Finite Group Databasebeta

← #11795891

Subgroups — #11795891

Order 1152.

274 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 96 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#10593765C211yesmaximal, characteristic
2C2×#63764C211yesmaximal, characteristic
3C3⋊D3×M32C211yesmaximal, characteristic
4#10590135C212yesmaximal, complemented
5C16×#157C212yesmaximal, complemented
6#64286C411yescharacteristic
7#64283C411yescharacteristic
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×#3708C412yescomplemented
10#63767C412yes—
11C8×#157C2212yes—
12#63764C412yescomplemented
13#63764C2211yescharacteristic
14#63764C2211yescharacteristic
15C32×M32C411yescharacteristic, complemented
16#63639C411yescharacteristic, complemented
17#63625C412yescomplemented
18C16×C3⋊D3C2212yes—
19D3×M32—62no—
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C22⋊#157C812yes—
22#3792C812yes—
23C4⋊#157C812yes—
24C4×#157C2×C412yes—
25#3788C812yes—
26#3787C2×C412yes—
27C2×C32×C8C2×C411yescharacteristic
28C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
29C8×C3⋊D3C2×C411yescharacteristic
30C8×C3⋊D3C2×C411yescharacteristic
31C8×C3⋊D3C2×C411yescharacteristic
32C8×C3⋊D3C2311yescharacteristic
33#3708C2×C412yes—
34#3708C2×C412yes—
35C32×C16C2×C412yes—
36C3⋊(C3⋊C16)C2×C412yes—
37#2108—91nomaximal, Sylow
38C2×D3×C8—62no—
39C3×M32—22no—
40#812—62no—
41#798—64no—
42D3×C16—64no—
43C22×C3⋊D3C2×C811yescharacteristic
44C2×#157C2×C814yes—
45C2×C32×C4C4211yescharacteristic
46C2×C3⋊Dic3C2×C811yescharacteristic
47C4×C3⋊D3C4211yescharacteristic
48C4×C3⋊D3C2×C811yescharacteristic
49C4×C3⋊D3C2×C811yescharacteristic
50C4×C3⋊D3C22×C411yescharacteristic
51#622C2×C814yes—
52C32×C8C4211yescharacteristic
53C32×C8C22×C411yescharacteristic
54C3⋊(C3⋊C8)C4211yescharacteristic
55C3⋊(C3⋊C8)C22×C411yescharacteristic
56C2×M32—91no—
57C22×C16—91no—
58#405—91no—
59#346—92no—
60C4×C16—92no—
61C2×C4×D3—62no—
62C2×C3×C8—22no—
63C2×C3⋊C8—62no—
64D3×C8—62no—
65D3×C8—62no—
66D3×C8—62no—
67D3×C8—62no—
68C3×C16—24no—
69C3⋊C16—64no—
70C22×C32C4×C811yescharacteristic
71C2×C3⋊D3—22no—
72C2×C3⋊D3C4×C811yescharacteristic
73C2×C3⋊D3C22×C811yescharacteristic
74#157—24no—
75C32×C4C4×C811yescharacteristic
76C32×C4C2×C4211yescharacteristic
77C3⋊Dic3C4×C811yescharacteristic
78C3⋊Dic3C22×C811yescharacteristic
79C2×M16—91no—
80C22×C8—91no—
81#117—91no—
82M32—91no—
83M32—92no—
84M32#15711yescharacteristic, complemented
85C2×C16—92no—
86C2×C16—91no—
87C2×C16—91no—
88C2×C16—92no—
89C2×C16—92no—
90#97—92no—
91C4×C8—92no—
92C22×D3—62no—
93C2×C3×C4—22no—
94C2×Dic3—62no—
95C4×D3—62no—
96C4×D3—62no—
97C4×D3—62no—
98C4×D3—62no—
99C3×C8—22no—
100C3×C8—22no—
101C3⋊C8—62no—
102C3⋊C8—62no—
103C2×C32—21no—
104C2×C32C2×C4×C811yescharacteristic
105C3⋊D3—21no—
106C3⋊D3#50412yes—
107C22×C4—91no—
108M16—92no—
109M16—92no—
110C2×C8—92no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8—91no—
114C2×C8—91no—
115C2×C8—91no—
116C2×C8C2×#15711yescharacteristic
117C4⋊C4—92no—
118C22⋊C4—92no—
119C42—92no—
120C16—92no—
121C16—92no—
122C16—92no—
123C16C2×#15712yes—
124C22×C3—22no—
125C2×D3—62no—
126C2×D3—62no—
127C2×D3—124no—
128C3×C4—22no—
129C3×C4—22no—
130Dic3—62no—
131Dic3—62no—
132C32#210811yescharacteristic, complemented, Sylow
133C23—91no—
134C2×C4—91no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—94no—
140C2×C4C4×#15711yescharacteristic
141C8—94no—
142C8—91no—
143C8—91no—
144C8C4×#15711yescharacteristic
145C8C22×#15711yescharacteristic
146C2×C3—22no—
147C2×C3—42no—
148D3—64no—
149D3—122no—
150C22—91no—
151C22—91no—
152C22—182no—
153C22C8×#15711yescharacteristic
154C4—91no—
155C4—91no—
156C4—184no—
157C4C8×#15711yescharacteristic
158C4C2×C4×#15711yescharacteristic
159C3—22no—
160C2—21no—
161C2—92no—
162C2—181no—
163C2C2×C8×#15711yescharacteristic
subgroupG/H
center, FrattiniC8C22×#157
commutator, socleC2×C32C2×C4×C8
FittingC32×M32C4
prime radicalC22×C3⋊D3C2×C8
cosocleC8×C3⋊D3C23
hypercenterM32#157
hypocenterC32#2108
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ M32

Complements

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

NH ≅ G/Ntype
4. #10590135C2semidirect
5. C16×#157C2semidirect
9. C2×#3708C4semidirect
12. #63764C4semidirect
15. C32×M32C4semidirect
16. #63639C4semidirect
17. #63625C4semidirect
84. M32#157semidirect
132. C32#2108semidirect

Maximal subgroups

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

subgroupindex
#105937652
C2×#637642
C3⋊D3×M322
#105901352
C16×#1572
#21089