Finite Group Databasebeta

← #26140809

Subgroups — #26140809

Order 12032.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094019C211yesmaximal, characteristic
2C2×#15689006C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
4#20241654C211yesmaximal, characteristic, complemented
5#20241641C211yesmaximal, characteristic, complemented
6#20241634C211yesmaximal, characteristic
7#20241632C211yesmaximal, characteristic
8#20241626C211yesmaximal, characteristic
9#20241624C211yesmaximal, characteristic
10#20241624C211yesmaximal, characteristic
11#20241624C211yesmaximal, characteristic
12Dic47⋊#95C211yesmaximal, characteristic, complemented
13#20241613C211yesmaximal, characteristic, complemented
14#95×Dic47C211yesmaximal, characteristic, complemented
15C47×#1436C211yesmaximal, characteristic, complemented
16C2×#13094019—24no—
17C2×#13094019—24no—
18C2×#13094019C418yescomplemented
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34#15689006—24no—
35C4×C4⋊Dic47—24no—
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
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C22×C4⋊C4×C47C2211yescharacteristic
50C22×C42×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C24×D47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64#13094019—232no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47C2×C414yes—
69C2×C4⋊Dic47D414yes—
70C2×C4⋊Dic47D414yes—
71C2×Dic47⋊C4—22no—
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4—22no—
74C2×Dic47⋊C4—22no—
75C2×Dic47⋊C4—41no—
76C2×Dic47⋊C4C2×C414yes—
77C2×(C2×D47)⋊C4—22no—
78C2×(C2×D47)⋊C4—22no—
79C2×(C2×D47)⋊C4—22no—
80C2×(C2×D47)⋊C4—22no—
81C2×(C2×D47)⋊C4—22no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—22no—
85C2×(C2×D47)⋊C4—22no—
86C2×(C2×D47)⋊C4—22no—
87C2×(C2×D47)⋊C4—22no—
88C2×(C2×D47)⋊C4—22no—
89C2×(C2×D47)⋊C4—22no—
90C2×(C2×D47)⋊C4—22no—
91C2×(C2×D47)⋊C4—41no—
92C2×(C2×D47)⋊C4—41no—
93C2×(C2×D47)⋊C4—41no—
94C2×(C2×D47)⋊C4—41no—
95C2×(C2×D47)⋊C4C2×C414yes—
96C2×(C2×D47)⋊C4C2×C414yes—
97C2×(C2×D47)⋊C4C2×C414yes—
98C2×C4×Dic47—22no—
99C2×C4×Dic47—22no—
100C2×C4×Dic47—22no—
101C2×C4×Dic47—22no—
102C2×C4×Dic47—22no—
103C2×C4×Dic47—22no—
104C2×C4×Dic47—22no—
105C2×C4×Dic47—22no—
106C2×C4×Dic47—41no—
107C2×C4×Dic47—41no—
108C2×C4×Dic47—41no—
109C2×C4×Dic47C2×C414yes—
110C47⋊#95—22no—
111C47⋊#95—22no—
112C47⋊#95—22no—
113C47⋊#95—22no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95—22no—
118C47⋊#95—22no—
119C47⋊#95—41no—
120C47⋊#95—41no—
121C47⋊#95—41no—
122C47⋊#95—41no—
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47—22no—
131C2×C4⋊C4×C47—22no—
132C2×C4⋊C4×C47C2×C414yes—
133C2×C42×C47—22no—
134C2×C42×C47—22no—
135C2×C42×C47—22no—
136#95×C47—22no—
137#95×C47—22no—
138#95×C47—22no—
139#95×C47—22no—
140#95×C47—22no—
141C24×C47C2411yescharacteristic
142C23×D47—21no—
143C23×D47—21no—
144C23×D47—21no—
145C23×D47—21no—
146C23×D47—21no—
147C23×D47—21no—
148C23×D47—21no—
149C23×D47—21no—
150C23×D47—21no—
151C23×D47—21no—
152C23×D47—21no—
153C23×D47—21no—
154C23×D47—21no—
155C23×D47—21no—
156C23×D47C22×C412yes—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47C22×C412yes—
197C22×C4×C47C22×C412yes—
198C22×C4×C47C22×C412yes—
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2×D412yes—
201C22×C4×C47#4112yes—
202C22×C4×C47#4112yes—
203C22×C4×C47#4112yes—
204C22×C4×C47#4112yes—
205C22×C4×C47#4112yes—
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×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47C22×C412yes—
246C22×Dic47C22×C412yes—
247C22×Dic47C22×C412yes—
248C22×Dic47C2×D412yes—
249C22×Dic47C2×D412yes—
250C22×Dic47C2×D412yes—
251C22×Dic47C2×D412yes—
252C22×Dic47#4112yes—
253C22×Dic47#4112yes—
254C22×Dic47#4112yes—
255C4⋊C4×C47—28no—
256C42×C47—28no—
257(C2×D47)⋊C4—28no—
258(C2×D47)⋊C4—28no—
259(C2×D47)⋊C4—28no—
260(C2×D47)⋊C4—44no—
261(C2×D47)⋊C4—44no—
262(C2×D47)⋊C4—44no—
263(C2×D47)⋊C4—44no—
264C4⋊Dic47—28no—
265C4⋊Dic47C22⋊C4116yescomplemented
266Dic47⋊C4—28no—
267Dic47⋊C4—44no—
268C4×Dic47—28no—
269C4×Dic47—44no—
270C4×Dic47—44no—
271C4×Dic47—44no—
272C23×C47C23×C411yescharacteristic
273C23×C47C22×D411yescharacteristic
274C23×C47C22×D411yescharacteristic
275C23×C47C2×#4111yescharacteristic
276C23×C47C2×#4111yescharacteristic
277C23×C47C2×#4111yescharacteristic
278C23×C47C2×#4111yescharacteristic
279C23×C47C2×#4111yescharacteristic
280C23×C47C2×#4111yescharacteristic
281C23×C47C2×#4111yescharacteristic
282C23×C47C2×#4111yescharacteristic
283C23×C47H(5,𝔽2)11yescharacteristic
284C23×C47H(5,𝔽2)11yescharacteristic
285C23×C472−1+411yescharacteristic
286C23×C472−1+411yescharacteristic
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—41no—
295C22×D47—41no—
296C22×D47—41no—
297C22×D47—41no—
298C22×D47—41no—
299C22×D47—41no—
300C22×D47—41no—
301C22×D47—41no—
302C22×D47—41no—
303C22×D47—41no—
304C22×D47—41no—
305C22×D47—41no—
306C22×D47—41no—
307C22×D47—41no—
308C22×D47—41no—
309C22×D47—41no—
310C22×D47—41no—
311C22×D47—41no—
312C22×D47—41no—
313C22×D47—41no—
314C22×D47—41no—
315C22×D47—41no—
316C22×D47—41no—
317C22×D47—41no—
318C22×D47—41no—
319C22×D47—41no—
320C22×D47—41no—
321C22×D47—41no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47C2×C22⋊C414yes—
370C2×C4×C47#12614yescomplemented
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—41no—
396C2×Dic47—41no—
397C2×Dic47—41no—
398C2×Dic47—41no—
399C2×Dic47—41no—
400C2×Dic47—41no—
401C2×Dic47—41no—
402C2×Dic47—41no—
403C2×Dic47—41no—
404C2×Dic47—41no—
405C2×Dic47—41no—
406C2×Dic47—41no—
407C2×Dic47—41no—
408C2×Dic47—41no—
409C2×Dic47—41no—
410C2×Dic47—41no—
411C2×Dic47—41no—
412C2×Dic47—41no—
413C2×Dic47—41no—
414C2×Dic47—41no—
415C2×Dic47—41no—
416C2×Dic47—41no—
417C2×Dic47—41no—
418C2×Dic47C2×C22⋊C414yes—
419C2×Dic47C2×C22⋊C414yes—
420#14101—471nomaximal, Sylow
421C22×C47C22×C22⋊C411yescharacteristic
422C22×C47C4×#4111yescharacteristic
423C22×C47C4×#4111yescharacteristic
424C22×C47C4×#4111yescharacteristic
425C22×C47C4×#4111yescharacteristic
426C22×C47#52011yescharacteristic
427C22×C47#52011yescharacteristic
428C22×C47#52511yescharacteristic
429C22×C47#52511yescharacteristic
430C22×C47C2×#12611yescharacteristic
431C22×C47#52911yescharacteristic
432C22×C47#52911yescharacteristic
433C22×C47#52911yescharacteristic
434C22×C47#53211yescharacteristic
435C22×C47#53211yescharacteristic
436C22×C47#53811yescharacteristic
437C22×C47#53911yescharacteristic
438C22×C47#54111yescharacteristic
439C22×C47#54211yescharacteristic
440C22×C47#54611yescharacteristic
441C22×C47#54611yescharacteristic
442C22×C47#54711yescharacteristic
443C22×C47#54711yescharacteristic
444C22×C47#54811yescharacteristic
445C22×C47#54811yescharacteristic
446C22×C47#55011yescharacteristic
447C22×C47#55011yescharacteristic
448C22×C47#55111yescharacteristic
449C22×C47#55111yescharacteristic
450C22×C47#55211yescharacteristic
451C22×C47#55211yescharacteristic
452C22×C47#55311yescharacteristic
453C22×C47#55311yescharacteristic
454C22×C47#55611yescharacteristic
455C22×C47#55611yescharacteristic
456C2×D47—42no—
457C2×D47—42no—
458C2×D47—42no—
459C2×D47—42no—
460C2×D47—42no—
461C2×D47—42no—
462C2×D47—42no—
463C2×D47—81no—
464C2×D47—81no—
465C2×D47—81no—
466C2×D47—81no—
467C2×D47—81no—
468C2×D47—81no—
469C2×D47—81no—
470C2×D47—81no—
471C4×C47—24no—
472C4×C47—24no—
473C4×C47—42no—
474C4×C47—42no—
475C4×C47—42no—
476C4×C47—42no—
477C4×C47—81no—
478Dic47—24no—
479Dic47—24no—
480Dic47—42no—
481Dic47—42no—
482Dic47—42no—
483Dic47—42no—
484Dic47—81no—
485C22×#126—471no—
486C2×#387—471no—
487C2×C4×C4⋊C4—471no—
488#1445—471no—
489#1441—471no—
490#1439—471no—
491#1439—471no—
492#1437—471no—
493#1437—471no—
494#1437—471no—
495#1437—471no—
496#1436D4711yescharacteristic, complemented
497C4⋊#95—471no—
498#1434—471no—
499C4×#95—471no—
500C2×C47#229711yescharacteristic
501C2×C47C4×#12611yescharacteristic
502C2×C47#233411yescharacteristic
503C2×C47#233911yescharacteristic
504C2×C47#234111yescharacteristic
505C2×C47#237311yescharacteristic
506C2×C47#237311yescharacteristic
507C2×C47#246711yescharacteristic
508C2×C47#246911yescharacteristic
509C2×C47#247911yescharacteristic
510C2×C47#248111yescharacteristic
511C2×C47#251211yescharacteristic
512C2×C47#251911yescharacteristic
513C2×C47#255411yescharacteristic
514C2×C47#256011yescharacteristic
515D47—82no—
516C2×#126—478no—
517C2×#126—944no—
518C2×#126—944no—
519C22×C4⋊C4—471no—
520C22×C4⋊C4—471no—
521C22×C4⋊C4—471no—
522C22×C4⋊C4—471no—
523C22×C4⋊C4C2×D4711yescharacteristic
524C22×C22⋊C4—471no—
525C22×C22⋊C4—471no—
526C22×C22⋊C4—471no—
527C22×C22⋊C4—471no—
528C22×C22⋊C4—471no—
529C22×C22⋊C4—471no—
530C22×C22⋊C4—471no—
531C22×C42—471no—
532C22×C42—471no—
533C22×C42—471no—
534C22×C42—471no—
535C22×C42C2×D4711yescharacteristic
536#387—944no—
537C4×C4⋊C4—944no—
538C2×#95—471no—
539C2×#95—471no—
540C2×#95—471no—
541C2×#95—471no—
542C2×#95—471no—
543C2×#95—471no—
544C2×#95—471no—
545C2×#95—471no—
546C2×#95—471no—
547C2×#95—471no—
548C2×#95—471no—
549C2×#95—471no—
550C2×#95—471no—
551C2×#95C2×D4711yescharacteristic
552C2×#95C2×D4711yescharacteristic
553C2×#95C2×D4711yescharacteristic
554C2×#95C2×D4711yescharacteristic
555C2×#95C2×D4711yescharacteristic
556C47#1410111yescharacteristic, complemented, Sylow
557C25—471no—
558C23×C4—471no—
559C23×C4—471no—
560C23×C4—471no—
561C23×C4—471no—
562C23×C4—471no—
563C23×C4—471no—
564C23×C4—471no—
565C23×C4C22×D4711yescharacteristic
566C23×C4C22×D4711yescharacteristic
567C23×C4C22×D4711yescharacteristic
568C23×C4C22×D4711yescharacteristic
569C23×C4C22×D4711yescharacteristic
570C23×C4C22×D4711yescharacteristic
571C23×C4C22×D4711yescharacteristic
572#126—9432no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—474no—
576C2×C4⋊C4—474no—
577C2×C4⋊C4—474no—
578C2×C4⋊C4—474no—
579C2×C4⋊C4—942no—
580C2×C4⋊C4—942no—
581C2×C4⋊C4—942no—
582C2×C4⋊C4—942no—
583C2×C4⋊C4—942no—
584C2×C4⋊C4—942no—
585C2×C4⋊C4—942no—
586C2×C4⋊C4—1881no—
587C2×C4⋊C4C4×D4714yes—
588C2×C22⋊C4—474no—
589C2×C22⋊C4—474no—
590C2×C22⋊C4—474no—
591C2×C22⋊C4—942no—
592C2×C22⋊C4—942no—
593C2×C22⋊C4—942no—
594C2×C22⋊C4—942no—
595C2×C22⋊C4—942no—
596C2×C22⋊C4—942no—
597C2×C22⋊C4—942no—
598C2×C22⋊C4—942no—
599C2×C22⋊C4—942no—
600C2×C22⋊C4—942no—
601C2×C22⋊C4—942no—
602C2×C22⋊C4—942no—
603C2×C22⋊C4—942no—
604C2×C22⋊C4—942no—
605C2×C22⋊C4—1881no—
606C2×C22⋊C4—1881no—
607C2×C22⋊C4—1881no—
608C2×C22⋊C4—1881no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—474no—
613C2×C42—942no—
614C2×C42—942no—
615C2×C42—942no—
616C2×C42—942no—
617C2×C42—942no—
618C2×C42—942no—
619C2×C42—942no—
620C2×C42—942no—
621C2×C42—1881no—
622C2×C42—1881no—
623C2×C42—1881no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—942no—
630#95—942no—
631#95—942no—
632#95—942no—
633#95—942no—
634#95—942no—
635#95—942no—
636#95—942no—
637#95—942no—
638#95—1881no—
639#95—1881no—
640#95—1881no—
641#95—1881no—
642C24—472no—
643C24—941no—
644C24—941no—
645C24—941no—
646C24—941no—
647C24—941no—
648C24—941no—
649C24—941no—
650C24—941no—
651C24—941no—
652C24—941no—
653C24—941no—
654C24—941no—
655C24—941no—
656C24—941no—
657C24C23×D4711yescharacteristic
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—472no—
698C22×C4—472no—
699C22×C4—472no—
700C22×C4—472no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—472no—
704C22×C4—472no—
705C22×C4—472no—
706C22×C4—472no—
707C22×C4—941no—
708C22×C4—941no—
709C22×C4—941no—
710C22×C4—941no—
711C22×C4—941no—
712C22×C4—941no—
713C22×C4—941no—
714C22×C4—941no—
715C22×C4—941no—
716C22×C4—941no—
717C22×C4—941no—
718C22×C4—941no—
719C22×C4—941no—
720C22×C4—941no—
721C22×C4—941no—
722C22×C4—941no—
723C22×C4—941no—
724C22×C4—941no—
725C22×C4—941no—
726C22×C4—941no—
727C22×C4—941no—
728C22×C4—941no—
729C22×C4—941no—
730C22×C4—941no—
731C22×C4—941no—
732C22×C4—941no—
733C22×C4—941no—
734C22×C4—941no—
735C22×C4—941no—
736C22×C4—941no—
737C22×C4—941no—
738C22×C4—941no—
739C22×C4—941no—
740C22×C4—941no—
741C22×C4—941no—
742C22×C4—941no—
743C22×C4—941no—
744C22×C4—941no—
745C22×C4—941no—
746C22×C4C2×C4×D4712yes—
747C22×C4C2×C4×D4712yes—
748C22×C4C2×C4×D4712yes—
749C22×C4#1062535012yes—
750C22×C4#1062535012yes—
751C22×C4D4×D4712yes—
752C22×C4D4×D4712yes—
753C22×C4#1062535212yes—
754C22×C4#1062535212yes—
755C22×C4#1062535412yes—
756C4⋊C4—28no—
757C4⋊C4—4716no—
758C4⋊C4—948no—
759C4⋊C4—948no—
760C4⋊C4—1884no—
761C22⋊C4—948no—
762C22⋊C4—948no—
763C22⋊C4—948no—
764C22⋊C4—1884no—
765C22⋊C4—1884no—
766C22⋊C4—1884no—
767C22⋊C4—1884no—
768C42—28no—
769C42—948no—
770C42—1884no—
771C42—1884no—
772C42—1884no—
773C23—942no—
774C23—942no—
775C23—942no—
776C23—942no—
777C23—942no—
778C23—942no—
779C23—942no—
780C23—1881no—
781C23—1881no—
782C23—1881no—
783C23—1881no—
784C23—1881no—
785C23—1881no—
786C23—1881no—
787C23—1881no—
788C23—1881no—
789C23—1881no—
790C23—1881no—
791C23—1881no—
792C23—1881no—
793C23—1881no—
794C23—1881no—
795C23—1881no—
796C23—1881no—
797C23—1881no—
798C23—1881no—
799C23—1881no—
800C23—1881no—
801C23—1881no—
802C23—1881no—
803C23—1881no—
804C23—1881no—
805C23—1881no—
806C23—1881no—
807C23—1881no—
808C23C22×C4×D4711yescharacteristic
809C23C2×D4×D4711yescharacteristic
810C23C2×D4×D4711yescharacteristic
811C23#41×D4711yescharacteristic
812C23#41×D4711yescharacteristic
813C23#41×D4711yescharacteristic
814C23C2×#1062535211yescharacteristic
815C23C2×#1062535211yescharacteristic
816C23C2×#1062535011yescharacteristic
817C23C2×#1062535011yescharacteristic
818C23C2×#1062535411yescharacteristic
819C23#1309407011yescharacteristic
820C23#1309407011yescharacteristic
821C23#1309407111yescharacteristic
822C23#1309407211yescharacteristic
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—474no—
871C2×C4—474no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—942no—
875C2×C4—942no—
876C2×C4—942no—
877C2×C4—942no—
878C2×C4—942no—
879C2×C4—942no—
880C2×C4—942no—
881C2×C4—942no—
882C2×C4—942no—
883C2×C4—942no—
884C2×C4—942no—
885C2×C4—942no—
886C2×C4—942no—
887C2×C4—942no—
888C2×C4—942no—
889C2×C4—942no—
890C2×C4—942no—
891C2×C4—942no—
892C2×C4—942no—
893C2×C4—942no—
894C2×C4—942no—
895C2×C4—942no—
896C2×C4—1881no—
897C2×C4—1881no—
898C2×C4—1881no—
899C2×C4—1881no—
900C2×C4—1881no—
901C2×C4—1881no—
902C2×C4—1881no—
903C2×C4—1881no—
904C2×C4—1881no—
905C2×C4—1881no—
906C2×C4—1881no—
907C2×C4—1881no—
908C2×C4—1881no—
909C2×C4—1881no—
910C2×C4—1881no—
911C2×C4—1881no—
912C2×C4—1881no—
913C2×C4—1881no—
914C2×C4—1881no—
915C2×C4—1881no—
916C2×C4—1881no—
917C2×C4—1881no—
918C2×C4—1881no—
919C2×C4C22⋊C4×D4714yes—
920C2×C4#1309401914yescomplemented
921C22—3761no—
922C22—3761no—
923C22—3761no—
924C22—3761no—
925C22—3761no—
926C22—3761no—
927C22—3761no—
928C22—3761no—
929C22—1882no—
930C22—1882no—
931C22—1882no—
932C22—1882no—
933C22—1882no—
934C22—1882no—
935C22—1882no—
936C22C2×C22⋊C4×D4711yescharacteristic
937C22C4×#1062535211yescharacteristic
938C22C4×#1062535211yescharacteristic
939C22C4×#1062535011yescharacteristic
940C22C4×#1062535411yescharacteristic
941C22#1568960311yescharacteristic
942C22#1568960511yescharacteristic
943C22#1568962911yescharacteristic
944C22#1568963111yescharacteristic
945C22C2×#1309401911yescharacteristic
946C22#1568965111yescharacteristic
947C22#1568965311yescharacteristic
948C22#1568966011yescharacteristic
949C22#1568966811yescharacteristic
950C22#1568966811yescharacteristic
951C22#1568971211yescharacteristic
952C22#1568971711yescharacteristic
953C22#1568973211yescharacteristic
954C22#1568974611yescharacteristic
955C22#1568976411yescharacteristic
956C22#1568976611yescharacteristic
957C22#1568977511yescharacteristic
958C22#1568977611yescharacteristic
959C22#1568978211yescharacteristic
960C22#1568978211yescharacteristic
961C22#1568979411yescharacteristic
962C22#1568979411yescharacteristic
963C22#1568979611yescharacteristic
964C22#1568979711yescharacteristic
965C22#1568980811yescharacteristic
966C22#1568981511yescharacteristic
967C22#1568981911yescharacteristic
968C22#1568982611yescharacteristic
969C22#1568984011yescharacteristic
970C22#1568984511yescharacteristic
971C4—24no—
972C4—24no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4—81no—
978C4—944no—
979C4—944no—
980C4—3761no—
981C4—1882no—
982C4—1882no—
983C4—1882no—
984C4—1882no—
985C2—3762no—
986C2#2024587311yescharacteristic
987C2C4×#1309401911yescharacteristic
988C2#2024616811yescharacteristic
989C2#2024621711yescharacteristic
990C2#2024622811yescharacteristic
991C2#2024650711yescharacteristic
992C2#2024651311yescharacteristic
993C2#2024743611yescharacteristic
994C2#2024746611yescharacteristic
995C2#2024761611yescharacteristic
996C2#2024764611yescharacteristic
997C2#2024797711yescharacteristic
998C2#2024806711yescharacteristic
999C2#2024844711yescharacteristic
1000C2#2024852911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1436C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenter#1436D47
hypocenterC47#14101
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#15689006C2semidirect
3. C2×C4×C4⋊Dic47C2semidirect
4. #20241654C2semidirect
5. #20241641C2semidirect
12. Dic47⋊#95C2semidirect
13. #20241613C2semidirect
14. #95×Dic47C2semidirect
15. C47×#1436C2semidirect
18. C2×#13094019C4semidirect
265. C4⋊Dic47C22⋊C4semidirect
370. C2×C4×C47#126semidirect
496. #1436D47semidirect
556. C47#14101semidirect
920. C2×C4#13094019semidirect

Maximal subgroups

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

subgroupindex
C22×#130940192
C2×#156890062
C2×C4×C4⋊Dic472
#202416542
#202416412
#202416342
#202416322
#202416262
#202416242
Dic47⋊#952
#202416132
#95×Dic472
C47×#14362
#1410147