Finite Group Databasebeta

← C4⋊C8×#157 #11784170

Subgroups — C4⋊C8×#157 #11784170

Order 1152.

454 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 136 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×C8×#157C212yesmaximal
2C42×#157C211yesmaximal, characteristic
3#10593726C211yesmaximal, characteristic
4C3⋊D3×C4⋊C8C211yesmaximal, characteristic
5#10590181C212yesmaximal
6C2×C4×#157C412yes—
7C2×C4×#157C412yes—
8C2×C4×#157C2211yescharacteristic
9C2×C4×#157C2211yescharacteristic
10C2×#3787C2212yes—
11C2×C8×C3⋊D3C2212yes—
12C42×C3⋊D3C2211yescharacteristic
13#63779C412yescomplemented
14C4⋊#622C412yescomplemented
15C8×#157—24no—
16C32×C4⋊C8C411yescharacteristic, complemented
17#63641C412yescomplemented
18C4⋊(C3⋊(C3⋊C8))C411yescharacteristic, complemented
19D3×C4⋊C8—62no—
20C22×#157C2×C412yes—
21C22×#157C2×C412yes—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×#622C2×C414yes—
26C4×#157—24no—
27C4×#157—21no—
28C4×#157—21no—
29C4×#157C818yescomplemented
30C4×#157D412yes—
31C4×#157Q812yes—
32#3787—22no—
33#3787—22no—
34C2×C32×C8C2×C412yes—
35C32×C42C2×C411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C2×C3⋊(C3⋊C8)C2×C412yes—
40C8×C3⋊D3—22no—
41C8×C3⋊D3—22no—
42C4×C4⋊C8—91nomaximal, Sylow
43C2×D3×C8—64no—
44C42×D3—62no—
45C3×C4⋊C8—22no—
46Dic3⋊C8—64no—
47C4⋊(C3⋊C8)—62no—
48C22×C3⋊D3C22×C411yescharacteristic
49C2×#157—22no—
50C2×#157—22no—
51C2×#157C4⋊C414yes—
52C2×#157C2×C814yes—
53C2×#157C2×C814yes—
54C2×#157M1614yes—
55C2×C32×C4C4211yescharacteristic
56C2×C32×C4C4211yescharacteristic
57C2×C32×C4C22×C411yescharacteristic
58C2×C3⋊Dic3C4211yescharacteristic
59C2×C3⋊Dic3C4211yescharacteristic
60C2×C3⋊Dic3C22×C411yescharacteristic
61C4×C3⋊D3—22no—
62C4×C3⋊D3C2×C814yes—
63C4×C3⋊D3C2×D411yescharacteristic
64C4×C3⋊D3C2×Q811yescharacteristic
65C4×C3⋊D3#4111yescharacteristic
66C4×C3⋊D3#4111yescharacteristic
67#622—24no—
68C32×C8—22no—
69C3⋊(C3⋊C8)—22no—
70C2×C4⋊C8—91no—
71C2×C4⋊C8—91no—
72C2×C4×C8—92no—
73C43—91no—
74#336—92no—
75C2×C4×D3—62no—
76C2×C4×D3—62no—
77C2×C4×D3—62no—
78C2×C3×C8—24no—
79C3×C42—22no—
80C4×Dic3—62no—
81C4×Dic3—62no—
82C4×Dic3—62no—
83C2×C3⋊C8—64no—
84D3×C8—124no—
85D3×C8—124no—
86C22×C32C2×C4211yescharacteristic
87C2×C3⋊D3C2×C4⋊C411yescharacteristic
88C2×C3⋊D3#11711yescharacteristic
89C2×C3⋊D3C22×C812yes—
90C2×C3⋊D3C2×M1612yes—
91#157—24no—
92#157C4⋊C818yesdirect product factor
93C32×C4—21no—
94C32×C4C4×C812yescomplemented
95C32×C4C4×D411yescharacteristic
96C32×C4C4×Q811yescharacteristic
97C3⋊Dic3—21no—
98C3⋊Dic3C4×C812yescomplemented
99C3⋊Dic3C4×D411yescharacteristic
100C3⋊Dic3C4×Q811yescharacteristic
101C22×C8—92no—
102C22×C8—92no—
103C2×C42—92no—
104C2×C42—91no—
105C2×C42—91no—
106C2×C42—92no—
107C2×C42—91no—
108C4⋊C8—92no—
109C4⋊C8—92no—
110C4⋊C8—92no—
111C4⋊C8—91no—
112C4⋊C8#15711yescharacteristic, direct product factor
113C4×C8—184no—
114C22×D3—62no—
115C2×C3×C4—22no—
116C2×C3×C4—22no—
117C2×C3×C4—22no—
118C2×Dic3—62no—
119C2×Dic3—62no—
120C2×Dic3—62no—
121C4×D3—68no—
122C4×D3—62no—
123C4×D3—62no—
124C4×D3—62no—
125C4×D3—62no—
126C4×D3—124no—
127C3×C8—44no—
128C3⋊C8—124no—
129C2×C32C4×C4⋊C411yescharacteristic
130C2×C32C2×C4×C811yescharacteristic
131C2×C32C4×M1611yescharacteristic
132C3⋊D3C2×C4⋊C812yes—
133C3⋊D3#43112yes—
134C22×C4—92no—
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—92no—
138C22×C4—91no—
139C2×C8—94no—
140C2×C8—92no—
141C2×C8—182no—
142C2×C8—182no—
143C2×C8—182no—
144C2×C8—182no—
145C2×C8C2×#15712yes—
146C42—92no—
147C42—98no—
148C42—92no—
149C42—91no—
150C42—91no—
151C42—91no—
152C42—184no—
153C42—181no—
154C42—181no—
155C42C2×#15711yescharacteristic
156C22×C3—22no—
157C2×D3—62no—
158C2×D3—62no—
159C2×D3—64no—
160C2×D3—64no—
161C3×C4—24no—
162C3×C4—22no—
163C3×C4—22no—
164C3×C4—42no—
165Dic3—64no—
166Dic3—62no—
167Dic3—62no—
168Dic3—122no—
169C32C4×C4⋊C811yescharacteristic, complemented, Sylow
170C23—91no—
171C2×C4—94no—
172C2×C4—94no—
173C2×C4—94no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—94no—
177C2×C4—91no—
178C2×C4—91no—
179C2×C4—91no—
180C2×C4—91no—
181C2×C4—94no—
182C2×C4—91no—
183C2×C4—182no—
184C2×C4—182no—
185C2×C4—182no—
186C2×C4C4×#15711yescharacteristic
187C2×C4C4×#15711yescharacteristic
188C2×C4C22×#15711yescharacteristic
189C8—22no—
190C8—184no—
191C8—182no—
192C2×C3—22no—
193C2×C3—22no—
194C2×C3—22no—
195D3—64no—
196D3—64no—
197C22—91no—
198C22—91no—
199C22—92no—
200C22—92no—
201C22C2×C4×#15711yescharacteristic
202C4—21no—
203C4—98no—
204C4—91no—
205C4—91no—
206C4—92no—
207C4—184no—
208C4—181no—
209C4C8×#15712yescomplemented
210C4D4×#15711yescharacteristic
211C4Q8×#15711yescharacteristic
212C3—22no—
213C2—92no—
214C2—92no—
215C2C4⋊C4×#15711yescharacteristic
216C2C2×C8×#15711yescharacteristic
217C2M16×#15711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutatorC2×C32C2×C4×C8
FittingC32×C4⋊C8C4
socleC22×C32C2×C42
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C8#157
hypocenterC32C4×C4⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
13. #63779C4semidirect
14. C4⋊#622C4semidirect
16. C32×C4⋊C8C4semidirect
17. #63641C4semidirect
18. C4⋊(C3⋊(C3⋊C8))C4semidirect
29. C4×#157C8semidirect
92. #157C4⋊C8direct (N × H)
94. C32×C4C4×C8semidirect
98. C3⋊Dic3C4×C8semidirect
112. C4⋊C8#157direct (N × H)
169. C32C4×C4⋊C8semidirect
209. C4C8×#157semidirect

Maximal subgroups

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

subgroupindex
C2×C8×#1572
C42×#1572
#105937262
C3⋊D3×C4⋊C82
#105901812
C4×C4⋊C89