Finite Group Databasebeta

← #11858524

Subgroups — #11858524

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×#3792C211yesmaximal, characteristic
2C2×#63957C212yesmaximal
3#10593511C214yesmaximal, complemented
4#10593507C218yesmaximal, complemented
5C23×C3⋊Dic3C2211yescharacteristic
6C2×#3792C418yescomplemented
7C2×#3792C2214yes—
8C22×#622C2212yes—
9C2×C3×#217—22no—
10C2×#3724C2214yes—
11#63957—22no—
12#63957—22no—
13#63957C2214yes—
14#63957C2214yes—
15C2×Dic32—22no—
16#63743C2218yescomplemented
17#63742C2218yescomplemented
18C2×#877—62no—
19C24×C32D411yescharacteristic
20C22×C3⋊Dic3C2×C414yes—
21C22×C3⋊Dic3D412yes—
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3Q814yes—
24C22×C3⋊Dic3C2311yescharacteristic
25C22×C3⋊Dic3C2312yes—
26C22×C3×Dic3—24no—
27#3792C2×C4116yescomplemented
28C2×#622C2×C418yescomplemented
29C2×#622C2314yes—
30C3×#217—24no—
31C3×#217—24no—
32#3724—24no—
33#3724C2318yes—
34Dic32—24no—
35Dic32—24no—
36#2911—91nomaximal, Sylow
37C23×Dic3—62no—
38C2×C3×C22⋊C4—62no—
39C2×#217—22no—
40C2×Dic3⋊C4—64no—
41C2×C4×Dic3—64no—
42#877—64no—
43#877—64no—
44#877—64no—
45#877—64no—
46C23×C32—42no—
47C23×C32C4⋊C414yes—
48C23×C32C2×D411yescharacteristic
49C23×C32C2×D412yes—
50C2×C3⋊Dic3C4⋊C418yes—
51C2×C3⋊Dic3C4⋊C414yes—
52C2×C3⋊Dic3C22×C412yes—
53C2×C3⋊Dic3C22×C414yes—
54C2×C3⋊Dic3C2×D411yescharacteristic
55C2×C3⋊Dic3C2×D412yes—
56C2×C3⋊Dic3C2×Q812yes—
57C2×C3⋊Dic3C2×Q814yes—
58C2×C3⋊Dic3C2411yescharacteristic
59C2×C3×Dic3—28no—
60C2×C3×Dic3—48no—
61#622C22×C418yes—
62C22×M16—91no—
63C2×#117—92no—
64#428—98no—
65#427—94no—
66C24×C3—22no—
67C22×C3×C4—64no—
68C22×Dic3—24no—
69C22×Dic3—62no—
70C22×Dic3—62no—
71C22×Dic3—62no—
72C22×Dic3—62no—
73C22×Dic3—62no—
74C22×Dic3—62no—
75C22×Dic3—68no—
76C22×Dic3—68no—
77C3×C22⋊C4—64no—
78C3×C22⋊C4—64no—
79#217—24no—
80#217—24no—
81Dic3⋊C4—68no—
82Dic3⋊C4—68no—
83C4×Dic3—68no—
84C4×Dic3—68no—
85C22×C32—24no—
86C22×C32—22no—
87C22×C32—44no—
88C22×C32C2×C4⋊C414yes—
89C22×C32C2×C4⋊C412yes—
90C22×C32C22×D411yescharacteristic
91C3⋊Dic3C2×C4⋊C412yes—
92C3⋊Dic3C2×C4⋊C414yes—
93C3⋊Dic3C23×C411yescharacteristic
94C3⋊Dic3C22×Q811yescharacteristic
95C3×Dic3—48no—
96C23×C4—91no—
97C2×M16—98no—
98C2×M16—94no—
99C22×C8—92no—
100#117—94no—
101#117—94no—
102#117—182no—
103#117—182no—
104C2×C4⋊C4—94no—
105C2×C22⋊C4—62no—
106C2×C42—182no—
107#107—98no—
108#106—98no—
109C23×C3—22no—
110C23×C3—22no—
111C23×C3—22no—
112C23×C3—28no—
113C23×C3—48no—
114C2×C3×C4—68no—
115C2×C3×C4—128no—
116C2×Dic3—28no—
117C2×Dic3—48no—
118C2×Dic3—68no—
119C2×Dic3—68no—
120C2×Dic3—68no—
121C2×Dic3—64no—
122C2×Dic3—64no—
123C2×Dic3—64no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—62no—
127C2×Dic3—64no—
128C2×Dic3—64no—
129C2×Dic3—64no—
130C2×Dic3—62no—
131C2×C32—24no—
132C2×C32—22no—
133C2×C32C22×C4⋊C411yescharacteristic
134C2×C32#57512yes—
135C24GO+(4,𝔽2)11yescharacteristic
136C22×C4—64no—
137C22×C4—92no—
138C22×C4—92no—
139C22×C4—91no—
140C22×C4—91no—
141C22×C4—94no—
142C22×C4—94no—
143M16—916no—
144C2×C8—94no—
145C2×C8—98no—
146C4⋊C4—98no—
147C4⋊C4—184no—
148C22⋊C4—64no—
149C22⋊C4—64no—
150C42—184no—
151C42—184no—
152C22×C3—28no—
153C22×C3—22no—
154C22×C3—24no—
155C22×C3—24no—
156C22×C3—24no—
157C22×C3—44no—
158C22×C3—44no—
159C22×C3—416no—
160C3×C4—128no—
161Dic3—48no—
162Dic3—64no—
163Dic3—64no—
164Dic3—64no—
165Dic3—62no—
166Dic3—62no—
167C32#291111yescharacteristic, complemented, Sylow
168C23—42no—
169C23#377314yes—
170C23C2×GO+(4,𝔽2)11yescharacteristic
171C23C2×GO+(4,𝔽2)12yes—
172C2×C4—68no—
173C2×C4—91no—
174C2×C4—92no—
175C2×C4—91no—
176C2×C4—92no—
177C2×C4—94no—
178C2×C4—98no—
179C2×C4—94no—
180C2×C4—92no—
181C2×C4—94no—
182C2×C4—128no—
183C8—98no—
184C2×C3—28no—
185C2×C3—22no—
186C2×C3—24no—
187C2×C3—44no—
188C2×C3—44no—
189C22—24no—
190C22—22no—
191C22—44no—
192C22C2×#377314yes—
193C22C2×#377312yes—
194C22C22×GO+(4,𝔽2)11yescharacteristic
195C4—91no—
196C4—92no—
197C4—94no—
198C4—91no—
199C4—128no—
200C3—22no—
201C2—24no—
202C2—22no—
203C2C22×#377311yescharacteristic
204C2#1059653212yes—
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
Fitting, prime radicalC24×C32D4
socleC22×C32C22×D4
cosocleC2×C3⋊Dic3C24
hypercenterC24GO+(4,𝔽2)
hypocenterC32#2911
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
3. #10593511C2semidirect
4. #10593507C2semidirect
6. C2×#3792C4semidirect
16. #63743C22semidirect
17. #63742C22semidirect
27. #3792C2×C4semidirect
28. C2×#622C2×C4semidirect
167. C32#2911semidirect

Maximal subgroups

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

subgroupindex
C22×#37922
C2×#639572
#105935112
#105935072
#29119