Finite Group Databasebeta

← #17898305

Subgroups — #17898305

Order 4352.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763576C211yesmaximal, characteristic, complemented
2C22×#10587634C211yesmaximal, characteristic, complemented
3#14537528C213yesmaximal, complemented
4D4×#63223C213yesmaximal, complemented
5#14537511C213yesmaximal, complemented
6#14537511C213yesmaximal, complemented
7#14537502C213yesmaximal, complemented
8#14537488C213yesmaximal, complemented
9#14537479C213yesmaximal, complemented
10C2×#11762881C213yesmaximal, complemented
11#14537352C211yesmaximal, characteristic, complemented
12#14537233C211yesmaximal, characteristic, complemented
13#14537233C211yesmaximal, characteristic, complemented
14#14537212C211yesmaximal, characteristic, complemented
15D4×#41×C17C211yesmaximal, characteristic
16#11763576—28no—
17C2×#10587634—28no—
18C2×#10587634C2211yescharacteristic
19C2×#10587634C2211yescharacteristic
20C2×#10587634C2211yescharacteristic
21C2×#10587634C2211yescharacteristic
22C2×#10587634C2213yescomplemented
23C2×#10587634C2213yescomplemented
24C2×#10587634C2213yescomplemented
25C2×#10587634C2213yescomplemented
26C22×#63223C2213yescomplemented
27C22×#63223C2213yescomplemented
28C22×#63223C2213yescomplemented
29C23×#3622C2213yescomplemented
30#11762887C2216yescomplemented
31#11762887C2216yescomplemented
32#11762881C2213yes—
33#11762881C2211yescharacteristic
34#11762881C2213yescomplemented
35#11762881C2216yescomplemented
36#11762881C2213yescomplemented
37#11762881C2213yescomplemented
38#11762881C2216yescomplemented
39#11762881C2216yescomplemented
40#11762881C2213yescomplemented
41#11762881C2213yescomplemented
42#11762881C2213yescomplemented
43D4×#3622C2216yescomplemented
44D4×#3622C2216yescomplemented
45#11762836C2213yescomplemented
46#11762836C2213yescomplemented
47#11762833C2213yescomplemented
48C2×C4⋊#3622C2213yescomplemented
49#11762776C2213yescomplemented
50#11762776C2213yescomplemented
51#11762776C2213yescomplemented
52#11762776C2213yescomplemented
53#11762773C2213yescomplemented
54#11762773C2213yescomplemented
55C2×C22⋊#3622C2213yescomplemented
56C2×C22⋊#3622C2213yescomplemented
57#11762765C2213yescomplemented
58#11762765C2213yescomplemented
59C4×#63223C2213yescomplemented
60C2×#10587474C2213yescomplemented
61C22×#41×C17C2211yescharacteristic
62C22×#41×C17C2211yescharacteristic
63C17×#550C411yescharacteristic
64D4×Q8×C17C411yescharacteristic
65C17×#548C411yescharacteristic
66C17×#548C411yescharacteristic
67C17×#547C413yes—
68C17×#546C413yes—
69C17×#546C413yes—
70D42×C17C413yes—
71C17×#532C2213yes—
72C17×#525C2213yes—
73C17×#525C2213yes—
74C4×#41×C17C2211yescharacteristic
75C2×C4×D4×C17C2213yes—
76C2×#41×C17—24no—
77C2×#41×C17—24no—
78C2×#41×C17—24no—
79C2×#41×C17—24no—
80C2×#41×C17C2×C413yes—
81C2×#41×C17C2×C413yes—
82C2×#41×C17C2×C411yescharacteristic
83C2×#41×C17C2×C411yescharacteristic
84C2×#41×C17C2313yes—
85C2×#41×C17C2313yes—
86C2×#41×C17C2311yescharacteristic
87C22×Q8×C17C2×C411yescharacteristic
88C22×Q8×C17C2×C411yescharacteristic
89C22×D4×C17C2×C413yes—
90C22×D4×C17C2×C413yes—
91C22×D4×C17C2×C413yes—
92C23×C4×C17C2313yes—
93C23×C4×C17C2313yes—
94C17×C4⋊Q8C2×C413yes—
95C17×#127C2×C413yes—
96C17×#124C2×C413yes—
97C17×#124C2×C413yes—
98C17×#123C2×C416yes—
99C17×#123C2×C416yes—
100C17×C22⋊Q8C2×C413yes—
101C17×C22⋊Q8C2×C413yes—
102C17×C22⋊Q8C2×C413yes—
103C17×C22⋊Q8C2×C413yes—
104C17×#121C2×C413yes—
105C17×#121C2×C413yes—
106C17×#121C2×C413yes—
107C17×#121C2×C413yes—
108C17×#121C2×C416yes—
109C17×#121C2×C416yes—
110C17×#120C2×C416yes—
111C17×#120C2×C416yes—
112C4×Q8×C17C2×C411yescharacteristic
113C4×Q8×C17C2×C411yescharacteristic
114C4×D4×C17C2×C413yes—
115C4×D4×C17C2×C413yes—
116C4×D4×C17C2×C413yes—
117C4×D4×C17C2×C413yes—
118C4×D4×C17C2×C413yes—
119C4×D4×C17C2×C413yes—
120C4×D4×C17C2311yescharacteristic
121C4×D4×C17C2313yes—
122C4×D4×C17C2313yes—
123C4×D4×C17C2313yes—
124C4×D4×C17C2316yes—
125C17×#117C2313yes—
126C2×C4⋊C4×C17C2×C413yes—
127C2×C22⋊C4×C17C2×C413yes—
128C2×C22⋊C4×C17C2×C413yes—
129C2×C42×C17C2313yes—
130#10587634—212no—
131#10587634—212no—
132#10587634—212no—
133#10587634—212no—
134#10587634—24no—
135#10587634—24no—
136#10587634—24no—
137#10587634D418yescomplemented
138C2×#63223—212no—
139C2×#63223—212no—
140C2×#63223—212no—
141C2×#63223C2313yes—
142C2×#63223C2313yes—
143C2×#63223C2313yes—
144C2×#63223C2311yescharacteristic
145C2×#63223C2313yes—
146C2×#63223C2313yes—
147C2×#63223C2313yes—
148C2×#63223C2316yes—
149C2×#63223C2313yes—
150C22×#3622—212no—
151C22×#3622C2313yes—
152C22×#3622C2313yes—
153C22×#3622C2313yes—
154C22×#3622C2311yescharacteristic
155C22×#3622C2313yes—
156C22×#3622C2313yes—
157C22×#3622C2313yes—
158C22×#3622C2316yes—
159C22×#3622C2313yes—
160C22⋊#3622C2311yescharacteristic
161C22⋊#3622C2311yescharacteristic
162C22⋊#3622C2313yes—
163C22⋊#3622C2313yes—
164C22⋊#3622C2313yes—
165C22⋊#3622C2313yes—
166C22⋊#3622C2313yes—
167C22⋊#3622C2313yes—
168C22⋊#3622C2316yes—
169C22⋊#3622C2316yes—
170C4⋊#3622C2311yescharacteristic
171C4⋊#3622C2313yes—
172C4⋊#3622C2313yes—
173C4⋊#3622C2313yes—
174C4⋊#3622C2316yes—
175#10587474C2311yescharacteristic
176#10587474C2313yes—
177#10587474C2313yes—
178#10587474C2313yes—
179C4×#3622C2316yes—
180C24×C17C22×C413yes—
181C24×C17C22×C413yes—
182#41×C17—24no—
183#41×C17—24no—
184#41×C17—212no—
185#41×C17—212no—
186#41×C17—26no—
187#41×C17—26no—
188#41×C17—26no—
189#41×C17—26no—
190#41×C17C2×D414yes—
191#41×C17#4114yes—
192C2×Q8×C17—24no—
193C2×Q8×C17—24no—
194C2×Q8×C17C22×C413yes—
195C2×Q8×C17C22×C413yes—
196C2×Q8×C17C22×C411yescharacteristic
197C2×D4×C17—212no—
198C2×D4×C17—212no—
199C2×D4×C17—46no—
200C2×D4×C17C22×C416yes—
201C2×D4×C17C22×C416yes—
202C2×D4×C17C22×C413yes—
203C2×D4×C17C22×C413yes—
204C2×D4×C17C22×C411yescharacteristic
205C2×D4×C17C22×C413yes—
206C2×D4×C17C22×C413yes—
207C2×D4×C17C22×C416yes—
208C2×D4×C17C22×C413yes—
209C2×D4×C17C22×C413yes—
210C22×C4×C17—26no—
211C22×C4×C17—26no—
212C22×C4×C17—26no—
213C22×C4×C17—26no—
214C22×C4×C17C22×C413yes—
215C22×C4×C17C22×C413yes—
216C22×C4×C17C22×C413yes—
217C22×C4×C17C22×C413yes—
218C22×C4×C17C22×C413yes—
219C22×C4×C17C22×C413yes—
220C22×C4×C17C22×C413yes—
221C22×C4×C17C22×C413yes—
222C22×C4×C17C2411yescharacteristic
223C22×C4×C17C2411yescharacteristic
224C22×C4×C17C2413yes—
225C22×C4×C17C2413yes—
226C22×C4×C17C2413yes—
227C4⋊C4×C17C22×C416yes—
228C4⋊C4×C17C22×C413yes—
229C4⋊C4×C17C22×C413yes—
230C4⋊C4×C17C22×C413yes—
231C4⋊C4×C17C22×C413yes—
232C4⋊C4×C17C22×C413yes—
233C4⋊C4×C17C22×C411yescharacteristic
234C22⋊C4×C17C22×C413yes—
235C22⋊C4×C17C22×C413yes—
236C22⋊C4×C17C22×C416yes—
237C22⋊C4×C17C22×C416yes—
238C22⋊C4×C17C22×C413yes—
239C22⋊C4×C17C22×C413yes—
240C22⋊C4×C17C22×C416yes—
241C22⋊C4×C17C22×C413yes—
242C22⋊C4×C17C22×C413yes—
243C22⋊C4×C17C22×C411yescharacteristic
244C22⋊C4×C17C22×C411yescharacteristic
245C42×C17C22×C413yes—
246C42×C17C22×C413yes—
247C42×C17C2413yes—
248C42×C17C2411yescharacteristic
249#63223—26no—
250#63223—26no—
251#63223—26no—
252#63223—22no—
253#63223—26no—
254#63223—26no—
255#63223—212no—
256#63223—26no—
257#63223C2×D4112yescomplemented
258C2×#3622—26no—
259C2×#3622—26no—
260C2×#3622—26no—
261C2×#3622—22no—
262C2×#3622—26no—
263C2×#3622—26no—
264C2×#3622—26no—
265C2×#3622—212no—
266C2×#3622C2×D4112yescomplemented
267C2×#3622C2413yes—
268C2×#3622C2411yescharacteristic
269C2×#3622C2411yescharacteristic
270C2×#3622C2411yescharacteristic
271C2×#3622C2413yes—
272C2×#3622C2413yes—
273C2×#3622C2413yes—
274C2×#3622C2411yescharacteristic
275#60146—171nomaximal, Sylow
276C23×C17—26no—
277C23×C17—26no—
278C23×C17—26no—
279C23×C17—43no—
280C23×C17—43no—
281C23×C17—43no—
282C23×C17C23×C411yescharacteristic
283C23×C17C23×C413yes—
284C23×C17C23×C413yes—
285C23×C17C23×C413yes—
286C23×C17C23×C411yescharacteristic
287Q8×C17—26no—
288Q8×C17—26no—
289Q8×C17C4×D414yes—
290D4×C17—212no—
291D4×C17—212no—
292D4×C17—22no—
293D4×C17—26no—
294D4×C17—26no—
295D4×C17—26no—
296D4×C17—43no—
297D4×C17—43no—
298D4×C17—46no—
299D4×C17C4×D4112yes—
300C2×C4×C17—26no—
301C2×C4×C17—26no—
302C2×C4×C17—26no—
303C2×C4×C17—26no—
304C2×C4×C17—26no—
305C2×C4×C17—26no—
306C2×C4×C17—21no—
307C2×C4×C17—21no—
308C2×C4×C17—23no—
309C2×C4×C17—23no—
310C2×C4×C17—21no—
311C2×C4×C17—21no—
312C2×C4×C17—23no—
313C2×C4×C17—23no—
314C2×C4×C17—43no—
315C2×C4×C17—43no—
316C2×C4×C17C23×C411yescharacteristic
317C2×C4×C17C23×C411yescharacteristic
318C2×C4×C17C23×C413yes—
319C2×C4×C17C23×C413yes—
320C2×C4×C17C23×C411yescharacteristic
321C2×C4×C17C23×C411yescharacteristic
322C2×C4×C17C23×C413yes—
323C2×C4×C17C23×C413yes—
324C2×C4×C17C23×C413yes—
325C2×C4×C17C22×D416yes—
326C2×C4×C17C2×#4116yes—
327C2×C4×C17C2511yescharacteristic
328#3622—21no—
329#3622—23no—
330#3622—21no—
331#3622—23no—
332#3622—21no—
333#3622—23no—
334#3622C22×D412yes—
335#3622C22×D416yes—
336C2×#568—171no—
337C22×#131—171no—
338D4×#41D1711yescharacteristic
339#2935—173no—
340D4×M16—173no—
341#2933—173no—
342#2933—173no—
343#2932—173no—
344#2930—173no—
345#2929—173no—
346C2×#435—173no—
347#2906—171no—
348#2880—171no—
349#2880—171no—
350#2875—171no—
351C22×C17—21no—
352C22×C17—23no—
353C22×C17—23no—
354C22×C17—21no—
355C22×C17—21no—
356C22×C17—23no—
357C22×C17—23no—
358C22×C17—21no—
359C22×C17—23no—
360C22×C17—23no—
361C22×C17—23no—
362C22×C17—23no—
363C22×C17—21no—
364C22×C17—412no—
365C22×C17—86no—
366C22×C17C2×C4×D416yes—
367C22×C17#56812yescomplemented
368C22×C17C24×C411yescharacteristic
369C4×C17—21no—
370C4×C17—21no—
371C4×C17—23no—
372C4×C17—23no—
373C4×C17—21no—
374C4×C17—23no—
375C4×C17—21no—
376C4×C17—23no—
377C4×C17C2×C4×D416yes—
378C4×C17C23×D411yescharacteristic
379C4×C17C22×#4111yescharacteristic
380C22×#41C2×D1711yescharacteristic
381C22×#41C2×D1711yescharacteristic
382#568—348no—
383C2×#131—171no—
384C2×#131—171no—
385C2×#131—171no—
386C2×#131—171no—
387C2×#131—173no—
388C2×#131—173no—
389C2×#131—173no—
390C2×#131—173no—
391C2×#131—348no—
392C22×M16—173no—
393C22×M16—173no—
394C22×M16—173no—
395C23×C8—173no—
396#550Dic1711yescharacteristic
397D4×Q8Dic1711yescharacteristic
398#548Dic1711yescharacteristic
399#548Dic1711yescharacteristic
400#547Dic1713yes—
401#546Dic1713yes—
402#546Dic1713yes—
403D42Dic1713yes—
404#532C2×D1713yes—
405#525C2×D1713yes—
406#525C2×D1713yes—
407C4×#41C2×D1711yescharacteristic
408C2×C4×D4C2×D1713yes—
409#436—176no—
410#436—176no—
411#435—171no—
412#435—173no—
413#435—173no—
414#435—173no—
415#435—173no—
416#435—173no—
417#435—173no—
418#435—173no—
419#435—176no—
420#435—176no—
421#435—176no—
422C8×D4—176no—
423C8×D4—176no—
424#424—173no—
425#424—173no—
426#423—173no—
427C2×C4⋊C8—173no—
428#408—173no—
429#408—173no—
430#408—173no—
431#408—173no—
432#407—173no—
433#407—173no—
434C2×C22⋊C8—173no—
435C2×C22⋊C8—173no—
436#405—173no—
437#405—173no—
438C4×M16—173no—
439C2×#97—173no—
440C2×C17—22no—
441C2×C17—26no—
442C2×C17—43no—
443C2×C17—43no—
444C2×C17—41no—
445C2×C17C22×C4×D411yescharacteristic
446C2×C17C2×#56811yescharacteristic
447C2×C17#357311yescharacteristic
448C2×#41—24no—
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—24no—
452C2×#41C2×Dic1713yes—
453C2×#41C2×Dic1713yes—
454C2×#41C2×Dic1711yescharacteristic
455C2×#41C2×Dic1711yescharacteristic
456C2×#41C22×D1713yes—
457C2×#41C22×D1713yes—
458C2×#41C22×D1711yescharacteristic
459C22×Q8C2×Dic1711yescharacteristic
460C22×Q8C2×Dic1711yescharacteristic
461C22×D4C2×Dic1713yes—
462C22×D4C2×Dic1713yes—
463C22×D4C2×Dic1713yes—
464C23×C4C22×D1713yes—
465C23×C4C22×D1713yes—
466#131—178no—
467#131—3412no—
468#131—3412no—
469#131—3412no—
470#131—3412no—
471#131—344no—
472#131—344no—
473#131—344no—
474C2×M16—173no—
475C2×M16—171no—
476C2×M16—173no—
477C2×M16—173no—
478C2×M16—173no—
479C2×M16—173no—
480C2×M16—173no—
481C2×M16—176no—
482C2×M16—173no—
483C2×M16—3412no—
484C2×M16—3412no—
485C2×M16—3412no—
486C22×C8—173no—
487C22×C8—171no—
488C22×C8—173no—
489C22×C8—173no—
490C22×C8—173no—
491C22×C8—173no—
492C22×C8—173no—
493C22×C8—176no—
494C22×C8—173no—
495C22×C8—3412no—
496C4⋊Q8C2×Dic1713yes—
497#127C2×Dic1713yes—
498#124C2×Dic1713yes—
499#124C2×Dic1713yes—
500#123C2×Dic1716yes—
501#123C2×Dic1716yes—
502C22⋊Q8C2×Dic1713yes—
503C22⋊Q8C2×Dic1713yes—
504C22⋊Q8C2×Dic1713yes—
505C22⋊Q8C2×Dic1713yes—
506#121C2×Dic1713yes—
507#121C2×Dic1713yes—
508#121C2×Dic1713yes—
509#121C2×Dic1713yes—
510#121C2×Dic1716yes—
511#121C2×Dic1716yes—
512#120C2×Dic1716yes—
513#120C2×Dic1716yes—
514C4×Q8C2×Dic1711yescharacteristic
515C4×Q8C2×Dic1711yescharacteristic
516C4×D4C2×Dic1713yes—
517C4×D4C2×Dic1713yes—
518C4×D4C2×Dic1713yes—
519C4×D4C2×Dic1713yes—
520C4×D4C2×Dic1713yes—
521C4×D4C2×Dic1713yes—
522C4×D4C22×D1711yescharacteristic
523C4×D4C22×D1713yes—
524C4×D4C22×D1713yes—
525C4×D4C22×D1713yes—
526C4×D4C22×D1716yes—
527#117C22×D1713yes—
528C2×C4⋊C4C2×Dic1713yes—
529C2×C22⋊C4C2×Dic1713yes—
530C2×C22⋊C4C2×Dic1713yes—
531C2×C42C22×D1713yes—
532C4⋊C8—171no—
533C4⋊C8—173no—
534C4⋊C8—173no—
535C4⋊C8—173no—
536C4⋊C8—176no—
537C22⋊C8—171no—
538C22⋊C8—171no—
539C22⋊C8—173no—
540C22⋊C8—173no—
541C22⋊C8—173no—
542C22⋊C8—173no—
543C22⋊C8—173no—
544C22⋊C8—173no—
545C22⋊C8—176no—
546C22⋊C8—176no—
547#97—171no—
548#97—173no—
549#97—173no—
550#97—173no—
551C4×C8—176no—
552C17#6014611yescharacteristic, complemented, Sylow
553C24C22×Dic1713yes—
554C24C22×Dic1713yes—
555#41—24no—
556#41—24no—
557#41—212no—
558#41—212no—
559#41—26no—
560#41—26no—
561#41—26no—
562#41—26no—
563#41D4×D1714yes—
564#41#6325414yes—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8C22×Dic1713yes—
568C2×Q8C22×Dic1713yes—
569C2×Q8C22×Dic1711yescharacteristic
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—46no—
573C2×D4C22×Dic1711yescharacteristic
574C2×D4C22×Dic1713yes—
575C2×D4C22×Dic1716yes—
576C2×D4C22×Dic1716yes—
577C2×D4C22×Dic1713yes—
578C2×D4C22×Dic1713yes—
579C2×D4C22×Dic1713yes—
580C2×D4C22×Dic1713yes—
581C2×D4C22×Dic1716yes—
582C2×D4C22×Dic1713yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—26no—
587C22×C4C22×Dic1713yes—
588C22×C4C22×Dic1713yes—
589C22×C4C22×Dic1713yes—
590C22×C4C22×Dic1713yes—
591C22×C4C22×Dic1713yes—
592C22×C4C22×Dic1713yes—
593C22×C4C22×Dic1713yes—
594C22×C4C22×Dic1713yes—
595C22×C4C23×D1711yescharacteristic
596C22×C4C23×D1713yes—
597C22×C4C23×D1713yes—
598C22×C4C23×D1711yescharacteristic
599C22×C4C23×D1713yes—
600M16—1712no—
601M16—342no—
602M16—346no—
603M16—346no—
604M16—346no—
605M16—3412no—
606M16—346no—
607M16—346no—
608M16—346no—
609C2×C8—1712no—
610C2×C8—173no—
611C2×C8—171no—
612C2×C8—173no—
613C2×C8—171no—
614C2×C8—171no—
615C2×C8—171no—
616C2×C8—173no—
617C2×C8—173no—
618C2×C8—342no—
619C2×C8—346no—
620C2×C8—346no—
621C2×C8—346no—
622C2×C8—3412no—
623C2×C8—346no—
624C2×C8—346no—
625C2×C8—346no—
626C4⋊C4C22×Dic1711yescharacteristic
627C4⋊C4C22×Dic1713yes—
628C4⋊C4C22×Dic1713yes—
629C4⋊C4C22×Dic1713yes—
630C4⋊C4C22×Dic1713yes—
631C4⋊C4C22×Dic1713yes—
632C4⋊C4C22×Dic1716yes—
633C22⋊C4C22×Dic1711yescharacteristic
634C22⋊C4C22×Dic1711yescharacteristic
635C22⋊C4C22×Dic1713yes—
636C22⋊C4C22×Dic1713yes—
637C22⋊C4C22×Dic1713yes—
638C22⋊C4C22×Dic1713yes—
639C22⋊C4C22×Dic1713yes—
640C22⋊C4C22×Dic1713yes—
641C22⋊C4C22×Dic1716yes—
642C22⋊C4C22×Dic1716yes—
643C22⋊C4C22×Dic1716yes—
644C42C22×Dic1713yes—
645C42C22×Dic1713yes—
646C42C23×D1713yes—
647C42C23×D1711yescharacteristic
648C23—26no—
649C23—26no—
650C23—26no—
651C23—43no—
652C23—43no—
653C23—43no—
654C23C23×Dic1711yescharacteristic
655C23C23×Dic1713yes—
656C23C23×Dic1713yes—
657C23C23×Dic1713yes—
658C23C23×Dic1711yescharacteristic
659Q8—26no—
660Q8—26no—
661Q8D4×Dic1714yes—
662D4—212no—
663D4—212no—
664D4—22no—
665D4—26no—
666D4—26no—
667D4—26no—
668D4—43no—
669D4—43no—
670D4—46no—
671D4D4×Dic17112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—26no—
676C2×C4—26no—
677C2×C4—26no—
678C2×C4—21no—
679C2×C4—23no—
680C2×C4—23no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—43no—
687C2×C4—43no—
688C2×C4C2×D4×D1716yes—
689C2×C4C2×#6325416yes—
690C2×C4C23×Dic1711yescharacteristic
691C2×C4C23×Dic1711yescharacteristic
692C2×C4C23×Dic1713yes—
693C2×C4C23×Dic1713yes—
694C2×C4C23×Dic1711yescharacteristic
695C2×C4C23×Dic1711yescharacteristic
696C2×C4C23×Dic1713yes—
697C2×C4C23×Dic1713yes—
698C2×C4C23×Dic1713yes—
699C2×C4C24×D1711yescharacteristic
700C8—172no—
701C8—176no—
702C8—341no—
703C8—343no—
704C8—343no—
705C8—341no—
706C8—341no—
707C8—343no—
708C22—21no—
709C22—23no—
710C22—23no—
711C22—21no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—23no—
717C22—23no—
718C22—23no—
719C22—23no—
720C22—21no—
721C22—412no—
722C22—86no—
723C22C2×D4×Dic1716yes—
724C22#1176357612yescomplemented
725C22C24×Dic1711yescharacteristic
726C4—21no—
727C4—21no—
728C4—23no—
729C4—23no—
730C4—21no—
731C4—23no—
732C4—21no—
733C4—23no—
734C4C2×D4×Dic1716yes—
735C4C22×D4×D1711yescharacteristic
736C4C22×#6325411yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×D4×Dic1711yescharacteristic
743C2C2×#1176357611yescharacteristic
744C2#1454349611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
Fitting, prime radicalD4×#41×C17C2
cosocleC2×C4×C17C25
hypercenterD4×#41D17
hypocenterC17#60146
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#11763576C2semidirect
2. C22×#10587634C2semidirect
3. #14537528C2semidirect
4. D4×#63223C2semidirect
5. #14537511C2semidirect
6. #14537511C2semidirect
7. #14537502C2semidirect
8. #14537488C2semidirect
9. #14537479C2semidirect
10. C2×#11762881C2semidirect
11. #14537352C2semidirect
12. #14537233C2semidirect
13. #14537233C2semidirect
14. #14537212C2semidirect
22. C2×#10587634C22semidirect
23. C2×#10587634C22semidirect
24. C2×#10587634C22semidirect
25. C2×#10587634C22semidirect
26. C22×#63223C22semidirect
27. C22×#63223C22semidirect
28. C22×#63223C22semidirect
29. C23×#3622C22semidirect
30. #11762887C22semidirect
31. #11762887C22semidirect
34. #11762881C22semidirect
35. #11762881C22semidirect
36. #11762881C22semidirect
37. #11762881C22semidirect
38. #11762881C22semidirect
39. #11762881C22semidirect
40. #11762881C22semidirect
41. #11762881C22semidirect
42. #11762881C22semidirect
43. D4×#3622C22semidirect
44. D4×#3622C22semidirect
45. #11762836C22semidirect
46. #11762836C22semidirect
47. #11762833C22semidirect
48. C2×C4⋊#3622C22semidirect
49. #11762776C22semidirect
50. #11762776C22semidirect
51. #11762776C22semidirect
52. #11762776C22semidirect
53. #11762773C22semidirect
54. #11762773C22semidirect
55. C2×C22⋊#3622C22semidirect
56. C2×C22⋊#3622C22semidirect
57. #11762765C22semidirect
58. #11762765C22semidirect
59. C4×#63223C22semidirect
60. C2×#10587474C22semidirect
137. #10587634D4semidirect
257. #63223C2×D4semidirect
266. C2×#3622C2×D4semidirect
367. C22×C17#568semidirect
552. C17#60146semidirect
724. C22#11763576semidirect

Maximal subgroups

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

subgroupindex
C2×#117635762
C22×#105876342
#145375282
D4×#632232
#145375112
#145375022
#145374882
#145374792
C2×#117628812
#145373522
#145372332
#145372122
D4×#41×C172
#6014617