Finite Group Databasebeta

← #17241346

Subgroups — #17241346

Order 4352.

2602 conjugacy classes of subgroups.

The subgroup lattice has 1762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763400C211yesmaximal, characteristic, complemented
2C2×#123×D17C211yesmaximal, characteristic, complemented
3#14537072C211yesmaximal, characteristic, complemented
4#14537065C211yesmaximal, characteristic, complemented
5#14535490C211yesmaximal, characteristic, complemented
6#14535488C211yesmaximal, characteristic, complemented
7#14535486C211yesmaximal, characteristic, complemented
8#14535484C211yesmaximal, characteristic, complemented
9#14535459C211yesmaximal, characteristic, complemented
10#14535457C211yesmaximal, characteristic, complemented
11#14535451C211yesmaximal, characteristic, complemented
12#14535152C211yesmaximal, characteristic, complemented
13#14535151C211yesmaximal, characteristic, complemented
14#14535148C211yesmaximal, characteristic, complemented
15#14535144C211yesmaximal, characteristic, complemented
16#14535140C211yesmaximal, characteristic, complemented
17#14535136C211yesmaximal, characteristic, complemented
18#14535135C211yesmaximal, characteristic, complemented
19#14535131C211yesmaximal, characteristic, complemented
20#14534590C211yesmaximal, characteristic, complemented
21#14534523C211yesmaximal, characteristic, complemented
22#14534135C211yesmaximal, characteristic, complemented
23#14534126C211yesmaximal, characteristic, complemented
24#14532168C211yesmaximal, characteristic, complemented
25#14532166C211yesmaximal, characteristic, complemented
26#14532164C211yesmaximal, characteristic, complemented
27#14532162C211yesmaximal, characteristic, complemented
28#14532138C211yesmaximal, characteristic, complemented
29#14532133C211yesmaximal, characteristic, complemented
30#14531399C211yesmaximal, characteristic, complemented
31C17×#2705C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763400—28no—
35C2×#10587584C2211yescharacteristic, complemented
36C2×#10587556C2211yescharacteristic, complemented
37C2×#10587576C2211yescharacteristic, complemented
38C2×#10587580C2211yescharacteristic
39C2×#10587580C2211yescharacteristic
40C2×#10587580C2211yescharacteristic
41C2×#10587572C2211yescharacteristic
42C2×#10587572C2211yescharacteristic, complemented
43C2×#10587615C2211yescharacteristic
44C2×#10587569C2211yescharacteristic
45C2×#10587569C2211yescharacteristic
46C2×#10587569C2211yescharacteristic
47C2×#10587569C2211yescharacteristic, complemented
48C2×#10587621C2211yescharacteristic
49#123×D17—28no—
50C2×#10587583C2211yescharacteristic
51C2×#10587583C2211yescharacteristic, complemented
52C2×#10587610C2211yescharacteristic, complemented
53C2×#10587582C2211yescharacteristic, complemented
54C2×#10587564C2211yescharacteristic, complemented
55C2×#10587581C2211yescharacteristic
56C2×#10587570C2211yescharacteristic
57C2×#10587570C2211yescharacteristic, complemented
58C2×#10587625C2211yescharacteristic
59C2×#10587625C2211yescharacteristic
60C2×#10587625C2211yescharacteristic, complemented
61C2×#10587624C2211yescharacteristic
62C2×#10587568C2211yescharacteristic
63C2×#10587568C2211yescharacteristic
64C2×#10587623C2211yescharacteristic
65C2×#10587623C2211yescharacteristic
66C2×C4×D68C2211yescharacteristic
67C2×#10587567C2211yescharacteristic
68C2×#10587578C2211yescharacteristic
69C2×#10587558C2211yescharacteristic
70C2×C4⋊C4×D17C2211yescharacteristic
71C2×C4⋊C4×D17C2211yescharacteristic
72C2×C22⋊C4×D17C2211yescharacteristic
73C2×C22⋊C4×D17C2211yescharacteristic
74C2×C22⋊C4×D17C2211yescharacteristic
75#11762744C2211yescharacteristic, complemented
76#11762743C2211yescharacteristic, complemented
77#11762742C2211yescharacteristic, complemented
78#11762741C2211yescharacteristic, complemented
79#11762739C2211yescharacteristic, complemented
80#11762738C2211yescharacteristic, complemented
81#11762737C2211yescharacteristic, complemented
82#11762733C2211yescharacteristic, complemented
83#11762733C2211yescharacteristic, complemented
84#11762732C2211yescharacteristic, complemented
85#11762732C2211yescharacteristic, complemented
86#11762732C2211yescharacteristic, complemented
87#11762732C2211yescharacteristic, complemented
88#11762732C2211yescharacteristic, complemented
89#11762732C2211yescharacteristic, complemented
90#11762731C2211yescharacteristic, complemented
91#11762731C2211yescharacteristic, complemented
92#11762731C2211yescharacteristic, complemented
93#11762731C2211yescharacteristic, complemented
94#11762731C2211yescharacteristic, complemented
95#11762731C2211yescharacteristic, complemented
96#11762727C2211yescharacteristic
97#11762727C2211yescharacteristic, complemented
98#11762726C2211yescharacteristic, complemented
99#11762726C2211yescharacteristic, complemented
100#11762725C2211yescharacteristic
101#11762725C2211yescharacteristic
102#11762725C2211yescharacteristic, complemented
103#11762725C2211yescharacteristic, complemented
104#11762725C2211yescharacteristic, complemented
105#11762725C2211yescharacteristic, complemented
106#11762724C2211yescharacteristic, complemented
107#11762724C2211yescharacteristic, complemented
108#11762723C2211yescharacteristic
109#11762723C2211yescharacteristic, complemented
110#11762722C2211yescharacteristic, complemented
111#11762721C2211yescharacteristic, complemented
112#11762718C2211yescharacteristic
113#11762718C2211yescharacteristic
114#11762718C2211yescharacteristic
115#11762718C2211yescharacteristic, complemented
116#11762717C2211yescharacteristic, complemented
117#11762712C2211yescharacteristic, complemented
118#11762711C2211yescharacteristic
119#11762711C2211yescharacteristic, complemented
120#11762710C2211yescharacteristic, complemented
121#11762709C2211yescharacteristic
122#11762709C2211yescharacteristic
123#11762709C2211yescharacteristic, complemented
124#11762709C2211yescharacteristic, complemented
125#11762709C2211yescharacteristic, complemented
126#11762709C2211yescharacteristic, complemented
127#11762708C2211yescharacteristic, complemented
128#11762707C2211yescharacteristic, complemented
129#11762706C2211yescharacteristic, complemented
130#11762706C2211yescharacteristic, complemented
131#11762705C2211yescharacteristic, complemented
132#11762704C2211yescharacteristic, complemented
133#11762704C2211yescharacteristic, complemented
134#11762703C2211yescharacteristic, complemented
135#11762702C2211yescharacteristic, complemented
136#11762701C2211yescharacteristic, complemented
137#11762700C2211yescharacteristic, complemented
138#11762699C2211yescharacteristic, complemented
139#11762698C2211yescharacteristic, complemented
140#11762697C2211yescharacteristic, complemented
141#11762695C2211yescharacteristic, complemented
142#11762693C2211yescharacteristic, complemented
143#11762691C2211yescharacteristic, complemented
144#11762688C2211yescharacteristic, complemented
145#11762687C2211yescharacteristic
146#11762687C2211yescharacteristic
147#11762687C2211yescharacteristic, complemented
148#11762685C2211yescharacteristic
149#11762685C2211yescharacteristic
150#11762685C2211yescharacteristic, complemented
151#11762684C2211yescharacteristic, complemented
152#11762684C2211yescharacteristic, complemented
153#11762684C2211yescharacteristic, complemented
154#11762683C2211yescharacteristic
155#11762683C2211yescharacteristic
156#11762683C2211yescharacteristic, complemented
157#11762683C2211yescharacteristic, complemented
158#11762683C2211yescharacteristic, complemented
159#11762681C2211yescharacteristic, complemented
160#11762680C2211yescharacteristic
161#11762680C2211yescharacteristic
162#11762680C2211yescharacteristic, complemented
163#11762668C2211yescharacteristic
164#11762668C2211yescharacteristic
165#11762668C2211yescharacteristic, complemented
166#11762667C2211yescharacteristic, complemented
167#11762666C2211yescharacteristic
168#11762666C2211yescharacteristic
169#11762666C2211yescharacteristic, complemented
170#11762664C2211yescharacteristic
171#11762664C2211yescharacteristic
172#11762664C2211yescharacteristic
173#11762664C2211yescharacteristic
174C2×C17×#126C2211yescharacteristic, complemented
175C2×C17×#123C2211yescharacteristic
176C17×#399C2211yescharacteristic, complemented
177C17×#396C2211yescharacteristic, complemented
178C17×#396C2211yescharacteristic, complemented
179C17×#394C2211yescharacteristic, complemented
180C17×#394C2211yescharacteristic, complemented
181C17×#392C2211yescharacteristic
182C17×#390C2211yescharacteristic
183C17×#390C2211yescharacteristic, complemented
184C17×#389C2211yescharacteristic, complemented
185C17×#388C2211yescharacteristic, complemented
186C17×#387C2211yescharacteristic, complemented
187C17×#386C2211yescharacteristic, complemented
188C17×#380C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C2×D4×D17—24no—
206C2×D4×D17—42no—
207C2×D4×D17—42no—
208C22×D68C2311yescharacteristic
209C22×D68C2311yescharacteristic
210C22×D68C2311yescharacteristic
211C22×D68C2311yescharacteristic
212C22×C4×D17—24no—
213C22×C4×D17—42no—
214C22×C4×D17—42no—
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×Dic34C2311yescharacteristic
224C17×#126—24no—
225C17×#123—24no—
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊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×C42×C17C2311yescharacteristic
250C2×C42×C17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263#10587625—42no—
264#10587625—42no—
265#10587625—42no—
266#10587624—42no—
267#10587623—42no—
268#10587623—42no—
269#10587621—24no—
270#10587615—24no—
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2311yescharacteristic
306C2×C4⋊Dic17C2311yescharacteristic
307C2×C4⋊Dic17C2311yescharacteristic
308C2×C4⋊Dic17C2311yescharacteristic
309C2×C4⋊Dic17C2311yescharacteristic
310C2×C4⋊Dic17C2311yescharacteristic
311C2×C4⋊Dic17C2311yescharacteristic
312C2×C4⋊Dic17C2311yescharacteristic
313C2×C4⋊Dic17C2311yescharacteristic
314#10587610—42no—
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×#63225C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×#63225C2311yescharacteristic
328C2×#63225C2311yescharacteristic
329C2×#63225C2311yescharacteristic
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×#63225C2311yescharacteristic
333C2×C4×Dic17C2311yescharacteristic
334C2×C4×Dic17C2311yescharacteristic
335C2×C4×Dic17C2311yescharacteristic
336C2×C4×Dic17C2311yescharacteristic
337#10587584—24no—
338#10587583—24no—
339#10587583—42no—
340#10587582—24no—
341#10587581—42no—
342#10587580—24no—
343#10587580—24no—
344#10587580—24no—
345#10587578—42no—
346C4⋊C4×D17—24no—
347C4⋊C4×D17D418yescomplemented
348#10587576—24no—
349#10587572—24no—
350#10587572—24no—
351#10587570—24no—
352#10587570—42no—
353#10587569—24no—
354#10587569—24no—
355#10587569—24no—
356#10587569—24no—
357#10587568—42no—
358#10587568—42no—
359#10587567—24no—
360C22⋊C4×D17—24no—
361C22⋊C4×D17—24no—
362C22⋊C4×D17—24no—
363#10587564—24no—
364C4×D68—24no—
365#10587558—42no—
366#10587556—24no—
367C17×#95C2311yescharacteristic
368C17×#95C2311yescharacteristic
369C17×#95C2311yescharacteristic
370C17×#95C2311yescharacteristic
371C17×#95C2311yescharacteristic
372C17×#95C2311yescharacteristic
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—22no—
399C23×D17—22no—
400C23×D17—22no—
401C23×D17—22no—
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
412C2×D4×C17—22no—
413C2×D4×C17—22no—
414C2×D4×C17—22no—
415C2×D4×C17—41no—
416C2×D4×C17—41no—
417C2×D4×C17—41no—
418C2×D4×C17—41no—
419C2×D4×C17—41no—
420C2×D4×C17—41no—
421C22×C4×C17—22no—
422C22×C4×C17—22no—
423C22×C4×C17—41no—
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C2×C22⋊D17—22no—
437C2×C22⋊D17—22no—
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
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—41no—
447C2×C22⋊D17—41no—
448C2×C22⋊D17—41no—
449C2×C22⋊D17—41no—
450C2×C22⋊D17—41no—
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—
460C22×Dic17—22no—
461C22×Dic17—22no—
462C22×Dic17—22no—
463C22×Dic17—41no—
464C22×Dic17—41no—
465C22×Dic17—41no—
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478D4×D17—416no—
479C2×D68—22no—
480C2×D68—22no—
481C2×D68—22no—
482C2×D68—22no—
483C2×D68—22no—
484C2×D68—22no—
485C2×D68—41no—
486C2×D68—41no—
487C2×D68—41no—
488C2×D68—41no—
489C2×D68—41no—
490C2×D68—41no—
491C2×C4×D17—22no—
492C2×C4×D17—22no—
493C2×C4×D17—22no—
494C2×C4×D17—22no—
495C2×C4×D17—22no—
496C2×C4×D17—22no—
497C2×C4×D17—22no—
498C2×C4×D17—22no—
499C2×C4×D17—22no—
500C2×C4×D17—41no—
501C2×C4×D17—41no—
502C2×C4×D17—41no—
503C2×C4×D17—41no—
504C2×C4×D17—41no—
505C2×C4×D17—41no—
506C2×C4×D17—41no—
507C2×C4×D17—41no—
508C2×C4×D17—41no—
509C2×C4×D17—41no—
510C2×C4×D17—416no—
511C2×C4×D17—41no—
512C2×C4×D17—41no—
513C2×C4×D17C2×D414yes—
514C2×C4×D17C2×D414yes—
515C2×C4×D17C2×D414yes—
516C2×Dic34—22no—
517C2×Dic34—41no—
518C2×Dic34—41no—
519C4⋊C4×C17—22no—
520C4⋊C4×C17—22no—
521C4⋊C4×C17—22no—
522C4⋊C4×C17—41no—
523C4⋊C4×C17—41no—
524C4⋊C4×C17—41no—
525C4⋊C4×C17—41no—
526C4⋊C4×C17—41no—
527C4⋊C4×C17C2×D414yes—
528C22⋊C4×C17—22no—
529C22⋊C4×C17—22no—
530C22⋊C4×C17—22no—
531C22⋊C4×C17—22no—
532C22⋊C4×C17—22no—
533C22⋊C4×C17—22no—
534C22⋊C4×C17—41no—
535C22⋊C4×C17—41no—
536C22⋊C4×C17—41no—
537C22⋊C4×C17—41no—
538C22⋊C4×C17—41no—
539C22⋊C4×C17—41no—
540C22⋊C4×C17—41no—
541C22⋊C4×C17—41no—
542C42×C17—22no—
543C42×C17—41no—
544C22⋊Dic17—22no—
545C22⋊Dic17—22no—
546C22⋊Dic17—22no—
547C22⋊Dic17—22no—
548C22⋊Dic17—22no—
549C22⋊Dic17—22no—
550C22⋊Dic17—41no—
551C22⋊Dic17—41no—
552C22⋊Dic17—41no—
553C22⋊Dic17—41no—
554C22⋊Dic17—41no—
555C22⋊Dic17—41no—
556#63227—22no—
557#63227—22no—
558#63227—22no—
559#63227—22no—
560#63227—22no—
561#63227—22no—
562#63227—22no—
563#63227—22no—
564#63227—22no—
565#63227—22no—
566#63227—22no—
567#63227—22no—
568#63227—22no—
569#63227—22no—
570#63227—22no—
571#63227—22no—
572#63227—22no—
573#63227—22no—
574#63227—41no—
575#63227—41no—
576#63227—41no—
577#63227—41no—
578#63227—41no—
579#63227—41no—
580#63227—41no—
581#63227—41no—
582#63227—41no—
583#63227—41no—
584#63227—41no—
585#63227—41no—
586#63227—41no—
587#63227—41no—
588C4⋊Dic17—22no—
589C4⋊Dic17—22no—
590C4⋊Dic17—22no—
591C4⋊Dic17—22no—
592C4⋊Dic17—22no—
593C4⋊Dic17—41no—
594C4⋊Dic17—41no—
595C4⋊Dic17—41no—
596C4⋊Dic17—41no—
597C4⋊Dic17—41no—
598C4⋊Dic17C2×D414yes—
599#63225—22no—
600#63225—22no—
601#63225—22no—
602#63225—22no—
603#63225—22no—
604#63225—22no—
605#63225—41no—
606#63225—41no—
607#63225—41no—
608#63225—41no—
609#63225—41no—
610#63225—41no—
611#63225—41no—
612#63225—41no—
613#63225—41no—
614#63225—41no—
615#63225C2×D414yes—
616#63225C2×D414yes—
617C4×Dic17—22no—
618C4×Dic17—41no—
619C4×Dic17—41no—
620C4×Dic17—41no—
621#36722—171nomaximal, Sylow
622C23×C17—21no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17—21no—
626C23×C17—21no—
627C23×C17—21no—
628C23×C17—21no—
629C23×C17—21no—
630C23×C17—21no—
631C23×C17—21no—
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×C17H(5,𝔽2)12yes—
643C23×C17C2511yescharacteristic
644C22×D17—21no—
645C22×D17—21no—
646C22×D17—21no—
647C22×D17—21no—
648C22×D17—28no—
649C22×D17—21no—
650C22×D17—21no—
651C22×D17—21no—
652C22×D17—21no—
653C22×D17—21no—
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—44no—
670C22×D17—44no—
671C22×D17—44no—
672C22×D17—44no—
673C22×D17—44no—
674C22×D17—44no—
675C22×D17—44no—
676C22×D17—44no—
677C22×D17—44no—
678C22×D17—82no—
679C22×D17—82no—
680C22×D17—82no—
681C22×D17—82no—
682C22×D17C22×D412yes—
683C22×D17H(5,𝔽2)12yes—
684C22×D17H(5,𝔽2)12yes—
685C22×D172−1+412yes—
686D4×C17—44no—
687D4×C17—82no—
688D4×C17—82no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—21no—
693C2×C4×C17—21no—
694C2×C4×C17—21no—
695C2×C4×C17—21no—
696C2×C4×C17—21no—
697C2×C4×C17—21no—
698C2×C4×C17—21no—
699C2×C4×C17—21no—
700C2×C4×C17—21no—
701C2×C4×C17—21no—
702C2×C4×C17—21no—
703C2×C4×C17—21no—
704C2×C4×C17—21no—
705C2×C4×C17—21no—
706C2×C4×C17—21no—
707C2×C4×C17—21no—
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—44no—
723C2×C4×C17C22×D412yes—
724C2×C4×C17C22×D412yes—
725C2×C4×C17C22×D412yes—
726C22⋊D17—44no—
727C22⋊D17—44no—
728C22⋊D17—44no—
729C22⋊D17—82no—
730C22⋊D17—82no—
731C22⋊D17—82no—
732C22⋊D17—82no—
733C22⋊D17—82no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—21no—
739C2×Dic17—21no—
740C2×Dic17—21no—
741C2×Dic17—21no—
742C2×Dic17—21no—
743C2×Dic17—21no—
744C2×Dic17—21no—
745C2×Dic17—21no—
746C2×Dic17—21no—
747C2×Dic17—21no—
748C2×Dic17—21no—
749C2×Dic17—21no—
750C2×Dic17—21no—
751C2×Dic17—21no—
752C2×Dic17—21no—
753C2×Dic17—21no—
754C2×Dic17—21no—
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—44no—
768C2×Dic17—82no—
769C2×Dic17C22×D412yes—
770C2×Dic17C22×D412yes—
771C2×Dic17C22×D412yes—
772D68—44no—
773D68—44no—
774D68—82no—
775D68—82no—
776C4×D17—28no—
777C4×D17—44no—
778C4×D17—44no—
779C4×D17—44no—
780C4×D17—44no—
781C4×D17—44no—
782C4×D17—44no—
783C4×D17—82no—
784Dic34—82no—
785C2×#539—171no—
786C22×#123—171no—
787#2848—171no—
788#2847—171no—
789#2707—171no—
790#2707—171no—
791#2707—171no—
792#2707—171no—
793#2705—171no—
794#2705—171no—
795#2705—171no—
796#2705D1711yescharacteristic, complemented
797#2682—171no—
798#2682—171no—
799#2682—171no—
800#2682—171no—
801#2681—171no—
802#2681—171no—
803#2681—171no—
804#2681—171no—
805#2626—171no—
806#2617—171no—
807#2579—171no—
808#2579—171no—
809#2411—171no—
810#2411—171no—
811#2411—171no—
812#2411—171no—
813#2408—171no—
814#2408—171no—
815#2316—171no—
816C22×C17—22no—
817C22×C17—22no—
818C22×C17—22no—
819C22×C17—41no—
820C22×C17—41no—
821C22×C17—41no—
822C22×C17—41no—
823C22×C17—41no—
824C22×C17—41no—
825C22×C17—41no—
826C22×C17—41no—
827C22×C17—41no—
828C22×C17—41no—
829C22×C17—41no—
830C22×C17—41no—
831C22×C17—41no—
832C22×C17—41no—
833C22×C17—41no—
834C22×C17—41no—
835C22×C17—41no—
836C22×C17—41no—
837C22×C17C23×D411yescharacteristic
838C22×C17C2×H(5,𝔽2)11yescharacteristic
839C22×C17C2×H(5,𝔽2)11yescharacteristic
840C22×C17C2×H(5,𝔽2)11yescharacteristic
841C22×C17C2×2−1+411yescharacteristic
842C22×C17#58511yescharacteristic
843C22×C17#58511yescharacteristic
844C2×D17—22no—
845C2×D17—22no—
846C2×D17—22no—
847C2×D17—22no—
848C2×D17—22no—
849C2×D17—22no—
850C2×D17—22no—
851C2×D17—22no—
852C2×D17—22no—
853C2×D17—416no—
854C2×D17—41no—
855C2×D17—41no—
856C2×D17—41no—
857C2×D17—41no—
858C2×D17—41no—
859C2×D17—41no—
860C2×D17—41no—
861C2×D17—41no—
862C2×D17—41no—
863C2×D17—41no—
864C2×D17—41no—
865C2×D17—41no—
866C2×D17—41no—
867C2×D17—41no—
868C2×D17—41no—
869C2×D17—41no—
870C2×D17—41no—
871C2×D17—41no—
872C2×D17—88no—
873C2×D17#53714yes—
874C4×C17—22no—
875C4×C17—22no—
876C4×C17—22no—
877C4×C17—41no—
878C4×C17—41no—
879C4×C17—41no—
880C4×C17—41no—
881C4×C17—41no—
882C4×C17—41no—
883C4×C17—41no—
884C4×C17—41no—
885C4×C17—41no—
886Dic17—22no—
887Dic17—22no—
888Dic17—22no—
889Dic17—41no—
890Dic17—41no—
891Dic17—41no—
892Dic17—41no—
893Dic17—41no—
894Dic17—41no—
895Dic17—41no—
896Dic17—41no—
897Dic17—41no—
898C23×D4—171no—
899C24×C4—171no—
900#539—348no—
901C2×#126—171no—
902C2×#126C2×D1711yescharacteristic, complemented
903C2×#125—171no—
904C2×#125—171no—
905C2×#123—171no—
906C2×#123—171no—
907C2×#123—171no—
908C2×#123—171no—
909C2×#123—171no—
910C2×#123—171no—
911C2×#123—171no—
912C2×#123—171no—
913C2×#123—171no—
914C2×#123—171no—
915C2×#123—171no—
916C2×#123—348no—
917C2×#123C2×D1711yescharacteristic
918C2×C22⋊Q8—171no—
919C2×C22⋊Q8—171no—
920C2×C22⋊Q8—171no—
921C2×C22⋊Q8—171no—
922C2×C22⋊Q8—171no—
923C2×#121—171no—
924C2×#121—171no—
925C2×#121—171no—
926C2×#121—171no—
927C2×#121—171no—
928C2×#121—171no—
929C2×#121—171no—
930C2×#120—171no—
931C2×#120—171no—
932C2×#120—171no—
933C2×#120—171no—
934C2×C4×D4—171no—
935C2×C4×D4—171no—
936C2×#117—171no—
937C2×#117—171no—
938C22×C4⋊C4—171no—
939C22×C4⋊C4—171no—
940C22×C22⋊C4—171no—
941C22×C22⋊C4—171no—
942C22×C22⋊C4—171no—
943#399—171no—
944#399C2×D1711yescharacteristic, complemented
945#398—171no—
946#398—171no—
947#398—171no—
948#398—171no—
949#397—171no—
950#397—171no—
951#396—171no—
952#396—171no—
953#396—171no—
954#396—171no—
955#396—171no—
956#396—171no—
957#396—171no—
958#396—171no—
959#396—171no—
960#396—171no—
961#396—171no—
962#396—171no—
963#396—171no—
964#396—171no—
965#396C2×D1711yescharacteristic, complemented
966#396C2×D1711yescharacteristic, complemented
967#394—171no—
968#394—171no—
969#394—171no—
970#394—171no—
971#394—171no—
972#394—171no—
973#394—171no—
974#394—171no—
975#394—171no—
976#394—171no—
977#394—171no—
978#394—171no—
979#394—171no—
980#394—171no—
981#394C2×D1711yescharacteristic, complemented
982#394C2×D1711yescharacteristic, complemented
983#393—171no—
984#393—171no—
985#392—171no—
986#392—171no—
987#392—171no—
988#392—171no—
989#392—171no—
990#392C2×D1711yescharacteristic
991#390—171no—
992#390—171no—
993#390—171no—
994#390—171no—
995#390—171no—
996#390—171no—
997#390—171no—
998#390—171no—
999#390—171no—
1000#390—171no—
1001#390C2×D1711yescharacteristic
1002#390C2×D1711yescharacteristic, complemented
1003#389—171no—
1004#389—171no—
1005#389—171no—
1006#389—171no—
1007#389—171no—
1008#389—171no—
1009#389—171no—
1010#389C2×D1711yescharacteristic, complemented
1011#388—171no—
1012#388—171no—
1013#388—171no—
1014#388—171no—
1015#388—171no—
1016#388—171no—
1017#388—171no—
1018#388C2×D1711yescharacteristic, complemented
1019#387—171no—
1020#387—171no—
1021#387—171no—
1022#387C2×D1711yescharacteristic, complemented
1023#386—171no—
1024#386—171no—
1025#386—171no—
1026#386—171no—
1027#386—171no—
1028#386—171no—
1029#386—171no—
1030#386C2×D1711yescharacteristic, complemented
1031#385—171no—
1032#385—171no—
1033#385—171no—
1034#385—171no—
1035#385—171no—
1036#385—171no—
1037#385—171no—
1038#385—171no—
1039#385—171no—
1040#385—171no—
1041#385—171no—
1042#385—171no—
1043#380—171no—
1044#380—171no—
1045#380—171no—
1046#380—171no—
1047#380—171no—
1048#380—171no—
1049#380—171no—
1050#380C2×D1711yescharacteristic, complemented
1051#379—171no—
1052#379—171no—
1053#379—171no—
1054#379—171no—
1055C2×C17—42no—
1056C2×C17—81no—
1057C2×C17—81no—
1058C2×C17C2×#53711yescharacteristic
1059C2×C17#348411yescharacteristic
1060C2×C17#348711yescharacteristic
1061C2×C17#353411yescharacteristic
1062C2×C17#353411yescharacteristic
1063C2×C17#353511yescharacteristic
1064C2×C17#353511yescharacteristic
1065D17—24no—
1066D17—42no—
1067D17—81no—
1068D17—81no—
1069C25—171no—
1070C25—171no—
1071C22×Q8—171no—
1072C22×D4—171no—
1073C22×D4—171no—
1074C22×D4—171no—
1075C22×D4—171no—
1076C22×D4—171no—
1077C22×D4—171no—
1078C22×D4—171no—
1079C22×D4—171no—
1080C22×D4—171no—
1081C22×D4—171no—
1082C22×D4—171no—
1083C22×D4—171no—
1084C22×D4—344no—
1085C22×D4—682no—
1086C22×D4—682no—
1087C22×D4C22×D1711yescharacteristic
1088C22×D4C22×D1711yescharacteristic
1089C22×D4C22×D1711yescharacteristic
1090C23×C4—171no—
1091C23×C4—171no—
1092C23×C4—171no—
1093C23×C4—171no—
1094C23×C4—171no—
1095C23×C4—171no—
1096C23×C4—171no—
1097C23×C4—171no—
1098C23×C4—171no—
1099C23×C4—171no—
1100C23×C4—344no—
1101C23×C4—682no—
1102C23×C4—682no—
1103C23×C4C22×D1711yescharacteristic
1104#126—24no—
1105#126—344no—
1106#125—344no—
1107#125—344no—
1108#123—24no—
1109#123—344no—
1110#123—344no—
1111#123—344no—
1112#123—344no—
1113#123—344no—
1114#123—344no—
1115#123—344no—
1116#123—344no—
1117#123—344no—
1118#123—344no—
1119#123—344no—
1120C22⋊Q8—344no—
1121C22⋊Q8—344no—
1122C22⋊Q8—344no—
1123C22⋊Q8—682no—
1124C22⋊Q8—682no—
1125#121—344no—
1126#121—682no—
1127#121—682no—
1128#121—682no—
1129#121—682no—
1130#121—682no—
1131#121—682no—
1132#120—682no—
1133#120—682no—
1134#120—682no—
1135#120—682no—
1136C4×D4—344no—
1137C4×D4—344no—
1138#117—682no—
1139#117—682no—
1140C2×C4⋊C4—171no—
1141C2×C4⋊C4—171no—
1142C2×C4⋊C4—171no—
1143C2×C4⋊C4—178no—
1144C2×C4⋊C4—171no—
1145C2×C4⋊C4—171no—
1146C2×C4⋊C4—171no—
1147C2×C4⋊C4—171no—
1148C2×C4⋊C4—171no—
1149C2×C4⋊C4—171no—
1150C2×C4⋊C4—171no—
1151C2×C4⋊C4—171no—
1152C2×C4⋊C4—171no—
1153C2×C4⋊C4—171no—
1154C2×C4⋊C4—171no—
1155C2×C4⋊C4—171no—
1156C2×C4⋊C4—171no—
1157C2×C4⋊C4—171no—
1158C2×C4⋊C4—171no—
1159C2×C4⋊C4—171no—
1160C2×C4⋊C4—171no—
1161C2×C4⋊C4—171no—
1162C2×C4⋊C4—171no—
1163C2×C4⋊C4—171no—
1164C2×C4⋊C4—171no—
1165C2×C4⋊C4—171no—
1166C2×C4⋊C4—171no—
1167C2×C4⋊C4—171no—
1168C2×C4⋊C4—171no—
1169C2×C4⋊C4—171no—
1170C2×C4⋊C4—344no—
1171C2×C4⋊C4C22×D1711yescharacteristic
1172C2×C4⋊C4C22×D1711yescharacteristic
1173C2×C4⋊C4C22×D1711yescharacteristic
1174C2×C4⋊C4C22×D1711yescharacteristic
1175C2×C4⋊C4C22×D1711yescharacteristic
1176C2×C4⋊C4C22×D1711yescharacteristic
1177C2×C4⋊C4C22×D1711yescharacteristic
1178C2×C4⋊C4C22×D1711yescharacteristic
1179C2×C4⋊C4C22×D1711yescharacteristic
1180C2×C22⋊C4—171no—
1181C2×C22⋊C4—171no—
1182C2×C22⋊C4—171no—
1183C2×C22⋊C4—171no—
1184C2×C22⋊C4—171no—
1185C2×C22⋊C4—171no—
1186C2×C22⋊C4—171no—
1187C2×C22⋊C4—171no—
1188C2×C22⋊C4—171no—
1189C2×C22⋊C4—171no—
1190C2×C22⋊C4—171no—
1191C2×C22⋊C4—171no—
1192C2×C22⋊C4—171no—
1193C2×C22⋊C4—171no—
1194C2×C22⋊C4—171no—
1195C2×C22⋊C4—171no—
1196C2×C22⋊C4—171no—
1197C2×C22⋊C4—171no—
1198C2×C22⋊C4—171no—
1199C2×C22⋊C4—171no—
1200C2×C22⋊C4—171no—
1201C2×C22⋊C4—171no—
1202C2×C22⋊C4—171no—
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—344no—
1225C2×C22⋊C4—344no—
1226C2×C22⋊C4—344no—
1227C2×C22⋊C4C22×D1711yescharacteristic
1228C2×C22⋊C4C22×D1711yescharacteristic
1229C2×C22⋊C4C22×D1711yescharacteristic
1230C2×C22⋊C4C22×D1711yescharacteristic
1231C2×C22⋊C4C22×D1711yescharacteristic
1232C2×C22⋊C4C22×D1711yescharacteristic
1233C2×C22⋊C4C22×D1711yescharacteristic
1234C2×C22⋊C4C22×D1711yescharacteristic
1235C2×C22⋊C4C22×D1711yescharacteristic
1236C2×C22⋊C4C22×D1711yescharacteristic
1237C2×C22⋊C4C22×D1711yescharacteristic
1238C2×C22⋊C4C22×D1711yescharacteristic
1239C2×C22⋊C4C22×D1711yescharacteristic
1240C2×C22⋊C4C22×D1711yescharacteristic
1241C2×C42—171no—
1242C2×C42—171no—
1243C2×C42—171no—
1244C2×C42—171no—
1245C2×C42C22×D1711yescharacteristic
1246C2×C42C22×D1711yescharacteristic
1247#95—171no—
1248#95—171no—
1249#95—171no—
1250#95—171no—
1251#95—171no—
1252#95—171no—
1253#95—171no—
1254#95—171no—
1255#95—171no—
1256#95—171no—
1257#95—171no—
1258#95—171no—
1259#95—171no—
1260#95—171no—
1261#95—171no—
1262#95—171no—
1263#95—171no—
1264#95—171no—
1265#95C22×D1711yescharacteristic
1266#95C22×D1711yescharacteristic
1267#95C22×D1711yescharacteristic
1268#95C22×D1711yescharacteristic
1269#95C22×D1711yescharacteristic
1270#95C22×D1711yescharacteristic
1271C17#3672211yescharacteristic, complemented, Sylow
1272C24—171no—
1273C24—171no—
1274C24—171no—
1275C24—171no—
1276C24—342no—
1277C24—342no—
1278C24—342no—
1279C24—342no—
1280C24—342no—
1281C24—342no—
1282C24—342no—
1283C24—342no—
1284C24—681no—
1285C24—681no—
1286C24—681no—
1287C24—681no—
1288C24—681no—
1289C24—681no—
1290C24C23×D1711yescharacteristic
1291C24C23×D1711yescharacteristic
1292C24C23×D1711yescharacteristic
1293C2×Q8—342no—
1294C2×Q8—681no—
1295C2×Q8—681no—
1296C2×D4—22no—
1297C2×D4—22no—
1298C2×D4—22no—
1299C2×D4—41no—
1300C2×D4—41no—
1301C2×D4—41no—
1302C2×D4—41no—
1303C2×D4—41no—
1304C2×D4—41no—
1305C2×D4—342no—
1306C2×D4—342no—
1307C2×D4—342no—
1308C2×D4—342no—
1309C2×D4—342no—
1310C2×D4—342no—
1311C2×D4—342no—
1312C2×D4—342no—
1313C2×D4—342no—
1314C2×D4—342no—
1315C2×D4—342no—
1316C2×D4—342no—
1317C2×D4—342no—
1318C2×D4—342no—
1319C2×D4—342no—
1320C2×D4—342no—
1321C2×D4—681no—
1322C2×D4—681no—
1323C2×D4—681no—
1324C2×D4—681no—
1325C2×D4—681no—
1326C2×D4—681no—
1327C2×D4—681no—
1328C2×D4—681no—
1329C2×D4—681no—
1330C2×D4—681no—
1331C2×D4—681no—
1332C2×D4—681no—
1333C2×D4—681no—
1334C2×D4—681no—
1335C2×D4—681no—
1336C2×D4—681no—
1337C2×D4—681no—
1338C2×D4—681no—
1339C2×D4—681no—
1340C2×D4—681no—
1341C2×D4—6816no—
1342C22×C4—22no—
1343C22×C4—22no—
1344C22×C4—41no—
1345C22×C4—171no—
1346C22×C4—171no—
1347C22×C4—171no—
1348C22×C4—174no—
1349C22×C4—174no—
1350C22×C4—174no—
1351C22×C4—171no—
1352C22×C4—171no—
1353C22×C4—171no—
1354C22×C4—171no—
1355C22×C4—171no—
1356C22×C4—171no—
1357C22×C4—171no—
1358C22×C4—171no—
1359C22×C4—171no—
1360C22×C4—342no—
1361C22×C4—342no—
1362C22×C4—342no—
1363C22×C4—342no—
1364C22×C4—342no—
1365C22×C4—342no—
1366C22×C4—342no—
1367C22×C4—342no—
1368C22×C4—342no—
1369C22×C4—342no—
1370C22×C4—342no—
1371C22×C4—342no—
1372C22×C4—681no—
1373C22×C4—681no—
1374C22×C4—681no—
1375C22×C4—681no—
1376C22×C4—681no—
1377C22×C4—681no—
1378C22×C4—681no—
1379C22×C4—681no—
1380C22×C4—681no—
1381C22×C4—681no—
1382C22×C4—681no—
1383C22×C4—681no—
1384C22×C4—6816no—
1385C22×C4—681no—
1386C22×C4—681no—
1387C22×C4—681no—
1388C22×C4C23×D1711yescharacteristic
1389C22×C4C23×D1711yescharacteristic
1390C22×C4C23×D1711yescharacteristic
1391C22×C4C23×D1711yescharacteristic
1392C22×C4C23×D1711yescharacteristic
1393C22×C4C23×D1711yescharacteristic
1394C22×C4C23×D1711yescharacteristic
1395C22×C4C23×D1711yescharacteristic
1396C22×C4C23×D1711yescharacteristic
1397C22×C4C23×D1711yescharacteristic
1398C22×C4C23×D1711yescharacteristic
1399C22×C4C23×D1711yescharacteristic
1400C4⋊C4—22no—
1401C4⋊C4—22no—
1402C4⋊C4—22no—
1403C4⋊C4—41no—
1404C4⋊C4—41no—
1405C4⋊C4—41no—
1406C4⋊C4—41no—
1407C4⋊C4—41no—
1408C4⋊C4—174no—
1409C4⋊C4—174no—
1410C4⋊C4—174no—
1411C4⋊C4—342no—
1412C4⋊C4—342no—
1413C4⋊C4—342no—
1414C4⋊C4—342no—
1415C4⋊C4—342no—
1416C4⋊C4—342no—
1417C4⋊C4—342no—
1418C4⋊C4—342no—
1419C4⋊C4—342no—
1420C4⋊C4—342no—
1421C4⋊C4—342no—
1422C4⋊C4—681no—
1423C4⋊C4—681no—
1424C4⋊C4—681no—
1425C4⋊C4—681no—
1426C4⋊C4—681no—
1427C4⋊C4—681no—
1428C4⋊C4—681no—
1429C4⋊C4—681no—
1430C4⋊C4—681no—
1431C4⋊C4—681no—
1432C4⋊C4—681no—
1433C4⋊C4—681no—
1434C4⋊C4—681no—
1435C4⋊C4—681no—
1436C4⋊C4—681no—
1437C4⋊C4D4×D1714yes—
1438C22⋊C4—22no—
1439C22⋊C4—22no—
1440C22⋊C4—22no—
1441C22⋊C4—22no—
1442C22⋊C4—22no—
1443C22⋊C4—22no—
1444C22⋊C4—41no—
1445C22⋊C4—41no—
1446C22⋊C4—41no—
1447C22⋊C4—41no—
1448C22⋊C4—41no—
1449C22⋊C4—41no—
1450C22⋊C4—41no—
1451C22⋊C4—41no—
1452C22⋊C4—342no—
1453C22⋊C4—342no—
1454C22⋊C4—342no—
1455C22⋊C4—342no—
1456C22⋊C4—342no—
1457C22⋊C4—342no—
1458C22⋊C4—342no—
1459C22⋊C4—342no—
1460C22⋊C4—342no—
1461C22⋊C4—342no—
1462C22⋊C4—342no—
1463C22⋊C4—342no—
1464C22⋊C4—342no—
1465C22⋊C4—342no—
1466C22⋊C4—342no—
1467C22⋊C4—342no—
1468C22⋊C4—342no—
1469C22⋊C4—342no—
1470C22⋊C4—342no—
1471C22⋊C4—342no—
1472C22⋊C4—342no—
1473C22⋊C4—342no—
1474C22⋊C4—342no—
1475C22⋊C4—342no—
1476C22⋊C4—681no—
1477C22⋊C4—681no—
1478C22⋊C4—681no—
1479C22⋊C4—681no—
1480C22⋊C4—681no—
1481C22⋊C4—681no—
1482C22⋊C4—681no—
1483C22⋊C4—681no—
1484C22⋊C4—681no—
1485C22⋊C4—681no—
1486C22⋊C4—681no—
1487C22⋊C4—681no—
1488C22⋊C4—681no—
1489C22⋊C4—681no—
1490C22⋊C4—681no—
1491C22⋊C4—681no—
1492C22⋊C4—681no—
1493C22⋊C4—681no—
1494C22⋊C4—681no—
1495C22⋊C4—681no—
1496C42—22no—
1497C42—41no—
1498C42—342no—
1499C42—681no—
1500C42—681no—
1501C42—681no—
1502C23—21no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—21no—
1518C23—21no—
1519C23—21no—
1520C23—21no—
1521C23—21no—
1522C23—172no—
1523C23—172no—
1524C23—172no—
1525C23—172no—
1526C23—348no—
1527C23—341no—
1528C23—341no—
1529C23—341no—
1530C23—341no—
1531C23—341no—
1532C23—341no—
1533C23—341no—
1534C23—341no—
1535C23—341no—
1536C23—341no—
1537C23—341no—
1538C23—341no—
1539C23—341no—
1540C23—341no—
1541C23—341no—
1542C23—341no—
1543C23—341no—
1544C23—341no—
1545C23—341no—
1546C23—341no—
1547C23—341no—
1548C23—341no—
1549C23—341no—
1550C23—341no—
1551C23—684no—
1552C23—684no—
1553C23—684no—
1554C23—684no—
1555C23—684no—
1556C23—684no—
1557C23—684no—
1558C23—684no—
1559C23—684no—
1560C23—1362no—
1561C23—1362no—
1562C23—1362no—
1563C23—1362no—
1564C23#1058769612yes—
1565C23C24×D1711yescharacteristic
1566Q8—1362no—
1567D4—44no—
1568D4—82no—
1569D4—82no—
1570D4—684no—
1571D4—684no—
1572D4—684no—
1573D4—684no—
1574D4—684no—
1575D4—1362no—
1576D4—1362no—
1577D4—1362no—
1578D4—1362no—
1579D4—1362no—
1580D4—1362no—
1581D4—1362no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—44no—
1616C2×C4—172no—
1617C2×C4—172no—
1618C2×C4—172no—
1619C2×C4—348no—
1620C2×C4—341no—
1621C2×C4—341no—
1622C2×C4—341no—
1623C2×C4—341no—
1624C2×C4—341no—
1625C2×C4—341no—
1626C2×C4—341no—
1627C2×C4—341no—
1628C2×C4—341no—
1629C2×C4—341no—
1630C2×C4—341no—
1631C2×C4—341no—
1632C2×C4—341no—
1633C2×C4—341no—
1634C2×C4—341no—
1635C2×C4—341no—
1636C2×C4—341no—
1637C2×C4—341no—
1638C2×C4—341no—
1639C2×C4—341no—
1640C2×C4—341no—
1641C2×C4—341no—
1642C2×C4—341no—
1643C2×C4—341no—
1644C2×C4—341no—
1645C2×C4—341no—
1646C2×C4—341no—
1647C2×C4—341no—
1648C2×C4—341no—
1649C2×C4—341no—
1650C2×C4—341no—
1651C2×C4—341no—
1652C2×C4—341no—
1653C2×C4—684no—
1654C2×C4—684no—
1655C2×C4—684no—
1656C2×C4—684no—
1657C2×C4—684no—
1658C2×C4—684no—
1659C2×C4—684no—
1660C2×C4—1362no—
1661C2×C4—1362no—
1662C2×C4C2×D4×D1712yes—
1663C2×C4C2×D4×D1712yes—
1664C2×C4C2×D4×D1712yes—
1665C22—22no—
1666C22—22no—
1667C22—22no—
1668C22—41no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—41no—
1676C22—41no—
1677C22—41no—
1678C22—41no—
1679C22—41no—
1680C22—41no—
1681C22—41no—
1682C22—41no—
1683C22—41no—
1684C22—41no—
1685C22—41no—
1686C22—174no—
1687C22—342no—
1688C22—342no—
1689C22—342no—
1690C22—342no—
1691C22—342no—
1692C22—342no—
1693C22—342no—
1694C22—342no—
1695C22—342no—
1696C22—6816no—
1697C22—681no—
1698C22—681no—
1699C22—681no—
1700C22—681no—
1701C22—681no—
1702C22—681no—
1703C22—681no—
1704C22—681no—
1705C22—681no—
1706C22—681no—
1707C22—681no—
1708C22—681no—
1709C22—681no—
1710C22—681no—
1711C22—681no—
1712C22—681no—
1713C22—681no—
1714C22—681no—
1715C22—1368no—
1716C22C22×D4×D1711yescharacteristic
1717C22H(5,𝔽2)×D1711yescharacteristic
1718C22H(5,𝔽2)×D1711yescharacteristic
1719C22C2×#1058769611yescharacteristic
1720C222−1+4×D1711yescharacteristic
1721C22#1176364411yescharacteristic
1722C22#1176364511yescharacteristic
1723C4—22no—
1724C4—22no—
1725C4—22no—
1726C4—41no—
1727C4—41no—
1728C4—41no—
1729C4—41no—
1730C4—41no—
1731C4—41no—
1732C4—41no—
1733C4—41no—
1734C4—41no—
1735C4—342no—
1736C4—342no—
1737C4—342no—
1738C4—681no—
1739C4—681no—
1740C4—681no—
1741C4—681no—
1742C4—681no—
1743C4—681no—
1744C4—681no—
1745C4—681no—
1746C4—681no—
1747C2—42no—
1748C2—81no—
1749C2—81no—
1750C2—344no—
1751C2—682no—
1752C2—1361no—
1753C2—1361no—
1754C2D17×#53711yescharacteristic
1755C2#1454241411yescharacteristic
1756C2#1454243711yescharacteristic
1757C2#1454296511yescharacteristic
1758C2#1454297711yescharacteristic
1759C2#1454298611yescharacteristic
1760C2#1454299111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2705C2
hypercenter#2705D17
hypocenterC17#36722
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2705

Complements

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

NH ≅ G/Ntype
1. C2×#11763400C2semidirect
2. C2×#123×D17C2semidirect
3. #14537072C2semidirect
4. #14537065C2semidirect
5. #14535490C2semidirect
6. #14535488C2semidirect
7. #14535486C2semidirect
8. #14535484C2semidirect
9. #14535459C2semidirect
10. #14535457C2semidirect
11. #14535451C2semidirect
12. #14535152C2semidirect
13. #14535151C2semidirect
14. #14535148C2semidirect
15. #14535144C2semidirect
16. #14535140C2semidirect
17. #14535136C2semidirect
18. #14535135C2semidirect
19. #14535131C2semidirect
20. #14534590C2semidirect
21. #14534523C2semidirect
22. #14534135C2semidirect
23. #14534126C2semidirect
24. #14532168C2semidirect
25. #14532166C2semidirect
26. #14532164C2semidirect
27. #14532162C2semidirect
28. #14532138C2semidirect
29. #14532133C2semidirect
30. #14531399C2semidirect
31. C17×#2705C2semidirect
35. C2×#10587584C22semidirect
36. C2×#10587556C22semidirect
37. C2×#10587576C22semidirect
42. C2×#10587572C22semidirect
47. C2×#10587569C22semidirect
51. C2×#10587583C22semidirect
52. C2×#10587610C22semidirect
53. C2×#10587582C22semidirect
54. C2×#10587564C22semidirect
57. C2×#10587570C22semidirect
60. C2×#10587625C22semidirect
75. #11762744C22semidirect
76. #11762743C22semidirect
77. #11762742C22semidirect
78. #11762741C22semidirect
79. #11762739C22semidirect
80. #11762738C22semidirect
81. #11762737C22semidirect
82. #11762733C22semidirect
83. #11762733C22semidirect
84. #11762732C22semidirect
85. #11762732C22semidirect
86. #11762732C22semidirect
87. #11762732C22semidirect
88. #11762732C22semidirect
89. #11762732C22semidirect
90. #11762731C22semidirect
91. #11762731C22semidirect
92. #11762731C22semidirect
93. #11762731C22semidirect
94. #11762731C22semidirect
95. #11762731C22semidirect
97. #11762727C22semidirect
98. #11762726C22semidirect
99. #11762726C22semidirect
102. #11762725C22semidirect
103. #11762725C22semidirect
104. #11762725C22semidirect
105. #11762725C22semidirect
106. #11762724C22semidirect
107. #11762724C22semidirect
109. #11762723C22semidirect
110. #11762722C22semidirect
111. #11762721C22semidirect
115. #11762718C22semidirect
116. #11762717C22semidirect
117. #11762712C22semidirect
119. #11762711C22semidirect
120. #11762710C22semidirect
123. #11762709C22semidirect
124. #11762709C22semidirect
125. #11762709C22semidirect
126. #11762709C22semidirect
127. #11762708C22semidirect
128. #11762707C22semidirect
129. #11762706C22semidirect
130. #11762706C22semidirect
131. #11762705C22semidirect
132. #11762704C22semidirect
133. #11762704C22semidirect
134. #11762703C22semidirect
135. #11762702C22semidirect
136. #11762701C22semidirect
137. #11762700C22semidirect
138. #11762699C22semidirect
139. #11762698C22semidirect
140. #11762697C22semidirect
141. #11762695C22semidirect
142. #11762693C22semidirect
143. #11762691C22semidirect
144. #11762688C22semidirect
147. #11762687C22semidirect
150. #11762685C22semidirect
151. #11762684C22semidirect
152. #11762684C22semidirect
153. #11762684C22semidirect
156. #11762683C22semidirect
157. #11762683C22semidirect
158. #11762683C22semidirect
159. #11762681C22semidirect
162. #11762680C22semidirect
165. #11762668C22semidirect
166. #11762667C22semidirect
169. #11762666C22semidirect
174. C2×C17×#126C22semidirect
176. C17×#399C22semidirect
177. C17×#396C22semidirect
178. C17×#396C22semidirect
179. C17×#394C22semidirect
180. C17×#394C22semidirect
183. C17×#390C22semidirect
184. C17×#389C22semidirect
185. C17×#388C22semidirect
186. C17×#387C22semidirect
187. C17×#386C22semidirect
188. C17×#380C22semidirect
347. C4⋊C4×D17D4semidirect
796. #2705D17semidirect
902. C2×#126C2×D17semidirect
944. #399C2×D17semidirect
965. #396C2×D17semidirect
966. #396C2×D17semidirect
981. #394C2×D17semidirect
982. #394C2×D17semidirect
1002. #390C2×D17semidirect
1010. #389C2×D17semidirect
1018. #388C2×D17semidirect
1022. #387C2×D17semidirect
1030. #386C2×D17semidirect
1050. #380C2×D17semidirect
1271. C17#36722semidirect

Maximal subgroups

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

subgroupindex
C2×#117634002
C2×#123×D172
#145370722
#145370652
#145354902
#145354882
#145354862
#145354842
#145354592
#145354572
#145354512
#145351522
#145351512
#145351482
#145351442
#145351402
#145351362
#145351352
#145351312
#145345902
#145345232
#145341352
#145341262
#145321682
#145321662
#145321642
#145321622
#145321382
#145321332
#145313992
C17×#27052
#3672217