Finite Group Databasebeta

← #11772287

Subgroups — #11772287

Order 1152.

258 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 53 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#10593762C211yesmaximal, characteristic
2#10590668C211yesmaximal, characteristic
3#10590625C211yesmaximal, characteristic
4C2×C8×C3⋊D3C2211yescharacteristic
5C4×#624C411yescharacteristic
6C2×#3710C411yescharacteristic
7#63773—21no—
8#63765—21no—
9#63764C412yescomplemented
10C3×#815—21no—
11C3×#812—21no—
12#63554—21no—
13#63544—21no—
14#63542C412yescomplemented
15D3×M32—61no—
16D3×#97—61no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×#624—21no—
19C2×C32×C8D411yescharacteristic
20C2×C3⋊(C3⋊C8)D411yescharacteristic
21C8×C3⋊D3C2×C411yescharacteristic
22C8×C3⋊D3C2×C411yescharacteristic
23C8×C3⋊D3D411yescharacteristic
24C8×C3⋊D3Q811yescharacteristic
25C3×C4×Dic3—21no—
26C2×C3×C3⋊C8—21no—
27Dic32C812yes—
28#3710—21no—
29#3710C812yes—
30#3708—22no—
31C3×C3⋊C16—22no—
32#1375—91nomaximal, Sylow
33C2×D3×C8—61no—
34C2×D3×C8—61no—
35C2×D3×C8—61no—
36C42×D3—61no—
37C3×M32—61no—
38C3×#97—61no—
39#815—21no—
40#815—61no—
41#812—21no—
42#803—61no—
43#798—62no—
44D3×C16—62no—
45C22×C3⋊D3M1611yescharacteristic
46C2×C32×C4C22⋊C411yescharacteristic
47C2×C3⋊Dic3C2×C811yescharacteristic
48C4×C3⋊D3C4211yescharacteristic
49C4×C3⋊D3C4⋊C411yescharacteristic
50C4×C3⋊D3C2×C811yescharacteristic
51C4×C3⋊D3M1611yescharacteristic
52C2×C3×Dic3—22no—
53#624—42no—
54C32×C8C22⋊C411yescharacteristic
55C32×C8C4⋊C411yescharacteristic
56C3⋊(C3⋊C8)C22⋊C411yescharacteristic
57C3⋊(C3⋊C8)C4⋊C411yescharacteristic
58C3×C3⋊C8—22no—
59C2×M32—91no—
60C2×M32—91no—
61C2×#97—91no—
62C2×C4×D3—61no—
63C2×C4×D3—61no—
64C2×C4×D3—62no—
65C2×C3×C8—21no—
66C2×C3×C8—21no—
67C2×C3×C8—61no—
68C3×C42—61no—
69C4×Dic3—21no—
70C4×Dic3—62no—
71C2×C3⋊C8—21no—
72C2×C3⋊C8—61no—
73C2×C3⋊C8—61no—
74D3×C8—62no—
75D3×C8—61no—
76D3×C8—61no—
77D3×C8—61no—
78D3×C8—61no—
79D3×C8—61no—
80D3×C8—61no—
81D3×C8—61no—
82D3×C8—61no—
83D3×C8—62no—
84C3×C16—62no—
85C3⋊C16—22no—
86C22×C32C22⋊C811yescharacteristic
87C2×C3⋊D3—22no—
88C2×C3⋊D3#9711yescharacteristic
89C2×C3⋊D3C4⋊C811yescharacteristic
90C32×C4#9511yescharacteristic
91C32×C4C22⋊C811yescharacteristic
92C3⋊Dic3C4×C811yescharacteristic
93C3⋊Dic3C4⋊C811yescharacteristic
94C3×Dic3—42no—
95C22×C8—91no—
96C22×C8—91no—
97C2×C42—91no—
98M32—61no—
99M32—181no—
100M32—181no—
101M32—181no—
102C2×C16—92no—
103C2×C16—92no—
104#97—61no—
105#97—181no—
106C22×D3—61no—
107C22×D3—61no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—62no—
111C2×Dic3—22no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C4×D3—61no—
115C4×D3—61no—
116C4×D3—61no—
117C4×D3—61no—
118C4×D3—61no—
119C4×D3—61no—
120C4×D3—61no—
121C4×D3—61no—
122C4×D3—124no—
123C3×C8—21no—
124C3×C8—21no—
125C3×C8—21no—
126C3×C8—21no—
127C3×C8—62no—
128C3⋊C8—22no—
129C3⋊C8—61no—
130C3⋊C8—61no—
131C3⋊C8—61no—
132C3⋊C8—61no—
133C2×C32—21no—
134C2×C32#33611yescharacteristic
135C3⋊D3—21no—
136C3⋊D3#34712yes—
137C22×C4—91no—
138C22×C4—181no—
139C2×C8—61no—
140C2×C8—92no—
141C2×C8—91no—
142C2×C8—91no—
143C2×C8—91no—
144C2×C8—91no—
145C2×C8—91no—
146C2×C8—181no—
147C2×C8GO+(4,𝔽2)11yescharacteristic
148C42—61no—
149C42—92no—
150C16—62no—
151C16—182no—
152C22×C3—21no—
153C22×C3—21no—
154C2×D3—61no—
155C2×D3—61no—
156C2×D3—61no—
157C2×D3—61no—
158C2×D3—64no—
159C2×D3—122no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—122no—
165Dic3—42no—
166Dic3—61no—
167Dic3—61no—
168Dic3—61no—
169Dic3—61no—
170C32#137511yescharacteristic, complemented, Sylow
171C23—91no—
172C2×C4—62no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—362no—
179C2×C4D32⋊C411yescharacteristic
180C8—62no—
181C8—91no—
182C8—91no—
183C8D32⋊C411yescharacteristic
184C8#377311yescharacteristic
185C2×C3—22no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—41no—
189D3—62no—
190D3—62no—
191D3—62no—
192D3—121no—
193C22—91no—
194C22—91no—
195C22—182no—
196C22D32⋊C811yescharacteristic
197C4—91no—
198C4—91no—
199C4—122no—
200C4D32⋊C811yescharacteristic
201C4#6373711yescharacteristic
202C3—21no—
203C3—21no—
204C2—21no—
205C2—92no—
206C2—181no—
207C2#1059004311yescharacteristic
subgroupG/H
centerC4#63737
commutatorC3⋊Dic3C4×C8
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#336
prime radicalC22×C3⋊D3M16
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1375
LCSG ▷ C3⋊Dic3 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
9. #63764C4semidirect
14. #63542C4semidirect
170. C32#1375semidirect

Maximal subgroups

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

subgroupindex
#105937622
#105906682
#105906252
#13759