Finite Group Databasebeta

← #26146369

Subgroups — #26146369

Order 12032.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689035C211yesmaximal, characteristic
2C2×#15689028C211yesmaximal, characteristic, complemented
3C2×#15689027C211yesmaximal, characteristic, complemented
4C2×#15688996C211yesmaximal, characteristic
5#20241651C211yesmaximal, characteristic, complemented
6#20241651C211yesmaximal, characteristic, complemented
7#20241647C211yesmaximal, characteristic, complemented
8#20241643C211yesmaximal, characteristic, complemented
9#20241631C211yesmaximal, characteristic
10#20241625C211yesmaximal, characteristic
11#20241625C211yesmaximal, characteristic
12#20241613C211yesmaximal, characteristic, complemented
13#20241612C211yesmaximal, characteristic, complemented
14#20241611C211yesmaximal, characteristic
15C2×C47×#385C211yesmaximal, characteristic
16C23×Dic94C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26#15689035C418yescomplemented
27#15689028—24no—
28#15689027—24no—
29#15688996—24no—
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
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C24×C4×C47C2211yescharacteristic
49C22×C4⋊C4×C47C2211yescharacteristic
50C22×C4⋊C4×C47C2211yescharacteristic
51C22×C22⋊C4×C47C2211yescharacteristic
52C22×C22⋊C4×C47C2211yescharacteristic
53C47×#385—24no—
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C22×Dic94—22no—
57C22×Dic94—22no—
58C22×Dic94—22no—
59C22×Dic94—22no—
60C22×Dic94—41no—
61C22×Dic94—41no—
62C22×Dic94C2×C414yescomplemented
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C2×Dic47⋊C4—22no—
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4—22no—
74C2×Dic47⋊C4—41no—
75C2×Dic47⋊C4—41no—
76C2×Dic47⋊C4—41no—
77C2×Dic47⋊C4—41no—
78C2×Dic47⋊C4—41no—
79C2×Dic47⋊C4—41no—
80C2×C22⋊Dic47—22no—
81C2×C22⋊Dic47—22no—
82C2×C22⋊Dic47—22no—
83C2×C22⋊Dic47—22no—
84C2×C22⋊Dic47—41no—
85C2×C22⋊Dic47—41no—
86C2×C22⋊Dic47—41no—
87C2×C22⋊Dic47—41no—
88C2×C22⋊Dic47—41no—
89C2×C22⋊Dic47C2×C414yes—
90C2×C22⋊Dic47C2×C414yes—
91C2×C22⋊Dic47Q814yescomplemented
92C2×C4×Dic47—22no—
93C2×C4×Dic47—22no—
94C2×C4×Dic47—22no—
95C2×C4×Dic47—22no—
96C2×C4×Dic47—41no—
97C2×C4×Dic47—41no—
98C47⋊#95—22no—
99C47⋊#95—22no—
100C47⋊#95—22no—
101C47⋊#95—22no—
102C47⋊#95—22no—
103C47⋊#95—22no—
104C47⋊#95—22no—
105C47⋊#95—41no—
106C47⋊#95—41no—
107C47⋊#95—41no—
108C47⋊#95—41no—
109C47⋊#95—41no—
110C47⋊#95—41no—
111C47⋊#95—41no—
112C47⋊#95C2×C414yescomplemented
113C47⋊#95C2×C414yescomplemented
114C47⋊#95C2×C414yescomplemented
115C47⋊#95D414yes—
116C25×C47C2311yescharacteristic
117C23×C4×C47—22no—
118C23×C4×C47—22no—
119C23×C4×C47—22no—
120C23×C4×C47—41no—
121C23×C4×C47—41no—
122C23×C4×C47—41no—
123C23×C4×C47—41no—
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×C47—22no—
133C2×C4⋊C4×C47—41no—
134C2×C4⋊C4×C47—41no—
135C2×C4⋊C4×C47—41no—
136C2×C22⋊C4×C47—22no—
137C2×C22⋊C4×C47—22no—
138C2×C22⋊C4×C47—22no—
139C2×C22⋊C4×C47—22no—
140C2×C22⋊C4×C47—41no—
141C2×C22⋊C4×C47C2×C414yes—
142#95×C47—22no—
143#95×C47D414yes—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47C22×C412yes—
157C24×C47C2×Q812yes—
158C24×C47#4112yes—
159C24×C47C2411yescharacteristic
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—44no—
196C22×C4×C47—44no—
197C22×C4×C47—44no—
198C22×C4×C47—44no—
199C22×C4×C47—44no—
200C22×C4×C47—44no—
201C22×C4×C47—44no—
202C22×C4×C47C22×C412yes—
203C22×C4×C47C22×C412yes—
204C22×C4×C47C2×D412yes—
205C22×C4×C47C2×D412yes—
206C22×C4×C47C2×D412yes—
207C22×C4×C47C2×D412yes—
208C22×C4×C47#4112yes—
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×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×Dic47C22×C412yes—
260C22×Dic47C2×D412yes—
261C22×Dic47C2×D412yes—
262C22×Dic47C2×Q812yes—
263C22×Dic47C2×Q812yes—
264C22×Dic47#4112yes—
265C2×Dic94—28no—
266C2×Dic94—28no—
267C2×Dic94—44no—
268C2×Dic94—44no—
269C2×Dic94—44no—
270C2×Dic94—44no—
271C2×Dic94—44no—
272C4⋊C4×C47—44no—
273C4⋊C4×C47—44no—
274C22⋊C4×C47—28no—
275C22⋊C4×C47—44no—
276C22⋊Dic47—28no—
277C22⋊Dic47—44no—
278C22⋊Dic47—44no—
279C22⋊Dic47—44no—
280Dic47⋊C4—44no—
281Dic47⋊C4—44no—
282Dic47⋊C4—44no—
283C4×Dic47—44no—
284C4×Dic47—44no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—41no—
319C23×C47C4×Q814yes—
320C23×C47C23×C411yescharacteristic
321C23×C47C22×D411yescharacteristic
322C23×C47C22×D411yescharacteristic
323C23×C47C22×Q811yescharacteristic
324C23×C47C2×#4111yescharacteristic
325C23×C47C2×#4111yescharacteristic
326C23×C47C2×#4111yescharacteristic
327C23×C47H(5,𝔽2)11yescharacteristic
328C23×C47H(5,𝔽2)11yescharacteristic
329C23×C47H(5,𝔽2)11yescharacteristic
330C23×C47H(5,𝔽2)11yescharacteristic
331C23×C47H(5,𝔽2)11yescharacteristic
332C23×C472−1+411yescharacteristic
333C23×C472−1+411yescharacteristic
334C23×C472−1+411yescharacteristic
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—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—416no—
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×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47C4×D414yes—
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—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
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×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—41no—
421C2×Dic47—41no—
422C2×Dic47—41no—
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×Dic47C4×D414yes—
434Dic94—416no—
435#14575—471nomaximal, Sylow
436C22×C47—24no—
437C22×C47—24no—
438C22×C47—24no—
439C22×C47—42no—
440C22×C47—42no—
441C22×C47—42no—
442C22×C47—42no—
443C22×C47—42no—
444C22×C47—42no—
445C22×C47—42no—
446C22×C47—42no—
447C22×C47—42no—
448C22×C47—42no—
449C22×C47—42no—
450C22×C47—42no—
451C22×C47C2×C4×D411yescharacteristic
452C22×C47C2×C4×D411yescharacteristic
453C22×C47C2×C4×Q811yescharacteristic
454C22×C47#51811yescharacteristic
455C22×C47#52011yescharacteristic
456C22×C47#52011yescharacteristic
457C22×C47#52011yescharacteristic
458C22×C47#53511yescharacteristic
459C22×C47#53511yescharacteristic
460C22×C47#53611yescharacteristic
461C22×C47#53611yescharacteristic
462C22×C47#53811yescharacteristic
463C22×C47#53911yescharacteristic
464C22×C47#54211yescharacteristic
465C22×C47#54211yescharacteristic
466C22×C47#54211yescharacteristic
467C22×C47#54211yescharacteristic
468C22×C47#54311yescharacteristic
469C22×C47#54411yescharacteristic
470C22×C47D4211yescharacteristic
471C22×C47#54611yescharacteristic
472C22×C47#54611yescharacteristic
473C22×C47#54611yescharacteristic
474C22×C47#54611yescharacteristic
475C22×C47D4×Q811yescharacteristic
476C22×C47D4×Q811yescharacteristic
477C22×C47#55111yescharacteristic
478C22×C47#55211yescharacteristic
479C22×C47#55211yescharacteristic
480C22×C47#55411yescharacteristic
481C22×C47#55411yescharacteristic
482C22×C47H(3,𝔽4)11yescharacteristic
483C22×C47#56211yescharacteristic
484C22×C47#56211yescharacteristic
485C22×C47#56311yescharacteristic
486C4×C47—24no—
487C4×C47—42no—
488C4×C47—42no—
489C4×C47—42no—
490C4×C47—42no—
491C4×C47—81no—
492Dic47—24no—
493Dic47—42no—
494Dic47—42no—
495Dic47—42no—
496Dic47—42no—
497Dic47—42no—
498Dic47—42no—
499Dic47—81no—
500C2×#393—471no—
501C2×#391—471no—
502C2×#391—471no—
503C2×#385—471no—
504C2×#385D4711yescharacteristic
505#1444—471no—
506#1444—471no—
507#1442—471no—
508#1442—471no—
509#1439—471no—
510#1437—471no—
511#1437—471no—
512#1434—471no—
513#1434—471no—
514C22⋊#95—471no—
515C2×C47—44no—
516C2×C47#232611yescharacteristic
517C2×C47#232611yescharacteristic
518C2×C47#232911yescharacteristic
519C2×C47#235811yescharacteristic
520C2×C47#236011yescharacteristic
521C2×C47#236011yescharacteristic
522C2×C47#237911yescharacteristic
523C2×C47#267011yescharacteristic
524C2×C47#267711yescharacteristic
525C2×C47#268711yescharacteristic
526C2×C47#268711yescharacteristic
527C2×C47#269211yescharacteristic
528C2×C47#269211yescharacteristic
529C2×C47#276311yescharacteristic
530C2×C47#276411yescharacteristic
531C23×Q8—471no—
532C24×C4C2×D4711yescharacteristic
533C22×C4⋊C4—471no—
534C22×C4⋊C4—471no—
535C22×C4⋊C4—471no—
536C22×C4⋊C4C2×D4711yescharacteristic
537C22×C4⋊C4C2×D4711yescharacteristic
538C22×C22⋊C4—471no—
539C22×C22⋊C4—471no—
540C22×C22⋊C4—471no—
541C22×C22⋊C4—471no—
542C22×C22⋊C4C2×D4711yescharacteristic
543C22×C22⋊C4C2×D4711yescharacteristic
544C22×C42—471no—
545C22×C42—471no—
546#393—478no—
547#391—944no—
548#391—944no—
549#385—24no—
550#385—944no—
551C2×#95—471no—
552C2×#95—471no—
553C2×#95—471no—
554C2×#95—471no—
555C2×#95—471no—
556C2×#95—471no—
557C2×#95—471no—
558C2×#95—471no—
559C2×#95—471no—
560C2×#95—471no—
561C2×#95—471no—
562C2×#95—471no—
563C2×#95—471no—
564C2×#95—471no—
565C2×#95—471no—
566C2×#95—471no—
567C2×#95—471no—
568C2×#95—471no—
569C2×#95C2×D4711yescharacteristic
570C2×#95C2×D4711yescharacteristic
571C47#1457511yescharacteristic, complemented, Sylow
572C25C22×D4711yescharacteristic
573C22×Q8—474no—
574C22×Q8—942no—
575C22×Q8—942no—
576C22×Q8—942no—
577C22×Q8—942no—
578C22×Q8—1881no—
579C22×Q8—1881no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4—41no—
586C23×C4—41no—
587C23×C4—471no—
588C23×C4—471no—
589C23×C4—471no—
590C23×C4—471no—
591C23×C4—471no—
592C23×C4—471no—
593C23×C4—471no—
594C23×C4—471no—
595C23×C4C22×D4711yescharacteristic
596C23×C4C22×D4711yescharacteristic
597C23×C4C22×D4711yescharacteristic
598C23×C4C22×D4711yescharacteristic
599C23×C4C22×D4711yescharacteristic
600C23×C4C22×D4711yescharacteristic
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—942no—
608C2×C4⋊C4—942no—
609C2×C4⋊C4—942no—
610C2×C4⋊C4—1881no—
611C2×C4⋊C4—1881no—
612C2×C4⋊C4—1881no—
613C2×C4⋊C4—1881no—
614C2×C4⋊C4—1881no—
615C2×C4⋊C4—1881no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—474no—
622C2×C22⋊C4—474no—
623C2×C22⋊C4—474no—
624C2×C22⋊C4—942no—
625C2×C22⋊C4—942no—
626C2×C22⋊C4—942no—
627C2×C22⋊C4—942no—
628C2×C22⋊C4—1881no—
629C2×C22⋊C4—1881no—
630C2×C22⋊C4—1881no—
631C2×C22⋊C4—1881no—
632C2×C22⋊C4—1881no—
633C2×C22⋊C4C4×D4714yes—
634C2×C42—942no—
635C2×C42—942no—
636C2×C42—942no—
637C2×C42—942no—
638C2×C42—1881no—
639C2×C42—1881no—
640#95—22no—
641#95—474no—
642#95—474no—
643#95—474no—
644#95—474no—
645#95—942no—
646#95—942no—
647#95—942no—
648#95—942no—
649#95—942no—
650#95—942no—
651#95—942no—
652#95—1881no—
653#95—1881no—
654#95—1881no—
655#95—1881no—
656#95—1881no—
657#95—1881no—
658#95—1881no—
659#95C22⋊D4714yes—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24C2×C4×D4712yes—
673C24#1062535212yes—
674C24Q8×D4712yes—
675C24C23×D4711yescharacteristic
676C2×Q8—948no—
677C2×Q8—948no—
678C2×Q8—1884no—
679C2×Q8—1884no—
680C2×Q8—1884no—
681C2×Q8—1884no—
682C2×Q8—1884no—
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—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—472no—
726C22×C4—472no—
727C22×C4—472no—
728C22×C4—472no—
729C22×C4—472no—
730C22×C4—472no—
731C22×C4—472no—
732C22×C4—472no—
733C22×C4—472no—
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×C4—941no—
747C22×C4—941no—
748C22×C4—941no—
749C22×C4—941no—
750C22×C4—941no—
751C22×C4—941no—
752C22×C4—941no—
753C22×C4—941no—
754C22×C4—941no—
755C22×C4—941no—
756C22×C4—941no—
757C22×C4—941no—
758C22×C4—941no—
759C22×C4—941no—
760C22×C4—941no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4—941no—
765C22×C4—941no—
766C22×C4—941no—
767C22×C4—941no—
768C22×C4—941no—
769C22×C4—941no—
770C22×C4—941no—
771C22×C4—941no—
772C22×C4—941no—
773C22×C4—941no—
774C22×C4—941no—
775C22×C4—941no—
776C22×C4—941no—
777C22×C4—941no—
778C22×C4—941no—
779C22×C4—941no—
780C22×C4—941no—
781C22×C4C2×C4×D4712yes—
782C22×C4C2×C4×D4712yes—
783C22×C4#1062535012yes—
784C22×C4D4×D4712yes—
785C22×C4C2×C22⋊D4712yes—
786C22×C4C2×C22⋊D4712yes—
787C22×C4C2×C22⋊D4712yes—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—1884no—
791C4⋊C4—1884no—
792C4⋊C4—1884no—
793C22⋊C4—28no—
794C22⋊C4—44no—
795C22⋊C4—948no—
796C22⋊C4—1884no—
797C22⋊C4—1884no—
798C22⋊C4—1884no—
799C42—1884no—
800C42—1884no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23#1309398914yes—
836C23C22×C4×D4711yescharacteristic
837C23C2×D4×D4711yescharacteristic
838C23C22×C22⋊D4711yescharacteristic
839C23C2×Q8×D4711yescharacteristic
840C23#41×D4711yescharacteristic
841C23C2×#1062535211yescharacteristic
842C23C2×#1062535011yescharacteristic
843C23#1309406911yescharacteristic
844C23#1309406911yescharacteristic
845C23#1309406911yescharacteristic
846C23#1309406911yescharacteristic
847C23#1309407011yescharacteristic
848C23#1309407111yescharacteristic
849C23#1309407111yescharacteristic
850C23#1309407211yescharacteristic
851Q8—18816no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—416no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—474no—
895C2×C4—942no—
896C2×C4—942no—
897C2×C4—942no—
898C2×C4—942no—
899C2×C4—942no—
900C2×C4—942no—
901C2×C4—942no—
902C2×C4—942no—
903C2×C4—942no—
904C2×C4—942no—
905C2×C4—942no—
906C2×C4—942no—
907C2×C4—942no—
908C2×C4—942no—
909C2×C4—942no—
910C2×C4—942no—
911C2×C4—942no—
912C2×C4—942no—
913C2×C4—942no—
914C2×C4—942no—
915C2×C4—942no—
916C2×C4—942no—
917C2×C4—942no—
918C2×C4—942no—
919C2×C4—1881no—
920C2×C4—1881no—
921C2×C4—1881no—
922C2×C4—1881no—
923C2×C4—1881no—
924C2×C4—1881no—
925C2×C4—1881no—
926C2×C4—1881no—
927C2×C4—1881no—
928C2×C4—1881no—
929C2×C4—1881no—
930C2×C4—1881no—
931C2×C4—1881no—
932C2×C4—1881no—
933C2×C4—1881no—
934C2×C4—1881no—
935C2×C4—1881no—
936C2×C4—1881no—
937C2×C4—1881no—
938C2×C4—1881no—
939C2×C4—1881no—
940C2×C4—1881no—
941C2×C4—1881no—
942C2×C4—1881no—
943C2×C4—1881no—
944C2×C4—1881no—
945C2×C4—1881no—
946C2×C4—1881no—
947C2×C4—1881no—
948C2×C4—1881no—
949C2×C4—1881no—
950C2×C4C4×C22⋊D4714yes—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22C4×D4×D4711yescharacteristic
967C22C2×C4×C22⋊D4711yescharacteristic
968C22C2×#1309398911yescharacteristic
969C22#1568959511yescharacteristic
970C22#1568960211yescharacteristic
971C22#1568960211yescharacteristic
972C22#1568960411yescharacteristic
973C22#1568968811yescharacteristic
974C22#1568969011yescharacteristic
975C22#1568969411yescharacteristic
976C22#1568969611yescharacteristic
977C22#1568970811yescharacteristic
978C22#1568971711yescharacteristic
979C22#1568973811yescharacteristic
980C22#1568973811yescharacteristic
981C22#1568974111yescharacteristic
982C22#1568974311yescharacteristic
983C22#1568974811yescharacteristic
984C22#1568975211yescharacteristic
985C22D4×C22⋊D4711yescharacteristic
986C22#1568976011yescharacteristic
987C22#1568976111yescharacteristic
988C22#1568976711yescharacteristic
989C22#1568976911yescharacteristic
990C22#1568978611yescharacteristic
991C22Q8×C22⋊D4711yescharacteristic
992C22#1568980211yescharacteristic
993C22#1568980811yescharacteristic
994C22#1568981011yescharacteristic
995C22#1568982711yescharacteristic
996C22#1568982811yescharacteristic
997C22#1568986611yescharacteristic
998C22#1568986911yescharacteristic
999C22#1568987011yescharacteristic
1000C22#1568987411yescharacteristic
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—81no—
1007C4—944no—
1008C4—3761no—
1009C4—1882no—
1010C4—1882no—
1011C4—1882no—
1012C4—1882no—
1013C4—1882no—
1014C4—1882no—
1015C2—44no—
1016C2#2024609411yescharacteristic
1017C2#2024610011yescharacteristic
1018C2#2024611911yescharacteristic
1019C2#2024636511yescharacteristic
1020C2#2024638811yescharacteristic
1021C2#2024639311yescharacteristic
1022C2#2024656111yescharacteristic
1023C2#2024961011yescharacteristic
1024C2#2024969911yescharacteristic
1025C2#2024980311yescharacteristic
1026C2#2024981211yescharacteristic
1027C2#2024987811yescharacteristic
1028C2#2024988711yescharacteristic
1029C2#2025080011yescharacteristic
1030C2#2025080911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#385C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#385D47
hypocenterC47#14575
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#15689028C2semidirect
3. C2×#15689027C2semidirect
5. #20241651C2semidirect
6. #20241651C2semidirect
7. #20241647C2semidirect
8. #20241643C2semidirect
12. #20241613C2semidirect
13. #20241612C2semidirect
26. #15689035C4semidirect
62. C22×Dic94C2×C4semidirect
91. C2×C22⋊Dic47Q8semidirect
112. C47⋊#95C2×C4semidirect
113. C47⋊#95C2×C4semidirect
114. C47⋊#95C2×C4semidirect
571. C47#14575semidirect

Maximal subgroups

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

subgroupindex
C2×#156890352
C2×#156890282
C2×#156890272
C2×#156889962
#202416512
#202416472
#202416432
#202416312
#202416252
#202416132
#202416122
#202416112
C2×C47×#3852
#1457547