Finite Group Databasebeta

← C2×#20257034 #27124440

Subgroups — C2×#20257034 #27124440

Order 12032.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094071C211yesmaximal, characteristic, complemented
2C23×Q8×D47C211yesmaximal, characteristic, complemented
3#20257034C2132yesmaximal, direct product factor
4C2×Q8×D188C211yesmaximal, characteristic, complemented
5C2×D4×Dic94C213yesmaximal, complemented
6C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
7C2×#15689786C213yesmaximal, complemented
8C2×#15689781C213yesmaximal, complemented
9C2×#15689780C211yesmaximal, characteristic, complemented
10C2×#15689779C213yesmaximal, complemented
11C2×#15689696C213yesmaximal, complemented
12C2×#15689693C213yesmaximal, complemented
13C2×#15689633C213yesmaximal, complemented
14C2×#15689632C213yesmaximal, complemented
15C2×#15689599C211yesmaximal, characteristic, complemented
16C2×C47×#548C211yesmaximal, characteristic, complemented
17C2×#13094071—216no—
18C2×#13094071C22116yescomplemented
19C22×#10625350C2213yes—
20C22×#10625352C2213yes—
21C22×#10625352C2213yescomplemented
22C23×Dic94C2213yes—
23C23×Dic94C2213yescomplemented
24C22×Q8×D47—216no—
25C22×Q8×D47C2211yescharacteristic
26C22×Q8×D47C2213yes—
27C22×Q8×D47C2213yes—
28C22×Q8×D47C2211yescharacteristic
29C22×Q8×D47C22116yescomplemented
30C22×Q8×D47C2211yescharacteristic, complemented
31C23×C4×D47C2213yes—
32Q8×D188C22116yescomplemented
33D4×Dic94C22148yescomplemented
34Q8×C22⋊D47C22116yescomplemented
35#15689786C22148yescomplemented
36#15689781C22148yescomplemented
37#15689780C22116yescomplemented
38#15689779C22148yescomplemented
39#15689696C22148yescomplemented
40#15689693C22148yescomplemented
41C2×#13094024C2213yescomplemented
42C2×#13094023C2216yescomplemented
43C2×#13094022C2213yescomplemented
44C2×#13094011C2213yescomplemented
45C2×#13094010C2216yescomplemented
46#15689633C22148yescomplemented
47#15689632C22148yescomplemented
48C2×#13094009C2213yes—
49C2×#13094006C2213yes—
50C2×#13094006C2216yes—
51C2×#13094004C2213yes—
52C2×#13094004C2213yescomplemented
53C2×#13094003C2213yes—
54C2×#13094003C2213yescomplemented
55C2×#13094002C2213yes—
56C2×#13094001C2213yes—
57C2×#13094001C2216yescomplemented
58C2×#13094001C2216yescomplemented
59C2×#13094000C2213yescomplemented
60C2×#13093997C2213yes—
61C2×#13093996C2213yes—
62C2×#13093995C2213yes—
63C2×#13093994C2211yescharacteristic
64C2×#13093992C2213yes—
65#15689599C22116yescomplemented
66C2×Q8×Dic47C2211yescharacteristic, complemented
67C2×C4×Dic94C2213yescomplemented
68C2×#13093989C2213yescomplemented
69C2×C4×D188C2213yes—
70C2×D4×Dic47C2216yes—
71C2×C4×C22⋊D47C2213yes—
72C2×C4×C22⋊D47C2213yes—
73C2×(C22⋊D47)⋊C4C2216yes—
74C2×#13093982C2213yes—
75C2×#13093981C2213yes—
76C22×#41×C47C2211yescharacteristic, complemented
77C23×Q8×C47C2211yescharacteristic
78C47×#548C22116yescomplemented
79C2×#124×C47C2213yescomplemented
80C2×C22⋊Q8×C47C2213yescomplemented
81C2×#121×C47C2213yes—
82C2×C4×Q8×C47C2211yescharacteristic, complemented
83C2×C4×D4×C47C2213yes—
84C24×D47C2311yescharacteristic
85#13094071—2128no—
86C2×#10625350—224no—
87C2×#10625350C23124yes—
88C2×#10625352—224no—
89C2×#10625352—224no—
90C2×#10625352C23124yes—
91C2×#10625352C23124yescomplemented
92C22×Dic94—224no—
93C22×Dic94—224no—
94C22×Dic94C23124yes—
95C22×Dic94C2313yes—
96C22×Dic94C2316yes—
97C22×Dic94C2313yes—
98C22×Dic94C2313yes—
99C22×Dic94C2313yes—
100C22×Dic94C23124yescomplemented
101C2×Q8×D47—28no—
102C2×Q8×D47—28no—
103C2×Q8×D47—2128no—
104C2×Q8×D47—224no—
105C2×Q8×D47—224no—
106C2×Q8×D47D4116yescomplemented
107C2×Q8×D47C2318yes—
108C2×Q8×D47C23124yes—
109C2×Q8×D47C23124yes—
110C2×Q8×D47C2318yes—
111C2×Q8×D47C2318yescomplemented
112C22×D188C2311yescharacteristic
113C22×D188C2311yescharacteristic
114C22×C22⋊D47C2313yes—
115C22×C22⋊D47C2311yescharacteristic
116C22×C22⋊D47C2313yes—
117C22×C22⋊D47C2313yes—
118C23×Dic47C2316yes—
119C23×Dic47C2313yes—
120C22×C4×D47—224no—
121C22×C4×D47C2313yes—
122C22×C4×D47C2313yes—
123C22×C4×D47C2313yes—
124C22×C4×D47C2313yes—
125C22×C4×D47C23124yes—
126C22×C4×D47C2313yes—
127#13094024C23124yescomplemented
128#13094023C23148yescomplemented
129#13094022C23124yescomplemented
130#13094011C23124yescomplemented
131#13094010C23148yescomplemented
132#13094009C23124yes—
133#13094006C23124yes—
134#13094006C23148yes—
135#13094004C23124yes—
136#13094004C23124yescomplemented
137#13094003C23124yes—
138#13094003C23124yescomplemented
139#13094002C23124yes—
140#13094001C23124yes—
141#13094001C23148yescomplemented
142#13094001C23148yescomplemented
143#13094000C23124yescomplemented
144#13093997C23124yes—
145#13093996C23124yes—
146#13093995C23124yes—
147#13093994C2318yes—
148#13093992C23124yes—
149Q8×Dic47C2318yescomplemented
150C4×Dic94C23124yescomplemented
151#13093989C23124yescomplemented
152C4×D188C23124yes—
153D4×Dic47C23148yes—
154C4×C22⋊D47C23124yes—
155C4×C22⋊D47C23124yes—
156(C22⋊D47)⋊C4C23148yes—
157#13093982C23124yes—
158#13093981C23124yes—
159C2×C4⋊Dic47C2313yes—
160C2×C4⋊Dic47C2316yes—
161C2×C4⋊Dic47C2313yes—
162C2×Dic47⋊C4C2313yes—
163C2×Dic47⋊C4C2313yes—
164C2×Dic47⋊C4C2316yes—
165C2×Dic47⋊C4C2313yes—
166C2×Dic47⋊C4C2313yes—
167C2×C22⋊Dic47C2313yes—
168C2×C22⋊Dic47C2313yes—
169C2×C22⋊Dic47C2316yes—
170C2×(C2×D47)⋊C4C2311yescharacteristic
171C2×(C2×D47)⋊C4C2313yes—
172C2×(C2×D47)⋊C4C2313yes—
173C2×(C2×D47)⋊C4C2311yescharacteristic
174C2×(C2×D47)⋊C4C2313yes—
175C2×(C2×D47)⋊C4C2313yes—
176C2×C4×Dic47C2313yes—
177C2×C4×Dic47C2316yes—
178C2×#41×C47—28no—
179C2×#41×C47C2318yescomplemented
180C22×Q8×C47—28no—
181C22×Q8×C47C2318yes—
182C22×Q8×C47C2313yes—
183C22×Q8×C47C2311yescharacteristic
184C22×D4×C47C2313yes—
185C22×D4×C47C2313yes—
186C23×C4×C47C2313yes—
187C23×C4×C47C2313yes—
188#124×C47C23124yescomplemented
189C22⋊Q8×C47C23124yescomplemented
190#121×C47C23124yes—
191C4×Q8×C47C2318yescomplemented
192C4×D4×C47C23124yes—
193C2×C4⋊C4×C47C2313yes—
194C2×C4⋊C4×C47C2313yes—
195C2×C22⋊C4×C47C2311yescharacteristic
196C2×C22⋊C4×C47C2313yes—
197C2×C22⋊C4×C47C2316yes—
198C2×C42×C47C2313yes—
199C24×C47C2413yes—
200C24×C47C2411yescharacteristic
201C23×D47—24no—
202C23×D47—24no—
203C23×D47—24no—
204C23×D47C2411yescharacteristic
205C23×D47C2414yes—
206C23×D47C2411yescharacteristic
207C23×D47C2411yescharacteristic
208#41×C47—232no—
209C2×Q8×C47—232no—
210C2×Q8×C47—212no—
211C2×Q8×C47C2×D418yes—
212C2×Q8×C47C24112yes—
213C2×Q8×C47C2414yes—
214C2×D4×C47—212no—
215C2×D4×C47—212no—
216C2×D4×C47C24112yes—
217C2×D4×C47C24112yes—
218C22×C4×C47—212no—
219C22×C4×C47—212no—
220C22×C4×C47C2411yescharacteristic
221C22×C4×C47C2413yes—
222C22×C4×C47C2413yes—
223C22×C4×C47C2411yescharacteristic
224C22×C4×C47C24112yes—
225C22×C4×C47C24112yes—
226C22×C4×C47C2413yes—
227C2×C22⋊D47—24no—
228C2×C22⋊D47—212no—
229C2×C22⋊D47—212no—
230C2×C22⋊D47—212no—
231C2×C22⋊D47C24112yes—
232C2×C22⋊D47C2414yes—
233C2×C22⋊D47C24112yes—
234C2×C22⋊D47C24112yes—
235C22×Dic47—212no—
236C22×Dic47—224no—
237C22×Dic47C2411yescharacteristic
238C22×Dic47C2413yes—
239C22×Dic47C2413yes—
240C22×Dic47C2413yes—
241C22×Dic47C24124yes—
242C22×Dic47C24112yes—
243C22×Dic47C2413yes—
244Q8×D47—232no—
245Q8×D47—232no—
246Q8×D47—296no—
247Q8×D47—296no—
248Q8×D47C2×D4164yescomplemented
249#10625352—296no—
250#10625352—296no—
251#10625350—296no—
252C2×D188—24no—
253C2×D188—24no—
254C2×D188C2414yes—
255C2×D188C2414yes—
256C2×C4×D47—212no—
257C2×C4×D47—212no—
258C2×C4×D47—212no—
259C2×C4×D47—212no—
260C2×C4×D47—296no—
261C2×C4×D47C2×D4124yes—
262C2×C4×D47C24112yes—
263C2×C4×D47C24112yes—
264C2×C4×D47C24112yes—
265C2×C4×D47C24112yes—
266C2×C4×D47C24112yes—
267C2×Dic94—212no—
268C2×Dic94—212no—
269C2×Dic94—224no—
270C2×Dic94—212no—
271C2×Dic94—296no—
272C2×Dic94—296no—
273C2×Dic94C2×D4124yes—
274C2×Dic94C24112yes—
275C2×Dic94C24124yes—
276C2×Dic94C24112yes—
277C2×Dic94C24112yes—
278C2×Dic94C24112yes—
279C4⋊C4×C47C24112yes—
280C4⋊C4×C47C24112yes—
281C22⋊C4×C47C2414yes—
282C22⋊C4×C47C24112yes—
283C22⋊C4×C47C24124yes—
284C42×C47C24112yes—
285C22⋊Dic47C24112yes—
286C22⋊Dic47C24112yes—
287C22⋊Dic47C24124yes—
288(C2×D47)⋊C4C2414yes—
289(C2×D47)⋊C4C24112yes—
290(C2×D47)⋊C4C24112yes—
291(C2×D47)⋊C4C2414yes—
292(C2×D47)⋊C4C24112yes—
293(C2×D47)⋊C4C24112yes—
294C4⋊Dic47C24112yes—
295C4⋊Dic47C24124yes—
296C4⋊Dic47C24112yes—
297Dic47⋊C4C24112yes—
298Dic47⋊C4C24112yes—
299Dic47⋊C4C24124yes—
300Dic47⋊C4C24112yes—
301Dic47⋊C4C24112yes—
302C4×Dic47C24112yes—
303C4×Dic47C24124yes—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—26no—
307C23×C47—26no—
308C23×C47—26no—
309C23×C472−1+414yescomplemented
310C23×C47C2516yes—
311C23×C47C2512yes—
312C23×C47C2511yescharacteristic
313C22×D47—232no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—28no—
319C22×D47—28no—
320C22×D47—28no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47C22×D414yes—
325C22×D472−1+414yescomplemented
326C22×D47C2512yes—
327C22×D47C2512yes—
328C22×D47C2512yes—
329Q8×C47—224no—
330Q8×C47C22×D4116yes—
331D4×C47—224no—
332D4×C47—224no—
333C2×C4×C47—22no—
334C2×C4×C47—26no—
335C2×C4×C47—22no—
336C2×C4×C47—26no—
337C2×C4×C47—224no—
338C2×C4×C47—224no—
339C2×C4×C47C22×D4112yes—
340C2×C4×C47C2516yes—
341C2×C4×C47C2512yes—
342C2×C4×C47C2516yes—
343C2×C4×C47C2512yes—
344C2×C4×C47C2516yes—
345C22⋊D47—28no—
346C22⋊D47—224no—
347C22⋊D47—224no—
348C22⋊D47—224no—
349C2×Dic47—26no—
350C2×Dic47—26no—
351C2×Dic47—26no—
352C2×Dic47—22no—
353C2×Dic47—224no—
354C2×Dic47—248no—
355C2×Dic47C22×D4112yes—
356C2×Dic47C2512yes—
357C2×Dic47C2516yes—
358C2×Dic47C2516yes—
359C2×Dic47C2516yes—
360C2×Dic47C2516yes—
361D188—28no—
362D188—28no—
363C4×D47—224no—
364C4×D47—224no—
365C4×D47—224no—
366C4×D47—224no—
367C4×D47C22×D4148yes—
368Dic94—224no—
369Dic94—224no—
370Dic94—224no—
371Dic94—248no—
372Dic94C22×D4148yes—
373C2×#3486—471nomaximal, Sylow
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—28no—
377C22×C47—26no—
378C22×C47—26no—
379C22×C47—26no—
380C22×C47—412no—
381C22×C47C23×D412yes—
382C22×C47C2×2−1+412yes—
383C22×C47C2×2−1+412yes—
384C22×C47C2×2−1+414yescomplemented
385C22×C47C2611yescharacteristic
386C2×D47—232no—
387C2×D47—22no—
388C2×D47—22no—
389C2×D47—22no—
390C2×D47—22no—
391C2×D47—28no—
392C2×D47—28no—
393C2×D47—22no—
394C2×D47—22no—
395C2×D47—22no—
396C2×D47—44no—
397C2×D47C23×D414yes—
398C2×D47C2×2−1+414yescomplemented
399C4×C47—22no—
400C4×C47—26no—
401C4×C47—22no—
402C4×C47—26no—
403C4×C47C23×D4112yes—
404Dic47—26no—
405Dic47—26no—
406Dic47—26no—
407Dic47—22no—
408Dic47C23×D4112yes—
409C22×2−1+4—471no—
410C24×Q8—471no—
411#3486—4732no—
412C2×D4×Q8—471no—
413C2×D4×Q8—473no—
414C2×D4×Q8—471no—
415C2×D4×Q8—473no—
416C2×#548—471no—
417C2×#548—473no—
418C2×#548—473no—
419C2×#548D4711yescharacteristic, complemented
420C2×#536—473no—
421C2×#536—473no—
422C2×#525—473no—
423C2×#525—473no—
424C2×#519—471no—
425C2×C47—24no—
426C2×C47—46no—
427C2×C47#348614yescomplemented
428C2×C47C24×D411yescharacteristic
429C2×C47C22×2−1+411yescharacteristic
430C2×C47C22×2−1+411yescharacteristic
431D47—24no—
432D47—24no—
433D47—42no—
434C2×2−1+4—4716no—
435C2×2−1+4—9416no—
436C22×#41—473no—
437C22×#41—473no—
438C22×#41—473no—
439C22×#41C2×D4711yescharacteristic, complemented
440C23×Q8—471no—
441C23×Q8—473no—
442C23×Q8—473no—
443C23×Q8—471no—
444C23×Q8—4716no—
445C23×Q8—471no—
446C23×Q8—473no—
447C23×Q8—473no—
448C23×Q8—9416no—
449C23×Q8C2×D4711yescharacteristic
450C24×C4—473no—
451D4×Q8—4716no—
452D4×Q8—4748no—
453D4×Q8—4716no—
454D4×Q8—4748no—
455#548—4716no—
456#548—4748no—
457#548—4748no—
458#548C2×D47116yescomplemented
459#536—4748no—
460#536—4748no—
461C2×C4⋊Q8—473no—
462C2×C4⋊Q8—476no—
463C2×C4⋊Q8—473no—
464C2×#124—473no—
465C2×#124—476no—
466C2×#124C2×D4713yescomplemented
467#525—4748no—
468#525—4748no—
469C2×#123—473no—
470C2×#123—476no—
471C2×#123—473no—
472C2×C22⋊Q8—473no—
473C2×C22⋊Q8—473no—
474C2×C22⋊Q8—473no—
475C2×C22⋊Q8—473no—
476C2×C22⋊Q8—473no—
477C2×C22⋊Q8—473no—
478C2×C22⋊Q8—473no—
479C2×C22⋊Q8—476no—
480C2×C22⋊Q8—476no—
481C2×C22⋊Q8C2×D4713yescomplemented
482C2×#121—473no—
483C2×#121—473no—
484C2×#121—473no—
485C2×#121C2×D4713yes—
486C2×#120—473no—
487C2×#120—471no—
488#519—4716no—
489C2×C4×Q8—471no—
490C2×C4×Q8—473no—
491C2×C4×Q8—473no—
492C2×C4×Q8C2×D4711yescharacteristic, complemented
493C2×C4×D4—476no—
494C2×C4×D4—473no—
495C2×C4×D4—473no—
496C2×C4×D4—476no—
497C2×C4×D4—473no—
498C2×C4×D4C2×D4713yes—
499C2×#117—473no—
500C2×#117—473no—
501C47C2×#348611yescharacteristic, complemented, Sylow
502C25—471no—
5032−1+4—94128no—
504C2×#41—28no—
505C2×#41—4724no—
506C2×#41—4724no—
507C2×#41—4724no—
508C2×#41—9424no—
509C2×#41—9424no—
510C2×#41—9424no—
511C2×#41C22×D4718yescomplemented
512C22×Q8—28no—
513C22×Q8—4716no—
514C22×Q8—478no—
515C22×Q8—4724no—
516C22×Q8—4724no—
517C22×Q8—478no—
518C22×Q8—478no—
519C22×Q8—473no—
520C22×Q8—476no—
521C22×Q8—473no—
522C22×Q8—473no—
523C22×Q8—473no—
524C22×Q8—4724no—
525C22×Q8—4724no—
526C22×Q8—9424no—
527C22×Q8—9424no—
528C22×Q8—9424no—
529C22×Q8—94128no—
530C22×Q8—9424no—
531C22×Q8—948no—
532C22×Q8—948no—
533C22×Q8C22×D4713yes—
534C22×Q8C22×D4718yes—
535C22×Q8C22×D4711yescharacteristic
536C22×D4—473no—
537C22×D4—471no—
538C22×D4—473no—
539C22×D4—473no—
540C22×D4—471no—
541C22×D4—471no—
542C22×D4C22×D4713yes—
543C22×D4C22×D4713yes—
544C23×C4—473no—
545C23×C4—473no—
546C23×C4—476no—
547C23×C4—473no—
548C23×C4—473no—
549C23×C4—473no—
550C23×C4—473no—
551C23×C4—4724no—
552C23×C4—9424no—
553C23×C4C22×D4713yes—
554C23×C4C22×D4713yes—
555C4⋊Q8—4724no—
556C4⋊Q8—4748no—
557C4⋊Q8—4724no—
558#124—4724no—
559#124—4748no—
560#124C22×D47124yescomplemented
561#123—4724no—
562#123—4748no—
563#123—4724no—
564C22⋊Q8—4724no—
565C22⋊Q8—4724no—
566C22⋊Q8—4724no—
567C22⋊Q8—4724no—
568C22⋊Q8—4724no—
569C22⋊Q8—4724no—
570C22⋊Q8—4724no—
571C22⋊Q8—4748no—
572C22⋊Q8—4748no—
573C22⋊Q8C22×D47124yescomplemented
574#121—4724no—
575#121—4724no—
576#121—4724no—
577#121C22×D47124yes—
578#120—4724no—
579#120—478no—
580C4×Q8—478no—
581C4×Q8—4724no—
582C4×Q8—4724no—
583C4×Q8C22×D4718yescomplemented
584C4×D4—4748no—
585C4×D4—4724no—
586C4×D4—4724no—
587C4×D4—4748no—
588C4×D4—4724no—
589C4×D4C22×D47124yes—
590#117—4724no—
591#117—4724no—
592C2×C4⋊C4—473no—
593C2×C4⋊C4—473no—
594C2×C4⋊C4—473no—
595C2×C4⋊C4—473no—
596C2×C4⋊C4—473no—
597C2×C4⋊C4—476no—
598C2×C4⋊C4—476no—
599C2×C4⋊C4—473no—
600C2×C4⋊C4C22×D4713yes—
601C2×C4⋊C4C22×D4713yes—
602C2×C22⋊C4—473no—
603C2×C22⋊C4—476no—
604C2×C22⋊C4—473no—
605C2×C22⋊C4—473no—
606C2×C22⋊C4—471no—
607C2×C22⋊C4—471no—
608C2×C22⋊C4—473no—
609C2×C22⋊C4—473no—
610C2×C22⋊C4—473no—
611C2×C22⋊C4C22×D4716yes—
612C2×C22⋊C4C22×D4711yescharacteristic
613C2×C22⋊C4C22×D4713yes—
614C2×C42—476no—
615C2×C42—473no—
616C2×C42C22×D4713yes—
617C24—471no—
618C24—471no—
619C24—474no—
620C24—471no—
621C24—944no—
622C24—944no—
623C24—944no—
624C24C23×D4713yes—
625C24C23×D4711yescharacteristic
626#41—232no—
627#41—9496no—
628#41—9496no—
629#41—9496no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—4764no—
633C2×Q8—4724no—
634C2×Q8—4712no—
635C2×Q8—4724no—
636C2×Q8—4712no—
637C2×Q8—4712no—
638C2×Q8—4712no—
639C2×Q8—9424no—
640C2×Q8—9412no—
641C2×Q8—9496no—
642C2×Q8—9496no—
643C2×Q8—9496no—
644C2×Q8—9496no—
645C2×Q8—9432no—
646C2×Q8—9432no—
647C2×Q8—9412no—
648C2×Q8—9412no—
649C2×Q8D4×D4718yes—
650C2×Q8C23×D47112yes—
651C2×Q8C23×D4714yes—
652C2×D4—212no—
653C2×D4—212no—
654C2×D4—4712no—
655C2×D4—474no—
656C2×D4—4712no—
657C2×D4—4712no—
658C2×D4—474no—
659C2×D4—474no—
660C2×D4—944no—
661C2×D4—944no—
662C2×D4—9412no—
663C2×D4—9412no—
664C2×D4—9412no—
665C2×D4—944no—
666C2×D4C23×D47112yes—
667C2×D4C23×D47112yes—
668C22×C4—212no—
669C22×C4—212no—
670C22×C4—473no—
671C22×C4—4724no—
672C22×C4—4712no—
673C22×C4—4712no—
674C22×C4—4724no—
675C22×C4—473no—
676C22×C4—471no—
677C22×C4—473no—
678C22×C4—473no—
679C22×C4—4712no—
680C22×C4—4712no—
681C22×C4—4712no—
682C22×C4—4712no—
683C22×C4—9412no—
684C22×C4—9496no—
685C22×C4—9412no—
686C22×C4—9412no—
687C22×C4—9424no—
688C22×C4—9412no—
689C22×C4—9412no—
690C22×C4C23×D47112yes—
691C22×C4C23×D47112yes—
692C22×C4C23×D4713yes—
693C22×C4C23×D4711yescharacteristic
694C22×C4C23×D4713yes—
695C22×C4C23×D4711yescharacteristic
696C22×C4C23×D4713yes—
697C4⋊C4—4712no—
698C4⋊C4—4712no—
699C4⋊C4—4712no—
700C4⋊C4—4724no—
701C4⋊C4—4712no—
702C4⋊C4—4712no—
703C4⋊C4—4724no—
704C4⋊C4—4712no—
705C4⋊C4C23×D47112yes—
706C4⋊C4C23×D47112yes—
707C22⋊C4—4712no—
708C22⋊C4—4712no—
709C22⋊C4—4724no—
710C22⋊C4—4712no—
711C22⋊C4—474no—
712C22⋊C4—474no—
713C22⋊C4—4712no—
714C22⋊C4—4712no—
715C22⋊C4—4712no—
716C22⋊C4C23×D47124yes—
717C22⋊C4C23×D4714yes—
718C22⋊C4C23×D47112yes—
719C42—4724no—
720C42—4712no—
721C42C23×D47112yes—
722C23—22no—
723C23—22no—
724C23—26no—
725C23—26no—
726C23—26no—
727C23—474no—
728C23—474no—
729C23—472no—
730C23—472no—
731C23—472no—
732C23—948no—
733C23—948no—
734C23—9432no—
735C23—942no—
736C23—942no—
737C23—942no—
738C23—942no—
739C23—948no—
740C23—942no—
741C23—942no—
742C23—942no—
743C23#1309407114yescomplemented
744C23C24×D4716yes—
745C23C24×D4712yes—
746C23C24×D4711yescharacteristic
747Q8—224no—
748Q8—4748no—
749Q8—9448no—
750Q8—9424no—
751Q8—9424no—
752Q8—9424no—
753Q8C2×D4×D47116yes—
754D4—224no—
755D4—224no—
756D4—948no—
757D4—948no—
758D4—9424no—
759D4—9424no—
760D4—9424no—
761D4—948no—
762C2×C4—22no—
763C2×C4—26no—
764C2×C4—22no—
765C2×C4—26no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—4712no—
769C2×C4—476no—
770C2×C4—4748no—
771C2×C4—476no—
772C2×C4—472no—
773C2×C4—476no—
774C2×C4—476no—
775C2×C4—9424no—
776C2×C4—9424no—
777C2×C4—9424no—
778C2×C4—9448no—
779C2×C4—946no—
780C2×C4—946no—
781C2×C4—946no—
782C2×C4—942no—
783C2×C4—9424no—
784C2×C4—9424no—
785C2×C4C2×D4×D47112yes—
786C2×C4C24×D4716yes—
787C2×C4C24×D4712yes—
788C2×C4C24×D4716yes—
789C2×C4C24×D4712yes—
790C2×C4C24×D4716yes—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—26no—
795C22—26no—
796C22—26no—
797C22—412no—
798C22—474no—
799C22—474no—
800C22—9432no—
801C22—948no—
802C22—948no—
803C22—942no—
804C22—942no—
805C22—942no—
806C22—942no—
807C22—942no—
808C22—942no—
809C22—942no—
810C22—1884no—
811C22C22×D4×D4712yes—
812C222−1+4×D4712yes—
813C22C2×#1309407112yes—
814C22C2×#1309407114yescomplemented
815C22C25×D4711yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—4712no—
821C4—946no—
822C4—946no—
823C4—946no—
824C4—942no—
825C4C22×D4×D47112yes—
826C2—24no—
827C2—46no—
828C2—944no—
829C2—944no—
830C2—1882no—
831C2#2025703414yesdirect product factor
832C2C23×D4×D4711yescharacteristic
833C2C2×2−1+4×D4711yescharacteristic
834C2C22×#1309407111yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#548C2
socleC23×C47C25
hypercenterC2×#548D47
hypocenterC47C2×#3486
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13094071C2semidirect
2. C23×Q8×D47C2semidirect
3. #20257034C2direct (N × H)
4. C2×Q8×D188C2semidirect
5. C2×D4×Dic94C2semidirect
6. C2×Q8×C22⋊D47C2semidirect
7. C2×#15689786C2semidirect
8. C2×#15689781C2semidirect
9. C2×#15689780C2semidirect
10. C2×#15689779C2semidirect
11. C2×#15689696C2semidirect
12. C2×#15689693C2semidirect
13. C2×#15689633C2semidirect
14. C2×#15689632C2semidirect
15. C2×#15689599C2semidirect
16. C2×C47×#548C2semidirect
18. C2×#13094071C22semidirect
21. C22×#10625352C22semidirect
23. C23×Dic94C22semidirect
29. C22×Q8×D47C22semidirect
30. C22×Q8×D47C22semidirect
32. Q8×D188C22semidirect
33. D4×Dic94C22semidirect
34. Q8×C22⋊D47C22semidirect
35. #15689786C22semidirect
36. #15689781C22semidirect
37. #15689780C22semidirect
38. #15689779C22semidirect
39. #15689696C22semidirect
40. #15689693C22semidirect
41. C2×#13094024C22semidirect
42. C2×#13094023C22semidirect
43. C2×#13094022C22semidirect
44. C2×#13094011C22semidirect
45. C2×#13094010C22semidirect
46. #15689633C22semidirect
47. #15689632C22semidirect
52. C2×#13094004C22semidirect
54. C2×#13094003C22semidirect
57. C2×#13094001C22semidirect
58. C2×#13094001C22semidirect
59. C2×#13094000C22semidirect
65. #15689599C22semidirect
66. C2×Q8×Dic47C22semidirect
67. C2×C4×Dic94C22semidirect
68. C2×#13093989C22semidirect
76. C22×#41×C47C22semidirect
78. C47×#548C22semidirect
79. C2×#124×C47C22semidirect
80. C2×C22⋊Q8×C47C22semidirect
82. C2×C4×Q8×C47C22semidirect
91. C2×#10625352C23semidirect
100. C22×Dic94C23semidirect
106. C2×Q8×D47D4semidirect
111. C2×Q8×D47C23semidirect
127. #13094024C23semidirect
128. #13094023C23semidirect
129. #13094022C23semidirect
130. #13094011C23semidirect
131. #13094010C23semidirect
136. #13094004C23semidirect
138. #13094003C23semidirect
141. #13094001C23semidirect
142. #13094001C23semidirect
143. #13094000C23semidirect
149. Q8×Dic47C23semidirect
150. C4×Dic94C23semidirect
151. #13093989C23semidirect
179. C2×#41×C47C23semidirect
188. #124×C47C23semidirect
189. C22⋊Q8×C47C23semidirect
191. C4×Q8×C47C23semidirect
248. Q8×D47C2×D4semidirect
309. C23×C472−1+4semidirect
325. C22×D472−1+4semidirect
384. C22×C47C2×2−1+4semidirect
398. C2×D47C2×2−1+4semidirect
419. C2×#548D47semidirect
427. C2×C47#3486semidirect
439. C22×#41C2×D47semidirect
458. #548C2×D47semidirect
466. C2×#124C2×D47semidirect
481. C2×C22⋊Q8C2×D47semidirect
492. C2×C4×Q8C2×D47semidirect
501. C47C2×#3486semidirect
511. C2×#41C22×D47semidirect
560. #124C22×D47semidirect
573. C22⋊Q8C22×D47semidirect
583. C4×Q8C22×D47semidirect
743. C23#13094071semidirect
814. C22C2×#13094071semidirect
831. C2#20257034direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940712
C23×Q8×D472
#202570342
C2×Q8×D1882
C2×D4×Dic942
C2×Q8×C22⋊D472
C2×#156897862
C2×#156897812
C2×#156897802
C2×#156897792
C2×#156896962
C2×#156896932
C2×#156896332
C2×#156896322
C2×#156895992
C2×C47×#5482
C2×#348647