Finite Group Databasebeta

← #14672460

Subgroups — #14672460

Order 2816.

420 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073821C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13066742C214yesmaximal
4C4×C11×#101C211yesmaximal, characteristic
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#66922C411yescharacteristic
7C2×C11×#101C2212yes—
8C4×C11×M16—21no—
9#10622843C2212yes—
10C2×#66900C2212yes—
11#10622592—21no—
12#10622592—21no—
13#10622589C412yes—
14C4×C4⋊Dic11C411yescharacteristic
15#10622541—21no—
16#10622541—21no—
17#10622537—21no—
18C11×#343—21no—
19#10622168—21no—
20C22×Q8×C11C2311yescharacteristic
21C22×Dic22—21no—
22C2×C11×M16—22no—
23C4×Q8×C11—41no—
24C4×Q8×C11—41no—
25C2×C11×C4⋊C4C2×C411yescharacteristic
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C412yes—
34C2×Dic11⋊C4—22no—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11C2×C412yes—
37C2×#4318—22no—
38#66922—41no—
39#66922—41no—
40C11×#101—22no—
41C11×#101Q814yescomplemented
42C11×#97—41no—
43C4×C8×C11—41no—
44#66900—24no—
45C11⋊#95—21no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C4⋊(C11⋊C8)—41no—
49C4⋊(C11⋊C8)—41no—
50#13302—111nomaximal, Sylow
51C2×Q8×C11—41no—
52C2×Q8×C11—41no—
53C2×Q8×C11C2×Q812yes—
54C2×Q8×C11#4112yes—
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—22no—
63C22×Dic11—22no—
64C2×Dic22—42no—
65C2×Dic22—82no—
66C11×M16—24no—
67C11×M16—42no—
68C2×C8×C11—42no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C42×C11—21no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C4⋊Dic11—24no—
79C4⋊Dic11—42no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82Dic11⋊C4—82no—
83Dic11⋊C4—82no—
84C4×Dic11—42no—
85#4318—42no—
86#4318—42no—
87C2×C11⋊C8—42no—
88#2567—111no—
89#1801—111no—
90C4×#101D1111yescharacteristic
91#1394—114no—
92C23×C11C2×C22⋊C411yescharacteristic
93Q8×C11—42no—
94Q8×C11—42no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11#9911yescharacteristic
109C2×C4×C11#9911yescharacteristic
110C2×C4×C11C4×Q812yes—
111C2×C4×C11C22⋊Q812yes—
112C2×C4×C11#12411yescharacteristic
113C2×C4×C11C4⋊Q811yescharacteristic
114C2×Dic11—24no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120Dic22—84no—
121C8×C11—44no—
122C11⋊C8—82no—
123C2×C4⋊Q8—111no—
124C2×C4×Q8C2×D1111yescharacteristic
125#423—221no—
126C2×#101—112no—
127C2×#101C2×D1112yes—
128C4×M16—21no—
129#395—221no—
130#395—221no—
131#391—112no—
132#389—221no—
133#389—221no—
134#384—112no—
135C4×C4⋊C4—111no—
136#343—21no—
137#343—221no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11#39111yescharacteristic
141C22×C11C2×#9911yescharacteristic
142C22×C11#41011yescharacteristic
143C4×C11—21no—
144C4×C11—22no—
145C4×C11—22no—
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11#35612yes—
152Dic11—44no—
153Dic11—82no—
154C22×Q8—221no—
155C22×Q8C22×D1111yescharacteristic
156C2×M16—22no—
157C2×M16—222no—
158C4⋊Q8—441no—
159C4⋊Q8—441no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—112no—
163C2×C4⋊C4—221no—
164C2×C4⋊C4—221no—
165C2×C4⋊C4—222no—
166C2×C4⋊C4—222no—
167C2×C4⋊C4C4×D1111yescharacteristic
168C2×C4⋊C4D4411yescharacteristic
169C2×C4⋊C4C22⋊D1111yescharacteristic
170C2×C42—112no—
171C2×C42C4×D1111yescharacteristic
172C2×C42D4411yescharacteristic
173C2×C42C22⋊D1111yescharacteristic
174C4⋊C8—441no—
175C4⋊C8—441no—
176#101—22no—
177#101—224no—
178#101Dic2214yescomplemented
179#97—41no—
180C4×C8—41no—
181#95—221no—
182#95—222no—
183#95—222no—
184C2×C11—21no—
185C2×C11—21no—
186C2×C11#199611yescharacteristic
187C2×C11C2×#35611yescharacteristic
188C2×C11#213411yescharacteristic
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—442no—
192C2×Q8—882no—
193C2×Q8C2×Dic2212yes—
194C2×Q8#433912yes—
195C22×C4—222no—
196C22×C4—222no—
197C22×C4(C2×D11)⋊C411yescharacteristic
198C22×C4(C2×D11)⋊C411yescharacteristic
199C22×C4(C2×D11)⋊C411yescharacteristic
200C22×C4(C2×D11)⋊C411yescharacteristic
201C22×C4C2×C4×D1111yescharacteristic
202C22×C4C2×D4411yescharacteristic
203C22×C4C2×C22⋊D1111yescharacteristic
204M16—24no—
205M16—42no—
206M16—442no—
207M16—442no—
208C2×C8—42no—
209C2×C8—442no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—224no—
214C4⋊C4—442no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C4⋊C4—882no—
218C4⋊C4—882no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—442no—
226C11#1330211yescharacteristic, complemented, Sylow
227C23C2×(C2×D11)⋊C411yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—884no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—224no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—442no—
249C2×C4—442no—
250C2×C4#6687011yescharacteristic
251C2×C4#6687011yescharacteristic
252C2×C4C4×Dic2212yes—
253C2×C4#6692211yescharacteristic
254C2×C4#6692811yescharacteristic
255C2×C4#6697712yes—
256C8—44no—
257C8—882no—
258C22—21no—
259C22—21no—
260C22#1062254211yescharacteristic
261C22C2×#6687011yescharacteristic
262C22#1062261911yescharacteristic
263C4—22no—
264C4—21no—
265C4—22no—
266C4—21no—
267C4—21no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—444no—
272C4—882no—
273C4#1062211612yes—
274C2—21no—
275C2—21no—
276C2#1306960111yescharacteristic
277C2C2×#1062211611yescharacteristic
278C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC4×C11×#101C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC22×Q8×C11C23
hypercenterC4×#101D11
hypocenterC11#13302
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
41. C11×#101Q8semidirect
178. #101Dic22semidirect
226. C11#13302semidirect

Maximal subgroups

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

subgroupindex
#130738212
#130686122
#130667422
C4×C11×#1012
#1330211