Finite Group Databasebeta

← #11771417

Subgroups — #11771417

Order 1152.

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

normal subgroups only

This group has 351 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#10592825C211yesmaximal, characteristic
2C3×#4553C212yesmaximal, complemented
3#67530—32nomaximal
4C22×C4×C3⋊D3C411yescharacteristic
5C2×C32×M16C2211yescharacteristic
6C2×#3748C411yescharacteristic
7#63647—22no—
8C3×#812—22no—
9#5126—32no—
10#5126—61no—
11C3×#349—32no—
12#4553D312yescomplemented
13C23×C3⋊D3C811yescharacteristic
14C22×C32×C4C2×C411yescharacteristic
15C22×C3⋊Dic3C811yescharacteristic
16C2×C4×C3⋊D3—21no—
17C2×C4×C3⋊D3—21no—
18C2×C4×C3⋊D3—41no—
19C2×C4×C3⋊D3—41no—
20C32×M16—41no—
21C2×C32×C8D412yes—
22#3748—41no—
23C2×C3⋊(C3⋊C8)—21no—
24C3×C3⋊C16—42no—
25#1320—91noSylow
26C22×C4×D3—32no—
27C22×C4×D3—61no—
28C2×C3×M16—21no—
29C2×C3×M16C2×D312yes—
30C2×#208—32no—
31C2×#208—61no—
32C3×M32—62no—
33(C2×D3)⋊C8—64no—
34(C2×D3)⋊C8—62no—
35(C2×D3)⋊C8—62no—
36#812—22no—
37C23×C32C2×C811yescharacteristic
38C22×C3⋊D3—21no—
39C22×C3⋊D3—42no—
40C22×C3⋊D3—41no—
41C2×C32×C4—21no—
42C2×C32×C4—21no—
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4M1611yescharacteristic
45C2×C3⋊Dic3—21no—
46C2×C3⋊Dic3—41no—
47C4×C3⋊D3—42no—
48C4×C3⋊D3—41no—
49C4×C3⋊D3—41no—
50C32×C8—22no—
51C3⋊(C3⋊C8)—41no—
52#407—91no—
53#349—32no—
54C23×D3—32no—
55C23×D3—61no—
56C22×C3×C4—21no—
57C22×C3×C4C4×D312yes—
58C22×Dic3—32no—
59C22×Dic3—61no—
60C2×C4×D3—62no—
61C2×C4×D3—62no—
62C2×C4×D3—62no—
63C2×C4×D3—62no—
64C2×C4×D3—122no—
65C2×C4×D3—122no—
66C2×C4×D3—122no—
67C2×C4×D3—122no—
68C3×M16—42no—
69C3×M16—42no—
70C2×C3×C8—22no—
71C2×C3×C8D1212yes—
72C2×C3×C8#6712yes—
73#208—122no—
74#208—122no—
75C2×C3⋊C8—62no—
76C2×C3⋊C8—62no—
77C3×C16—122no—
78C3⋊C16—42no—
79C22×C32—21no—
80C22×C32—41no—
81C22×C32C22⋊C811yescharacteristic
82C2×C3⋊D3—22no—
83C2×C3⋊D3—41no—
84C2×C3⋊D3—42no—
85C2×C3⋊D3—41no—
86C2×C3⋊D3—42no—
87C32×C4—21no—
88C32×C4#9911yescharacteristic
89C32×C4#10011yescharacteristic
90C3⋊Dic3—41no—
91C23×C4—91no—
92C2×M16—91no—
93C2×M16D3211yescharacteristic
94M32—62no—
95C22⋊C8—182no—
96C23×C3—21no—
97C23×C3D3×C812yes—
98C22×D3—62no—
99C22×D3—62no—
100C22×D3—124no—
101C22×D3—124no—
102C22×D3—122no—
103C22×D3—122no—
104C2×C3×C4—22no—
105C2×C3×C4—22no—
106C2×C3×C4—22no—
107C2×C3×C4—22no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4ΓL(1,𝔽25)12yes—
111C2×C3×C4(C2×D3)⋊C412yes—
112C2×Dic3—62no—
113C2×Dic3—62no—
114C2×Dic3—122no—
115C2×Dic3—122no—
116C4×D3—124no—
117C4×D3—124no—
118C4×D3—122no—
119C4×D3—122no—
120C4×D3—122no—
121C4×D3—122no—
122C3×C8—22no—
123C3×C8—22no—
124C3×C8—42no—
125C3⋊C8—122no—
126C3⋊C8—122no—
127C2×C32—21no—
128C2×C32—41no—
129C2×C32#32311yescharacteristic
130C3⋊D3—42no—
131C24—91no—
132C22×C4—91no—
133C22×C4—181no—
134C22×C4—181no—
135C22×C4—361no—
136C22×C4—361no—
137C22×C4#62411yescharacteristic
138M16—41no—
139M16—361no—
140C2×C8—181no—
141C2×C8#62612yes—
142C16—122no—
143C22×C3—22no—
144C22×C3—22no—
145C22×C3—21no—
146C22×C3—42no—
147C22×C3—42no—
148C22×C3(C2×D3)⋊C812yes—
149C2×D3—64no—
150C2×D3—64no—
151C2×D3—122no—
152C2×D3—122no—
153C2×D3—122no—
154C2×D3—124no—
155C2×D3—124no—
156C2×D3—124no—
157C2×D3—122no—
158C2×D3—124no—
159C3×C4—22no—
160C3×C4—22no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4#80612yes—
164C3×C4#82312yes—
165Dic3—122no—
166Dic3—122no—
167C32#132011yescharacteristic, complemented, Sylow
168C23—181no—
169C23—361no—
170C23—362no—
171C23#371011yescharacteristic
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—181no—
175C2×C4—362no—
176C2×C4—361no—
177C2×C4—361no—
178C2×C4—361no—
179C2×C4#371211yescharacteristic
180C2×C4#372211yescharacteristic
181C8—22no—
182C8—361no—
183C2×C3—22no—
184C2×C3—22no—
185C2×C3—21no—
186C2×C3—42no—
187C2×C3—42no—
188C2×C3#446812yes—
189D3—124no—
190D3—124no—
191C22—21no—
192C22—41no—
193C22—182no—
194C22—361no—
195C22—362no—
196C22—362no—
197C22—361no—
198C22#6355711yescharacteristic
199C4—21no—
200C4—361no—
201C4#6355911yescharacteristic
202C4#6358111yescharacteristic
203C3—21no—
204C3#6753012yescomplemented
205C2—21no—
206C2—41no—
207C2—362no—
208C2#1058914611yescharacteristic
subgroupG/H
centerC4#63581
commutatorC23×C32C2×C8
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#323
prime radicalC23×C3⋊D3C8
hypocenterC32#1320
LCSG ▷ C23×C32 ▷ 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
167. C32#1320semidirect
204. C3#67530semidirect

Maximal subgroups

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

subgroupindex
#105928252
C3×#45532
#675303