Finite Group Databasebeta

← #11858310

Subgroups — #11858310

Order 1152.

814 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 202 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
1C22×#3792C212yesmaximal
2C2×#64086C211yesmaximal, characteristic
3#10593805C214yesmaximal, complemented
4#10593743C218yesmaximal, complemented
5C23×C3⋊Dic3C2211yescharacteristic
6C2×#3792—28no—
7C2×#3792C2214yes—
8C2×#3792C2214yes—
9C22×#622C2214yes—
10C2×C32×C22⋊C4C411yescharacteristic
11C2×#3757C411yescharacteristic
12C2×#3750C412yes—
13C2×C4×C3⋊Dic3C2212yes—
14#64086C414yes—
15#64086C2214yes—
16#63779C2218yescomplemented
17C4⋊#622C2218yescomplemented
18C2×#877—62no—
19C24×C32C2×C411yescharacteristic
20C22×C32×C4C2×C412yes—
21C22×C3⋊Dic3C2×C412yes—
22C22×C3⋊Dic3C2×C412yes—
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D414yes—
25C22×C3⋊Dic3Q814yes—
26C22×C3⋊Dic3C2312yes—
27C22×C3⋊Dic3C2311yescharacteristic
28#3792—28no—
29#3792—28no—
30C2×#622—28no—
31C2×#622C2318yes—
32C32×C22⋊C4C2×C414yes—
33#3757C2×C414yes—
34#3750C2×C418yes—
35C4×C3⋊Dic3C2×C414yes—
36C4×C3⋊Dic3C2314yes—
37#2905—91nomaximal, Sylow
38C23×Dic3—62no—
39C2×C3×C22⋊C4—22no—
40C2×#217—62no—
41C2×Dic3⋊C4—64no—
42C2×C4×Dic3—64no—
43#877—68no—
44#877—68no—
45C23×C32—42no—
46C23×C32C4⋊C414yes—
47C23×C32C22×C412yes—
48C23×C32C22×C411yescharacteristic
49C2×C32×C4—42no—
50C2×C32×C4C22×C414yes—
51C2×C3⋊Dic3—42no—
52C2×C3⋊Dic3C4⋊C418yes—
53C2×C3⋊Dic3C4⋊C414yes—
54C2×C3⋊Dic3C22×C414yes—
55C2×C3⋊Dic3C22×C411yescharacteristic
56C2×C3⋊Dic3C22×C412yes—
57C2×C3⋊Dic3C2×D414yes—
58C2×C3⋊Dic3C2×D412yes—
59C2×C3⋊Dic3C2×Q814yes—
60C2×C3⋊Dic3C2×Q812yes—
61C2×C3⋊Dic3C2411yescharacteristic
62#622—28no—
63C22×M16—92no—
64C2×#117—91no—
65#424—98no—
66#423—94no—
67C24×C3—22no—
68C22×C3×C4—24no—
69C22×Dic3—64no—
70C22×Dic3—64no—
71C22×Dic3—62no—
72C22×Dic3—62no—
73C22×Dic3—68no—
74C22×Dic3—68no—
75C22×Dic3—64no—
76C3×C22⋊C4—28no—
77#217—68no—
78Dic3⋊C4—616no—
79C4×Dic3—68no—
80C4×Dic3—68no—
81C22×C32—22no—
82C22×C32—24no—
83C22×C32—44no—
84C22×C32C2×C4⋊C412yes—
85C22×C32C2×C4⋊C414yes—
86C22×C32C23×C411yescharacteristic
87C32×C4—24no—
88C3⋊Dic3—24no—
89C3⋊Dic3C2×C4⋊C412yes—
90C3⋊Dic3C2×C4⋊C414yes—
91C3⋊Dic3C22×D411yescharacteristic
92C3⋊Dic3C22×Q811yescharacteristic
93C23×C4—91no—
94C2×M16—94no—
95C2×M16—94no—
96C2×M16—188no—
97C22×C8—94no—
98#117—94no—
99#117—94no—
100C2×C4⋊C4—92no—
101C2×C22⋊C4—91no—
102C2×C22⋊C4#15711yescharacteristic
103C2×C42—92no—
104C4⋊C8—98no—
105C4⋊C8—98no—
106C23×C3—22no—
107C23×C3—24no—
108C23×C3—28no—
109C23×C3—48no—
110C2×C3×C4—28no—
111C2×C3×C4—48no—
112C2×Dic3—68no—
113C2×Dic3—616no—
114C2×Dic3—62no—
115C2×Dic3—64no—
116C2×Dic3—68no—
117C2×Dic3—64no—
118C2×Dic3—64no—
119C2×Dic3—68no—
120C2×Dic3—62no—
121C2×Dic3—68no—
122C2×Dic3—128no—
123C2×C32—22no—
124C2×C32—24no—
125C2×C32C22×C4⋊C411yescharacteristic
126C2×C32#56812yes—
127C24C2×#15711yescharacteristic
128C22×C4—91no—
129C22×C4—91no—
130C22×C4—92no—
131C22×C4—92no—
132C22×C4—94no—
133C22×C4—94no—
134C22×C4—92no—
135C22×C4C2×#15712yes—
136M16—188no—
137M16—188no—
138C2×C8—98no—
139C2×C8—188no—
140C4⋊C4—98no—
141C22⋊C4—94no—
142C22⋊C4C2×#15714yes—
143C42—94no—
144C42—94no—
145C22×C3—28no—
146C22×C3—24no—
147C22×C3—28no—
148C22×C3—22no—
149C22×C3—48no—
150C22×C3—416no—
151C3×C4—48no—
152Dic3—64no—
153Dic3—68no—
154Dic3—62no—
155Dic3—62no—
156Dic3—128no—
157C32#290511yescharacteristic, complemented, Sylow
158C23—42no—
159C23C4⋊#15714yes—
160C23C22×#15712yes—
161C23C22×#15711yescharacteristic
162C2×C4—42no—
163C2×C4—94no—
164C2×C4—92no—
165C2×C4—92no—
166C2×C4—94no—
167C2×C4—94no—
168C2×C4—98no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—92no—
172C2×C4—94no—
173C2×C4—362no—
174C2×C4C22×#15714yes—
175C8—188no—
176C2×C3—28no—
177C2×C3—22no—
178C2×C3—24no—
179C2×C3—48no—
180C22—22no—
181C22—24no—
182C22—44no—
183C22C2×C4⋊#15712yes—
184C22C2×C4⋊#15714yes—
185C22C23×#15711yescharacteristic
186C4—24no—
187C4—91no—
188C4—94no—
189C4—92no—
190C4—91no—
191C4—184no—
192C3—22no—
193C2—22no—
194C2—24no—
195C2C22×C4⋊#15711yescharacteristic
196C2#1059664012yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC2×C32×C22⋊C4C4
prime radicalC24×C32C2×C4
cosocleC2×C3⋊Dic3C24
hypercenterC2×C22⋊C4#157
hypocenterC32#2905
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #10593805C2semidirect
4. #10593743C2semidirect
16. #63779C22semidirect
17. C4⋊#622C22semidirect
157. C32#2905semidirect

Maximal subgroups

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

subgroupindex
C22×#37922
C2×#640862
#105938052
#105937432
#29059