Finite Group Databasebeta

← C22×C8×#157 #11857103

Subgroups — C22×C8×#157 #11857103

Order 1152.

1098 conjugacy classes of subgroups; only the 418 normal subgroups are shown.

normal subgroups only

This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 418 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×C4×#157C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic
3C22×C8×C3⋊D3C211yesmaximal, characteristic
4C2×C8×#157C2112yesmaximal, direct product factor
5C23×#157C412yes—
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#622C412yescomplemented
8C2×C4×#157C416yes—
9C2×C4×#157C2216yes—
10C2×#3787C416yescomplemented
11C2×#3787C2216yes—
12C22×C32×C8C411yescharacteristic, complemented
13C22×C3⋊(C3⋊C8)C411yescharacteristic, complemented
14C2×C8×C3⋊D3C416yescomplemented
15C2×C8×C3⋊D3C2216yes—
16C8×#157C22116yesdirect product factor
17C22×D3×C8—62no—
18C23×C3⋊D3C2×C411yescharacteristic
19C22×#157C8116yesdirect product factor
20C22×#157C2×C4112yes—
21C22×C32×C4C2×C411yescharacteristic
22C22×C3⋊Dic3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C413yes—
24C2×C4×C3⋊D3C2×C413yes—
25C2×C4×C3⋊D3C2×C413yes—
26C2×C4×C3⋊D3C2313yes—
27C2×#622C2×C4112yescomplemented
28C4×#157C2×C4112yes—
29C4×#157C2314yes—
30#3787C2×C4112yescomplemented
31#3787C2314yes—
32C2×C32×C8C2×C416yescomplemented
33C2×C3⋊(C3⋊C8)C2×C416yescomplemented
34C8×C3⋊D3C2×C4112yescomplemented
35C8×C3⋊D3C2314yes—
36C22×C4×C8—91nomaximal, Sylow
37C22×C4×D3—62no—
38C22×C3×C8—22no—
39C22×C3⋊C8—62no—
40C2×D3×C8—612no—
41C2×D3×C8—612no—
42C23×C32C4211yescharacteristic
43C22×C3⋊D3C4213yes—
44C22×C3⋊D3C2×C818yes—
45C22×C3⋊D3C22×C413yes—
46C2×#157C2×C8148yesdirect product factor
47C2×#157C22×C418yes—
48C2×C32×C4C4213yes—
49C2×C32×C4C22×C413yes—
50C2×C3⋊Dic3C4213yes—
51C2×C3⋊Dic3C22×C413yes—
52C4×C3⋊D3C4216yes—
53C4×C3⋊D3C22×C413yes—
54C4×C3⋊D3C22×C413yes—
55C4×C3⋊D3C22×C413yes—
56C4×C3⋊D3C2411yescharacteristic
57#622C22×C418yescomplemented
58C32×C8C22×C414yescomplemented
59C3⋊(C3⋊C8)C22×C414yescomplemented
60C23×C8—91no—
61C23×C8—91no—
62C22×C42—91no—
63C2×C4×C8—912no—
64C23×D3—62no—
65C22×C3×C4—22no—
66C22×Dic3—62no—
67C2×C4×D3—66no—
68C2×C4×D3—66no—
69C2×C4×D3—66no—
70C2×C4×D3—66no—
71C2×C3×C8—212no—
72C2×C3⋊C8—612no—
73D3×C8—624no—
74D3×C8—68no—
75C22×C32C4×C814yescomplemented
76C22×C32C2×C4213yes—
77C2×C3⋊D3C4×C8112yescomplemented
78C2×C3⋊D3C2×C4213yes—
79C2×C3⋊D3C22×C8112yes—
80C2×C3⋊D3C23×C411yescharacteristic
81#157C22×C8116yesdirect product factor
82C32×C4C2×C4213yes—
83C32×C4C23×C411yescharacteristic
84C3⋊Dic3C2×C4213yes—
85C3⋊Dic3C23×C411yescharacteristic
86C23×C4—92no—
87C23×C4—91no—
88C22×C8—96no—
89C22×C8—96no—
90C22×C8—92no—
91C22×C8—91no—
92C22×C8—96no—
93C22×C8—96no—
94C22×C8#15711yescharacteristic, direct product factor
95C2×C42—96no—
96C2×C42—96no—
97C4×C8—916no—
98C23×C3—22no—
99C22×D3—66no—
100C22×D3—616no—
101C22×D3—66no—
102C2×C3×C4—26no—
103C2×C3×C4—26no—
104C2×Dic3—66no—
105C2×Dic3—66no—
106C4×D3—612no—
107C4×D3—66no—
108C4×D3—66no—
109C4×D3—66no—
110C4×D3—62no—
111C3×C8—28no—
112C3⋊C8—68no—
113C2×C32C2×C4×C816yescomplemented
114C2×C32C22×C4211yescharacteristic
115C3⋊D3C2×C4×C816yescomplemented
116C3⋊D3C23×C812yes—
117C24—91no—
118C22×C4—916no—
119C22×C4—912no—
120C22×C4—91no—
121C22×C4—93no—
122C22×C4—93no—
123C22×C4—93no—
124C22×C4—93no—
125C22×C4C2×#15711yescharacteristic
126C2×C8—94no—
127C2×C8—912no—
128C2×C8—912no—
129C2×C8—96no—
130C2×C8—94no—
131C2×C8—912no—
132C2×C8C2×#15716yesdirect product factor
133C42—94no—
134C42—912no—
135C22×C3—28no—
136C22×C3—26no—
137C2×D3—66no—
138C2×D3—62no—
139C2×D3—624no—
140C2×D3—624no—
141C3×C4—26no—
142C3×C4—22no—
143Dic3—66no—
144Dic3—62no—
145C32C22×C4×C811yescharacteristic, complemented, Sylow
146C23—98no—
147C23—93no—
148C23—93no—
149C23C4×#15711yescharacteristic
150C2×C4—98no—
151C2×C4—948no—
152C2×C4—93no—
153C2×C4—93no—
154C2×C4—93no—
155C2×C4—93no—
156C2×C4—96no—
157C2×C4—91no—
158C2×C4—93no—
159C2×C4C4×#15713yes—
160C2×C4C22×#15713yes—
161C8—98no—
162C8—94no—
163C8C22×#15714yesdirect product factor
164C2×C3—22no—
165C2×C3—212no—
166D3—64no—
167D3—612no—
168C22—91no—
169C22—93no—
170C22—912no—
171C22—912no—
172C22C8×#15714yesdirect product factor
173C22C2×C4×#15713yes—
174C4—916no—
175C4—91no—
176C4—93no—
177C4C2×C4×#15713yes—
178C4C23×#15711yescharacteristic
179C3—22no—
180C2—92no—
181C2—96no—
182C2C2×C8×#15716yesdirect product factor
183C2C22×C4×#15711yescharacteristic
subgroupG/H
center, hypercenterC22×C8#157
commutator, hypocenterC32C22×C4×C8
FrattiniC4C23×#157
FittingC22×C32×C8C4
socleC23×C32C42
prime radicalC23×C3⋊D3C2×C4
cosocleC4×C3⋊D3C24
LCSG ▷ C32
UCSC1 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C8×#157C2direct (N × H)
7. C22×#622C4semidirect
10. C2×#3787C4semidirect
12. C22×C32×C8C4semidirect
13. C22×C3⋊(C3⋊C8)C4semidirect
14. C2×C8×C3⋊D3C4semidirect
16. C8×#157C22direct (N × H)
19. C22×#157C8direct (N × H)
27. C2×#622C2×C4semidirect
30. #3787C2×C4semidirect
32. C2×C32×C8C2×C4semidirect
33. C2×C3⋊(C3⋊C8)C2×C4semidirect
34. C8×C3⋊D3C2×C4semidirect
46. C2×#157C2×C8direct (N × H)
57. #622C22×C4semidirect
58. C32×C8C22×C4semidirect
59. C3⋊(C3⋊C8)C22×C4semidirect
75. C22×C32C4×C8semidirect
77. C2×C3⋊D3C4×C8semidirect
81. #157C22×C8direct (N × H)
94. C22×C8#157direct (N × H)
113. C2×C32C2×C4×C8semidirect
115. C3⋊D3C2×C4×C8semidirect
132. C2×C8C2×#157direct (N × H)
145. C32C22×C4×C8semidirect
163. C8C22×#157direct (N × H)
172. C22C8×#157direct (N × H)
182. C2C2×C8×#157direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C22×#37872
C22×C8×C3⋊D32
C2×C8×#1572
C22×C4×C89