Finite Group Databasebeta

← #11790811

Subgroups — #11790811

Order 1152.

630 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 70 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#10596196C211yesmaximal, characteristic
2C2×#63785C214yesmaximal, complemented
3#10593733C211yesmaximal, characteristic, complemented
4#10593729C211yesmaximal, characteristic, complemented
5C2×#3832C2212yes—
6C2×C4×#157C2212yes—
7C2×#3788C2212yes—
8C32×C4⋊Q8C411yescharacteristic, complemented
9#64156C412yescomplemented
10#64104—22no—
11#64102—22no—
12#64083C411yescharacteristic, complemented
13C42×C3⋊D3C2211yescharacteristic
14#63785—28no—
15#63781—22no—
16#63779—22no—
17#5725—62no—
18C22×#157—22no—
19C2×C32×Q8C2×C412yes—
20#3832—24no—
21#3832—24no—
22C2×C4⋊(C3⋊D3)—22no—
23C2×C4⋊(C3⋊D3)—22no—
24C2×C4⋊(C3⋊D3)C2×C412yes—
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3D412yes—
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×#622—22no—
29C4×#157—22no—
30C4×#157D414yescomplemented
31#3788—24no—
32C32×C4⋊C4—22no—
33C32×C42C2×C411yescharacteristic
34#3752—24no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D412yes—
37#1963—91nomaximal, Sylow
38C2×#239—64no—
39C3×C4⋊Q8—22no—
40#947—64no—
41#895—68no—
42#893—68no—
43#874—62no—
44C42×D3—62no—
45C22×C3⋊D3—22no—
46C22×C3⋊D3C2×D411yescharacteristic
47C2×#157—24no—
48C2×#157—44no—
49C32×Q8—24no—
50C2×C32×C4—22no—
51C2×C32×C4C22⋊C412yes—
52C2×C32×C4C22×C411yescharacteristic
53C2×C3⋊Dic3C22⋊C412yes—
54C2×C3⋊Dic3C2×D411yescharacteristic
55C4⋊(C3⋊D3)—24no—
56C4⋊(C3⋊D3)—44no—
57C4⋊(C3⋊D3)—44no—
58C4×C3⋊D3—42no—
59C4×C3⋊D3—42no—
60C4×C3⋊D3—42no—
61C4×C3⋊D3C2×D412yes—
62C4×C3⋊D3#4112yes—
63#622—42no—
64#532—91no—
65#423—91no—
66C2×#104—94no—
67#376—91no—
68C2×C3×Q8—24no—
69#239—128no—
70#239—128no—
71C2×D12—64no—
72C2×D12—68no—
73C2×D12—68no—
74C2×C4×D3—62no—
75C2×C4×D3—64no—
76C2×C4×D3—68no—
77C3×C4⋊C4—28no—
78C3×C42—22no—
79(C2×D3)⋊C4—616no—
80C4×Dic3—64no—
81C4×Dic3—62no—
82C22×C32C2×C22⋊C411yescharacteristic
83C2×C3⋊D3—22no—
84C2×C3⋊D3—42no—
85C2×C3⋊D3—44no—
86C2×C3⋊D3#12112yes—
87#157—44no—
88C32×C4—22no—
89C32×C4—42no—
90C32×C4C4×D412yes—
91C3⋊Dic3—22no—
92C3⋊Dic3#12411yescharacteristic
93C3⋊Dic3#12711yescharacteristic
94C2×#41—92no—
95C2×M16—92no—
96C4⋊Q8#15711yescharacteristic, complemented
97#127—91no—
98#124—92no—
99#121—182no—
100C4×D4—182no—
101C2×C42—91no—
102C2×C42—92no—
103C4⋊C8—182no—
104#104—188no—
105#95—182no—
106C22×D3—62no—
107C22×D3—68no—
108C3×Q8—48no—
109C2×C3×C4—28no—
110C2×C3×C4—22no—
111C2×C3×C4—24no—
112C2×Dic3—62no—
113C2×Dic3—64no—
114D12—128no—
115D12—1216no—
116D12—1216no—
117C4×D3—64no—
118C4×D3—64no—
119C4×D3—128no—
120C4×D3—128no—
121C4×D3—128no—
122C2×C32#39011yescharacteristic
123C2×C32#42112yes—
124C3⋊D3—22no—
125C3⋊D3—82no—
126#41—184no—
127#41—184no—
128C2×Q8C2×#15712yes—
129C2×D4—92no—
130C2×D4—182no—
131C2×D4—182no—
132C22×C4—91no—
133C22×C4—92no—
134C22×C4—182no—
135C22×C4—182no—
136M16—184no—
137C2×C8—182no—
138C4⋊C4—22no—
139C22⋊C4—184no—
140C42—91no—
141C42—92no—
142C42—94no—
143C42—182no—
144C42C2×#15711yescharacteristic
145C22×C3—22no—
146C2×D3—64no—
147C2×D3—124no—
148C2×D3—128no—
149C2×D3—1216no—
150C3×C4—28no—
151C3×C4—24no—
152C3×C4—48no—
153Dic3—62no—
154Dic3—62no—
155Dic3—124no—
156C32#196311yescharacteristic, complemented, Sylow
157C23—91no—
158C23—182no—
159Q8—24no—
160D4—184no—
161D4—364no—
162D4—364no—
163C2×C4—22no—
164C2×C4—91no—
165C2×C4—92no—
166C2×C4—92no—
167C2×C4—92no—
168C2×C4—184no—
169C2×C4—362no—
170C2×C4—362no—
171C2×C4—362no—
172C2×C4—364no—
173C2×C4C22⋊#15712yes—
174C2×C4C22×#15711yescharacteristic
175C8—362no—
176C2×C3—22no—
177C2×C3—24no—
178D3—124no—
179D3—248no—
180C22—92no—
181C22—182no—
182C22—362no—
183C22—364no—
184C22C2×C22⋊#15711yescharacteristic
185C4—22no—
186C4—42no—
187C4—91no—
188C4—91no—
189C4—182no—
190C4—364no—
191C4D4×#15712yes—
192C3—22no—
193C2—182no—
194C2—722no—
195C2#1059382711yescharacteristic
196C2#1059383112yes—
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radical#10596196C2
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊Q8#157
hypocenterC32#1963
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63785C2semidirect
3. #10593733C2semidirect
4. #10593729C2semidirect
8. C32×C4⋊Q8C4semidirect
9. #64156C4semidirect
12. #64083C4semidirect
30. C4×#157D4semidirect
96. C4⋊Q8#157semidirect
156. C32#1963semidirect

Maximal subgroups

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

subgroupindex
#105961962
C2×#637852
#105937332
#105937292
#19639