Finite Group Databasebeta

← #11781980

Subgroups — #11781980

Order 1152.

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

normal subgroups only

This group has 260 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#10593756C211yesmaximal, characteristic
2#10593388C211yesmaximal, characteristic
3#10590566C212yesmaximal
4#10590041C211yesmaximal, characteristic
5#10590038C212yesmaximal
6#64096C2211yescharacteristic
7#63873C2212yes—
8C2×#3719—22no—
9#63777—21no—
10C4⋊#622—21no—
11C4⋊#622C2211yescharacteristic
12C4×#622C2211yescharacteristic
13#63743—21no—
14#63743—21no—
15C3×#810—22no—
16#63572C2212yes—
17#4795—62no—
18C2×#634D411yescharacteristic
19C2×C3×Dic6—22no—
20C2×#622—21no—
21C2×#622D411yescharacteristic
22C2×#622D411yescharacteristic
23C32×C4⋊C4D411yescharacteristic
24#3750—21no—
25C4×C3⋊Dic3—21no—
26C4×C3⋊Dic3C2311yescharacteristic
27C2×C3×C3⋊C8—22no—
28#3724—22no—
29#3724—22no—
30#3719—44no—
31#1694—91nomaximal, Sylow
32#944—62no—
33C2×#216—62no—
34C2×Dic12—62no—
35#887—62no—
36C3×#103—62no—
37Dic3⋊C8—62no—
38#810—22no—
39C2×C32×C4—21no—
40C2×C32×C4C2×D411yescharacteristic
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3C2×D411yescharacteristic
43C2×C3⋊Dic3#4111yescharacteristic
44#634—22no—
45C2×C3×Dic3—42no—
46C3×Dic6—42no—
47C3×Dic6—42no—
48#622—21no—
49#622—41no—
50#622Q1612yescomplemented
51C3×C3⋊C8—42no—
52#500—91no—
53#462—92no—
54#446—91no—
55#334—91no—
56#332—92no—
57C2×C3×Q8—62no—
58C2×Dic6—22no—
59C2×Dic6—62no—
60C2×C3×C8—62no—
61C3×C4⋊C4—22no—
62#216—124no—
63Dic3⋊C4—122no—
64Dic3⋊C4—122no—
65Dic3⋊C4—122no—
66C4×Dic3—62no—
67C4×Dic3—122no—
68C2×C3⋊C8—22no—
69Dic12—124no—
70C22×C32#12111yescharacteristic
71C32×C4—41no—
72C32×C4AGL(1,ℤ/8)12yes—
73C3⋊Dic3—21no—
74C3⋊Dic3—41no—
75C3⋊Dic3C2×Q1611yescharacteristic
76C3⋊Dic3#13711yescharacteristic
77C3×Dic3—82no—
78C2×Q16—182no—
79C4⋊Q8—92no—
80C4×Q8—91no—
81#107—181no—
82#107—181no—
83C4⋊C8—92no—
84C4⋊C8—91no—
85C4⋊C8—181no—
86#103—62no—
87#97—181no—
88C4×C8—91no—
89C3×Q8—122no—
90C3×Q8—122no—
91C2×C3×C4—22no—
92C2×C3×C4—42no—
93C2×C3×C4—122no—
94C2×Dic3—42no—
95C2×Dic3—62no—
96C2×Dic3—62no—
97C2×Dic3—122no—
98Dic6—42no—
99Dic6—42no—
100Dic6—64no—
101Dic6—122no—
102C3×C8—122no—
103C3⋊C8—42no—
104C2×C32#46211yescharacteristic
105C2×C32#46911yescharacteristic
106C2×C32#47311yescharacteristic
107C2×Q8—62no—
108C2×Q8—91no—
109Q16—364no—
110C2×C8—62no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8—181no—
114C4⋊C4—181no—
115C4⋊C4—182no—
116C4⋊C4—182no—
117C4⋊C4GO+(4,𝔽2)11yescharacteristic
118C42—91no—
119C42—181no—
120C22×C3—22no—
121C3×C4—22no—
122C3×C4—22no—
123C3×C4—82no—
124C3×C4—242no—
125Dic3—62no—
126Dic3—62no—
127Dic3—82no—
128Dic3—122no—
129Dic3—124no—
130C32#169411yescharacteristic, complemented, Sylow
131Q8—122no—
132Q8—122no—
133Q8—182no—
134C2×C4—21no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—122no—
138C2×C4—181no—
139C2×C4C2×GO+(4,𝔽2)11yescharacteristic
140C8—92no—
141C8—122no—
142C8—181no—
143C8—361no—
144C2×C3—22no—
145C2×C3—22no—
146C2×C3—22no—
147C22#6424211yescharacteristic
148C4—41no—
149C4—91no—
150C4—91no—
151C4—181no—
152C4—242no—
153C4—361no—
154C4#6422412yes—
155C3—22no—
156C2#1059342911yescharacteristic
157C2#1059346811yescharacteristic
158C2#1059347711yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socle, prime radicalC22×C32#121
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1694
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
50. #622Q16semidirect
130. C32#1694semidirect

Maximal subgroups

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

subgroupindex
#105937562
#105933882
#105905662
#105900412
#105900382
#16949