Finite Group Databasebeta

← #26139067

Subgroups — #26139067

Order 12032.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094002C211yesmaximal, characteristic
2C22×#13093989C211yesmaximal, characteristic, complemented
3C2×#15689027C211yesmaximal, characteristic, complemented
4C2×#15688982C211yesmaximal, characteristic
5C2×#15688970C211yesmaximal, characteristic
6#20241639C211yesmaximal, characteristic, complemented
7#20241632C211yesmaximal, characteristic
8#20241630C211yesmaximal, characteristic
9#20241624C211yesmaximal, characteristic
10#20241624C211yesmaximal, characteristic
11#20241620C211yesmaximal, characteristic, complemented
12#20241619C211yesmaximal, characteristic, complemented
13Dic47⋊#95C211yesmaximal, characteristic, complemented
14Dic47⋊#95C211yesmaximal, characteristic, complemented
15C47×#1441C211yesmaximal, characteristic, complemented
16C23×Dic94C2211yescharacteristic
17C23×C4×D47C2211yescharacteristic
18C2×#13094002—24no—
19C2×#13094002—24no—
20C2×#13094002C418yescomplemented
21C2×#13093989—24no—
22C2×#13093989—24no—
23C2×#13093989—24no—
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39#15689027—24no—
40#15688982—24no—
41#15688970—24no—
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C22×C4⋊C4×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C2×#95×C47C2211yescharacteristic
59C2×#95×C47C2211yescharacteristic
60C24×D47C2311yescharacteristic
61C22×Dic94—22no—
62C22×Dic94—22no—
63C22×Dic94—22no—
64C22×Dic94—22no—
65C22×Dic94C2×C414yes—
66C22×Dic94D414yes—
67C22×Dic94D414yes—
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C22×C4×D47—22no—
76C22×C4×D47—22no—
77C22×C4×D47—22no—
78C22×C4×D47—22no—
79C22×C4×D47—22no—
80C22×C4×D47—22no—
81C22×C4×D47C2×C414yes—
82#13094002—232no—
83#13093989—232no—
84C2×Dic47⋊C4—22no—
85C2×Dic47⋊C4—22no—
86C2×Dic47⋊C4—22no—
87C2×Dic47⋊C4—22no—
88C2×Dic47⋊C4—22no—
89C2×Dic47⋊C4—22no—
90C2×Dic47⋊C4—22no—
91C2×Dic47⋊C4—22no—
92C2×Dic47⋊C4—22no—
93C2×Dic47⋊C4—22no—
94C2×Dic47⋊C4—22no—
95C2×Dic47⋊C4—22no—
96C2×Dic47⋊C4C2×C414yes—
97C2×Dic47⋊C4C2×C414yes—
98C2×Dic47⋊C4D414yes—
99C2×(C2×D47)⋊C4—22no—
100C2×(C2×D47)⋊C4—22no—
101C2×(C2×D47)⋊C4—22no—
102C2×(C2×D47)⋊C4—22no—
103C2×(C2×D47)⋊C4—22no—
104C2×(C2×D47)⋊C4—22no—
105C2×(C2×D47)⋊C4—22no—
106C2×(C2×D47)⋊C4—22no—
107C2×(C2×D47)⋊C4—22no—
108C2×(C2×D47)⋊C4—22no—
109C2×(C2×D47)⋊C4—22no—
110C2×(C2×D47)⋊C4—22no—
111C2×(C2×D47)⋊C4—22no—
112C2×(C2×D47)⋊C4—41no—
113C2×(C2×D47)⋊C4—41no—
114C2×(C2×D47)⋊C4C2×C414yes—
115C2×(C2×D47)⋊C4C2×C414yes—
116C2×(C2×D47)⋊C4Q814yescomplemented
117C2×C4×Dic47—22no—
118C2×C4×Dic47—22no—
119C2×C4×Dic47—22no—
120C2×C4×Dic47—22no—
121C2×C4×Dic47—22no—
122C2×C4×Dic47—22no—
123C2×C4×Dic47—22no—
124C2×C4×Dic47—22no—
125C2×C4×Dic47—22no—
126C2×C4×Dic47—22no—
127C2×C4×Dic47—22no—
128C2×C4×Dic47D414yes—
129C47⋊#95—22no—
130C47⋊#95—22no—
131C47⋊#95—22no—
132C47⋊#95—22no—
133C47⋊#95—22no—
134C47⋊#95—22no—
135C47⋊#95—22no—
136C47⋊#95—22no—
137C47⋊#95—22no—
138C47⋊#95—41no—
139C47⋊#95—41no—
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C2×C4⋊C4×C47—22no—
148C2×C4⋊C4×C47—22no—
149C2×C4⋊C4×C47—22no—
150C2×C4⋊C4×C47—22no—
151C2×C4⋊C4×C47—22no—
152C2×C4⋊C4×C47C2×C414yes—
153#95×C47—22no—
154#95×C47—22no—
155#95×C47—22no—
156#95×C47—41no—
157#95×C47—41no—
158C24×C47C2411yescharacteristic
159C23×D47—21no—
160C23×D47—21no—
161C23×D47—21no—
162C23×D47—21no—
163C23×D47—21no—
164C23×D47—21no—
165C23×D47—21no—
166C23×D47—21no—
167C23×D47—21no—
168C23×D47—21no—
169C23×D47—21no—
170C23×D47—21no—
171C23×D47C22×C412yes—
172C23×D47C2×Q812yes—
173C23×D47#4112yes—
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×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47C22×C412yes—
216C22×C4×C47C22×C412yes—
217C22×C4×C47C22×C412yes—
218C22×C4×C47C2×D412yes—
219C22×C4×C47C2×D412yes—
220C22×C4×C47C2×D412yes—
221C22×C4×C47C2×D412yes—
222C22×C4×C47C2×Q812yes—
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×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47—21no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47—21no—
253C22×Dic47—21no—
254C22×Dic47—21no—
255C22×Dic47—21no—
256C22×Dic47C22×C412yes—
257C22×Dic47C22×C412yes—
258C22×Dic47C22×C412yes—
259C22×Dic47C2×D412yes—
260C22×Dic47C2×D412yes—
261C22×Dic47C2×D412yes—
262C22×Dic47C2×D412yes—
263C22×Dic47C2×D412yes—
264C22×Dic47C2×D412yes—
265C22×Dic47C2×D412yes—
266C22×Dic47C2×D412yes—
267C22×Dic47C2×Q812yes—
268C22×Dic47#4112yes—
269C22×Dic47#4112yes—
270C22×Dic47#4112yes—
271C22×Dic47#4112yes—
272C2×C4×D47—28no—
273C2×C4×D47—28no—
274C2×C4×D47—28no—
275C2×C4×D47—44no—
276C2×C4×D47—44no—
277C2×C4×D47—44no—
278C2×C4×D47—44no—
279C2×Dic94—28no—
280C2×Dic94—28no—
281C2×Dic94—28no—
282C2×Dic94—28no—
283C2×Dic94—28no—
284C2×Dic94—28no—
285C2×Dic94C22⋊C4116yescomplemented
286C4⋊C4×C47—28no—
287C4⋊C4×C47—28no—
288(C2×D47)⋊C4—28no—
289(C2×D47)⋊C4—28no—
290(C2×D47)⋊C4—28no—
291(C2×D47)⋊C4—28no—
292(C2×D47)⋊C4—44no—
293(C2×D47)⋊C4—44no—
294Dic47⋊C4—28no—
295Dic47⋊C4—28no—
296Dic47⋊C4—28no—
297Dic47⋊C4—28no—
298Dic47⋊C4—44no—
299C4×Dic47—28no—
300C4×Dic47—28no—
301C4×Dic47—28no—
302C4×Dic47—44no—
303C23×C47C23×C411yescharacteristic
304C23×C47C22×D411yescharacteristic
305C23×C47C22×D411yescharacteristic
306C23×C47C22×D411yescharacteristic
307C23×C47C22×D411yescharacteristic
308C23×C47C22×Q811yescharacteristic
309C23×C47C2×#4111yescharacteristic
310C23×C47C2×#4111yescharacteristic
311C23×C47C2×#4111yescharacteristic
312C23×C47C2×#4111yescharacteristic
313C23×C47C2×#4111yescharacteristic
314C23×C47H(5,𝔽2)11yescharacteristic
315C23×C472−1+411yescharacteristic
316C23×C472−1+411yescharacteristic
317C23×C472−1+411yescharacteristic
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—22no—
332C22×D47—22no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—41no—
337C22×D47—41no—
338C22×D47—41no—
339C22×D47—41no—
340C22×D47—41no—
341C22×D47—41no—
342C22×D47—41no—
343C22×D47—41no—
344C22×D47—41no—
345C22×D47—41no—
346C22×D47—41no—
347C22×D47—41no—
348C22×D47—41no—
349C22×D47—41no—
350C22×D47—41no—
351C22×D47—41no—
352C22×D47C4×Q814yescomplemented
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
396C2×C4×C47—41no—
397C2×C4×C47—41no—
398C2×C4×C47—41no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47C2×C22⋊C414yes—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—22no—
406C2×Dic47—22no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47—22no—
410C2×Dic47—22no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
414C2×Dic47—22no—
415C2×Dic47—22no—
416C2×Dic47—22no—
417C2×Dic47—22no—
418C2×Dic47—22no—
419C2×Dic47—22no—
420C2×Dic47—22no—
421C2×Dic47—22no—
422C2×Dic47—22no—
423C2×Dic47—41no—
424C2×Dic47—41no—
425C2×Dic47—41no—
426C2×Dic47—41no—
427C2×Dic47—41no—
428C2×Dic47—41no—
429C2×Dic47—41no—
430C2×Dic47—41no—
431C2×Dic47—41no—
432C2×Dic47—41no—
433C2×Dic47—41no—
434C2×Dic47—41no—
435C2×Dic47—41no—
436C2×Dic47—41no—
437C2×Dic47—41no—
438C2×Dic47—41no—
439C2×Dic47—41no—
440C2×Dic47—41no—
441C2×Dic47—41no—
442C2×Dic47C2×C22⋊C414yes—
443C2×Dic47C2×C22⋊C414yes—
444C2×Dic47C4×D414yes—
445C2×Dic47C4×D414yes—
446C2×Dic47#12014yes—
447C2×Dic47#12114yes—
448C2×Dic47#12114yes—
449C2×Dic47C22⋊Q814yescomplemented
450C2×Dic47#12314yes—
451C4×D47—416no—
452Dic94—232no—
453#13969—471nomaximal, Sylow
454C22×C47C22×C22⋊C411yescharacteristic
455C22×C47C2×C4×D411yescharacteristic
456C22×C47C2×C4×D411yescharacteristic
457C22×C47C2×C4×Q811yescharacteristic
458C22×C47C4×#4111yescharacteristic
459C22×C47#51911yescharacteristic
460C22×C47#52011yescharacteristic
461C22×C47C2×#12011yescharacteristic
462C22×C47C2×#12111yescharacteristic
463C22×C47C2×#12111yescharacteristic
464C22×C47C2×C22⋊Q811yescharacteristic
465C22×C47C2×#12311yescharacteristic
466C22×C47#52511yescharacteristic
467C22×C47#52911yescharacteristic
468C22×C47#53311yescharacteristic
469C22×C47#53611yescharacteristic
470C22×C47#53711yescharacteristic
471C22×C47#54111yescharacteristic
472C22×C47#54211yescharacteristic
473C22×C47#54611yescharacteristic
474C22×C47#54711yescharacteristic
475C22×C47#54811yescharacteristic
476C22×C47#54811yescharacteristic
477C22×C47#54811yescharacteristic
478C22×C47#54811yescharacteristic
479C22×C47#54811yescharacteristic
480C22×C47D4×Q811yescharacteristic
481C22×C47D4×Q811yescharacteristic
482C22×C47D4×Q811yescharacteristic
483C22×C47#55011yescharacteristic
484C22×C47#55011yescharacteristic
485C22×C47#55211yescharacteristic
486C22×C47#55211yescharacteristic
487C22×C47#55411yescharacteristic
488C22×C47#55611yescharacteristic
489C2×D47—24no—
490C2×D47—24no—
491C2×D47—24no—
492C2×D47—42no—
493C2×D47—42no—
494C2×D47—42no—
495C2×D47—42no—
496C2×D47—42no—
497C2×D47—42no—
498C2×D47—42no—
499C2×D47—42no—
500C2×D47—42no—
501C2×D47—42no—
502C2×D47—42no—
503C2×D47—42no—
504C4×C47—24no—
505C4×C47—42no—
506C4×C47—42no—
507C4×C47—42no—
508C4×C47—42no—
509C4×C47—42no—
510C4×C47—81no—
511Dic47—24no—
512Dic47—24no—
513Dic47—42no—
514Dic47—42no—
515Dic47—42no—
516Dic47—81no—
517Dic47#38618yes—
518C22×C22⋊Q8—471no—
519C22×C4×Q8—471no—
520C2×#391—471no—
521C2×#380—471no—
522C2×C4×C22⋊C4—471no—
523#1441—471no—
524#1441D4711yescharacteristic, complemented
525#1439—471no—
526#1439—471no—
527#1437—471no—
528#1437—471no—
529#1436—471no—
530#1436—471no—
531C4⋊#95—471no—
532C4⋊#95—471no—
533C2×C47C2×#38611yescharacteristic
534C2×C47C4×C22⋊Q811yescharacteristic
535C2×C47#232311yescharacteristic
536C2×C47Q8×C22⋊C411yescharacteristic
537C2×C47#234111yescharacteristic
538C2×C47#236011yescharacteristic
539C2×C47#236211yescharacteristic
540C2×C47#240711yescharacteristic
541C2×C47#240911yescharacteristic
542C2×C47#242111yescharacteristic
543C2×C47#242311yescharacteristic
544C2×C47#242611yescharacteristic
545C2×C47#242911yescharacteristic
546C2×C47#253611yescharacteristic
547C2×C47#253811yescharacteristic
548D47—44no—
549C23×Q8—471no—
550C24×C4—471no—
551C2×C22⋊Q8—478no—
552C2×C22⋊Q8—944no—
553C2×C22⋊Q8—944no—
554C2×C4×Q8—944no—
555C2×C4×Q8—944no—
556C2×C4×Q8—944no—
557C22×C4⋊C4—471no—
558C22×C4⋊C4—471no—
559C22×C4⋊C4—471no—
560C22×C4⋊C4—471no—
561C22×C4⋊C4—471no—
562C22×C4⋊C4C2×D4711yescharacteristic
563C22×C4⋊C4C2×D4711yescharacteristic
564C22×C22⋊C4—471no—
565C22×C22⋊C4—471no—
566C22×C22⋊C4—471no—
567C22×C22⋊C4—471no—
568C22×C22⋊C4—471no—
569C22×C22⋊C4—471no—
570C22×C42—471no—
571C22×C42—471no—
572C22×C42—471no—
573C22×C42—471no—
574#391—944no—
575#380—944no—
576C4×C22⋊C4—944no—
577C2×#95—471no—
578C2×#95—471no—
579C2×#95—471no—
580C2×#95—471no—
581C2×#95—471no—
582C2×#95—471no—
583C2×#95—471no—
584C2×#95—471no—
585C2×#95—471no—
586C2×#95—471no—
587C2×#95—471no—
588C2×#95C2×D4711yescharacteristic
589C2×#95C2×D4711yescharacteristic
590C2×#95C2×D4711yescharacteristic
591C2×#95C2×D4711yescharacteristic
592C2×#95C2×D4711yescharacteristic
593C47#1396911yescharacteristic, complemented, Sylow
594C25—471no—
595C22×Q8—474no—
596C22×Q8—474no—
597C22×Q8—474no—
598C22×Q8—942no—
599C22×Q8—942no—
600C22×Q8—942no—
601C22×Q8—942no—
602C23×C4—471no—
603C23×C4—471no—
604C23×C4—471no—
605C23×C4—471no—
606C23×C4—471no—
607C23×C4—471no—
608C23×C4—474no—
609C23×C4—471no—
610C23×C4—942no—
611C23×C4—942no—
612C23×C4—942no—
613C23×C4—942no—
614C23×C4—942no—
615C23×C4—942no—
616C23×C4C22×D4711yescharacteristic
617C23×C4C22×D4711yescharacteristic
618C23×C4C22×D4711yescharacteristic
619C23×C4C22×D4711yescharacteristic
620C23×C4C22×D4711yescharacteristic
621C23×C4C22×D4711yescharacteristic
622C23×C4C22×D4711yescharacteristic
623C22⋊Q8—9432no—
624C4×Q8—9432no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—474no—
631C2×C4⋊C4—474no—
632C2×C4⋊C4—474no—
633C2×C4⋊C4—942no—
634C2×C4⋊C4—942no—
635C2×C4⋊C4—942no—
636C2×C4⋊C4—942no—
637C2×C4⋊C4—942no—
638C2×C4⋊C4—942no—
639C2×C4⋊C4—942no—
640C2×C4⋊C4—942no—
641C2×C4⋊C4—942no—
642C2×C4⋊C4—942no—
643C2×C4⋊C4—942no—
644C2×C4⋊C4—942no—
645C2×C4⋊C4C4×D4714yes—
646C2×C22⋊C4—474no—
647C2×C22⋊C4—474no—
648C2×C22⋊C4—474no—
649C2×C22⋊C4—942no—
650C2×C22⋊C4—942no—
651C2×C22⋊C4—942no—
652C2×C22⋊C4—942no—
653C2×C22⋊C4—942no—
654C2×C22⋊C4—942no—
655C2×C22⋊C4—942no—
656C2×C22⋊C4—942no—
657C2×C22⋊C4—942no—
658C2×C22⋊C4—942no—
659C2×C22⋊C4—942no—
660C2×C22⋊C4—942no—
661C2×C22⋊C4—942no—
662C2×C22⋊C4—1881no—
663C2×C22⋊C4—1881no—
664C2×C42—474no—
665C2×C42—942no—
666C2×C42—942no—
667C2×C42—942no—
668C2×C42—942no—
669C2×C42—942no—
670C2×C42—942no—
671C2×C42—942no—
672C2×C42—942no—
673C2×C42—942no—
674C2×C42—942no—
675C2×C42—942no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—41no—
680#95—41no—
681#95—942no—
682#95—942no—
683#95—942no—
684#95—942no—
685#95—942no—
686#95—942no—
687#95—942no—
688#95—942no—
689#95—942no—
690#95—1881no—
691#95—1881no—
692C24—472no—
693C24—472no—
694C24—472no—
695C24—941no—
696C24—941no—
697C24—941no—
698C24—941no—
699C24—941no—
700C24—941no—
701C24—941no—
702C24—941no—
703C24—941no—
704C24—941no—
705C24—941no—
706C24—941no—
707C24C23×D4711yescharacteristic
708C2×Q8—4716no—
709C2×Q8—948no—
710C2×Q8—948no—
711C2×Q8—948no—
712C2×Q8—948no—
713C2×Q8—948no—
714C2×Q8—948no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—472no—
757C22×C4—472no—
758C22×C4—472no—
759C22×C4—472no—
760C22×C4—472no—
761C22×C4—472no—
762C22×C4—472no—
763C22×C4—472no—
764C22×C4—472no—
765C22×C4—472no—
766C22×C4—472no—
767C22×C4—472no—
768C22×C4—472no—
769C22×C4—472no—
770C22×C4—472no—
771C22×C4—472no—
772C22×C4—948no—
773C22×C4—948no—
774C22×C4—948no—
775C22×C4—941no—
776C22×C4—941no—
777C22×C4—941no—
778C22×C4—941no—
779C22×C4—941no—
780C22×C4—941no—
781C22×C4—941no—
782C22×C4—941no—
783C22×C4—941no—
784C22×C4—941no—
785C22×C4—941no—
786C22×C4—941no—
787C22×C4—941no—
788C22×C4—941no—
789C22×C4—941no—
790C22×C4—941no—
791C22×C4—941no—
792C22×C4—941no—
793C22×C4—941no—
794C22×C4—941no—
795C22×C4—941no—
796C22×C4—941no—
797C22×C4—941no—
798C22×C4—941no—
799C22×C4—941no—
800C22×C4—941no—
801C22×C4—941no—
802C22×C4—941no—
803C22×C4—941no—
804C22×C4—941no—
805C22×C4—941no—
806C22×C4—941no—
807C22×C4—941no—
808C22×C4—1884no—
809C22×C4—1884no—
810C22×C4—1884no—
811C22×C4—1884no—
812C22×C4C2×C4×D4712yes—
813C22×C4C2×C4×D4712yes—
814C22×C4C2×C4×D4712yes—
815C22×C4D4×D4712yes—
816C22×C4D4×D4712yes—
817C22×C4D4×D4712yes—
818C22×C4D4×D4712yes—
819C22×C4Q8×D4712yes—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—948no—
823C4⋊C4—948no—
824C4⋊C4—948no—
825C4⋊C4—948no—
826C4⋊C4—1884no—
827C22⋊C4—948no—
828C22⋊C4—948no—
829C22⋊C4—948no—
830C22⋊C4—948no—
831C22⋊C4—1884no—
832C22⋊C4—1884no—
833C42—948no—
834C42—948no—
835C42—948no—
836C42—1884no—
837C23—474no—
838C23—942no—
839C23—942no—
840C23—942no—
841C23—942no—
842C23—942no—
843C23—942no—
844C23—942no—
845C23—942no—
846C23—942no—
847C23—942no—
848C23—942no—
849C23—942no—
850C23—942no—
851C23—942no—
852C23—942no—
853C23—942no—
854C23—942no—
855C23—942no—
856C23—1881no—
857C23—1881no—
858C23—1881no—
859C23—1881no—
860C23—1881no—
861C23—1881no—
862C23—1881no—
863C23—1881no—
864C23—1881no—
865C23—1881no—
866C23—1881no—
867C23—1881no—
868C23—1881no—
869C23—1881no—
870C23—1881no—
871C23—1881no—
872C23C22×C4×D4711yescharacteristic
873C23C2×D4×D4711yescharacteristic
874C23C2×D4×D4711yescharacteristic
875C23C2×D4×D4711yescharacteristic
876C23C2×D4×D4711yescharacteristic
877C23C2×Q8×D4711yescharacteristic
878C23#41×D4711yescharacteristic
879C23#41×D4711yescharacteristic
880C23#41×D4711yescharacteristic
881C23#41×D4711yescharacteristic
882C23#41×D4711yescharacteristic
883C23#1309406911yescharacteristic
884C23#1309407111yescharacteristic
885C23#1309407211yescharacteristic
886C23#1309407211yescharacteristic
887Q8—9432no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—474no—
937C2×C4—474no—
938C2×C4—474no—
939C2×C4—474no—
940C2×C4—474no—
941C2×C4—474no—
942C2×C4—474no—
943C2×C4—474no—
944C2×C4—474no—
945C2×C4—942no—
946C2×C4—942no—
947C2×C4—942no—
948C2×C4—942no—
949C2×C4—942no—
950C2×C4—942no—
951C2×C4—942no—
952C2×C4—942no—
953C2×C4—942no—
954C2×C4—942no—
955C2×C4—942no—
956C2×C4—942no—
957C2×C4—942no—
958C2×C4—942no—
959C2×C4—942no—
960C2×C4—942no—
961C2×C4—942no—
962C2×C4—942no—
963C2×C4—942no—
964C2×C4—942no—
965C2×C4—942no—
966C2×C4—18816no—
967C2×C4—1881no—
968C2×C4—1881no—
969C2×C4—1881no—
970C2×C4—1881no—
971C2×C4—1881no—
972C2×C4—1881no—
973C2×C4—1881no—
974C2×C4—1881no—
975C2×C4—1881no—
976C2×C4—1881no—
977C2×C4—1881no—
978C2×C4—1881no—
979C2×C4—1881no—
980C2×C4—1881no—
981C2×C4—1881no—
982C2×C4—1881no—
983C2×C4—1881no—
984C2×C4—1881no—
985C2×C4—1881no—
986C2×C4C22⋊C4×D4714yes—
987C22—944no—
988C22—944no—
989C22—944no—
990C22—1882no—
991C22—1882no—
992C22—1882no—
993C22—1882no—
994C22—1882no—
995C22—1882no—
996C22—1882no—
997C22—1882no—
998C22—1882no—
999C22—1882no—
1000C22—1882no—
1001C22—1882no—
1002C22C2×C22⋊C4×D4711yescharacteristic
1003C22C4×D4×D4711yescharacteristic
1004C22C4×D4×D4711yescharacteristic
1005C22C4×Q8×D4711yescharacteristic
1006C22#1568959111yescharacteristic
1007C22#1568959911yescharacteristic
1008C22#1568960411yescharacteristic
1009C22#120×D4711yescharacteristic
1010C22#121×D4711yescharacteristic
1011C22#121×D4711yescharacteristic
1012C22C22⋊Q8×D4711yescharacteristic
1013C22#123×D4711yescharacteristic
1014C22#1568963111yescharacteristic
1015C22#1568965611yescharacteristic
1016C22#1568967911yescharacteristic
1017C22#1568969811yescharacteristic
1018C22#1568970011yescharacteristic
1019C22#1568973211yescharacteristic
1020C22#1568974311yescharacteristic
1021C22#1568976211yescharacteristic
1022C22#1568977111yescharacteristic
1023C22#1568978111yescharacteristic
1024C22#1568978311yescharacteristic
1025C22#1568978311yescharacteristic
1026C22#1568978311yescharacteristic
1027C22#1568978311yescharacteristic
1028C22#1568978611yescharacteristic
1029C22#1568978811yescharacteristic
1030C22#1568978811yescharacteristic
1031C22#1568979111yescharacteristic
1032C22#1568979111yescharacteristic
1033C22#1568980511yescharacteristic
1034C22#1568980511yescharacteristic
1035C22#1568982711yescharacteristic
1036C22#1568984011yescharacteristic
1037C4—24no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—81no—
1044C4—478no—
1045C4—944no—
1046C4—944no—
1047C4—3761no—
1048C4—1882no—
1049C4—1882no—
1050C4—1882no—
1051C2—1884no—
1052C2#386×D4711yescharacteristic
1053C2#2024592211yescharacteristic
1054C2#2024606511yescharacteristic
1055C2#2024622211yescharacteristic
1056C2#2024622511yescharacteristic
1057C2#2024639011yescharacteristic
1058C2#2024641011yescharacteristic
1059C2#2024672811yescharacteristic
1060C2#2024674811yescharacteristic
1061C2#2024688611yescharacteristic
1062C2#2024690811yescharacteristic
1063C2#2024694911yescharacteristic
1064C2#2024698211yescharacteristic
1065C2#2024829411yescharacteristic
1066C2#2024830511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1441C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenter#1441D47
hypocenterC47#13969
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C22×#13093989C2semidirect
3. C2×#15689027C2semidirect
6. #20241639C2semidirect
11. #20241620C2semidirect
12. #20241619C2semidirect
13. Dic47⋊#95C2semidirect
14. Dic47⋊#95C2semidirect
15. C47×#1441C2semidirect
20. C2×#13094002C4semidirect
116. C2×(C2×D47)⋊C4Q8semidirect
285. C2×Dic94C22⋊C4semidirect
352. C22×D47C4×Q8semidirect
449. C2×Dic47C22⋊Q8semidirect
524. #1441D47semidirect
593. C47#13969semidirect

Maximal subgroups

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

subgroupindex
C22×#130940022
C22×#130939892
C2×#156890272
C2×#156889822
C2×#156889702
#202416392
#202416322
#202416302
#202416242
#202416202
#202416192
Dic47⋊#952
C47×#14412
#1396947