Finite Group Databasebeta

← C2×#20246138 #26375129

Subgroups — C2×#20246138 #26375129

Order 12032.

2678 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×#13094001C211yesmaximal, characteristic
2#20246138C2116yesmaximal, direct product factor
3C2×#15689029C211yesmaximal, characteristic, complemented
4C2×#15689027C211yesmaximal, characteristic, complemented
5C2×#15689016C211yesmaximal, characteristic
6C2×#15689011C211yesmaximal, characteristic
7C2×#15689011C211yesmaximal, characteristic
8C2×#15689010C211yesmaximal, characteristic, complemented
9C2×#15689008C211yesmaximal, characteristic, complemented
10C2×#15689005C211yesmaximal, characteristic, complemented
11C2×#15689004C211yesmaximal, characteristic, complemented
12C2×#15688984C211yesmaximal, characteristic
13C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic47C211yesmaximal, characteristic
16C2×C47×#388C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C2×#13094001C4116yescomplemented
20C2×#13094001C2218yes—
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35#15689029C2218yescomplemented
36#15689027C2218yescomplemented
37#15689016C2218yes—
38#15689011C2218yes—
39#15689011C2218yes—
40#15689010C2218yescomplemented
41#15689008C2218yescomplemented
42#15689005C2218yescomplemented
43#15689004C2218yescomplemented
44#15688984C2218yes—
45C4⋊C4×Dic47C2218yescomplemented
46C4×Dic47⋊C4C2218yescomplemented
47C22⋊C4×Dic47C2218yes—
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×C47⋊#95C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C22⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C42×C47C2211yescharacteristic
65C47×#388C2218yes—
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C22×Dic94—42no—
69C22×Dic94—42no—
70C22×Dic94C2×C418yes—
71C22×Dic94C2314yes—
72C23×Dic47—42no—
73C23×Dic47—42no—
74C23×Dic47C2×C418yes—
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2314yes—
84#13094001C2×C4164yescomplemented
85C2×C4⋊Dic47—42no—
86C2×C4⋊Dic47C2×C418yes—
87C2×C4⋊Dic47C2314yes—
88C2×C4⋊Dic47C2314yes—
89C2×Dic47⋊C4—24no—
90C2×Dic47⋊C4—42no—
91C2×Dic47⋊C4C2×C418yes—
92C2×Dic47⋊C4C2×C418yes—
93C2×Dic47⋊C4C2314yes—
94C2×Dic47⋊C4C2314yes—
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×C22⋊Dic47—24no—
98C2×C22⋊Dic47—42no—
99C2×C22⋊Dic47C2×C418yes—
100C2×C22⋊Dic47C2314yes—
101C2×C22⋊Dic47C2314yes—
102C2×C22⋊Dic47C2314yes—
103C2×C4×Dic47—24no—
104C2×C4×Dic47—24no—
105C2×C4×Dic47—42no—
106C2×C4×Dic47—42no—
107C2×C4×Dic47—42no—
108C2×C4×Dic47C2314yes—
109C2×C4×Dic47C2314yes—
110C2×C4×Dic47C2314yes—
111C2×C4×Dic47C2314yes—
112C2×C4×Dic47C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C25×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C2×C4⋊C4×C47—24no—
133C2×C4⋊C4×C47C2314yes—
134C2×C22⋊C4×C47—24no—
135C2×C22⋊C4×C47—42no—
136C2×C22⋊C4×C47C2×C418yes—
137C2×C22⋊C4×C47C2314yes—
138C2×C22⋊C4×C47C2314yes—
139C2×C22⋊C4×C47C2314yes—
140C2×C42×C47—42no—
141C2×C42×C47C2314yes—
142#95×C47C2314yes—
143#95×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×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47C22×C414yes—
169C22×C4×C47C22×C414yes—
170C22×C4×C47#4114yes—
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—416no—
197C22×Dic47—44no—
198C22×Dic47—44no—
199C22×Dic47C22×C414yes—
200C22×Dic47C22×C414yes—
201C22×Dic47C22×C414yes—
202C22×Dic47C22×C414yes—
203C22×Dic47C22×C4116yes—
204C22×Dic47#4114yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C22×Dic47C2412yes—
210C22×Dic47C2412yes—
211C22×Dic47C2412yes—
212C22×Dic47C2412yes—
213C2×Dic94—416no—
214C2×Dic94—44no—
215C2×Dic94—44no—
216C2×Dic94C22×C4116yes—
217C4⋊C4×C47—28no—
218C22⋊C4×C47—28no—
219C22⋊C4×C47—44no—
220C22⋊C4×C47C22×C4116yes—
221C42×C47—44no—
222C22⋊Dic47—28no—
223C22⋊Dic47—44no—
224C22⋊Dic47C22×C4116yes—
225C4⋊Dic47—44no—
226C4⋊Dic47C22×C4116yes—
227Dic47⋊C4—28no—
228Dic47⋊C4—44no—
229Dic47⋊C4C22×C4116yes—
230Dic47⋊C4C22×C4116yes—
231C4×Dic47—28no—
232C4×Dic47—28no—
233C4×Dic47—44no—
234C4×Dic47—44no—
235C4×Dic47—44no—
236C23×C47—28no—
237C23×C47—28no—
238C23×C47—28no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—44no—
246C23×C47—44no—
247C23×C47—44no—
248C23×C47—44no—
249C23×C47C23×C414yes—
250C23×C47C23×C412yes—
251C23×C47C2×#4112yes—
252C23×C47C2×#4112yes—
253C23×C47H(5,𝔽2)12yes—
254C23×C47H(5,𝔽2)12yes—
255C23×C472−1+412yes—
256C23×C472−1+412yes—
257C23×C47C2511yescharacteristic
258C2×C4×C47—28no—
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—44no—
277C2×C4×C47—44no—
278C2×C4×C47—44no—
279C2×C4×C47C23×C414yes—
280C2×C4×C47C23×C414yes—
281C2×C4×C47C2×#4114yes—
282C2×Dic47—28no—
283C2×Dic47—28no—
284C2×Dic47—28no—
285C2×Dic47—28no—
286C2×Dic47—28no—
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—22no—
306C2×Dic47—416no—
307C2×Dic47—44no—
308C2×Dic47—44no—
309C2×Dic47—44no—
310C2×Dic47C23×C414yes—
311C2×Dic47C23×C414yes—
312C2×Dic47C23×C414yes—
313C2×Dic47C23×C414yes—
314C2×Dic47C2×#4114yes—
315Dic94—416no—
316C2×#2332—471nomaximal, Sylow
317C22×C47—24no—
318C22×C47—24no—
319C22×C47—24no—
320C22×C47—416no—
321C22×C47—42no—
322C22×C47—42no—
323C22×C47—42no—
324C22×C47—42no—
325C22×C47C4×#4114yes—
326C22×C47#51814yes—
327C22×C47#51914yes—
328C22×C47#53914yes—
329C22×C47#53914yes—
330C22×C47#54214yes—
331C22×C47#54214yes—
332C22×C47C24×C411yescharacteristic
333C22×C47C22×#4111yescharacteristic
334C22×C47C22×#4111yescharacteristic
335C22×C47C2×H(5,𝔽2)11yescharacteristic
336C22×C47C2×H(5,𝔽2)11yescharacteristic
337C22×C47C2×2−1+411yescharacteristic
338C22×C47C2×2−1+411yescharacteristic
339C4×C47—24no—
340C4×C47—24no—
341C4×C47—24no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47—42no—
345Dic47—24no—
346Dic47—24no—
347Dic47—24no—
348Dic47—24no—
349Dic47—24no—
350Dic47—42no—
351Dic47—42no—
352Dic47—42no—
353C22×C22⋊Q8—471no—
354#2332—4716no—
355C2×#391—471no—
356C2×#391—471no—
357C2×#388—471no—
358C2×#388—471no—
359C2×#388—471no—
360C2×#388D4711yescharacteristic
361C2×#387—471no—
362C2×#387—471no—
363C2×#387—471no—
364C2×#387—471no—
365C2×#381—471no—
366C2×C4×C4⋊C4—471no—
367C2×C4×C4⋊C4—471no—
368C2×C4×C22⋊C4—471no—
369C2×C47—44no—
370C2×C47#233218yescomplemented
371C2×C47C2×C4×#4111yescharacteristic
372C2×C47C2×#51811yescharacteristic
373C2×C47C2×#51911yescharacteristic
374C2×C47C2×#53911yescharacteristic
375C2×C47C2×#53911yescharacteristic
376C2×C47C2×#54211yescharacteristic
377C2×C47C2×#54211yescharacteristic
378C23×Q8—471no—
379C24×C4—471no—
380C2×C22⋊Q8—4716no—
381C2×C22⋊Q8—478no—
382C22×C4⋊C4—471no—
383C22×C4⋊C4—471no—
384C22×C4⋊C4—471no—
385C22×C4⋊C4—471no—
386C22×C4⋊C4—471no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4C2×D4711yescharacteristic
389C22×C22⋊C4—471no—
390C22×C22⋊C4—471no—
391C22×C22⋊C4—471no—
392C22×C22⋊C4C2×D4711yescharacteristic
393C22×C22⋊C4C2×D4711yescharacteristic
394C22×C22⋊C4C2×D4711yescharacteristic
395C22×C42—471no—
396C22×C42—471no—
397C22×C42—471no—
398C22×C42—471no—
399C22×C42—471no—
400C22×C42C2×D4711yescharacteristic
401#391—478no—
402#391—478no—
403#388—478no—
404#388—478no—
405#388—478no—
406#388C2×D4718yes—
407#387—478no—
408#387—478no—
409#387—478no—
410#387—478no—
411#381—478no—
412C4×C4⋊C4—478no—
413C4×C4⋊C4—478no—
414C4×C22⋊C4—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—
427C2×#95C2×D4711yescharacteristic
428C2×#95C2×D4711yescharacteristic
429C47C2×#233211yescharacteristic, complemented, Sylow
430C25C22×D4711yescharacteristic
431C22×Q8—478no—
432C22×Q8—474no—
433C22×Q8—1882no—
434C22×Q8—1882no—
435C23×C4—471no—
436C23×C4—471no—
437C23×C4—471no—
438C23×C4—471no—
439C23×C4—471no—
440C23×C4—478no—
441C23×C4—474no—
442C23×C4—471no—
443C23×C4—471no—
444C23×C4—471no—
445C23×C4—1882no—
446C23×C4—1882no—
447C23×C4C22×D4711yescharacteristic
448C23×C4C22×D4711yescharacteristic
449C23×C4C22×D4711yescharacteristic
450C23×C4C22×D4711yescharacteristic
451C23×C4C22×D4711yescharacteristic
452C23×C4C22×D4711yescharacteristic
453C22⋊Q8—4764no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—478no—
456C2×C4⋊C4—478no—
457C2×C4⋊C4—478no—
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—1882no—
466C2×C4⋊C4—1882no—
467C2×C4⋊C4C22×D4714yes—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—478no—
471C2×C22⋊C4—474no—
472C2×C22⋊C4—474no—
473C2×C22⋊C4—474no—
474C2×C22⋊C4—944no—
475C2×C22⋊C4—1882no—
476C2×C22⋊C4C4×D4718yes—
477C2×C22⋊C4C22×D4714yes—
478C2×C22⋊C4C22×D4714yes—
479C2×C22⋊C4C22×D4714yes—
480C2×C42—42no—
481C2×C42—474no—
482C2×C42—474no—
483C2×C42—474no—
484C2×C42—474no—
485C2×C42—474no—
486C2×C42—944no—
487C2×C42—944no—
488C2×C42—1882no—
489C2×C42—1882no—
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—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24C2×C4×D4714yes—
513C24C23×D4712yes—
514C24C23×D4711yescharacteristic
515C2×Q8—4716no—
516C2×Q8—18816no—
517C2×Q8—1884no—
518C2×Q8—1884no—
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—474no—
539C22×C4—472no—
540C22×C4—472no—
541C22×C4—472no—
542C22×C4—472no—
543C22×C4—472no—
544C22×C4—4716no—
545C22×C4—472no—
546C22×C4—472no—
547C22×C4—472no—
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—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—18816no—
568C22×C4—1884no—
569C22×C4—1884no—
570C22×C4C2×C4×D4714yes—
571C22×C4C2×C4×D4714yes—
572C22×C4#1062535214yes—
573C22×C4C23×D4712yes—
574C22×C4C23×D4712yes—
575C22×C4C23×D4712yes—
576C22×C4C23×D4712yes—
577C22×C4C23×D4712yes—
578C22×C4C23×D4712yes—
579C4⋊C4—28no—
580C4⋊C4—4716no—
581C4⋊C4—4716no—
582C4⋊C4—4716no—
583C4⋊C4—948no—
584C4⋊C4—1884no—
585C4⋊C4—1884no—
586C22⋊C4—28no—
587C22⋊C4—44no—
588C22⋊C4—4716no—
589C22⋊C4—948no—
590C22⋊C4—1884no—
591C22⋊C4C2×C4×D47116yes—
592C42—44no—
593C42—948no—
594C42—948no—
595C42—1884no—
596C42—1884no—
597C42—1884no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23C22×C4×D4714yes—
612C23C22×C4×D4712yes—
613C23#41×D4712yes—
614C23C2×#1062535212yes—
615C23#1309406912yes—
616C23#1309407012yes—
617C23#1309407112yes—
618C23#1309407112yes—
619C23C24×D4711yescharacteristic
620Q8—18816no—
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—28no—
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—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—474no—
643C2×C4—474no—
644C2×C4—474no—
645C2×C4—474no—
646C2×C4—474no—
647C2×C4—948no—
648C2×C4—948no—
649C2×C4—948no—
650C2×C4—948no—
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—948no—
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—18816no—
672C2×C4—1884no—
673C2×C4—1884no—
674C2×C4—1884no—
675C2×C4C22×C4×D4714yes—
676C2×C4C22×C4×D4714yes—
677C2×C4C2×#1062535214yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—416no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22C4×#1062535214yes—
687C22#1568959514yes—
688C22#1568960014yes—
689C22#1568971614yes—
690C22#1568971814yes—
691C22#1568973914yes—
692C22#1568974214yes—
693C22C23×C4×D4711yescharacteristic
694C22C2×#41×D4711yescharacteristic
695C22C22×#1062535211yescharacteristic
696C22C2×#1309406911yescharacteristic
697C22C2×#1309407011yescharacteristic
698C22C2×#1309407111yescharacteristic
699C22C2×#1309407111yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—944no—
707C4—944no—
708C4—944no—
709C4—944no—
710C4—944no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C2—44no—
715C2#2024613818yesdirect product factor
716C2C2×C4×#1062535211yescharacteristic
717C2C2×#1568959511yescharacteristic
718C2C2×#1568960011yescharacteristic
719C2C2×#1568971611yescharacteristic
720C2C2×#1568971811yescharacteristic
721C2C2×#1568973911yescharacteristic
722C2C2×#1568974211yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC25×C47C23
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2332
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #20246138C2direct (N × H)
3. C2×#15689029C2semidirect
4. C2×#15689027C2semidirect
8. C2×#15689010C2semidirect
9. C2×#15689008C2semidirect
10. C2×#15689005C2semidirect
11. C2×#15689004C2semidirect
13. C2×C4⋊C4×Dic47C2semidirect
14. C2×C4×Dic47⋊C4C2semidirect
19. C2×#13094001C4semidirect
35. #15689029C22semidirect
36. #15689027C22semidirect
40. #15689010C22semidirect
41. #15689008C22semidirect
42. #15689005C22semidirect
43. #15689004C22semidirect
45. C4⋊C4×Dic47C22semidirect
46. C4×Dic47⋊C4C22semidirect
84. #13094001C2×C4semidirect
370. C2×C47#2332semidirect
429. C47C2×#2332semidirect
715. C2#20246138direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940012
#202461382
C2×#156890292
C2×#156890272
C2×#156890162
C2×#156890112
C2×#156890102
C2×#156890082
C2×#156890052
C2×#156890042
C2×#156889842
C2×C4⋊C4×Dic472
C2×C4×Dic47⋊C42
C2×C22⋊C4×Dic472
C2×C47×#3882
C2×#233247