Finite Group Databasebeta

← C2×#20257065 #27124678

Subgroups — C2×#20257065 #27124678

Order 12032.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094072C211yesmaximal, characteristic, complemented
2C23×#10625354C211yesmaximal, characteristic, complemented
3#20257065C2132yesmaximal, direct product factor
4C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
5C2×#15689785C211yesmaximal, characteristic, complemented
6C2×#15689784C211yesmaximal, characteristic, complemented
7C2×#15689776C213yesmaximal, complemented
8C2×#15689775C213yesmaximal, complemented
9C2×#15689769C213yesmaximal, complemented
10C2×#15689764C213yesmaximal, complemented
11C2×#15689703C213yesmaximal, complemented
12C2×#15689698C213yesmaximal, complemented
13C2×#15689632C213yesmaximal, complemented
14C2×C22⋊Q8×D47C213yesmaximal, complemented
15C2×#15689605C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C47C211yesmaximal, characteristic, complemented
17C2×#13094072—216no—
18C2×#13094072C22116yescomplemented
19C22×#10625354—216no—
20C22×#10625354C2213yes—
21C22×#10625354C2211yescharacteristic
22C22×#10625354C2213yes—
23C22×#10625354C2211yescharacteristic
24C22×#10625354C22116yescomplemented
25C22×#10625354C2213yescomplemented
26C22×#10625350C2213yescomplemented
27C22×#10625350C2213yescomplemented
28C22×Q8×D47C2211yescharacteristic, complemented
29C22×Q8×D47C2213yescomplemented
30C23×D188C2213yes—
31C23×C4×D47C2213yes—
32Q8×C22⋊D47C22116yescomplemented
33#15689785C22116yescomplemented
34#15689784C22116yescomplemented
35#15689776C22148yescomplemented
36#15689775C22148yescomplemented
37#15689769C22148yescomplemented
38#15689764C22148yescomplemented
39#15689703C22148yescomplemented
40#15689698C22148yescomplemented
41C2×#13094022C2213yescomplemented
42C2×#13094013C2213yescomplemented
43C2×#13094012C2213yescomplemented
44#15689632C22148yescomplemented
45C2×#13094009C2216yescomplemented
46C2×#13094009C2216yescomplemented
47C2×#13094009C2213yescomplemented
48C2×#13094006C2213yescomplemented
49C2×#13094004C2213yescomplemented
50C2×#13094003C2213yes—
51C2×#13094002C2216yescomplemented
52C2×#13094002C2213yescomplemented
53C2×#13094001C2213yes—
54C2×#13094000C2213yescomplemented
55C2×#13094000C2213yescomplemented
56C22⋊Q8×D47C22148yescomplemented
57C2×#13093999C2216yescomplemented
58C2×#13093999C2213yescomplemented
59C2×#13093998C2213yescomplemented
60C2×#13093997C2216yescomplemented
61C2×#13093997C2213yescomplemented
62C2×#13093996C2211yescharacteristic
63C2×#13093994C2213yes—
64C2×#13093992C2213yes—
65#15689605C22116yescomplemented
66C2×Q8×Dic47C2211yescharacteristic, complemented
67C2×C4×D188C2213yescomplemented
68C2×C4×D188C2213yescomplemented
69C2×#13093986C2213yescomplemented
70C2×C4×C22⋊D47C2213yes—
71C2×C4×C22⋊D47C2213yescomplemented
72C2×#13093981C2213yescomplemented
73C2×C4⋊C4×D47C2213yescomplemented
74C2×C4⋊C4×D47C2216yescomplemented
75C2×C22⋊C4×D47C2216yes—
76C23×Q8×C47C2211yescharacteristic
77C23×Q8×C47C2211yescharacteristic, complemented
78D4×Q8×C47C22116yescomplemented
79C2×C4⋊Q8×C47C2213yescomplemented
80C2×C22⋊Q8×C47C2213yes—
81C2×C22⋊Q8×C47C2213yescomplemented
82C2×C4×Q8×C47C2211yescharacteristic, complemented
83C2×C4×D4×C47C2213yes—
84C24×D47C2313yes—
85#13094072—2128no—
86C2×#10625354—28no—
87C2×#10625354—2128no—
88C2×#10625354—224no—
89C2×#10625354—224no—
90C2×#10625354—224no—
91C2×#10625354D4116yescomplemented
92C2×#10625354C23124yes—
93C2×#10625354C2318yes—
94C2×#10625354C23124yes—
95C2×#10625354C2318yes—
96C2×#10625354C23124yescomplemented
97C2×#10625350—224no—
98C2×#10625350—224no—
99C2×#10625350C23124yescomplemented
100C2×#10625350C23124yescomplemented
101C22×Dic94C2313yes—
102C22×Dic94C2313yes—
103C2×Q8×D47—28no—
104C2×Q8×D47—224no—
105C2×Q8×D47C2318yescomplemented
106C2×Q8×D47C23124yescomplemented
107C22×D188—224no—
108C22×D188C23124yes—
109C22×D188C2313yes—
110C22×D188C2316yes—
111C22×D188C2313yes—
112C22×D188C2313yes—
113C22×D188C2313yes—
114C22×C22⋊D47C2311yescharacteristic
115C22×C22⋊D47C2313yes—
116C22×C22⋊D47C2311yescharacteristic
117C22×C22⋊D47C2313yes—
118C23×Dic47C2311yescharacteristic
119C22×C4×D47—224no—
120C22×C4×D47C2316yes—
121C22×C4×D47C2313yes—
122C22×C4×D47C2313yes—
123C22×C4×D47C2313yes—
124C22×C4×D47C2313yes—
125C22×C4×D47C23124yes—
126C22×C4×D47C2316yes—
127C22×C4×D47C2313yes—
128#13094022C23124yescomplemented
129#13094013C23124yescomplemented
130#13094012C23124yescomplemented
131#13094009C23148yescomplemented
132#13094009C23148yescomplemented
133#13094009C23124yescomplemented
134#13094006C23124yescomplemented
135#13094004C23124yescomplemented
136#13094003C23124yes—
137#13094002C23148yescomplemented
138#13094002C23124yescomplemented
139#13094001C23124yes—
140#13094000C23124yescomplemented
141#13094000C23124yescomplemented
142#13093999C23148yescomplemented
143#13093999C23124yescomplemented
144#13093998C23124yescomplemented
145#13093997C23148yescomplemented
146#13093997C23124yescomplemented
147#13093996C2318yes—
148#13093994C23124yes—
149#13093992C23124yes—
150Q8×Dic47C2318yescomplemented
151C4×D188C23124yescomplemented
152C4×D188C23124yescomplemented
153#13093986C23124yescomplemented
154C4×C22⋊D47C23124yes—
155C4×C22⋊D47C23124yescomplemented
156#13093981C23124yescomplemented
157C2×C4⋊Dic47C2313yes—
158C2×C4⋊Dic47C2313yes—
159C2×Dic47⋊C4C2313yes—
160C2×Dic47⋊C4C2313yes—
161C2×Dic47⋊C4C2316yes—
162C2×Dic47⋊C4C2311yescharacteristic
163C2×Dic47⋊C4C2313yes—
164C4⋊C4×D47C23148yescomplemented
165C4⋊C4×D47C23124yescomplemented
166C2×C22⋊Dic47C2313yes—
167C2×C22⋊Dic47C2311yescharacteristic
168C2×(C2×D47)⋊C4C2316yes—
169C2×(C2×D47)⋊C4C2316yes—
170C2×(C2×D47)⋊C4C2313yes—
171C2×(C2×D47)⋊C4C2313yes—
172C2×(C2×D47)⋊C4C2313yes—
173C2×(C2×D47)⋊C4C2313yes—
174C2×(C2×D47)⋊C4C2311yescharacteristic
175C2×(C2×D47)⋊C4C2313yes—
176C22⋊C4×D47C23148yes—
177C2×C4×Dic47C2313yes—
178C22×Q8×C47—28no—
179C22×Q8×C47—28no—
180C22×Q8×C47C2318yes—
181C22×Q8×C47C2313yes—
182C22×Q8×C47C2313yes—
183C22×Q8×C47C2311yescharacteristic
184C22×Q8×C47C2318yescomplemented
185C22×D4×C47C2311yescharacteristic
186C23×C4×C47C2313yes—
187C23×C4×C47C2313yes—
188C4⋊Q8×C47C23124yescomplemented
189C22⋊Q8×C47C23124yes—
190C22⋊Q8×C47C23124yescomplemented
191C4×Q8×C47C2318yescomplemented
192C4×D4×C47C23124yes—
193C2×C4⋊C4×C47C2313yes—
194C2×C4⋊C4×C47C2313yes—
195C2×C4⋊C4×C47C2316yes—
196C2×C22⋊C4×C47C2313yes—
197C2×C22⋊C4×C47C2313yes—
198C2×C42×C47C2313yes—
199C24×C47C2411yescharacteristic
200C24×C47C2411yescharacteristic
201C23×D47—212no—
202C23×D47—212no—
203C23×D47—46no—
204C23×D47C2413yes—
205C23×D47C2411yescharacteristic
206C23×D47C24112yes—
207C23×D47C2413yes—
208C2×Q8×C47—232no—
209C2×Q8×C47—232no—
210C2×Q8×C47—212no—
211C2×Q8×C47—212no—
212C2×Q8×C47C2×D418yes—
213C2×Q8×C47C24112yes—
214C2×Q8×C47C24112yes—
215C2×Q8×C47C2414yes—
216C2×D4×C47—24no—
217C2×D4×C47C2414yes—
218C22×C4×C47—212no—
219C22×C4×C47—212no—
220C22×C4×C47C2411yescharacteristic
221C22×C4×C47C2413yes—
222C22×C4×C47C2413yes—
223C22×C4×C47C2413yes—
224C22×C4×C47C24112yes—
225C22×C4×C47C24112yes—
226C22×C4×C47C2413yes—
227C2×C22⋊D47—24no—
228C2×C22⋊D47—212no—
229C2×C22⋊D47—24no—
230C2×C22⋊D47—46no—
231C2×C22⋊D47C2414yes—
232C2×C22⋊D47C24112yes—
233C2×C22⋊D47C2414yes—
234C2×C22⋊D47C24112yes—
235C22×Dic47—24no—
236C22×Dic47C2411yescharacteristic
237C22×Dic47C2413yes—
238C22×Dic47C2413yes—
239C22×Dic47C2411yescharacteristic
240C22×Dic47C2414yes—
241C22×Dic47C2411yescharacteristic
242#10625354—232no—
243#10625354—296no—
244#10625354—296no—
245#10625354—296no—
246#10625354C2×D4164yescomplemented
247Q8×D47—232no—
248Q8×D47—296no—
249#10625350—296no—
250#10625350—296no—
251C2×D188—224no—
252C2×D188—212no—
253C2×D188—212no—
254C2×D188—296no—
255C2×D188—46no—
256C2×D188C2×D4124yes—
257C2×D188C24112yes—
258C2×D188C24124yes—
259C2×D188C24112yes—
260C2×D188C24112yes—
261C2×D188C24112yes—
262C2×C4×D47—212no—
263C2×C4×D47—224no—
264C2×C4×D47—212no—
265C2×C4×D47—212no—
266C2×C4×D47—212no—
267C2×C4×D47—296no—
268C2×C4×D47—412no—
269C2×C4×D47C2×D4124yes—
270C2×C4×D47C24124yes—
271C2×C4×D47C24112yes—
272C2×C4×D47C24112yes—
273C2×C4×D47C24112yes—
274C2×C4×D47C24112yes—
275C2×C4×D47C24124yes—
276C2×C4×D47C24112yes—
277C2×Dic94—212no—
278C2×Dic94—212no—
279C2×Dic94C24112yes—
280C2×Dic94C24112yes—
281C4⋊C4×C47C24112yes—
282C4⋊C4×C47C24112yes—
283C4⋊C4×C47C24124yes—
284C22⋊C4×C47C24112yes—
285C22⋊C4×C47C24112yes—
286C42×C47C24112yes—
287C22⋊Dic47C24112yes—
288C22⋊Dic47C2414yes—
289(C2×D47)⋊C4C24124yes—
290(C2×D47)⋊C4C24124yes—
291(C2×D47)⋊C4C24112yes—
292(C2×D47)⋊C4C24112yes—
293(C2×D47)⋊C4C24112yes—
294(C2×D47)⋊C4C24112yes—
295(C2×D47)⋊C4C2414yes—
296(C2×D47)⋊C4C24112yes—
297C4⋊Dic47C24112yes—
298C4⋊Dic47C24112yes—
299Dic47⋊C4C24112yes—
300Dic47⋊C4C24112yes—
301Dic47⋊C4C24124yes—
302Dic47⋊C4C2414yes—
303Dic47⋊C4C24112yes—
304C4×Dic47C24112yes—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C472−1+414yescomplemented
311C23×C47C2512yes—
312C23×C47C2512yes—
313C23×C47C2511yescharacteristic
314C22×D47—26no—
315C22×D47—26no—
316C22×D47—22no—
317C22×D47—26no—
318C22×D47—22no—
319C22×D47—26no—
320C22×D47—224no—
321C22×D47—22no—
322C22×D47—26no—
323C22×D47—224no—
324C22×D47—412no—
325C22×D47—448no—
326C22×D47C22×D4112yes—
327C22×D47C2516yes—
328C22×D47C2512yes—
329C22×D47C2516yes—
330Q8×C47—224no—
331Q8×C47—224no—
332Q8×C47C22×D4116yes—
333D4×C47—28no—
334C2×C4×C47—26no—
335C2×C4×C47—26no—
336C2×C4×C47—22no—
337C2×C4×C47—26no—
338C2×C4×C47—224no—
339C2×C4×C47—224no—
340C2×C4×C47C22×D4112yes—
341C2×C4×C47C2516yes—
342C2×C4×C47C2516yes—
343C2×C4×C47C2512yes—
344C2×C4×C47C2516yes—
345C2×C4×C47C2516yes—
346C22⋊D47—28no—
347C22⋊D47—224no—
348C22⋊D47—28no—
349C22⋊D47—412no—
350C2×Dic47—26no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47—26no—
354C2×Dic47—28no—
355C2×Dic47C22×D414yes—
356C2×Dic47C2512yes—
357C2×Dic47C2516yes—
358C2×Dic47C2512yes—
359C2×Dic47C2516yes—
360C2×Dic47C2512yes—
361D188—248no—
362D188—224no—
363D188—224no—
364D188—412no—
365D188C22×D4148yes—
366C4×D47—224no—
367C4×D47—248no—
368C4×D47—224no—
369C4×D47—224no—
370C4×D47—224no—
371C4×D47—424no—
372C4×D47C22×D4148yes—
373Dic94—224no—
374Dic94—224no—
375C2×#3489—471nomaximal, Sylow
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—28no—
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—22no—
382C22×C47—44no—
383C22×C47C23×D412yes—
384C22×C47C2×2−1+412yes—
385C22×C47C2×2−1+414yescomplemented
386C22×C47#58512yes—
387C22×C47C2611yescharacteristic
388C2×D47—26no—
389C2×D47—26no—
390C2×D47—224no—
391C2×D47—22no—
392C2×D47—26no—
393C2×D47—22no—
394C2×D47—26no—
395C2×D47—22no—
396C2×D47—26no—
397C2×D47—448no—
398C2×D47—44no—
399C2×D47—412no—
400C2×D47C23×D4112yes—
401C4×C47—26no—
402C4×C47—26no—
403C4×C47—22no—
404C4×C47—26no—
405C4×C47C23×D4112yes—
406Dic47—26no—
407Dic47—22no—
408Dic47—22no—
409Dic47—26no—
410Dic47C23×D414yes—
411C22×2−1+4—471no—
412C23×#41—471no—
413#3489—4732no—
414C2×D4×Q8—471no—
415C2×D4×Q8D4711yescharacteristic, complemented
416C2×#548—471no—
417C2×#548—471no—
418C2×#547—473no—
419C2×#547—473no—
420C2×#546—473no—
421C2×#546—473no—
422C2×#537—473no—
423C2×#536—473no—
424C2×#525—473no—
425C22×C22⋊Q8—473no—
426C2×#520—471no—
427C2×C47—24no—
428C2×C47—42no—
429C2×C47#348914yescomplemented
430C2×C47C24×D411yescharacteristic
431C2×C47C22×2−1+411yescharacteristic
432C2×C47C2×#58511yescharacteristic
433D47—212no—
434D47—42no—
435D47—46no—
436C2×2−1+4—4716no—
437C2×2−1+4—9416no—
438C22×#41—471no—
439C22×#41—473no—
440C22×#41—473no—
441C22×#41—471no—
442C22×#41—4716no—
443C22×#41—473no—
444C22×#41—473no—
445C22×#41—473no—
446C22×#41—9416no—
447C23×Q8—473no—
448C23×Q8—471no—
449C23×Q8C2×D4711yescharacteristic
450C23×Q8C2×D4711yescharacteristic, complemented
451C23×D4—473no—
452C24×C4—473no—
453D4×Q8—4716no—
454D4×Q8C2×D47116yescomplemented
455#548—4716no—
456#548—4716no—
457#547—4748no—
458#547—4748no—
459#546—4748no—
460#546—4748no—
461#537—4748no—
462#536—4748no—
463C2×C4⋊Q8—473no—
464C2×C4⋊Q8C2×D4713yescomplemented
465C2×#124—473no—
466C2×#124—473no—
467#525—4748no—
468C2×#123—473no—
469C2×#123—476no—
470C2×#123—476no—
471C2×#123—473no—
472C2×C22⋊Q8—473no—
473C2×C22⋊Q8—473no—
474C2×C22⋊Q8—473no—
475C2×C22⋊Q8—4748no—
476C2×C22⋊Q8—476no—
477C2×C22⋊Q8—473no—
478C2×C22⋊Q8—473no—
479C2×C22⋊Q8—473no—
480C2×C22⋊Q8C2×D4713yes—
481C2×C22⋊Q8C2×D4713yescomplemented
482C2×#121—471no—
483C2×#121—473no—
484C2×#121—476no—
485C2×#121—473no—
486C2×#121—473no—
487C2×#121—476no—
488C2×#120—473no—
489C2×#120—473no—
490#520—4716no—
491C2×C4×Q8—471no—
492C2×C4×Q8C2×D4711yescharacteristic, complemented
493C2×C4×D4—473no—
494C2×C4×D4—473no—
495C2×C4×D4—473no—
496C2×C4×D4—473no—
497C2×C4×D4—473no—
498C2×C4×D4C2×D4713yes—
499C2×#117—473no—
500C22×C4⋊C4—473no—
501C22×C4⋊C4—476no—
502C22×C22⋊C4—476no—
503C47C2×#348911yescharacteristic, complemented, Sylow
504C25—473no—
5052−1+4—94128no—
506C2×#41—4716no—
507C2×#41—478no—
508C2×#41—4724no—
509C2×#41—4724no—
510C2×#41—4724no—
511C2×#41—478no—
512C2×#41—4724no—
513C2×#41—4724no—
514C2×#41—9424no—
515C2×#41—9424no—
516C2×#41—9424no—
517C2×#41—9424no—
518C2×#41—9424no—
519C2×#41—94128no—
520C2×#41—948no—
521C22×Q8—28no—
522C22×Q8—28no—
523C22×Q8—4724no—
524C22×Q8—478no—
525C22×Q8—473no—
526C22×Q8—473no—
527C22×Q8—9424no—
528C22×Q8—948no—
529C22×Q8C22×D4713yes—
530C22×Q8C22×D4713yes—
531C22×Q8C22×D4718yes—
532C22×Q8C22×D4711yescharacteristic
533C22×Q8C22×D4718yescomplemented
534C22×D4—471no—
535C22×D4—473no—
536C22×D4—471no—
537C22×D4—473no—
538C22×D4—473no—
539C22×D4—473no—
540C22×D4—476no—
541C22×D4—473no—
542C22×D4—4724no—
543C22×D4—473no—
544C22×D4—9424no—
545C22×D4C22×D4711yescharacteristic
546C23×C4—473no—
547C23×C4—471no—
548C23×C4—476no—
549C23×C4—473no—
550C23×C4—473no—
551C23×C4—473no—
552C23×C4—473no—
553C23×C4—4724no—
554C23×C4—476no—
555C23×C4—9424no—
556C23×C4C22×D4713yes—
557C23×C4C22×D4713yes—
558C4⋊Q8—4724no—
559C4⋊Q8C22×D47124yescomplemented
560#124—4724no—
561#124—4724no—
562#123—4724no—
563#123—4748no—
564#123—4748no—
565#123—4724no—
566C22⋊Q8—4724no—
567C22⋊Q8—4724no—
568C22⋊Q8—4724no—
569C22⋊Q8—4748no—
570C22⋊Q8—4724no—
571C22⋊Q8—4724no—
572C22⋊Q8—4724no—
573C22⋊Q8C22×D47124yes—
574C22⋊Q8C22×D47124yescomplemented
575#121—478no—
576#121—4724no—
577#121—4748no—
578#121—4724no—
579#121—4724no—
580#121—4748no—
581#120—4724no—
582#120—4724no—
583C4×Q8—478no—
584C4×Q8C22×D4718yescomplemented
585C4×D4—4724no—
586C4×D4—4724no—
587C4×D4—4724no—
588C4×D4—4724no—
589C4×D4—4724no—
590C4×D4C22×D47124yes—
591#117—4724no—
592C2×C4⋊C4—473no—
593C2×C4⋊C4—473no—
594C2×C4⋊C4—473no—
595C2×C4⋊C4—473no—
596C2×C4⋊C4—476no—
597C2×C4⋊C4—471no—
598C2×C4⋊C4—473no—
599C2×C4⋊C4—4724no—
600C2×C4⋊C4—4748no—
601C2×C4⋊C4C22×D4713yes—
602C2×C4⋊C4C22×D4716yes—
603C2×C4⋊C4C22×D4713yes—
604C2×C22⋊C4—473no—
605C2×C22⋊C4—471no—
606C2×C22⋊C4—476no—
607C2×C22⋊C4—476no—
608C2×C22⋊C4—473no—
609C2×C22⋊C4—473no—
610C2×C22⋊C4—471no—
611C2×C22⋊C4—473no—
612C2×C22⋊C4—473no—
613C2×C22⋊C4—473no—
614C2×C22⋊C4—4748no—
615C2×C22⋊C4C22×D4713yes—
616C2×C22⋊C4C22×D4713yes—
617C2×C42—473no—
618C2×C42C22×D4713yes—
619C24—473no—
620C24—473no—
621C24—471no—
622C24—4712no—
623C24—9412no—
624C24—9412no—
625C24—1886no—
626C24C23×D4711yescharacteristic
627C24C23×D4711yescharacteristic
628#41—4764no—
629#41—9496no—
630#41—9496no—
631#41—9496no—
632#41—9496no—
633#41—9496no—
634#41—9432no—
635C2×Q8—232no—
636C2×Q8—232no—
637C2×Q8—212no—
638C2×Q8—212no—
639C2×Q8—4712no—
640C2×Q8—4712no—
641C2×Q8—9412no—
642C2×Q8—9496no—
643C2×Q8—9432no—
644C2×Q8—9412no—
645C2×Q8D4×D4718yes—
646C2×Q8C23×D47112yes—
647C2×Q8C23×D47112yes—
648C2×Q8C23×D4714yes—
649C2×D4—24no—
650C2×D4—474no—
651C2×D4—4712no—
652C2×D4—474no—
653C2×D4—4712no—
654C2×D4—4724no—
655C2×D4—4712no—
656C2×D4—4712no—
657C2×D4—4724no—
658C2×D4—4712no—
659C2×D4—4712no—
660C2×D4—9496no—
661C2×D4—9424no—
662C2×D4—9412no—
663C2×D4—944no—
664C2×D4—9412no—
665C2×D4—944no—
666C2×D4—9412no—
667C2×D4—1886no—
668C2×D4—1886no—
669C2×D4C23×D4714yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—471no—
673C22×C4—4724no—
674C22×C4—4712no—
675C22×C4—474no—
676C22×C4—471no—
677C22×C4—473no—
678C22×C4—473no—
679C22×C4—471no—
680C22×C4—4724no—
681C22×C4—4712no—
682C22×C4—4712no—
683C22×C4—4712no—
684C22×C4—4712no—
685C22×C4—4724no—
686C22×C4—9412no—
687C22×C4—9496no—
688C22×C4—9412no—
689C22×C4—9424no—
690C22×C4—944no—
691C22×C4—9412no—
692C22×C4—9412no—
693C22×C4—18812no—
694C22×C4C23×D47112yes—
695C22×C4C23×D47112yes—
696C22×C4C23×D4711yescharacteristic
697C22×C4C23×D4713yes—
698C22×C4C23×D4713yes—
699C22×C4C23×D4713yes—
700C22×C4C23×D4713yes—
701C4⋊C4—4712no—
702C4⋊C4—4712no—
703C4⋊C4—4724no—
704C4⋊C4—474no—
705C4⋊C4—4712no—
706C4⋊C4—4712no—
707C4⋊C4—4712no—
708C4⋊C4C23×D47112yes—
709C4⋊C4C23×D47124yes—
710C4⋊C4C23×D47112yes—
711C22⋊C4—4712no—
712C22⋊C4—474no—
713C22⋊C4—4724no—
714C22⋊C4—4724no—
715C22⋊C4—4712no—
716C22⋊C4—4712no—
717C22⋊C4—474no—
718C22⋊C4—4712no—
719C22⋊C4—4712no—
720C22⋊C4—4712no—
721C22⋊C4C23×D47112yes—
722C22⋊C4C23×D47112yes—
723C42—4712no—
724C42C23×D47112yes—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—4712no—
731C23—476no—
732C23—476no—
733C23—472no—
734C23—9424no—
735C23—946no—
736C23—946no—
737C23—942no—
738C23—946no—
739C23—942no—
740C23—946no—
741C23—9424no—
742C23—942no—
743C23—946no—
744C23—18812no—
745C23—18848no—
746C23#1309407214yescomplemented
747C23C24×D4712yes—
748C23C24×D4712yes—
749C23C24×D4711yescharacteristic
750Q8—224no—
751Q8—224no—
752Q8—9424no—
753Q8—9424no—
754Q8C2×D4×D47116yes—
755D4—28no—
756D4—4748no—
757D4—9448no—
758D4—9424no—
759D4—948no—
760D4—9424no—
761D4—948no—
762D4—9424no—
763D4—18812no—
764D4—18812no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—474no—
772C2×C4—472no—
773C2×C4—4748no—
774C2×C4—472no—
775C2×C4—476no—
776C2×C4—476no—
777C2×C4—472no—
778C2×C4—9424no—
779C2×C4—9424no—
780C2×C4—9448no—
781C2×C4—948no—
782C2×C4—942no—
783C2×C4—946no—
784C2×C4—942no—
785C2×C4—946no—
786C2×C4—9424no—
787C2×C4—9424no—
788C2×C4—18824no—
789C2×C4C2×D4×D47112yes—
790C2×C4C24×D4712yes—
791C2×C4C24×D4716yes—
792C2×C4C24×D4716yes—
793C2×C4C24×D4716yes—
794C2×C4C24×D4716yes—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—4712no—
803C22—9424no—
804C22—946no—
805C22—946no—
806C22—942no—
807C22—946no—
808C22—942no—
809C22—946no—
810C22—942no—
811C22—946no—
812C22—18848no—
813C22—18812no—
814C22—1884no—
815C22C22×D4×D4712yes—
816C22C2×#1309407212yes—
817C22C2×#1309407214yescomplemented
818C22#1568996012yes—
819C22C25×D4711yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—474no—
825C4—942no—
826C4—946no—
827C4—942no—
828C4—946no—
829C4C22×D4×D47112yes—
830C2—24no—
831C2—42no—
832C2—9412no—
833C2—1886no—
834C2—1882no—
835C2#2025706514yesdirect product factor
836C2C23×D4×D4711yescharacteristic
837C2C22×#1309407211yescharacteristic
838C2C2×#1568996011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×D4×Q8×C47C2
socleC23×C47C25
hypercenterC2×D4×Q8D47
hypocenterC47C2×#3489
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13094072C2semidirect
2. C23×#10625354C2semidirect
3. #20257065C2direct (N × H)
4. C2×Q8×C22⋊D47C2semidirect
5. C2×#15689785C2semidirect
6. C2×#15689784C2semidirect
7. C2×#15689776C2semidirect
8. C2×#15689775C2semidirect
9. C2×#15689769C2semidirect
10. C2×#15689764C2semidirect
11. C2×#15689703C2semidirect
12. C2×#15689698C2semidirect
13. C2×#15689632C2semidirect
14. C2×C22⋊Q8×D47C2semidirect
15. C2×#15689605C2semidirect
16. C2×D4×Q8×C47C2semidirect
18. C2×#13094072C22semidirect
24. C22×#10625354C22semidirect
25. C22×#10625354C22semidirect
26. C22×#10625350C22semidirect
27. C22×#10625350C22semidirect
28. C22×Q8×D47C22semidirect
29. C22×Q8×D47C22semidirect
32. Q8×C22⋊D47C22semidirect
33. #15689785C22semidirect
34. #15689784C22semidirect
35. #15689776C22semidirect
36. #15689775C22semidirect
37. #15689769C22semidirect
38. #15689764C22semidirect
39. #15689703C22semidirect
40. #15689698C22semidirect
41. C2×#13094022C22semidirect
42. C2×#13094013C22semidirect
43. C2×#13094012C22semidirect
44. #15689632C22semidirect
45. C2×#13094009C22semidirect
46. C2×#13094009C22semidirect
47. C2×#13094009C22semidirect
48. C2×#13094006C22semidirect
49. C2×#13094004C22semidirect
51. C2×#13094002C22semidirect
52. C2×#13094002C22semidirect
54. C2×#13094000C22semidirect
55. C2×#13094000C22semidirect
56. C22⋊Q8×D47C22semidirect
57. C2×#13093999C22semidirect
58. C2×#13093999C22semidirect
59. C2×#13093998C22semidirect
60. C2×#13093997C22semidirect
61. C2×#13093997C22semidirect
65. #15689605C22semidirect
66. C2×Q8×Dic47C22semidirect
67. C2×C4×D188C22semidirect
68. C2×C4×D188C22semidirect
69. C2×#13093986C22semidirect
71. C2×C4×C22⋊D47C22semidirect
72. C2×#13093981C22semidirect
73. C2×C4⋊C4×D47C22semidirect
74. C2×C4⋊C4×D47C22semidirect
77. C23×Q8×C47C22semidirect
78. D4×Q8×C47C22semidirect
79. C2×C4⋊Q8×C47C22semidirect
81. C2×C22⋊Q8×C47C22semidirect
82. C2×C4×Q8×C47C22semidirect
91. C2×#10625354D4semidirect
96. C2×#10625354C23semidirect
99. C2×#10625350C23semidirect
100. C2×#10625350C23semidirect
105. C2×Q8×D47C23semidirect
106. C2×Q8×D47C23semidirect
128. #13094022C23semidirect
129. #13094013C23semidirect
130. #13094012C23semidirect
131. #13094009C23semidirect
132. #13094009C23semidirect
133. #13094009C23semidirect
134. #13094006C23semidirect
135. #13094004C23semidirect
137. #13094002C23semidirect
138. #13094002C23semidirect
140. #13094000C23semidirect
141. #13094000C23semidirect
142. #13093999C23semidirect
143. #13093999C23semidirect
144. #13093998C23semidirect
145. #13093997C23semidirect
146. #13093997C23semidirect
150. Q8×Dic47C23semidirect
151. C4×D188C23semidirect
152. C4×D188C23semidirect
153. #13093986C23semidirect
155. C4×C22⋊D47C23semidirect
156. #13093981C23semidirect
164. C4⋊C4×D47C23semidirect
165. C4⋊C4×D47C23semidirect
184. C22×Q8×C47C23semidirect
188. C4⋊Q8×C47C23semidirect
190. C22⋊Q8×C47C23semidirect
191. C4×Q8×C47C23semidirect
246. #10625354C2×D4semidirect
310. C23×C472−1+4semidirect
385. C22×C47C2×2−1+4semidirect
415. C2×D4×Q8D47semidirect
429. C2×C47#3489semidirect
450. C23×Q8C2×D47semidirect
454. D4×Q8C2×D47semidirect
464. C2×C4⋊Q8C2×D47semidirect
481. C2×C22⋊Q8C2×D47semidirect
492. C2×C4×Q8C2×D47semidirect
503. C47C2×#3489semidirect
533. C22×Q8C22×D47semidirect
559. C4⋊Q8C22×D47semidirect
574. C22⋊Q8C22×D47semidirect
584. C4×Q8C22×D47semidirect
746. C23#13094072semidirect
817. C22C2×#13094072semidirect
835. C2#20257065direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940722
C23×#106253542
#202570652
C2×Q8×C22⋊D472
C2×#156897852
C2×#156897842
C2×#156897762
C2×#156897752
C2×#156897692
C2×#156897642
C2×#156897032
C2×#156896982
C2×#156896322
C2×C22⋊Q8×D472
C2×#156896052
C2×D4×Q8×C472
C2×#348947