Finite Group Databasebeta

← #11770882

Subgroups — #11770882

Order 1152.

416 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 44 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#10593811C211yesmaximal, characteristic
2C4×C22⋊#157C211yesmaximal, characteristic
3#10592425C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157—21no—
6C2×C22⋊#157—21no—
7C2×C4×#157C412yescomplemented
8C2×#3743—21no—
9#63781—21no—
10#63781—21no—
11#63781C412yescomplemented
12C32×C22⋊C8C411yescharacteristic, complemented
13#63657C411yescharacteristic, complemented
14#63647—21no—
15#4726—62no—
16C23×C3⋊D3D411yescharacteristic
17C22×#157—22no—
18C22×#157—22no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3Q811yescharacteristic
21C2×C4×C3⋊D3—42no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C22⋊#157—24no—
27C22⋊#157—42no—
28C4×#157—42no—
29C2×C32×C8—21no—
30C2×C3⋊(C3⋊C8)—21no—
31#3743—42no—
32#1284—91nomaximal, Sylow
33C22×C4×D3—62no—
34C2×ΓL(1,𝔽25)—64no—
35C3×C22⋊C8—22no—
36#830—62no—
37(C2×D3)⋊C8—64no—
38C23×C32C4⋊C411yescharacteristic
39C22×C3⋊D3—22no—
40C22×C3⋊D3—22no—
41C22×C3⋊D3—41no—
42C22×C3⋊D3C22⋊C411yescharacteristic
43C22×C3⋊D3C22⋊C411yescharacteristic
44C2×#157—24no—
45C2×#157—42no—
46C2×#157—42no—
47C2×#157—42no—
48C2×#157—42no—
49C2×#157—42no—
50C2×C32×C4—41no—
51C2×C32×C4C4211yescharacteristic
52C2×C32×C4C22⋊C411yescharacteristic
53C2×C3⋊Dic3—41no—
54C2×C3⋊Dic3C4⋊C411yescharacteristic
55C2×C3⋊Dic3C4⋊C411yescharacteristic
56C4×C3⋊D3—22no—
57C4×C3⋊D3—22no—
58C4×C3⋊D3—41no—
59C4×C3⋊D3—41no—
60C32×C8—41no—
61C3⋊(C3⋊C8)—41no—
62#407—91no—
63#381—91no—
64C4×C22⋊C4—91no—
65C23×D3—62no—
66C22×C3×C4—22no—
67C22×Dic3—62no—
68C2×C4×D3—62no—
69C2×C4×D3—62no—
70C2×C4×D3—62no—
71C2×C4×D3—62no—
72C2×C4×D3—128no—
73C2×C3×C8—24no—
74C2×C3⋊C8—64no—
75ΓL(1,𝔽25)—128no—
76C22×C32—21no—
77C22×C32—21no—
78C22×C32—21no—
79C22×C32#9511yescharacteristic
80C2×C3⋊D3—21no—
81C2×C3⋊D3—21no—
82C2×C3⋊D3—21no—
83C2×C3⋊D3—21no—
84C2×C3⋊D3—44no—
85C2×C3⋊D3#9912yes—
86C2×C3⋊D3#10412yes—
87#157—44no—
88#157—82no—
89C32×C4—21no—
90C32×C4—21no—
91C3⋊Dic3—21no—
92C3⋊Dic3—21no—
93C23×C4—91no—
94C2×M16—181no—
95C2×C22⋊C4—181no—
96C2×C22⋊C4—181no—
97C2×C42—92no—
98C22⋊C8—91no—
99C22⋊C8—181no—
100C22⋊C8#15711yescharacteristic, complemented
101#95—92no—
102#95—181no—
103#95—181no—
104C23×C3—22no—
105C22×D3—62no—
106C22×D3—62no—
107C22×D3—124no—
108C22×D3—124no—
109C22×D3—124no—
110C2×C3×C4—22no—
111C2×C3×C4—22no—
112C2×C3×C4—44no—
113C2×Dic3—62no—
114C2×Dic3—62no—
115C2×Dic3—124no—
116C4×D3—68no—
117C4×D3—124no—
118C4×D3—124no—
119C4×D3—124no—
120C3×C8—44no—
121C3⋊C8—124no—
122C2×C32—41no—
123C2×C32H(3,ℤ/4)11yescharacteristic
124C2×C32#33911yescharacteristic
125C2×C32#34211yescharacteristic
126C3⋊D3—22no—
127C3⋊D3—22no—
128C24—91no—
129C22×C4—91no—
130C22×C4—91no—
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—91no—
134C22×C4—182no—
135C22×C4—182no—
136C22×C4—362no—
137C22×C4C2×#15711yescharacteristic
138M16—362no—
139C2×C8—21no—
140C2×C8—181no—
141C22⋊C4—184no—
142C22⋊C4—362no—
143C42—362no—
144C22×C3—24no—
145C22×C3—22no—
146C22×C3—42no—
147C22×C3—42no—
148C2×D3—64no—
149C2×D3—64no—
150C2×D3—122no—
151C2×D3—122no—
152C2×D3—122no—
153C2×D3—122no—
154C2×D3—1216no—
155C3×C4—24no—
156C3×C4—42no—
157Dic3—64no—
158Dic3—122no—
159C32#128411yescharacteristic, complemented, Sylow
160C23—91no—
161C23—91no—
162C23—182no—
163C23—182no—
164C23—361no—
165C23C4⋊#15711yescharacteristic
166C2×C4—41no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—182no—
170C2×C4—182no—
171C2×C4—184no—
172C2×C4—361no—
173C2×C4—361no—
174C2×C4—361no—
175C2×C4—362no—
176C2×C4—362no—
177C2×C4—362no—
178C2×C4—362no—
179C2×C4—362no—
180C2×C4C4×#15711yescharacteristic
181C2×C4C22⋊#15711yescharacteristic
182C8—41no—
183C8—361no—
184C2×C3—22no—
185C2×C3—22no—
186C2×C3—22no—
187C2×C3—44no—
188D3—124no—
189D3—124no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—92no—
194C22—92no—
195C22—181no—
196C22—181no—
197C22—181no—
198C22—181no—
199C22—364no—
200C22#6378111yescharacteristic
201C4—21no—
202C4—21no—
203C4—181no—
204C4—181no—
205C4—364no—
206C4—722no—
207C3—22no—
208C2—41no—
209C2—182no—
210C2—182no—
211C2#1059015511yescharacteristic
212C2#1059018411yescharacteristic
213C2#1059018911yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC32×C22⋊C8C4
socleC22×C32#95
prime radicalC23×C3⋊D3D4
cosocleC22×C4×C3⋊D3C22
hypercenterC22⋊C8#157
hypocenterC32#1284
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
7. C2×C4×#157C4semidirect
11. #63781C4semidirect
12. C32×C22⋊C8C4semidirect
13. #63657C4semidirect
100. C22⋊C8#157semidirect
159. C32#1284semidirect

Maximal subgroups

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

subgroupindex
#105938112
C4×C22⋊#1572
#105924252
#12849