Finite Group Databasebeta

← #14663093

Subgroups — #14663093

Order 2816.

418 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 131 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#13070419C212yesmaximal, complemented
2#13066540C214yesmaximal, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic
4C23×C8×C11C412yes—
5C2×C4×D4×C11C411yescharacteristic
6C8×D4×C11—22no—
7C8×D4×C11—22no—
8C2×C11×C4⋊C8C411yescharacteristic
9C2×C11×C22⋊C8C2212yes—
10C2×C4×C8×C11C2211yescharacteristic
11C22⋊(C11⋊C16)C2214yes—
12C4⋊(C11⋊C16)—22no—
13#10622099—22no—
14C22×D4×C11C811yescharacteristic
15C23×C4×C11C2×C412yes—
16C22×C8×C11—22no—
17C22×C8×C11—22no—
18C22×C8×C11—44no—
19C22×C8×C11C2×C411yescharacteristic
20C22×C8×C11C2×C412yes—
21C22×C8×C11C2311yescharacteristic
22C4×D4×C11—22no—
23C4×D4×C11—22no—
24C2×C11×C4⋊C4C811yescharacteristic
25C2×C11×C22⋊C4C812yes—
26C2×C42×C11C2×C411yescharacteristic
27C11×C4⋊C8—22no—
28C11×C22⋊C8—24no—
29C4×C8×C11D412yes—
30C4×C8×C11D412yes—
31C2×C11⋊C16—24no—
32#11488—111nomaximal, Sylow
33C24×C11C2×C812yes—
34C2×D4×C11—24no—
35C2×D4×C11—22no—
36C22×C4×C11—22no—
37C22×C4×C11—22no—
38C22×C4×C11—42no—
39C22×C4×C11—42no—
40C22×C4×C11C2×C811yescharacteristic
41C22×C4×C11C2×C812yes—
42C22×C4×C11C2×C811yescharacteristic
43C22×C4×C11C22×C411yescharacteristic
44C2×C8×C11—22no—
45C2×C8×C11—22no—
46C2×C8×C11—41no—
47C2×C8×C11—42no—
48C2×C8×C11—44no—
49C2×C8×C11—44no—
50C2×C8×C11C22⋊C411yescharacteristic
51C2×C8×C11C22⋊C411yescharacteristic
52C2×C8×C11C2×D412yes—
53C11×C4⋊C4—22no—
54C11×C22⋊C4—24no—
55C42×C11C22⋊C412yes—
56C42×C11M1612yes—
57C11⋊C16—44no—
58C2×C8×D4D1111yescharacteristic
59#2163—112no—
60#1314—114no—
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—42no—
64C23×C11—42no—
65C23×C11M3214yes—
66C23×C11C22×C811yescharacteristic
67D4×C11—28no—
68C2×C4×C11—22no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—41no—
73C2×C4×C11—44no—
74C2×C4×C11—42no—
75C2×C4×C11—42no—
76C2×C4×C11—42no—
77C2×C4×C11C22⋊C812yes—
78C2×C4×C11C22⋊C812yes—
79C2×C4×C11C2×C22⋊C411yescharacteristic
80C2×C4×C11C2×M1611yescharacteristic
81C8×C11—22no—
82C8×C11—21no—
83C8×C11—42no—
84C8×C11#10012yes—
85C23×C8Dic1112yes—
86C2×C4×D4Dic1111yescharacteristic
87C8×D4—22no—
88C8×D4—22no—
89C2×C4⋊C8Dic1111yescharacteristic
90C2×C22⋊C8C2×D1112yes—
91C2×C4×C8C2×D1111yescharacteristic
92C4⋊C16—222no—
93C22⋊C16—114no—
94#346—222no—
95C22×C11—21no—
96C22×C11—21no—
97C22×C11—24no—
98C22×C11—44no—
99C22×C11—44no—
100C22×C11—42no—
101C22×C11—42no—
102C22×C11C2×C22⋊C811yescharacteristic
103C22×C11C2×M3212yes—
104C4×C11—22no—
105C4×C11—22no—
106C4×C11—21no—
107C4×C11—42no—
108C4×C11#41011yescharacteristic
109C4×C11C2×#10011yescharacteristic
110C22×D4C11⋊C811yescharacteristic
111C23×C4C2×Dic1112yes—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—44no—
115C22×C8C2×Dic1111yescharacteristic
116C22×C8C2×Dic1112yes—
117C22×C8C22×D1111yescharacteristic
118C4×D4—22no—
119C4×D4—22no—
120C2×C4⋊C4C11⋊C811yescharacteristic
121C2×C22⋊C4C11⋊C812yes—
122C2×C42C2×Dic1111yescharacteristic
123C2×C16—224no—
124C4⋊C8—22no—
125C22⋊C8—24no—
126C4×C8C22⋊D1112yes—
127C4×C8C22⋊D1112yes—
128C2×C11—22no—
129C2×C11—44no—
130C2×C11#146011yescharacteristic
131C2×C11#211211yescharacteristic
132C2×C11#211511yescharacteristic
133C24C2×C11⋊C812yes—
134C2×D4—24no—
135C2×D4—22no—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—42no—
139C22×C4—42no—
140C22×C4C2×C11⋊C811yescharacteristic
141C22×C4C2×C11⋊C812yes—
142C22×C4C2×C11⋊C811yescharacteristic
143C22×C4C22×Dic1111yescharacteristic
144C2×C8—22no—
145C2×C8—22no—
146C2×C8—41no—
147C2×C8—44no—
148C2×C8—44no—
149C2×C8—42no—
150C2×C8C22⋊Dic1111yescharacteristic
151C2×C8C22⋊Dic1111yescharacteristic
152C2×C8C2×C22⋊D1112yes—
153C4⋊C4—22no—
154C22⋊C4—24no—
155C42#431812yes—
156C42C22⋊Dic1112yes—
157C16—444no—
158C11#1148811yescharacteristic, complemented, Sylow
159C23—22no—
160C23—22no—
161C23—42no—
162C23—42no—
163C23#6687614yes—
164C23C22×C11⋊C811yescharacteristic
165D4—28no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4C22⋊(C11⋊C8)12yes—
176C2×C4C22⋊(C11⋊C8)12yes—
177C2×C4C2×#431811yescharacteristic
178C2×C4C2×C22⋊Dic1111yescharacteristic
179C8—21no—
180C8—22no—
181C8—42no—
182C8#6689712yes—
183C22—21no—
184C22—21no—
185C22—24no—
186C22—44no—
187C22—44no—
188C22—42no—
189C22—42no—
190C22C2×#6687612yes—
191C22C2×C22⋊(C11⋊C8)11yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—42no—
196C4C2×#6689711yescharacteristic
197C4#1062285311yescharacteristic
198C2—22no—
199C2—44no—
200C2#1306693711yescharacteristic
201C2#1307022711yescharacteristic
202C2#1307023711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic11
commutatorC23×C11C22×C8
FrattiniC22×C8C22×D11
FittingC2×C8×D4×C11C2
socleC22×C11C2×C22⋊C8
prime radicalC22×D4×C11C8
cosocleC22×C8×C11C23
hypercenterC2×C8×D4D11
hypocenterC11#11488
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. #13070419C2semidirect
2. #13066540C2semidirect
158. C11#11488semidirect

Maximal subgroups

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

subgroupindex
#130704192
#130665402
C2×C8×D4×C112
#1148811