Finite Group Databasebeta

← #11800168

Subgroups — #11800168

Order 1152.

276 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 43 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#10590886C211yesmaximal, characteristic
2#10590874C211yesmaximal, characteristic, complemented
3#10590175C211yesmaximal, characteristic, complemented
4#10590061C214yesmaximal, complemented
5C2×C3×D24—21no—
6#63914—21no—
7#63872—21no—
8C2×#3713C2212yes—
9C2×#3708C2212yes—
10C8×C3⋊Dic3C2211yescharacteristic
11C3×#817—21no—
12#63576C2212yes—
13#5151—61no—
14#4858—61no—
15C2×C3×D12—22no—
16C2×#625—42no—
17C2×C32×C8D411yescharacteristic
18C4×C3⋊Dic3D411yescharacteristic
19C2×C3⋊(C3⋊C8)C2311yescharacteristic
20C3×C4⋊Dic3—22no—
21C3×D24—42no—
22Dic3⋊Dic3—42no—
23#3713—24no—
24#3708—22no—
25#2244—91nomaximal, Sylow
26C2×C3×D8—61no—
27#940—62no—
28C2×#213—62no—
29C2×D24—21no—
30#890—62no—
31C3×#106—61no—
32#817—21no—
33C8×Dic3—61no—
34C8×Dic3—61no—
35#807—62no—
36C22×C3×D3—42no—
37C2×C32×C4C2×D411yescharacteristic
38C2×C3⋊Dic3D812yes—
39C2×C3×Dic3—42no—
40C3×D12—42no—
41C3×D12—42no—
42#625—84no—
43C32×C8SD1612yes—
44C3⋊(C3⋊C8)#4112yes—
45#499—91no—
46#493—91no—
47#357—94no—
48#346—91no—
49C2×C3×D4—62no—
50C2×#67—124no—
51C2×D12—22no—
52C3×D8—122no—
53C2×C3×C8—21no—
54C2×C3×C8—21no—
55C3×C4⋊C4—62no—
56#213—124no—
57C4⋊Dic3—22no—
58C4⋊Dic3—122no—
59Dic3⋊C4—122no—
60C4×Dic3—61no—
61C4×Dic3—61no—
62C2×C3⋊C8—61no—
63C2×C3⋊C8—61no—
64D24—42no—
65C22×C32C2×D811yescharacteristic
66C2×C3×D3—82no—
67C2×C3×D3—84no—
68C32×C4#12411yescharacteristic
69C32×C4C2×SD1611yescharacteristic
70C3⋊Dic3—22no—
71C3×Dic3—82no—
72C2×D8—61no—
73C2×D8—92no—
74#127—181no—
75#125—181no—
76C2×C16—92no—
77#107—92no—
78#106—61no—
79C4×C8—91no—
80C23×C3—122no—
81C22×D3—42no—
82C3×D4—122no—
83C3×D4—122no—
84C2×C3×C4—21no—
85C2×C3×C4—21no—
86C2×C3×C4—122no—
87#67—248no—
88C2×Dic3—42no—
89C2×Dic3—62no—
90C2×Dic3—62no—
91D12—42no—
92D12—42no—
93C3×C8—22no—
94C3×C8—22no—
95C3⋊C8—62no—
96C3⋊C8—62no—
97C2×C32#48611yescharacteristic
98C2×C32#50912yes—
99C3×D3—162no—
100C2×D4—62no—
101C2×D4—362no—
102D8—122no—
103D8—184no—
104C2×C8—91no—
105C2×C8GO+(4,𝔽2)11yescharacteristic
106C4⋊C4—62no—
107C4⋊C4—362no—
108C42—91no—
109C16—182no—
110C22×C3—21no—
111C22×C3—21no—
112C22×C3—244no—
113C22×C3—242no—
114C2×D3—82no—
115C2×D3—84no—
116C3×C4—21no—
117C3×C4—21no—
118C3×C4—21no—
119C3×C4—21no—
120C3×C4—242no—
121Dic3—64no—
122Dic3—82no—
123Dic3—122no—
124C32#224411yescharacteristic, complemented, Sylow
125C23—122no—
126D4—122no—
127D4—122no—
128D4—724no—
129C2×C4—92no—
130C2×C4—122no—
131C2×C4C2×GO+(4,𝔽2)11yescharacteristic
132C8—92no—
133C8#377512yes—
134C2×C3—21no—
135C2×C3—21no—
136C2×C3—22no—
137C2×C3—22no—
138C2×C3—482no—
139D3—162no—
140C22—242no—
141C22—244no—
142C22#6422511yescharacteristic
143C4—182no—
144C4—242no—
145C4#6422111yescharacteristic
146C4C2×#377511yescharacteristic
147C3—21no—
148C3—21no—
149C2—482no—
150C2#1059327712yes—
151C2#1059336611yescharacteristic
subgroupG/H
centerC22#64225
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C2×D8
prime radical#10590886C2
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2244
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10590874C2semidirect
3. #10590175C2semidirect
4. #10590061C2semidirect
124. C32#2244semidirect

Maximal subgroups

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

subgroupindex
#105908862
#105908742
#105901752
#105900612
#22449