Finite Group Databasebeta

← #14664965

Subgroups — #14664965

Order 2816.

326 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 61 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#13078989C211yesmaximal, characteristic
2#13070426C212yesmaximal, complemented
3#13066649C211yesmaximal, characteristic, complemented
4#13066648C212yesmaximal, complemented
5C11×#1355C211yesmaximal, characteristic, complemented
6D11×#127C411yescharacteristic
7#10623219C411yescharacteristic
8C11×#490C2211yescharacteristic
9#10622684C411yescharacteristic
10#10622680C411yescharacteristic
11#10622383—22no—
12#10622373—22no—
13#10622326C2211yescharacteristic
14#10622320C2211yescharacteristic
15C11×#347C2212yescomplemented
16#10622152—22no—
17#10622149—22no—
18#10622104C2212yescomplemented
19C2×D4×D11—21no—
20C2×D4×D11—41no—
21C11×#127C2×C411yescharacteristic
22C11×#125C2×C411yescharacteristic
23#66993—21no—
24#66993—41no—
25C2×#4313D412yes—
26#66949—41no—
27#66945—21no—
28#66941—21no—
29#66940—41no—
30#66927C2×C411yescharacteristic
31C42×D11C2×C411yescharacteristic
32#66923C2×C411yescharacteristic
33C11×M32—22no—
34C11×#102—22no—
35C11×#97C2311yescharacteristic
36#66896—22no—
37#66885—22no—
38C8×Dic11D412yes—
39#66876—22no—
40#66873—22no—
41#66867C2×C411yescharacteristic
42#11915—111nomaximal, Sylow
43C23×D11—41no—
44C2×D4×C11—21no—
45C2×D4×C11—41no—
46C2×C22⋊D11—42no—
47C2×C22⋊D11—41no—
48D4×D11—44no—
49D4×D11—84no—
50C2×D44—21no—
51C2×D44—41no—
52C2×C4×D11—21no—
53C2×C4×D11C22⋊C411yescharacteristic
54C2×Dic22—41no—
55C2×C8×C11C2×D412yes—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—41no—
58C42×C11C22×C411yescharacteristic
59(C2×D11)⋊C4—41no—
60C4⋊Dic11—21no—
61Dic11⋊C4—41no—
62Dic11⋊C4—41no—
63C4×Dic11—21no—
64C4×Dic11—41no—
65C4×Dic11C22⋊C411yescharacteristic
66C2×C11⋊C8C22⋊C412yes—
67#4313—42no—
68C11×C16—42no—
69C11⋊C16—42no—
70#3138—111no—
71#2165—112no—
72#1355—111no—
73#1355—112no—
74#1355D1111yescharacteristic, complemented
75C23×C11—41no—
76C22×D11—41no—
77C22×D11—82no—
78C22×D11—84no—
79C22×D11#10011yescharacteristic
80D4×C11—42no—
81D4×C11—82no—
82C2×C4×C11—21no—
83C2×C4×C11—41no—
84C2×C4×C11C2×C22⋊C411yescharacteristic
85C22⋊D11—82no—
86C22⋊D11—84no—
87C2×Dic11—21no—
88C2×Dic11—41no—
89C2×Dic11#10011yescharacteristic
90D44—42no—
91D44—82no—
92C4×D11—22no—
93C4×D11—42no—
94Dic22—82no—
95C8×C11—22no—
96C11⋊C8—22no—
97#533—111no—
98C2×#127—111no—
99#490—111no—
100#490—111no—
101#490—111no—
102#490C2×D1111yescharacteristic
103#486—222no—
104#418—222no—
105C4×M16—111no—
106#364—222no—
107#349—222no—
108#347—112no—
109#347C2×D1112yescomplemented
110C22×C11—82no—
111C22×C11—81no—
112C22×C11C2×#10011yescharacteristic
113C2×D11—21no—
114C2×D11—41no—
115C2×D11—82no—
116C2×D11—81no—
117C2×D11—164no—
118C4×C11—41no—
119C4×C11—81no—
120C4×C11#42112yes—
121Dic11—22no—
122Dic11—21no—
123Dic11—81no—
124C22×D4—221no—
125C22×D4—441no—
126C2×M16—112no—
127C4⋊Q8—221no—
128#127—111no—
129#127—221no—
130#127—441no—
131#127C4×D1111yescharacteristic
132#125—111no—
133#125C4×D1111yescharacteristic
134C22⋊Q8—441no—
135C4×Q8—441no—
136#117—221no—
137C2×C42—111no—
138M32—22no—
139M32—222no—
140#102—22no—
141#102—222no—
142#102—222no—
143#102—222no—
144#97—111no—
145#97C22×D1111yescharacteristic
146C4×C8—112no—
147C2×C11—21no—
148C2×C11—161no—
149C2×C11#153311yescharacteristic
150D11—41no—
151D11—161no—
152C24—441no—
153C2×Q8—441no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—221no—
157C2×D4—441no—
158C2×D4—441no—
159C2×D4—444no—
160C2×D4—442no—
161C2×D4—884no—
162C22×C4—111no—
163C22×C4—221no—
164M16—442no—
165C2×C8—112no—
166C2×C8D4×D1112yes—
167C4⋊C4—21no—
168C4⋊C4—41no—
169C4⋊C4—221no—
170C4⋊C4—441no—
171C4⋊C4—441no—
172C22⋊C4—441no—
173C42—111no—
174C42—221no—
175C42—441no—
176C42C2×C4×D1111yescharacteristic
177C16—42no—
178C16—442no—
179C11#1191511yescharacteristic, complemented, Sylow
180C23—41no—
181C23—111no—
182C23—441no—
183C23—882no—
184C23—884no—
185Q8—882no—
186D4—42no—
187D4—82no—
188D4—442no—
189D4—882no—
190D4—882no—
191D4—884no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—111no—
195C2×C4—221no—
196C2×C4—222no—
197C2×C4—442no—
198C2×C4—441no—
199C2×C4C22⋊C4×D1111yescharacteristic
200C8—22no—
201C8—222no—
202C22—82no—
203C22—81no—
204C22—221no—
205C22—441no—
206C22—882no—
207C22—881no—
208C22—1764no—
209C22D11×#10011yescharacteristic
210C4—41no—
211C4—81no—
212C4—222no—
213C4—221no—
214C4—881no—
215C4#1062243412yes—
216C2—21no—
217C2—161no—
218C2—441no—
219C2—1761no—
220C2#1306723811yescharacteristic
subgroupG/H
centerC2#13067238
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#1355C2
socleC2×C11#1533
prime radicalD11×#127C4
cosocleC11×#97C23
hypercenter#1355D11
hypocenterC11#11915
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. #13070426C2semidirect
3. #13066649C2semidirect
4. #13066648C2semidirect
5. C11×#1355C2semidirect
15. C11×#347C22semidirect
18. #10622104C22semidirect
74. #1355D11semidirect
109. #347C2×D11semidirect
179. C11#11915semidirect

Maximal subgroups

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

subgroupindex
#130789892
#130704262
#130666492
#130666482
C11×#13552
#1191511