Finite Group Databasebeta

← #11772543

Subgroups — #11772543

Order 1152.

230 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 47 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#10593771C211yesmaximal, characteristic
2#10590714C211yesmaximal, characteristic
3#10590625C211yesmaximal, characteristic
4#64283—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#63849—21no—
7#63771—21no—
8#63770C412yescomplemented
9C3×#818—21no—
10C3×#812—21no—
11#63574C412yes—
12#63544C412yescomplemented
13#63542—21no—
14D3×M32—61no—
15#4880—61no—
16C2×C4×C3⋊D3D411yescharacteristic
17#3792—41no—
18#3788—22no—
19#3787—41no—
20C2×C32×C8D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
22C8×C3⋊D3C2×C411yescharacteristic
23C8×C3⋊D3C2×C411yescharacteristic
24C8×C3⋊D3D411yescharacteristic
25C8×C3⋊D3Q811yescharacteristic
26C3×C4⋊Dic3—22no—
27#3722—41no—
28Dic32—41no—
29C3×C3⋊C16—22no—
30#1389—91nomaximal, Sylow
31C2×D3×C8—61no—
32C2×D3×C8—61no—
33#892—62no—
34C3×M32—61no—
35C3×#107—61no—
36#818—21no—
37#812—21no—
38#808—62no—
39#798—62no—
40D3×C16—62no—
41C22×C3⋊D3SD1611yescharacteristic
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C3⋊Dic3D811yescharacteristic
44C4×C3⋊D3C22⋊C411yescharacteristic
45C4×C3⋊D3C4⋊C411yescharacteristic
46C4×C3⋊D3SD1611yescharacteristic
47C4×C3⋊D3Q1611yescharacteristic
48C2×C3×Dic3—42no—
49#622—42no—
50C32×C8C22⋊C411yescharacteristic
51C32×C8C4⋊C411yescharacteristic
52C3⋊(C3⋊C8)C4211yescharacteristic
53C3⋊(C3⋊C8)C4⋊C411yescharacteristic
54C2×M32—91no—
55C2×#108—91no—
56#427—91no—
57C2×C4×D3—61no—
58C2×C4×D3—61no—
59C2×C3×C8—21no—
60C2×C3×C8—21no—
61C3×C4⋊C4—62no—
62(C2×D3)⋊C4—122no—
63C4⋊Dic3—22no—
64C4×Dic3—122no—
65C2×C3⋊C8—61no—
66C2×C3⋊C8—61no—
67D3×C8—61no—
68D3×C8—61no—
69D3×C8—61no—
70D3×C8—61no—
71D3×C8—61no—
72D3×C8—61no—
73D3×C8—61no—
74D3×C8—61no—
75C3×C16—62no—
76C3⋊C16—22no—
77C22×C32#10211yescharacteristic
78C2×C3⋊D3—41no—
79C2×C3⋊D3#10311yescharacteristic
80C2×C3⋊D3#10611yescharacteristic
81C32×C4#9511yescharacteristic
82C32×C4#10311yescharacteristic
83C3⋊Dic3#10211yescharacteristic
84C3⋊Dic3#10711yescharacteristic
85C3×Dic3—82no—
86C2×M16—181no—
87C22×C8—91no—
88#117—181no—
89M32—61no—
90M32—92no—
91C2×C16—181no—
92#108—92no—
93#108—181no—
94#107—61no—
95#106—92no—
96C22×D3—61no—
97C22×D3—61no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—122no—
101C2×Dic3—42no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104C4×D3—61no—
105C4×D3—61no—
106C4×D3—61no—
107C4×D3—61no—
108C4×D3—61no—
109C4×D3—61no—
110C4×D3—61no—
111C4×D3—61no—
112C3×C8—21no—
113C3×C8—21no—
114C3×C8—21no—
115C3×C8—21no—
116C3⋊C8—61no—
117C3⋊C8—61no—
118C3⋊C8—61no—
119C3⋊C8—61no—
120C2×C32—21no—
121C2×C32#34011yescharacteristic
122C3⋊D3—21no—
123C3⋊D3—21no—
124C22×C4—91no—
125M16—182no—
126M16—361no—
127C2×C8—91no—
128C2×C8—91no—
129C2×C8—91no—
130C2×C8—91no—
131C2×C8—91no—
132C2×C8—361no—
133C2×C8GO+(4,𝔽2)11yescharacteristic
134C4⋊C4—62no—
135C22⋊C4—361no—
136C42—361no—
137C16—62no—
138C22×C3—21no—
139C22×C3—21no—
140C2×D3—61no—
141C2×D3—61no—
142C2×D3—61no—
143C2×D3—61no—
144C2×D3—122no—
145C2×D3—121no—
146C2×D3—121no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—21no—
150C3×C4—21no—
151C3×C4—242no—
152Dic3—61no—
153Dic3—61no—
154Dic3—61no—
155Dic3—61no—
156Dic3—82no—
157C32#138911yescharacteristic, complemented, Sylow
158C23—91no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—122no—
165C2×C4D32⋊C411yescharacteristic
166C8—91no—
167C8—91no—
168C8—362no—
169C8D32⋊C411yescharacteristic
170C8#377311yescharacteristic
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—21no—
174C2×C3—21no—
175C2×C3—41no—
176D3—62no—
177D3—121no—
178D3—121no—
179D3—121no—
180C22—91no—
181C22—91no—
182C22—361no—
183C22#6372911yescharacteristic
184C4—91no—
185C4—91no—
186C4—242no—
187C4#6373011yescharacteristic
188C4#6373711yescharacteristic
189C3—21no—
190C3—21no—
191C2—21no—
192C2—181no—
193C2—181no—
194C2#1059004911yescharacteristic
subgroupG/H
centerC2#10590049
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#340
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1389
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
8. #63770C4semidirect
12. #63544C4semidirect
157. C32#1389semidirect

Maximal subgroups

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

subgroupindex
#105937712
#105907142
#105906252
#13899