Finite Group Databasebeta

← #11773813

Subgroups — #11773813

Order 1152.

738 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 84 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×#64102C211yesmaximal, characteristic
2#10593795C212yesmaximal, complemented
3#10590204C214yesmaximal, complemented
4C22×C4⋊(C3⋊D3)C411yescharacteristic
5C22×C4×C3⋊D3C412yes—
6C2×C32×C4⋊C4C411yescharacteristic
7C2×#3752C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9#64102—22no—
10#64102—22no—
11C22⋊#622C2214yes—
12C4⋊#622—22no—
13C4×#622—22no—
14C2×#893—62no—
15C23×C3⋊D3C2×C412yes—
16C22×C32×C4C2×C412yes—
17C22×C32×C4C2×C411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C22×C3⋊Dic3C2311yescharacteristic
20C2×C4⋊(C3⋊D3)—22no—
21C2×C4⋊(C3⋊D3)—22no—
22C2×C4⋊(C3⋊D3)C814yescomplemented
23C2×C4×C3⋊D3—22no—
24C2×C4×C3⋊D3—22no—
25C2×C4×C3⋊D3—44no—
26C2×#622—24no—
27C32×C4⋊C4—22no—
28#3752—24no—
29C4×C3⋊Dic3D412yes—
30C4×C3⋊Dic3D412yes—
31#1460—91nomaximal, Sylow
32C22×D12—62no—
33C22×C4×D3—64no—
34C2×C3×C4⋊C4—22no—
35C2×(C2×D3)⋊C4—64no—
36C2×C4×Dic3—62no—
37#893—68no—
38#893—68no—
39C23×C32C22×C411yescharacteristic
40C22×C3⋊D3—22no—
41C22×C3⋊D3—22no—
42C22×C3⋊D3—42no—
43C22×C3⋊D3—42no—
44C22×C3⋊D3C2×C814yes—
45C2×C32×C4—22no—
46C2×C32×C4—42no—
47C2×C32×C4C22⋊C412yes—
48C2×C32×C4C2×C812yes—
49C2×C32×C4M1612yes—
50C2×C3⋊Dic3—22no—
51C2×C3⋊Dic3—41no—
52C2×C3⋊Dic3C22⋊C411yescharacteristic
53C2×C3⋊Dic3C22⋊C411yescharacteristic
54C2×C3⋊Dic3C2×D412yes—
55C4⋊(C3⋊D3)—28no—
56C4×C3⋊D3—44no—
57C4×C3⋊D3—44no—
58#622—44no—
59C2×C4×D4—91no—
60#431—92no—
61#323—94no—
62C23×D3—64no—
63C22×C3×C4—24no—
64C22×C3×C4—22no—
65C22×Dic3—62no—
66C22×Dic3—62no—
67C2×D12—68no—
68C2×D12—68no—
69C2×D12—68no—
70C2×C4×D3—68no—
71C2×C4×D3—68no—
72C2×C4×D3—1216no—
73C3×C4⋊C4—28no—
74(C2×D3)⋊C4—616no—
75C4×Dic3—64no—
76C4×Dic3—64no—
77C22×C32—21no—
78C22×C32—21no—
79C22×C32C2×C22⋊C411yescharacteristic
80C22×C32C22×C811yescharacteristic
81C22×C32C2×M1611yescharacteristic
82C2×C3⋊D3—24no—
83C2×C3⋊D3—44no—
84C2×C3⋊D3—42no—
85C2×C3⋊D3—42no—
86C2×C3⋊D3—44no—
87C32×C4—42no—
88C32×C4C22⋊C814yes—
89C3⋊Dic3—21no—
90C3⋊Dic3—22no—
91C3⋊Dic3#10012yes—
92C22×D4—91no—
93C23×C4—92no—
94C4×D4—182no—
95C4×D4—182no—
96C2×C4⋊C4#15711yescharacteristic
97C2×C22⋊C4—92no—
98C2×C42—91no—
99C4⋊C8—182no—
100C22⋊C8—94no—
101C4×C8—182no—
102C23×C3—22no—
103C22×D3—68no—
104C22×D3—68no—
105C22×D3—68no—
106C22×D3—128no—
107C22×D3—128no—
108C2×C3×C4—28no—
109C2×C3×C4—24no—
110C2×C3×C4—24no—
111C2×C3×C4—24no—
112C2×C3×C4—48no—
113C2×Dic3—62no—
114C2×Dic3—62no—
115C2×Dic3—64no—
116C2×Dic3—68no—
117C2×Dic3—124no—
118D12—632no—
119C4×D3—1216no—
120C4×D3—1216no—
121C2×C32—21no—
122C2×C32—21no—
123C2×C32C2×C22⋊C811yescharacteristic
124C2×C32#41011yescharacteristic
125C2×C32C2×#10011yescharacteristic
126C3⋊D3—44no—
127C24—92no—
128C2×D4—94no—
129C2×D4—182no—
130C2×D4—182no—
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—182no—
134C22×C4—182no—
135C22×C4—364no—
136C22×C4C2×#15712yes—
137C22×C4C2×#15711yescharacteristic
138C2×C8—184no—
139C4⋊C4—22no—
140C22⋊C4—184no—
141C42—92no—
142C42—92no—
143C22×C3—24no—
144C22×C3—24no—
145C22×C3—22no—
146C22×C3—22no—
147C22×C3—22no—
148C2×D3—616no—
149C2×D3—128no—
150C2×D3—1216no—
151C2×D3—1216no—
152C2×D3—128no—
153C3×C4—28no—
154C3×C4—48no—
155Dic3—64no—
156Dic3—64no—
157Dic3—124no—
158C32#146011yescharacteristic, complemented, Sylow
159C23—94no—
160C23—182no—
161C23—182no—
162C23—362no—
163C23—362no—
164C23C22×#15711yescharacteristic
165D4—188no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—91no—
169C2×C4—92no—
170C2×C4—91no—
171C2×C4—182no—
172C2×C4—364no—
173C2×C4—364no—
174C2×C4—361no—
175C2×C4#378712yes—
176C2×C4#378812yes—
177C2×C4C22⋊#15712yes—
178C8—364no—
179C2×C3—24no—
180C2×C3—24no—
181C2×C3—22no—
182C2×C3—22no—
183C2×C3—22no—
184D3—1216no—
185C22—21no—
186C22—21no—
187C22—184no—
188C22—364no—
189C22—364no—
190C22—362no—
191C22—362no—
192C22C2×#378711yescharacteristic
193C22C2×#378811yescharacteristic
194C22C2×C22⋊#15711yescharacteristic
195C4—42no—
196C4—92no—
197C4—181no—
198C4—182no—
199C4#6377814yes—
200C3—22no—
201C2—21no—
202C2—21no—
203C2—364no—
204C2C2×#6377811yescharacteristic
205C2#1059382511yescharacteristic
206C2#1059383211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC22×C32C22×C8
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1460
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593795C2semidirect
3. #10590204C2semidirect
22. C2×C4⋊(C3⋊D3)C8semidirect
158. C32#1460semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
#105937952
#105902042
#14609