Finite Group Databasebeta

← C4×#63768 #11784439

Subgroups — C4×#63768 #11784439

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×#63768C212yesmaximal
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#63768C418yesdirect 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×#106—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⋊D3SD1614yes—
54C4×C3⋊D3C22×C412yes—
55C4×C3⋊D3#4112yes—
56C32×C8—21no—
57C32×C8C4212yescomplemented
58C3⋊(C3⋊C8)—21no—
59C3⋊(C3⋊C8)C4212yescomplemented
60C2×#106—92no—
61C2×C4×C8—91no—
62C4×C4⋊C4—92no—
63#340—92no—
64C2×C4×D3—62no—
65C2×C4×D3—62no—
66C2×C4×D3—62no—
67C2×C3×C8—22no—
68C2×C3×C8—22no—
69C3×C42—22no—
70C4×Dic3—62no—
71C4×Dic3—62no—
72C4×Dic3—62no—
73C2×C3⋊C8—62no—
74C2×C3⋊C8—62no—
75D3×C8—68no—
76D3×C8—68no—
77C22×C32C2×C4⋊C411yescharacteristic
78C2×C3⋊D3C4×D412yes—
79C2×C3⋊D3C2×SD1612yes—
80C2×C3⋊D3#13512yes—
81#157—48no—
82C32×C4—21no—
83C32×C4#10612yescomplemented
84C32×C4C2×C4211yescharacteristic
85C32×C4#11711yescharacteristic
86C3⋊Dic3—21no—
87C3⋊Dic3#10612yescomplemented
88C3⋊Dic3C4×Q812yes—
89C22×C8—91no—
90C22×C8—91no—
91C2×C4⋊C4—94no—
92C2×C42—91no—
93C2×C42—182no—
94#106—98no—
95C4×C8—91no—
96C4×C8—91no—
97C4×C8—91no—
98C4×C8#15711yescharacteristic, complemented
99#95—182no—
100C22×D3—62no—
101C2×C3×C4—22no—
102C2×C3×C4—22no—
103C2×C3×C4—22no—
104C2×Dic3—62no—
105C2×Dic3—62no—
106C2×Dic3—62no—
107C4×D3—68no—
108C4×D3—64no—
109C4×D3—64no—
110C4×D3—68no—
111C3×C8—24no—
112C3×C8—24no—
113C3⋊C8—64no—
114C3⋊C8—64no—
115C2×C32C4×C4⋊C411yescharacteristic
116C2×C32C2×#10611yescharacteristic
117C2×C32#42711yescharacteristic
118C3⋊D3C4×SD1614yes—
119C22×C4—91no—
120C22×C4—91no—
121C22×C4—91no—
122C22×C4—184no—
123C2×C8—91no—
124C2×C8—94no—
125C2×C8—91no—
126C2×C8—182no—
127C2×C8C2×#15711yescharacteristic
128C2×C8C2×#15711yescharacteristic
129C4⋊C4—98no—
130C4⋊C4—184no—
131C42—91no—
132C42—91no—
133C42—91no—
134C42—364no—
135C42C2×#15711yescharacteristic
136C22×C3—22no—
137C2×D3—64no—
138C2×D3—64no—
139C2×D3—64no—
140C3×C4—24no—
141C3×C4—24no—
142C3×C4—22no—
143C3×C4—22no—
144Dic3—64no—
145Dic3—64no—
146Dic3—64no—
147C32C4×#10611yescharacteristic, complemented, Sylow
148C23—91no—
149C2×C4—91no—
150C2×C4—91no—
151C2×C4—94no—
152C2×C4—92no—
153C2×C4—92no—
154C2×C4—91no—
155C2×C4—182no—
156C2×C4—188no—
157C2×C4—364no—
158C2×C4—364no—
159C2×C4C4⋊#15711yescharacteristic
160C2×C4C4⋊#15711yescharacteristic
161C2×C4C22×#15711yescharacteristic
162C8—21no—
163C8—92no—
164C8—181no—
165C8C4×#15712yescomplemented
166C2×C3—22no—
167C2×C3—22no—
168C2×C3—22no—
169D3—68no—
170C22—92no—
171C22—92no—
172C22—92no—
173C22C2×C4⋊#15711yescharacteristic
174C4—21no—
175C4—92no—
176C4—92no—
177C4—181no—
178C4—368no—
179C4#6376812yesdirect product factor
180C4C2×C4×#15711yescharacteristic
181C4#6428611yescharacteristic
182C3—22no—
183C2—94no—
184C2C4×C4⋊#15711yescharacteristic
185C2C2×#6376811yescharacteristic
186C2#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×#106
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. #63768C4direct (N × H)
12. C32×C4×C8C4semidirect
13. C8×C3⋊Dic3C4semidirect
14. C8×C3⋊Dic3C4semidirect
15. C4×C3⋊(C3⋊C8)C4semidirect
57. C32×C8C42semidirect
59. C3⋊(C3⋊C8)C42semidirect
83. C32×C4#106semidirect
87. C3⋊Dic3#106semidirect
98. C4×C8#157semidirect
147. C32C4×#106semidirect
165. C8C4×#157semidirect
179. C4#63768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#637682
C4×C4⋊#1572
C4×C8×C3⋊D32
#105901822
C4×#1069