Finite Group Databasebeta

← C4×#63769 #11784466

Subgroups — C4×#63769 #11784466

Order 1152.

442 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 110 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×#63769C212yesmaximal
2C4×C4⋊#157C212yesmaximal
3C4×C8×C3⋊D3C211yesmaximal, characteristic
4#10590182C212yesmaximal
5C2×C4⋊#157C2214yes—
6C2×C4×#157—22no—
7C2×C8×C3⋊D3C2211yescharacteristic
8C2×C8×C3⋊D3C2211yescharacteristic
9C42×C3⋊D3C2211yescharacteristic
10#63781—22no—
11#63769C418yesdirect product factor
12C32×C4×C8C411yescharacteristic, complemented
13C8×C3⋊Dic3C411yescharacteristic, complemented
14C8×C3⋊Dic3C411yescharacteristic, complemented
15C4×C3⋊(C3⋊C8)C411yescharacteristic, complemented
16C4×D3×C8—62no—
17C22×#157—24no—
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C2×C4×C3⋊D3C2311yescharacteristic
21C4⋊#157—24no—
22C4⋊#157C2×C418yes—
23C4×#157—44no—
24C2×C32×C8C2×C411yescharacteristic
25C2×C32×C8C2×C411yescharacteristic
26C32×C42C2×C411yescharacteristic
27C4×C3⋊Dic3C2×C411yescharacteristic
28C4×C3⋊Dic3Q811yescharacteristic
29C4×C3⋊Dic3Q811yescharacteristic
30C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
31C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
32C8×C3⋊D3—22no—
33C8×C3⋊D3C2×C414yes—
34C4×#107—91nomaximal, Sylow
35C2×D3×C8—62no—
36C2×D3×C8—62no—
37C42×D3—62no—
38C3×C4×C8—22no—
39C8×Dic3—62no—
40C8×Dic3—62no—
41C4×C3⋊C8—62no—
42C22×C3⋊D3C2×D411yescharacteristic
43C2×#157—28no—
44C2×#157—44no—
45C2×#157—44no—
46C2×C32×C4C4⋊C411yescharacteristic
47C2×C32×C4C4⋊C411yescharacteristic
48C2×C32×C4C22×C411yescharacteristic
49C2×C3⋊Dic3C4⋊C411yescharacteristic
50C2×C3⋊Dic3C4⋊C411yescharacteristic
51C2×C3⋊Dic3C2×Q811yescharacteristic
52C4×C3⋊D3—22no—
53C4×C3⋊D3D812yes—
54C4×C3⋊D3Q1612yes—
55C4×C3⋊D3C22×C412yes—
56C4×C3⋊D3#4112yes—
57C32×C8—21no—
58C32×C8C4212yescomplemented
59C3⋊(C3⋊C8)—21no—
60C3⋊(C3⋊C8)C4212yescomplemented
61C2×#107—92no—
62C2×C4×C8—91no—
63C4×C4⋊C4—92no—
64#340—92no—
65C2×C4×D3—62no—
66C2×C4×D3—62no—
67C2×C4×D3—62no—
68C2×C3×C8—22no—
69C2×C3×C8—22no—
70C3×C42—22no—
71C4×Dic3—62no—
72C4×Dic3—62no—
73C4×Dic3—62no—
74C2×C3⋊C8—62no—
75C2×C3⋊C8—62no—
76D3×C8—68no—
77D3×C8—68no—
78C22×C32C2×C4⋊C411yescharacteristic
79C2×C3⋊D3C4×D412yes—
80C2×C3⋊D3C2×D811yescharacteristic
81C2×C3⋊D3C2×Q1611yescharacteristic
82C2×C3⋊D3#13512yes—
83#157—48no—
84C32×C4—21no—
85C32×C4#10712yescomplemented
86C32×C4C2×C4211yescharacteristic
87C32×C4#11711yescharacteristic
88C3⋊Dic3—21no—
89C3⋊Dic3#10712yescomplemented
90C3⋊Dic3C4×Q812yes—
91C22×C8—91no—
92C22×C8—91no—
93C2×C4⋊C4—94no—
94C2×C42—91no—
95C2×C42—182no—
96#107—98no—
97C4×C8—91no—
98C4×C8—91no—
99C4×C8—91no—
100C4×C8#15711yescharacteristic, complemented
101#95—182no—
102C22×D3—62no—
103C2×C3×C4—22no—
104C2×C3×C4—22no—
105C2×C3×C4—22no—
106C2×Dic3—62no—
107C2×Dic3—62no—
108C2×Dic3—62no—
109C4×D3—64no—
110C4×D3—64no—
111C4×D3—64no—
112C4×D3—64no—
113C4×D3—68no—
114C3×C8—24no—
115C3×C8—24no—
116C3⋊C8—64no—
117C3⋊C8—64no—
118C2×C32C4×C4⋊C411yescharacteristic
119C2×C32C2×#10711yescharacteristic
120C2×C32#42711yescharacteristic
121C3⋊D3C4×D812yes—
122C3⋊D3C4×Q1612yes—
123C22×C4—91no—
124C22×C4—91no—
125C22×C4—91no—
126C22×C4—184no—
127C2×C8—91no—
128C2×C8—94no—
129C2×C8—91no—
130C2×C8—182no—
131C2×C8C2×#15711yescharacteristic
132C2×C8C2×#15711yescharacteristic
133C4⋊C4—98no—
134C4⋊C4—184no—
135C42—91no—
136C42—91no—
137C42—91no—
138C42—364no—
139C42C2×#15711yescharacteristic
140C22×C3—22no—
141C2×D3—64no—
142C2×D3—62no—
143C2×D3—62no—
144C2×D3—64no—
145C3×C4—24no—
146C3×C4—24no—
147C3×C4—22no—
148C3×C4—22no—
149Dic3—64no—
150Dic3—64no—
151Dic3—64no—
152C32C4×#10711yescharacteristic, complemented, Sylow
153C23—91no—
154C2×C4—91no—
155C2×C4—91no—
156C2×C4—92no—
157C2×C4—92no—
158C2×C4—92no—
159C2×C4—92no—
160C2×C4—91no—
161C2×C4—182no—
162C2×C4—188no—
163C2×C4—364no—
164C2×C4—364no—
165C2×C4C4⋊#15711yescharacteristic
166C2×C4C4⋊#15711yescharacteristic
167C2×C4C22×#15711yescharacteristic
168C8—21no—
169C8—92no—
170C8—181no—
171C8C4×#15712yescomplemented
172C2×C3—22no—
173C2×C3—22no—
174C2×C3—22no—
175D3—64no—
176D3—64no—
177C22—92no—
178C22—91no—
179C22—91no—
180C22—92no—
181C22C2×C4⋊#15711yescharacteristic
182C4—21no—
183C4—92no—
184C4—92no—
185C4—181no—
186C4—368no—
187C4#6376912yesdirect product factor
188C4C2×C4×#15711yescharacteristic
189C4#6428611yescharacteristic
190C3—22no—
191C2—92no—
192C2—92no—
193C2C4×C4⋊#15711yescharacteristic
194C2C2×#6376911yescharacteristic
195C2#1059376811yescharacteristic
subgroupG/H
centerC2×C4C4⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×C4×C8C4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4×C8#157
hypocenterC32C4×#107
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
11. #63769C4direct (N × H)
12. C32×C4×C8C4semidirect
13. C8×C3⋊Dic3C4semidirect
14. C8×C3⋊Dic3C4semidirect
15. C4×C3⋊(C3⋊C8)C4semidirect
58. C32×C8C42semidirect
60. C3⋊(C3⋊C8)C42semidirect
85. C32×C4#107semidirect
89. C3⋊Dic3#107semidirect
100. C4×C8#157semidirect
152. C32C4×#107semidirect
171. C8C4×#157semidirect
187. C4#63769direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#637692
C4×C4⋊#1572
C4×C8×C3⋊D32
#105901822
C4×#1079