Finite Group Databasebeta

← #26225411

Subgroups — #26225411

Order 12032.

1486 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2#20245771C211yesmaximal, characteristic, complemented
3#20243834C214yesmaximal, complemented
4#20243690C214yesmaximal, complemented
5#20243485C212yesmaximal, complemented
6#20243331C212yesmaximal, complemented
7C2×C47×#407C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9#15689634—21no—
10#15689634—21no—
11#15689634—21no—
12#15689634—21no—
13#15689634C412yescomplemented
14#15689634C412yescomplemented
15#15689634C2212yes—
16#15689634C2212yes—
17C2×#13094007—21no—
18C2×#13094003C411yescharacteristic, complemented
19C2×#13094003C411yescharacteristic, complemented
20C2×#13093998C411yescharacteristic, complemented
21C2×#13093998C411yescharacteristic, complemented
22C2×#13093993—21no—
23C2×C4×C22⋊D47—21no—
24C2×C4×C22⋊D47—21no—
25C2×#13093983C2211yescharacteristic
26C2×#13093983C2212yescomplemented
27C2×#13093950C2218yescomplemented
28#15688986—21no—
29#15688983—21no—
30#15688983—21no—
31#15688979—21no—
32C4×C22⋊Dic47C2212yes—
33C4×C22⋊Dic47C2212yescomplemented
34#15688884C2218yescomplemented
35C24×C4×C47C2211yescharacteristic
36C22×M16×C47C2212yescomplemented
37C47×#407—21no—
38C47×#407—21no—
39C47×#407C2212yes—
40C47×#407C2212yescomplemented
41C2×C22⋊C8×C47—21no—
42C2×C22⋊C8×C47—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—44no—
46C2×#10625350C2×C412yes—
47C2×#10625350C2312yes—
48C22×Dic94C2×C411yescharacteristic
49C22×D188C2×C411yescharacteristic
50C22×C22⋊D47—21no—
51C22×C22⋊D47—21no—
52C22×C22⋊D47—21no—
53C22×C4×D47—21no—
54#13094007—22no—
55#13094007—22no—
56#13094007—22no—
57#13094007—22no—
58#13094003—21no—
59#13094003—21no—
60#13094003—21no—
61#13094003—21no—
62#13094003C2×C412yes—
63#13094003C2×C412yes—
64#13094003C2×C412yes—
65#13094003C2×C412yes—
66#13093998—21no—
67#13093998—21no—
68#13093998—21no—
69#13093998—21no—
70#13093998C2×C412yes—
71#13093998C2×C412yes—
72#13093998C2×C412yes—
73#13093998C2×C412yes—
74#13093993—22no—
75#13093993—22no—
76#13093993—22no—
77#13093993—22no—
78C4×C22⋊D47—22no—
79C4×C22⋊D47—22no—
80C4×C22⋊D47—22no—
81C4×C22⋊D47—22no—
82C4×C22⋊D47—22no—
83C4×C22⋊D47—22no—
84C4×C22⋊D47—22no—
85C4×C22⋊D47—22no—
86#13093983—21no—
87#13093983—21no—
88#13093983—44no—
89#13093983C2×C412yes—
90#13093983C2312yes—
91C2×C4⋊Dic47—22no—
92C2×C4⋊Dic47C2×C411yescharacteristic
93C2×C4⋊Dic47C2×C411yescharacteristic
94C2×Dic47⋊C4—21no—
95C2×Dic47⋊C4—21no—
96C2×C22⋊Dic47—21no—
97C2×C22⋊Dic47—21no—
98C2×C22⋊Dic47—21no—
99C2×C22⋊Dic47—22no—
100C2×C22⋊Dic47—22no—
101C2×C22⋊Dic47—22no—
102C2×(C2×D47)⋊C4—21no—
103C2×(C2×D47)⋊C4—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47C2314yes—
106#13093950—48no—
107C47⋊#95—22no—
108C47⋊#95—22no—
109C25×C47D411yescharacteristic
110C23×C4×C47—44no—
111C23×C4×C47C2×C411yescharacteristic
112C23×C4×C47C2×C411yescharacteristic
113C23×C4×C47C2×C411yescharacteristic
114C23×C4×C47C2×C411yescharacteristic
115C23×C4×C47D411yescharacteristic
116C23×C4×C47D411yescharacteristic
117C23×C4×C47D411yescharacteristic
118C23×C4×C47D411yescharacteristic
119C23×C4×C47D411yescharacteristic
120C23×C4×C47D411yescharacteristic
121C23×C4×C47D411yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C2×M16×C47—22no—
126C2×M16×C47—44no—
127C2×M16×C47C2314yes—
128C22×C8×C47—22no—
129C22⋊C8×C47—22no—
130C22⋊C8×C47—22no—
131C22⋊C8×C47—22no—
132C22⋊C8×C47—22no—
133C24×C47—42no—
134C24×C47—42no—
135C24×C47—42no—
136C24×C47C22⋊C411yescharacteristic
137C24×C47C22⋊C411yescharacteristic
138C24×C47C22⋊C411yescharacteristic
139C24×C47C22⋊C411yescharacteristic
140C24×C47C2×D411yescharacteristic
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C23×D47—21no—
144C22×C4×C47—24no—
145C22×C4×C47—24no—
146C22×C4×C47—24no—
147C22×C4×C47—42no—
148C22×C4×C47—42no—
149C22×C4×C47—42no—
150C22×C4×C47—42no—
151C22×C4×C47—42no—
152C22×C4×C47—42no—
153C22×C4×C47—42no—
154C22×C4×C47—42no—
155C22×C4×C47—42no—
156C22×C4×C47—42no—
157C22×C4×C47—42no—
158C22×C4×C47C22⋊C411yescharacteristic
159C22×C4×C47C22⋊C411yescharacteristic
160C22×C4×C47C22⋊C411yescharacteristic
161C22×C4×C47C22⋊C411yescharacteristic
162C22×C4×C47C22⋊C411yescharacteristic
163C22×C4×C47C22⋊C411yescharacteristic
164C22×C4×C47C22⋊C411yescharacteristic
165C22×C4×C47C22⋊C411yescharacteristic
166C22×C4×C47C22⋊C411yescharacteristic
167C22×C4×C47C22⋊C411yescharacteristic
168C22×C4×C47C22⋊C411yescharacteristic
169C22×C4×C47C22⋊C411yescharacteristic
170C22×C4×C47C22×C411yescharacteristic
171C22×C4×C47C22×C411yescharacteristic
172C22×C4×C47C22×C411yescharacteristic
173C22×C4×C47C22×C411yescharacteristic
174C22×C4×C47C22×C411yescharacteristic
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2411yescharacteristic
186C2×C22⋊D47—22no—
187C2×C22⋊D47—22no—
188C2×C22⋊D47—22no—
189C2×C22⋊D47—22no—
190C2×C22⋊D47—22no—
191C2×C22⋊D47—22no—
192C2×C22⋊D47—44no—
193C2×C22⋊D47—44no—
194C2×C22⋊D47—44no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—24no—
199#10625350—28no—
200#10625350—44no—
201#10625350—44no—
202#10625350—44no—
203C2×D188—21no—
204C2×D188—42no—
205C2×D188C22×C412yes—
206C2×C4×D47—22no—
207C2×C4×D47—22no—
208C2×C4×D47—44no—
209C2×Dic94—21no—
210C2×Dic94—42no—
211C2×Dic94C22×C412yes—
212M16×C47—28no—
213M16×C47—44no—
214C2×C8×C47—24no—
215C2×C8×C47—44no—
216C22⋊Dic47—22no—
217C22⋊Dic47—22no—
218C22⋊Dic47—22no—
219C22⋊Dic47—22no—
220C22⋊Dic47—22no—
221C22⋊Dic47—22no—
222C22⋊Dic47—44no—
223C22⋊Dic47—44no—
224C22⋊Dic47—44no—
225(C2×D47)⋊C4—22no—
226(C2×D47)⋊C4—22no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4—22no—
229C4⋊Dic47—21no—
230C4⋊Dic47—21no—
231C4⋊Dic47—44no—
232C4⋊Dic47C22×C412yes—
233C4⋊Dic47C22×C412yes—
234Dic47⋊C4—22no—
235Dic47⋊C4—22no—
236Dic47⋊C4—22no—
237Dic47⋊C4—22no—
238C4×Dic47—22no—
239C4×Dic47—22no—
240C4×Dic47—28no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—22no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—416no—
263C23×C47C2×C22⋊C411yescharacteristic
264C23×C47C2×C22⋊C411yescharacteristic
265C23×C47C2×C22⋊C411yescharacteristic
266C23×C47C2×C22⋊C411yescharacteristic
267C23×C47C2×C22⋊C411yescharacteristic
268C23×C47C2×C22⋊C411yescharacteristic
269C23×C47C22×D411yescharacteristic
270C22×D47—22no—
271C22×D47—42no—
272C22×D47—42no—
273C22×D47—42no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
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—22no—
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—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47C2×C22⋊C411yescharacteristic
302C2×C4×C47C2×C22⋊C411yescharacteristic
303C2×C4×C47C2×C22⋊C411yescharacteristic
304C2×C4×C47C2×C22⋊C411yescharacteristic
305C2×C4×C47C2×C22⋊C411yescharacteristic
306C2×C4×C47C2×C22⋊C411yescharacteristic
307C2×C4×C47C23×C411yescharacteristic
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47H(5,𝔽2)14yes—
310C22⋊D47—44no—
311C22⋊D47—44no—
312C22⋊D47—44no—
313C22⋊D47—44no—
314C22⋊D47—44no—
315C22⋊D47—44no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—44no—
323C2×Dic47—44no—
324C2×Dic47—44no—
325D188—24no—
326D188—42no—
327C4×D47—44no—
328C4×D47—44no—
329Dic94—24no—
330Dic94—42no—
331C8×C47—44no—
332#21774—471nomaximal, Sylow
333C22×C47—21no—
334C22×C47—21no—
335C22×C47—21no—
336C22×C47—21no—
337C22×C47—21no—
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—21no—
341C22×C47—21no—
342C22×C47—21no—
343C22×C47—21no—
344C22×C47—21no—
345C22×C47—21no—
346C22×C47—21no—
347C22×C47—21no—
348C22×C47—21no—
349C22×C47—21no—
350C22×C47—21no—
351C22×C47—44no—
352C22×C47—44no—
353C22×C47—44no—
354C22×C47—44no—
355C22×C47—44no—
356C22×C47—44no—
357C22×C47—44no—
358C22×C47#42112yes—
359C22×C47#42112yes—
360C22×C47C22×C22⋊C411yescharacteristic
361C22×C47#53412yes—
362C2×D47—42no—
363C2×D47—42no—
364C2×D47—42no—
365C2×D47—84no—
366C4×C47—21no—
367C4×C47—21no—
368C4×C47—21no—
369C4×C47—21no—
370C4×C47—21no—
371C4×C47—21no—
372C4×C47#51812yes—
373C4×C47#53412yes—
374Dic47—42no—
375Dic47—42no—
376Dic47—42no—
377Dic47—84no—
378C2×#525—471no—
379C2×#407D4711yescharacteristic, complemented
380#2280—471no—
381#1897—474no—
382#1871—474no—
383#1826—472no—
384#1789—472no—
385C2×C47—22no—
386C2×C47—22no—
387C2×C47—22no—
388C2×C47—41no—
389C2×C47—41no—
390C2×C47—41no—
391C2×C47—41no—
392C2×C47#230811yescharacteristic
393C2×C47C2×#42111yescharacteristic
394C2×C47C2×#42111yescharacteristic
395D47—82no—
396C22×#41—471no—
397C24×C4C2×D4711yescharacteristic
398C22×M16C2×D4712yescomplemented
399#525—472no—
400#525—472no—
401#525—472no—
402#525—472no—
403#525—941no—
404#525—941no—
405#525—941no—
406#525—941no—
407C2×#123—941no—
408C2×C22⋊Q8—471no—
409C2×C22⋊Q8—471no—
410C2×#121—471no—
411C2×#121—471no—
412C2×#120—941no—
413C2×C4×D4—941no—
414C2×C4×D4—941no—
415C2×#117—472no—
416C2×#117—471no—
417C2×#104—478no—
418#407—21no—
419#407—21no—
420#407C2×D4712yes—
421#407C2×D4712yescomplemented
422C2×C22⋊C8—21no—
423C2×C22⋊C8—21no—
424#381—941no—
425#380—941no—
426#380—941no—
427#379—941no—
428C4×C22⋊C4—472no—
429C4×C22⋊C4—472no—
430#339—478no—
431C47#2177411yescharacteristic, complemented, Sylow
432C25D18811yescharacteristic
433C2×#41—472no—
434C2×#41—472no—
435C2×#41—941no—
436C2×#41—941no—
437C2×#41—1884no—
438C22×Q8—471no—
439C22×D4—471no—
440C22×D4—941no—
441C22×D4—941no—
442C22×D4—941no—
443C23×C4—44no—
444C23×C4—941no—
445C23×C4C4×D4711yescharacteristic
446C23×C4C4×D4711yescharacteristic
447C23×C4C4×D4711yescharacteristic
448C23×C4C4×D4711yescharacteristic
449C23×C4D18811yescharacteristic
450C23×C4D18811yescharacteristic
451C23×C4D18811yescharacteristic
452C23×C4C22⋊D4711yescharacteristic
453C23×C4C22⋊D4711yescharacteristic
454C23×C4C22⋊D4711yescharacteristic
455C23×C4C22⋊D4711yescharacteristic
456C23×C4C22×D4711yescharacteristic
457C23×C4C22×D4711yescharacteristic
458C23×C4C22×D4711yescharacteristic
459C2×M16—22no—
460C2×M16—44no—
461C2×M16C22×D4714yes—
462C22×C8—22no—
463#123—942no—
464#123—942no—
465#123—942no—
466#123—942no—
467C22⋊Q8—472no—
468C22⋊Q8—472no—
469C22⋊Q8—472no—
470C22⋊Q8—472no—
471C22⋊Q8—941no—
472C22⋊Q8—941no—
473C22⋊Q8—941no—
474C22⋊Q8—941no—
475#121—472no—
476#121—472no—
477#121—472no—
478#121—472no—
479#121—941no—
480#121—941no—
481#121—941no—
482#121—941no—
483#120—942no—
484#120—942no—
485#120—942no—
486#120—942no—
487C4×D4—942no—
488C4×D4—942no—
489C4×D4—942no—
490C4×D4—942no—
491C4×D4—942no—
492C4×D4—942no—
493C4×D4—942no—
494C4×D4—942no—
495#117—472no—
496#117—472no—
497#117—941no—
498#117—941no—
499#117—1884no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—942no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—942no—
511C2×C22⋊C4—942no—
512C2×C22⋊C4—942no—
513C2×C42—474no—
514C2×C42—941no—
515#104—1888no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520#95—942no—
521#95—942no—
522C24—42no—
523C24—42no—
524C24—42no—
525C24—941no—
526C24(C2×D47)⋊C411yescharacteristic
527C24(C2×D47)⋊C411yescharacteristic
528C24(C2×D47)⋊C411yescharacteristic
529C24(C2×D47)⋊C411yescharacteristic
530C24C2×D18811yescharacteristic
531C24C2×D18811yescharacteristic
532C24C2×D18811yescharacteristic
533#41—948no—
534#41—1884no—
535#41—1884no—
536#41—1884no—
537C2×Q8—472no—
538C2×Q8—941no—
539C2×Q8—1882no—
540C2×D4—472no—
541C2×D4—942no—
542C2×D4—942no—
543C2×D4—942no—
544C2×D4—942no—
545C2×D4—942no—
546C2×D4—942no—
547C2×D4—941no—
548C2×D4—1882no—
549C2×D4—1884no—
550C2×D4—1884no—
551C2×D4—1884no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—941no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—944no—
572C22×C4—1884no—
573C22×C4(C2×D47)⋊C411yescharacteristic
574C22×C4(C2×D47)⋊C411yescharacteristic
575C22×C4(C2×D47)⋊C411yescharacteristic
576C22×C4(C2×D47)⋊C411yescharacteristic
577C22×C4(C2×D47)⋊C411yescharacteristic
578C22×C4(C2×D47)⋊C411yescharacteristic
579C22×C4(C2×D47)⋊C411yescharacteristic
580C22×C4(C2×D47)⋊C411yescharacteristic
581C22×C4(C2×D47)⋊C411yescharacteristic
582C22×C4(C2×D47)⋊C411yescharacteristic
583C22×C4(C2×D47)⋊C411yescharacteristic
584C22×C4(C2×D47)⋊C411yescharacteristic
585C22×C4C2×C4×D4711yescharacteristic
586C22×C4C2×C4×D4711yescharacteristic
587C22×C4C2×C4×D4711yescharacteristic
588C22×C4C2×C4×D4711yescharacteristic
589C22×C4C2×C4×D4711yescharacteristic
590C22×C4C2×C4×D4711yescharacteristic
591C22×C4C2×D18811yescharacteristic
592C22×C4C2×D18811yescharacteristic
593C22×C4C2×D18811yescharacteristic
594C22×C4C2×C22⋊D4711yescharacteristic
595C22×C4C2×C22⋊D4711yescharacteristic
596C22×C4C2×C22⋊D4711yescharacteristic
597C22×C4C2×C22⋊D4711yescharacteristic
598C22×C4C2×C22⋊D4711yescharacteristic
599C22×C4C2×C22⋊D4711yescharacteristic
600C22×C4C23×D4711yescharacteristic
601M16—28no—
602M16—44no—
603C2×C8—24no—
604C2×C8—44no—
605C4⋊C4—472no—
606C4⋊C4—472no—
607C4⋊C4—942no—
608C4⋊C4—942no—
609C4⋊C4—942no—
610C4⋊C4—942no—
611C4⋊C4—941no—
612C4⋊C4—941no—
613C4⋊C4—1884no—
614C22⋊C4—942no—
615C22⋊C4—942no—
616C22⋊C4—942no—
617C22⋊C4—942no—
618C22⋊C4—942no—
619C22⋊C4—942no—
620C22⋊C4—942no—
621C22⋊C4—942no—
622C22⋊C4—942no—
623C22⋊C4—942no—
624C22⋊C4—1884no—
625C22⋊C4—1884no—
626C22⋊C4—1884no—
627C42—942no—
628C42—942no—
629C42—948no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—416no—
652C23—942no—
653C23—1882no—
654C23—1882no—
655C23—1882no—
656C23C2×(C2×D47)⋊C411yescharacteristic
657C23C2×(C2×D47)⋊C411yescharacteristic
658C23C2×(C2×D47)⋊C411yescharacteristic
659C23C2×(C2×D47)⋊C411yescharacteristic
660C23C2×(C2×D47)⋊C411yescharacteristic
661C23C2×(C2×D47)⋊C411yescharacteristic
662C23C22×D18811yescharacteristic
663Q8—944no—
664Q8—1882no—
665D4—944no—
666D4—1882no—
667D4—1884no—
668D4—1884no—
669D4—1884no—
670D4—1884no—
671D4—1884no—
672D4—1884no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
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—41no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—1884no—
704C2×C4—1884no—
705C2×C4—1884no—
706C2×C4—1884no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4—1882no—
710C2×C4—1884no—
711C2×C4C2×(C2×D47)⋊C411yescharacteristic
712C2×C4C2×(C2×D47)⋊C411yescharacteristic
713C2×C4C2×(C2×D47)⋊C411yescharacteristic
714C2×C4C2×(C2×D47)⋊C411yescharacteristic
715C2×C4C2×(C2×D47)⋊C411yescharacteristic
716C2×C4C2×(C2×D47)⋊C411yescharacteristic
717C2×C4C22×C4×D4711yescharacteristic
718C2×C4C22×C22⋊D4711yescharacteristic
719C2×C4#1309406914yes—
720C8—44no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—3764no—
747C22—1882no—
748C22—1882no—
749C22—1882no—
750C22#1568913912yes—
751C22#1568913912yes—
752C22C22×(C2×D47)⋊C411yescharacteristic
753C22#1568968512yes—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—3764no—
761C4—1882no—
762C4—1882no—
763C4—1882no—
764C4#1568959612yes—
765C4#1568968212yes—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—41no—
772C2—41no—
773C2—3762no—
774C2#2024596311yescharacteristic
775C2C2×#1568913911yescharacteristic
776C2C2×#1568913911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#407C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenterC2×#407D47
hypocenterC47#21774
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #20245771C2semidirect
3. #20243834C2semidirect
4. #20243690C2semidirect
5. #20243485C2semidirect
6. #20243331C2semidirect
7. C2×C47×#407C2semidirect
13. #15689634C4semidirect
14. #15689634C4semidirect
18. C2×#13094003C4semidirect
19. C2×#13094003C4semidirect
20. C2×#13093998C4semidirect
21. C2×#13093998C4semidirect
26. C2×#13093983C22semidirect
27. C2×#13093950C22semidirect
33. C4×C22⋊Dic47C22semidirect
34. #15688884C22semidirect
36. C22×M16×C47C22semidirect
40. C47×#407C22semidirect
379. C2×#407D47semidirect
398. C22×M16C2×D47semidirect
421. #407C2×D47semidirect
431. C47#21774semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
#202457712
#202438342
#202436902
#202434852
#202433312
C2×C47×#4072
#2177447