Finite Group Databasebeta

← #10593501

Subgroups — #10593501

Order 576.

171 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 171 conjugacy classes of subgroups — too many to draw. Only its 31 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
1#63982C211yesmaximal, characteristic
2#63957C211yesmaximal, characteristic
3C22⋊#622C211yesmaximal, characteristic
4#63743C211yesmaximal, characteristic, complemented
5#63742C211yesmaximal, characteristic, complemented
6#63740C211yesmaximal, characteristic, complemented
7#63740C211yesmaximal, characteristic, complemented
8C22×C3⋊Dic3C2211yescharacteristic
9C2×#627C2211yescharacteristic
10C2×#622C2211yescharacteristic
11C2×#622C2211yescharacteristic
12C3×#217—21no—
13C3×#217—21no—
14#3724C2211yescharacteristic
15#3724C2211yescharacteristic
16#3724C2211yescharacteristic
17Dic3⋊Dic3—21no—
18Dic32—21no—
19#878—61no—
20#877—61no—
21C23×C32D411yescharacteristic
22C2×C3⋊Dic3—21no—
23C2×C3⋊Dic3—21no—
24C2×C3⋊Dic3D411yescharacteristic
25C2×C3⋊Dic3C2311yescharacteristic
26C2×C3×Dic3—21no—
27C2×C3×Dic3—21no—
28C2×C3×Dic3—21no—
29C2×C3×Dic3—21no—
30#627—21no—
31#627—21no—
32#622—21no—
33#622—21no—
34#485—91nomaximal, Sylow
35C22×Dic3—61no—
36C22×Dic3—61no—
37C2×Dic6—61no—
38C3×C22⋊C4—61no—
39C3×C22⋊C4—61no—
40#217—21no—
41#217—21no—
42C4⋊Dic3—61no—
43Dic3⋊C4—61no—
44Dic3⋊C4—61no—
45Dic3⋊C4—61no—
46Dic3⋊C4—61no—
47C4×Dic3—61no—
48C4×Dic3—61no—
49C22×C32—21no—
50C22×C32—21no—
51C22×C32—21no—
52C22×C32C2×D411yescharacteristic
53C3⋊Dic3—21no—
54C3⋊Dic3#4111yescharacteristic
55C3⋊Dic3#4111yescharacteristic
56C3×Dic3—41no—
57C3×Dic3—41no—
58C3×Dic3—41no—
59C3×Dic3—41no—
60C22⋊Q8—91no—
61#117—91no—
62#107—91no—
63#106—91no—
64#103—91no—
65#103—91no—
66C22⋊C8—91no—
67C23×C3—21no—
68C23×C3—21no—
69C2×C3×C4—61no—
70C2×C3×C4—61no—
71C2×C3×C4—61no—
72C2×C3×C4—61no—
73C2×Dic3—21no—
74C2×Dic3—21no—
75C2×Dic3—21no—
76C2×Dic3—21no—
77C2×Dic3—61no—
78C2×Dic3—61no—
79C2×Dic3—61no—
80C2×Dic3—61no—
81C2×Dic3—62no—
82C2×Dic3—62no—
83C2×Dic3—121no—
84C2×Dic3—121no—
85Dic6—121no—
86Dic6—121no—
87C2×C32—41no—
88C2×C32#12311yescharacteristic
89C2×C32#13511yescharacteristic
90C2×C32#13711yescharacteristic
91C2×Q8—91no—
92C22×C4—91no—
93C2×C8—91no—
94C2×C8—91no—
95C4⋊C4—91no—
96C4⋊C4—91no—
97C4⋊C4—91no—
98C4⋊C4—181no—
99C22⋊C4—61no—
100C22⋊C4—61no—
101C42—181no—
102C22×C3—22no—
103C22×C3—22no—
104C22×C3—21no—
105C22×C3—21no—
106C22×C3—41no—
107C22×C3—41no—
108C22×C3—41no—
109C22×C3—41no—
110C3×C4—121no—
111C3×C4—121no—
112C3×C4—121no—
113C3×C4—121no—
114Dic3—41no—
115Dic3—41no—
116Dic3—41no—
117Dic3—41no—
118Dic3—61no—
119Dic3—61no—
120Dic3—61no—
121Dic3—61no—
122Dic3—62no—
123Dic3—121no—
124C32#48511yescharacteristic, complemented, Sylow
125C23GO+(4,𝔽2)11yescharacteristic
126Q8—181no—
127Q8—181no—
128C2×C4—61no—
129C2×C4—61no—
130C2×C4—61no—
131C2×C4—61no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—181no—
135C2×C4—181no—
136C8—181no—
137C8—181no—
138C2×C3—21no—
139C2×C3—21no—
140C2×C3—21no—
141C2×C3—21no—
142C2×C3—21no—
143C2×C3—21no—
144C2×C3—42no—
145C2×C3—42no—
146C22—21no—
147C22—21no—
148C22—21no—
149C22C2×GO+(4,𝔽2)11yescharacteristic
150C4—91no—
151C4—91no—
152C4—121no—
153C4—121no—
154C4—121no—
155C4—121no—
156C4—181no—
157C3—21no—
158C3—21no—
159C2—41no—
160C2#6423311yescharacteristic
161C2#6423711yescharacteristic
162C2#6423911yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
Fitting, prime radicalC23×C32D4
socleC22×C32C2×D4
hypercenterC23GO+(4,𝔽2)
hypocenterC32#485
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
4. #63743C2semidirect
5. #63742C2semidirect
6. #63740C2semidirect
7. #63740C2semidirect
124. C32#485semidirect

Maximal subgroups

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

subgroupindex
#639822
#639572
C22⋊#6222
#637432
#637422
#637402
#4859