Finite Group Databasebeta

← C2×#20246247 #26375503

Subgroups — C2×#20246247 #26375503

Order 12032.

3006 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093982C211yesmaximal, characteristic
2#20246247C2116yesmaximal, direct product factor
3C2×#15689009C211yesmaximal, characteristic, complemented
4C2×#15689008C211yesmaximal, characteristic, complemented
5C2×#15689006C211yesmaximal, characteristic, complemented
6C2×#15688997C211yesmaximal, characteristic
7C2×#15688994C211yesmaximal, characteristic
8C2×#15688990C211yesmaximal, characteristic, complemented
9C2×#15688988C211yesmaximal, characteristic, complemented
10C2×#15688985C211yesmaximal, characteristic
11C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
13C2×#15688970C211yesmaximal, characteristic
14C2×#15688968C211yesmaximal, characteristic, complemented
15C2×#95×D47C211yesmaximal, characteristic
16C2×C47×#387C211yesmaximal, characteristic, complemented
17C23×C4×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×#13093982C4116yescomplemented
21C2×#13093982C2218yes—
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35#15689009C2218yescomplemented
36#15689008C2218yescomplemented
37#15689006C2218yescomplemented
38#15688997C2218yes—
39#15688994C2218yes—
40#15688990C2218yescomplemented
41#15688988C2218yescomplemented
42#15688985C2218yes—
43C4×Dic47⋊C4C2218yescomplemented
44C4×(C2×D47)⋊C4C2218yes—
45#15688970C2218yes—
46#15688968C2218yescomplemented
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
59#95×D47C2218yes—
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C42×C47C2211yescharacteristic
63C47×#387C2218yescomplemented
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C24×D47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C22×C4×D47—24no—
77C22×C4×D47—24no—
78C22×C4×D47—24no—
79C22×C4×D47—24no—
80C22×C4×D47—24no—
81C22×C4×D47—24no—
82C22×C4×D47—42no—
83C22×C4×D47—42no—
84C22×C4×D47C2×C418yes—
85C22×C4×D47C2314yes—
86C22×C4×D47C2314yes—
87C22×C4×D47C2314yes—
88#13093982C2×C4164yescomplemented
89C2×C4⋊Dic47—42no—
90C2×C4⋊Dic47C2×C418yescomplemented
91C2×C4⋊Dic47C2314yes—
92C2×C4⋊Dic47C2314yes—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4—24no—
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×(C2×D47)⋊C4—24no—
98C2×(C2×D47)⋊C4—24no—
99C2×(C2×D47)⋊C4C2×C418yes—
100C2×(C2×D47)⋊C4C2×C418yes—
101C2×(C2×D47)⋊C4C2314yes—
102C2×(C2×D47)⋊C4C2314yes—
103C2×(C2×D47)⋊C4C2314yes—
104C2×(C2×D47)⋊C4C2314yes—
105C2×C4×Dic47—24no—
106C2×C4×Dic47—24no—
107C2×C4×Dic47—42no—
108C2×C4×Dic47C2×C418yescomplemented
109C2×C4×Dic47C2×C418yescomplemented
110C2×C4×Dic47C2314yes—
111C2×C4×Dic47C2314yes—
112C2×C4×Dic47C2314yes—
113C2×C4×Dic47C2314yes—
114C2×C4×Dic47C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
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—42no—
135C2×C4⋊C4×C47C2×C418yescomplemented
136C2×C4⋊C4×C47C2314yes—
137C2×C4⋊C4×C47C2314yes—
138C2×C42×C47—42no—
139C2×C42×C47C2314yes—
140#95×C47C2314yes—
141#95×C47C2314yes—
142#95×C47C2314yes—
143#95×C47C2314yes—
144C24×C47C2411yescharacteristic
145C23×D47—22no—
146C23×D47—22no—
147C23×D47—22no—
148C23×D47—22no—
149C23×D47C22×C414yes—
150C23×D47#4114yes—
151C23×D47#4114yes—
152C23×D47C2412yes—
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×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47C22×C414yes—
171C22×C4×C47C22×C414yes—
172C22×C4×C47C22×C414yes—
173C22×C4×C47#4114yes—
174C22×C4×C47C2412yes—
175C22×C4×C47C2412yes—
176C22×C4×C47C2412yes—
177C22×C4×C47C2412yes—
178C22×C4×C47C2412yes—
179C22×C4×C47C2412yes—
180C22×C4×C47C2412yes—
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—22no—
198C22×Dic47C22×C414yes—
199C22×Dic47C22×C414yes—
200C22×Dic47C22×C414yes—
201C22×Dic47#4114yes—
202C22×Dic47C2412yes—
203C22×Dic47C2412yes—
204C22×Dic47C2412yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C2×C4×D47—232no—
210C2×C4×D47—28no—
211C2×C4×D47—28no—
212C2×C4×D47—28no—
213C2×C4×D47—28no—
214C2×C4×D47—28no—
215C2×C4×D47—28no—
216C2×C4×D47—44no—
217C2×C4×D47—44no—
218C2×C4×D47—416no—
219C2×C4×D47—416no—
220C2×C4×D47C22×C4116yes—
221C4⋊C4×C47—44no—
222C4⋊C4×C47C22×C4116yescomplemented
223C42×C47—44no—
224(C2×D47)⋊C4—28no—
225(C2×D47)⋊C4—28no—
226(C2×D47)⋊C4C22×C4116yes—
227(C2×D47)⋊C4C22×C4116yes—
228C4⋊Dic47—44no—
229C4⋊Dic47C22×C4116yescomplemented
230Dic47⋊C4—28no—
231Dic47⋊C4—28no—
232C4×Dic47—28no—
233C4×Dic47—28no—
234C4×Dic47—44no—
235C4×Dic47C22×C4116yescomplemented
236C4×Dic47C22×C4116yescomplemented
237C23×C47C23×C412yes—
238C23×C47C2×#4112yes—
239C23×C47C2×#4112yes—
240C23×C47C2×#4112yes—
241C23×C47C2×#4112yes—
242C23×C47H(5,𝔽2)12yes—
243C23×C472−1+412yes—
244C23×C47C2511yescharacteristic
245C22×D47—28no—
246C22×D47—28no—
247C22×D47—28no—
248C22×D47—28no—
249C22×D47—28no—
250C22×D47—28no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—22no—
254C22×D47—22no—
255C22×D47#117116yes—
256C22×D47C23×C414yes—
257C22×D47C2×#4114yes—
258C22×D47C2×#4114yes—
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×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×C47C23×C414yes—
284C2×C4×C47C23×C414yes—
285C2×C4×C47C23×C414yes—
286C2×C4×C47C2×#4114yes—
287C2×Dic47—28no—
288C2×Dic47—28no—
289C2×Dic47—28no—
290C2×Dic47—28no—
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×Dic47C23×C414yes—
312C2×Dic47C23×C414yes—
313C2×Dic47C23×C414yes—
314C2×Dic47C2×#4114yes—
315C4×D47—232no—
316C4×D47—416no—
317C4×D47—416no—
318C2×#2343—471nomaximal, Sylow
319C22×C47C2×#11714yes—
320C22×C47C4×#4114yes—
321C22×C47#52014yes—
322C22×C47#55114yes—
323C22×C47#55114yes—
324C22×C47#55214yes—
325C22×C47#55214yes—
326C22×C47C24×C411yescharacteristic
327C22×C47C22×#4111yescharacteristic
328C22×C47C22×#4111yescharacteristic
329C22×C47C22×#4111yescharacteristic
330C22×C47C22×#4111yescharacteristic
331C22×C47C2×H(5,𝔽2)11yescharacteristic
332C22×C47C2×2−1+411yescharacteristic
333C2×D47—232no—
334C2×D47—24no—
335C2×D47—24no—
336C2×D47—24no—
337C2×D47—24no—
338C2×D47—24no—
339C2×D47—24no—
340C2×D47C2×#11718yes—
341C4×C47—24no—
342C4×C47—24no—
343C4×C47—24no—
344C4×C47—24no—
345C4×C47—42no—
346C4×C47—42no—
347C4×C47—42no—
348Dic47—24no—
349Dic47—24no—
350Dic47—24no—
351Dic47—24no—
352Dic47—42no—
353Dic47—42no—
354Dic47—42no—
355C22×#117—471no—
356#2343—4716no—
357C2×#387—471no—
358C2×#387—471no—
359C2×#387—471no—
360C2×#387D4711yescharacteristic, complemented
361C2×#385—471no—
362C2×#385—471no—
363C2×#383—471no—
364C2×#382—471no—
365C2×#381—471no—
366C2×C4×C4⋊C4—471no—
367C2×C4×C22⋊C4—471no—
368C2×C4×C22⋊C4—471no—
369C2×#376—471no—
370C22×#95—471no—
371C2×C47#234318yescomplemented
372C2×C47C22×#11711yescharacteristic
373C2×C47C2×C4×#4111yescharacteristic
374C2×C47C2×#52011yescharacteristic
375C2×C47C2×#55111yescharacteristic
376C2×C47C2×#55111yescharacteristic
377C2×C47C2×#55211yescharacteristic
378C2×C47C2×#55211yescharacteristic
379D47—28no—
380C24×C4—471no—
381C24×C4—471no—
382C24×C4—471no—
383C2×#117—4716no—
384C2×#117—478no—
385C22×C4⋊C4—471no—
386C22×C4⋊C4—471no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4—471no—
389C22×C4⋊C4C2×D4711yescharacteristic
390C22×C4⋊C4C2×D4711yescharacteristic
391C22×C22⋊C4—471no—
392C22×C22⋊C4—471no—
393C22×C22⋊C4—471no—
394C22×C22⋊C4—471no—
395C22×C42—471no—
396C22×C42—471no—
397C22×C42—471no—
398C22×C42—471no—
399C22×C42—471no—
400C22×C42C2×D4711yescharacteristic
401#387—478no—
402#387—478no—
403#387—478no—
404#387C2×D4718yescomplemented
405#385—478no—
406#385—478no—
407#383—478no—
408#382—478no—
409#381—478no—
410C4×C4⋊C4—478no—
411C4×C22⋊C4—478no—
412C4×C22⋊C4—478no—
413#376—478no—
414C2×#95—471no—
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—478no—
427C2×#95C2×D4711yescharacteristic
428C2×#95C2×D4711yescharacteristic
429C2×#95C2×D4711yescharacteristic
430C2×#95C2×D4711yescharacteristic
431C47C2×#234311yescharacteristic, complemented, Sylow
432C25—471no—
433C23×C4—471no—
434C23×C4—471no—
435C23×C4—471no—
436C23×C4—471no—
437C23×C4—478no—
438C23×C4—474no—
439C23×C4—471no—
440C23×C4—471no—
441C23×C4—471no—
442C23×C4—474no—
443C23×C4—474no—
444C23×C4—944no—
445C23×C4—944no—
446C23×C4—944no—
447C23×C4—944no—
448C23×C4—944no—
449C23×C4—944no—
450C23×C4—1882no—
451C23×C4—1882no—
452C23×C4C22×D4711yescharacteristic
453C23×C4C22×D4711yescharacteristic
454C23×C4C22×D4711yescharacteristic
455C23×C4C22×D4711yescharacteristic
456C23×C4C22×D4711yescharacteristic
457C23×C4C22×D4711yescharacteristic
458C23×C4C22×D4711yescharacteristic
459#117—4764no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—478no—
462C2×C4⋊C4—474no—
463C2×C4⋊C4—474no—
464C2×C4⋊C4—474no—
465C2×C4⋊C4—474no—
466C2×C4⋊C4—944no—
467C2×C4⋊C4—944no—
468C2×C4⋊C4—1882no—
469C2×C4⋊C4C4×D4718yescomplemented
470C2×C4⋊C4C22×D4714yes—
471C2×C4⋊C4C22×D4714yes—
472C2×C22⋊C4—478no—
473C2×C22⋊C4—478no—
474C2×C22⋊C4—474no—
475C2×C22⋊C4—474no—
476C2×C22⋊C4—474no—
477C2×C22⋊C4—474no—
478C2×C22⋊C4—944no—
479C2×C22⋊C4—944no—
480C2×C42—42no—
481C2×C42—478no—
482C2×C42—478no—
483C2×C42—474no—
484C2×C42—474no—
485C2×C42—474no—
486C2×C42—474no—
487C2×C42—474no—
488C2×C42—944no—
489C2×C42—944no—
490C2×C42—1882no—
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—
504#95C22×D4714yes—
505#95C22×D4714yes—
506#95C22×D4714yes—
507#95C22×D4714yes—
508C24—474no—
509C24—474no—
510C24—474no—
511C24—472no—
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—474no—
535C22×C4—474no—
536C22×C4—474no—
537C22×C4—474no—
538C22×C4—472no—
539C22×C4—472no—
540C22×C4—472no—
541C22×C4—472no—
542C22×C4—4716no—
543C22×C4—472no—
544C22×C4—472no—
545C22×C4—472no—
546C22×C4—948no—
547C22×C4—9432no—
548C22×C4—948no—
549C22×C4—948no—
550C22×C4—948no—
551C22×C4—948no—
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—942no—
569C22×C4—948no—
570C22×C4—1884no—
571C22×C4—1884no—
572C22×C4—18816no—
573C22×C4—18816no—
574C22×C4C2×C4×D4714yes—
575C22×C4C2×C4×D4714yes—
576C22×C4C2×C4×D4714yes—
577C22×C4#1062535414yes—
578C22×C4C23×D4712yes—
579C22×C4C23×D4712yes—
580C22×C4C23×D4712yes—
581C22×C4C23×D4712yes—
582C22×C4C23×D4712yes—
583C22×C4C23×D4712yes—
584C22×C4C23×D4712yes—
585C4⋊C4—44no—
586C4⋊C4—4716no—
587C4⋊C4—948no—
588C4⋊C4—948no—
589C4⋊C4—1884no—
590C4⋊C4C2×C4×D47116yescomplemented
591C22⋊C4—4716no—
592C22⋊C4—4716no—
593C22⋊C4—948no—
594C22⋊C4—948no—
595C42—44no—
596C42—4716no—
597C42—4716no—
598C42—948no—
599C42—948no—
600C42—1884no—
601C23—4716no—
602C23—474no—
603C23—474no—
604C23—474no—
605C23—948no—
606C23—948no—
607C23—948no—
608C23—948no—
609C23—948no—
610C23—948no—
611C23—942no—
612C23—942no—
613C23—942no—
614C23—942no—
615C23C22×C4×D4712yes—
616C23#41×D4712yes—
617C23#41×D4712yes—
618C23#41×D4712yes—
619C23C2×#1062535412yes—
620C23#1309406912yes—
621C23#1309407112yes—
622C23C24×D4711yescharacteristic
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—28no—
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—22no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—474no—
648C2×C4—474no—
649C2×C4—474no—
650C2×C4—474no—
651C2×C4—9432no—
652C2×C4—948no—
653C2×C4—948no—
654C2×C4—948no—
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—942no—
672C2×C4—942no—
673C2×C4—18816no—
674C2×C4—18816no—
675C2×C4—1884no—
676C2×C4—1884no—
677C2×C4—1884no—
678C2×C4C22×C4×D4714yes—
679C2×C4C22×C4×D4714yes—
680C2×C4C22×C4×D4714yes—
681C2×C4C2×#1062535414yes—
682C22—478no—
683C22—944no—
684C22—944no—
685C22—944no—
686C22—944no—
687C22—944no—
688C22—944no—
689C22—9432no—
690C22#117×D4714yes—
691C22C4×#1062535414yes—
692C22#1568960214yes—
693C22#1568980014yes—
694C22#1568980114yes—
695C22#1568980914yes—
696C22#1568981114yes—
697C22C23×C4×D4711yescharacteristic
698C22C2×#41×D4711yescharacteristic
699C22C2×#41×D4711yescharacteristic
700C22C2×#41×D4711yescharacteristic
701C22C22×#1062535411yescharacteristic
702C22C2×#1309406911yescharacteristic
703C22C2×#1309407111yescharacteristic
704C4—24no—
705C4—24no—
706C4—24no—
707C4—24no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—944no—
712C4—944no—
713C4—944no—
714C4—944no—
715C4—1882no—
716C4—1882no—
717C4—1882no—
718C2—948no—
719C2#2024624718yesdirect product factor
720C2C2×#117×D4711yescharacteristic
721C2C2×C4×#1062535411yescharacteristic
722C2C2×#1568960211yescharacteristic
723C2C2×#1568980011yescharacteristic
724C2C2×#1568980111yescharacteristic
725C2C2×#1568980911yescharacteristic
726C2C2×#1568981111yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#387C2
socleC24×C47C24
prime radicalC24×D47C23
cosocleC23×C47C25
hypercenterC2×#387D47
hypocenterC47C2×#2343
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #20246247C2direct (N × H)
3. C2×#15689009C2semidirect
4. C2×#15689008C2semidirect
5. C2×#15689006C2semidirect
8. C2×#15688990C2semidirect
9. C2×#15688988C2semidirect
11. C2×C4×Dic47⋊C4C2semidirect
14. C2×#15688968C2semidirect
16. C2×C47×#387C2semidirect
20. C2×#13093982C4semidirect
35. #15689009C22semidirect
36. #15689008C22semidirect
37. #15689006C22semidirect
40. #15688990C22semidirect
41. #15688988C22semidirect
43. C4×Dic47⋊C4C22semidirect
46. #15688968C22semidirect
63. C47×#387C22semidirect
88. #13093982C2×C4semidirect
90. C2×C4⋊Dic47C2×C4semidirect
108. C2×C4×Dic47C2×C4semidirect
109. C2×C4×Dic47C2×C4semidirect
135. C2×C4⋊C4×C47C2×C4semidirect
222. C4⋊C4×C47C22×C4semidirect
229. C4⋊Dic47C22×C4semidirect
235. C4×Dic47C22×C4semidirect
236. C4×Dic47C22×C4semidirect
360. C2×#387D47semidirect
371. C2×C47#2343semidirect
404. #387C2×D47semidirect
431. C47C2×#2343semidirect
469. C2×C4⋊C4C4×D47semidirect
590. C4⋊C4C2×C4×D47semidirect
719. C2#20246247direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939822
#202462472
C2×#156890092
C2×#156890082
C2×#156890062
C2×#156889972
C2×#156889942
C2×#156889902
C2×#156889882
C2×#156889852
C2×C4×Dic47⋊C42
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×#156889682
C2×#95×D472
C2×C47×#3872
C2×#234347