Finite Group Databasebeta

← #26226334

Subgroups — #26226334

Order 12032.

950 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245769C211yesmaximal, characteristic
2#20244004C211yesmaximal, characteristic, complemented
3#20244003C211yesmaximal, characteristic, complemented
4#20244002C211yesmaximal, characteristic, complemented
5#20243999C211yesmaximal, characteristic, complemented
6#20243994C211yesmaximal, characteristic, complemented
7#20243993C211yesmaximal, characteristic, complemented
8#20243991C211yesmaximal, characteristic, complemented
9#20243371C211yesmaximal, characteristic, complemented
10#20243369C211yesmaximal, characteristic, complemented
11#20243297C211yesmaximal, characteristic
12#20243297C211yesmaximal, characteristic
13#20243155C211yesmaximal, characteristic, complemented
14#20243153C211yesmaximal, characteristic, complemented
15C47×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C2×#13093981C2211yescharacteristic
18C2×#13093981C2211yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
20C2×Dic47⋊C8C2211yescharacteristic, complemented
21C2×Dic47⋊C8C2211yescharacteristic, complemented
22C2×C22⋊(C47⋊C8)C2211yescharacteristic
23C2×C22⋊(C47⋊C8)C2211yescharacteristic
24C2×(C2×D47)⋊C8C2211yescharacteristic
25C2×(C2×D47)⋊C8C2211yescharacteristic
26C2×(C2×D47)⋊C8C2211yescharacteristic
27C2×(C2×D47)⋊C8C2211yescharacteristic
28C2×(C2×D47)⋊C8C2211yescharacteristic
29C2×(C2×D47)⋊C8C2211yescharacteristic
30C2×(C2×D47)⋊C8C2211yescharacteristic
31C2×(C2×D47)⋊C8C2211yescharacteristic
32C2×#13093935C2211yescharacteristic, complemented
33C2×#13093934C2211yescharacteristic, complemented
34C2×C8×Dic47C2211yescharacteristic, complemented
35#15688985C411yescharacteristic
36#15688985C411yescharacteristic
37#15688982C411yescharacteristic
38#15688982C411yescharacteristic
39#15688981C411yescharacteristic
40#15688981C411yescharacteristic
41#15688978C411yescharacteristic
42#15688978C411yescharacteristic
43C4×(C2×D47)⋊C4C2211yescharacteristic
44C4×(C2×D47)⋊C4C2211yescharacteristic
45C4×C22⋊Dic47C2211yescharacteristic
46#15688878C2211yescharacteristic, complemented
47#15688878C2211yescharacteristic, complemented
48#15688877C2211yescharacteristic, complemented
49#15688877C2211yescharacteristic, complemented
50#15688877C2211yescharacteristic, complemented
51#15688877C2211yescharacteristic, complemented
52C2×C4⋊C8×C47C2211yescharacteristic, complemented
53C2×C22⋊C8×C47C2211yescharacteristic
54C2×C22⋊C8×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic, complemented
56C4×C22⋊C4×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic, complemented
58C47×#336C2211yescharacteristic, complemented
59C24×D47C2×C411yescharacteristic
60C23×Dic47C2×C411yescharacteristic
61C22×C4×D47—22no—
62C22×C4×D47—22no—
63C22×C4×D47—41no—
64C22×C4×D47—41no—
65C22×C4×D47—41no—
66C22×C4×D47—41no—
67C22×C4×D47C2×C411yescharacteristic
68C22×C4×D47C2×C411yescharacteristic
69C22×C4×D47C2311yescharacteristic
70C22×C4×D47C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13093981—41no—
76#13093981—41no—
77#13093981—41no—
78#13093981—41no—
79C2×Dic47⋊C4C2×C411yescharacteristic
80C2×Dic47⋊C4C2×C411yescharacteristic
81C2×Dic47⋊C4C2×C411yescharacteristic
82C2×Dic47⋊C4C2×C411yescharacteristic
83C2×C22⋊Dic47C2×C411yescharacteristic
84C2×C22⋊Dic47C2×C411yescharacteristic
85C2×(C2×D47)⋊C4C2×C411yescharacteristic
86C2×(C2×D47)⋊C4C2×C411yescharacteristic
87C2×(C2×D47)⋊C4C2×C411yescharacteristic
88C2×(C2×D47)⋊C4C2×C411yescharacteristic
89C2×(C2×D47)⋊C4C2×C411yescharacteristic
90C2×(C2×D47)⋊C4C2×C411yescharacteristic
91C2×(C2×D47)⋊C4C2×C411yescharacteristic
92C2×(C2×D47)⋊C4C2×C411yescharacteristic
93C2×C4×Dic47C2311yescharacteristic
94C2×C4×Dic47C2311yescharacteristic
95C4⋊(C47⋊C8)—41no—
96Dic47⋊C8—41no—
97Dic47⋊C8—41no—
98C22⋊(C47⋊C8)—41no—
99C22⋊(C47⋊C8)—41no—
100(C2×D47)⋊C8—22no—
101(C2×D47)⋊C8—22no—
102(C2×D47)⋊C8—22no—
103(C2×D47)⋊C8—22no—
104(C2×D47)⋊C8—41no—
105(C2×D47)⋊C8—41no—
106(C2×D47)⋊C8—41no—
107(C2×D47)⋊C8—41no—
108#13093935—41no—
109#13093934—41no—
110C8×Dic47—41no—
111C47⋊#95C2×C411yescharacteristic
112C47⋊#95C2×C411yescharacteristic
113C47⋊#95C2×C411yescharacteristic
114C47⋊#95C2×C411yescharacteristic
115C47⋊#95C2×C411yescharacteristic
116C47⋊#95C2×C411yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C22×C8×C47C2311yescharacteristic
119C22×C8×C47C2311yescharacteristic
120C22×C8×C47C2311yescharacteristic
121C22×C8×C47C2311yescharacteristic
122C2×C22⋊C4×C47C2×C411yescharacteristic
123C2×C22⋊C4×C47C2×C411yescharacteristic
124C2×C42×C47C2311yescharacteristic
125C2×C42×C47C2311yescharacteristic
126C4⋊C8×C47—41no—
127C22⋊C8×C47—41no—
128C22⋊C8×C47—41no—
129C4×C8×C47—41no—
130#95×C47C2×C411yescharacteristic
131#95×C47C2×C411yescharacteristic
132C24×C47C22×C411yescharacteristic
133C23×D47—22no—
134C23×D47—22no—
135C23×D47—22no—
136C23×D47—41no—
137C23×D47—41no—
138C23×D47—41no—
139C23×D47—41no—
140C23×D47C22×C411yescharacteristic
141C23×D47C22×C411yescharacteristic
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×C47C22×C411yescharacteristic
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C22×C411yescharacteristic
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C2411yescharacteristic
154C22×Dic47—22no—
155C22×Dic47—41no—
156C22×Dic47—41no—
157C22×Dic47C22×C411yescharacteristic
158C22×Dic47C22×C411yescharacteristic
159C22×Dic47C22×C411yescharacteristic
160C22×Dic47C22×C411yescharacteristic
161C22×Dic47C22×C411yescharacteristic
162C22×Dic47C22×C411yescharacteristic
163C2×C4×D47—21no—
164C2×C4×D47—21no—
165C2×C4×D47—21no—
166C2×C4×D47—21no—
167C2×C4×D47—22no—
168C2×C4×D47—21no—
169C2×C4×D47—21no—
170C2×C4×D47—21no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—21no—
174C2×C4×D47—22no—
175C2×C4×D47—44no—
176C2×C4×D47—44no—
177C2×C4×D47—44no—
178C2×C4×D47—44no—
179C2×C4×D47—41no—
180C2×C4×D47—41no—
181C2×C4×D47—41no—
182C2×C4×D47—41no—
183C2×C4×D47#4112yes—
184C2×C4×D47#4112yes—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C22⋊C4×C47—22no—
198C22⋊C4×C47—41no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C22⋊Dic47—22no—
204C22⋊Dic47—41no—
205(C2×D47)⋊C4—22no—
206(C2×D47)⋊C4—22no—
207(C2×D47)⋊C4—41no—
208(C2×D47)⋊C4—41no—
209(C2×D47)⋊C4—41no—
210(C2×D47)⋊C4—41no—
211(C2×D47)⋊C4—41no—
212(C2×D47)⋊C4—41no—
213Dic47⋊C4—41no—
214Dic47⋊C4—41no—
215Dic47⋊C4—41no—
216Dic47⋊C4—41no—
217C4×Dic47—21no—
218C4×Dic47—21no—
219C4×Dic47—21no—
220C4×Dic47—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47#13112yes—
240C23×C47C23×C411yescharacteristic
241C22×D47—21no—
242C22×D47—21no—
243C22×D47—21no—
244C22×D47—21no—
245C22×D47—21no—
246C22×D47—21no—
247C22×D47—21no—
248C22×D47—21no—
249C22×D47—21no—
250C22×D47—21no—
251C22×D47—21no—
252C22×D47—21no—
253C22×D47—44no—
254C22×D47—44no—
255C22×D47—44no—
256C22×D47—44no—
257C22×D47—44no—
258C22×D47—44no—
259C22×D47—44no—
260C22×D47#11712yes—
261C22×D47#13112yes—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47C2×#4111yescharacteristic
282C2×C4×C47C2×#4111yescharacteristic
283C2×C4×C47H(5,𝔽2)11yescharacteristic
284C2×C4×C47H(5,𝔽2)11yescharacteristic
285C2×C4×C47H(5,𝔽2)11yescharacteristic
286C2×C4×C47H(5,𝔽2)11yescharacteristic
287C2×Dic47—21no—
288C2×Dic47—21no—
289C2×Dic47—21no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—21no—
293C2×Dic47—21no—
294C2×Dic47—21no—
295C2×Dic47—21no—
296C2×Dic47—21no—
297C2×Dic47—21no—
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—21no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—44no—
305C2×Dic47#11712yes—
306C4×D47—22no—
307C4×D47—22no—
308C4×D47—22no—
309C4×D47—22no—
310C4×D47—44no—
311C4×D47—44no—
312C4×D47—41no—
313C4×D47—41no—
314C4×D47—41no—
315C4×D47—41no—
316C8×C47—41no—
317C8×C47—41no—
318C8×C47—41no—
319C8×C47—41no—
320C47⋊C8—41no—
321C47⋊C8—41no—
322C47⋊C8—41no—
323C47⋊C8—41no—
324#21908—471nomaximal, Sylow
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47C2×#11711yescharacteristic
333C22×C47#51811yescharacteristic
334C22×C47#51811yescharacteristic
335C22×C47C2×#13111yescharacteristic
336C22×C47C2×#13111yescharacteristic
337C22×C47#56811yescharacteristic
338C22×C47#56811yescharacteristic
339C2×D47—22no—
340C2×D47—22no—
341C2×D47—22no—
342C2×D47—22no—
343C2×D47—22no—
344C2×D47—22no—
345C2×D47—416no—
346C2×D47—41no—
347C2×D47—41no—
348C2×D47—41no—
349C2×D47—41no—
350C2×D47—41no—
351C2×D47—41no—
352C2×D47—41no—
353C2×D47—41no—
354C4×C47—41no—
355C4×C47—41no—
356C4×C47—41no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47#53811yescharacteristic
360C4×C47#53811yescharacteristic
361C4×C47#53811yescharacteristic
362C4×C47#53811yescharacteristic
363Dic47—22no—
364Dic47—41no—
365Dic47—41no—
366Dic47—41no—
367Dic47—41no—
368Dic47—41no—
369#2280—471no—
370#1924—471no—
371#1924—471no—
372#1924—471no—
373#1924—471no—
374#1923—471no—
375#1923—471no—
376#1923—471no—
377#1923D4711yescharacteristic, complemented
378#1798—471no—
379#1798—471no—
380#1779—471no—
381#1779—471no—
382#1750—471no—
383#1750—471no—
384C2×C47—42no—
385C2×C47#231211yescharacteristic
386C2×C47#292411yescharacteristic
387C2×C47#292411yescharacteristic
388C2×C47#297611yescharacteristic
389C2×C47#297611yescharacteristic
390C2×C47#297711yescharacteristic
391C2×C47#297811yescharacteristic
392D47—42no—
393D47—42no—
394C24×C4—471no—
395C2×#117—471no—
396C2×#117—471no—
397C2×C4⋊C8—471no—
398C2×C4⋊C8—471no—
399C2×C4⋊C8—471no—
400C2×C4⋊C8C2×D4711yescharacteristic, complemented
401C2×C22⋊C8—471no—
402C2×C22⋊C8—471no—
403C2×C22⋊C8—471no—
404C2×C22⋊C8—471no—
405C2×C22⋊C8—471no—
406C2×C22⋊C8—471no—
407C2×C22⋊C8—471no—
408C2×C22⋊C8—471no—
409C2×C22⋊C8—471no—
410C2×C22⋊C8—471no—
411C2×C22⋊C8C2×D4711yescharacteristic
412C2×C22⋊C8C2×D4711yescharacteristic
413C2×#97—471no—
414C2×#97—471no—
415C2×C4×C8—471no—
416C2×C4×C8C2×D4711yescharacteristic, complemented
417#381—471no—
418#381—471no—
419#380—471no—
420#380—471no—
421#380—471no—
422#380—471no—
423#379—471no—
424#379—471no—
425C4×C22⋊C4—471no—
426C4×C22⋊C4—471no—
427C4×C22⋊C4—471no—
428C4×C22⋊C4C2×D4711yescharacteristic
429#336—471no—
430#336—471no—
431#336—471no—
432#336—471no—
433#336—471no—
434#336—471no—
435#336C2×D4711yescharacteristic, complemented
436#336C2×D4711yescharacteristic, complemented
437C47#2190811yescharacteristic, complemented, Sylow
438C25—471no—
439C23×C4—471no—
440C23×C4—471no—
441C23×C4—471no—
442C23×C4—471no—
443C23×C4—471no—
444C23×C4—942no—
445C23×C4—942no—
446C23×C4—1881no—
447C23×C4—1881no—
448C23×C4—1881no—
449C23×C4—1881no—
450C23×C4C22×D4711yescharacteristic
451C22×C8—471no—
452C22×C8—471no—
453C22×C8—471no—
454C22×C8—471no—
455C22×C8C22×D4711yescharacteristic
456C22×C8C22×D4711yescharacteristic
457C22×C8C22×D4711yescharacteristic
458C22×C8C22×D4711yescharacteristic
459#117—1881no—
460#117—1881no—
461#117—1881no—
462#117—1881no—
463C2×C4⋊C4—471no—
464C2×C4⋊C4—471no—
465C2×C4⋊C4—471no—
466C2×C4⋊C4—471no—
467C2×C22⋊C4—471no—
468C2×C22⋊C4—471no—
469C2×C22⋊C4—471no—
470C2×C22⋊C4—471no—
471C2×C22⋊C4—471no—
472C2×C22⋊C4—471no—
473C2×C22⋊C4—471no—
474C2×C22⋊C4—471no—
475C2×C22⋊C4—471no—
476C2×C22⋊C4—471no—
477C2×C22⋊C4C4×D4711yescharacteristic
478C2×C22⋊C4C4×D4711yescharacteristic
479C2×C42—471no—
480C2×C42—471no—
481C2×C42C22×D4711yescharacteristic
482C2×C42C22×D4711yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—1881no—
485C4⋊C8—1881no—
486C4⋊C8—1881no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—942no—
490C22⋊C8—942no—
491C22⋊C8—942no—
492C22⋊C8—942no—
493C22⋊C8—1881no—
494C22⋊C8—1881no—
495C22⋊C8—1881no—
496C22⋊C8—1881no—
497C22⋊C8—1881no—
498C22⋊C8—1881no—
499#97—1881no—
500#97—1881no—
501C4×C8—41no—
502C4×C8—1881no—
503#95—471no—
504#95—471no—
505#95—471no—
506#95—471no—
507#95—471no—
508#95—471no—
509#95C4×D4711yescharacteristic
510#95C4×D4711yescharacteristic
511C24—471no—
512C24—471no—
513C24—942no—
514C24—942no—
515C24—942no—
516C24—1881no—
517C24—1881no—
518C24—1881no—
519C24—1881no—
520C24C2×C4×D4711yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—471no—
528C22×C4—472no—
529C22×C4—472no—
530C22×C4—471no—
531C22×C4—471no—
532C22×C4—471no—
533C22×C4—471no—
534C22×C4—471no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4—941no—
541C22×C4—941no—
542C22×C4—941no—
543C22×C4—941no—
544C22×C4—941no—
545C22×C4—941no—
546C22×C4—941no—
547C22×C4—941no—
548C22×C4—1881no—
549C22×C4—1881no—
550C22×C4—1881no—
551C22×C4—1881no—
552C22×C4—1884no—
553C22×C4—1884no—
554C22×C4—1884no—
555C22×C4—1884no—
556C22×C4—1881no—
557C22×C4—1881no—
558C22×C4C2×C4×D4711yescharacteristic
559C22×C4C2×C4×D4711yescharacteristic
560C22×C4C2×C4×D4711yescharacteristic
561C22×C4C2×C4×D4711yescharacteristic
562C22×C4C2×C4×D4711yescharacteristic
563C22×C4C23×D4711yescharacteristic
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—941no—
577C2×C8—941no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8—941no—
581C2×C8—941no—
582C2×C8—941no—
583C2×C8—941no—
584C2×C8—941no—
585C2×C8—941no—
586C2×C8—941no—
587C2×C8—941no—
588C4⋊C4—1881no—
589C4⋊C4—1881no—
590C4⋊C4—1881no—
591C4⋊C4—1881no—
592C22⋊C4—22no—
593C22⋊C4—41no—
594C22⋊C4—942no—
595C22⋊C4—942no—
596C22⋊C4—942no—
597C22⋊C4—1881no—
598C22⋊C4—1881no—
599C22⋊C4—1881no—
600C22⋊C4—1881no—
601C22⋊C4—1881no—
602C22⋊C4—1881no—
603C22⋊C4—1881no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—941no—
609C42—941no—
610C42—941no—
611C42—941no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—472no—
619C23—472no—
620C23—941no—
621C23—941no—
622C23—941no—
623C23—941no—
624C23—941no—
625C23—941no—
626C23—941no—
627C23—941no—
628C23—941no—
629C23—941no—
630C23—941no—
631C23—941no—
632C23—1884no—
633C23—1884no—
634C23—1884no—
635C23—1884no—
636C23—1884no—
637C23—1884no—
638C23—1884no—
639C23#1309403012yes—
640C23C22×C4×D4711yescharacteristic
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—472no—
661C2×C4—941no—
662C2×C4—941no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—941no—
668C2×C4—941no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—941no—
672C2×C4—941no—
673C2×C4—941no—
674C2×C4—941no—
675C2×C4—941no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—941no—
679C2×C4—941no—
680C2×C4—941no—
681C2×C4—941no—
682C2×C4—1884no—
683C2×C4—1884no—
684C2×C4—1884no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4—1881no—
688C2×C4—1881no—
689C2×C4#41×D4711yescharacteristic
690C2×C4#41×D4711yescharacteristic
691C2×C4#1309406911yescharacteristic
692C2×C4#1309406911yescharacteristic
693C2×C4#1309407011yescharacteristic
694C2×C4#1309407011yescharacteristic
695C8—41no—
696C8—41no—
697C8—41no—
698C8—41no—
699C8—1881no—
700C8—1881no—
701C8—1881no—
702C8—1881no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—942no—
711C22—942no—
712C22—942no—
713C22—942no—
714C22—942no—
715C22—942no—
716C22—18816no—
717C22—1881no—
718C22—1881no—
719C22—1881no—
720C22—1881no—
721C22—1881no—
722C22—1881no—
723C22—1881no—
724C22—1881no—
725C22#117×D4711yescharacteristic
726C22#1568959511yescharacteristic
727C22#1568959511yescharacteristic
728C22#131×D4711yescharacteristic
729C22C2×#1309403011yescharacteristic
730C22#1568988811yescharacteristic
731C22#1568988911yescharacteristic
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—942no—
738C4—1881no—
739C4—1881no—
740C4—1881no—
741C4—1881no—
742C4—1881no—
743C4#1568970511yescharacteristic
744C4#1568970711yescharacteristic
745C4#1568970911yescharacteristic
746C4#1568971211yescharacteristic
747C2—42no—
748C2—1882no—
749C2—1882no—
750C2#2024598211yescharacteristic
751C2#2025204111yescharacteristic
752C2#2025204411yescharacteristic
753C2#2025243011yescharacteristic
754C2#2025243511yescharacteristic
755C2#2025244111yescharacteristic
756C2#2025244511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1923C2
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1923D47
hypocenterC47#21908
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #20244004C2semidirect
3. #20244003C2semidirect
4. #20244002C2semidirect
5. #20243999C2semidirect
6. #20243994C2semidirect
7. #20243993C2semidirect
8. #20243991C2semidirect
9. #20243371C2semidirect
10. #20243369C2semidirect
13. #20243155C2semidirect
14. #20243153C2semidirect
15. C47×#1923C2semidirect
19. C2×C4⋊(C47⋊C8)C22semidirect
20. C2×Dic47⋊C8C22semidirect
21. C2×Dic47⋊C8C22semidirect
32. C2×#13093935C22semidirect
33. C2×#13093934C22semidirect
34. C2×C8×Dic47C22semidirect
46. #15688878C22semidirect
47. #15688878C22semidirect
48. #15688877C22semidirect
49. #15688877C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
52. C2×C4⋊C8×C47C22semidirect
55. C2×C4×C8×C47C22semidirect
57. C47×#336C22semidirect
58. C47×#336C22semidirect
377. #1923D47semidirect
400. C2×C4⋊C8C2×D47semidirect
416. C2×C4×C8C2×D47semidirect
435. #336C2×D47semidirect
436. #336C2×D47semidirect
437. C47#21908semidirect

Maximal subgroups

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

subgroupindex
#202457692
#202440042
#202440032
#202440022
#202439992
#202439942
#202439932
#202439912
#202433712
#202433692
#202432972
#202431552
#202431532
C47×#19232
#2190847