Finite Group Databasebeta

← #11796054

Subgroups — #11796054

Order 1152.

486 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 78 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×#64116C211yesmaximal, characteristic
2C2×#63773C212yesmaximal, complemented
3#10590180C214yesmaximal, complemented
4C2×#3828C411yescharacteristic
5C2×C32×M16C411yescharacteristic
6C22×C3⋊(C3⋊C8)C2211yescharacteristic
7#64116—22no—
8#64116—22no—
9C2×#3743C2212yes—
10C2×C8×C3⋊D3C412yes—
11#63773—22no—
12#63773C2214yes—
13C2×#3708—22no—
14C2×#907—62no—
15C22×C32×C4C2×C411yescharacteristic
16C2×#638C812yes—
17#3828—22no—
18#3828—22no—
19C2×C4⋊(C3⋊D3)C811yescharacteristic
20C2×C4×C3⋊D3C2×C412yes—
21C2×#634C811yescharacteristic
22C32×M16—22no—
23C2×C32×C8C2×C412yes—
24C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
25C2×C3⋊(C3⋊C8)D412yes—
26C2×C3⋊(C3⋊C8)D412yes—
27C2×C3⋊(C3⋊C8)C2311yescharacteristic
28#3743—24no—
29C8×C3⋊D3—22no—
30C8×C3⋊D3—22no—
31#3708—24no—
32#2115—91nomaximal, Sylow
33C2×#235—62no—
34C2×C3×M16—22no—
35C22×C3⋊C8—62no—
36#907—68no—
37#907—68no—
38C2×ΓL(1,𝔽25)—64no—
39C2×D3×C8—64no—
40C23×C32C2×C811yescharacteristic
41C22×C3⋊D3C2×C812yes—
42C2×C32×C4C22⋊C412yes—
43C2×C32×C4C2×C811yescharacteristic
44C2×C32×C4M1612yes—
45C2×C32×C4C22×C411yescharacteristic
46#638—24no—
47C2×C3⋊Dic3C2×C812yes—
48C4⋊(C3⋊D3)—22no—
49C4×C3⋊D3—22no—
50C4×C3⋊D3—22no—
51#634—22no—
52C32×C8—22no—
53C3⋊(C3⋊C8)C22⋊C411yescharacteristic
54C3⋊(C3⋊C8)C22⋊C411yescharacteristic
55C3⋊(C3⋊C8)C2×D412yes—
56C2×#131—91no—
57C2×M32—92no—
58#349—94no—
59C22×C3×C4—22no—
60C2×#67—64no—
61#235—68no—
62#235—68no—
63C2×D12—62no—
64C2×C4×D3—64no—
65C2×Dic6—62no—
66C3×M16—28no—
67C2×C3×C8—24no—
68C2×C3⋊C8—62no—
69C2×C3⋊C8—62no—
70C2×C3⋊C8—64no—
71C2×C3⋊C8—64no—
72ΓL(1,𝔽25)—616no—
73D3×C8—68no—
74D3×C8—68no—
75C22×C32—41no—
76C22×C32C22⋊C812yes—
77C22×C32C22×C811yescharacteristic
78C2×C3⋊D3—22no—
79C2×C3⋊D3—42no—
80C32×C4C22⋊C812yes—
81C32×C4C2×C22⋊C411yescharacteristic
82C32×C4C2×M1611yescharacteristic
83C3⋊Dic3—22no—
84C2×#41—91no—
85#131—182no—
86#131—182no—
87C2×M16—92no—
88C2×M16#15711yescharacteristic
89C22×C8—91no—
90C22×C8—92no—
91M32—94no—
92M32—182no—
93C2×C16—182no—
94C23×C3—22no—
95C22×D3—64no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×C3×C4—24no—
99C2×C3×C4—24no—
100#67—616no—
101C2×Dic3—64no—
102D12—68no—
103C4×D3—68no—
104C4×D3—68no—
105Dic6—68no—
106C3×C8—28no—
107C3⋊C8—62no—
108C3⋊C8—62no—
109C3⋊C8—64no—
110C2×C32—21no—
111C2×C32—22no—
112C2×C32C2×C22⋊C811yescharacteristic
113C3⋊D3—42no—
114#41—182no—
115#41—182no—
116C2×Q8—91no—
117C2×D4—92no—
118C2×D4—91no—
119C22×C4—92no—
120C22×C4C2×#15711yescharacteristic
121M16—22no—
122M16—184no—
123C2×C8—91no—
124C2×C8—91no—
125C2×C8—92no—
126C2×C8—92no—
127C2×C8—182no—
128C2×C8—182no—
129C2×C8C2×#15712yes—
130C16—184no—
131C22×C3—22no—
132C22×C3—24no—
133C22×C3—44no—
134C2×D3—68no—
135C2×D3—128no—
136C3×C4—22no—
137C3×C4—24no—
138C3×C4—22no—
139Dic3—68no—
140C32#211511yescharacteristic, complemented, Sylow
141C23—92no—
142C23#378711yescharacteristic
143Q8—182no—
144D4—184no—
145D4—182no—
146C2×C4—92no—
147C2×C4—182no—
148C2×C4—182no—
149C2×C4#378711yescharacteristic
150C2×C4#378812yes—
151C2×C4C22⋊#15712yes—
152C2×C4C22×#15711yescharacteristic
153C8—22no—
154C8—92no—
155C8—91no—
156C8—91no—
157C2×C3—24no—
158C2×C3—22no—
159C2×C3—44no—
160D3—128no—
161C22—41no—
162C22—182no—
163C22—362no—
164C22#6377812yes—
165C22C2×#378711yescharacteristic
166C4—182no—
167C4#6377812yes—
168C4C2×#378811yescharacteristic
169C4C2×C22⋊#15711yescharacteristic
170C3—22no—
171C2—21no—
172C2—22no—
173C2—362no—
174C2C2×#6377811yescharacteristic
subgroupG/H
centerC4C2×C22⋊#157
commutatorC22×C32C22×C8
FrattiniC2×C4C22×#157
FittingC2×C32×M16C4
socleC2×C32C2×C22⋊C8
prime radicalC2×#3828C4
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×M16#157
hypocenterC32#2115
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63773C2semidirect
3. #10590180C2semidirect
140. C32#2115semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
C2×#637732
#105901802
#21159