Finite Group Databasebeta

← C2×#20246512 #26375970

Subgroups — C2×#20246512 #26375970

Order 12032.

2726 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246512C2116yesmaximal, direct product factor
2C2×#15689022C211yesmaximal, characteristic, complemented
3C2×#15689016C211yesmaximal, characteristic
4C2×#15689016C211yesmaximal, characteristic
5C2×#15689016C211yesmaximal, characteristic
6C2×#15689009C211yesmaximal, characteristic, complemented
7C2×#15689009C211yesmaximal, characteristic, complemented
8C2×#15689009C211yesmaximal, characteristic, complemented
9C2×#15688998C211yesmaximal, characteristic
10C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic47C211yesmaximal, characteristic
14C2×C22⋊C4×Dic47C211yesmaximal, characteristic
15C2×#15688969C211yesmaximal, characteristic, complemented
16C22×#126×C47C211yesmaximal, characteristic
17C24×Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28C22×C4×Dic47C2211yescharacteristic
29C22×C4×Dic47C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33#15689022C2218yescomplemented
34#15689016C2218yes—
35#15689016C2218yes—
36#15689016C2218yes—
37#15689009C2218yescomplemented
38#15689009C2218yescomplemented
39#15689009C2218yescomplemented
40#15688998C2218yes—
41C4⋊C4×Dic47C2218yescomplemented
42C4⋊C4×Dic47C2218yescomplemented
43C4×C4⋊Dic47C2218yescomplemented
44C22⋊C4×Dic47C2218yes—
45C22⋊C4×Dic47C2218yes—
46#15688969C2218yescomplemented
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×#126×C47C4116yescomplemented
60C2×#126×C47C2218yes—
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C42×C47C2211yescharacteristic
68C23×Dic47—24no—
69C23×Dic47—24no—
70C23×Dic47—42no—
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2314yes—
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C2×C4⋊Dic47—24no—
81C2×C4⋊Dic47—24no—
82C2×C4⋊Dic47—24no—
83C2×C4⋊Dic47—24no—
84C2×C4⋊Dic47—42no—
85C2×C4⋊Dic47C2314yes—
86C2×C4⋊Dic47C2314yes—
87C2×C4⋊Dic47C2314yes—
88C2×C4⋊Dic47C2314yes—
89C2×C4⋊Dic47C2314yes—
90C2×C22⋊Dic47—24no—
91C2×C22⋊Dic47—24no—
92C2×C22⋊Dic47—42no—
93C2×C22⋊Dic47C2314yes—
94C2×C22⋊Dic47C2314yes—
95C2×C22⋊Dic47C2314yes—
96C2×C4×Dic47—24no—
97C2×C4×Dic47—24no—
98C2×C4×Dic47—24no—
99C2×C4×Dic47—24no—
100C2×C4×Dic47—42no—
101C2×C4×Dic47—42no—
102C2×C4×Dic47—42no—
103C2×C4×Dic47C2314yes—
104C2×C4×Dic47C2314yes—
105C2×C4×Dic47C2314yes—
106C2×C4×Dic47C2314yes—
107C2×C4×Dic47C2314yes—
108C2×C4×Dic47C2314yes—
109C2×C4×Dic47C2314yes—
110C47⋊#95C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C25×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129#126×C47C2×C4164yescomplemented
130C2×C4⋊C4×C47C2×C418yescomplemented
131C2×C4⋊C4×C47C2×C418yescomplemented
132C2×C4⋊C4×C47C2×C418yescomplemented
133C2×C4⋊C4×C47C2314yes—
134C2×C4⋊C4×C47C2314yes—
135C2×C4⋊C4×C47C2314yes—
136C2×C22⋊C4×C47C2×C418yes—
137C2×C22⋊C4×C47C2×C418yes—
138C2×C22⋊C4×C47C2×C418yes—
139C2×C22⋊C4×C47C2314yes—
140C2×C22⋊C4×C47C2314yes—
141C2×C22⋊C4×C47C2314yes—
142C2×C42×C47C2×C418yescomplemented
143C2×C42×C47C2314yes—
144C24×C47—22no—
145C24×C47—22no—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—22no—
149C24×C47—22no—
150C24×C47C22×C414yes—
151C24×C47C2412yes—
152C24×C47C2411yescharacteristic
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47C22×C414yes—
166C22×C4×C47C22×C414yes—
167C22×C4×C47C22×C414yes—
168C22×C4×C47C22×C414yes—
169C22×C4×C47C22×C414yes—
170C22×C4×C47C22×C414yes—
171C22×C4×C47C2412yes—
172C22×C4×C47C2412yes—
173C22×C4×C47C2412yes—
174C22×C4×C47C2412yes—
175C22×C4×C47C2412yes—
176C22×C4×C47C2412yes—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—28no—
198C22×Dic47—28no—
199C22×Dic47—44no—
200C22×Dic47—416no—
201C22×Dic47#4114yes—
202C22×Dic47#4114yes—
203C22×Dic47#4114yes—
204C22×Dic47#4114yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C22×Dic47C2412yes—
210C22×Dic47C2412yes—
211C22×Dic47C2412yes—
212C22×Dic47C2412yes—
213C4⋊C4×C47C22×C4116yescomplemented
214C4⋊C4×C47C22×C4116yescomplemented
215C4⋊C4×C47C22×C4116yescomplemented
216C22⋊C4×C47C22×C4116yes—
217C22⋊C4×C47C22×C4116yes—
218C22⋊C4×C47C22×C4116yes—
219C42×C47C22×C4116yescomplemented
220C22⋊Dic47—28no—
221C22⋊Dic47—28no—
222C22⋊Dic47—44no—
223C4⋊Dic47—28no—
224C4⋊Dic47—28no—
225C4⋊Dic47—28no—
226C4⋊Dic47—28no—
227C4⋊Dic47—44no—
228C4×Dic47—28no—
229C4×Dic47—28no—
230C4×Dic47—28no—
231C4×Dic47—28no—
232C4×Dic47—44no—
233C4×Dic47—44no—
234C4×Dic47—44no—
235C23×C47—28no—
236C23×C47—28no—
237C23×C47—28no—
238C23×C47—22no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—44no—
245C23×C47—44no—
246C23×C47—44no—
247C23×C47—44no—
248C23×C47C23×C414yes—
249C23×C47C23×C412yes—
250C23×C47C2×#4112yes—
251C23×C47C2×#4112yes—
252C23×C47C2×#4112yes—
253C23×C47C2×#4112yes—
254C23×C47H(5,𝔽2)12yes—
255C23×C472−1+412yes—
256C23×C47C2511yescharacteristic
257C2×C4×C47—28no—
258C2×C4×C47—28no—
259C2×C4×C47—28no—
260C2×C4×C47—28no—
261C2×C4×C47—28no—
262C2×C4×C47—28no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47C23×C414yes—
276C2×C4×C47C23×C414yes—
277C2×C4×C47C23×C414yes—
278C2×C4×C47C23×C414yes—
279C2×C4×C47C23×C414yes—
280C2×C4×C47C23×C414yes—
281C2×Dic47—28no—
282C2×Dic47—28no—
283C2×Dic47—28no—
284C2×Dic47—28no—
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—416no—
306C2×Dic47—44no—
307C2×Dic47—44no—
308C2×Dic47—44no—
309C2×Dic47—44no—
310C2×Dic47C2×#4114yes—
311C2×Dic47C2×#4114yes—
312C2×Dic47C2×#4114yes—
313C2×Dic47C2×#4114yes—
314C2×#2373—471nomaximal, Sylow
315C22×C47—24no—
316C22×C47—24no—
317C22×C47—24no—
318C22×C47—416no—
319C22×C47—42no—
320C22×C47—42no—
321C22×C47—42no—
322C22×C47—42no—
323C22×C47C4×#4114yes—
324C22×C47C4×#4114yes—
325C22×C47#52014yes—
326C22×C47#55114yes—
327C22×C47#55214yes—
328C22×C47#55314yes—
329C22×C47#55614yes—
330C22×C47C24×C411yescharacteristic
331C22×C47C22×#4111yescharacteristic
332C22×C47C22×#4111yescharacteristic
333C22×C47C22×#4111yescharacteristic
334C22×C47C22×#4111yescharacteristic
335C22×C47C2×H(5,𝔽2)11yescharacteristic
336C22×C47C2×2−1+411yescharacteristic
337C4×C47—24no—
338C4×C47—24no—
339C4×C47—24no—
340C4×C47—24no—
341C4×C47—24no—
342C4×C47—24no—
343Dic47—24no—
344Dic47—24no—
345Dic47—24no—
346Dic47—24no—
347Dic47—42no—
348Dic47—42no—
349Dic47—42no—
350Dic47—42no—
351C22×#126D4711yescharacteristic
352#2373—4716no—
353C2×#389—471no—
354C2×#388—471no—
355C2×#388—471no—
356C2×#388—471no—
357C2×#387—471no—
358C2×#387—471no—
359C2×#387—471no—
360C2×#385—471no—
361C2×C4×C4⋊C4—471no—
362C2×C4×C4⋊C4—471no—
363C2×C4×C4⋊C4—471no—
364C2×C4×C22⋊C4—471no—
365C2×C4×C22⋊C4—471no—
366C2×#376—471no—
367C2×C47—44no—
368C2×C47#237318yescomplemented
369C2×C47C2×C4×#4111yescharacteristic
370C2×C47C2×C4×#4111yescharacteristic
371C2×C47C2×#52011yescharacteristic
372C2×C47C2×#55111yescharacteristic
373C2×C47C2×#55211yescharacteristic
374C2×C47C2×#55311yescharacteristic
375C2×C47C2×#55611yescharacteristic
376C24×C4—471no—
377C2×#126Dic47116yescomplemented
378C2×#126C2×D4718yes—
379C22×C4⋊C4—471no—
380C22×C4⋊C4—471no—
381C22×C4⋊C4—471no—
382C22×C4⋊C4—471no—
383C22×C4⋊C4—471no—
384C22×C4⋊C4C2×D4711yescharacteristic
385C22×C4⋊C4C2×D4711yescharacteristic
386C22×C4⋊C4C2×D4711yescharacteristic
387C22×C22⋊C4—471no—
388C22×C22⋊C4—471no—
389C22×C22⋊C4—471no—
390C22×C22⋊C4C2×D4711yescharacteristic
391C22×C22⋊C4C2×D4711yescharacteristic
392C22×C22⋊C4C2×D4711yescharacteristic
393C22×C42—471no—
394C22×C42—471no—
395C22×C42—471no—
396C22×C42—471no—
397C22×C42—471no—
398C22×C42—471no—
399C22×C42—471no—
400C22×C42C2×D4711yescharacteristic
401#389—478no—
402#388—478no—
403#388—478no—
404#388—478no—
405#387—478no—
406#387—478no—
407#387—478no—
408#385—478no—
409C4×C4⋊C4—478no—
410C4×C4⋊C4—478no—
411C4×C4⋊C4—478no—
412C4×C22⋊C4—478no—
413C4×C22⋊C4—478no—
414#376—478no—
415C2×#95—471no—
416C2×#95—471no—
417C2×#95—471no—
418C2×#95—471no—
419C2×#95—471no—
420C2×#95—471no—
421C2×#95—471no—
422C2×#95—471no—
423C2×#95—471no—
424C2×#95—471no—
425C2×#95—471no—
426C2×#95—471no—
427C47C2×#237311yescharacteristic, complemented, Sylow
428C25C22×D4711yescharacteristic
429C23×C4—471no—
430C23×C4—471no—
431C23×C4—471no—
432C23×C4—471no—
433C23×C4—471no—
434C23×C4—471no—
435C23×C4—471no—
436C23×C4—471no—
437C23×C4—474no—
438C23×C4—944no—
439C23×C4—944no—
440C23×C4—1882no—
441C23×C4C22×D4711yescharacteristic
442C23×C4C22×D4711yescharacteristic
443C23×C4C22×D4711yescharacteristic
444C23×C4C22×D4711yescharacteristic
445C23×C4C22×D4711yescharacteristic
446C23×C4C22×D4711yescharacteristic
447#126C2×Dic47164yescomplemented
448C2×C4⋊C4—474no—
449C2×C4⋊C4—474no—
450C2×C4⋊C4—474no—
451C2×C4⋊C4—474no—
452C2×C4⋊C4—474no—
453C2×C4⋊C4—944no—
454C2×C4⋊C4—944no—
455C2×C4⋊C4—944no—
456C2×C4⋊C4—944no—
457C2×C4⋊C4—1882no—
458C2×C4⋊C4C2×Dic4718yescomplemented
459C2×C4⋊C4C2×Dic4718yescomplemented
460C2×C4⋊C4C2×Dic4718yescomplemented
461C2×C4⋊C4C22×D4714yes—
462C2×C4⋊C4C22×D4714yes—
463C2×C4⋊C4C22×D4714yes—
464C2×C22⋊C4—474no—
465C2×C22⋊C4—474no—
466C2×C22⋊C4—474no—
467C2×C22⋊C4—944no—
468C2×C22⋊C4—944no—
469C2×C22⋊C4—1882no—
470C2×C22⋊C4C2×Dic4718yes—
471C2×C22⋊C4C2×Dic4718yes—
472C2×C22⋊C4C2×Dic4718yes—
473C2×C22⋊C4C22×D4714yes—
474C2×C22⋊C4C22×D4714yes—
475C2×C22⋊C4C22×D4714yes—
476C2×C42—474no—
477C2×C42—474no—
478C2×C42—474no—
479C2×C42—474no—
480C2×C42—474no—
481C2×C42—474no—
482C2×C42—474no—
483C2×C42—944no—
484C2×C42—944no—
485C2×C42—944no—
486C2×C42—944no—
487C2×C42—1882no—
488C2×C42—1882no—
489C2×C42—1882no—
490C2×C42C2×Dic4718yescomplemented
491C2×C42C22×D4714yes—
492#95—474no—
493#95—474no—
494#95—474no—
495#95—474no—
496#95—474no—
497#95—474no—
498#95—474no—
499#95—474no—
500#95—474no—
501#95—474no—
502#95—474no—
503#95—474no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24C22×Dic4714yes—
511C24C23×D4712yes—
512C24C23×D4711yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—474no—
526C22×C4—474no—
527C22×C4—474no—
528C22×C4—474no—
529C22×C4—472no—
530C22×C4—472no—
531C22×C4—472no—
532C22×C4—472no—
533C22×C4—472no—
534C22×C4—472no—
535C22×C4—472no—
536C22×C4—472no—
537C22×C4—948no—
538C22×C4—948no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—942no—
558C22×C4—942no—
559C22×C4—1884no—
560C22×C4—18816no—
561C22×C4C22×Dic4714yes—
562C22×C4C22×Dic4714yes—
563C22×C4C22×Dic4714yes—
564C22×C4C22×Dic4714yes—
565C22×C4C22×Dic4714yes—
566C22×C4C22×Dic4714yes—
567C22×C4C23×D4712yes—
568C22×C4C23×D4712yes—
569C22×C4C23×D4712yes—
570C22×C4C23×D4712yes—
571C22×C4C23×D4712yes—
572C22×C4C23×D4712yes—
573C4⋊C4—948no—
574C4⋊C4—948no—
575C4⋊C4—948no—
576C4⋊C4—948no—
577C4⋊C4—1884no—
578C4⋊C4C22×Dic47116yescomplemented
579C4⋊C4C22×Dic47116yescomplemented
580C4⋊C4C22×Dic47116yescomplemented
581C22⋊C4—948no—
582C22⋊C4—948no—
583C22⋊C4—1884no—
584C22⋊C4C22×Dic47116yes—
585C22⋊C4C22×Dic47116yes—
586C22⋊C4C22×Dic47116yes—
587C42—948no—
588C42—948no—
589C42—948no—
590C42—948no—
591C42—1884no—
592C42—1884no—
593C42—1884no—
594C42C22×Dic47116yescomplemented
595C23—28no—
596C23—28no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23C23×Dic4714yes—
609C23C23×Dic4712yes—
610C23#41×D4712yes—
611C23#41×D4712yes—
612C23#41×D4712yes—
613C23#41×D4712yes—
614C23#1309407012yes—
615C23#1309407112yes—
616C23C24×D4711yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—474no—
636C2×C4—474no—
637C2×C4—474no—
638C2×C4—474no—
639C2×C4—948no—
640C2×C4—948no—
641C2×C4—948no—
642C2×C4—948no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—18816no—
664C2×C4—1884no—
665C2×C4—1884no—
666C2×C4—1884no—
667C2×C4—1884no—
668C2×C4C23×Dic4714yes—
669C2×C4C23×Dic4714yes—
670C2×C4C23×Dic4714yes—
671C2×C4C23×Dic4714yes—
672C2×C4C23×Dic4714yes—
673C2×C4C23×Dic4714yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—416no—
682C22#41×Dic4714yes—
683C22#41×Dic4714yes—
684C22#1568960614yes—
685C22#1568979814yes—
686C22#1568980914yes—
687C22#1568982414yes—
688C22#1568984014yes—
689C22C24×Dic4711yescharacteristic
690C22C2×#41×D4711yescharacteristic
691C22C2×#41×D4711yescharacteristic
692C22C2×#41×D4711yescharacteristic
693C22C2×#41×D4711yescharacteristic
694C22C2×#1309407011yescharacteristic
695C22C2×#1309407111yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—24no—
701C4—24no—
702C4—944no—
703C4—944no—
704C4—944no—
705C4—944no—
706C4—1882no—
707C4—1882no—
708C4—1882no—
709C4—1882no—
710C2—44no—
711C2#2024651218yesdirect product factor
712C2C2×#41×Dic4711yescharacteristic
713C2C2×#41×Dic4711yescharacteristic
714C2C2×#1568960611yescharacteristic
715C2C2×#1568979811yescharacteristic
716C2C2×#1568980911yescharacteristic
717C2C2×#1568982411yescharacteristic
718C2C2×#1568984011yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC22×#126×C47C2
socleC24×C47C24
prime radicalC25×C47C23
cosocleC23×C47C25
hypercenterC22×#126D47
hypocenterC47C2×#2373
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. #20246512C2direct (N × H)
2. C2×#15689022C2semidirect
6. C2×#15689009C2semidirect
7. C2×#15689009C2semidirect
8. C2×#15689009C2semidirect
10. C2×C4⋊C4×Dic47C2semidirect
11. C2×C4⋊C4×Dic47C2semidirect
12. C2×C4×C4⋊Dic47C2semidirect
15. C2×#15688969C2semidirect
33. #15689022C22semidirect
37. #15689009C22semidirect
38. #15689009C22semidirect
39. #15689009C22semidirect
41. C4⋊C4×Dic47C22semidirect
42. C4⋊C4×Dic47C22semidirect
43. C4×C4⋊Dic47C22semidirect
46. #15688969C22semidirect
59. C2×#126×C47C4semidirect
129. #126×C47C2×C4semidirect
130. C2×C4⋊C4×C47C2×C4semidirect
131. C2×C4⋊C4×C47C2×C4semidirect
132. C2×C4⋊C4×C47C2×C4semidirect
142. C2×C42×C47C2×C4semidirect
213. C4⋊C4×C47C22×C4semidirect
214. C4⋊C4×C47C22×C4semidirect
215. C4⋊C4×C47C22×C4semidirect
219. C42×C47C22×C4semidirect
368. C2×C47#2373semidirect
377. C2×#126Dic47semidirect
427. C47C2×#2373semidirect
447. #126C2×Dic47semidirect
458. C2×C4⋊C4C2×Dic47semidirect
459. C2×C4⋊C4C2×Dic47semidirect
460. C2×C4⋊C4C2×Dic47semidirect
490. C2×C42C2×Dic47semidirect
578. C4⋊C4C22×Dic47semidirect
579. C4⋊C4C22×Dic47semidirect
580. C4⋊C4C22×Dic47semidirect
594. C42C22×Dic47semidirect
711. C2#20246512direct (N × H)

Maximal subgroups

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

subgroupindex
#202465122
C2×#156890222
C2×#156890162
C2×#156890092
C2×#156889982
C2×C4⋊C4×Dic472
C2×C4×C4⋊Dic472
C2×C22⋊C4×Dic472
C2×#156889692
C22×#126×C472
C2×#237347