Finite Group Databasebeta

← #10593411

Subgroups — #10593411

Order 576.

306 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 49 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
2C2×#3773C212yesmaximal
3#63883C211yesmaximal, characteristic
4#63781C211yesmaximal, characteristic
5#63737C212yesmaximal
6C22×#157C2212yes—
7C2×C4×C3⋊D3C2211yescharacteristic
8C2×C3×Dic6—21no—
9C2×#627—21no—
10C2×#624C2211yescharacteristic
11C2×#624C2212yes—
12C2×#624C2211yescharacteristic
13#3797—24no—
14#3773—24no—
15C3×Dic3⋊C4—21no—
16Dic3⋊Dic3—21no—
17C2×D3×Q8—61no—
18D3×C4⋊C4—61no—
19C22×C3⋊D3C2311yescharacteristic
20C2×#157—22no—
21C2×#157—22no—
22C2×#157Q814yescomplemented
23C2×C32×C4D411yescharacteristic
24C2×C3⋊Dic3D411yescharacteristic
25C4×C3⋊D3—22no—
26C2×C3×Dic3—21no—
27C2×C3×Dic3—22no—
28C2×C3×Dic3—21no—
29C3×Dic6—24no—
30#627—24no—
31#624—22no—
32#624—21no—
33#624—22no—
34#624D414yes—
35#624Q812yescomplemented
36#395—91nomaximal, Sylow
37C2×C3×Q8—61no—
38D3×Q8—68no—
39C2×C4×D3—61no—
40C2×C4×D3—62no—
41C2×C4×D3—61no—
42C2×C4×D3—61no—
43C2×C4×D3—61no—
44C2×Dic6—21no—
45C2×Dic6—62no—
46C3×C4⋊C4—61no—
47C4⋊Dic3—61no—
48Dic3⋊C4—21no—
49Dic3⋊C4—61no—
50C22×C32C2×D411yescharacteristic
51C2×C3⋊D3C2×D412yes—
52C2×C3⋊D3C2×Q812yes—
53C2×C3⋊D3C2×Q811yescharacteristic
54C2×C3⋊D3#4111yescharacteristic
55#157—24no—
56C32×C4—21no—
57C3⋊Dic3—21no—
58C3×Dic3—24no—
59C3×Dic3—22no—
60C3×Dic3—41no—
61C22×Q8—91no—
62C2×C4⋊C4—91no—
63C2×C4⋊C4—92no—
64#95—91no—
65#95—92no—
66C22×D3—61no—
67C22×D3—61no—
68C3×Q8—64no—
69C2×C3×C4—21no—
70C2×C3×C4—21no—
71C2×C3×C4—61no—
72C2×C3×C4—62no—
73C2×C3×C4—61no—
74C2×Dic3—21no—
75C2×Dic3—22no—
76C2×Dic3—21no—
77C2×Dic3—61no—
78C2×Dic3—61no—
79C4×D3—64no—
80C4×D3—62no—
81C4×D3—62no—
82C4×D3—64no—
83C4×D3—64no—
84C4×D3—122no—
85C4×D3—122no—
86Dic6—24no—
87Dic6—68no—
88C2×C32#12011yescharacteristic
89C2×C32C22⋊Q811yescharacteristic
90C2×C32C4⋊Q811yescharacteristic
91C3⋊D3C22⋊Q812yes—
92C3⋊D3C4⋊Q812yes—
93C2×Q8—61no—
94C2×Q8—181no—
95C2×Q8—184no—
96C22×C4—91no—
97C22×C4—92no—
98C22×C4—91no—
99C22×C4—92no—
100C22×C4—91no—
101C4⋊C4—61no—
102C4⋊C4—181no—
103C4⋊C4—184no—
104C22×C3—21no—
105C22×C3—21no—
106C2×D3—62no—
107C2×D3—61no—
108C2×D3—61no—
109C2×D3—62no—
110C2×D3—61no—
111C2×D3—62no—
112C2×D3—62no—
113C2×D3—61no—
114C3×C4—22no—
115C3×C4—41no—
116C3×C4—64no—
117C3×C4—62no—
118C3×C4—121no—
119Dic3—24no—
120Dic3—22no—
121Dic3—41no—
122Dic3—62no—
123Dic3—121no—
124C32#39511yescharacteristic, complemented, Sylow
125C23—91no—
126Q8—64no—
127Q8—184no—
128C2×C4—61no—
129C2×C4—62no—
130C2×C4—61no—
131C2×C4—94no—
132C2×C4—92no—
133C2×C4—94no—
134C2×C4—91no—
135C2×C4—182no—
136C2×C4—182no—
137C2×C4—181no—
138C2×C4—182no—
139C2×C4—182no—
140C2×C4—182no—
141C2×C4GO+(4,𝔽2)11yescharacteristic
142C2×C3—21no—
143C2×C3—21no—
144C2×C3—21no—
145C2×C3—21no—
146C2×C3—21no—
147C2×C3—21no—
148D3—62no—
149D3—62no—
150D3—62no—
151D3—62no—
152C22—91no—
153C22—91no—
154C22—92no—
155C22—92no—
156C22C2×GO+(4,𝔽2)11yescharacteristic
157C4—21no—
158C4—62no—
159C4—64no—
160C4—121no—
161C4—184no—
162C4—181no—
163C3—21no—
164C3—21no—
165C2—92no—
166C2—92no—
167C2D32⋊Q811yescharacteristic
168C2#6422211yescharacteristic
169C2#6424111yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, prime radical, cosocleC22×C3⋊D3C23
FittingC2×C32×C4D4
socleC22×C32C2×D4
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#395
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
22. C2×#157Q8semidirect
35. #624Q8semidirect
124. C32#395semidirect

Maximal subgroups

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

subgroupindex
C2×#37972
C2×#37732
#638832
#637812
#637372
#3959