Finite Group Databasebeta

← #26137581

Subgroups — #26137581

Order 12032.

2470 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C2×#15689023C212yesmaximal
3C2×#15688974C211yesmaximal, characteristic, complemented
4C2×#15688968C211yesmaximal, characteristic, complemented
5#20241625C212yesmaximal, complemented
6#20241624C212yesmaximal, complemented
7Dic47⋊#95C212yesmaximal, complemented
8#20241611C211yesmaximal, characteristic, complemented
9(C2×D47)⋊#95C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C211yesmaximal, characteristic, complemented
11C47×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C2×C4×C22⋊D47—24no—
15C2×C4×C22⋊D47—24no—
16C2×C4×C22⋊D47C418yescomplemented
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×C22⋊Dic47C2211yescharacteristic
20C22×C22⋊Dic47C2212yes—
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C22×(C2×D47)⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2212yes—
24C22×C4×Dic47C2212yes—
25C22×C4×Dic47C2212yes—
26C22×C4×Dic47C2211yescharacteristic
27#15689023C4116yescomplemented
28#15688974—24no—
29#15688968—24no—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
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—24no—
45C22×C22⋊D47C2×C418yes—
46C22×C22⋊D47C2×C414yes—
47C23×Dic47C2312yes—
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2312yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C22×C4×D47—22no—
53C22×C4×D47—22no—
54C22×C4×D47—42no—
55C22×C4×D47—42no—
56C22×C4×D47C2×C414yes—
57C4×C22⋊D47—232no—
58C2×Dic47⋊C4—24no—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4C2×C414yes—
63C2×Dic47⋊C4C2×C418yescomplemented
64C2×C22⋊Dic47—22no—
65C2×C22⋊Dic47—22no—
66C2×C22⋊Dic47—42no—
67C2×C22⋊Dic47—42no—
68C2×C22⋊Dic47C2×C414yes—
69C2×C22⋊Dic47C2×C418yescomplemented
70C2×(C2×D47)⋊C4—22no—
71C2×(C2×D47)⋊C4—22no—
72C2×(C2×D47)⋊C4—42no—
73C2×(C2×D47)⋊C4—42no—
74C2×(C2×D47)⋊C4—42no—
75C2×(C2×D47)⋊C4—42no—
76C2×(C2×D47)⋊C4C2×C414yes—
77C2×(C2×D47)⋊C4C2×C418yescomplemented
78C2×(C2×D47)⋊C4C2×C418yescomplemented
79C2×C4×Dic47—24no—
80C2×C4×Dic47—24no—
81C2×C4×Dic47—24no—
82C2×C4×Dic47—42no—
83C2×C4×Dic47—42no—
84C2×C4×Dic47C2×C414yes—
85C2×C4×Dic47C2×C418yescomplemented
86C2×C4×Dic47D414yes—
87C2×C4×Dic47D414yes—
88C47⋊#95—22no—
89C47⋊#95—22no—
90C47⋊#95—24no—
91C47⋊#95—42no—
92C47⋊#95—42no—
93C47⋊#95—42no—
94C25×C47C2311yescharacteristic
95C23×C4×C47—22no—
96C23×C4×C47—22no—
97C23×C4×C47—42no—
98C23×C4×C47—42no—
99C23×C4×C47C2×C414yes—
100C23×C4×C47C2312yes—
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2312yes—
103C23×C4×C47C2311yescharacteristic
104C2×C22⋊C4×C47—42no—
105C2×C22⋊C4×C47—42no—
106C2×C22⋊C4×C47C2×C418yescomplemented
107#95×C47—22no—
108#95×C47—22no—
109#95×C47—42no—
110C24×C47—21no—
111C24×C47—21no—
112C24×C47—22no—
113C24×C47—21no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—21no—
117C24×C47—21no—
118C24×C47—21no—
119C24×C47C22×C414yes—
120C24×C47C22×C412yes—
121C24×C47C2411yescharacteristic
122C23×D47—21no—
123C23×D47—21no—
124C23×D47—22no—
125C23×D47—21no—
126C23×D47—21no—
127C23×D47—22no—
128C23×D47—22no—
129C23×D47—21no—
130C23×D47—21no—
131C23×D47C22×C412yes—
132C23×D47C22×C414yes—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
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—28no—
152C22×C4×C47—44no—
153C22×C4×C47—44no—
154C22×C4×C47—48no—
155C22×C4×C47—48no—
156C22×C4×C47C22×C414yes—
157C22×C4×C47C22×C414yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C22×C412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C2×C22⋊D47—28no—
163C2×C22⋊D47—28no—
164C2×C22⋊D47—216no—
165C2×C22⋊D47—216no—
166C2×C22⋊D47C42116yescomplemented
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47C22×C414yes—
188C22×Dic47C22×C414yes—
189C22×Dic47C22×C412yes—
190C22×Dic47C22×C412yes—
191C22×Dic47C22×C412yes—
192C22×Dic47C22×C414yes—
193C22×Dic47C2×D412yes—
194C22×Dic47C2×D412yes—
195C22×Dic47C2×D412yes—
196C22×Dic47C2×D412yes—
197C22×Dic47#4114yes—
198C2×C4×D47—28no—
199C2×C4×D47—44no—
200C2×C4×D47—44no—
201C2×C4×D47—48no—
202C2×C4×D47—48no—
203C22⋊C4×C47—48no—
204C22⋊Dic47—28no—
205C22⋊Dic47—48no—
206(C2×D47)⋊C4—28no—
207(C2×D47)⋊C4—48no—
208(C2×D47)⋊C4—48no—
209Dic47⋊C4—28no—
210Dic47⋊C4—216no—
211C4×Dic47—216no—
212C4×Dic47—48no—
213C4×Dic47C22⋊C4116yescomplemented
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—24no—
217C23×C47—24no—
218C23×C47—24no—
219C23×C47—24no—
220C23×C47—22no—
221C23×C47—22no—
222C23×C47—24no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—24no—
226C23×C47—42no—
227C23×C47—42no—
228C23×C47—41no—
229C23×C47—41no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—42no—
233C23×C47—42no—
234C23×C47—42no—
235C23×C47—42no—
236C23×C47C2×C4214yes—
237C23×C47C23×C411yescharacteristic
238C23×C47C23×C412yes—
239C23×C47C22×D411yescharacteristic
240C23×C47C22×D411yescharacteristic
241C23×C47C2×#4112yes—
242C23×C47H(5,𝔽2)12yes—
243C23×C47H(5,𝔽2)12yes—
244C23×C47H(5,𝔽2)11yescharacteristic
245C23×C47H(5,𝔽2)11yescharacteristic
246C23×C472−1+411yescharacteristic
247C23×C472−1+411yescharacteristic
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—24no—
251C22×D47—24no—
252C22×D47—24no—
253C22×D47—24no—
254C22×D47—22no—
255C22×D47—22no—
256C22×D47—24no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—24no—
260C22×D47—42no—
261C22×D47—42no—
262C22×D47—41no—
263C22×D47—41no—
264C22×D47—41no—
265C22×D47—41no—
266C22×D47—42no—
267C22×D47—42no—
268C22×D47—42no—
269C22×D47—42no—
270C22×D47C2×C4214yes—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—24no—
274C2×C4×C47—24no—
275C2×C4×C47—22no—
276C2×C4×C47—24no—
277C2×C4×C47—24no—
278C2×C4×C47—24no—
279C2×C4×C47—24no—
280C2×C4×C47—24no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—24no—
284C2×C4×C47—416no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47C2×C22⋊C414yes—
296C22⋊D47—232no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—24no—
305C2×Dic47—24no—
306C2×Dic47—24no—
307C2×Dic47—24no—
308C2×Dic47—24no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—24no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47C2×C4214yes—
323C2×Dic47C2×C22⋊C414yes—
324C2×Dic47C2×C22⋊C414yes—
325C2×Dic47#11714yes—
326C2×Dic47C4×D418yes—
327C2×Dic47C4×D418yes—
328C4×D47—416no—
329#13785—471nomaximal, Sylow
330C22×C47—24no—
331C22×C47—24no—
332C22×C47—24no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—42no—
337C22×C47—44no—
338C22×C47—44no—
339C22×C47—44no—
340C22×C47—44no—
341C22×C47C22×C4211yescharacteristic
342C22×C47C22×C22⋊C411yescharacteristic
343C22×C47C2×#11711yescharacteristic
344C22×C47C2×C4×D412yes—
345C22×C47C2×C4×D412yes—
346C22×C47#51812yes—
347C22×C47#51811yescharacteristic
348C22×C47#51811yescharacteristic
349C22×C47#51812yes—
350C22×C47#52012yes—
351C22×C47#52011yescharacteristic
352C22×C47#52011yescharacteristic
353C22×C47#52012yes—
354C22×C47#53512yes—
355C22×C47#53512yes—
356C22×C47#53511yescharacteristic
357C22×C47#53611yescharacteristic
358C22×C47#53711yescharacteristic
359C22×C47#53711yescharacteristic
360C22×C47#54012yes—
361C22×C47#54012yes—
362C22×C47#54212yes—
363C22×C47#54212yes—
364C2×D47—24no—
365C2×D47—24no—
366C2×D47—24no—
367C2×D47—42no—
368C2×D47—42no—
369C2×D47—42no—
370C2×D47—42no—
371C2×D47—44no—
372C2×D47—44no—
373C2×D47—44no—
374C2×D47—44no—
375C4×C47—24no—
376C4×C47—42no—
377C4×C47—44no—
378C4×C47—44no—
379Dic47—24no—
380Dic47—42no—
381Dic47—44no—
382Dic47—44no—
383Dic47C4×C22⋊C418yes—
384C22×C4×D4—471no—
385C2×#390—472no—
386C2×C4×C4⋊C4—471no—
387C2×#376—471no—
388#1437—472no—
389#1437—472no—
390C4⋊#95—472no—
391C22⋊#95—471no—
392C22⋊#95—471no—
393C22⋊#95—471no—
394C22⋊#95D4711yescharacteristic, complemented
395C2×C47—44no—
396C2×C47C2×C4×C22⋊C411yescharacteristic
397C2×C47#227511yescharacteristic
398C2×C47#227511yescharacteristic
399C2×C47#230911yescharacteristic
400C2×C47#231111yescharacteristic
401C2×C47#231911yescharacteristic
402C2×C47#231911yescharacteristic
403C2×C47#232412yes—
404C2×C47#232412yes—
405C2×C47#232612yes—
406C2×C47#232812yes—
407D47—44no—
408C23×D4—471no—
409C24×C4—471no—
410C24×C4C2×D4711yescharacteristic
411C2×C4×D4—478no—
412C2×C4×D4—944no—
413C2×C4×D4—944no—
414C22×C4⋊C4—471no—
415C22×C4⋊C4—472no—
416C22×C22⋊C4—471no—
417C22×C22⋊C4—471no—
418C22×C22⋊C4—472no—
419C22×C22⋊C4—472no—
420C22×C22⋊C4—472no—
421C22×C22⋊C4C2×D4712yes—
422C22×C42—471no—
423C22×C42—472no—
424C22×C42—472no—
425#390—4716no—
426C4×C4⋊C4—944no—
427#376—944no—
428C2×#95—471no—
429C2×#95—471no—
430C2×#95—472no—
431C2×#95—472no—
432C2×#95—472no—
433C2×#95—472no—
434C2×#95C2×D4711yescharacteristic
435C2×#95C2×D4711yescharacteristic
436C2×#95C2×D4712yes—
437C47#1378511yescharacteristic, complemented, Sylow
438C25—471no—
439C25C22×D4711yescharacteristic
440C22×D4—474no—
441C22×D4—478no—
442C22×D4—942no—
443C22×D4—942no—
444C22×D4—944no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—471no—
450C23×C4—471no—
451C23×C4—472no—
452C23×C4—472no—
453C23×C4—471no—
454C23×C4—474no—
455C23×C4—942no—
456C23×C4—942no—
457C23×C4—1882no—
458C23×C4—1882no—
459C23×C4C4×D4714yes—
460C23×C4C22×D4712yes—
461C23×C4C22×D4712yes—
462C23×C4C22×D4711yescharacteristic
463C23×C4C22×D4711yescharacteristic
464C4×D4—9432no—
465C2×C4⋊C4—474no—
466C2×C4⋊C4—478no—
467C2×C4⋊C4—942no—
468C2×C4⋊C4—942no—
469C2×C4⋊C4—944no—
470C2×C4⋊C4—944no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—474no—
474C2×C22⋊C4—474no—
475C2×C22⋊C4—478no—
476C2×C22⋊C4—478no—
477C2×C22⋊C4—478no—
478C2×C22⋊C4—942no—
479C2×C22⋊C4—942no—
480C2×C22⋊C4—942no—
481C2×C22⋊C4—942no—
482C2×C22⋊C4—1882no—
483C2×C22⋊C4—1882no—
484C2×C22⋊C4—1882no—
485C2×C22⋊C4—1882no—
486C2×C22⋊C4—1882no—
487C2×C22⋊C4—1882no—
488C2×C22⋊C4C4×D4718yescomplemented
489C2×C42—474no—
490C2×C42—474no—
491C2×C42—474no—
492C2×C42—478no—
493C2×C42—944no—
494C2×C42—944no—
495C2×C42—944no—
496C2×C42—1882no—
497C2×C42—1882no—
498#95—22no—
499#95—22no—
500#95—42no—
501#95—944no—
502#95—942no—
503#95—942no—
504#95—1882no—
505#95—1882no—
506#95—1882no—
507C24—21no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—22no—
512C24—22no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—474no—
517C24—472no—
518C24—941no—
519C24—941no—
520C24—942no—
521C24—941no—
522C24—942no—
523C24—942no—
524C24—941no—
525C24—941no—
526C24—941no—
527C24C2×C4×D4714yes—
528C24C2×C4×D4712yes—
529C24C23×D4711yescharacteristic
530C2×D4—4716no—
531C2×D4—948no—
532C2×D4—948no—
533C2×D4—9416no—
534C2×D4—9416no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
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—28no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—472no—
559C22×C4—474no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—474no—
563C22×C4—472no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—474no—
567C22×C4—474no—
568C22×C4—472no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—941no—
576C22×C4—941no—
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—948no—
590C22×C4—1884no—
591C22×C4—1884no—
592C22×C4—1888no—
593C22×C4—1888no—
594C22×C4C2×C4×D4714yes—
595C22×C4C2×C4×D4714yes—
596C22×C4C2×C4×D4712yes—
597C22×C4C2×C4×D4712yes—
598C22×C4D4×D4712yes—
599C22×C4D4×D4712yes—
600C4⋊C4—9416no—
601C4⋊C4—948no—
602C22⋊C4—48no—
603C22⋊C4—948no—
604C22⋊C4—948no—
605C22⋊C4—1888no—
606C22⋊C4—1888no—
607C22⋊C4—1888no—
608C42—4716no—
609C42—9416no—
610C42—1888no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—474no—
634C23—942no—
635C23—942no—
636C23—944no—
637C23—944no—
638C23—944no—
639C23—944no—
640C23—942no—
641C23—942no—
642C23—944no—
643C23—942no—
644C23—942no—
645C23—944no—
646C23—1882no—
647C23—1882no—
648C23—1882no—
649C23—1882no—
650C23—1881no—
651C23—1881no—
652C23—1881no—
653C23—1881no—
654C23—1882no—
655C23—1882no—
656C23C42×D4714yes—
657C23C22×C4×D4711yescharacteristic
658C23C22×C4×D4712yes—
659C23C2×D4×D4711yescharacteristic
660C23C2×D4×D4711yescharacteristic
661C23#41×D4712yes—
662C23#1309406912yes—
663C23#1309406912yes—
664C23#1309406911yescharacteristic
665C23#1309407011yescharacteristic
666C23#1309407111yescharacteristic
667C23#1309407211yescharacteristic
668D4—9432no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—416no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—474no—
694C2×C4—474no—
695C2×C4—474no—
696C2×C4—478no—
697C2×C4—478no—
698C2×C4—474no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—944no—
707C2×C4—944no—
708C2×C4—944no—
709C2×C4—944no—
710C2×C4—944no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—944no—
714C2×C4—18816no—
715C2×C4—1882no—
716C2×C4—1882no—
717C2×C4—1882no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4—1882no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4C22⋊C4×D4714yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—42no—
736C22—42no—
737C22—944no—
738C22—944no—
739C22—944no—
740C22—1882no—
741C22—1882no—
742C22—1884no—
743C22—1884no—
744C22—1884no—
745C22—1884no—
746C22—1882no—
747C22—1882no—
748C22C2×C42×D4711yescharacteristic
749C22C2×C22⋊C4×D4711yescharacteristic
750C22#117×D4711yescharacteristic
751C22C4×D4×D4712yes—
752C22C4×D4×D4712yes—
753C22#1568959512yes—
754C22#1568959611yescharacteristic
755C22#1568959611yescharacteristic
756C22#1568959612yes—
757C22#1568960212yes—
758C22#1568960311yescharacteristic
759C22#1568960411yescharacteristic
760C22#1568960412yes—
761C22#1568968812yes—
762C22#1568968812yes—
763C22#1568968911yescharacteristic
764C22#1568969611yescharacteristic
765C22#1568970211yescharacteristic
766C22#1568970311yescharacteristic
767C22#1568972312yes—
768C22#1568972512yes—
769C22#1568974112yes—
770C22#1568974312yes—
771C4—24no—
772C4—44no—
773C4—44no—
774C4—42no—
775C4—478no—
776C4—944no—
777C4—1884no—
778C4—1884no—
779C4—1882no—
780C2—44no—
781C2—1884no—
782C2C4×C22⋊C4×D4711yescharacteristic
783C2#2024574611yescharacteristic
784C2#2024574711yescharacteristic
785C2#2024596911yescharacteristic
786C2#2024597711yescharacteristic
787C2#2024602811yescharacteristic
788C2#2024603011yescharacteristic
789C2#2024607812yes—
790C2#2024608012yes—
791C2#2024609412yes—
792C2#2024610912yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC22⋊#95D47
hypocenterC47#13785
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#15688974C2semidirect
4. C2×#15688968C2semidirect
5. #20241625C2semidirect
6. #20241624C2semidirect
7. Dic47⋊#95C2semidirect
8. #20241611C2semidirect
9. (C2×D47)⋊#95C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C47×C22⋊#95C2semidirect
16. C2×C4×C22⋊D47C4semidirect
27. #15689023C4semidirect
63. C2×Dic47⋊C4C2×C4semidirect
69. C2×C22⋊Dic47C2×C4semidirect
77. C2×(C2×D47)⋊C4C2×C4semidirect
78. C2×(C2×D47)⋊C4C2×C4semidirect
85. C2×C4×Dic47C2×C4semidirect
106. C2×C22⋊C4×C47C2×C4semidirect
166. C2×C22⋊D47C42semidirect
213. C4×Dic47C22⋊C4semidirect
394. C22⋊#95D47semidirect
437. C47#13785semidirect
488. 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×C4×C22⋊D472
C2×#156890232
C2×#156889742
C2×#156889682
#202416252
#202416242
Dic47⋊#952
#202416112
(C2×D47)⋊#952
C47×C22⋊#952
#1378547