Finite Group Databasebeta

← #11858525

Subgroups — #11858525

Order 1152.

822 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 191 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
1C22×#3788C211yesmaximal, characteristic
2#10594969C212yesmaximal
3#10593511C214yesmaximal, complemented
4#10593394C218yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#622C2212yes—
7C2×#3788C418yescomplemented
8C2×#3788C2214yes—
9C3×#926—22no—
10#63974—22no—
11#63957C2214yes—
12#63900C2214yes—
13C4×#624—22no—
14#63874C2214yes—
15#63849—22no—
16#63743C2218yescomplemented
17#63742C2218yescomplemented
18D3×#117—62no—
19C23×C3⋊D3D411yescharacteristic
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3C2311yescharacteristic
22C2×C4×C3⋊D3C2×C414yes—
23C2×C4×C3⋊D3D412yes—
24C2×C4×C3⋊D3Q814yes—
25C2×C4×C3⋊D3C2312yes—
26C2×#624—24no—
27C2×#622C2×C418yescomplemented
28C2×#622C2314yes—
29#3788C2×C4116yescomplemented
30C3×#217—24no—
31C3×C4⋊Dic3—24no—
32C3×C4×Dic3—24no—
33#3724C2318yes—
34#3722—24no—
35Dic32—24no—
36#2911—91nomaximal, Sylow
37C22×C4×D3—62no—
38C3×#117—62no—
39#926—22no—
40#892—64no—
41D3×C4⋊C4—64no—
42D3×C22⋊C4—64no—
43#877—64no—
44#872—64no—
45C42×D3—64no—
46C23×C32C2×D411yescharacteristic
47C22×C3⋊D3—42no—
48C22×C3⋊D3C4⋊C414yes—
49C22×C3⋊D3C2×D412yes—
50C2×C32×C4C4⋊C414yes—
51C2×C32×C4C2×D412yes—
52C2×C3⋊Dic3C22×C412yes—
53C2×C3⋊Dic3C2×D411yescharacteristic
54C2×C3⋊Dic3C2×Q812yes—
55C2×C3⋊Dic3C2411yescharacteristic
56C4×C3⋊D3C4⋊C418yes—
57C4×C3⋊D3C22×C414yes—
58C4×C3⋊D3C2×Q814yes—
59C2×C3×Dic3—28no—
60#624—48no—
61#622C22×C418yes—
62C22×M16—91no—
63C2×#117—92no—
64#428—98no—
65#427—94no—
66C23×D3—62no—
67C22×C3×C4—22no—
68C22×Dic3—62no—
69C2×C4×D3—62no—
70C2×C4×D3—62no—
71C2×C4×D3—62no—
72C2×C4×D3—62no—
73C2×C4×D3—68no—
74C2×C4×D3—68no—
75C2×C4×D3—68no—
76C3×C4⋊C4—64no—
77C3×C22⋊C4—64no—
78C3×C42—64no—
79#217—24no—
80(C2×D3)⋊C4—68no—
81C4⋊Dic3—24no—
82Dic3⋊C4—68no—
83C4×Dic3—24no—
84C4×Dic3—68no—
85C22×C32—22no—
86C22×C32C2×C4⋊C412yes—
87C22×C32C22×D411yescharacteristic
88C2×C3⋊D3—24no—
89C2×C3⋊D3—44no—
90C2×C3⋊D3C2×C4⋊C414yes—
91C32×C4C2×C4⋊C414yes—
92C3⋊Dic3C2×C4⋊C412yes—
93C3⋊Dic3C23×C411yescharacteristic
94C3⋊Dic3C22×Q811yescharacteristic
95C3×Dic3—48no—
96C23×C4—91no—
97C2×M16—98no—
98C2×M16—94no—
99C22×C8—92no—
100#117—62no—
101#117—94no—
102#117—94no—
103#117—182no—
104C2×C4⋊C4—94no—
105C2×C22⋊C4—182no—
106C2×C42—182no—
107#107—98no—
108#106—98no—
109C23×C3—22no—
110C22×D3—62no—
111C22×D3—68no—
112C22×D3—62no—
113C22×D3—128no—
114C2×C3×C4—22no—
115C2×C3×C4—22no—
116C2×C3×C4—28no—
117C2×C3×C4—68no—
118C2×Dic3—28no—
119C2×Dic3—64no—
120C2×Dic3—62no—
121C2×Dic3—64no—
122C2×Dic3—62no—
123C4×D3—68no—
124C4×D3—68no—
125C4×D3—64no—
126C4×D3—64no—
127C4×D3—64no—
128C4×D3—64no—
129C4×D3—1216no—
130C2×C32—22no—
131C2×C32C22×C4⋊C411yescharacteristic
132C2×C32#57512yes—
133C3⋊D3—24no—
134C24—91no—
135C22×C4—91no—
136C22×C4—92no—
137C22×C4—92no—
138C22×C4—94no—
139C22×C4—94no—
140C22×C4—184no—
141C22×C4GO+(4,𝔽2)11yescharacteristic
142M16—916no—
143C2×C8—94no—
144C2×C8—98no—
145C4⋊C4—64no—
146C4⋊C4—98no—
147C22⋊C4—64no—
148C22⋊C4—184no—
149C42—64no—
150C42—184no—
151C22×C3—22no—
152C22×C3—24no—
153C22×C3—44no—
154C2×D3—64no—
155C2×D3—64no—
156C2×D3—68no—
157C2×D3—124no—
158C2×D3—1216no—
159C3×C4—24no—
160C3×C4—24no—
161C3×C4—128no—
162Dic3—48no—
163Dic3—64no—
164Dic3—62no—
165Dic3—62no—
166C32#291111yescharacteristic, complemented, Sylow
167C23—92no—
168C23—94no—
169C23—362no—
170C23C2×GO+(4,𝔽2)11yescharacteristic
171C2×C4—68no—
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—92no—
175C2×C4—92no—
176C2×C4—94no—
177C2×C4—98no—
178C2×C4—94no—
179C2×C4—368no—
180C2×C4#377314yes—
181C2×C4C2×GO+(4,𝔽2)12yes—
182C8—98no—
183C2×C3—24no—
184C2×C3—22no—
185C2×C3—44no—
186D3—68no—
187D3—124no—
188C22—22no—
189C22—94no—
190C22—184no—
191C22—364no—
192C22C2×#377312yes—
193C22C22×GO+(4,𝔽2)11yescharacteristic
194C4—91no—
195C4—92no—
196C4—91no—
197C4—128no—
198C4C2×#377314yes—
199C3—22no—
200C2—22no—
201C2—184no—
202C2#1059650212yes—
203C2C22×#377311yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2911
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10593511C2semidirect
4. #10593394C2semidirect
7. C2×#3788C4semidirect
16. #63743C22semidirect
17. #63742C22semidirect
27. C2×#622C2×C4semidirect
29. #3788C2×C4semidirect
166. C32#2911semidirect

Maximal subgroups

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

subgroupindex
C22×#37882
#105949692
#105935112
#105933942
#29119