Finite Group Databasebeta

← #11771430

Subgroups — #11771430

Order 1152.

303 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 303 conjugacy classes of subgroups — too many to draw. Only its 58 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#10592828C211yesmaximal, characteristic
2C3×#4553C212yesmaximal, complemented
3#67531—32nomaximal
4C2×#3828C411yescharacteristic
5C2×C32×M16C2211yescharacteristic
6C22×C3⋊(C3⋊C8)C411yescharacteristic
7#63647—22no—
8C3×#812—22no—
9#5129—32no—
10#5129—61no—
11C3×#349—32no—
12#4553D312yescomplemented
13C22×C32×C4C2×C411yescharacteristic
14C2×#638—21no—
15#3828—41no—
16#3828—41no—
17C2×C4⋊(C3⋊D3)C811yescharacteristic
18C2×C4×C3⋊D3—21no—
19C2×#634C811yescharacteristic
20C32×M16—41no—
21C2×C32×C8D412yes—
22C2×C3⋊(C3⋊C8)—21no—
23C2×C3⋊(C3⋊C8)—41no—
24C3×C3⋊C16—42no—
25#1321—91noSylow
26C2×#235—32no—
27C2×#235—61no—
28C2×C3×M16—21no—
29C2×C3×M16C2×D312yes—
30C22×C3⋊C8—32no—
31C22×C3⋊C8—61no—
32C3×M32—62no—
33(C2×D3)⋊C8—64no—
34(C2×D3)⋊C8—62no—
35(C2×D3)⋊C8—62no—
36#812—22no—
37C23×C32M1611yescharacteristic
38C22×C3⋊D3—21no—
39C2×C32×C4—21no—
40C2×C32×C4—21no—
41C2×C32×C4C22⋊C411yescharacteristic
42C2×C32×C4C2×C811yescharacteristic
43#638—42no—
44C2×C3⋊Dic3—21no—
45C4⋊(C3⋊D3)—41no—
46C4×C3⋊D3—41no—
47C4×C3⋊D3—41no—
48#634—41no—
49C32×C8—22no—
50C3⋊(C3⋊C8)—41no—
51#408—91no—
52#349—32no—
53C22×C3×C4—21no—
54C22×C3×C4C4×D312yes—
55C2×#67—62no—
56C2×#67—62no—
57#235—122no—
58#235—122no—
59#235—122no—
60#235—122no—
61C2×D12—32no—
62C2×D12—61no—
63C2×C4×D3—62no—
64C2×C4×D3—62no—
65C2×Dic6—32no—
66C2×Dic6—61no—
67C3×M16—42no—
68C3×M16—42no—
69C2×C3×C8—22no—
70C2×C3×C8D1212yes—
71C2×C3×C8#6712yes—
72C2×C3⋊C8—62no—
73C2×C3⋊C8—62no—
74C2×C3⋊C8—122no—
75C2×C3⋊C8—122no—
76C3×C16—122no—
77C3⋊C16—42no—
78C22×C32—21no—
79C22×C32—41no—
80C22×C32C22⋊C811yescharacteristic
81C2×C3⋊D3—42no—
82C2×C3⋊D3—41no—
83C32×C4—21no—
84C32×C4#9911yescharacteristic
85C32×C4#10011yescharacteristic
86C3⋊Dic3—41no—
87C2×#41—91no—
88C2×M16D3211yescharacteristic
89C22×C8—91no—
90M32—62no—
91C22⋊C8—182no—
92C23×C3—21no—
93C23×C3ΓL(1,𝔽25)12yes—
94C22×D3—62no—
95C22×D3—62no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×C3×C4—22no—
99C2×C3×C4—22no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4D3×C812yes—
103C2×C3×C4(C2×D3)⋊C412yes—
104#67—124no—
105#67—124no—
106C2×Dic3—62no—
107C2×Dic3—62no—
108D12—122no—
109D12—122no—
110C4×D3—122no—
111C4×D3—122no—
112C4×D3—122no—
113C4×D3—122no—
114Dic6—122no—
115Dic6—122no—
116C3×C8—22no—
117C3×C8—22no—
118C3×C8—42no—
119C3⋊C8—122no—
120C3⋊C8—122no—
121C2×C32—21no—
122C2×C32—41no—
123C2×C32#32311yescharacteristic
124C3⋊D3—81no—
125#41—361no—
126#41—361no—
127C2×Q8—91no—
128C2×D4—91no—
129C2×D4—181no—
130C22×C4—181no—
131C22×C4#62411yescharacteristic
132M16—41no—
133C2×C8—181no—
134C2×C8—361no—
135C2×C8#62612yes—
136C16—122no—
137C22×C3—22no—
138C22×C3—22no—
139C22×C3—21no—
140C22×C3—42no—
141C22×C3—42no—
142C22×C3(C2×D3)⋊C812yes—
143C2×D3—122no—
144C2×D3—124no—
145C2×D3—124no—
146C2×D3—122no—
147C3×C4—22no—
148C3×C4—22no—
149C3×C4—21no—
150C3×C4—21no—
151C3×C4#80612yes—
152C3×C4#82312yes—
153Dic3—122no—
154Dic3—122no—
155C32#132111yescharacteristic, complemented, Sylow
156C23—181no—
157C23#371211yescharacteristic
158Q8—361no—
159D4—361no—
160D4—362no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—181no—
164C2×C4—361no—
165C2×C4—361no—
166C2×C4#371011yescharacteristic
167C2×C4#372211yescharacteristic
168C8—22no—
169C8—361no—
170C2×C3—22no—
171C2×C3—22no—
172C2×C3—21no—
173C2×C3—42no—
174C2×C3—42no—
175C2×C3#446812yes—
176D3—242no—
177D3—242no—
178C22—21no—
179C22—41no—
180C22—362no—
181C22—361no—
182C22#6355711yescharacteristic
183C4—21no—
184C4—361no—
185C4#6355911yescharacteristic
186C4#6358111yescharacteristic
187C3—21no—
188C3#6753112yescomplemented
189C2—21no—
190C2—41no—
191C2—721no—
192C2#1058914611yescharacteristic
subgroupG/H
centerC4#63581
commutatorC2×C32×C4C2×C8
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#323
prime radicalC2×#3828C4
hypocenterC32#1321
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#4553C2semidirect
12. #4553D3semidirect
155. C32#1321semidirect
188. C3#67531semidirect

Maximal subgroups

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

subgroupindex
#105928282
C3×#45532
#675313