Finite Group Databasebeta

← #26144971

Subgroups — #26144971

Order 12032.

1146 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689006C211yesmaximal, characteristic
2#20241652C211yesmaximal, characteristic
3#20241649C211yesmaximal, characteristic
4#20241646C211yesmaximal, characteristic
5#20241646C211yesmaximal, characteristic
6#20241645C211yesmaximal, characteristic
7#20241640C211yesmaximal, characteristic
8#20241622C211yesmaximal, characteristic
9#20241621C211yesmaximal, characteristic
10#20241620C211yesmaximal, characteristic
11#20241617C211yesmaximal, characteristic
12Dic47⋊#95C211yesmaximal, characteristic
13#20241615C211yesmaximal, characteristic
14#20241614C211yesmaximal, characteristic
15C47×#1436C211yesmaximal, characteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23#15689006C418yescomplemented
24C2×C47⋊#95C2211yescharacteristic
25C2×C47⋊#95C2211yescharacteristic
26C2×C47⋊#95C2211yescharacteristic
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C22×C4⋊C4×C47C2211yescharacteristic
46C22×C42×C47C2211yescharacteristic
47C2×#95×C47C2211yescharacteristic
48C2×#95×C47C2211yescharacteristic
49C2×#95×C47C2211yescharacteristic
50C2×#95×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C2×C4⋊Dic47—22no—
61C2×C4⋊Dic47—22no—
62C2×C4⋊Dic47—22no—
63C2×C4⋊Dic47—41no—
64C2×C4⋊Dic47—41no—
65C2×C4⋊Dic47C2×C414yes—
66C2×Dic47⋊C4—22no—
67C2×Dic47⋊C4—41no—
68C2×Dic47⋊C4—41no—
69C2×Dic47⋊C4—41no—
70C2×Dic47⋊C4—41no—
71C2×Dic47⋊C4—41no—
72C2×Dic47⋊C4—41no—
73C2×Dic47⋊C4—41no—
74C2×Dic47⋊C4C2×C414yes—
75C2×C4×Dic47—22no—
76C2×C4×Dic47—41no—
77C2×C4×Dic47—41no—
78C2×C4×Dic47—41no—
79C2×C4×Dic47—41no—
80C2×C4×Dic47C2×C414yes—
81C47⋊#95—22no—
82C47⋊#95—22no—
83C47⋊#95—22no—
84C47⋊#95—22no—
85C47⋊#95—22no—
86C47⋊#95—22no—
87C47⋊#95—22no—
88C47⋊#95—41no—
89C47⋊#95—41no—
90C47⋊#95—41no—
91C47⋊#95—41no—
92C47⋊#95—41no—
93C47⋊#95—41no—
94C47⋊#95—41no—
95C47⋊#95—41no—
96C47⋊#95—41no—
97C47⋊#95—41no—
98C47⋊#95—41no—
99C47⋊#95C2×C414yes—
100C47⋊#95C2×C414yes—
101C47⋊#95C2×C414yes—
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108C23×C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47—41no—
110C2×C4⋊C4×C47—41no—
111C2×C4⋊C4×C47Q814yes—
112C2×C42×C47—22no—
113C2×C42×C47—41no—
114C2×C42×C47—41no—
115#95×C47—22no—
116#95×C47—22no—
117#95×C47—41no—
118#95×C47—41no—
119#95×C47C2×C414yes—
120C24×C47C2411yescharacteristic
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×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
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—21no—
161C22×C4×C47—21no—
162C22×C4×C47C22×C412yes—
163C22×C4×C47C22×C412yes—
164C22×C4×C47C22×C412yes—
165C22×C4×C47C2×Q812yes—
166C22×C4×C47C2×Q812yes—
167C22×C4×C47C2×Q812yes—
168C22×C4×C47#4112yes—
169C22×C4×C47#4112yes—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47C22×C412yes—
220C22×Dic47C22×C412yes—
221C22×Dic47C22×C412yes—
222C22×Dic47C22×C412yes—
223C22×Dic47#4112yes—
224C22×Dic47#4112yes—
225C22×Dic47#4112yes—
226C4⋊C4×C47—44no—
227C42×C47—44no—
228C4⋊Dic47—28no—
229C4⋊Dic47—44no—
230Dic47⋊C4—44no—
231Dic47⋊C4—44no—
232Dic47⋊C4—44no—
233C4×Dic47—44no—
234C4×Dic47—44no—
235C23×C47C23×C411yescharacteristic
236C23×C47C22×Q811yescharacteristic
237C23×C47C2×#4111yescharacteristic
238C23×C47C2×#4111yescharacteristic
239C23×C47C2×#4111yescharacteristic
240C23×C47C2×#4111yescharacteristic
241C23×C47C2×#4111yescharacteristic
242C23×C47H(5,𝔽2)11yescharacteristic
243C23×C47H(5,𝔽2)11yescharacteristic
244C23×C47H(5,𝔽2)11yescharacteristic
245C23×C47H(5,𝔽2)11yescharacteristic
246C23×C47H(5,𝔽2)11yescharacteristic
247C23×C472−1+411yescharacteristic
248C23×C472−1+411yescharacteristic
249C23×C472−1+411yescharacteristic
250C2×C4×C47—22no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
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×C47C4×Q814yes—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—41no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—41no—
343C2×Dic47—41no—
344C2×Dic47—41no—
345C2×Dic47—41no—
346C2×Dic47—41no—
347C2×Dic47—41no—
348C2×Dic47—41no—
349C2×Dic47—41no—
350C2×Dic47—41no—
351C2×Dic47—41no—
352C2×Dic47—41no—
353C2×Dic47—41no—
354C2×Dic47#11714yes—
355#14464—471nomaximal, Sylow
356C22×C47C2×#11711yescharacteristic
357C22×C47C2×C4×Q811yescharacteristic
358C22×C47C4×#4111yescharacteristic
359C22×C47#51811yescharacteristic
360C22×C47#52011yescharacteristic
361C22×C47#52011yescharacteristic
362C22×C47#52011yescharacteristic
363C22×C47#53811yescharacteristic
364C22×C47#53811yescharacteristic
365C22×C47#53811yescharacteristic
366C22×C47#53811yescharacteristic
367C22×C47#53911yescharacteristic
368C22×C47#53911yescharacteristic
369C22×C47#53911yescharacteristic
370C22×C47#53911yescharacteristic
371C22×C47#54011yescharacteristic
372C22×C47#54211yescharacteristic
373C22×C47#54311yescharacteristic
374C22×C47#54411yescharacteristic
375C22×C47#55211yescharacteristic
376C22×C47#55211yescharacteristic
377C22×C47#55211yescharacteristic
378C22×C47#55311yescharacteristic
379C22×C47#55411yescharacteristic
380C22×C47#55411yescharacteristic
381C22×C47#55511yescharacteristic
382C22×C47#55511yescharacteristic
383C22×C47#55611yescharacteristic
384C22×C47#55711yescharacteristic
385C22×C47#55711yescharacteristic
386C22×C47#55911yescharacteristic
387C22×C47#56011yescharacteristic
388C22×C47#56311yescharacteristic
389C22×C47#56311yescharacteristic
390C22×C47#56311yescharacteristic
391C4×C47—24no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47—42no—
397C4×C47—81no—
398Dic47—24no—
399Dic47—42no—
400Dic47—42no—
401Dic47—42no—
402Dic47—42no—
403Dic47—81no—
404Dic47—81no—
405Dic47—81no—
406C2×#387—471no—
407#1444—471no—
408#1443—471no—
409#1442—471no—
410#1442—471no—
411#1442—471no—
412#1441—471no—
413#1436—471no—
414#1436—471no—
415#1436—471no—
416#1436D4711yescharacteristic
417C4⋊#95—471no—
418C4⋊#95—471no—
419#1434—471no—
420#1434—471no—
421C2×C47#231811yescharacteristic
422C2×C47#232911yescharacteristic
423C2×C47#233511yescharacteristic
424C2×C47#234611yescharacteristic
425C2×C47#235511yescharacteristic
426C2×C47#237011yescharacteristic
427C2×C47#238311yescharacteristic
428C2×C47#277111yescharacteristic
429C2×C47#277411yescharacteristic
430C2×C47#277511yescharacteristic
431C2×C47#278411yescharacteristic
432C2×C47#278711yescharacteristic
433C2×C47#279111yescharacteristic
434C2×C47#280311yescharacteristic
435C2×C47#280911yescharacteristic
436C22×C4⋊C4—471no—
437C22×C4⋊C4—471no—
438C22×C4⋊C4—471no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4C2×D4711yescharacteristic
442C22×C42—471no—
443C22×C42—471no—
444C22×C42C2×D4711yescharacteristic
445#387—478no—
446C2×#95—471no—
447C2×#95—471no—
448C2×#95—471no—
449C2×#95—471no—
450C2×#95—471no—
451C2×#95—471no—
452C2×#95—471no—
453C2×#95—471no—
454C2×#95—471no—
455C2×#95—471no—
456C2×#95—471no—
457C2×#95—471no—
458C2×#95—471no—
459C2×#95—471no—
460C2×#95—471no—
461C2×#95—471no—
462C2×#95—471no—
463C2×#95—471no—
464C2×#95—471no—
465C2×#95—471no—
466C2×#95—471no—
467C2×#95C2×D4711yescharacteristic
468C2×#95C2×D4711yescharacteristic
469C2×#95C2×D4711yescharacteristic
470C2×#95C2×D4711yescharacteristic
471C2×#95C2×D4711yescharacteristic
472C47#1446411yescharacteristic, complemented, Sylow
473C23×C4—471no—
474C23×C4—471no—
475C23×C4—471no—
476C23×C4—471no—
477C23×C4—471no—
478C23×C4—471no—
479C23×C4—471no—
480C23×C4—471no—
481C23×C4C22×D4711yescharacteristic
482C23×C4C22×D4711yescharacteristic
483C23×C4C22×D4711yescharacteristic
484C23×C4C22×D4711yescharacteristic
485C23×C4C22×D4711yescharacteristic
486C23×C4C22×D4711yescharacteristic
487C23×C4C22×D4711yescharacteristic
488C2×C4⋊C4—41no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—474no—
492C2×C4⋊C4—942no—
493C2×C4⋊C4—942no—
494C2×C4⋊C4—942no—
495C2×C4⋊C4—942no—
496C2×C4⋊C4—1881no—
497C2×C4⋊C4—1881no—
498C2×C4⋊C4—1881no—
499C2×C4⋊C4—1881no—
500C2×C4⋊C4—1881no—
501C2×C4⋊C4—1881no—
502C2×C4⋊C4—1881no—
503C2×C4⋊C4—1881no—
504C2×C4⋊C4—1881no—
505C2×C4⋊C4Dic9414yes—
506C2×C42—22no—
507C2×C42—41no—
508C2×C42—41no—
509C2×C42—474no—
510C2×C42—942no—
511C2×C42—1881no—
512C2×C42—1881no—
513C2×C42—1881no—
514C2×C42—1881no—
515#95—22no—
516#95—22no—
517#95—41no—
518#95—41no—
519#95—474no—
520#95—474no—
521#95—474no—
522#95—942no—
523#95—942no—
524#95—942no—
525#95—942no—
526#95—942no—
527#95—942no—
528#95—942no—
529#95—1881no—
530#95—1881no—
531#95—1881no—
532#95—1881no—
533#95—1881no—
534#95—1881no—
535#95—1881no—
536#95—1881no—
537#95—1881no—
538#95—1881no—
539#95—1881no—
540#95C4×D4714yes—
541C24C23×D4711yescharacteristic
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—472no—
584C22×C4—472no—
585C22×C4—472no—
586C22×C4—472no—
587C22×C4—472no—
588C22×C4—472no—
589C22×C4—472no—
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—941no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—941no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—941no—
624C22×C4—941no—
625C22×C4—941no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4—941no—
633C22×C4—941no—
634C22×C4—941no—
635C22×C4—941no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—941no—
639C22×C4C2×Dic9412yes—
640C22×C4C2×Dic9412yes—
641C22×C4C2×Dic9412yes—
642C22×C4C2×C4×D4712yes—
643C22×C4C2×C4×D4712yes—
644C22×C4C2×C4×D4712yes—
645C22×C4#1062535012yes—
646C22×C4#1062535212yes—
647C4⋊C4—44no—
648C4⋊C4—948no—
649C4⋊C4—1884no—
650C4⋊C4—1884no—
651C4⋊C4—1884no—
652C4⋊C4—1884no—
653C42—44no—
654C42—1884no—
655C42—1884no—
656C23C22×C4×D4711yescharacteristic
657C23C22×Dic9411yescharacteristic
658C23#41×D4711yescharacteristic
659C23#41×D4711yescharacteristic
660C23#41×D4711yescharacteristic
661C23C2×#1062535211yescharacteristic
662C23C2×#1062535011yescharacteristic
663C23#1309406911yescharacteristic
664C23#1309406911yescharacteristic
665C23#1309406911yescharacteristic
666C23#1309407011yescharacteristic
667C23#1309407011yescharacteristic
668C23#1309407111yescharacteristic
669C23#1309407211yescharacteristic
670C23#1309407211yescharacteristic
671C2×C4—22no—
672C2×C4—22no—
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—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
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—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—474no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1881no—
741C2×C4—1881no—
742C2×C4—1881no—
743C2×C4—1881no—
744C2×C4—1881no—
745C2×C4—1881no—
746C2×C4—1881no—
747C2×C4—1881no—
748C2×C4—1881no—
749C2×C4—1881no—
750C2×C4—1881no—
751C2×C4—1881no—
752C2×C4—1881no—
753C2×C4—1881no—
754C2×C4—1881no—
755C2×C4—1881no—
756C2×C4—1881no—
757C2×C4—1881no—
758C2×C4—1881no—
759C2×C4—1881no—
760C2×C4—1881no—
761C2×C4—1881no—
762C2×C4—1881no—
763C2×C4—1881no—
764C2×C4—1881no—
765C2×C4—1881no—
766C2×C4—1881no—
767C2×C4—1881no—
768C2×C4—1881no—
769C2×C4—1881no—
770C2×C4—1881no—
771C2×C4—1881no—
772C2×C4—1881no—
773C2×C4—1881no—
774C2×C4—1881no—
775C2×C4C4×Dic9414yes—
776C22#117×D4711yescharacteristic
777C22C2×C4×Dic9411yescharacteristic
778C22C4×#1062535211yescharacteristic
779C22#1568959511yescharacteristic
780C22#1568960211yescharacteristic
781C22#1568960411yescharacteristic
782C22#1568960511yescharacteristic
783C22#1568970611yescharacteristic
784C22#1568970811yescharacteristic
785C22#1568970911yescharacteristic
786C22#1568971211yescharacteristic
787C22#1568971511yescharacteristic
788C22#1568971911yescharacteristic
789C22#1568971911yescharacteristic
790C22#1568972111yescharacteristic
791C22#1568972511yescharacteristic
792C22#1568974611yescharacteristic
793C22#1568974911yescharacteristic
794C22#1568975111yescharacteristic
795C22#1568980811yescharacteristic
796C22#1568980911yescharacteristic
797C22#1568981011yescharacteristic
798C22#1568981711yescharacteristic
799C22#1568983011yescharacteristic
800C22#1568983211yescharacteristic
801C22#1568983511yescharacteristic
802C22#1568983711yescharacteristic
803C22#1568984511yescharacteristic
804C22#1568984911yescharacteristic
805C22#1568984911yescharacteristic
806C22#1568985611yescharacteristic
807C22#1568986111yescharacteristic
808C22#1568987211yescharacteristic
809C22#1568987411yescharacteristic
810C22#1568987711yescharacteristic
811C4—24no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—81no—
818C4—944no—
819C4—3761no—
820C4—3761no—
821C4—3761no—
822C4—1882no—
823C4—1882no—
824C4—1882no—
825C4—1882no—
826C2#2024602011yescharacteristic
827C2#2024611611yescharacteristic
828C2#2024617311yescharacteristic
829C2#2024627011yescharacteristic
830C2#2024634611yescharacteristic
831C2#2024648611yescharacteristic
832C2#2024657911yescharacteristic
833C2#2025090611yescharacteristic
834C2#2025095011yescharacteristic
835C2#2025096111yescharacteristic
836C2#2025108611yescharacteristic
837C2#2025112211yescharacteristic
838C2#2025117611yescharacteristic
839C2#2025131911yescharacteristic
840C2#2025137411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1436C2
socle, prime radical, cosocleC24×C47C24
hypercenter#1436D47
hypocenterC47#14464
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
23. #15689006C4semidirect
472. C47#14464semidirect

Maximal subgroups

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

subgroupindex
C2×#156890062
#202416522
#202416492
#202416462
#202416452
#202416402
#202416222
#202416212
#202416202
#202416172
Dic47⋊#952
#202416152
#202416142
C47×#14362
#1446447