Finite Group Databasebeta

← #10593312

Subgroups — #10593312

Order 576.

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

normal subgroups only

This group has 338 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#64283C211yesmaximal, characteristic, complemented
3#63818C211yesmaximal, characteristic, complemented
4#63727C214yesmaximal, complemented
5C22×D32C412yes—
6C2×C4×C3⋊D3C2211yescharacteristic
7C2×C3×D12—21no—
8C2×#625—21no—
9#3802—21no—
10#3802—21no—
11#3802C412yes—
12#3802C2212yes—
13#3792—21no—
14#3788C2212yescomplemented
15#3787—21no—
16C3×#208—21no—
17#3712C2212yescomplemented
18#3710—21no—
19C2×D3×D4—61no—
20D3×M16—61no—
21C22×C3⋊D3C2×C411yescharacteristic
22C22×C3×D3—22no—
23C2×D32—22no—
24C2×D32—44no—
25C2×D32C2×C414yes—
26C2×C32×C4D411yescharacteristic
27C2×C3⋊Dic3D411yescharacteristic
28C4×C3⋊D3C2×C411yescharacteristic
29C4×C3⋊D3D411yescharacteristic
30C4×C3⋊D3D411yescharacteristic
31C4×C3⋊D3C2311yescharacteristic
32C3×D12—22no—
33C3×D12—22no—
34#625—22no—
35#625—22no—
36#622—22no—
37C3×C3⋊C8—22no—
38C2×#100—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⋊D3C22×C411yescharacteristic
57C2×C3×D3—24no—
58C2×C3×D3—44no—
59D32—44no—
60D32—44no—
61C32×C4C22⋊C411yescharacteristic
62C32×C4C2×D411yescharacteristic
63C3⋊Dic3C22⋊C411yescharacteristic
64C3⋊Dic3C2×D411yescharacteristic
65C22×D4—91no—
66C2×M16—91no—
67C2×M16—91no—
68#100—94no—
69C23×C3—62no—
70C22×D3—22no—
71C22×D3—64no—
72C22×D3—61no—
73C22×D3—61no—
74C22×D3—64no—
75C22×D3—128no—
76C3×D4—62no—
77C3×D4—62no—
78C2×C3×C4—21no—
79C2×C3×C4—21no—
80#67—64no—
81#67—64no—
82C2×Dic3—61no—
83C2×Dic3—61no—
84D12—22no—
85D12—22no—
86C4×D3—61no—
87C4×D3—61no—
88C4×D3—61no—
89C4×D3—61no—
90C4×D3—61no—
91C4×D3—61no—
92C4×D3—61no—
93C4×D3—61no—
94C3×C8—62no—
95C3⋊C8—22no—
96C2×C32—21no—
97C2×C32C2×C22⋊C411yescharacteristic
98C3⋊D3—21no—
99C3⋊D3#10012yescomplemented
100C3×D3—44no—
101C24—92no—
102C2×D4—61no—
103C2×D4—92no—
104C2×D4—92no—
105C2×D4—181no—
106C2×D4—181no—
107C2×D4—181no—
108C22×C4—91no—
109M16—61no—
110M16—92no—
111M16—92no—
112M16—181no—
113C2×C8—181no—
114C2×C8—181no—
115C22×C3—21no—
116C22×C3—21no—
117C22×C3—64no—
118C22×C3—124no—
119C2×D3—24no—
120C2×D3—44no—
121C2×D3—61no—
122C2×D3—61no—
123C2×D3—61no—
124C2×D3—61no—
125C2×D3—64no—
126C2×D3—122no—
127C2×D3—128no—
128C2×D3—128no—
129C3×C4—21no—
130C3×C4—21no—
131C3×C4—21no—
132C3×C4—21no—
133Dic3—61no—
134Dic3—61no—
135Dic3—61no—
136Dic3—61no—
137C32C2×#10011yescharacteristic, complemented, Sylow
138C23—62no—
139C23—94no—
140C23—91no—
141C23—182no—
142C23—364no—
143D4—62no—
144D4—62no—
145D4—182no—
146D4—182no—
147C2×C4—91no—
148C2×C4—91no—
149C2×C4—91no—
150C2×C4—91no—
151C2×C4—91no—
152C2×C4GO+(4,𝔽2)11yescharacteristic
153C8—62no—
154C8—182no—
155C2×C3—22no—
156C2×C3—21no—
157C2×C3—21no—
158C2×C3—41no—
159C2×C3—124no—
160D3—44no—
161D3—62no—
162D3—62no—
163D3—62no—
164D3—121no—
165C22—64no—
166C22—91no—
167C22—91no—
168C22—124no—
169C22—182no—
170C22—364no—
171C22—364no—
172C22D32⋊C411yescharacteristic
173C4—91no—
174C4—91no—
175C4D32⋊C411yescharacteristic
176C4C2×GO+(4,𝔽2)11yescharacteristic
177C3—21no—
178C3—21no—
179C2—21no—
180C2—92no—
181C2—124no—
182C2—181no—
183C2C2×D32⋊C411yescharacteristic
subgroupG/H
centerC2C2×D32⋊C4
commutatorC2×C3⋊D3C22×C4
FrattiniC4C2×GO+(4,𝔽2)
FittingC2×C32×C4D4
socleC2×C32C2×C22⋊C4
prime radicalC2×#3802C2
cosocleC4×C3⋊D3C23
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32C2×#100
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #64283C2semidirect
3. #63818C2semidirect
4. #63727C2semidirect
14. #3788C22semidirect
17. #3712C22semidirect
99. C3⋊D3#100semidirect
137. C32C2×#100semidirect

Maximal subgroups

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

subgroupindex
C2×#38022
#642832
#638182
#637272
C2×#1009