Finite Group Databasebeta

← #11772371

Subgroups — #11772371

Order 1152.

282 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C2×#63769C211yesmaximal, characteristic
2C2×#63764C211yesmaximal, characteristic
3C3⋊D3×#107C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6C4⋊C4×C3⋊D3—21no—
7C2×#3708—21no—
8#63769—21no—
9#63769C412yescomplemented
10#63764—21no—
11#63764C412yescomplemented
12C32×#107C411yescharacteristic, complemented
13#63645C411yescharacteristic, complemented
14#63634—21no—
15D3×#107—62no—
16C22×#157—41no—
17C2×C4×C3⋊D3—41no—
18C2×C4×C3⋊D3D411yescharacteristic
19C4⋊#157—22no—
20C4⋊#157—41no—
21C2×C32×C8C2×C411yescharacteristic
22C32×C4⋊C4—21no—
23C4⋊(C3⋊Dic3)—21no—
24#3750—41no—
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3C2×C411yescharacteristic
28C8×C3⋊D3D411yescharacteristic
29C8×C3⋊D3Q811yescharacteristic
30#3708—22no—
31#1380—91nomaximal, Sylow
32C2×D3×C8—62no—
33D3×C4⋊C4—64no—
34C3×#107—22no—
35#818—62no—
36#807—64no—
37C22×C3⋊D3D811yescharacteristic
38C2×#157—42no—
39C2×#157—81no—
40C2×#157—81no—
41C2×C32×C4—41no—
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C3⋊Dic3—41no—
44C2×C3⋊Dic3SD1611yescharacteristic
45C4×C3⋊D3—81no—
46C4×C3⋊D3—81no—
47C4×C3⋊D3C22⋊C411yescharacteristic
48C4×C3⋊D3C4⋊C411yescharacteristic
49C4×C3⋊D3SD1611yescharacteristic
50C4×C3⋊D3Q1611yescharacteristic
51C32×C8C4211yescharacteristic
52C32×C8C4⋊C411yescharacteristic
53C3⋊(C3⋊C8)C22⋊C411yescharacteristic
54C3⋊(C3⋊C8)C4⋊C411yescharacteristic
55C22×C16—91no—
56C2×#107—91no—
57C2×#107—91no—
58C2×C4×D3—62no—
59C2×C4×D3—124no—
60C2×C3×C8—22no—
61C3×C4⋊C4—24no—
62C4⋊Dic3—64no—
63Dic3⋊C4—124no—
64C2×C3⋊C8—62no—
65D3×C8—62no—
66D3×C8—62no—
67D3×C8—62no—
68D3×C8—62no—
69C22×C32#10211yescharacteristic
70C2×C3⋊D3#10211yescharacteristic
71C2×C3⋊D3#10711yescharacteristic
72C2×C3⋊D3D1611yescharacteristic
73C2×C3⋊D3SD3211yescharacteristic
74C2×C3⋊D3SD3211yescharacteristic
75C2×C3⋊D3Q3211yescharacteristic
76#157—82no—
77C32×C4—81no—
78C32×C4#9511yescharacteristic
79C32×C4#10311yescharacteristic
80C3⋊Dic3—81no—
81C3⋊Dic3#10311yescharacteristic
82C3⋊Dic3#10611yescharacteristic
83C22×C8—91no—
84C2×C4⋊C4—181no—
85C2×C4⋊C4—181no—
86C2×C16—92no—
87C2×C16—181no—
88C2×C16—181no—
89#107—92no—
90#107—91no—
91#107—181no—
92#107—181no—
93#107#15711yescharacteristic, complemented
94C22×D3—62no—
95C2×C3×C4—22no—
96C2×C3×C4—44no—
97C2×Dic3—62no—
98C2×Dic3—124no—
99C4×D3—62no—
100C4×D3—62no—
101C4×D3—62no—
102C4×D3—62no—
103C4×D3—244no—
104C4×D3—244no—
105C3×C8—22no—
106C3×C8—22no—
107C3⋊C8—62no—
108C3⋊C8—62no—
109C2×C32#34011yescharacteristic
110C2×C32#35711yescharacteristic
111C2×C32#35811yescharacteristic
112C3⋊D3#35711yescharacteristic
113C3⋊D3#35811yescharacteristic
114C3⋊D3#36611yescharacteristic
115C3⋊D3#36711yescharacteristic
116C22×C4—91no—
117C22×C4—361no—
118C22×C4—361no—
119C2×C8—91no—
120C2×C8—91no—
121C2×C8—91no—
122C2×C8—91no—
123C2×C8—91no—
124C2×C8C2×#15711yescharacteristic
125C4⋊C4—21no—
126C4⋊C4—182no—
127C4⋊C4—181no—
128C4⋊C4—361no—
129C4⋊C4—361no—
130C16—182no—
131C22×C3—22no—
132C2×D3—62no—
133C2×D3—62no—
134C2×D3—62no—
135C2×D3—62no—
136C2×D3—62no—
137C2×D3—62no—
138C3×C4—22no—
139C3×C4—22no—
140C3×C4—84no—
141Dic3—62no—
142Dic3—62no—
143Dic3—244no—
144C32#138011yescharacteristic, complemented, Sylow
145C23—91no—
146C2×C4—41no—
147C2×C4—91no—
148C2×C4—91no—
149C2×C4—91no—
150C2×C4—91no—
151C2×C4—91no—
152C2×C4—362no—
153C2×C4—361no—
154C2×C4—721no—
155C2×C4—721no—
156C2×C4—721no—
157C2×C4—721no—
158C2×C4C22⋊#15711yescharacteristic
159C8—91no—
160C8—91no—
161C8C4×#15711yescharacteristic
162C8C4⋊#15711yescharacteristic
163C2×C3—22no—
164C2×C3—22no—
165C2×C3—22no—
166D3—62no—
167D3—62no—
168D3—62no—
169D3—62no—
170C22—91no—
171C22—91no—
172C22—91no—
173C22—91no—
174C22—91no—
175C22—91no—
176C22#6378211yescharacteristic
177C4—81no—
178C4—91no—
179C4—91no—
180C4—722no—
181C4—721no—
182C4#6378111yescharacteristic
183C4#6378411yescharacteristic
184C3—22no—
185C2—91no—
186C2—91no—
187C2—91no—
188C2—91no—
189C2#1059016311yescharacteristic
190C2#1059019311yescharacteristic
191C2#1059019711yescharacteristic
subgroupG/H
centerC22#63782
commutatorC32×C8C42
FrattiniC2×C8C2×#157
FittingC32×#107C4
socleC22×C32#102
prime radicalC22×C3⋊D3D8
cosocleC2×C8×C3⋊D3C22
hypercenter#107#157
hypocenterC32#1380
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
9. #63769C4semidirect
11. #63764C4semidirect
12. C32×#107C4semidirect
13. #63645C4semidirect
93. #107#157semidirect
144. C32#1380semidirect

Maximal subgroups

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

subgroupindex
C2×#637692
C2×#637642
C3⋊D3×#1072
#13809