Finite Group Databasebeta

← #26138229

Subgroups — #26138229

Order 12032.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689016C212yesmaximal
2C2×#15688993C211yesmaximal, characteristic, complemented
3C2×#15688983C211yesmaximal, characteristic
4C2×#15688983C211yesmaximal, characteristic
5C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
6#20241645C212yesmaximal, complemented
7#20241633C212yesmaximal
8#20241622C212yesmaximal, complemented
9#20241618C211yesmaximal, characteristic, complemented
10#20241618C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2212yes—
15C22×C4⋊Dic47C2212yes—
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2212yes—
19C22×C22⋊Dic47C2212yes—
20C22×C4×Dic47C2212yes—
21#15689016—28no—
22#15688993—24no—
23#15688983—24no—
24#15688983—24no—
25C4×C4⋊Dic47—24no—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C24×C4×C47C2211yescharacteristic
34C22×C22⋊C4×C47C2211yescharacteristic
35C22×C22⋊C4×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C4×C22⋊C4×C47C418yescomplemented
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2211yescharacteristic
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2312yes—
44C23×Dic47C2312yes—
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—22no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—24no—
53C2×C4⋊Dic47—24no—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47—24no—
58C2×C4⋊Dic47—24no—
59C2×C4⋊Dic47—42no—
60C2×C4⋊Dic47—42no—
61C2×C4⋊Dic47D414yes—
62C2×C4⋊Dic47D414yes—
63C2×C22⋊Dic47—24no—
64C2×C22⋊Dic47—24no—
65C2×C22⋊Dic47—24no—
66C2×C22⋊Dic47—24no—
67C2×C22⋊Dic47—42no—
68C2×C22⋊Dic47—42no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—42no—
72C47⋊#95—24no—
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—24no—
76C47⋊#95—24no—
77C47⋊#95—24no—
78C47⋊#95—42no—
79C25×C47C2311yescharacteristic
80C23×C4×C47—22no—
81C23×C4×C47—22no—
82C23×C4×C47—22no—
83C23×C4×C47—22no—
84C23×C4×C47—22no—
85C23×C4×C47—22no—
86C23×C4×C47C2×C414yes—
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C2×C22⋊C4×C47—22no—
94C2×C22⋊C4×C47—22no—
95C2×C22⋊C4×C47C2×C414yes—
96C2×C22⋊C4×C47C2×C414yes—
97C2×C22⋊C4×C47D414yes—
98C2×C22⋊C4×C47Q814yes—
99C2×C42×C47—22no—
100C2×C42×C47—22no—
101C2×C42×C47—22no—
102C2×C42×C47—22no—
103C2×C42×C47C2×C414yes—
104C2×C42×C47C2×C414yes—
105#95×C47C2×C414yes—
106#95×C47C2×C414yes—
107C24×C47—21no—
108C24×C47—21no—
109C24×C47—21no—
110C24×C47—21no—
111C24×C47—21no—
112C24×C47—21no—
113C24×C47—21no—
114C24×C47—21no—
115C24×C47—21no—
116C24×C47—21no—
117C24×C47—21no—
118C24×C47—21no—
119C24×C47C22×C412yes—
120C24×C47C2×D412yes—
121C24×C47C2×Q812yes—
122C24×C47C2411yescharacteristic
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—28no—
148C22×C4×C47—28no—
149C22×C4×C47—28no—
150C22×C4×C47—44no—
151C22×C4×C47—44no—
152C22×C4×C47—44no—
153C22×C4×C47—44no—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C22×C412yes—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C22×C412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×D412yes—
163C22×C4×C47C2×D412yes—
164C22×C4×C47C2×Q812yes—
165C22×C4×C47C2×Q812yes—
166C22×C4×C47#4112yes—
167C22×C4×C47#4112yes—
168C22×C4×C47#4112yes—
169C22×C4×C47#4112yes—
170C22×C4×C47#4112yes—
171C22×C4×C47#4112yes—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
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×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47C2×D414yes—
199C22×Dic47C2×D414yes—
200C22⋊C4×C47—28no—
201C22⋊C4×C47C4⋊C4116yescomplemented
202C42×C47—28no—
203C42×C47—28no—
204C22⋊Dic47—48no—
205C22⋊Dic47—48no—
206C4⋊Dic47—28no—
207C4⋊Dic47—28no—
208C4⋊Dic47—48no—
209C4⋊Dic47—48no—
210C4⋊Dic47—44no—
211C4⋊Dic47—44no—
212C4×Dic47—48no—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—22no—
221C23×C47—22no—
222C23×C47—22no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—22no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—22no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47C2×C4⋊C414yes—
248C23×C47C23×C411yescharacteristic
249C23×C47C22×D411yescharacteristic
250C23×C47C22×D411yescharacteristic
251C23×C47C22×D411yescharacteristic
252C23×C47C22×Q811yescharacteristic
253C23×C47C2×#4111yescharacteristic
254C23×C47C2×#4111yescharacteristic
255C23×C47C2×#4111yescharacteristic
256C23×C47C2×#4111yescharacteristic
257C23×C47C2×#4111yescharacteristic
258C23×C47C2×#4111yescharacteristic
259C23×C47H(5,𝔽2)11yescharacteristic
260C23×C47H(5,𝔽2)11yescharacteristic
261C23×C472−1+411yescharacteristic
262C23×C472−1+411yescharacteristic
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—416no—
296C2×C4×C47C2×C4⋊C414yes—
297C2×C4×C47C2×C4⋊C414yes—
298C2×C4×C47#11714yes—
299C2×C4×C47#11714yes—
300C2×C4×C47C4×D414yes—
301C2×C4×C47C4×D414yes—
302C2×C4×C47#12114yes—
303C2×C4×C47#12314yes—
304C2×C4×C47#12414yes—
305C2×C4×C47#12614yes—
306C2×Dic47—24no—
307C2×Dic47—24no—
308C2×Dic47—24no—
309C2×Dic47—24no—
310C2×Dic47—24no—
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×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334#13876—471nomaximal, Sylow
335C22×C47—24no—
336C22×C47—24no—
337C22×C47—24no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47C22×C4⋊C411yescharacteristic
351C22×C47C2×#11711yescharacteristic
352C22×C47C2×#11711yescharacteristic
353C22×C47C2×C4×D411yescharacteristic
354C22×C47C2×C4×D411yescharacteristic
355C22×C47#52011yescharacteristic
356C22×C47#52011yescharacteristic
357C22×C47C2×#12111yescharacteristic
358C22×C47C2×#12311yescharacteristic
359C22×C47C2×#12411yescharacteristic
360C22×C47C2×#12611yescharacteristic
361C22×C47#53211yescharacteristic
362C22×C47#53211yescharacteristic
363C22×C47#53311yescharacteristic
364C22×C47#53311yescharacteristic
365C22×C47#54011yescharacteristic
366C22×C47#54111yescharacteristic
367C22×C47#54211yescharacteristic
368C22×C47#54211yescharacteristic
369C22×C47D4211yescharacteristic
370C22×C47D4211yescharacteristic
371C22×C47#54611yescharacteristic
372C22×C47#54711yescharacteristic
373C22×C47#54711yescharacteristic
374C22×C47#54711yescharacteristic
375C22×C47#54811yescharacteristic
376C22×C47D4×Q811yescharacteristic
377C22×C47D4×Q811yescharacteristic
378C22×C47#55011yescharacteristic
379C22×C47#55211yescharacteristic
380C22×C47#55311yescharacteristic
381C22×C47#55411yescharacteristic
382C22×C47#55411yescharacteristic
383C22×C47#55511yescharacteristic
384C22×C47#55611yescharacteristic
385C4×C47—24no—
386C4×C47—24no—
387C4×C47—24no—
388C4×C47—42no—
389C4×C47—42no—
390C4×C47#38818yescomplemented
391Dic47—44no—
392Dic47—44no—
393Dic47—82no—
394Dic47—82no—
395C2×#388—472no—
396C2×#384—471no—
397C2×#380—471no—
398C2×#380—471no—
399C2×C4×C4⋊C4—471no—
400C2×C4×C22⋊C4D4711yescharacteristic
401#1442—472no—
402#1439—472no—
403#1436—472no—
404C4⋊#95—471no—
405C4⋊#95—471no—
406C2×C47—44no—
407C2×C47#228511yescharacteristic
408C2×C47C2×#38811yescharacteristic
409C2×C47#231411yescharacteristic
410C2×C47D4×C4⋊C411yescharacteristic
411C2×C47D4×C4⋊C411yescharacteristic
412C2×C47#235211yescharacteristic
413C2×C47#235411yescharacteristic
414C2×C47#242211yescharacteristic
415C2×C47#242311yescharacteristic
416C2×C47#242811yescharacteristic
417C2×C47#242911yescharacteristic
418C2×C47#249111yescharacteristic
419C2×C47#249211yescharacteristic
420C2×C47#249611yescharacteristic
421C2×C47#249711yescharacteristic
422C24×C4C2×D4711yescharacteristic
423C22×C4⋊C4—471no—
424C22×C4⋊C4—471no—
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4—472no—
428C22×C4⋊C4—472no—
429C22×C22⋊C4—472no—
430C22×C22⋊C4—472no—
431C22×C22⋊C4C2×D4711yescharacteristic
432C22×C22⋊C4C2×D4711yescharacteristic
433C22×C42—472no—
434C22×C42C2×D4711yescharacteristic
435C22×C42C2×D4711yescharacteristic
436#388—948no—
437#384—944no—
438#380—944no—
439#380—944no—
440C4×C4⋊C4—944no—
441C4×C22⋊C4Dic4718yescomplemented
442C2×#95—472no—
443C2×#95—472no—
444C2×#95—472no—
445C2×#95—472no—
446C2×#95—472no—
447C2×#95—472no—
448C2×#95—472no—
449C2×#95C2×D4711yescharacteristic
450C2×#95C2×D4711yescharacteristic
451C47#1387611yescharacteristic, complemented, Sylow
452C25C22×D4711yescharacteristic
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—472no—
460C23×C4—472no—
461C23×C4—472no—
462C23×C4—472no—
463C23×C4C2×Dic4714yes—
464C23×C4C22×D4711yescharacteristic
465C23×C4C22×D4711yescharacteristic
466C23×C4C22×D4711yescharacteristic
467C23×C4C22×D4711yescharacteristic
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470C2×C4⋊C4—474no—
471C2×C4⋊C4—474no—
472C2×C4⋊C4—942no—
473C2×C4⋊C4—942no—
474C2×C4⋊C4—942no—
475C2×C4⋊C4—942no—
476C2×C4⋊C4—944no—
477C2×C4⋊C4—944no—
478C2×C4⋊C4—944no—
479C2×C4⋊C4—944no—
480C2×C4⋊C4—942no—
481C2×C4⋊C4—942no—
482C2×C4⋊C4—942no—
483C2×C4⋊C4—942no—
484C2×C4⋊C4—942no—
485C2×C4⋊C4—942no—
486C2×C4⋊C4—1882no—
487C2×C4⋊C4—1882no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—944no—
491C2×C22⋊C4—944no—
492C2×C22⋊C4—944no—
493C2×C22⋊C4—944no—
494C2×C22⋊C4—1882no—
495C2×C22⋊C4—1882no—
496C2×C22⋊C4Dic9414yes—
497C2×C22⋊C4D18814yes—
498C2×C22⋊C4C2×Dic4714yes—
499C2×C22⋊C4C2×Dic4714yes—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—944no—
505C2×C42—944no—
506C2×C42—1882no—
507C2×C42C2×Dic4714yes—
508C2×C42C2×Dic4714yes—
509#95—944no—
510#95—944no—
511#95—944no—
512#95—944no—
513#95—944no—
514#95—944no—
515#95—1882no—
516#95C2×Dic4714yes—
517#95C2×Dic4714yes—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C2×Dic9412yes—
531C24C2×D18812yes—
532C24C22×Dic4712yes—
533C24C23×D4711yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—474no—
566C22×C4—474no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
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—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4C2×Dic9412yes—
594C22×C4C2×Dic9412yes—
595C22×C4C2×D18812yes—
596C22×C4C2×D18812yes—
597C22×C4#1062535012yes—
598C22×C4#1062535012yes—
599C22×C4#1062535012yes—
600C22×C4#1062535012yes—
601C22×C4D4×D4712yes—
602C22×C4D4×D4712yes—
603C22×C4#1062535212yes—
604C22×C4#1062535212yes—
605C22×C4C22×Dic4712yes—
606C22×C4C22×Dic4712yes—
607C22×C4C22×Dic4712yes—
608C22×C4C22×Dic4712yes—
609C22×C4C22×Dic4712yes—
610C22×C4C22×Dic4712yes—
611C4⋊C4—948no—
612C4⋊C4—948no—
613C4⋊C4—1888no—
614C4⋊C4—1888no—
615C4⋊C4—1884no—
616C4⋊C4—1884no—
617C22⋊C4—28no—
618C22⋊C4—1888no—
619C22⋊C4—1888no—
620C22⋊C4C4⋊Dic47116yescomplemented
621C42—28no—
622C42—28no—
623C42—1888no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C2×C4⋊Dic4714yes—
659C23C23×Dic4711yescharacteristic
660C23C2×D4×D4711yescharacteristic
661C23C2×D4×D4711yescharacteristic
662C23C22×D18811yescharacteristic
663C23C22×Dic9411yescharacteristic
664C23C2×#1062535211yescharacteristic
665C23C2×#1062535211yescharacteristic
666C23C2×#1062535011yescharacteristic
667C23C2×#1062535011yescharacteristic
668C23C2×#1062535011yescharacteristic
669C23C2×#1062535011yescharacteristic
670C23#1309407011yescharacteristic
671C23#1309407011yescharacteristic
672C23#1309407111yescharacteristic
673C23#1309407111yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—416no—
707C2×C4—944no—
708C2×C4—944no—
709C2×C4—944no—
710C2×C4—944no—
711C2×C4—944no—
712C2×C4—944no—
713C2×C4—1882no—
714C2×C4—1882no—
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×C4—1882no—
726C2×C4—1882no—
727C2×C4—1882no—
728C2×C4—1882no—
729C2×C4—1882no—
730C2×C4—1882no—
731C2×C4—1882no—
732C2×C4—1882no—
733C2×C4—1882no—
734C2×C4—1882no—
735C2×C4C2×C4⋊Dic4714yes—
736C2×C4C2×C4⋊Dic4714yes—
737C2×C4#1309398314yes—
738C2×C4#1309398314yes—
739C2×C4D4×Dic4714yes—
740C2×C4D4×Dic4714yes—
741C2×C4#1309399714yes—
742C2×C4#1309400614yes—
743C2×C4#1309401014yes—
744C2×C4#1309401714yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C22×C4⋊Dic4711yescharacteristic
761C22C2×#1309398311yescharacteristic
762C22C2×#1309398311yescharacteristic
763C22C2×D4×Dic4711yescharacteristic
764C22C2×D4×Dic4711yescharacteristic
765C22#1568960611yescharacteristic
766C22#1568960611yescharacteristic
767C22C2×#1309399711yescharacteristic
768C22C2×#1309400611yescharacteristic
769C22C2×#1309401011yescharacteristic
770C22C2×#1309401711yescharacteristic
771C22#1568967311yescharacteristic
772C22#1568967311yescharacteristic
773C22#1568968011yescharacteristic
774C22#1568968011yescharacteristic
775C22#1568972811yescharacteristic
776C22#1568973511yescharacteristic
777C22#1568974411yescharacteristic
778C22#1568974411yescharacteristic
779C22D4×D18811yescharacteristic
780C22D4×D18811yescharacteristic
781C22#1568976911yescharacteristic
782C22#1568977711yescharacteristic
783C22#1568977711yescharacteristic
784C22#1568977811yescharacteristic
785C22#1568978211yescharacteristic
786C22D4×Dic9411yescharacteristic
787C22D4×Dic9411yescharacteristic
788C22#1568979411yescharacteristic
789C22#1568981311yescharacteristic
790C22#1568981911yescharacteristic
791C22#1568983011yescharacteristic
792C22#1568983011yescharacteristic
793C22#1568983811yescharacteristic
794C22#1568984311yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—3762no—
801C4—3762no—
802C4—1884no—
803C4—1884no—
804C4#1568901618yescomplemented
805C2—44no—
806C2#2024579511yescharacteristic
807C2C2×#1568901611yescharacteristic
808C2#2024599711yescharacteristic
809C2D4×C4⋊Dic4711yescharacteristic
810C2D4×C4⋊Dic4711yescharacteristic
811C2#2024631711yescharacteristic
812C2#2024633711yescharacteristic
813C2#2024690211yescharacteristic
814C2#2024691311yescharacteristic
815C2#2024697611yescharacteristic
816C2#2024698711yescharacteristic
817C2#2024775111yescharacteristic
818C2#2024776211yescharacteristic
819C2#2024781011yescharacteristic
820C2#2024782111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×C4×C22⋊C4D47
hypocenterC47#13876
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15688993C2semidirect
5. C2×C4×C4⋊Dic47C2semidirect
6. #20241645C2semidirect
8. #20241622C2semidirect
9. #20241618C2semidirect
10. #20241618C2semidirect
38. C4×C22⋊C4×C47C4semidirect
201. C22⋊C4×C47C4⋊C4semidirect
390. C4×C47#388semidirect
441. C4×C22⋊C4Dic47semidirect
451. C47#13876semidirect
620. C22⋊C4C4⋊Dic47semidirect
804. C4#15689016semidirect

Maximal subgroups

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

subgroupindex
C2×#156890162
C2×#156889932
C2×#156889832
C2×C4×C4⋊Dic472
#202416452
#202416332
#202416222
#202416182
C2×C4×C22⋊C4×C472
#1387647