Finite Group Databasebeta

← #14646765

Subgroups — #14646765

Order 2816.

388 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 119 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#13067379C212yesmaximal, complemented
2#13067251C212yesmaximal
3#13066527C212yesmaximal, complemented
4C11×#2931C211yesmaximal, characteristic
5C2×C11×#131C412yes—
6C11×#532C2211yescharacteristic
7C11×#436—22no—
8C8×D4×C11—22no—
9C11×#423C2211yescharacteristic
10C11×#408C412yes—
11C2×C4×C8×C11C2211yescharacteristic
12#10622539C2214yes—
13#10622178—24no—
14#10622096—22no—
15#10622095—22no—
16C2×C11×#41C2×C412yes—
17C11×#131—44no—
18C2×C11×M16—22no—
19C2×C11×M16C2×C412yes—
20C22×C8×C11—22no—
21C22×C8×C11C2×C411yescharacteristic
22C22×C8×C11C2×C411yescharacteristic
23C11×C4⋊Q8Q811yescharacteristic
24C11×#127Q811yescharacteristic
25C11×#124D412yes—
26C11×#121—22no—
27C4×D4×C11—22no—
28C2×C42×C11C2311yescharacteristic
29C11×C4⋊C8—22no—
30C11×C22⋊C8—24no—
31C4×C8×C11D412yes—
32C4×C8×C11D412yes—
33C22⋊(C11⋊C8)—24no—
34C4⋊(C11⋊C8)—24no—
35#66867—24no—
36#8630—111nomaximal, Sylow
37C11×#41—42no—
38C11×#41—42no—
39C2×Q8×C11C4⋊C412yes—
40C2×D4×C11—22no—
41C2×D4×C11—22no—
42C2×D4×C11C4⋊C412yes—
43C22×C4×C11—22no—
44C22×C4×C11C22×C411yescharacteristic
45C22×C4×C11#4112yes—
46C11×M16—42no—
47C11×M16—44no—
48C2×C8×C11—22no—
49C2×C8×C11—22no—
50C2×C8×C11—41no—
51C2×C8×C11—44no—
52C2×C8×C11C22⋊C412yes—
53C2×C8×C11C22⋊C411yescharacteristic
54C2×C8×C11C22⋊C411yescharacteristic
55C11×C4⋊C4—22no—
56C11×C22⋊C4—24no—
57C42×C11C2×D412yes—
58C42×C11C2×D411yescharacteristic
59C42×C11C2×Q811yescharacteristic
60C2×C11⋊C8—44no—
61#2931D1111yescharacteristic
62#1568—112no—
63#1536—112no—
64#1307—112no—
65C23×C11—22no—
66C23×C11#11711yescharacteristic
67Q8×C11—42no—
68D4×C11—42no—
69D4×C11—44no—
70D4×C11—44no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—42no—
75C2×C4×C11—42no—
76C2×C4×C11—42no—
77C2×C4×C11C2×C22⋊C411yescharacteristic
78C2×C4×C11C2×C4⋊C411yescharacteristic
79C2×C4×C11#12112yes—
80C2×C4×C11C22⋊Q812yes—
81C8×C11—21no—
82C8×C11—22no—
83C8×C11—42no—
84C8×C11#10012yes—
85C11⋊C8—84no—
86C2×#131Dic1112yes—
87#532C2×D1111yescharacteristic
88#436—22no—
89C8×D4—22no—
90#432—114no—
91#423C2×D1111yescharacteristic
92#408Dic1112yes—
93C2×C4×C8C2×D1111yescharacteristic
94#335—222no—
95#334—222no—
96#329—224no—
97C22×C11—21no—
98C22×C11—22no—
99C22×C11—42no—
100C22×C11—44no—
101C22×C11#38011yescharacteristic
102C4×C11—21no—
103C4×C11—22no—
104C4×C11—22no—
105C4×C11—42no—
106C4×C11C2×#10011yescharacteristic
107C4×C11#41311yescharacteristic
108C2×#41C2×Dic1112yes—
109#131—44no—
110C2×M16—22no—
111C2×M16C2×Dic1112yes—
112C22×C8—22no—
113C22×C8C2×Dic1111yescharacteristic
114C22×C8C2×Dic1111yescharacteristic
115C4⋊Q8Dic2211yescharacteristic
116#127Dic2211yescharacteristic
117#124D4412yes—
118#121—22no—
119C4×D4—22no—
120C2×C42C22×D1111yescharacteristic
121C4⋊C8—22no—
122C4⋊C8—224no—
123C22⋊C8—24no—
124C22⋊C8—224no—
125#97—224no—
126C4×C8C22⋊D1112yes—
127C4×C8C22⋊D1112yes—
128C2×C11—41no—
129C2×C11—82no—
130C2×C11#180011yescharacteristic
131C2×C11#181412yes—
132#41—42no—
133#41—42no—
134C2×Q8C4⋊Dic1112yes—
135C2×D4—22no—
136C2×D4—22no—
137C2×D4C4⋊Dic1112yes—
138C22×C4—22no—
139C22×C4#433912yes—
140C22×C4C22×Dic1111yescharacteristic
141M16—44no—
142M16—42no—
143C2×C8—22no—
144C2×C8—22no—
145C2×C8—41no—
146C2×C8—44no—
147C2×C8—444no—
148C2×C8C22⋊Dic1112yes—
149C2×C8C22⋊Dic1111yescharacteristic
150C2×C8C22⋊Dic1111yescharacteristic
151C4⋊C4—22no—
152C22⋊C4—24no—
153C42C2×Dic2211yescharacteristic
154C42C2×D4411yescharacteristic
155C42C2×C22⋊D1112yes—
156C11#863011yescharacteristic, complemented, Sylow
157C23—22no—
158C23#6697911yescharacteristic
159Q8—42no—
160D4—42no—
161D4—44no—
162D4—44no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4#6697712yes—
170C2×C4C2×C4⋊Dic1111yescharacteristic
171C2×C4#6698312yes—
172C2×C4C2×C22⋊Dic1111yescharacteristic
173C8—21no—
174C8—22no—
175C8—42no—
176C8—884no—
177C8#6689712yes—
178C22—21no—
179C22—22no—
180C22—42no—
181C22—44no—
182C22#1062282511yescharacteristic
183C4—21no—
184C4—22no—
185C4—22no—
186C4—42no—
187C4C2×#6689711yescharacteristic
188C4#1062285011yescharacteristic
189C2—41no—
190C2—82no—
191C2#1306860811yescharacteristic
192C2#1306867012yes—
subgroupG/H
centerC22#10622825
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2931C2
socleC22×C11#380
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#2931D11
hypocenterC11#8630
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2931

Complements

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

NH ≅ G/Ntype
1. #13067379C2semidirect
3. #13066527C2semidirect
156. C11#8630semidirect

Maximal subgroups

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

subgroupindex
#130673792
#130672512
#130665272
C11×#29312
#863011