Finite Group Databasebeta

← #17241855

Subgroups — #17241855

Order 4352.

2184 conjugacy classes of subgroups.

The subgroup lattice has 1636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763426C211yesmaximal, characteristic, complemented
2C2×#11763396C211yesmaximal, characteristic, complemented
3#14537112C211yesmaximal, characteristic, complemented
4#14537081C211yesmaximal, characteristic, complemented
5#14535704C211yesmaximal, characteristic, complemented
6#14535615C211yesmaximal, characteristic, complemented
7#14535594C211yesmaximal, characteristic, complemented
8#14535551C211yesmaximal, characteristic, complemented
9#14535386C211yesmaximal, characteristic, complemented
10#14535358C211yesmaximal, characteristic, complemented
11#14535337C211yesmaximal, characteristic, complemented
12#14535262C211yesmaximal, characteristic, complemented
13#14535186C211yesmaximal, characteristic, complemented
14#14535181C211yesmaximal, characteristic, complemented
15#14535163C211yesmaximal, characteristic, complemented
16#14535078C211yesmaximal, characteristic, complemented
17#14535071C211yesmaximal, characteristic, complemented
18#14535009C211yesmaximal, characteristic, complemented
19#14534987C211yesmaximal, characteristic, complemented
20#14534933C211yesmaximal, characteristic, complemented
21#14534909C211yesmaximal, characteristic, complemented
22#14534467C211yesmaximal, characteristic, complemented
23#14534425C211yesmaximal, characteristic, complemented
24#14534389C211yesmaximal, characteristic, complemented
25#14534385C211yesmaximal, characteristic, complemented
26#14534268C211yesmaximal, characteristic, complemented
27#14533941C211yesmaximal, characteristic, complemented
28#14532206C211yesmaximal, characteristic, complemented
29#14532172C211yesmaximal, characteristic, complemented
30#14531224C211yesmaximal, characteristic, complemented
31C17×#2688C211yesmaximal, characteristic, complemented
32#11763426—28no—
33#11763396—28no—
34C2×#10587574C2211yescharacteristic, complemented
35C2×#10587584C2211yescharacteristic
36C2×#10587584C2211yescharacteristic
37C2×#10587565C2211yescharacteristic
38C2×#10587565C2211yescharacteristic, complemented
39C2×#10587622C2211yescharacteristic
40C2×#10587622C2211yescharacteristic
41C2×#10587622C2211yescharacteristic, complemented
42C2×#10587571C2211yescharacteristic
43C2×#10587571C2211yescharacteristic
44C2×#10587571C2211yescharacteristic
45C2×#10587572C2211yescharacteristic
46C2×#10587572C2211yescharacteristic
47C2×#10587621C2211yescharacteristic
48C2×#10587621C2211yescharacteristic, complemented
49C2×#10587610C2211yescharacteristic
50C2×#10587610C2211yescharacteristic, complemented
51C2×#10587564C2211yescharacteristic
52C2×#10587564C2211yescharacteristic, complemented
53C2×#10587564C2211yescharacteristic, complemented
54C2×#10587625C2211yescharacteristic
55C2×#10587625C2211yescharacteristic
56C2×#10587625C2211yescharacteristic
57C2×#10587623C2211yescharacteristic
58C2×#10587623C2211yescharacteristic
59C2×#10587623C2211yescharacteristic
60C2×#10587573C2211yescharacteristic, complemented
61C2×D4×Dic17C2211yescharacteristic
62C2×D4×Dic17C2211yescharacteristic
63C2×#10587612C2211yescharacteristic, complemented
64C2×#10587563C2211yescharacteristic
65C22×#63227C2211yescharacteristic
66C22×C4×Dic17C2211yescharacteristic, complemented
67#11762751C2211yescharacteristic, complemented
68#11762744C2211yescharacteristic
69#11762744C2211yescharacteristic
70#11762743C2211yescharacteristic, complemented
71#11762743C2211yescharacteristic, complemented
72#11762738C2211yescharacteristic
73#11762738C2211yescharacteristic
74#11762737C2211yescharacteristic
75#11762737C2211yescharacteristic, complemented
76#11762737C2211yescharacteristic, complemented
77#11762735C2211yescharacteristic
78#11762734C2211yescharacteristic
79#11762734C2211yescharacteristic
80#11762733C2211yescharacteristic
81#11762733C2211yescharacteristic
82#11762732C2211yescharacteristic, complemented
83#11762731C2211yescharacteristic
84#11762730C2211yescharacteristic, complemented
85#11762730C2211yescharacteristic, complemented
86#11762729C2211yescharacteristic, complemented
87#11762725C2211yescharacteristic
88#11762725C2211yescharacteristic
89#11762725C2211yescharacteristic
90#11762724C2211yescharacteristic
91#11762724C2211yescharacteristic
92#11762724C2211yescharacteristic
93#11762724C2211yescharacteristic
94#11762724C2211yescharacteristic
95#11762723C2211yescharacteristic
96#11762723C2211yescharacteristic
97#11762723C2211yescharacteristic
98#11762723C2211yescharacteristic, complemented
99#11762722C2211yescharacteristic
100#11762722C2211yescharacteristic
101#11762722C2211yescharacteristic
102#11762722C2211yescharacteristic
103#11762722C2211yescharacteristic
104#11762721C2211yescharacteristic, complemented
105#11762721C2211yescharacteristic, complemented
106#11762717C2211yescharacteristic
107#11762717C2211yescharacteristic
108#11762717C2211yescharacteristic
109#11762713C2211yescharacteristic, complemented
110#11762713C2211yescharacteristic, complemented
111#11762713C2211yescharacteristic, complemented
112#11762713C2211yescharacteristic, complemented
113#11762712C2211yescharacteristic, complemented
114#11762709C2211yescharacteristic
115#11762709C2211yescharacteristic
116#11762709C2211yescharacteristic
117#11762709C2211yescharacteristic
118#11762709C2211yescharacteristic
119#11762709C2211yescharacteristic
120#11762708C2211yescharacteristic, complemented
121#11762706C2211yescharacteristic, complemented
122#11762706C2211yescharacteristic, complemented
123#11762706C2211yescharacteristic, complemented
124#11762704C2211yescharacteristic, complemented
125#11762703C2211yescharacteristic
126#11762703C2211yescharacteristic, complemented
127#11762702C2211yescharacteristic, complemented
128#11762702C2211yescharacteristic, complemented
129#11762702C2211yescharacteristic, complemented
130#11762701C2211yescharacteristic
131#11762701C2211yescharacteristic
132#11762701C2211yescharacteristic
133#11762701C2211yescharacteristic
134#11762698C2211yescharacteristic
135#11762698C2211yescharacteristic
136#11762698C2211yescharacteristic
137#11762698C2211yescharacteristic
138#11762698C2211yescharacteristic
139#11762698C2211yescharacteristic
140#11762698C2211yescharacteristic
141#11762697C2211yescharacteristic
142#11762697C2211yescharacteristic, complemented
143#11762697C2211yescharacteristic, complemented
144#11762697C2211yescharacteristic, complemented
145#11762694C2211yescharacteristic, complemented
146#11762692C2211yescharacteristic, complemented
147#11762692C2211yescharacteristic, complemented
148#11762691C2211yescharacteristic, complemented
149#11762691C2211yescharacteristic, complemented
150#11762690C2211yescharacteristic, complemented
151#11762689C2211yescharacteristic
152#11762689C2211yescharacteristic, complemented
153#11762689C2211yescharacteristic, complemented
154#11762688C2211yescharacteristic
155#11762688C2211yescharacteristic
156#11762688C2211yescharacteristic
157#11762688C2211yescharacteristic
158#11762686C2211yescharacteristic
159#11762682C2211yescharacteristic
160#11762682C2211yescharacteristic, complemented
161#11762681C2211yescharacteristic, complemented
162#11762681C2211yescharacteristic, complemented
163#11762673C2211yescharacteristic, complemented
164#11762672C2211yescharacteristic
165#11762667C2211yescharacteristic, complemented
166#11762667C2211yescharacteristic, complemented
167#11762664C2211yescharacteristic
168#11762664C2211yescharacteristic
169#11762664C2211yescharacteristic
170#11762660C2211yescharacteristic, complemented
171C22⋊C4×Dic17C2211yescharacteristic
172C22⋊C4×Dic17C2211yescharacteristic, complemented
173#11762654C2211yescharacteristic, complemented
174C2×C17×#121C2211yescharacteristic
175C2×C17×#121C2211yescharacteristic
176C17×#400C2211yescharacteristic, complemented
177C17×#397C2211yescharacteristic, complemented
178C17×#397C2211yescharacteristic, complemented
179C17×#394C2211yescharacteristic
180C17×#392C2211yescharacteristic
181C17×#392C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic, complemented
185C17×#386C2211yescharacteristic, complemented
186C17×#386C2211yescharacteristic, complemented
187C17×#385C2211yescharacteristic, complemented
188C17×#381C2211yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C22×Dic34C2311yescharacteristic
210C22×Dic34C2311yescharacteristic
211C22×Dic34C2311yescharacteristic
212C22×Dic34C2311yescharacteristic
213C17×#121—24no—
214C17×#121—24no—
215C2×C4⋊C4×C17C2311yescharacteristic
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C22⋊C4×C17C2311yescharacteristic
219C2×C22⋊C4×C17C2311yescharacteristic
220C2×C22⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊Dic17C2311yescharacteristic
232C2×C22⋊Dic17C2311yescharacteristic
233C2×C22⋊Dic17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252#10587625—24no—
253#10587625—24no—
254#10587625—42no—
255#10587623—24no—
256#10587623—24no—
257#10587623—42no—
258#10587622—24no—
259#10587622—24no—
260#10587622—24no—
261#10587621—24no—
262#10587621—24no—
263D4×Dic17—24no—
264D4×Dic17D418yescomplemented
265C2×#63227—24no—
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
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
288#10587612—24no—
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296#10587610—24no—
297#10587610—24no—
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×C4×Dic17—42no—
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328#10587584—24no—
329#10587584—24no—
330#10587574—24no—
331#10587573—24no—
332#10587572—24no—
333#10587572—24no—
334#10587571—24no—
335#10587571—24no—
336#10587571—42no—
337#10587565—24no—
338#10587565—24no—
339#10587564—24no—
340#10587564—24no—
341#10587564—42no—
342#10587563—42no—
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349C17×#95C2311yescharacteristic
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379C24×C17C2411yescharacteristic
380C24×C17C2411yescharacteristic
381C24×C17C2411yescharacteristic
382C24×C17C2411yescharacteristic
383C23×D17—22no—
384C23×D17—41no—
385C23×D17—41no—
386C23×D17—41no—
387C23×D17—41no—
388C23×D17—41no—
389C23×D17—41no—
390C23×D17C2411yescharacteristic
391C23×D17C2411yescharacteristic
392C2×D4×C17—22no—
393C2×D4×C17—22no—
394C2×D4×C17—22no—
395C2×D4×C17—22no—
396C2×D4×C17—41no—
397C2×D4×C17—41no—
398C2×D4×C17—41no—
399C2×D4×C17—41no—
400C2×D4×C17—41no—
401C2×D4×C17—41no—
402C2×D4×C17—41no—
403C2×D4×C17—41no—
404C2×D4×C17—41no—
405C2×D4×C17—41no—
406C2×D4×C17—41no—
407C2×D4×C17—41no—
408C2×D4×C17—41no—
409C2×D4×C17C2×D414yes—
410C22×C4×C17—22no—
411C22×C4×C17—22no—
412C22×C4×C17—41no—
413C22×C4×C17—41no—
414C22×C4×C17—41no—
415C22×C4×C17—41no—
416C22×C4×C17—41no—
417C22×C4×C17—41no—
418C22×C4×C17—41no—
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C2×C22⋊D17—22no—
431C2×C22⋊D17—22no—
432C2×C22⋊D17—22no—
433C2×C22⋊D17—22no—
434C2×C22⋊D17—22no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17—41no—
446C2×C22⋊D17—41no—
447C2×C22⋊D17—41no—
448C22×Dic17—22no—
449C22×Dic17—22no—
450C22×Dic17—41no—
451C22×Dic17—41no—
452C22×Dic17—41no—
453C22×Dic17—41no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17—41no—
458C22×Dic17C2×D414yes—
459C22×Dic17C2×D414yes—
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C2×Dic34—22no—
475C2×Dic34—22no—
476C2×Dic34—22no—
477C2×Dic34—22no—
478C2×Dic34—41no—
479C2×Dic34—41no—
480C2×Dic34—41no—
481C2×Dic34—41no—
482C2×Dic34—41no—
483C2×Dic34—41no—
484C2×Dic34—41no—
485C2×Dic34—41no—
486C4⋊C4×C17—22no—
487C4⋊C4×C17—22no—
488C4⋊C4×C17—41no—
489C22⋊C4×C17—22no—
490C22⋊C4×C17—22no—
491C22⋊C4×C17—22no—
492C22⋊C4×C17—22no—
493C22⋊C4×C17—41no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17—41no—
501C22⋊C4×C17—41no—
502C22⋊Dic17—22no—
503C22⋊Dic17—22no—
504C22⋊Dic17—22no—
505C22⋊Dic17—22no—
506C22⋊Dic17—22no—
507C22⋊Dic17—22no—
508C22⋊Dic17—22no—
509C22⋊Dic17—22no—
510C22⋊Dic17—22no—
511C22⋊Dic17—22no—
512C22⋊Dic17—22no—
513C22⋊Dic17—22no—
514C22⋊Dic17—41no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17—41no—
518C22⋊Dic17—41no—
519C22⋊Dic17—41no—
520C22⋊Dic17—41no—
521C22⋊Dic17C2×D414yes—
522C22⋊Dic17C2×D414yes—
523#63227—22no—
524#63227—22no—
525#63227—22no—
526#63227—22no—
527#63227—22no—
528#63227—22no—
529#63227—22no—
530#63227—22no—
531#63227—22no—
532#63227—41no—
533#63227—41no—
534#63227—41no—
535#63227—41no—
536#63227—41no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227—41no—
544#63227—41no—
545C4⋊Dic17—22no—
546C4⋊Dic17—22no—
547C4⋊Dic17—22no—
548C4⋊Dic17—22no—
549C4⋊Dic17—41no—
550C4⋊Dic17—41no—
551C4⋊Dic17C2×D414yes—
552#63225—22no—
553#63225—22no—
554#63225—22no—
555#63225—22no—
556#63225—22no—
557#63225—22no—
558#63225—22no—
559#63225—22no—
560#63225—22no—
561#63225—22no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568#63225—41no—
569#63225—41no—
570C4×Dic17—22no—
571C4×Dic17—22no—
572C4×Dic17—22no—
573C4×Dic17—22no—
574C4×Dic17—22no—
575C4×Dic17—22no—
576C4×Dic17—41no—
577C4×Dic17—41no—
578C4×Dic17—41no—
579C4×Dic17—41no—
580C4×Dic17C2×D414yes—
581#36745—171nomaximal, Sylow
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17C22×D412yes—
609C23×C17C22×D412yes—
610C23×C17C2511yescharacteristic
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
625C22×D17—44no—
626C22×D17—82no—
627C22×D17—82no—
628C22×D17—82no—
629C22×D17—82no—
630C22×D17—82no—
631C22×D17—82no—
632D4×C17—44no—
633D4×C17—44no—
634D4×C17—82no—
635D4×C17—82no—
636D4×C17—82no—
637D4×C17—82no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—44no—
671C2×C4×C17—44no—
672C2×C4×C17—82no—
673C2×C4×C17C22×D412yes—
674C22⋊D17—82no—
675C22⋊D17—82no—
676C22⋊D17—82no—
677C22⋊D17—82no—
678C22⋊D17—82no—
679C22⋊D17—82no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—44no—
718C2×Dic17—44no—
719C2×Dic17—44no—
720C2×Dic17—82no—
721C2×Dic17C22×D412yes—
722C2×Dic17C22×D412yes—
723C2×Dic17C22×D412yes—
724C2×Dic17C22×D412yes—
725C2×Dic17H(5,𝔽2)12yes—
726Dic34—44no—
727Dic34—82no—
728Dic34—82no—
729Dic34—82no—
730C2×#542—171no—
731C2×#538—171no—
732#2854—171no—
733#2850—171no—
734#2723—171no—
735#2716—171no—
736#2715—171no—
737#2712—171no—
738#2700—171no—
739#2698—171no—
740#2696—171no—
741#2691—171no—
742#2688D1711yescharacteristic, complemented
743#2686—171no—
744#2685—171no—
745#2684—171no—
746#2676—171no—
747#2674—171no—
748#2670—171no—
749#2668—171no—
750#2663—171no—
751#2661—171no—
752#2610—171no—
753#2604—171no—
754#2602—171no—
755#2601—171no—
756#2592—171no—
757#2561—171no—
758#2415—171no—
759#2411—171no—
760#2290—171no—
761C22×C17—22no—
762C22×C17—22no—
763C22×C17—22no—
764C22×C17—22no—
765C22×C17—22no—
766C22×C17—22no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17—41no—
775C22×C17—41no—
776C22×C17—41no—
777C22×C17—41no—
778C22×C17—41no—
779C22×C17—41no—
780C22×C17—41no—
781C22×C17—41no—
782C22×C17—41no—
783C22×C17—41no—
784C22×C17—41no—
785C22×C17—41no—
786C22×C17—41no—
787C22×C17—41no—
788C22×C17—41no—
789C22×C17C23×D411yescharacteristic
790C22×C17C2×H(5,𝔽2)11yescharacteristic
791C22×C17#58511yescharacteristic
792C22×C17#58511yescharacteristic
793C22×C17#58511yescharacteristic
794C22×C17#58511yescharacteristic
795C22×C17#58511yescharacteristic
796C2×D17—41no—
797C2×D17—41no—
798C2×D17—41no—
799C2×D17—41no—
800C2×D17—41no—
801C2×D17—41no—
802C2×D17—41no—
803C2×D17—41no—
804C2×D17—41no—
805C2×D17—41no—
806C2×D17—41no—
807C2×D17—41no—
808C2×D17—41no—
809C2×D17—41no—
810C2×D17—88no—
811C4×C17—22no—
812C4×C17—41no—
813C4×C17—41no—
814C4×C17—41no—
815C4×C17—41no—
816C4×C17—41no—
817C4×C17—41no—
818C4×C17—41no—
819C4×C17—41no—
820C4×C17—41no—
821C4×C17—41no—
822Dic17—22no—
823Dic17—22no—
824Dic17—22no—
825Dic17—22no—
826Dic17—22no—
827Dic17—41no—
828Dic17—41no—
829Dic17—41no—
830Dic17—41no—
831Dic17—41no—
832Dic17—41no—
833Dic17—41no—
834Dic17—41no—
835Dic17—41no—
836#542—348no—
837#538—348no—
838C2×C4⋊Q8—171no—
839C2×#126—171no—
840C2×#126—171no—
841C2×#126—171no—
842C2×#126—171no—
843C2×#124—171no—
844C2×#124—171no—
845C2×#124—171no—
846C2×#124—171no—
847C2×#124—171no—
848C2×#124—171no—
849C2×#123—171no—
850C2×#123—171no—
851C2×#123—171no—
852C2×#123—171no—
853C2×C22⋊Q8—171no—
854C2×C22⋊Q8—171no—
855C2×C22⋊Q8—171no—
856C2×C22⋊Q8—171no—
857C2×C22⋊Q8—171no—
858C2×#121—171no—
859C2×#121—171no—
860C2×#121—171no—
861C2×#121C2×D1711yescharacteristic
862C2×#121C2×D1711yescharacteristic
863C2×#120—171no—
864C2×#120—171no—
865C2×#120—171no—
866C2×C4×Q8—171no—
867C2×C4×D4—171no—
868C2×C4×D4—171no—
869C2×#117—171no—
870C2×#117—171no—
871C22×C22⋊C4—171no—
872C22×C42—171no—
873#400—171no—
874#400C2×D1711yescharacteristic, complemented
875#399—171no—
876#399—171no—
877#398—171no—
878#398—171no—
879#397—171no—
880#397—171no—
881#397—171no—
882#397—171no—
883#397—171no—
884#397—171no—
885#397—171no—
886#397—171no—
887#397C2×D1711yescharacteristic, complemented
888#397C2×D1711yescharacteristic, complemented
889#396—171no—
890#396—171no—
891#396—171no—
892#396—171no—
893#395—171no—
894#395—171no—
895#395—171no—
896#394—171no—
897#394—171no—
898#394—171no—
899#394—171no—
900#394—171no—
901#394—171no—
902#394—171no—
903#394—171no—
904#394—171no—
905#394—171no—
906#394—171no—
907#394—171no—
908#394C2×D1711yescharacteristic
909#393—171no—
910#393—171no—
911#393—171no—
912#393—171no—
913#393—171no—
914#393—171no—
915#393—171no—
916#392—171no—
917#392—171no—
918#392—171no—
919#392C2×D1711yescharacteristic
920#392C2×D1711yescharacteristic, complemented
921#391—171no—
922#391—171no—
923#391—171no—
924#391—171no—
925#390—171no—
926#390—171no—
927#390—171no—
928#390—171no—
929#390—171no—
930#390—171no—
931#390—171no—
932#389—171no—
933#389—171no—
934#389—171no—
935#389—171no—
936#389—171no—
937#388—171no—
938#388—171no—
939#388—171no—
940#388—171no—
941#388—171no—
942#388—171no—
943#388—171no—
944#388—171no—
945#388—171no—
946#388—171no—
947#388—171no—
948#388—171no—
949#388—171no—
950#388—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#387—171no—
958#387—171no—
959#387—171no—
960#387—171no—
961#387—171no—
962#387—171no—
963#386—171no—
964#386—171no—
965#386—171no—
966#386—171no—
967#386—171no—
968#386—171no—
969#386—171no—
970#386—171no—
971#386C2×D1711yescharacteristic
972#386C2×D1711yescharacteristic
973#386C2×D1711yescharacteristic, complemented
974#386C2×D1711yescharacteristic, complemented
975#386C2×D1711yescharacteristic, complemented
976#385—171no—
977#385—171no—
978#385—171no—
979#385—171no—
980#385C2×D1711yescharacteristic, complemented
981#382—171no—
982#381—171no—
983#381C2×D1711yescharacteristic
984#380—171no—
985#380—171no—
986#379—171no—
987#379—171no—
988#379—171no—
989C4×C4⋊C4—171no—
990C4×C22⋊C4—171no—
991C4×C22⋊C4—171no—
992#376—171no—
993C2×C17—42no—
994C2×C17—42no—
995C2×C17—81no—
996C2×C17—81no—
997C2×C17#344911yescharacteristic
998C2×C17#349611yescharacteristic
999C2×C17#350011yescharacteristic
1000C2×C17#353311yescharacteristic
1001C2×C17#354011yescharacteristic
1002C2×C17#356611yescharacteristic
1003C2×C17#356811yescharacteristic
1004D17—81no—
1005D17—81no—
1006C25—171no—
1007C22×Q8—171no—
1008C22×Q8—171no—
1009C22×Q8—171no—
1010C22×Q8—171no—
1011C22×D4—171no—
1012C22×D4—171no—
1013C22×D4—171no—
1014C22×D4—171no—
1015C22×D4—171no—
1016C22×D4—171no—
1017C22×D4C22×D1711yescharacteristic
1018C22×D4C22×D1711yescharacteristic
1019C22×D4C22×D1711yescharacteristic
1020C22×D4C22×D1711yescharacteristic
1021C22×D4C22×D1711yescharacteristic
1022C22×D4C22×D1711yescharacteristic
1023C23×C4—171no—
1024C23×C4—171no—
1025C23×C4—171no—
1026C23×C4—171no—
1027C23×C4C22×D1711yescharacteristic
1028C23×C4C22×D1711yescharacteristic
1029C23×C4C22×D1711yescharacteristic
1030C4⋊Q8—344no—
1031#126—344no—
1032#126—344no—
1033#126—344no—
1034#126—344no—
1035#124—344no—
1036#124—344no—
1037#124—344no—
1038#124—344no—
1039#124—344no—
1040#124—682no—
1041#123—344no—
1042#123—344no—
1043#123—344no—
1044#123—344no—
1045C22⋊Q8—344no—
1046C22⋊Q8—344no—
1047C22⋊Q8—344no—
1048C22⋊Q8—344no—
1049C22⋊Q8—682no—
1050#121—24no—
1051#121—24no—
1052#121—344no—
1053#121—344no—
1054#121—682no—
1055#120—344no—
1056#120—344no—
1057#120—682no—
1058C4×Q8—344no—
1059C4×D4—178no—
1060C4×D4—344no—
1061#117—344no—
1062#117—682no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—171no—
1069C2×C4⋊C4—171no—
1070C2×C4⋊C4—171no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—171no—
1075C2×C4⋊C4—171no—
1076C2×C4⋊C4—171no—
1077C2×C4⋊C4—171no—
1078C2×C4⋊C4—171no—
1079C2×C4⋊C4—171no—
1080C2×C4⋊C4—171no—
1081C2×C4⋊C4—171no—
1082C2×C4⋊C4—171no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—171no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4C22×D1711yescharacteristic
1089C2×C4⋊C4C22×D1711yescharacteristic
1090C2×C4⋊C4C22×D1711yescharacteristic
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—344no—
1135C2×C22⋊C4C22×D1711yescharacteristic
1136C2×C22⋊C4C22×D1711yescharacteristic
1137C2×C22⋊C4C22×D1711yescharacteristic
1138C2×C22⋊C4C22×D1711yescharacteristic
1139C2×C22⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4C22×D1711yescharacteristic
1141C2×C22⋊C4C22×D1711yescharacteristic
1142C2×C22⋊C4C22×D1711yescharacteristic
1143C2×C22⋊C4C22×D1711yescharacteristic
1144C2×C22⋊C4C22×D1711yescharacteristic
1145C2×C22⋊C4C22×D1711yescharacteristic
1146C2×C22⋊C4C22×D1711yescharacteristic
1147C2×C22⋊C4C22×D1711yescharacteristic
1148C2×C42—171no—
1149C2×C42—171no—
1150C2×C42—171no—
1151C2×C42—171no—
1152C2×C42—171no—
1153C2×C42—171no—
1154C2×C42—171no—
1155C2×C42—171no—
1156C2×C42—171no—
1157C2×C42—171no—
1158C2×C42—171no—
1159C2×C42—682no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95C22×D1711yescharacteristic
1187#95C22×D1711yescharacteristic
1188#95C22×D1711yescharacteristic
1189#95C22×D1711yescharacteristic
1190#95C22×D1711yescharacteristic
1191#95C22×D1711yescharacteristic
1192#95C22×D1711yescharacteristic
1193#95C22×D1711yescharacteristic
1194#95C22×D1711yescharacteristic
1195#95C22×D1711yescharacteristic
1196C17#3674511yescharacteristic, complemented, Sylow
1197C24—171no—
1198C24—171no—
1199C24—342no—
1200C24—681no—
1201C24—681no—
1202C24—681no—
1203C24—681no—
1204C24—681no—
1205C24—681no—
1206C24C23×D1711yescharacteristic
1207C24C23×D1711yescharacteristic
1208C24C23×D1711yescharacteristic
1209C24C23×D1711yescharacteristic
1210C2×Q8—342no—
1211C2×Q8—342no—
1212C2×Q8—342no—
1213C2×Q8—342no—
1214C2×Q8—681no—
1215C2×Q8—681no—
1216C2×Q8—681no—
1217C2×Q8—681no—
1218C2×Q8—681no—
1219C2×Q8—681no—
1220C2×Q8—681no—
1221C2×Q8—681no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—22no—
1226C2×D4—41no—
1227C2×D4—41no—
1228C2×D4—41no—
1229C2×D4—41no—
1230C2×D4—41no—
1231C2×D4—41no—
1232C2×D4—41no—
1233C2×D4—41no—
1234C2×D4—41no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—41no—
1238C2×D4—41no—
1239C2×D4—342no—
1240C2×D4—342no—
1241C2×D4—342no—
1242C2×D4—342no—
1243C2×D4—342no—
1244C2×D4—681no—
1245C2×D4—681no—
1246C2×D4—681no—
1247C2×D4—681no—
1248C2×D4—681no—
1249C2×D4—681no—
1250C2×D4—681no—
1251C2×D4—681no—
1252C2×D4—681no—
1253C2×D4—681no—
1254C2×D4—681no—
1255C2×D4—681no—
1256C2×D4—681no—
1257C2×D4D4×D1714yes—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—41no—
1266C22×C4—41no—
1267C22×C4—171no—
1268C22×C4—171no—
1269C22×C4—171no—
1270C22×C4—171no—
1271C22×C4—171no—
1272C22×C4—174no—
1273C22×C4—174no—
1274C22×C4—171no—
1275C22×C4—171no—
1276C22×C4—171no—
1277C22×C4—171no—
1278C22×C4—171no—
1279C22×C4—171no—
1280C22×C4—171no—
1281C22×C4—171no—
1282C22×C4—171no—
1283C22×C4—342no—
1284C22×C4—342no—
1285C22×C4—681no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—681no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4—681no—
1292C22×C4—681no—
1293C22×C4C23×D1711yescharacteristic
1294C22×C4C23×D1711yescharacteristic
1295C22×C4C23×D1711yescharacteristic
1296C22×C4C23×D1711yescharacteristic
1297C22×C4C23×D1711yescharacteristic
1298C22×C4C23×D1711yescharacteristic
1299C22×C4C23×D1711yescharacteristic
1300C22×C4C23×D1711yescharacteristic
1301C22×C4C23×D1711yescharacteristic
1302C22×C4C23×D1711yescharacteristic
1303C22×C4C23×D1711yescharacteristic
1304C4⋊C4—22no—
1305C4⋊C4—22no—
1306C4⋊C4—41no—
1307C4⋊C4—174no—
1308C4⋊C4—342no—
1309C4⋊C4—342no—
1310C4⋊C4—342no—
1311C4⋊C4—342no—
1312C4⋊C4—342no—
1313C4⋊C4—342no—
1314C4⋊C4—342no—
1315C4⋊C4—342no—
1316C4⋊C4—342no—
1317C4⋊C4—342no—
1318C4⋊C4—342no—
1319C4⋊C4—342no—
1320C4⋊C4—342no—
1321C4⋊C4—342no—
1322C4⋊C4—681no—
1323C4⋊C4—681no—
1324C4⋊C4—681no—
1325C4⋊C4—681no—
1326C4⋊C4—681no—
1327C4⋊C4—681no—
1328C4⋊C4—681no—
1329C4⋊C4—681no—
1330C4⋊C4—681no—
1331C4⋊C4—681no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—41no—
1342C22⋊C4—41no—
1343C22⋊C4—41no—
1344C22⋊C4—41no—
1345C22⋊C4—174no—
1346C22⋊C4—174no—
1347C22⋊C4—342no—
1348C22⋊C4—342no—
1349C22⋊C4—342no—
1350C22⋊C4—342no—
1351C22⋊C4—342no—
1352C22⋊C4—342no—
1353C22⋊C4—342no—
1354C22⋊C4—342no—
1355C22⋊C4—342no—
1356C22⋊C4—342no—
1357C22⋊C4—342no—
1358C22⋊C4—342no—
1359C22⋊C4—342no—
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—681no—
1369C22⋊C4—681no—
1370C22⋊C4—681no—
1371C22⋊C4—681no—
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—681no—
1385C22⋊C4—681no—
1386C22⋊C4—681no—
1387C22⋊C4—681no—
1388C42—174no—
1389C42—342no—
1390C42—342no—
1391C42—342no—
1392C42—342no—
1393C42—342no—
1394C42—342no—
1395C42—681no—
1396C42—681no—
1397C42—681no—
1398C42—681no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—341no—
1426C23—341no—
1427C23—341no—
1428C23—341no—
1429C23—341no—
1430C23—341no—
1431C23—341no—
1432C23—341no—
1433C23—341no—
1434C23—341no—
1435C23—341no—
1436C23—341no—
1437C23—341no—
1438C23—341no—
1439C23—684no—
1440C23—1362no—
1441C23—1362no—
1442C23—1362no—
1443C23—1362no—
1444C23—1362no—
1445C23—1362no—
1446C23C2×D4×D1712yes—
1447C23C2×D4×D1712yes—
1448C23C24×D1711yescharacteristic
1449Q8—684no—
1450Q8—1362no—
1451Q8—1362no—
1452Q8—1362no—
1453D4—44no—
1454D4—44no—
1455D4—82no—
1456D4—82no—
1457D4—82no—
1458D4—82no—
1459D4—1362no—
1460D4—1362no—
1461D4—1362no—
1462D4—1362no—
1463D4—1362no—
1464D4—1362no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—44no—
1498C2×C4—44no—
1499C2×C4—82no—
1500C2×C4—172no—
1501C2×C4—172no—
1502C2×C4—172no—
1503C2×C4—172no—
1504C2×C4—172no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—684no—
1543C2×C4—684no—
1544C2×C4—684no—
1545C2×C4—1362no—
1546C2×C4C2×D4×D1712yes—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—22no—
1552C22—22no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—41no—
1569C22—41no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—41no—
1575C22—681no—
1576C22—681no—
1577C22—681no—
1578C22—681no—
1579C22—681no—
1580C22—681no—
1581C22—681no—
1582C22—681no—
1583C22—681no—
1584C22—681no—
1585C22—681no—
1586C22—681no—
1587C22—681no—
1588C22—681no—
1589C22—1368no—
1590C22C22×D4×D1711yescharacteristic
1591C22H(5,𝔽2)×D1711yescharacteristic
1592C22#1176364411yescharacteristic
1593C22#1176364411yescharacteristic
1594C22#1176364411yescharacteristic
1595C22#1176364511yescharacteristic
1596C22#1176364511yescharacteristic
1597C4—22no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—342no—
1609C4—342no—
1610C4—342no—
1611C4—342no—
1612C4—342no—
1613C4—681no—
1614C4—681no—
1615C4—681no—
1616C4—681no—
1617C4—681no—
1618C4—681no—
1619C4—681no—
1620C4—681no—
1621C4—681no—
1622C2—42no—
1623C2—42no—
1624C2—81no—
1625C2—81no—
1626C2—1361no—
1627C2—1361no—
1628C2#1454211011yescharacteristic
1629C2#1454254411yescharacteristic
1630C2#1454257011yescharacteristic
1631C2#1454294411yescharacteristic
1632C2#1454305111yescharacteristic
1633C2#1454346111yescharacteristic
1634C2#1454347711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2688C2
hypercenter#2688D17
hypocenterC17#36745
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2688

Complements

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

NH ≅ G/Ntype
1. C2×#11763426C2semidirect
2. C2×#11763396C2semidirect
3. #14537112C2semidirect
4. #14537081C2semidirect
5. #14535704C2semidirect
6. #14535615C2semidirect
7. #14535594C2semidirect
8. #14535551C2semidirect
9. #14535386C2semidirect
10. #14535358C2semidirect
11. #14535337C2semidirect
12. #14535262C2semidirect
13. #14535186C2semidirect
14. #14535181C2semidirect
15. #14535163C2semidirect
16. #14535078C2semidirect
17. #14535071C2semidirect
18. #14535009C2semidirect
19. #14534987C2semidirect
20. #14534933C2semidirect
21. #14534909C2semidirect
22. #14534467C2semidirect
23. #14534425C2semidirect
24. #14534389C2semidirect
25. #14534385C2semidirect
26. #14534268C2semidirect
27. #14533941C2semidirect
28. #14532206C2semidirect
29. #14532172C2semidirect
30. #14531224C2semidirect
31. C17×#2688C2semidirect
34. C2×#10587574C22semidirect
38. C2×#10587565C22semidirect
41. C2×#10587622C22semidirect
48. C2×#10587621C22semidirect
50. C2×#10587610C22semidirect
52. C2×#10587564C22semidirect
53. C2×#10587564C22semidirect
60. C2×#10587573C22semidirect
63. C2×#10587612C22semidirect
66. C22×C4×Dic17C22semidirect
67. #11762751C22semidirect
70. #11762743C22semidirect
71. #11762743C22semidirect
75. #11762737C22semidirect
76. #11762737C22semidirect
82. #11762732C22semidirect
84. #11762730C22semidirect
85. #11762730C22semidirect
86. #11762729C22semidirect
98. #11762723C22semidirect
104. #11762721C22semidirect
105. #11762721C22semidirect
109. #11762713C22semidirect
110. #11762713C22semidirect
111. #11762713C22semidirect
112. #11762713C22semidirect
113. #11762712C22semidirect
120. #11762708C22semidirect
121. #11762706C22semidirect
122. #11762706C22semidirect
123. #11762706C22semidirect
124. #11762704C22semidirect
126. #11762703C22semidirect
127. #11762702C22semidirect
128. #11762702C22semidirect
129. #11762702C22semidirect
142. #11762697C22semidirect
143. #11762697C22semidirect
144. #11762697C22semidirect
145. #11762694C22semidirect
146. #11762692C22semidirect
147. #11762692C22semidirect
148. #11762691C22semidirect
149. #11762691C22semidirect
150. #11762690C22semidirect
152. #11762689C22semidirect
153. #11762689C22semidirect
160. #11762682C22semidirect
161. #11762681C22semidirect
162. #11762681C22semidirect
163. #11762673C22semidirect
165. #11762667C22semidirect
166. #11762667C22semidirect
170. #11762660C22semidirect
172. C22⋊C4×Dic17C22semidirect
173. #11762654C22semidirect
176. C17×#400C22semidirect
177. C17×#397C22semidirect
178. C17×#397C22semidirect
181. C17×#392C22semidirect
184. C17×#386C22semidirect
185. C17×#386C22semidirect
186. C17×#386C22semidirect
187. C17×#385C22semidirect
264. D4×Dic17D4semidirect
742. #2688D17semidirect
874. #400C2×D17semidirect
887. #397C2×D17semidirect
888. #397C2×D17semidirect
920. #392C2×D17semidirect
973. #386C2×D17semidirect
974. #386C2×D17semidirect
975. #386C2×D17semidirect
980. #385C2×D17semidirect
1196. C17#36745semidirect

Maximal subgroups

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

subgroupindex
C2×#117634262
C2×#117633962
#145371122
#145370812
#145357042
#145356152
#145355942
#145355512
#145353862
#145353582
#145353372
#145352622
#145351862
#145351812
#145351632
#145350782
#145350712
#145350092
#145349872
#145349332
#145349092
#145344672
#145344252
#145343892
#145343852
#145342682
#145339412
#145322062
#145321722
#145312242
C17×#26882
#3674517