Finite Group Databasebeta

← #11770809

Subgroups — #11770809

Order 1152.

466 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 64 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×#63781C211yesmaximal, characteristic
2#10593800C211yesmaximal, characteristic
3C3⋊D3×C22⋊C8C211yesmaximal, characteristic
4C23×#157C412yes—
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3787—21no—
7C2×C8×C3⋊D3—21no—
8C22⋊#622C412yescomplemented
9#63781—21no—
10#63781—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×#157—22no—
19C22×#157—42no—
20C22×#157—42no—
21C22×#157C814yescomplemented
22C22×C32×C4C2×C411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C2×C4×C3⋊D3—42no—
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3Q811yescharacteristic
29C2×#622—22no—
30#3787—42no—
31C2×C32×C8—21no—
32C2×C3⋊(C3⋊C8)—21no—
33C8×C3⋊D3—42no—
34#1280—91nomaximal, Sylow
35C22×C4×D3—62no—
36C2×D3×C8—64no—
37C3×C22⋊C8—22no—
38#830—62no—
39(C2×D3)⋊C8—64no—
40C23×C32C4211yescharacteristic
41C22×C3⋊D3—22no—
42C22×C3⋊D3—21no—
43C22×C3⋊D3—21no—
44C22×C3⋊D3C22⋊C411yescharacteristic
45C22×C3⋊D3C4⋊C411yescharacteristic
46C22×C3⋊D3C2×C812yes—
47C22×C3⋊D3M1612yes—
48C2×#157—24no—
49C2×#157—44no—
50C2×#157—42no—
51C2×#157—42no—
52C2×#157—44no—
53C2×C32×C4—41no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4C4⋊C411yescharacteristic
56C2×C3⋊Dic3—41no—
57C2×C3⋊Dic3C22⋊C411yescharacteristic
58C2×C3⋊Dic3C4⋊C411yescharacteristic
59C4×C3⋊D3—22no—
60C4×C3⋊D3—22no—
61C4×C3⋊D3—41no—
62C4×C3⋊D3—41no—
63#622—42no—
64C32×C8—41no—
65C3⋊(C3⋊C8)—41no—
66C2×C22⋊C8—91no—
67C2×C22⋊C8—91no—
68C2×#95—91no—
69C23×D3—62no—
70C22×C3×C4—22no—
71C22×Dic3—62no—
72C2×C4×D3—62no—
73C2×C4×D3—62no—
74C2×C4×D3—62no—
75C2×C4×D3—62no—
76C2×C4×D3—128no—
77C2×C3×C8—24no—
78C2×C3⋊C8—64no—
79D3×C8—128no—
80C22×C32—21no—
81C22×C32—21no—
82C22×C32#9511yescharacteristic
83C22×C32C4×C811yescharacteristic
84C22×C32#9711yescharacteristic
85C2×C3⋊D3—21no—
86C2×C3⋊D3—21no—
87C2×C3⋊D3—22no—
88C2×C3⋊D3—22no—
89C2×C3⋊D3—22no—
90C2×C3⋊D3—22no—
91C2×C3⋊D3C22⋊C812yes—
92C2×C3⋊D3#9912yes—
93C2×C3⋊D3#10011yescharacteristic
94C2×C3⋊D3#10111yescharacteristic
95C2×C3⋊D3C4⋊C812yes—
96#157—44no—
97C32×C4—21no—
98C32×C4—21no—
99C3⋊Dic3—21no—
100C3⋊Dic3—21no—
101C23×C4—91no—
102C23×C4—92no—
103C22×C8—181no—
104C22×C8—181no—
105C22⋊C8—92no—
106C22⋊C8—91no—
107C22⋊C8—181no—
108C22⋊C8—181no—
109C22⋊C8#15711yescharacteristic, complemented
110#95—181no—
111#95—181no—
112C23×C3—22no—
113C22×D3—62no—
114C22×D3—62no—
115C22×D3—64no—
116C22×D3—64no—
117C22×D3—124no—
118C22×D3—122no—
119C22×D3—122no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×C3×C4—44no—
123C2×Dic3—62no—
124C2×Dic3—62no—
125C2×Dic3—124no—
126C4×D3—68no—
127C4×D3—124no—
128C4×D3—124no—
129C4×D3—124no—
130C3×C8—44no—
131C3⋊C8—124no—
132C2×C32—21no—
133C2×C32—21no—
134C2×C32#33611yescharacteristic
135C2×C32#34211yescharacteristic
136C2×C32#34311yescharacteristic
137C3⋊D3—22no—
138C3⋊D3#32312yes—
139C3⋊D3#32412yes—
140C24—91no—
141C22×C4—91no—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—94no—
147C22×C4—182no—
148C22×C4—182no—
149C22×C4—362no—
150C22×C4—362no—
151C22×C4—362no—
152C22×C4C2×#15711yescharacteristic
153C2×C8—21no—
154C2×C8—182no—
155C2×C8—181no—
156C2×C8—362no—
157C2×C8—362no—
158C22×C3—22no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—42no—
162C22×C3—42no—
163C2×D3—64no—
164C2×D3—64no—
165C2×D3—62no—
166C2×D3—62no—
167C2×D3—64no—
168C2×D3—124no—
169C2×D3—124no—
170C2×D3—124no—
171C2×D3—124no—
172C2×D3—122no—
173C2×D3—122no—
174C3×C4—24no—
175C3×C4—42no—
176Dic3—64no—
177Dic3—122no—
178C32#128011yescharacteristic, complemented, Sylow
179C23—91no—
180C23—92no—
181C23—92no—
182C23—91no—
183C23—182no—
184C23—181no—
185C23—181no—
186C23C4×#15711yescharacteristic
187C2×C4—41no—
188C2×C4—91no—
189C2×C4—91no—
190C2×C4—182no—
191C2×C4—182no—
192C2×C4—184no—
193C2×C4—361no—
194C2×C4—361no—
195C2×C4—361no—
196C2×C4—362no—
197C2×C4—362no—
198C2×C4—364no—
199C2×C4—364no—
200C2×C4C4⋊#15711yescharacteristic
201C2×C4C22⋊#15711yescharacteristic
202C8—41no—
203C8—361no—
204C8—362no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—22no—
208C2×C3—42no—
209C2×C3—42no—
210D3—64no—
211D3—64no—
212D3—124no—
213C22—21no—
214C22—21no—
215C22—92no—
216C22—92no—
217C22—91no—
218C22—91no—
219C22—92no—
220C22—182no—
221C22—182no—
222C22—182no—
223C22—182no—
224C22—181no—
225C22—181no—
226C22C8×#15711yescharacteristic
227C22#6376711yescharacteristic
228C22#6378111yescharacteristic
229C4—21no—
230C4—21no—
231C4—181no—
232C4—181no—
233C4—364no—
234C3—22no—
235C2—21no—
236C2—21no—
237C2—92no—
238C2—92no—
239C2—182no—
240C2#1059015511yescharacteristic
241C2#1059018111yescharacteristic
242C2#1059018811yescharacteristic
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#1280
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
8. C22⋊#622C4semidirect
12. C32×C22⋊C8C4semidirect
13. #63657C4semidirect
21. C22×#157C8semidirect
109. C22⋊C8#157semidirect
178. C32#1280semidirect

Maximal subgroups

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

subgroupindex
C2×#637812
#105938002
C3⋊D3×C22⋊C82
#12809