Finite Group Databasebeta

← (C22⋊D47)⋊#95 #26137745

Subgroups — (C22⋊D47)⋊#95 #26137745

Order 12032.

3562 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C22×(C22⋊D47)⋊C4C212yesmaximal
3C22×C47⋊#95C211yesmaximal, characteristic, complemented
4C2×#95×D47C211yesmaximal, characteristic, complemented
5Dic47⋊#95C212yesmaximal, complemented
6Dic47⋊#95C211yesmaximal, characteristic, complemented
7#20241610C212yesmaximal, complemented
8(C2×D47)⋊#95C212yesmaximal, complemented
9(C2×D47)⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic47C211yesmaximal, characteristic, complemented
11C47×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C24×Dic47C2212yes—
14C23×C4×D47C2212yes—
15C23×C4×D47C2211yescharacteristic
16C2×C4×C22⋊D47—28no—
17C2×C4×C22⋊D47C418yescomplemented
18C2×(C22⋊D47)⋊C4—28no—
19C2×(C22⋊D47)⋊C4—28no—
20C2×(C22⋊D47)⋊C4C4116yescomplemented
21C22×Dic47⋊C4C2212yes—
22C22×Dic47⋊C4C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×(C2×D47)⋊C4C2212yes—
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×C4×Dic47C2212yes—
27C22×C4×Dic47C2211yescharacteristic
28C2×C47⋊#95—24no—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2211yescharacteristic
36#95×D47—24no—
37C24×C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2212yes—
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2211yescharacteristic
41C2×#95×C47C2212yes—
42C24×D47C2311yescharacteristic
43C22×C22⋊D47C2×C418yes—
44C22×C22⋊D47C2×C414yes—
45C22×C22⋊D47D414yes—
46C22×C22⋊D47D418yes—
47C22×C22⋊D47Q814yes—
48C23×Dic47—24no—
49C23×Dic47—24no—
50C23×Dic47—24no—
51C23×Dic47—24no—
52C23×Dic47—42no—
53C23×Dic47—42no—
54C23×Dic47C2×C418yescomplemented
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2312yes—
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2312yes—
59C23×Dic47C2311yescharacteristic
60C22×C4×D47—24no—
61C22×C4×D47—24no—
62C22×C4×D47—24no—
63C22×C4×D47—22no—
64C22×C4×D47—22no—
65C22×C4×D47—24no—
66C22×C4×D47—24no—
67C22×C4×D47—42no—
68C22×C4×D47—42no—
69C22×C4×D47—42no—
70C22×C4×D47C2×C418yescomplemented
71C22×C4×D47C2×C414yescomplemented
72C4×C22⋊D47—232no—
73(C22⋊D47)⋊C4—264no—
74C2×Dic47⋊C4—24no—
75C2×Dic47⋊C4—24no—
76C2×Dic47⋊C4—24no—
77C2×Dic47⋊C4C2×C418yescomplemented
78C2×Dic47⋊C4C2×C414yescomplemented
79C2×C22⋊Dic47—24no—
80C2×C22⋊Dic47C2×C414yescomplemented
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4—24no—
84C2×(C2×D47)⋊C4C2×C418yescomplemented
85C2×(C2×D47)⋊C4C2×C414yescomplemented
86C2×C4×Dic47—24no—
87C2×C4×Dic47—24no—
88C2×C4×Dic47—24no—
89C2×C4×Dic47C2×C418yescomplemented
90C2×C4×Dic47C2×C414yescomplemented
91C47⋊#95—22no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—24no—
95C47⋊#95—42no—
96C47⋊#95—42no—
97C47⋊#95D414yescomplemented
98C25×C47C2311yescharacteristic
99C23×C4×C47—24no—
100C23×C4×C47—22no—
101C23×C4×C47—22no—
102C23×C4×C47—42no—
103C23×C4×C47C2×C414yescomplemented
104C23×C4×C47C2312yes—
105C23×C4×C47C2312yes—
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108C2×C22⋊C4×C47—24no—
109C2×C22⋊C4×C47—24no—
110C2×C22⋊C4×C47C2×C418yescomplemented
111#95×C47—22no—
112#95×C47—22no—
113#95×C47—42no—
114C24×C47—21no—
115C24×C47—21no—
116C24×C47—22no—
117C24×C47—22no—
118C24×C47—21no—
119C24×C47—21no—
120C24×C47C22×C414yes—
121C24×C47C22×C412yes—
122C24×C47C2×D412yes—
123C24×C47C2×D414yes—
124C24×C47C2×Q812yes—
125C24×C47C2411yescharacteristic
126C23×D47—21no—
127C23×D47—22no—
128C23×D47—21no—
129C23×D47—22no—
130C23×D47—21no—
131C23×D47—21no—
132C23×D47C22×C414yes—
133C23×D47C22×C412yes—
134C23×D47C2×D412yes—
135C23×D47C2×D414yes—
136C23×D47C2×Q812yes—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—28no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—21no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—28no—
157C22×C4×C47—44no—
158C22×C4×C47—48no—
159C22×C4×C47—48no—
160C22×C4×C47C22×C414yes—
161C22×C4×C47C22×C414yes—
162C22×C4×C47C22×C412yes—
163C22×C4×C47C22×C412yes—
164C22×C4×C47C2×D412yes—
165C22×C4×C47#4112yes—
166C2×C22⋊D47C42116yes—
167C2×C22⋊D47C22⋊C4132yes—
168C2×C22⋊D47C22⋊C4116yes—
169C2×C22⋊D47C4⋊C4132yes—
170C2×C22⋊D47C4⋊C4116yes—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—216no—
176C22×Dic47—21no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—21no—
184C22×Dic47—22no—
185C22×Dic47—21no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—21no—
190C22×Dic47—216no—
191C22×Dic47—48no—
192C22×Dic47—48no—
193C22×Dic47—48no—
194C22×Dic47—48no—
195C22×Dic47—48no—
196C22×Dic47C22×C412yes—
197C22×Dic47C22×C414yes—
198C22×Dic47C22×C412yes—
199C22×Dic47C22×C414yes—
200C22×Dic47C22×C414yes—
201C22×Dic47C22×C412yes—
202C22×Dic47C2×D414yes—
203C22×Dic47C2×D412yes—
204C22×Dic47C2×D414yes—
205C22×Dic47C2×Q812yes—
206C22×Dic47#4114yes—
207C2×C4×D47—216no—
208C2×C4×D47—28no—
209C2×C4×D47—28no—
210C2×C4×D47—216no—
211C2×C4×D47—48no—
212C2×C4×D47—44no—
213C2×C4×D47—48no—
214C2×C4×D47—48no—
215C2×C4×D47—48no—
216C2×C4×D47—48no—
217C2×C4×D47—48no—
218C2×C4×D47—48no—
219C22⋊C4×C47—216no—
220C22⋊Dic47—28no—
221(C2×D47)⋊C4—216no—
222(C2×D47)⋊C4—28no—
223Dic47⋊C4—216no—
224Dic47⋊C4—28no—
225C4×Dic47—216no—
226C4×Dic47—28no—
227C23×C47—24no—
228C23×C47—22no—
229C23×C47—24no—
230C23×C47—22no—
231C23×C47—24no—
232C23×C47—22no—
233C23×C47—24no—
234C23×C47—22no—
235C23×C47—22no—
236C23×C47—24no—
237C23×C47—24no—
238C23×C47—24no—
239C23×C47—24no—
240C23×C47—24no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—24no—
244C23×C47—22no—
245C23×C47C2×C4214yes—
246C23×C47C2×C22⋊C414yes—
247C23×C47C2×C22⋊C418yes—
248C23×C47C2×C4⋊C418yes—
249C23×C47C2×C4⋊C414yes—
250C23×C47C23×C412yes—
251C23×C47C23×C411yescharacteristic
252C23×C47C22×D412yes—
253C23×C47C22×D411yescharacteristic
254C23×C47C22×D411yescharacteristic
255C23×C47C22×Q811yescharacteristic
256C23×C47C2×#4112yes—
257C23×C47C2×#4111yescharacteristic
258C23×C47H(5,𝔽2)12yes—
259C23×C47H(5,𝔽2)11yescharacteristic
260C23×C472−1+411yescharacteristic
261C22×D47—24no—
262C22×D47—22no—
263C22×D47—24no—
264C22×D47—22no—
265C22×D47—24no—
266C22×D47—22no—
267C22×D47—24no—
268C22×D47—22no—
269C22×D47—24no—
270C22×D47—22no—
271C22×D47—24no—
272C22×D47—24no—
273C22×D47—24no—
274C22×D47—24no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—24no—
278C22×D47—22no—
279C22×D47C2×C4214yes—
280C22×D47C2×C22⋊C418yes—
281C22×D47C2×C22⋊C414yes—
282C22×D47C2×C4⋊C414yes—
283C22×D47C2×C4⋊C418yes—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—24no—
287C2×C4×C47—24no—
288C2×C4×C47—24no—
289C2×C4×C47—22no—
290C2×C4×C47—24no—
291C2×C4×C47—24no—
292C2×C4×C47—22no—
293C2×C4×C47—24no—
294C2×C4×C47—24no—
295C2×C4×C47—22no—
296C2×C4×C47—24no—
297C2×C4×C47—416no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47C4×D414yescomplemented
309C22⋊D47#95164yescomplemented
310C2×Dic47—24no—
311C2×Dic47—24no—
312C2×Dic47—24no—
313C2×Dic47—24no—
314C2×Dic47—24no—
315C2×Dic47—24no—
316C2×Dic47—22no—
317C2×Dic47—24no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—24no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—24no—
324C2×Dic47—22no—
325C2×Dic47—432no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47C2×C4214yes—
335C2×Dic47C2×C22⋊C418yes—
336C2×Dic47C2×C22⋊C414yes—
337C2×Dic47C2×C4⋊C414yes—
338C2×Dic47C2×C4⋊C418yes—
339C2×Dic47C4×D418yescomplemented
340C4×D47—432no—
341C4×D47—416no—
342D4×#95—471nomaximal, Sylow
343C22×C47—28no—
344C22×C47—24no—
345C22×C47—24no—
346C22×C47—28no—
347C22×C47—24no—
348C22×C47—28no—
349C22×C47—24no—
350C22×C47—28no—
351C22×C47—24no—
352C22×C47—24no—
353C22×C47C2×#9518yescomplemented
354C22×C47C22×C4211yescharacteristic
355C22×C47C22×C22⋊C411yescharacteristic
356C22×C47C22×C22⋊C412yes—
357C22×C47C22×C4⋊C411yescharacteristic
358C22×C47C22×C4⋊C412yes—
359C22×C47C2×C4×D412yes—
360C22×C47C2×C4×D411yescharacteristic
361C22×C47C4×#4112yes—
362C22×C47C4×#4111yescharacteristic
363C22×C47#51812yes—
364C22×C47#51811yescharacteristic
365C22×C47#52012yes—
366C22×C47#52011yescharacteristic
367C22×C47D4212yes—
368C22×C47D4211yescharacteristic
369C22×C47#54612yes—
370C22×C47#54612yes—
371C22×C47#54612yes—
372C22×C47#54712yes—
373C22×C47#54711yescharacteristic
374C22×C47D4×Q811yescharacteristic
375C22×C47#55412yes—
376C22×C47#55411yescharacteristic
377C2×D47—24no—
378C2×D47—28no—
379C2×D47—24no—
380C2×D47—28no—
381C2×D47—24no—
382C2×D47—28no—
383C2×D47—24no—
384C2×D47—28no—
385C2×D47—24no—
386C2×D47—24no—
387C2×D47C2×#9518yescomplemented
388C4×C47—24no—
389C4×C47—44no—
390C4×C47—42no—
391C4×C47—44no—
392Dic47—28no—
393Dic47—42no—
394Dic47—44no—
395Dic47—42no—
396Dic47C2×#9518yescomplemented
397C22×C4×D4—471no—
398C22×C4×D4—472no—
399C22×#95—471no—
400C22×#95—471no—
401C4⋊#95—472no—
402C4⋊#95—471no—
403C22⋊#95—472no—
404C22⋊#95—471no—
405C22⋊#95—472no—
406C22⋊#95D4711yescharacteristic, complemented
407C4×#95—471no—
408C2×C47—28no—
409C2×C47C22×#9511yescharacteristic
410C2×C47C42×D411yescharacteristic
411C2×C47#227511yescharacteristic
412C2×C47D4×C22⋊C411yescharacteristic
413C2×C47D4×C22⋊C412yes—
414C2×C47#233911yescharacteristic
415C2×C47#233912yes—
416C2×C47D4×C4⋊C411yescharacteristic
417C2×C47D4×C4⋊C412yes—
418C2×C47#234911yescharacteristic
419C2×C47#234912yes—
420D47—28no—
421C23×D4—471no—
422C24×C4—472no—
423C24×C4—472no—
424C24×C4—471no—
425C24×C4C2×D4711yescharacteristic
426C2×C4×D4—478no—
427C2×C4×D4—4716no—
428C2×C4×D4—948no—
429C2×C4×D4—948no—
430C2×C4×D4—948no—
431C22×C4⋊C4—471no—
432C22×C4⋊C4—472no—
433C22×C22⋊C4—471no—
434C22×C22⋊C4—471no—
435C22×C22⋊C4—472no—
436C22×C22⋊C4C2×D4712yes—
437C22×C42—472no—
438C22×C42—471no—
439C2×#95—471no—
440C2×#95—472no—
441C2×#95—472no—
442C2×#95—472no—
443C2×#95—471no—
444C2×#95—472no—
445C2×#95—472no—
446C2×#95—944no—
447C2×#95—944no—
448C2×#95C2×D4711yescharacteristic
449C2×#95C2×D4711yescharacteristic
450C2×#95C2×D4712yes—
451C47D4×#9511yescharacteristic, complemented, Sylow
452C25—471no—
453C25C22×D4711yescharacteristic
454C22×D4—474no—
455C22×D4—478no—
456C22×D4—474no—
457C22×D4—478no—
458C22×D4—474no—
459C23×C4—24no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—42no—
463C23×C4—471no—
464C23×C4—472no—
465C23×C4—471no—
466C23×C4—472no—
467C23×C4—471no—
468C23×C4—478no—
469C23×C4—478no—
470C23×C4—474no—
471C23×C4—944no—
472C23×C4—944no—
473C23×C4—944no—
474C23×C4—944no—
475C23×C4—944no—
476C23×C4—944no—
477C23×C4—944no—
478C23×C4—944no—
479C23×C4—944no—
480C23×C4—942no—
481C23×C4—942no—
482C23×C4—1882no—
483C23×C4—1882no—
484C23×C4—1882no—
485C23×C4—1882no—
486C23×C4—1882no—
487C23×C4C4×D4714yescomplemented
488C23×C4C22×D4712yes—
489C23×C4C22×D4711yescharacteristic
490C23×C4C22×D4712yes—
491C23×C4C22×D4711yescharacteristic
492C4×D4—9464no—
493C4×D4—9432no—
494C2×C4⋊C4—474no—
495C2×C4⋊C4—478no—
496C2×C4⋊C4—944no—
497C2×C4⋊C4—944no—
498C2×C4⋊C4—944no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—474no—
502C2×C22⋊C4—474no—
503C2×C22⋊C4—478no—
504C2×C22⋊C4—944no—
505C2×C22⋊C4—944no—
506C2×C22⋊C4—944no—
507C2×C22⋊C4—944no—
508C2×C22⋊C4C4×D4718yescomplemented
509C2×C42—478no—
510C2×C42—474no—
511C2×C42—944no—
512C2×C42—944no—
513C2×C42—944no—
514#95—22no—
515#95—22no—
516#95—42no—
517#95—474no—
518#95—944no—
519#95—944no—
520#95—944no—
521#95—942no—
522#95—1882no—
523#95—1882no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—22no—
528C24—21no—
529C24—21no—
530C24—474no—
531C24—472no—
532C24—474no—
533C24—472no—
534C24—472no—
535C24—941no—
536C24—942no—
537C24—941no—
538C24—942no—
539C24—941no—
540C24—941no—
541C24C2×C4×D4712yes—
542C24C2×C4×D4714yes—
543C24D4×D4712yes—
544C24D4×D4714yes—
545C24Q8×D4712yes—
546C24C23×D4711yescharacteristic
547C2×D4—4716no—
548C2×D4—4732no—
549C2×D4—4716no—
550C2×D4—4716no—
551C2×D4—4732no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—28no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—28no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—474no—
576C22×C4—472no—
577C22×C4—474no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—474no—
581C22×C4—474no—
582C22×C4—474no—
583C22×C4—472no—
584C22×C4—474no—
585C22×C4—472no—
586C22×C4—9416no—
587C22×C4—948no—
588C22×C4—9416no—
589C22×C4—9416no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—942no—
594C22×C4—9416no—
595C22×C4—942no—
596C22×C4—941no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—941no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—941no—
607C22×C4—942no—
608C22×C4—941no—
609C22×C4—948no—
610C22×C4—1884no—
611C22×C4—1888no—
612C22×C4—1888no—
613C22×C4—1888no—
614C22×C4—1888no—
615C22×C4—1888no—
616C22×C4—1888no—
617C22×C4—1888no—
618C22×C4—1888no—
619C22×C4—1888no—
620C22×C4—1888no—
621C22×C4—1888no—
622C22×C4—1888no—
623C22×C4C2×C4×D4714yes—
624C22×C4C2×C4×D4712yes—
625C22×C4C2×C4×D4714yes—
626C22×C4C2×C4×D4712yes—
627C22×C4D4×D4712yes—
628C22×C4#1062535212yes—
629C4⋊C4—9416no—
630C4⋊C4—948no—
631C22⋊C4—216no—
632C22⋊C4—9416no—
633C22⋊C4—948no—
634C22⋊C4—948no—
635C42—948no—
636C42—9416no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—474no—
656C23—474no—
657C23—478no—
658C23—474no—
659C23—478no—
660C23—944no—
661C23—942no—
662C23—944no—
663C23—944no—
664C23—944no—
665C23—944no—
666C23—942no—
667C23—942no—
668C23—944no—
669C23—942no—
670C23—944no—
671C23—942no—
672C23—944no—
673C23—942no—
674C23—944no—
675C23—942no—
676C23—944no—
677C23—942no—
678C23C42×D4714yes—
679C23C22⋊C4×D4718yes—
680C23C22⋊C4×D4714yes—
681C23C4⋊C4×D4714yes—
682C23C4⋊C4×D4718yes—
683C23C22×C4×D4712yes—
684C23C22×C4×D4711yescharacteristic
685C23C2×D4×D4711yescharacteristic
686C23C2×D4×D4712yes—
687C23C2×D4×D4711yescharacteristic
688C23C2×Q8×D4711yescharacteristic
689C23#41×D4712yes—
690C23C2×#1062535211yescharacteristic
691C23#1309406912yes—
692C23#1309407011yescharacteristic
693C23#1309407111yescharacteristic
694D4—4764no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—416no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—474no—
720C2×C4—474no—
721C2×C4—478no—
722C2×C4—474no—
723C2×C4—478no—
724C2×C4—478no—
725C2×C4—944no—
726C2×C4—944no—
727C2×C4—944no—
728C2×C4—944no—
729C2×C4—944no—
730C2×C4—944no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—944no—
734C2×C4—944no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—944no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—18816no—
741C2×C4—18832no—
742C2×C4—18832no—
743C2×C4—1882no—
744C2×C4—1882no—
745C2×C4—1882no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4—1882no—
750C2×C4—1882no—
751C2×C4(C22⋊D47)⋊C414yescomplemented
752C22—24no—
753C22—28no—
754C22—24no—
755C22—28no—
756C22—24no—
757C22—28no—
758C22—24no—
759C22—28no—
760C22—24no—
761C22—24no—
762C22—478no—
763C22—944no—
764C22—948no—
765C22—944no—
766C22—948no—
767C22—944no—
768C22—948no—
769C22—944no—
770C22—948no—
771C22—944no—
772C22—944no—
773C22#95×D4718yescomplemented
774C22C2×C42×D4711yescharacteristic
775C22C2×C22⋊C4×D4711yescharacteristic
776C22C2×C22⋊C4×D4712yes—
777C22C2×C4⋊C4×D4711yescharacteristic
778C22C2×C4⋊C4×D4712yes—
779C22C4×D4×D4712yes—
780C22C2×(C22⋊D47)⋊C411yescharacteristic
781C22C4×#1062535212yes—
782C22#1568959111yescharacteristic
783C22#1568959512yes—
784C22#1568959611yescharacteristic
785C22#1568960212yes—
786C22#1568960311yescharacteristic
787C22#1568975512yes—
788C22#1568975711yescharacteristic
789C22#1568976012yes—
790C22#1568976212yes—
791C22#1568976512yes—
792C22#1568977112yes—
793C22#1568977311yescharacteristic
794C22#1568978611yescharacteristic
795C22#1568982712yes—
796C22#1568983111yescharacteristic
797C4—24no—
798C4—42no—
799C4—44no—
800C4—44no—
801C4—478no—
802C4—948no—
803C4—1882no—
804C4—1884no—
805C4—1882no—
806C2—28no—
807C2—948no—
808C2C2×#95×D4711yescharacteristic
809C2C4×(C22⋊D47)⋊C411yescharacteristic
810C2#2024574711yescharacteristic
811C2#2024620411yescharacteristic
812C2#2024620612yes—
813C2#2024621211yescharacteristic
814C2#2024621412yes—
815C2#2024628411yescharacteristic
816C2#2024628612yes—
817C2#2024629211yescharacteristic
818C2#2024629412yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC22⋊#95D47
hypocenterC47D4×#95
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C22×C47⋊#95C2semidirect
4. C2×#95×D47C2semidirect
5. Dic47⋊#95C2semidirect
6. Dic47⋊#95C2semidirect
7. #20241610C2semidirect
8. (C2×D47)⋊#95C2semidirect
9. (C2×D47)⋊#95C2semidirect
10. #95×Dic47C2semidirect
11. C47×C22⋊#95C2semidirect
17. C2×C4×C22⋊D47C4semidirect
20. C2×(C22⋊D47)⋊C4C4semidirect
54. C23×Dic47C2×C4semidirect
70. C22×C4×D47C2×C4semidirect
71. C22×C4×D47C2×C4semidirect
77. C2×Dic47⋊C4C2×C4semidirect
78. C2×Dic47⋊C4C2×C4semidirect
80. C2×C22⋊Dic47C2×C4semidirect
84. C2×(C2×D47)⋊C4C2×C4semidirect
85. C2×(C2×D47)⋊C4C2×C4semidirect
89. C2×C4×Dic47C2×C4semidirect
90. C2×C4×Dic47C2×C4semidirect
97. C47⋊#95D4semidirect
103. C23×C4×C47C2×C4semidirect
110. C2×C22⋊C4×C47C2×C4semidirect
308. C2×C4×C47C4×D4semidirect
309. C22⋊D47#95semidirect
339. C2×Dic47C4×D4semidirect
353. C22×C47C2×#95semidirect
387. C2×D47C2×#95semidirect
396. Dic47C2×#95semidirect
406. C22⋊#95D47semidirect
451. C47D4×#95semidirect
487. C23×C4C4×D47semidirect
508. C2×C22⋊C4C4×D47semidirect
751. C2×C4(C22⋊D47)⋊C4semidirect
773. C22#95×D47semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C22×(C22⋊D47)⋊C42
C22×C47⋊#952
C2×#95×D472
Dic47⋊#952
#202416102
(C2×D47)⋊#952
#95×Dic472
C47×C22⋊#952
D4×#9547