Finite Group Databasebeta

← #26138992

Subgroups — #26138992

Order 12032.

2590 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2C2×#15688999C212yesmaximal
3C2×#15688980C211yesmaximal, characteristic, complemented
4C2×#95×D47C211yesmaximal, characteristic, complemented
5#20241642C211yesmaximal, characteristic, complemented
6#20241638C211yesmaximal, characteristic, complemented
7#20241633C211yesmaximal, characteristic, complemented
8#20241613C212yesmaximal, complemented
9#20241610C212yesmaximal, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C47×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C23×C4×D47C2212yes—
15C23×C4×D47C2211yescharacteristic
16C2×(C22⋊D47)⋊C4—24no—
17C2×(C22⋊D47)⋊C4—24no—
18C2×(C22⋊D47)⋊C4C418yescomplemented
19C22×C4⋊Dic47C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×C22⋊Dic47C2212yes—
22C22×(C2×D47)⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25#15688999—28no—
26#15688980—24no—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35#95×D47—24no—
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2212yes—
38C22×C22⋊C4×C47C2211yescharacteristic
39C2×#95×C47C2212yes—
40C2×#95×C47C2211yescharacteristic
41C24×D47C2311yescharacteristic
42C22×C22⋊D47—22no—
43C22×C22⋊D47—22no—
44C22×C22⋊D47—22no—
45C22×C22⋊D47—22no—
46C22×C22⋊D47C2×C414yes—
47C22×C22⋊D47D414yes—
48C22×C22⋊D47Q814yes—
49C23×Dic47—22no—
50C23×Dic47—22no—
51C23×Dic47—42no—
52C23×Dic47—42no—
53C23×Dic47C2×C414yescomplemented
54C23×Dic47C2312yes—
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2312yes—
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C22×C4×D47—24no—
60C22×C4×D47—24no—
61C22×C4×D47—24no—
62C22×C4×D47—24no—
63C22×C4×D47—24no—
64C22×C4×D47—42no—
65C22×C4×D47—42no—
66C22×C4×D47—42no—
67C22×C4×D47—42no—
68C22×C4×D47C2×C414yes—
69C22×C4×D47D414yes—
70C22×C4×D47D414yes—
71(C22⋊D47)⋊C4—232no—
72C2×C4⋊Dic47—22no—
73C2×C4⋊Dic47—42no—
74C2×Dic47⋊C4—22no—
75C2×Dic47⋊C4—22no—
76C2×Dic47⋊C4C2×C414yescomplemented
77C2×C22⋊Dic47—24no—
78C2×C22⋊Dic47—24no—
79C2×C22⋊Dic47—42no—
80C2×(C2×D47)⋊C4—22no—
81C2×(C2×D47)⋊C4—22no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4—24no—
84C2×(C2×D47)⋊C4—24no—
85C2×(C2×D47)⋊C4C2×C414yes—
86C2×C4×Dic47—22no—
87C2×C4×Dic47—22no—
88C2×C4×Dic47C2×C414yescomplemented
89C47⋊#95—22no—
90C47⋊#95—24no—
91C47⋊#95—24no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—24no—
95C47⋊#95—42no—
96C47⋊#95—42no—
97C25×C47C2311yescharacteristic
98C23×C4×C47C2312yes—
99C23×C4×C47C2311yescharacteristic
100C23×C4×C47C2312yes—
101C23×C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—42no—
104C2×C22⋊C4×C47—22no—
105C2×C22⋊C4×C47—22no—
106C2×C22⋊C4×C47—24no—
107C2×C22⋊C4×C47—24no—
108C2×C22⋊C4×C47—42no—
109C2×C22⋊C4×C47C2×C414yescomplemented
110#95×C47—22no—
111#95×C47—24no—
112C24×C47—21no—
113C24×C47—21no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—21no—
117C24×C47—21no—
118C24×C47—22no—
119C24×C47—22no—
120C24×C47C22×C412yes—
121C24×C47C2×D412yes—
122C24×C47C2×Q812yes—
123C24×C47C2411yescharacteristic
124C23×D47—22no—
125C23×D47—22no—
126C23×D47—22no—
127C23×D47—22no—
128C23×D47C22×C412yes—
129C23×D47C2×D412yes—
130C23×D47C2×D412yes—
131C23×D47C2×D412yes—
132C23×D47C2×Q812yes—
133C23×D47#4112yes—
134C23×D47#4112yes—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
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×C47C22×C412yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47#4114yes—
159C2×C22⋊D47—28no—
160C2×C22⋊D47—28no—
161C2×C22⋊D47—28no—
162C2×C22⋊D47—28no—
163C2×C22⋊D47—28no—
164C2×C22⋊D47—28no—
165C2×C22⋊D47C4⋊C4116yescomplemented
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—28no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—48no—
191C22×Dic47—48no—
192C22×Dic47—44no—
193C22×Dic47—44no—
194C22×Dic47C22×C412yes—
195C22×Dic47C22×C412yes—
196C22×Dic47C22×C412yes—
197C22×Dic47C2×D412yes—
198C22×Dic47C2×D412yes—
199C22×Dic47C2×D412yes—
200C22×Dic47C2×Q812yes—
201C22×Dic47#4114yes—
202C2×C4×D47—216no—
203C2×C4×D47—48no—
204C2×C4×D47—44no—
205C2×C4×D47—44no—
206C2×C4×D47—48no—
207C2×C4×D47—48no—
208C2×C4×D47—48no—
209C2×C4×D47—48no—
210C2×C4×D47—48no—
211C2×C4×D47—48no—
212C2×C4×D47—48no—
213C2×C4×D47C22⋊C4116yescomplemented
214C4⋊C4×C47—44no—
215C22⋊C4×C47—28no—
216C22⋊C4×C47—48no—
217C22⋊Dic47—48no—
218(C2×D47)⋊C4—28no—
219(C2×D47)⋊C4—48no—
220C4⋊Dic47—44no—
221Dic47⋊C4—28no—
222C4×Dic47—28no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—22no—
231C23×C47—24no—
232C23×C47—24no—
233C23×C47—24no—
234C23×C47—24no—
235C23×C47—42no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—42no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—42no—
242C23×C47—42no—
243C23×C47—42no—
244C23×C47—42no—
245C23×C47C2×C4⋊C414yes—
246C23×C47C23×C411yescharacteristic
247C23×C47C22×D411yescharacteristic
248C23×C47C22×D411yescharacteristic
249C23×C47C22×D411yescharacteristic
250C23×C47C22×Q811yescharacteristic
251C23×C47C2×#4111yescharacteristic
252C23×C47C2×#4111yescharacteristic
253C23×C47C2×#4112yes—
254C23×C47C2×#4112yes—
255C23×C47H(5,𝔽2)12yes—
256C23×C47H(5,𝔽2)12yes—
257C22×D47—24no—
258C22×D47—24no—
259C22×D47—24no—
260C22×D47—22no—
261C22×D47—22no—
262C22×D47—24no—
263C22×D47—22no—
264C22×D47—22no—
265C22×D47—24no—
266C22×D47—24no—
267C22×D47—24no—
268C22×D47—24no—
269C22×D47—24no—
270C22×D47—24no—
271C22×D47—24no—
272C22×D47—24no—
273C22×D47C2×C22⋊C414yes—
274C22×D47C2×C4⋊C414yes—
275C22×D47#11714yes—
276C22×D47#12114yes—
277C22×D47#12114yes—
278C22×D47C22⋊Q814yes—
279C22×D47C22⋊Q814yes—
280C2×C4×C47—24no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—24no—
284C2×C4×C47—22no—
285C2×C4×C47—24no—
286C2×C4×C47—24no—
287C2×C4×C47—24no—
288C2×C4×C47—24no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47C2×C22⋊C414yes—
304C22⋊D47—232no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—24no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—24no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—24no—
317C2×Dic47—24no—
318C2×Dic47—24no—
319C2×Dic47—24no—
320C2×Dic47—416no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—41no—
325C2×Dic47—41no—
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×Dic47—42no—
335C2×Dic47C2×C22⋊C414yes—
336C2×Dic47C2×C4⋊C414yes—
337C4×D47—416no—
338C4×D47—432no—
339#13960—471nomaximal, Sylow
340C22×C47—28no—
341C22×C47—24no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—44no—
346C22×C47—44no—
347C22×C47—44no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47C22×C22⋊C411yescharacteristic
352C22×C47C22×C4⋊C411yescharacteristic
353C22×C47C2×#11711yescharacteristic
354C22×C47C4×#4112yes—
355C22×C47#51812yes—
356C22×C47C2×#12111yescharacteristic
357C22×C47C2×#12111yescharacteristic
358C22×C47C2×C22⋊Q811yescharacteristic
359C22×C47C2×C22⋊Q811yescharacteristic
360C22×C47#52512yes—
361C22×C47#53211yescharacteristic
362C22×C47#53211yescharacteristic
363C22×C47#53412yes—
364C22×C47#53411yescharacteristic
365C22×C47#53411yescharacteristic
366C22×C47#54612yes—
367C22×C47#54612yes—
368C22×C47#55112yes—
369C22×C47#55112yes—
370C22×C47#55312yes—
371C22×C47#55312yes—
372C22×C47#55412yes—
373C22×C47#55412yes—
374C2×D47—24no—
375C2×D47—24no—
376C2×D47—24no—
377C2×D47—28no—
378C2×D47—28no—
379C2×D47—28no—
380C2×D47—28no—
381C2×D47—24no—
382C2×D47—24no—
383C2×D47—24no—
384C2×D47#38018yes—
385C4×C47—24no—
386C4×C47—44no—
387C4×C47—42no—
388C4×C47—82no—
389Dic47—24no—
390Dic47—24no—
391Dic47—42no—
392Dic47—44no—
393Dic47—82no—
394C22×C4×D4—471no—
395C2×#386—472no—
396C2×#380—471no—
397C22×#95—471no—
398#1441—471no—
399#1441—471no—
400#1439—471no—
401#1439D4711yescharacteristic, complemented
402#1434—472no—
403C22⋊#95—472no—
404C22⋊#95—472no—
405C2×C47—44no—
406C2×C47C2×#38011yescharacteristic
407C2×C47#229711yescharacteristic
408C2×C47#230811yescharacteristic
409C2×C47#234912yes—
410C2×C47#235312yes—
411C2×C47#253412yes—
412C2×C47#254311yescharacteristic
413C2×C47#254311yescharacteristic
414C2×C47#256411yescharacteristic
415C2×C47#256411yescharacteristic
416C2×C47#257912yes—
417D47—28no—
418C23×D4—471no—
419C24×C4—471no—
420C24×C4—471no—
421C24×C4—472no—
422C2×C4×D4—478no—
423C2×C4×D4—944no—
424C2×C4×D4—944no—
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4C2×D4711yescharacteristic
428C22×C22⋊C4—471no—
429C22×C22⋊C4—472no—
430C22×C22⋊C4—472no—
431C22×C22⋊C4C2×D4712yes—
432C22×C22⋊C4C2×D4711yescharacteristic
433C22×C42—471no—
434#386—948no—
435#380—944no—
436C2×#95—472no—
437C2×#95—472no—
438C2×#95—472no—
439C2×#95—472no—
440C2×#95—472no—
441C2×#95—471no—
442C2×#95—472no—
443C2×#95—472no—
444C2×#95—944no—
445C2×#95C2×D4712yes—
446C2×#95C2×D4711yescharacteristic
447C47#1396011yescharacteristic, complemented, Sylow
448C25—471no—
449C25C22×D4711yescharacteristic
450C22×D4—474no—
451C22×D4—474no—
452C22×D4—474no—
453C22×D4—942no—
454C22×D4—942no—
455C22×D4—942no—
456C22×D4—942no—
457C23×C4—471no—
458C23×C4—471no—
459C23×C4—474no—
460C23×C4—474no—
461C23×C4—474no—
462C23×C4—471no—
463C23×C4—472no—
464C23×C4—474no—
465C23×C4—472no—
466C23×C4—944no—
467C23×C4—944no—
468C23×C4—944no—
469C23×C4—944no—
470C23×C4—942no—
471C23×C4—942no—
472C23×C4—944no—
473C23×C4—1882no—
474C23×C4—1882no—
475C23×C4—1882no—
476C23×C4—1882no—
477C23×C4—1882no—
478C23×C4—1882no—
479C23×C4C22×D4712yes—
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4712yes—
482C23×C4C22×D4711yescharacteristic
483C4×D4—9432no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—474no—
487C2×C4⋊C4—942no—
488C2×C4⋊C4—942no—
489C2×C4⋊C4—942no—
490C2×C4⋊C4—1882no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—474no—
497C2×C22⋊C4—942no—
498C2×C22⋊C4—942no—
499C2×C22⋊C4—944no—
500C2×C22⋊C4—944no—
501C2×C22⋊C4—944no—
502C2×C22⋊C4—944no—
503C2×C22⋊C4—944no—
504C2×C22⋊C4—1882no—
505C2×C22⋊C4C4×D4714yescomplemented
506C2×C42—474no—
507C2×C42—942no—
508C2×C42—942no—
509#95—22no—
510#95—24no—
511#95—944no—
512#95—944no—
513#95—944no—
514#95—944no—
515#95—944no—
516#95—942no—
517#95—1882no—
518#95—1882no—
519C24—21no—
520C24—21no—
521C24—22no—
522C24—21no—
523C24—21no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—472no—
528C24—472no—
529C24—472no—
530C24—472no—
531C24—472no—
532C24—472no—
533C24—472no—
534C24—942no—
535C24—942no—
536C24—942no—
537C24—942no—
538C24C2×C4×D4712yes—
539C24D4×D4712yes—
540C24Q8×D4712yes—
541C24C23×D4711yescharacteristic
542C2×D4—4716no—
543C2×D4—948no—
544C2×D4—948no—
545C2×D4—948no—
546C2×D4—948no—
547C2×D4—948no—
548C2×D4—948no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
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—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—472no—
569C22×C4—472no—
570C22×C4—472no—
571C22×C4—472no—
572C22×C4—472no—
573C22×C4—472no—
574C22×C4—4716no—
575C22×C4—472no—
576C22×C4—474no—
577C22×C4—9416no—
578C22×C4—948no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—942no—
594C22×C4—942no—
595C22×C4—942no—
596C22×C4—942no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—1888no—
603C22×C4—1888no—
604C22×C4—1884no—
605C22×C4—1884no—
606C22×C4—1888no—
607C22×C4—1888no—
608C22×C4—1888no—
609C22×C4—1888no—
610C22×C4—1888no—
611C22×C4—1888no—
612C22×C4—1888no—
613C22×C4—1888no—
614C22×C4—1884no—
615C22×C4—1884no—
616C22×C4C2×C4×D4712yes—
617C22×C4C2×C4×D4712yes—
618C22×C4D4×D4712yes—
619C22×C4D4×D4712yes—
620C22×C4#1062535214yes—
621C4⋊C4—44no—
622C4⋊C4—948no—
623C4⋊C4—1884no—
624C22⋊C4—28no—
625C22⋊C4—48no—
626C22⋊C4—948no—
627C22⋊C4—1888no—
628C22⋊C4—1888no—
629C42—948no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—24no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—41no—
648C23—41no—
649C23—42no—
650C23—41no—
651C23—41no—
652C23—474no—
653C23—474no—
654C23—474no—
655C23—474no—
656C23—474no—
657C23—474no—
658C23—474no—
659C23—944no—
660C23—944no—
661C23—944no—
662C23—944no—
663C23—944no—
664C23—944no—
665C23—944no—
666C23—944no—
667C23—944no—
668C23—944no—
669C23—944no—
670C23—942no—
671C23—942no—
672C23—944no—
673C23—942no—
674C23—942no—
675C23C4⋊C4×D4714yes—
676C23C22×C4×D4711yescharacteristic
677C23C2×D4×D4711yescharacteristic
678C23C2×D4×D4711yescharacteristic
679C23C2×D4×D4711yescharacteristic
680C23C2×Q8×D4711yescharacteristic
681C23#41×D4712yes—
682C23#41×D4711yescharacteristic
683C23#41×D4711yescharacteristic
684C23C2×#1062535212yes—
685C23#1309406912yes—
686C23#1309407012yes—
687D4—9432no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—474no—
712C2×C4—474no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—944no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—944no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—944no—
724C2×C4—944no—
725C2×C4—942no—
726C2×C4—944no—
727C2×C4—944no—
728C2×C4—18816no—
729C2×C4—18832no—
730C2×C4—18816no—
731C2×C4—1882no—
732C2×C4—1882no—
733C2×C4—1882no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1882no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4—1882no—
742C2×C4—1882no—
743C2×C4—1881no—
744C2×C4—1881no—
745C2×C4C22⋊C4×D4714yes—
746C22—28no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—44no—
751C22—42no—
752C22—44no—
753C22—42no—
754C22—44no—
755C22—42no—
756C22—42no—
757C22—478no—
758C22—948no—
759C22—944no—
760C22—944no—
761C22—948no—
762C22—944no—
763C22—948no—
764C22—944no—
765C22—948no—
766C22—944no—
767C22—944no—
768C22C2×C22⋊C4×D4711yescharacteristic
769C22C2×C4⋊C4×D4711yescharacteristic
770C22#117×D4711yescharacteristic
771C22C4×#1062535212yes—
772C22#1568959512yes—
773C22#121×D4711yescharacteristic
774C22#121×D4711yescharacteristic
775C22C22⋊Q8×D4711yescharacteristic
776C22C22⋊Q8×D4711yescharacteristic
777C22#1568963312yes—
778C22#1568967111yescharacteristic
779C22#1568967211yescharacteristic
780C22#1568968112yes—
781C22#1568968311yescharacteristic
782C22#1568968411yescharacteristic
783C22#1568976012yes—
784C22#1568976512yes—
785C22#1568979612yes—
786C22#1568980312yes—
787C22#1568982012yes—
788C22#1568982412yes—
789C22#1568982712yes—
790C22#1568983112yes—
791C4—24no—
792C4—42no—
793C4—44no—
794C4—82no—
795C4—944no—
796C4—944no—
797C4—3762no—
798C4—1882no—
799C4—1884no—
800C2—44no—
801C2—948no—
802C2#380×D4711yescharacteristic
803C2#2024587511yescharacteristic
804C2#2024596211yescharacteristic
805C2#2024629412yes—
806C2#2024632312yes—
807C2#2024827312yes—
808C2#2024834311yescharacteristic
809C2#2024834511yescharacteristic
810C2#2024856311yescharacteristic
811C2#2024856511yescharacteristic
812C2#2024873012yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1439C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenter#1439D47
hypocenterC47#13960
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#15688980C2semidirect
4. C2×#95×D47C2semidirect
5. #20241642C2semidirect
6. #20241638C2semidirect
7. #20241633C2semidirect
8. #20241613C2semidirect
9. #20241610C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C47×#1439C2semidirect
18. C2×(C22⋊D47)⋊C4C4semidirect
53. C23×Dic47C2×C4semidirect
76. C2×Dic47⋊C4C2×C4semidirect
88. C2×C4×Dic47C2×C4semidirect
109. C2×C22⋊C4×C47C2×C4semidirect
165. C2×C22⋊D47C4⋊C4semidirect
213. C2×C4×D47C22⋊C4semidirect
401. #1439D47semidirect
447. C47#13960semidirect
505. C2×C22⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D47)⋊C42
C2×#156889992
C2×#156889802
C2×#95×D472
#202416422
#202416382
#202416332
#202416132
#202416102
(C2×D47)⋊#952
C47×#14392
#1396047