Finite Group Databasebeta

← #14759004

Subgroups — #14759004

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66867C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic
3#13069590C212yesmaximal, complemented
4#13069437C212yesmaximal, complemented
5#13069040C214yesmaximal
6#13068446C214yesmaximal, complemented
7C2×C11×#533C211yesmaximal, characteristic
8C11×#533—24no—
9C11×#533C418yescomplemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#125—21no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×Q8×C11—21no—
16C2×C4×Q8×C11C2212yes—
17C2×C11×#117—21no—
18C22×C42×C11C2211yescharacteristic
19C23×C11⋊C8C2212yes—
20C2×#66899C2218yes—
21#10622825C2212yes—
22#10622824—21no—
23C4×C22⋊Dic11—21no—
24#10622550—21no—
25#10622549C2212yes—
26C4×C4⋊Dic11C2212yes—
27#10622545—21no—
28C2×#66867—24no—
29C2×#66867C2212yes—
30C2×#66867C2212yes—
31#10622167C2218yes—
32C22×Q8×C11—21no—
33C22×Q8×C11C2312yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8C2×C414yes—
40C11×C4⋊Q8C2×C414yes—
41C11×#125—28no—
42C11×C22⋊Q8—28no—
43C11×C22⋊Q8—24no—
44C11×C22⋊Q8C2×C418yes—
45C4×Q8×C11—28no—
46C4×Q8×C11—24no—
47C4×Q8×C11C2×C418yes—
48C11×#117—28no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—22no—
56C2×C42×C11—22no—
57C2×C42×C11C2×C414yes—
58C2×C42×C11D411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D414yes—
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64C2×C4⋊Dic11C2314yes—
65C2×C4×Dic11—22no—
66C22×C11⋊C8—24no—
67C22×C11⋊C8—28no—
68C22×C11⋊C8C2314yes—
69#66899—216no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74#66867—24no—
75#66867—24no—
76#21407—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C2×Q8×C11—24no—
79C2×Q8×C11—22no—
80C2×Q8×C11—28no—
81C2×Q8×C11—44no—
82C2×Q8×C11C22×C414yes—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—42no—
88C22×C4×C11C22⋊C414yes—
89C22×C4×C11C22⋊C414yes—
90C22×C4×C11C22×C412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—28no—
103C11×C4⋊C4—28no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4C22×C414yes—
106C11×C22⋊C4—28no—
107C42×C11—28no—
108C42×C11C22⋊C414yes—
109C42×C11C22⋊C414yes—
110C42×C11C22×C412yes—
111C42×C11C22×C412yes—
112C42×C11C2×D412yes—
113C42×C11C2×D412yes—
114C22⋊Dic11—44no—
115C4⋊Dic11—28no—
116C4×Dic11—44no—
117C2×C11⋊C8—216no—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8#4118yes—
121C2×#533D1111yescharacteristic
122C22×#97—111no—
123#2283—111no—
124#1993—112no—
125#1960—112no—
126#1892—114no—
127#1763—114no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11C2×C22⋊C412yes—
131C23×C11#13714yes—
132C23×C11C22×D411yescharacteristic
133Q8×C11—28no—
134Q8×C11—48no—
135Q8×C11—44no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—28no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—44no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11C2×C22⋊C412yes—
150C2×C4×C11C2×C22⋊C412yes—
151C2×C4×C11C2×C22⋊C412yes—
152C2×C4×C11C2×C22⋊C412yes—
153C2×C4×C11C2×C22⋊C412yes—
154C2×C4×C11C23×C411yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C2×#4114yes—
157C2×Dic11—44no—
158C2×Dic11—44no—
159C2×Dic11—44no—
160C11⋊C8—28no—
161C23×C8—112no—
162#533—24no—
163#533Dic1118yescomplemented
164C2×C4⋊Q8C2×D1111yescharacteristic
165C2×C4⋊Q8C2×D1111yescharacteristic
166C2×#125—21no—
167C2×C22⋊Q8—21no—
168C2×C22⋊Q8C2×D1112yes—
169C2×C4×Q8—21no—
170C2×C4×Q8C2×D1112yes—
171C2×#117—21no—
172C22×C42C2×D1111yescharacteristic
173C2×#103—118no—
174C2×#97—112no—
175C2×#97—112no—
176C2×#97—224no—
177#383—221no—
178#382—112no—
179#381—221no—
180#380—112no—
181C4×C4⋊C4—112no—
182C4×C22⋊C4—221no—
183#376—221no—
184#340—118no—
185C22×C11—22no—
186C22×C11—28no—
187C22×C11—22no—
188C22×C11#41914yes—
189C22×C11C22×C22⋊C411yescharacteristic
190C22×C11#53212yes—
191C22×C11C2×#13712yes—
192C22×C11#57512yes—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—22no—
198C4×C11—44no—
199C4×C11—44no—
200C4×C11C4×#4112yes—
201C4×C11#52512yes—
202Dic11—84no—
203C22×Q8—21no—
204C22×Q8C22×D1112yes—
205C23×C4C22⋊D1111yescharacteristic
206C23×C4C22⋊D1111yescharacteristic
207C23×C4C22×D1111yescharacteristic
208C22×C8—114no—
209C22×C8—228no—
210C22×C8—224no—
211C4⋊Q8—22no—
212C4⋊Q8—22no—
213C4⋊Q8C2×Dic1114yes—
214C4⋊Q8C2×Dic1114yes—
215#125—28no—
216C22⋊Q8—28no—
217C22⋊Q8—24no—
218C22⋊Q8C2×Dic1118yes—
219C4×Q8—28no—
220C4×Q8—24no—
221C4×Q8C2×Dic1118yes—
222#117—28no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—114no—
229C2×C4⋊C4C22×D1112yes—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—222no—
232C2×C42—22no—
233C2×C42—222no—
234C2×C42C2×Dic1114yes—
235C2×C42C22⋊D1111yescharacteristic
236C2×C42C22⋊D1111yescharacteristic
237C2×C42C22⋊D1114yes—
238C2×C42C22×D1111yescharacteristic
239C2×C42C22×D1111yescharacteristic
240#103—2216no—
241#97—224no—
242#97—224no—
243#95—222no—
244#95—222no—
245#95—222no—
246#95—222no—
247C2×C11—24no—
248C2×C11#229711yescharacteristic
249C2×C11C2×#41911yescharacteristic
250C2×C11#289611yescharacteristic
251C2×C11#318114yes—
252C24C2×C22⋊D1111yescharacteristic
253C2×Q8—24no—
254C2×Q8—22no—
255C2×Q8—28no—
256C2×Q8—44no—
257C2×Q8C22×Dic1114yes—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—42no—
263C22×C4—224no—
264C22×C4C22⋊Dic1114yes—
265C22×C4C22⋊Dic1114yes—
266C22×C4C22×Dic1112yes—
267C22×C4C2×C22⋊D1111yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272C22×C4C2×C22⋊D1112yes—
273C22×C4C23×D1111yescharacteristic
274C2×C8—118no—
275C2×C8—2216no—
276C2×C8—224no—
277C2×C8—224no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—28no—
282C4⋊C4—28no—
283C4⋊C4—22no—
284C4⋊C4—228no—
285C4⋊C4C22×Dic1114yes—
286C22⋊C4—28no—
287C22⋊C4—444no—
288C42—28no—
289C42—444no—
290C42C22⋊Dic1114yes—
291C42C22⋊Dic1114yes—
292C42C22×Dic1112yes—
293C42C22×Dic1112yes—
294C42C2×C22⋊D1112yes—
295C42C2×C22⋊D1112yes—
296C11#2140711yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23#6699514yes—
300C23C2×C22⋊Dic1112yes—
301C23C22×C22⋊D1111yescharacteristic
302Q8—28no—
303Q8—48no—
304Q8—44no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—28no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—444no—
319C2×C4—444no—
320C2×C4—444no—
321C2×C4C2×C22⋊Dic1112yes—
322C2×C4C2×C22⋊Dic1112yes—
323C2×C4C2×C22⋊Dic1112yes—
324C2×C4C2×C22⋊Dic1112yes—
325C2×C4C2×C22⋊Dic1112yes—
326C2×C4#41×D1114yes—
327C2×C4C23×Dic1111yescharacteristic
328C2×C4C22×C22⋊D1111yescharacteristic
329C8—228no—
330C22—22no—
331C22—28no—
332C22—22no—
333C22#1062283814yes—
334C22C2×#6699512yes—
335C22#1062335312yes—
336C22#1062336312yes—
337C22C22×C22⋊Dic1111yescharacteristic
338C4—22no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—22no—
343C4—44no—
344C4—44no—
345C4—884no—
346C4#41×Dic1112yes—
347C4#1062335912yes—
348C2—24no—
349C2#1307110711yescharacteristic
350C2C2×#1062283811yescharacteristic
351C2#1307713511yescharacteristic
352C2#1307931914yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#533D11
hypocenterC11#21407
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
3. #13069590C2semidirect
4. #13069437C2semidirect
6. #13068446C2semidirect
9. C11×#533C4semidirect
163. #533Dic11semidirect
296. C11#21407semidirect

Maximal subgroups

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

subgroupindex
C22×#668672
#130710142
#130695902
#130694372
#130690402
#130684462
C2×C11×#5332
#2140711