Finite Group Databasebeta

← C2×#20248470 #26386369

Subgroups — C2×#20248470 #26386369

Order 12032.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094014C211yesmaximal, characteristic, complemented
2#20248470C2116yesmaximal, direct product factor
3C2×#15689059C211yesmaximal, characteristic
4C2×#15689056C211yesmaximal, characteristic, complemented
5C2×#15689046C211yesmaximal, characteristic
6C2×#15689042C211yesmaximal, characteristic, complemented
7C2×#15689030C211yesmaximal, characteristic, complemented
8C2×#15689018C211yesmaximal, characteristic, complemented
9C2×#15689018C211yesmaximal, characteristic, complemented
10C2×#15689017C211yesmaximal, characteristic
11C2×#15689017C211yesmaximal, characteristic
12C2×#15689004C211yesmaximal, characteristic, complemented
13C2×#15688996C211yesmaximal, characteristic
14C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic47C211yesmaximal, characteristic
16C22×C22⋊Q8×C47C211yesmaximal, characteristic
17C2×#13094014—28no—
18C2×#13094014C2218yescomplemented
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C22⋊Dic47C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37#15689059C2218yes—
38#15689056C2218yescomplemented
39#15689046C2218yes—
40#15689042C2218yescomplemented
41#15689030C2218yescomplemented
42#15689018C2218yescomplemented
43#15689018C2218yescomplemented
44#15689017C2218yes—
45#15689017C2218yes—
46#15689004C2218yescomplemented
47#15688996C2218yes—
48C4⋊C4×Dic47C2218yescomplemented
49C4×C22⋊Dic47C2218yes—
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
60C23×Q8×C47C2211yescharacteristic
61C24×C4×C47C2211yescharacteristic
62C2×C22⋊Q8×C47—28no—
63C2×C22⋊Q8×C47C2218yes—
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic
66C22×C4⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77#13094014—232no—
78C2×C4⋊Dic47—24no—
79C2×C4⋊Dic47—24no—
80C2×C4⋊Dic47C2314yes—
81C2×C4⋊Dic47C2314yes—
82C2×Dic47⋊C4—24no—
83C2×Dic47⋊C4—24no—
84C2×Dic47⋊C4—24no—
85C2×Dic47⋊C4—24no—
86C2×Dic47⋊C4—24no—
87C2×Dic47⋊C4—24no—
88C2×Dic47⋊C4—24no—
89C2×Dic47⋊C4—42no—
90C2×Dic47⋊C4C2314yes—
91C2×Dic47⋊C4C2314yes—
92C2×Dic47⋊C4C2314yes—
93C2×Dic47⋊C4C2314yes—
94C2×Dic47⋊C4C2314yes—
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×Dic47⋊C4C2314yes—
98C2×C22⋊Dic47—24no—
99C2×C22⋊Dic47—24no—
100C2×C22⋊Dic47—42no—
101C2×C22⋊Dic47Q818yescomplemented
102C2×C22⋊Dic47C2314yes—
103C2×C22⋊Dic47C2314yes—
104C2×C22⋊Dic47C2314yes—
105C2×C22⋊Dic47C2314yes—
106C2×C4×Dic47—24no—
107C2×C4×Dic47—24no—
108C2×C4×Dic47—42no—
109C2×C4×Dic47—42no—
110C2×C4×Dic47C2314yes—
111C2×C4×Dic47C2314yes—
112C2×C4×Dic47C2314yes—
113C2×C4×Dic47C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C25×C47C2311yescharacteristic
125C22×Q8×C47—24no—
126C22×Q8×C47—24no—
127C22×Q8×C47—42no—
128C22×Q8×C47C2314yes—
129C23×C4×C47—24no—
130C23×C4×C47—24no—
131C23×C4×C47—42no—
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2314yes—
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C22⋊Q8×C47—232no—
140C2×C4⋊C4×C47—24no—
141C2×C4⋊C4×C47—24no—
142C2×C4⋊C4×C47D418yes—
143C2×C4⋊C4×C47C2314yes—
144C2×C4⋊C4×C47C2314yes—
145C2×C4⋊C4×C47C2314yes—
146C2×C22⋊C4×C47—24no—
147C2×C22⋊C4×C47—24no—
148C2×C22⋊C4×C47C2314yes—
149C2×C22⋊C4×C47C2314yes—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47C2×Q814yes—
157C24×C47C2412yes—
158C24×C47C2411yescharacteristic
159C2×Q8×C47—28no—
160C2×Q8×C47—28no—
161C2×Q8×C47—44no—
162C2×Q8×C47—416no—
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×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—28no—
178C22×C4×C47—28no—
179C22×C4×C47—44no—
180C22×C4×C47—416no—
181C22×C4×C47C2×D414yes—
182C22×C4×C47C2×D414yes—
183C22×C4×C47C2×D414yes—
184C22×C4×C47#4114yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2412yes—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
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×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47C2×Q814yes—
212C22×Dic47C2×Q814yes—
213C22×Dic47#4114yes—
214C22×Dic47#4114yes—
215C22×Dic47C2412yes—
216C22×Dic47C2412yes—
217C22×Dic47C2412yes—
218C22×Dic47C2412yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C4⋊C4×C47—28no—
224C4⋊C4×C47—28no—
225C4⋊C4×C47C2×D4116yes—
226C22⋊C4×C47—28no—
227C22⋊C4×C47—28no—
228C22⋊Dic47—28no—
229C22⋊Dic47—28no—
230C22⋊Dic47—44no—
231C22⋊Dic47C2×Q8116yescomplemented
232C4⋊Dic47—28no—
233C4⋊Dic47—28no—
234Dic47⋊C4—28no—
235Dic47⋊C4—28no—
236Dic47⋊C4—28no—
237Dic47⋊C4—28no—
238Dic47⋊C4—28no—
239Dic47⋊C4—28no—
240Dic47⋊C4—28no—
241Dic47⋊C4—44no—
242C4×Dic47—28no—
243C4×Dic47—28no—
244C4×Dic47—44no—
245C4×Dic47—44no—
246C23×C47—28no—
247C23×C47—28no—
248C23×C47—28no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—44no—
256C23×C47—44no—
257C23×C47—44no—
258C23×C47—44no—
259C23×C47C22×D412yes—
260C23×C47C22×Q814yes—
261C23×C47C22×Q812yes—
262C23×C47C2×#4112yes—
263C23×C47C2×#4112yes—
264C23×C47C2×#4112yes—
265C23×C47H(5,𝔽2)12yes—
266C23×C472−1+412yes—
267C23×C47C2511yescharacteristic
268Q8×C47—416no—
269C2×C4×C47—28no—
270C2×C4×C47—28no—
271C2×C4×C47—28no—
272C2×C4×C47—28no—
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—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—416no—
288C2×C4×C47—44no—
289C2×C4×C47—44no—
290C2×C4×C47C22×D414yes—
291C2×C4×C47C22×D414yes—
292C2×C4×C47C22×D414yes—
293C2×C4×C47C2×#4114yes—
294C2×Dic47—28no—
295C2×Dic47—28no—
296C2×Dic47—28no—
297C2×Dic47—28no—
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—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—44no—
319C2×Dic47—44no—
320C2×Dic47—44no—
321C2×Dic47—44no—
322C2×Dic47C22×Q814yes—
323C2×Dic47C22×Q814yes—
324C2×Dic47C2×#4114yes—
325C2×Dic47C2×#4114yes—
326C2×#2556—471nomaximal, Sylow
327C22×C47—24no—
328C22×C47—24no—
329C22×C47—24no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47—42no—
334C22×C47—416no—
335C22×C47#53214yes—
336C22×C47#53314yes—
337C22×C47#53914yes—
338C22×C47#54614yes—
339C22×C47D4×Q814yes—
340C22×C47#55214yes—
341C22×C47#55414yes—
342C22×C47C23×D411yescharacteristic
343C22×C47C23×Q811yescharacteristic
344C22×C47C22×#4111yescharacteristic
345C22×C47C22×#4111yescharacteristic
346C22×C47C22×#4111yescharacteristic
347C22×C47C2×H(5,𝔽2)11yescharacteristic
348C22×C47C2×2−1+411yescharacteristic
349C4×C47—24no—
350C4×C47—24no—
351C4×C47—24no—
352C4×C47—24no—
353C4×C47—42no—
354C4×C47—42no—
355Dic47—24no—
356Dic47—24no—
357Dic47—24no—
358Dic47—24no—
359Dic47—42no—
360Dic47—42no—
361Dic47—42no—
362Dic47—42no—
363C22×#125—471no—
364C22×C22⋊Q8D4711yescharacteristic
365#2556—4716no—
366C2×#399—471no—
367C2×#398—471no—
368C2×#396—471no—
369C2×#395—471no—
370C2×#391—471no—
371C2×#389—471no—
372C2×#389—471no—
373C2×#388—471no—
374C2×#388—471no—
375C2×#387—471no—
376C2×#385—471no—
377C2×C4×C4⋊C4—471no—
378C2×C4×C22⋊C4—471no—
379C2×C47—44no—
380C2×C47#255618yescomplemented
381C2×C47C2×#53211yescharacteristic
382C2×C47C2×#53311yescharacteristic
383C2×C47C2×#53911yescharacteristic
384C2×C47C2×#54611yescharacteristic
385C2×C47C2×D4×Q811yescharacteristic
386C2×C47C2×#55211yescharacteristic
387C2×C47C2×#55411yescharacteristic
388C23×Q8C2×D4711yescharacteristic
389C24×C4C2×D4711yescharacteristic
390C2×#125—478no—
391C2×#125—948no—
392C2×C22⋊Q8—28no—
393C2×C22⋊Q8C2×D4718yes—
394C22×C4⋊C4—471no—
395C22×C4⋊C4—471no—
396C22×C4⋊C4—471no—
397C22×C4⋊C4—471no—
398C22×C4⋊C4—471no—
399C22×C4⋊C4—471no—
400C22×C4⋊C4—471no—
401C22×C4⋊C4—471no—
402C22×C4⋊C4—471no—
403C22×C4⋊C4—471no—
404C22×C4⋊C4C2×D4711yescharacteristic
405C22×C4⋊C4C2×D4711yescharacteristic
406C22×C4⋊C4C2×D4711yescharacteristic
407C22×C22⋊C4—471no—
408C22×C22⋊C4—471no—
409C22×C22⋊C4—471no—
410C22×C22⋊C4—471no—
411C22×C22⋊C4C2×D4711yescharacteristic
412C22×C22⋊C4C2×D4711yescharacteristic
413C22×C42—471no—
414C22×C42—471no—
415C22×C42—471no—
416C22×C42—471no—
417#399—478no—
418#398—478no—
419#396—478no—
420#395—478no—
421#391—478no—
422#389—478no—
423#389—478no—
424#388—478no—
425#388—478no—
426#387—478no—
427#385—478no—
428C4×C4⋊C4—478no—
429C4×C22⋊C4—478no—
430C2×#95—471no—
431C2×#95—471no—
432C2×#95—471no—
433C2×#95—471no—
434C2×#95—471no—
435C2×#95—471no—
436C2×#95—471no—
437C2×#95—471no—
438C2×#95—471no—
439C2×#95—471no—
440C47C2×#255611yescharacteristic, complemented, Sylow
441C25C22×D4711yescharacteristic
442C22×Q8—24no—
443C22×Q8—24no—
444C22×Q8—42no—
445C22×Q8C22×D4714yes—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—42no—
449C23×C4—471no—
450C23×C4—471no—
451C23×C4—471no—
452C23×C4—471no—
453C23×C4—471no—
454C23×C4—471no—
455C23×C4—471no—
456C23×C4—471no—
457C23×C4C22×D4711yescharacteristic
458C23×C4C22×D4711yescharacteristic
459C23×C4C22×D4714yes—
460C23×C4C22×D4711yescharacteristic
461C23×C4C22×D4711yescharacteristic
462C23×C4C22×D4711yescharacteristic
463C23×C4C22×D4711yescharacteristic
464#125—9432no—
465C22⋊Q8—232no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—474no—
469C2×C4⋊C4—474no—
470C2×C4⋊C4—474no—
471C2×C4⋊C4—474no—
472C2×C4⋊C4—474no—
473C2×C4⋊C4—474no—
474C2×C4⋊C4—474no—
475C2×C4⋊C4—474no—
476C2×C4⋊C4—474no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—944no—
479C2×C4⋊C4—944no—
480C2×C4⋊C4—944no—
481C2×C4⋊C4—944no—
482C2×C4⋊C4—944no—
483C2×C4⋊C4—944no—
484C2×C4⋊C4—944no—
485C2×C4⋊C4—944no—
486C2×C4⋊C4—944no—
487C2×C4⋊C4—1882no—
488C2×C4⋊C4C22⋊D4718yes—
489C2×C4⋊C4C22×D4714yes—
490C2×C4⋊C4C22×D4714yes—
491C2×C4⋊C4C22×D4714yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—478no—
495C2×C22⋊C4—474no—
496C2×C22⋊C4—474no—
497C2×C22⋊C4—474no—
498C2×C22⋊C4—474no—
499C2×C22⋊C4—944no—
500C2×C22⋊C4—944no—
501C2×C22⋊C4—1882no—
502C2×C22⋊C4C22×D4714yes—
503C2×C22⋊C4C22×D4714yes—
504C2×C42—474no—
505C2×C42—474no—
506C2×C42—474no—
507C2×C42—474no—
508C2×C42—944no—
509C2×C42—944no—
510C2×C42—1882no—
511C2×C42—1882no—
512#95—474no—
513#95—474no—
514#95—474no—
515#95—474no—
516#95—474no—
517#95—474no—
518#95—474no—
519#95—474no—
520#95—474no—
521#95—474no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24Q8×D4714yes—
529C24C23×D4712yes—
530C24C23×D4711yescharacteristic
531C2×Q8—28no—
532C2×Q8—28no—
533C2×Q8—44no—
534C2×Q8—416no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—44no—
552C22×C4—416no—
553C22×C4—474no—
554C22×C4—474no—
555C22×C4—474no—
556C22×C4—474no—
557C22×C4—472no—
558C22×C4—472no—
559C22×C4—472no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—472no—
563C22×C4—472no—
564C22×C4—472no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4#1062535214yes—
586C22×C4C2×C22⋊D4714yes—
587C22×C4C2×C22⋊D4714yes—
588C22×C4C2×C22⋊D4714yes—
589C22×C4C23×D4712yes—
590C22×C4C23×D4712yes—
591C22×C4C23×D4712yes—
592C22×C4C23×D4712yes—
593C22×C4C23×D4712yes—
594C22×C4C23×D4712yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—948no—
598C4⋊C4—948no—
599C4⋊C4—948no—
600C4⋊C4—948no—
601C4⋊C4—948no—
602C4⋊C4—948no—
603C4⋊C4—948no—
604C4⋊C4—948no—
605C4⋊C4—948no—
606C4⋊C4—1884no—
607C4⋊C4C2×C22⋊D47116yes—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—4716no—
611C22⋊C4—948no—
612C22⋊C4—948no—
613C22⋊C4—1884no—
614C42—948no—
615C42—948no—
616C42—1884no—
617C42—1884no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23C22×C22⋊D4712yes—
632C23C2×Q8×D4714yes—
633C23C2×Q8×D4712yes—
634C23#41×D4712yes—
635C23#41×D4712yes—
636C23C2×#1062535212yes—
637C23#1309406912yes—
638C23#1309407212yes—
639C23C24×D4711yescharacteristic
640Q8—416no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—416no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—474no—
663C2×C4—474no—
664C2×C4—474no—
665C2×C4—474no—
666C2×C4—948no—
667C2×C4—948no—
668C2×C4—948no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—948no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—1884no—
691C2×C4—1884no—
692C2×C4—1884no—
693C2×C4—1884no—
694C2×C4C22×C22⋊D4714yes—
695C2×C4C22×C22⋊D4714yes—
696C2×C4C22×C22⋊D4714yes—
697C2×C4C2×#1062535214yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—416no—
704C22—42no—
705C22—42no—
706C22#1568966914yes—
707C22#1568967514yes—
708C22#1568971914yes—
709C22#1568976714yes—
710C22Q8×C22⋊D4714yes—
711C22#1568980714yes—
712C22#1568982714yes—
713C22C23×C22⋊D4711yescharacteristic
714C22C22×Q8×D4711yescharacteristic
715C22C2×#41×D4711yescharacteristic
716C22C2×#41×D4711yescharacteristic
717C22C22×#1062535211yescharacteristic
718C22C2×#1309406911yescharacteristic
719C22C2×#1309407211yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—944no—
727C4—944no—
728C4—944no—
729C4—944no—
730C4—1882no—
731C4—1882no—
732C4—1882no—
733C4—1882no—
734C2—44no—
735C2#2024847018yesdirect product factor
736C2C2×#1568966911yescharacteristic
737C2C2×#1568967511yescharacteristic
738C2C2×#1568971911yescharacteristic
739C2C2×#1568976711yescharacteristic
740C2C2×Q8×C22⋊D4711yescharacteristic
741C2C2×#1568980711yescharacteristic
742C2C2×#1568982711yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×C22⋊Q8×C47C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC22×C22⋊Q8D47
hypocenterC47C2×#2556
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13094014C2semidirect
2. #20248470C2direct (N × H)
4. C2×#15689056C2semidirect
6. C2×#15689042C2semidirect
7. C2×#15689030C2semidirect
8. C2×#15689018C2semidirect
9. C2×#15689018C2semidirect
12. C2×#15689004C2semidirect
14. C2×C4⋊C4×Dic47C2semidirect
18. C2×#13094014C22semidirect
38. #15689056C22semidirect
40. #15689042C22semidirect
41. #15689030C22semidirect
42. #15689018C22semidirect
43. #15689018C22semidirect
46. #15689004C22semidirect
48. C4⋊C4×Dic47C22semidirect
101. C2×C22⋊Dic47Q8semidirect
231. C22⋊Dic47C2×Q8semidirect
380. C2×C47#2556semidirect
440. C47C2×#2556semidirect
735. C2#20248470direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940142
#202484702
C2×#156890592
C2×#156890562
C2×#156890462
C2×#156890422
C2×#156890302
C2×#156890182
C2×#156890172
C2×#156890042
C2×#156889962
C2×C4⋊C4×Dic472
C2×C4×C22⋊Dic472
C22×C22⋊Q8×C472
C2×#255647