Finite Group Databasebeta

← #11800601

Subgroups — #11800601

Order 1152.

273 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 273 conjugacy classes of subgroups — too many to draw. Only its 68 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×#63626C211yesmaximal, characteristic, complemented
2C3×#4904C211yesmaximal, characteristic, complemented
3C3×#4499C211yesmaximal, characteristic, complemented
4#10589074C212yesmaximal, complemented
5#10589071C212yesmaximal, complemented
6#71509—31nomaximal
7#69373—31nomaximal
8C2×#3745—21no—
9C3×#904—21no—
10C2×C32×C16C2211yescharacteristic
11#63626—21no—
12#63626C2212yes—
13C3×Dic24C2211yescharacteristic, complemented
14C3×#800—21no—
15C3×D48C2211yescharacteristic, complemented
16C3×C3⋊C32C2212yescomplemented
17C3×#508—31no—
18#4904D311yescharacteristic, complemented
19C2×D48—31no—
20C2×D48—31no—
21C2×D48—61no—
22C3×M64—31no—
23#4521—32no—
24#4519—32no—
25#4499D311yescharacteristic, complemented
26#4449—32no—
27D96—32no—
28C2×C4⋊(C3⋊D3)—41no—
29C3×#235—41no—
30C2×C32×C8D411yescharacteristic
31#3745—22no—
32#3745—41no—
33C3×Dic12—21no—
34C3×D24—21no—
35C3×#204—41no—
36C32×C16D411yescharacteristic
37C32×C16C2311yescharacteristic
38#2263—91noSylow
39C3×#135—61no—
40#904—21no—
41C2×D24—62no—
42C2×D24—61no—
43C2×D24—61no—
44C3×Q32—31no—
45C3×SD32—61no—
46C3×D16—31no—
47C2×C3×C16—21no—
48C2×C3×C16C2×D311yescharacteristic
49C2×C3×C16C2×D311yescharacteristic
50Dic24C2×D311yescharacteristic, complemented
51#800—21no—
52D48—32no—
53D48—32no—
54D48—62no—
55D48—62no—
56D48—61no—
57D48—61no—
58D48C2×D311yescharacteristic, complemented
59C3×C32—32no—
60C3⋊C32C2×D312yescomplemented
61C22×C3⋊D3—81no—
62C2×C32×C4D811yescharacteristic
63C4⋊(C3⋊D3)—42no—
64C4⋊(C3⋊D3)—81no—
65C3×#67—81no—
66C3×D12—41no—
67C3×C4×D3—81no—
68C3×Dic6—41no—
69C32×C8D811yescharacteristic
70C32×C8C2×D411yescharacteristic
71#508—31no—
72C2×D16—91no—
73SD64—92no—
74D32—92no—
75M64—31no—
76C3×#41—121no—
77#235—41no—
78C2×D12—122no—
79C2×D12—121no—
80C2×D12—121no—
81C3×Q16—61no—
82C3×SD16—121no—
83C3×D8—61no—
84C2×C3×C8—21no—
85C2×C3×C8D1211yescharacteristic
86C2×C3×C8#6711yescharacteristic
87Dic12—21no—
88D24—21no—
89D24—64no—
90D24—62no—
91D24—62no—
92D24—122no—
93D24—121no—
94D24—121no—
95#204—41no—
96C3×C16—21no—
97C3×C16—21no—
98C3×C16D1211yescharacteristic
99C3×C16#6711yescharacteristic
100C3×C16C22×D311yescharacteristic
101C3×C16C22×D311yescharacteristic
102C22×C32D1611yescharacteristic
103C2×C3⋊D3—82no—
104C2×C3⋊D3—162no—
105C2×C3×D3—81no—
106C32×C4D1611yescharacteristic
107C32×C4C2×D811yescharacteristic
108C3×Dic3—81no—
109#135—61no—
110C2×D8—181no—
111Q32—31no—
112SD32—61no—
113D16—31no—
114D16—92no—
115D16—181no—
116C2×C16D3211yescharacteristic
117C32—32no—
118C22×D3—242no—
119C22×D3—241no—
120C22×D3—241no—
121C3×Q8—121no—
122C3×D4—121no—
123C3×D4—241no—
124C2×C3×C4—21no—
125C2×C3×C4—241no—
126C2×C3×C4D2411yescharacteristic
127C2×C3×C4#21311yescharacteristic
128#67—81no—
129D12—41no—
130D12—124no—
131D12—122no—
132D12—122no—
133D12—242no—
134D12—241no—
135D12—241no—
136C4×D3—81no—
137Dic6—41no—
138C3×C8—21no—
139C3×C8—21no—
140C3×C8D2411yescharacteristic
141C3×C8#21311yescharacteristic
142C3×C8C2×D1211yescharacteristic
143C3×C8C2×#6711yescharacteristic
144C2×C32—21no—
145C2×C32C2×D1611yescharacteristic
146C3⋊D3—162no—
147C3×D3—161no—
148#41—121no—
149C2×D4—361no—
150Q16—61no—
151SD16—121no—
152D8—61no—
153D8—182no—
154D8—361no—
155C2×C8#62611yescharacteristic
156C16#62611yescharacteristic
157C16C2×D3211yescharacteristic
158C22×C3—21no—
159C22×C3—241no—
160C22×C3D4811yescharacteristic
161C22×C3#82611yescharacteristic
162C2×D3—81no—
163C2×D3—244no—
164C2×D3—242no—
165C2×D3—242no—
166C2×D3—484no—
167C2×D3—482no—
168C2×D3—482no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—241no—
172C3×C4D4811yescharacteristic
173C3×C4#82611yescharacteristic
174C3×C4C2×D2411yescharacteristic
175C3×C4C2×#21311yescharacteristic
176Dic3—81no—
177C32#226311yescharacteristic, complemented, Sylow
178C23—721no—
179Q8—121no—
180D4—121no—
181D4—241no—
182D4—362no—
183D4—721no—
184C2×C4—241no—
185C2×C4#371411yescharacteristic
186C8#371411yescharacteristic
187C8C2×#62611yescharacteristic
188C2×C3—22no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—481no—
193C2×C3C2×D4811yescharacteristic
194C2×C3C2×#82611yescharacteristic
195D3—161no—
196D3—484no—
197D3—482no—
198D3—482no—
199C22—241no—
200C22—722no—
201C22—1442no—
202C22#6354611yescharacteristic
203C4—241no—
204C4#6354611yescharacteristic
205C4C2×#371411yescharacteristic
206C3—21no—
207C3#6937311yescharacteristic, complemented
208C3#7150911yescharacteristic, complemented
209C2—21no—
210C2—481no—
211C2—1442no—
212C2C2×#6354611yescharacteristic
subgroupG/H
centerC2C2×#63546
commutator, cosocleC32×C16C23
FrattiniC16C2×D32
FittingC2×C32×C16C22
socleC2×C32C2×D16
hypercenterC2×C16D32
hypocenterC32#2263
LCSG ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×#63626C2semidirect
2. C3×#4904C2semidirect
3. C3×#4499C2semidirect
4. #10589074C2semidirect
5. #10589071C2semidirect
13. C3×Dic24C22semidirect
15. C3×D48C22semidirect
16. C3×C3⋊C32C22semidirect
18. #4904D3semidirect
25. #4499D3semidirect
50. Dic24C2×D3semidirect
58. D48C2×D3semidirect
60. C3⋊C32C2×D3semidirect
177. C32#2263semidirect
207. C3#69373semidirect
208. C3#71509semidirect

Maximal subgroups

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

subgroupindex
C2×#636262
C3×#49042
C3×#44992
#105890742
#105890712
#715093
#693733