Finite Group Databasebeta

← C2×#14541046 #17911187

Subgroups — C2×#14541046 #17911187

Order 4352.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763468C211yesmaximal, characteristic
2#14541046C2116yesmaximal, direct product factor
3C2×#11763166C211yesmaximal, characteristic, complemented
4C2×#11763144C211yesmaximal, characteristic, complemented
5C2×#11763133C211yesmaximal, characteristic, complemented
6C2×#11763113C211yesmaximal, characteristic, complemented
7C2×#11763065C211yesmaximal, characteristic, complemented
8C2×#11763057C211yesmaximal, characteristic, complemented
9C2×#11763031C211yesmaximal, characteristic, complemented
10C2×#11762969C211yesmaximal, characteristic, complemented
11C2×#11762964C211yesmaximal, characteristic, complemented
12C2×C4×#63231C211yesmaximal, characteristic, complemented
13C2×#11762887C211yesmaximal, characteristic, complemented
14C2×#11762808C211yesmaximal, characteristic, complemented
15C2×#11762817C211yesmaximal, characteristic, complemented
16C2×C17×#552C211yesmaximal, characteristic, complemented
17C22×#63252C2211yescharacteristic
18C23×Dic34C2211yescharacteristic
19C22×#63231C2211yescharacteristic
20C22×#63231C2211yescharacteristic
21C22×#63230C2211yescharacteristic
22C22×#63223C2211yescharacteristic
23C22×#63223C2211yescharacteristic
24#11763468—24no—
25#11763468C2218yes—
26C2×#10587561C2211yescharacteristic
27C2×#10587571—21no—
28C2×#10587610C2211yescharacteristic
29C2×#10587582—21no—
30C2×#10587616C2211yescharacteristic
31C2×#10587625—21no—
32C2×C4×Dic34C2211yescharacteristic
33C2×#10587567—21no—
34#11763166C2218yescomplemented
35#11763144C2218yescomplemented
36#11763133C2218yescomplemented
37#11763113C2218yescomplemented
38#11763065C2218yescomplemented
39#11763057C2218yescomplemented
40#11763031C2218yescomplemented
41#11762969C2218yescomplemented
42#11762964C2218yescomplemented
43C4×#63231C2218yescomplemented
44#11762887C2218yescomplemented
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49#11762817C2218yescomplemented
50#11762808C2218yescomplemented
51C2×#10587506C2211yescharacteristic
52C2×#10587481C2211yescharacteristic
53C2×#10587481C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#552—24no—
65C17×#552C2218yescomplemented
66C2×C17×#126—21no—
67C2×C17×#125—21no—
68C2×C17×#125C2211yescharacteristic
69C2×C17×#123—21no—
70C2×C17×C22⋊Q8C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×D4×C17C2211yescharacteristic
74C2×C17×#117—21no—
75C2×C17×#117C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17D411yescharacteristic
79C23×C4×C17—21no—
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C22×C22⋊D17—21no—
83C22×C22⋊D17—21no—
84C23×Dic17—21no—
85C2×#63252—22no—
86C2×#63252—24no—
87C2×#63252—42no—
88C2×#63252C2314yes—
89C22×D68C2311yescharacteristic
90C22×C4×D17—21no—
91C22×Dic34—24no—
92C22×Dic34—22no—
93C22×Dic34—21no—
94C22×Dic34—42no—
95C22×Dic34C2311yescharacteristic
96C22×Dic34C2314yes—
97C22×Dic34C2311yescharacteristic
98C17×#126—28no—
99C17×#125—28no—
100C17×#125—22no—
101C17×#125C2314yes—
102C17×#123—28no—
103C17×C22⋊Q8—22no—
104C17×C22⋊Q8—22no—
105C17×C22⋊Q8C2314yes—
106C17×C22⋊Q8C2314yes—
107C4×Q8×C17—22no—
108C4×Q8×C17C2314yes—
109C4×D4×C17D414yes—
110C4×D4×C17C2314yes—
111C17×#117—22no—
112C17×#117—28no—
113C17×#117C2314yes—
114C2×C4⋊C4×C17—21no—
115C2×C4⋊C4×C17—22no—
116C2×C4⋊C4×C17—21no—
117C2×C4⋊C4×C17—21no—
118C2×C4⋊C4×C17—21no—
119C2×C4⋊C4×C17—21no—
120C2×C4⋊C4×C17—21no—
121C2×C4⋊C4×C17D411yescharacteristic
122C2×C4⋊C4×C17C2311yescharacteristic
123C2×C4⋊C4×C17C2311yescharacteristic
124C2×C4⋊C4×C17C2314yes—
125C2×C4⋊C4×C17C2311yescharacteristic
126C2×C22⋊C4×C17—21no—
127C2×C22⋊C4×C17—21no—
128C2×C22⋊C4×C17—21no—
129C2×C22⋊C4×C17D411yescharacteristic
130C2×C22⋊C4×C17D411yescharacteristic
131C2×C42×C17—21no—
132C2×C42×C17—21no—
133C2×C42×C17C2311yescharacteristic
134C2×C22⋊Dic17—21no—
135C2×#63231—24no—
136C2×#63231—42no—
137C2×#63231C2314yes—
138C2×#63231C2314yes—
139C2×#63230—42no—
140C2×#63230C2314yes—
141#10587625—28no—
142#10587616—22no—
143#10587616C2314yes—
144C2×#63227—21no—
145C2×#63227—21no—
146C2×#63227—21no—
147C2×C4⋊Dic17C2311yescharacteristic
148#10587610—22no—
149#10587610C2314yes—
150C2×#63225—21no—
151C2×#63225—21no—
152C2×C4×Dic17—21no—
153C2×#63223—42no—
154C2×#63223—42no—
155C2×#63223C2314yes—
156C2×#63223C2314yes—
157C22×#3622C2311yescharacteristic
158C22×#3622C2311yescharacteristic
159C22×#3622C2311yescharacteristic
160C22×#3622C2311yescharacteristic
161#10587582—28no—
162#10587571—28no—
163#10587567—28no—
164#10587561—22no—
165#10587561C2314yes—
166C4×Dic34—22no—
167C4×Dic34C2314yes—
168#10587506C2314yes—
169C22⋊#3622C2314yes—
170C22⋊#3622C2314yes—
171#10587481C2314yes—
172#10587481C2314yes—
173#10587481C2314yes—
174#10587481C2314yes—
175#10587481C2314yes—
176#10587481C2314yes—
177#10587480C2314yes—
178#10587480C2314yes—
179#10587480C2314yes—
180#10587479C2314yes—
181#10587478C2314yes—
182#10587478C2314yes—
183C4⋊#3622C2314yes—
184C4×#3622C2314yes—
185C24×C17C2×D411yescharacteristic
186C24×C17C2×D411yescharacteristic
187C23×D17—21no—
188C2×Q8×C17—21no—
189C2×Q8×C17—22no—
190C2×Q8×C17—22no—
191C2×Q8×C17C2412yes—
192C2×D4×C17—42no—
193C2×D4×C17C2×D414yes—
194C22×C4×C17—22no—
195C22×C4×C17—22no—
196C22×C4×C17—22no—
197C22×C4×C17—22no—
198C22×C4×C17—24no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—44no—
204C22×C4×C17C2×D412yes—
205C22×C4×C17C2×D412yes—
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2×D411yescharacteristic
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17C2×D411yescharacteristic
210C22×C4×C17C2412yes—
211C22×C4×C17C2412yes—
212C22×C4×C17C2411yescharacteristic
213C2×C22⋊D17—24no—
214C2×C22⋊D17—24no—
215C2×C22⋊D17—44no—
216C2×C22⋊D17—44no—
217C22×Dic17—21no—
218C22×Dic17—24no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—44no—
222#63252—28no—
223#63252—44no—
224#63252—48no—
225C2×D68—22no—
226C2×D68—22no—
227C2×D68—21no—
228C2×D68C2412yes—
229C2×C4×D17—24no—
230C2×C4×D17—44no—
231C2×Dic34—21no—
232C2×Dic34—22no—
233C2×Dic34—22no—
234C2×Dic34—22no—
235C2×Dic34—28no—
236C2×Dic34—21no—
237C2×Dic34—24no—
238C2×Dic34—44no—
239C2×Dic34—48no—
240C2×Dic34—44no—
241C2×Dic34#4114yes—
242C2×Dic34C2412yes—
243C2×Dic34C2412yes—
244C4⋊C4×C17—21no—
245C4⋊C4×C17—21no—
246C4⋊C4×C17—24no—
247C4⋊C4×C17—24no—
248C4⋊C4×C17—24no—
249C4⋊C4×C17—24no—
250C4⋊C4×C17—24no—
251C4⋊C4×C17—24no—
252C4⋊C4×C17—21no—
253C4⋊C4×C17C2×D414yes—
254C4⋊C4×C17C2412yes—
255C4⋊C4×C17C2412yes—
256C4⋊C4×C17C2412yes—
257C22⋊C4×C17—24no—
258C22⋊C4×C17—24no—
259C22⋊C4×C17—24no—
260C22⋊C4×C17C2×D414yes—
261C22⋊C4×C17C2×D414yes—
262C42×C17—24no—
263C42×C17—24no—
264C42×C17C2×D412yes—
265C42×C17C2412yes—
266C22⋊Dic17—24no—
267#63231—28no—
268#63231—44no—
269#63230—44no—
270#63227—24no—
271#63227—24no—
272#63227—24no—
273C4⋊Dic17—21no—
274C4⋊Dic17C2412yes—
275#63225—24no—
276#63225—24no—
277C4×Dic17—24no—
278#63223—44no—
279#63223—44no—
280C2×#3622—22no—
281C2×#3622—22no—
282C2×#3622—22no—
283C2×#3622—22no—
284C2×#3622C2412yes—
285C2×#3622C2412yes—
286C2×#3622C2412yes—
287C2×#3622C2412yes—
288C2×#3327—171nomaximal, Sylow
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17C22×D412yes—
296C23×C17C22×D412yes—
297C23×C17C22×D411yescharacteristic
298C22×D17—22no—
299C22×D17—42no—
300C22×D17—42no—
301C22×D17—42no—
302Q8×C17—22no—
303Q8×C17—22no—
304Q8×C17—42no—
305D4×C17—44no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—24no—
311C2×C4×C17—24no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—48no—
321C2×C4×C17—42no—
322C2×C4×C17—42no—
323C2×C4×C17—42no—
324C2×C4×C17—42no—
325C2×C4×C17C22×D412yes—
326C2×C4×C17C22×D412yes—
327C2×C4×C17C22×D412yes—
328C2×C4×C17C22×D412yes—
329C2×C4×C17C22×D411yescharacteristic
330C2×C4×C17C2×#4112yes—
331C2×C4×C17H(5,𝔽2)12yes—
332C2×C4×C17C2511yescharacteristic
333C22⋊D17—48no—
334C22⋊D17—48no—
335C2×Dic17—24no—
336C2×Dic17—22no—
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—48no—
340C2×Dic17—42no—
341C2×Dic17—42no—
342D68—22no—
343D68—22no—
344D68—42no—
345C4×D17—48no—
346Dic34—24no—
347Dic34—22no—
348Dic34—22no—
349Dic34—22no—
350Dic34—48no—
351Dic34—42no—
352Dic34C2×#4114yes—
353#3622—22no—
354#3622—22no—
355#3622—22no—
356#3622—22no—
357C2×#552D1711yescharacteristic, complemented
358C2×#548—171no—
359#3327—1716no—
360C2×#488—171no—
361C2×#484—171no—
362C2×#482—171no—
363C2×#479—171no—
364C2×#470—171no—
365C2×#468—171no—
366C2×#464—171no—
367C2×#452—171no—
368C2×#451—171no—
369C2×C4×Q16—171no—
370C2×#436—171no—
371C2×#417—171no—
372C2×#419—171no—
373C22×C17—22no—
374C22×C17—22no—
375C22×C17—22no—
376C22×C17—22no—
377C22×C17—22no—
378C22×C17—22no—
379C22×C17—44no—
380C22×C17—44no—
381C22×C17#54612yes—
382C22×C17#57512yes—
383C22×C17#57812yes—
384C22×C17C23×D411yescharacteristic
385C2×D17—42no—
386C2×D17—42no—
387C2×D17—42no—
388C2×D17—84no—
389C4×C17—22no—
390C4×C17—22no—
391C4×C17—22no—
392C4×C17—22no—
393C4×C17—42no—
394C4×C17—42no—
395C4×C17—42no—
396C4×C17—42no—
397C4×C17#54612yes—
398C4×C17C22×#4111yescharacteristic
399C4×C17C2×H(5,𝔽2)11yescharacteristic
400Dic17—24no—
401Dic17—42no—
402Dic17—42no—
403C22×#41—171no—
404C23×Q8—171no—
405C22×Q16—171no—
406C22×Q16—171no—
407C22×SD16—171no—
408C22×M16—171no—
409C22×M16—171no—
410#552—24no—
411#552C2×D1718yescomplemented
412#548—178no—
413#548—344no—
414C2×#126—21no—
415C2×#125—21no—
416C2×#125C2×D1711yescharacteristic
417C2×#124—171no—
418C2×#124—341no—
419C2×#123—21no—
420C2×C22⋊Q8—171no—
421C2×C22⋊Q8—341no—
422C2×C22⋊Q8C2×D1711yescharacteristic
423C2×C22⋊Q8C2×D1711yescharacteristic
424C2×#121—171no—
425C2×#121—341no—
426C2×C4×Q8—171no—
427C2×C4×Q8C2×D1711yescharacteristic
428C2×C4×D4—341no—
429C2×C4×D4C2×D1711yescharacteristic
430C2×#117—21no—
431C2×#117C2×D1711yescharacteristic
432C22×C4⋊C4C2×D1711yescharacteristic
433#488—178no—
434#484—178no—
435#482—178no—
436#479—178no—
437#470—178no—
438#468—178no—
439#464—178no—
440#452—178no—
441#451—178no—
442C4×Q16—178no—
443#436—178no—
444C2×#107—171no—
445C2×#107—171no—
446C2×#106—171no—
447C2×C4⋊C8—171no—
448#419—178no—
449#417—178no—
450C2×#103—171no—
451C2×#103—171no—
452C2×#103—171no—
453C2×#103—171no—
454C2×#103—171no—
455C2×#103—171no—
456C2×#103—171no—
457C2×#102—171no—
458C2×#102—171no—
459C2×#102—171no—
460C2×C22⋊C8—171no—
461C2×C22⋊C8—171no—
462C2×C4×C8—171no—
463C2×C17—42no—
464C2×C17—42no—
465C2×C17#332714yescomplemented
466C2×C17C2×#54611yescharacteristic
467C2×C17C2×#57511yescharacteristic
468C2×C17C2×#57811yescharacteristic
469D17—82no—
470C2×#41—174no—
471C2×#41—344no—
472C2×#41—342no—
473C2×#41—682no—
474C22×Q8—171no—
475C22×Q8—171no—
476C22×Q8—174no—
477C22×Q8—344no—
478C22×Q8—341no—
479C22×Q8—342no—
480C22×Q8—682no—
481C22×Q8C22×D1711yescharacteristic
482C22×D4—171no—
483C22×D4—341no—
484C22×D4—341no—
485C22×D4C22⋊D1711yescharacteristic
486C23×C4—21no—
487C23×C4—341no—
488C23×C4—341no—
489C23×C4C22×D1711yescharacteristic
490C23×C4C22×D1711yescharacteristic
491C2×Q16—174no—
492C2×Q16—174no—
493C2×Q16—344no—
494C2×Q16—682no—
495C2×SD16—174no—
496C2×SD16—682no—
497C2×M16—174no—
498C2×M16—174no—
499C2×M16—682no—
500C2×M16—682no—
501C22×C8—171no—
502C22×C8—171no—
503C22×C8—171no—
504C22×C8—171no—
505#126—28no—
506#125—28no—
507#125—22no—
508#125C22×D1714yes—
509#124—174no—
510#124—348no—
511#124—342no—
512#123—28no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—174no—
516C22⋊Q8—342no—
517C22⋊Q8—348no—
518C22⋊Q8C22×D1714yes—
519C22⋊Q8C22×D1714yes—
520#121—174no—
521#121—348no—
522#121—342no—
523C4×Q8—22no—
524C4×Q8—174no—
525C4×Q8—342no—
526C4×Q8C22×D1714yes—
527C4×D4—348no—
528C4×D4C22⋊D1714yes—
529C4×D4C22×D1714yes—
530#117—22no—
531#117—28no—
532#117C22×D1714yes—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—171no—
541C2×C4⋊C4—341no—
542C2×C4⋊C4—341no—
543C2×C4⋊C4C22⋊D1711yescharacteristic
544C2×C4⋊C4C22×D1711yescharacteristic
545C2×C4⋊C4C22×D1711yescharacteristic
546C2×C4⋊C4C22×D1714yes—
547C2×C4⋊C4C22×D1711yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—341no—
552C2×C22⋊C4—341no—
553C2×C22⋊C4—341no—
554C2×C22⋊C4—341no—
555C2×C22⋊C4C22⋊D1711yescharacteristic
556C2×C22⋊C4C22⋊D1711yescharacteristic
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—341no—
560C2×C42C22×D1711yescharacteristic
561#107—174no—
562#107—174no—
563#106—174no—
564C4⋊C8—174no—
565#103—174no—
566#103—174no—
567#103—174no—
568#103—174no—
569#103—174no—
570#103—174no—
571#103—174no—
572#102—174no—
573#102—174no—
574#102—174no—
575C22⋊C8—174no—
576C22⋊C8—174no—
577C4×C8—174no—
578C17C2×#332711yescharacteristic, complemented, Sylow
579C24—341no—
580C24C2×C22⋊D1711yescharacteristic
581C24C2×C22⋊D1711yescharacteristic
582#41—348no—
583#41—684no—
584#41—688no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—174no—
589C2×Q8—172no—
590C2×Q8—172no—
591C2×Q8—348no—
592C2×Q8—342no—
593C2×Q8—341no—
594C2×Q8—344no—
595C2×Q8—341no—
596C2×Q8—342no—
597C2×Q8—342no—
598C2×Q8—684no—
599C2×Q8—684no—
600C2×Q8—688no—
601C2×Q8C23×D1712yes—
602C2×D4—42no—
603C2×D4—172no—
604C2×D4—344no—
605C2×D4—344no—
606C2×D4—342no—
607C2×D4—342no—
608C2×D4—341no—
609C2×D4—684no—
610C2×D4—684no—
611C2×D4C2×C22⋊D1714yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—44no—
622C22×C4—341no—
623C22×C4—344no—
624C22×C4—341no—
625C22×C4—341no—
626C22×C4—344no—
627C22×C4—684no—
628C22×C4—684no—
629C22×C4C2×C22⋊D1712yes—
630C22×C4C2×C22⋊D1712yes—
631C22×C4C2×C22⋊D1711yescharacteristic
632C22×C4C2×C22⋊D1711yescharacteristic
633C22×C4C2×C22⋊D1711yescharacteristic
634C22×C4C2×C22⋊D1711yescharacteristic
635C22×C4C23×D1712yes—
636C22×C4C23×D1712yes—
637C22×C4C23×D1711yescharacteristic
638Q16—348no—
639Q16—684no—
640SD16—684no—
641M16—684no—
642M16—684no—
643C2×C8—172no—
644C2×C8—172no—
645C2×C8—172no—
646C2×C8—172no—
647C2×C8—342no—
648C2×C8—342no—
649C2×C8—342no—
650C2×C8—342no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—172no—
661C4⋊C4—341no—
662C4⋊C4—344no—
663C4⋊C4—344no—
664C4⋊C4C2×C22⋊D1714yes—
665C4⋊C4C23×D1712yes—
666C4⋊C4C23×D1712yes—
667C4⋊C4C23×D1712yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—344no—
672C22⋊C4—344no—
673C22⋊C4—344no—
674C22⋊C4—344no—
675C22⋊C4C2×C22⋊D1714yes—
676C22⋊C4C2×C22⋊D1714yes—
677C42—24no—
678C42—24no—
679C42—344no—
680C42C2×C22⋊D1712yes—
681C42C23×D1712yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—342no—
689C23—682no—
690C23—682no—
691C23—682no—
692C23C22×C22⋊D1712yes—
693C23C22×C22⋊D1712yes—
694C23C22×C22⋊D1711yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—174no—
699Q8—342no—
700Q8—344no—
701Q8—342no—
702Q8—342no—
703Q8—688no—
704Q8—682no—
705D4—44no—
706D4—342no—
707D4—342no—
708D4—688no—
709D4—688no—
710D4—682no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—342no—
731C2×C4—344no—
732C2×C4—342no—
733C2×C4—342no—
734C2×C4—688no—
735C2×C4—688no—
736C2×C4—682no—
737C2×C4—682no—
738C2×C4#41×D1712yes—
739C2×C4#1058769612yes—
740C2×C4C22×C22⋊D1712yes—
741C2×C4C22×C22⋊D1712yes—
742C2×C4C22×C22⋊D1712yes—
743C2×C4C22×C22⋊D1712yes—
744C2×C4C22×C22⋊D1711yescharacteristic
745C2×C4C24×D1711yescharacteristic
746C8—342no—
747C8—342no—
748C8—342no—
749C8—342no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—682no—
759C22—682no—
760C22—682no—
761C22—1364no—
762C22#1176344712yes—
763C22#1176360712yes—
764C22#1176362412yes—
765C22C23×C22⋊D1711yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—344no—
775C4—682no—
776C4—682no—
777C4#1176344712yes—
778C4C2×#41×D1711yescharacteristic
779C4C2×#1058769611yescharacteristic
780C2—42no—
781C2—42no—
782C2—1362no—
783C2#1454104614yesdirect product factor
784C2C2×#1176344711yescharacteristic
785C2C2×#1176360711yescharacteristic
786C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#552C2
socleC23×C17C22×D4
prime radicalC2×#11763468C2
hypercenterC2×#552D17
hypocenterC17C2×#3327
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #14541046C2direct (N × H)
3. C2×#11763166C2semidirect
4. C2×#11763144C2semidirect
5. C2×#11763133C2semidirect
6. C2×#11763113C2semidirect
7. C2×#11763065C2semidirect
8. C2×#11763057C2semidirect
9. C2×#11763031C2semidirect
10. C2×#11762969C2semidirect
11. C2×#11762964C2semidirect
12. C2×C4×#63231C2semidirect
13. C2×#11762887C2semidirect
14. C2×#11762808C2semidirect
15. C2×#11762817C2semidirect
16. C2×C17×#552C2semidirect
34. #11763166C22semidirect
35. #11763144C22semidirect
36. #11763133C22semidirect
37. #11763113C22semidirect
38. #11763065C22semidirect
39. #11763057C22semidirect
40. #11763031C22semidirect
41. #11762969C22semidirect
42. #11762964C22semidirect
43. C4×#63231C22semidirect
44. #11762887C22semidirect
49. #11762817C22semidirect
50. #11762808C22semidirect
65. C17×#552C22semidirect
357. C2×#552D17semidirect
411. #552C2×D17semidirect
465. C2×C17#3327semidirect
578. C17C2×#3327semidirect
783. C2#14541046direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634682
#145410462
C2×#117631662
C2×#117631442
C2×#117631332
C2×#117631132
C2×#117630652
C2×#117630572
C2×#117630312
C2×#117629692
C2×#117629642
C2×C4×#632312
C2×#117628872
C2×#117628082
C2×#117628172
C2×C17×#5522
C2×#332717