Finite Group Databasebeta

← #26139500

Subgroups — #26139500

Order 12032.

1614 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689021C211yesmaximal, characteristic
2C2×#15689021C211yesmaximal, characteristic
3C2×#15689021C211yesmaximal, characteristic
4C2×#15689020C212yesmaximal
5C2×#15688993C211yesmaximal, characteristic
6C2×C4×C4⋊Dic47C211yesmaximal, characteristic
7#20241652C212yesmaximal
8#20241642C212yesmaximal
9#20241622C212yesmaximal
10#20241618C211yesmaximal, characteristic
11C4×#95×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2212yes—
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×Dic47⋊C4C2212yes—
20C22×Dic47⋊C4C2212yes—
21C22×C4×Dic47C2212yes—
22#15689021—24no—
23#15689021—24no—
24#15689021C418yescomplemented
25#15689020—28no—
26#15688993—24no—
27C4×C4⋊Dic47—24no—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C22×C42×C47C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C2×#95×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2211yescharacteristic
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2312yes—
44C23×Dic47C2312yes—
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—24no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—24no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47—24no—
55C2×C4⋊Dic47—24no—
56C2×C4⋊Dic47—42no—
57C2×C4⋊Dic47—42no—
58C2×C4⋊Dic47C2×C414yes—
59C2×C4⋊Dic47C2×C414yes—
60C2×C4⋊Dic47D414yes—
61C2×C4⋊Dic47D414yes—
62C2×C4⋊Dic47Q814yes—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4—24no—
69C2×Dic47⋊C4—42no—
70C2×Dic47⋊C4—42no—
71C2×Dic47⋊C4C2×C418yes—
72C2×C4×Dic47—24no—
73C2×C4×Dic47—24no—
74C2×C4×Dic47—42no—
75C47⋊#95—24no—
76C47⋊#95—24no—
77C47⋊#95—24no—
78C47⋊#95—24no—
79C47⋊#95—42no—
80C47⋊#95C2×C418yes—
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C2×C42×C47—22no—
89C2×C42×C47—22no—
90C2×C42×C47—22no—
91C2×C42×C47—22no—
92C2×C42×C47—22no—
93C2×C42×C47—22no—
94C2×C42×C47—22no—
95C2×C42×C47C2×C414yes—
96C2×C42×C47Q814yes—
97#95×C47—22no—
98#95×C47—22no—
99#95×C47D414yes—
100#95×C47Q814yes—
101C24×C47C2411yescharacteristic
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
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—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47C22×C412yes—
133C22×C4×C47C22×C412yes—
134C22×C4×C47C22×C412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×D412yes—
139C22×C4×C47C2×D412yes—
140C22×C4×C47C2×Q812yes—
141C22×C4×C47C2×Q812yes—
142C22×C4×C47C2×Q812yes—
143C22×C4×C47C2×Q812yes—
144C22×C4×C47C2×Q812yes—
145C22×C4×C47C2×Q812yes—
146C22×C4×C47C2×Q812yes—
147C22×C4×C47#4112yes—
148C22×C4×C47#4112yes—
149C22×C4×C47#4112yes—
150C22×C4×C47#4112yes—
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—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
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—22no—
174C22×Dic47C22×C414yes—
175C22×Dic47C22×C414yes—
176C22×Dic47C2×D414yes—
177C22×Dic47C2×D414yes—
178C22×Dic47C2×Q814yes—
179C42×C47—28no—
180C42×C47—28no—
181C42×C47—44no—
182C4⋊Dic47—28no—
183C4⋊Dic47—28no—
184C4⋊Dic47—48no—
185C4⋊Dic47—48no—
186C4⋊Dic47—44no—
187C4⋊Dic47C4⋊C4116yescomplemented
188Dic47⋊C4—216no—
189Dic47⋊C4—48no—
190Dic47⋊C4—48no—
191C4×Dic47—48no—
192C23×C47C23×C411yescharacteristic
193C23×C47C22×D411yescharacteristic
194C23×C47C22×D411yescharacteristic
195C23×C47C22×D411yescharacteristic
196C23×C47C22×Q811yescharacteristic
197C23×C47C22×Q811yescharacteristic
198C23×C47C22×Q811yescharacteristic
199C23×C47C2×#4111yescharacteristic
200C23×C47C2×#4111yescharacteristic
201C23×C47C2×#4111yescharacteristic
202C23×C47C2×#4111yescharacteristic
203C23×C47H(5,𝔽2)11yescharacteristic
204C23×C47H(5,𝔽2)11yescharacteristic
205C23×C472−1+411yescharacteristic
206C23×C472−1+411yescharacteristic
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
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—22no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47C2×C4⋊C414yes—
247C2×C4×C47C4×D414yes—
248C2×C4×C47C4×D414yes—
249C2×C4×C47C4×Q814yes—
250C2×C4×C47C4×Q814yes—
251C2×C4×C47#12114yes—
252C2×C4×C47C22⋊Q814yes—
253C2×C4×C47#12514yes—
254C2×C4×C47C4⋊Q814yes—
255C2×C4×C47C4⋊Q814yes—
256C2×Dic47—24no—
257C2×Dic47—24no—
258C2×Dic47—24no—
259C2×Dic47—24no—
260C2×Dic47—24no—
261C2×Dic47—24no—
262C2×Dic47—24no—
263C2×Dic47—24no—
264C2×Dic47—24no—
265C2×Dic47—24no—
266C2×Dic47—24no—
267C2×Dic47—24no—
268C2×Dic47—42no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—42no—
274C2×Dic47—42no—
275C2×Dic47—42no—
276C2×Dic47—42no—
277C2×Dic47—42no—
278C2×Dic47—42no—
279C2×Dic47—42no—
280C2×Dic47—42no—
281C2×Dic47—42no—
282C2×Dic47—42no—
283C2×Dic47C2×C4⋊C418yes—
284#14005—471nomaximal, Sylow
285C22×C47C22×C4⋊C411yescharacteristic
286C22×C47C2×C4×D411yescharacteristic
287C22×C47C2×C4×D411yescharacteristic
288C22×C47C2×C4×Q811yescharacteristic
289C22×C47C2×C4×Q811yescharacteristic
290C22×C47#52011yescharacteristic
291C22×C47#52011yescharacteristic
292C22×C47C2×#12111yescharacteristic
293C22×C47C2×C22⋊Q811yescharacteristic
294C22×C47C2×#12511yescharacteristic
295C22×C47C2×C4⋊Q811yescharacteristic
296C22×C47C2×C4⋊Q811yescharacteristic
297C22×C47#53211yescharacteristic
298C22×C47#53311yescharacteristic
299C22×C47#53311yescharacteristic
300C22×C47#54011yescharacteristic
301C22×C47#54111yescharacteristic
302C22×C47#54411yescharacteristic
303C22×C47#54411yescharacteristic
304C22×C47D4211yescharacteristic
305C22×C47D4211yescharacteristic
306C22×C47#54611yescharacteristic
307C22×C47#54711yescharacteristic
308C22×C47#54711yescharacteristic
309C22×C47#54811yescharacteristic
310C22×C47D4×Q811yescharacteristic
311C22×C47D4×Q811yescharacteristic
312C22×C47D4×Q811yescharacteristic
313C22×C47#55011yescharacteristic
314C22×C47#55211yescharacteristic
315C22×C47#55311yescharacteristic
316C22×C47#55411yescharacteristic
317C22×C47#55411yescharacteristic
318C22×C47#55711yescharacteristic
319C22×C47Q8211yescharacteristic
320C4×C47—24no—
321C4×C47—24no—
322C4×C47—24no—
323C4×C47—42no—
324C4×C47—42no—
325C4×C47—42no—
326C4×C47#38918yescomplemented
327Dic47—28no—
328Dic47—44no—
329Dic47—44no—
330Dic47—82no—
331C2×#389—471no—
332C2×#389—471no—
333C2×#389—471no—
334C2×#389—472no—
335C2×#384—471no—
336C2×C4×C4⋊C4—471no—
337#1444—472no—
338#1441—472no—
339#1436—472no—
340C4⋊#95—471no—
341C4×#95D4711yescharacteristic
342C2×C47C2×#38911yescharacteristic
343C2×C47C4×C4⋊Q811yescharacteristic
344C2×C47#233011yescharacteristic
345C2×C47D4×C4⋊C411yescharacteristic
346C2×C47Q8×C4⋊C411yescharacteristic
347C2×C47#236011yescharacteristic
348C2×C47#236111yescharacteristic
349C2×C47#242811yescharacteristic
350C2×C47#242911yescharacteristic
351C2×C47#244011yescharacteristic
352C2×C47#244111yescharacteristic
353C2×C47#250611yescharacteristic
354C2×C47#250711yescharacteristic
355C2×C47#255011yescharacteristic
356C2×C47#255111yescharacteristic
357C22×C4⋊C4—471no—
358C22×C4⋊C4—472no—
359C22×C4⋊C4—471no—
360C22×C4⋊C4—471no—
361C22×C4⋊C4—471no—
362C22×C4⋊C4—472no—
363C22×C4⋊C4—472no—
364C22×C4⋊C4—472no—
365C22×C4⋊C4—472no—
366C22×C42—472no—
367C22×C42C2×D4711yescharacteristic
368C22×C42C2×D4711yescharacteristic
369C22×C42C2×D4711yescharacteristic
370#389—478no—
371#389—944no—
372#389—944no—
373#389—948no—
374#384—944no—
375C4×C4⋊C4—944no—
376C2×#95—472no—
377C2×#95—472no—
378C2×#95—472no—
379C2×#95—472no—
380C2×#95—472no—
381C2×#95—472no—
382C2×#95C2×D4711yescharacteristic
383C2×#95C2×D4711yescharacteristic
384C2×#95C2×D4711yescharacteristic
385C2×#95C2×D4711yescharacteristic
386C47#1400511yescharacteristic, complemented, Sylow
387C23×C4—472no—
388C23×C4—472no—
389C23×C4—472no—
390C23×C4—472no—
391C23×C4C22×D4711yescharacteristic
392C23×C4C22×D4711yescharacteristic
393C23×C4C22×D4711yescharacteristic
394C23×C4C22×D4711yescharacteristic
395C23×C4C22×D4711yescharacteristic
396C23×C4C22×D4711yescharacteristic
397C23×C4C22×D4711yescharacteristic
398C2×C4⋊C4—474no—
399C2×C4⋊C4—474no—
400C2×C4⋊C4—474no—
401C2×C4⋊C4—478no—
402C2×C4⋊C4—474no—
403C2×C4⋊C4—474no—
404C2×C4⋊C4—944no—
405C2×C4⋊C4—944no—
406C2×C4⋊C4—942no—
407C2×C4⋊C4—942no—
408C2×C4⋊C4—942no—
409C2×C4⋊C4—942no—
410C2×C4⋊C4—944no—
411C2×C4⋊C4—944no—
412C2×C4⋊C4—944no—
413C2×C4⋊C4—944no—
414C2×C4⋊C4—944no—
415C2×C4⋊C4—944no—
416C2×C4⋊C4—944no—
417C2×C4⋊C4—944no—
418C2×C4⋊C4—942no—
419C2×C4⋊C4—942no—
420C2×C4⋊C4—942no—
421C2×C4⋊C4—1882no—
422C2×C4⋊C4—1882no—
423C2×C4⋊C4—1882no—
424C2×C4⋊C4—1882no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—944no—
433C2×C42—944no—
434C2×C42—1882no—
435C2×C42Dic9414yes—
436C2×C42C4×D4714yes—
437#95—22no—
438#95—22no—
439#95—478no—
440#95—944no—
441#95—944no—
442#95—944no—
443#95—944no—
444#95—1882no—
445#95Dic9414yes—
446#95D18814yes—
447C24C23×D4711yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
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—474no—
479C22×C4—474no—
480C22×C4—474no—
481C22×C4—474no—
482C22×C4—474no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—942no—
493C22×C4—942no—
494C22×C4—942no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4—942no—
498C22×C4—942no—
499C22×C4—942no—
500C22×C4—942no—
501C22×C4—942no—
502C22×C4—942no—
503C22×C4—942no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4C2×Dic9412yes—
507C22×C4C2×Dic9412yes—
508C22×C4C2×Dic9412yes—
509C22×C4C2×Dic9412yes—
510C22×C4C2×Dic9412yes—
511C22×C4C2×Dic9412yes—
512C22×C4C2×C4×D4712yes—
513C22×C4C2×C4×D4712yes—
514C22×C4C2×C4×D4712yes—
515C22×C4C2×D18812yes—
516C22×C4C2×D18812yes—
517C22×C4C2×D18812yes—
518C22×C4#1062535012yes—
519C22×C4#1062535012yes—
520C22×C4#1062535012yes—
521C22×C4D4×D4712yes—
522C22×C4D4×D4712yes—
523C22×C4#1062535212yes—
524C22×C4Q8×D4712yes—
525C4⋊C4—4716no—
526C4⋊C4—948no—
527C4⋊C4—9416no—
528C4⋊C4—948no—
529C4⋊C4—1888no—
530C4⋊C4—1888no—
531C4⋊C4—1888no—
532C4⋊C4—1888no—
533C4⋊C4—1884no—
534C42—28no—
535C42—28no—
536C42—44no—
537C42—1888no—
538C23C22×C4×D4711yescharacteristic
539C23C2×D4×D4711yescharacteristic
540C23C2×D4×D4711yescharacteristic
541C23C22×D18811yescharacteristic
542C23C2×Q8×D4711yescharacteristic
543C23C22×Dic9411yescharacteristic
544C23C22×Dic9411yescharacteristic
545C23C2×#1062535211yescharacteristic
546C23C2×#1062535011yescharacteristic
547C23C2×#1062535011yescharacteristic
548C23C2×#1062535011yescharacteristic
549C23#1309407011yescharacteristic
550C23#1309407011yescharacteristic
551C23#1309407111yescharacteristic
552C23#1309407111yescharacteristic
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—478no—
593C2×C4—944no—
594C2×C4—944no—
595C2×C4—944no—
596C2×C4—944no—
597C2×C4—944no—
598C2×C4—944no—
599C2×C4—944no—
600C2×C4—944no—
601C2×C4—944no—
602C2×C4—944no—
603C2×C4—944no—
604C2×C4—944no—
605C2×C4—1882no—
606C2×C4—1882no—
607C2×C4—1882no—
608C2×C4—1882no—
609C2×C4—1882no—
610C2×C4—1882no—
611C2×C4—1882no—
612C2×C4—1882no—
613C2×C4—1882no—
614C2×C4—1882no—
615C2×C4—1882no—
616C2×C4—1882no—
617C2×C4—1882no—
618C2×C4—1882no—
619C2×C4—1882no—
620C2×C4C4⋊C4×D4714yes—
621C2×C4(C22⋊D47)⋊C414yes—
622C2×C4C4×D18814yes—
623C2×C4C4×Dic9414yes—
624C2×C4C4×Dic9414yes—
625C2×C4#1309399714yes—
626C2×C4#1309400114yes—
627C2×C4#1309401414yes—
628C2×C4#1309402314yes—
629C2×C4#1309402414yes—
630C22C2×C4⋊C4×D4711yescharacteristic
631C22C2×(C22⋊D47)⋊C411yescharacteristic
632C22C2×C4×D18811yescharacteristic
633C22C2×C4×Dic9411yescharacteristic
634C22C2×C4×Dic9411yescharacteristic
635C22#1568960311yescharacteristic
636C22#1568960311yescharacteristic
637C22C2×#1309399711yescharacteristic
638C22C2×#1309400111yescharacteristic
639C22C2×#1309401411yescharacteristic
640C22C2×#1309402311yescharacteristic
641C22C2×#1309402411yescharacteristic
642C22#1568967311yescharacteristic
643C22#1568968011yescharacteristic
644C22#1568968011yescharacteristic
645C22#1568972811yescharacteristic
646C22#1568973511yescharacteristic
647C22#1568975111yescharacteristic
648C22#1568975111yescharacteristic
649C22D4×D18811yescharacteristic
650C22D4×D18811yescharacteristic
651C22#1568976911yescharacteristic
652C22#1568977711yescharacteristic
653C22#1568977811yescharacteristic
654C22#1568978211yescharacteristic
655C22D4×Dic9411yescharacteristic
656C22D4×Dic9411yescharacteristic
657C22Q8×D18811yescharacteristic
658C22#1568979411yescharacteristic
659C22#1568981311yescharacteristic
660C22#1568981911yescharacteristic
661C22#1568983011yescharacteristic
662C22#1568983311yescharacteristic
663C22#1568985111yescharacteristic
664C22Q8×Dic9411yescharacteristic
665C4—24no—
666C4—24no—
667C4—24no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—948no—
672C4—3762no—
673C4—1884no—
674C4—1884no—
675C4#1568902018yescomplemented
676C2C2×#1568902011yescharacteristic
677C2C4×#1309402411yescharacteristic
678C2#2024612911yescharacteristic
679C2C4⋊C4×D18811yescharacteristic
680C2C4⋊C4×Dic9411yescharacteristic
681C2#2024639111yescharacteristic
682C2#2024640211yescharacteristic
683C2#2024697611yescharacteristic
684C2#2024698711yescharacteristic
685C2#2024709011yescharacteristic
686C2#2024710111yescharacteristic
687C2#2024790411yescharacteristic
688C2#2024791511yescharacteristic
689C2#2024840911yescharacteristic
690C2#2024841411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC4×#95×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC4×#95D47
hypocenterC47#14005
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
24. #15689021C4semidirect
187. C4⋊Dic47C4⋊C4semidirect
326. C4×C47#389semidirect
386. C47#14005semidirect
675. C4#15689020semidirect

Maximal subgroups

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

subgroupindex
C2×#156890212
C2×#156890202
C2×#156889932
C2×C4×C4⋊Dic472
#202416522
#202416422
#202416222
#202416182
C4×#95×C472
#1400547