Finite Group Databasebeta

← #11771231

Subgroups — #11771231

Order 1152.

390 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 46 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#10593812C211yesmaximal, characteristic
2#10593803C211yesmaximal, characteristic
3#10592825C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C412yes—
6C2×C4⋊#157—21no—
7C2×#3788—21no—
8C2×C32×M16C411yescharacteristic, complemented
9C2×#3748C411yescharacteristic, complemented
10C22⋊#622C412yescomplemented
11#63781—21no—
12#63778—21no—
13#63647—21no—
14#63647—21no—
15#5126—62no—
16C23×C3⋊D3C2×C411yescharacteristic
17C22×#157—22no—
18C22×C32×C4C2×C411yescharacteristic
19C22×C3⋊Dic3C2×C411yescharacteristic
20C2×C4×C3⋊D3—41no—
21C2×C4×C3⋊D3—41no—
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3Q811yescharacteristic
26C22⋊#157—42no—
27C2×#622—22no—
28C4⋊#157—41no—
29C4⋊#157—41no—
30#3788—41no—
31#3788—41no—
32C32×M16—41no—
33C2×C32×C8—21no—
34#3748—41no—
35C2×C3⋊(C3⋊C8)—21no—
36#1305—91nomaximal, Sylow
37C22×C4×D3—62no—
38C2×C3×M16—22no—
39C2×#208—62no—
40(C2×D3)⋊C8—64no—
41(C2×D3)⋊C8—64no—
42C23×C32C4211yescharacteristic
43C22×C3⋊D3—21no—
44C22×C3⋊D3—21no—
45C22×C3⋊D3—41no—
46C22×C3⋊D3—41no—
47C22×C3⋊D3C22⋊C411yescharacteristic
48C22×C3⋊D3C4⋊C411yescharacteristic
49C2×#157—42no—
50C2×#157—42no—
51C2×#157—42no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4C4⋊C411yescharacteristic
56C2×C3⋊Dic3—41no—
57C2×C3⋊Dic3C22⋊C411yescharacteristic
58C2×C3⋊Dic3C4⋊C411yescharacteristic
59C4×C3⋊D3—21no—
60C4×C3⋊D3—21no—
61C4×C3⋊D3—21no—
62C4×C3⋊D3—21no—
63C4×C3⋊D3—41no—
64C4×C3⋊D3—41no—
65#622—42no—
66C32×C8—41no—
67C3⋊(C3⋊C8)—41no—
68#407—91no—
69#407—91no—
70#380—91no—
71C23×D3—62no—
72C22×C3×C4—22no—
73C22×Dic3—62no—
74C2×C4×D3—62no—
75C2×C4×D3—62no—
76C2×C4×D3—62no—
77C2×C4×D3—62no—
78C2×C4×D3—124no—
79C2×C4×D3—124no—
80C3×M16—44no—
81C2×C3×C8—24no—
82#208—124no—
83C2×C3⋊C8—64no—
84C22×C32—21no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32#9511yescharacteristic
88C2×C3⋊D3—21no—
89C2×C3⋊D3—21no—
90C2×C3⋊D3—21no—
91C2×C3⋊D3—21no—
92C2×C3⋊D3—21no—
93C2×C3⋊D3—42no—
94C2×C3⋊D3—42no—
95C2×C3⋊D3#10011yescharacteristic
96C2×C3⋊D3#10111yescharacteristic
97#157—82no—
98C32×C4—21no—
99C32×C4#9911yescharacteristic
100C32×C4#9911yescharacteristic
101C3⋊Dic3—21no—
102C3⋊Dic3—21no—
103C23×C4—91no—
104C2×M16—91no—
105C2×M16—181no—
106C2×M16#15711yescharacteristic, complemented
107C2×C4⋊C4—181no—
108C2×C22⋊C4—92no—
109C22⋊C8—92no—
110C22⋊C8—181no—
111C22⋊C8—181no—
112C22⋊C8—181no—
113#95—181no—
114C23×C3—22no—
115C22×D3—62no—
116C22×D3—62no—
117C22×D3—122no—
118C22×D3—122no—
119C22×D3—124no—
120C22×D3—124no—
121C2×C3×C4—24no—
122C2×C3×C4—24no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×Dic3—62no—
126C2×Dic3—62no—
127C2×Dic3—124no—
128C4×D3—122no—
129C4×D3—122no—
130C4×D3—122no—
131C4×D3—122no—
132C4×D3—124no—
133C4×D3—124no—
134C3×C8—44no—
135C3⋊C8—124no—
136C2×C32—41no—
137C2×C32#34211yescharacteristic
138C2×C32#34311yescharacteristic
139C2×C32#34411yescharacteristic
140C3⋊D3—21no—
141C3⋊D3—21no—
142C3⋊D3—41no—
143C24—91no—
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—91no—
147C22×C4—91no—
148C22×C4—91no—
149C22×C4—182no—
150C22×C4—361no—
151C22×C4—361no—
152C22×C4C2×#15711yescharacteristic
153M16—41no—
154M16—361no—
155M16—361no—
156M16—361no—
157C2×C8—21no—
158C2×C8—182no—
159C2×C8—181no—
160C4⋊C4—361no—
161C4⋊C4—361no—
162C22⋊C4—362no—
163C22×C3—24no—
164C22×C3—22no—
165C22×C3—42no—
166C22×C3—42no—
167C2×D3—62no—
168C2×D3—62no—
169C2×D3—64no—
170C2×D3—122no—
171C2×D3—122no—
172C2×D3—122no—
173C2×D3—122no—
174C2×D3—128no—
175C2×D3—128no—
176C3×C4—24no—
177C3×C4—22no—
178C3×C4—22no—
179Dic3—122no—
180Dic3—122no—
181C32#130511yescharacteristic, complemented, Sylow
182C23—91no—
183C23—91no—
184C23—181no—
185C23—181no—
186C23—361no—
187C23—361no—
188C23C4×#15711yescharacteristic
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—181no—
194C2×C4—181no—
195C2×C4—181no—
196C2×C4—181no—
197C2×C4—361no—
198C2×C4—361no—
199C2×C4—361no—
200C2×C4—362no—
201C2×C4—362no—
202C2×C4—362no—
203C2×C4C4⋊#15711yescharacteristic
204C2×C4C22⋊#15711yescharacteristic
205C8—41no—
206C8—362no—
207C8—361no—
208C2×C3—22no—
209C2×C3—22no—
210C2×C3—22no—
211C2×C3—44no—
212D3—122no—
213D3—122no—
214D3—124no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—91no—
219C22—91no—
220C22—181no—
221C22—181no—
222C22—181no—
223C22—181no—
224C22—181no—
225C22—362no—
226C22—362no—
227C22#6378111yescharacteristic
228C4—21no—
229C4—181no—
230C4—181no—
231C4—722no—
232C4#6377411yescharacteristic
233C4#6378611yescharacteristic
234C3—22no—
235C2—41no—
236C2—181no—
237C2—181no—
238C2—361no—
239C2#1059018811yescharacteristic
240C2#1059019111yescharacteristic
241C2#1059020611yescharacteristic
subgroupG/H
centerC22#63781
commutatorC23×C32C42
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypercenterC2×M16#157
hypocenterC32#1305
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
8. C2×C32×M16C4semidirect
9. C2×#3748C4semidirect
10. C22⋊#622C4semidirect
106. C2×M16#157semidirect
181. C32#1305semidirect

Maximal subgroups

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

subgroupindex
#105938122
#105938032
#105928252
#13059