Finite Group Databasebeta

← #26217029

Subgroups — #26217029

Order 12032.

1462 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689604C211yesmaximal, characteristic
2C2×#15689164C211yesmaximal, characteristic, complemented
3C2×#107×D47C211yesmaximal, characteristic, complemented
4C2×#15689088C211yesmaximal, characteristic
5#20245977C211yesmaximal, characteristic
6#20243589C211yesmaximal, characteristic, complemented
7#20243588C211yesmaximal, characteristic, complemented
8#20243585C211yesmaximal, characteristic, complemented
9#20243584C211yesmaximal, characteristic, complemented
10#20243577C211yesmaximal, characteristic, complemented
11#20243576C211yesmaximal, characteristic, complemented
12#20243574C211yesmaximal, characteristic, complemented
13#20243106C211yesmaximal, characteristic, complemented
14#20243103C211yesmaximal, characteristic, complemented
15C47×#1852C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19#15689604—24no—
20#15689604—24no—
21C2×#13093989—21no—
22C2×#13093986—21no—
23C2×C4×C22⋊D47—21no—
24C2×C4×C22⋊D47—21no—
25C2×#13093983C2211yescharacteristic
26C2×#13093982C2211yescharacteristic
27C2×#13093982C2211yescharacteristic
28C2×#13093982C2211yescharacteristic
29C2×C4⋊C4×D47C2211yescharacteristic
30C2×C4⋊C4×D47C2211yescharacteristic
31C2×C4⋊C4×D47C2211yescharacteristic
32#15689164—24no—
33C2×#13093958C2211yescharacteristic
34C2×#13093957C2211yescharacteristic
35C2×#13093957C2211yescharacteristic
36C2×#13093957C2211yescharacteristic
37#107×D47—24no—
38C2×#13093956C2211yescharacteristic
39C2×#13093955C2211yescharacteristic
40#15689088C418yescomplemented
41C2×C22⋊(C47⋊C8)C2211yescharacteristic
42C2×(C2×D47)⋊C8C2211yescharacteristic
43C2×(C2×D47)⋊C8C2211yescharacteristic
44#15689027—21no—
45#15689023—21no—
46#15689001—21no—
47#15688999—21no—
48#15688983C2211yescharacteristic
49#15688980C2211yescharacteristic
50#15688980C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55#15688885C2211yescharacteristic
56#15688885C2211yescharacteristic
57C22×C4⋊C4×C47C2211yescharacteristic
58C2×#107×C47C2211yescharacteristic
59C2×#107×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C47×#380C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#340C2211yescharacteristic
64C2×#10625350—22no—
65C2×#10625350—22no—
66C2×#10625350—22no—
67C2×#10625350—22no—
68C2×#10625350C2×C414yes—
69C2×#10625350Q814yes—
70C22×Dic94D411yescharacteristic
71C22×D188D411yescharacteristic
72C22×C22⋊D47D411yescharacteristic
73C22×C22⋊D47D411yescharacteristic
74C22×C4×D47—21no—
75C22×C4×D47—21no—
76C22×C4×D47—21no—
77C22×C4×D47C2311yescharacteristic
78C22×C4×D47C2311yescharacteristic
79C2×#10625324—22no—
80C2×#10625324—22no—
81C2×#10625324C2×C414yescomplemented
82C22×C47⋊C8C2311yescharacteristic
83C22×C47⋊C8C2311yescharacteristic
84C2×C8×D47—22no—
85C2×C8×D47—22no—
86C2×C8×D47C2×C414yescomplemented
87#13093989—28no—
88#13093986—28no—
89C4×C22⋊D47—28no—
90C4×C22⋊D47—28no—
91#13093983—22no—
92#13093983—22no—
93#13093982—22no—
94#13093982—22no—
95#13093982—22no—
96#13093982—22no—
97#13093982—22no—
98#13093982D414yes—
99C2×C4⋊Dic47C2311yescharacteristic
100C2×C4⋊Dic47C2311yescharacteristic
101C2×C4⋊Dic47C2311yescharacteristic
102C2×C4⋊Dic47C2311yescharacteristic
103C2×Dic47⋊C4—21no—
104C2×Dic47⋊C4—21no—
105C2×Dic47⋊C4—21no—
106C4⋊C4×D47—22no—
107C4⋊C4×D47—22no—
108C4⋊C4×D47—22no—
109C4⋊C4×D47—22no—
110C4⋊C4×D47—22no—
111C4⋊C4×D47D414yes—
112C2×C22⋊Dic47—21no—
113C2×C22⋊Dic47—21no—
114C2×(C2×D47)⋊C4—21no—
115C2×(C2×D47)⋊C4—21no—
116C2×(C2×D47)⋊C4—21no—
117C2×(C2×D47)⋊C4—21no—
118C2×(C2×D47)⋊C4—21no—
119C2×C4×Dic47—21no—
120C2×C4×Dic47—21no—
121C2×C4×Dic47—21no—
122C2×C4×Dic47—21no—
123#13093958—22no—
124#13093957—22no—
125#13093957—22no—
126#13093957—22no—
127#13093956—22no—
128#13093955—22no—
129C22⋊(C47⋊C8)C2×C414yescomplemented
130(C2×D47)⋊C8C2×C414yescomplemented
131(C2×D47)⋊C8C2×C414yescomplemented
132C47⋊#95—21no—
133C47⋊#95—21no—
134C47⋊#95—21no—
135C23×C4×C47—21no—
136C23×C4×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139C2×C4⋊C4×C47—21no—
140C2×C4⋊C4×C47—22no—
141C2×C4⋊C4×C47—22no—
142C2×C4⋊C4×C47C2311yescharacteristic
143C2×C4⋊C4×C47C2311yescharacteristic
144C2×C4⋊C4×C47C2311yescharacteristic
145C2×C4⋊C4×C47C2311yescharacteristic
146C2×C22⋊C4×C47—21no—
147#107×C47—22no—
148#107×C47—22no—
149C22⋊C8×C47C2×C414yescomplemented
150#95×C47—21no—
151C24×C47C2×D411yescharacteristic
152C23×D47C2×D411yescharacteristic
153C23×D47C2×D411yescharacteristic
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—24no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—81no—
164C22×C4×C47—81no—
165C22×C4×C47C22×C412yes—
166C22×C4×C47C2×D411yescharacteristic
167C22×C4×C47C2×Q812yes—
168C22×C4×C47C2411yescharacteristic
169C2×C22⋊D47—22no—
170C2×C22⋊D47—22no—
171C2×C22⋊D47—22no—
172C2×C22⋊D47—22no—
173C2×C22⋊D47C4⋊C414yes—
174C2×C22⋊D47C4⋊C414yes—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47C2×D411yescharacteristic
180C22×Dic47C2×D411yescharacteristic
181#10625350—28no—
182#10625350—28no—
183#10625350—28no—
184#10625350—28no—
185C2×D188—22no—
186C2×D188—22no—
187C2×D188C4⋊C414yes—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—21no—
191C2×C4×D47—21no—
192C2×C4×D47—24no—
193C2×C4×D47—24no—
194C2×C4×D47—42no—
195C2×C4×D47—81no—
196C2×C4×D47—81no—
197C2×C4×D47—81no—
198C2×C4×D47—81no—
199C2×C4×D47—81no—
200C2×C4×D47—81no—
201C2×C4×D47C22×C412yes—
202C2×C4×D47C22×C412yes—
203C2×C4×D47C2×D412yes—
204C2×C4×D47C2×D412yes—
205C2×C4×D47C2×Q812yes—
206C2×C4×D47C2×Q812yes—
207C2×C4×D47#4112yes—
208C2×C4×D47#4112yes—
209C2×Dic94—22no—
210C2×Dic94—22no—
211C2×Dic94C4⋊C414yes—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47C22×C412yes—
217C2×C8×C47C22×C412yes—
218C4⋊C4×C47—24no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47C2×D412yes—
226C4⋊C4×C47C2×D412yes—
227C22⋊C4×C47—81no—
228C22⋊Dic47—24no—
229C22⋊Dic47—81no—
230(C2×D47)⋊C4—24no—
231(C2×D47)⋊C4—24no—
232(C2×D47)⋊C4—42no—
233(C2×D47)⋊C4—81no—
234(C2×D47)⋊C4—81no—
235C4⋊Dic47—21no—
236C4⋊Dic47—21no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—21no—
241C4⋊Dic47C2×D412yes—
242C4⋊Dic47C2×D412yes—
243Dic47⋊C4—24no—
244Dic47⋊C4—24no—
245Dic47⋊C4—42no—
246C4×Dic47—24no—
247C4×Dic47—24no—
248C4×Dic47—24no—
249C4×Dic47—42no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8C22×C412yes—
255C2×C47⋊C8C22×C412yes—
256#10625324—28no—
257C8×D47—28no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47C2×C4⋊C412yes—
265C23×C47C22×D411yescharacteristic
266C22×D47—21no—
267C22×D47—21no—
268C22×D47—21no—
269C22×D47—21no—
270C22×D47—21no—
271C22×D47—21no—
272C22×D47—21no—
273C22×D47—21no—
274C22×D47—21no—
275C22×D47—21no—
276C22×D47C2×C4⋊C412yes—
277C22×D47C2×C4⋊C412yes—
278C22×D47#12012yes—
279C22×D47#12312yes—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—84no—
299C2×C4×C47C2×C4⋊C412yes—
300C2×C4×C47C23×C411yescharacteristic
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C22×Q811yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C22⋊D47—28no—
307C22⋊D47—28no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—41no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47C2×C4⋊C412yes—
323C2×Dic47C2×C4⋊C412yes—
324C2×Dic47#12012yes—
325C2×Dic47#12312yes—
326D188—28no—
327C4×D47—22no—
328C4×D47—22no—
329C4×D47—22no—
330C4×D47—22no—
331C4×D47—84no—
332C4×D47—84no—
333C4×D47—84no—
334C4×D47C4×D414yes—
335C4×D47C4×D414yes—
336C4×D47C22⋊Q814yes—
337C4×D47C22⋊Q814yes—
338Dic94—28no—
339C8×C47—22no—
340C8×C47—22no—
341C47⋊C8—22no—
342C47⋊C8—22no—
343#20847—471nomaximal, Sylow
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47C22×C4⋊C411yescharacteristic
352C22×C47C2×#12011yescharacteristic
353C22×C47C2×#12311yescharacteristic
354C22×C47#57611yescharacteristic
355C22×C47#57611yescharacteristic
356C22×C47#57811yescharacteristic
357C22×C47#57811yescharacteristic
358C2×D47—22no—
359C2×D47—22no—
360C2×D47—22no—
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—41no—
368C2×D47—41no—
369C2×D47—41no—
370C2×D47—41no—
371C2×D47#38514yes—
372C4×C47—22no—
373C4×C47—42no—
374C4×C47—42no—
375C4×C47—81no—
376C4×C47—81no—
377C4×C47C2×C4×D411yescharacteristic
378C4×C47C2×C4×D411yescharacteristic
379C4×C47C2×C22⋊Q811yescharacteristic
380C4×C47C2×C22⋊Q811yescharacteristic
381Dic47—22no—
382Dic47—42no—
383Dic47—42no—
384Dic47—81no—
385Dic47—81no—
386Dic47#38514yes—
387C2×#520—471no—
388C2×#428—471no—
389C22×#107—471no—
390C2×#408—471no—
391#2311—471no—
392#1854—471no—
393#1854—471no—
394#1854—471no—
395#1854—471no—
396#1852—471no—
397#1852—471no—
398#1852—471no—
399#1852D4711yescharacteristic, complemented
400#1736—471no—
401#1735—471no—
402C2×C47—42no—
403C2×C47C2×#38511yescharacteristic
404C2×C47#291311yescharacteristic
405C2×C47#291311yescharacteristic
406C2×C47#300811yescharacteristic
407C2×C47#301111yescharacteristic
408C2×C47#309811yescharacteristic
409C2×C47#309811yescharacteristic
410D47—24no—
411D47—42no—
412C22×#41—471no—
413C22×M16—471no—
414C23×C8—471no—
415#520—944no—
416#520—944no—
417C2×C4×Q8—941no—
418C2×C4×D4—941no—
419C2×C4×D4—941no—
420C2×C4×D4—941no—
421C2×#117—471no—
422C2×#117—471no—
423C2×#117—471no—
424C2×#117—471no—
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4—471no—
428C22×C4⋊C4C2×D4711yescharacteristic
429#428—944no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#107—471no—
433C2×#107—471no—
434C2×#107—944no—
435C2×#107C2×D4711yescharacteristic
436C2×#107C2×D4711yescharacteristic
437C2×#106—471no—
438C2×#106—471no—
439#408—478no—
440C2×C22⋊C8—471no—
441C2×C22⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×C22⋊C8C2×D4711yescharacteristic
444#391—941no—
445#390—941no—
446#386—941no—
447#386—941no—
448#380—471no—
449#380—471no—
450#380—471no—
451#380C2×D4711yescharacteristic
452#340—471no—
453#340—471no—
454#340—471no—
455#340—471no—
456#340—471no—
457#340—471no—
458#340C2×D4711yescharacteristic
459#340C2×D4711yescharacteristic
460C47#2084711yescharacteristic, complemented, Sylow
461C2×#41—474no—
462C2×#41—474no—
463C2×#41—942no—
464C2×#41—942no—
465C2×#41—942no—
466C2×#41—942no—
467C22×Q8—471no—
468C22×D4—471no—
469C22×D4—471no—
470C22×D4—471no—
471C23×C4—21no—
472C23×C4—471no—
473C23×C4—471no—
474C23×C4—941no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4C22×D4711yescharacteristic
478C2×M16—474no—
479C2×M16—942no—
480C2×M16—942no—
481C22×C8—471no—
482C22×C8—471no—
483C22×C8—474no—
484C22×C8—942no—
485C22×C8—942no—
486C22×C8C22×D4711yescharacteristic
487C22×C8C22×D4711yescharacteristic
488C4×Q8—948no—
489C4×D4—948no—
490C4×D4—948no—
491C4×D4—948no—
492#117—474no—
493#117—942no—
494#117—942no—
495#117—942no—
496#117—942no—
497#117—942no—
498#117—942no—
499#117—942no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—942no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—942no—
511C2×C4⋊C4—942no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—942no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4C22×D4711yescharacteristic
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C4⋊C4C22×D4711yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—941no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—941no—
529C2×C42—941no—
530C2×C42—941no—
531C2×C42—941no—
532#107—22no—
533#107—22no—
534#107—942no—
535#107—942no—
536#107—942no—
537#107—942no—
538#106—942no—
539#106—942no—
540C22⋊C8—474no—
541C22⋊C8—474no—
542C22⋊C8—474no—
543C22⋊C8C4×D4714yescomplemented
544#95—21no—
545#95—941no—
546#95—941no—
547#95—941no—
548C24—471no—
549C24—471no—
550C24D4×D4711yescharacteristic
551#41—948no—
552#41—948no—
553#41—948no—
554#41—948no—
555C2×Q8—474no—
556C2×Q8—942no—
557C2×Q8—942no—
558C2×D4—474no—
559C2×D4—474no—
560C2×D4—474no—
561C2×D4—942no—
562C2×D4—942no—
563C2×D4—942no—
564C2×D4—942no—
565C2×D4—942no—
566C2×D4—942no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—81no—
577C22×C4—81no—
578C22×C4—471no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—472no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—472no—
585C22×C4—471no—
586C22×C4—472no—
587C22×C4—472no—
588C22×C4—944no—
589C22×C4—944no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—3761no—
599C22×C4—3761no—
600C22×C4—3761no—
601C22×C4—3761no—
602C22×C4—3761no—
603C22×C4—3761no—
604C22×C4—1882no—
605C22×C4C2×C4×D4712yes—
606C22×C4D4×D4711yescharacteristic
607C22×C4Q8×D4712yes—
608C22×C4C23×D4711yescharacteristic
609M16—948no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—472no—
615C2×C8—472no—
616C2×C8—948no—
617C2×C8—941no—
618C2×C8—941no—
619C2×C8—941no—
620C2×C8—941no—
621C2×C8C2×C4×D4712yes—
622C2×C8C2×C4×D4712yes—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—472no—
631C4⋊C4—472no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—941no—
635C4⋊C4—941no—
636C4⋊C4—941no—
637C4⋊C4—941no—
638C4⋊C4—941no—
639C4⋊C4—941no—
640C4⋊C4—1882no—
641C4⋊C4D4×D4712yes—
642C4⋊C4D4×D4712yes—
643C22⋊C4—81no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—3761no—
648C22⋊C4—3761no—
649C22⋊C4—3761no—
650C22⋊C4—1882no—
651C42—944no—
652C42—944no—
653C42—944no—
654C42—1882no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—472no—
662C23—472no—
663C23—472no—
664C23—472no—
665C23—941no—
666C23—941no—
667C23—941no—
668C23—941no—
669C23—941no—
670C23—941no—
671C23—941no—
672C23—941no—
673C23—941no—
674C23—941no—
675C23C4⋊C4×D4712yes—
676C23C2×D4×D4711yescharacteristic
677Q8—948no—
678D4—948no—
679D4—948no—
680D4—948no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—84no—
700C2×C4—472no—
701C2×C4—472no—
702C2×C4—472no—
703C2×C4—474no—
704C2×C4—474no—
705C2×C4—474no—
706C2×C4—474no—
707C2×C4—472no—
708C2×C4—941no—
709C2×C4—941no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—3764no—
717C2×C4—3764no—
718C2×C4—3764no—
719C2×C4—1881no—
720C2×C4—1881no—
721C2×C4—1881no—
722C2×C4—1881no—
723C2×C4—1881no—
724C2×C4—1881no—
725C2×C4—1881no—
726C2×C4—1881no—
727C2×C4—1881no—
728C2×C4—1881no—
729C2×C4C4⋊C4×D4712yes—
730C2×C4C22×C4×D4711yescharacteristic
731C2×C4C2×D4×D4711yescharacteristic
732C2×C4C2×D4×D4711yescharacteristic
733C2×C4C2×Q8×D4711yescharacteristic
734C2×C4#41×D4711yescharacteristic
735C2×C4#41×D4711yescharacteristic
736C8—22no—
737C8—22no—
738C8—942no—
739C8—942no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—474no—
748C22—942no—
749C22—942no—
750C22—942no—
751C22—942no—
752C22—942no—
753C22—942no—
754C22—942no—
755C22—942no—
756C22—942no—
757C22—1881no—
758C22—1881no—
759C22—1881no—
760C22—1881no—
761C22C2×C4⋊C4×D4711yescharacteristic
762C22#120×D4711yescharacteristic
763C22#123×D4711yescharacteristic
764C22#1568992411yescharacteristic
765C22#1568992711yescharacteristic
766C22#1568993611yescharacteristic
767C22#1568993911yescharacteristic
768C4—22no—
769C4—42no—
770C4—42no—
771C4—81no—
772C4—81no—
773C4—474no—
774C4—942no—
775C4—3761no—
776C4—3761no—
777C4—1882no—
778C4—1882no—
779C4C4×D4×D4711yescharacteristic
780C4C4×D4×D4711yescharacteristic
781C4C22⋊Q8×D4711yescharacteristic
782C4C22⋊Q8×D4711yescharacteristic
783C2—42no—
784C2—944no—
785C2—1882no—
786C2#385×D4711yescharacteristic
787C2#2025198411yescharacteristic
788C2#2025198711yescharacteristic
789C2#2025265111yescharacteristic
790C2#2025267811yescharacteristic
791C2#2025336111yescharacteristic
792C2#2025336711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1852C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#1852D47
hypocenterC47#20847
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#15689164C2semidirect
3. C2×#107×D47C2semidirect
6. #20243589C2semidirect
7. #20243588C2semidirect
8. #20243585C2semidirect
9. #20243584C2semidirect
10. #20243577C2semidirect
11. #20243576C2semidirect
12. #20243574C2semidirect
13. #20243106C2semidirect
14. #20243103C2semidirect
15. C47×#1852C2semidirect
40. #15689088C4semidirect
81. C2×#10625324C2×C4semidirect
86. C2×C8×D47C2×C4semidirect
129. C22⋊(C47⋊C8)C2×C4semidirect
130. (C2×D47)⋊C8C2×C4semidirect
131. (C2×D47)⋊C8C2×C4semidirect
149. C22⋊C8×C47C2×C4semidirect
399. #1852D47semidirect
460. C47#20847semidirect
543. C22⋊C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896042
C2×#156891642
C2×#107×D472
C2×#156890882
#202459772
#202435892
#202435882
#202435852
#202435842
#202435772
#202435762
#202435742
#202431062
#202431032
C47×#18522
#2084747