Finite Group Databasebeta

← #11771924

Subgroups — #11771924

Order 1152.

364 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 30 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#10592372C211yesmaximal, characteristic
2#10590206C211yesmaximal, characteristic
3#10590204C211yesmaximal, characteristic
4C22×#634C411yescharacteristic, complemented
5C2×C22⋊#157—21no—
6C2×#3752—21no—
7C2×#3752C2211yescharacteristic
8C22⋊#622—21no—
9C32×#95C411yescharacteristic, complemented
10#63658—21no—
11#4673—62no—
12C23×C3⋊D3D411yescharacteristic
13C22×#157—41no—
14C22×C32×C4—21no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C3⋊Dic3—21no—
17C22×C3⋊Dic3D411yescharacteristic
18C2×#634—41no—
19C2×#634—42no—
20C22⋊#157—22no—
21C22⋊#157—41no—
22C2×#622—41no—
23#3752—41no—
24#3752—42no—
25#1351—91nomaximal, Sylow
26C22×Dic6—62no—
27C2×(C2×D3)⋊C4—62no—
28C2×(C2×D3)⋊C4—64no—
29C3×#95—22no—
30C3⋊#95—64no—
31C23×C32C22⋊C411yescharacteristic
32C22×C3⋊D3—21no—
33C22×C3⋊D3—21no—
34C22×C3⋊D3—41no—
35C22×C3⋊D3—41no—
36C22×C3⋊D3SD1611yescharacteristic
37C22×C3⋊D3Q1611yescharacteristic
38C2×#157—42no—
39C2×#157—81no—
40C2×#157—81no—
41C2×C32×C4—21no—
42C2×C32×C4—41no—
43C2×C32×C4—41no—
44C2×C32×C4—41no—
45C2×C32×C4—41no—
46C2×C3⋊Dic3—22no—
47C2×C3⋊Dic3—21no—
48C2×C3⋊Dic3—41no—
49C2×C3⋊Dic3—41no—
50C2×C3⋊Dic3—41no—
51#634—42no—
52#634—42no—
53#622—81no—
54#393—91no—
55#342—91no—
56#323—91no—
57C23×D3—62no—
58C22×C3×C4—24no—
59C22×C3×C4—22no—
60C22×Dic3—62no—
61C22×Dic3—64no—
62C2×Dic6—128no—
63C2×Dic6—124no—
64(C2×D3)⋊C4—128no—
65(C2×D3)⋊C4—124no—
66C22×C32—21no—
67C22×C32—21no—
68C22×C32#9911yescharacteristic
69C22×C32#10311yescharacteristic
70C22×C32#10411yescharacteristic
71C2×C3⋊D3—21no—
72C2×C3⋊D3—21no—
73C2×C3⋊D3—41no—
74C2×C3⋊D3—41no—
75C2×C3⋊D3—41no—
76C2×C3⋊D3—41no—
77C2×C3⋊D3—81no—
78#157—82no—
79C32×C4—41no—
80C32×C4—81no—
81C3⋊Dic3—42no—
82C3⋊Dic3—41no—
83C22×Q8—91no—
84C2×C22⋊C4—91no—
85C2×C22⋊C4—181no—
86C2×C22⋊C4—181no—
87C22⋊C8—181no—
88#95—181no—
89#95#15711yescharacteristic, complemented
90C23×C3—22no—
91C22×D3—62no—
92C22×D3—62no—
93C22×D3—122no—
94C22×D3—122no—
95C22×D3—124no—
96C22×D3—124no—
97C2×C3×C4—24no—
98C2×C3×C4—44no—
99C2×C3×C4—44no—
100C2×C3×C4—44no—
101C2×C3×C4—44no—
102C2×Dic3—68no—
103C2×Dic3—122no—
104C2×Dic3—124no—
105C2×Dic3—124no—
106C2×Dic3—124no—
107Dic6—128no—
108Dic6—128no—
109C2×C32—21no—
110C2×C32—21no—
111C2×C32#32811yescharacteristic
112C2×C32AΣL(1,𝔽16)11yescharacteristic
113C2×C32#35411yescharacteristic
114C3⋊D3—41no—
115C3⋊D3—41no—
116C24—91no—
117C2×Q8—361no—
118C2×Q8—362no—
119C22×C4—21no—
120C22×C4—91no—
121C22×C4—181no—
122C22×C4—361no—
123C22×C4C2×#15711yescharacteristic
124C2×C8—361no—
125C22⋊C4—182no—
126C22⋊C4—361no—
127C22⋊C4—362no—
128C22⋊C4—361no—
129C22×C3—24no—
130C22×C3—24no—
131C22×C3—22no—
132C22×C3—22no—
133C22×C3—22no—
134C2×D3—122no—
135C2×D3—122no—
136C2×D3—124no—
137C2×D3—124no—
138C2×D3—242no—
139C2×D3—242no—
140C2×D3—244no—
141C3×C4—44no—
142C3×C4—84no—
143Dic3—128no—
144Dic3—242no—
145C32#135111yescharacteristic, complemented, Sylow
146C23—91no—
147C23—91no—
148C23—181no—
149C23—181no—
150C23—361no—
151C23—361no—
152C23C22⋊#15711yescharacteristic
153Q8—362no—
154Q8—362no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—182no—
161C2×C4—181no—
162C2×C4—361no—
163C2×C4—361no—
164C2×C4—361no—
165C2×C4—362no—
166C2×C4—721no—
167C2×C4—721no—
168C8—721no—
169C2×C3—24no—
170C2×C3—24no—
171C2×C3—22no—
172C2×C3—22no—
173C2×C3—22no—
174D3—242no—
175D3—242no—
176C22—21no—
177C22—21no—
178C22—181no—
179C22—181no—
180C22—361no—
181C22—361no—
182C22—361no—
183C22—361no—
184C22—721no—
185C22#6377411yescharacteristic
186C22#6378311yescharacteristic
187C22#6378411yescharacteristic
188C4—41no—
189C4—81no—
190C4—361no—
191C4—362no—
192C4—722no—
193C3—22no—
194C2—21no—
195C2—21no—
196C2—361no—
197C2—361no—
198C2#1059014311yescharacteristic
199C2#1059015311yescharacteristic
200C2#1059015811yescharacteristic
subgroupG/H
centerC22#63774
commutatorC22×C32×C4C2×C4
FrattiniC22×C4C2×#157
FittingC32×#95C4
socleC22×C32#99
prime radicalC23×C3⋊D3D4
cosocleC2×#3752C22
hypercenter#95#157
hypocenterC32#1351
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C22×#634C4semidirect
9. C32×#95C4semidirect
89. #95#157semidirect
145. C32#1351semidirect

Maximal subgroups

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

subgroupindex
#105923722
#105902062
#105902042
#13519