Finite Group Databasebeta

← #11770840

Subgroups — #11770840

Order 1152.

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

normal subgroups only

This group has 430 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
1C4×C22⋊#157C211yesmaximal, characteristic
2C2×#63778C211yesmaximal, characteristic
3C3⋊D3×C22⋊C8C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C412yes—
6C22×#622C412yescomplemented
7C2×C4×#157—21no—
8C2×C8×C3⋊D3—21no—
9#63781—21no—
10#63778—21no—
11#63778—21no—
12C32×C22⋊C8C411yescharacteristic, complemented
13#63657C411yescharacteristic, complemented
14#63647—21no—
15D3×C22⋊C8—62no—
16C23×C3⋊D3C2×C411yescharacteristic
17C22×#157—22no—
18C22×C32×C4C2×C411yescharacteristic
19C22×C3⋊Dic3C2×C411yescharacteristic
20C2×C4×C3⋊D3—42no—
21C2×C4×C3⋊D3D411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3Q811yescharacteristic
25C22⋊#157—22no—
26C22⋊#157C814yescomplemented
27C2×#622—22no—
28C2×#622—42no—
29C4×#157—42no—
30C2×C32×C8—21no—
31C2×C3⋊(C3⋊C8)—21no—
32C8×C3⋊D3—42no—
33#1282—91nomaximal, Sylow
34C22×C4×D3—62no—
35C2×D3×C8—64no—
36C3×C22⋊C8—22no—
37#830—62no—
38(C2×D3)⋊C8—64no—
39C23×C32C4211yescharacteristic
40C22×C3⋊D3—41no—
41C22×C3⋊D3—41no—
42C22×C3⋊D3C22⋊C411yescharacteristic
43C22×C3⋊D3C4⋊C411yescharacteristic
44C22×C3⋊D3C2×C812yes—
45C22×C3⋊D3M1612yes—
46C2×#157—24no—
47C2×#157—42no—
48C2×#157—42no—
49C2×C32×C4—41no—
50C2×C32×C4C22⋊C411yescharacteristic
51C2×C32×C4C4⋊C411yescharacteristic
52C2×C3⋊Dic3—22no—
53C2×C3⋊Dic3C22⋊C411yescharacteristic
54C2×C3⋊Dic3C4⋊C411yescharacteristic
55C4×C3⋊D3—22no—
56C4×C3⋊D3—22no—
57C4×C3⋊D3—41no—
58C4×C3⋊D3—41no—
59#622—42no—
60C32×C8—41no—
61C3⋊(C3⋊C8)—41no—
62C2×C22⋊C8—91no—
63C2×C22⋊C8—91no—
64C4×C22⋊C4—91no—
65C23×D3—62no—
66C22×C3×C4—22no—
67C22×Dic3—62no—
68C2×C4×D3—62no—
69C2×C4×D3—62no—
70C2×C4×D3—62no—
71C2×C4×D3—62no—
72C2×C4×D3—128no—
73C2×C3×C8—24no—
74C2×C3⋊C8—64no—
75D3×C8—128no—
76C22×C32—21no—
77C22×C32—21no—
78C22×C32#9511yescharacteristic
79C22×C32C4×C811yescharacteristic
80C22×C32#9711yescharacteristic
81C2×C3⋊D3—21no—
82C2×C3⋊D3—21no—
83C2×C3⋊D3—21no—
84C2×C3⋊D3—21no—
85C2×C3⋊D3—42no—
86C2×C3⋊D3—42no—
87C2×C3⋊D3C22⋊C812yes—
88C2×C3⋊D3C4⋊C812yes—
89#157—44no—
90C32×C4—21no—
91C32×C4—21no—
92C3⋊Dic3—21no—
93C3⋊Dic3#9912yes—
94C23×C4—91no—
95C22×C8—92no—
96C22×C8—181no—
97C2×C22⋊C4—92no—
98C2×C42—181no—
99C22⋊C8—91no—
100C22⋊C8—181no—
101C22⋊C8—181no—
102C22⋊C8—181no—
103C22⋊C8#15711yescharacteristic, complemented
104#95—181no—
105C23×C3—22no—
106C22×D3—62no—
107C22×D3—62no—
108C22×D3—64no—
109C22×D3—64no—
110C22×D3—124no—
111C22×D3—124no—
112C2×C3×C4—22no—
113C2×C3×C4—22no—
114C2×C3×C4—44no—
115C2×Dic3—62no—
116C2×Dic3—62no—
117C2×Dic3—124no—
118C4×D3—68no—
119C4×D3—124no—
120C4×D3—124no—
121C4×D3—124no—
122C3×C8—44no—
123C3⋊C8—124no—
124C2×C32—21no—
125C2×C32—21no—
126C2×C32#33611yescharacteristic
127C2×C32#34211yescharacteristic
128C2×C32#34411yescharacteristic
129C3⋊D3—22no—
130C3⋊D3—22no—
131C24—91no—
132C22×C4—91no—
133C22×C4—91no—
134C22×C4—91no—
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—182no—
138C22×C4—362no—
139C22×C4C2×#15711yescharacteristic
140C2×C8—21no—
141C2×C8—182no—
142C2×C8—181no—
143C2×C8—362no—
144C2×C8—362no—
145C22⋊C4—94no—
146C22⋊C4—182no—
147C42—362no—
148C22×C3—22no—
149C22×C3—22no—
150C22×C3—22no—
151C22×C3—42no—
152C22×C3—42no—
153C2×D3—64no—
154C2×D3—64no—
155C2×D3—64no—
156C2×D3—64no—
157C2×D3—122no—
158C2×D3—122no—
159C2×D3—128no—
160C2×D3—128no—
161C3×C4—24no—
162C3×C4—42no—
163Dic3—64no—
164Dic3—122no—
165C32#128211yescharacteristic, complemented, Sylow
166C23—91no—
167C23—91no—
168C23—92no—
169C23—92no—
170C23—361no—
171C23—361no—
172C23C4×#15711yescharacteristic
173C2×C4—41no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—182no—
177C2×C4—182no—
178C2×C4—182no—
179C2×C4—184no—
180C2×C4—361no—
181C2×C4—361no—
182C2×C4—362no—
183C2×C4—362no—
184C2×C4C4⋊#15711yescharacteristic
185C2×C4C22⋊#15711yescharacteristic
186C8—41no—
187C8—361no—
188C8—362no—
189C2×C3—22no—
190C2×C3—22no—
191C2×C3—22no—
192C2×C3—42no—
193C2×C3—42no—
194D3—68no—
195D3—124no—
196C22—21no—
197C22—21no—
198C22—92no—
199C22—92no—
200C22—181no—
201C22—181no—
202C22—181no—
203C22—181no—
204C22—362no—
205C22—362no—
206C22C8×#15711yescharacteristic
207C22#6376711yescharacteristic
208C22#6378111yescharacteristic
209C4—21no—
210C4—21no—
211C4—92no—
212C4—181no—
213C4—364no—
214C3—22no—
215C2—21no—
216C2—21no—
217C2—182no—
218C2—182no—
219C2#1059015511yescharacteristic
220C2#1059018111yescharacteristic
221C2#1059019111yescharacteristic
subgroupG/H
centerC22#63781
commutatorC22×C32C4×C8
FrattiniC22×C4C2×#157
FittingC32×C22⋊C8C4
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypercenterC22⋊C8#157
hypocenterC32#1282
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
6. C22×#622C4semidirect
12. C32×C22⋊C8C4semidirect
13. #63657C4semidirect
26. C22⋊#157C8semidirect
103. C22⋊C8#157semidirect
165. C32#1282semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#1572
C2×#637782
C3⋊D3×C22⋊C82
#12829