Finite Group Databasebeta

← #14664968

Subgroups — #14664968

Order 2816.

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

normal subgroups only

This group has 274 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#13078995C211yesmaximal, characteristic
2#13070426C212yesmaximal
3#13066651C211yesmaximal, characteristic, complemented
4#13066650C212yesmaximal, complemented
5C11×#1356C211yesmaximal, characteristic, complemented
6D11×C4⋊Q8C411yescharacteristic
7#10623219C411yescharacteristic
8C11×#491C2211yescharacteristic
9#10622695C411yescharacteristic
10#10622682C411yescharacteristic
11#10622415—22no—
12#10622405—22no—
13#10622320C2211yescharacteristic
14#10622316C2211yescharacteristic
15C11×#347C2212yes—
16#10622152—22no—
17#10622149—22no—
18#10622104C2212yes—
19C2×Q8×D11—21no—
20C11×C4⋊Q8C2×C411yescharacteristic
21C11×#125C2×C411yescharacteristic
22#66997—21no—
23C2×#4313D412yes—
24#66949—41no—
25#66945—21no—
26C4⋊C4×D11—41no—
27#66941—21no—
28#66941—41no—
29#66940—41no—
30C42×D11C2×C411yescharacteristic
31#66923C2×C411yescharacteristic
32#66922C2×C411yescharacteristic
33C11×M32—22no—
34C11×#103—22no—
35C11×#97C2311yescharacteristic
36#66899—22no—
37#66880—22no—
38C8×Dic11D412yes—
39#66876—22no—
40#66874—22no—
41#66867C2×C411yescharacteristic
42#11916—111nomaximal, Sylow
43C2×Q8×C11—21no—
44Q8×D11—44no—
45C2×C4×D11—21no—
46C2×C4×D11—41no—
47C2×C4×D11C22⋊C411yescharacteristic
48C2×Dic22—21no—
49C2×Dic22—41no—
50C2×Dic22—41no—
51C2×C8×C11C2×D412yes—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—41no—
54C11×C4⋊C4—41no—
55C42×C11C22×C411yescharacteristic
56(C2×D11)⋊C4—41no—
57C4⋊Dic11—21no—
58C4⋊Dic11—41no—
59Dic11⋊C4—41no—
60Dic11⋊C4—41no—
61Dic11⋊C4—42no—
62C4×Dic11—21no—
63C4×Dic11—41no—
64C4×Dic11C22⋊C411yescharacteristic
65C2×C11⋊C8C22⋊C412yes—
66#4313—42no—
67C11×C16—42no—
68C11⋊C16—42no—
69#3139—111no—
70#2165—112no—
71#1356—111no—
72#1356—112no—
73#1356D1111yescharacteristic, complemented
74C22×D11#10011yescharacteristic
75Q8×C11—42no—
76C2×C4×C11—21no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11C2×C22⋊C411yescharacteristic
80C2×Dic11—21no—
81C2×Dic11—41no—
82C2×Dic11—41no—
83C2×Dic11#10011yescharacteristic
84C4×D11—22no—
85C4×D11—42no—
86C4×D11—82no—
87Dic22—42no—
88Dic22—82no—
89Dic22—82no—
90C8×C11—22no—
91C11⋊C8—22no—
92#533—111no—
93C2×C4⋊Q8—111no—
94#491—111no—
95#491—111no—
96#491—111no—
97#491C2×D1111yescharacteristic
98#487—222no—
99#419—222no—
100C4×M16—111no—
101#364—222no—
102#349—222no—
103#347—112no—
104#347C2×D1112yes—
105C22×C11C2×#10011yescharacteristic
106C2×D11—21no—
107C2×D11—41no—
108C4×C11—41no—
109C4×C11—81no—
110C4×C11—81no—
111C4×C11#42112yes—
112Dic11—22no—
113Dic11—21no—
114Dic11—81no—
115Dic11—81no—
116C22×Q8—221no—
117C2×M16—112no—
118C4⋊Q8—111no—
119C4⋊Q8—221no—
120C4⋊Q8—221no—
121C4⋊Q8—441no—
122C4⋊Q8C4×D1111yescharacteristic
123#125—111no—
124#125C4×D1111yescharacteristic
125C22⋊Q8—441no—
126C4×Q8—441no—
127#117—221no—
128C2×C4⋊C4—441no—
129C2×C42—111no—
130M32—22no—
131M32—222no—
132#103—22no—
133#103—222no—
134#103—222no—
135#103—222no—
136#97—111no—
137#97C22×D1111yescharacteristic
138C4×C8—112no—
139C2×C11—21no—
140C2×C11#153311yescharacteristic
141D11—41no—
142C2×Q8—21no—
143C2×Q8—221no—
144C2×Q8—441no—
145C2×Q8—441no—
146C2×Q8—444no—
147C22×C4—111no—
148C22×C4—221no—
149C22×C4—441no—
150M16—442no—
151C2×C8—112no—
152C2×C8D4×D1112yes—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—221no—
157C4⋊C4—441no—
158C4⋊C4—441no—
159C4⋊C4—442no—
160C4⋊C4—441no—
161C22⋊C4—441no—
162C42—111no—
163C42—221no—
164C42—441no—
165C42C2×C4×D1111yescharacteristic
166C16—42no—
167C16—442no—
168C11#1191611yescharacteristic, complemented, Sylow
169C23—111no—
170Q8—42no—
171Q8—442no—
172Q8—882no—
173Q8—882no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—111no—
178C2×C4—221no—
179C2×C4—222no—
180C2×C4—442no—
181C2×C4—441no—
182C2×C4—441no—
183C2×C4—882no—
184C2×C4C22⋊C4×D1111yescharacteristic
185C8—22no—
186C8—222no—
187C22—221no—
188C22—441no—
189C22D11×#10011yescharacteristic
190C4—41no—
191C4—81no—
192C4—81no—
193C4—222no—
194C4—221no—
195C4—881no—
196C4—881no—
197C4#1062243412yes—
198C2—21no—
199C2—441no—
200C2#1306723811yescharacteristic
subgroupG/H
centerC2#13067238
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#1356C2
socleC2×C11#1533
prime radicalC22×D11#100
cosocleC11×#97C23
hypercenter#1356D11
hypocenterC11#11916
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
3. #13066651C2semidirect
4. #13066650C2semidirect
5. C11×#1356C2semidirect
73. #1356D11semidirect
168. C11#11916semidirect

Maximal subgroups

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

subgroupindex
#130789952
#130704262
#130666512
#130666502
C11×#13562
#1191611