Finite Group Databasebeta

← C2×#20249302 #26383221

Subgroups — C2×#20249302 #26383221

Order 12032.

2482 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094019C211yesmaximal, characteristic
2C22×C4×Dic94C211yesmaximal, characteristic, complemented
3#20249302C2116yesmaximal, direct product factor
4C2×#15689057C211yesmaximal, characteristic, complemented
5C2×#15689057C211yesmaximal, characteristic, complemented
6C2×#15689055C211yesmaximal, characteristic, complemented
7C2×#15689052C211yesmaximal, characteristic
8C2×#15689047C211yesmaximal, characteristic
9C2×#15689045C211yesmaximal, characteristic
10C2×#15689043C211yesmaximal, characteristic, complemented
11C2×#15689036C211yesmaximal, characteristic
12C2×#15689015C211yesmaximal, characteristic
13C2×#15689014C211yesmaximal, characteristic
14C2×#15689004C211yesmaximal, characteristic, complemented
15C2×#15688987C211yesmaximal, characteristic, complemented
16C2×C47×#387C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C2×#13094019—28no—
19C2×#13094019C2218yes—
20C2×C4×Dic94—28no—
21C2×C4×Dic94C2218yescomplemented
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41#15689057C2218yescomplemented
42#15689057C2218yescomplemented
43#15689055C2218yescomplemented
44#15689052C2218yes—
45#15689047C2218yes—
46#15689045C2218yes—
47#15689043C2218yescomplemented
48#15689036C2218yes—
49#15689015C2218yes—
50#15689014C2218yes—
51#15689004C2218yescomplemented
52#15688987C2218yescomplemented
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C42×C47C2211yescharacteristic
64C47×#387C2218yescomplemented
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C24×D47C2311yescharacteristic
70C22×Dic94—24no—
71C22×Dic94—24no—
72C22×Dic94—24no—
73C22×Dic94C2314yes—
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81#13094019—232no—
82C4×Dic94—232no—
83C2×C4⋊Dic47—24no—
84C2×C4⋊Dic47—24no—
85C2×C4⋊Dic47—42no—
86C2×C4⋊Dic47C2314yes—
87C2×C4⋊Dic47C2314yes—
88C2×C4⋊Dic47C2314yes—
89C2×Dic47⋊C4—24no—
90C2×Dic47⋊C4—24no—
91C2×Dic47⋊C4—24no—
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4—42no—
94C2×Dic47⋊C4—42no—
95C2×Dic47⋊C4—42no—
96C2×Dic47⋊C4C2314yes—
97C2×Dic47⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×(C2×D47)⋊C4—24no—
104C2×(C2×D47)⋊C4—24no—
105C2×(C2×D47)⋊C4—24no—
106C2×(C2×D47)⋊C4—24no—
107C2×(C2×D47)⋊C4—24no—
108C2×(C2×D47)⋊C4—42no—
109C2×(C2×D47)⋊C4—42no—
110C2×(C2×D47)⋊C4C2314yes—
111C2×(C2×D47)⋊C4C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×C4×Dic47—24no—
118C2×C4×Dic47D418yes—
119C2×C4×Dic47C2314yes—
120C2×C4×Dic47C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47—24no—
137C2×C4⋊C4×C47—24no—
138C2×C4⋊C4×C47C2314yes—
139C2×C4⋊C4×C47C2314yes—
140C2×C42×C47—24no—
141C2×C42×C47C2314yes—
142#95×C47C2314yes—
143#95×C47C2314yes—
144#95×C47C2314yes—
145#95×C47C2314yes—
146C24×C47C2411yescharacteristic
147C23×D47—22no—
148C23×D47—22no—
149C23×D47—22no—
150C23×D47—22no—
151C23×D47—22no—
152C23×D47—22no—
153C23×D47—22no—
154C23×D47C2412yes—
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×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47C2×D414yes—
175C22×C4×C47#4114yes—
176C22×C4×C47C2412yes—
177C22×C4×C47C2412yes—
178C22×C4×C47C2412yes—
179C22×C4×C47C2412yes—
180C22×C4×C47C2412yes—
181C22×C4×C47C2412yes—
182C22×C4×C47C2412yes—
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—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47C2×D414yes—
202C22×Dic47C2×D414yes—
203C22×Dic47#4114yes—
204C22×Dic47C2412yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C22×Dic47C2412yes—
210C22×Dic47C2412yes—
211C2×Dic94—232no—
212C2×Dic94—28no—
213C2×Dic94—28no—
214C2×Dic94—28no—
215C4⋊C4×C47—28no—
216C4⋊C4×C47—28no—
217C42×C47—28no—
218(C2×D47)⋊C4—28no—
219(C2×D47)⋊C4—28no—
220(C2×D47)⋊C4—28no—
221(C2×D47)⋊C4—28no—
222(C2×D47)⋊C4—28no—
223(C2×D47)⋊C4—44no—
224(C2×D47)⋊C4—44no—
225C4⋊Dic47—28no—
226C4⋊Dic47—28no—
227C4⋊Dic47—44no—
228Dic47⋊C4—28no—
229Dic47⋊C4—28no—
230Dic47⋊C4—28no—
231Dic47⋊C4—28no—
232Dic47⋊C4—44no—
233Dic47⋊C4—44no—
234Dic47⋊C4—44no—
235C4×Dic47—28no—
236C4×Dic47C2×D4116yes—
237C23×C47C22×D412yes—
238C23×C47C2×#4112yes—
239C23×C47C2×#4112yes—
240C23×C47H(5,𝔽2)12yes—
241C23×C472−1+412yes—
242C23×C472−1+412yes—
243C23×C472−1+412yes—
244C23×C47C2511yescharacteristic
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—44no—
253C22×D47—44no—
254C22×D47—44no—
255C22×D47—44no—
256C22×D47—44no—
257C22×D47—44no—
258C22×D47—44no—
259C2×C4×C47—28no—
260C2×C4×C47—28no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
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×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—44no—
281C2×C4×C47—44no—
282C2×C4×C47—44no—
283C2×C4×C47—44no—
284C2×C4×C47—44no—
285C2×C4×C47C22×D414yes—
286C2×C4×C47C2×#4114yes—
287C2×Dic47—28no—
288C2×Dic47—28no—
289C2×Dic47—28no—
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—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—44no—
309C2×Dic47—44no—
310C2×Dic47—44no—
311C2×Dic47—44no—
312C2×Dic47C22×D414yes—
313C2×Dic47C22×D414yes—
314C2×Dic47C2×#4114yes—
315Dic94—232no—
316C2×#2637—471nomaximal, Sylow
317C22×C47#52514yes—
318C22×C47#53614yes—
319C22×C47#53714yes—
320C22×C47#54114yes—
321C22×C47#54114yes—
322C22×C47#54214yes—
323C22×C47#54214yes—
324C22×C47C23×D411yescharacteristic
325C22×C47C22×#4111yescharacteristic
326C22×C47C22×#4111yescharacteristic
327C22×C47C2×H(5,𝔽2)11yescharacteristic
328C22×C47C2×2−1+411yescharacteristic
329C22×C47C2×2−1+411yescharacteristic
330C22×C47C2×2−1+411yescharacteristic
331C2×D47—42no—
332C2×D47—42no—
333C2×D47—42no—
334C2×D47—42no—
335C2×D47—42no—
336C2×D47—42no—
337C2×D47—42no—
338C2×D47—88no—
339C4×C47—24no—
340C4×C47—24no—
341C4×C47—42no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47—42no—
346Dic47—24no—
347Dic47—24no—
348Dic47—24no—
349Dic47—42no—
350Dic47—42no—
351Dic47—42no—
352Dic47—42no—
353C22×#126—471no—
354C22×C4×Q8—471no—
355#2637—4716no—
356C2×#398—471no—
357C2×#398—471no—
358C2×#398—471no—
359C2×#397—471no—
360C2×#396—471no—
361C2×#396—471no—
362C2×#395—471no—
363C2×#393—471no—
364C2×#388—471no—
365C2×#388—471no—
366C2×#387—471no—
367C2×#387D4711yescharacteristic, complemented
368C2×#382—471no—
369C2×C47#263718yescomplemented
370C2×C47C2×#52511yescharacteristic
371C2×C47C2×#53611yescharacteristic
372C2×C47C2×#53711yescharacteristic
373C2×C47C2×#54111yescharacteristic
374C2×C47C2×#54111yescharacteristic
375C2×C47C2×#54211yescharacteristic
376C2×C47C2×#54211yescharacteristic
377D47—82no—
378C23×Q8—471no—
379C2×#126—478no—
380C2×#126—948no—
381C2×C4×Q8—478no—
382C2×C4×Q8—948no—
383C22×C4⋊C4—471no—
384C22×C4⋊C4—471no—
385C22×C4⋊C4—471no—
386C22×C4⋊C4—471no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4—471no—
389C22×C4⋊C4—471no—
390C22×C4⋊C4—471no—
391C22×C4⋊C4—471no—
392C22×C4⋊C4—471no—
393C22×C4⋊C4C2×D4711yescharacteristic
394C22×C4⋊C4C2×D4711yescharacteristic
395C22×C22⋊C4—471no—
396C22×C22⋊C4—471no—
397C22×C22⋊C4—471no—
398C22×C22⋊C4—471no—
399C22×C22⋊C4—471no—
400C22×C22⋊C4—471no—
401C22×C22⋊C4—471no—
402C22×C42—471no—
403C22×C42—471no—
404C22×C42C2×D4711yescharacteristic
405#398—478no—
406#398—478no—
407#398—478no—
408#397—478no—
409#396—478no—
410#396—478no—
411#395—478no—
412#393—478no—
413#388—478no—
414#388—478no—
415#387—478no—
416#387C2×D4718yescomplemented
417#382—478no—
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×#95C2×D4711yescharacteristic
427C2×#95C2×D4711yescharacteristic
428C2×#95C2×D4711yescharacteristic
429C2×#95C2×D4711yescharacteristic
430C47C2×#263711yescharacteristic, complemented, Sylow
431C25—471no—
432C22×Q8—474no—
433C22×Q8—944no—
434C22×Q8—944no—
435C22×Q8—944no—
436C23×C4—471no—
437C23×C4—471no—
438C23×C4—471no—
439C23×C4—471no—
440C23×C4—471no—
441C23×C4—471no—
442C23×C4—471no—
443C23×C4C22×D4711yescharacteristic
444C23×C4C22×D4711yescharacteristic
445C23×C4C22×D4711yescharacteristic
446C23×C4C22×D4711yescharacteristic
447C23×C4C22×D4711yescharacteristic
448C23×C4C22×D4711yescharacteristic
449C23×C4C22×D4711yescharacteristic
450#126—9432no—
451C4×Q8—9432no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—474no—
455C2×C4⋊C4—474no—
456C2×C4⋊C4—474no—
457C2×C4⋊C4—474no—
458C2×C4⋊C4—474no—
459C2×C4⋊C4—474no—
460C2×C4⋊C4—474no—
461C2×C4⋊C4—474no—
462C2×C4⋊C4—474no—
463C2×C4⋊C4—474no—
464C2×C4⋊C4—944no—
465C2×C4⋊C4—944no—
466C2×C4⋊C4—944no—
467C2×C4⋊C4—944no—
468C2×C4⋊C4—944no—
469C2×C4⋊C4—944no—
470C2×C4⋊C4—1882no—
471C2×C4⋊C4—1882no—
472C2×C4⋊C4—1882no—
473C2×C4⋊C4—1882no—
474C2×C4⋊C4C22×D4714yes—
475C2×C4⋊C4C22×D4714yes—
476C2×C22⋊C4—474no—
477C2×C22⋊C4—474no—
478C2×C22⋊C4—474no—
479C2×C22⋊C4—474no—
480C2×C22⋊C4—474no—
481C2×C22⋊C4—474no—
482C2×C22⋊C4—474no—
483C2×C22⋊C4—944no—
484C2×C22⋊C4—944no—
485C2×C22⋊C4—944no—
486C2×C22⋊C4—944no—
487C2×C22⋊C4—944no—
488C2×C22⋊C4—1882no—
489C2×C22⋊C4—1882no—
490C2×C42—24no—
491C2×C42—478no—
492C2×C42—474no—
493C2×C42—474no—
494C2×C42—944no—
495C2×C42C22×D4714yes—
496#95—474no—
497#95—474no—
498#95—474no—
499#95—474no—
500#95—474no—
501#95—474no—
502#95—474no—
503#95—474no—
504#95C22×D4714yes—
505#95C22×D4714yes—
506#95C22×D4714yes—
507#95C22×D4714yes—
508C24—472no—
509C24—942no—
510C24—942no—
511C24—942no—
512C24—942no—
513C24—942no—
514C24—942no—
515C24—942no—
516C24C23×D4711yescharacteristic
517C2×Q8—948no—
518C2×Q8—948no—
519C2×Q8—9432no—
520C2×Q8—948no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—474no—
541C22×C4—474no—
542C22×C4—474no—
543C22×C4—472no—
544C22×C4—472no—
545C22×C4—472no—
546C22×C4—472no—
547C22×C4—472no—
548C22×C4—472no—
549C22×C4—472no—
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—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4#1062535014yes—
569C22×C4D4×D4714yes—
570C22×C4C23×D4712yes—
571C22×C4C23×D4712yes—
572C22×C4C23×D4712yes—
573C22×C4C23×D4712yes—
574C22×C4C23×D4712yes—
575C22×C4C23×D4712yes—
576C22×C4C23×D4712yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—948no—
580C4⋊C4—948no—
581C4⋊C4—948no—
582C4⋊C4—948no—
583C4⋊C4—948no—
584C4⋊C4—948no—
585C4⋊C4—1884no—
586C4⋊C4—1884no—
587C4⋊C4—1884no—
588C4⋊C4—1884no—
589C22⋊C4—948no—
590C22⋊C4—948no—
591C22⋊C4—948no—
592C22⋊C4—948no—
593C22⋊C4—948no—
594C22⋊C4—1884no—
595C22⋊C4—1884no—
596C42—28no—
597C42—4716no—
598C42—948no—
599C23—942no—
600C23—942no—
601C23—942no—
602C23—942no—
603C23—942no—
604C23—942no—
605C23—942no—
606C23—1884no—
607C23—1884no—
608C23—1884no—
609C23—1884no—
610C23—1884no—
611C23—1884no—
612C23—1884no—
613C23C2×D4×D4712yes—
614C23#41×D4712yes—
615C23C2×#1062535012yes—
616C23#1309407012yes—
617C23#1309407112yes—
618C23#1309407112yes—
619C23#1309407212yes—
620C23C24×D4711yescharacteristic
621Q8—9432no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—28no—
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—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—474no—
649C2×C4—474no—
650C2×C4—474no—
651C2×C4—948no—
652C2×C4—948no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—948no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—1884no—
673C2×C4—1884no—
674C2×C4—1884no—
675C2×C4—1884no—
676C2×C4C2×D4×D4714yes—
677C2×C4C2×#1062535014yes—
678C22—3768no—
679C22—1882no—
680C22—1882no—
681C22—1882no—
682C22—1882no—
683C22—1882no—
684C22—1882no—
685C22—1882no—
686C22#1568963214yes—
687C22#1568969514yes—
688C22#1568970314yes—
689C22#1568973114yes—
690C22#1568973214yes—
691C22#1568973914yes—
692C22#1568974414yes—
693C22C22×D4×D4711yescharacteristic
694C22C2×#41×D4711yescharacteristic
695C22C22×#1062535011yescharacteristic
696C22C2×#1309407011yescharacteristic
697C22C2×#1309407111yescharacteristic
698C22C2×#1309407111yescharacteristic
699C22C2×#1309407211yescharacteristic
700C4—24no—
701C4—24no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—944no—
708C4—944no—
709C4—944no—
710C4—1882no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C2—3762no—
715C2#2024930218yesdirect product factor
716C2C2×#1568963211yescharacteristic
717C2C2×#1568969511yescharacteristic
718C2C2×#1568970311yescharacteristic
719C2C2×#1568973111yescharacteristic
720C2C2×#1568973211yescharacteristic
721C2C2×#1568973911yescharacteristic
722C2C2×#1568974411yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#387C2
socleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#387D47
hypocenterC47C2×#2637
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic94C2semidirect
3. #20249302C2direct (N × H)
4. C2×#15689057C2semidirect
5. C2×#15689057C2semidirect
6. C2×#15689055C2semidirect
10. C2×#15689043C2semidirect
14. C2×#15689004C2semidirect
15. C2×#15688987C2semidirect
16. C2×C47×#387C2semidirect
21. C2×C4×Dic94C22semidirect
41. #15689057C22semidirect
42. #15689057C22semidirect
43. #15689055C22semidirect
47. #15689043C22semidirect
51. #15689004C22semidirect
52. #15688987C22semidirect
64. C47×#387C22semidirect
367. C2×#387D47semidirect
369. C2×C47#2637semidirect
416. #387C2×D47semidirect
430. C47C2×#2637semidirect
715. C2#20249302direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940192
C22×C4×Dic942
#202493022
C2×#156890572
C2×#156890552
C2×#156890522
C2×#156890472
C2×#156890452
C2×#156890432
C2×#156890362
C2×#156890152
C2×#156890142
C2×#156890042
C2×#156889872
C2×C47×#3872
C2×#263747