Finite Group Databasebeta

← #10593431

Subgroups — #10593431

Order 576.

202 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 41 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×#3775C211yesmaximal, characteristic
2C4×#625C211yesmaximal, characteristic
3#63838C211yesmaximal, characteristic, complemented
4#63777C211yesmaximal, characteristic, complemented
5#63743C211yesmaximal, characteristic, complemented
6#63740C211yesmaximal, characteristic, complemented
7#63739C211yesmaximal, characteristic
8C2×C3×C4×D3—21no—
9C2×#627C2211yescharacteristic
10C2×#625C2211yescharacteristic
11C2×#622C2211yescharacteristic
12C2×#622C2211yescharacteristic
13#3775C414yescomplemented
14C4×C3⋊Dic3C2211yescharacteristic
15C3×Dic3⋊C4—21no—
16#3724C2211yescharacteristic
17#3724C2211yescharacteristic
18(C2×D3)⋊Dic3—21no—
19Dic32—21no—
20C4×#67—61no—
21#887—61no—
22C22×C3×D3—21no—
23C2×C32×C4D411yescharacteristic
24C2×C3⋊Dic3D411yescharacteristic
25C2×C3⋊Dic3C2311yescharacteristic
26C2×C3×Dic3—21no—
27C2×C3×Dic3—21no—
28C2×C3×Dic3—21no—
29C3×C4×D3—42no—
30#627—21no—
31#627C2×C412yescomplemented
32#625—21no—
33#625C2×C412yes—
34#622—21no—
35#622C2×C412yescomplemented
36#440—91nomaximal, Sylow
37C22×C3×C4—61no—
38C2×#67—61no—
39C2×C4×D3—21no—
40C2×Dic6—61no—
41C3×C4⋊C4—61no—
42#217—61no—
43(C2×D3)⋊C4—61no—
44Dic3⋊C4—21no—
45Dic3⋊C4—61no—
46Dic3⋊C4—61no—
47C4×Dic3—61no—
48C4×Dic3—61no—
49C4×Dic3—61no—
50C4×Dic3—61no—
51C22×C32C2×D411yescharacteristic
52C2×C3×D3—22no—
53C2×C3×D3—41no—
54C2×C3×D3—41no—
55C32×C4—21no—
56C3⋊Dic3—21no—
57C3⋊Dic3C22×C411yescharacteristic
58C3⋊Dic3#4111yescharacteristic
59C3×Dic3—22no—
60C3×Dic3—41no—
61C3×Dic3—41no—
62C2×SD16—91no—
63C4×Q8—91no—
64C4×D4—91no—
65#107—91no—
66#103—91no—
67#102—91no—
68#97—91no—
69C23×C3—61no—
70C22×D3—21no—
71C2×C3×C4—21no—
72C2×C3×C4—21no—
73C2×C3×C4—61no—
74C2×C3×C4—61no—
75C2×C3×C4—61no—
76C2×C3×C4—122no—
77#67—62no—
78#67—62no—
79C2×Dic3—21no—
80C2×Dic3—21no—
81C2×Dic3—21no—
82C2×Dic3—61no—
83C2×Dic3—61no—
84C2×Dic3—61no—
85C2×Dic3—61no—
86C4×D3—42no—
87Dic6—62no—
88Dic6—62no—
89C2×C32C4×D411yescharacteristic
90C2×C32AGL(1,ℤ/8)11yescharacteristic
91C2×C32#13711yescharacteristic
92C3×D3—42no—
93C2×Q8—91no—
94C2×D4—91no—
95C22×C4—61no—
96SD16—94no—
97C2×C8—91no—
98C2×C8—91no—
99C4⋊C4—61no—
100C4⋊C4—91no—
101C4⋊C4—91no—
102C22⋊C4—181no—
103C42—91no—
104C42—181no—
105C22×C3—21no—
106C22×C3—21no—
107C22×C3—62no—
108C22×C3—121no—
109C22×C3—121no—
110C2×D3—22no—
111C2×D3—41no—
112C2×D3—41no—
113C3×C4—22no—
114C3×C4—41no—
115C3×C4—62no—
116C3×C4—121no—
117C3×C4—121no—
118Dic3—22no—
119Dic3—41no—
120Dic3—41no—
121Dic3—61no—
122Dic3—61no—
123Dic3—61no—
124Dic3—61no—
125Dic3—62no—
126Dic3—121no—
127C32#44011yescharacteristic, complemented, Sylow
128C23—61no—
129Q8—92no—
130Q8—181no—
131D4—92no—
132D4—181no—
133C2×C4—61no—
134C2×C4—61no—
135C2×C4—61no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—122no—
139C2×C4GO+(4,𝔽2)11yescharacteristic
140C8—92no—
141C8—181no—
142C2×C3—21no—
143C2×C3—21no—
144C2×C3—21no—
145C2×C3—21no—
146C2×C3—21no—
147C2×C3—21no—
148C2×C3—122no—
149D3—42no—
150C22—62no—
151C22—121no—
152C22—121no—
153C22C2×GO+(4,𝔽2)11yescharacteristic
154C4—21no—
155C4—62no—
156C4—91no—
157C4—91no—
158C4—121no—
159C4—121no—
160C4—181no—
161C3—21no—
162C3—21no—
163C2—122no—
164C2#6422611yescharacteristic
165C2C4×GO+(4,𝔽2)11yescharacteristic
166C2#6423611yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C4
FittingC2×C32×C4D4
socleC22×C32C2×D4
prime radicalC2×#625C22
cosocleC2×C3⋊Dic3C23
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#440
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #63838C2semidirect
4. #63777C2semidirect
5. #63743C2semidirect
6. #63740C2semidirect
13. #3775C4semidirect
31. #627C2×C4semidirect
35. #622C2×C4semidirect
127. C32#440semidirect

Maximal subgroups

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

subgroupindex
C2×#37752
C4×#6252
#638382
#637772
#637432
#637402
#637392
#4409