Finite Group Databasebeta

← C2×#20247523 #26383868

Subgroups — C2×#20247523 #26383868

Order 12032.

2942 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×#13094014C211yesmaximal, characteristic, complemented
2#20247523C2116yesmaximal, direct product factor
3C2×#15689061C211yesmaximal, characteristic, complemented
4C2×#15689056C211yesmaximal, characteristic, complemented
5C2×#15689054C211yesmaximal, characteristic, complemented
6C2×#15689053C211yesmaximal, characteristic, complemented
7C2×#15689018C211yesmaximal, characteristic, complemented
8C2×#15689009C211yesmaximal, characteristic, complemented
9C2×#15689004C211yesmaximal, characteristic, complemented
10C2×#15688996C211yesmaximal, characteristic
11C2×#15688996C211yesmaximal, characteristic
12C2×#15688996C211yesmaximal, characteristic
13C2×#15688996C211yesmaximal, characteristic
14C2×#15688983C211yesmaximal, characteristic
15C2×C4×C22⋊Dic47C211yesmaximal, characteristic
16C23×C4⋊C4×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
35#15689061C2218yescomplemented
36#15689056C2218yescomplemented
37#15689054C2218yescomplemented
38#15689053C2218yescomplemented
39#15689018C2218yescomplemented
40#15689009C2218yescomplemented
41#15689004C2218yescomplemented
42#15688996C2218yes—
43#15688996C2218yes—
44#15688996C2218yes—
45#15688996C2218yes—
46#15688983C2218yes—
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
60C24×C4×C47C2211yescharacteristic
61C24×C4×C47C2211yescharacteristic
62C24×C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47—28no—
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic
66C22×C4⋊C4×C47C2211yescharacteristic
67C22×C4⋊C4×C47C2218yes—
68C22×C4⋊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—42no—
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—42no—
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—24no—
101C2×C22⋊Dic47Q818yes—
102C2×C22⋊Dic47C2314yes—
103C2×C22⋊Dic47C2314yes—
104C2×C22⋊Dic47C2314yes—
105C2×C22⋊Dic47C2314yes—
106C2×C4×Dic47—24no—
107C2×C4×Dic47—42no—
108C2×C4×Dic47C2314yes—
109C2×C4×Dic47C2314yes—
110C47⋊#95C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C25×C47C2311yescharacteristic
123C23×C4×C47—24no—
124C23×C4×C47—24no—
125C23×C4×C47—24no—
126C23×C4×C47—24no—
127C23×C4×C47—24no—
128C23×C4×C47—24no—
129C23×C4×C47—24no—
130C23×C4×C47—42no—
131C23×C4×C47—42no—
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2314yes—
135C23×C4×C47C2314yes—
136C23×C4×C47C2314yes—
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C2×C4⋊C4×C47—24no—
142C2×C4⋊C4×C47—24no—
143C2×C4⋊C4×C47—24no—
144C2×C4⋊C4×C47—232no—
145C2×C4⋊C4×C47D418yes—
146C2×C4⋊C4×C47C2314yes—
147C2×C4⋊C4×C47C2314yes—
148C2×C4⋊C4×C47C2314yes—
149C2×C4⋊C4×C47C2314yes—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47C2×Q814yes—
155C24×C47#4114yes—
156C24×C47#4114yes—
157C24×C47C2412yes—
158C24×C47C2411yescharacteristic
159C22×C4×C47—232no—
160C22×C4×C47—22no—
161C22×C4×C47—28no—
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—28no—
170C22×C4×C47—28no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—28no—
174C22×C4×C47—28no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—28no—
180C22×C4×C47—28no—
181C22×C4×C47—44no—
182C22×C4×C47—44no—
183C22×C4×C47—416no—
184C22×C4×C47—416no—
185C22×C4×C47C2×D414yes—
186C22×C4×C47C2×D414yes—
187C22×C4×C47C2×D414yes—
188C22×C4×C47#4114yes—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
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×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47C2×Q814yes—
218C22×Dic47C2×Q814yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C4⋊C4×C47—28no—
228C4⋊C4×C47—28no—
229C4⋊C4×C47—28no—
230C4⋊C4×C47C2×D4116yes—
231C22⋊Dic47—28no—
232C22⋊Dic47—28no—
233C22⋊Dic47—28no—
234C22⋊Dic47C2×Q8116yes—
235C4⋊Dic47—28no—
236C4⋊Dic47—44no—
237Dic47⋊C4—28no—
238Dic47⋊C4—28no—
239Dic47⋊C4—28no—
240Dic47⋊C4—28no—
241Dic47⋊C4—28no—
242Dic47⋊C4—28no—
243Dic47⋊C4—44no—
244Dic47⋊C4—44no—
245C4×Dic47—28no—
246C4×Dic47—44no—
247C23×C47—28no—
248C23×C47—28no—
249C23×C47—28no—
250C23×C47—28no—
251C23×C47—28no—
252C23×C47—28no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47#125116yescomplemented
258C23×C47C22×D412yes—
259C23×C47C22×Q814yes—
260C23×C47C22×Q812yes—
261C23×C47C2×#4114yes—
262C23×C47C2×#4112yes—
263C23×C47C2×#4114yes—
264C23×C47C2×#4112yes—
265C23×C47C2×#4112yes—
266C23×C47H(5,𝔽2)12yes—
267C23×C472−1+412yes—
268C23×C47C2511yescharacteristic
269C2×C4×C47—232no—
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—416no—
290C2×C4×C47—44no—
291C2×C4×C47—44no—
292C2×C4×C47C22×D414yes—
293C2×C4×C47C22×D414yes—
294C2×C4×C47C22×D414yes—
295C2×C4×C47C2×#4114yes—
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—22no—
319C2×Dic47—22no—
320C2×Dic47—44no—
321C2×Dic47—44no—
322C2×Dic47—44no—
323C2×Dic47—44no—
324C2×Dic47—44no—
325C2×Dic47—44no—
326C2×Dic47C22×Q814yes—
327C2×Dic47C22×Q814yes—
328C2×#2473—471nomaximal, Sylow
329C22×C47—24no—
330C22×C47—24no—
331C22×C47—24no—
332C22×C47—24no—
333C22×C47—24no—
334C22×C47—24no—
335C22×C47—232no—
336C22×C47#52514yes—
337C22×C47C2×#12514yes—
338C22×C47C2×#12518yescomplemented
339C22×C47#53914yes—
340C22×C47#54614yes—
341C22×C47D4×Q814yes—
342C22×C47#55214yes—
343C22×C47#55414yes—
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—42no—
360Dic47—42no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365C22×#125—471no—
366C23×C4⋊C4D4711yescharacteristic
367#2473—4716no—
368C2×#400—471no—
369C2×#398—471no—
370C2×#398—471no—
371C2×#398—471no—
372C2×#389—471no—
373C2×#387—471no—
374C2×#387—471no—
375C2×#385—471no—
376C2×#385—471no—
377C2×#385—471no—
378C2×#385—471no—
379C2×#380—471no—
380C2×C4×C22⋊C4—471no—
381C2×C47—28no—
382C2×C47#247318yescomplemented
383C2×C47C2×#52511yescharacteristic
384C2×C47C22×#12511yescharacteristic
385C2×C47C2×#53911yescharacteristic
386C2×C47C2×#54611yescharacteristic
387C2×C47C2×D4×Q811yescharacteristic
388C2×C47C2×#55211yescharacteristic
389C2×C47C2×#55411yescharacteristic
390C24×C4C2×D4711yescharacteristic
391C24×C4C2×D4711yescharacteristic
392C24×C4C2×D4711yescharacteristic
393C2×#125—478no—
394C2×#125—948no—
395C22×C4⋊C4—28no—
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⋊C4—471no—
405C22×C4⋊C4—471no—
406C22×C4⋊C4C2×D4711yescharacteristic
407C22×C4⋊C4C2×D4711yescharacteristic
408C22×C4⋊C4C2×D4718yes—
409C22×C4⋊C4C2×D4711yescharacteristic
410C22×C4⋊C4C2×D4711yescharacteristic
411C22×C22⋊C4—471no—
412C22×C22⋊C4—471no—
413C22×C22⋊C4—471no—
414C22×C22⋊C4—471no—
415C22×C42—471no—
416C22×C42—471no—
417#400—478no—
418#398—478no—
419#398—478no—
420#398—478no—
421#389—478no—
422#387—478no—
423#387—478no—
424#385—478no—
425#385—478no—
426#385—478no—
427#385—478no—
428#380—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×#247311yescharacteristic, complemented, Sylow
443C25C22×D4711yescharacteristic
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—24no—
449C23×C4—24no—
450C23×C4—24no—
451C23×C4—42no—
452C23×C4—42no—
453C23×C4—471no—
454C23×C4—471no—
455C23×C4—471no—
456C23×C4—471no—
457C23×C4—471no—
458C23×C4—471no—
459C23×C4—471no—
460C23×C4—471no—
461C23×C4C22×D4714yes—
462C23×C4C22×D4711yescharacteristic
463C23×C4C22×D4711yescharacteristic
464C23×C4C22×D4714yes—
465C23×C4C22×D4714yes—
466C23×C4C22×D4711yescharacteristic
467C23×C4C22×D4711yescharacteristic
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470#125—9432no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—232no—
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—474no—
482C2×C4⋊C4—474no—
483C2×C4⋊C4—474no—
484C2×C4⋊C4—474no—
485C2×C4⋊C4—944no—
486C2×C4⋊C4—944no—
487C2×C4⋊C4—944no—
488C2×C4⋊C4—944no—
489C2×C4⋊C4—944no—
490C2×C4⋊C4—944no—
491C2×C4⋊C4—944no—
492C2×C4⋊C4—1882no—
493C2×C4⋊C4—1882no—
494C2×C4⋊C4—1882no—
495C2×C4⋊C4C22⋊D4718yes—
496C2×C4⋊C4C22×D4714yes—
497C2×C4⋊C4C22×D4714yes—
498C2×C4⋊C4C22×D4714yes—
499C2×C4⋊C4C22×D4714yes—
500C2×C22⋊C4—478no—
501C2×C22⋊C4—474no—
502C2×C22⋊C4—474no—
503C2×C22⋊C4—474no—
504C2×C22⋊C4—474no—
505C2×C22⋊C4—944no—
506C2×C22⋊C4—944no—
507C2×C22⋊C4—944no—
508C2×C42—474no—
509C2×C42—474no—
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#1062535014yes—
529C24#1062535214yes—
530C24Q8×D4714yes—
531C24C23×D4712yes—
532C24C23×D4711yescharacteristic
533C22×C4—232no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—28no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—416no—
558C22×C4—416no—
559C22×C4—474no—
560C22×C4—474no—
561C22×C4—472no—
562C22×C4—472no—
563C22×C4—472no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—472no—
567C22×C4—472no—
568C22×C4—472no—
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—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4#1062535014yes—
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—28no—
604C4⋊C4—948no—
605C4⋊C4—948no—
606C4⋊C4—948no—
607C4⋊C4—948no—
608C4⋊C4—948no—
609C4⋊C4—948no—
610C4⋊C4—948no—
611C4⋊C4—1884no—
612C4⋊C4—1884no—
613C4⋊C4—1884no—
614C4⋊C4C2×C22⋊D47116yes—
615C22⋊C4—4716no—
616C22⋊C4—948no—
617C22⋊C4—948no—
618C22⋊C4—948no—
619C42—948no—
620C42—1884no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—28no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—28no—
631C23#13094014116yescomplemented
632C23C22×C22⋊D4712yes—
633C23C2×Q8×D4714yes—
634C23C2×Q8×D4712yes—
635C23C2×#1062535214yes—
636C23C2×#1062535212yes—
637C23C2×#1062535014yes—
638C23C2×#1062535012yes—
639C23C2×#1062535012yes—
640C23#1309406912yes—
641C23#1309407212yes—
642C23C24×D4711yescharacteristic
643C2×C4—232no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
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—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—416no—
663C2×C4—416no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—474no—
667C2×C4—474no—
668C2×C4—948no—
669C2×C4—948no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
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—1884no—
693C2×C4—1884no—
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×#1062535014yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—232no—
709C22#1568963414yes—
710C22C2×#1309401414yes—
711C22C2×#1309401418yescomplemented
712C22#1568972014yes—
713C22#1568976714yes—
714C22Q8×C22⋊D4714yes—
715C22#1568980814yes—
716C22#1568982814yes—
717C22C23×C22⋊D4711yescharacteristic
718C22C22×Q8×D4711yescharacteristic
719C22C22×#1062535211yescharacteristic
720C22C22×#1062535011yescharacteristic
721C22C22×#1062535011yescharacteristic
722C22C2×#1309406911yescharacteristic
723C22C2×#1309407211yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—944no—
731C4—944no—
732C4—1882no—
733C4—1882no—
734C4—1882no—
735C4—1882no—
736C4—1882no—
737C4—1882no—
738C2—28no—
739C2#2024752318yesdirect product factor
740C2C2×#1568963411yescharacteristic
741C2C22×#1309401411yescharacteristic
742C2C2×#1568972011yescharacteristic
743C2C2×#1568976711yescharacteristic
744C2C2×Q8×C22⋊D4711yescharacteristic
745C2C2×#1568980811yescharacteristic
746C2C2×#1568982811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC23×C4⋊C4×C47C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC23×C4⋊C4D47
hypocenterC47C2×#2473
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#13094014C2semidirect
2. #20247523C2direct (N × H)
3. C2×#15689061C2semidirect
4. C2×#15689056C2semidirect
5. C2×#15689054C2semidirect
6. C2×#15689053C2semidirect
7. C2×#15689018C2semidirect
8. C2×#15689009C2semidirect
9. C2×#15689004C2semidirect
18. C2×#13094014C22semidirect
35. #15689061C22semidirect
36. #15689056C22semidirect
37. #15689054C22semidirect
38. #15689053C22semidirect
39. #15689018C22semidirect
40. #15689009C22semidirect
41. #15689004C22semidirect
257. C23×C47#125semidirect
338. C22×C47C2×#125semidirect
382. C2×C47#2473semidirect
442. C47C2×#2473semidirect
631. C23#13094014semidirect
711. C22C2×#13094014semidirect
739. C2#20247523direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940142
#202475232
C2×#156890612
C2×#156890562
C2×#156890542
C2×#156890532
C2×#156890182
C2×#156890092
C2×#156890042
C2×#156889962
C2×#156889832
C2×C4×C22⋊Dic472
C23×C4⋊C4×C472
C2×#247347