Finite Group Databasebeta

← C2×#10590216 #11775666

Subgroups — C2×#10590216 #11775666

Order 1152.

614 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C2×#64156C211yesmaximal, characteristic
2C2×#63777C212yesmaximal, complemented
3#10590216C214yesmaximal, direct product factor
4C22×C32×Q8C411yescharacteristic
5C22×C4⋊(C3⋊D3)C411yescharacteristic
6C22×#622—22no—
7#64156—22no—
8#64156C412yes—
9#64156C2212yes—
10C2×#3752—22no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#63777—22no—
13#63777C2214yescomplemented
14C2×#947—62no—
15C23×C3⋊D3—21no—
16C2×C32×Q8—21no—
17C2×C32×Q8—42no—
18C2×C32×Q8C2×C412yes—
19C22×C32×C4—21no—
20C22×C32×C4C2×C411yescharacteristic
21C22×C3⋊Dic3D412yes—
22C2×C4⋊(C3⋊D3)—21no—
23C2×C4⋊(C3⋊D3)—42no—
24C2×C4⋊(C3⋊D3)C2×C412yes—
25C2×#622—28no—
26C2×#622—24no—
27#3752—24no—
28#3752—24no—
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D412yes—
31C4×C3⋊Dic3C2311yescharacteristic
32C2×#329—91nomaximal, Sylow
33C22×C3×Q8—22no—
34C22×D12—62no—
35#947—64no—
36#947—64no—
37#947—68no—
38C2×(C2×D3)⋊C4—68no—
39C2×C4×Dic3—62no—
40C23×C32C22⋊C411yescharacteristic
41C22×C3⋊D3—22no—
42C22×C3⋊D3—42no—
43C22×C3⋊D3—44no—
44C32×Q8—42no—
45C32×Q8—42no—
46C2×C32×C4—22no—
47C2×C32×C4—22no—
48C2×C32×C4—42no—
49C2×C32×C4C22⋊C411yescharacteristic
50C2×C32×C4C22×C411yescharacteristic
51C2×C3⋊Dic3—24no—
52C2×C3⋊Dic3C22⋊C412yes—
53C2×C3⋊Dic3C2×D412yes—
54C4⋊(C3⋊D3)—42no—
55C4⋊(C3⋊D3)—42no—
56#622—28no—
57C2×#124—91no—
58C2×#97—92no—
59#329—94no—
60C23×D3—64no—
61C2×C3×Q8—24no—
62C2×C3×Q8—24no—
63C2×C3×Q8—48no—
64C22×C3×C4—24no—
65C22×C3×C4—22no—
66C22×Dic3—64no—
67C2×D12—64no—
68C2×D12—64no—
69C2×D12—128no—
70(C2×D3)⋊C4—616no—
71(C2×D3)⋊C4—616no—
72C4×Dic3—62no—
73C4×Dic3—64no—
74C4×Dic3—62no—
75C22×C32#10012yes—
76C22×C32#10414yes—
77C22×C32C2×C22⋊C411yescharacteristic
78C2×C3⋊D3—42no—
79C2×C3⋊D3—44no—
80C2×C3⋊D3—84no—
81C32×C4—21no—
82C32×C4—21no—
83C32×C4—42no—
84C3⋊Dic3—22no—
85C3⋊Dic3—22no—
86C22×Q8#15711yescharacteristic
87C22×D4—91no—
88C22×C8—182no—
89#124—92no—
90#124—92no—
91#124—182no—
92C2×C22⋊C4—182no—
93C2×C42—91no—
94#97—94no—
95#97—182no—
96C23×C3—22no—
97C22×D3—68no—
98C22×D3—128no—
99C22×D3—1216no—
100C3×Q8—48no—
101C3×Q8—48no—
102C2×C3×C4—28no—
103C2×C3×C4—28no—
104C2×C3×C4—22no—
105C2×C3×C4—22no—
106C2×C3×C4—48no—
107C2×Dic3—64no—
108C2×Dic3—64no—
109C2×Dic3—128no—
110D12—128no—
111D12—128no—
112C2×C32#32914yescomplemented
113C2×C32C2×#10011yescharacteristic
114C2×C32C2×#10412yes—
115C3⋊D3—82no—
116C24—181no—
117C2×Q8—21no—
118C2×Q8—42no—
119C2×Q8C2×#15712yes—
120C2×D4—92no—
121C2×D4—181no—
122C2×D4—362no—
123C22×C4—21no—
124C22×C4—92no—
125C22×C4C2×#15711yescharacteristic
126C2×C8—184no—
127C2×C8—188no—
128C22⋊C4—184no—
129C22⋊C4—184no—
130C42—91no—
131C42—91no—
132C42—92no—
133C22×C3—22no—
134C22×C3—28no—
135C22×C3—24no—
136C2×D3—128no—
137C2×D3—1216no—
138C2×D3—2416no—
139C3×C4—24no—
140C3×C4—24no—
141C3×C4—48no—
142Dic3—124no—
143Dic3—124no—
144C32C2×#32911yescharacteristic, complemented, Sylow
145C23—182no—
146C23—364no—
147C23—362no—
148C23C22⋊#15711yescharacteristic
149Q8—42no—
150Q8—42no—
151D4—362no—
152D4—362no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—92no—
157C2×C4—92no—
158C2×C4—184no—
159C2×C4C22⋊#15711yescharacteristic
160C2×C4C22×#15711yescharacteristic
161C8—188no—
162C2×C3—28no—
163C2×C3—24no—
164C2×C3—22no—
165D3—248no—
166C22—364no—
167C22—362no—
168C22—724no—
169C22#6378514yes—
170C22#6378812yes—
171C22C2×C22⋊#15711yescharacteristic
172C4—21no—
173C4—21no—
174C4—42no—
175C4—182no—
176C4—182no—
177C3—22no—
178C2—722no—
179C2#1059021614yesdirect product factor
180C2C2×#6378512yes—
181C2C2×#6378811yescharacteristic
subgroupG/H
centerC23C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×Q8C4
socleC23×C32C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×Q8#157
hypocenterC32C2×#329
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63777C2semidirect
3. #10590216C2direct (N × H)
13. #63777C22semidirect
112. C2×C32#329semidirect
144. C32C2×#329semidirect
179. C2#10590216direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641562
C2×#637772
#105902162
C2×#3299