Finite Group Databasebeta

← #11771097

Subgroups — #11771097

Order 1152.

504 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 48 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
2#10593803C211yesmaximal, characteristic
3#10592365C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157—21no—
6C2×C4×#157—21no—
7C2×#3788C412yescomplemented
8C2×#3752—21no—
9C2×C4×C3⋊Dic3—21no—
10C22⋊#622—21no—
11#63781C412yescomplemented
12#63778—21no—
13C32×#95C411yescharacteristic, complemented
14#63658C411yescharacteristic, complemented
15#4666—62no—
16C23×C3⋊D3D411yescharacteristic
17C22×#157—22no—
18C22×C32×C4—21no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3—21no—
21C22×C3⋊Dic3D411yescharacteristic
22C2×C4×C3⋊D3—42no—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3Q811yescharacteristic
27C22⋊#157—22no—
28C22⋊#157—22no—
29C2×#622—22no—
30C4×#157—42no—
31#3788—42no—
32#3752—24no—
33C4×C3⋊Dic3—42no—
34#1297—91nomaximal, Sylow
35C22×C4×D3—62no—
36C2×(C2×D3)⋊C4—64no—
37C2×C4×Dic3—64no—
38C3×#95—22no—
39C3⋊#95—62no—
40C23×C32C22⋊C411yescharacteristic
41C22×C3⋊D3—22no—
42C22×C3⋊D3—21no—
43C22×C3⋊D3—21no—
44C22×C3⋊D3—41no—
45C22×C3⋊D3C22⋊C411yescharacteristic
46C22×C3⋊D3C4⋊C411yescharacteristic
47C2×#157—24no—
48C2×#157—42no—
49C2×#157—42no—
50C2×C32×C4—22no—
51C2×C32×C4—41no—
52C2×C32×C4—41no—
53C2×C32×C4—41no—
54C2×C32×C4C4211yescharacteristic
55C2×C32×C4C4⋊C411yescharacteristic
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3—41no—
60C2×C3⋊Dic3C22⋊C411yescharacteristic
61C2×C3⋊Dic3C4⋊C411yescharacteristic
62C4×C3⋊D3—22no—
63C4×C3⋊D3—22no—
64C4×C3⋊D3—41no—
65C4×C3⋊D3—41no—
66#622—42no—
67#407—91no—
68C4×C22⋊C4—91no—
69C4×C22⋊C4—91no—
70C23×D3—62no—
71C22×C3×C4—24no—
72C22×C3×C4—22no—
73C22×Dic3—62no—
74C22×Dic3—64no—
75C2×C4×D3—62no—
76C2×C4×D3—62no—
77C2×C4×D3—62no—
78C2×C4×D3—62no—
79C2×C4×D3—128no—
80(C2×D3)⋊C4—616no—
81C4×Dic3—128no—
82C22×C32—21no—
83C22×C32—21no—
84C22×C32#9511yescharacteristic
85C22×C32#10411yescharacteristic
86C22×C32#10411yescharacteristic
87C2×C3⋊D3—21no—
88C2×C3⋊D3—21no—
89C2×C3⋊D3—21no—
90C2×C3⋊D3—21no—
91C2×C3⋊D3—21no—
92C2×C3⋊D3—42no—
93C2×C3⋊D3—42no—
94C2×C3⋊D3#10412yes—
95#157—44no—
96C32×C4—21no—
97C32×C4—21no—
98C32×C4—42no—
99C3⋊Dic3—21no—
100C3⋊Dic3—42no—
101C3⋊Dic3#9912yes—
102C23×C4—91no—
103C2×M16—92no—
104C2×C22⋊C4—181no—
105C2×C22⋊C4—181no—
106C2×C42—181no—
107C2×C42—181no—
108C22⋊C8—181no—
109C22⋊C8—181no—
110#95—92no—
111#95—91no—
112#95#15711yescharacteristic, complemented
113C23×C3—22no—
114C22×D3—62no—
115C22×D3—62no—
116C22×D3—68no—
117C22×D3—122no—
118C22×D3—122no—
119C22×D3—124no—
120C2×C3×C4—28no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—44no—
124C2×C3×C4—44no—
125C2×C3×C4—44no—
126C2×Dic3—62no—
127C2×Dic3—62no—
128C2×Dic3—68no—
129C2×Dic3—68no—
130C2×Dic3—124no—
131C2×Dic3—124no—
132C4×D3—124no—
133C4×D3—124no—
134C4×D3—124no—
135C4×D3—124no—
136C2×C32—21no—
137C2×C32—21no—
138C2×C32#33911yescharacteristic
139C2×C32#33911yescharacteristic
140C2×C32#34211yescharacteristic
141C3⋊D3—22no—
142C3⋊D3—41no—
143C24—91no—
144C22×C4—21no—
145C22×C4—91no—
146C22×C4—91no—
147C22×C4—91no—
148C22×C4—91no—
149C22×C4—91no—
150C22×C4—182no—
151C22×C4—181no—
152C22×C4—362no—
153C22×C4C2×#15711yescharacteristic
154M16—362no—
155C2×C8—182no—
156C22⋊C4—184no—
157C22⋊C4—182no—
158C22⋊C4—182no—
159C42—362no—
160C42—362no—
161C22×C3—24no—
162C22×C3—24no—
163C22×C3—22no—
164C22×C3—22no—
165C22×C3—22no—
166C2×D3—64no—
167C2×D3—64no—
168C2×D3—122no—
169C2×D3—122no—
170C2×D3—122no—
171C2×D3—122no—
172C2×D3—128no—
173C2×D3—128no—
174C3×C4—42no—
175C3×C4—42no—
176C3×C4—48no—
177Dic3—64no—
178Dic3—64no—
179Dic3—128no—
180C32#129711yescharacteristic, complemented, Sylow
181C23—91no—
182C23—91no—
183C23—182no—
184C23—181no—
185C23—181no—
186C23—361no—
187C23C22⋊#15711yescharacteristic
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—182no—
195C2×C4—182no—
196C2×C4—182no—
197C2×C4—182no—
198C2×C4—184no—
199C2×C4—361no—
200C2×C4—361no—
201C2×C4—361no—
202C2×C4—362no—
203C2×C4—362no—
204C2×C4—361no—
205C2×C4C4×#15711yescharacteristic
206C2×C4C4⋊#15711yescharacteristic
207C8—362no—
208C2×C3—24no—
209C2×C3—24no—
210C2×C3—22no—
211C2×C3—22no—
212C2×C3—22no—
213D3—124no—
214D3—124no—
215C22—21no—
216C22—21no—
217C22—92no—
218C22—181no—
219C22—181no—
220C22—181no—
221C22—181no—
222C22—181no—
223C22—362no—
224C22—362no—
225C22#6378111yescharacteristic
226C22#6378311yescharacteristic
227C22#6378511yescharacteristic
228C4—21no—
229C4—21no—
230C4—42no—
231C4—92no—
232C4—181no—
233C4—362no—
234C4—364no—
235C3—22no—
236C2—21no—
237C2—21no—
238C2—182no—
239C2—361no—
240C2#1059015111yescharacteristic
241C2#1059015511yescharacteristic
242C2#1059016411yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC32×#95C4
socleC22×C32#95
prime radicalC23×C3⋊D3D4
cosocleC22×C4×C3⋊D3C22
hypercenter#95#157
hypocenterC32#1297
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
7. C2×#3788C4semidirect
11. #63781C4semidirect
13. C32×#95C4semidirect
14. #63658C4semidirect
112. #95#157semidirect
180. C32#1297semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#1572
#105938032
#105923652
#12979