Finite Group Databasebeta

← #26222072

Subgroups — #26222072

Order 12032.

1344 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689279C211yesmaximal, characteristic
2C2×#15689228C211yesmaximal, characteristic, complemented
3C2×C4×#10625337C211yesmaximal, characteristic, complemented
4#20246070C211yesmaximal, characteristic
5#20243729C211yesmaximal, characteristic, complemented
6#20243729C211yesmaximal, characteristic, complemented
7#20243700C211yesmaximal, characteristic
8#20243656C211yesmaximal, characteristic, complemented
9#20243642C211yesmaximal, characteristic, complemented
10#20243587C211yesmaximal, characteristic
11#20243323C211yesmaximal, characteristic
12#20243218C211yesmaximal, characteristic, complemented
13C4×#13093948C211yesmaximal, characteristic, complemented
14#20243154C211yesmaximal, characteristic
15C2×C47×#519C211yesmaximal, characteristic
16C22×#10625337C2211yescharacteristic
17C22×#10625337C2211yescharacteristic
18C2×#13094003C2211yescharacteristic
19C2×C4×Dic94C2211yescharacteristic
20#15689279C418yescomplemented
21#15689228—24no—
22C4×#10625337—24no—
23C2×#13093957C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×#13093948C2211yescharacteristic
26C2×#13093948C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093948C2211yescharacteristic
31C2×#13093947C2211yescharacteristic
32C2×#13093947C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35C2×#13093935C2211yescharacteristic
36C2×C4×C47⋊C8C2211yescharacteristic
37#15689029C2211yescharacteristic
38#15689021C2211yescharacteristic
39#15689018—21no—
40#15689017—21no—
41#15689011—21no—
42#15689004—21no—
43#15688983C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51C23×Q8×C47C2211yescharacteristic
52C47×#519—24no—
53C47×#519—24no—
54C2×C4×Q8×C47—21no—
55C2×C4×Q8×C47—21no—
56C2×C4×Q8×C47C2211yescharacteristic
57C2×C4×Q8×C47C2211yescharacteristic
58C2×C4×Q8×C47C2211yescharacteristic
59C2×C4×Q8×C47C2211yescharacteristic
60C2×#117×C47—21no—
61C2×#117×C47—21no—
62C2×#117×C47C2211yescharacteristic
63C2×#117×C47C2211yescharacteristic
64C22×Dic94C2311yescharacteristic
65C2×#10625337—22no—
66C2×#10625337—22no—
67C2×#10625337—22no—
68C2×#10625337—22no—
69C2×#10625337C2×C414yes—
70C2×#10625337C2×C414yes—
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13094003—22no—
76#13094003C2×C414yes—
77C4×Dic94—22no—
78C4×Dic94—22no—
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89#13093957—22no—
90#13093955—22no—
91#13093948—22no—
92#13093948—22no—
93#13093948—22no—
94#13093948—22no—
95#13093948C2×C414yes—
96#13093948C2×C414yes—
97#13093947—22no—
98#13093947—22no—
99C22⋊(C47⋊C8)—22no—
100C22⋊(C47⋊C8)C2×C414yes—
101#13093935—22no—
102C4×C47⋊C8—22no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C22×Q8×C47—22no—
109C22×Q8×C47—22no—
110C22×Q8×C47—22no—
111C22×Q8×C47—22no—
112C22×Q8×C47—21no—
113C22×Q8×C47—22no—
114C22×Q8×C47C2×C414yes—
115C22×Q8×C47C2311yescharacteristic
116C22×Q8×C47C2311yescharacteristic
117C23×C4×C47—21no—
118C23×C4×C47C2311yescharacteristic
119C4×Q8×C47—28no—
120C4×Q8×C47—28no—
121C4×Q8×C47—22no—
122C4×Q8×C47—22no—
123C4×Q8×C47—22no—
124C4×Q8×C47—22no—
125C4×Q8×C47—22no—
126C4×Q8×C47—22no—
127C4×Q8×C47D414yes—
128C4×Q8×C47D414yes—
129#117×C47—28no—
130#117×C47—28no—
131#117×C47—22no—
132#117×C47—22no—
133#117×C47—22no—
134#117×C47—22no—
135C2×C4⋊C4×C47—21no—
136C2×C4⋊C4×C47—21no—
137C2×C4⋊C4×C47—21no—
138C2×C4⋊C4×C47—21no—
139C2×C4⋊C4×C47D411yescharacteristic
140C2×C4⋊C4×C47D411yescharacteristic
141C2×C4⋊C4×C47C2311yescharacteristic
142C2×C4⋊C4×C47C2311yescharacteristic
143C2×C22⋊C4×C47—21no—
144C2×C22⋊C4×C47D411yescharacteristic
145C2×C22⋊C4×C47D411yescharacteristic
146C2×C42×C47—21no—
147C2×C42×C47—21no—
148C2×C42×C47—21no—
149C2×C42×C47—21no—
150C2×C42×C47—21no—
151C2×C42×C47C2311yescharacteristic
152C2×C42×C47C2311yescharacteristic
153C24×C47C2×D411yescharacteristic
154C2×Q8×C47—24no—
155C2×Q8×C47—28no—
156C2×Q8×C47—28no—
157C2×Q8×C47—24no—
158C2×Q8×C47—28no—
159C2×Q8×C47—28no—
160C2×Q8×C47—24no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47C22×C412yes—
168C2×Q8×C47C22×C412yes—
169C2×Q8×C47C2×D412yes—
170C2×Q8×C47C2×D412yes—
171C2×Q8×C47#4112yes—
172C2×Q8×C47#4112yes—
173C22×C4×C47—24no—
174C22×C4×C47—24no—
175C22×C4×C47—24no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47C22×C412yes—
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47#4112yes—
191C22×C4×C47C2411yescharacteristic
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C2×Dic94—21no—
197C2×Dic94—21no—
198C2×Dic94—21no—
199C2×Dic94—21no—
200C2×Dic94—21no—
201C2×Dic94C22×C412yes—
202C4⋊C4×C47—24no—
203C4⋊C4×C47—24no—
204C4⋊C4×C47—24no—
205C4⋊C4×C47—24no—
206C4⋊C4×C47—22no—
207C4⋊C4×C47—22no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47C2×D412yes—
211C4⋊C4×C47C2×D412yes—
212C22⋊C4×C47—24no—
213C22⋊C4×C47—22no—
214C22⋊C4×C47—22no—
215C42×C47—24no—
216C42×C47—24no—
217C42×C47—24no—
218C42×C47—24no—
219C42×C47—24no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47C2×D412yes—
223C42×C47C2×D412yes—
224C22⋊Dic47—24no—
225C22⋊Dic47—81no—
226#10625337—28no—
227#10625337—28no—
228C4⋊Dic47—21no—
229C4⋊Dic47—21no—
230C4⋊Dic47—21no—
231C4⋊Dic47—21no—
232C4⋊Dic47—21no—
233C4⋊Dic47C22×C412yes—
234Dic47⋊C4—24no—
235Dic47⋊C4—42no—
236Dic47⋊C4—81no—
237C4×Dic47—42no—
238C4×Dic47—81no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C2×C47⋊C8—21no—
244C2×C47⋊C8—21no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8C22×C412yes—
250C2×C47⋊C8C22×C412yes—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47C4×D412yes—
258C23×C47C22×D411yescharacteristic
259Q8×C47—216no—
260Q8×C47—22no—
261Q8×C47—22no—
262Q8×C47—22no—
263Q8×C47—22no—
264Q8×C47—22no—
265Q8×C47—22no—
266Q8×C47C4×D414yes—
267Q8×C47C4×D414yes—
268C2×C4×C47—216no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—21no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47C4×D412yes—
298C2×C4×C47#12012yes—
299C2×C4×C47#12012yes—
300C2×C4×C47C23×C411yescharacteristic
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C2×#4111yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—41no—
318Dic94—22no—
319Dic94—22no—
320Dic94—41no—
321Dic94—41no—
322C47⋊C8—22no—
323C47⋊C8—22no—
324C47⋊C8—41no—
325C47⋊C8—41no—
326#21463—471nomaximal, Sylow
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47C2×C4×D411yescharacteristic
335C22×C47C2×#12011yescharacteristic
336C22×C47#52511yescharacteristic
337C22×C47#57711yescharacteristic
338C22×C47#57811yescharacteristic
339C22×C47#57811yescharacteristic
340C22×C47#57811yescharacteristic
341C4×C47—22no—
342C4×C47—22no—
343C4×C47—24no—
344C4×C47—24no—
345C4×C47—22no—
346C4×C47—41no—
347C4×C47—42no—
348C4×C47—41no—
349C4×C47—42no—
350C4×C47C2×C4×D411yescharacteristic
351C4×C47C2×C4×D411yescharacteristic
352C4×C47#52511yescharacteristic
353C4×C47#52511yescharacteristic
354Dic47—42no—
355Dic47—42no—
356Dic47—81no—
357Dic47—81no—
358C2×#519D4711yescharacteristic
359C2×#451—471no—
360C2×#441—471no—
361C2×C4×Q16—471no—
362#2323—471no—
363#1878—471no—
364#1878—471no—
365#1873—471no—
366#1865—471no—
367#1863—471no—
368#1854—471no—
369#1787—471no—
370#1763—471no—
371C4×#103—471no—
372#1750—471no—
373C2×C47—42no—
374C2×C47C4×#12011yescharacteristic
375C2×C47#294711yescharacteristic
376C2×C47#295011yescharacteristic
377C2×C47#301111yescharacteristic
378C2×C47#301311yescharacteristic
379C2×C47#312111yescharacteristic
380C2×C47#312711yescharacteristic
381C23×Q8C2×D4711yescharacteristic
382C22×Q16—471no—
383C22×Q16—471no—
384C2×C22⋊Q8—471no—
385#519—24no—
386#519—24no—
387C2×C4×Q8—21no—
388C2×C4×Q8—21no—
389C2×C4×Q8—471no—
390C2×C4×Q8C2×D4711yescharacteristic
391C2×C4×Q8C2×D4711yescharacteristic
392C2×C4×Q8C2×D4711yescharacteristic
393C2×C4×Q8C2×D4711yescharacteristic
394C2×#117—21no—
395C2×#117—21no—
396C2×#117C2×D4711yescharacteristic
397C2×#117C2×D4711yescharacteristic
398#451—478no—
399#441—944no—
400C4×Q16—944no—
401C2×#107—471no—
402C2×#106—471no—
403C2×#103—471no—
404C2×#103—471no—
405C2×#103—471no—
406C2×#103—471no—
407C2×#103—471no—
408C2×#103—471no—
409C2×#103—471no—
410C2×#103—471no—
411C2×C22⋊C8—471no—
412C2×C22⋊C8—471no—
413C2×#97—471no—
414C2×C4×C8—471no—
415#391—471no—
416#389—471no—
417#389—941no—
418#388—941no—
419#388—941no—
420#387—941no—
421#380—471no—
422C4×C4⋊C4—471no—
423#340—471no—
424#340—471no—
425#340—471no—
426#340—471no—
427#336—471no—
428#336—471no—
429C47#2146311yescharacteristic, complemented, Sylow
430C22×Q8—22no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—22no—
434C22×Q8—22no—
435C22×Q8—21no—
436C22×Q8—471no—
437C22×Q8C4×D4714yes—
438C22×Q8C22×D4711yescharacteristic
439C22×Q8C22×D4711yescharacteristic
440C23×C4—21no—
441C23×C4C22×D4711yescharacteristic
442C2×Q16—474no—
443C2×Q16—474no—
444C2×Q16—942no—
445C2×Q16—942no—
446C2×Q16—942no—
447C2×Q16—942no—
448C22×C8—471no—
449C22×C8—471no—
450C22×C8—471no—
451C22×C8—471no—
452C22⋊Q8—474no—
453C22⋊Q8—942no—
454C4×Q8—28no—
455C4×Q8—28no—
456C4×Q8—22no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—22no—
462C4×Q8—942no—
463C4×Q8—942no—
464C4×Q8C22⋊D4714yes—
465C4×Q8C22⋊D4714yes—
466#117—28no—
467#117—28no—
468#117—22no—
469#117—22no—
470#117—22no—
471#117—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—471no—
477C2×C4⋊C4—471no—
478C2×C4⋊C4—471no—
479C2×C4⋊C4—941no—
480C2×C4⋊C4—941no—
481C2×C4⋊C4—941no—
482C2×C4⋊C4C22⋊D4711yescharacteristic
483C2×C4⋊C4C22⋊D4711yescharacteristic
484C2×C4⋊C4C22×D4711yescharacteristic
485C2×C4⋊C4C22×D4711yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—941no—
488C2×C22⋊C4—941no—
489C2×C22⋊C4C22⋊D4711yescharacteristic
490C2×C22⋊C4C22⋊D4711yescharacteristic
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—941no—
497C2×C42—941no—
498C2×C42C22×D4711yescharacteristic
499C2×C42C22×D4711yescharacteristic
500#107—942no—
501#106—942no—
502#103—474no—
503#103—474no—
504#103—942no—
505#103—942no—
506#103—942no—
507#103—942no—
508#103—942no—
509#103—942no—
510C22⋊C8—474no—
511C22⋊C8—942no—
512#97—942no—
513C4×C8—942no—
514#95—941no—
515#95—941no—
516#95—941no—
517#95—941no—
518#95—941no—
519C24C2×C22⋊D4711yescharacteristic
520C2×Q8—24no—
521C2×Q8—28no—
522C2×Q8—28no—
523C2×Q8—24no—
524C2×Q8—28no—
525C2×Q8—28no—
526C2×Q8—24no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—472no—
534C2×Q8—941no—
535C2×Q8—941no—
536C2×Q8—941no—
537C2×Q8—941no—
538C2×Q8—941no—
539C2×Q8C2×C4×D4712yes—
540C2×Q8C2×C4×D4712yes—
541C2×Q8#1062535012yes—
542C2×Q8#1062535012yes—
543C2×Q8C2×C22⋊D4712yes—
544C2×Q8C2×C22⋊D4712yes—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4C2×C4×D4712yes—
561C22×C4#1062535012yes—
562C22×C4C2×C22⋊D4711yescharacteristic
563C22×C4C2×C22⋊D4711yescharacteristic
564C22×C4C2×C22⋊D4711yescharacteristic
565C22×C4C2×C22⋊D4711yescharacteristic
566C22×C4C2×C22⋊D4711yescharacteristic
567C22×C4C23×D4711yescharacteristic
568Q16—948no—
569Q16—948no—
570C2×C8—472no—
571C2×C8—472no—
572C2×C8—941no—
573C2×C8—941no—
574C2×C8—941no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8—941no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8—941no—
581C2×C8—941no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—472no—
591C4⋊C4—944no—
592C4⋊C4—941no—
593C4⋊C4—941no—
594C4⋊C4—941no—
595C4⋊C4—941no—
596C4⋊C4—941no—
597C4⋊C4—3761no—
598C4⋊C4—1882no—
599C4⋊C4C2×C22⋊D4712yes—
600C4⋊C4C2×C22⋊D4712yes—
601C22⋊C4—24no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—944no—
605C22⋊C4—3761no—
606C42—24no—
607C42—24no—
608C42—24no—
609C42—24no—
610C42—24no—
611C42—21no—
612C42—21no—
613C42—3761no—
614C42—1882no—
615C42C2×C22⋊D4712yes—
616C42C2×C22⋊D4712yes—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C4×C22⋊D4712yes—
624C23C22×C22⋊D4711yescharacteristic
625Q8—216no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—942no—
633Q8—942no—
634Q8—1881no—
635Q8—1881no—
636Q8C4×C22⋊D4714yes—
637Q8C4×C22⋊D4714yes—
638C2×C4—216no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—1881no—
670C2×C4—1881no—
671C2×C4—1881no—
672C2×C4—1881no—
673C2×C4—1881no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4—1881no—
679C2×C4C4×C22⋊D4712yes—
680C2×C4#1309399312yes—
681C2×C4#1309399312yes—
682C2×C4C22×C4×D4711yescharacteristic
683C2×C4C22×C22⋊D4711yescharacteristic
684C2×C4C22×C22⋊D4711yescharacteristic
685C2×C4C2×#1062535011yescharacteristic
686C2×C4C2×#1062535011yescharacteristic
687C2×C4C2×#1062535011yescharacteristic
688C8—942no—
689C8—942no—
690C8—1881no—
691C8—1881no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22C2×C4×C22⋊D4711yescharacteristic
700C22C2×#1309399311yescharacteristic
701C22#1568963411yescharacteristic
702C22#1568993111yescharacteristic
703C22#1568993811yescharacteristic
704C22#1568993811yescharacteristic
705C22#1568993811yescharacteristic
706C4—22no—
707C4—22no—
708C4—24no—
709C4—24no—
710C4—22no—
711C4—41no—
712C4—42no—
713C4—41no—
714C4—42no—
715C4—3761no—
716C4—3761no—
717C4—1882no—
718C4—1882no—
719C4C2×C4×C22⋊D4711yescharacteristic
720C4C2×C4×C22⋊D4711yescharacteristic
721C4#1568963411yescharacteristic
722C4#1568963411yescharacteristic
723C2—42no—
724C2C4×#1309399311yescharacteristic
725C2#2025223111yescharacteristic
726C2#2025225411yescharacteristic
727C2#2025268311yescharacteristic
728C2#2025270311yescharacteristic
729C2#2025361711yescharacteristic
730C2#2025368811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#519C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterC2×#519D47
hypocenterC47#21463
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#15689228C2semidirect
3. C2×C4×#10625337C2semidirect
5. #20243729C2semidirect
6. #20243729C2semidirect
8. #20243656C2semidirect
9. #20243642C2semidirect
12. #20243218C2semidirect
13. C4×#13093948C2semidirect
20. #15689279C4semidirect
429. C47#21463semidirect

Maximal subgroups

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

subgroupindex
C2×#156892792
C2×#156892282
C2×C4×#106253372
#202460702
#202437292
#202437002
#202436562
#202436422
#202435872
#202433232
#202432182
C4×#130939482
#202431542
C2×C47×#5192
#2146347