Finite Group Databasebeta

← #11781162

Subgroups — #11781162

Order 1152.

264 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593750C211yesmaximal, characteristic
2#10593388C211yesmaximal, characteristic
3#10590566C212yesmaximal
4#10590042C211yesmaximal, characteristic
5#10590038C212yesmaximal
6#64096C2211yescharacteristic
7#63873C2212yes—
8C2×#3719—22no—
9#63779—21no—
10C4⋊#622C2211yescharacteristic
11C4×#622—21no—
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#1674—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—21no—
45#634D812yes—
46C2×C3×Dic3—42no—
47C3×Dic6—42no—
48C3×Dic6—42no—
49#622—21no—
50#622—41no—
51#622Q1612yescomplemented
52C3×C3⋊C8—42no—
53#500—91no—
54#462—92no—
55C8×Q8—91no—
56#335—91no—
57#332—92no—
58C2×C3×Q8—62no—
59C2×Dic6—22no—
60C2×Dic6—62no—
61C2×C3×C8—62no—
62C3×C4⋊C4—22no—
63#216—124no—
64Dic3⋊C4—122no—
65Dic3⋊C4—122no—
66Dic3⋊C4—122no—
67C4×Dic3—62no—
68C4×Dic3—122no—
69C2×C3⋊C8—22no—
70Dic12—124no—
71C22×C32#12111yescharacteristic
72C32×C4—41no—
73C32×C4C2×D811yescharacteristic
74C32×C4#13511yescharacteristic
75C3⋊Dic3—22no—
76C3⋊Dic3—21no—
77C3⋊Dic3C2×Q1611yescharacteristic
78C3⋊Dic3#13711yescharacteristic
79C3×Dic3—82no—
80C2×Q16—182no—
81C4⋊Q8—92no—
82C4×Q8—91no—
83#107—181no—
84#107—181no—
85C4⋊C8—92no—
86C4⋊C8—91no—
87C4⋊C8—181no—
88#103—62no—
89C4×C8—91no—
90C4×C8—181no—
91C3×Q8—122no—
92C3×Q8—122no—
93C2×C3×C4—22no—
94C2×C3×C4—42no—
95C2×C3×C4—122no—
96C2×Dic3—42no—
97C2×Dic3—62no—
98C2×Dic3—62no—
99C2×Dic3—122no—
100Dic6—42no—
101Dic6—42no—
102Dic6—64no—
103Dic6—122no—
104C3×C8—122no—
105C3⋊C8—42no—
106C2×C32#46211yescharacteristic
107C2×C32#46611yescharacteristic
108C2×C32#47311yescharacteristic
109C2×Q8—62no—
110C2×Q8—91no—
111Q16—364no—
112C2×C8—62no—
113C2×C8—91no—
114C2×C8—91no—
115C2×C8—181no—
116C4⋊C4—181no—
117C4⋊C4—182no—
118C4⋊C4—182no—
119C4⋊C4GO+(4,𝔽2)11yescharacteristic
120C42—91no—
121C42—181no—
122C22×C3—22no—
123C3×C4—22no—
124C3×C4—22no—
125C3×C4—82no—
126C3×C4—242no—
127Dic3—62no—
128Dic3—62no—
129Dic3—82no—
130Dic3—124no—
131Dic3—122no—
132C32#167411yescharacteristic, complemented, Sylow
133Q8—92no—
134Q8—122no—
135Q8—122no—
136Q8—181no—
137C2×C4—21no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—122no—
141C2×C4—181no—
142C2×C4C2×GO+(4,𝔽2)11yescharacteristic
143C8—92no—
144C8—122no—
145C8—181no—
146C8—361no—
147C2×C3—22no—
148C2×C3—22no—
149C2×C3—22no—
150C22#6424211yescharacteristic
151C4—41no—
152C4—91no—
153C4—91no—
154C4—182no—
155C4—181no—
156C4—242no—
157C4#6422311yescharacteristic
158C4#6422511yescharacteristic
159C3—22no—
160C2#1059342311yescharacteristic
161C2#1059346811yescharacteristic
162C2#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#1674
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
51. #622Q16semidirect
132. C32#1674semidirect

Maximal subgroups

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

subgroupindex
#105937502
#105933882
#105905662
#105900422
#105900382
#16749