Finite Group Databasebeta

← #11771082

Subgroups — #11771082

Order 1152.

326 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593735C211yesmaximal, characteristic
2#10593726C211yesmaximal, characteristic
3C3⋊D3×C4⋊C8C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C4⋊#157—21no—
6C2×C4⋊#157C412yes—
7C2×#3787—21no—
8C2×C8×C3⋊D3—21no—
9C42×C3⋊D3C2211yescharacteristic
10#63779C412yescomplemented
11C4⋊#622—21no—
12C32×C4⋊C8C411yescharacteristic, complemented
13#63641—21no—
14C4⋊(C3⋊(C3⋊C8))C411yescharacteristic, complemented
15D3×C4⋊C8—62no—
16C22×#157—22no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C2×#622—22no—
21C4⋊#157—42no—
22C4⋊#157—41no—
23C4⋊#157—41no—
24C4⋊#157—41no—
25C4⋊#157—41no—
26#3787—41no—
27#3787—41no—
28C2×C32×C8—21no—
29C32×C42C2×C411yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3Q811yescharacteristic
33C2×C3⋊(C3⋊C8)—21no—
34C8×C3⋊D3—41no—
35C8×C3⋊D3—41no—
36#1296—91nomaximal, Sylow
37C2×D3×C8—64no—
38C42×D3—62no—
39C3×C4⋊C8—22no—
40Dic3⋊C8—64no—
41C4⋊(C3⋊C8)—62no—
42C22×C3⋊D3C22⋊C411yescharacteristic
43C2×#157—42no—
44C2×#157—42no—
45C2×#157—42no—
46C2×C32×C4C4211yescharacteristic
47C2×C32×C4C22⋊C411yescharacteristic
48C2×C32×C4C4⋊C411yescharacteristic
49C2×C3⋊Dic3C22⋊C411yescharacteristic
50C2×C3⋊Dic3C4⋊C411yescharacteristic
51C2×C3⋊Dic3C4⋊C411yescharacteristic
52C4×C3⋊D3—21no—
53C4×C3⋊D3—21no—
54C4×C3⋊D3D811yescharacteristic
55C4×C3⋊D3D811yescharacteristic
56C4×C3⋊D3SD1611yescharacteristic
57C4×C3⋊D3SD1611yescharacteristic
58C4×C3⋊D3SD1611yescharacteristic
59C4×C3⋊D3SD1611yescharacteristic
60C4×C3⋊D3Q1611yescharacteristic
61C4×C3⋊D3Q1611yescharacteristic
62#622—42no—
63C32×C8—41no—
64C3⋊(C3⋊C8)—41no—
65C2×C4⋊C8—91no—
66C2×C4⋊C8—91no—
67#384—91no—
68C2×C4×D3—62no—
69C2×C4×D3—62no—
70C2×C4×D3—62no—
71C2×C3×C8—24no—
72C3×C42—22no—
73C4×Dic3—62no—
74C4×Dic3—62no—
75C4×Dic3—62no—
76C2×C3⋊C8—64no—
77D3×C8—124no—
78D3×C8—124no—
79C22×C32#9511yescharacteristic
80C2×C3⋊D3#10011yescharacteristic
81C2×C3⋊D3#10111yescharacteristic
82C2×C3⋊D3#10211yescharacteristic
83C2×C3⋊D3#10211yescharacteristic
84C2×C3⋊D3#10311yescharacteristic
85C2×C3⋊D3#10311yescharacteristic
86#157—82no—
87C32×C4—21no—
88C32×C4#10211yescharacteristic
89C32×C4#10311yescharacteristic
90C32×C4#10611yescharacteristic
91C32×C4#10711yescharacteristic
92C3⋊Dic3—21no—
93C3⋊Dic3#10211yescharacteristic
94C3⋊Dic3#10311yescharacteristic
95C3⋊Dic3#10611yescharacteristic
96C3⋊Dic3#10711yescharacteristic
97C22×C8—181no—
98C22×C8—181no—
99C2×C4⋊C4—92no—
100C2×C4⋊C4—181no—
101C2×C4⋊C4—181no—
102C2×C42—91no—
103C4⋊C8—92no—
104C4⋊C8—91no—
105C4⋊C8—181no—
106C4⋊C8—181no—
107C4⋊C8#15711yescharacteristic, complemented
108C22×D3—62no—
109C2×C3×C4—22no—
110C2×C3×C4—22no—
111C2×C3×C4—22no—
112C2×Dic3—62no—
113C2×Dic3—62no—
114C2×Dic3—62no—
115C4×D3—62no—
116C4×D3—62no—
117C4×D3—62no—
118C4×D3—62no—
119C4×D3—62no—
120C4×D3—62no—
121C4×D3—62no—
122C4×D3—62no—
123C4×D3—122no—
124C4×D3—122no—
125C3×C8—44no—
126C3⋊C8—124no—
127C2×C32#34011yescharacteristic
128C2×C32#34011yescharacteristic
129C2×C32#34311yescharacteristic
130C3⋊D3#33111yescharacteristic
131C3⋊D3#33211yescharacteristic
132C3⋊D3#33211yescharacteristic
133C3⋊D3#33311yescharacteristic
134C22×C4—91no—
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—182no—
138C2×C8—21no—
139C2×C8—182no—
140C2×C8—181no—
141C2×C8—361no—
142C2×C8—361no—
143C2×C8—361no—
144C2×C8—361no—
145C4⋊C4—361no—
146C4⋊C4—361no—
147C4⋊C4—361no—
148C4⋊C4—361no—
149C4⋊C4—362no—
150C42—91no—
151C42—91no—
152C42—91no—
153C42C2×#15711yescharacteristic
154C22×C3—22no—
155C2×D3—62no—
156C2×D3—62no—
157C2×D3—62no—
158C2×D3—62no—
159C2×D3—62no—
160C2×D3—62no—
161C3×C4—22no—
162C3×C4—22no—
163C3×C4—22no—
164C3×C4—22no—
165C3×C4—42no—
166Dic3—62no—
167Dic3—62no—
168Dic3—62no—
169Dic3—62no—
170Dic3—122no—
171C32#129611yescharacteristic, complemented, Sylow
172C23—91no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—91no—
179C2×C4—91no—
180C2×C4—91no—
181C2×C4—91no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—181no—
185C2×C4—181no—
186C2×C4—362no—
187C2×C4—362no—
188C2×C4—362no—
189C2×C4C4×#15711yescharacteristic
190C2×C4C4⋊#15711yescharacteristic
191C2×C4C22⋊#15711yescharacteristic
192C8—41no—
193C8—362no—
194C8—361no—
195C2×C3—22no—
196C2×C3—22no—
197C2×C3—22no—
198D3—62no—
199D3—62no—
200D3—62no—
201D3—62no—
202C22—91no—
203C22—91no—
204C22—91no—
205C22—91no—
206C22—91no—
207C22—91no—
208C22#6378111yescharacteristic
209C4—21no—
210C4—91no—
211C4—91no—
212C4—91no—
213C4—91no—
214C4—181no—
215C4—722no—
216C4#6376811yescharacteristic
217C4#6376911yescharacteristic
218C4#6378211yescharacteristic
219C4#6378411yescharacteristic
220C3—22no—
221C2—91no—
222C2—91no—
223C2—91no—
224C2—91no—
225C2#1059016311yescharacteristic
226C2#1059018211yescharacteristic
227C2#1059018811yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC42C2×#157
FittingC32×C4⋊C8C4
socleC22×C32#95
prime radicalC22×C3⋊D3C22⋊C4
cosocleC42×C3⋊D3C22
hypercenterC4⋊C8#157
hypocenterC32#1296
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
10. #63779C4semidirect
12. C32×C4⋊C8C4semidirect
14. C4⋊(C3⋊(C3⋊C8))C4semidirect
107. C4⋊C8#157semidirect
171. C32#1296semidirect

Maximal subgroups

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

subgroupindex
#105937352
#105937262
C3⋊D3×C4⋊C82
#12969