Finite Group Databasebeta

← #14960590

Subgroups — #14960590

Order 2816.

2326 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623031C211yesmaximal, characteristic, complemented
2#13076903C212yesmaximal
3#13075078C218yesmaximal, complemented
4#13074927C218yesmaximal, complemented
5#13074429C212yesmaximal, complemented
6#13073774C212yesmaximal
7#13072903C212yesmaximal, complemented
8#13072890C212yesmaximal
9#13072256C212yesmaximal, complemented
10#13071219C211yesmaximal, characteristic, complemented
11C22×C11×C22⋊Q8C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C2×C11×C22⋊Q8—28no—
15C2×C11×C22⋊Q8C2218yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C2×#66997C2214yescomplemented
22C2×#66979C2212yes—
23C2×#66977C2212yes—
24C2×#66977C2212yes—
25C2×#66977C2214yes—
26#10623031—28no—
27C2×#66943C2214yescomplemented
28C2×#66941C2214yescomplemented
29#10622860C2214yes—
30#10622843C2214yescomplemented
31#10622842C2218yescomplemented
32#10622825C2212yes—
33#10622825C2214yes—
34#10622824C2214yes—
35#10622824C2212yes—
36#10622823C2214yes—
37#10622823C2214yes—
38#10622823C2218yes—
39C4×C22⋊Dic11C2212yes—
40#10622599C2214yescomplemented
41#10622599C2214yescomplemented
42#10622597C2218yescomplemented
43#10622596C2214yescomplemented
44#10622594C2218yescomplemented
45#10622592C2214yescomplemented
46#10622591C2218yescomplemented
47#10622566C2214yes—
48#10622566C2214yes—
49#10622562C2214yes—
50#10622560C2214yes—
51#10622558C2218yes—
52#10622557C2218yes—
53C25×C11C2311yescharacteristic
54C22×Q8×C11—24no—
55C22×Q8×C11—44no—
56C22×Q8×C11C2314yes—
57C23×C4×C11—24no—
58C23×C4×C11—44no—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2314yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×Dic22C2312yes—
67C22×Dic22C2312yes—
68C11×C22⋊Q8—232no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4D418yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2314yes—
79C2×C22⋊Dic11C2314yes—
80C2×C22⋊Dic11C2318yes—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2318yes—
83#66997—48no—
84#66979—28no—
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2312yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2314yes—
90#66977—28no—
91#66977—28no—
92#66977—48no—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×C4×Dic11C2314yes—
98C2×C4×Dic11C2314yes—
99#66943—216no—
100#66941—216no—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2318yes—
108C11⋊#95C2314yes—
109#36708—111nomaximal, Sylow
110C24×C11—22no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—42no—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C2×Q8×C11—28no—
117C2×Q8×C11—28no—
118C2×Q8×C11—44no—
119C2×Q8×C11—416no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—28no—
127C22×C4×C11—28no—
128C22×C4×C11—42no—
129C22×C4×C11—44no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—416no—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×Dic11C2418yes—
143C22×Dic11C2414yes—
144C22×Dic11C2414yes—
145C2×Dic22—24no—
146C2×Dic22—24no—
147C2×Dic22—44no—
148C2×Dic22—44no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4C2×D4116yes—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—28no—
154C22⋊Dic11—28no—
155C22⋊Dic11—216no—
156C22⋊Dic11—28no—
157C22⋊Dic11—48no—
158C4⋊Dic11—24no—
159C4⋊Dic11—24no—
160C4⋊Dic11—24no—
161C4⋊Dic11—24no—
162C4⋊Dic11—44no—
163Dic11⋊C4—28no—
164Dic11⋊C4—28no—
165Dic11⋊C4—216no—
166Dic11⋊C4—48no—
167C4×Dic11—28no—
168C4×Dic11—44no—
169C2×#544—111no—
170C22×C22⋊Q8D1111yescharacteristic
171#2848—112no—
172#2690—118no—
173#2677—118no—
174#2627—112no—
175#2561—112no—
176#2484—112no—
177#2482—112no—
178#2434—112no—
179#2313—111no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—28no—
183C23×C11—22no—
184C23×C11—24no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—416no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11C22×D412yes—
191C23×C112−1+414yes—
192C23×C112−1+414yes—
193C23×C11C2511yescharacteristic
194Q8×C11—416no—
195C2×C4×C11—28no—
196C2×C4×C11—28no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11—416no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11C22×D414yes—
212C2×C4×C11C22×D414yes—
213C2×C4×C11C22×D414yes—
214C2×C4×C11H(5,𝔽2)14yes—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—28no—
218C2×Dic11—28no—
219C2×Dic11—28no—
220C2×Dic11—28no—
221C2×Dic11—28no—
222Dic22—84no—
223Dic22—84no—
224C23×Q8C2×D1111yescharacteristic
225C24×C4C2×D1111yescharacteristic
226#544—228no—
227C2×C4⋊Q8—114no—
228C2×C4⋊Q8—114no—
229C2×#125—114no—
230C2×C22⋊Q8—28no—
231C2×C22⋊Q8—112no—
232C2×C22⋊Q8—112no—
233C2×C22⋊Q8—114no—
234C2×C22⋊Q8C2×D1118yes—
235C2×#117—112no—
236C22×C4⋊C4C2×D1111yescharacteristic
237C22×C4⋊C4C2×D1111yescharacteristic
238C22×C4⋊C4C2×D1111yescharacteristic
239C22×C22⋊C4C2×D1111yescharacteristic
240C22×C22⋊C4C2×D1111yescharacteristic
241#400—114no—
242#400—114no—
243#399—114no—
244#398—118no—
245#398—114no—
246#397—114no—
247#397—114no—
248#395—118no—
249#395—114no—
250#393—114no—
251#391—114no—
252#388—118no—
253#388—118no—
254#387—118no—
255#387—118no—
256#385—118no—
257#385—114no—
258#385—114no—
259#381—114no—
260#381—112no—
261#380—112no—
262#380—114no—
263#379—114no—
264C4×C22⋊C4—112no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—28no—
268C22×C11—24no—
269C22×C11—28no—
270C22×C11—416no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—44no—
274C22×C11#53614yes—
275C22×C11C23×D411yescharacteristic
276C22×C11C2×H(5,𝔽2)12yes—
277C22×C11C2×2−1+412yes—
278C22×C11C2×2−1+412yes—
279C4×C11—24no—
280C4×C11—24no—
281C4×C11—24no—
282C4×C11—24no—
283C4×C11—42no—
284C4×C11—42no—
285Dic11—44no—
286Dic11—44no—
287Dic11—48no—
288C25C22×D1111yescharacteristic
289C22×Q8—24no—
290C22×Q8—44no—
291C22×Q8—112no—
292C22×Q8—112no—
293C22×Q8C22×D1114yes—
294C23×C4—24no—
295C23×C4—44no—
296C23×C4C22×D1111yescharacteristic
297C23×C4C22×D1111yescharacteristic
298C23×C4C22×D1114yes—
299C23×C4C22×D1111yescharacteristic
300C23×C4C22×D1111yescharacteristic
301C23×C4C22×D1111yescharacteristic
302C23×C4C22×D1111yescharacteristic
303C4⋊Q8—2216no—
304C4⋊Q8—448no—
305#125—2216no—
306C22⋊Q8—232no—
307C22⋊Q8—228no—
308C22⋊Q8—228no—
309C22⋊Q8—448no—
310#117—228no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—114no—
318C2×C4⋊C4—114no—
319C2×C4⋊C4—118no—
320C2×C4⋊C4—114no—
321C2×C4⋊C4—118no—
322C2×C4⋊C4C22⋊D1118yes—
323C2×C4⋊C4C22×D1114yes—
324C2×C4⋊C4C22×D1114yes—
325C2×C4⋊C4C22×D1114yes—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—114no—
329C2×C22⋊C4—114no—
330C2×C22⋊C4—118no—
331C2×C22⋊C4—118no—
332C2×C22⋊C4C22×D1114yes—
333C2×C22⋊C4C22×D1114yes—
334C2×C42—114no—
335C2×C42—114no—
336#95—114no—
337#95—114no—
338#95—118no—
339#95—114no—
340#95—114no—
341#95—118no—
342#95—118no—
343#95—118no—
344C2×C11—24no—
345C2×C11—44no—
346C2×C11C2×#53611yescharacteristic
347C2×C11#348411yescharacteristic
348C2×C11#348611yescharacteristic
349C2×C11#353814yes—
350C24—24no—
351C24—22no—
352C24—24no—
353C24—42no—
354C24C23×D1112yes—
355C24C23×D1111yescharacteristic
356C2×Q8—28no—
357C2×Q8—28no—
358C2×Q8—44no—
359C2×Q8—416no—
360C2×Q8—224no—
361C2×Q8—224no—
362C2×Q8—444no—
363C2×Q8—444no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—28no—
371C22×C4—28no—
372C22×C4—42no—
373C22×C4—44no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—416no—
377C22×C4—118no—
378C22×C4—114no—
379C22×C4—114no—
380C22×C4C2×C22⋊D1114yes—
381C22×C4C2×C22⋊D1114yes—
382C22×C4C2×C22⋊D1114yes—
383C22×C4C23×D1112yes—
384C22×C4C23×D1112yes—
385C22×C4C23×D1112yes—
386C22×C4C23×D1112yes—
387C22×C4C23×D1112yes—
388C22×C4C23×D1112yes—
389C4⋊C4—28no—
390C4⋊C4—28no—
391C4⋊C4—2216no—
392C4⋊C4—224no—
393C4⋊C4—224no—
394C4⋊C4—224no—
395C4⋊C4—224no—
396C4⋊C4—228no—
397C4⋊C4—228no—
398C4⋊C4—444no—
399C4⋊C4—448no—
400C4⋊C4C2×C22⋊D11116yes—
401C22⋊C4—28no—
402C22⋊C4—28no—
403C22⋊C4—2216no—
404C22⋊C4—228no—
405C22⋊C4—228no—
406C22⋊C4—448no—
407C42—228no—
408C42—444no—
409C11#3670811yescharacteristic, complemented, Sylow
410C23—22no—
411C23—22no—
412C23—28no—
413C23—24no—
414C23—22no—
415C23—24no—
416C23—22no—
417C23—416no—
418C23—44no—
419C23—44no—
420C23#6704014yes—
421C23#6704314yes—
422C23C22×C22⋊D1112yes—
423C23C24×D1111yescharacteristic
424Q8—416no—
425Q8—884no—
426Q8—884no—
427C2×C4—28no—
428C2×C4—28no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—416no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—228no—
444C2×C4—228no—
445C2×C4—228no—
446C2×C4—228no—
447C2×C4—228no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4#6703714yes—
451C2×C4C22×C22⋊D1114yes—
452C2×C4C22×C22⋊D1114yes—
453C2×C4C22×C22⋊D1114yes—
454C22—22no—
455C22—22no—
456C22—28no—
457C22—24no—
458C22—28no—
459C22—416no—
460C22—42no—
461C22—42no—
462C22—44no—
463C22#1062335614yes—
464C22C2×#6703712yes—
465C22C2×#6704012yes—
466C22C2×#6704312yes—
467C22C23×C22⋊D1111yescharacteristic
468C4—24no—
469C4—24no—
470C4—24no—
471C4—24no—
472C4—42no—
473C4—42no—
474C4—444no—
475C4—444no—
476C4—448no—
477C2—24no—
478C2—44no—
479C2C2×#1062335611yescharacteristic
480C2#1308225111yescharacteristic
481C2#1308226711yescharacteristic
482C2#1308286114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×C22⋊Q8C2
prime radicalC25×C11C23
hypercenterC22×C22⋊Q8D11
hypocenterC11#36708
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10623031C2semidirect
3. #13075078C2semidirect
4. #13074927C2semidirect
5. #13074429C2semidirect
7. #13072903C2semidirect
9. #13072256C2semidirect
10. #13071219C2semidirect
21. C2×#66997C22semidirect
27. C2×#66943C22semidirect
28. C2×#66941C22semidirect
30. #10622843C22semidirect
31. #10622842C22semidirect
40. #10622599C22semidirect
41. #10622599C22semidirect
42. #10622597C22semidirect
43. #10622596C22semidirect
44. #10622594C22semidirect
45. #10622592C22semidirect
46. #10622591C22semidirect
409. C11#36708semidirect

Maximal subgroups

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

subgroupindex
C2×#106230312
#130769032
#130750782
#130749272
#130744292
#130737742
#130729032
#130728902
#130722562
#130712192
C22×C11×C22⋊Q82
#3670811