Finite Group Databasebeta

← #11771037

Subgroups — #11771037

Order 1152.

469 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 469 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×#63657C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3#67687—32nomaximal
4C23×C32×C4C2211yescharacteristic
5C22×C3⋊(C3⋊C8)C412yes—
6C2×C3×#208—22no—
7#63657—22no—
8C3×#830—22no—
9C3×#830C414yes—
10C3×#407—32no—
11#5207D312yes—
12C2×#830—32no—
13C2×#830—61no—
14C24×C32Q811yescharacteristic
15C22×C32×C4—42no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C32×C4C2×C412yes—
18C22×C32×C4D412yes—
19C22×C32×C4D411yescharacteristic
20C2×C3⋊(C3⋊C8)—22no—
21C2×C3⋊(C3⋊C8)—42no—
22C3×#208—44no—
23C2×C3×C3⋊C8—24no—
24#1293—91noSylow
25C23×C3×C4—21no—
26C23×C3×C4C2×D312yes—
27C2×C3×M16—62no—
28C2×#208—22no—
29C22×C3⋊C8—34no—
30C22×C3⋊C8—62no—
31C3×C22⋊C8—34no—
32C3×C22⋊C8—62no—
33#830—22no—
34#830—64no—
35#830—62no—
36#830—62no—
37#830Dic314yes—
38C23×C32—22no—
39C23×C32—41no—
40C23×C32—41no—
41C23×C32C4⋊C411yescharacteristic
42C23×C32C4⋊C412yes—
43C2×C32×C4—22no—
44C2×C32×C4—24no—
45C2×C32×C4—42no—
46C2×C32×C4—41no—
47C2×C32×C4C4211yescharacteristic
48C2×C32×C4C22⋊C411yescharacteristic
49C2×C32×C4C22⋊C412yes—
50C3⋊(C3⋊C8)—42no—
51C3×C3⋊C8—44no—
52#407—32no—
53C2×C22⋊C8—91no—
54C24×C3—21no—
55C24×C3Dic612yes—
56C22×C3×C4—22no—
57C22×C3×C4—21no—
58C22×C3×C4—21no—
59C22×C3×C4—22no—
60C22×C3×C4—44no—
61C22×C3×C4—44no—
62C22×C3×C4C4×D312yes—
63C22×C3×C4C4×D312yes—
64C22×C3×C4D1212yes—
65C22×C3×C4C2×Dic312yes—
66C22×C3×C4#6712yes—
67C22×C3×C4#6712yes—
68C3×M16—124no—
69C2×C3×C8—64no—
70#208—44no—
71C2×C3⋊C8—24no—
72C2×C3⋊C8—64no—
73C2×C3⋊C8—64no—
74C2×C3⋊C8—124no—
75C2×C3⋊C8—124no—
76C22×C32—21no—
77C22×C32—21no—
78C22×C32—22no—
79C22×C32—22no—
80C22×C32—22no—
81C22×C32—44no—
82C22×C32#9511yescharacteristic
83C22×C32#10812yes—
84C32×C4—21no—
85C32×C4—22no—
86C32×C4#9912yes—
87C23×C4D3211yescharacteristic
88C2×M16—62no—
89C22×C8—92no—
90C22⋊C8—34no—
91C22⋊C8—62no—
92C22⋊C8—182no—
93C23×C3—24no—
94C23×C3—24no—
95C23×C3—22no—
96C23×C3—21no—
97C23×C3—42no—
98C23×C3—42no—
99C23×C3—42no—
100C23×C3—42no—
101C23×C3Dic3⋊C412yes—
102C23×C3Dic3⋊C412yes—
103C23×C3C4⋊Dic312yes—
104C2×C3×C4—24no—
105C2×C3×C4—24no—
106C2×C3×C4—24no—
107C2×C3×C4—24no—
108C2×C3×C4—21no—
109C2×C3×C4—22no—
110C2×C3×C4—21no—
111C2×C3×C4—44no—
112C2×C3×C4—42no—
113C2×C3×C4—42no—
114C2×C3×C4—42no—
115C2×C3×C4—44no—
116C2×C3×C4—42no—
117C2×C3×C4C4×Dic312yes—
118C2×C3×C4(C2×D3)⋊C412yes—
119C2×C3×C4(C2×D3)⋊C412yes—
120C2×C3×C4#21712yes—
121C3×C8—124no—
122C3⋊C8—44no—
123C3⋊C8—124no—
124C3⋊C8—124no—
125C2×C32—22no—
126C2×C32—42no—
127C2×C32#33811yescharacteristic
128C2×C32#34111yescharacteristic
129C2×C32#34211yescharacteristic
130C24#62711yescharacteristic
131C22×C4—42no—
132C22×C4D3×Dic312yes—
133C22×C4#62411yescharacteristic
134C22×C4#62511yescharacteristic
135C22×C4#62612yes—
136M16—124no—
137C2×C8—64no—
138C2×C8—182no—
139C2×C8—362no—
140C22×C3—22no—
141C22×C3—22no—
142C22×C3—22no—
143C22×C3—22no—
144C22×C3—24no—
145C22×C3—22no—
146C22×C3—22no—
147C22×C3—22no—
148C22×C3—22no—
149C22×C3—22no—
150C22×C3—22no—
151C22×C3—22no—
152C22×C3—21no—
153C22×C3—42no—
154C22×C3—42no—
155C22×C3—48no—
156C22×C3—48no—
157C22×C3#82214yes—
158C22×C3C3⋊#9512yes—
159C3×C4—22no—
160C3×C4—22no—
161C3×C4—22no—
162C3×C4—22no—
163C3×C4—22no—
164C3×C4—42no—
165C3×C4#80614yes—
166C32#129311yescharacteristic, complemented, Sylow
167C23—22no—
168C23—41no—
169C23—41no—
170C23Dic3⋊Dic312yes—
171C23#372411yescharacteristic
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—42no—
175C2×C4—41no—
176C2×C4Dic3211yescharacteristic
177C2×C4(C2×D3)⋊Dic312yes—
178C2×C4#372211yescharacteristic
179C8—124no—
180C8—362no—
181C2×C3—24no—
182C2×C3—24no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—44no—
187C2×C3—42no—
188C2×C3—42no—
189C2×C3#452712yes—
190C2×C3#455812yes—
191C2×C3C3⋊#33812yes—
192C22—21no—
193C22—21no—
194C22—22no—
195C22—22no—
196C22—22no—
197C22—44no—
198C22#6357812yes—
199C22#6357911yescharacteristic
200C4—22no—
201C4—21no—
202C4#6358112yes—
203C3—21no—
204C3#6768712yescomplemented
205C2—22no—
206C2—42no—
207C2#1058915911yescharacteristic
208C2#1058916511yescharacteristic
209C2#1058918711yescharacteristic
subgroupG/H
centerC22#63579
commutatorC2×C32×C4C42
Frattini, hypercenterC23×C4D32
Fitting, cosocleC23×C32×C4C22
socleC22×C32#95
prime radicalC24×C32Q8
hypocenterC32#1293
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
166. C32#1293semidirect
204. C3#67687semidirect

Maximal subgroups

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

subgroupindex
C2×#636572
C3×#52072
#676873