Finite Group Databasebeta

← #14752566

Subgroups — #14752566

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622332C211yesmaximal, characteristic
2C22×Dic11⋊C8C211yesmaximal, characteristic
3#13071010C211yesmaximal, characteristic
4#13068490C212yesmaximal, complemented
5#13068489C212yesmaximal, complemented
6#13068474C212yesmaximal, complemented
7#13068472C212yesmaximal, complemented
8#13068395C211yesmaximal, characteristic
9#13068394C211yesmaximal, characteristic
10C8×C22⋊Dic11C211yesmaximal, characteristic
11C8×C11×C22⋊C4C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C2×C11×C22⋊C8C2211yescharacteristic
16C2×C4×C8×C11C2212yes—
17C4×C11×C22⋊C4C2211yescharacteristic
18C4×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20C2×#66879C2212yes—
21C2×#66879C2212yes—
22C2×Dic11⋊C8C418yescomplemented
23C2×Dic11⋊C8C2211yescharacteristic
24C2×Dic11⋊C8C2211yescharacteristic
25C2×Dic11⋊C8C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2212yes—
28C2×C8×Dic11C2212yes—
29#10622556C412yes—
30#10622555C412yes—
31#10622545C2212yes—
32C4×Dic11⋊C4C2212yes—
33C2×#66867C2212yes—
34#10622332C418yescomplemented
35#10622264C412yes—
36#10622263C412yes—
37C11×#336C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40#10622162C2212yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2×C411yescharacteristic
43C23×Dic11C2×C411yescharacteristic
44C22×C8×C11—42no—
45C22×C8×C11C2×C414yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C2×C11×C22⋊C4C2×C412yes—
50C2×C42×C11C2312yes—
51C2×C22⋊Dic11C2×C412yes—
52C2×Dic11⋊C4C2×C414yes—
53C2×C4×Dic11C2×C411yescharacteristic
54C2×C4×Dic11C2×C411yescharacteristic
55C2×C4×Dic11C2×C414yes—
56C2×C4×Dic11C2×C414yes—
57C2×C4×Dic11C2312yes—
58C2×C4×Dic11C2311yescharacteristic
59C2×C4×Dic11C2311yescharacteristic
60C22×C11⋊C8—42no—
61C22×C11⋊C8C2×C414yes—
62C22×C11⋊C8C2311yescharacteristic
63C22×C11⋊C8C2312yes—
64C22×C11⋊C8C2311yescharacteristic
65C11×C22⋊C8C2×C414yes—
66C4×C8×C11—42no—
67C11×#95C2×C412yes—
68C11⋊#95C2×C412yes—
69C11⋊#95C2×C414yes—
70C11⋊#95C2×C414yes—
71C11⋊#95C2×C414yes—
72C22⋊(C11⋊C8)C2×C414yes—
73#66879—42no—
74#66879C2×C418yes—
75Dic11⋊C8C2×C418yes—
76Dic11⋊C8C2×C414yes—
77Dic11⋊C8C2×C414yes—
78Dic11⋊C8C2×C414yes—
79Dic11⋊C8C2×C414yes—
80C8×Dic11—42no—
81#66867—42no—
82#20544—111nomaximal, Sylow
83C24×C11C22×C411yescharacteristic
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11C22×C414yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C412yes—
89C22×C4×C11C22×C412yes—
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—24no—
92C22×Dic11—42no—
93C22×Dic11C4214yes—
94C22×Dic11C4214yes—
95C22×Dic11C22×C414yes—
96C22×Dic11C22×C411yescharacteristic
97C22×Dic11C22×C411yescharacteristic
98C22×Dic11C22×C411yescharacteristic
99C22×Dic11C22×C411yescharacteristic
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—44no—
105C2×C8×C11C22×C412yes—
106C2×C8×C11C22×C412yes—
107C2×C8×C11C22×C414yes—
108C11×C22⋊C4—24no—
109C42×C11—22no—
110C42×C11—22no—
111C22⋊Dic11—24no—
112Dic11⋊C4—44no—
113C4×Dic11—22no—
114C4×Dic11—22no—
115C4×Dic11C4214yes—
116C4×Dic11C4214yes—
117C4×Dic11C22×C412yes—
118C4×Dic11C22×C412yes—
119C4×Dic11C22×C412yes—
120C4×Dic11C22×C412yes—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—44no—
126C2×C11⋊C8C22×C412yes—
127C2×C11⋊C8C22×C412yes—
128C2×C11⋊C8C22×C414yes—
129C2×#432—111no—
130C22×C4⋊C8—111no—
131#2283—111no—
132#1771—112no—
133#1771—112no—
134#1768—112no—
135#1768—112no—
136#1752—111no—
137#1752—111no—
138C8×C22⋊C4—111no—
139C8×C22⋊C4D1111yescharacteristic
140C23×C11—22no—
141C23×C11—22no—
142C23×C11C2×C4212yes—
143C23×C11#13114yes—
144C23×C11C23×C411yescharacteristic
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11C2×C4212yes—
153C2×C4×C11C23×C411yescharacteristic
154C2×C4×C11C23×C411yescharacteristic
155C2×C4×C11H(5,𝔽2)12yes—
156C2×C4×C112−1+412yes—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—28no—
162C2×Dic11—24no—
163C2×Dic11—24no—
164C2×Dic11—24no—
165C2×Dic11—44no—
166C2×Dic11C2×C4212yes—
167C2×Dic11C2×C4212yes—
168C2×Dic11C2×C4212yes—
169C2×Dic11C2×C4212yes—
170C8×C11—22no—
171C8×C11—22no—
172C8×C11—24no—
173C11⋊C8—22no—
174C11⋊C8—22no—
175C11⋊C8—24no—
176C23×C8—111no—
177C23×C8C2×D1111yescharacteristic
178C22×C42—111no—
179#432—118no—
180C2×C4⋊C8—111no—
181C2×C4⋊C8—111no—
182C2×C4⋊C8—111no—
183C2×C4⋊C8—111no—
184C2×C4⋊C8—112no—
185C2×C4⋊C8—118no—
186C2×C22⋊C8—111no—
187C2×C22⋊C8C2×D1111yescharacteristic
188C2×#97—112no—
189C2×#97—112no—
190C2×#97—112no—
191C2×C4×C8—112no—
192C2×C4×C8C2×D1112yes—
193#383—112no—
194#382—112no—
195#381—112no—
196#380—112no—
197C4×C4⋊C4—112no—
198C4×C22⋊C4—111no—
199C4×C22⋊C4C2×D1111yescharacteristic
200#376—112no—
201#336—112no—
202#336—112no—
203#336—112no—
204#336C2×D1112yes—
205C22×C11—22no—
206C22×C11—28no—
207C22×C11—22no—
208C22×C11#40514yes—
209C22×C11C22×C4211yescharacteristic
210C22×C11#52012yes—
211C22×C11C2×#13112yes—
212C22×C11#56812yes—
213C4×C11—22no—
214C4×C11—44no—
215C4×C11#51811yescharacteristic
216C4×C11#51911yescharacteristic
217C4×C11#52012yes—
218Dic11—22no—
219Dic11—22no—
220Dic11—22no—
221Dic11—22no—
222Dic11—44no—
223C23×C4—111no—
224C23×C4—111no—
225C23×C4C22×D1111yescharacteristic
226C22×C8—42no—
227C22×C8—111no—
228C22×C8—111no—
229C22×C8—112no—
230C22×C8—114no—
231C22×C8—442no—
232C22×C8C4×D1114yes—
233C22×C8C22×D1111yescharacteristic
234C22×C8C22×D1111yescharacteristic
235C22×C8C22×D1112yes—
236C2×C4⋊C4—114no—
237C2×C22⋊C4—112no—
238C2×C22⋊C4C4×D1112yes—
239C2×C42—111no—
240C2×C42—111no—
241C2×C42—114no—
242C2×C42—114no—
243C2×C42—111no—
244C2×C42—111no—
245C2×C42—112no—
246C2×C42C22×D1112yes—
247C4⋊C8—114no—
248C4⋊C8—114no—
249C4⋊C8—114no—
250C4⋊C8—114no—
251C4⋊C8—118no—
252C22⋊C8—114no—
253C22⋊C8C4×D1114yes—
254#97—118no—
255#97—442no—
256#97—442no—
257C4×C8—42no—
258C4×C8—442no—
259#95—114no—
260#95—114no—
261#95—112no—
262#95—114no—
263#95C4×D1112yes—
264C2×C11—24no—
265C2×C11#227411yescharacteristic
266C2×C11C2×#40511yescharacteristic
267C2×C11#287311yescharacteristic
268C2×C11#299214yes—
269C24C2×C4×D1111yescharacteristic
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—114no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—114no—
278C22×C4—114no—
279C22×C4—224no—
280C22×C4—442no—
281C22×C4C2×C4×D1114yes—
282C22×C4C2×C4×D1111yescharacteristic
283C22×C4C2×C4×D1112yes—
284C22×C4C2×C4×D1112yes—
285C22×C4C23×D1111yescharacteristic
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—44no—
291C2×C8—114no—
292C2×C8—112no—
293C2×C8—112no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8—444no—
299C2×C8C2×C4×D1114yes—
300C2×C8C2×C4×D1112yes—
301C2×C8C2×C4×D1112yes—
302C4⋊C4—444no—
303C22⋊C4—24no—
304C22⋊C4—224no—
305C42—22no—
306C42—22no—
307C42—114no—
308C42—114no—
309C42—112no—
310C42—112no—
311C42—112no—
312C42—112no—
313C42—222no—
314C42—222no—
315C11#2054411yescharacteristic, complemented, Sylow
316C23—22no—
317C23—22no—
318C23C42×D1112yes—
319C23#6695414yes—
320C23C22×C4×D1111yescharacteristic
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—112no—
329C2×C4—112no—
330C2×C4—112no—
331C2×C4—112no—
332C2×C4—222no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—222no—
336C2×C4—228no—
337C2×C4—224no—
338C2×C4—224no—
339C2×C4—224no—
340C2×C4—444no—
341C2×C4C42×D1112yes—
342C2×C4C22×C4×D1111yescharacteristic
343C2×C4C22×C4×D1111yescharacteristic
344C2×C4#6703712yes—
345C2×C4#6704312yes—
346C8—22no—
347C8—22no—
348C8—24no—
349C8—222no—
350C8—222no—
351C8—224no—
352C22—22no—
353C22—22no—
354C22—28no—
355C22#1062230214yes—
356C22C2×C42×D1111yescharacteristic
357C22#1062307712yes—
358C22C2×#6695412yes—
359C22#1062328112yes—
360C4—22no—
361C4—44no—
362C4—222no—
363C4—222no—
364C4—222no—
365C4—222no—
366C4—444no—
367C4#1062301711yescharacteristic
368C4#1062304711yescharacteristic
369C4#1062307712yes—
370C2—24no—
371C2#1307097111yescharacteristic
372C2C2×#1062230211yescharacteristic
373C2#1307703211yescharacteristic
374C2#1307774914yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC8×C11×C22⋊C4C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC8×C22⋊C4D11
hypocenterC11#20544
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #13068490C2semidirect
5. #13068489C2semidirect
6. #13068474C2semidirect
7. #13068472C2semidirect
22. C2×Dic11⋊C8C4semidirect
34. #10622332C4semidirect
315. C11#20544semidirect

Maximal subgroups

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

subgroupindex
C2×#106223322
C22×Dic11⋊C82
#130710102
#130684902
#130684892
#130684742
#130684722
#130683952
#130683942
C8×C22⋊Dic112
C8×C11×C22⋊C42
#2054411