Finite Group Databasebeta

← #10593318

Subgroups — #10593318

Order 576.

342 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 47 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×#3802C211yesmaximal, characteristic
2#64286C211yesmaximal, characteristic, complemented
3#63818C211yesmaximal, characteristic, complemented
4#63729C214yesmaximal, complemented
5C22×D32—21no—
6C2×C4×C3⋊D3C2211yescharacteristic
7C2×C3×D12—21no—
8C2×#625C412yescomplemented
9#3802—21no—
10#3802—21no—
11#3802C412yescomplemented
12#3802C2212yes—
13C22⋊#157—21no—
14C4⋊#157C2212yescomplemented
15C4×#157—21no—
16C3×#208—21no—
17#3712—21no—
18#3710C2212yescomplemented
19C2×D3×D4—61no—
20D3×M16—61no—
21C22×C3⋊D3D411yescharacteristic
22C22×C3×D3—22no—
23C2×D32—22no—
24C2×D32—22no—
25C2×D32—44no—
26C2×#157—22no—
27C2×C32×C4D411yescharacteristic
28C2×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊D3C2×C411yescharacteristic
30C4×C3⋊D3D411yescharacteristic
31C4×C3⋊D3D411yescharacteristic
32C4×C3⋊D3C2311yescharacteristic
33C3×D12—22no—
34C3×D12—22no—
35#625—22no—
36#625C2×C414yes—
37C3×C3⋊C8—22no—
38#418—91nomaximal, Sylow
39C23×D3—62no—
40C2×C3×D4—61no—
41C2×#67—62no—
42D3×D4—62no—
43D3×D4—62no—
44D3×D4—62no—
45D3×D4—62no—
46C2×D12—21no—
47C2×C4×D3—61no—
48C2×C4×D3—61no—
49C3×M16—61no—
50#208—21no—
51ΓL(1,𝔽25)—62no—
52D3×C8—62no—
53C22×C32C22⋊C411yescharacteristic
54C2×C3⋊D3—22no—
55C2×C3⋊D3C22⋊C411yescharacteristic
56C2×C3⋊D3C2×D411yescharacteristic
57C2×C3×D3—24no—
58C2×C3×D3—44no—
59D32—44no—
60D32—44no—
61#157—42no—
62C32×C4C22⋊C411yescharacteristic
63C32×C4C2×D411yescharacteristic
64C3⋊Dic3C22⋊C411yescharacteristic
65C3⋊Dic3C22×C411yescharacteristic
66C22×D4—91no—
67C2×M16—91no—
68#117—91no—
69#102—94no—
70C23×C3—62no—
71C22×D3—22no—
72C22×D3—61no—
73C22×D3—61no—
74C22×D3—64no—
75C22×D3—64no—
76C22×D3—128no—
77C3×D4—62no—
78C3×D4—62no—
79C2×C3×C4—21no—
80C2×C3×C4—21no—
81#67—64no—
82#67—64no—
83C2×Dic3—61no—
84C2×Dic3—61no—
85D12—22no—
86D12—22no—
87C4×D3—61no—
88C4×D3—61no—
89C4×D3—61no—
90C4×D3—61no—
91C4×D3—61no—
92C4×D3—61no—
93C4×D3—61no—
94C4×D3—61no—
95C3×C8—62no—
96C3⋊C8—22no—
97C2×C32—21no—
98C2×C32C2×C22⋊C411yescharacteristic
99C3⋊D3—21no—
100C3⋊D3AGL(1,ℤ/8)12yes—
101C3×D3—44no—
102C24—181no—
103C2×D4—61no—
104C2×D4—92no—
105C2×D4—92no—
106C2×D4—92no—
107C2×D4—181no—
108C2×D4—181no—
109C22×C4—91no—
110M16—61no—
111M16—181no—
112C2×C8—92no—
113C4⋊C4—92no—
114C22⋊C4—181no—
115C42—181no—
116C22×C3—21no—
117C22×C3—21no—
118C22×C3—64no—
119C22×C3—124no—
120C2×D3—24no—
121C2×D3—44no—
122C2×D3—61no—
123C2×D3—61no—
124C2×D3—61no—
125C2×D3—61no—
126C2×D3—64no—
127C2×D3—122no—
128C2×D3—128no—
129C2×D3—128no—
130C3×C4—21no—
131C3×C4—21no—
132C3×C4—21no—
133C3×C4—21no—
134Dic3—61no—
135Dic3—61no—
136Dic3—61no—
137Dic3—61no—
138C32#41811yescharacteristic, complemented, Sylow
139C23—62no—
140C23—91no—
141C23—182no—
142C23—182no—
143C23—364no—
144D4—62no—
145D4—62no—
146D4—94no—
147D4—182no—
148C2×C4—91no—
149C2×C4—91no—
150C2×C4—91no—
151C2×C4—91no—
152C2×C4—91no—
153C2×C4—182no—
154C2×C4GO+(4,𝔽2)11yescharacteristic
155C8—62no—
156C2×C3—22no—
157C2×C3—21no—
158C2×C3—21no—
159C2×C3—41no—
160C2×C3—124no—
161D3—44no—
162D3—62no—
163D3—62no—
164D3—62no—
165D3—121no—
166C22—64no—
167C22—91no—
168C22—91no—
169C22—124no—
170C22—182no—
171C22—364no—
172C22—364no—
173C22D32⋊C411yescharacteristic
174C4—91no—
175C4—91no—
176C4—362no—
177C4D32⋊C411yescharacteristic
178C4C2×GO+(4,𝔽2)11yescharacteristic
179C3—21no—
180C3—21no—
181C2—21no—
182C2—92no—
183C2—124no—
184C2—181no—
185C2C2×D32⋊C411yescharacteristic
subgroupG/H
centerC2C2×D32⋊C4
commutatorC3⋊Dic3C22×C4
FrattiniC4C2×GO+(4,𝔽2)
FittingC2×C32×C4D4
socleC2×C32C2×C22⋊C4
prime radicalC2×#3802C2
cosocleC4×C3⋊D3C23
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#418
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #64286C2semidirect
3. #63818C2semidirect
4. #63729C2semidirect
8. C2×#625C4semidirect
11. #3802C4semidirect
14. C4⋊#157C22semidirect
18. #3710C22semidirect
138. C32#418semidirect

Maximal subgroups

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

subgroupindex
C2×#38022
#642862
#638182
#637292
#4189