Finite Group Databasebeta

← #17241401

Subgroups — #17241401

Order 4352.

2644 conjugacy classes of subgroups.

The subgroup lattice has 1818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763393C211yesmaximal, characteristic, complemented
2C2×#11763321C211yesmaximal, characteristic, complemented
3#14537075C211yesmaximal, characteristic, complemented
4#14537065C211yesmaximal, characteristic, complemented
5#14535452C211yesmaximal, characteristic, complemented
6#14535407C211yesmaximal, characteristic, complemented
7#14535381C211yesmaximal, characteristic, complemented
8#14535368C211yesmaximal, characteristic, complemented
9#14535204C211yesmaximal, characteristic, complemented
10#14535148C211yesmaximal, characteristic, complemented
11#14535135C211yesmaximal, characteristic, complemented
12#14535134C211yesmaximal, characteristic, complemented
13#14535119C211yesmaximal, characteristic, complemented
14#14535107C211yesmaximal, characteristic, complemented
15#14535106C211yesmaximal, characteristic, complemented
16#14535102C211yesmaximal, characteristic, complemented
17#14535034C211yesmaximal, characteristic, complemented
18#14535004C211yesmaximal, characteristic, complemented
19#14535000C211yesmaximal, characteristic, complemented
20#14534995C211yesmaximal, characteristic, complemented
21#14534675C211yesmaximal, characteristic, complemented
22#14534631C211yesmaximal, characteristic, complemented
23#14534411C211yesmaximal, characteristic, complemented
24#14534381C211yesmaximal, characteristic, complemented
25#14534369C211yesmaximal, characteristic, complemented
26#14533756C211yesmaximal, characteristic, complemented
27#14533678C211yesmaximal, characteristic, complemented
28#14532126C211yesmaximal, characteristic, complemented
29#14532101C211yesmaximal, characteristic, complemented
30#14531428C211yesmaximal, characteristic, complemented
31C17×#2610C211yesmaximal, characteristic, complemented
32C22×#63252C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic, complemented
34#11763393—28no—
35C2×#10587626C2211yescharacteristic
36C2×#10587562C2211yescharacteristic, complemented
37C2×#10587565C2211yescharacteristic, complemented
38C2×#10587633C2211yescharacteristic
39C2×#10587633C2211yescharacteristic, complemented
40#11763321—28no—
41C2×#10587580C2211yescharacteristic
42C2×#10587572C2211yescharacteristic
43C2×#10587572C2211yescharacteristic, complemented
44C2×#10587572C2211yescharacteristic, complemented
45C2×#10587569C2211yescharacteristic
46C2×#10587569C2211yescharacteristic
47C2×#10587583C2211yescharacteristic, complemented
48C2×#10587583C2211yescharacteristic, complemented
49C2×#10587564C2211yescharacteristic, complemented
50C2×#10587632C2211yescharacteristic, complemented
51C2×#10587581C2211yescharacteristic
52C2×#10587581C2211yescharacteristic
53C2×#10587570C2211yescharacteristic
54C2×#10587570C2211yescharacteristic
55C2×#10587570C2211yescharacteristic
56C2×#10587625C2211yescharacteristic
57C2×#10587625C2211yescharacteristic
58C2×#10587625C2211yescharacteristic, complemented
59C2×#10587568C2211yescharacteristic
60C2×#10587568C2211yescharacteristic
61C2×#10587568C2211yescharacteristic
62C2×#10587568C2211yescharacteristic
63C2×#10587568C2211yescharacteristic, complemented
64C2×#10587568C2211yescharacteristic, complemented
65C2×#10587623C2211yescharacteristic
66C2×#10587623C2211yescharacteristic
67C2×#10587623C2211yescharacteristic, complemented
68C2×#10587623C2211yescharacteristic, complemented
69C2×C4×D68C2211yescharacteristic
70C2×C4×D68C2211yescharacteristic
71C2×C4×D68C2211yescharacteristic, complemented
72C2×C4×D68C2211yescharacteristic, complemented
73C2×#10587567C2211yescharacteristic, complemented
74C2×C22⋊C4×D17C2211yescharacteristic, complemented
75#11762751C2211yescharacteristic, complemented
76#11762744C2211yescharacteristic, complemented
77#11762742C2211yescharacteristic, complemented
78#11762741C2211yescharacteristic, complemented
79#11762741C2211yescharacteristic, complemented
80#11762736C2211yescharacteristic, complemented
81#11762736C2211yescharacteristic, complemented
82#11762735C2211yescharacteristic, complemented
83#11762732C2211yescharacteristic, complemented
84#11762732C2211yescharacteristic, complemented
85#11762732C2211yescharacteristic, complemented
86#11762731C2211yescharacteristic, complemented
87#11762731C2211yescharacteristic, complemented
88#11762731C2211yescharacteristic, complemented
89#11762727C2211yescharacteristic
90#11762727C2211yescharacteristic, complemented
91#11762727C2211yescharacteristic, complemented
92#11762727C2211yescharacteristic, complemented
93#11762726C2211yescharacteristic
94#11762726C2211yescharacteristic
95#11762725C2211yescharacteristic
96#11762725C2211yescharacteristic
97#11762725C2211yescharacteristic
98#11762725C2211yescharacteristic
99#11762725C2211yescharacteristic, complemented
100#11762725C2211yescharacteristic, complemented
101#11762725C2211yescharacteristic, complemented
102#11762725C2211yescharacteristic, complemented
103#11762724C2211yescharacteristic
104#11762724C2211yescharacteristic, complemented
105#11762724C2211yescharacteristic, complemented
106#11762724C2211yescharacteristic, complemented
107#11762722C2211yescharacteristic, complemented
108#11762721C2211yescharacteristic, complemented
109#11762719C2211yescharacteristic
110#11762719C2211yescharacteristic
111#11762718C2211yescharacteristic
112#11762718C2211yescharacteristic
113#11762718C2211yescharacteristic
114#11762718C2211yescharacteristic, complemented
115#11762718C2211yescharacteristic, complemented
116#11762718C2211yescharacteristic, complemented
117#11762717C2211yescharacteristic
118#11762717C2211yescharacteristic
119#11762716C2211yescharacteristic, complemented
120#11762713C2211yescharacteristic, complemented
121#11762712C2211yescharacteristic, complemented
122#11762711C2211yescharacteristic
123#11762711C2211yescharacteristic
124#11762711C2211yescharacteristic
125#11762711C2211yescharacteristic, complemented
126#11762709C2211yescharacteristic
127#11762709C2211yescharacteristic, complemented
128#11762707C2211yescharacteristic, complemented
129#11762707C2211yescharacteristic, complemented
130#11762704C2211yescharacteristic, complemented
131#11762703C2211yescharacteristic, complemented
132#11762700C2211yescharacteristic, complemented
133#11762700C2211yescharacteristic, complemented
134#11762700C2211yescharacteristic, complemented
135#11762699C2211yescharacteristic, complemented
136#11762698C2211yescharacteristic, complemented
137#11762698C2211yescharacteristic, complemented
138#11762698C2211yescharacteristic, complemented
139#11762698C2211yescharacteristic, complemented
140#11762698C2211yescharacteristic, complemented
141#11762695C2211yescharacteristic, complemented
142#11762693C2211yescharacteristic, complemented
143#11762689C2211yescharacteristic
144#11762688C2211yescharacteristic
145#11762687C2211yescharacteristic
146#11762687C2211yescharacteristic
147#11762687C2211yescharacteristic, complemented
148#11762687C2211yescharacteristic, complemented
149#11762686C2211yescharacteristic, complemented
150#11762685C2211yescharacteristic
151#11762685C2211yescharacteristic
152#11762685C2211yescharacteristic
153#11762685C2211yescharacteristic, complemented
154#11762685C2211yescharacteristic, complemented
155#11762685C2211yescharacteristic, complemented
156#11762685C2211yescharacteristic, complemented
157#11762684C2211yescharacteristic, complemented
158#11762684C2211yescharacteristic, complemented
159#11762683C2211yescharacteristic, complemented
160#11762683C2211yescharacteristic, complemented
161#11762683C2211yescharacteristic, complemented
162#11762682C2211yescharacteristic, complemented
163#11762671C2211yescharacteristic, complemented
164#11762671C2211yescharacteristic, complemented
165#11762671C2211yescharacteristic, complemented
166#11762671C2211yescharacteristic, complemented
167#11762668C2211yescharacteristic, complemented
168#11762668C2211yescharacteristic, complemented
169#11762668C2211yescharacteristic, complemented
170#11762667C2211yescharacteristic, complemented
171#11762664C2211yescharacteristic, complemented
172#11762664C2211yescharacteristic, complemented
173C4×C4⋊Dic17C2211yescharacteristic, complemented
174C2×C17×#124C2211yescharacteristic, complemented
175C2×C17×#117C2211yescharacteristic, complemented
176C17×#395C2211yescharacteristic, complemented
177C17×#394C2211yescharacteristic, complemented
178C17×#393C2211yescharacteristic, complemented
179C17×#392C2211yescharacteristic
180C17×#390C2211yescharacteristic
181C17×#390C2211yescharacteristic, complemented
182C17×#388C2211yescharacteristic, complemented
183C17×#388C2211yescharacteristic, complemented
184C17×#388C2211yescharacteristic, complemented
185C17×#388C2211yescharacteristic, complemented
186C17×#386C2211yescharacteristic
187C17×#386C2211yescharacteristic, complemented
188C17×#376C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×Q8×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C2×#63252—24no—
210C2×#63252—42no—
211C2×#63252—42no—
212C22×D68C2311yescharacteristic
213C22×D68C2311yescharacteristic
214C22×D68C2311yescharacteristic
215C22×D68C2311yescharacteristic
216C22×D68C2311yescharacteristic
217C22×D68C2311yescharacteristic
218C22×D68C2311yescharacteristic
219C22×D68C2311yescharacteristic
220C22×C4×D17—24no—
221C22×C4×D17—42no—
222C22×C4×D17—42no—
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C22×C4×D17C2311yescharacteristic
229C22×C4×D17C2311yescharacteristic
230C22×Dic34C2311yescharacteristic
231C17×#124—24no—
232C17×#117—24no—
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C42×C17C2311yescharacteristic
252C2×C42×C17C2311yescharacteristic
253C2×C42×C17C2311yescharacteristic
254C2×C42×C17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264#10587633—24no—
265#10587633—42no—
266#10587632—24no—
267#10587626—42no—
268#10587625—24no—
269#10587625—42no—
270#10587625—42no—
271#10587623—24no—
272#10587623—42no—
273#10587623—42no—
274#10587623—42no—
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×#63227C2311yescharacteristic
303C2×#63227C2311yescharacteristic
304C2×#63227C2311yescharacteristic
305C2×#63227C2311yescharacteristic
306C2×#63227C2311yescharacteristic
307C2×#63227C2311yescharacteristic
308C2×#63227C2311yescharacteristic
309C2×#63227C2311yescharacteristic
310C2×#63227C2311yescharacteristic
311C2×#63227C2311yescharacteristic
312C2×C4⋊Dic17C2311yescharacteristic
313C2×C4⋊Dic17C2311yescharacteristic
314C2×C4⋊Dic17C2311yescharacteristic
315C2×C4⋊Dic17C2311yescharacteristic
316C2×C4⋊Dic17C2311yescharacteristic
317C2×C4⋊Dic17C2311yescharacteristic
318C2×C4⋊Dic17C2311yescharacteristic
319C2×C4⋊Dic17C2311yescharacteristic
320C2×C4⋊Dic17C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×#63225C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×#63225C2311yescharacteristic
328C2×#63225C2311yescharacteristic
329C2×#63225C2311yescharacteristic
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333C2×C4×Dic17C2311yescharacteristic
334C2×C4×Dic17C2311yescharacteristic
335#10587583—24no—
336#10587583—24no—
337#10587581—24no—
338#10587581—24no—
339#10587580—42no—
340#10587572—24no—
341#10587572—24no—
342#10587572—24no—
343#10587570—24no—
344#10587570—24no—
345#10587570—42no—
346#10587569—24no—
347#10587569—42no—
348#10587568—24no—
349#10587568—24no—
350#10587568—24no—
351#10587568—42no—
352#10587568—42no—
353#10587568—42no—
354#10587567—24no—
355C22⋊C4×D17—24no—
356#10587565—24no—
357#10587564—42no—
358#10587562—24no—
359C4×D68—24no—
360C4×D68—24no—
361C4×D68—24no—
362C4×D68D418yescomplemented
363C17×#95C2311yescharacteristic
364C17×#95C2311yescharacteristic
365C17×#95C2311yescharacteristic
366C17×#95C2311yescharacteristic
367C17×#95C2311yescharacteristic
368C17×#95C2311yescharacteristic
369C17×#95C2311yescharacteristic
370C17×#95C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C24×C17C2411yescharacteristic
394C23×D17—22no—
395C23×D17—22no—
396C23×D17—22no—
397C23×D17—22no—
398C23×D17—41no—
399C23×D17—41no—
400C23×D17—41no—
401C23×D17—41no—
402C23×D17—41no—
403C23×D17—41no—
404C23×D17—41no—
405C23×D17—41no—
406C23×D17—41no—
407C23×D17—41no—
408C23×D17C2411yescharacteristic
409C23×D17C2411yescharacteristic
410C23×D17C2411yescharacteristic
411C23×D17C2411yescharacteristic
412C23×D17C2411yescharacteristic
413C2×Q8×C17—22no—
414C2×Q8×C17—41no—
415C2×Q8×C17—41no—
416C2×D4×C17—22no—
417C2×D4×C17—22no—
418C2×D4×C17—22no—
419C2×D4×C17—41no—
420C2×D4×C17—41no—
421C2×D4×C17—41no—
422C2×D4×C17—41no—
423C2×D4×C17—41no—
424C2×D4×C17—41no—
425C22×C4×C17—22no—
426C22×C4×C17—22no—
427C22×C4×C17—22no—
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C22×C4×C17C2411yescharacteristic
438C22×C4×C17C2411yescharacteristic
439C22×C4×C17C2411yescharacteristic
440C2×C22⋊D17—22no—
441C2×C22⋊D17—22no—
442C2×C22⋊D17—22no—
443C2×C22⋊D17—22no—
444C2×C22⋊D17—22no—
445C2×C22⋊D17—22no—
446C2×C22⋊D17—22no—
447C2×C22⋊D17—22no—
448C2×C22⋊D17—22no—
449C2×C22⋊D17—22no—
450C2×C22⋊D17—22no—
451C2×C22⋊D17—41no—
452C2×C22⋊D17—41no—
453C2×C22⋊D17—41no—
454C2×C22⋊D17—41no—
455C2×C22⋊D17—41no—
456C2×C22⋊D17—41no—
457C2×C22⋊D17—41no—
458C2×C22⋊D17—41no—
459C2×C22⋊D17—41no—
460C2×C22⋊D17—41no—
461C2×C22⋊D17—41no—
462C2×C22⋊D17—41no—
463C2×C22⋊D17—41no—
464C2×C22⋊D17—41no—
465C2×C22⋊D17—41no—
466C2×C22⋊D17—41no—
467C2×C22⋊D17—41no—
468C2×C22⋊D17—41no—
469C2×C22⋊D17—41no—
470C2×C22⋊D17—41no—
471C2×C22⋊D17—41no—
472C2×C22⋊D17—41no—
473C22×Dic17—22no—
474C22×Dic17—22no—
475C22×Dic17—22no—
476C22×Dic17—41no—
477C22×Dic17—41no—
478C22×Dic17—41no—
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488C22×Dic17C2411yescharacteristic
489C22×Dic17C2411yescharacteristic
490#63252—416no—
491C2×D68—22no—
492C2×D68—22no—
493C2×D68—22no—
494C2×D68—22no—
495C2×D68—22no—
496C2×D68—22no—
497C2×D68—22no—
498C2×D68—22no—
499C2×D68—22no—
500C2×D68—41no—
501C2×D68—41no—
502C2×D68—41no—
503C2×D68—41no—
504C2×D68—41no—
505C2×D68—41no—
506C2×D68—41no—
507C2×D68—41no—
508C2×D68—41no—
509C2×D68—41no—
510C2×D68—41no—
511C2×D68—41no—
512C2×D68—41no—
513C2×D68—41no—
514C2×D68C2×D414yes—
515C2×C4×D17—22no—
516C2×C4×D17—22no—
517C2×C4×D17—22no—
518C2×C4×D17—22no—
519C2×C4×D17—22no—
520C2×C4×D17—22no—
521C2×C4×D17—22no—
522C2×C4×D17—41no—
523C2×C4×D17—41no—
524C2×C4×D17—41no—
525C2×C4×D17—41no—
526C2×C4×D17—41no—
527C2×C4×D17—41no—
528C2×C4×D17—41no—
529C2×C4×D17—41no—
530C2×C4×D17—41no—
531C2×C4×D17—41no—
532C2×C4×D17—416no—
533C2×C4×D17—41no—
534C2×C4×D17—41no—
535C2×C4×D17C2×D414yes—
536C2×C4×D17C2×D414yes—
537C2×Dic34—22no—
538C2×Dic34—22no—
539C2×Dic34—41no—
540C4⋊C4×C17—22no—
541C4⋊C4×C17—22no—
542C4⋊C4×C17—41no—
543C4⋊C4×C17—41no—
544C22⋊C4×C17—22no—
545C22⋊C4×C17—22no—
546C22⋊C4×C17—22no—
547C22⋊C4×C17—22no—
548C22⋊C4×C17—22no—
549C22⋊C4×C17—22no—
550C22⋊C4×C17—22no—
551C22⋊C4×C17—22no—
552C22⋊C4×C17—41no—
553C22⋊C4×C17—41no—
554C22⋊C4×C17—41no—
555C22⋊C4×C17—41no—
556C22⋊C4×C17—41no—
557C22⋊C4×C17—41no—
558C42×C17—22no—
559C42×C17—41no—
560C42×C17—41no—
561C42×C17C2×D414yes—
562C22⋊Dic17—22no—
563C22⋊Dic17—22no—
564C22⋊Dic17—22no—
565C22⋊Dic17—41no—
566C22⋊Dic17—41no—
567C22⋊Dic17—41no—
568C22⋊Dic17—41no—
569C22⋊Dic17—41no—
570C22⋊Dic17—41no—
571#63227—22no—
572#63227—22no—
573#63227—22no—
574#63227—22no—
575#63227—22no—
576#63227—22no—
577#63227—22no—
578#63227—22no—
579#63227—22no—
580#63227—22no—
581#63227—22no—
582#63227—22no—
583#63227—22no—
584#63227—22no—
585#63227—22no—
586#63227—22no—
587#63227—41no—
588#63227—41no—
589#63227—41no—
590#63227—41no—
591#63227—41no—
592#63227—41no—
593#63227—41no—
594#63227—41no—
595#63227—41no—
596#63227—41no—
597#63227—41no—
598#63227—41no—
599#63227—41no—
600#63227—41no—
601#63227—41no—
602#63227—41no—
603#63227—41no—
604#63227—41no—
605#63227—41no—
606#63227C2×D414yes—
607#63227C2×D414yes—
608C4⋊Dic17—22no—
609C4⋊Dic17—22no—
610C4⋊Dic17—22no—
611C4⋊Dic17—22no—
612C4⋊Dic17—41no—
613C4⋊Dic17—41no—
614C4⋊Dic17—41no—
615C4⋊Dic17—41no—
616C4⋊Dic17C2×D414yes—
617#63225—22no—
618#63225—22no—
619#63225—22no—
620#63225—22no—
621#63225—22no—
622#63225—41no—
623#63225—41no—
624#63225—41no—
625#63225—41no—
626#63225—41no—
627#63225—41no—
628C4×Dic17—22no—
629C4×Dic17—41no—
630C4×Dic17—41no—
631#36724—171nomaximal, Sylow
632C23×C17—21no—
633C23×C17—21no—
634C23×C17—21no—
635C23×C17—21no—
636C23×C17—21no—
637C23×C17—21no—
638C23×C17—21no—
639C23×C17—21no—
640C23×C17—21no—
641C23×C17—21no—
642C23×C17—21no—
643C23×C17—21no—
644C23×C17—21no—
645C23×C17—21no—
646C23×C17—21no—
647C23×C17—21no—
648C23×C17—21no—
649C23×C17—21no—
650C23×C17—21no—
651C23×C17—21no—
652C23×C17H(5,𝔽2)12yes—
653C23×C17C2511yescharacteristic
654C22×D17—21no—
655C22×D17—21no—
656C22×D17—21no—
657C22×D17—21no—
658C22×D17—21no—
659C22×D17—21no—
660C22×D17—21no—
661C22×D17—21no—
662C22×D17—21no—
663C22×D17—21no—
664C22×D17—21no—
665C22×D17—21no—
666C22×D17—21no—
667C22×D17—21no—
668C22×D17—21no—
669C22×D17—21no—
670C22×D17—21no—
671C22×D17—21no—
672C22×D17—21no—
673C22×D17—21no—
674C22×D17—21no—
675C22×D17—21no—
676C22×D17—21no—
677C22×D17—21no—
678C22×D17—21no—
679C22×D17—21no—
680C22×D17—21no—
681C22×D17—21no—
682C22×D17—21no—
683C22×D17—21no—
684C22×D17—21no—
685C22×D17—21no—
686C22×D17—44no—
687C22×D17—44no—
688C22×D17—44no—
689C22×D17—44no—
690C22×D17—44no—
691C22×D17—44no—
692C22×D17—44no—
693C22×D17—44no—
694C22×D17—82no—
695C22×D17—82no—
696C22×D17—82no—
697C22×D17—82no—
698C22×D17—82no—
699C22×D17—82no—
700C22×D17C22×D412yes—
701C22×D17C22×D412yes—
702C22×D17H(5,𝔽2)12yes—
703Q8×C17—82no—
704D4×C17—82no—
705D4×C17—82no—
706D4×C17—82no—
707C2×C4×C17—28no—
708C2×C4×C17—21no—
709C2×C4×C17—21no—
710C2×C4×C17—21no—
711C2×C4×C17—21no—
712C2×C4×C17—21no—
713C2×C4×C17—21no—
714C2×C4×C17—21no—
715C2×C4×C17—21no—
716C2×C4×C17—21no—
717C2×C4×C17—21no—
718C2×C4×C17—21no—
719C2×C4×C17—21no—
720C2×C4×C17—21no—
721C2×C4×C17—21no—
722C2×C4×C17—21no—
723C2×C4×C17—21no—
724C2×C4×C17—21no—
725C2×C4×C17—21no—
726C2×C4×C17—21no—
727C2×C4×C17—21no—
728C2×C4×C17—21no—
729C2×C4×C17—21no—
730C2×C4×C17—21no—
731C2×C4×C17—21no—
732C2×C4×C17—21no—
733C2×C4×C17—21no—
734C2×C4×C17—21no—
735C2×C4×C17—21no—
736C2×C4×C17—21no—
737C2×C4×C17—21no—
738C2×C4×C17—21no—
739C2×C4×C17—21no—
740C2×C4×C17C22×D412yes—
741C2×C4×C17C22×D412yes—
742C2×C4×C17C22×D412yes—
743C2×C4×C17H(5,𝔽2)12yes—
744C22⋊D17—44no—
745C22⋊D17—44no—
746C22⋊D17—44no—
747C22⋊D17—82no—
748C22⋊D17—82no—
749C22⋊D17—82no—
750C22⋊D17—82no—
751C22⋊D17—82no—
752C22⋊D17—82no—
753C22⋊D17—82no—
754C22⋊D17—82no—
755C2×Dic17—21no—
756C2×Dic17—21no—
757C2×Dic17—21no—
758C2×Dic17—21no—
759C2×Dic17—21no—
760C2×Dic17—21no—
761C2×Dic17—21no—
762C2×Dic17—21no—
763C2×Dic17—21no—
764C2×Dic17—21no—
765C2×Dic17—21no—
766C2×Dic17—21no—
767C2×Dic17—21no—
768C2×Dic17—21no—
769C2×Dic17—21no—
770C2×Dic17—21no—
771C2×Dic17—21no—
772C2×Dic17—21no—
773C2×Dic17—21no—
774C2×Dic17—21no—
775C2×Dic17—21no—
776C2×Dic17—21no—
777C2×Dic17—21no—
778C2×Dic17—21no—
779C2×Dic17—21no—
780C2×Dic17—21no—
781C2×Dic17—21no—
782C2×Dic17—21no—
783C2×Dic17—21no—
784C2×Dic17—21no—
785C2×Dic17—21no—
786C2×Dic17—44no—
787C2×Dic17—82no—
788C2×Dic17C22×D412yes—
789C2×Dic17C22×D412yes—
790D68—44no—
791D68—44no—
792D68—44no—
793D68—44no—
794D68—44no—
795D68—82no—
796D68—82no—
797D68—82no—
798C4×D17—44no—
799C4×D17—44no—
800C4×D17—44no—
801C4×D17—44no—
802C4×D17—44no—
803C4×D17—44no—
804C4×D17—82no—
805Dic34—44no—
806C2×#538—171no—
807C2×#525—171no—
808#2849—171no—
809#2847—171no—
810#2705—171no—
811#2702—171no—
812#2700—171no—
813#2699—171no—
814#2687—171no—
815#2682—171no—
816#2681—171no—
817#2681—171no—
818#2679—171no—
819#2678—171no—
820#2678—171no—
821#2678—171no—
822#2672—171no—
823#2670—171no—
824#2669—171no—
825#2669—171no—
826#2635—171no—
827#2630—171no—
828#2610D1711yescharacteristic, complemented
829#2603—171no—
830#2601—171no—
831#2600—171no—
832#2544—171no—
833#2534—171no—
834#2407—171no—
835#2404—171no—
836#2319—171no—
837C22×C17—22no—
838C22×C17—22no—
839C22×C17—22no—
840C22×C17—41no—
841C22×C17—41no—
842C22×C17—41no—
843C22×C17—41no—
844C22×C17—41no—
845C22×C17—41no—
846C22×C17—41no—
847C22×C17—41no—
848C22×C17—41no—
849C22×C17—41no—
850C22×C17—41no—
851C22×C17—41no—
852C22×C17—41no—
853C22×C17—41no—
854C22×C17—41no—
855C22×C17—41no—
856C22×C17—41no—
857C22×C17—41no—
858C22×C17C23×D411yescharacteristic
859C22×C17C2×H(5,𝔽2)11yescharacteristic
860C22×C17C2×H(5,𝔽2)11yescharacteristic
861C22×C17C2×H(5,𝔽2)11yescharacteristic
862C22×C17#58511yescharacteristic
863C22×C17#58511yescharacteristic
864C22×C17#58511yescharacteristic
865C2×D17—22no—
866C2×D17—22no—
867C2×D17—22no—
868C2×D17—22no—
869C2×D17—22no—
870C2×D17—22no—
871C2×D17—22no—
872C2×D17—22no—
873C2×D17—22no—
874C2×D17—416no—
875C2×D17—41no—
876C2×D17—41no—
877C2×D17—41no—
878C2×D17—41no—
879C2×D17—41no—
880C2×D17—41no—
881C2×D17—41no—
882C2×D17—41no—
883C2×D17—41no—
884C2×D17—41no—
885C2×D17—41no—
886C2×D17—41no—
887C2×D17—41no—
888C2×D17—41no—
889C2×D17—41no—
890C2×D17—41no—
891C2×D17—41no—
892C2×D17—41no—
893C2×D17—41no—
894C2×D17—41no—
895C2×D17—41no—
896C2×D17—41no—
897C2×D17—41no—
898C2×D17—41no—
899C2×D17—41no—
900C2×D17—41no—
901C2×D17—88no—
902C4×C17—22no—
903C4×C17—22no—
904C4×C17—22no—
905C4×C17—22no—
906C4×C17—41no—
907C4×C17—41no—
908C4×C17—41no—
909C4×C17—41no—
910C4×C17—41no—
911C4×C17—41no—
912C4×C17—41no—
913C4×C17—41no—
914Dic17—22no—
915Dic17—22no—
916Dic17—41no—
917Dic17—41no—
918Dic17—41no—
919Dic17—41no—
920Dic17—41no—
921Dic17—41no—
922Dic17—41no—
923Dic17—41no—
924Dic17—41no—
925C22×#41—171no—
926C24×C4—171no—
927#538—348no—
928C2×#127—171no—
929C2×#126—171no—
930C2×#126—171no—
931C2×#124—171no—
932C2×#124—171no—
933C2×#124C2×D1711yescharacteristic, complemented
934#525—348no—
935C2×#123—171no—
936C2×#123—171no—
937C2×#123—171no—
938C2×#123—171no—
939C2×#123—171no—
940C2×#123—171no—
941C2×C22⋊Q8—171no—
942C2×C22⋊Q8—171no—
943C2×C22⋊Q8—171no—
944C2×C22⋊Q8—171no—
945C2×#121—171no—
946C2×#121—171no—
947C2×#121—171no—
948C2×#121—171no—
949C2×#121—171no—
950C2×#121—171no—
951C2×#121—171no—
952C2×#121—171no—
953C2×#120—171no—
954C2×#120—171no—
955C2×#120—171no—
956C2×#120—171no—
957C2×#120—171no—
958C2×#120—171no—
959C2×#120—171no—
960C2×#120—171no—
961C2×#120—171no—
962C2×#120—171no—
963C2×C4×D4—171no—
964C2×C4×D4—171no—
965C2×C4×D4—171no—
966C2×C4×D4—171no—
967C2×C4×D4—171no—
968C2×#117C2×D1711yescharacteristic, complemented
969C22×C22⋊C4—171no—
970#400—171no—
971#399—171no—
972#398—171no—
973#398—171no—
974#398—171no—
975#397—171no—
976#397—171no—
977#397—171no—
978#396—171no—
979#396—171no—
980#396—171no—
981#396—171no—
982#396—171no—
983#396—171no—
984#395C2×D1711yescharacteristic, complemented
985#394—171no—
986#394—171no—
987#394—171no—
988#394—171no—
989#394—171no—
990#394—171no—
991#394—171no—
992#394—171no—
993#394—171no—
994#394—171no—
995#394—171no—
996#394—171no—
997#394—171no—
998#394—171no—
999#394—171no—
1000#394—171no—
1001#394—171no—
1002#394—171no—
1003#394C2×D1711yescharacteristic, complemented
1004#393—171no—
1005#393—171no—
1006#393C2×D1711yescharacteristic, complemented
1007#392—171no—
1008#392—171no—
1009#392—171no—
1010#392—171no—
1011#392—171no—
1012#392—171no—
1013#392—171no—
1014#392—171no—
1015#392—171no—
1016#392—171no—
1017#392C2×D1711yescharacteristic
1018#391—171no—
1019#391—171no—
1020#390—171no—
1021#390—171no—
1022#390—171no—
1023#390—171no—
1024#390—171no—
1025#390—171no—
1026#390—171no—
1027#390C2×D1711yescharacteristic
1028#390C2×D1711yescharacteristic, complemented
1029#389—171no—
1030#389—171no—
1031#389—171no—
1032#388—171no—
1033#388—171no—
1034#388—171no—
1035#388—171no—
1036#388—171no—
1037#388—171no—
1038#388—171no—
1039#388—171no—
1040#388—171no—
1041#388—171no—
1042#388C2×D1711yescharacteristic, complemented
1043#388C2×D1711yescharacteristic, complemented
1044#388C2×D1711yescharacteristic, complemented
1045#388C2×D1711yescharacteristic, complemented
1046#387—171no—
1047#387—171no—
1048#386—171no—
1049#386—171no—
1050#386—171no—
1051#386—171no—
1052#386—171no—
1053#386—171no—
1054#386—171no—
1055#386—171no—
1056#386—171no—
1057#386—171no—
1058#386—171no—
1059#386—171no—
1060#386—171no—
1061#386—171no—
1062#386C2×D1711yescharacteristic
1063#386C2×D1711yescharacteristic, complemented
1064#385—171no—
1065#385—171no—
1066#385—171no—
1067#385—171no—
1068#385—171no—
1069#385—171no—
1070#381—171no—
1071#381—171no—
1072#381—171no—
1073#381—171no—
1074#380—171no—
1075#380—171no—
1076#380—171no—
1077#380—171no—
1078#379—171no—
1079#379—171no—
1080C4×C4⋊C4—171no—
1081#376C2×D1711yescharacteristic, complemented
1082C2×C17—42no—
1083C2×C17—81no—
1084C2×C17—81no—
1085C2×C17#344911yescharacteristic
1086C2×C17#348411yescharacteristic
1087C2×C17#348811yescharacteristic
1088C2×C17#353311yescharacteristic
1089C2×C17#353411yescharacteristic
1090C2×C17#354011yescharacteristic
1091C2×C17#354211yescharacteristic
1092D17—42no—
1093D17—42no—
1094D17—42no—
1095D17—81no—
1096D17—81no—
1097C25—171no—
1098C25—171no—
1099C2×#41—344no—
1100C2×#41—682no—
1101C2×#41—682no—
1102C22×Q8—171no—
1103C22×Q8C22×D1711yescharacteristic
1104C22×D4—171no—
1105C22×D4—171no—
1106C22×D4—171no—
1107C22×D4—171no—
1108C22×D4—171no—
1109C22×D4—171no—
1110C22×D4—171no—
1111C22×D4—171no—
1112C22×D4—171no—
1113C22×D4—171no—
1114C22×D4—171no—
1115C22×D4—171no—
1116C22×D4—171no—
1117C22×D4—171no—
1118C22×D4—171no—
1119C22×D4—171no—
1120C22×D4—171no—
1121C22×D4—171no—
1122C22×D4—171no—
1123C22×D4C22×D1711yescharacteristic
1124C22×D4C22×D1711yescharacteristic
1125C22×D4C22×D1711yescharacteristic
1126C23×C4—171no—
1127C23×C4—171no—
1128C23×C4—171no—
1129C23×C4—171no—
1130C23×C4—171no—
1131C23×C4—171no—
1132C23×C4—171no—
1133C23×C4—171no—
1134C23×C4—171no—
1135C23×C4—344no—
1136C23×C4—682no—
1137C23×C4—682no—
1138C23×C4C22×D1711yescharacteristic
1139#127—682no—
1140#126—344no—
1141#126—344no—
1142#124—24no—
1143#124—344no—
1144#124—682no—
1145#123—344no—
1146#123—344no—
1147#123—344no—
1148#123—344no—
1149#123—682no—
1150#123—682no—
1151C22⋊Q8—344no—
1152C22⋊Q8—344no—
1153C22⋊Q8—344no—
1154C22⋊Q8—682no—
1155#121—344no—
1156#121—344no—
1157#121—344no—
1158#121—344no—
1159#121—344no—
1160#121—682no—
1161#121—682no—
1162#121—682no—
1163#120—344no—
1164#120—344no—
1165#120—344no—
1166#120—344no—
1167#120—682no—
1168#120—682no—
1169#120—682no—
1170#120—682no—
1171#120—682no—
1172#120—682no—
1173C4×D4—178no—
1174C4×D4—344no—
1175C4×D4—344no—
1176C4×D4—344no—
1177C4×D4—344no—
1178#117—24no—
1179C2×C4⋊C4—171no—
1180C2×C4⋊C4—171no—
1181C2×C4⋊C4—171no—
1182C2×C4⋊C4—171no—
1183C2×C4⋊C4—171no—
1184C2×C4⋊C4—171no—
1185C2×C4⋊C4—171no—
1186C2×C4⋊C4—171no—
1187C2×C4⋊C4—171no—
1188C2×C4⋊C4—171no—
1189C2×C4⋊C4—171no—
1190C2×C4⋊C4—171no—
1191C2×C4⋊C4—171no—
1192C2×C4⋊C4—171no—
1193C2×C4⋊C4—171no—
1194C2×C4⋊C4—171no—
1195C2×C4⋊C4—171no—
1196C2×C4⋊C4—171no—
1197C2×C4⋊C4—171no—
1198C2×C4⋊C4—171no—
1199C2×C4⋊C4C22×D1711yescharacteristic
1200C2×C4⋊C4C22×D1711yescharacteristic
1201C2×C4⋊C4C22×D1711yescharacteristic
1202C2×C4⋊C4C22×D1711yescharacteristic
1203C2×C22⋊C4—171no—
1204C2×C22⋊C4—171no—
1205C2×C22⋊C4—171no—
1206C2×C22⋊C4—171no—
1207C2×C22⋊C4—171no—
1208C2×C22⋊C4—171no—
1209C2×C22⋊C4—171no—
1210C2×C22⋊C4—171no—
1211C2×C22⋊C4—171no—
1212C2×C22⋊C4—171no—
1213C2×C22⋊C4—171no—
1214C2×C22⋊C4—171no—
1215C2×C22⋊C4—171no—
1216C2×C22⋊C4—171no—
1217C2×C22⋊C4—171no—
1218C2×C22⋊C4—171no—
1219C2×C22⋊C4—171no—
1220C2×C22⋊C4—171no—
1221C2×C22⋊C4—171no—
1222C2×C22⋊C4—171no—
1223C2×C22⋊C4—171no—
1224C2×C22⋊C4—171no—
1225C2×C22⋊C4—171no—
1226C2×C22⋊C4—171no—
1227C2×C22⋊C4—171no—
1228C2×C22⋊C4—171no—
1229C2×C22⋊C4—171no—
1230C2×C22⋊C4—171no—
1231C2×C22⋊C4—171no—
1232C2×C22⋊C4—171no—
1233C2×C22⋊C4—171no—
1234C2×C22⋊C4—171no—
1235C2×C22⋊C4—171no—
1236C2×C22⋊C4—171no—
1237C2×C22⋊C4—171no—
1238C2×C22⋊C4—171no—
1239C2×C22⋊C4—171no—
1240C2×C22⋊C4—171no—
1241C2×C22⋊C4—171no—
1242C2×C22⋊C4—171no—
1243C2×C22⋊C4—171no—
1244C2×C22⋊C4—171no—
1245C2×C22⋊C4—171no—
1246C2×C22⋊C4—171no—
1247C2×C22⋊C4—171no—
1248C2×C22⋊C4—171no—
1249C2×C22⋊C4—344no—
1250C2×C22⋊C4C22×D1711yescharacteristic
1251C2×C22⋊C4C22×D1711yescharacteristic
1252C2×C22⋊C4C22×D1711yescharacteristic
1253C2×C22⋊C4C22×D1711yescharacteristic
1254C2×C22⋊C4C22×D1711yescharacteristic
1255C2×C22⋊C4C22×D1711yescharacteristic
1256C2×C22⋊C4C22×D1711yescharacteristic
1257C2×C22⋊C4C22×D1711yescharacteristic
1258C2×C22⋊C4C22×D1711yescharacteristic
1259C2×C22⋊C4C22×D1711yescharacteristic
1260C2×C22⋊C4C22×D1711yescharacteristic
1261C2×C22⋊C4C22×D1711yescharacteristic
1262C2×C22⋊C4C22×D1711yescharacteristic
1263C2×C22⋊C4C22×D1711yescharacteristic
1264C2×C42—171no—
1265C2×C42—171no—
1266C2×C42—171no—
1267C2×C42C22×D1711yescharacteristic
1268C2×C42C22×D1711yescharacteristic
1269C2×C42C22×D1711yescharacteristic
1270C2×C42C22×D1711yescharacteristic
1271#95—171no—
1272#95—171no—
1273#95—171no—
1274#95—171no—
1275#95—171no—
1276#95—171no—
1277#95—171no—
1278#95—171no—
1279#95—171no—
1280#95—171no—
1281#95—171no—
1282#95—171no—
1283#95—171no—
1284#95—171no—
1285#95—171no—
1286#95—171no—
1287#95—171no—
1288#95—171no—
1289#95—171no—
1290#95—171no—
1291#95C22×D1711yescharacteristic
1292#95C22×D1711yescharacteristic
1293#95C22×D1711yescharacteristic
1294#95C22×D1711yescharacteristic
1295#95C22×D1711yescharacteristic
1296#95C22×D1711yescharacteristic
1297#95C22×D1711yescharacteristic
1298#95C22×D1711yescharacteristic
1299C17#3672411yescharacteristic, complemented, Sylow
1300C24—171no—
1301C24—171no—
1302C24—171no—
1303C24—171no—
1304C24—171no—
1305C24—342no—
1306C24—342no—
1307C24—342no—
1308C24—342no—
1309C24—681no—
1310C24—681no—
1311C24—681no—
1312C24—681no—
1313C24—681no—
1314C24—681no—
1315C24—681no—
1316C24—681no—
1317C24—681no—
1318C24—681no—
1319C24C23×D1711yescharacteristic
1320C24C23×D1711yescharacteristic
1321C24C23×D1711yescharacteristic
1322#41—6816no—
1323C2×Q8—22no—
1324C2×Q8—41no—
1325C2×Q8—41no—
1326C2×Q8—342no—
1327C2×Q8—342no—
1328C2×Q8—681no—
1329C2×D4—22no—
1330C2×D4—22no—
1331C2×D4—22no—
1332C2×D4—41no—
1333C2×D4—41no—
1334C2×D4—41no—
1335C2×D4—41no—
1336C2×D4—41no—
1337C2×D4—41no—
1338C2×D4—174no—
1339C2×D4—342no—
1340C2×D4—342no—
1341C2×D4—342no—
1342C2×D4—342no—
1343C2×D4—342no—
1344C2×D4—342no—
1345C2×D4—342no—
1346C2×D4—342no—
1347C2×D4—342no—
1348C2×D4—342no—
1349C2×D4—342no—
1350C2×D4—342no—
1351C2×D4—342no—
1352C2×D4—342no—
1353C2×D4—342no—
1354C2×D4—342no—
1355C2×D4—342no—
1356C2×D4—342no—
1357C2×D4—342no—
1358C2×D4—342no—
1359C2×D4—681no—
1360C2×D4—681no—
1361C2×D4—681no—
1362C2×D4—681no—
1363C2×D4—681no—
1364C2×D4—681no—
1365C2×D4—681no—
1366C2×D4—681no—
1367C2×D4—681no—
1368C2×D4—681no—
1369C2×D4—681no—
1370C2×D4—681no—
1371C2×D4—681no—
1372C2×D4—681no—
1373C2×D4—681no—
1374C2×D4—681no—
1375C2×D4—681no—
1376C2×D4—681no—
1377C2×D4—681no—
1378C2×D4—681no—
1379C2×D4—681no—
1380C2×D4—681no—
1381C2×D4—681no—
1382C2×D4—681no—
1383C2×D4—681no—
1384C2×D4—681no—
1385C2×D4—681no—
1386C2×D4—681no—
1387C2×D4—681no—
1388C2×D4—681no—
1389C2×D4—681no—
1390C2×D4—681no—
1391C2×D4—681no—
1392C2×D4—681no—
1393C2×D4—681no—
1394C2×D4—681no—
1395C22×C4—22no—
1396C22×C4—22no—
1397C22×C4—22no—
1398C22×C4—171no—
1399C22×C4—171no—
1400C22×C4—174no—
1401C22×C4—174no—
1402C22×C4—171no—
1403C22×C4—171no—
1404C22×C4—171no—
1405C22×C4—171no—
1406C22×C4—171no—
1407C22×C4—171no—
1408C22×C4—171no—
1409C22×C4—171no—
1410C22×C4—171no—
1411C22×C4—342no—
1412C22×C4—342no—
1413C22×C4—342no—
1414C22×C4—342no—
1415C22×C4—342no—
1416C22×C4—342no—
1417C22×C4—342no—
1418C22×C4—342no—
1419C22×C4—342no—
1420C22×C4—342no—
1421C22×C4—681no—
1422C22×C4—681no—
1423C22×C4—681no—
1424C22×C4—681no—
1425C22×C4—681no—
1426C22×C4—681no—
1427C22×C4—681no—
1428C22×C4—681no—
1429C22×C4—681no—
1430C22×C4—681no—
1431C22×C4—681no—
1432C22×C4—681no—
1433C22×C4—6816no—
1434C22×C4—681no—
1435C22×C4—681no—
1436C22×C4—681no—
1437C22×C4C23×D1711yescharacteristic
1438C22×C4C23×D1711yescharacteristic
1439C22×C4C23×D1711yescharacteristic
1440C22×C4C23×D1711yescharacteristic
1441C22×C4C23×D1711yescharacteristic
1442C22×C4C23×D1711yescharacteristic
1443C22×C4C23×D1711yescharacteristic
1444C22×C4C23×D1711yescharacteristic
1445C22×C4C23×D1711yescharacteristic
1446C22×C4C23×D1711yescharacteristic
1447C22×C4C23×D1711yescharacteristic
1448C22×C4C23×D1711yescharacteristic
1449C4⋊C4—22no—
1450C4⋊C4—22no—
1451C4⋊C4—41no—
1452C4⋊C4—41no—
1453C4⋊C4—174no—
1454C4⋊C4—342no—
1455C4⋊C4—342no—
1456C4⋊C4—342no—
1457C4⋊C4—342no—
1458C4⋊C4—342no—
1459C4⋊C4—342no—
1460C4⋊C4—342no—
1461C4⋊C4—342no—
1462C4⋊C4—342no—
1463C4⋊C4—681no—
1464C4⋊C4—681no—
1465C4⋊C4—681no—
1466C4⋊C4—681no—
1467C4⋊C4—681no—
1468C4⋊C4—681no—
1469C4⋊C4—681no—
1470C4⋊C4—681no—
1471C4⋊C4—681no—
1472C4⋊C4—681no—
1473C22⋊C4—22no—
1474C22⋊C4—22no—
1475C22⋊C4—22no—
1476C22⋊C4—22no—
1477C22⋊C4—22no—
1478C22⋊C4—22no—
1479C22⋊C4—22no—
1480C22⋊C4—22no—
1481C22⋊C4—41no—
1482C22⋊C4—41no—
1483C22⋊C4—41no—
1484C22⋊C4—41no—
1485C22⋊C4—41no—
1486C22⋊C4—41no—
1487C22⋊C4—174no—
1488C22⋊C4—174no—
1489C22⋊C4—342no—
1490C22⋊C4—342no—
1491C22⋊C4—342no—
1492C22⋊C4—342no—
1493C22⋊C4—342no—
1494C22⋊C4—342no—
1495C22⋊C4—342no—
1496C22⋊C4—342no—
1497C22⋊C4—342no—
1498C22⋊C4—342no—
1499C22⋊C4—342no—
1500C22⋊C4—342no—
1501C22⋊C4—342no—
1502C22⋊C4—342no—
1503C22⋊C4—342no—
1504C22⋊C4—342no—
1505C22⋊C4—342no—
1506C22⋊C4—342no—
1507C22⋊C4—342no—
1508C22⋊C4—681no—
1509C22⋊C4—681no—
1510C22⋊C4—681no—
1511C22⋊C4—681no—
1512C22⋊C4—681no—
1513C22⋊C4—681no—
1514C22⋊C4—681no—
1515C22⋊C4—681no—
1516C22⋊C4—681no—
1517C22⋊C4—681no—
1518C22⋊C4—681no—
1519C22⋊C4—681no—
1520C22⋊C4—681no—
1521C22⋊C4—681no—
1522C22⋊C4—681no—
1523C22⋊C4—681no—
1524C22⋊C4—681no—
1525C22⋊C4—681no—
1526C22⋊C4—681no—
1527C22⋊C4—681no—
1528C22⋊C4—681no—
1529C22⋊C4—681no—
1530C22⋊C4—681no—
1531C22⋊C4—681no—
1532C22⋊C4—681no—
1533C42—22no—
1534C42—41no—
1535C42—41no—
1536C42—342no—
1537C42—681no—
1538C42—681no—
1539C42D4×D1714yes—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—21no—
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—21no—
1557C23—21no—
1558C23—21no—
1559C23—21no—
1560C23—172no—
1561C23—172no—
1562C23—172no—
1563C23—341no—
1564C23—341no—
1565C23—341no—
1566C23—341no—
1567C23—341no—
1568C23—341no—
1569C23—341no—
1570C23—341no—
1571C23—341no—
1572C23—341no—
1573C23—341no—
1574C23—341no—
1575C23—341no—
1576C23—341no—
1577C23—341no—
1578C23—341no—
1579C23—341no—
1580C23—341no—
1581C23—341no—
1582C23—341no—
1583C23—341no—
1584C23—341no—
1585C23—341no—
1586C23—341no—
1587C23—341no—
1588C23—341no—
1589C23—341no—
1590C23—341no—
1591C23—341no—
1592C23—341no—
1593C23—341no—
1594C23—341no—
1595C23—684no—
1596C23—684no—
1597C23—684no—
1598C23—684no—
1599C23—684no—
1600C23—684no—
1601C23—684no—
1602C23—684no—
1603C23—1362no—
1604C23—1362no—
1605C23—1362no—
1606C23—1362no—
1607C23—1362no—
1608C23—1362no—
1609C23#1058769612yes—
1610C23C24×D1711yescharacteristic
1611Q8—82no—
1612Q8—684no—
1613D4—82no—
1614D4—82no—
1615D4—82no—
1616D4—684no—
1617D4—684no—
1618D4—684no—
1619D4—684no—
1620D4—684no—
1621D4—684no—
1622D4—684no—
1623D4—684no—
1624D4—1362no—
1625D4—1362no—
1626D4—1362no—
1627D4—1362no—
1628D4—1362no—
1629D4—1362no—
1630D4—1362no—
1631D4—1362no—
1632D4—1362no—
1633D4—1362no—
1634D4—1362no—
1635C2×C4—28no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—172no—
1669C2×C4—172no—
1670C2×C4—341no—
1671C2×C4—341no—
1672C2×C4—341no—
1673C2×C4—341no—
1674C2×C4—341no—
1675C2×C4—341no—
1676C2×C4—341no—
1677C2×C4—341no—
1678C2×C4—341no—
1679C2×C4—341no—
1680C2×C4—341no—
1681C2×C4—341no—
1682C2×C4—341no—
1683C2×C4—341no—
1684C2×C4—341no—
1685C2×C4—341no—
1686C2×C4—341no—
1687C2×C4—341no—
1688C2×C4—341no—
1689C2×C4—341no—
1690C2×C4—341no—
1691C2×C4—341no—
1692C2×C4—341no—
1693C2×C4—341no—
1694C2×C4—341no—
1695C2×C4—341no—
1696C2×C4—341no—
1697C2×C4—341no—
1698C2×C4—341no—
1699C2×C4—341no—
1700C2×C4—341no—
1701C2×C4—684no—
1702C2×C4—684no—
1703C2×C4—684no—
1704C2×C4—684no—
1705C2×C4—684no—
1706C2×C4—684no—
1707C2×C4—684no—
1708C2×C4—1362no—
1709C2×C4—1362no—
1710C2×C4C2×D4×D1712yes—
1711C2×C4C2×D4×D1712yes—
1712C2×C4C2×D4×D1712yes—
1713C2×C4#1058769612yes—
1714C22—22no—
1715C22—22no—
1716C22—22no—
1717C22—41no—
1718C22—41no—
1719C22—41no—
1720C22—41no—
1721C22—41no—
1722C22—41no—
1723C22—41no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—41no—
1733C22—41no—
1734C22—41no—
1735C22—342no—
1736C22—342no—
1737C22—342no—
1738C22—342no—
1739C22—342no—
1740C22—342no—
1741C22—342no—
1742C22—342no—
1743C22—342no—
1744C22—6816no—
1745C22—681no—
1746C22—681no—
1747C22—681no—
1748C22—681no—
1749C22—681no—
1750C22—681no—
1751C22—681no—
1752C22—681no—
1753C22—681no—
1754C22—681no—
1755C22—681no—
1756C22—681no—
1757C22—681no—
1758C22—681no—
1759C22—681no—
1760C22—681no—
1761C22—681no—
1762C22—681no—
1763C22—681no—
1764C22—681no—
1765C22—681no—
1766C22—681no—
1767C22—681no—
1768C22—681no—
1769C22—681no—
1770C22—681no—
1771C22—1368no—
1772C22C22×D4×D1711yescharacteristic
1773C22H(5,𝔽2)×D1711yescharacteristic
1774C22C2×#1058769611yescharacteristic
1775C22C2×#1058769611yescharacteristic
1776C22#1176364411yescharacteristic
1777C22#1176364511yescharacteristic
1778C22#1176364511yescharacteristic
1779C4—22no—
1780C4—22no—
1781C4—22no—
1782C4—22no—
1783C4—41no—
1784C4—41no—
1785C4—41no—
1786C4—41no—
1787C4—41no—
1788C4—41no—
1789C4—41no—
1790C4—41no—
1791C4—342no—
1792C4—342no—
1793C4—681no—
1794C4—681no—
1795C4—681no—
1796C4—681no—
1797C4—681no—
1798C4—681no—
1799C4—681no—
1800C4—681no—
1801C4—681no—
1802C2—42no—
1803C2—81no—
1804C2—81no—
1805C2—682no—
1806C2—682no—
1807C2—682no—
1808C2—1361no—
1809C2—1361no—
1810C2#1454211111yescharacteristic
1811C2#1454241711yescharacteristic
1812C2#1454245111yescharacteristic
1813C2#1454295611yescharacteristic
1814C2#1454297711yescharacteristic
1815C2#1454305411yescharacteristic
1816C2#1454310711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2610C2
hypercenter#2610D17
hypocenterC17#36724
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2610

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11763393C2semidirect
2. C2×#11763321C2semidirect
3. #14537075C2semidirect
4. #14537065C2semidirect
5. #14535452C2semidirect
6. #14535407C2semidirect
7. #14535381C2semidirect
8. #14535368C2semidirect
9. #14535204C2semidirect
10. #14535148C2semidirect
11. #14535135C2semidirect
12. #14535134C2semidirect
13. #14535119C2semidirect
14. #14535107C2semidirect
15. #14535106C2semidirect
16. #14535102C2semidirect
17. #14535034C2semidirect
18. #14535004C2semidirect
19. #14535000C2semidirect
20. #14534995C2semidirect
21. #14534675C2semidirect
22. #14534631C2semidirect
23. #14534411C2semidirect
24. #14534381C2semidirect
25. #14534369C2semidirect
26. #14533756C2semidirect
27. #14533678C2semidirect
28. #14532126C2semidirect
29. #14532101C2semidirect
30. #14531428C2semidirect
31. C17×#2610C2semidirect
33. C23×C4×D17C22semidirect
36. C2×#10587562C22semidirect
37. C2×#10587565C22semidirect
39. C2×#10587633C22semidirect
43. C2×#10587572C22semidirect
44. C2×#10587572C22semidirect
47. C2×#10587583C22semidirect
48. C2×#10587583C22semidirect
49. C2×#10587564C22semidirect
50. C2×#10587632C22semidirect
58. C2×#10587625C22semidirect
63. C2×#10587568C22semidirect
64. C2×#10587568C22semidirect
67. C2×#10587623C22semidirect
68. C2×#10587623C22semidirect
71. C2×C4×D68C22semidirect
72. C2×C4×D68C22semidirect
73. C2×#10587567C22semidirect
74. C2×C22⋊C4×D17C22semidirect
75. #11762751C22semidirect
76. #11762744C22semidirect
77. #11762742C22semidirect
78. #11762741C22semidirect
79. #11762741C22semidirect
80. #11762736C22semidirect
81. #11762736C22semidirect
82. #11762735C22semidirect
83. #11762732C22semidirect
84. #11762732C22semidirect
85. #11762732C22semidirect
86. #11762731C22semidirect
87. #11762731C22semidirect
88. #11762731C22semidirect
90. #11762727C22semidirect
91. #11762727C22semidirect
92. #11762727C22semidirect
99. #11762725C22semidirect
100. #11762725C22semidirect
101. #11762725C22semidirect
102. #11762725C22semidirect
104. #11762724C22semidirect
105. #11762724C22semidirect
106. #11762724C22semidirect
107. #11762722C22semidirect
108. #11762721C22semidirect
114. #11762718C22semidirect
115. #11762718C22semidirect
116. #11762718C22semidirect
119. #11762716C22semidirect
120. #11762713C22semidirect
121. #11762712C22semidirect
125. #11762711C22semidirect
127. #11762709C22semidirect
128. #11762707C22semidirect
129. #11762707C22semidirect
130. #11762704C22semidirect
131. #11762703C22semidirect
132. #11762700C22semidirect
133. #11762700C22semidirect
134. #11762700C22semidirect
135. #11762699C22semidirect
136. #11762698C22semidirect
137. #11762698C22semidirect
138. #11762698C22semidirect
139. #11762698C22semidirect
140. #11762698C22semidirect
141. #11762695C22semidirect
142. #11762693C22semidirect
147. #11762687C22semidirect
148. #11762687C22semidirect
149. #11762686C22semidirect
153. #11762685C22semidirect
154. #11762685C22semidirect
155. #11762685C22semidirect
156. #11762685C22semidirect
157. #11762684C22semidirect
158. #11762684C22semidirect
159. #11762683C22semidirect
160. #11762683C22semidirect
161. #11762683C22semidirect
162. #11762682C22semidirect
163. #11762671C22semidirect
164. #11762671C22semidirect
165. #11762671C22semidirect
166. #11762671C22semidirect
167. #11762668C22semidirect
168. #11762668C22semidirect
169. #11762668C22semidirect
170. #11762667C22semidirect
171. #11762664C22semidirect
172. #11762664C22semidirect
173. C4×C4⋊Dic17C22semidirect
174. C2×C17×#124C22semidirect
175. C2×C17×#117C22semidirect
176. C17×#395C22semidirect
177. C17×#394C22semidirect
178. C17×#393C22semidirect
181. C17×#390C22semidirect
182. C17×#388C22semidirect
183. C17×#388C22semidirect
184. C17×#388C22semidirect
185. C17×#388C22semidirect
187. C17×#386C22semidirect
188. C17×#376C22semidirect
362. C4×D68D4semidirect
828. #2610D17semidirect
933. C2×#124C2×D17semidirect
968. C2×#117C2×D17semidirect
984. #395C2×D17semidirect
1003. #394C2×D17semidirect
1006. #393C2×D17semidirect
1028. #390C2×D17semidirect
1042. #388C2×D17semidirect
1043. #388C2×D17semidirect
1044. #388C2×D17semidirect
1045. #388C2×D17semidirect
1063. #386C2×D17semidirect
1081. #376C2×D17semidirect
1299. C17#36724semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633932
C2×#117633212
#145370752
#145370652
#145354522
#145354072
#145353812
#145353682
#145352042
#145351482
#145351352
#145351342
#145351192
#145351072
#145351062
#145351022
#145350342
#145350042
#145350002
#145349952
#145346752
#145346312
#145344112
#145343812
#145343692
#145337562
#145336782
#145321262
#145321012
#145314282
C17×#26102
#3672417