Finite Group Databasebeta

← #11773841

Subgroups — #11773841

Order 1152.

326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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×Q8×#157C211yesmaximal, characteristic
2#10596484C212yesmaximal
3#10593260C214yesmaximal
4C2×Q8×C3⋊D3C411yescharacteristic
5Q8×#157—22no—
6Q8×#157—22no—
7C2×C4⋊#157C411yescharacteristic
8C2×C4⋊#157C2212yes—
9C2×C4×#157C412yes—
10C2×C4×#157C2211yescharacteristic
11C22⋊AGL(1,𝔽9)C2214yes—
12C4⋊AGL(1,𝔽9)—22no—
13C4×AGL(1,𝔽9)—22no—
14C22×#157C2×C411yescharacteristic
15C22×#157C2×C412yes—
16C22×#157C2311yescharacteristic
17C2×AGL(1,𝔽9)—24no—
18C2×C32×Q8C811yescharacteristic, complemented
19Q8×C3⋊D3—22no—
20Q8×C3⋊D3—22no—
21C2×C4×C3⋊D3C2×C412yes—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×#634C811yescharacteristic, complemented
24C2×#634C812yescomplemented
25C4⋊#157—24no—
26C4⋊#157—22no—
27C4×#157—22no—
28C4×#157—22no—
29C4×#157D412yes—
30C4×#157D412yes—
31#1461—91nomaximal, Sylow
32C2×D3×Q8—121no—
33C22×C3⋊D3C22×C411yescharacteristic
34C2×#157—22no—
35C2×#157—22no—
36C2×#157—41no—
37C2×#157—42no—
38C2×#157C22⋊C411yescharacteristic
39C2×#157C22⋊C411yescharacteristic
40C2×#157C2×D412yes—
41AGL(1,𝔽9)—44no—
42C32×Q8—22no—
43C2×C32×C4C2×C812yes—
44C2×C32×C4C2×C811yescharacteristic
45C2×C3⋊Dic3C2×C812yes—
46C2×C3⋊Dic3C2×C811yescharacteristic
47C4×C3⋊D3—22no—
48C4×C3⋊D3—22no—
49C4×C3⋊D3C22⋊C412yes—
50C4×C3⋊D3M1612yes—
51#634—22no—
52#634—24no—
53C2×C4×Q8—91no—
54#431—92no—
55#324—94no—
56C2×C3×Q8—41no—
57D3×Q8—124no—
58D3×Q8—124no—
59C2×C4×D3—121no—
60C2×C4×D3—122no—
61C2×Dic6—122no—
62C2×Dic6—121no—
63C22×C32C22×C811yescharacteristic
64C2×C3⋊D3—21no—
65C2×C3⋊D3—21no—
66C2×C3⋊D3C2×C22⋊C411yescharacteristic
67C2×C3⋊D3C2×M1611yescharacteristic
68#157—22no—
69#157—21no—
70#157—42no—
71#157#10112yes—
72C32×C4—22no—
73C32×C4C22⋊C812yes—
74C3⋊Dic3—22no—
75C3⋊Dic3C22⋊C812yes—
76C22×Q8—91no—
77C4×Q8—182no—
78C4×Q8—182no—
79C2×C4⋊C4—91no—
80C2×C4⋊C4—92no—
81C2×C42—91no—
82C2×C42—92no—
83C4⋊C8—182no—
84C22⋊C8—94no—
85C4×C8—182no—
86C22×D3—121no—
87C3×Q8—44no—
88C2×C3×C4—42no—
89C2×C3×C4—41no—
90C2×Dic3—121no—
91C2×Dic3—122no—
92C4×D3—122no—
93C4×D3—122no—
94C4×D3—124no—
95C4×D3—124no—
96Dic6—128no—
97Dic6—124no—
98C2×C32—21no—
99C2×C32C2×C22⋊C811yescharacteristic
100C3⋊D3—21no—
101C3⋊D3#41011yescharacteristic
102C3⋊D3C2×#10111yescharacteristic
103C2×Q8—92no—
104C2×Q8—91no—
105C2×Q8—182no—
106C2×Q8—182no—
107C2×Q8AGL(1,𝔽9)11yescharacteristic, complemented
108C22×C4—91no—
109C22×C4—91no—
110C22×C4—91no—
111C22×C4—92no—
112C22×C4—92no—
113C2×C8—184no—
114C4⋊C4—182no—
115C4⋊C4—184no—
116C42—92no—
117C42—92no—
118C42—182no—
119C42—182no—
120C22×C3—41no—
121C2×D3—121no—
122C2×D3—121no—
123C2×D3—122no—
124C2×D3—122no—
125C3×C4—44no—
126C3×C4—42no—
127Dic3—122no—
128Dic3—124no—
129C32#146111yescharacteristic, complemented, Sylow
130C23—91no—
131Q8—22no—
132Q8—184no—
133Q8—182no—
134C2×C4—91no—
135C2×C4—91no—
136C2×C4—92no—
137C2×C4—92no—
138C2×C4—91no—
139C2×C4—92no—
140C2×C4—92no—
141C2×C4—182no—
142C2×C4—182no—
143C2×C4—182no—
144C2×C4—182no—
145C2×C4—361no—
146C2×C4—362no—
147C2×C4C2×AGL(1,𝔽9)12yes—
148C2×C4C2×AGL(1,𝔽9)11yescharacteristic
149C8—364no—
150C2×C3—42no—
151C2×C3—41no—
152D3—121no—
153D3—121no—
154D3—122no—
155C22—91no—
156C22—91no—
157C22—181no—
158C22—181no—
159C22C22×AGL(1,𝔽9)11yescharacteristic
160C4—22no—
161C4—92no—
162C4—92no—
163C4—182no—
164C4—181no—
165C4—182no—
166C4—362no—
167C4C22⋊AGL(1,𝔽9)12yes—
168C3—41no—
169C2—21no—
170C2—91no—
171C2—91no—
172C2—181no—
173C2C2×C22⋊AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC2C2×C22⋊AGL(1,𝔽9)
commutatorC22×C32C22×C8
FrattiniC22C22×AGL(1,𝔽9)
FittingC2×C32×Q8C8
socleC2×C32C2×C22⋊C8
prime radicalC22×C3⋊D3C22×C4
cosocleC22×#157C23
hypercenterC2×Q8AGL(1,𝔽9)
hypocenterC32#1461
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
18. C2×C32×Q8C8semidirect
23. C2×#634C8semidirect
24. C2×#634C8semidirect
107. C2×Q8AGL(1,𝔽9)semidirect
129. C32#1461semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#1572
#105964842
#105932602
#14619