Finite Group Databasebeta

← #26138995

Subgroups — #26138995

Order 12032.

2590 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C2×#15688999C212yesmaximal
3C2×#15688982C211yesmaximal, characteristic, complemented
4C2×#95×D47C211yesmaximal, characteristic, complemented
5#20241639C212yesmaximal, complemented
6#20241631C212yesmaximal, complemented
7#20241612C211yesmaximal, characteristic, complemented
8#20241612C211yesmaximal, characteristic, complemented
9#20241611C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C47×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C23×C4×D47C2212yes—
14C23×C4×D47C2211yescharacteristic
15C2×C4×C22⋊D47—24no—
16C2×C4×C22⋊D47—24no—
17C2×C4×C22⋊D47C418yescomplemented
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2212yes—
20C22×C22⋊Dic47C2212yes—
21C22×C22⋊Dic47C2211yescharacteristic
22C22×(C2×D47)⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25#15688999—28no—
26#15688982—24no—
27C2×C47⋊#95C2211yescharacteristic
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—
36C24×C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2212yes—
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2212yes—
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×Dic47C2312yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2312yes—
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54C22×C4×D47—24no—
55C22×C4×D47—24no—
56C22×C4×D47—24no—
57C22×C4×D47—24no—
58C22×C4×D47—24no—
59C22×C4×D47—42no—
60C22×C4×D47—42no—
61C22×C4×D47—42no—
62C22×C4×D47—42no—
63C22×C4×D47C2×C414yes—
64C22×C4×D47D414yes—
65C22×C4×D47D414yes—
66C4×C22⋊D47—232no—
67C2×Dic47⋊C4—22no—
68C2×Dic47⋊C4—22no—
69C2×Dic47⋊C4—24no—
70C2×Dic47⋊C4—42no—
71C2×Dic47⋊C4—42no—
72C2×Dic47⋊C4C2×C414yescomplemented
73C2×C22⋊Dic47—22no—
74C2×C22⋊Dic47—22no—
75C2×C22⋊Dic47—24no—
76C2×C22⋊Dic47—24no—
77C2×C22⋊Dic47—42no—
78C2×C22⋊Dic47C2×C414yescomplemented
79C2×(C2×D47)⋊C4—22no—
80C2×(C2×D47)⋊C4—22no—
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4—24no—
84C2×(C2×D47)⋊C4C2×C414yes—
85C2×C4×Dic47—22no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47C2×C414yescomplemented
88C47⋊#95—22no—
89C47⋊#95—22no—
90C47⋊#95—24no—
91C47⋊#95—24no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—24no—
95C47⋊#95—42no—
96C25×C47C2311yescharacteristic
97C23×C4×C47—22no—
98C23×C4×C47—22no—
99C23×C4×C47—42no—
100C23×C4×C47—42no—
101C23×C4×C47C2×C414yescomplemented
102C23×C4×C47C2312yes—
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2312yes—
105C23×C4×C47C2311yescharacteristic
106C2×C22⋊C4×C47—24no—
107C2×C22⋊C4×C47—24no—
108C2×C22⋊C4×C47—42no—
109#95×C47—22no—
110#95×C47—22no—
111#95×C47—42no—
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—28no—
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—44no—
156C22×C4×C47—44no—
157C22×C4×C47—48no—
158C22×C4×C47—48no—
159C22×C4×C47C22×C412yes—
160C22×C4×C47C22×C412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×D412yes—
163C22×C4×C47#4114yes—
164C2×C22⋊D47—28no—
165C2×C22⋊D47—28no—
166C2×C22⋊D47—28no—
167C2×C22⋊D47—28no—
168C2×C22⋊D47—28no—
169C2×C22⋊D47—28no—
170C2×C22⋊D47C4⋊C4116yescomplemented
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
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—44no—
204C2×C4×D47—44no—
205C2×C4×D47—48no—
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
214C22⋊C4×C47—48no—
215C22⋊Dic47—28no—
216C22⋊Dic47—48no—
217(C2×D47)⋊C4—28no—
218(C2×D47)⋊C4—48no—
219Dic47⋊C4—28no—
220Dic47⋊C4—48no—
221C4×Dic47—28no—
222C23×C47—22no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—22no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—24no—
233C23×C47—24no—
234C23×C47—24no—
235C23×C47—24no—
236C23×C47—42no—
237C23×C47—42no—
238C23×C47—42no—
239C23×C47—42no—
240C23×C47—42no—
241C23×C47—42no—
242C23×C47—42no—
243C23×C47—42no—
244C23×C47C2×C4⋊C414yes—
245C23×C47C23×C411yescharacteristic
246C23×C47C22×D411yescharacteristic
247C23×C47C22×D411yescharacteristic
248C23×C47C22×D411yescharacteristic
249C23×C47C22×Q811yescharacteristic
250C23×C47C2×#4111yescharacteristic
251C23×C47C2×#4111yescharacteristic
252C23×C47C2×#4112yes—
253C23×C47C2×#4112yes—
254C23×C47H(5,𝔽2)12yes—
255C23×C47H(5,𝔽2)12yes—
256C22×D47—22no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—22no—
260C22×D47—24no—
261C22×D47—24no—
262C22×D47—24no—
263C22×D47—24no—
264C22×D47—24no—
265C22×D47—24no—
266C22×D47—24no—
267C22×D47—24no—
268C22×D47—24no—
269C22×D47—24no—
270C22×D47—24no—
271C22×D47—24no—
272C22×D47C2×C22⋊C414yes—
273C22×D47C2×C4⋊C414yes—
274C22×D47#11714yes—
275C22×D47#12114yes—
276C22×D47#12114yes—
277C22×D47C22⋊Q814yes—
278C22×D47C22⋊Q814yes—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—24no—
282C2×C4×C47—24no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—24no—
287C2×C4×C47—24no—
288C2×C4×C47—24no—
289C2×C4×C47—416no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
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—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—24no—
314C2×Dic47—24no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—24no—
319C2×Dic47—24no—
320C2×Dic47—24no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—42no—
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×C22⋊C414yes—
335C2×Dic47C2×C4⋊C414yes—
336C4×D47—416no—
337C4×D47—432no—
338#13960—471nomaximal, Sylow
339C22×C47—24no—
340C22×C47—24no—
341C22×C47—24no—
342C22×C47—42no—
343C22×C47—44no—
344C22×C47—44no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—44no—
348C22×C47—44no—
349C22×C47—42no—
350C22×C47C22×C22⋊C411yescharacteristic
351C22×C47C22×C4⋊C411yescharacteristic
352C22×C47C2×#11711yescharacteristic
353C22×C47C4×#4111yescharacteristic
354C22×C47C4×#4111yescharacteristic
355C22×C47#51811yescharacteristic
356C22×C47#51811yescharacteristic
357C22×C47C2×#12111yescharacteristic
358C22×C47C2×#12111yescharacteristic
359C22×C47C2×C22⋊Q811yescharacteristic
360C22×C47C2×C22⋊Q811yescharacteristic
361C22×C47#52512yes—
362C22×C47#53212yes—
363C22×C47#53412yes—
364C22×C47#53412yes—
365C22×C47#54612yes—
366C22×C47#54612yes—
367C22×C47#55112yes—
368C22×C47#55112yes—
369C22×C47#55312yes—
370C22×C47#55312yes—
371C22×C47#55412yes—
372C22×C47#55412yes—
373C2×D47—24no—
374C2×D47—28no—
375C2×D47—28no—
376C2×D47—24no—
377C2×D47—24no—
378C2×D47—24no—
379C2×D47—24no—
380C2×D47—28no—
381C2×D47—28no—
382C2×D47—24no—
383C2×D47#38018yes—
384C4×C47—24no—
385C4×C47—42no—
386C4×C47—44no—
387C4×C47—82no—
388Dic47—24no—
389Dic47—24no—
390Dic47—44no—
391Dic47—42no—
392Dic47—82no—
393C22×C4×D4—471no—
394C2×#386—472no—
395C2×#380—471no—
396C22×#95—471no—
397#1441—472no—
398#1439—472no—
399#1434—471no—
400#1434—471no—
401C22⋊#95—472no—
402C22⋊#95—471no—
403C22⋊#95D4711yescharacteristic, complemented
404C2×C47—44no—
405C2×C47C2×#38011yescharacteristic
406C2×C47#229711yescharacteristic
407C2×C47#230811yescharacteristic
408C2×C47#234911yescharacteristic
409C2×C47#234911yescharacteristic
410C2×C47#235311yescharacteristic
411C2×C47#235311yescharacteristic
412C2×C47#253412yes—
413C2×C47#254312yes—
414C2×C47#256412yes—
415C2×C47#257912yes—
416D47—28no—
417C23×D4—471no—
418C24×C4—471no—
419C24×C4—472no—
420C24×C4C2×D4711yescharacteristic
421C2×C4×D4—478no—
422C2×C4×D4—944no—
423C2×C4×D4—944no—
424C22×C4⋊C4—471no—
425C22×C4⋊C4—472no—
426C22×C22⋊C4—471no—
427C22×C22⋊C4—471no—
428C22×C22⋊C4—472no—
429C22×C22⋊C4—472no—
430C22×C22⋊C4C2×D4712yes—
431C22×C42—471no—
432#386—948no—
433#380—944no—
434C2×#95—472no—
435C2×#95—472no—
436C2×#95—471no—
437C2×#95—471no—
438C2×#95—472no—
439C2×#95—472no—
440C2×#95—472no—
441C2×#95—472no—
442C2×#95—944no—
443C2×#95C2×D4711yescharacteristic
444C2×#95C2×D4711yescharacteristic
445C2×#95C2×D4712yes—
446C47#1396011yescharacteristic, complemented, Sylow
447C25—471no—
448C25C22×D4711yescharacteristic
449C22×D4—474no—
450C22×D4—474no—
451C22×D4—474no—
452C22×D4—942no—
453C22×D4—942no—
454C22×D4—942no—
455C22×D4—942no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—42no—
459C23×C4—42no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—474no—
463C23×C4—474no—
464C23×C4—474no—
465C23×C4—471no—
466C23×C4—472no—
467C23×C4—472no—
468C23×C4—944no—
469C23×C4—944no—
470C23×C4—944no—
471C23×C4—944no—
472C23×C4—944no—
473C23×C4—1882no—
474C23×C4—1882no—
475C23×C4—1882no—
476C23×C4—1882no—
477C23×C4C4×D4714yescomplemented
478C23×C4C22×D4712yes—
479C23×C4C22×D4711yescharacteristic
480C23×C4C22×D4712yes—
481C23×C4C22×D4711yescharacteristic
482C4×D4—9432no—
483C2×C4⋊C4—474no—
484C2×C4⋊C4—942no—
485C2×C4⋊C4—942no—
486C2×C4⋊C4—944no—
487C2×C4⋊C4—1882no—
488C2×C4⋊C4—1882no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—474no—
493C2×C22⋊C4—474no—
494C2×C22⋊C4—942no—
495C2×C22⋊C4—942no—
496C2×C22⋊C4—942no—
497C2×C22⋊C4—942no—
498C2×C22⋊C4—944no—
499C2×C22⋊C4—944no—
500C2×C22⋊C4—944no—
501C2×C22⋊C4—944no—
502C2×C22⋊C4—944no—
503C2×C22⋊C4—1882no—
504C2×C42—474no—
505C2×C42—942no—
506C2×C42—942no—
507#95—22no—
508#95—22no—
509#95—42no—
510#95—944no—
511#95—944no—
512#95—944no—
513#95—944no—
514#95—944no—
515#95—942no—
516#95—942no—
517#95—1882no—
518C24—21no—
519C24—21no—
520C24—22no—
521C24—21no—
522C24—21no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—472no—
527C24—472no—
528C24—472no—
529C24—472no—
530C24—472no—
531C24—472no—
532C24—472no—
533C24—942no—
534C24—942no—
535C24—942no—
536C24—942no—
537C24C2×C4×D4712yes—
538C24D4×D4712yes—
539C24Q8×D4712yes—
540C24C23×D4711yescharacteristic
541C2×D4—4716no—
542C2×D4—948no—
543C2×D4—948no—
544C2×D4—948no—
545C2×D4—948no—
546C2×D4—948no—
547C2×D4—948no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—28no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—472no—
573C22×C4—472no—
574C22×C4—472no—
575C22×C4—472no—
576C22×C4—472no—
577C22×C4—472no—
578C22×C4—4716no—
579C22×C4—472no—
580C22×C4—474no—
581C22×C4—9416no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—941no—
591C22×C4—941no—
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—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—1884no—
606C22×C4—1884no—
607C22×C4—1888no—
608C22×C4—1888no—
609C22×C4—1888no—
610C22×C4—1888no—
611C22×C4—1888no—
612C22×C4—1888no—
613C22×C4—1888no—
614C22×C4—1888no—
615C22×C4C2×C4×D4712yes—
616C22×C4C2×C4×D4712yes—
617C22×C4#1062535014yes—
618C22×C4D4×D4712yes—
619C22×C4D4×D4712yes—
620C4⋊C4—948no—
621C4⋊C4—1888no—
622C22⋊C4—48no—
623C22⋊C4—948no—
624C22⋊C4—948no—
625C22⋊C4—1888no—
626C22⋊C4—1888no—
627C42—948no—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—474no—
651C23—474no—
652C23—474no—
653C23—474no—
654C23—474no—
655C23—474no—
656C23—474no—
657C23—944no—
658C23—944no—
659C23—944no—
660C23—944no—
661C23—944no—
662C23—944no—
663C23—944no—
664C23—944no—
665C23—942no—
666C23—942no—
667C23—942no—
668C23—942no—
669C23—944no—
670C23—944no—
671C23—944no—
672C23—944no—
673C23C4⋊C4×D4714yes—
674C23C22×C4×D4711yescharacteristic
675C23C2×D4×D4711yescharacteristic
676C23C2×D4×D4711yescharacteristic
677C23C2×D4×D4711yescharacteristic
678C23C2×Q8×D4711yescharacteristic
679C23#41×D4712yes—
680C23#41×D4711yescharacteristic
681C23#41×D4711yescharacteristic
682C23C2×#1062535012yes—
683C23#1309406912yes—
684C23#1309406912yes—
685D4—9432no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—416no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—474no—
711C2×C4—474no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—944no—
721C2×C4—944no—
722C2×C4—944no—
723C2×C4—944no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—944no—
728C2×C4—18816no—
729C2×C4—18832no—
730C2×C4—1882no—
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×C4C22⋊C4×D4714yes—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—44no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—44no—
755C22—478no—
756C22—944no—
757C22—944no—
758C22—948no—
759C22—944no—
760C22—944no—
761C22—944no—
762C22—948no—
763C22—944no—
764C22—948no—
765C22—948no—
766C22C2×C22⋊C4×D4711yescharacteristic
767C22C2×C4⋊C4×D4711yescharacteristic
768C22#117×D4711yescharacteristic
769C22#1568959111yescharacteristic
770C22C4×#1062535011yescharacteristic
771C22#1568959611yescharacteristic
772C22#1568959611yescharacteristic
773C22#121×D4711yescharacteristic
774C22#121×D4711yescharacteristic
775C22C22⋊Q8×D4711yescharacteristic
776C22C22⋊Q8×D4711yescharacteristic
777C22#1568963212yes—
778C22#1568967012yes—
779C22#1568968312yes—
780C22#1568968312yes—
781C22#1568976212yes—
782C22#1568976312yes—
783C22#1568980112yes—
784C22#1568980212yes—
785C22#1568981812yes—
786C22#1568982312yes—
787C22#1568982712yes—
788C22#1568982812yes—
789C4—24no—
790C4—42no—
791C4—44no—
792C4—82no—
793C4—944no—
794C4—944no—
795C4—3762no—
796C4—1882no—
797C4—1884no—
798C2—44no—
799C2—948no—
800C2#380×D4711yescharacteristic
801C2#2024587411yescharacteristic
802C2#2024596411yescharacteristic
803C2#2024629211yescharacteristic
804C2#2024629511yescharacteristic
805C2#2024632511yescharacteristic
806C2#2024633111yescharacteristic
807C2#2024827612yes—
808C2#2024834712yes—
809C2#2024857312yes—
810C2#2024873312yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC22⋊#95D47
hypocenterC47#13960
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#15688982C2semidirect
4. C2×#95×D47C2semidirect
5. #20241639C2semidirect
6. #20241631C2semidirect
7. #20241612C2semidirect
8. #20241612C2semidirect
9. #20241611C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C47×C22⋊#95C2semidirect
17. C2×C4×C22⋊D47C4semidirect
72. C2×Dic47⋊C4C2×C4semidirect
78. C2×C22⋊Dic47C2×C4semidirect
87. C2×C4×Dic47C2×C4semidirect
101. C23×C4×C47C2×C4semidirect
170. C2×C22⋊D47C4⋊C4semidirect
213. C2×C4×D47C22⋊C4semidirect
403. C22⋊#95D47semidirect
446. C47#13960semidirect
477. C23×C4C4×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
C2×#156889992
C2×#156889822
C2×#95×D472
#202416392
#202416312
#202416122
#202416112
(C2×D47)⋊#952
C47×C22⋊#952
#1396047