Finite Group Databasebeta

← C2×#41×C22⋊D47 #27123235

Subgroups — C2×#41×C22⋊D47 #27123235

Order 12032.

12314 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D47C211yesmaximal, characteristic, complemented
2#41×C22⋊D47C2132yesmaximal, direct product factor
3C2×#15689792C211yesmaximal, characteristic, complemented
4C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
5C2×#15689784C211yesmaximal, characteristic, complemented
6C2×#15689780C211yesmaximal, characteristic, complemented
7C2×#15689772C213yesmaximal, complemented
8C2×#15689767C213yesmaximal, complemented
9C2×#15689761C213yesmaximal, complemented
10C2×D4×C22⋊D47C213yesmaximal, complemented
11C2×#15689669C213yesmaximal, complemented
12C2×#15689634C213yesmaximal, complemented
13C2×#15689630C213yesmaximal, complemented
14C2×#41×Dic47C211yesmaximal, characteristic, complemented
15C22×C4×C22⋊D47C213yesmaximal, complemented
16C23×#41×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic, complemented
18C22×#10625350C2213yescomplemented
19C22×#10625352C2213yescomplemented
20C2×#41×D47—216no—
21C2×#41×D47C22116yescomplemented
22C22×Q8×D47C2211yescharacteristic, complemented
23C23×C22⋊D47C2213yes—
24C22×D4×D47C2213yescomplemented
25C23×C4×D47C2213yescomplemented
26#15689792C22116yescomplemented
27Q8×C22⋊D47C22116yescomplemented
28#15689784C22116yescomplemented
29#15689780C22116yescomplemented
30#15689772C22148yescomplemented
31#15689767C22148yescomplemented
32#15689761C22148yescomplemented
33D4×C22⋊D47C22148yescomplemented
34#15689669C22148yescomplemented
35C2×#13094022C2213yescomplemented
36C2×#13094020C2213yescomplemented
37C2×#13094013C2213yescomplemented
38C2×#13094011C2213yescomplemented
39#15689634C22148yescomplemented
40#15689630C22148yescomplemented
41C2×#13094007C2216yescomplemented
42C2×#13094005C2216yescomplemented
43C2×#13094003C2213yescomplemented
44C2×#13094003C2213yescomplemented
45C2×#13094000C2213yescomplemented
46C2×#13094000C2213yescomplemented
47C2×#13093998C2213yescomplemented
48C2×#13093998C2213yescomplemented
49C2×#13093996C2216yescomplemented
50C2×#13093996C2216yescomplemented
51C2×#13093995C2213yescomplemented
52C2×#13093995C2213yescomplemented
53C2×#13093993C2216yescomplemented
54C2×#13093992C2216yescomplemented
55#41×Dic47C22116yescomplemented
56C2×Q8×Dic47C2211yescharacteristic, complemented
57C2×Q8×Dic47C2211yescharacteristic, complemented
58C2×D4×Dic47C2213yescomplemented
59C2×D4×Dic47C2213yescomplemented
60C2×C4×C22⋊D47C2211yescharacteristic
61C2×C4×C22⋊D47C2213yes—
62C2×C4×C22⋊D47C2213yescomplemented
63C2×C4×C22⋊D47C2213yescomplemented
64C2×C4×C22⋊D47C2213yescomplemented
65C2×C4×C22⋊D47C2213yescomplemented
66C2×C4×C22⋊D47C2213yescomplemented
67C2×C4×C22⋊D47C2213yescomplemented
68C2×C4×C22⋊D47C2216yescomplemented
69C2×C4×C22⋊D47C22148yescomplemented
70C2×#13093983C2213yescomplemented
71C22×Dic47⋊C4C2213yescomplemented
72C22×C22⋊Dic47C2213yescomplemented
73C22×(C2×D47)⋊C4C2213yescomplemented
74C22×C4×Dic47C2213yescomplemented
75C22×#41×C47—216no—
76C22×#41×C47C2211yescharacteristic
77C22×#41×C47C2213yescomplemented
78C22×#41×C47C2211yescharacteristic, complemented
79C22×#41×C47C2213yescomplemented
80C22×#41×C47C22116yescomplemented
81C23×Q8×C47C2211yescharacteristic, complemented
82C23×D4×C47C2213yescomplemented
83C24×C4×C47C2213yescomplemented
84C24×D47C2313yes—
85C2×#10625354—28no—
86C2×#10625354C2318yescomplemented
87C2×#10625350—224no—
88C2×#10625350C23124yescomplemented
89C2×#10625352—224no—
90C2×#10625352C23124yescomplemented
91#41×D47—2128no—
92C22×Dic94C2313yes—
93C2×Q8×D47—28no—
94C2×Q8×D47C2318yescomplemented
95C22×D188C2313yes—
96C22×C22⋊D47—224no—
97C22×C22⋊D47C23124yes—
98C22×C22⋊D47C2313yes—
99C22×C22⋊D47C2313yes—
100C22×C22⋊D47C2313yes—
101C22×C22⋊D47C2316yes—
102C22×C22⋊D47C2316yes—
103C22×C22⋊D47C2311yescharacteristic
104C2×D4×D47—224no—
105C2×D4×D47C23124yescomplemented
106C23×Dic47C2313yes—
107C23×Dic47C2313yes—
108C23×Dic47C2313yes—
109C22×C4×D47—224no—
110C22×C4×D47C2311yescharacteristic
111C22×C4×D47C2313yes—
112C22×C4×D47C2313yes—
113C22×C4×D47C2313yes—
114C22×C4×D47C23124yescomplemented
115#13094022C23124yescomplemented
116#13094020C23124yescomplemented
117#13094013C23124yescomplemented
118#13094011C23124yescomplemented
119#13094007C23148yescomplemented
120#13094005C23148yescomplemented
121#13094003C23124yescomplemented
122#13094003C23124yescomplemented
123#13094000C23124yescomplemented
124#13094000C23124yescomplemented
125#13093998C23124yescomplemented
126#13093998C23124yescomplemented
127#13093996C23148yescomplemented
128#13093996C23148yescomplemented
129#13093995C23124yescomplemented
130#13093995C23124yescomplemented
131#13093993C23148yescomplemented
132#13093992C23148yescomplemented
133Q8×Dic47C2318yescomplemented
134Q8×Dic47C2318yescomplemented
135D4×Dic47C23124yescomplemented
136D4×Dic47C23124yescomplemented
137C4×C22⋊D47C23124yes—
138C4×C22⋊D47C2318yes—
139C4×C22⋊D47C23124yescomplemented
140C4×C22⋊D47C23124yescomplemented
141C4×C22⋊D47C23124yescomplemented
142C4×C22⋊D47C23124yescomplemented
143C4×C22⋊D47C23124yescomplemented
144C4×C22⋊D47C23124yescomplemented
145C4×C22⋊D47C23148yescomplemented
146#13093983C23124yescomplemented
147C2×C4⋊Dic47C2313yes—
148C2×C4⋊Dic47C2313yes—
149C2×Dic47⋊C4C2311yescharacteristic
150C2×Dic47⋊C4C2313yes—
151C2×Dic47⋊C4C2313yes—
152C2×Dic47⋊C4C2313yes—
153C2×Dic47⋊C4C2316yes—
154C2×Dic47⋊C4C23124yescomplemented
155C2×C22⋊Dic47C2311yescharacteristic
156C2×C22⋊Dic47C2313yes—
157C2×C22⋊Dic47C2313yes—
158C2×C22⋊Dic47C2313yes—
159C2×C22⋊Dic47C2316yes—
160C2×C22⋊Dic47C2316yes—
161C2×C22⋊Dic47C23124yescomplemented
162C2×(C2×D47)⋊C4C2311yescharacteristic
163C2×(C2×D47)⋊C4C2313yes—
164C2×(C2×D47)⋊C4C2313yes—
165C2×(C2×D47)⋊C4C2313yes—
166C2×(C2×D47)⋊C4C2316yes—
167C2×(C2×D47)⋊C4C23124yescomplemented
168C2×C4×Dic47C2311yescharacteristic
169C2×C4×Dic47C2313yes—
170C2×C4×Dic47C2313yes—
171C2×C4×Dic47C2313yes—
172C2×C4×Dic47C23124yescomplemented
173C25×C47C2313yes—
174C2×#41×C47—2128no—
175C2×#41×C47—28no—
176C2×#41×C47—224no—
177C2×#41×C47—224no—
178C2×#41×C47D4116yescomplemented
179C2×#41×C47C2318yes—
180C2×#41×C47C23124yescomplemented
181C2×#41×C47C2318yescomplemented
182C2×#41×C47C23124yescomplemented
183C22×Q8×C47—28no—
184C22×Q8×C47C2313yes—
185C22×Q8×C47C2311yescharacteristic
186C22×Q8×C47C2318yescomplemented
187C22×D4×C47—224no—
188C22×D4×C47C2316yes—
189C22×D4×C47C2313yes—
190C22×D4×C47C2313yes—
191C22×D4×C47C23124yescomplemented
192C23×C4×C47—224no—
193C23×C4×C47C2313yes—
194C23×C4×C47C2311yescharacteristic
195C23×C4×C47C2313yes—
196C23×C4×C47C2313yes—
197C23×C4×C47C2313yes—
198C23×C4×C47C2313yes—
199C23×C4×C47C23124yescomplemented
200C24×C47—212no—
201C24×C47—212no—
202C24×C47—46no—
203C24×C47C2413yes—
204C24×C47C24112yes—
205C24×C47C2413yes—
206C24×C47C2411yescharacteristic
207C23×D47—212no—
208C23×D47—212no—
209C23×D47—46no—
210C23×D47C2413yes—
211C23×D47C24112yes—
212C23×D47C2411yescharacteristic
213#41×C47—232no—
214#41×C47—296no—
215#41×C47—296no—
216#41×C47C2×D4164yescomplemented
217C2×Q8×C47—232no—
218C2×Q8×C47—212no—
219C2×Q8×C47C2×D418yescomplemented
220C2×Q8×C47C24112yes—
221C2×Q8×C47C2414yes—
222C2×D4×C47—224no—
223C2×D4×C47—296no—
224C2×D4×C47—212no—
225C2×D4×C47C2×D4124yescomplemented
226C2×D4×C47C24124yes—
227C2×D4×C47C24112yes—
228C2×D4×C47C24112yes—
229C22×C4×C47—212no—
230C22×C4×C47—24no—
231C22×C4×C47—212no—
232C22×C4×C47—212no—
233C22×C4×C47—212no—
234C22×C4×C47—296no—
235C22×C4×C47C2×D4124yescomplemented
236C22×C4×C47C2411yescharacteristic
237C22×C4×C47C2413yes—
238C22×C4×C47C2414yes—
239C22×C4×C47C24112yes—
240C22×C4×C47C24112yes—
241C22×C4×C47C24112yes—
242C22×C4×C47C24112yes—
243C22×C4×C47C2413yes—
244C22×C4×C47C2411yescharacteristic
245C22×C4×C47C24112yes—
246C2×C22⋊D47—224no—
247C2×C22⋊D47—212no—
248C2×C22⋊D47—212no—
249C2×C22⋊D47—296no—
250C2×C22⋊D47—212no—
251C2×C22⋊D47—412no—
252C2×C22⋊D47#4118yesdirect product factor
253C2×C22⋊D47C24112yes—
254C2×C22⋊D47C24112yes—
255C2×C22⋊D47C24112yes—
256C2×C22⋊D47C24124yes—
257C2×C22⋊D47C24124yes—
258C2×C22⋊D47C2414yes—
259C22×Dic47—212no—
260C22×Dic47—212no—
261C22×Dic47—46no—
262C22×Dic47C2411yescharacteristic
263C22×Dic47C2413yes—
264C22×Dic47C2413yes—
265C22×Dic47C24112yes—
266C22×Dic47C2411yescharacteristic
267C22×Dic47C2413yes—
268C22×Dic47C24112yes—
269C22×Dic47C24112yes—
270C22×Dic47C2411yescharacteristic
271#10625354—232no—
272Q8×D47—232no—
273#10625352—296no—
274D4×D47—296no—
275#10625350—296no—
276C2×D188—212no—
277C2×D188C24112yes—
278C2×C4×D47—24no—
279C2×C4×D47—212no—
280C2×C4×D47—212no—
281C2×C4×D47—212no—
282C2×C4×D47—296no—
283C2×C4×D47C2414yes—
284C2×C4×D47C24112yes—
285C2×C4×D47C24112yes—
286C2×C4×D47C24112yes—
287C2×Dic94—212no—
288C2×Dic94C24112yes—
289C22⋊Dic47C2414yes—
290C22⋊Dic47C24112yes—
291C22⋊Dic47C24112yes—
292C22⋊Dic47C24112yes—
293C22⋊Dic47C24124yes—
294C22⋊Dic47C24124yes—
295(C2×D47)⋊C4C2414yes—
296(C2×D47)⋊C4C24112yes—
297(C2×D47)⋊C4C24112yes—
298(C2×D47)⋊C4C24112yes—
299(C2×D47)⋊C4C24124yes—
300C4⋊Dic47C24112yes—
301C4⋊Dic47C24112yes—
302Dic47⋊C4C2414yes—
303Dic47⋊C4C24112yes—
304Dic47⋊C4C24112yes—
305Dic47⋊C4C24112yes—
306Dic47⋊C4C24124yes—
307C4×Dic47C2414yes—
308C4×Dic47C24112yes—
309C4×Dic47C24112yes—
310C4×Dic47C24112yes—
311C23×C47—22no—
312C23×C47—26no—
313C23×C47—26no—
314C23×C47—22no—
315C23×C47—224no—
316C23×C47—26no—
317C23×C47—26no—
318C23×C47—224no—
319C23×C47—26no—
320C23×C47—412no—
321C23×C47—448no—
322C23×C47C22×D4112yes—
323C23×C47C2×#4114yescomplemented
324C23×C47C2516yes—
325C23×C47C2516yes—
326C23×C47C2512yes—
327C23×C47C2511yescharacteristic
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—26no—
331C22×D47—224no—
332C22×D47—26no—
333C22×D47—26no—
334C22×D47—224no—
335C22×D47—412no—
336C22×D47—448no—
337C22×D47C2×#4114yescomplemented
338C22×D47C2516yes—
339C22×D47C2512yes—
340Q8×C47—224no—
341Q8×C47C22×D4116yescomplemented
342D4×C47—248no—
343D4×C47—224no—
344D4×C47C22×D4148yescomplemented
345C2×C4×C47—22no—
346C2×C4×C47—26no—
347C2×C4×C47—224no—
348C2×C4×C47—28no—
349C2×C4×C47—224no—
350C2×C4×C47—224no—
351C2×C4×C47—224no—
352C2×C4×C47C22×D4112yes—
353C2×C4×C47C22×D414yes—
354C2×C4×C47C22×D4148yescomplemented
355C2×C4×C47C2512yes—
356C2×C4×C47C2516yes—
357C2×C4×C47C2512yes—
358C2×C4×C47C2516yes—
359C22⋊D47—248no—
360C22⋊D47—224no—
361C22⋊D47—224no—
362C22⋊D47—224no—
363C22⋊D47—424no—
364C22⋊D47C2×#41116yesdirect product factor
365C2×Dic47—26no—
366C2×Dic47—22no—
367C2×Dic47—224no—
368C2×Dic47—26no—
369C2×Dic47—22no—
370C2×Dic47—26no—
371C2×Dic47—224no—
372C2×Dic47—412no—
373C2×Dic47C2×#4114yescomplemented
374C2×Dic47C2512yes—
375C2×Dic47C2516yes—
376C2×Dic47C2516yes—
377C2×Dic47C2516yes—
378C2×Dic47C2512yes—
379C2×Dic47C2512yes—
380D188—224no—
381C4×D47—28no—
382C4×D47—224no—
383C4×D47—224no—
384C4×D47—224no—
385Dic94—224no—
386C2×D4×#41—471nomaximal, Sylow
387C22×C47—22no—
388C22×C47—26no—
389C22×C47—26no—
390C22×C47—22no—
391C22×C47—224no—
392C22×C47—28no—
393C22×C47—26no—
394C22×C47—26no—
395C22×C47—26no—
396C22×C47—448no—
397C22×C47—412no—
398C22×C47C23×D4112yes—
399C22×C47C23×D412yes—
400C22×C47C22×#4112yes—
401C22×C47C22×#4114yescomplemented
402C22×C47#58512yes—
403C22×C47C2611yescharacteristic
404C2×D47—22no—
405C2×D47—22no—
406C2×D47—28no—
407C2×D47—26no—
408C2×D47—26no—
409C2×D47—26no—
410C2×D47—448no—
411C2×D47—412no—
412C2×D47C22×#4114yescomplemented
413C4×C47—22no—
414C4×C47—26no—
415C4×C47C23×D4112yes—
416C4×C47C23×D414yes—
417Dic47—26no—
418Dic47—22no—
419Dic47—26no—
420Dic47—22no—
421Dic47—26no—
422Dic47C22×#4114yescomplemented
423C23×#41—471no—
424C23×#41D4711yescharacteristic, complemented
425D4×#41—4732no—
426C2×#550—471no—
427C2×D4×Q8—471no—
428C2×#548—471no—
429C2×#548—471no—
430C2×#547—473no—
431C2×#546—473no—
432C2×#546—473no—
433C2×D42—473no—
434C2×#532—473no—
435C2×#525—473no—
436C2×#525—473no—
437C2×C4×#41—471no—
438C22×C4×D4—473no—
439C2×C47—212no—
440C2×C47—24no—
441C2×C47—46no—
442C2×C47D4×#4114yescomplemented
443C2×C47C24×D411yescharacteristic
444C2×C47C23×#4111yescharacteristic
445C2×C47C2×#58511yescharacteristic
446D47—24no—
447D47—46no—
448C22×#41—216no—
449C22×#41—4716no—
450C22×#41—471no—
451C22×#41—473no—
452C22×#41—473no—
453C22×#41—9416no—
454C22×#41C2×D4711yescharacteristic
455C22×#41C2×D4713yescomplemented
456C22×#41C2×D4713yescomplemented
457C22×#41C2×D4711yescharacteristic, complemented
458C22×#41C2×D47116yescomplemented
459C23×Q8—471no—
460C23×Q8C2×D4711yescharacteristic, complemented
461C23×D4—473no—
462C23×D4—473no—
463C23×D4C2×D4713yescomplemented
464C24×C4—473no—
465C24×C4C2×D4713yescomplemented
466#550—4716no—
467D4×Q8—4716no—
468#548—4716no—
469#548—4716no—
470#547—4748no—
471#546—4748no—
472#546—4748no—
473D42—4748no—
474#532—4748no—
475C2×C4⋊Q8—473no—
476C2×#127—473no—
477C2×#124—473no—
478C2×#124—473no—
479#525—4748no—
480#525—4748no—
481C2×#123—476no—
482C2×#123—476no—
483C2×C22⋊Q8—473no—
484C2×C22⋊Q8—473no—
485C2×C22⋊Q8—473no—
486C2×C22⋊Q8—473no—
487C2×#121—473no—
488C2×#121—473no—
489C2×#121—476no—
490C2×#121—476no—
491C2×#121—473no—
492C2×#121—473no—
493C2×#120—476no—
494C2×#120—476no—
495C4×#41—4716no—
496C2×C4×Q8—471no—
497C2×C4×Q8—471no—
498C2×C4×D4—473no—
499C2×C4×D4—473no—
500C2×C4×D4—471no—
501C2×C4×D4—473no—
502C2×C4×D4—473no—
503C2×C4×D4—473no—
504C2×C4×D4—473no—
505C2×C4×D4—473no—
506C2×C4×D4—473no—
507C2×C4×D4—473no—
508C2×C4×D4—476no—
509C2×C4×D4—4748no—
510C2×#117—473no—
511C22×C4⋊C4—473no—
512C22×C22⋊C4—473no—
513C22×C22⋊C4—473no—
514C22×C42—473no—
515C47C2×D4×#4111yescharacteristic, complemented, Sylow
516C25—473no—
517C25C22×D4713yes—
518C2×#41—2128no—
519C2×#41—28no—
520C2×#41—224no—
521C2×#41—224no—
522C2×#41—478no—
523C2×#41—4724no—
524C2×#41—4724no—
525C2×#41—94128no—
526C2×#41—948no—
527C2×#41—9424no—
528C2×#41—9424no—
529C2×#41C22⋊D47116yesdirect product factor
530C2×#41C22×D4718yes—
531C2×#41C22×D47124yescomplemented
532C2×#41C22×D47124yescomplemented
533C2×#41C22×D4718yescomplemented
534C22×Q8—28no—
535C22×Q8—478no—
536C22×Q8—473no—
537C22×Q8—948no—
538C22×Q8C22×D4713yes—
539C22×Q8C22×D4711yescharacteristic
540C22×Q8C22×D4718yescomplemented
541C22×D4—224no—
542C22×D4—471no—
543C22×D4—473no—
544C22×D4—473no—
545C22×D4—473no—
546C22×D4—4724no—
547C22×D4—476no—
548C22×D4—476no—
549C22×D4—4724no—
550C22×D4—473no—
551C22×D4—9424no—
552C22×D4—9424no—
553C22×D4C22×D4716yes—
554C22×D4C22×D4713yes—
555C22×D4C22×D4713yes—
556C22×D4C22×D47124yescomplemented
557C23×C4—224no—
558C23×C4—473no—
559C23×C4—473no—
560C23×C4—473no—
561C23×C4—473no—
562C23×C4—473no—
563C23×C4—4724no—
564C23×C4—471no—
565C23×C4—473no—
566C23×C4—9424no—
567C23×C4C22×D4713yes—
568C23×C4C22×D4713yes—
569C23×C4C22×D4713yes—
570C23×C4C22×D4711yescharacteristic
571C23×C4C22×D4713yes—
572C23×C4C22×D4713yes—
573C23×C4C22×D47124yescomplemented
574C4⋊Q8—4724no—
575#127—4724no—
576#124—4724no—
577#124—4724no—
578#123—4748no—
579#123—4748no—
580C22⋊Q8—4724no—
581C22⋊Q8—4724no—
582C22⋊Q8—4724no—
583C22⋊Q8—4724no—
584#121—4724no—
585#121—4724no—
586#121—4748no—
587#121—4748no—
588#121—4724no—
589#121—4724no—
590#120—4748no—
591#120—4748no—
592C4×Q8—478no—
593C4×Q8—478no—
594C4×D4—4724no—
595C4×D4—4724no—
596C4×D4—478no—
597C4×D4—4724no—
598C4×D4—4724no—
599C4×D4—4724no—
600C4×D4—4724no—
601C4×D4—4724no—
602C4×D4—4724no—
603C4×D4—4724no—
604C4×D4—4748no—
605#117—4724no—
606C2×C4⋊C4—471no—
607C2×C4⋊C4—473no—
608C2×C4⋊C4—473no—
609C2×C4⋊C4—473no—
610C2×C4⋊C4—4724no—
611C2×C4⋊C4—473no—
612C2×C4⋊C4—473no—
613C2×C4⋊C4—476no—
614C2×C22⋊C4—471no—
615C2×C22⋊C4—473no—
616C2×C22⋊C4—473no—
617C2×C22⋊C4—473no—
618C2×C22⋊C4—4724no—
619C2×C22⋊C4—476no—
620C2×C22⋊C4—476no—
621C2×C22⋊C4—471no—
622C2×C22⋊C4—473no—
623C2×C22⋊C4—473no—
624C2×C22⋊C4—473no—
625C2×C22⋊C4—4724no—
626C2×C22⋊C4—476no—
627C2×C42—473no—
628C2×C42—473no—
629C2×C42—4724no—
630C2×C42—473no—
631C2×C42—471no—
632C24—212no—
633C24—212no—
634C24—46no—
635C24—471no—
636C24—473no—
637C24—4712no—
638C24—9412no—
639C24—9412no—
640C24—1886no—
641C24C23×D4713yes—
642C24C23×D47112yes—
643C24C23×D4713yes—
644C24C23×D4711yescharacteristic
645#41—232no—
646#41—296no—
647#41—296no—
648#41—9432no—
649#41—9496no—
650#41—9496no—
651#41C2×C22⋊D47164yesdirect product factor
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—4712no—
655C2×Q8—9432no—
656C2×Q8—9412no—
657C2×Q8C2×C22⋊D4718yescomplemented
658C2×Q8C23×D47112yes—
659C2×Q8C23×D4714yes—
660C2×D4—224no—
661C2×D4—296no—
662C2×D4—212no—
663C2×D4—478no—
664C2×D4—474no—
665C2×D4—4712no—
666C2×D4—4712no—
667C2×D4—4712no—
668C2×D4—4724no—
669C2×D4—4724no—
670C2×D4—4712no—
671C2×D4—9412no—
672C2×D4—9496no—
673C2×D4—9412no—
674C2×D4—9424no—
675C2×D4—9412no—
676C2×D4—9496no—
677C2×D4—9412no—
678C2×D4—18812no—
679C2×D4C2×C22⋊D47124yescomplemented
680C2×D4C23×D47124yes—
681C2×D4C23×D47112yes—
682C2×D4C23×D47112yes—
683C22×C4—212no—
684C22×C4—24no—
685C22×C4—212no—
686C22×C4—212no—
687C22×C4—212no—
688C22×C4—296no—
689C22×C4—471no—
690C22×C4—471no—
691C22×C4—473no—
692C22×C4—473no—
693C22×C4—4712no—
694C22×C4—471no—
695C22×C4—473no—
696C22×C4—4712no—
697C22×C4—4712no—
698C22×C4—474no—
699C22×C4—4712no—
700C22×C4—4712no—
701C22×C4—4712no—
702C22×C4—9412no—
703C22×C4—9412no—
704C22×C4—944no—
705C22×C4—9412no—
706C22×C4—9412no—
707C22×C4—9412no—
708C22×C4—9496no—
709C22×C4—1886no—
710C22×C4C2×C22⋊D47124yescomplemented
711C22×C4C23×D4711yescharacteristic
712C22×C4C23×D4713yes—
713C22×C4C23×D47112yes—
714C22×C4C23×D4714yes—
715C22×C4C23×D47112yes—
716C22×C4C23×D47112yes—
717C22×C4C23×D47112yes—
718C22×C4C23×D4713yes—
719C22×C4C23×D47112yes—
720C22×C4C23×D4711yescharacteristic
721C4⋊C4—474no—
722C4⋊C4—4712no—
723C4⋊C4—4712no—
724C4⋊C4—4712no—
725C4⋊C4—4724no—
726C4⋊C4—4712no—
727C4⋊C4—4712no—
728C22⋊C4—474no—
729C22⋊C4—4712no—
730C22⋊C4—4712no—
731C22⋊C4—4712no—
732C22⋊C4—4724no—
733C22⋊C4—4724no—
734C22⋊C4—474no—
735C22⋊C4—4712no—
736C22⋊C4—4712no—
737C22⋊C4—4712no—
738C22⋊C4—4724no—
739C42—474no—
740C42—4712no—
741C42—4712no—
742C42—4712no—
743C23—22no—
744C23—26no—
745C23—26no—
746C23—22no—
747C23—224no—
748C23—26no—
749C23—26no—
750C23—224no—
751C23—26no—
752C23—412no—
753C23—448no—
754C23—474no—
755C23—472no—
756C23—476no—
757C23—9424no—
758C23—942no—
759C23—942no—
760C23—9424no—
761C23—946no—
762C23—946no—
763C23—946no—
764C23—18812no—
765C23—18848no—
766C23C22×C22⋊D47112yes—
767C23#41×D4714yescomplemented
768C23C24×D4716yes—
769C23C24×D4716yes—
770C23C24×D4712yes—
771C23C24×D4711yescharacteristic
772Q8—224no—
773Q8—9424no—
774Q8C22×C22⋊D47116yescomplemented
775D4—248no—
776D4—224no—
777D4—4716no—
778D4—9424no—
779D4—9424no—
780D4—9448no—
781D4—9424no—
782D4—9424no—
783D4—18824no—
784D4C22×C22⋊D47148yescomplemented
785C2×C4—22no—
786C2×C4—26no—
787C2×C4—224no—
788C2×C4—28no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—224no—
792C2×C4—474no—
793C2×C4—472no—
794C2×C4—472no—
795C2×C4—476no—
796C2×C4—476no—
797C2×C4—472no—
798C2×C4—476no—
799C2×C4—9424no—
800C2×C4—942no—
801C2×C4—946no—
802C2×C4—9424no—
803C2×C4—946no—
804C2×C4—942no—
805C2×C4—946no—
806C2×C4—948no—
807C2×C4—9424no—
808C2×C4—9424no—
809C2×C4—9424no—
810C2×C4—18812no—
811C2×C4C22×C22⋊D4714yes—
812C2×C4C22×C22⋊D47112yes—
813C2×C4C22×C22⋊D47148yescomplemented
814C2×C4C24×D4712yes—
815C2×C4C24×D4716yes—
816C2×C4C24×D4712yes—
817C2×C4C24×D4716yes—
818C22—28no—
819C22—224no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—22no—
824C22—26no—
825C22—26no—
826C22—26no—
827C22—448no—
828C22—412no—
829C22—474no—
830C22—948no—
831C22—942no—
832C22—942no—
833C22—946no—
834C22—946no—
835C22—946no—
836C22—18848no—
837C22—18812no—
838C22C23×C22⋊D47112yes—
839C22C23×C22⋊D4712yes—
840C22C2×#41×D4712yes—
841C22C2×#41×D4714yescomplemented
842C22#1568995912yes—
843C22C25×D4711yescharacteristic
844C4—22no—
845C4—26no—
846C4—474no—
847C4—942no—
848C4—946no—
849C4—946no—
850C4—942no—
851C4—946no—
852C4C23×C22⋊D4714yes—
853C4C23×C22⋊D47112yes—
854C2—24no—
855C2—212no—
856C2—46no—
857C2—944no—
858C2—1886no—
859C2#41×C22⋊D4714yesdirect product factor
860C2C24×C22⋊D4711yescharacteristic
861C2C22×#41×D4711yescharacteristic
862C2C2×#1568995911yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC23×#41×C47C2
socleC23×C47C25
hypercenterC23×#41D47
hypocenterC47C2×D4×#41
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C22×#41×D47C2semidirect
2. #41×C22⋊D47C2direct (N × H)
3. C2×#15689792C2semidirect
4. C2×Q8×C22⋊D47C2semidirect
5. C2×#15689784C2semidirect
6. C2×#15689780C2semidirect
7. C2×#15689772C2semidirect
8. C2×#15689767C2semidirect
9. C2×#15689761C2semidirect
10. C2×D4×C22⋊D47C2semidirect
11. C2×#15689669C2semidirect
12. C2×#15689634C2semidirect
13. C2×#15689630C2semidirect
14. C2×#41×Dic47C2semidirect
15. C22×C4×C22⋊D47C2semidirect
16. C23×#41×C47C2semidirect
17. C22×#10625354C22semidirect
18. C22×#10625350C22semidirect
19. C22×#10625352C22semidirect
21. C2×#41×D47C22semidirect
22. C22×Q8×D47C22semidirect
24. C22×D4×D47C22semidirect
25. C23×C4×D47C22semidirect
26. #15689792C22semidirect
27. Q8×C22⋊D47C22semidirect
28. #15689784C22semidirect
29. #15689780C22semidirect
30. #15689772C22semidirect
31. #15689767C22semidirect
32. #15689761C22semidirect
33. D4×C22⋊D47C22semidirect
34. #15689669C22semidirect
35. C2×#13094022C22semidirect
36. C2×#13094020C22semidirect
37. C2×#13094013C22semidirect
38. C2×#13094011C22semidirect
39. #15689634C22semidirect
40. #15689630C22semidirect
41. C2×#13094007C22semidirect
42. C2×#13094005C22semidirect
43. C2×#13094003C22semidirect
44. C2×#13094003C22semidirect
45. C2×#13094000C22semidirect
46. C2×#13094000C22semidirect
47. C2×#13093998C22semidirect
48. C2×#13093998C22semidirect
49. C2×#13093996C22semidirect
50. C2×#13093996C22semidirect
51. C2×#13093995C22semidirect
52. C2×#13093995C22semidirect
53. C2×#13093993C22semidirect
54. C2×#13093992C22semidirect
55. #41×Dic47C22semidirect
56. C2×Q8×Dic47C22semidirect
57. C2×Q8×Dic47C22semidirect
58. C2×D4×Dic47C22semidirect
59. C2×D4×Dic47C22semidirect
62. C2×C4×C22⋊D47C22semidirect
63. C2×C4×C22⋊D47C22semidirect
64. C2×C4×C22⋊D47C22semidirect
65. C2×C4×C22⋊D47C22semidirect
66. C2×C4×C22⋊D47C22semidirect
67. C2×C4×C22⋊D47C22semidirect
68. C2×C4×C22⋊D47C22semidirect
69. C2×C4×C22⋊D47C22semidirect
70. C2×#13093983C22semidirect
71. C22×Dic47⋊C4C22semidirect
72. C22×C22⋊Dic47C22semidirect
73. C22×(C2×D47)⋊C4C22semidirect
74. C22×C4×Dic47C22semidirect
77. C22×#41×C47C22semidirect
78. C22×#41×C47C22semidirect
79. C22×#41×C47C22semidirect
80. C22×#41×C47C22semidirect
81. C23×Q8×C47C22semidirect
82. C23×D4×C47C22semidirect
83. C24×C4×C47C22semidirect
86. C2×#10625354C23semidirect
88. C2×#10625350C23semidirect
90. C2×#10625352C23semidirect
94. C2×Q8×D47C23semidirect
105. C2×D4×D47C23semidirect
114. C22×C4×D47C23semidirect
115. #13094022C23semidirect
116. #13094020C23semidirect
117. #13094013C23semidirect
118. #13094011C23semidirect
119. #13094007C23semidirect
120. #13094005C23semidirect
121. #13094003C23semidirect
122. #13094003C23semidirect
123. #13094000C23semidirect
124. #13094000C23semidirect
125. #13093998C23semidirect
126. #13093998C23semidirect
127. #13093996C23semidirect
128. #13093996C23semidirect
129. #13093995C23semidirect
130. #13093995C23semidirect
131. #13093993C23semidirect
132. #13093992C23semidirect
133. Q8×Dic47C23semidirect
134. Q8×Dic47C23semidirect
135. D4×Dic47C23semidirect
136. D4×Dic47C23semidirect
139. C4×C22⋊D47C23semidirect
140. C4×C22⋊D47C23semidirect
141. C4×C22⋊D47C23semidirect
142. C4×C22⋊D47C23semidirect
143. C4×C22⋊D47C23semidirect
144. C4×C22⋊D47C23semidirect
145. C4×C22⋊D47C23semidirect
146. #13093983C23semidirect
154. C2×Dic47⋊C4C23semidirect
161. C2×C22⋊Dic47C23semidirect
167. C2×(C2×D47)⋊C4C23semidirect
172. C2×C4×Dic47C23semidirect
178. C2×#41×C47D4semidirect
180. C2×#41×C47C23semidirect
181. C2×#41×C47C23semidirect
182. C2×#41×C47C23semidirect
186. C22×Q8×C47C23semidirect
191. C22×D4×C47C23semidirect
199. C23×C4×C47C23semidirect
216. #41×C47C2×D4semidirect
219. C2×Q8×C47C2×D4semidirect
225. C2×D4×C47C2×D4semidirect
235. C22×C4×C47C2×D4semidirect
252. C2×C22⋊D47#41direct (N × H)
323. C23×C47C2×#41semidirect
337. C22×D47C2×#41semidirect
341. Q8×C47C22×D4semidirect
344. D4×C47C22×D4semidirect
354. C2×C4×C47C22×D4semidirect
364. C22⋊D47C2×#41direct (N × H)
373. C2×Dic47C2×#41semidirect
401. C22×C47C22×#41semidirect
412. C2×D47C22×#41semidirect
422. Dic47C22×#41semidirect
424. C23×#41D47semidirect
442. C2×C47D4×#41semidirect
455. C22×#41C2×D47semidirect
456. C22×#41C2×D47semidirect
457. C22×#41C2×D47semidirect
458. C22×#41C2×D47semidirect
460. C23×Q8C2×D47semidirect
463. C23×D4C2×D47semidirect
465. C24×C4C2×D47semidirect
515. C47C2×D4×#41semidirect
529. C2×#41C22⋊D47direct (N × H)
531. C2×#41C22×D47semidirect
532. C2×#41C22×D47semidirect
533. C2×#41C22×D47semidirect
540. C22×Q8C22×D47semidirect
556. C22×D4C22×D47semidirect
573. C23×C4C22×D47semidirect
651. #41C2×C22⋊D47direct (N × H)
657. C2×Q8C2×C22⋊D47semidirect
679. C2×D4C2×C22⋊D47semidirect
710. C22×C4C2×C22⋊D47semidirect
767. C23#41×D47semidirect
774. Q8C22×C22⋊D47semidirect
784. D4C22×C22⋊D47semidirect
813. C2×C4C22×C22⋊D47semidirect
841. C22C2×#41×D47semidirect
859. C2#41×C22⋊D47direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D472
#41×C22⋊D472
C2×#156897922
C2×Q8×C22⋊D472
C2×#156897842
C2×#156897802
C2×#156897722
C2×#156897672
C2×#156897612
C2×D4×C22⋊D472
C2×#156896692
C2×#156896342
C2×#156896302
C2×#41×Dic472
C22×C4×C22⋊D472
C23×#41×C472
C2×D4×#4147