Finite Group Databasebeta

← #11800077

Subgroups — #11800077

Order 1152.

329 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 329 conjugacy classes of subgroups — too many to draw. Only its 78 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#10592573C211yesmaximal, characteristic
2#10590905C211yesmaximal, characteristic
3C3×#4492C212yesmaximal
4#10589118C212yesmaximal
5#10589102C211yesmaximal, characteristic
6#69215—32nomaximal
7#64097—21no—
8C2×C3×Dic12C2212yes—
9#63873—21no—
10C2×#3718—21no—
11C32×#107C2211yescharacteristic
12#63645C2211yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14#63634—21no—
15C2×C3×C3⋊C16C2212yes—
16#5183—32no—
17#4874—32no—
18#4874—61no—
19C3×#358—32no—
20#4564—32no—
21#4503—32no—
22Dic3×C16—32no—
23#4492D312yes—
24C2×#634—41no—
25C2×C3×Dic6—22no—
26C2×C32×C8C2311yescharacteristic
27C32×C4⋊C4—21no—
28C4⋊(C3⋊Dic3)—21no—
29#3750—41no—
30C4×C3⋊Dic3D411yescharacteristic
31C2×C3⋊(C3⋊C8)D411yescharacteristic
32C3×Dic12—22no—
33C3×Dic12—22no—
34#3724—41no—
35#3724—41no—
36#3718—42no—
37C3×C3⋊C16—22no—
38#2241—91noSylow
39C2×C3×Q16—32no—
40#944—62no—
41C2×#216—62no—
42C2×Dic12C2×D312yes—
43#888—62no—
44#888—62no—
45C2×C3×C16—32no—
46C3×#107—21no—
47C3×#107C2×D312yes—
48#818—32no—
49#818—61no—
50C8×Dic3—32no—
51C8×Dic3—61no—
52C2×C3⋊C16C2×D312yes—
53#807—62no—
54#807—62no—
55C2×C32×C4—41no—
56C2×C32×C4C2×D411yescharacteristic
57C2×C3⋊Dic3—41no—
58C2×C3⋊Dic3D811yescharacteristic
59C2×C3⋊Dic3D811yescharacteristic
60#634—82no—
61C2×C3×Dic3—42no—
62C3×Dic6—42no—
63C3×Dic6—42no—
64C32×C8#4112yes—
65C3⋊(C3⋊C8)SD1612yes—
66#500—91no—
67#494—91no—
68#358—32no—
69#358—92no—
70C4×C16—91no—
71C2×C3×Q8—62no—
72C2×Dic6—22no—
73C2×Dic6—122no—
74C2×Dic6—122no—
75C3×Q16—62no—
76C3×Q16—62no—
77C2×C3×C8—21no—
78C2×C3×C8C22×D312yes—
79C3×C4⋊C4—22no—
80C3×C4⋊C4—22no—
81#216—124no—
82C4⋊Dic3—62no—
83C4⋊Dic3—62no—
84Dic3⋊C4—122no—
85Dic3⋊C4—122no—
86Dic3⋊C4—122no—
87Dic3⋊C4—122no—
88C4×Dic3—32no—
89C4×Dic3—61no—
90C2×C3⋊C8—32no—
91C2×C3⋊C8—61no—
92Dic12—22no—
93Dic12—22no—
94C3×C16—62no—
95C3⋊C16—22no—
96C22×C32C2×D811yescharacteristic
97C32×C4—81no—
98C32×C4#12411yescharacteristic
99C32×C4C2×SD1611yescharacteristic
100C3⋊Dic3—81no—
101C3⋊Dic3SD3212yes—
102C3⋊Dic3Q3212yes—
103C3×Dic3—82no—
104C2×Q16—32no—
105C2×Q16—181no—
106C4⋊Q8—181no—
107C4⋊Q8—181no—
108C2×C16—32no—
109#107—91no—
110#107—181no—
111#107D3211yescharacteristic
112C4×C8—91no—
113C3×Q8—122no—
114C3×Q8—122no—
115C2×C3×C4—21no—
116C2×C3×C4—42no—
117C2×C3×C4—42no—
118C2×C3×C4—122no—
119C2×C3×C4D3×D412yes—
120C2×Dic3—32no—
121C2×Dic3—32no—
122C2×Dic3—42no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—122no—
126C2×Dic3—122no—
127Dic6—42no—
128Dic6—42no—
129Dic6—244no—
130Dic6—244no—
131C3×C8—22no—
132C3×C8#23512yes—
133C3×C8#23712yes—
134C3⋊C8—34no—
135C3⋊C8—62no—
136C2×C32#48611yescharacteristic
137C2×C32C2×SD3211yescharacteristic
138C2×C32C2×Q3211yescharacteristic
139C2×Q8—62no—
140C2×Q8—361no—
141Q16—62no—
142Q16—62no—
143Q16—362no—
144C2×C8—91no—
145C2×C8C2×D3211yescharacteristic
146C4⋊C4—21no—
147C4⋊C4—181no—
148C4⋊C4—361no—
149C4⋊C4—361no—
150C4⋊C4—361no—
151C42—91no—
152C16—62no—
153C22×C3—21no—
154C22×C3D3×D812yes—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—82no—
158C3×C4—82no—
159C3×C4—242no—
160C3×C4#88512yes—
161C3×C4D3×SD1612yes—
162Dic3—34no—
163Dic3—34no—
164Dic3—62no—
165Dic3—62no—
166Dic3—82no—
167Dic3—242no—
168Dic3—242no—
169C32#224111yescharacteristic, complemented, Sylow
170Q8—122no—
171Q8—122no—
172Q8—722no—
173C2×C4—41no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—122no—
177C2×C4—361no—
178C2×C4#381111yescharacteristic
179C8—92no—
180C8#379512yes—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3#476012yes—
185C2×C3D3×SD3212yes—
186C2×C3D3×Q3212yes—
187C22#6392611yescharacteristic
188C4—81no—
189C4—92no—
190C4—92no—
191C4—242no—
192C4—721no—
193C4#6391311yescharacteristic
194C4#6394011yescharacteristic
195C3—21no—
196C3#6921512yescomplemented
197C2#1059055211yescharacteristic
198C2#1059102911yescharacteristic
199C2#1059104311yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socle, prime radicalC22×C32C2×D8
hypercenter#107D32
hypocenterC32#2241
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
169. C32#2241semidirect
196. C3#69215semidirect

Maximal subgroups

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

subgroupindex
#105925732
#105909052
C3×#44922
#105891182
#105891022
#692153