Finite Group Databasebeta

← #11800608

Subgroups — #11800608

Order 1152.

203 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 203 conjugacy classes of subgroups — too many to draw. Only its 35 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
1#10590629C211yesmaximal, characteristic, complemented
2C2×#63545C211yesmaximal, characteristic, complemented
3#10590166C211yesmaximal, characteristic, complemented
4#10590025C212yesmaximal, complemented
5#10590024C212yesmaximal, complemented
6C3×#904—21no—
7C2×C3×D24—21no—
8C2×C3⋊(C3⋊C16)C2211yescharacteristic
9#63550C2211yescharacteristic, complemented
10#63547—21no—
11#63545—21no—
12#63545C2212yes—
13#63545C2211yescharacteristic, complemented
14#63540C2212yescomplemented
15#5194—61no—
16C2×#826—61no—
17C3×#235—41no—
18C2×C3×D12—41no—
19C2×C32×C8D411yescharacteristic
20C3×Dic12—21no—
21C3×D24—22no—
22C3×D24—21no—
23C3×D24—41no—
24C3×#204—41no—
25C3⋊(C3⋊C16)D411yescharacteristic
26C3⋊(C3⋊C16)C2311yescharacteristic
27#2263—91nomaximal, Sylow
28C3×#135—61no—
29C2×C3×D8—61no—
30#904—21no—
31C2×D24—21no—
32#829—61no—
33#828—61no—
34#827—61no—
35#826—62no—
36#826—61no—
37#826—62no—
38C2×C3⋊C16—61no—
39C2×C3⋊C16—61no—
40C22×C3×D3—81no—
41C2×C32×C4D811yescharacteristic
42C3×#67—81no—
43C3×D12—41no—
44C3×D12—42no—
45C3×D12—81no—
46C3×C4×D3—81no—
47C3×Dic6—41no—
48C32×C8D811yescharacteristic
49C32×C8C2×D411yescharacteristic
50#508—91no—
51C2×D16—91no—
52SD64—92no—
53D32—92no—
54M64—91no—
55C3×#41—121no—
56C2×C3×D4—121no—
57#235—41no—
58C2×D12—41no—
59C3×Q16—61no—
60C3×SD16—121no—
61C3×D8—62no—
62C3×D8—61no—
63C3×D8—121no—
64C2×C3×C8—21no—
65C2×C3×C8—21no—
66Dic12—21no—
67D24—22no—
68D24—21no—
69D24—41no—
70#204—41no—
71C3⋊C16—61no—
72C3⋊C16—61no—
73C3⋊C16—61no—
74C3⋊C16—61no—
75C22×C32D1611yescharacteristic
76C2×C3×D3—81no—
77C2×C3×D3—82no—
78C2×C3×D3—162no—
79C32×C4D1611yescharacteristic
80C32×C4C2×D811yescharacteristic
81C3×Dic3—81no—
82#135—61no—
83C2×D8—61no—
84Q32—91no—
85SD32—181no—
86D16—91no—
87D16—92no—
88D16—181no—
89C2×C16—91no—
90C32—92no—
91C23×C3—241no—
92C22×D3—81no—
93C3×Q8—121no—
94C3×D4—122no—
95C3×D4—121no—
96C3×D4—241no—
97C3×D4—241no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—241no—
101#67—81no—
102D12—41no—
103D12—42no—
104D12—81no—
105C4×D3—81no—
106Dic6—41no—
107C3×C8—21no—
108C3×C8—21no—
109C3×C8—21no—
110C3×C8—21no—
111C2×C32—21no—
112C2×C32C2×D1611yescharacteristic
113C3×D3—161no—
114C3×D3—162no—
115#41—121no—
116C2×D4—121no—
117Q16—61no—
118SD16—121no—
119D8—62no—
120D8—61no—
121D8—121no—
122C2×C8GO+(4,𝔽2)11yescharacteristic
123C16—91no—
124C16—91no—
125C22×C3—21no—
126C22×C3—21no—
127C22×C3—241no—
128C22×C3—242no—
129C22×C3—482no—
130C2×D3—81no—
131C2×D3—82no—
132C2×D3—162no—
133C3×C4—21no—
134C3×C4—21no—
135C3×C4—21no—
136C3×C4—21no—
137C3×C4—241no—
138Dic3—81no—
139C32#226311yescharacteristic, complemented, Sylow
140C23—241no—
141Q8—121no—
142D4—122no—
143D4—121no—
144D4—241no—
145D4—241no—
146C2×C4—241no—
147C2×C4#377411yescharacteristic
148C8#377411yescharacteristic
149C8C2×GO+(4,𝔽2)11yescharacteristic
150C2×C3—22no—
151C2×C3—21no—
152C2×C3—21no—
153C2×C3—41no—
154C2×C3—482no—
155C2×C3—481no—
156D3—162no—
157D3—161no—
158C22—241no—
159C22—242no—
160C22—482no—
161C22#6373411yescharacteristic
162C4—241no—
163C4#6373411yescharacteristic
164C4C2×#377411yescharacteristic
165C3—21no—
166C3—21no—
167C2—21no—
168C2—482no—
169C2—481no—
170C2C2×#6373411yescharacteristic
subgroupG/H
centerC2C2×#63734
commutator, cosocleC3⋊(C3⋊C16)C23
FrattiniC8C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×D16
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2263
LCSG ▷ C3⋊(C3⋊C16) ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #10590629C2semidirect
2. C2×#63545C2semidirect
3. #10590166C2semidirect
4. #10590025C2semidirect
5. #10590024C2semidirect
9. #63550C22semidirect
13. #63545C22semidirect
14. #63540C22semidirect
139. C32#2263semidirect

Maximal subgroups

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

subgroupindex
#105906292
C2×#635452
#105901662
#105900252
#105900242
#22639