Finite Group Databasebeta

← #10593315

Subgroups — #10593315

Order 576.

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

normal subgroups only

This group has 258 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×#3797C211yesmaximal, characteristic
2#64283C211yesmaximal, characteristic
3#63818C211yesmaximal, characteristic
4#63728C214yesmaximal, complemented
5C2×C4×C3⋊D3C2211yescharacteristic
6C2×C3×Dic6—21no—
7C2×#627—21no—
8C2×#624C412yes—
9#3797—21no—
10#3797—21no—
11#3797C412yes—
12#3797C2212yes—
13#3792—21no—
14#3788C2212yes—
15#3787—21no—
16C3×#208—21no—
17#3712C2212yes—
18#3710—21no—
19C2×D3×Q8—61no—
20D3×M16—61no—
21C22×C3⋊D3C2×C411yescharacteristic
22C2×C32×C4D411yescharacteristic
23C2×C3⋊Dic3D411yescharacteristic
24C4×C3⋊D3C2×C411yescharacteristic
25C4×C3⋊D3D411yescharacteristic
26C4×C3⋊D3D411yescharacteristic
27C4×C3⋊D3C2311yescharacteristic
28C2×C3×Dic3—22no—
29C3×Dic6—22no—
30C3×Dic6—22no—
31#627—22no—
32#627—22no—
33#624—22no—
34#624C2×C414yes—
35#622—22no—
36C3×C3⋊C8—22no—
37C2×#101—91nomaximal, Sylow
38C2×C3×Q8—61no—
39D3×Q8—62no—
40D3×Q8—62no—
41D3×Q8—62no—
42D3×Q8—62no—
43C2×C4×D3—62no—
44C2×C4×D3—61no—
45C2×C4×D3—61no—
46C2×Dic6—21no—
47C2×Dic6—62no—
48C3×M16—61no—
49#208—21no—
50ΓL(1,𝔽25)—62no—
51D3×C8—62no—
52C22×C32C22⋊C411yescharacteristic
53C2×C3⋊D3—22no—
54C2×C3⋊D3C22⋊C411yescharacteristic
55C2×C3⋊D3C22×C411yescharacteristic
56C32×C4C22⋊C411yescharacteristic
57C32×C4C2×D411yescharacteristic
58C3⋊Dic3C22⋊C411yescharacteristic
59C3⋊Dic3C2×D411yescharacteristic
60C3×Dic3—24no—
61C22×Q8—91no—
62C2×M16—91no—
63C2×M16—91no—
64#101—94no—
65C22×D3—61no—
66C22×D3—61no—
67C3×Q8—62no—
68C3×Q8—62no—
69C2×C3×C4—21no—
70C2×C3×C4—21no—
71C2×C3×C4—62no—
72C2×Dic3—22no—
73C2×Dic3—61no—
74C2×Dic3—61no—
75C4×D3—64no—
76C4×D3—61no—
77C4×D3—61no—
78C4×D3—61no—
79C4×D3—61no—
80C4×D3—61no—
81C4×D3—61no—
82C4×D3—61no—
83C4×D3—61no—
84C4×D3—64no—
85Dic6—22no—
86Dic6—22no—
87Dic6—64no—
88Dic6—64no—
89C3×C8—62no—
90C3⋊C8—22no—
91C2×C32—21no—
92C2×C32C2×C22⋊C411yescharacteristic
93C3⋊D3—21no—
94C3⋊D3#10112yescomplemented
95C2×Q8—61no—
96C2×Q8—92no—
97C2×Q8—92no—
98C2×Q8—181no—
99C2×Q8—181no—
100C2×Q8—181no—
101C22×C4—92no—
102C22×C4—91no—
103M16—61no—
104M16—92no—
105M16—92no—
106M16—181no—
107C2×C8—181no—
108C2×C8—181no—
109C22×C3—21no—
110C22×C3—21no—
111C2×D3—61no—
112C2×D3—61no—
113C2×D3—61no—
114C2×D3—61no—
115C2×D3—64no—
116C2×D3—122no—
117C3×C4—21no—
118C3×C4—21no—
119C3×C4—21no—
120C3×C4—21no—
121C3×C4—64no—
122Dic3—24no—
123Dic3—61no—
124Dic3—61no—
125Dic3—61no—
126Dic3—61no—
127C32C2×#10111yescharacteristic, complemented, Sylow
128C23—91no—
129Q8—62no—
130Q8—62no—
131Q8—182no—
132Q8—182no—
133C2×C4—62no—
134C2×C4—94no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—182no—
141C2×C4GO+(4,𝔽2)11yescharacteristic
142C8—62no—
143C8—182no—
144C2×C3—22no—
145C2×C3—21no—
146C2×C3—21no—
147C2×C3—41no—
148D3—62no—
149D3—62no—
150D3—62no—
151D3—121no—
152C22—91no—
153C22—91no—
154C22—182no—
155C22D32⋊C411yescharacteristic
156C4—64no—
157C4—91no—
158C4—91no—
159C4D32⋊C411yescharacteristic
160C4C2×GO+(4,𝔽2)11yescharacteristic
161C3—21no—
162C3—21no—
163C2—21no—
164C2—92no—
165C2—181no—
166C2C2×D32⋊C411yescharacteristic
subgroupG/H
centerC2C2×D32⋊C4
commutatorC2×C3⋊D3C22×C4
FrattiniC4C2×GO+(4,𝔽2)
FittingC2×C32×C4D4
socleC2×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×C4
cosocleC4×C3⋊D3C23
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32C2×#101
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
4. #63728C2semidirect
94. C3⋊D3#101semidirect
127. C32C2×#101semidirect

Maximal subgroups

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

subgroupindex
C2×#37972
#642832
#638182
#637282
C2×#1019