Finite Group Databasebeta

← #11808040

Subgroups — #11808040

Order 1152.

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

normal subgroups only

This group has 702 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×#126C211yesmaximal, characteristic
2#10593759C213yesmaximal, complemented
3#10593758C213yesmaximal, complemented
4#10593747C213yesmaximal
5#10593746C213yesmaximal
6#10593737C211yesmaximal, characteristic, complemented
7#10593735C211yesmaximal, characteristic, complemented
8C23×#157C2211yescharacteristic
9C2×C22⋊#157C2213yes—
10C2×C4⋊#157C2213yes—
11C2×C4⋊#157C2213yes—
12C2×C4⋊#157C2213yes—
13C2×C4×#157C2213yes—
14C32×#126C411yescharacteristic, complemented
15#64107C413yescomplemented
16C4⋊C4×C3⋊D3C2213yes—
17C22⋊C4×C3⋊D3C2213yes—
18#64088C413yescomplemented
19#64085C411yescharacteristic, complemented
20C42×C3⋊D3C2211yescharacteristic
21#63781C2213yes—
22#63781C2213yes—
23#63781C2213yes—
24#63781C2213yes—
25D3×#126—62no—
26C23×C3⋊D3C2311yescharacteristic
27C22×#157—43no—
28C22×#157C2313yes—
29C22×#157C2313yes—
30C22×#157C2311yescharacteristic
31C22×#157C2311yescharacteristic
32C2×C4×C3⋊D3C2313yes—
33C2×C4×C3⋊D3C2313yes—
34C22⋊#157—43no—
35C4⋊#157—43no—
36C4⋊#157—43no—
37C4⋊#157—43no—
38C4×#157—43no—
39C32×C4⋊C4C2×C413yescomplemented
40C32×C22⋊C4C2×C413yes—
41C32×C42C2×C411yescharacteristic, complemented
42#3757C2×C413yes—
43#3752C2×C413yes—
44#3752C2×C413yes—
45C4⋊(C3⋊Dic3)C2×C413yescomplemented
46#3750C2×C413yescomplemented
47#3750C2×C413yescomplemented
48C4×C3⋊Dic3C2×C413yescomplemented
49#2383—91nomaximal, Sylow
50C3×#126—22no—
51#898—66no—
52D3×C4⋊C4—66no—
53D3×C22⋊C4—66no—
54#879—66no—
55#876—62no—
56C42×D3—62no—
57C23×C32C22×C411yescharacteristic
58C22×C3⋊D3—23no—
59C22×C3⋊D3—23no—
60C22×C3⋊D3C22×C411yescharacteristic
61C22×C3⋊D3C2411yescharacteristic
62C2×#157—23no—
63C2×#157—23no—
64C2×#157—23no—
65C2×#157—23no—
66C2×#157—23no—
67C2×#157—23no—
68C2×#157—26no—
69C2×#157—44no—
70C2×C32×C4C22×C413yes—
71C2×C32×C4C22×C413yes—
72C2×C3⋊Dic3C22×C413yes—
73C2×C3⋊Dic3C22×C413yes—
74C4×C3⋊D3—23no—
75C4×C3⋊D3—23no—
76C4×C3⋊D3—23no—
77C4×C3⋊D3—23no—
78C2×#126—91no—
79#389—93no—
80#388—93no—
81#387—93no—
82#385—93no—
83#384—91no—
84#383—91no—
85C23×D3—62no—
86C2×C4×D3—66no—
87C2×C4×D3—66no—
88C3×C4⋊C4—26no—
89C3×C22⋊C4—26no—
90C3×C42—22no—
91#217—66no—
92(C2×D3)⋊C4—66no—
93(C2×D3)⋊C4—66no—
94C4⋊Dic3—66no—
95Dic3⋊C4—66no—
96Dic3⋊C4—66no—
97C4×Dic3—66no—
98C22×C32—23no—
99C22×C32C23×C411yescharacteristic
100C2×C3⋊D3—23no—
101C2×C3⋊D3—41no—
102C2×C3⋊D3—43no—
103C2×C3⋊D3H(5,𝔽2)13yes—
104C2×C3⋊D32−1+413yes—
105#157—43no—
106#157—41no—
107#157—41no—
108#157—43no—
109C32×C4—23no—
110C32×C4—23no—
111C3⋊Dic3—23no—
112C3⋊Dic3—23no—
113C23×C4—91no—
114#126—93no—
115#126—93no—
116#126—91no—
117#126#15711yescharacteristic, complemented
118C2×C4⋊C4—93no—
119C2×C4⋊C4—93no—
120C2×C4⋊C4—93no—
121C2×C4⋊C4—93no—
122C2×C22⋊C4—93no—
123C2×C22⋊C4—93no—
124C2×C42—91no—
125C2×C42—93no—
126#95—93no—
127#95—93no—
128#95—93no—
129#95—93no—
130C23×C3—22no—
131C22×D3—62no—
132C22×D3—62no—
133C22×D3—126no—
134C22×D3—126no—
135C2×C3×C4—26no—
136C2×C3×C4—26no—
137C2×Dic3—66no—
138C2×Dic3—66no—
139C4×D3—126no—
140C4×D3—126no—
141C4×D3—126no—
142C4×D3—126no—
143C2×C32—41no—
144C2×C32#52013yes—
145C3⋊D3—41no—
146C3⋊D3#56011yescharacteristic
147C3⋊D3#56313yes—
148C24—91no—
149C22×C4—93no—
150C22×C4—93no—
151C22×C4—93no—
152C22×C4—91no—
153C22×C4—91no—
154C22×C4—93no—
155C22×C4—363no—
156C4⋊C4—93no—
157C4⋊C4—93no—
158C4⋊C4—93no—
159C4⋊C4—363no—
160C4⋊C4—363no—
161C4⋊C4—363no—
162C4⋊C4C2×#15713yescomplemented
163C22⋊C4—93no—
164C22⋊C4—93no—
165C22⋊C4—93no—
166C22⋊C4—363no—
167C22⋊C4C2×#15713yes—
168C42—93no—
169C42—363no—
170C42C2×#15711yescharacteristic, complemented
171C22×C3—22no—
172C22×C3—46no—
173C2×D3—66no—
174C2×D3—66no—
175C2×D3—126no—
176C2×D3—242no—
177C2×D3—246no—
178C3×C4—46no—
179C3×C4—46no—
180Dic3—126no—
181Dic3—126no—
182C32#238311yescharacteristic, complemented, Sylow
183C23—91no—
184C23—91no—
185C23—183no—
186C23—183no—
187C23C22×#15711yescharacteristic
188C2×C4—93no—
189C2×C4—93no—
190C2×C4—183no—
191C2×C4—183no—
192C2×C4—183no—
193C2×C4—183no—
194C2×C4—183no—
195C2×C4—183no—
196C2×C4—183no—
197C2×C4—183no—
198C2×C4—183no—
199C2×C4—183no—
200C2×C4—186no—
201C2×C4—364no—
202C2×C4C22×#15713yes—
203C2×C4C22×#15713yes—
204C2×C3—26no—
205C2×C3—82no—
206D3—62no—
207D3—66no—
208D3—242no—
209C22—23no—
210C22—93no—
211C22—93no—
212C22—183no—
213C22—361no—
214C22—363no—
215C22C23×#15711yescharacteristic
216C4—23no—
217C4—23no—
218C4—183no—
219C4—183no—
220C4—361no—
221C4—361no—
222C4—363no—
223C4—363no—
224C3—22no—
225C2—41no—
226C2—91no—
227C2—93no—
228C2—361no—
229C2#1059665013yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#126C4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenter#126#157
hypocenterC32#2383
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
2. #10593759C2semidirect
3. #10593758C2semidirect
6. #10593737C2semidirect
7. #10593735C2semidirect
14. C32×#126C4semidirect
15. #64107C4semidirect
18. #64088C4semidirect
19. #64085C4semidirect
39. C32×C4⋊C4C2×C4semidirect
41. C32×C42C2×C4semidirect
45. C4⋊(C3⋊Dic3)C2×C4semidirect
46. #3750C2×C4semidirect
47. #3750C2×C4semidirect
48. C4×C3⋊Dic3C2×C4semidirect
117. #126#157semidirect
162. C4⋊C4C2×#157semidirect
170. C42C2×#157semidirect
182. C32#2383semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1262
#105937592
#105937582
#105937472
#105937462
#105937372
#105937352
#23839