Finite Group Databasebeta

← C2×#63730 #10593320

Subgroups — C2×#63730 #10593320

Order 576.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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×#3797C211yesmaximal, characteristic
2C2×C4⋊#157C211yesmaximal, characteristic
3C2×#3710C211yesmaximal, characteristic
4#63730C214yesmaximal, direct product factor
5C22×#157—21no—
6C2×C4×C3⋊D3C2211yescharacteristic
7C2×C3×Dic6—21no—
8C2×#627C412yescomplemented
9C2×#624—21no—
10#3797—21no—
11#3797—21no—
12#3797C412yescomplemented
13#3797C2212yes—
14C4⋊#157—21no—
15C4⋊#157C2212yes—
16C2×C3×C3⋊C8—21no—
17#3710—21no—
18#3710C2212yes—
19C2×D3×Q8—61no—
20C2×D3×C8—61no—
21C22×C3⋊D3D411yescharacteristic
22C2×#157—22no—
23C2×#157—42no—
24C2×C32×C4D411yescharacteristic
25C2×C3⋊Dic3C2×C411yescharacteristic
26C4×C3⋊D3C2×C411yescharacteristic
27C4×C3⋊D3D411yescharacteristic
28C4×C3⋊D3D411yescharacteristic
29C4×C3⋊D3C2311yescharacteristic
30C2×C3×Dic3—22no—
31C3×Dic6—22no—
32C3×Dic6—22no—
33#627—22no—
34#627C2×C414yescomplemented
35#624—22no—
36#624—22no—
37C3×C3⋊C8—22no—
38C2×#103—91nomaximal, Sylow
39C2×C3×Q8—61no—
40D3×Q8—62no—
41D3×Q8—62no—
42D3×Q8—62no—
43D3×Q8—62no—
44C2×C4×D3—61no—
45C2×C4×D3—61no—
46C2×C4×D3—62no—
47C2×Dic6—21no—
48C2×Dic6—62no—
49C2×C3×C8—61no—
50C2×C3⋊C8—21no—
51D3×C8—62no—
52D3×C8—62no—
53C22×C32C22⋊C411yescharacteristic
54C2×C3⋊D3C22⋊C411yescharacteristic
55C2×C3⋊D3SD1612yes—
56C2×C3⋊D3Q1612yes—
57C2×C3⋊D3C2×D411yescharacteristic
58#157—42no—
59C32×C4C22⋊C411yescharacteristic
60C32×C4C2×D411yescharacteristic
61C3⋊Dic3C22⋊C411yescharacteristic
62C3⋊Dic3C22×C411yescharacteristic
63C3×Dic3—24no—
64C22×Q8—91no—
65C22×C8—91no—
66C2×C4⋊C4—91no—
67#103—94no—
68C22×D3—61no—
69C22×D3—61no—
70C3×Q8—62no—
71C3×Q8—62no—
72C2×C3×C4—21no—
73C2×C3×C4—21no—
74C2×C3×C4—62no—
75C2×Dic3—22no—
76C2×Dic3—61no—
77C2×Dic3—61no—
78C4×D3—61no—
79C4×D3—61no—
80C4×D3—61no—
81C4×D3—61no—
82C4×D3—61no—
83C4×D3—61no—
84C4×D3—61no—
85C4×D3—61no—
86C4×D3—64no—
87C4×D3—64no—
88Dic6—22no—
89Dic6—22no—
90Dic6—64no—
91Dic6—64no—
92C3×C8—62no—
93C3⋊C8—22no—
94C2×C32#10312yescomplemented
95C2×C32C2×C22⋊C411yescharacteristic
96C3⋊D3#10312yescomplemented
97C3⋊D3C2×SD1611yescharacteristic
98C3⋊D3C2×Q1611yescharacteristic
99C2×Q8—61no—
100C2×Q8—92no—
101C2×Q8—92no—
102C2×Q8—92no—
103C2×Q8—181no—
104C2×Q8—181no—
105C22×C4—91no—
106C22×C4—181no—
107C22×C4—181no—
108C2×C8—61no—
109C2×C8—92no—
110C2×C8—181no—
111C4⋊C4—92no—
112C4⋊C4—181no—
113C22×C3—21no—
114C22×C3—21no—
115C2×D3—61no—
116C2×D3—61no—
117C2×D3—61no—
118C2×D3—61no—
119C2×D3—62no—
120C2×D3—62no—
121C2×D3—62no—
122C2×D3—62no—
123C3×C4—21no—
124C3×C4—21no—
125C3×C4—21no—
126C3×C4—21no—
127C3×C4—64no—
128Dic3—24no—
129Dic3—61no—
130Dic3—61no—
131Dic3—61no—
132Dic3—61no—
133C32C2×#10311yescharacteristic, complemented, Sylow
134C23—91no—
135Q8—62no—
136Q8—62no—
137Q8—94no—
138Q8—182no—
139C2×C4—62no—
140C2×C4—91no—
141C2×C4—91no—
142C2×C4—91no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—182no—
146C2×C4—182no—
147C2×C4—182no—
148C2×C4—362no—
149C2×C4GO+(4,𝔽2)11yescharacteristic
150C8—62no—
151C2×C3—21no—
152C2×C3—21no—
153C2×C3—22no—
154C2×C3—22no—
155D3—62no—
156D3—62no—
157D3—61no—
158D3—61no—
159D3—61no—
160D3—61no—
161C22—91no—
162C22—91no—
163C22—92no—
164C22—92no—
165C22D32⋊C411yescharacteristic
166C4—64no—
167C4—91no—
168C4—91no—
169C4—362no—
170C4D32⋊C411yescharacteristic
171C4C2×GO+(4,𝔽2)11yescharacteristic
172C3—21no—
173C3—21no—
174C2—91no—
175C2—91no—
176C2—92no—
177C2#6373012yesdirect product factor
178C2C2×D32⋊C411yescharacteristic
subgroupG/H
centerC22D32⋊C4
commutatorC3⋊Dic3C22×C4
FrattiniC4C2×GO+(4,𝔽2)
FittingC2×C32×C4D4
socleC22×C32C22⋊C4
prime radicalC22×C3⋊D3D4
cosocleC4×C3⋊D3C23
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32C2×#103
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #63730C2direct (N × H)
8. C2×#627C4semidirect
12. #3797C4semidirect
34. #627C2×C4semidirect
94. C2×C32#103semidirect
96. C3⋊D3#103semidirect
133. C32C2×#103semidirect
177. C2#63730direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#37972
C2×C4⋊#1572
C2×#37102
#637302
C2×#1039