Finite Group Databasebeta

← #11771509

Subgroups — #11771509

Order 1152.

255 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 255 conjugacy classes of subgroups — too many to draw. Only its 58 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#10592817C211yesmaximal, characteristic
2C3×#4553C212yesmaximal
3#67532—32nomaximal
4C2×C32×M16C2211yescharacteristic
5C2×C4×C3⋊Dic3C411yescharacteristic
6C2×#3748C411yescharacteristic
7#63641—22no—
8C3×#812—22no—
9#5118—32no—
10#5118—61no—
11C3×#349—32no—
12#4553D312yes—
13C22×C32×C4C2×C411yescharacteristic
14C22×C3⋊Dic3—21no—
15C32×M16—41no—
16C2×C32×C8D412yes—
17C4×C3⋊Dic3—21no—
18C4×C3⋊Dic3C811yescharacteristic
19C4×C3⋊Dic3C811yescharacteristic
20#3748—41no—
21C2×C3⋊(C3⋊C8)—21no—
22C3×C3⋊C16—42no—
23#1327—91noSylow
24C2×C3×M16—21no—
25C2×C3×M16C2×D312yes—
26C2×C4×Dic3—32no—
27C2×C4×Dic3—61no—
28C2×#208—32no—
29C2×#208—61no—
30C3×M32—62no—
31Dic3⋊C8—64no—
32Dic3⋊C8—62no—
33Dic3⋊C8—62no—
34#812—22no—
35C23×C32M1611yescharacteristic
36C2×C32×C4—21no—
37C2×C32×C4—21no—
38C2×C32×C4C22⋊C411yescharacteristic
39C2×C32×C4C2×C811yescharacteristic
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—42no—
43C32×C8—22no—
44C3⋊(C3⋊C8)—41no—
45#423—91no—
46#349—32no—
47C22×C3×C4—21no—
48C22×C3×C4C4×D312yes—
49C22×Dic3—62no—
50C22×Dic3—62no—
51C3×M16—42no—
52C3×M16—42no—
53C2×C3×C8—22no—
54C2×C3×C8D1212yes—
55C2×C3×C8#6712yes—
56C4×Dic3—32no—
57C4×Dic3—32no—
58C4×Dic3—61no—
59C4×Dic3—61no—
60C4×Dic3—62no—
61C4×Dic3—62no—
62#208—122no—
63#208—122no—
64C2×C3⋊C8—62no—
65C2×C3⋊C8—62no—
66C3×C16—122no—
67C3⋊C16—42no—
68C22×C32—21no—
69C22×C32—41no—
70C22×C32C22⋊C811yescharacteristic
71C32×C4—21no—
72C32×C4#9911yescharacteristic
73C32×C4#10111yescharacteristic
74C3⋊Dic3—22no—
75C3⋊Dic3—41no—
76C2×M16—91no—
77C2×M16D3211yescharacteristic
78C2×C42—91no—
79M32—62no—
80C4⋊C8—182no—
81C23×C3—21no—
82C23×C3ΓL(1,𝔽25)12yes—
83C2×C3×C4—22no—
84C2×C3×C4—22no—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×C3×C4—21no—
88C2×C3×C4—21no—
89C2×C3×C4D3×C812yes—
90C2×C3×C4(C2×D3)⋊C412yes—
91C2×Dic3—62no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C2×Dic3—62no—
95C2×Dic3—124no—
96C2×Dic3—124no—
97C3×C8—22no—
98C3×C8—22no—
99C3×C8—42no—
100C3⋊C8—122no—
101C3⋊C8—122no—
102C2×C32—21no—
103C2×C32—41no—
104C2×C32#32411yescharacteristic
105C22×C4—181no—
106C22×C4#62411yescharacteristic
107M16—41no—
108M16—361no—
109C2×C8—181no—
110C2×C8#62612yes—
111C42—91no—
112C42—91no—
113C42—181no—
114C16—122no—
115C22×C3—22no—
116C22×C3—22no—
117C22×C3—21no—
118C22×C3—42no—
119C22×C3—42no—
120C22×C3(C2×D3)⋊C812yes—
121C3×C4—22no—
122C3×C4—22no—
123C3×C4—21no—
124C3×C4—21no—
125C3×C4#80612yes—
126C3×C4#82412yes—
127Dic3—64no—
128Dic3—64no—
129Dic3—122no—
130Dic3—122no—
131C32#132711yescharacteristic, complemented, Sylow
132C23#371211yescharacteristic
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—181no—
136C2×C4—181no—
137C2×C4—362no—
138C2×C4#371011yescharacteristic
139C2×C4#372211yescharacteristic
140C8—22no—
141C8—361no—
142C2×C3—22no—
143C2×C3—22no—
144C2×C3—21no—
145C2×C3—42no—
146C2×C3—42no—
147C2×C3#446912yes—
148C22—21no—
149C22—41no—
150C22#6355711yescharacteristic
151C4—21no—
152C4—182no—
153C4—361no—
154C4#6356111yescharacteristic
155C4#6358111yescharacteristic
156C3—21no—
157C3#6753212yescomplemented
158C2—21no—
159C2—41no—
160C2#1058914811yescharacteristic
subgroupG/H
centerC4#63581
commutatorC2×C32×C4C2×C8
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#324
prime radicalC23×C32M16
hypocenterC32#1327
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
131. C32#1327semidirect
157. C3#67532semidirect

Maximal subgroups

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

subgroupindex
#105928172
C3×#45532
#675323