Finite Group Databasebeta

← #11797029

Subgroups — #11797029

Order 1152.

385 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 385 conjugacy classes of subgroups — too many to draw. Only its 114 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#10592388C211yesmaximal, characteristic
2C2×#63544C211yesmaximal, characteristic
3C2×#63542C211yesmaximal, characteristic
4C3×C4⋊(C3⋊C16)C212yesmaximal, complemented
5#10589133C212yesmaximal, complemented
6#69285—32nomaximal
7C2×#3743C411yescharacteristic
8C2×C8×C3⋊D3C2211yescharacteristic
9#64081C411yescharacteristic
10C32×C4×C8C2211yescharacteristic
11#63642C411yescharacteristic
12C8×C3⋊Dic3C2211yescharacteristic
13#63630C411yescharacteristic
14C2×C3×C3⋊C16C2212yes—
15C2×C3×C3⋊C16C2212yes—
16#63544—22no—
17#63542—22no—
18C2×#798—32no—
19C2×D3×C16—32no—
20#4689—32no—
21#4689—61no—
22C3×C4⋊C16—32no—
23Dic3⋊C16—32no—
24Dic3⋊C16—32no—
25C4⋊(C3⋊C16)D312yescomplemented
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C32×C8C2×C411yescharacteristic
28C2×C32×C8C2311yescharacteristic
29C32×C42C2×C411yescharacteristic
30#3752C812yes—
31#3750C812yes—
32C4×C3⋊Dic3C2×C411yescharacteristic
33C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
34C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
35#3743—22no—
36C8×C3⋊D3D412yes—
37C8×C3⋊D3Q812yes—
38C3×C3⋊C16—22no—
39C3×C3⋊C16—22no—
40#2151—91noSylow
41C2×ΓL(1,𝔽25)—32no—
42C2×ΓL(1,𝔽25)—61no—
43C2×D3×C8—32no—
44C2×D3×C8—61no—
45#872—32no—
46#872—61no—
47C2×C3×C16—32no—
48C2×C3×C16—32no—
49C3×C4×C8—21no—
50C3×C4×C8C2×D312yes—
51#815—32no—
52#815—61no—
53C8×Dic3—32no—
54C8×Dic3—61no—
55C2×C3⋊C16C2×D312yes—
56C2×C3⋊C16C2×D312yes—
57#803—32no—
58#803—61no—
59#798—64no—
60D3×C16—64no—
61C22×C3⋊D3C2×C811yescharacteristic
62C2×C32×C4C2×C812yes—
63C2×C32×C4C22×C411yescharacteristic
64C2×C3⋊Dic3C2×C812yes—
65C2×C3⋊Dic3C2×C811yescharacteristic
66C4×C3⋊D3C4⋊C412yes—
67C4×C3⋊D3M1612yes—
68C32×C8—21no—
69C32×C8C2×D411yescharacteristic
70C32×C8C2×Q811yescharacteristic
71C3⋊(C3⋊C8)—21no—
72C3⋊(C3⋊C8)C4⋊C412yes—
73C2×M32—91no—
74C22×C16—91no—
75#405—91no—
76C4⋊C16—32no—
77C4⋊C16—92no—
78C2×C4×D3—32no—
79C2×C4×D3—61no—
80C2×C3×C8—21no—
81C2×C3×C8—21no—
82C2×C3×C8C4×D312yes—
83C2×C3×C8C22×D312yes—
84C3×C42—21no—
85C3×C42C4×D312yes—
86(C2×D3)⋊C4—32no—
87(C2×D3)⋊C4—32no—
88(C2×D3)⋊C4—62no—
89Dic3⋊C4—32no—
90Dic3⋊C4—32no—
91Dic3⋊C4—62no—
92C4×Dic3—32no—
93C4×Dic3—61no—
94C2×C3⋊C8—32no—
95C2×C3⋊C8—32no—
96C2×C3⋊C8—61no—
97C2×C3⋊C8—61no—
98ΓL(1,𝔽25)—64no—
99ΓL(1,𝔽25)—64no—
100D3×C8—34no—
101D3×C8—34no—
102D3×C8—62no—
103D3×C8—62no—
104C3×C16—62no—
105C3×C16—62no—
106C3⋊C16—22no—
107C3⋊C16—22no—
108C22×C32C22×C811yescharacteristic
109C2×C3⋊D3—22no—
110C2×C3⋊D3C4⋊C812yes—
111C32×C4—22no—
112C32×C4C2×C4⋊C411yescharacteristic
113C32×C4C2×M1611yescharacteristic
114C3⋊Dic3—22no—
115C3⋊Dic3C4⋊C812yes—
116C2×M16—91no—
117C22×C8—91no—
118#117—91no—
119M32—182no—
120C2×C16—32no—
121C2×C16—32no—
122C2×C16—182no—
123#97—91no—
124#97—91no—
125C4×C8—91no—
126C4×C8D3211yescharacteristic
127C22×D3—32no—
128C22×D3—61no—
129C2×C3×C4—22no—
130C2×C3×C4—21no—
131C2×C3×C4D3×C812yes—
132C2×C3×C4D3×C812yes—
133C2×C3×C4C2×C4×D312yes—
134C2×Dic3—32no—
135C2×Dic3—32no—
136C2×Dic3—32no—
137C2×Dic3—61no—
138C2×Dic3—62no—
139C4×D3—34no—
140C4×D3—34no—
141C4×D3—62no—
142C4×D3—62no—
143C3×C8—22no—
144C3×C8—22no—
145C3×C8—21no—
146C3×C8—21no—
147C3×C8D3×D412yes—
148C3×C8D3×Q812yes—
149C3⋊C8—34no—
150C3⋊C8—62no—
151C3⋊C8—62no—
152C3⋊C8—62no—
153C2×C32C2×C4⋊C811yescharacteristic
154C2×C32#50412yes—
155C3⋊D3—22no—
156C22×C4—91no—
157M16—182no—
158C2×C8—91no—
159C2×C8—92no—
160C2×C8—92no—
161C2×C8—91no—
162C2×C8#62411yescharacteristic
163C2×C8C2×D3211yescharacteristic
164C4⋊C4—92no—
165C22⋊C4—92no—
166C42—91no—
167C42#62411yescharacteristic
168C16—62no—
169C16—62no—
170C22×C3—21no—
171C22×C3C2×D3×C812yes—
172C2×D3—34no—
173C2×D3—62no—
174C2×D3—62no—
175C2×D3—62no—
176C2×D3—122no—
177C3×C4—22no—
178C3×C4—22no—
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—42no—
182C3×C4D3×C4⋊C412yes—
183C3×C4D3×M1612yes—
184Dic3—34no—
185Dic3—62no—
186Dic3—62no—
187Dic3—62no—
188Dic3—122no—
189C32#215111yescharacteristic, complemented, Sylow
190C23—91no—
191C2×C4—91no—
192C2×C4—92no—
193C2×C4—92no—
194C2×C4—92no—
195C2×C4#371012yes—
196C2×C4C2×#62411yescharacteristic
197C8—21no—
198C8—92no—
199C8—181no—
200C8#379711yescharacteristic
201C8#380211yescharacteristic
202C2×C3—21no—
203C2×C3—22no—
204C2×C3D3×C4⋊C812yes—
205C2×C3#490112yes—
206C2×C3#490712yes—
207D3—64no—
208D3—122no—
209C22—92no—
210C22—182no—
211C22C2×#371011yescharacteristic
212C4—22no—
213C4—92no—
214C4—182no—
215C4#6381811yescharacteristic
216C4#6390011yescharacteristic
217C3—21no—
218C3#6928512yescomplemented
219C2—182no—
220C2#1059033111yescharacteristic
221C2#1059062412yes—
subgroupG/H
center, FrattiniC2×C8C2×D32
commutator, socleC22×C32C22×C8
FittingC32×C4×C8C22
prime radicalC22×C3⋊D3C2×C8
cosocleC2×C32×C8C23
hypercenterC4×C8D32
hypocenterC32#2151
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
4. C3×C4⋊(C3⋊C16)C2semidirect
5. #10589133C2semidirect
25. C4⋊(C3⋊C16)D3semidirect
189. C32#2151semidirect
218. C3#69285semidirect

Maximal subgroups

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

subgroupindex
#105923882
C2×#635442
C2×#635422
C3×C4⋊(C3⋊C16)2
#105891332
#692853