Finite Group Databasebeta

← #11772642

Subgroups — #11772642

Order 1152.

244 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 37 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#10593824C211yesmaximal, characteristic
2#10593822C211yesmaximal, characteristic
3#10593818C211yesmaximal, characteristic
4C2×#3830C2211yescharacteristic
5C2×#3792—21no—
6C2×#3792C411yescharacteristic, complemented
7C22×#622C411yescharacteristic, complemented
8#64286—21no—
9#63788—21no—
10C22⋊#622—21no—
11#63786—21no—
12#63786C412yes—
13#63780C412yescomplemented
14#63778—21no—
15C2×C32×D4Q811yescharacteristic
16C2×#638C2×C411yescharacteristic
17C2×#638D411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C22×C3⋊Dic3D411yescharacteristic
20#3830—41no—
21#3830—41no—
22C2×C4×C3⋊D3D411yescharacteristic
23C2×#634C2×C411yescharacteristic
24C22⋊#157—22no—
25#3792—22no—
26#3792—41no—
27#3792—41no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622—41no—
31C2×#622—41no—
32C4⋊#157—41no—
33C4×#157—41no—
34#1395—91nomaximal, Sylow
35C2×#237—121no—
36C23×C32C4⋊C411yescharacteristic
37C23×C32C4⋊C411yescharacteristic
38C22×C3⋊D3C22⋊C411yescharacteristic
39C2×#157—42no—
40C32×D4—41no—
41C2×C32×C4C4⋊C411yescharacteristic
42#638—41no—
43#638—41no—
44C2×C3⋊Dic3—21no—
45C2×C3⋊Dic3—21no—
46C2×C3⋊Dic3—21no—
47C2×C3⋊Dic3—21no—
48C2×C3⋊Dic3C4211yescharacteristic
49C2×C3⋊Dic3C22⋊C411yescharacteristic
50C2×C3⋊Dic3C22⋊C411yescharacteristic
51C4×C3⋊D3—21no—
52C4×C3⋊D3—21no—
53#634—41no—
54#622—42no—
55#622—41no—
56#622—41no—
57#413—91no—
58#410—91no—
59#408—91no—
60C2×C3×D4—41no—
61C2×#67—121no—
62C2×#67—121no—
63C22×Dic3—121no—
64C22×Dic3—121no—
65#237—124no—
66#237—124no—
67C2×C4×D3—121no—
68C2×Dic6—121no—
69C22×C32—21no—
70C22×C32—21no—
71C22×C32—41no—
72C22×C32—41no—
73C22×C32#9511yescharacteristic
74C2×C3⋊D3—21no—
75C2×C3⋊D3—41no—
76#157—82no—
77C32×C4—21no—
78C3⋊Dic3—21no—
79C3⋊Dic3—21no—
80C3⋊Dic3#9911yescharacteristic
81C3⋊Dic3#9911yescharacteristic
82C2×#41—91no—
83C2×M16—91no—
84C2×M16—181no—
85C22×C8—91no—
86#117—181no—
87#101—92no—
88#100—181no—
89#99—92no—
90#99—181no—
91C22⋊C8—181no—
92C22⋊C8—181no—
93C23×C3—41no—
94C23×C3—41no—
95C22×D3—121no—
96C3×D4—44no—
97C2×C3×C4—41no—
98#67—124no—
99#67—124no—
100C2×Dic3—121no—
101C2×Dic3—121no—
102C2×Dic3—121no—
103C2×Dic3—122no—
104C2×Dic3—122no—
105C2×Dic3—122no—
106C2×Dic3—122no—
107C4×D3—122no—
108C4×D3—122no—
109Dic6—124no—
110C2×C32—21no—
111C2×C32—41no—
112C2×C32—41no—
113C2×C32#34211yescharacteristic
114C3⋊D3—41no—
115#41—361no—
116#41—361no—
117C2×Q8—91no—
118C2×D4—91no—
119C2×D4—91no—
120C2×D4PSU(3,𝔽2)11yescharacteristic
121C22×C4—91no—
122C22×C4—91no—
123C22×C4—91no—
124M16—182no—
125M16—361no—
126M16—361no—
127C2×C8—181no—
128C2×C8—181no—
129C2×C8—361no—
130C2×C8—361no—
131C4⋊C4—361no—
132C22⋊C4—182no—
133C42—361no—
134C22×C3—42no—
135C22×C3—42no—
136C22×C3—41no—
137C22×C3—82no—
138C22×C3—82no—
139C2×D3—122no—
140C2×D3—242no—
141C3×C4—42no—
142Dic3—121no—
143Dic3—121no—
144Dic3—122no—
145Dic3—122no—
146C32#139511yescharacteristic, complemented, Sylow
147C23—91no—
148C23#377711yescharacteristic
149C23#377711yescharacteristic
150Q8—361no—
151D4—41no—
152D4—361no—
153D4—361no—
154C2×C4—91no—
155C2×C4—91no—
156C2×C4—91no—
157C2×C4—181no—
158C2×C4—181no—
159C2×C4—181no—
160C2×C4—181no—
161C2×C4—181no—
162C2×C4—181no—
163C2×C4—362no—
164C2×C4#377711yescharacteristic
165C8—361no—
166C8—361no—
167C8—362no—
168C2×C3—42no—
169C2×C3—41no—
170C2×C3—82no—
171C2×C3—82no—
172D3—242no—
173C22—21no—
174C22—21no—
175C22—41no—
176C22—41no—
177C22—181no—
178C22—361no—
179C22#6374711yescharacteristic
180C4—21no—
181C4—91no—
182C4—91no—
183C4—181no—
184C4—181no—
185C4—722no—
186C3—41no—
187C2—21no—
188C2—41no—
189C2—41no—
190C2—361no—
191C2#1059009811yescharacteristic
subgroupG/H
centerC2#10590098
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC2×D4PSU(3,𝔽2)
FittingC2×C32×D4Q8
socleC2×C32#342
prime radical, cosocleC2×#3830C22
hypocenterC32#1395
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
6. C2×#3792C4semidirect
7. C22×#622C4semidirect
13. #63780C4semidirect
146. C32#1395semidirect

Maximal subgroups

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

subgroupindex
#105938242
#105938222
#105938182
#13959