Finite Group Databasebeta

← #11799431

Subgroups — #11799431

Order 1152.

322 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 66 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#10592606C211yesmaximal, characteristic
2#10590933C212yesmaximal
3C2×#63550C211yesmaximal, characteristic, complemented
4C3×#4517C212yesmaximal, complemented
5#10589144C211yesmaximal, characteristic, complemented
6#69270—32nomaximal
7#64110C2211yescharacteristic
8C2×C3×Dic12C2212yes—
9#63833—22no—
10C32×M32C2211yescharacteristic
11C2×C3⋊(C3⋊C16)C2211yescharacteristic
12#63625—21no—
13C16×C3⋊D3—21no—
14C3×#819C2212yes—
15#63560—22no—
16#63550—21no—
17#63550—21no—
18#5192—32no—
19C2×#829—32no—
20#4907—32no—
21#4907—61no—
22#4896—32no—
23C3×#362—32no—
24#4517D312yescomplemented
25#4493—32no—
26#3828D411yescharacteristic
27C2×C3×Dic6—22no—
28C2×C32×C8C2311yescharacteristic
29#3748D411yescharacteristic
30#3743—21no—
31C8×C3⋊D3—21no—
32C3×#208—22no—
33C3×Dic12—22no—
34C3×Dic12—22no—
35#3719—42no—
36#3717—42no—
37C32×C16—21no—
38C3⋊(C3⋊C16)D411yescharacteristic
39C3⋊(C3⋊C16)D411yescharacteristic
40#2222—91noSylow
41C2×C3×Q16—32no—
42#942—62no—
43#909—62no—
44C2×Dic12C2×D312yes—
45#901—32no—
46#901—61no—
47C3×M32—21no—
48C3×M32C2×D312yes—
49C3×#108—32no—
50#836—62no—
51#829—62no—
52#829—62no—
53#824—62no—
54#819C2×D312yes—
55C2×C3⋊C16—32no—
56C2×C3⋊C16—61no—
57#798—62no—
58#798—62no—
59D3×C16—62no—
60D3×C16—62no—
61C2×C32×C4C2×D411yescharacteristic
62#638—21no—
63C4⋊(C3⋊D3)D811yescharacteristic
64C4×C3⋊D3—21no—
65#634D811yescharacteristic
66C2×C3×Dic3—42no—
67C3×Dic6—42no—
68C3×Dic6—42no—
69C32×C8C2×D411yescharacteristic
70C32×C8#4111yescharacteristic
71C3⋊(C3⋊C8)—21no—
72C3×C3⋊C8—42no—
73C2×Q32—91no—
74#504—91no—
75#473—92no—
76#368—91no—
77#362—32no—
78C2×C3×Q8—62no—
79#235—32no—
80#235—61no—
81C2×Dic6—22no—
82C3×Q16—62no—
83C3×Q16—62no—
84C3×M16—62no—
85C2×C3×C8—21no—
86C2×C3×C8C22×D312yes—
87#216—122no—
88#215—122no—
89#208—22no—
90#208—32no—
91#208—61no—
92Dic12—22no—
93Dic12—22no—
94Dic12—122no—
95#204—122no—
96ΓL(1,𝔽25)—62no—
97ΓL(1,𝔽25)—62no—
98D3×C8—62no—
99D3×C8—62no—
100C3×C16—22no—
101C3×C16—22no—
102C3⋊C16—32no—
103C3⋊C16—32no—
104C3⋊C16—61no—
105C3⋊C16—61no—
106C22×C32#13511yescharacteristic
107C2×C3⋊D3—21no—
108C32×C4#12111yescharacteristic
109C32×C4C2×D811yescharacteristic
110C3⋊Dic3—21no—
111C3×Dic3—82no—
112#137—182no—
113C2×Q16—32no—
114#131—91no—
115Q32—181no—
116Q32—181no—
117M32—181no—
118M32D3211yescharacteristic
119C2×C16—91no—
120C2×C16—181no—
121#108—32no—
122#101—182no—
123C3×Q8—122no—
124C3×Q8—122no—
125C2×C3×C4—21no—
126C2×C3×C4—122no—
127C2×C3×C4D3×D412yes—
128#67—62no—
129#67—62no—
130C2×Dic3—42no—
131D12—32no—
132D12—61no—
133C4×D3—62no—
134C4×D3—62no—
135Dic6—32no—
136Dic6—42no—
137Dic6—42no—
138Dic6—61no—
139C3×C8—21no—
140C3×C8—21no—
141C3×C8—122no—
142C3×C8#23512yes—
143C3×C8D3×D412yes—
144C3⋊C8—42no—
145C3⋊C8—62no—
146C3⋊C8—62no—
147C2×C32—21no—
148C2×C32#46611yescharacteristic
149C3⋊D3—41no—
150#41—91no—
151C2×Q8—62no—
152Q16—62no—
153Q16—62no—
154Q16—362no—
155SD16—362no—
156M16—62no—
157M16—91no—
158M16—181no—
159C2×C8—181no—
160C2×C8C2×D3211yescharacteristic
161C16—21no—
162C16—91no—
163C16—91no—
164C22×C3—21no—
165C22×C3#91612yes—
166C2×D3—62no—
167C2×D3—62no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—242no—
171C3×C4#88412yes—
172C3×C4D3×D812yes—
173Dic3—62no—
174Dic3—62no—
175Dic3—82no—
176C32#222211yescharacteristic, complemented, Sylow
177Q8—91no—
178Q8—122no—
179Q8—122no—
180D4—91no—
181D4—181no—
182C2×C4—122no—
183C2×C4—181no—
184C2×C4#380211yescharacteristic
185C8—122no—
186C8—181no—
187C8#379811yescharacteristic
188C8#381111yescharacteristic
189C2×C3—22no—
190C2×C3—21no—
191C2×C3—41no—
192C2×C3#477512yes—
193D3—122no—
194D3—122no—
195C22—181no—
196C22#6380911yescharacteristic
197C4—181no—
198C4—242no—
199C4#6379711yescharacteristic
200C4#6391211yescharacteristic
201C3—21no—
202C3#6927012yescomplemented
203C2—21no—
204C2—361no—
205C2#1059083911yescharacteristic
subgroupG/H
centerC2#10590839
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#466
prime radical#3828D4
hypercenterM32D32
hypocenterC32#2222
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
3. C2×#63550C2semidirect
4. C3×#4517C2semidirect
5. #10589144C2semidirect
24. #4517D3semidirect
176. C32#2222semidirect
202. C3#69270semidirect

Maximal subgroups

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

subgroupindex
#105926062
#105909332
C2×#635502
C3×#45172
#105891442
#692703