Finite Group Databasebeta

← #11797440

Subgroups — #11797440

Order 1152.

308 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×#3708C211yesmaximal, characteristic, complemented
2C2×#63764C211yesmaximal, characteristic, complemented
3#10592424C211yesmaximal, characteristic
4C22⋊#3708C211yesmaximal, characteristic, complemented
5#10590177C211yesmaximal, characteristic, complemented
6#10590176C211yesmaximal, characteristic, complemented
7#10590174C211yesmaximal, characteristic, complemented
8C4×#638C411yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C8×C3⋊D3C2211yescharacteristic
11C2×#3708—22no—
12C2×#3708C2211yescharacteristic
13C2×#3708C2211yescharacteristic
14C2×#3708C2211yescharacteristic
15C2×#3708C2211yescharacteristic
16#63764—22no—
17C32×C22⋊C8C411yescharacteristic
18#63647C411yescharacteristic
19#63641C411yescharacteristic
20C8×C3⋊Dic3C2211yescharacteristic
21#67⋊C8—62no—
22C22×C32×C4C2×C411yescharacteristic
23C2×#638C811yescharacteristic
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C32×C8C2×C411yescharacteristic
26C2×C32×C8C2×C411yescharacteristic
27#3757C811yescharacteristic
28#3752C811yescharacteristic
29#3750C811yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C2×C3⋊(C3⋊C8)—21no—
32C2×C3⋊(C3⋊C8)—21no—
33C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
34C2×C3⋊(C3⋊C8)C2311yescharacteristic
35C8×C3⋊D3—21no—
36C8×C3⋊D3—21no—
37#3708—21no—
38#3708—21no—
39#3708—21no—
40#3708D412yescomplemented
41D4×C16—91nomaximal, Sylow
42C4×#67—62no—
43C22×C3⋊C8—62no—
44C2×D3×C8—62no—
45C3×C22⋊C8—22no—
46(C2×D3)⋊C8—62no—
47Dic3⋊C8—62no—
48C8×Dic3—62no—
49C23×C32C2×C811yescharacteristic
50C22×C3⋊D3C2×C811yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4C2×C811yescharacteristic
54C2×C32×C4C22×C411yescharacteristic
55#638C1614yescomplemented
56C2×C3⋊Dic3C2×C811yescharacteristic
57C2×C3⋊Dic3C2×C811yescharacteristic
58C2×C3⋊Dic3C2×C811yescharacteristic
59C4×C3⋊D3—21no—
60C4×C3⋊D3—21no—
61C32×C8—21no—
62C32×C8—21no—
63C3⋊(C3⋊C8)—21no—
64C3⋊(C3⋊C8)C2×D411yescharacteristic
65C3⋊(C3⋊C8)#4111yescharacteristic
66C22×C16—91no—
67C22×C16—91no—
68C8×D4—91no—
69C4⋊C16—91no—
70C22⋊C16—91no—
71C22⋊C16—91no—
72C4×C16—91no—
73C22×C3×C4—22no—
74C2×#67—62no—
75C2×C4×D3—62no—
76C2×C3×C8—22no—
77C2×C3×C8—22no—
78#217—62no—
79(C2×D3)⋊C4—62no—
80Dic3⋊C4—62no—
81C4×Dic3—62no—
82C2×C3⋊C8—62no—
83C2×C3⋊C8—62no—
84C2×C3⋊C8—122no—
85C2×C3⋊C8—122no—
86D3×C8—122no—
87D3×C8—122no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32C2×C1612yescomplemented
91C22×C32C22×C811yescharacteristic
92C2×C3⋊D3—21no—
93C2×C3⋊D3—21no—
94C2×C3⋊D3C2×C1612yescomplemented
95C32×C4—21no—
96C32×C4C4×D411yescharacteristic
97C32×C4#13111yescharacteristic
98C3⋊Dic3—21no—
99C3⋊Dic3—21no—
100C3⋊Dic3C2×C1612yescomplemented
101C22×C8—91no—
102C22×C8—91no—
103C4×D4—91no—
104C2×C16—91no—
105C2×C16—91no—
106C2×C16—91no—
107C2×C16—91no—
108C2×C16—182no—
109C2×C16—182no—
110C4⋊C8—91no—
111C22⋊C8—91no—
112C22⋊C8#15711yescharacteristic
113C4×C8—91no—
114C23×C3—22no—
115C22×D3—62no—
116C2×C3×C4—22no—
117C2×C3×C4—22no—
118C2×C3×C4—42no—
119C2×C3×C4—42no—
120#67—68no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C4×D3—122no—
125C4×D3—122no—
126C3×C8—42no—
127C3×C8—42no—
128C3⋊C8—62no—
129C3⋊C8—62no—
130C3⋊C8—122no—
131C2×C32—22no—
132C2×C32C8×D411yescharacteristic
133C2×C32C22×C1611yescharacteristic
134C2×C32#50411yescharacteristic
135C3⋊D3—22no—
136C2×D4—91no—
137C22×C4—91no—
138C22×C4C2×#15711yescharacteristic
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—181no—
142C2×C8—181no—
143C2×C8—181no—
144C2×C8—181no—
145C2×C8C2×#15711yescharacteristic
146C2×C8C2×#15711yescharacteristic
147C4⋊C4—91no—
148C22⋊C4—91no—
149C22⋊C4—91no—
150C42—91no—
151C16—92no—
152C16—181no—
153C16—181no—
154C16—181no—
155C22×C3—24no—
156C22×C3—22no—
157C22×C3—42no—
158C22×C3—42no—
159C2×D3—64no—
160C2×D3—122no—
161C2×D3—122no—
162C3×C4—22no—
163C3×C4—22no—
164C3×C4—42no—
165Dic3—64no—
166Dic3—122no—
167Dic3—122no—
168C32D4×C1611yescharacteristic, complemented, Sylow
169C23—91no—
170C23#378711yescharacteristic
171D4—94no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—181no—
178C2×C4—181no—
179C2×C4#378711yescharacteristic
180C2×C4C22×#15711yescharacteristic
181C8—21no—
182C8—21no—
183C8—91no—
184C8—91no—
185C8—181no—
186C2×C3—22no—
187C2×C3—22no—
188C2×C3—22no—
189C2×C3—44no—
190D3—124no—
191C22—21no—
192C22—21no—
193C22—92no—
194C22—181no—
195C22—181no—
196C22#6376412yescomplemented
197C22C2×#378711yescharacteristic
198C4—21no—
199C4—92no—
200C4—181no—
201C4—181no—
202C4#6428711yescharacteristic
203C4D4×#15711yescharacteristic
204C3—22no—
205C2—22no—
206C2—182no—
207C2#1059373911yescharacteristic
208C2C2×#6376411yescharacteristic
209C2#1059377211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutatorC2×C32C22×C16
FittingC32×C22⋊C8C4
socleC22×C32C22×C8
prime radicalC2×#638C8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22⋊C8#157
hypocenterC32D4×C16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×#3708C2semidirect
2. C2×#63764C2semidirect
4. C22⋊#3708C2semidirect
5. #10590177C2semidirect
6. #10590176C2semidirect
7. #10590174C2semidirect
40. #3708D4semidirect
55. #638C16semidirect
90. C22×C32C2×C16semidirect
94. C2×C3⋊D3C2×C16semidirect
100. C3⋊Dic3C2×C16semidirect
168. C32D4×C16semidirect
196. C22#63764semidirect

Maximal subgroups

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

subgroupindex
C22×#37082
C2×#637642
#105924242
C22⋊#37082
#105901772
#105901762
#105901742
D4×C169