Finite Group Databasebeta

← #26137855

Subgroups — #26137855

Order 12032.

1778 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689022C211yesmaximal, characteristic
2C2×C4⋊C4×Dic47C212yesmaximal
3C2×C4⋊C4×Dic47C211yesmaximal, characteristic
4C2×C4⋊C4×Dic47C211yesmaximal, characteristic
5C2×C4×C4⋊Dic47C211yesmaximal, characteristic
6#20241622C212yesmaximal
7#20241620C212yesmaximal
8#20241617C211yesmaximal, characteristic
9#20241613C212yesmaximal
10C4×C47⋊#95C211yesmaximal, characteristic
11C2×C47×#389C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4×Dic47C2212yes—
16C22×C4×Dic47C2212yes—
17C22×C4×Dic47C2211yescharacteristic
18C22×C4×Dic47C2211yescharacteristic
19C22×C4×Dic47C2212yes—
20#15689022C418yescomplemented
21C4⋊C4×Dic47—24no—
22C4⋊C4×Dic47—28no—
23C4⋊C4×Dic47C418yescomplemented
24C4×C4⋊Dic47—24no—
25C2×C47⋊#95C2211yescharacteristic
26C2×C47⋊#95C2211yescharacteristic
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2212yes—
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C47×#389C418yescomplemented
40C2×#95×C47C2212yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2312yes—
44C23×Dic47C2312yes—
45C23×Dic47C2311yescharacteristic
46C23×Dic47C2311yescharacteristic
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—24no—
50C2×C4⋊Dic47—24no—
51C2×C4⋊Dic47C2×C414yes—
52C2×C4⋊Dic47C2×C418yes—
53C2×C4⋊Dic47C2×C414yes—
54C2×C4⋊Dic47D414yes—
55C2×C4⋊Dic47Q814yes—
56C2×C4×Dic47—22no—
57C2×C4×Dic47—22no—
58C2×C4×Dic47—22no—
59C2×C4×Dic47—22no—
60C2×C4×Dic47—24no—
61C2×C4×Dic47—24no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—24no—
64C2×C4×Dic47—24no—
65C2×C4×Dic47—24no—
66C2×C4×Dic47—42no—
67C2×C4×Dic47—42no—
68C2×C4×Dic47C2×C414yes—
69C2×C4×Dic47C2×C418yes—
70C2×C4×Dic47C2×C414yes—
71C47⋊#95—22no—
72C47⋊#95—24no—
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—22no—
76C47⋊#95—22no—
77C47⋊#95—42no—
78C47⋊#95C2×C418yes—
79C47⋊#95C2×C418yes—
80C47⋊#95D414yes—
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2312yes—
83C23×C4×C47C2312yes—
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47—24no—
87C2×C4⋊C4×C47—22no—
88C2×C4⋊C4×C47—24no—
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47C2×C414yes—
91C2×C4⋊C4×C47C2×C418yes—
92C2×C4⋊C4×C47C2×C414yes—
93C2×C4⋊C4×C47C2×C414yes—
94C2×C4⋊C4×C47C2×C414yes—
95C2×C42×C47—22no—
96C2×C42×C47—22no—
97C2×C42×C47C2×C414yes—
98#95×C47C2×C418yes—
99C24×C47C2411yescharacteristic
100C22×C4×C47—21no—
101C22×C4×C47—22no—
102C22×C4×C47—21no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—21no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—22no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—22no—
120C22×C4×C47C22×C412yes—
121C22×C4×C47C22×C414yes—
122C22×C4×C47C22×C414yes—
123C22×C4×C47C22×C414yes—
124C22×C4×C47C22×C414yes—
125C22×C4×C47C22×C412yes—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C22×C412yes—
128C22×C4×C47C22×C412yes—
129C22×C4×C47C2×D412yes—
130C22×C4×C47C2×D412yes—
131C22×C4×C47C2×Q812yes—
132C22×C4×C47#4112yes—
133C22×C4×C47#4112yes—
134C22×C4×C47#4112yes—
135C22×Dic47—21no—
136C22×Dic47—22no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—22no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—22no—
147C22×Dic47—21no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—21no—
160C22×Dic47—22no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—22no—
164C22×Dic47—21no—
165C22×Dic47C22×C412yes—
166C22×Dic47C22×C412yes—
167C22×Dic47C22×C414yes—
168C22×Dic47C22×C414yes—
169C22×Dic47C22×C412yes—
170C22×Dic47C22×C412yes—
171C22×Dic47C2×D414yes—
172C22×Dic47C2×D412yes—
173C22×Dic47C2×D412yes—
174C22×Dic47C2×Q814yes—
175C22×Dic47#4112yes—
176C22×Dic47#4112yes—
177C4⋊C4×C47—216no—
178C4⋊C4×C47—28no—
179C4⋊C4×C47C42116yescomplemented
180C42×C47—28no—
181C4⋊Dic47—28no—
182C4⋊Dic47—216no—
183C4⋊Dic47C4⋊C4116yescomplemented
184C4×Dic47—28no—
185C4×Dic47—28no—
186C4×Dic47—216no—
187C4×Dic47—48no—
188C4×Dic47—48no—
189C23×C47C23×C411yescharacteristic
190C23×C47C23×C411yescharacteristic
191C23×C47C23×C411yescharacteristic
192C23×C47C22×D411yescharacteristic
193C23×C47C22×D411yescharacteristic
194C23×C47C22×Q811yescharacteristic
195C23×C47C2×#4111yescharacteristic
196C23×C47C2×#4111yescharacteristic
197C23×C47C2×#4111yescharacteristic
198C23×C47C2×#4111yescharacteristic
199C23×C47C2×#4111yescharacteristic
200C23×C47H(5,𝔽2)11yescharacteristic
201C23×C472−1+411yescharacteristic
202C23×C472−1+411yescharacteristic
203C23×C472−1+411yescharacteristic
204C2×C4×C47—24no—
205C2×C4×C47—24no—
206C2×C4×C47—22no—
207C2×C4×C47—24no—
208C2×C4×C47—24no—
209C2×C4×C47—24no—
210C2×C4×C47—24no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—24no—
218C2×C4×C47—24no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—24no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—41no—
225C2×C4×C47—42no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—42no—
229C2×C4×C47—41no—
230C2×C4×C47C2×C4218yes—
231C2×C4×C47C2×C4214yes—
232C2×C4×C47C2×C4⋊C414yes—
233C2×C4×C47#11714yes—
234C2×C4×C47C4×D414yes—
235C2×C4×C47C4×D414yes—
236C2×C4×C47C4×D414yes—
237C2×C4×C47C4×Q814yes—
238C2×C4×C47C4×Q814yes—
239C2×Dic47—22no—
240C2×Dic47—24no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—24no—
244C2×Dic47—22no—
245C2×Dic47—24no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—24no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—24no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—24no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—24no—
260C2×Dic47—24no—
261C2×Dic47—22no—
262C2×Dic47—22no—
263C2×Dic47—22no—
264C2×Dic47—22no—
265C2×Dic47—24no—
266C2×Dic47—42no—
267C2×Dic47—41no—
268C2×Dic47—42no—
269C2×Dic47—41no—
270C2×Dic47—42no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—42no—
275C2×Dic47—41no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47C2×C4⋊C418yes—
279C2×Dic47C4×D414yes—
280C2×Dic47C4×D414yes—
281#13821—471nomaximal, Sylow
282C22×C47C22×C4211yescharacteristic
283C22×C47C22×C4⋊C411yescharacteristic
284C22×C47C2×#11711yescharacteristic
285C22×C47C2×C4×D411yescharacteristic
286C22×C47C2×C4×D411yescharacteristic
287C22×C47C2×C4×D411yescharacteristic
288C22×C47C2×C4×D411yescharacteristic
289C22×C47C2×C4×D411yescharacteristic
290C22×C47C2×C4×Q811yescharacteristic
291C22×C47C2×C4×Q811yescharacteristic
292C22×C47C4×#4111yescharacteristic
293C22×C47C4×#4111yescharacteristic
294C22×C47C4×#4111yescharacteristic
295C22×C47#51911yescharacteristic
296C22×C47#51911yescharacteristic
297C22×C47#51911yescharacteristic
298C22×C47#52011yescharacteristic
299C22×C47#52011yescharacteristic
300C22×C47#52011yescharacteristic
301C22×C47D4211yescharacteristic
302C22×C47#54711yescharacteristic
303C22×C47#54711yescharacteristic
304C22×C47#54711yescharacteristic
305C22×C47#54811yescharacteristic
306C22×C47#54811yescharacteristic
307C22×C47D4×Q811yescharacteristic
308C22×C47#55211yescharacteristic
309C22×C47#55211yescharacteristic
310C22×C47#55311yescharacteristic
311C22×C47#55311yescharacteristic
312C22×C47#55411yescharacteristic
313C22×C47#55611yescharacteristic
314C22×C47#55611yescharacteristic
315C22×C47#55711yescharacteristic
316C22×C47#55711yescharacteristic
317C4×C47—24no—
318C4×C47—28no—
319C4×C47—44no—
320C4×C47—42no—
321C4×C47C4×C4⋊C418yescomplemented
322Dic47—24no—
323Dic47—28no—
324Dic47—24no—
325Dic47—42no—
326Dic47—44no—
327Dic47—42no—
328C2×#389—471no—
329C2×#389D4711yescharacteristic
330C2×C4×C4⋊C4—471no—
331C2×C4×C4⋊C4—471no—
332C2×C4×C4⋊C4—471no—
333C2×C4×C4⋊C4—472no—
334#1436—472no—
335#1436—472no—
336C4⋊#95—471no—
337#1434—472no—
338C4×#95—471no—
339C2×C47C2×C4×C4⋊C411yescharacteristic
340C2×C47C42×D411yescharacteristic
341C2×C47#227611yescharacteristic
342C2×C47#234411yescharacteristic
343C2×C47#234711yescharacteristic
344C2×C47D4×C4⋊C411yescharacteristic
345C2×C47#235111yescharacteristic
346C2×C47#236111yescharacteristic
347C2×C47#236111yescharacteristic
348C2×C47#236211yescharacteristic
349C2×C47#236211yescharacteristic
350C2×C47#236511yescharacteristic
351C2×C47#236511yescharacteristic
352C2×C47#237011yescharacteristic
353C2×C47#237011yescharacteristic
354C22×C4⋊C4—471no—
355C22×C4⋊C4—471no—
356C22×C4⋊C4—472no—
357C22×C4⋊C4C2×D4711yescharacteristic
358C22×C4⋊C4C2×D4712yes—
359C22×C4⋊C4C2×D4711yescharacteristic
360C22×C42—471no—
361C22×C42—471no—
362C22×C42—472no—
363C22×C42—472no—
364C22×C42—472no—
365C22×C42C2×D4711yescharacteristic
366#389—478no—
367#389Dic4718yescomplemented
368C4×C4⋊C4—478no—
369C4×C4⋊C4—948no—
370C4×C4⋊C4—944no—
371C4×C4⋊C4—944no—
372C2×#95—471no—
373C2×#95—472no—
374C2×#95—472no—
375C2×#95—471no—
376C2×#95—471no—
377C2×#95—471no—
378C2×#95—472no—
379C2×#95—472no—
380C2×#95—472no—
381C2×#95—472no—
382C2×#95C2×D4712yes—
383C47#1382111yescharacteristic, complemented, Sylow
384C23×C4—471no—
385C23×C4—472no—
386C23×C4—471no—
387C23×C4—472no—
388C23×C4—471no—
389C23×C4—471no—
390C23×C4C22×D4712yes—
391C23×C4C22×D4711yescharacteristic
392C23×C4C22×D4712yes—
393C23×C4C22×D4711yescharacteristic
394C23×C4C22×D4711yescharacteristic
395C2×C4⋊C4—24no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—474no—
400C2×C4⋊C4—474no—
401C2×C4⋊C4—474no—
402C2×C4⋊C4—478no—
403C2×C4⋊C4—474no—
404C2×C4⋊C4—944no—
405C2×C4⋊C4—944no—
406C2×C4⋊C4—942no—
407C2×C4⋊C4—942no—
408C2×C4⋊C4C4×D4714yes—
409C2×C4⋊C4C4×D4714yes—
410C2×C4⋊C4C2×Dic4714yes—
411C2×C4⋊C4C2×Dic4718yes—
412C2×C4⋊C4C2×Dic4714yes—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—478no—
416C2×C42—474no—
417C2×C42—474no—
418C2×C42—944no—
419C2×C42—944no—
420C2×C42—942no—
421C2×C42—942no—
422C2×C42—942no—
423C2×C42—942no—
424C2×C42—944no—
425C2×C42—944no—
426C2×C42—944no—
427C2×C42—944no—
428C2×C42—1882no—
429C2×C42—1882no—
430C2×C42C2×Dic4714yes—
431#95—478no—
432#95—478no—
433#95—474no—
434#95—942no—
435#95—942no—
436#95—944no—
437#95—944no—
438#95—944no—
439#95—942no—
440#95—1882no—
441#95C2×Dic4718yes—
442C24C23×D4711yescharacteristic
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—474no—
464C22×C4—472no—
465C22×C4—472no—
466C22×C4—472no—
467C22×C4—472no—
468C22×C4—474no—
469C22×C4—474no—
470C22×C4—472no—
471C22×C4—472no—
472C22×C4—472no—
473C22×C4—472no—
474C22×C4—474no—
475C22×C4—941no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—941no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—942no—
483C22×C4—941no—
484C22×C4—942no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—941no—
491C22×C4—941no—
492C22×C4—942no—
493C22×C4—941no—
494C22×C4—941no—
495C22×C4—941no—
496C22×C4—941no—
497C22×C4—941no—
498C22×C4—942no—
499C22×C4—941no—
500C22×C4—942no—
501C22×C4—941no—
502C22×C4—941no—
503C22×C4—942no—
504C22×C4—941no—
505C22×C4C2×C4×D4714yes—
506C22×C4C2×C4×D4714yes—
507C22×C4C2×C4×D4712yes—
508C22×C4C2×C4×D4712yes—
509C22×C4D4×D4712yes—
510C22×C4D4×D4712yes—
511C22×C4#1062535212yes—
512C22×C4#1062535212yes—
513C22×C4Q8×D4712yes—
514C22×C4#1062535412yes—
515C22×C4C22×Dic4712yes—
516C22×C4C22×Dic4714yes—
517C22×C4C22×Dic4714yes—
518C22×C4C22×Dic4712yes—
519C22×C4C22×Dic4712yes—
520C4⋊C4—216no—
521C4⋊C4—28no—
522C4⋊C4—4716no—
523C4⋊C4—9416no—
524C4⋊C4—948no—
525C4⋊C4C4×Dic47116yescomplemented
526C42—28no—
527C42—9416no—
528C42—948no—
529C42—948no—
530C42—1888no—
531C42—1888no—
532C23C22×C4×D4711yescharacteristic
533C23C22×C4×D4711yescharacteristic
534C23C23×Dic4711yescharacteristic
535C23C2×D4×D4711yescharacteristic
536C23C2×D4×D4711yescharacteristic
537C23C2×Q8×D4711yescharacteristic
538C23#41×D4711yescharacteristic
539C23#41×D4711yescharacteristic
540C23C2×#1062535211yescharacteristic
541C23C2×#1062535211yescharacteristic
542C23C2×#1062535411yescharacteristic
543C23#1309407011yescharacteristic
544C23#1309407111yescharacteristic
545C23#1309407211yescharacteristic
546C23#1309407211yescharacteristic
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—478no—
574C2×C4—474no—
575C2×C4—474no—
576C2×C4—944no—
577C2×C4—942no—
578C2×C4—942no—
579C2×C4—944no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—942no—
583C2×C4—944no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—942no—
587C2×C4—944no—
588C2×C4—942no—
589C2×C4—944no—
590C2×C4—942no—
591C2×C4—942no—
592C2×C4—944no—
593C2×C4—942no—
594C2×C4—942no—
595C2×C4—944no—
596C2×C4—942no—
597C2×C4—944no—
598C2×C4—942no—
599C2×C4—942no—
600C2×C4—942no—
601C2×C4—942no—
602C2×C4—944no—
603C2×C4—1882no—
604C2×C4—1881no—
605C2×C4—1882no—
606C2×C4—1881no—
607C2×C4—1882no—
608C2×C4—1881no—
609C2×C4—1881no—
610C2×C4—1881no—
611C2×C4—1882no—
612C2×C4—1881no—
613C2×C4—1881no—
614C2×C4—1881no—
615C2×C4C2×C4×Dic4718yes—
616C2×C4C2×C4×Dic4714yes—
617C2×C4C4⋊C4×D4714yes—
618C2×C4#1309398214yes—
619C2×C4#1309398614yes—
620C2×C4D4×Dic4714yes—
621C2×C4D4×Dic4714yes—
622C2×C4#1309398914yes—
623C2×C4Q8×Dic4714yes—
624C22C22×C4×Dic4711yescharacteristic
625C22C2×C4⋊C4×D4711yescharacteristic
626C22C2×#1309398211yescharacteristic
627C22C4×D4×D4711yescharacteristic
628C22C4×D4×D4711yescharacteristic
629C22C2×#1309398611yescharacteristic
630C22C2×D4×Dic4711yescharacteristic
631C22C2×D4×Dic4711yescharacteristic
632C22C2×#1309398911yescharacteristic
633C22C2×Q8×Dic4711yescharacteristic
634C22C4×#1062535211yescharacteristic
635C22C4×#1062535211yescharacteristic
636C22#41×Dic4711yescharacteristic
637C22#1568959911yescharacteristic
638C22#1568959911yescharacteristic
639C22#1568960111yescharacteristic
640C22#1568960511yescharacteristic
641C22#1568960511yescharacteristic
642C22#1568960611yescharacteristic
643C22#1568975711yescharacteristic
644C22#1568977311yescharacteristic
645C22#1568977511yescharacteristic
646C22#1568977611yescharacteristic
647C22#1568977911yescharacteristic
648C22#1568978311yescharacteristic
649C22#1568978811yescharacteristic
650C22#1568980711yescharacteristic
651C22#1568981111yescharacteristic
652C22#1568982511yescharacteristic
653C22#1568982611yescharacteristic
654C22#1568982911yescharacteristic
655C22#1568984411yescharacteristic
656C22#1568984711yescharacteristic
657C22#1568984811yescharacteristic
658C22#1568985011yescharacteristic
659C4—24no—
660C4—28no—
661C4—44no—
662C4—42no—
663C4—948no—
664C4—944no—
665C4—944no—
666C4—1882no—
667C4—1884no—
668C4—1882no—
669C4C4⋊C4×Dic4718yescomplemented
670C2C2×C4⋊C4×Dic4711yescharacteristic
671C2C4×D4×Dic4711yescharacteristic
672C2#2024575311yescharacteristic
673C2#2024625611yescharacteristic
674C2#2024628011yescharacteristic
675C2#2024628911yescharacteristic
676C2#2024630711yescharacteristic
677C2#2024640311yescharacteristic
678C2#2024640811yescharacteristic
679C2#2024641411yescharacteristic
680C2#2024641911yescharacteristic
681C2#2024644111yescharacteristic
682C2#2024644811yescharacteristic
683C2#2024648311yescharacteristic
684C2#2024648811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C47×#389C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×#389D47
hypocenterC47#13821
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
20. #15689022C4semidirect
23. C4⋊C4×Dic47C4semidirect
39. C47×#389C4semidirect
179. C4⋊C4×C47C42semidirect
183. C4⋊Dic47C4⋊C4semidirect
321. C4×C47C4×C4⋊C4semidirect
367. #389Dic47semidirect
383. C47#13821semidirect
525. C4⋊C4C4×Dic47semidirect
669. C4C4⋊C4×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890222
C2×C4⋊C4×Dic472
C2×C4×C4⋊Dic472
#202416222
#202416202
#202416172
#202416132
C4×C47⋊#952
C2×C47×#3892
#1382147