Finite Group Databasebeta

← C2×#20249085 #26387167

Subgroups — C2×#20249085 #26387167

Order 12032.

2638 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×#13094014C211yesmaximal, characteristic, complemented
2C22×#13093982C211yesmaximal, characteristic
3#20249085C2116yesmaximal, direct product factor
4C2×#15689065C211yesmaximal, characteristic, complemented
5C2×#15689058C211yesmaximal, characteristic
6C2×#15689056C211yesmaximal, characteristic, complemented
7C2×#15689052C211yesmaximal, characteristic
8C2×#15689018C211yesmaximal, characteristic, complemented
9C2×#15689014C211yesmaximal, characteristic
10C2×#15689013C211yesmaximal, characteristic
11C2×#15689009C211yesmaximal, characteristic, complemented
12C2×#15689005C211yesmaximal, characteristic, complemented
13C2×#15688997C211yesmaximal, characteristic
14C2×#15688994C211yesmaximal, characteristic
15C2×#15688969C211yesmaximal, characteristic, complemented
16C2×C47×#389C211yesmaximal, characteristic, complemented
17C23×C4×D47C2211yescharacteristic
18C2×#13094014—28no—
19C2×#13094014C2218yescomplemented
20C2×#13093982—28no—
21C2×#13093982C2218yes—
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39#15689065C2218yescomplemented
40#15689058C2218yes—
41#15689056C2218yescomplemented
42#15689052C2218yes—
43#15689018C2218yescomplemented
44#15689014C2218yes—
45#15689013C2218yes—
46#15689009C2218yescomplemented
47#15689005C2218yescomplemented
48#15688997C2218yes—
49#15688994C2218yes—
50#15688969C2218yescomplemented
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×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C42×C47C2211yescharacteristic
66C47×#389C2218yescomplemented
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C24×D47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C22×C4×D47—24no—
78C22×C4×D47—24no—
79C22×C4×D47—24no—
80C22×C4×D47C2314yes—
81#13094014—232no—
82#13093982—232no—
83C2×C4⋊Dic47—24no—
84C2×C4⋊Dic47—24no—
85C2×C4⋊Dic47C2314yes—
86C2×C4⋊Dic47C2314yes—
87C2×Dic47⋊C4—24no—
88C2×Dic47⋊C4—24no—
89C2×Dic47⋊C4—24no—
90C2×Dic47⋊C4—24no—
91C2×Dic47⋊C4—24no—
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4C2314yes—
94C2×Dic47⋊C4C2314yes—
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×Dic47⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×(C2×D47)⋊C4—24no—
100C2×(C2×D47)⋊C4—24no—
101C2×(C2×D47)⋊C4—24no—
102C2×(C2×D47)⋊C4—24no—
103C2×(C2×D47)⋊C4—24no—
104C2×(C2×D47)⋊C4—24no—
105C2×(C2×D47)⋊C4C2314yes—
106C2×(C2×D47)⋊C4C2314yes—
107C2×(C2×D47)⋊C4C2314yes—
108C2×(C2×D47)⋊C4C2314yes—
109C2×(C2×D47)⋊C4C2314yes—
110C2×(C2×D47)⋊C4C2314yes—
111C2×C4×Dic47—24no—
112C2×C4×Dic47—24no—
113C2×C4×Dic47D418yes—
114C2×C4×Dic47C2314yes—
115C2×C4×Dic47C2314yes—
116C2×C4×Dic47C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C2×C4⋊C4×C47—24no—
135C2×C4⋊C4×C47—24no—
136C2×C4⋊C4×C47—24no—
137C2×C4⋊C4×C47—24no—
138C2×C4⋊C4×C47C2314yes—
139C2×C4⋊C4×C47C2314yes—
140C2×C4⋊C4×C47C2314yes—
141C2×C4⋊C4×C47C2314yes—
142C2×C42×C47—24no—
143C2×C42×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#4114yes—
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×C47C2×D414yes—
174C22×C4×C47#4114yes—
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×C4×D47—232no—
212C2×C4×D47—28no—
213C2×C4×D47—28no—
214C2×C4×D47—28no—
215C4⋊C4×C47—28no—
216C4⋊C4×C47—28no—
217C4⋊C4×C47—28no—
218C4⋊C4×C47—28no—
219C42×C47—28no—
220(C2×D47)⋊C4—28no—
221(C2×D47)⋊C4—28no—
222(C2×D47)⋊C4—28no—
223(C2×D47)⋊C4—28no—
224(C2×D47)⋊C4—28no—
225(C2×D47)⋊C4—28no—
226C4⋊Dic47—28no—
227C4⋊Dic47—28no—
228Dic47⋊C4—28no—
229Dic47⋊C4—28no—
230Dic47⋊C4—28no—
231Dic47⋊C4—28no—
232Dic47⋊C4—28no—
233Dic47⋊C4—28no—
234C4×Dic47—28no—
235C4×Dic47—28no—
236C4×Dic47C2×D4116yes—
237C23×C47C22×D412yes—
238C23×C47C2×#4112yes—
239C23×C47C2×#4112yes—
240C23×C47C2×#4112yes—
241C23×C47C2×#4112yes—
242C23×C472−1+412yes—
243C23×C472−1+412yes—
244C23×C47C2511yescharacteristic
245C22×D47—28no—
246C22×D47—28no—
247C22×D47—28no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—22no—
254C22×D47—44no—
255C22×D47—44no—
256C22×D47—44no—
257C22×D47—44no—
258C22×D47C2×#4114yes—
259C2×C4×C47—28no—
260C2×C4×C47—28no—
261C2×C4×C47—28no—
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×C47C22×D414yes—
285C2×C4×C47C2×#4114yes—
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—
315C4×D47—232no—
316C2×#2611—471nomaximal, Sylow
317C22×C47#52514yes—
318C22×C47#53214yes—
319C22×C47#53614yes—
320C22×C47#55214yes—
321C22×C47#55214yes—
322C22×C47#55214yes—
323C22×C47#55214yes—
324C22×C47C23×D411yescharacteristic
325C22×C47C22×#4111yescharacteristic
326C22×C47C22×#4111yescharacteristic
327C22×C47C22×#4111yescharacteristic
328C22×C47C22×#4111yescharacteristic
329C22×C47C2×2−1+411yescharacteristic
330C22×C47C2×2−1+411yescharacteristic
331C2×D47—24no—
332C2×D47—24no—
333C2×D47—24no—
334C2×D47—416no—
335C2×D47—42no—
336C2×D47—42no—
337C2×D47—42no—
338C2×D47—42no—
339C4×C47—24no—
340C4×C47—24no—
341C4×C47—24no—
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×#125—471no—
354C22×#117—471no—
355#2611—4716no—
356C2×#400—471no—
357C2×#399—471no—
358C2×#398—471no—
359C2×#397—471no—
360C2×#389—471no—
361C2×#389D4711yescharacteristic, complemented
362C2×#388—471no—
363C2×#388—471no—
364C2×#387—471no—
365C2×#387—471no—
366C2×#385—471no—
367C2×#385—471no—
368C2×#376—471no—
369C2×C47#261118yescomplemented
370C2×C47C2×#52511yescharacteristic
371C2×C47C2×#53211yescharacteristic
372C2×C47C2×#53611yescharacteristic
373C2×C47C2×#55211yescharacteristic
374C2×C47C2×#55211yescharacteristic
375C2×C47C2×#55211yescharacteristic
376C2×C47C2×#55211yescharacteristic
377D47—44no—
378C24×C4—471no—
379C2×#125—478no—
380C2×#125—948no—
381C2×#117—478no—
382C2×#117—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⋊C4C2×D4711yescharacteristic
392C22×C4⋊C4C2×D4711yescharacteristic
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×C42—471no—
402C22×C42—471no—
403C22×C42—471no—
404C22×C42C2×D4711yescharacteristic
405#400—478no—
406#399—478no—
407#398—478no—
408#397—478no—
409#389—478no—
410#389C2×D4718yescomplemented
411#388—478no—
412#388—478no—
413#387—478no—
414#387—478no—
415#385—478no—
416#385—478no—
417#376—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×#95—471no—
427C2×#95—471no—
428C2×#95C2×D4711yescharacteristic
429C2×#95C2×D4711yescharacteristic
430C47C2×#261111yescharacteristic, complemented, Sylow
431C25—471no—
432C23×C4—471no—
433C23×C4—471no—
434C23×C4—471no—
435C23×C4—471no—
436C23×C4—471no—
437C23×C4—471no—
438C23×C4—471no—
439C23×C4—474no—
440C23×C4—944no—
441C23×C4—944no—
442C23×C4—944no—
443C23×C4C22×D4711yescharacteristic
444C23×C4C22×D4711yescharacteristic
445C23×C4C22×D4711yescharacteristic
446C23×C4C22×D4711yescharacteristic
447C23×C4C22×D4711yescharacteristic
448C23×C4C22×D4711yescharacteristic
449C23×C4C22×D4711yescharacteristic
450#125—9432no—
451#117—9432no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
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—944no—
471C2×C4⋊C4—944no—
472C2×C4⋊C4C22×D4714yes—
473C2×C4⋊C4C22×D4714yes—
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—944no—
483C2×C22⋊C4—944no—
484C2×C22⋊C4—944no—
485C2×C22⋊C4—944no—
486C2×C22⋊C4—944no—
487C2×C22⋊C4—944no—
488C2×C42—24no—
489C2×C42—478no—
490C2×C42—474no—
491C2×C42—474no—
492C2×C42—474no—
493C2×C42—944no—
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#95—474no—
505#95—474no—
506#95C22×D4714yes—
507#95C22×D4714yes—
508C24—474no—
509C24—472no—
510C24—942no—
511C24—942no—
512C24—942no—
513C24—942no—
514C24—942no—
515C24—942no—
516C24C23×D4711yescharacteristic
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—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—474no—
536C22×C4—474no—
537C22×C4—474no—
538C22×C4—472no—
539C22×C4—472no—
540C22×C4—472no—
541C22×C4—472no—
542C22×C4—472no—
543C22×C4—472no—
544C22×C4—472no—
545C22×C4—948no—
546C22×C4—948no—
547C22×C4—9432no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—948no—
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#1062535014yes—
568C22×C4D4×D4714yes—
569C22×C4#1062535214yes—
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—28no—
580C4⋊C4—28no—
581C4⋊C4—948no—
582C4⋊C4—948no—
583C4⋊C4—948no—
584C4⋊C4—948no—
585C4⋊C4—948no—
586C4⋊C4—948no—
587C4⋊C4—948no—
588C4⋊C4—948no—
589C22⋊C4—948no—
590C22⋊C4—948no—
591C22⋊C4—948no—
592C22⋊C4—948no—
593C22⋊C4—948no—
594C22⋊C4—948no—
595C42—28no—
596C42—4716no—
597C42—948no—
598C42—948no—
599C23—474no—
600C23—948no—
601C23—948no—
602C23—948no—
603C23—942no—
604C23—942no—
605C23—942no—
606C23—942no—
607C23—942no—
608C23—942no—
609C23—1884no—
610C23—1884no—
611C23—1884no—
612C23—1884no—
613C23C2×D4×D4712yes—
614C23#41×D4712yes—
615C23#41×D4712yes—
616C23C2×#1062535212yes—
617C23C2×#1062535012yes—
618C23#1309407212yes—
619C23#1309407212yes—
620C23C24×D4711yescharacteristic
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—28no—
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—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—474no—
647C2×C4—474no—
648C2×C4—474no—
649C2×C4—9432no—
650C2×C4—948no—
651C2×C4—948no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—948no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
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—1884no—
672C2×C4—1884no—
673C2×C4—1884no—
674C2×C4—1884no—
675C2×C4C2×D4×D4714yes—
676C2×C4C2×#1062535214yes—
677C2×C4C2×#1062535014yes—
678C22—944no—
679C22—944no—
680C22—944no—
681C22—1882no—
682C22—1882no—
683C22—1882no—
684C22—1882no—
685C22—18816no—
686C22#1568963214yes—
687C22#1568966814yes—
688C22#1568969814yes—
689C22#1568980514yes—
690C22#1568980714yes—
691C22#1568980814yes—
692C22#1568981414yes—
693C22C22×D4×D4711yescharacteristic
694C22C2×#41×D4711yescharacteristic
695C22C2×#41×D4711yescharacteristic
696C22C22×#1062535211yescharacteristic
697C22C22×#1062535011yescharacteristic
698C22C2×#1309407211yescharacteristic
699C22C2×#1309407211yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—944no—
708C4—944no—
709C4—944no—
710C4—1882no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C2—1884no—
715C2#2024908518yesdirect product factor
716C2C2×#1568963211yescharacteristic
717C2C2×#1568966811yescharacteristic
718C2C2×#1568969811yescharacteristic
719C2C2×#1568980511yescharacteristic
720C2C2×#1568980711yescharacteristic
721C2C2×#1568980811yescharacteristic
722C2C2×#1568981411yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#389C2
socleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#389D47
hypocenterC47C2×#2611
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#13094014C2semidirect
3. #20249085C2direct (N × H)
4. C2×#15689065C2semidirect
6. C2×#15689056C2semidirect
8. C2×#15689018C2semidirect
11. C2×#15689009C2semidirect
12. C2×#15689005C2semidirect
15. C2×#15688969C2semidirect
16. C2×C47×#389C2semidirect
19. C2×#13094014C22semidirect
39. #15689065C22semidirect
41. #15689056C22semidirect
43. #15689018C22semidirect
46. #15689009C22semidirect
47. #15689005C22semidirect
50. #15688969C22semidirect
66. C47×#389C22semidirect
361. C2×#389D47semidirect
369. C2×C47#2611semidirect
410. #389C2×D47semidirect
430. C47C2×#2611semidirect
715. C2#20249085direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940142
C22×#130939822
#202490852
C2×#156890652
C2×#156890582
C2×#156890562
C2×#156890522
C2×#156890182
C2×#156890142
C2×#156890132
C2×#156890092
C2×#156890052
C2×#156889972
C2×#156889942
C2×#156889692
C2×C47×#3892
C2×#261147