Finite Group Databasebeta

← C2×#20247405 #26384249

Subgroups — C2×#20247405 #26384249

Order 12032.

2854 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093989C211yesmaximal, characteristic, complemented
2#20247405C2116yesmaximal, direct product factor
3C2×#15689046C211yesmaximal, characteristic
4C2×#15689043C211yesmaximal, characteristic, complemented
5C2×#15689042C211yesmaximal, characteristic, complemented
6C2×#15689035C211yesmaximal, characteristic
7C2×#15689030C211yesmaximal, characteristic, complemented
8C2×#15689018C211yesmaximal, characteristic, complemented
9C2×#15689011C211yesmaximal, characteristic
10C2×#15689011C211yesmaximal, characteristic
11C2×#15689009C211yesmaximal, characteristic, complemented
12C2×#15689004C211yesmaximal, characteristic, complemented
13C2×#15689004C211yesmaximal, characteristic, complemented
14C2×#15688996C211yesmaximal, characteristic
15C2×C4×C22⋊Dic47C211yesmaximal, characteristic
16C22×C22⋊Q8×C47C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C2×#13093989—28no—
19C2×#13093989C2218yescomplemented
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35#15689046C2218yes—
36#15689043C2218yescomplemented
37#15689042C2218yescomplemented
38#15689035C2218yes—
39#15689030C2218yescomplemented
40#15689018C2218yescomplemented
41#15689011C2218yes—
42#15689011C2218yes—
43#15689009C2218yescomplemented
44#15689004C2218yescomplemented
45#15689004C2218yescomplemented
46#15688996C2218yes—
47C4×C22⋊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
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
69C22×Dic94—24no—
70C22×Dic94—24no—
71C22×Dic94—24no—
72C22×Dic94C2314yes—
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81#13093989—232no—
82C2×C4⋊Dic47—42no—
83C2×C4⋊Dic47C2314yes—
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×C22⋊Dic47—24no—
97C2×C22⋊Dic47—24no—
98C2×C22⋊Dic47—42no—
99C2×C22⋊Dic47Q818yescomplemented
100C2×C22⋊Dic47C2314yes—
101C2×C22⋊Dic47C2314yes—
102C2×C22⋊Dic47C2314yes—
103C2×C22⋊Dic47C2314yes—
104C2×C4×Dic47—24no—
105C2×C4×Dic47—24no—
106C2×C4×Dic47—24no—
107C2×C4×Dic47—42no—
108C2×C4×Dic47C2314yes—
109C2×C4×Dic47C2314yes—
110C2×C4×Dic47C2314yes—
111C2×C4×Dic47C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
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—
223C2×Dic94—232no—
224C2×Dic94—28no—
225C2×Dic94—28no—
226C2×Dic94—28no—
227C4⋊C4×C47—28no—
228C4⋊C4×C47—28no—
229C4⋊C4×C47C2×D4116yes—
230C22⋊C4×C47—28no—
231C22⋊C4×C47—28no—
232C22⋊Dic47—28no—
233C22⋊Dic47—28no—
234C22⋊Dic47—44no—
235C22⋊Dic47C2×Q8116yescomplemented
236C4⋊Dic47—44no—
237Dic47⋊C4—28no—
238Dic47⋊C4—28no—
239Dic47⋊C4—28no—
240Dic47⋊C4—28no—
241Dic47⋊C4—28no—
242Dic47⋊C4—44no—
243C4×Dic47—28no—
244C4×Dic47—28no—
245C4×Dic47—28no—
246C4×Dic47—44no—
247C23×C47—28no—
248C23×C47—28no—
249C23×C47—28no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—44no—
257C23×C47—44no—
258C23×C47—44no—
259C23×C47—44no—
260C23×C47C22×D412yes—
261C23×C47C22×Q814yes—
262C23×C47C22×Q812yes—
263C23×C47C2×#4112yes—
264C23×C47C2×#4112yes—
265C23×C47C2×#4112yes—
266C23×C47H(5,𝔽2)12yes—
267C23×C472−1+412yes—
268C23×C47C2511yescharacteristic
269Q8×C47—416no—
270C2×C4×C47—28no—
271C2×C4×C47—28no—
272C2×C4×C47—28no—
273C2×C4×C47—28no—
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—22no—
288C2×C4×C47—416no—
289C2×C4×C47—44no—
290C2×C4×C47—44no—
291C2×C4×C47C22×D414yes—
292C2×C4×C47C22×D414yes—
293C2×C4×C47C22×D414yes—
294C2×C4×C47C2×#4114yes—
295C2×Dic47—28no—
296C2×Dic47—28no—
297C2×Dic47—28no—
298C2×Dic47—28no—
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—22no—
319C2×Dic47—44no—
320C2×Dic47—44no—
321C2×Dic47—44no—
322C2×Dic47—44no—
323C2×Dic47C22×Q814yes—
324C2×Dic47C22×Q814yes—
325C2×Dic47C2×#4114yes—
326C2×Dic47C2×#4114yes—
327Dic94—232no—
328C2×#2465—471nomaximal, Sylow
329C22×C47—24no—
330C22×C47—24no—
331C22×C47—24no—
332C22×C47—42no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—416no—
337C22×C47#52514yes—
338C22×C47#53314yes—
339C22×C47#54214yes—
340C22×C47#54614yes—
341C22×C47D4×Q814yes—
342C22×C47#55414yes—
343C22×C47#55614yes—
344C22×C47C23×D411yescharacteristic
345C22×C47C23×Q811yescharacteristic
346C22×C47C22×#4111yescharacteristic
347C22×C47C22×#4111yescharacteristic
348C22×C47C22×#4111yescharacteristic
349C22×C47C2×H(5,𝔽2)11yescharacteristic
350C22×C47C2×2−1+411yescharacteristic
351C4×C47—24no—
352C4×C47—24no—
353C4×C47—24no—
354C4×C47—24no—
355C4×C47—42no—
356C4×C47—42no—
357Dic47—24no—
358Dic47—24no—
359Dic47—24no—
360Dic47—24no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365C22×C22⋊Q8D4711yescharacteristic
366C22×C4×Q8—471no—
367#2465—4716no—
368C2×#396—471no—
369C2×#395—471no—
370C2×#395—471no—
371C2×#393—471no—
372C2×#391—471no—
373C2×#389—471no—
374C2×#388—471no—
375C2×#388—471no—
376C2×#387—471no—
377C2×#387—471no—
378C2×#387—471no—
379C2×#385—471no—
380C2×C4×C22⋊C4—471no—
381C2×C47—44no—
382C2×C47#246518yescomplemented
383C2×C47C2×#52511yescharacteristic
384C2×C47C2×#53311yescharacteristic
385C2×C47C2×#54211yescharacteristic
386C2×C47C2×#54611yescharacteristic
387C2×C47C2×D4×Q811yescharacteristic
388C2×C47C2×#55411yescharacteristic
389C2×C47C2×#55611yescharacteristic
390C23×Q8—471no—
391C23×Q8C2×D4711yescharacteristic
392C24×C4C2×D4711yescharacteristic
393C2×C22⋊Q8—28no—
394C2×C22⋊Q8C2×D4718yes—
395C2×C4×Q8—478no—
396C2×C4×Q8—948no—
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#396—478no—
418#395—478no—
419#395—478no—
420#393—478no—
421#391—478no—
422#389—478no—
423#388—478no—
424#388—478no—
425#387—478no—
426#387—478no—
427#387—478no—
428#385—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—
440C2×#95—471no—
441C2×#95—471no—
442C47C2×#246511yescharacteristic, complemented, Sylow
443C25C22×D4711yescharacteristic
444C22×Q8—24no—
445C22×Q8—24no—
446C22×Q8—42no—
447C22×Q8—474no—
448C22×Q8—944no—
449C22×Q8—944no—
450C22×Q8—944no—
451C22×Q8C22×D4714yes—
452C23×C4—24no—
453C23×C4—24no—
454C23×C4—42no—
455C23×C4—471no—
456C23×C4—471no—
457C23×C4—471no—
458C23×C4—471no—
459C23×C4—471no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—471no—
463C23×C4C22×D4711yescharacteristic
464C23×C4C22×D4711yescharacteristic
465C23×C4C22×D4714yes—
466C23×C4C22×D4711yescharacteristic
467C23×C4C22×D4711yescharacteristic
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470C22⋊Q8—232no—
471C4×Q8—9432no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—474no—
475C2×C4⋊C4—474no—
476C2×C4⋊C4—474no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—474no—
479C2×C4⋊C4—474no—
480C2×C4⋊C4—474no—
481C2×C4⋊C4—944no—
482C2×C4⋊C4—944no—
483C2×C4⋊C4—944no—
484C2×C4⋊C4—944no—
485C2×C4⋊C4—944no—
486C2×C4⋊C4—1882no—
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—944no—
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—
522#95—474no—
523#95—474no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24Q8×D4714yes—
531C24C23×D4712yes—
532C24C23×D4711yescharacteristic
533C2×Q8—28no—
534C2×Q8—28no—
535C2×Q8—44no—
536C2×Q8—416no—
537C2×Q8—948no—
538C2×Q8—948no—
539C2×Q8—9432no—
540C2×Q8—948no—
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—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—44no—
558C22×C4—416no—
559C22×C4—474no—
560C22×C4—474no—
561C22×C4—474no—
562C22×C4—474no—
563C22×C4—472no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—472no—
567C22×C4—472no—
568C22×C4—472no—
569C22×C4—472no—
570C22×C4—472no—
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—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4#1062535214yes—
592C22×C4C2×C22⋊D4714yes—
593C22×C4C2×C22⋊D4714yes—
594C22×C4C2×C22⋊D4714yes—
595C22×C4C23×D4712yes—
596C22×C4C23×D4712yes—
597C22×C4C23×D4712yes—
598C22×C4C23×D4712yes—
599C22×C4C23×D4712yes—
600C22×C4C23×D4712yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—948no—
604C4⋊C4—948no—
605C4⋊C4—948no—
606C4⋊C4—948no—
607C4⋊C4—948no—
608C4⋊C4—1884no—
609C4⋊C4—1884no—
610C4⋊C4C2×C22⋊D47116yes—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—4716no—
614C22⋊C4—948no—
615C22⋊C4—948no—
616C22⋊C4—1884no—
617C42—948no—
618C42—948no—
619C42—948no—
620C42—1884no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23C22×C22⋊D4712yes—
635C23C2×Q8×D4714yes—
636C23C2×Q8×D4712yes—
637C23#41×D4712yes—
638C23#41×D4712yes—
639C23C2×#1062535212yes—
640C23#1309406912yes—
641C23#1309407212yes—
642C23C24×D4711yescharacteristic
643Q8—416no—
644Q8—9432no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
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—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—416no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—474no—
667C2×C4—474no—
668C2×C4—474no—
669C2×C4—474no—
670C2×C4—948no—
671C2×C4—948no—
672C2×C4—948no—
673C2×C4—948no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—942no—
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—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—1884no—
695C2×C4—1884no—
696C2×C4—1884no—
697C2×C4—1884no—
698C2×C4C22×C22⋊D4714yes—
699C2×C4C22×C22⋊D4714yes—
700C2×C4C22×C22⋊D4714yes—
701C2×C4C2×#1062535214yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—416no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22#1568963014yes—
711C22#1568967514yes—
712C22#1568974314yes—
713C22#1568976714yes—
714C22Q8×C22⋊D4714yes—
715C22#1568982714yes—
716C22#1568984414yes—
717C22C23×C22⋊D4711yescharacteristic
718C22C22×Q8×D4711yescharacteristic
719C22C2×#41×D4711yescharacteristic
720C22C2×#41×D4711yescharacteristic
721C22C22×#1062535211yescharacteristic
722C22C2×#1309406911yescharacteristic
723C22C2×#1309407211yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—944no—
731C4—944no—
732C4—944no—
733C4—944no—
734C4—1882no—
735C4—1882no—
736C4—1882no—
737C4—1882no—
738C2—44no—
739C2#2024740518yesdirect product factor
740C2C2×#1568963011yescharacteristic
741C2C2×#1568967511yescharacteristic
742C2C2×#1568974311yescharacteristic
743C2C2×#1568976711yescharacteristic
744C2C2×Q8×C22⋊D4711yescharacteristic
745C2C2×#1568982711yescharacteristic
746C2C2×#1568984411yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×C22⋊Q8×C47C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC22×C22⋊Q8D47
hypocenterC47C2×#2465
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×#13093989C2semidirect
2. #20247405C2direct (N × H)
4. C2×#15689043C2semidirect
5. C2×#15689042C2semidirect
7. C2×#15689030C2semidirect
8. C2×#15689018C2semidirect
11. C2×#15689009C2semidirect
12. C2×#15689004C2semidirect
13. C2×#15689004C2semidirect
19. C2×#13093989C22semidirect
36. #15689043C22semidirect
37. #15689042C22semidirect
39. #15689030C22semidirect
40. #15689018C22semidirect
43. #15689009C22semidirect
44. #15689004C22semidirect
45. #15689004C22semidirect
99. C2×C22⋊Dic47Q8semidirect
235. C22⋊Dic47C2×Q8semidirect
382. C2×C47#2465semidirect
442. C47C2×#2465semidirect
739. C2#20247405direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939892
#202474052
C2×#156890462
C2×#156890432
C2×#156890422
C2×#156890352
C2×#156890302
C2×#156890182
C2×#156890112
C2×#156890092
C2×#156890042
C2×#156889962
C2×C4×C22⋊Dic472
C22×C22⋊Q8×C472
C2×#246547