Finite Group Databasebeta

← #11770880

Subgroups — #11770880

Order 1152.

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

normal subgroups only

This group has 444 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
1C4×C22⋊#157C211yesmaximal, characteristic
2#10593803C211yesmaximal, characteristic
3#10592363C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157—21no—
6C2×C4×#157C412yescomplemented
7C2×#3788—21no—
8C2×#3752—21no—
9C22⋊#622—21no—
10#63781—21no—
11#63778C412yescomplemented
12C32×#95C411yescharacteristic, complemented
13#63658—21no—
14#63658C411yescharacteristic, complemented
15#4664—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—42no—
33#1284—91nomaximal, Sylow
34C22×C4×D3—62no—
35C2×(C2×D3)⋊C4—64no—
36C3×#95—22no—
37C3⋊#95—62no—
38C3⋊#95—64no—
39C23×C32C22⋊C411yescharacteristic
40C22×C3⋊D3—22no—
41C22×C3⋊D3—21no—
42C22×C3⋊D3—21no—
43C22×C3⋊D3—41no—
44C22×C3⋊D3C22⋊C411yescharacteristic
45C22×C3⋊D3C4⋊C411yescharacteristic
46C2×#157—24no—
47C2×#157—42no—
48C2×#157—42no—
49C2×C32×C4—41no—
50C2×C32×C4—41no—
51C2×C32×C4—41no—
52C2×C32×C4—41no—
53C2×C32×C4C4211yescharacteristic
54C2×C32×C4C4⋊C411yescharacteristic
55C2×C3⋊Dic3—41no—
56C2×C3⋊Dic3—41no—
57C2×C3⋊Dic3—41no—
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3C22⋊C411yescharacteristic
60C2×C3⋊Dic3C4⋊C411yescharacteristic
61C4×C3⋊D3—22no—
62C4×C3⋊D3—22no—
63C4×C3⋊D3—41no—
64C4×C3⋊D3—41no—
65#622—42no—
66#407—91no—
67#381—91no—
68C4×C22⋊C4—91no—
69C23×D3—62no—
70C22×C3×C4—24no—
71C22×C3×C4—22no—
72C22×Dic3—62no—
73C22×Dic3—64no—
74C2×C4×D3—62no—
75C2×C4×D3—62no—
76C2×C4×D3—62no—
77C2×C4×D3—62no—
78C2×C4×D3—128no—
79(C2×D3)⋊C4—128no—
80C22×C32—21no—
81C22×C32—21no—
82C22×C32#9511yescharacteristic
83C22×C32#10411yescharacteristic
84C22×C32#10411yescharacteristic
85C2×C3⋊D3—21no—
86C2×C3⋊D3—21no—
87C2×C3⋊D3—21no—
88C2×C3⋊D3—21no—
89C2×C3⋊D3—21no—
90C2×C3⋊D3—42no—
91C2×C3⋊D3—42no—
92C2×C3⋊D3#9912yes—
93#157—44no—
94C32×C4—21no—
95C32×C4—21no—
96C32×C4—81no—
97C3⋊Dic3—21no—
98C3⋊Dic3—21no—
99C3⋊Dic3—81no—
100C23×C4—91no—
101C2×M16—181no—
102C2×C22⋊C4—181no—
103C2×C22⋊C4—181no—
104C2×C42—92no—
105C22⋊C8—92no—
106C22⋊C8—181no—
107#95—91no—
108#95—181no—
109#95—181no—
110#95#15711yescharacteristic, complemented
111C23×C3—22no—
112C22×D3—62no—
113C22×D3—62no—
114C22×D3—68no—
115C22×D3—122no—
116C22×D3—122no—
117C22×D3—124no—
118C2×C3×C4—22no—
119C2×C3×C4—22no—
120C2×C3×C4—44no—
121C2×C3×C4—44no—
122C2×C3×C4—44no—
123C2×C3×C4—44no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—124no—
127C2×Dic3—124no—
128C2×Dic3—124no—
129C2×Dic3—124no—
130C4×D3—124no—
131C4×D3—124no—
132C4×D3—124no—
133C4×D3—124no—
134C2×C32—21no—
135C2×C32—21no—
136C2×C32H(3,ℤ/4)11yescharacteristic
137C2×C32#33911yescharacteristic
138C2×C32#34211yescharacteristic
139C3⋊D3—22no—
140C3⋊D3—41no—
141C24—91no—
142C22×C4—21no—
143C22×C4—91no—
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—91no—
147C22×C4—91no—
148C22×C4—182no—
149C22×C4—181no—
150C22×C4—362no—
151C22×C4C2×#15711yescharacteristic
152M16—362no—
153C2×C8—182no—
154C22⋊C4—182no—
155C22⋊C4—182no—
156C22⋊C4—362no—
157C42—362no—
158C22×C3—24no—
159C22×C3—24no—
160C22×C3—22no—
161C22×C3—22no—
162C22×C3—22no—
163C2×D3—64no—
164C2×D3—64no—
165C2×D3—122no—
166C2×D3—122no—
167C2×D3—122no—
168C2×D3—122no—
169C2×D3—128no—
170C2×D3—128no—
171C3×C4—42no—
172C3×C4—42no—
173C3×C4—84no—
174Dic3—122no—
175Dic3—122no—
176Dic3—244no—
177C32#128411yescharacteristic, complemented, Sylow
178C23—91no—
179C23—91no—
180C23—182no—
181C23—181no—
182C23—181no—
183C23—361no—
184C23C22⋊#15711yescharacteristic
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—91no—
190C2×C4—91no—
191C2×C4—182no—
192C2×C4—182no—
193C2×C4—184no—
194C2×C4—361no—
195C2×C4—361no—
196C2×C4—361no—
197C2×C4—362no—
198C2×C4—362no—
199C2×C4—361no—
200C2×C4—361no—
201C2×C4—361no—
202C2×C4C4×#15711yescharacteristic
203C2×C4C4⋊#15711yescharacteristic
204C8—362no—
205C2×C3—24no—
206C2×C3—24no—
207C2×C3—22no—
208C2×C3—22no—
209C2×C3—22no—
210D3—124no—
211D3—124no—
212C22—21no—
213C22—21no—
214C22—92no—
215C22—181no—
216C22—181no—
217C22—181no—
218C22—181no—
219C22—181no—
220C22—362no—
221C22—362no—
222C22#6378111yescharacteristic
223C22#6378311yescharacteristic
224C22#6378511yescharacteristic
225C4—21no—
226C4—21no—
227C4—81no—
228C4—181no—
229C4—181no—
230C4—364no—
231C4—721no—
232C3—22no—
233C2—21no—
234C2—21no—
235C2—182no—
236C2—361no—
237C2#1059015211yescharacteristic
238C2#1059015511yescharacteristic
239C2#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#1284
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
6. C2×C4×#157C4semidirect
11. #63778C4semidirect
12. C32×#95C4semidirect
14. #63658C4semidirect
110. #95#157semidirect
177. C32#1284semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#1572
#105938032
#105923632
#12849