Finite Group Databasebeta

← C8×C4⋊#157 #11784256

Subgroups — C8×C4⋊#157 #11784256

Order 1152.

458 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 126 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
2C4×C4⋊#157C211yesmaximal, characteristic
3#10593726C211yesmaximal, characteristic
4C4×C8×C3⋊D3C211yesmaximal, characteristic
5#10590181C212yesmaximal
6C2×C4⋊#157C412yes—
7C2×C4×#157C2212yes—
8C2×#3787C2212yes—
9C2×C8×C3⋊D3C2211yescharacteristic
10C2×C8×C3⋊D3C2211yescharacteristic
11C42×C3⋊D3C2211yescharacteristic
12#63781C412yes—
13#63779C412yescomplemented
14C4⋊#622C412yescomplemented
15C8×#157—24no—
16C32×C4×C8C411yescharacteristic, complemented
17C8×C3⋊Dic3C411yescharacteristic, complemented
18C8×C3⋊Dic3C411yescharacteristic, complemented
19C4×C3⋊(C3⋊C8)C411yescharacteristic, complemented
20C4×D3×C8—62no—
21C22×#157C2×C414yes—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×#622C2×C414yes—
26C4⋊#157C818yesdirect product factor
27C4×#157—22no—
28C4×#157—22no—
29#3787—22no—
30#3787—22no—
31C2×C32×C8C2×C411yescharacteristic
32C2×C32×C8C2×C411yescharacteristic
33C32×C42C2×C411yescharacteristic
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
38C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
39C8×C3⋊D3—21no—
40C8×C3⋊D3—21no—
41C8×C3⋊D3D412yes—
42C8×C3⋊D3Q812yes—
43C8×C4⋊C4—91nomaximal, Sylow
44C2×D3×C8—62no—
45C2×D3×C8—62no—
46C42×D3—62no—
47C3×C4×C8—22no—
48C8×Dic3—62no—
49C8×Dic3—62no—
50C4×C3⋊C8—62no—
51C22×C3⋊D3C22×C411yescharacteristic
52C2×#157—24no—
53C2×#157—24no—
54C2×#157C2×C818yes—
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—21no—
69C32×C8C4⋊C412yescomplemented
70C3⋊(C3⋊C8)—21no—
71C3⋊(C3⋊C8)C4⋊C412yescomplemented
72C2×C4⋊C8—91no—
73C2×C4×C8—91no—
74C2×C4×C8—92no—
75C4×C4⋊C4—91no—
76#336—92no—
77C2×C4×D3—62no—
78C2×C4×D3—62no—
79C2×C4×D3—62no—
80C2×C3×C8—22no—
81C2×C3×C8—22no—
82C3×C42—22no—
83C4×Dic3—62no—
84C4×Dic3—62no—
85C4×Dic3—62no—
86C2×C3⋊C8—62no—
87C2×C3⋊C8—62no—
88D3×C8—64no—
89D3×C8—64no—
90D3×C8—64no—
91D3×C8—64no—
92C22×C32C2×C4211yescharacteristic
93C2×C3⋊D3C4×D411yescharacteristic
94C2×C3⋊D3C4×Q811yescharacteristic
95C2×C3⋊D3C22×C812yes—
96C2×C3⋊D3#13112yes—
97#157—28no—
98C32×C4—21no—
99C32×C4C4×C812yescomplemented
100C32×C4C2×C4⋊C411yescharacteristic
101C32×C4#11711yescharacteristic
102C3⋊Dic3—21no—
103C3⋊Dic3C4×C812yescomplemented
104C3⋊Dic3C4×D411yescharacteristic
105C3⋊Dic3C4×Q811yescharacteristic
106C22×C8—91no—
107C22×C8—92no—
108C22×C8—91no—
109C2×C4⋊C4—92no—
110C2×C42—91no—
111C2×C42—92no—
112C4⋊C8—92no—
113C4⋊C8—92no—
114C4×C8—91no—
115C4×C8—91no—
116C4×C8—91no—
117C4×C8—184no—
118C4×C8#15711yescharacteristic, complemented
119#95—92no—
120C22×D3—62no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—62no—
127C4×D3—68no—
128C4×D3—62no—
129C4×D3—62no—
130C4×D3—62no—
131C4×D3—62no—
132C4×D3—68no—
133C3×C8—24no—
134C3×C8—24no—
135C3⋊C8—64no—
136C3⋊C8—64no—
137C2×C32C4×C4⋊C411yescharacteristic
138C2×C32C2×C4×C811yescharacteristic
139C2×C32#40511yescharacteristic
140C3⋊D3C8×D412yes—
141C3⋊D3C8×Q812yes—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4—94no—
145C22×C4—91no—
146C2×C8—91no—
147C2×C8—92no—
148C2×C8—92no—
149C2×C8—94no—
150C2×C8—91no—
151C2×C8—181no—
152C2×C8—181no—
153C2×C8—182no—
154C2×C8—182no—
155C2×C8C2×#15711yescharacteristic
156C2×C8C2×#15711yescharacteristic
157C4⋊C4—98no—
158C42—91no—
159C42—91no—
160C42—91no—
161C42—182no—
162C42—182no—
163C42C2×#15711yescharacteristic
164C22×C3—22no—
165C2×D3—62no—
166C2×D3—62no—
167C2×D3—64no—
168C2×D3—64no—
169C3×C4—24no—
170C3×C4—24no—
171C3×C4—22no—
172C3×C4—22no—
173Dic3—64no—
174Dic3—62no—
175Dic3—62no—
176Dic3—64no—
177C32C8×C4⋊C411yescharacteristic, complemented, Sylow
178C23—91no—
179C2×C4—91no—
180C2×C4—91no—
181C2×C4—94no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—98no—
187C2×C4—91no—
188C2×C4—182no—
189C2×C4—184no—
190C2×C4—184no—
191C2×C4C4×#15711yescharacteristic
192C2×C4C4×#15711yescharacteristic
193C2×C4C22×#15711yescharacteristic
194C8—21no—
195C8—92no—
196C8—184no—
197C8—181no—
198C8C4⋊#15712yesdirect product factor
199C2×C3—22no—
200C2×C3—22no—
201C2×C3—22no—
202D3—64no—
203D3—64no—
204C22—91no—
205C22—91no—
206C22—92no—
207C22—92no—
208C22C2×C4×#15711yescharacteristic
209C4—21no—
210C4—91no—
211C4—91no—
212C4—92no—
213C4—188no—
214C4—181no—
215C4C8×#15712yescomplemented
216C4C2×C4⋊#15711yescharacteristic
217C4#6428611yescharacteristic
218C3—22no—
219C2—92no—
220C2—92no—
221C2C4×C4⋊#15711yescharacteristic
222C2C2×C8×#15711yescharacteristic
223C2#1059376511yescharacteristic
subgroupG/H
centerC2×C8C2×#157
commutatorC2×C32C2×C4×C8
FrattiniC2×C4C22×#157
FittingC32×C4×C8C4
socleC22×C32C2×C42
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC4×C8#157
hypocenterC32C8×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ 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. C8×C3⋊Dic3C4semidirect
18. C8×C3⋊Dic3C4semidirect
19. C4×C3⋊(C3⋊C8)C4semidirect
26. C4⋊#157C8direct (N × H)
69. C32×C8C4⋊C4semidirect
71. C3⋊(C3⋊C8)C4⋊C4semidirect
99. C32×C4C4×C8semidirect
103. C3⋊Dic3C4×C8semidirect
118. C4×C8#157semidirect
177. C32C8×C4⋊C4semidirect
198. C8C4⋊#157direct (N × H)
215. 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
C4×C4⋊#1572
#105937262
C4×C8×C3⋊D32
#105901812
C8×C4⋊C49