Finite Group Databasebeta

← #26137620

Subgroups — #26137620

Order 12032.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689016C211yesmaximal, characteristic
2C2×#15689016C211yesmaximal, characteristic
3C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic47C211yesmaximal, characteristic
5#20241625C211yesmaximal, characteristic
6#20241625C211yesmaximal, characteristic
7#20241622C211yesmaximal, characteristic, complemented
8#20241622C211yesmaximal, characteristic, complemented
9#20241620C211yesmaximal, characteristic, complemented
10#20241620C211yesmaximal, characteristic, complemented
11#20241617C211yesmaximal, characteristic, complemented
12#20241613C211yesmaximal, characteristic, complemented
13#20241611C211yesmaximal, characteristic
14#95×Dic47C211yesmaximal, characteristic, complemented
15C2×C47×#385C211yesmaximal, characteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2211yescharacteristic
19C22×C22⋊Dic47C2211yescharacteristic
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15689016C418yescomplemented
29#15689016C418yescomplemented
30C4⋊C4×Dic47—24no—
31C4×C22⋊Dic47—24no—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C24×C4×C47C2211yescharacteristic
49C22×C4⋊C4×C47C2211yescharacteristic
50C22×C4⋊C4×C47C2211yescharacteristic
51C22×C22⋊C4×C47C2211yescharacteristic
52C22×C22⋊C4×C47C2211yescharacteristic
53C47×#385C418yescomplemented
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—41no—
67C2×C4⋊Dic47—41no—
68C2×C4⋊Dic47C2×C414yescomplemented
69C2×C4⋊Dic47C2×C414yescomplemented
70C2×C22⋊Dic47—22no—
71C2×C22⋊Dic47—22no—
72C2×C22⋊Dic47—22no—
73C2×C22⋊Dic47—22no—
74C2×C22⋊Dic47—41no—
75C2×C22⋊Dic47—41no—
76C2×C22⋊Dic47—41no—
77C2×C22⋊Dic47—41no—
78C2×C22⋊Dic47C2×C414yes—
79C2×C22⋊Dic47C2×C414yes—
80C2×C22⋊Dic47C2×C414yes—
81C2×C22⋊Dic47C2×C414yes—
82C2×C4×Dic47—22no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47—41no—
88C2×C4×Dic47—41no—
89C2×C4×Dic47—41no—
90C2×C4×Dic47—41no—
91C2×C4×Dic47—41no—
92C2×C4×Dic47—41no—
93C2×C4×Dic47—41no—
94C2×C4×Dic47—41no—
95C2×C4×Dic47—41no—
96C2×C4×Dic47—41no—
97C2×C4×Dic47C2×C414yescomplemented
98C2×C4×Dic47C2×C414yescomplemented
99C2×C4×Dic47D414yes—
100C47⋊#95—22no—
101C47⋊#95—22no—
102C47⋊#95—22no—
103C47⋊#95—22no—
104C47⋊#95—22no—
105C47⋊#95—22no—
106C47⋊#95—41no—
107C47⋊#95—41no—
108C47⋊#95—41no—
109C47⋊#95—41no—
110C47⋊#95—41no—
111C47⋊#95—41no—
112C47⋊#95C2×C414yescomplemented
113C47⋊#95C2×C414yescomplemented
114C47⋊#95C2×C414yescomplemented
115C47⋊#95C2×C414yescomplemented
116C25×C47C2311yescharacteristic
117C23×C4×C47—22no—
118C23×C4×C47—22no—
119C23×C4×C47—41no—
120C23×C4×C47—41no—
121C23×C4×C47—41no—
122C23×C4×C47—41no—
123C23×C4×C47C2×C414yes—
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47—22no—
131C2×C4⋊C4×C47—22no—
132C2×C4⋊C4×C47—41no—
133C2×C4⋊C4×C47—41no—
134C2×C4⋊C4×C47C2×C414yes—
135C2×C4⋊C4×C47C2×C414yes—
136C2×C22⋊C4×C47—41no—
137C2×C22⋊C4×C47—41no—
138C2×C22⋊C4×C47C2×C414yes—
139C2×C22⋊C4×C47C2×C414yes—
140C2×C22⋊C4×C47C2×C414yes—
141C2×C22⋊C4×C47C2×C414yes—
142#95×C47C2×C414yes—
143#95×C47C2×C414yes—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47C22×C412yes—
157C24×C47C22×C412yes—
158C24×C47C22×C412yes—
159C24×C47C2411yescharacteristic
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—28no—
191C22×C4×C47—44no—
192C22×C4×C47—44no—
193C22×C4×C47—44no—
194C22×C4×C47—44no—
195C22×C4×C47—44no—
196C22×C4×C47—44no—
197C22×C4×C47C22×C412yes—
198C22×C4×C47C22×C412yes—
199C22×C4×C47C22×C412yes—
200C22×C4×C47C22×C412yes—
201C22×C4×C47C22×C412yes—
202C22×C4×C47C22×C412yes—
203C22×C4×C47C22×C412yes—
204C22×C4×C47C22×C412yes—
205C22×C4×C47C22×C412yes—
206C22×C4×C47C22×C412yes—
207C22×C4×C47C2×D412yes—
208C22×C4×C47#4112yes—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47—21no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47—21no—
253C22×Dic47C22×C412yes—
254C22×Dic47C22×C412yes—
255C22×Dic47C22×C412yes—
256C22×Dic47C22×C412yes—
257C22×Dic47C22×C412yes—
258C22×Dic47C22×C412yes—
259C22×Dic47C22×C412yes—
260C22×Dic47C22×C412yes—
261C22×Dic47C2×D412yes—
262C22×Dic47C2×D412yes—
263C22×Dic47#4112yes—
264C22×Dic47#4112yes—
265C4⋊C4×C47—28no—
266C4⋊C4×C47—44no—
267C22⋊C4×C47—44no—
268C22⋊C4×C47C42116yescomplemented
269C22⋊Dic47—28no—
270C22⋊Dic47—28no—
271C22⋊Dic47—44no—
272C22⋊Dic47—44no—
273C4⋊Dic47—28no—
274C4⋊Dic47—44no—
275C4×Dic47—28no—
276C4×Dic47—44no—
277C4×Dic47—44no—
278C4×Dic47—44no—
279C4×Dic47—44no—
280C4×Dic47—44no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47C2×C4214yes—
316C23×C47C23×C411yescharacteristic
317C23×C47C23×C411yescharacteristic
318C23×C47C23×C411yescharacteristic
319C23×C47C22×D411yescharacteristic
320C23×C47C2×#4111yescharacteristic
321C23×C47C2×#4111yescharacteristic
322C23×C47C2×#4111yescharacteristic
323C23×C47H(5,𝔽2)11yescharacteristic
324C23×C47H(5,𝔽2)11yescharacteristic
325C23×C47H(5,𝔽2)11yescharacteristic
326C23×C47H(5,𝔽2)11yescharacteristic
327C23×C47H(5,𝔽2)11yescharacteristic
328C23×C472−1+411yescharacteristic
329C23×C472−1+411yescharacteristic
330C23×C472−1+411yescharacteristic
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—416no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47C2×C4214yes—
372C2×C4×C47C2×C4214yes—
373C2×C4×C47C4×D414yes—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—41no—
405C2×Dic47—41no—
406C2×Dic47—41no—
407C2×Dic47—41no—
408C2×Dic47—41no—
409C2×Dic47—41no—
410C2×Dic47—41no—
411C2×Dic47—41no—
412C2×Dic47—41no—
413C2×Dic47—41no—
414C2×Dic47—41no—
415C2×Dic47—41no—
416C2×Dic47—41no—
417C2×Dic47—41no—
418C2×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—41no—
421C2×Dic47—41no—
422C2×Dic47—41no—
423C2×Dic47—41no—
424C2×Dic47—41no—
425C2×Dic47—41no—
426C2×Dic47—41no—
427C2×Dic47—41no—
428C2×Dic47C4×D414yes—
429C2×Dic47C4×D414yes—
430#13789—471nomaximal, Sylow
431C22×C47—24no—
432C22×C47—24no—
433C22×C47—24no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47—42no—
439C22×C47—42no—
440C22×C47—42no—
441C22×C47—42no—
442C22×C47—42no—
443C22×C47—42no—
444C22×C47—42no—
445C22×C47—42no—
446C22×C47C22×C4211yescharacteristic
447C22×C47C2×C4×D411yescharacteristic
448C22×C47C2×C4×D411yescharacteristic
449C22×C47C2×C4×D411yescharacteristic
450C22×C47C4×#4111yescharacteristic
451C22×C47C4×#4111yescharacteristic
452C22×C47C4×#4111yescharacteristic
453C22×C47#51811yescharacteristic
454C22×C47#51811yescharacteristic
455C22×C47#51811yescharacteristic
456C22×C47#51811yescharacteristic
457C22×C47#51911yescharacteristic
458C22×C47#52011yescharacteristic
459C22×C47#52011yescharacteristic
460C22×C47#52011yescharacteristic
461C22×C47#52011yescharacteristic
462C22×C47#52011yescharacteristic
463C22×C47#52011yescharacteristic
464C22×C47#52011yescharacteristic
465C22×C47#53411yescharacteristic
466C22×C47#53511yescharacteristic
467C22×C47#53611yescharacteristic
468C22×C47#53711yescharacteristic
469C22×C47#53811yescharacteristic
470C22×C47#53811yescharacteristic
471C22×C47#53811yescharacteristic
472C22×C47#53911yescharacteristic
473C22×C47#53911yescharacteristic
474C22×C47#53911yescharacteristic
475C22×C47#54011yescharacteristic
476C22×C47#54111yescharacteristic
477C22×C47#54211yescharacteristic
478C22×C47#54211yescharacteristic
479C22×C47#54211yescharacteristic
480C22×C47#54211yescharacteristic
481C4×C47—24no—
482C4×C47—24no—
483C4×C47—24no—
484C4×C47—42no—
485C4×C47—42no—
486C4×C47—42no—
487Dic47—24no—
488Dic47—24no—
489Dic47—42no—
490Dic47—42no—
491Dic47—42no—
492Dic47—42no—
493Dic47—42no—
494Dic47—42no—
495C2×#388—471no—
496C2×#388—471no—
497C2×#385D4711yescharacteristic
498C2×C4×C4⋊C4—471no—
499C2×C4×C22⋊C4—471no—
500#1437—471no—
501#1437—471no—
502#1436—471no—
503#1436—471no—
504#1436—471no—
505#1436—471no—
506C4⋊#95—471no—
507#1434—471no—
508C22⋊#95—471no—
509C4×#95—471no—
510C2×C47—44no—
511C2×C47C42×D411yescharacteristic
512C2×C47#227411yescharacteristic
513C2×C47#227511yescharacteristic
514C2×C47#232111yescharacteristic
515C2×C47#232211yescharacteristic
516C2×C47#232311yescharacteristic
517C2×C47#232411yescharacteristic
518C2×C47#232511yescharacteristic
519C2×C47#232611yescharacteristic
520C2×C47#233211yescharacteristic
521C2×C47#233411yescharacteristic
522C2×C47#233411yescharacteristic
523C2×C47#233511yescharacteristic
524C2×C47#233511yescharacteristic
525C2×C47#233711yescharacteristic
526C24×C4C2×D4711yescharacteristic
527C22×C4⋊C4—471no—
528C22×C4⋊C4—471no—
529C22×C4⋊C4C2×D4711yescharacteristic
530C22×C4⋊C4C2×D4711yescharacteristic
531C22×C22⋊C4—471no—
532C22×C22⋊C4—471no—
533C22×C22⋊C4—471no—
534C22×C22⋊C4—471no—
535C22×C22⋊C4C2×D4711yescharacteristic
536C22×C22⋊C4C2×D4711yescharacteristic
537C22×C42—471no—
538C22×C42—471no—
539C22×C42—471no—
540C22×C42—471no—
541C22×C42—471no—
542C22×C42—471no—
543#388—478no—
544#388—478no—
545#385Dic4718yescomplemented
546C4×C4⋊C4—944no—
547C4×C22⋊C4—944no—
548C2×#95—471no—
549C2×#95—471no—
550C2×#95—471no—
551C2×#95—471no—
552C2×#95—471no—
553C2×#95—471no—
554C2×#95—471no—
555C2×#95—471no—
556C2×#95—471no—
557C2×#95—471no—
558C2×#95—471no—
559C2×#95—471no—
560C2×#95—471no—
561C2×#95—471no—
562C2×#95—471no—
563C2×#95—471no—
564C2×#95C2×D4711yescharacteristic
565C2×#95C2×D4711yescharacteristic
566C47#1378911yescharacteristic, complemented, Sylow
567C25C22×D4711yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—471no—
575C23×C4—471no—
576C23×C4—471no—
577C23×C4—471no—
578C23×C4—471no—
579C23×C4—471no—
580C23×C4—471no—
581C23×C4—471no—
582C23×C4C2×Dic4714yes—
583C23×C4C22×D4711yescharacteristic
584C23×C4C22×D4711yescharacteristic
585C23×C4C22×D4711yescharacteristic
586C23×C4C22×D4711yescharacteristic
587C23×C4C22×D4711yescharacteristic
588C23×C4C22×D4711yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—474no—
594C2×C4⋊C4—474no—
595C2×C4⋊C4—942no—
596C2×C4⋊C4—942no—
597C2×C4⋊C4—1881no—
598C2×C4⋊C4—1881no—
599C2×C4⋊C4C2×Dic4714yes—
600C2×C4⋊C4C2×Dic4714yes—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—474no—
604C2×C22⋊C4—474no—
605C2×C22⋊C4—474no—
606C2×C22⋊C4—474no—
607C2×C22⋊C4—942no—
608C2×C22⋊C4—942no—
609C2×C22⋊C4—942no—
610C2×C22⋊C4—942no—
611C2×C22⋊C4—1881no—
612C2×C22⋊C4—1881no—
613C2×C22⋊C4—1881no—
614C2×C22⋊C4—1881no—
615C2×C22⋊C4C4×D4714yes—
616C2×C22⋊C4C4×D4714yes—
617C2×C22⋊C4C2×Dic4714yes—
618C2×C22⋊C4C2×Dic4714yes—
619C2×C42—474no—
620C2×C42—474no—
621C2×C42—474no—
622C2×C42—942no—
623C2×C42—942no—
624C2×C42—942no—
625C2×C42—942no—
626C2×C42—942no—
627C2×C42—1881no—
628C2×C42—1881no—
629C2×C42—1881no—
630C2×C42—1881no—
631C2×C42—1881no—
632C2×C42—1881no—
633C2×C42—1881no—
634C2×C42—1881no—
635C2×C42—1881no—
636C2×C42—1881no—
637#95—474no—
638#95—474no—
639#95—474no—
640#95—474no—
641#95—942no—
642#95—942no—
643#95—942no—
644#95—942no—
645#95—942no—
646#95—942no—
647#95—1881no—
648#95—1881no—
649#95—1881no—
650#95—1881no—
651#95—1881no—
652#95—1881no—
653#95C2×Dic4714yes—
654#95C2×Dic4714yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×C4×D4712yes—
668C24C2×C4×D4712yes—
669C24C22×Dic4712yes—
670C24C23×D4711yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—28no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—472no—
709C22×C4—472no—
710C22×C4—472no—
711C22×C4—472no—
712C22×C4—472no—
713C22×C4—472no—
714C22×C4—472no—
715C22×C4—472no—
716C22×C4—472no—
717C22×C4—472no—
718C22×C4—472no—
719C22×C4—472no—
720C22×C4—941no—
721C22×C4—941no—
722C22×C4—941no—
723C22×C4—941no—
724C22×C4—941no—
725C22×C4—941no—
726C22×C4—941no—
727C22×C4—941no—
728C22×C4—941no—
729C22×C4—941no—
730C22×C4—941no—
731C22×C4—941no—
732C22×C4—941no—
733C22×C4—941no—
734C22×C4—941no—
735C22×C4—941no—
736C22×C4—941no—
737C22×C4—941no—
738C22×C4—941no—
739C22×C4—941no—
740C22×C4—941no—
741C22×C4—941no—
742C22×C4—941no—
743C22×C4—941no—
744C22×C4—941no—
745C22×C4—941no—
746C22×C4—941no—
747C22×C4—941no—
748C22×C4—941no—
749C22×C4—941no—
750C22×C4—941no—
751C22×C4—941no—
752C22×C4—941no—
753C22×C4—941no—
754C22×C4—941no—
755C22×C4—941no—
756C22×C4—941no—
757C22×C4—941no—
758C22×C4—941no—
759C22×C4—941no—
760C22×C4—941no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4C2×C4×D4712yes—
765C22×C4C2×C4×D4712yes—
766C22×C4C2×C4×D4712yes—
767C22×C4C2×C4×D4712yes—
768C22×C4D4×D4712yes—
769C22×C4#1062535212yes—
770C22×C4C22×Dic4712yes—
771C22×C4C22×Dic4712yes—
772C22×C4C22×Dic4712yes—
773C22×C4C22×Dic4712yes—
774C22×C4C22×Dic4712yes—
775C22×C4C22×Dic4712yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—948no—
779C4⋊C4—1884no—
780C22⋊C4—44no—
781C22⋊C4—948no—
782C22⋊C4—948no—
783C22⋊C4—1884no—
784C22⋊C4—1884no—
785C22⋊C4C4×Dic47116yescomplemented
786C42—948no—
787C42—1884no—
788C42—1884no—
789C42—1884no—
790C42—1884no—
791C42—1884no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4×Dic4714yes—
827C23C22×C4×D4711yescharacteristic
828C23C22×C4×D4711yescharacteristic
829C23C23×Dic4711yescharacteristic
830C23C2×D4×D4711yescharacteristic
831C23#41×D4711yescharacteristic
832C23#41×D4711yescharacteristic
833C23C2×#1062535211yescharacteristic
834C23#1309406911yescharacteristic
835C23#1309406911yescharacteristic
836C23#1309406911yescharacteristic
837C23#1309406911yescharacteristic
838C23#1309407011yescharacteristic
839C23#1309407111yescharacteristic
840C23#1309407211yescharacteristic
841C23#1309407211yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—416no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—474no—
883C2×C4—474no—
884C2×C4—942no—
885C2×C4—942no—
886C2×C4—942no—
887C2×C4—942no—
888C2×C4—942no—
889C2×C4—942no—
890C2×C4—942no—
891C2×C4—942no—
892C2×C4—942no—
893C2×C4—942no—
894C2×C4—942no—
895C2×C4—942no—
896C2×C4—942no—
897C2×C4—942no—
898C2×C4—942no—
899C2×C4—942no—
900C2×C4—942no—
901C2×C4—942no—
902C2×C4—942no—
903C2×C4—942no—
904C2×C4—942no—
905C2×C4—942no—
906C2×C4—942no—
907C2×C4—942no—
908C2×C4—942no—
909C2×C4—942no—
910C2×C4—942no—
911C2×C4—942no—
912C2×C4—942no—
913C2×C4—942no—
914C2×C4—1881no—
915C2×C4—1881no—
916C2×C4—1881no—
917C2×C4—1881no—
918C2×C4—1881no—
919C2×C4—1881no—
920C2×C4—1881no—
921C2×C4—1881no—
922C2×C4—1881no—
923C2×C4—1881no—
924C2×C4—1881no—
925C2×C4—1881no—
926C2×C4—1881no—
927C2×C4—1881no—
928C2×C4—1881no—
929C2×C4—1881no—
930C2×C4—1881no—
931C2×C4—1881no—
932C2×C4—1881no—
933C2×C4—1881no—
934C2×C4—1881no—
935C2×C4—1881no—
936C2×C4—1881no—
937C2×C4—1881no—
938C2×C4C2×C4×Dic4714yes—
939C2×C4C2×C4×Dic4714yes—
940C2×C4D4×Dic4714yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4×Dic4711yescharacteristic
957C22C4×D4×D4711yescharacteristic
958C22C4×D4×D4711yescharacteristic
959C22C2×D4×Dic4711yescharacteristic
960C22C4×#1062535211yescharacteristic
961C22C4×#1062535211yescharacteristic
962C22#41×Dic4711yescharacteristic
963C22#1568959511yescharacteristic
964C22#1568959511yescharacteristic
965C22#1568959811yescharacteristic
966C22#1568959811yescharacteristic
967C22#1568960111yescharacteristic
968C22#1568960211yescharacteristic
969C22#1568960211yescharacteristic
970C22#1568960411yescharacteristic
971C22#1568960411yescharacteristic
972C22#1568960411yescharacteristic
973C22#1568960411yescharacteristic
974C22#1568960611yescharacteristic
975C22#1568968311yescharacteristic
976C22#1568968811yescharacteristic
977C22#1568969611yescharacteristic
978C22#1568970311yescharacteristic
979C22#1568970811yescharacteristic
980C22#1568970811yescharacteristic
981C22#1568970911yescharacteristic
982C22#1568971611yescharacteristic
983C22#1568971911yescharacteristic
984C22#1568971911yescharacteristic
985C22#1568972511yescharacteristic
986C22#1568973311yescharacteristic
987C22#1568974111yescharacteristic
988C22#1568974311yescharacteristic
989C22#1568974311yescharacteristic
990C22#1568974611yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—944no—
998C4—944no—
999C4—1882no—
1000C4—1882no—
1001C4—1882no—
1002C4—1882no—
1003C4—1882no—
1004C4—1882no—
1005C2—44no—
1006C2C4×D4×Dic4711yescharacteristic
1007C2#2024574511yescharacteristic
1008C2#2024574911yescharacteristic
1009C2#2024604911yescharacteristic
1010C2#2024605511yescharacteristic
1011C2#2024607211yescharacteristic
1012C2#2024608011yescharacteristic
1013C2#2024608511yescharacteristic
1014C2#2024609411yescharacteristic
1015C2#2024614611yescharacteristic
1016C2#2024615811yescharacteristic
1017C2#2024616411yescharacteristic
1018C2#2024617311yescharacteristic
1019C2#2024618211yescharacteristic
1020C2#2024620211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C47×#385C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#385D47
hypocenterC47#13789
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic47C2semidirect
7. #20241622C2semidirect
8. #20241622C2semidirect
9. #20241620C2semidirect
10. #20241620C2semidirect
11. #20241617C2semidirect
12. #20241613C2semidirect
14. #95×Dic47C2semidirect
28. #15689016C4semidirect
29. #15689016C4semidirect
53. C47×#385C4semidirect
68. C2×C4⋊Dic47C2×C4semidirect
69. C2×C4⋊Dic47C2×C4semidirect
97. C2×C4×Dic47C2×C4semidirect
98. C2×C4×Dic47C2×C4semidirect
112. C47⋊#95C2×C4semidirect
113. C47⋊#95C2×C4semidirect
114. C47⋊#95C2×C4semidirect
115. C47⋊#95C2×C4semidirect
268. C22⋊C4×C47C42semidirect
545. #385Dic47semidirect
566. C47#13789semidirect
785. C22⋊C4C4×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890162
C2×C4⋊C4×Dic472
C2×C4×C22⋊Dic472
#202416252
#202416222
#202416202
#202416172
#202416132
#202416112
#95×Dic472
C2×C47×#3852
#1378947