Finite Group Databasebeta

← #26140009

Subgroups — #26140009

Order 12032.

1586 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×#15689022C211yesmaximal, characteristic
2C2×#15689022C211yesmaximal, characteristic
3C2×#15689021C212yesmaximal
4C2×#15689021C211yesmaximal, characteristic
5C2×C4×Dic47⋊C4C211yesmaximal, characteristic
6#20241644C212yesmaximal
7#20241640C212yesmaximal
8#20241621C212yesmaximal
9#20241617C211yesmaximal, characteristic
10#20241617C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4⋊Dic47C2212yes—
16C22×Dic47⋊C4C2212yes—
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21#15689022—24no—
22#15689022C418yescomplemented
23#15689021—28no—
24#15689021—24no—
25C4×Dic47⋊C4—24no—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C42×C47C2212yes—
38C22×C42×C47C2211yescharacteristic
39C4×C4⋊C4×C47—24no—
40C2×#95×C47C2212yes—
41C23×Dic47C2312yes—
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2312yes—
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2311yescharacteristic
46C23×Dic47C2311yescharacteristic
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—24no—
50C2×C4⋊Dic47—24no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—24no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47—24no—
56C2×C4⋊Dic47—42no—
57C2×C4⋊Dic47C2×C414yes—
58C2×C4⋊Dic47C2×C418yes—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4—22no—
62C2×Dic47⋊C4—22no—
63C2×Dic47⋊C4—22no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4D414yes—
68C2×C4×Dic47—22no—
69C2×C4×Dic47—22no—
70C2×C4×Dic47—22no—
71C2×C4×Dic47—22no—
72C2×C4×Dic47—22no—
73C2×C4×Dic47C2×C414yes—
74C47⋊#95—22no—
75C47⋊#95—22no—
76C47⋊#95—24no—
77C47⋊#95—24no—
78C47⋊#95—24no—
79C47⋊#95—24no—
80C47⋊#95—24no—
81C47⋊#95—42no—
82C47⋊#95C2×C418yes—
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2312yes—
85C23×C4×C47C2312yes—
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C2×C4⋊C4×C47—22no—
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47C2×C414yes—
91C2×C4⋊C4×C47D414yes—
92C2×C4⋊C4×C47Q814yes—
93C2×C4⋊C4×C47Q814yes—
94C2×C42×C47—22no—
95C2×C42×C47—22no—
96C2×C42×C47—24no—
97C2×C42×C47—24no—
98C2×C42×C47—42no—
99C2×C42×C47D414yes—
100#95×C47—24no—
101C24×C47C2411yescharacteristic
102C22×C4×C47—21no—
103C22×C4×C47—22no—
104C22×C4×C47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—21no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—21no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—22no—
122C22×C4×C47C22×C414yes—
123C22×C4×C47C22×C412yes—
124C22×C4×C47C2×D412yes—
125C22×C4×C47C2×D414yes—
126C22×C4×C47C2×D412yes—
127C22×C4×C47C2×D412yes—
128C22×C4×C47C2×D412yes—
129C22×C4×C47C2×D412yes—
130C22×C4×C47C2×Q814yes—
131C22×C4×C47C2×Q814yes—
132C22×C4×C47C2×Q812yes—
133C22×C4×C47C2×Q812yes—
134C22×C4×C47#4112yes—
135C22×C4×C47#4112yes—
136C22×C4×C47#4112yes—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—21no—
148C22×Dic47—22no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—22no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—22no—
156C22×Dic47—22no—
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—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47C22×C412yes—
173C22×Dic47C22×C414yes—
174C22×Dic47C22×C412yes—
175C22×Dic47C2×D412yes—
176C22×Dic47C2×D412yes—
177C22×Dic47#4112yes—
178C22×Dic47#4112yes—
179C4⋊C4×C47—28no—
180C4⋊C4×C47C4⋊C4116yescomplemented
181C42×C47—28no—
182C42×C47—48no—
183C4⋊Dic47—28no—
184C4⋊Dic47—216no—
185C4⋊Dic47—48no—
186C4⋊Dic47—44no—
187Dic47⋊C4—28no—
188Dic47⋊C4—28no—
189Dic47⋊C4—48no—
190C4×Dic47—28no—
191C4×Dic47—44no—
192C23×C47C23×C411yescharacteristic
193C23×C47C22×D411yescharacteristic
194C23×C47C22×D411yescharacteristic
195C23×C47C22×D411yescharacteristic
196C23×C47C22×Q811yescharacteristic
197C23×C47C22×Q811yescharacteristic
198C23×C47C2×#4111yescharacteristic
199C23×C47C2×#4111yescharacteristic
200C23×C47C2×#4111yescharacteristic
201C23×C47C2×#4111yescharacteristic
202C23×C47C2×#4111yescharacteristic
203C23×C47H(5,𝔽2)11yescharacteristic
204C23×C472−1+411yescharacteristic
205C23×C472−1+411yescharacteristic
206C23×C472−1+411yescharacteristic
207C2×C4×C47—24no—
208C2×C4×C47—24no—
209C2×C4×C47—22no—
210C2×C4×C47—22no—
211C2×C4×C47—24no—
212C2×C4×C47—22no—
213C2×C4×C47—24no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—24no—
217C2×C4×C47—22no—
218C2×C4×C47—24no—
219C2×C4×C47—22no—
220C2×C4×C47—24no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—42no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47C2×C4⋊C418yes—
234C2×C4×C47C2×C4⋊C414yes—
235C2×C4×C47C4×D414yes—
236C2×C4×C47C4×Q814yes—
237C2×C4×C47#12114yes—
238C2×C4×C47#12114yes—
239C2×C4×C47C22⋊Q814yes—
240C2×C4×C47#12514yes—
241C2×C4×C47C4⋊Q814yes—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—42no—
263C2×Dic47—42no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—41no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—41no—
276C2×Dic47—42no—
277C2×Dic47—42no—
278C2×Dic47—42no—
279C2×Dic47—42no—
280C2×Dic47—42no—
281C2×Dic47—42no—
282C2×Dic47—42no—
283C2×Dic47C4×D414yes—
284#14046—471nomaximal, Sylow
285C22×C47C22×C4⋊C411yescharacteristic
286C22×C47C2×C4×D411yescharacteristic
287C22×C47C2×C4×D411yescharacteristic
288C22×C47C2×C4×Q811yescharacteristic
289C22×C47C4×#4111yescharacteristic
290C22×C47#51911yescharacteristic
291C22×C47#52011yescharacteristic
292C22×C47C2×#12111yescharacteristic
293C22×C47C2×#12111yescharacteristic
294C22×C47C2×C22⋊Q811yescharacteristic
295C22×C47#52511yescharacteristic
296C22×C47C2×#12511yescharacteristic
297C22×C47#52911yescharacteristic
298C22×C47C2×C4⋊Q811yescharacteristic
299C22×C47#53211yescharacteristic
300C22×C47#53611yescharacteristic
301C22×C47#53711yescharacteristic
302C22×C47#54111yescharacteristic
303C22×C47#54211yescharacteristic
304C22×C47D4211yescharacteristic
305C22×C47#54711yescharacteristic
306C22×C47#54711yescharacteristic
307C22×C47#54811yescharacteristic
308C22×C47#54811yescharacteristic
309C22×C47D4×Q811yescharacteristic
310C22×C47D4×Q811yescharacteristic
311C22×C47#55211yescharacteristic
312C22×C47#55311yescharacteristic
313C22×C47#55411yescharacteristic
314C22×C47#55411yescharacteristic
315C22×C47#55611yescharacteristic
316C22×C47#55711yescharacteristic
317C22×C47#55711yescharacteristic
318C22×C47#55711yescharacteristic
319C22×C47#55711yescharacteristic
320C4×C47—28no—
321C4×C47—24no—
322C4×C47—42no—
323C4×C47—44no—
324C4×C47#38918yescomplemented
325Dic47—24no—
326Dic47—42no—
327Dic47—42no—
328Dic47—42no—
329Dic47—44no—
330Dic47—82no—
331C2×#389—472no—
332C2×#389—471no—
333C2×#389—471no—
334C2×#389—471no—
335C2×C4×C4⋊C4—471no—
336C2×C4×C4⋊C4D4711yescharacteristic
337#1442—472no—
338#1441—472no—
339#1436—472no—
340C4⋊#95—471no—
341C4⋊#95—471no—
342C2×C47C2×#38911yescharacteristic
343C2×C47C4×#12111yescharacteristic
344C2×C47#232311yescharacteristic
345C2×C47D4×C4⋊C411yescharacteristic
346C2×C47#235111yescharacteristic
347C2×C47#236511yescharacteristic
348C2×C47#237011yescharacteristic
349C2×C47#241511yescharacteristic
350C2×C47#241611yescharacteristic
351C2×C47#245211yescharacteristic
352C2×C47#245311yescharacteristic
353C2×C47#250611yescharacteristic
354C2×C47#250911yescharacteristic
355C2×C47#254611yescharacteristic
356C2×C47#258411yescharacteristic
357C22×C4⋊C4—471no—
358C22×C4⋊C4—471no—
359C22×C4⋊C4—472no—
360C22×C4⋊C4—472no—
361C22×C4⋊C4—471no—
362C22×C4⋊C4—471no—
363C22×C4⋊C4—472no—
364C22×C4⋊C4C2×D4711yescharacteristic
365C22×C4⋊C4C2×D4711yescharacteristic
366C22×C42—471no—
367C22×C42—471no—
368C22×C42C2×D4712yes—
369C22×C42C2×D4711yescharacteristic
370#389—478no—
371#389—948no—
372#389—944no—
373#389—944no—
374C4×C4⋊C4—24no—
375C4×C4⋊C4—944no—
376C2×#95—472no—
377C2×#95—472no—
378C2×#95—472no—
379C2×#95—472no—
380C2×#95—471no—
381C2×#95—472no—
382C2×#95—472no—
383C2×#95—471no—
384C2×#95—472no—
385C2×#95C2×D4712yes—
386C47#1404611yescharacteristic, complemented, Sylow
387C23×C4—471no—
388C23×C4—472no—
389C23×C4—471no—
390C23×C4—471no—
391C23×C4—471no—
392C23×C4—472no—
393C23×C4C22×D4712yes—
394C23×C4C22×D4711yescharacteristic
395C23×C4C22×D4712yes—
396C23×C4C22×D4711yescharacteristic
397C23×C4C22×D4711yescharacteristic
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—478no—
401C2×C4⋊C4—474no—
402C2×C4⋊C4—474no—
403C2×C4⋊C4—942no—
404C2×C4⋊C4—942no—
405C2×C4⋊C4—944no—
406C2×C4⋊C4—944no—
407C2×C4⋊C4—942no—
408C2×C4⋊C4—942no—
409C2×C4⋊C4—942no—
410C2×C4⋊C4—942no—
411C2×C4⋊C4—942no—
412C2×C4⋊C4—944no—
413C2×C4⋊C4—944no—
414C2×C4⋊C4—942no—
415C2×C4⋊C4—942no—
416C2×C4⋊C4—944no—
417C2×C4⋊C4—944no—
418C2×C4⋊C4—944no—
419C2×C4⋊C4—942no—
420C2×C4⋊C4—1882no—
421C2×C4⋊C4Dic9414yes—
422C2×C4⋊C4Dic9414yes—
423C2×C4⋊C4C4×D4714yes—
424C2×C4⋊C4C22⋊D4714yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—42no—
430C2×C42—474no—
431C2×C42—942no—
432C2×C42—942no—
433C2×C42—942no—
434C2×C42—942no—
435C2×C42—942no—
436C2×C42D18814yes—
437#95—24no—
438#95—478no—
439#95—944no—
440#95—944no—
441#95—944no—
442#95—942no—
443#95—942no—
444#95—944no—
445#95—944no—
446#95—1882no—
447C24C23×D4711yescharacteristic
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—472no—
469C22×C4—472no—
470C22×C4—472no—
471C22×C4—472no—
472C22×C4—474no—
473C22×C4—472no—
474C22×C4—472no—
475C22×C4—941no—
476C22×C4—941no—
477C22×C4—941no—
478C22×C4—941no—
479C22×C4—942no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4—941no—
484C22×C4—941no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—941no—
491C22×C4—941no—
492C22×C4—942no—
493C22×C4—942no—
494C22×C4—941no—
495C22×C4—941no—
496C22×C4—941no—
497C22×C4—941no—
498C22×C4—941no—
499C22×C4—941no—
500C22×C4—941no—
501C22×C4—941no—
502C22×C4—941no—
503C22×C4—942no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4C2×Dic9414yes—
511C22×C4C2×Dic9414yes—
512C22×C4C2×Dic9412yes—
513C22×C4C2×Dic9412yes—
514C22×C4C2×C4×D4714yes—
515C22×C4C2×C4×D4712yes—
516C22×C4C2×D18812yes—
517C22×C4C2×D18812yes—
518C22×C4C2×D18812yes—
519C22×C4#1062535012yes—
520C22×C4#1062535012yes—
521C22×C4D4×D4712yes—
522C22×C4#1062535412yes—
523C22×C4C2×C22⋊D4714yes—
524C22×C4C2×C22⋊D4712yes—
525C4⋊C4—28no—
526C4⋊C4—9416no—
527C4⋊C4—948no—
528C4⋊C4—948no—
529C4⋊C4—948no—
530C4⋊C4—1888no—
531C4⋊C4—1884no—
532C4⋊C4—1888no—
533C4⋊C4Dic47⋊C4116yescomplemented
534C42—28no—
535C42—48no—
536C42—948no—
537C42—1884no—
538C23C22×C4×D4711yescharacteristic
539C23C2×D4×D4711yescharacteristic
540C23C22×C22⋊D4711yescharacteristic
541C23C22×D18811yescharacteristic
542C23C22×Dic9411yescharacteristic
543C23C22×Dic9411yescharacteristic
544C23#41×D4711yescharacteristic
545C23#41×D4711yescharacteristic
546C23C2×#1062535011yescharacteristic
547C23C2×#1062535011yescharacteristic
548C23C2×#1062535411yescharacteristic
549C23#1309406911yescharacteristic
550C23#1309407111yescharacteristic
551C23#1309407111yescharacteristic
552C23#1309407211yescharacteristic
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—474no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—942no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—942no—
587C2×C4—942no—
588C2×C4—942no—
589C2×C4—942no—
590C2×C4—944no—
591C2×C4—942no—
592C2×C4—944no—
593C2×C4—944no—
594C2×C4—942no—
595C2×C4—942no—
596C2×C4—942no—
597C2×C4—942no—
598C2×C4—1882no—
599C2×C4—1882no—
600C2×C4—1882no—
601C2×C4—1882no—
602C2×C4—1882no—
603C2×C4—1882no—
604C2×C4—1882no—
605C2×C4—1881no—
606C2×C4—1881no—
607C2×C4—1881no—
608C2×C4—1881no—
609C2×C4—1881no—
610C2×C4—1881no—
611C2×C4—1881no—
612C2×C4—1881no—
613C2×C4—1882no—
614C2×C4—1882no—
615C2×C4—1882no—
616C2×C4—1882no—
617C2×C4—1881no—
618C2×C4—1881no—
619C2×C4—1881no—
620C2×C4—1881no—
621C2×C4C2×Dic47⋊C418yes—
622C2×C4C2×Dic47⋊C414yes—
623C2×C4C4×D18814yes—
624C2×C4C4×Dic9414yes—
625C2×C4#1309399814yes—
626C2×C4#1309399914yes—
627C2×C4#1309400314yes—
628C2×C4#1309401614yes—
629C2×C4#1309402414yes—
630C22C22×Dic47⋊C411yescharacteristic
631C22C4×D4×D4711yescharacteristic
632C22C2×C4×D18811yescharacteristic
633C22C2×C4×Dic9411yescharacteristic
634C22C4×#1062535411yescharacteristic
635C22#1568959911yescharacteristic
636C22#1568960211yescharacteristic
637C22C2×#1309399811yescharacteristic
638C22C2×#1309399911yescharacteristic
639C22C2×#1309400311yescharacteristic
640C22#1568963511yescharacteristic
641C22C2×#1309401611yescharacteristic
642C22#1568966011yescharacteristic
643C22C2×#1309402411yescharacteristic
644C22#1568967011yescharacteristic
645C22#1568969911yescharacteristic
646C22#1568970411yescharacteristic
647C22#1568973111yescharacteristic
648C22#1568973811yescharacteristic
649C22D4×C22⋊D4711yescharacteristic
650C22#1568977211yescharacteristic
651C22#1568977411yescharacteristic
652C22#1568978011yescharacteristic
653C22#1568978411yescharacteristic
654C22D4×Dic9411yescharacteristic
655C22D4×Dic9411yescharacteristic
656C22#1568981211yescharacteristic
657C22#1568982111yescharacteristic
658C22#1568983211yescharacteristic
659C22#1568983211yescharacteristic
660C22#1568984111yescharacteristic
661C22#1568984911yescharacteristic
662C22#1568984911yescharacteristic
663C22#1568985211yescharacteristic
664C22#1568985211yescharacteristic
665C4—28no—
666C4—24no—
667C4—42no—
668C4—44no—
669C4—944no—
670C4—3762no—
671C4—1882no—
672C4—1882no—
673C4—1882no—
674C4—1884no—
675C4#1568902118yescomplemented
676C2C2×#1568902111yescharacteristic
677C2C4×#1309399911yescharacteristic
678C2#2024607111yescharacteristic
679C2D4×Dic47⋊C411yescharacteristic
680C2#2024630611yescharacteristic
681C2#2024644711yescharacteristic
682C2#2024648011yescharacteristic
683C2#2024681111yescharacteristic
684C2#2024682211yescharacteristic
685C2#2024723211yescharacteristic
686C2#2024724311yescharacteristic
687C2#2024789811yescharacteristic
688C2#2024793111yescharacteristic
689C2#2024837611yescharacteristic
690C2#2024877111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C4⋊C4×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47#14046
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #15689022C4semidirect
180. C4⋊C4×C47C4⋊C4semidirect
324. C4×C47#389semidirect
386. C47#14046semidirect
533. C4⋊C4Dic47⋊C4semidirect
675. C4#15689021semidirect

Maximal subgroups

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

subgroupindex
C2×#156890222
C2×#156890212
C2×C4×Dic47⋊C42
#202416442
#202416402
#202416212
#202416172
C2×C4×C4⋊C4×C472
#1404647