Finite Group Databasebeta

← #14663113

Subgroups — #14663113

Order 2816.

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

normal subgroups only

This group has 330 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
2#13066556C214yesmaximal
3C2×C8×Q8×C11C211yesmaximal, characteristic
4C2×C4×Q8×C11C411yescharacteristic
5C8×Q8×C11—22no—
6C8×Q8×C11—22no—
7C2×C11×C4⋊C8C411yescharacteristic
8C2×C11×C4⋊C8C2212yes—
9C2×C4×C8×C11C412yes—
10C2×C4×C8×C11C2211yescharacteristic
11C22⋊(C11⋊C16)C2214yes—
12C4⋊(C11⋊C16)—22no—
13#10622099—22no—
14C22×Q8×C11C811yescharacteristic
15C22×C8×C11C2×C411yescharacteristic
16C22×C8×C11C2×C412yes—
17C22×C8×C11C2311yescharacteristic
18C4×Q8×C11—22no—
19C4×Q8×C11—22no—
20C2×C11×C4⋊C4C811yescharacteristic
21C2×C11×C4⋊C4C812yes—
22C2×C42×C11C2×C412yes—
23C2×C42×C11C2×C411yescharacteristic
24C11×C4⋊C8—24no—
25C11×C4⋊C8—22no—
26C4×C8×C11—22no—
27C4×C8×C11—22no—
28C4×C8×C11D412yes—
29C4×C8×C11D412yes—
30C2×C11⋊C16—24no—
31#11494—111nomaximal, Sylow
32C2×Q8×C11—22no—
33C2×Q8×C11—24no—
34C22×C4×C11C2×C811yescharacteristic
35C22×C4×C11C2×C812yes—
36C22×C4×C11C2×C812yes—
37C22×C4×C11C2×C811yescharacteristic
38C22×C4×C11C22×C411yescharacteristic
39C2×C8×C11—22no—
40C2×C8×C11—22no—
41C2×C8×C11—41no—
42C2×C8×C11—42no—
43C2×C8×C11C22⋊C411yescharacteristic
44C2×C8×C11C22⋊C411yescharacteristic
45C2×C8×C11C2×D412yes—
46C11×C4⋊C4—24no—
47C11×C4⋊C4—22no—
48C42×C11—22no—
49C42×C11—22no—
50C42×C11C22⋊C412yes—
51C42×C11M1612yes—
52C11⋊C16—44no—
53C2×C8×Q8D1111yescharacteristic
54#2163—112no—
55#1322—114no—
56C23×C11C22×C811yescharacteristic
57Q8×C11—28no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—41no—
65C2×C4×C11—42no—
66C2×C4×C11C22⋊C812yes—
67C2×C4×C11C22⋊C812yes—
68C2×C4×C11M3214yes—
69C2×C4×C11C2×C22⋊C411yescharacteristic
70C2×C4×C11C2×M1611yescharacteristic
71C8×C11—22no—
72C8×C11—21no—
73C8×C11—42no—
74C8×C11#10112yes—
75C2×C4×Q8Dic1111yescharacteristic
76C8×Q8—22no—
77C8×Q8—22no—
78C2×C4⋊C8Dic1111yescharacteristic
79C2×C4⋊C8C2×D1112yes—
80C2×C4×C8Dic1112yes—
81C2×C4×C8C2×D1111yescharacteristic
82C4⋊C16—222no—
83C22⋊C16—114no—
84#346—222no—
85C22×C11—21no—
86C22×C11—21no—
87C22×C11C2×C22⋊C811yescharacteristic
88C22×C11C2×M3212yes—
89C4×C11—22no—
90C4×C11—24no—
91C4×C11—22no—
92C4×C11—21no—
93C4×C11—42no—
94C4×C11#41011yescharacteristic
95C4×C11C2×#10111yescharacteristic
96C22×Q8C11⋊C811yescharacteristic
97C22×C8C2×Dic1111yescharacteristic
98C22×C8C2×Dic1112yes—
99C22×C8C22×D1111yescharacteristic
100C4×Q8—22no—
101C4×Q8—22no—
102C2×C4⋊C4C11⋊C812yes—
103C2×C4⋊C4C11⋊C811yescharacteristic
104C2×C42C2×Dic1112yes—
105C2×C42C2×Dic1111yescharacteristic
106C2×C16—224no—
107C4⋊C8—24no—
108C4⋊C8—22no—
109C4×C8—22no—
110C4×C8—22no—
111C4×C8C22⋊D1112yes—
112C4×C8C22⋊D1112yes—
113C2×C11—22no—
114C2×C11#146111yescharacteristic
115C2×C11#211211yescharacteristic
116C2×C11#211511yescharacteristic
117C2×Q8—24no—
118C2×Q8—22no—
119C22×C4C2×C11⋊C812yes—
120C22×C4C2×C11⋊C811yescharacteristic
121C22×C4C2×C11⋊C812yes—
122C22×C4C2×C11⋊C811yescharacteristic
123C22×C4C22×Dic1111yescharacteristic
124C2×C8—22no—
125C2×C8—22no—
126C2×C8—41no—
127C2×C8—42no—
128C2×C8C22⋊Dic1111yescharacteristic
129C2×C8C22⋊Dic1111yescharacteristic
130C2×C8C2×C22⋊D1112yes—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C42—22no—
134C42—22no—
135C42#431812yes—
136C42C22⋊Dic1112yes—
137C16—444no—
138C11#1149411yescharacteristic, complemented, Sylow
139C23C22×C11⋊C811yescharacteristic
140Q8—28no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4#6687614yes—
150C2×C4C22⋊(C11⋊C8)12yes—
151C2×C4C22⋊(C11⋊C8)12yes—
152C2×C4C2×#431811yescharacteristic
153C2×C4C2×C22⋊Dic1111yescharacteristic
154C8—21no—
155C8—22no—
156C8—42no—
157C8#6690012yes—
158C22—21no—
159C22—21no—
160C22C2×#6687612yes—
161C22C2×C22⋊(C11⋊C8)11yescharacteristic
162C4—24no—
163C4—22no—
164C4—22no—
165C4—21no—
166C4—42no—
167C4C2×#6690011yescharacteristic
168C4#1062285311yescharacteristic
169C2—22no—
170C2#1306694011yescharacteristic
171C2#1307022711yescharacteristic
172C2#1307023711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic11
commutator, prime radicalC23×C11C22×C8
FrattiniC22×C8C22×D11
FittingC2×C8×Q8×C11C2
socleC22×C11C2×C22⋊C8
cosocleC22×C8×C11C23
hypercenterC2×C8×Q8D11
hypocenterC11#11494
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
138. C11#11494semidirect

Maximal subgroups

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

subgroupindex
#130704192
#130665562
C2×C8×Q8×C112
#1149411