Finite Group Databasebeta

← #11781158

Subgroups — #11781158

Order 1152.

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

normal subgroups only

This group has 363 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#10590388C212yesmaximal
3#10590312C211yesmaximal, characteristic
4C3×#4486C212yesmaximal
5#10589100C211yesmaximal, characteristic
6#68467—32nomaximal
7C4×#634C2211yescharacteristic
8C3×#869C2212yes—
9C2×#3719—22no—
10C32×C4⋊C8C2211yescharacteristic
11#63641—21no—
12C8×C3⋊Dic3—21no—
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×C4⋊(C3⋊C8)C2212yes—
15#63576—21no—
16#63576—21no—
17#63566—22no—
18#5090—32no—
19#5078—32no—
20#4849—32no—
21#4830—32no—
22#4830—61no—
23C3×#332—32no—
24#4486D312yes—
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#3719—44no—
39#1674—91noSylow
40C3×C4⋊Q8—32no—
41C2×#216—62no—
42C2×Dic12—62no—
43#869C2×D312yes—
44C4×Dic6—32no—
45C4×Dic6—61no—
46C3×C4⋊C8—21no—
47C3×C4⋊C8—32no—
48C3×C4⋊C8C2×D312yes—
49#835—62no—
50#816—62no—
51Dic3⋊C8—62no—
52Dic3⋊C8—62no—
53C8×Dic3—62no—
54C8×Dic3—62no—
55#807—62no—
56#807—62no—
57C4⋊(C3⋊C8)C2×D312yes—
58C4×C3⋊C8—32no—
59C4×C3⋊C8—61no—
60C2×C32×C4C2×D411yescharacteristic
61C2×C32×C4C2×D411yescharacteristic
62C2×C32×C4#4111yescharacteristic
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3—21no—
65#634—21no—
66#634D812yes—
67C2×C3×Dic3—42no—
68C3×Dic6—42no—
69C3×Dic6—42no—
70C32×C8—41no—
71C3⋊(C3⋊C8)—21no—
72C3⋊(C3⋊C8)Q1612yescomplemented
73C3×C3⋊C8—42no—
74#500—91no—
75#462—92no—
76C8×Q8—91no—
77#335—91no—
78#332—32no—
79C2×C3×Q8—62no—
80C2×Dic6—22no—
81C2×Dic6—32no—
82C2×Dic6—61no—
83C2×C3×C8—22no—
84C2×C3×C8—22no—
85C2×C3×C8—62no—
86C3×C4⋊C4—62no—
87C3×C4⋊C4—62no—
88C3×C42—21no—
89C3×C42C22×D312yes—
90#216—124no—
91C4⋊Dic3—22no—
92C4⋊Dic3—22no—
93C4⋊Dic3—32no—
94C4⋊Dic3—61no—
95Dic3⋊C4—62no—
96Dic3⋊C4—62no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C2×C3⋊C8—22no—
100C2×C3⋊C8—32no—
101C2×C3⋊C8—32no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—61no—
104Dic12—124no—
105C22×C32#12111yescharacteristic
106C32×C4—21no—
107C32×C4C2×D811yescharacteristic
108C32×C4C2×Q1611yescharacteristic
109C32×C4#13511yescharacteristic
110C32×C4#13711yescharacteristic
111C3⋊Dic3—22no—
112C3⋊Dic3—41no—
113C3×Dic3—82no—
114C2×Q16—182no—
115C4⋊Q8—32no—
116C4×Q8—91no—
117#107—181no—
118#107—181no—
119C4⋊C8—32no—
120C4⋊C8—181no—
121C4⋊C8D3211yescharacteristic
122#103—182no—
123C4×C8—91no—
124C4×C8—181no—
125C3×Q8—122no—
126C3×Q8—122no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—122no—
131C2×C3×C4#23512yes—
132C2×C3×C4D3×D412yes—
133C2×C3×C4D3×D412yes—
134C2×Dic3—42no—
135C2×Dic3—62no—
136C2×Dic3—62no—
137C2×Dic3—62no—
138C2×Dic3—62no—
139Dic6—34no—
140Dic6—42no—
141Dic6—42no—
142Dic6—62no—
143Dic6—62no—
144Dic6—62no—
145C3×C8—42no—
146C3×C8—42no—
147C3×C8—122no—
148C3⋊C8—34no—
149C3⋊C8—42no—
150C3⋊C8—62no—
151C3⋊C8—62no—
152C3⋊C8—121no—
153C2×C32#46211yescharacteristic
154C2×C32#46611yescharacteristic
155C2×C32#47311yescharacteristic
156C2×Q8—62no—
157C2×Q8—91no—
158Q16—364no—
159C2×C8—21no—
160C2×C8—62no—
161C2×C8—91no—
162C2×C8—91no—
163C4⋊C4—62no—
164C4⋊C4—62no—
165C4⋊C4—91no—
166C4⋊C4—181no—
167C42—181no—
168C42C2×D3211yescharacteristic
169C22×C3—21no—
170C22×C3#88412yes—
171C3×C4—22no—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—41no—
177C3×C4—242no—
178C3×C4D3×D812yes—
179C3×C4#91512yes—
180C3×C4#91612yes—
181C3×C4D3×Q1612yes—
182Dic3—64no—
183Dic3—64no—
184Dic3—82no—
185Dic3—122no—
186Dic3—122no—
187C32#167411yescharacteristic, complemented, Sylow
188Q8—92no—
189Q8—122no—
190Q8—122no—
191Q8—181no—
192C2×C4—122no—
193C2×C4—181no—
194C2×C4—181no—
195C2×C4#379811yescharacteristic
196C2×C4#380211yescharacteristic
197C2×C4#381111yescharacteristic
198C8—41no—
199C8—92no—
200C8—122no—
201C8—181no—
202C2×C3—21no—
203C2×C3—21no—
204C2×C3—21no—
205C2×C3#475512yes—
206C2×C3#477512yes—
207C2×C3#479512yes—
208C22#6391211yescharacteristic
209C4—21no—
210C4—182no—
211C4—242no—
212C4—361no—
213C4#6379711yescharacteristic
214C4#6380911yescharacteristic
215C4#6393111yescharacteristic
216C4#6394411yescharacteristic
217C3—21no—
218C3#6846712yescomplemented
219C2#1059056611yescharacteristic
220C2#1059083911yescharacteristic
221C2#1059099311yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1674
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
72. C3⋊(C3⋊C8)Q16semidirect
187. C32#1674semidirect
218. C3#68467semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105903882
#105903122
C3×#44862
#105891002
#684673