Finite Group Databasebeta

← #26138780

Subgroups — #26138780

Order 12032.

1794 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic47C211yesmaximal, characteristic
2C2×#15689030C211yesmaximal, characteristic
3C2×#15689021C211yesmaximal, characteristic
4C2×#15689019C211yesmaximal, characteristic
5#20241640C212yesmaximal
6#20241640C212yesmaximal
7#20241617C211yesmaximal, characteristic
8Dic47⋊#95C212yesmaximal
9#20241614C212yesmaximal
10C4×C47⋊#95C211yesmaximal, characteristic
11C2×C47×#391C211yesmaximal, characteristic
12C2×Q8×Dic47—24no—
13C2×Q8×Dic47—24no—
14C2×Q8×Dic47C418yescomplemented
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C4⋊Dic47C2212yes—
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×Dic47⋊C4C2212yes—
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2212yes—
23#15689030—24no—
24#15689021—24no—
25#15689019—24no—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2211yescharacteristic
36C23×Q8×C47C2211yescharacteristic
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C47×#391—24no—
40C2×#95×C47C2212yes—
41C2×#95×C47C2212yes—
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2311yescharacteristic
46C23×Dic47C2312yes—
47C23×Dic47C2311yescharacteristic
48Q8×Dic47—232no—
49C2×C4⋊Dic47—24no—
50C2×C4⋊Dic47—24no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—22no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47C2×C418yes—
55C2×C4⋊Dic47C2×C414yes—
56C2×C4⋊Dic47D414yes—
57C2×C4⋊Dic47D414yes—
58C2×Dic47⋊C4—24no—
59C2×Dic47⋊C4—24no—
60C2×Dic47⋊C4—24no—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4—42no—
63C2×Dic47⋊C4—42no—
64C2×C4×Dic47—22no—
65C2×C4×Dic47—22no—
66C2×C4×Dic47—24no—
67C2×C4×Dic47—24no—
68C2×C4×Dic47—22no—
69C2×C4×Dic47—22no—
70C2×C4×Dic47—22no—
71C2×C4×Dic47C2×C414yes—
72C2×C4×Dic47C2×C418yes—
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—22no—
76C47⋊#95—24no—
77C47⋊#95—24no—
78C47⋊#95—22no—
79C47⋊#95—22no—
80C47⋊#95—24no—
81C47⋊#95—42no—
82C47⋊#95Q814yescomplemented
83C22×Q8×C47—22no—
84C22×Q8×C47—22no—
85C22×Q8×C47—22no—
86C22×Q8×C47—22no—
87C22×Q8×C47C2×C414yes—
88C22×Q8×C47D414yes—
89C22×Q8×C47Q814yes—
90C23×C4×C47C2312yes—
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2312yes—
94C23×C4×C47C2311yescharacteristic
95C2×C4⋊C4×C47—22no—
96C2×C4⋊C4×C47—22no—
97C2×C4⋊C4×C47—22no—
98C2×C42×C47—22no—
99C2×C42×C47—22no—
100C2×C42×C47—22no—
101#95×C47—24no—
102#95×C47—24no—
103C24×C47C2411yescharacteristic
104C2×Q8×C47—28no—
105C2×Q8×C47—28no—
106C2×Q8×C47—28no—
107C2×Q8×C47—28no—
108C2×Q8×C47—28no—
109C2×Q8×C47—28no—
110C2×Q8×C47C4⋊C4116yescomplemented
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47C22×C414yes—
135C22×C4×C47C22×C412yes—
136C22×C4×C47C2×D414yes—
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×D412yes—
139C22×C4×C47C2×D412yes—
140C22×C4×C47C2×Q812yes—
141C22×C4×C47C2×Q814yes—
142C22×C4×C47C2×Q812yes—
143C22×C4×C47#4112yes—
144C22×C4×C47#4112yes—
145C22×C4×C47#4112yes—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—22no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47C22×C412yes—
180C22×Dic47C22×C414yes—
181C22×Dic47C22×C412yes—
182C22×Dic47C2×D414yes—
183C22×Dic47C2×D414yes—
184C22×Dic47C2×Q812yes—
185C22×Dic47C2×Q812yes—
186C22×Dic47#4112yes—
187C22×Dic47#4112yes—
188C4⋊C4×C47—44no—
189C42×C47—44no—
190C4⋊Dic47—216no—
191C4⋊Dic47—44no—
192C4⋊Dic47C22⋊C4116yes—
193Dic47⋊C4—48no—
194Dic47⋊C4—48no—
195C4×Dic47—28no—
196C4×Dic47—216no—
197C4×Dic47—44no—
198C23×C47C23×C411yescharacteristic
199C23×C47C22×D411yescharacteristic
200C23×C47C22×D411yescharacteristic
201C23×C47C22×D411yescharacteristic
202C23×C47C22×Q811yescharacteristic
203C23×C47C22×Q811yescharacteristic
204C23×C47C2×#4111yescharacteristic
205C23×C47C2×#4111yescharacteristic
206C23×C47C2×#4111yescharacteristic
207C23×C47C2×#4111yescharacteristic
208C23×C47C2×#4111yescharacteristic
209C23×C47H(5,𝔽2)11yescharacteristic
210C23×C472−1+411yescharacteristic
211C23×C472−1+411yescharacteristic
212C23×C472−1+411yescharacteristic
213Q8×C47—232no—
214C2×C4×C47—24no—
215C2×C4×C47—24no—
216C2×C4×C47—24no—
217C2×C4×C47—24no—
218C2×C4×C47—24no—
219C2×C4×C47—24no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47—42no—
240C2×C4×C47—42no—
241C2×C4×C47C2×C22⋊C414yes—
242C2×C4×C47C2×C4⋊C418yes—
243C2×C4×C47C2×C4⋊C414yes—
244C2×C4×C47#11714yes—
245C2×C4×C47#12114yes—
246C2×C4×C47#12114yes—
247C2×C4×C47C22⋊Q814yes—
248C2×C4×C47C22⋊Q814yes—
249C2×Dic47—22no—
250C2×Dic47—24no—
251C2×Dic47—22no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—24no—
256C2×Dic47—24no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—22no—
263C2×Dic47—22no—
264C2×Dic47—22no—
265C2×Dic47—22no—
266C2×Dic47—22no—
267C2×Dic47—22no—
268C2×Dic47—22no—
269C2×Dic47—22no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—41no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—41no—
280C2×Dic47—41no—
281C2×Dic47—41no—
282C2×Dic47—42no—
283C2×Dic47—42no—
284C2×Dic47—42no—
285C2×Dic47—42no—
286C2×Dic47—42no—
287C2×Dic47—42no—
288C2×Dic47—42no—
289C2×Dic47C2×C22⋊C418yes—
290C2×Dic47C4×Q814yes—
291#13935—471nomaximal, Sylow
292C22×C47C22×C22⋊C411yescharacteristic
293C22×C47C22×C4⋊C411yescharacteristic
294C22×C47C2×#11711yescharacteristic
295C22×C47C2×C4×Q811yescharacteristic
296C22×C47C4×#4111yescharacteristic
297C22×C47#51911yescharacteristic
298C22×C47#52011yescharacteristic
299C22×C47C2×#12111yescharacteristic
300C22×C47C2×#12111yescharacteristic
301C22×C47C2×C22⋊Q811yescharacteristic
302C22×C47C2×C22⋊Q811yescharacteristic
303C22×C47#52911yescharacteristic
304C22×C47#52911yescharacteristic
305C22×C47#53311yescharacteristic
306C22×C47#53311yescharacteristic
307C22×C47#54111yescharacteristic
308C22×C47#54111yescharacteristic
309C22×C47#54211yescharacteristic
310C22×C47#54211yescharacteristic
311C22×C47#54611yescharacteristic
312C22×C47#54611yescharacteristic
313C22×C47#54711yescharacteristic
314C22×C47#54711yescharacteristic
315C22×C47#54811yescharacteristic
316C22×C47#54811yescharacteristic
317C22×C47#54811yescharacteristic
318C22×C47#54811yescharacteristic
319C22×C47D4×Q811yescharacteristic
320C22×C47D4×Q811yescharacteristic
321C22×C47D4×Q811yescharacteristic
322C22×C47#55011yescharacteristic
323C22×C47#55711yescharacteristic
324C22×C47#55711yescharacteristic
325C22×C47#55711yescharacteristic
326C22×C47Q8211yescharacteristic
327C4×C47—28no—
328C4×C47—42no—
329C4×C47—42no—
330C4×C47—82no—
331C4×C47#38018yes—
332Dic47—28no—
333Dic47—24no—
334Dic47—42no—
335Dic47—42no—
336Dic47—42no—
337Dic47—82no—
338C22×C4×Q8—471no—
339C2×#391—471no—
340C2×#391D4711yescharacteristic
341C2×#389—471no—
342C2×#389—471no—
343#1441—472no—
344#1441—472no—
345C4⋊#95—472no—
346C4⋊#95—471no—
347#1434—472no—
348C4×#95—471no—
349C2×C47C2×#38011yescharacteristic
350C2×C47#229511yescharacteristic
351C2×C47#232011yescharacteristic
352C2×C47#233911yescharacteristic
353C2×C47Q8×C22⋊C411yescharacteristic
354C2×C47Q8×C4⋊C411yescharacteristic
355C2×C47#235111yescharacteristic
356C2×C47#242611yescharacteristic
357C2×C47#242611yescharacteristic
358C2×C47#242911yescharacteristic
359C2×C47#242911yescharacteristic
360C2×C47#245111yescharacteristic
361C2×C47#245111yescharacteristic
362C2×C47#245311yescharacteristic
363C2×C47#245311yescharacteristic
364C23×Q8C2×D4711yescharacteristic
365C2×C4×Q8—478no—
366C2×C4×Q8—944no—
367C2×C4×Q8—944no—
368C22×C4⋊C4—471no—
369C22×C4⋊C4—472no—
370C22×C4⋊C4—471no—
371C22×C4⋊C4—472no—
372C22×C4⋊C4—472no—
373C22×C4⋊C4C2×D4711yescharacteristic
374C22×C42—471no—
375C22×C42—472no—
376C22×C42—471no—
377C22×C42C2×D4711yescharacteristic
378#391—24no—
379#391—944no—
380#389—944no—
381#389—944no—
382C2×#95—471no—
383C2×#95—471no—
384C2×#95—471no—
385C2×#95—471no—
386C2×#95—472no—
387C2×#95—472no—
388C2×#95—472no—
389C2×#95—472no—
390C2×#95—472no—
391C2×#95—472no—
392C2×#95C2×D4712yes—
393C2×#95C2×D4712yes—
394C47#1393511yescharacteristic, complemented, Sylow
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8Dic9414yes—
400C22×Q8C4×D4714yes—
401C22×Q8C22⋊D4714yes—
402C23×C4—472no—
403C23×C4—471no—
404C23×C4—471no—
405C23×C4—471no—
406C23×C4—471no—
407C23×C4—472no—
408C23×C4C22×D4712yes—
409C23×C4C22×D4711yescharacteristic
410C23×C4C22×D4711yescharacteristic
411C23×C4C22×D4712yes—
412C23×C4C22×D4711yescharacteristic
413C4×Q8—9432no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—474no—
418C2×C4⋊C4—474no—
419C2×C4⋊C4—474no—
420C2×C4⋊C4—478no—
421C2×C4⋊C4—944no—
422C2×C4⋊C4—944no—
423C2×C4⋊C4—944no—
424C2×C4⋊C4—944no—
425C2×C4⋊C4—944no—
426C2×C4⋊C4—942no—
427C2×C4⋊C4—942no—
428C2×C4⋊C4—944no—
429C2×C4⋊C4—942no—
430C2×C4⋊C4—1882no—
431C2×C4⋊C4—1882no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—478no—
436C2×C42—474no—
437C2×C42—944no—
438C2×C42—944no—
439C2×C42—942no—
440C2×C42—942no—
441C2×C42—942no—
442C2×C42—942no—
443C2×C42—942no—
444#95—24no—
445#95—24no—
446#95—474no—
447#95—942no—
448#95—942no—
449#95—944no—
450#95—944no—
451#95—944no—
452#95—942no—
453#95—944no—
454#95—944no—
455#95—1882no—
456C24C23×D4711yescharacteristic
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—28no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8Dic47⋊C4116yescomplemented
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—472no—
488C22×C4—474no—
489C22×C4—474no—
490C22×C4—474no—
491C22×C4—472no—
492C22×C4—472no—
493C22×C4—472no—
494C22×C4—472no—
495C22×C4—472no—
496C22×C4—941no—
497C22×C4—941no—
498C22×C4—942no—
499C22×C4—942no—
500C22×C4—942no—
501C22×C4—941no—
502C22×C4—942no—
503C22×C4—941no—
504C22×C4—941no—
505C22×C4—941no—
506C22×C4—941no—
507C22×C4—941no—
508C22×C4—941no—
509C22×C4—941no—
510C22×C4—941no—
511C22×C4—941no—
512C22×C4—941no—
513C22×C4—941no—
514C22×C4—941no—
515C22×C4—941no—
516C22×C4—941no—
517C22×C4—941no—
518C22×C4—941no—
519C22×C4—941no—
520C22×C4—941no—
521C22×C4—941no—
522C22×C4—942no—
523C22×C4—942no—
524C22×C4—942no—
525C22×C4—942no—
526C22×C4—942no—
527C22×C4—942no—
528C22×C4—942no—
529C22×C4C2×Dic9414yes—
530C22×C4C2×Dic9412yes—
531C22×C4C2×C4×D4714yes—
532C22×C4C2×C4×D4712yes—
533C22×C4D4×D4712yes—
534C22×C4D4×D4712yes—
535C22×C4#1062535212yes—
536C22×C4#1062535212yes—
537C22×C4Q8×D4712yes—
538C22×C4#1062535412yes—
539C22×C4C2×C22⋊D4714yes—
540C22×C4C2×C22⋊D4712yes—
541C4⋊C4—44no—
542C4⋊C4—4716no—
543C4⋊C4—9416no—
544C4⋊C4—1888no—
545C4⋊C4—1888no—
546C4⋊C4—1884no—
547C42—44no—
548C42—9416no—
549C42—948no—
550C42—1884no—
551C23C22×C4×D4711yescharacteristic
552C23C2×D4×D4711yescharacteristic
553C23C2×D4×D4711yescharacteristic
554C23C22×C22⋊D4711yescharacteristic
555C23C2×Q8×D4711yescharacteristic
556C23C22×Dic9411yescharacteristic
557C23#41×D4711yescharacteristic
558C23#41×D4711yescharacteristic
559C23C2×#1062535211yescharacteristic
560C23C2×#1062535211yescharacteristic
561C23C2×#1062535411yescharacteristic
562C23#1309407011yescharacteristic
563C23#1309407111yescharacteristic
564C23#1309407211yescharacteristic
565C23#1309407211yescharacteristic
566Q8—232no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—478no—
595C2×C4—474no—
596C2×C4—944no—
597C2×C4—944no—
598C2×C4—944no—
599C2×C4—944no—
600C2×C4—942no—
601C2×C4—942no—
602C2×C4—942no—
603C2×C4—942no—
604C2×C4—942no—
605C2×C4—944no—
606C2×C4—942no—
607C2×C4—944no—
608C2×C4—942no—
609C2×C4—942no—
610C2×C4—942no—
611C2×C4—942no—
612C2×C4—942no—
613C2×C4—942no—
614C2×C4—942no—
615C2×C4—942no—
616C2×C4—942no—
617C2×C4—1882no—
618C2×C4—1882no—
619C2×C4—1882no—
620C2×C4—1882no—
621C2×C4—1882no—
622C2×C4—1882no—
623C2×C4—1882no—
624C2×C4—1881no—
625C2×C4—1881no—
626C2×C4—1881no—
627C2×C4—1881no—
628C2×C4—1881no—
629C2×C4—1881no—
630C2×C4—1881no—
631C2×C4—1881no—
632C2×C4—1881no—
633C2×C4—1881no—
634C2×C4—1881no—
635C2×C4—1881no—
636C2×C4C22⋊C4×D4714yes—
637C2×C4C2×Dic47⋊C418yes—
638C2×C4C2×Dic47⋊C414yes—
639C2×C4#1309398014yes—
640C2×C4#1309399614yes—
641C2×C4#1309399614yes—
642C2×C4#1309400114yes—
643C2×C4#1309400114yes—
644C22C2×C22⋊C4×D4711yescharacteristic
645C22C22×Dic47⋊C411yescharacteristic
646C22C2×#1309398011yescharacteristic
647C22C4×Q8×D4711yescharacteristic
648C22C4×#1062535411yescharacteristic
649C22#1568959911yescharacteristic
650C22#1568960511yescharacteristic
651C22C2×#1309399611yescharacteristic
652C22C2×#1309399611yescharacteristic
653C22C2×#1309400111yescharacteristic
654C22C2×#1309400111yescharacteristic
655C22#1568965211yescharacteristic
656C22#1568965911yescharacteristic
657C22#1568967511yescharacteristic
658C22#1568967811yescharacteristic
659C22#1568973311yescharacteristic
660C22#1568973411yescharacteristic
661C22#1568974211yescharacteristic
662C22#1568974611yescharacteristic
663C22#1568976411yescharacteristic
664C22#1568976611yescharacteristic
665C22#1568977511yescharacteristic
666C22#1568977611yescharacteristic
667C22#1568978011yescharacteristic
668C22#1568978111yescharacteristic
669C22#1568978311yescharacteristic
670C22#1568978411yescharacteristic
671C22#1568978611yescharacteristic
672C22Q8×C22⋊D4711yescharacteristic
673C22#1568978811yescharacteristic
674C22#1568979211yescharacteristic
675C22#1568984911yescharacteristic
676C22#1568984911yescharacteristic
677C22#1568985211yescharacteristic
678C22Q8×Dic9411yescharacteristic
679C4—28no—
680C4—42no—
681C4—42no—
682C4—82no—
683C4—948no—
684C4—944no—
685C4—3762no—
686C4—1882no—
687C4—1882no—
688C4—1882no—
689C4#1568898118yes—
690C2C2×#1568898111yescharacteristic
691C2#2024586311yescharacteristic
692C2#2024603311yescharacteristic
693C2#2024621711yescharacteristic
694C2#2024622211yescharacteristic
695C2Q8×Dic47⋊C411yescharacteristic
696C2#2024630611yescharacteristic
697C2#2024695611yescharacteristic
698C2#2024695711yescharacteristic
699C2#2024698911yescharacteristic
700C2#2024699011yescharacteristic
701C2#2024722911yescharacteristic
702C2#2024723011yescharacteristic
703C2#2024725111yescharacteristic
704C2#2024725211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#391C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×#391D47
hypocenterC47#13935
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
14. C2×Q8×Dic47C4semidirect
82. C47⋊#95Q8semidirect
110. C2×Q8×C47C4⋊C4semidirect
394. C47#13935semidirect
463. C2×Q8Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic472
C2×#156890302
C2×#156890212
C2×#156890192
#202416402
#202416172
Dic47⋊#952
#202416142
C4×C47⋊#952
C2×C47×#3912
#1393547