Finite Group Databasebeta

← #10593831

Subgroups — #10593831

Order 576.

318 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 48 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×#3832C211yesmaximal, characteristic
2#64286C211yesmaximal, characteristic, complemented
3#64283C211yesmaximal, characteristic, complemented
4#63785C214yesmaximal, complemented
5C2×C32×Q8C411yescharacteristic, complemented
6#3832—21no—
7#3832—21no—
8#3832C412yescomplemented
9#3832C2212yes—
10C2×C4⋊(C3⋊D3)—21no—
11C2×C4⋊(C3⋊D3)C411yescharacteristic, complemented
12C2×C4×C3⋊D3—21no—
13C2×C4×C3⋊D3C2211yescharacteristic
14C22⋊#157—21no—
15#3792—21no—
16C4⋊#157—21no—
17C4×#157C2212yescomplemented
18#3788C2212yescomplemented
19#3787—21no—
20C2×#239—62no—
21C22×C3⋊D3—21no—
22C22×C3⋊D3D411yescharacteristic
23C2×#157—22no—
24C32×Q8—21no—
25C32×Q8C2×C412yes—
26C2×C32×C4—21no—
27C2×C32×C4C2×C411yescharacteristic
28C2×C3⋊Dic3D411yescharacteristic
29C4⋊(C3⋊D3)—22no—
30C4⋊(C3⋊D3)—22no—
31C4⋊(C3⋊D3)—21no—
32C4⋊(C3⋊D3)C2×C412yes—
33C4×C3⋊D3—22no—
34C4×C3⋊D3—22no—
35C4×C3⋊D3C2×C411yescharacteristic
36C4×C3⋊D3D411yescharacteristic
37C4×C3⋊D3D411yescharacteristic
38C4×C3⋊D3C2311yescharacteristic
39#622—22no—
40#421—91nomaximal, Sylow
41C2×C3×Q8—22no—
42#239—64no—
43#239—64no—
44#239—64no—
45#239—64no—
46C2×D12—62no—
47C2×D12—64no—
48C2×C4×D3—62no—
49C2×C4×D3—64no—
50C22×C32C22⋊C411yescharacteristic
51C2×C3⋊D3—22no—
52C2×C3⋊D3—41no—
53C2×C3⋊D3—42no—
54C2×C3⋊D3C22⋊C411yescharacteristic
55C2×C3⋊D3C2×D411yescharacteristic
56#157—42no—
57C32×C4—22no—
58C32×C4C22⋊C411yescharacteristic
59C32×C4C22×C411yescharacteristic
60C3⋊Dic3C22⋊C411yescharacteristic
61C3⋊Dic3C2×D411yescharacteristic
62C2×#41—91no—
63C2×M16—91no—
64#117—91no—
65#104—94no—
66C22×D3—62no—
67C22×D3—64no—
68C3×Q8—24no—
69C3×Q8—24no—
70C2×C3×C4—24no—
71C2×C3×C4—22no—
72C2×Dic3—62no—
73D12—64no—
74D12—68no—
75D12—68no—
76D12—64no—
77C4×D3—62no—
78C4×D3—62no—
79C4×D3—62no—
80C4×D3—62no—
81C4×D3—68no—
82C4×D3—68no—
83C2×C32—21no—
84C2×C32C2×C22⋊C411yescharacteristic
85C3⋊D3—21no—
86C3⋊D3—21no—
87C3⋊D3—42no—
88#41—92no—
89#41—92no—
90#41—181no—
91#41—181no—
92C2×Q8#15711yescharacteristic, complemented
93C2×D4—91no—
94C2×D4—181no—
95C22×C4—91no—
96C22×C4—181no—
97M16—92no—
98M16—181no—
99C2×C8—181no—
100C4⋊C4—181no—
101C22⋊C4—181no—
102C42—92no—
103C22×C3—22no—
104C2×D3—62no—
105C2×D3—62no—
106C2×D3—68no—
107C2×D3—124no—
108C2×D3—128no—
109C3×C4—28no—
110C3×C4—22no—
111C3×C4—22no—
112Dic3—62no—
113Dic3—62no—
114C32#42111yescharacteristic, complemented, Sylow
115C23—91no—
116C23—181no—
117Q8—21no—
118Q8C2×#15712yes—
119D4—92no—
120D4—182no—
121D4—182no—
122D4—181no—
123C2×C4—21no—
124C2×C4—91no—
125C2×C4—91no—
126C2×C4—91no—
127C2×C4—91no—
128C2×C4—91no—
129C2×C4—182no—
130C2×C4—182no—
131C2×C4—182no—
132C2×C4C2×#15711yescharacteristic
133C8—182no—
134C2×C3—24no—
135C2×C3—22no—
136D3—122no—
137D3—122no—
138D3—128no—
139C22—91no—
140C22—91no—
141C22—182no—
142C22—361no—
143C22—362no—
144C22C22⋊#15711yescharacteristic
145C4—22no—
146C4—91no—
147C4—91no—
148C4—362no—
149C4C22⋊#15711yescharacteristic
150C4C22×#15711yescharacteristic
151C3—22no—
152C2—21no—
153C2—181no—
154C2—181no—
155C2—362no—
156C2C2×C22⋊#15711yescharacteristic
subgroupG/H
centerC2C2×C22⋊#157
commutatorC32×C4C22×C4
FrattiniC4C22×#157
FittingC2×C32×Q8C4
socleC2×C32C2×C22⋊C4
prime radicalC2×#3832C2
cosocleC4×C3⋊D3C23
hypercenterC2×Q8#157
hypocenterC32#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #64286C2semidirect
3. #64283C2semidirect
4. #63785C2semidirect
5. C2×C32×Q8C4semidirect
8. #3832C4semidirect
11. C2×C4⋊(C3⋊D3)C4semidirect
17. C4×#157C22semidirect
18. #3788C22semidirect
92. C2×Q8#157semidirect
114. C32#421semidirect

Maximal subgroups

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

subgroupindex
C2×#38322
#642862
#642832
#637852
#4219