Finite Group Databasebeta

← #26139075

Subgroups — #26139075

Order 12032.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094000C211yesmaximal, characteristic
2C22×Q8×Dic47C211yesmaximal, characteristic, complemented
3C2×#15688980C211yesmaximal, characteristic
4C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
5#20241642C212yesmaximal, complemented
6#20241634C212yesmaximal
7#20241624C212yesmaximal
8#20241623C212yesmaximal, complemented
9#20241618C211yesmaximal, characteristic, complemented
10#20241617C211yesmaximal, characteristic, complemented
11C2×C47×#391C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C2×#13094000—24no—
14C2×#13094000—24no—
15C2×#13094000C418yescomplemented
16C2×Q8×Dic47—24no—
17C2×Q8×Dic47—24no—
18C2×Q8×Dic47—24no—
19C22×C4⋊Dic47C2212yes—
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×Dic47⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×(C2×D47)⋊C4C2212yes—
25C22×(C2×D47)⋊C4C2212yes—
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×C4×Dic47C2212yes—
28C22×C4×Dic47C2211yescharacteristic
29#15688980—24no—
30C4×(C2×D47)⋊C4—24no—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2212yes—
37C2×C47⋊#95C2212yes—
38C23×Q8×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic
41C47×#391—24no—
42C2×#95×C47C2212yes—
43C2×#95×C47C2212yes—
44C24×D47C2311yescharacteristic
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C23×Dic47C2312yes—
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2311yescharacteristic
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47—22no—
54C22×C4×D47—22no—
55C22×C4×D47—22no—
56C22×C4×D47C2×C414yes—
57#13094000—232no—
58Q8×Dic47—232no—
59C2×C4⋊Dic47—24no—
60C2×C4⋊Dic47—22no—
61C2×C4⋊Dic47—22no—
62C2×C4⋊Dic47—22no—
63C2×C4⋊Dic47—22no—
64C2×C4⋊Dic47—24no—
65C2×C4⋊Dic47—24no—
66C2×C4⋊Dic47C2×C414yes—
67C2×C4⋊Dic47D414yes—
68C2×Dic47⋊C4—24no—
69C2×Dic47⋊C4—24no—
70C2×Dic47⋊C4C2×C418yes—
71C2×(C2×D47)⋊C4—22no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—24no—
74C2×(C2×D47)⋊C4—22no—
75C2×(C2×D47)⋊C4—22no—
76C2×(C2×D47)⋊C4—22no—
77C2×(C2×D47)⋊C4—22no—
78C2×(C2×D47)⋊C4—24no—
79C2×(C2×D47)⋊C4—24no—
80C2×(C2×D47)⋊C4—42no—
81C2×(C2×D47)⋊C4C2×C418yes—
82C2×(C2×D47)⋊C4Q814yescomplemented
83C2×C4×Dic47—24no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47—24no—
87C2×C4×Dic47—24no—
88C2×C4×Dic47D414yes—
89C47⋊#95—24no—
90C47⋊#95—22no—
91C47⋊#95—22no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—42no—
95C47⋊#95—42no—
96C22×Q8×C47—22no—
97C22×Q8×C47—22no—
98C22×Q8×C47—22no—
99C22×Q8×C47—22no—
100C22×Q8×C47C2×C414yes—
101C22×Q8×C47D414yes—
102C22×Q8×C47D414yes—
103C23×C4×C47C2312yes—
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2312yes—
107C23×C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47—22no—
109C2×C4⋊C4×C47—22no—
110C2×C4⋊C4×C47—22no—
111C2×C42×C47—22no—
112C2×C42×C47—22no—
113C2×C42×C47—22no—
114#95×C47—24no—
115#95×C47—24no—
116C24×C47C2411yescharacteristic
117C23×D47—21no—
118C23×D47—21no—
119C23×D47—21no—
120C23×D47—21no—
121C23×D47—21no—
122C23×D47—21no—
123C23×D47—21no—
124C23×D47—21no—
125C23×D47—21no—
126C23×D47—21no—
127C23×D47—21no—
128C23×D47—21no—
129C23×D47C22×C412yes—
130C23×D47C2×Q812yes—
131C23×D47#4112yes—
132C2×Q8×C47—28no—
133C2×Q8×C47—28no—
134C2×Q8×C47—28no—
135C2×Q8×C47—28no—
136C2×Q8×C47—28no—
137C2×Q8×C47—28no—
138C2×Q8×C47C22⋊C4116yescomplemented
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47C22×C414yes—
163C22×C4×C47C22×C412yes—
164C22×C4×C47C2×D414yes—
165C22×C4×C47C2×D414yes—
166C22×C4×C47C2×D412yes—
167C22×C4×C47C2×D412yes—
168C22×C4×C47C2×D412yes—
169C22×C4×C47C2×D412yes—
170C22×C4×C47C2×Q812yes—
171C22×C4×C47#4112yes—
172C22×C4×C47#4112yes—
173C22×C4×C47#4112yes—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—22no—
181C22×Dic47—21no—
182C22×Dic47—22no—
183C22×Dic47—21no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—22no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—22no—
197C22×Dic47—21no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—21no—
201C22×Dic47—22no—
202C22×Dic47C22×C414yes—
203C22×Dic47C22×C412yes—
204C22×Dic47C2×D414yes—
205C22×Dic47C2×D412yes—
206C22×Dic47C2×D412yes—
207C22×Dic47C2×Q812yes—
208C22×Dic47#4112yes—
209C2×C4×D47—28no—
210C2×C4×D47—28no—
211C2×C4×D47—28no—
212C2×C4×D47—44no—
213C2×C4×D47—44no—
214C2×C4×D47—44no—
215C2×C4×D47—44no—
216C4⋊C4×C47—44no—
217C42×C47—44no—
218(C2×D47)⋊C4—28no—
219(C2×D47)⋊C4—216no—
220(C2×D47)⋊C4—28no—
221(C2×D47)⋊C4—48no—
222C4⋊Dic47—216no—
223C4⋊Dic47—28no—
224C4⋊Dic47—28no—
225Dic47⋊C4—216no—
226C4×Dic47—216no—
227C4×Dic47—28no—
228C23×C47C23×C411yescharacteristic
229C23×C47C22×D411yescharacteristic
230C23×C47C22×D411yescharacteristic
231C23×C47C22×D411yescharacteristic
232C23×C47C22×D411yescharacteristic
233C23×C47C22×Q811yescharacteristic
234C23×C47C2×#4111yescharacteristic
235C23×C47C2×#4111yescharacteristic
236C23×C47C2×#4111yescharacteristic
237C23×C47C2×#4111yescharacteristic
238C23×C47C2×#4111yescharacteristic
239C23×C47H(5,𝔽2)11yescharacteristic
240C23×C472−1+411yescharacteristic
241C23×C472−1+411yescharacteristic
242C23×C472−1+411yescharacteristic
243C22×D47—22no—
244C22×D47—22no—
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—22no—
254C22×D47—22no—
255C22×D47—22no—
256C22×D47—22no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—41no—
262C22×D47—41no—
263C22×D47—41no—
264C22×D47—41no—
265C22×D47—41no—
266C22×D47—41no—
267C22×D47—41no—
268C22×D47—41no—
269C22×D47—41no—
270C22×D47—41no—
271C22×D47—41no—
272C22×D47—41no—
273C22×D47—41no—
274C22×D47—41no—
275C22×D47—41no—
276C22×D47—41no—
277C22×D47C4×Q814yescomplemented
278Q8×C47—232no—
279C2×C4×C47—24no—
280C2×C4×C47—24no—
281C2×C4×C47—24no—
282C2×C4×C47—24no—
283C2×C4×C47—24no—
284C2×C4×C47—24no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
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×C47C2×C22⋊C418yes—
307C2×C4×C47C2×C22⋊C414yes—
308C2×C4×C47C4×D414yes—
309C2×C4×C47C4×D414yes—
310C2×C4×C47#12014yes—
311C2×C4×C47#12114yes—
312C2×C4×C47#12114yes—
313C2×C4×C47#12314yes—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—24no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—24no—
325C2×Dic47—24no—
326C2×Dic47—24no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—24no—
331C2×Dic47—24no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—41no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—41no—
348C2×Dic47C22⋊Q814yescomplemented
349C4×D47—416no—
350#13969—471nomaximal, Sylow
351C22×C47C22×C22⋊C411yescharacteristic
352C22×C47C2×C4×D411yescharacteristic
353C22×C47C2×C4×D411yescharacteristic
354C22×C47C2×C4×Q811yescharacteristic
355C22×C47C4×#4111yescharacteristic
356C22×C47#51911yescharacteristic
357C22×C47#52011yescharacteristic
358C22×C47C2×#12011yescharacteristic
359C22×C47C2×#12111yescharacteristic
360C22×C47C2×#12111yescharacteristic
361C22×C47C2×C22⋊Q811yescharacteristic
362C22×C47C2×#12311yescharacteristic
363C22×C47#52511yescharacteristic
364C22×C47#52911yescharacteristic
365C22×C47#53311yescharacteristic
366C22×C47#53611yescharacteristic
367C22×C47#53711yescharacteristic
368C22×C47#54111yescharacteristic
369C22×C47#54211yescharacteristic
370C22×C47#54611yescharacteristic
371C22×C47#54711yescharacteristic
372C22×C47#54811yescharacteristic
373C22×C47#54811yescharacteristic
374C22×C47#54811yescharacteristic
375C22×C47#54811yescharacteristic
376C22×C47#54811yescharacteristic
377C22×C47D4×Q811yescharacteristic
378C22×C47D4×Q811yescharacteristic
379C22×C47D4×Q811yescharacteristic
380C22×C47#55011yescharacteristic
381C22×C47#55011yescharacteristic
382C22×C47#55211yescharacteristic
383C22×C47#55211yescharacteristic
384C22×C47#55411yescharacteristic
385C22×C47#55611yescharacteristic
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—24no—
389C2×D47—42no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C4×C47—28no—
402C4×C47—42no—
403C4×C47—42no—
404C4×C47—82no—
405C4×C47#38618yes—
406Dic47—24no—
407Dic47—44no—
408Dic47—42no—
409Dic47—44no—
410Dic47—42no—
411C22×C22⋊Q8—471no—
412C22×C4×Q8—471no—
413C2×#391D4711yescharacteristic, complemented
414C2×#380—471no—
415C2×C4×C22⋊C4—471no—
416#1441—472no—
417#1439—472no—
418#1437—472no—
419#1436—472no—
420C4⋊#95—471no—
421C4⋊#95—471no—
422C2×C47C2×#38611yescharacteristic
423C2×C47C4×C22⋊Q811yescharacteristic
424C2×C47#232311yescharacteristic
425C2×C47Q8×C22⋊C411yescharacteristic
426C2×C47#234111yescharacteristic
427C2×C47#236011yescharacteristic
428C2×C47#236211yescharacteristic
429C2×C47#240711yescharacteristic
430C2×C47#240911yescharacteristic
431C2×C47#242111yescharacteristic
432C2×C47#242311yescharacteristic
433C2×C47#242611yescharacteristic
434C2×C47#242911yescharacteristic
435C2×C47#253611yescharacteristic
436C2×C47#253811yescharacteristic
437D47—44no—
438C23×Q8C2×D4711yescharacteristic
439C24×C4—471no—
440C2×C22⋊Q8—478no—
441C2×C22⋊Q8—944no—
442C2×C22⋊Q8—944no—
443C2×C4×Q8—944no—
444C2×C4×Q8—944no—
445C2×C4×Q8—944no—
446C22×C4⋊C4—471no—
447C22×C4⋊C4—472no—
448C22×C4⋊C4—471no—
449C22×C4⋊C4—472no—
450C22×C4⋊C4C2×D4711yescharacteristic
451C22×C22⋊C4—472no—
452C22×C22⋊C4—471no—
453C22×C22⋊C4—471no—
454C22×C22⋊C4—472no—
455C22×C42—471no—
456C22×C42—472no—
457C22×C42C2×D4711yescharacteristic
458#391—24no—
459#380—944no—
460C4×C22⋊C4—944no—
461C2×#95—472no—
462C2×#95—472no—
463C2×#95—471no—
464C2×#95—472no—
465C2×#95—471no—
466C2×#95—472no—
467C2×#95—472no—
468C2×#95C2×D4712yes—
469C2×#95C2×D4712yes—
470C47#1396911yescharacteristic, complemented, Sylow
471C25—471no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8C4×D4714yes—
477C22×Q8D18814yes—
478C22×Q8C22⋊D4714yes—
479C23×C4—471no—
480C23×C4—472no—
481C23×C4—471no—
482C23×C4—472no—
483C23×C4—471no—
484C23×C4—474no—
485C23×C4—942no—
486C23×C4—942no—
487C23×C4—942no—
488C23×C4—942no—
489C23×C4—942no—
490C23×C4—942no—
491C23×C4C22×D4712yes—
492C23×C4C22×D4711yescharacteristic
493C23×C4C22×D4711yescharacteristic
494C23×C4C22×D4712yes—
495C23×C4C22×D4711yescharacteristic
496C22⋊Q8—9432no—
497C4×Q8—9432no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—478no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—944no—
505C2×C4⋊C4—944no—
506C2×C4⋊C4—944no—
507C2×C4⋊C4—942no—
508C2×C4⋊C4—944no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—942no—
511C2×C4⋊C4—944no—
512C2×C4⋊C4—942no—
513C2×C22⋊C4—478no—
514C2×C22⋊C4—474no—
515C2×C22⋊C4—942no—
516C2×C22⋊C4—942no—
517C2×C22⋊C4—942no—
518C2×C22⋊C4—942no—
519C2×C22⋊C4—944no—
520C2×C22⋊C4—942no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—944no—
524C2×C22⋊C4—1882no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—474no—
529C2×C42—944no—
530C2×C42—944no—
531C2×C42—944no—
532C2×C42—942no—
533C2×C42—942no—
534#95—24no—
535#95—24no—
536#95—944no—
537#95—942no—
538#95—942no—
539#95—944no—
540#95—944no—
541#95—1882no—
542#95—1882no—
543C24—472no—
544C24—472no—
545C24—472no—
546C24—941no—
547C24—941no—
548C24—941no—
549C24—941no—
550C24—941no—
551C24—941no—
552C24—941no—
553C24—941no—
554C24—941no—
555C24—941no—
556C24—941no—
557C24—941no—
558C24C23×D4711yescharacteristic
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—28no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8—28no—
565C2×Q8(C2×D47)⋊C4116yescomplemented
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—472no—
590C22×C4—472no—
591C22×C4—472no—
592C22×C4—474no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—474no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—941no—
606C22×C4—942no—
607C22×C4—941no—
608C22×C4—942no—
609C22×C4—941no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—941no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—941no—
618C22×C4—942no—
619C22×C4—941no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—942no—
623C22×C4—941no—
624C22×C4—948no—
625C22×C4—948no—
626C22×C4—948no—
627C22×C4—1884no—
628C22×C4—1884no—
629C22×C4—1884no—
630C22×C4—1884no—
631C22×C4C2×C4×D4714yes—
632C22×C4C2×C4×D4712yes—
633C22×C4C2×D18814yes—
634C22×C4C2×D18812yes—
635C22×C4D4×D4712yes—
636C22×C4D4×D4712yes—
637C22×C4#1062535212yes—
638C22×C4#1062535212yes—
639C22×C4Q8×D4712yes—
640C22×C4#1062535412yes—
641C22×C4C2×C22⋊D4714yes—
642C22×C4C2×C22⋊D4712yes—
643C4⋊C4—44no—
644C4⋊C4—9416no—
645C4⋊C4—9416no—
646C4⋊C4—948no—
647C4⋊C4—948no—
648C22⋊C4—948no—
649C22⋊C4—948no—
650C22⋊C4—9416no—
651C22⋊C4—1888no—
652C42—44no—
653C42—9416no—
654C42—948no—
655C23—474no—
656C23—942no—
657C23—942no—
658C23—942no—
659C23—942no—
660C23—942no—
661C23—942no—
662C23—942no—
663C23—942no—
664C23—942no—
665C23—942no—
666C23—942no—
667C23—942no—
668C23—942no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—942no—
673C23—942no—
674C23—1881no—
675C23—1881no—
676C23—1881no—
677C23—1881no—
678C23—1881no—
679C23—1881no—
680C23—1881no—
681C23—1881no—
682C23—1881no—
683C23—1881no—
684C23—1881no—
685C23—1881no—
686C23—1881no—
687C23—1881no—
688C23—1881no—
689C23—1881no—
690C23C22×C4×D4711yescharacteristic
691C23C2×D4×D4711yescharacteristic
692C23C2×D4×D4711yescharacteristic
693C23C22×C22⋊D4711yescharacteristic
694C23C22×D18811yescharacteristic
695C23C2×Q8×D4711yescharacteristic
696C23#41×D4711yescharacteristic
697C23#41×D4711yescharacteristic
698C23C2×#1062535211yescharacteristic
699C23C2×#1062535211yescharacteristic
700C23C2×#1062535411yescharacteristic
701C23#1309407011yescharacteristic
702C23#1309407111yescharacteristic
703C23#1309407211yescharacteristic
704C23#1309407211yescharacteristic
705Q8—232no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—474no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—944no—
741C2×C4—944no—
742C2×C4—944no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—944no—
747C2×C4—944no—
748C2×C4—944no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—1881no—
753C2×C4—1881no—
754C2×C4—1882no—
755C2×C4—1882no—
756C2×C4—1881no—
757C2×C4—1882no—
758C2×C4—1882no—
759C2×C4—1882no—
760C2×C4—1881no—
761C2×C4—1882no—
762C2×C4—1881no—
763C2×C4—1881no—
764C2×C4—1881no—
765C2×C4—1881no—
766C2×C4—1882no—
767C2×C4—1882no—
768C2×C4—18816no—
769C2×C4C2×(C2×D47)⋊C418yes—
770C2×C4C2×(C2×D47)⋊C414yes—
771C2×C4(C22⋊D47)⋊C414yes—
772C2×C4(C22⋊D47)⋊C414yes—
773C2×C4#1309399414yes—
774C2×C4#1309399614yes—
775C2×C4#1309399614yes—
776C2×C4#1309400814yes—
777C22—944no—
778C22—944no—
779C22—944no—
780C22—1882no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22—1882no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22—1882no—
790C22—1882no—
791C22—1882no—
792C22C22×(C2×D47)⋊C411yescharacteristic
793C22C2×(C22⋊D47)⋊C411yescharacteristic
794C22C2×(C22⋊D47)⋊C411yescharacteristic
795C22C4×Q8×D4711yescharacteristic
796C22C4×#1062535411yescharacteristic
797C22#1568959911yescharacteristic
798C22#1568960511yescharacteristic
799C22C2×#1309399411yescharacteristic
800C22C2×#1309399611yescharacteristic
801C22C2×#1309399611yescharacteristic
802C22C22⋊Q8×D4711yescharacteristic
803C22C2×#1309400811yescharacteristic
804C22#1568963611yescharacteristic
805C22#1568965211yescharacteristic
806C22#1568967811yescharacteristic
807C22#1568969611yescharacteristic
808C22#1568970311yescharacteristic
809C22#1568973411yescharacteristic
810C22#1568974211yescharacteristic
811C22#1568976611yescharacteristic
812C22#1568977611yescharacteristic
813C22#1568978011yescharacteristic
814C22#1568978111yescharacteristic
815C22#1568978411yescharacteristic
816C22#1568978511yescharacteristic
817C22#1568978511yescharacteristic
818C22Q8×C22⋊D4711yescharacteristic
819C22#1568978811yescharacteristic
820C22Q8×D18811yescharacteristic
821C22#1568979211yescharacteristic
822C22#1568979511yescharacteristic
823C22#1568980711yescharacteristic
824C22#1568981511yescharacteristic
825C22#1568983111yescharacteristic
826C22#1568984411yescharacteristic
827C4—28no—
828C4—42no—
829C4—42no—
830C4—82no—
831C4—944no—
832C4—1882no—
833C4—1884no—
834C4—1882no—
835C4—1884no—
836C4#1568900018yes—
837C2—1884no—
838C2C2×#1568900011yescharacteristic
839C2#2024592611yescharacteristic
840C2#2024607311yescharacteristic
841C2Q8×(C2×D47)⋊C411yescharacteristic
842C2#2024622611yescharacteristic
843C2#2024639811yescharacteristic
844C2#2024642011yescharacteristic
845C2#2024673611yescharacteristic
846C2#2024675111yescharacteristic
847C2#2024688911yescharacteristic
848C2#2024691111yescharacteristic
849C2#2024695711yescharacteristic
850C2#2024699011yescharacteristic
851C2#2024829511yescharacteristic
852C2#2024830711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#391C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#391D47
hypocenterC47#13969
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic47C2semidirect
5. #20241642C2semidirect
8. #20241623C2semidirect
9. #20241618C2semidirect
10. #20241617C2semidirect
11. C2×C47×#391C2semidirect
15. C2×#13094000C4semidirect
82. C2×(C2×D47)⋊C4Q8semidirect
138. C2×Q8×C47C22⋊C4semidirect
277. C22×D47C4×Q8semidirect
348. C2×Dic47C22⋊Q8semidirect
413. C2×#391D47semidirect
470. C47#13969semidirect
565. C2×Q8(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130940002
C22×Q8×Dic472
C2×#156889802
C2×C4×(C2×D47)⋊C42
#202416422
#202416342
#202416242
#202416232
#202416182
#202416172
C2×C47×#3912
#1396947