Finite Group Databasebeta

← #11772986

Subgroups — #11772986

Order 1152.

147 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 147 conjugacy classes of subgroups — too many to draw. Only its 27 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×#63545C211yesmaximal, characteristic
2#10590166C211yesmaximal, characteristic, complemented
3#10589144C211yesmaximal, characteristic, complemented
4C2×C3×D24—21no—
5C2×C3⋊(C3⋊C16)C2211yescharacteristic
6C3×#819—21no—
7#63545—21no—
8#63545C412yes—
9#63540—21no—
10C2×#826—61no—
11#4493—61no—
12C2×C3×D12—41no—
13C2×C32×C8D411yescharacteristic
14C3×#208—41no—
15C3×D24—22no—
16C3×D24—41no—
17C3⋊(C3⋊C16)C2×C411yescharacteristic
18C3⋊(C3⋊C16)D411yescharacteristic
19#1419—91nomaximal, Sylow
20C2×C3×D8—61no—
21C2×D24—21no—
22C3×#108—61no—
23#826—62no—
24#826—62no—
25#819—21no—
26C2×C3⋊C16—61no—
27C2×C3⋊C16—61no—
28C22×C3×D3—81no—
29C2×C32×C4D811yescharacteristic
30C3×D12—42no—
31C3×D12—81no—
32C32×C8C22⋊C411yescharacteristic
33C32×C8SD1611yescharacteristic
34C3×C3⋊C8—81no—
35C2×D16—91no—
36M64—91no—
37#368—91no—
38C2×C3×D4—121no—
39C2×D12—41no—
40C3×D8—62no—
41C3×D8—121no—
42C3×M16—121no—
43C2×C3×C8—21no—
44C2×C3×C8—21no—
45#208—41no—
46D24—22no—
47D24—41no—
48C3⋊C16—61no—
49C3⋊C16—61no—
50C3⋊C16—61no—
51C3⋊C16—61no—
52C22×C32SD3211yescharacteristic
53C2×C3×D3—82no—
54C2×C3×D3—162no—
55C32×C4#10211yescharacteristic
56C32×C4D1611yescharacteristic
57C2×D8—61no—
58D16—92no—
59D16—181no—
60C2×C16—91no—
61#108—61no—
62C32—181no—
63C23×C3—241no—
64C22×D3—81no—
65C3×D4—122no—
66C3×D4—241no—
67C2×C3×C4—21no—
68C2×C3×C4—21no—
69D12—42no—
70D12—81no—
71C3×C8—21no—
72C3×C8—21no—
73C3×C8—21no—
74C3×C8—21no—
75C3×C8—241no—
76C3⋊C8—81no—
77C2×C32—21no—
78C2×C32#35711yescharacteristic
79C3×D3—162no—
80C2×D4—121no—
81D8—62no—
82D8—121no—
83M16—121no—
84C2×C8GO+(4,𝔽2)11yescharacteristic
85C16—91no—
86C16—91no—
87C22×C3—21no—
88C22×C3—21no—
89C22×C3—242no—
90C22×C3—482no—
91C2×D3—82no—
92C2×D3—162no—
93C3×C4—21no—
94C3×C4—21no—
95C3×C4—21no—
96C3×C4—21no—
97C32#141911yescharacteristic, complemented, Sylow
98C23—241no—
99D4—122no—
100D4—241no—
101C2×C4#377411yescharacteristic
102C8—241no—
103C8D32⋊C411yescharacteristic
104C8#377511yescharacteristic
105C2×C3—22no—
106C2×C3—21no—
107C2×C3—21no—
108C2×C3—41no—
109C2×C3—482no—
110D3—162no—
111C22—242no—
112C22—482no—
113C22#6373511yescharacteristic
114C4#6373411yescharacteristic
115C4#6373911yescharacteristic
116C3—21no—
117C3—21no—
118C2—21no—
119C2—482no—
120C2#1059006111yescharacteristic
subgroupG/H
centerC2#10590061
commutatorC3⋊(C3⋊C16)C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#357
prime radicalC2×#63545C2
cosocleC2×C3⋊(C3⋊C16)C22
hypocenterC32#1419
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
2. #10590166C2semidirect
3. #10589144C2semidirect
97. C32#1419semidirect

Maximal subgroups

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

subgroupindex
C2×#635452
#105901662
#105891442
#14199