Finite Group Databasebeta

← #37570666

Subgroups — #37570666

Order 24448.

122 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 23 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#27132830C211yesmaximal, characteristic
2#27132456C211yesmaximal, characteristic, complemented
3#331×C191C211yesmaximal, characteristic, complemented
4#20259367C411yescharacteristic, complemented
5#20259348—21no—
6#20259250—21no—
7#20259239C411yescharacteristic, complemented
8#20259237—21no—
9#127×C191C2211yescharacteristic
10C4⋊C8×C191—21no—
11#15690287—21no—
12#15690286—41no—
13C2×C22⋊D191—41no—
14D4×D191—41no—
15#15690275—41no—
16#15690272—41no—
17#15690271—21no—
18C22⋊Dic191—41no—
19C2×D4×C191—41no—
20C2×D4×C191C2×C411yescharacteristic
21C2×D4×C191D411yescharacteristic
22C2×C8×C191—41no—
23C42×C191D411yescharacteristic
24C22×D191—41no—
25Dic382—21no—
26D764—21no—
27C22⋊D191—42no—
28C22⋊D191—41no—
29C2×Dic191—41no—
30C2×Dic191—81no—
31C4×D191—41no—
32C191⋊C8—41no—
33C23×C191—21no—
34C23×C191—21no—
35D4×C191—41no—
36D4×C191—41no—
37D4×C191—81no—
38D4×C191—81no—
39C2×C4×C191—21no—
40C2×C4×C191C22⋊C411yescharacteristic
41C8×C191—81no—
42C22×C191—41no—
43C22×C191—41no—
44C22×C191—81no—
45C22×C191—81no—
46C22×C191#9911yescharacteristic
47C2×D191—41no—
48C2×D191—161no—
49C4×C191—21no—
50C4×C191—21no—
51C4×C191—21no—
52Dic191—41no—
53Dic191—161no—
54C2×C191—21no—
55C2×C191—81no—
56C2×C191—81no—
57C2×C191AΣL(1,𝔽16)11yescharacteristic
58D191—81no—
59C191#140211yescharacteristic, complemented, Sylow
60#1402—1911nomaximal, Sylow
61#453—1911no—
62#353—1911no—
63#331D19111yescharacteristic, complemented
64H(5,𝔽2)—1911no—
65AGL(1,ℤ/8)—3821no—
66#127C2×D19111yescharacteristic
67C4⋊C8—21no—
68#104—3821no—
69#100—1911no—
70#99—3821no—
71#41—3821no—
72#41—7641no—
73C2×D4—41no—
74C2×D4—7641no—
75C2×D4—7641no—
76C2×D4C4×D19111yescharacteristic
77C2×D4D76411yescharacteristic
78SD16—7641no—
79D8—7641no—
80M16—3821no—
81C2×C8—41no—
82C22⋊C4—7641no—
83C42C22⋊D19111yescharacteristic
84C23—21no—
85C23—21no—
86C23—7641no—
87Q8—3821no—
88D4—41no—
89D4—41no—
90D4—81no—
91D4—81no—
92D4—3821no—
93D4—7642no—
94D4—7641no—
95C2×C4—21no—
96C2×C4—15281no—
97C2×C4—7641no—
98C2×C4—7641no—
99C2×C4(C2×D191)⋊C411yescharacteristic
100C8—81no—
101C8—7641no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—81no—
106C22—30561no—
107C22—7641no—
108C22#2025923611yescharacteristic
109C4—21no—
110C4—21no—
111C4—21no—
112C4—30561no—
113C4—7641no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—15281no—
118C2#2713245111yescharacteristic
subgroupG/H
centerC2#27132451
commutatorC2×D4×C191C2×C4
Frattini#127C2×D191
Fitting#331×C191C2
socleC2×C191AΣL(1,𝔽16)
prime radical#27132830C2
cosocle#127×C191C22
hypercenter#331D191
hypocenterC191#1402
LCSG ▷ C2×D4×C191 ▷ C2×C4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #27132456C2semidirect
3. #331×C191C2semidirect
4. #20259367C4semidirect
7. #20259239C4semidirect
59. C191#1402semidirect
63. #331D191semidirect

Maximal subgroups

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

subgroupindex
#271328302
#271324562
#331×C1912
#1402191