Finite Group Databasebeta

← #11807989

Subgroups — #11807989

Order 1152.

634 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 152 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
1C3⋊D3×#125C211yesmaximal, characteristic
2#10593759C214yesmaximal
3#10593758C214yesmaximal
4#10593758C214yesmaximal
5#10593736C212yesmaximal
6C2×C4⋊#157C2212yes—
7C2×C4⋊#157C2212yes—
8C2×C4⋊#157C2214yes—
9C2×C4×#157C2214yes—
10C32×#125C411yescharacteristic, complemented
11C4⋊C4×C3⋊D3C2212yes—
12C4⋊C4×C3⋊D3C2214yes—
13#64099C412yescomplemented
14#64098C414yescomplemented
15C42×C3⋊D3C2211yescharacteristic
16#64079C411yescharacteristic, complemented
17#63781C2214yes—
18#63781C2214yes—
19#63781C2214yes—
20#63781C2214yes—
21D3×#125—62no—
22C22×#157C2314yes—
23C22×#157C2314yes—
24C2×C4×C3⋊D3C2314yes—
25C2×C4×C3⋊D3C2312yes—
26C2×C4×C3⋊D3C2311yescharacteristic
27C4⋊#157—44no—
28C4⋊#157—42no—
29C4⋊#157—42no—
30C4×#157—44no—
31C32×C4⋊C4C2×C414yes—
32C32×C4⋊C4C2×C412yes—
33C32×C42C2×C411yescharacteristic
34C4⋊(C3⋊Dic3)C2×C412yes—
35C4⋊(C3⋊Dic3)C2×C414yes—
36#3750C2×C414yes—
37#3750C2×C414yes—
38#3750C2×C414yes—
39C4×C3⋊Dic3C2×C412yes—
40C4×C3⋊Dic3C2×C411yescharacteristic
41#2382—91nomaximal, Sylow
42C3×#125—22no—
43D3×C4⋊C4—64no—
44D3×C4⋊C4—68no—
45#890—64no—
46#889—68no—
47C42×D3—62no—
48#870—62no—
49C22×C3⋊D3C2411yescharacteristic
50C2×#157—24no—
51C2×#157—24no—
52C2×#157—24no—
53C2×#157—24no—
54C2×#157—24no—
55C2×#157—24no—
56C2×C32×C4C22×C412yes—
57C2×C32×C4C22×C411yescharacteristic
58C2×C32×C4C22×C414yes—
59C2×C3⋊Dic3C22×C411yescharacteristic
60C2×C3⋊Dic3C22×C412yes—
61C2×C3⋊Dic3C22×C414yes—
62C4×C3⋊D3—21no—
63C4×C3⋊D3—21no—
64C4×C3⋊D3—24no—
65C4×C3⋊D3—22no—
66C4×C3⋊D3—24no—
67C4×C3⋊D3—22no—
68C2×#125—91no—
69#389—94no—
70#387—94no—
71#387—94no—
72#382—92no—
73C2×C4×D3—62no—
74C2×C4×D3—64no—
75C2×C4×D3—68no—
76C3×C4⋊C4—28no—
77C3×C4⋊C4—24no—
78C3×C42—22no—
79C4⋊Dic3—64no—
80C4⋊Dic3—68no—
81Dic3⋊C4—68no—
82Dic3⋊C4—68no—
83Dic3⋊C4—68no—
84C4×Dic3—64no—
85C4×Dic3—62no—
86C22×C32C23×C411yescharacteristic
87C2×C3⋊D3H(5,𝔽2)12yes—
88C2×C3⋊D32−1+411yescharacteristic
89C2×C3⋊D32−1+411yescharacteristic
90C2×C3⋊D32−1+412yes—
91#157—44no—
92#157—44no—
93C32×C4—21no—
94C32×C4—24no—
95C32×C4—22no—
96C3⋊Dic3—21no—
97C3⋊Dic3—24no—
98C3⋊Dic3—22no—
99#125—94no—
100#125—92no—
101#125—91no—
102#125#15711yescharacteristic, complemented
103C2×C4⋊C4—92no—
104C2×C4⋊C4—94no—
105C2×C4⋊C4—92no—
106C2×C4⋊C4—92no—
107C2×C4⋊C4—94no—
108C2×C42—91no—
109C2×C42—94no—
110#95—94no—
111#95—94no—
112#95—94no—
113#95—94no—
114C22×D3—62no—
115C2×C3×C4—22no—
116C2×C3×C4—24no—
117C2×C3×C4—28no—
118C2×Dic3—62no—
119C2×Dic3—64no—
120C2×Dic3—68no—
121C4×D3—64no—
122C4×D3—64no—
123C4×D3—128no—
124C4×D3—124no—
125C4×D3—124no—
126C4×D3—128no—
127C2×C32#51911yescharacteristic
128C2×C32#52012yes—
129C3⋊D3#56211yescharacteristic
130C3⋊D3#56312yes—
131C3⋊D3#56411yescharacteristic
132C22×C4—91no—
133C22×C4—92no—
134C22×C4—94no—
135C22×C4—94no—
136C22×C4—94no—
137C4⋊C4—94no—
138C4⋊C4—94no—
139C4⋊C4—94no—
140C4⋊C4—94no—
141C4⋊C4—92no—
142C4⋊C4—364no—
143C4⋊C4—362no—
144C4⋊C4—362no—
145C4⋊C4C2×#15712yes—
146C4⋊C4C2×#15714yes—
147C42—92no—
148C42—91no—
149C42—364no—
150C42C2×#15711yescharacteristic
151C22×C3—22no—
152C2×D3—62no—
153C2×D3—62no—
154C2×D3—64no—
155C2×D3—64no—
156C3×C4—24no—
157C3×C4—44no—
158C3×C4—48no—
159Dic3—64no—
160Dic3—124no—
161Dic3—128no—
162C32#238211yescharacteristic, complemented, Sylow
163C23—91no—
164C2×C4—91no—
165C2×C4—92no—
166C2×C4—94no—
167C2×C4—184no—
168C2×C4—182no—
169C2×C4—181no—
170C2×C4—181no—
171C2×C4—184no—
172C2×C4—182no—
173C2×C4—184no—
174C2×C4—184no—
175C2×C4—184no—
176C2×C4—184no—
177C2×C4—184no—
178C2×C4—184no—
179C2×C4C22×#15711yescharacteristic
180C2×C4C22×#15712yes—
181C2×C4C22×#15714yes—
182C2×C3—22no—
183C2×C3—24no—
184D3—62no—
185D3—64no—
186D3—62no—
187C22—91no—
188C22—91no—
189C22—92no—
190C22—92no—
191C22C23×#15711yescharacteristic
192C4—21no—
193C4—24no—
194C4—22no—
195C4—181no—
196C4—182no—
197C4—184no—
198C4—364no—
199C4—364no—
200C3—22no—
201C2—91no—
202C2—92no—
203C2—91no—
204C2#1059664611yescharacteristic
205C2#1059665012yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#125C4
prime radical, cosocleC22×C3⋊D3C24
hypercenter#125#157
hypocenterC32#2382
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
10. C32×#125C4semidirect
13. #64099C4semidirect
14. #64098C4semidirect
16. #64079C4semidirect
102. #125#157semidirect
162. C32#2382semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1252
#105937592
#105937582
#105937362
#23829