Finite Group Databasebeta

← #14664772

Subgroups — #14664772

Order 2816.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#13078271C211yesmaximal, characteristic
2#13068662C211yesmaximal, characteristic
3#13066605C214yesmaximal, complemented
4C11×#2115C211yesmaximal, characteristic
5C2×C11×#131C2211yescharacteristic
6#10623356—21no—
7C22×Dic44C411yescharacteristic, complemented
8C2×C11×M32—21no—
9#10622853—21no—
10#10622750C412yescomplemented
11#10622750C2212yes—
12#10622733—21no—
13#10622729—21no—
14#10622729—21no—
15#10622719—21no—
16#10622719C411yescharacteristic, complemented
17C11×#349—21no—
18C11×#349C2212yes—
19#10622195C2212yes—
20C2×C11×#41D411yescharacteristic
21C22×Dic22—21no—
22C11×#131—41no—
23C11×#131—41no—
24C2×C11×M16C2×C411yescharacteristic
25C2×C11×M16D411yescharacteristic
26C2×C11×M16C2311yescharacteristic
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C22×C8×C11D411yescharacteristic
30#66997—41no—
31#66989—41no—
32#66988—41no—
33#66988—41no—
34#66979—21no—
35#66979—22no—
36#66977—22no—
37#66977—22no—
38C2×Dic44—21no—
39C2×Dic44—41no—
40C2×Dic44—41no—
41C2×Dic44C2×C412yes—
42C11×M32—22no—
43C11×M32—41no—
44C2×C11×C16—41no—
45#66898—41no—
46#66898—41no—
47#66882—21no—
48#66882—41no—
49#66881—41no—
50#66881C2×C412yes—
51#66880—22no—
52#66880—22no—
53#11869—111nomaximal, Sylow
54C11×#41—41no—
55C11×#41—41no—
56C2×Q8×C11SD1611yescharacteristic
57C2×D4×C11D811yescharacteristic
58C2×D4×C11D811yescharacteristic
59C2×D4×C11SD1611yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—41no—
64C2×Dic22—22no—
65C2×Dic22—42no—
66C2×Dic22—42no—
67C2×Dic22—41no—
68C11×M16—41no—
69C11×M16—41no—
70C11×M16—41no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—21no—
77C2×C8×C11C22⋊C411yescharacteristic
78C2×C8×C11C22⋊C411yescharacteristic
79C2×C8×C11C22×C411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C22⋊Dic11—42no—
82C22⋊Dic11—41no—
83C22⋊Dic11—42no—
84C22⋊Dic11—42no—
85C4⋊Dic11—22no—
86C4⋊Dic11—42no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89C4×Dic11—42no—
90C4×Dic11—41no—
91Dic44—42no—
92Dic44—41no—
93Dic44—41no—
94C11×C16—42no—
95#3059—111no—
96#2115D1111yescharacteristic
97#1812—111no—
98#1340—114no—
99C23×C11#10211yescharacteristic
100C23×C11#10211yescharacteristic
101C23×C11C2×D811yescharacteristic
102Q8×C11—41no—
103D4×C11—41no—
104D4×C11—41no—
105D4×C11—41no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11#10211yescharacteristic
113C2×C4×C11#10211yescharacteristic
114C2×C4×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11C2×SD1611yescharacteristic
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—82no—
119C2×Dic11—82no—
120Dic22—42no—
121Dic22—42no—
122Dic22—82no—
123C8×C11—21no—
124C8×C11—21no—
125C8×C11—21no—
126C8×C11#9911yescharacteristic
127C8×C11#9911yescharacteristic
128C22×Q16—111no—
129C2×#131C2×D1111yescharacteristic
130#536—221no—
131C2×M32—21no—
132#470—112no—
133#470—112no—
134#467—221no—
135#467—221no—
136#427—111no—
137#427—221no—
138#419—221no—
139#410—221no—
140#349—21no—
141#349C2×D1112yes—
142H(3,ℤ/4)—112no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11C2×#10211yescharacteristic
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11C2×#9911yescharacteristic
154C4×C11#42111yescharacteristic
155Dic11—82no—
156Dic11—82no—
157Dic11—162no—
158C2×#41D4411yescharacteristic
159C22×Q8—221no—
160C2×Q16—112no—
161C2×Q16—221no—
162C2×Q16—441no—
163C2×Q16—441no—
164#131—41no—
165#131—41no—
166C2×M16C4×D1111yescharacteristic
167C2×M16C22⋊D1111yescharacteristic
168C2×M16C22×D1111yescharacteristic
169C22×C8C4×D1111yescharacteristic
170C22×C8D4411yescharacteristic
171C22×C8C22⋊D1111yescharacteristic
172C4⋊Q8—441no—
173#124—441no—
174#123—441no—
175#123—441no—
176C22⋊Q8—222no—
177C22⋊Q8—222no—
178#117—221no—
179#117—222no—
180M32—22no—
181M32—41no—
182C2×C16—41no—
183#107—221no—
184#107—441no—
185#106—112no—
186#106—441no—
187#103—222no—
188#103—222no—
189#99—441no—
190#99—441no—
191C2×C11—21no—
192C2×C11—41no—
193C2×C11—41no—
194C2×C11—41no—
195C2×C11#151911yescharacteristic
196#41—41no—
197#41—41no—
198C2×Q8—222no—
199C2×Q8—442no—
200C2×Q8—442no—
201C2×Q8—441no—
202C2×Q8#431411yescharacteristic
203C2×D4#431411yescharacteristic
204C2×D4D8811yescharacteristic
205C2×D4D8811yescharacteristic
206C22×C4—441no—
207C22×C4(C2×D11)⋊C411yescharacteristic
208C22×C4(C2×D11)⋊C411yescharacteristic
209C22×C4C2×D4411yescharacteristic
210Q16—442no—
211Q16—441no—
212Q16—441no—
213M16—41no—
214M16—41no—
215M16—41no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8(C2×D11)⋊C411yescharacteristic
223C2×C8(C2×D11)⋊C411yescharacteristic
224C2×C8C2×C4×D1111yescharacteristic
225C2×C8C2×C22⋊D1111yescharacteristic
226C4⋊C4—222no—
227C4⋊C4—442no—
228C4⋊C4—442no—
229C4⋊C4—442no—
230C22⋊C4—441no—
231C22⋊C4—442no—
232C22⋊C4—442no—
233C22⋊C4—442no—
234C42—442no—
235C42—441no—
236C16—42no—
237C11#1186911yescharacteristic, complemented, Sylow
238C23#6688511yescharacteristic
239C23#6688511yescharacteristic
240C23C2×D8811yescharacteristic
241Q8—41no—
242Q8—442no—
243Q8—442no—
244Q8—882no—
245D4—41no—
246D4—41no—
247D4—41no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—882no—
257C2×C4—882no—
258C2×C4#6688511yescharacteristic
259C2×C4#6688511yescharacteristic
260C2×C4C2×#431411yescharacteristic
261C2×C4C2×(C2×D11)⋊C411yescharacteristic
262C8—21no—
263C8—21no—
264C8—21no—
265C8#6687011yescharacteristic
266C8#6687011yescharacteristic
267C22—21no—
268C22—21no—
269C22—21no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22C2×#6688511yescharacteristic
274C4—21no—
275C4—21no—
276C4—21no—
277C4—882no—
278C4—882no—
279C4—1762no—
280C4C2×#6687011yescharacteristic
281C4#1062275211yescharacteristic
282C2—21no—
283C2—41no—
284C2—41no—
285C2—41no—
286C2#1306718511yescharacteristic
subgroupG/H
centerC2#13067185
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#2115C2
socleC2×C11#1519
prime radicalC2×C11×#41D4
cosocleC2×C11×M16C23
hypercenter#2115D11
hypocenterC11#11869
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #2115

Complements

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

NH ≅ G/Ntype
3. #13066605C2semidirect
7. C22×Dic44C4semidirect
10. #10622750C4semidirect
16. #10622719C4semidirect
237. C11#11869semidirect

Maximal subgroups

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

subgroupindex
#130782712
#130686622
#130666052
C11×#21152
#1186911