Finite Group Databasebeta

← #14664964

Subgroups — #14664964

Order 2816.

272 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 75 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#13079275C211yesmaximal, characteristic
2#13070221C211yesmaximal, characteristic
3#13066650C214yesmaximal, complemented
4C11×#2166C211yesmaximal, characteristic
5#10623049C412yes—
6C11×#405C2211yescharacteristic
7#10622750—21no—
8#10622729—21no—
9C2×#66876—21no—
10#10622329—21no—
11#10622316C2212yes—
12#10622312C411yescharacteristic
13C4×Dic44—21no—
14#10622296C411yescharacteristic
15C11×#364—21no—
16C11×#349—21no—
17C11×#347C2212yes—
18#10622104—21no—
19#10622104C2212yes—
20C2×C11×M16D411yescharacteristic
21C22×C8×C11D411yescharacteristic
22C11×#117C2×C411yescharacteristic
23#66977—22no—
24C2×Dic44—21no—
25C2×Dic44—21no—
26#66942—42no—
27#66932—42no—
28#66923C2×C412yes—
29#66922C2×C412yes—
30C4×Dic22—22no—
31C11×M32—22no—
32C11×#97D411yescharacteristic
33C11×#97C2311yescharacteristic
34C4×C8×C11C2×C411yescharacteristic
35C4×C8×C11D411yescharacteristic
36#66882—21no—
37#66881—21no—
38#66880—22no—
39#66880—22no—
40#66876—22no—
41#66876—22no—
42C2×C11⋊C16—22no—
43#11914—111nomaximal, Sylow
44C22×C4×C11C22⋊C411yescharacteristic
45C2×Dic22—22no—
46C11×M16—41no—
47C2×C8×C11—21no—
48C2×C8×C11—21no—
49C2×C8×C11C22⋊C411yescharacteristic
50C2×C8×C11C22⋊C411yescharacteristic
51C2×C8×C11C2×D411yescharacteristic
52C2×C8×C11C2×D411yescharacteristic
53C11×C4⋊C4—21no—
54C11×C22⋊C4—21no—
55C42×C11C22⋊C411yescharacteristic
56C42×C11C22×C411yescharacteristic
57C22⋊Dic11—42no—
58C4⋊Dic11—22no—
59C4⋊Dic11—42no—
60Dic11⋊C4—42no—
61Dic11⋊C4—42no—
62Dic11⋊C4—42no—
63C4×Dic11—42no—
64Dic44—42no—
65Dic44—41no—
66Dic44—41no—
67C11×C16—42no—
68C11⋊C16—24no—
69#3177—111no—
70#2166D1111yescharacteristic
71#2110—111no—
72#1356—114no—
73C23×C11#10011yescharacteristic
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11#10011yescharacteristic
79C2×C4×C11C2×C22⋊C411yescharacteristic
80C2×Dic11—42no—
81C2×Dic11—42no—
82Dic22—42no—
83Dic22—42no—
84C8×C11—21no—
85C8×C11—21no—
86C8×C11—21no—
87C8×C11#10411yescharacteristic
88C8×C11#10411yescharacteristic
89#541—112no—
90C2×M32—221no—
91#499—111no—
92#494—111no—
93#491—112no—
94#470—221no—
95#467—221no—
96#441—221no—
97C4×Q16—221no—
98#405C2×D1111yescharacteristic
99#364—21no—
100#349—21no—
101#347—112no—
102#347—221no—
103#347C2×D1112yes—
104C22×C11—21no—
105C22×C11—41no—
106C22×C11C2×#10011yescharacteristic
107C4×C11—21no—
108C4×C11—41no—
109C4×C11—41no—
110C4×C11C2×#10411yescharacteristic
111C4×C11#42111yescharacteristic
112Dic11—82no—
113Dic11—82no—
114C2×Q16—221no—
115C2×Q16—221no—
116C2×M16C22⋊D1111yescharacteristic
117C22×C8D4411yescharacteristic
118C4⋊Q8—112no—
119#126—442no—
120#125—112no—
121#125—442no—
122C22⋊Q8—222no—
123C4×Q8—222no—
124#117C4×D1111yescharacteristic
125M32—22no—
126M32—222no—
127M32—222no—
128C2×C16—222no—
129#107—221no—
130#106—221no—
131#103—222no—
132#103—222no—
133#97D4411yescharacteristic
134#97C22×D1111yescharacteristic
135C4×C8C4×D1111yescharacteristic
136C4×C8C22⋊D1111yescharacteristic
137C2×C11—21no—
138C2×C11—41no—
139C2×C11#153011yescharacteristic
140C2×Q8—222no—
141C22×C4(C2×D11)⋊C411yescharacteristic
142Q16—442no—
143Q16—441no—
144Q16—441no—
145M16—41no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8(C2×D11)⋊C411yescharacteristic
149C2×C8(C2×D11)⋊C411yescharacteristic
150C2×C8C2×D4411yescharacteristic
151C2×C8C2×C22⋊D1111yescharacteristic
152C4⋊C4—21no—
153C4⋊C4—222no—
154C4⋊C4—442no—
155C4⋊C4—442no—
156C4⋊C4—442no—
157C4⋊C4—442no—
158C22⋊C4—21no—
159C22⋊C4—442no—
160C42—442no—
161C42(C2×D11)⋊C411yescharacteristic
162C42C2×C4×D1111yescharacteristic
163C16—42no—
164C16—224no—
165C11#1191411yescharacteristic, complemented, Sylow
166C23#6688711yescharacteristic
167Q8—442no—
168Q8—442no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—442no—
174C2×C4—442no—
175C2×C4#6688711yescharacteristic
176C2×C4C2×(C2×D11)⋊C411yescharacteristic
177C8—21no—
178C8—21no—
179C8—21no—
180C8#6688911yescharacteristic
181C8#6688911yescharacteristic
182C22—21no—
183C22—41no—
184C22C2×#6688711yescharacteristic
185C4—21no—
186C4—41no—
187C4—41no—
188C4—882no—
189C4—882no—
190C4#1062261811yescharacteristic
191C4C2×#6688911yescharacteristic
192C2—21no—
193C2—41no—
194C2#1306722811yescharacteristic
subgroupG/H
centerC2#13067228
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#2166C2
socleC2×C11#1530
prime radicalC23×C11#100
cosocleC11×#97C23
hypercenter#2166D11
hypocenterC11#11914
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
3. #13066650C2semidirect
165. C11#11914semidirect

Maximal subgroups

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

subgroupindex
#130792752
#130702212
#130666502
C11×#21662
#1191411