Finite Group Databasebeta

← #26121558

Subgroups — #26121558

Order 12032.

1518 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093982C211yesmaximal, characteristic
2C22×(C2×D47)⋊C8C211yesmaximal, characteristic
3C2×#15688980C211yesmaximal, characteristic
4C2×#15688886C211yesmaximal, characteristic, complemented
5C2×#15688885C211yesmaximal, characteristic, complemented
6C2×#15688885C211yesmaximal, characteristic, complemented
7C2×C47×#340C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C23×C47⋊C8C2211yescharacteristic
10C2×#13093982—22no—
11C2×#13093982—22no—
12C2×#13093982—22no—
13C2×#13093982—22no—
14C2×#13093982—22no—
15C2×#13093982C414yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×(C2×D47)⋊C4—21no—
19C22×(C2×D47)⋊C4—21no—
20C22×C4×Dic47—21no—
21C2×(C2×D47)⋊C8—22no—
22C2×(C2×D47)⋊C8—22no—
23C2×(C2×D47)⋊C8C414yescomplemented
24#15688980—22no—
25#15688980C414yescomplemented
26C2×C47⋊#95—21no—
27#15688886—22no—
28#15688885—22no—
29#15688885—22no—
30C23×C8×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C47×#340—22no—
34C24×D47D411yescharacteristic
35C23×Dic47—21no—
36C23×Dic47—21no—
37C23×Dic47D411yescharacteristic
38C22×C4×D47—21no—
39C22×C4×D47—21no—
40C22×C4×D47—21no—
41C22×C4×D47—21no—
42C22×C4×D47—21no—
43C22×C4×D47—21no—
44C22×C4×D47—21no—
45C22×C4×D47—21no—
46C22×C4×D47C2×C412yes—
47C22×C4×D47C2×C412yes—
48C22×C4×D47C2×C412yes—
49C22×C4×D47D412yes—
50C22×C4×D47D412yes—
51C22×C4×D47Q812yes—
52C22×C47⋊C8—21no—
53C22×C47⋊C8—21no—
54C22×C47⋊C8—21no—
55C22×C47⋊C8—21no—
56C22×C47⋊C8—21no—
57C22×C47⋊C8—21no—
58C22×C47⋊C8C2×C412yes—
59#13093982—28no—
60#13093982—28no—
61#13093982—28no—
62#13093982—28no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47—21no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47C2×C412yes—
72C2×C4⋊Dic47C2×C412yes—
73C2×C4⋊Dic47D412yes—
74C2×C4⋊Dic47D412yes—
75C2×(C2×D47)⋊C4—24no—
76C2×(C2×D47)⋊C4—24no—
77C2×(C2×D47)⋊C4—24no—
78C2×(C2×D47)⋊C4—24no—
79C2×(C2×D47)⋊C4—42no—
80C2×(C2×D47)⋊C4—42no—
81C2×C4×Dic47—24no—
82C2×C4×Dic47—24no—
83C2×C4×Dic47—24no—
84(C2×D47)⋊C8—28no—
85C47⋊#95—24no—
86C23×C4×C47—21no—
87C23×C4×C47—21no—
88C23×C4×C47C2311yescharacteristic
89C22×C8×C47—21no—
90C22×C8×C47—21no—
91C22×C8×C47—21no—
92C22×C8×C47—21no—
93C22×C8×C47—21no—
94C22×C8×C47—21no—
95C22×C8×C47C2×C412yes—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47C2×C412yes—
105C2×C4⋊C4×C47C2×C412yes—
106C2×C4⋊C4×C47D412yes—
107C2×C4⋊C4×C47D412yes—
108C24×C47C2×D411yescharacteristic
109C23×D47—21no—
110C23×D47—21no—
111C23×D47—21no—
112C23×D47—21no—
113C23×D47—21no—
114C23×D47—21no—
115C23×D47—21no—
116C23×D47—21no—
117C23×D47—21no—
118C23×D47—21no—
119C23×D47—21no—
120C23×D47—21no—
121C23×D47C22⋊C412yes—
122C23×D47C22⋊C412yes—
123C23×D47C4⋊C412yes—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—41no—
129C22×C4×C47—41no—
130C22×C4×C47—41no—
131C22×C4×C47—41no—
132C22×C4×C47—41no—
133C22×C4×C47—41no—
134C22×C4×C47—41no—
135C22×C4×C47—41no—
136C22×C4×C47—41no—
137C22×C4×C47—41no—
138C22×C4×C47C22×C411yescharacteristic
139C22×C4×C47C22×C411yescharacteristic
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×Q811yescharacteristic
148C22×C4×C47#4111yescharacteristic
149C22×C4×C47#4111yescharacteristic
150C22×C4×C47#4111yescharacteristic
151C22×C4×C47#4111yescharacteristic
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—41no—
161C22×Dic47—41no—
162C22×Dic47—41no—
163C22×Dic47—41no—
164C22×Dic47—41no—
165C22×Dic47—41no—
166C22×Dic47—41no—
167C22×Dic47—41no—
168C22×Dic47—41no—
169C22×Dic47—41no—
170C22×Dic47C22⋊C412yes—
171C22×Dic47C22⋊C412yes—
172C22×Dic47C4⋊C412yes—
173C2×C4×D47—22no—
174C2×C4×D47—22no—
175C2×C4×D47—22no—
176C2×C4×D47—22no—
177C2×C4×D47—22no—
178C2×C4×D47—22no—
179C2×C4×D47—22no—
180C2×C4×D47—22no—
181C2×C4×D47—22no—
182C2×C4×D47—22no—
183C2×C4×D47—22no—
184C2×C4×D47—22no—
185C2×C4×D47—22no—
186C2×C4×D47—22no—
187C2×C4×D47—22no—
188C2×C4×D47—22no—
189C2×C4×D47—22no—
190C2×C4×D47—22no—
191C2×C4×D47—22no—
192C2×C4×D47—22no—
193C2×C4×D47—22no—
194C2×C4×D47—22no—
195C2×C4×D47—22no—
196C2×C4×D47—22no—
197C2×C4×D47C4214yes—
198C2×C4×D47C22⋊C414yes—
199C2×C4×D47C4⋊C414yes—
200C2×C4×D47C4⋊C414yes—
201C2×C8×C47—22no—
202C2×C8×C47—22no—
203C2×C8×C47—22no—
204C2×C8×C47—41no—
205C2×C8×C47—41no—
206C2×C8×C47—41no—
207C2×C8×C47—41no—
208C4⋊C4×C47—22no—
209C4⋊C4×C47—22no—
210C4⋊C4×C47—22no—
211C4⋊C4×C47—22no—
212C4⋊C4×C47—22no—
213C4⋊C4×C47—41no—
214C4⋊C4×C47—41no—
215C4⋊C4×C47C22⋊C414yescomplemented
216(C2×D47)⋊C4—216no—
217(C2×D47)⋊C4—48no—
218C4⋊Dic47—22no—
219C4⋊Dic47—22no—
220C4⋊Dic47—22no—
221C4⋊Dic47—22no—
222C4⋊Dic47—22no—
223C4⋊Dic47—41no—
224C4⋊Dic47—41no—
225C4⋊Dic47C22⋊C414yescomplemented
226C4×Dic47—216no—
227C2×C47⋊C8—22no—
228C2×C47⋊C8—22no—
229C2×C47⋊C8—22no—
230C2×C47⋊C8—41no—
231C2×C47⋊C8—41no—
232C2×C47⋊C8—41no—
233C2×C47⋊C8—41no—
234C23×C47C2×C22⋊C411yescharacteristic
235C23×C47C2×C22⋊C411yescharacteristic
236C23×C47C2×C4⋊C411yescharacteristic
237C23×C47#12011yescharacteristic
238C23×C47#12011yescharacteristic
239C23×C47#12311yescharacteristic
240C23×C47#12311yescharacteristic
241C23×C47#13511yescharacteristic
242C23×C47#13511yescharacteristic
243C23×C47#13511yescharacteristic
244C23×C47#13511yescharacteristic
245C23×C47AGL(1,ℤ/8)11yescharacteristic
246C23×C47AGL(1,ℤ/8)11yescharacteristic
247C23×C47#13711yescharacteristic
248C23×C47#13711yescharacteristic
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—22no—
262C22×D47—22no—
263C22×D47—22no—
264C22×D47—22no—
265C22×D47—22no—
266C22×D47—22no—
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×D47—41no—
278C22×D47—41no—
279C22×D47—41no—
280C22×D47—41no—
281C22×D47—41no—
282C22×D47—41no—
283C22×D47#9514yes—
284C2×C4×C47—24no—
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—81no—
295C2×C4×C47—81no—
296C2×C4×C47—81no—
297C2×C4×C47—81no—
298C2×C4×C47C2×C4211yescharacteristic
299C2×C4×C47C2×C22⋊C411yescharacteristic
300C2×C4×C47C2×C22⋊C411yescharacteristic
301C2×C4×C47C2×C22⋊C411yescharacteristic
302C2×C4×C47C2×C4⋊C411yescharacteristic
303C2×C4×C47C2×C4⋊C411yescharacteristic
304C2×C4×C47#11711yescharacteristic
305C2×C4×C47#11711yescharacteristic
306C2×C4×C47C4×D411yescharacteristic
307C2×C4×C47C4×D411yescharacteristic
308C2×C4×C47C4×D411yescharacteristic
309C2×C4×C47C4×D411yescharacteristic
310C2×C4×C47C4×D411yescharacteristic
311C2×C4×C47C4×D411yescharacteristic
312C2×C4×C47C4×D411yescharacteristic
313C2×C4×C47C4×D411yescharacteristic
314C2×C4×C47#12011yescharacteristic
315C2×C4×C47#12011yescharacteristic
316C2×C4×C47#12111yescharacteristic
317C2×C4×C47#12111yescharacteristic
318C2×C4×C47#12111yescharacteristic
319C2×C4×C47#12111yescharacteristic
320C2×C4×C47C22⋊Q811yescharacteristic
321C2×C4×C47C22⋊Q811yescharacteristic
322C2×C4×C47C22⋊Q811yescharacteristic
323C2×C4×C47C22⋊Q811yescharacteristic
324C2×C4×C47#12311yescharacteristic
325C2×C4×C47#12311yescharacteristic
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—24no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—81no—
343C2×Dic47—81no—
344C2×Dic47—81no—
345C2×Dic47—81no—
346C2×Dic47#9514yes—
347C4×D47—24no—
348C4×D47—24no—
349C4×D47—24no—
350C4×D47—24no—
351C4×D47—24no—
352C4×D47—24no—
353C4×D47—24no—
354C4×D47—24no—
355C8×C47—42no—
356C47⋊C8—42no—
357#10731—471nomaximal, Sylow
358C22×C47C2×#9511yescharacteristic
359C22×C47#37911yescharacteristic
360C22×C47#38111yescharacteristic
361C22×C47#38511yescharacteristic
362C22×C47#38511yescharacteristic
363C22×C47#38611yescharacteristic
364C22×C47#38611yescharacteristic
365C22×C47#41611yescharacteristic
366C22×C47#41611yescharacteristic
367C22×C47#41611yescharacteristic
368C22×C47#41611yescharacteristic
369C22×C47#41711yescharacteristic
370C22×C47#41711yescharacteristic
371C22×C47#41811yescharacteristic
372C22×C47#41911yescharacteristic
373C22×C47#42711yescharacteristic
374C22×C47#42711yescharacteristic
375C22×C47#42811yescharacteristic
376C22×C47#42811yescharacteristic
377C22×C47#44911yescharacteristic
378C22×C47#44911yescharacteristic
379C22×C47#44911yescharacteristic
380C22×C47#44911yescharacteristic
381C22×C47#45211yescharacteristic
382C22×C47#45211yescharacteristic
383C22×C47#45211yescharacteristic
384C22×C47#45211yescharacteristic
385C22×C47#48211yescharacteristic
386C22×C47#48211yescharacteristic
387C22×C47#48211yescharacteristic
388C22×C47#48211yescharacteristic
389C22×C47#48511yescharacteristic
390C22×C47#48511yescharacteristic
391C22×C47#48511yescharacteristic
392C22×C47#48511yescharacteristic
393C2×D47—24no—
394C2×D47—24no—
395C2×D47—24no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—42no—
403C2×D47—42no—
404C2×D47—42no—
405C2×D47—42no—
406C2×D47—42no—
407C2×D47—42no—
408C4×C47—44no—
409C4×C47—82no—
410C4×C47C4×C22⋊C411yescharacteristic
411C4×C47C4×C22⋊C411yescharacteristic
412C4×C47#38011yescharacteristic
413C4×C47#38011yescharacteristic
414C4×C47#38511yescharacteristic
415C4×C47#38511yescharacteristic
416C4×C47#38611yescharacteristic
417C4×C47#38611yescharacteristic
418Dic47—24no—
419Dic47—44no—
420Dic47—82no—
421C22×#117—471no—
422C22×C22⋊C8—471no—
423C2×#380—471no—
424C2×#340—471no—
425C2×#340—471no—
426C2×#340—471no—
427C2×#340D4711yescharacteristic, complemented
428C2×C47C22⋊#9511yescharacteristic
429C2×C47#173511yescharacteristic
430C2×C47#173611yescharacteristic
431C2×C47#178811yescharacteristic
432C2×C47#178811yescharacteristic
433C2×C47#182511yescharacteristic
434C2×C47#182511yescharacteristic
435C2×C47#185411yescharacteristic
436C2×C47#185411yescharacteristic
437C2×C47#185411yescharacteristic
438C2×C47#185411yescharacteristic
439C2×C47#187311yescharacteristic
440C2×C47#187311yescharacteristic
441C2×C47#187511yescharacteristic
442C2×C47#187511yescharacteristic
443D47—44no—
444C24×C4—471no—
445C23×C8—471no—
446C23×C8C2×D4711yescharacteristic
447C2×#117—474no—
448C2×#117—942no—
449C2×#117—942no—
450C2×#117—942no—
451C2×#117—942no—
452C2×#117—942no—
453C22×C4⋊C4—471no—
454C22×C4⋊C4—471no—
455C22×C4⋊C4C2×D4711yescharacteristic
456C22×C4⋊C4C2×D4711yescharacteristic
457C22×C22⋊C4—941no—
458C22×C22⋊C4—941no—
459C22×C42—941no—
460C2×C22⋊C8—474no—
461C2×C22⋊C8—942no—
462C2×C22⋊C8—942no—
463#380—474no—
464#380—942no—
465C2×#95—941no—
466#340—22no—
467#340—942no—
468#340—942no—
469#340—942no—
470C47#1073111yescharacteristic, complemented, Sylow
471C25—471no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—471no—
475C23×C4—472no—
476C23×C4—472no—
477C23×C4—472no—
478C23×C4—472no—
479C23×C4—472no—
480C23×C4—472no—
481C23×C4—941no—
482C23×C4—941no—
483C23×C4—941no—
484C23×C4—941no—
485C23×C4—941no—
486C23×C4—941no—
487C23×C4—941no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4C22×D4711yescharacteristic
492C22×C8—21no—
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—21no—
498C22×C8—472no—
499C22×C8—941no—
500C22×C8—941no—
501C22×C8—941no—
502C22×C8—941no—
503C22×C8—941no—
504C22×C8—941no—
505C22×C8C4×D4712yes—
506#117—948no—
507#117—948no—
508#117—948no—
509#117—948no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—472no—
519C2×C4⋊C4—472no—
520C2×C4⋊C4—472no—
521C2×C4⋊C4—472no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4C4×D4712yes—
531C2×C4⋊C4C4×D4712yes—
532C2×C4⋊C4D18812yes—
533C2×C4⋊C4C22⋊D4712yes—
534C2×C22⋊C4—944no—
535C2×C22⋊C4—944no—
536C2×C22⋊C4—944no—
537C2×C22⋊C4—944no—
538C2×C22⋊C4—1882no—
539C2×C22⋊C4—1882no—
540C2×C42—944no—
541C2×C42—944no—
542C2×C42—944no—
543C22⋊C8—948no—
544#95—944no—
545C24—472no—
546C24—472no—
547C24—472no—
548C24—941no—
549C24—941no—
550C24—941no—
551C24—941no—
552C24—941no—
553C24—941no—
554C24—941no—
555C24—941no—
556C24—941no—
557C24—941no—
558C24—941no—
559C24—941no—
560C24D4×D4711yescharacteristic
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—472no—
576C22×C4—472no—
577C22×C4—472no—
578C22×C4—474no—
579C22×C4—474no—
580C22×C4—474no—
581C22×C4—474no—
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—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—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—1881no—
615C22×C4—1881no—
616C22×C4—1881no—
617C22×C4—1881no—
618C22×C4—1881no—
619C22×C4—1881no—
620C22×C4—1881no—
621C22×C4—1881no—
622C22×C4—1881no—
623C22×C4—1881no—
624C22×C4C2×C4×D4711yescharacteristic
625C22×C4C2×C4×D4711yescharacteristic
626C22×C4C2×C4×D4711yescharacteristic
627C22×C4C2×D18811yescharacteristic
628C22×C4#1062535011yescharacteristic
629C22×C4#1062535011yescharacteristic
630C22×C4D4×D4711yescharacteristic
631C22×C4D4×D4711yescharacteristic
632C22×C4D4×D4711yescharacteristic
633C22×C4D4×D4711yescharacteristic
634C22×C4#1062535211yescharacteristic
635C22×C4Q8×D4711yescharacteristic
636C22×C4#1062535411yescharacteristic
637C22×C4C2×C22⋊D4711yescharacteristic
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—942no—
646C2×C8—942no—
647C2×C8—942no—
648C2×C8—1881no—
649C2×C8—1881no—
650C2×C8—1881no—
651C2×C8—1881no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—474no—
660C4⋊C4—942no—
661C4⋊C4—942no—
662C4⋊C4—942no—
663C4⋊C4—942no—
664C4⋊C4—942no—
665C4⋊C4—1881no—
666C4⋊C4—1881no—
667C4⋊C4(C2×D47)⋊C414yescomplemented
668C22⋊C4—9416no—
669C22⋊C4—1888no—
670C42—9416no—
671C23—474no—
672C23—942no—
673C23—942no—
674C23—942no—
675C23—942no—
676C23—942no—
677C23—942no—
678C23—942no—
679C23—942no—
680C23—942no—
681C23—942no—
682C23—942no—
683C23—942no—
684C23—942no—
685C23—942no—
686C23—942no—
687C23—942no—
688C23—942no—
689C23—942no—
690C23—1881no—
691C23—1881no—
692C23—1881no—
693C23—1881no—
694C23—1881no—
695C23—1881no—
696C23—1881no—
697C23—1881no—
698C23—1881no—
699C23—1881no—
700C23—1881no—
701C23—1881no—
702C23—1881no—
703C23—1881no—
704C23—1881no—
705C23—1881no—
706C23C22⋊C4×D4711yescharacteristic
707C23C22⋊C4×D4711yescharacteristic
708C23C4⋊C4×D4711yescharacteristic
709C23#1309399211yescharacteristic
710C23#1309399411yescharacteristic
711C23#1309400611yescharacteristic
712C23#1309400911yescharacteristic
713C23#1309404311yescharacteristic
714C23#1309404511yescharacteristic
715C23#1309404511yescharacteristic
716C23#1309404711yescharacteristic
717C23#1309404811yescharacteristic
718C23#1309405111yescharacteristic
719C23#1309405311yescharacteristic
720C23#1309405611yescharacteristic
721C2×C4—24no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—474no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—944no—
743C2×C4—944no—
744C2×C4—944no—
745C2×C4—944no—
746C2×C4—944no—
747C2×C4—944no—
748C2×C4—944no—
749C2×C4—944no—
750C2×C4—944no—
751C2×C4—3761no—
752C2×C4—3761no—
753C2×C4—3761no—
754C2×C4—3761no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4—1882no—
758C2×C4—1882no—
759C2×C4—1882no—
760C2×C4—1882no—
761C2×C4—1882no—
762C2×C4—1882no—
763C2×C4—1882no—
764C2×C4C42×D4711yescharacteristic
765C2×C4C22⋊C4×D4711yescharacteristic
766C2×C4C22⋊C4×D4711yescharacteristic
767C2×C4C2×(C2×D47)⋊C411yescharacteristic
768C2×C4C4⋊C4×D4711yescharacteristic
769C2×C4C4⋊C4×D4711yescharacteristic
770C2×C4#1309398111yescharacteristic
771C2×C4#1309398211yescharacteristic
772C2×C4(C22⋊D47)⋊C411yescharacteristic
773C2×C4(C22⋊D47)⋊C411yescharacteristic
774C2×C4C4×C22⋊D4711yescharacteristic
775C2×C4C4×C22⋊D4711yescharacteristic
776C2×C4#1309398611yescharacteristic
777C2×C4#1309398611yescharacteristic
778C2×C4C4×D18811yescharacteristic
779C2×C4C4×D18811yescharacteristic
780C2×C4#1309399211yescharacteristic
781C2×C4#1309399411yescharacteristic
782C2×C4#1309399511yescharacteristic
783C2×C4#1309399711yescharacteristic
784C2×C4#1309399711yescharacteristic
785C2×C4#1309399911yescharacteristic
786C2×C4#1309400011yescharacteristic
787C2×C4#1309400211yescharacteristic
788C2×C4#1309400211yescharacteristic
789C2×C4#1309400411yescharacteristic
790C2×C4#1309400611yescharacteristic
791C2×C4#1309400911yescharacteristic
792C8—42no—
793C8—1882no—
794C22—944no—
795C22—944no—
796C22—944no—
797C22—1882no—
798C22—1882no—
799C22—1882no—
800C22—1882no—
801C22—1882no—
802C22—1882no—
803C22—1882no—
804C22—1882no—
805C22—1882no—
806C22—1882no—
807C22—1882no—
808C22—1882no—
809C22#95×D4711yescharacteristic
810C22#1568897811yescharacteristic
811C22#1568898511yescharacteristic
812C22#1568899411yescharacteristic
813C22#1568899711yescharacteristic
814C22#1568899911yescharacteristic
815C22#1568900111yescharacteristic
816C22#1568911611yescharacteristic
817C22#1568911611yescharacteristic
818C22#1568911811yescharacteristic
819C22#1568911811yescharacteristic
820C22#1568912111yescharacteristic
821C22#1568912311yescharacteristic
822C22#1568912611yescharacteristic
823C22#1568913011yescharacteristic
824C22#1568915811yescharacteristic
825C22#1568916011yescharacteristic
826C22#1568916211yescharacteristic
827C22#1568916411yescharacteristic
828C22#1568926511yescharacteristic
829C22#1568926711yescharacteristic
830C22#1568926911yescharacteristic
831C22#1568927111yescharacteristic
832C22#1568928211yescharacteristic
833C22#1568928411yescharacteristic
834C22#1568928611yescharacteristic
835C22#1568928811yescharacteristic
836C22#1568944511yescharacteristic
837C22#1568944611yescharacteristic
838C22#1568944911yescharacteristic
839C22#1568945011yescharacteristic
840C22#1568946211yescharacteristic
841C22#1568946311yescharacteristic
842C22#1568946611yescharacteristic
843C22#1568946711yescharacteristic
844C4—44no—
845C4—82no—
846C4—944no—
847C4—3762no—
848C4—1884no—
849C4#1568897011yescharacteristic
850C4C4×(C2×D47)⋊C411yescharacteristic
851C4#1568898011yescharacteristic
852C4#1568898211yescharacteristic
853C4#1568899411yescharacteristic
854C4#1568899711yescharacteristic
855C4#1568899911yescharacteristic
856C4#1568900111yescharacteristic
857C2—1884no—
858C2(C2×D47)⋊#9511yescharacteristic
859C2#2024310311yescharacteristic
860C2#2024310611yescharacteristic
861C2#2024332511yescharacteristic
862C2#2024332711yescharacteristic
863C2#2024348111yescharacteristic
864C2#2024348211yescharacteristic
865C2#2024358411yescharacteristic
866C2#2024358611yescharacteristic
867C2#2024358811yescharacteristic
868C2#2024359011yescharacteristic
869C2#2024369711yescharacteristic
870C2#2024369911yescharacteristic
871C2#2024370711yescharacteristic
872C2#2024370911yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socleC24×C47C2×D4
prime radicalC24×D47D4
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#10731
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#15688886C2semidirect
5. C2×#15688885C2semidirect
6. C2×#15688885C2semidirect
7. C2×C47×#340C2semidirect
15. C2×#13093982C4semidirect
23. C2×(C2×D47)⋊C8C4semidirect
25. #15688980C4semidirect
215. C4⋊C4×C47C22⋊C4semidirect
225. C4⋊Dic47C22⋊C4semidirect
427. C2×#340D47semidirect
470. C47#10731semidirect
667. C4⋊C4(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130939822
C22×(C2×D47)⋊C82
C2×#156889802
C2×#156888862
C2×#156888852
C2×C47×#3402
#1073147