Finite Group Databasebeta

← #14646799

Subgroups — #14646799

Order 2816.

404 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 127 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#13067375C212yesmaximal, complemented
2#13067351C212yesmaximal
3C11⋊#1309C212yesmaximal, 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#10622537C2214yes—
13#10622184—22no—
14#10622182—22no—
15#10622096—22no—
16#10622096—22no—
17C2×C11×#41C2×C412yes—
18C11×#131—44no—
19C2×C11×M16—22no—
20C2×C11×M16C2×C412yes—
21C22×C8×C11—22no—
22C22×C8×C11C2×C411yescharacteristic
23C22×C8×C11C2×C411yescharacteristic
24C11×C4⋊Q8D411yescharacteristic
25C11×#127D411yescharacteristic
26C11×#124Q812yes—
27C11×#121—22no—
28C4×D4×C11—22no—
29C2×C42×C11C2311yescharacteristic
30C2×#4318—24no—
31C11×C4⋊C8—22no—
32C11×C22⋊C8—24no—
33C4×C8×C11D412yes—
34C4×C8×C11D412yes—
35C4⋊(C11⋊C8)—24no—
36C4⋊(C11⋊C8)—24no—
37#8638—111nomaximal, Sylow
38C11×#41—42no—
39C11×#41—42no—
40C2×Q8×C11C4⋊C412yes—
41C2×D4×C11—22no—
42C2×D4×C11—22no—
43C2×D4×C11C4⋊C412yes—
44C22×C4×C11—22no—
45C22×C4×C11C22×C411yescharacteristic
46C22×C4×C11#4112yes—
47C11×M16—42no—
48C11×M16—44no—
49C2×C8×C11—22no—
50C2×C8×C11—22no—
51C2×C8×C11—41no—
52C2×C8×C11—44no—
53C2×C8×C11C22⋊C412yes—
54C2×C8×C11C22⋊C411yescharacteristic
55C2×C8×C11C22⋊C411yescharacteristic
56C11×C4⋊C4—22no—
57C11×C22⋊C4—24no—
58C42×C11C2×D412yes—
59C42×C11C2×D411yescharacteristic
60C42×C11C2×Q811yescharacteristic
61#4318—84no—
62C2×C11⋊C8—44no—
63#2931D1111yescharacteristic
64#1567—112no—
65#1560—112no—
66#1309—112no—
67C23×C11—22no—
68C23×C11#11711yescharacteristic
69Q8×C11—42no—
70D4×C11—42no—
71D4×C11—44no—
72D4×C11—42no—
73D4×C11—42no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—42no—
80C2×C4×C11—42no—
81C2×C4×C11C2×C22⋊C411yescharacteristic
82C2×C4×C11C2×C4⋊C411yescharacteristic
83C2×C4×C11#12112yes—
84C2×C4×C11C22⋊Q812yes—
85C8×C11—21no—
86C8×C11—22no—
87C8×C11—42no—
88C8×C11#10012yes—
89C11⋊C8—84no—
90C2×#131Dic1112yes—
91#532C2×D1111yescharacteristic
92#436—22no—
93C8×D4—22no—
94#423—114no—
95#423C2×D1111yescharacteristic
96#408Dic1112yes—
97C2×C4×C8C2×D1111yescharacteristic
98#335—222no—
99#335—222no—
100#333—222no—
101#331—222no—
102C22×C11—21no—
103C22×C11—22no—
104C22×C11—42no—
105C22×C11—44no—
106C22×C11#38011yescharacteristic
107C4×C11—21no—
108C4×C11—22no—
109C4×C11—42no—
110C4×C11C2×#10011yescharacteristic
111C4×C11#41311yescharacteristic
112C4×C11#47212yes—
113C4×C11#47312yes—
114C2×#41C2×Dic1112yes—
115#131—44no—
116C2×M16—22no—
117C2×M16—224no—
118C2×M16C2×Dic1112yes—
119C22×C8—22no—
120C22×C8C2×Dic1111yescharacteristic
121C22×C8C2×Dic1111yescharacteristic
122C4⋊Q8D4411yescharacteristic
123#127D4411yescharacteristic
124#124Dic2212yes—
125#121—22no—
126C4×D4—22no—
127C2×C42C22×D1111yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—224no—
130C4⋊C8—224no—
131C22⋊C8—24no—
132C4×C8C22⋊D1112yes—
133C4×C8C22⋊D1112yes—
134C2×C11—41no—
135C2×C11—82no—
136C2×C11#180011yescharacteristic
137C2×C11#181612yes—
138#41—42no—
139#41—42no—
140C2×Q8C4⋊Dic1112yes—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4C4⋊Dic1112yes—
144C22×C4—22no—
145C22×C4#433912yes—
146C22×C4C22×Dic1111yescharacteristic
147M16—44no—
148M16—42no—
149M16—884no—
150C2×C8—22no—
151C2×C8—22no—
152C2×C8—41no—
153C2×C8—44no—
154C2×C8—444no—
155C2×C8C22⋊Dic1112yes—
156C2×C8C22⋊Dic1111yescharacteristic
157C2×C8C22⋊Dic1111yescharacteristic
158C4⋊C4—22no—
159C22⋊C4—24no—
160C42C2×Dic2211yescharacteristic
161C42C2×D4411yescharacteristic
162C42C2×C22⋊D1112yes—
163C11#863811yescharacteristic, complemented, Sylow
164C23—22no—
165C23#6697911yescharacteristic
166Q8—42no—
167D4—42no—
168D4—44no—
169D4—42no—
170D4—42no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4#6697712yes—
179C2×C4C2×C4⋊Dic1111yescharacteristic
180C2×C4#6698312yes—
181C2×C4C2×C22⋊Dic1111yescharacteristic
182C8—21no—
183C8—22no—
184C8—42no—
185C8—884no—
186C8#6689712yes—
187C22—21no—
188C22—22no—
189C22—42no—
190C22—44no—
191C22#1062282511yescharacteristic
192C4—21no—
193C4—22no—
194C4—42no—
195C4#1062275512yes—
196C4#1062275612yes—
197C4C2×#6689711yescharacteristic
198C4#1062285011yescharacteristic
199C2—41no—
200C2—82no—
201C2#1306860811yescharacteristic
202C2#1306868012yes—
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#8638
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. #13067375C2semidirect
3. C11⋊#1309C2semidirect
163. C11#8638semidirect

Maximal subgroups

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

subgroupindex
#130673752
#130673512
C11⋊#13092
C11×#29312
#863811