Finite Group Databasebeta

← #26121578

Subgroups — #26121578

Order 12032.

1510 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093980C211yesmaximal, characteristic
2C2×#15688984C211yesmaximal, characteristic
3C2×#15688984C211yesmaximal, characteristic
4C2×#15688890C211yesmaximal, characteristic
5C2×#15688889C211yesmaximal, characteristic
6C2×#15688889C211yesmaximal, characteristic
7C2×C47×#342C211yesmaximal, characteristic
8C24×Dic47C2211yescharacteristic
9C2×#13093980—22no—
10C2×#13093980—22no—
11C2×#13093980—22no—
12C2×#13093980—22no—
13C2×#13093980—22no—
14C2×#13093980C414yescomplemented
15C22×Dic47⋊C4—21no—
16C22×C22⋊Dic47C2211yescharacteristic
17C22×C22⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2211yescharacteristic
19C22×C4×Dic47—21no—
20#15688984—22no—
21#15688984—22no—
22#15688984—21no—
23#15688984—21no—
24#15688984C414yescomplemented
25C2×C47⋊#95—22no—
26C2×C47⋊#95C414yescomplemented
27#15688890—22no—
28#15688889—22no—
29#15688889—22no—
30C22×C22⋊C4×C47C2211yescharacteristic
31C22×C22⋊C4×C47C2211yescharacteristic
32C22×C22⋊C4×C47C2211yescharacteristic
33C47×#342—22no—
34C23×Dic47—21no—
35C23×Dic47—21no—
36C23×Dic47—21no—
37C23×Dic47—21no—
38C23×Dic47—21no—
39C23×Dic47—21no—
40C23×Dic47—21no—
41C23×Dic47—21no—
42C23×Dic47—21no—
43C23×Dic47—21no—
44C23×Dic47C2×C412yes—
45C23×Dic47C2×C412yes—
46C23×Dic47C2×C412yes—
47C23×Dic47C2×C412yes—
48C23×Dic47D412yes—
49C23×Dic47D411yescharacteristic
50C23×Dic47D411yescharacteristic
51C23×Dic47D412yes—
52C23×Dic47Q812yes—
53#13093980—28no—
54#13093980—28no—
55#13093980—28no—
56#13093980—28no—
57C2×Dic47⋊C4—24no—
58C2×Dic47⋊C4—24no—
59C2×Dic47⋊C4—24no—
60C2×C22⋊Dic47—21no—
61C2×C22⋊Dic47—21no—
62C2×C22⋊Dic47—21no—
63C2×C22⋊Dic47—21no—
64C2×C22⋊Dic47—21no—
65C2×C22⋊Dic47—21no—
66C2×C22⋊Dic47—21no—
67C2×C22⋊Dic47—21no—
68C2×C22⋊Dic47—21no—
69C2×C22⋊Dic47—21no—
70C2×C22⋊Dic47—21no—
71C2×C22⋊Dic47—21no—
72C2×C22⋊Dic47—21no—
73C2×C22⋊Dic47—21no—
74C2×C22⋊Dic47C2×C412yes—
75C2×C22⋊Dic47C2×C412yes—
76C2×C22⋊Dic47D412yes—
77C2×C22⋊Dic47D412yes—
78C2×C4×Dic47—24no—
79C2×C4×Dic47—24no—
80C2×C4×Dic47—24no—
81C47⋊#95—28no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C25×C47C2311yescharacteristic
85C23×C4×C47—21no—
86C23×C4×C47—21no—
87C23×C4×C47C2×C412yes—
88C2×C22⋊C4×C47—21no—
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C22⋊C4×C47—21no—
94C2×C22⋊C4×C47—21no—
95C2×C22⋊C4×C47—21no—
96C2×C22⋊C4×C47—21no—
97C2×C22⋊C4×C47—21no—
98C2×C22⋊C4×C47—21no—
99C2×C22⋊C4×C47—21no—
100C2×C22⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47C2×C412yes—
103C2×C22⋊C4×C47C2×C412yes—
104C2×C22⋊C4×C47D412yes—
105C2×C22⋊C4×C47D412yes—
106C24×C47—44no—
107C24×C47C22×C411yescharacteristic
108C24×C47C22×C411yescharacteristic
109C24×C47C22×C411yescharacteristic
110C24×C47C2×D411yescharacteristic
111C24×C47C2×D411yescharacteristic
112C24×C47C2×D411yescharacteristic
113C24×C47C2×D411yescharacteristic
114C24×C47C2×D411yescharacteristic
115C24×C47C2×D411yescharacteristic
116C24×C47C2×D411yescharacteristic
117C24×C47C2×Q811yescharacteristic
118C24×C47#4111yescharacteristic
119C24×C47#4111yescharacteristic
120C24×C47#4111yescharacteristic
121C24×C47#4111yescharacteristic
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—44no—
130C22×C4×C47—44no—
131C22×C4×C47—41no—
132C22×C4×C47—41no—
133C22×C4×C47—44no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—22no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—44no—
174C22×Dic47—44no—
175C22×Dic47—41no—
176C22×Dic47—41no—
177C22×Dic47—44no—
178C22×Dic47C4214yes—
179C22×Dic47C22⋊C414yes—
180C22×Dic47C22⋊C412yes—
181C22×Dic47C22⋊C412yes—
182C22×Dic47C22⋊C412yes—
183C22×Dic47C22⋊C412yes—
184C22×Dic47C4⋊C414yes—
185C22×Dic47C4⋊C414yes—
186C22×Dic47C4⋊C412yes—
187C22×Dic47C4⋊C412yes—
188C22⋊C4×C47—22no—
189C22⋊C4×C47—22no—
190C22⋊C4×C47—22no—
191C22⋊C4×C47—22no—
192C22⋊C4×C47—22no—
193C22⋊C4×C47—41no—
194C22⋊C4×C47—41no—
195C22⋊C4×C47—41no—
196C22⋊C4×C47—41no—
197C22⋊C4×C47—41no—
198C22⋊C4×C47—41no—
199C22⋊C4×C47C22⋊C414yes—
200C22⋊Dic47—22no—
201C22⋊Dic47—22no—
202C22⋊Dic47—22no—
203C22⋊Dic47—22no—
204C22⋊Dic47—22no—
205C22⋊Dic47—41no—
206C22⋊Dic47—41no—
207C22⋊Dic47—41no—
208C22⋊Dic47—41no—
209C22⋊Dic47—41no—
210C22⋊Dic47—41no—
211C22⋊Dic47C22⋊C414yes—
212Dic47⋊C4—216no—
213C4×Dic47—216no—
214C23×C47—24no—
215C23×C47—24no—
216C23×C47—24no—
217C23×C47—42no—
218C23×C47—42no—
219C23×C47—42no—
220C23×C47—42no—
221C23×C47—42no—
222C23×C47—42no—
223C23×C47—42no—
224C23×C47—42no—
225C23×C47—42no—
226C23×C47—42no—
227C23×C47—42no—
228C23×C47—42no—
229C23×C47C2×C4211yescharacteristic
230C23×C47C2×C22⋊C411yescharacteristic
231C23×C47C2×C22⋊C411yescharacteristic
232C23×C47C2×C22⋊C411yescharacteristic
233C23×C47C2×C22⋊C411yescharacteristic
234C23×C47C2×C22⋊C411yescharacteristic
235C23×C47C2×C4⋊C411yescharacteristic
236C23×C47C2×C4⋊C411yescharacteristic
237C23×C47C2×C4⋊C411yescharacteristic
238C23×C47#11711yescharacteristic
239C23×C47#11711yescharacteristic
240C23×C47C4×D411yescharacteristic
241C23×C47C4×D411yescharacteristic
242C23×C47C4×D411yescharacteristic
243C23×C47C4×D411yescharacteristic
244C23×C47C4×D411yescharacteristic
245C23×C47C4×D411yescharacteristic
246C23×C47C4×D411yescharacteristic
247C23×C47C4×D411yescharacteristic
248C23×C47#12011yescharacteristic
249C23×C47#12011yescharacteristic
250C23×C47#12011yescharacteristic
251C23×C47#12011yescharacteristic
252C23×C47#12111yescharacteristic
253C23×C47#12111yescharacteristic
254C23×C47#12111yescharacteristic
255C23×C47#12111yescharacteristic
256C23×C47C22⋊Q811yescharacteristic
257C23×C47C22⋊Q811yescharacteristic
258C23×C47C22⋊Q811yescharacteristic
259C23×C47C22⋊Q811yescharacteristic
260C23×C47#12311yescharacteristic
261C23×C47#12311yescharacteristic
262C23×C47#12311yescharacteristic
263C23×C47#12311yescharacteristic
264C2×C4×C47—24no—
265C2×C4×C47—44no—
266C2×C4×C47—44no—
267C2×C4×C47—44no—
268C2×C4×C47—44no—
269C2×C4×C47—42no—
270C2×C4×C47—42no—
271C2×C4×C47—44no—
272C2×C4×C47—82no—
273C2×C4×C47—82no—
274C2×C4×C47—82no—
275C2×C4×C47—82no—
276C2×Dic47—24no—
277C2×Dic47—24no—
278C2×Dic47—22no—
279C2×Dic47—22no—
280C2×Dic47—24no—
281C2×Dic47—24no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—22no—
285C2×Dic47—22no—
286C2×Dic47—24no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—24no—
290C2×Dic47—24no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—24no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—24no—
297C2×Dic47—44no—
298C2×Dic47—44no—
299C2×Dic47—44no—
300C2×Dic47—44no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—44no—
304C2×Dic47—82no—
305C2×Dic47—82no—
306C2×Dic47—82no—
307C2×Dic47—82no—
308C2×Dic47#9514yes—
309C2×Dic47#9514yes—
310#10736—471nomaximal, Sylow
311C22×C47—22no—
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—22no—
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—22no—
322C22×C47—22no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47C2×#9511yescharacteristic
346C22×C47C4×C22⋊C411yescharacteristic
347C22×C47C4×C22⋊C411yescharacteristic
348C22×C47#37911yescharacteristic
349C22×C47#38011yescharacteristic
350C22×C47#38011yescharacteristic
351C22×C47#38111yescharacteristic
352C22×C47#38511yescharacteristic
353C22×C47#38511yescharacteristic
354C22×C47#38511yescharacteristic
355C22×C47#38511yescharacteristic
356C22×C47#38611yescharacteristic
357C22×C47#38611yescharacteristic
358C22×C47#38611yescharacteristic
359C22×C47#38611yescharacteristic
360C22×C47#41014yes—
361C4×C47—44no—
362C4×C47—82no—
363C4×C47—82no—
364Dic47—24no—
365Dic47—24no—
366Dic47—44no—
367Dic47—82no—
368Dic47—82no—
369C22×#117—471no—
370C2×#381—471no—
371C2×#381—471no—
372C2×#342—471no—
373C2×#342—471no—
374C2×#342—471no—
375C2×#342D4711yescharacteristic
376C2×C47—21no—
377C2×C47—21no—
378C2×C47—21no—
379C2×C47—21no—
380C2×C47—21no—
381C2×C47—21no—
382C2×C47—21no—
383C2×C47—21no—
384C2×C47—21no—
385C2×C47—21no—
386C2×C47—21no—
387C2×C47—21no—
388C2×C47C22⋊#9511yescharacteristic
389C2×C47#174012yes—
390C2×C47#189912yes—
391C2×C47#189912yes—
392C24×C4—471no—
393C2×#117—474no—
394C2×#117—942no—
395C2×#117—942no—
396C2×#117—942no—
397C2×#117—942no—
398C2×#117—942no—
399C22×C4⋊C4—941no—
400C22×C22⋊C4—471no—
401C22×C22⋊C4—471no—
402C22×C22⋊C4—471no—
403C22×C22⋊C4C2×D4711yescharacteristic
404C22×C22⋊C4C2×D4711yescharacteristic
405C22×C22⋊C4C2×D4711yescharacteristic
406C22×C42—941no—
407#381—474no—
408#381—941no—
409#381—942no—
410#381—941no—
411#381—942no—
412C2×#95—474no—
413C2×#95—942no—
414#342—22no—
415#342—942no—
416#342—942no—
417#342—942no—
418C47#1073611yescharacteristic, complemented, Sylow
419C25C22×D4711yescharacteristic
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—472no—
423C23×C4—472no—
424C23×C4—472no—
425C23×C4—471no—
426C23×C4—472no—
427C23×C4—472no—
428C23×C4—471no—
429C23×C4—472no—
430C23×C4—472no—
431C23×C4—941no—
432C23×C4—941no—
433C23×C4—941no—
434C23×C4—941no—
435C23×C4—941no—
436C23×C4—941no—
437C23×C4—941no—
438C23×C4—941no—
439C23×C4—941no—
440C23×C4—941no—
441C23×C4C4×D4712yes—
442#117—948no—
443#117—948no—
444#117—948no—
445#117—948no—
446C2×C4⋊C4—944no—
447C2×C4⋊C4—944no—
448C2×C4⋊C4—944no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—472no—
464C2×C22⋊C4—472no—
465C2×C22⋊C4—472no—
466C2×C22⋊C4—472no—
467C2×C22⋊C4—941no—
468C2×C22⋊C4—941no—
469C2×C22⋊C4—941no—
470C2×C22⋊C4—941no—
471C2×C22⋊C4—941no—
472C2×C22⋊C4—941no—
473C2×C22⋊C4—941no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—941no—
476C2×C22⋊C4—941no—
477C2×C22⋊C4—941no—
478C2×C22⋊C4—941no—
479C2×C22⋊C4—941no—
480C2×C22⋊C4—941no—
481C2×C22⋊C4C4×D4712yes—
482C2×C22⋊C4C4×D4712yes—
483C2×C22⋊C4D18812yes—
484C2×C22⋊C4C22⋊D4712yes—
485C2×C42—944no—
486C2×C42—944no—
487C2×C42—944no—
488#95—944no—
489#95—944no—
490#95—948no—
491C24—44no—
492C24C2×C4×D4711yescharacteristic
493C24C2×C4×D4711yescharacteristic
494C24C2×C4×D4711yescharacteristic
495C24C2×D18811yescharacteristic
496C24#1062535011yescharacteristic
497C24#1062535011yescharacteristic
498C24D4×D4711yescharacteristic
499C24D4×D4711yescharacteristic
500C24D4×D4711yescharacteristic
501C24D4×D4711yescharacteristic
502C24D4×D4711yescharacteristic
503C24#1062535211yescharacteristic
504C24Q8×D4711yescharacteristic
505C24#1062535411yescharacteristic
506C24C2×C22⋊D4711yescharacteristic
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—44no—
519C22×C4—474no—
520C22×C4—474no—
521C22×C4—472no—
522C22×C4—472no—
523C22×C4—472no—
524C22×C4—472no—
525C22×C4—474no—
526C22×C4—474no—
527C22×C4—472no—
528C22×C4—472no—
529C22×C4—942no—
530C22×C4—942no—
531C22×C4—942no—
532C22×C4—942no—
533C22×C4—942no—
534C22×C4—942no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—941no—
542C22×C4—941no—
543C22×C4—942no—
544C22×C4—941no—
545C22×C4—941no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—942no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—942no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—1884no—
569C22×C4—1881no—
570C22×C4—1881no—
571C22×C4—1884no—
572C22×C4—1884no—
573C4⋊C4—9416no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—474no—
586C22⋊C4—942no—
587C22⋊C4—942no—
588C22⋊C4—942no—
589C22⋊C4—942no—
590C22⋊C4—942no—
591C22⋊C4—1881no—
592C22⋊C4—1881no—
593C22⋊C4—1881no—
594C22⋊C4—1881no—
595C22⋊C4—1881no—
596C22⋊C4—1881no—
597C22⋊C4(C2×D47)⋊C414yes—
598C42—9416no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23C42×D4711yescharacteristic
615C23C22⋊C4×D4711yescharacteristic
616C23C22⋊C4×D4711yescharacteristic
617C23C22⋊C4×D4711yescharacteristic
618C23C22⋊C4×D4711yescharacteristic
619C23C2×(C2×D47)⋊C411yescharacteristic
620C23C4⋊C4×D4711yescharacteristic
621C23C4⋊C4×D4711yescharacteristic
622C23C4⋊C4×D4711yescharacteristic
623C23#1309398111yescharacteristic
624C23#1309398211yescharacteristic
625C23(C22⋊D47)⋊C411yescharacteristic
626C23(C22⋊D47)⋊C411yescharacteristic
627C23C4×C22⋊D4711yescharacteristic
628C23C4×C22⋊D4711yescharacteristic
629C23#1309398611yescharacteristic
630C23#1309398611yescharacteristic
631C23C4×D18811yescharacteristic
632C23C4×D18811yescharacteristic
633C23#1309399211yescharacteristic
634C23#1309399211yescharacteristic
635C23#1309399411yescharacteristic
636C23#1309399411yescharacteristic
637C23#1309399511yescharacteristic
638C23#1309399711yescharacteristic
639C23#1309399711yescharacteristic
640C23#1309399911yescharacteristic
641C23#1309400011yescharacteristic
642C23#1309400211yescharacteristic
643C23#1309400211yescharacteristic
644C23#1309400411yescharacteristic
645C23#1309400611yescharacteristic
646C23#1309400611yescharacteristic
647C23#1309400911yescharacteristic
648C23#1309400911yescharacteristic
649C2×C4—24no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—44no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—44no—
657C2×C4—82no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4—474no—
662C2×C4—474no—
663C2×C4—944no—
664C2×C4—944no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—944no—
668C2×C4—944no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—944no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—944no—
677C2×C4—944no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—944no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—944no—
684C2×C4—3762no—
685C2×C4—3762no—
686C2×C4—3762no—
687C2×C4—3762no—
688C2×C4—1884no—
689C2×C4—1882no—
690C2×C4—1882no—
691C2×C4—1884no—
692C2×C4—1884no—
693C2×C4—1884no—
694C2×C4—1884no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22#95×D4711yescharacteristic
730C22#1568897011yescharacteristic
731C22C4×(C2×D47)⋊C411yescharacteristic
732C22#1568897811yescharacteristic
733C22#1568898011yescharacteristic
734C22#1568898211yescharacteristic
735C22#1568898511yescharacteristic
736C22#1568899411yescharacteristic
737C22#1568899411yescharacteristic
738C22#1568899711yescharacteristic
739C22#1568899711yescharacteristic
740C22#1568899911yescharacteristic
741C22#1568899911yescharacteristic
742C22#1568900111yescharacteristic
743C22#1568900111yescharacteristic
744C22#1568909514yes—
745C4—44no—
746C4—82no—
747C4—82no—
748C4—944no—
749C4—944no—
750C4—3762no—
751C4—3762no—
752C4—1884no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—21no—
765C2(C2×D47)⋊#9511yescharacteristic
766C2#2024311912yes—
767C2#2024384312yes—
768C2#2024384512yes—
subgroupG/H
centerC23C22⋊C4×D47
commutatorC23×C47C2×C42
FrattiniC25C22×D47
FittingC2×C47×#342C2
socleC23×C47C2×C22⋊C4
prime radical, cosocleC25×C47C23
hypercenterC2×#342D47
hypocenterC47#10736
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
14. C2×#13093980C4semidirect
24. #15688984C4semidirect
26. C2×C47⋊#95C4semidirect
418. C47#10736semidirect

Maximal subgroups

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

subgroupindex
C22×#130939802
C2×#156889842
C2×#156888902
C2×#156888892
C2×C47×#3422
#1073647