Finite Group Databasebeta

← #26145241

Subgroups — #26145241

Order 12032.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689016C211yesmaximal, characteristic
2C2×#15688998C211yesmaximal, characteristic
3#20241651C211yesmaximal, characteristic, complemented
4#20241644C211yesmaximal, characteristic, complemented
5#20241644C211yesmaximal, characteristic, complemented
6#20241640C211yesmaximal, characteristic, complemented
7#20241631C211yesmaximal, characteristic
8#20241631C211yesmaximal, characteristic
9#20241621C211yesmaximal, characteristic, complemented
10#20241618C211yesmaximal, characteristic, complemented
11#20241617C211yesmaximal, characteristic, complemented
12#20241614C211yesmaximal, characteristic, complemented
13#20241610C211yesmaximal, characteristic
14#20241610C211yesmaximal, characteristic
15C2×C47×#388C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26#15689016C418yescomplemented
27#15688998—24no—
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
45C2×C47⋊#95C2211yescharacteristic
46C22×C4⋊C4×C47C2211yescharacteristic
47C22×C22⋊C4×C47C2211yescharacteristic
48C22×C22⋊C4×C47C2211yescharacteristic
49C22×C22⋊C4×C47C2211yescharacteristic
50C22×C42×C47C2211yescharacteristic
51C47×#388—24no—
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C23×Dic47—22no—
55C23×Dic47—22no—
56C23×Dic47—22no—
57C23×Dic47—41no—
58C23×Dic47—41no—
59C23×Dic47—41no—
60C23×Dic47—41no—
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C2×C4⋊Dic47—22no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47—22no—
72C2×C4⋊Dic47—22no—
73C2×C4⋊Dic47—41no—
74C2×C4⋊Dic47—41no—
75C2×C4⋊Dic47—41no—
76C2×C4⋊Dic47—41no—
77C2×C4⋊Dic47C2×C414yescomplemented
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—41no—
80C2×Dic47⋊C4—41no—
81C2×Dic47⋊C4—41no—
82C2×Dic47⋊C4—41no—
83C2×Dic47⋊C4—41no—
84C2×C22⋊Dic47—22no—
85C2×C22⋊Dic47—41no—
86C2×C22⋊Dic47—41no—
87C2×C22⋊Dic47—41no—
88C2×C22⋊Dic47—41no—
89C2×C22⋊Dic47—41no—
90C2×C22⋊Dic47—41no—
91C2×C22⋊Dic47C2×C414yes—
92C2×C22⋊Dic47C2×C414yes—
93C2×C4×Dic47—41no—
94C2×C4×Dic47—41no—
95C2×C4×Dic47C2×C414yescomplemented
96C47⋊#95—22no—
97C47⋊#95—22no—
98C47⋊#95—22no—
99C47⋊#95—22no—
100C47⋊#95—22no—
101C47⋊#95—41no—
102C47⋊#95—41no—
103C47⋊#95—41no—
104C47⋊#95—41no—
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
114C25×C47C2311yescharacteristic
115C23×C4×C47C2311yescharacteristic
116C23×C4×C47C2311yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C23×C4×C47C2311yescharacteristic
119C23×C4×C47C2311yescharacteristic
120C23×C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47—22no—
122C2×C4⋊C4×C47—22no—
123C2×C4⋊C4×C47—41no—
124C2×C22⋊C4×C47—22no—
125C2×C22⋊C4×C47—22no—
126C2×C22⋊C4×C47—22no—
127C2×C22⋊C4×C47—22no—
128C2×C22⋊C4×C47—41no—
129C2×C22⋊C4×C47—41no—
130C2×C22⋊C4×C47C2×C414yes—
131C2×C22⋊C4×C47D414yes—
132C2×C22⋊C4×C47Q814yes—
133C2×C42×C47—22no—
134C2×C42×C47—22no—
135C2×C42×C47—41no—
136#95×C47—22no—
137#95×C47—22no—
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—21no—
141C24×C47—21no—
142C24×C47—21no—
143C24×C47—21no—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47C22×C412yes—
151C24×C47C2×D412yes—
152C24×C47C2×Q812yes—
153C24×C47C2411yescharacteristic
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×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×C47C22×C412yes—
189C22×C4×C47C22×C412yes—
190C22×C4×C47C2×D412yes—
191C22×C4×C47C2×D412yes—
192C22×C4×C47C2×Q812yes—
193C22×C4×C47C2×Q812yes—
194C22×C4×C47#4112yes—
195C22×C4×C47#4112yes—
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×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—44no—
247C22×Dic47—44no—
248C22×Dic47—44no—
249C22×Dic47—44no—
250C22×Dic47—44no—
251C22×Dic47—44no—
252C22×Dic47—44no—
253C22×Dic47C22×C412yes—
254C22×Dic47C22×C412yes—
255C22×Dic47C22×C412yes—
256C22×Dic47C22×C412yes—
257C22×Dic47#4112yes—
258C22×Dic47#4112yes—
259C4⋊C4×C47—44no—
260C22⋊C4×C47—44no—
261C22⋊C4×C47—44no—
262C22⋊C4×C47C4⋊C4116yescomplemented
263C42×C47—44no—
264C22⋊Dic47—44no—
265C22⋊Dic47—44no—
266C22⋊Dic47—44no—
267C4⋊Dic47—44no—
268C4⋊Dic47—44no—
269C4⋊Dic47—44no—
270Dic47⋊C4—44no—
271Dic47⋊C4—44no—
272C4×Dic47—44no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47C2×C4⋊C414yes—
308C23×C47C23×C411yescharacteristic
309C23×C47C22×D411yescharacteristic
310C23×C47C22×Q811yescharacteristic
311C23×C47C2×#4111yescharacteristic
312C23×C47C2×#4111yescharacteristic
313C23×C47C2×#4111yescharacteristic
314C23×C47C2×#4111yescharacteristic
315C23×C47H(5,𝔽2)11yescharacteristic
316C23×C47H(5,𝔽2)11yescharacteristic
317C23×C47H(5,𝔽2)11yescharacteristic
318C23×C47H(5,𝔽2)11yescharacteristic
319C23×C47H(5,𝔽2)11yescharacteristic
320C23×C47H(5,𝔽2)11yescharacteristic
321C23×C472−1+411yescharacteristic
322C23×C472−1+411yescharacteristic
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—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
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×C47C2×C4⋊C414yes—
364C2×C4×C47C2×C4⋊C414yes—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
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—416no—
384C2×Dic47—41no—
385C2×Dic47—41no—
386C2×Dic47—41no—
387C2×Dic47—41no—
388C2×Dic47—41no—
389C2×Dic47—41no—
390C2×Dic47—41no—
391C2×Dic47—41no—
392C2×Dic47—41no—
393C2×Dic47—41no—
394C2×Dic47—41no—
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×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—41no—
421C2×Dic47—41no—
422#14488—471nomaximal, Sylow
423C22×C47—24no—
424C22×C47—24no—
425C22×C47—24no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—42no—
429C22×C47—42no—
430C22×C47—42no—
431C22×C47—42no—
432C22×C47—42no—
433C22×C47—42no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47C22×C4⋊C411yescharacteristic
439C22×C47C4×#4111yescharacteristic
440C22×C47C4×#4111yescharacteristic
441C22×C47#51811yescharacteristic
442C22×C47#51811yescharacteristic
443C22×C47#52011yescharacteristic
444C22×C47#52011yescharacteristic
445C22×C47#53511yescharacteristic
446C22×C47#53611yescharacteristic
447C22×C47#53811yescharacteristic
448C22×C47#53811yescharacteristic
449C22×C47#53811yescharacteristic
450C22×C47#53911yescharacteristic
451C22×C47#54011yescharacteristic
452C22×C47#54211yescharacteristic
453C22×C47#54211yescharacteristic
454C22×C47#54211yescharacteristic
455C22×C47#54411yescharacteristic
456C22×C47#54411yescharacteristic
457C22×C47#54611yescharacteristic
458C22×C47#54611yescharacteristic
459C22×C47#54611yescharacteristic
460C22×C47#54611yescharacteristic
461C22×C47#55111yescharacteristic
462C22×C47#55211yescharacteristic
463C22×C47#55311yescharacteristic
464C22×C47#55411yescharacteristic
465C22×C47#55411yescharacteristic
466C22×C47#55411yescharacteristic
467C22×C47#55411yescharacteristic
468C22×C47#55611yescharacteristic
469C22×C47#56011yescharacteristic
470C22×C47#56011yescharacteristic
471C22×C47#56211yescharacteristic
472C22×C47#56211yescharacteristic
473C4×C47—24no—
474C4×C47—24no—
475C4×C47—42no—
476C4×C47—42no—
477C4×C47—81no—
478C4×C47—81no—
479Dic47—42no—
480Dic47—42no—
481Dic47—42no—
482Dic47—42no—
483Dic47—42no—
484Dic47—42no—
485Dic47—81no—
486Dic47—81no—
487C2×#388—471no—
488C2×#388D4711yescharacteristic
489C2×#385—471no—
490#1444—471no—
491#1442—471no—
492#1442—471no—
493#1441—471no—
494#1439—471no—
495#1439—471no—
496#1436—471no—
497C4⋊#95—471no—
498C4⋊#95—471no—
499#1434—471no—
500C22⋊#95—471no—
501C22⋊#95—471no—
502C2×C47—44no—
503C2×C47#231711yescharacteristic
504C2×C47#233511yescharacteristic
505C2×C47#233711yescharacteristic
506C2×C47#234911yescharacteristic
507C2×C47#234911yescharacteristic
508C2×C47#237311yescharacteristic
509C2×C47#237711yescharacteristic
510C2×C47#268511yescharacteristic
511C2×C47#268711yescharacteristic
512C2×C47#270011yescharacteristic
513C2×C47#270311yescharacteristic
514C2×C47#274211yescharacteristic
515C2×C47#276811yescharacteristic
516C2×C47#278811yescharacteristic
517C2×C47#279011yescharacteristic
518C24×C4—471no—
519C22×C4⋊C4—471no—
520C22×C4⋊C4—471no—
521C22×C4⋊C4—471no—
522C22×C4⋊C4—471no—
523C22×C4⋊C4—471no—
524C22×C4⋊C4C2×D4711yescharacteristic
525C22×C22⋊C4—471no—
526C22×C22⋊C4—471no—
527C22×C22⋊C4—471no—
528C22×C22⋊C4C2×D4711yescharacteristic
529C22×C22⋊C4C2×D4711yescharacteristic
530C22×C22⋊C4C2×D4711yescharacteristic
531C22×C42—471no—
532C22×C42C2×D4711yescharacteristic
533#388—24no—
534#388—478no—
535#385—944no—
536C2×#95—471no—
537C2×#95—471no—
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×#95—471no—
552C2×#95—471no—
553C2×#95—471no—
554C2×#95C2×D4711yescharacteristic
555C2×#95C2×D4711yescharacteristic
556C47#1448811yescharacteristic, complemented, Sylow
557C25C22×D4711yescharacteristic
558C23×C4—471no—
559C23×C4—471no—
560C23×C4—471no—
561C23×C4—471no—
562C23×C4—471no—
563C23×C4—471no—
564C23×C4—471no—
565C23×C4—471no—
566C23×C4—942no—
567C23×C4—942no—
568C23×C4—942no—
569C23×C4—1881no—
570C23×C4—1881no—
571C23×C4—1881no—
572C23×C4—1881no—
573C23×C4C22×D4711yescharacteristic
574C23×C4C22×D4711yescharacteristic
575C23×C4C22×D4711yescharacteristic
576C23×C4C22×D4711yescharacteristic
577C23×C4C22×D4711yescharacteristic
578C23×C4C22×D4711yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—474no—
583C2×C4⋊C4—942no—
584C2×C4⋊C4—942no—
585C2×C4⋊C4—942no—
586C2×C4⋊C4—942no—
587C2×C4⋊C4—942no—
588C2×C4⋊C4—1881no—
589C2×C4⋊C4—1881no—
590C2×C4⋊C4—1881no—
591C2×C4⋊C4—1881no—
592C2×C4⋊C4—1881no—
593C2×C4⋊C4—1881no—
594C2×C4⋊C4—1881no—
595C2×C4⋊C4—1881no—
596C2×C4⋊C4—1881no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—474no—
604C2×C22⋊C4—474no—
605C2×C22⋊C4—942no—
606C2×C22⋊C4—1881no—
607C2×C22⋊C4—1881no—
608C2×C22⋊C4—1881no—
609C2×C22⋊C4—1881no—
610C2×C22⋊C4—1881no—
611C2×C22⋊C4—1881no—
612C2×C22⋊C4Dic9414yes—
613C2×C22⋊C4C4×D4714yes—
614C2×C22⋊C4C22⋊D4714yes—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—41no—
618C2×C42—474no—
619C2×C42—1881no—
620C2×C42—1881no—
621#95—22no—
622#95—22no—
623#95—474no—
624#95—474no—
625#95—942no—
626#95—942no—
627#95—942no—
628#95—942no—
629#95—942no—
630#95—1881no—
631#95—1881no—
632#95—1881no—
633#95—1881no—
634#95—1881no—
635#95—1881no—
636#95—1881no—
637#95—1881no—
638#95—1881no—
639#95—1881no—
640#95—1881no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×Dic9412yes—
654C24C2×C4×D4712yes—
655C24C2×C22⋊D4712yes—
656C24C23×D4711yescharacteristic
657C22×C4—21no—
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—472no—
692C22×C4—472no—
693C22×C4—472no—
694C22×C4—472no—
695C22×C4—472no—
696C22×C4—472no—
697C22×C4—941no—
698C22×C4—941no—
699C22×C4—941no—
700C22×C4—941no—
701C22×C4—941no—
702C22×C4—941no—
703C22×C4—941no—
704C22×C4—941no—
705C22×C4—941no—
706C22×C4—941no—
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×C4—941no—
747C22×C4—1884no—
748C22×C4—1884no—
749C22×C4—1884no—
750C22×C4—1884no—
751C22×C4—1884no—
752C22×C4—1884no—
753C22×C4—1884no—
754C22×C4C2×Dic9412yes—
755C22×C4C2×Dic9412yes—
756C22×C4C2×C4×D4712yes—
757C22×C4C2×C4×D4712yes—
758C22×C4#1062535212yes—
759C22×C4#1062535212yes—
760C22×C4C2×C22⋊D4712yes—
761C22×C4C2×C22⋊D4712yes—
762C4⋊C4—44no—
763C4⋊C4—1884no—
764C4⋊C4—1884no—
765C4⋊C4—1884no—
766C4⋊C4—1884no—
767C4⋊C4—1884no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—1884no—
771C22⋊C4—1884no—
772C22⋊C4—1884no—
773C22⋊C4Dic47⋊C4116yescomplemented
774C42—44no—
775C42—1884no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×Dic47⋊C414yes—
811C23C22×C4×D4711yescharacteristic
812C23C22×C22⋊D4711yescharacteristic
813C23C22×Dic9411yescharacteristic
814C23#41×D4711yescharacteristic
815C23#41×D4711yescharacteristic
816C23C2×#1062535211yescharacteristic
817C23C2×#1062535211yescharacteristic
818C23#1309406911yescharacteristic
819C23#1309406911yescharacteristic
820C23#1309407011yescharacteristic
821C23#1309407011yescharacteristic
822C23#1309407011yescharacteristic
823C23#1309407011yescharacteristic
824C23#1309407111yescharacteristic
825C23#1309407111yescharacteristic
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—41no—
845C2×C4—41no—
846C2×C4—41no—
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—942no—
867C2×C4—942no—
868C2×C4—942no—
869C2×C4—942no—
870C2×C4—942no—
871C2×C4—942no—
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—1881no—
885C2×C4—1881no—
886C2×C4—1881no—
887C2×C4—1881no—
888C2×C4—1881no—
889C2×C4—1881no—
890C2×C4—1881no—
891C2×C4—1881no—
892C2×C4—1881no—
893C2×C4—1881no—
894C2×C4—1881no—
895C2×C4—1881no—
896C2×C4—1881no—
897C2×C4—1881no—
898C2×C4—18816no—
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×C4—1881no—
920C2×C4—1881no—
921C2×C4—1881no—
922C2×C4—1881no—
923C2×C4C2×Dic47⋊C414yes—
924C2×C4C2×Dic47⋊C414yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×Dic47⋊C411yescharacteristic
941C22C4×#1062535211yescharacteristic
942C22C4×#1062535211yescharacteristic
943C22#1568959511yescharacteristic
944C22#1568959511yescharacteristic
945C22#1568960311yescharacteristic
946C22#1568960311yescharacteristic
947C22#1568968711yescharacteristic
948C22#1568969411yescharacteristic
949C22#1568971011yescharacteristic
950C22#1568971211yescharacteristic
951C22#1568971211yescharacteristic
952C22#1568971711yescharacteristic
953C22#1568972611yescharacteristic
954C22#1568973711yescharacteristic
955C22#1568974111yescharacteristic
956C22#1568974211yescharacteristic
957C22#1568975111yescharacteristic
958C22#1568975111yescharacteristic
959C22#1568976111yescharacteristic
960C22#1568976111yescharacteristic
961C22#1568976711yescharacteristic
962C22#1568976711yescharacteristic
963C22#1568979811yescharacteristic
964C22#1568981011yescharacteristic
965C22#1568982511yescharacteristic
966C22#1568983011yescharacteristic
967C22#1568983011yescharacteristic
968C22#1568983211yescharacteristic
969C22#1568983211yescharacteristic
970C22#1568984211yescharacteristic
971C22#1568986111yescharacteristic
972C22#1568986411yescharacteristic
973C22#1568986711yescharacteristic
974C22#1568987011yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—3761no—
982C4—3761no—
983C4—1882no—
984C4—1882no—
985C4—1882no—
986C4—1882no—
987C4—1882no—
988C4—1882no—
989C2—44no—
990C2#2024600811yescharacteristic
991C2#2024618511yescharacteristic
992C2#2024619511yescharacteristic
993C2#2024629311yescharacteristic
994C2#2024629311yescharacteristic
995C2#2024651511yescharacteristic
996C2#2024654111yescharacteristic
997C2#2024977311yescharacteristic
998C2#2024980311yescharacteristic
999C2#2024998011yescharacteristic
1000C2#2025002711yescharacteristic
1001C2#2025051411yescharacteristic
1002C2#2025087211yescharacteristic
1003C2#2025113111yescharacteristic
1004C2#2025115811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#388C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#388D47
hypocenterC47#14488
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. #20241651C2semidirect
4. #20241644C2semidirect
5. #20241644C2semidirect
6. #20241640C2semidirect
9. #20241621C2semidirect
10. #20241618C2semidirect
11. #20241617C2semidirect
12. #20241614C2semidirect
26. #15689016C4semidirect
77. C2×C4⋊Dic47C2×C4semidirect
95. C2×C4×Dic47C2×C4semidirect
112. C47⋊#95C2×C4semidirect
113. C47⋊#95C2×C4semidirect
262. C22⋊C4×C47C4⋊C4semidirect
556. C47#14488semidirect
773. C22⋊C4Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156890162
C2×#156889982
#202416512
#202416442
#202416402
#202416312
#202416212
#202416182
#202416172
#202416142
#202416102
C2×C47×#3882
#1448847