Finite Group Databasebeta

← #14664974

Subgroups — #14664974

Order 2816.

280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 79 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#13070428C212yesmaximal, complemented
2#13066651C212yesmaximal, complemented
3#13066649C212yesmaximal, complemented
4C11×#3142C211yesmaximal, characteristic
5C11×#532C411yescharacteristic
6C2×C11×#125C411yescharacteristic
7C11×#491C411yescharacteristic
8C11×#491C2211yescharacteristic
9C11×#490C411yescharacteristic
10C11×#490C2211yescharacteristic
11C11×#488—22no—
12C11×#417—22no—
13C4×C11×M16C2211yescharacteristic
14#10622191—22no—
15#10622104C2214yes—
16#10622101—22no—
17C2×C11×#41—21no—
18C2×C11×M16D412yes—
19C11×C4⋊Q8C2×C411yescharacteristic
20C11×#127C2×C411yescharacteristic
21C11×#125—21no—
22C11×#125—41no—
23C11×#125C2×C411yescharacteristic
24C11×#125C2×C411yescharacteristic
25C11×#124—21no—
26C11×#121—41no—
27C4×D4×C11—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—41no—
30C2×C42×C11C2×C411yescharacteristic
31C11×#103—22no—
32C11×#103—22no—
33C11×#102—22no—
34C11×#102—22no—
35C11×#97C2×C411yescharacteristic
36C11×#97C2311yescharacteristic
37C4×C8×C11D412yes—
38#66876—24no—
39#11917—111nomaximal, Sylow
40C11×#41—44no—
41C2×Q8×C11—21no—
42C2×D4×C11—21no—
43C2×D4×C11—41no—
44C2×D4×C11—41no—
45C22×C4×C11—21no—
46C22×C4×C11—41no—
47C22×C4×C11—41no—
48C22×C4×C11C22⋊C411yescharacteristic
49C11×M16—42no—
50C2×C8×C11C22⋊C412yes—
51C2×C8×C11C2×D412yes—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—42no—
55C11×C4⋊C4—41no—
56C11×C4⋊C4—41no—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—41no—
59C11×C22⋊C4—42no—
60C42×C11—21no—
61C42×C11C22⋊C411yescharacteristic
62C42×C11C22×C411yescharacteristic
63C11⋊C16—44no—
64#3142D1111yescharacteristic
65#2165—112no—
66#1356—112no—
67#1355—112no—
68C23×C11—41no—
69C23×C11#10011yescharacteristic
70Q8×C11—42no—
71D4×C11—42no—
72D4×C11—82no—
73D4×C11—82no—
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11—82no—
81C2×C4×C11—81no—
82C2×C4×C11—82no—
83C2×C4×C11#10011yescharacteristic
84C2×C4×C11C2×C22⋊C411yescharacteristic
85C8×C11—22no—
86C8×C11—22no—
87#532Dic1111yescharacteristic
88C2×#125Dic1111yescharacteristic
89#491Dic1111yescharacteristic
90#491C2×D1111yescharacteristic
91#490Dic1111yescharacteristic
92#490C2×D1111yescharacteristic
93#488—22no—
94#417—22no—
95C4×M16C2×D1111yescharacteristic
96#364—222no—
97#349—222no—
98#347—114no—
99C22×C11—21no—
100C22×C11—41no—
101C22×C11—82no—
102C22×C11—81no—
103C22×C11C2×#10011yescharacteristic
104C4×C11—21no—
105C4×C11—41no—
106C4×C11—41no—
107C4×C11—81no—
108C4×C11—81no—
109C4×C11—81no—
110C4×C11#42112yes—
111C2×#41—21no—
112C2×M16C22⋊D1112yes—
113C4⋊Q8C2×Dic1111yescharacteristic
114#127C2×Dic1111yescharacteristic
115#125—21no—
116#125—41no—
117#125C2×Dic1111yescharacteristic
118#125C2×Dic1111yescharacteristic
119#124—21no—
120#121—41no—
121C4×D4—41no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—41no—
124C2×C42C2×Dic1111yescharacteristic
125M32—224no—
126#103—22no—
127#103—22no—
128#102—22no—
129#102—22no—
130#97C2×Dic1111yescharacteristic
131#97C22×D1111yescharacteristic
132C4×C8C22⋊D1112yes—
133C2×C11—21no—
134C2×C11—41no—
135C2×C11—161no—
136C2×C11#153311yescharacteristic
137#41—44no—
138C2×Q8—21no—
139C2×D4—21no—
140C2×D4—41no—
141C2×D4—41no—
142C22×C4—21no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4C22⋊Dic1111yescharacteristic
146M16—42no—
147C2×C8C22⋊Dic1112yes—
148C2×C8C2×C22⋊D1112yes—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—42no—
155C4⋊C4—41no—
156C22⋊C4—42no—
157C42—21no—
158C42C22⋊Dic1111yescharacteristic
159C42C22×Dic1111yescharacteristic
160C16—444no—
161C11#1191711yescharacteristic, complemented, Sylow
162C23—41no—
163C23#6689711yescharacteristic
164Q8—42no—
165D4—42no—
166D4—82no—
167D4—82no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—82no—
175C2×C4—81no—
176C2×C4—82no—
177C2×C4#6689711yescharacteristic
178C2×C4C2×C22⋊Dic1111yescharacteristic
179C8—22no—
180C8—22no—
181C22—21no—
182C22—41no—
183C22—82no—
184C22—81no—
185C22C2×#6689711yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—81no—
190C4—81no—
191C4—81no—
192C4#1062284912yes—
193C2—21no—
194C2—41no—
195C2—161no—
196C2#1306724011yescharacteristic
subgroupG/H
centerC2#13067240
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#3142C2
socleC2×C11#1533
prime radicalC11×#532C4
cosocleC11×#97C23
hypercenter#3142D11
hypocenterC11#11917
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. #13070428C2semidirect
2. #13066651C2semidirect
3. #13066649C2semidirect
161. C11#11917semidirect

Maximal subgroups

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

subgroupindex
#130704282
#130666512
#130666492
C11×#31422
#1191711