Finite Group Databasebeta

← #11781223

Subgroups — #11781223

Order 1152.

339 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 339 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592529C211yesmaximal, characteristic
2#10590312C211yesmaximal, characteristic
3#10590284C212yesmaximal
4C3×#4481C212yesmaximal
5#10589100C211yesmaximal, characteristic
6#68509—32nomaximal
7C4×#634C2211yescharacteristic
8C3×#869C2212yes—
9C32×C4⋊C8C2211yescharacteristic
10#63641—21no—
11C8×C3⋊Dic3—21no—
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×C4⋊(C3⋊C8)C2212yes—
14#63576—21no—
15#63576—21no—
16#63575—22no—
17#63567—22no—
18#5091—32no—
19#5078—32no—
20#4850—32no—
21#4830—32no—
22#4830—61no—
23C3×#333—32no—
24#4481D312yes—
25#4479—32no—
26C2×#634D411yescharacteristic
27C2×C3×Dic6—22no—
28C2×C32×C8—21no—
29C32×C42C2311yescharacteristic
30C4⋊(C3⋊Dic3)D411yescharacteristic
31#3750—21no—
32C4×C3⋊Dic3—21no—
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C3×C4⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C2×C3×C3⋊C8—22no—
38#1676—91noSylow
39C3×C4⋊Q8—32no—
40#869C2×D312yes—
41C4×Dic6—32no—
42C4×Dic6—61no—
43C3×C4⋊C8—21no—
44C3×C4⋊C8—32no—
45C3×C4⋊C8C2×D312yes—
46#818—62no—
47#816—62no—
48Dic3⋊C8—62no—
49Dic3⋊C8—62no—
50C8×Dic3—62no—
51C8×Dic3—62no—
52#810—62no—
53#807—62no—
54#807—62no—
55#807—62no—
56C4⋊(C3⋊C8)C2×D312yes—
57C4×C3⋊C8—32no—
58C4×C3⋊C8—61no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C32×C4C2×D411yescharacteristic
61C2×C32×C4#4111yescharacteristic
62C2×C3⋊Dic3—21no—
63C2×C3⋊Dic3—21no—
64#634—21no—
65#634Q1612yes—
66C2×C3×Dic3—42no—
67C3×Dic6—82no—
68C32×C8—41no—
69C3⋊(C3⋊C8)—21no—
70C3⋊(C3⋊C8)Q1612yes—
71C3×C3⋊C8—42no—
72#500—91no—
73#477—92no—
74C8×Q8—91no—
75#335—91no—
76#333—32no—
77C2×C3×Q8—62no—
78C2×Dic6—22no—
79C2×Dic6—32no—
80C2×Dic6—61no—
81C2×C3×C8—22no—
82C2×C3×C8—22no—
83C2×C3×C8—62no—
84C3×C4⋊C4—62no—
85C3×C4⋊C4—62no—
86C3×C42—21no—
87C3×C42C22×D312yes—
88C4⋊Dic3—22no—
89C4⋊Dic3—22no—
90C4⋊Dic3—32no—
91C4⋊Dic3—61no—
92Dic3⋊C4—62no—
93Dic3⋊C4—62no—
94C4×Dic3—62no—
95C4×Dic3—62no—
96C2×C3⋊C8—22no—
97C2×C3⋊C8—32no—
98C2×C3⋊C8—32no—
99C2×C3⋊C8—61no—
100C2×C3⋊C8—61no—
101C22×C32#12111yescharacteristic
102C32×C4—21no—
103C32×C4C2×Q1611yescharacteristic
104C32×C4C2×Q1611yescharacteristic
105C32×C4#13511yescharacteristic
106C32×C4#13711yescharacteristic
107C3⋊Dic3—22no—
108C3⋊Dic3—41no—
109C3×Dic3—82no—
110C4⋊Q8—32no—
111C4×Q8—91no—
112#107—181no—
113#107—181no—
114#107—182no—
115C4⋊C8—32no—
116C4⋊C8—181no—
117C4⋊C8D3211yescharacteristic
118#103—182no—
119C4×C8—91no—
120C4×C8—181no—
121C3×Q8—242no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—122no—
126C2×C3×C4#23512yes—
127C2×C3×C4D3×D412yes—
128C2×C3×C4D3×D412yes—
129C2×Dic3—42no—
130C2×Dic3—62no—
131C2×Dic3—62no—
132C2×Dic3—62no—
133C2×Dic3—62no—
134Dic6—34no—
135Dic6—62no—
136Dic6—62no—
137Dic6—62no—
138Dic6—82no—
139C3×C8—42no—
140C3×C8—42no—
141C3×C8—122no—
142C3⋊C8—34no—
143C3⋊C8—42no—
144C3⋊C8—62no—
145C3⋊C8—62no—
146C3⋊C8—121no—
147C2×C32#46211yescharacteristic
148C2×C32#46711yescharacteristic
149C2×C32#47211yescharacteristic
150C2×Q8—62no—
151C2×Q8—91no—
152C2×C8—21no—
153C2×C8—62no—
154C2×C8—91no—
155C2×C8—91no—
156C4⋊C4—62no—
157C4⋊C4—62no—
158C4⋊C4—91no—
159C4⋊C4—181no—
160C42—181no—
161C42C2×D3211yescharacteristic
162C22×C3—21no—
163C22×C3#88412yes—
164C3×C4—22no—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—41no—
170C3×C4—242no—
171C3×C4#91512yes—
172C3×C4#91612yes—
173C3×C4D3×Q1612yes—
174C3×C4D3×Q1612yes—
175Dic3—64no—
176Dic3—64no—
177Dic3—82no—
178Dic3—122no—
179Dic3—122no—
180C32#167611yescharacteristic, complemented, Sylow
181Q8—92no—
182Q8—181no—
183Q8—242no—
184C2×C4—122no—
185C2×C4—181no—
186C2×C4—181no—
187C2×C4#379811yescharacteristic
188C2×C4#380211yescharacteristic
189C2×C4#381111yescharacteristic
190C8—41no—
191C8—92no—
192C8—122no—
193C8—181no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3#474912yes—
198C2×C3#479512yes—
199C2×C3#481312yes—
200C22#6391211yescharacteristic
201C4—21no—
202C4—182no—
203C4—242no—
204C4—361no—
205C4#6380211yescharacteristic
206C4#6380911yescharacteristic
207C4#6393111yescharacteristic
208C4#6394411yescharacteristic
209C3—21no—
210C3#6850912yescomplemented
211C2#1059056611yescharacteristic
212C2#1059085511yescharacteristic
213C2#1059098811yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1676
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
180. C32#1676semidirect
210. C3#68509semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105903122
#105902842
C3×#44812
#105891002
#685093