Finite Group Databasebeta

← C2×#548×D47 #27123208

Subgroups — C2×#548×D47 #27123208

Order 12032.

12142 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D47C211yesmaximal, characteristic, complemented
2C23×Q8×D47C211yesmaximal, characteristic, complemented
3C2×#15689785C211yesmaximal, characteristic, complemented
4C2×#15689784C211yesmaximal, characteristic, complemented
5C2×#15689783C213yesmaximal, complemented
6C2×#15689782C213yesmaximal, complemented
7C2×#15689781C213yesmaximal, complemented
8C2×#15689780C211yesmaximal, characteristic, complemented
9C2×#15689779C213yesmaximal, complemented
10#548×D47C2132yesmaximal, direct product factor
11C2×#124×D47C213yesmaximal, complemented
12C2×C22⋊Q8×D47C213yesmaximal, complemented
13C2×#121×D47C213yesmaximal, complemented
14C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
15C2×C4×D4×D47C213yesmaximal, complemented
16C2×C47×#548C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic, complemented
18C22×#10625350C2213yescomplemented
19C22×#10625352C2213yescomplemented
20C2×#41×D47—216no—
21C2×#41×D47C22116yescomplemented
22C23×Dic94C2213yescomplemented
23C22×Q8×D47—216no—
24C22×Q8×D47C2213yes—
25C22×Q8×D47C2211yescharacteristic
26C22×Q8×D47C2211yescharacteristic, complemented
27C22×Q8×D47C2213yescomplemented
28C22×Q8×D47C22116yescomplemented
29C22×D4×D47C2213yes—
30C22×D4×D47C2213yes—
31C23×C4×D47C2213yes—
32C23×C4×D47C2213yes—
33#15689785C22116yescomplemented
34#15689784C22116yescomplemented
35#15689783C22148yescomplemented
36#15689782C22148yescomplemented
37#15689781C22148yescomplemented
38#15689780C22116yescomplemented
39#15689779C22148yescomplemented
40C2×#13094013C2213yescomplemented
41C2×#13094012C2213yescomplemented
42C2×#13094011C2213yescomplemented
43C2×#13094010C2216yescomplemented
44C2×#13094010C2216yescomplemented
45#124×D47C22148yescomplemented
46C2×#13094004C2213yescomplemented
47C2×#13094003C2213yescomplemented
48C2×#13094002C2216yescomplemented
49C2×#13094001C2216yescomplemented
50C2×#13094000C2213yescomplemented
51C22⋊Q8×D47C22148yescomplemented
52C2×#13093999C2213yescomplemented
53C2×#13093998C2213yescomplemented
54C2×#13093997C2216yescomplemented
55C2×#13093996C2216yescomplemented
56C2×#13093995C2213yescomplemented
57#121×D47C22148yescomplemented
58C2×Q8×Dic47C2211yescharacteristic, complemented
59C2×C4×Dic94C2213yescomplemented
60C2×#13093989C2213yescomplemented
61C4×Q8×D47C22116yescomplemented
62C2×C4×D188C2213yescomplemented
63C2×D4×Dic47C2213yescomplemented
64C2×#13093986C2213yescomplemented
65C2×C4×C22⋊D47C2213yescomplemented
66C2×C4×C22⋊D47C2213yescomplemented
67C2×(C22⋊D47)⋊C4C2213yescomplemented
68C2×(C22⋊D47)⋊C4C2213yescomplemented
69C4×D4×D47C22148yescomplemented
70C2×C4⋊C4×D47C2213yes—
71C2×C4⋊C4×D47C2213yes—
72C2×C22⋊C4×D47C2211yescharacteristic
73C2×C22⋊C4×D47C2213yes—
74C2×C22⋊C4×D47C2216yes—
75C2×C42×D47C2213yes—
76C22×#41×C47C2211yescharacteristic, complemented
77C23×Q8×C47C2211yescharacteristic, complemented
78C47×#548C22116yescomplemented
79C2×#124×C47C2213yescomplemented
80C2×C22⋊Q8×C47C2213yescomplemented
81C2×#121×C47C2213yescomplemented
82C2×C4×Q8×C47C2211yescharacteristic, complemented
83C2×C4×D4×C47C2213yescomplemented
84C24×D47C2313yes—
85C24×D47C2311yescharacteristic
86C2×#10625354—28no—
87C2×#10625354C2318yescomplemented
88C2×#10625350—224no—
89C2×#10625350C23124yescomplemented
90C2×#10625352—224no—
91C2×#10625352C23124yescomplemented
92#41×D47—2128no—
93C22×Dic94—224no—
94C22×Dic94C2316yes—
95C22×Dic94C2313yes—
96C22×Dic94C2313yes—
97C22×Dic94C23124yescomplemented
98C2×Q8×D47—28no—
99C2×Q8×D47—2128no—
100C2×Q8×D47—224no—
101C2×Q8×D47—224no—
102C2×Q8×D47D4116yescomplemented
103C2×Q8×D47C23124yes—
104C2×Q8×D47C2318yes—
105C2×Q8×D47C2318yescomplemented
106C2×Q8×D47C23124yescomplemented
107C22×D188C2313yes—
108C22×D188C2313yes—
109C22×C22⋊D47C2313yes—
110C22×C22⋊D47C2313yes—
111C22×C22⋊D47C2316yes—
112C2×D4×D47—224no—
113C2×D4×D47—224no—
114C2×D4×D47C23124yes—
115C2×D4×D47C23124yes—
116C23×Dic47C2313yes—
117C23×Dic47C2313yes—
118C22×C4×D47—224no—
119C22×C4×D47—224no—
120C22×C4×D47C2311yescharacteristic
121C22×C4×D47C2313yes—
122C22×C4×D47C2313yes—
123C22×C4×D47C2311yescharacteristic
124C22×C4×D47C23124yes—
125C22×C4×D47C23124yes—
126C22×C4×D47C2313yes—
127C22×C4×D47C2313yes—
128C22×C4×D47C2313yes—
129C22×C4×D47C2313yes—
130C22×C4×D47C2313yes—
131#13094013C23124yescomplemented
132#13094012C23124yescomplemented
133#13094011C23124yescomplemented
134#13094010C23148yescomplemented
135#13094010C23148yescomplemented
136#13094004C23124yescomplemented
137#13094003C23124yescomplemented
138#13094002C23148yescomplemented
139#13094001C23148yescomplemented
140#13094000C23124yescomplemented
141#13093999C23124yescomplemented
142#13093998C23124yescomplemented
143#13093997C23148yescomplemented
144#13093996C23148yescomplemented
145#13093995C23124yescomplemented
146Q8×Dic47C2318yescomplemented
147C4×Dic94C23124yescomplemented
148#13093989C23124yescomplemented
149C4×D188C23124yescomplemented
150D4×Dic47C23124yescomplemented
151#13093986C23124yescomplemented
152C4×C22⋊D47C23124yescomplemented
153C4×C22⋊D47C23124yescomplemented
154(C22⋊D47)⋊C4C23124yescomplemented
155(C22⋊D47)⋊C4C23124yescomplemented
156C2×C4⋊Dic47C2313yes—
157C2×C4⋊Dic47C2313yes—
158C2×Dic47⋊C4C2313yes—
159C2×Dic47⋊C4C2313yes—
160C2×Dic47⋊C4C2316yes—
161C4⋊C4×D47C23124yes—
162C4⋊C4×D47C23124yes—
163C2×C22⋊Dic47C2311yescharacteristic
164C2×C22⋊Dic47C2313yes—
165C2×C22⋊Dic47C2316yes—
166C2×(C2×D47)⋊C4C2311yescharacteristic
167C2×(C2×D47)⋊C4C2313yes—
168C2×(C2×D47)⋊C4C2311yescharacteristic
169C2×(C2×D47)⋊C4C2313yes—
170C2×(C2×D47)⋊C4C2316yes—
171C2×(C2×D47)⋊C4C2316yes—
172C22⋊C4×D47C2318yes—
173C22⋊C4×D47C23124yes—
174C22⋊C4×D47C23148yes—
175C2×C4×Dic47C2313yes—
176C2×C4×Dic47C2313yes—
177C2×C4×Dic47C2313yes—
178C42×D47C23124yes—
179C2×#41×C47—28no—
180C2×#41×C47C2318yescomplemented
181C22×Q8×C47—28no—
182C22×Q8×C47C2313yes—
183C22×Q8×C47C2311yescharacteristic
184C22×Q8×C47C2318yescomplemented
185C22×D4×C47C2313yes—
186C22×D4×C47C2313yes—
187C23×C4×C47C2313yes—
188C23×C4×C47C2313yes—
189#124×C47C23124yescomplemented
190C22⋊Q8×C47C23124yescomplemented
191#121×C47C23124yescomplemented
192C4×Q8×C47C2318yescomplemented
193C4×D4×C47C23124yescomplemented
194C2×C4⋊C4×C47C2313yes—
195C2×C4⋊C4×C47C2313yes—
196C2×C22⋊C4×C47C2311yescharacteristic
197C2×C22⋊C4×C47C2313yes—
198C2×C22⋊C4×C47C2316yes—
199C2×C42×C47C2313yes—
200C24×C47C2413yes—
201C24×C47C2411yescharacteristic
202C23×D47—24no—
203C23×D47—24no—
204C23×D47—212no—
205C23×D47—212no—
206C23×D47—212no—
207C23×D47#4118yescomplemented
208C23×D47C24112yes—
209C23×D47C2413yes—
210C23×D47C2414yes—
211C23×D47C2411yescharacteristic
212C23×D47C2411yescharacteristic
213#41×C47—232no—
214C2×Q8×C47—232no—
215C2×Q8×C47—212no—
216C2×Q8×C47C2×D418yescomplemented
217C2×Q8×C47C24112yes—
218C2×Q8×C47C2414yes—
219C2×D4×C47—212no—
220C2×D4×C47—212no—
221C2×D4×C47C24112yes—
222C2×D4×C47C24112yes—
223C22×C4×C47—212no—
224C22×C4×C47—212no—
225C22×C4×C47C2411yescharacteristic
226C22×C4×C47C2413yes—
227C22×C4×C47C2413yes—
228C22×C4×C47C2411yescharacteristic
229C22×C4×C47C24112yes—
230C22×C4×C47C24112yes—
231C22×C4×C47C2413yes—
232C2×C22⋊D47—212no—
233C2×C22⋊D47—212no—
234C2×C22⋊D47—224no—
235C2×C22⋊D47C24112yes—
236C2×C22⋊D47C24112yes—
237C2×C22⋊D47C24124yes—
238C22×Dic47—212no—
239C22×Dic47—212no—
240C22×Dic47C2411yescharacteristic
241C22×Dic47C2413yes—
242C22×Dic47C2413yes—
243C22×Dic47C2411yescharacteristic
244C22×Dic47C24112yes—
245C22×Dic47C24112yes—
246C22×Dic47C2413yes—
247#10625354—232no—
248Q8×D47—232no—
249Q8×D47—296no—
250Q8×D47—296no—
251Q8×D47C2×D4164yescomplemented
252#10625352—296no—
253D4×D47—296no—
254D4×D47—296no—
255#10625350—296no—
256C2×D188—212no—
257C2×D188—212no—
258C2×D188C24112yes—
259C2×D188C24112yes—
260C2×C4×D47—24no—
261C2×C4×D47—212no—
262C2×C4×D47—212no—
263C2×C4×D47—24no—
264C2×C4×D47—212no—
265C2×C4×D47—212no—
266C2×C4×D47—212no—
267C2×C4×D47—212no—
268C2×C4×D47—296no—
269C2×C4×D47—296no—
270C2×C4×D47C2×D4124yes—
271C2×C4×D47C2414yes—
272C2×C4×D47C24112yes—
273C2×C4×D47C24112yes—
274C2×C4×D47C2414yes—
275C2×C4×D47C24112yes—
276C2×C4×D47C24112yes—
277C2×C4×D47C24112yes—
278C2×C4×D47C24112yes—
279C2×C4×D47C24112yes—
280C2×Dic94—212no—
281C2×Dic94—224no—
282C2×Dic94—296no—
283C2×Dic94C2×D4124yescomplemented
284C2×Dic94C24124yes—
285C2×Dic94C24112yes—
286C2×Dic94C24112yes—
287C4⋊C4×C47C24112yes—
288C4⋊C4×C47C24112yes—
289C22⋊C4×C47C2414yes—
290C22⋊C4×C47C24112yes—
291C22⋊C4×C47C24124yes—
292C42×C47C24112yes—
293C22⋊Dic47C2414yes—
294C22⋊Dic47C24112yes—
295C22⋊Dic47C24124yes—
296(C2×D47)⋊C4C2414yes—
297(C2×D47)⋊C4C24112yes—
298(C2×D47)⋊C4C2414yes—
299(C2×D47)⋊C4C24112yes—
300(C2×D47)⋊C4C24124yes—
301(C2×D47)⋊C4C24124yes—
302C4⋊Dic47C24112yes—
303C4⋊Dic47C24112yes—
304Dic47⋊C4C24112yes—
305Dic47⋊C4C24112yes—
306Dic47⋊C4C24124yes—
307C4×Dic47C24112yes—
308C4×Dic47C24112yes—
309C4×Dic47C24112yes—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—26no—
313C23×C47—26no—
314C23×C47—26no—
315C23×C47C2×#4114yescomplemented
316C23×C47C2516yes—
317C23×C47C2512yes—
318C23×C47C2511yescharacteristic
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—232no—
322C22×D47—28no—
323C22×D47—28no—
324C22×D47—26no—
325C22×D47—26no—
326C22×D47—26no—
327C22×D47—224no—
328C22×D47—224no—
329C22×D47—224no—
330C22×D47—448no—
331C22×D47C22×D414yes—
332C22×D47C2×#4114yes—
333C22×D47C2×#41116yescomplemented
334C22×D47C2×#4114yescomplemented
335C22×D472−1+414yes—
336C22×D47C2516yes—
337C22×D47C2512yes—
338C22×D47C2512yes—
339Q8×C47—224no—
340Q8×C47C22×D4116yescomplemented
341D4×C47—224no—
342D4×C47—224no—
343C2×C4×C47—26no—
344C2×C4×C47—22no—
345C2×C4×C47—26no—
346C2×C4×C47—22no—
347C2×C4×C47—224no—
348C2×C4×C47—224no—
349C2×C4×C47C22×D4112yes—
350C2×C4×C47C2512yes—
351C2×C4×C47C2516yes—
352C2×C4×C47C2512yes—
353C2×C4×C47C2516yes—
354C2×C4×C47C2516yes—
355C22⋊D47—224no—
356C22⋊D47—224no—
357C22⋊D47—248no—
358C2×Dic47—26no—
359C2×Dic47—22no—
360C2×Dic47—26no—
361C2×Dic47—22no—
362C2×Dic47—224no—
363C2×Dic47—224no—
364C2×Dic47C22×D4112yes—
365C2×Dic47C2512yes—
366C2×Dic47C2516yes—
367C2×Dic47C2512yes—
368C2×Dic47C2516yes—
369C2×Dic47C2516yes—
370D188—224no—
371D188—224no—
372C4×D47—28no—
373C4×D47—224no—
374C4×D47—224no—
375C4×D47—28no—
376C4×D47—224no—
377C4×D47—224no—
378C4×D47—224no—
379C4×D47—224no—
380C4×D47C22×D4148yes—
381Dic94—224no—
382Dic94—248no—
383Dic94C22×D4148yescomplemented
384C22×#548—471nomaximal, Sylow
385C22×C47—22no—
386C22×C47—22no—
387C22×C47—28no—
388C22×C47—26no—
389C22×C47—26no—
390C22×C47—26no—
391C22×C47—412no—
392C22×C47C23×D412yes—
393C22×C47C22×#4112yes—
394C22×C47C22×#4114yescomplemented
395C22×C47C2×2−1+412yes—
396C22×C47C2611yescharacteristic
397C2×D47—22no—
398C2×D47—22no—
399C2×D47—28no—
400C2×D47—232no—
401C2×D47—26no—
402C2×D47—26no—
403C2×D47—26no—
404C2×D47—412no—
405C2×D47—448no—
406C2×D47#548116yesdirect product factor
407C2×D47C23×D414yes—
408C2×D47C22×#4114yes—
409C2×D47C22×#4114yescomplemented
410C2×D47C2×2−1+414yes—
411C4×C47—26no—
412C4×C47—22no—
413C4×C47—26no—
414C4×C47—22no—
415C4×C47C23×D4112yes—
416Dic47—26no—
417Dic47—22no—
418Dic47—26no—
419Dic47—22no—
420Dic47C23×D4112yes—
421C23×#41—471no—
422C24×Q8—471no—
423C2×#548—471no—
424C2×#548—471no—
425C2×#548—4732no—
426C2×#548—473no—
427C2×#548—473no—
428C2×#548—473no—
429C2×#548—471no—
430C2×#548—473no—
431C2×#548D4711yescharacteristic, direct product factor
432C22×#124—473no—
433C22×C22⋊Q8—473no—
434C22×#121—473no—
435C22×C4×Q8—471no—
436C22×C4×D4—473no—
437C2×C47—24no—
438C2×C47—46no—
439C2×C47C2×#54814yescomplemented
440C2×C47C24×D411yescharacteristic
441C2×C47C23×#4111yescharacteristic
442C2×C47C22×2−1+411yescharacteristic
443D47—24no—
444D47—46no—
445D47C2×#54818yesdirect product factor
446C22×#41—4716no—
447C22×#41—471no—
448C22×#41—473no—
449C22×#41—473no—
450C22×#41—9416no—
451C22×#41C2×D4711yescharacteristic, complemented
452C23×Q8—471no—
453C23×Q8—473no—
454C23×Q8—473no—
455C23×Q8—471no—
456C23×Q8—4716no—
457C23×Q8—473no—
458C23×Q8—9416no—
459C23×Q8C2×D4711yescharacteristic, complemented
460C23×D4—473no—
461C23×D4—473no—
462C24×C4—473no—
463C24×C4—473no—
464#548—4716no—
465#548—4716no—
466#548—4748no—
467#548—4748no—
468#548—4748no—
469#548—4716no—
470#548—4748no—
471#548C2×D47116yesdirect product factor
472C2×#124—473no—
473C2×#124—473no—
474C2×#124—4748no—
475C2×#124—476no—
476C2×#124—476no—
477C2×#124—473no—
478C2×#124C2×D4713yescomplemented
479C2×C22⋊Q8—473no—
480C2×C22⋊Q8—473no—
481C2×C22⋊Q8—4748no—
482C2×C22⋊Q8—476no—
483C2×C22⋊Q8—473no—
484C2×C22⋊Q8—476no—
485C2×C22⋊Q8C2×D4713yescomplemented
486C2×#121—473no—
487C2×#121—476no—
488C2×#121—473no—
489C2×#121—4748no—
490C2×#121—473no—
491C2×#121—476no—
492C2×#121C2×D4713yescomplemented
493C2×C4×Q8—471no—
494C2×C4×Q8—4716no—
495C2×C4×Q8—473no—
496C2×C4×Q8—473no—
497C2×C4×Q8C2×D4711yescharacteristic, complemented
498C2×C4×D4—473no—
499C2×C4×D4—473no—
500C2×C4×D4—473no—
501C2×C4×D4—4748no—
502C2×C4×D4—473no—
503C2×C4×D4—473no—
504C2×C4×D4—473no—
505C2×C4×D4—473no—
506C2×C4×D4C2×D4713yescomplemented
507C22×C4⋊C4—473no—
508C22×C4⋊C4—473no—
509C22×C22⋊C4—471no—
510C22×C22⋊C4—473no—
511C22×C22⋊C4—476no—
512C22×C42—473no—
513C47C22×#54811yescharacteristic, complemented, Sylow
514C25—471no—
515C25—473no—
516C2×#41—28no—
517C2×#41—478no—
518C2×#41—4724no—
519C2×#41—4724no—
520C2×#41—9424no—
521C2×#41—9424no—
522C2×#41—94128no—
523C2×#41—948no—
524C2×#41C22×D4718yescomplemented
525C22×Q8—28no—
526C22×Q8—4716no—
527C22×Q8—478no—
528C22×Q8—4724no—
529C22×Q8—4724no—
530C22×Q8—478no—
531C22×Q8—473no—
532C22×Q8—476no—
533C22×Q8—473no—
534C22×Q8—4724no—
535C22×Q8—9424no—
536C22×Q8—9424no—
537C22×Q8—94128no—
538C22×Q8—9424no—
539C22×Q8—948no—
540C22×Q8C22×D4713yes—
541C22×Q8C22×D4711yescharacteristic
542C22×Q8C22×D4718yescomplemented
543C22×D4—473no—
544C22×D4—473no—
545C22×D4—476no—
546C22×D4—4724no—
547C22×D4—4724no—
548C22×D4—473no—
549C22×D4—473no—
550C22×D4—9424no—
551C22×D4—9424no—
552C22×D4C22×D4713yes—
553C22×D4C22×D4713yes—
554C23×C4—473no—
555C23×C4—473no—
556C23×C4—473no—
557C23×C4—471no—
558C23×C4—473no—
559C23×C4—473no—
560C23×C4—471no—
561C23×C4—473no—
562C23×C4—4724no—
563C23×C4—473no—
564C23×C4—473no—
565C23×C4—4724no—
566C23×C4—473no—
567C23×C4—9424no—
568C23×C4—9424no—
569C23×C4C22×D4713yes—
570C23×C4C22×D4713yes—
571#124—4724no—
572#124—4724no—
573#124—4748no—
574#124—4748no—
575#124—4724no—
576#124C22×D47124yescomplemented
577C22⋊Q8—4724no—
578C22⋊Q8—4724no—
579C22⋊Q8—4748no—
580C22⋊Q8—4724no—
581C22⋊Q8—4748no—
582C22⋊Q8C22×D47124yescomplemented
583#121—4724no—
584#121—4748no—
585#121—4724no—
586#121—4724no—
587#121—4748no—
588#121C22×D47124yescomplemented
589C4×Q8—478no—
590C4×Q8—4724no—
591C4×Q8—4724no—
592C4×Q8C22×D4718yescomplemented
593C4×D4—4724no—
594C4×D4—4724no—
595C4×D4—4724no—
596C4×D4—4724no—
597C4×D4—4724no—
598C4×D4—4724no—
599C4×D4—4724no—
600C4×D4C22×D47124yescomplemented
601C2×C4⋊C4—473no—
602C2×C4⋊C4—473no—
603C2×C4⋊C4—473no—
604C2×C4⋊C4—476no—
605C2×C4⋊C4—473no—
606C2×C4⋊C4—4724no—
607C2×C4⋊C4—4724no—
608C2×C4⋊C4C22×D4713yes—
609C2×C4⋊C4C22×D4713yes—
610C2×C22⋊C4—471no—
611C2×C22⋊C4—473no—
612C2×C22⋊C4—476no—
613C2×C22⋊C4—471no—
614C2×C22⋊C4—471no—
615C2×C22⋊C4—473no—
616C2×C22⋊C4—473no—
617C2×C22⋊C4—476no—
618C2×C22⋊C4—476no—
619C2×C22⋊C4—478no—
620C2×C22⋊C4—4724no—
621C2×C22⋊C4—4748no—
622C2×C22⋊C4C22×D4711yescharacteristic
623C2×C22⋊C4C22×D4713yes—
624C2×C22⋊C4C22×D4716yes—
625C2×C42—473no—
626C2×C42—473no—
627C2×C42—473no—
628C2×C42—4724no—
629C2×C42C22×D4713yes—
630C24—471no—
631C24—478no—
632C24—474no—
633C24—471no—
634C24—4712no—
635C24—473no—
636C24—944no—
637C24—944no—
638C24—9412no—
639C24—9412no—
640C24—9412no—
641C24C23×D4713yes—
642C24C23×D4711yescharacteristic
643#41—232no—
644#41—9496no—
645#41—9496no—
646#41—9432no—
647C2×Q8—232no—
648C2×Q8—212no—
649C2×Q8—4764no—
650C2×Q8—4724no—
651C2×Q8—4712no—
652C2×Q8—4724no—
653C2×Q8—4712no—
654C2×Q8—9424no—
655C2×Q8—9496no—
656C2×Q8—9496no—
657C2×Q8—9496no—
658C2×Q8—9432no—
659C2×Q8—9412no—
660C2×Q8D4×D4718yescomplemented
661C2×Q8C23×D47112yes—
662C2×Q8C23×D4714yes—
663C2×D4—212no—
664C2×D4—212no—
665C2×D4—4712no—
666C2×D4—4712no—
667C2×D4—4724no—
668C2×D4—4712no—
669C2×D4—4712no—
670C2×D4—9412no—
671C2×D4—9496no—
672C2×D4—9424no—
673C2×D4—9496no—
674C2×D4—9412no—
675C2×D4—9412no—
676C2×D4—9412no—
677C2×D4C23×D47112yes—
678C2×D4C23×D47112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—473no—
682C22×C4—4724no—
683C22×C4—4712no—
684C22×C4—4712no—
685C22×C4—4712no—
686C22×C4—471no—
687C22×C4—473no—
688C22×C4—473no—
689C22×C4—471no—
690C22×C4—474no—
691C22×C4—4712no—
692C22×C4—4712no—
693C22×C4—474no—
694C22×C4—4712no—
695C22×C4—4712no—
696C22×C4—4712no—
697C22×C4—4712no—
698C22×C4—9412no—
699C22×C4—9496no—
700C22×C4—9412no—
701C22×C4—9496no—
702C22×C4—944no—
703C22×C4—944no—
704C22×C4—9412no—
705C22×C4—9412no—
706C22×C4—9412no—
707C22×C4—9412no—
708C22×C4—9412no—
709C22×C4—9412no—
710C22×C4C23×D47112yes—
711C22×C4C23×D47112yes—
712C22×C4C23×D4711yescharacteristic
713C22×C4C23×D4713yes—
714C22×C4C23×D4713yes—
715C22×C4C23×D4711yescharacteristic
716C22×C4C23×D4713yes—
717C4⋊C4—4712no—
718C4⋊C4—4712no—
719C4⋊C4—4724no—
720C4⋊C4—4712no—
721C4⋊C4—4712no—
722C4⋊C4C23×D47112yes—
723C4⋊C4C23×D47112yes—
724C22⋊C4—474no—
725C22⋊C4—4712no—
726C22⋊C4—4724no—
727C22⋊C4—474no—
728C22⋊C4—474no—
729C22⋊C4—4712no—
730C22⋊C4—4712no—
731C22⋊C4—4724no—
732C22⋊C4—4724no—
733C22⋊C4C23×D4714yes—
734C22⋊C4C23×D47112yes—
735C22⋊C4C23×D47124yes—
736C42—4712no—
737C42—4712no—
738C42—4712no—
739C42C23×D47112yes—
740C23—22no—
741C23—22no—
742C23—26no—
743C23—26no—
744C23—26no—
745C23—474no—
746C23—474no—
747C23—474no—
748C23—472no—
749C23—474no—
750C23—4716no—
751C23—472no—
752C23—476no—
753C23—948no—
754C23—9432no—
755C23—948no—
756C23—9424no—
757C23—9424no—
758C23—9424no—
759C23—942no—
760C23—942no—
761C23—946no—
762C23—946no—
763C23—946no—
764C23—18848no—
765C23#41×D4714yescomplemented
766C23C24×D4716yes—
767C23C24×D4712yes—
768C23C24×D4711yescharacteristic
769Q8—224no—
770Q8—4748no—
771Q8—9448no—
772Q8—9424no—
773Q8C2×D4×D47116yescomplemented
774D4—224no—
775D4—224no—
776D4—9424no—
777D4—9448no—
778D4—9424no—
779D4—9424no—
780D4—9424no—
781C2×C4—22no—
782C2×C4—26no—
783C2×C4—26no—
784C2×C4—22no—
785C2×C4—224no—
786C2×C4—224no—
787C2×C4—4712no—
788C2×C4—476no—
789C2×C4—4748no—
790C2×C4—472no—
791C2×C4—476no—
792C2×C4—476no—
793C2×C4—472no—
794C2×C4—9424no—
795C2×C4—9424no—
796C2×C4—948no—
797C2×C4—948no—
798C2×C4—9424no—
799C2×C4—9424no—
800C2×C4—9424no—
801C2×C4—9424no—
802C2×C4—942no—
803C2×C4—946no—
804C2×C4—946no—
805C2×C4—942no—
806C2×C4—9424no—
807C2×C4—9424no—
808C2×C4C2×D4×D47112yes—
809C2×C4C24×D4712yes—
810C2×C4C24×D4716yes—
811C2×C4C24×D4716yes—
812C2×C4C24×D4712yes—
813C2×C4C24×D4716yes—
814C22—28no—
815C22—22no—
816C22—22no—
817C22—26no—
818C22—26no—
819C22—26no—
820C22—412no—
821C22—4716no—
822C22—474no—
823C22—474no—
824C22—474no—
825C22—474no—
826C22—9432no—
827C22—948no—
828C22—942no—
829C22—942no—
830C22—946no—
831C22—946no—
832C22—946no—
833C22—18848no—
834C22—18812no—
835C22C22×D4×D4712yes—
836C22C2×#41×D4712yes—
837C22C2×#41×D4714yescomplemented
838C222−1+4×D4712yes—
839C22C25×D4711yescharacteristic
840C4—22no—
841C4—26no—
842C4—26no—
843C4—22no—
844C4—4712no—
845C4—942no—
846C4—946no—
847C4—946no—
848C4—942no—
849C4C22×D4×D47112yes—
850C2—24no—
851C2—46no—
852C2—478no—
853C2—944no—
854C2—1886no—
855C2#548×D4714yesdirect product factor
856C2C23×D4×D4711yescharacteristic
857C2C22×#41×D4711yescharacteristic
858C2C2×2−1+4×D4711yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#548C2
socleC23×C47C25
hypercenterC2×#548D47
hypocenterC47C22×#548
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#41×D47C2semidirect
2. C23×Q8×D47C2semidirect
3. C2×#15689785C2semidirect
4. C2×#15689784C2semidirect
5. C2×#15689783C2semidirect
6. C2×#15689782C2semidirect
7. C2×#15689781C2semidirect
8. C2×#15689780C2semidirect
9. C2×#15689779C2semidirect
10. #548×D47C2direct (N × H)
11. C2×#124×D47C2semidirect
12. C2×C22⋊Q8×D47C2semidirect
13. C2×#121×D47C2semidirect
14. C2×C4×Q8×D47C2semidirect
15. C2×C4×D4×D47C2semidirect
16. C2×C47×#548C2semidirect
17. C22×#10625354C22semidirect
18. C22×#10625350C22semidirect
19. C22×#10625352C22semidirect
21. C2×#41×D47C22semidirect
22. C23×Dic94C22semidirect
26. C22×Q8×D47C22semidirect
27. C22×Q8×D47C22semidirect
28. C22×Q8×D47C22semidirect
33. #15689785C22semidirect
34. #15689784C22semidirect
35. #15689783C22semidirect
36. #15689782C22semidirect
37. #15689781C22semidirect
38. #15689780C22semidirect
39. #15689779C22semidirect
40. C2×#13094013C22semidirect
41. C2×#13094012C22semidirect
42. C2×#13094011C22semidirect
43. C2×#13094010C22semidirect
44. C2×#13094010C22semidirect
45. #124×D47C22semidirect
46. C2×#13094004C22semidirect
47. C2×#13094003C22semidirect
48. C2×#13094002C22semidirect
49. C2×#13094001C22semidirect
50. C2×#13094000C22semidirect
51. C22⋊Q8×D47C22semidirect
52. C2×#13093999C22semidirect
53. C2×#13093998C22semidirect
54. C2×#13093997C22semidirect
55. C2×#13093996C22semidirect
56. C2×#13093995C22semidirect
57. #121×D47C22semidirect
58. C2×Q8×Dic47C22semidirect
59. C2×C4×Dic94C22semidirect
60. C2×#13093989C22semidirect
61. C4×Q8×D47C22semidirect
62. C2×C4×D188C22semidirect
63. C2×D4×Dic47C22semidirect
64. C2×#13093986C22semidirect
65. C2×C4×C22⋊D47C22semidirect
66. C2×C4×C22⋊D47C22semidirect
67. C2×(C22⋊D47)⋊C4C22semidirect
68. C2×(C22⋊D47)⋊C4C22semidirect
69. C4×D4×D47C22semidirect
76. C22×#41×C47C22semidirect
77. C23×Q8×C47C22semidirect
78. C47×#548C22semidirect
79. C2×#124×C47C22semidirect
80. C2×C22⋊Q8×C47C22semidirect
81. C2×#121×C47C22semidirect
82. C2×C4×Q8×C47C22semidirect
83. C2×C4×D4×C47C22semidirect
87. C2×#10625354C23semidirect
89. C2×#10625350C23semidirect
91. C2×#10625352C23semidirect
97. C22×Dic94C23semidirect
102. C2×Q8×D47D4semidirect
105. C2×Q8×D47C23semidirect
106. C2×Q8×D47C23semidirect
131. #13094013C23semidirect
132. #13094012C23semidirect
133. #13094011C23semidirect
134. #13094010C23semidirect
135. #13094010C23semidirect
136. #13094004C23semidirect
137. #13094003C23semidirect
138. #13094002C23semidirect
139. #13094001C23semidirect
140. #13094000C23semidirect
141. #13093999C23semidirect
142. #13093998C23semidirect
143. #13093997C23semidirect
144. #13093996C23semidirect
145. #13093995C23semidirect
146. Q8×Dic47C23semidirect
147. C4×Dic94C23semidirect
148. #13093989C23semidirect
149. C4×D188C23semidirect
150. D4×Dic47C23semidirect
151. #13093986C23semidirect
152. C4×C22⋊D47C23semidirect
153. C4×C22⋊D47C23semidirect
154. (C22⋊D47)⋊C4C23semidirect
155. (C22⋊D47)⋊C4C23semidirect
180. C2×#41×C47C23semidirect
184. C22×Q8×C47C23semidirect
189. #124×C47C23semidirect
190. C22⋊Q8×C47C23semidirect
191. #121×C47C23semidirect
192. C4×Q8×C47C23semidirect
193. C4×D4×C47C23semidirect
207. C23×D47#41semidirect
216. C2×Q8×C47C2×D4semidirect
251. Q8×D47C2×D4semidirect
283. C2×Dic94C2×D4semidirect
315. C23×C47C2×#41semidirect
333. C22×D47C2×#41semidirect
334. C22×D47C2×#41semidirect
340. Q8×C47C22×D4semidirect
383. Dic94C22×D4semidirect
394. C22×C47C22×#41semidirect
406. C2×D47#548direct (N × H)
409. C2×D47C22×#41semidirect
431. C2×#548D47direct (N × H)
439. C2×C47C2×#548semidirect
445. D47C2×#548direct (N × H)
451. C22×#41C2×D47semidirect
459. C23×Q8C2×D47semidirect
471. #548C2×D47direct (N × H)
478. C2×#124C2×D47semidirect
485. C2×C22⋊Q8C2×D47semidirect
492. C2×#121C2×D47semidirect
497. C2×C4×Q8C2×D47semidirect
506. C2×C4×D4C2×D47semidirect
513. C47C22×#548semidirect
524. C2×#41C22×D47semidirect
542. C22×Q8C22×D47semidirect
576. #124C22×D47semidirect
582. C22⋊Q8C22×D47semidirect
588. #121C22×D47semidirect
592. C4×Q8C22×D47semidirect
600. C4×D4C22×D47semidirect
660. C2×Q8D4×D47semidirect
765. C23#41×D47semidirect
773. Q8C2×D4×D47semidirect
837. C22C2×#41×D47semidirect
855. C2#548×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
C23×Q8×D472
C2×#156897852
C2×#156897842
C2×#156897832
C2×#156897822
C2×#156897812
C2×#156897802
C2×#156897792
#548×D472
C2×#124×D472
C2×C22⋊Q8×D472
C2×#121×D472
C2×C4×Q8×D472
C2×C4×D4×D472
C2×C47×#5482
C22×#54847