Finite Group Databasebeta

← #11798954

Subgroups — #11798954

Order 1152.

363 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 363 conjugacy classes of subgroups — too many to draw. Only its 76 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#10592572C211yesmaximal, characteristic
2#10590905C211yesmaximal, characteristic
3C2×#63551C212yesmaximal
4C3×#4492C212yesmaximal
5#10589133C211yesmaximal, characteristic
6#69236—32nomaximal
7C2×#3746C2211yescharacteristic
8#64096—21no—
9C2×C3×Dic12C2212yes—
10#63873—21no—
11C2×#3718—21no—
12C32×#107C2211yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14#63637—21no—
15C2×C3×C3⋊C16C2212yes—
16#63551—24no—
17#5183—32no—
18C2×#829—32no—
19C2×Dic24—32no—
20#4873—32no—
21#4873—61no—
22C3×#358—32no—
23Dic3⋊C16—32no—
24#4492D312yes—
25C2×#634—21no—
26C2×C3×Dic6—22no—
27C2×C32×C8C2311yescharacteristic
28C32×C4⋊C4—21no—
29#3750—41no—
30C4×C3⋊Dic3—41no—
31C4×C3⋊Dic3D411yescharacteristic
32C2×C3⋊(C3⋊C8)D411yescharacteristic
33#3746—21no—
34#3746D412yes—
35C3×Dic12—22no—
36C3×Dic12—22no—
37#3724—41no—
38#3724—41no—
39#3718—42no—
40C3×C3⋊C16—22no—
41#2209—91noSylow
42C2×C3×Q16—32no—
43#944—62no—
44C2×#216—62no—
45C2×Dic12—32no—
46C2×Dic12—61no—
47C2×Dic12C2×D312yes—
48#887—62no—
49#887—62no—
50C2×C3×C16—32no—
51C3×#107—21no—
52C3×#107C2×D312yes—
53#829—64no—
54C8×Dic3—32no—
55C8×Dic3—61no—
56C2×C3⋊C16C2×D312yes—
57#810—62no—
58#810—62no—
59Dic24—64no—
60C2×C32×C4—41no—
61C2×C32×C4C2×D411yescharacteristic
62C2×C3⋊Dic3—41no—
63C2×C3⋊Dic3D811yescharacteristic
64C2×C3⋊Dic3D811yescharacteristic
65#634—22no—
66#634—41no—
67C2×C3×Dic3—42no—
68C3×Dic6—42no—
69C3×Dic6—42no—
70C32×C8C2×D411yescharacteristic
71C32×C8#4111yescharacteristic
72C3⋊(C3⋊C8)—21no—
73C2×Q32—92no—
74#494—91no—
75C4×Q16—91no—
76C4⋊C16—91no—
77#358—32no—
78C2×C3×Q8—62no—
79C2×Dic6—22no—
80C2×Dic6—62no—
81C2×Dic6—62no—
82C3×Q16—62no—
83C3×Q16—62no—
84C2×C3×C8—21no—
85C2×C3×C8C22×D312yes—
86C3×C4⋊C4—22no—
87C3×C4⋊C4—22no—
88#216—124no—
89Dic3⋊C4—122no—
90Dic3⋊C4—122no—
91Dic3⋊C4—122no—
92Dic3⋊C4—122no—
93C4×Dic3—32no—
94C4×Dic3—61no—
95C4×Dic3—122no—
96C4×Dic3—122no—
97C2×C3⋊C8—32no—
98C2×C3⋊C8—61no—
99Dic12—22no—
100Dic12—22no—
101Dic12—34no—
102Dic12—62no—
103Dic12—62no—
104Dic12—62no—
105C3×C16—62no—
106C3⋊C16—22no—
107C22×C32C2×D811yescharacteristic
108C32×C4—81no—
109C32×C4#12111yescharacteristic
110C32×C4AGL(1,ℤ/8)11yescharacteristic
111C3⋊Dic3—21no—
112C3⋊Dic3—42no—
113C3⋊Dic3Q3212yescomplemented
114C3×Dic3—82no—
115C2×Q16—32no—
116C2×Q16—91no—
117C2×Q16—181no—
118C4⋊Q8—181no—
119C4×Q8—181no—
120Q32—184no—
121C2×C16—32no—
122#107D3211yescharacteristic
123#103—181no—
124C4×C8—91no—
125C3×Q8—122no—
126C3×Q8—122no—
127C2×C3×C4—21no—
128C2×C3×C4—42no—
129C2×C3×C4—42no—
130C2×C3×C4—122no—
131C2×C3×C4D3×D412yes—
132C2×Dic3—32no—
133C2×Dic3—32no—
134C2×Dic3—42no—
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—122no—
138C2×Dic3—122no—
139Dic6—42no—
140Dic6—42no—
141Dic6—64no—
142Dic6—64no—
143Dic6—122no—
144Dic6—122no—
145C3×C8—21no—
146C3×C8—21no—
147C3×C8#23512yes—
148C3×C8D3×D412yes—
149C3⋊C8—62no—
150C3⋊C8—121no—
151C2×C32#45911yescharacteristic
152C2×C32C2×Q3211yescharacteristic
153C2×C32#51011yescharacteristic
154C2×Q8—62no—
155C2×Q8—181no—
156Q16—62no—
157Q16—62no—
158Q16—92no—
159Q16—181no—
160Q16—362no—
161C2×C8—91no—
162C2×C8C2×D3211yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—361no—
165C4⋊C4—361no—
166C4⋊C4—361no—
167C42—91no—
168C42—361no—
169C16—62no—
170C22×C3—21no—
171C22×C3D3×D812yes—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4—82no—
175C3×C4—82no—
176C3×C4—242no—
177C3×C4#88412yes—
178C3×C4#91412yes—
179Dic3—34no—
180Dic3—62no—
181Dic3—62no—
182Dic3—82no—
183Dic3—121no—
184Dic3—124no—
185Dic3—124no—
186C32#220911yescharacteristic, complemented, Sylow
187Q8—122no—
188Q8—122no—
189Q8—182no—
190Q8—361no—
191C2×C4—41no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—122no—
195C2×C4—361no—
196C2×C4#381111yescharacteristic
197C8—181no—
198C8#379811yescharacteristic
199C8#380211yescharacteristic
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3#478612yes—
204C2×C3#491512yes—
205C2×C3D3×Q3212yes—
206C22#6392611yescharacteristic
207C4—81no—
208C4—92no—
209C4—181no—
210C4—242no—
211C4—362no—
212C4#6391211yescharacteristic
213C4#6394111yescharacteristic
214C3—21no—
215C3#6923612yescomplemented
216C2#1059055111yescharacteristic
217C2#1059103011yescharacteristic
218C2#1059104311yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socle, prime radicalC22×C32C2×D8
hypercenter#107D32
hypocenterC32#2209
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
113. C3⋊Dic3Q32semidirect
186. C32#2209semidirect
215. C3#69236semidirect

Maximal subgroups

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

subgroupindex
#105925722
#105909052
C2×#635512
C3×#44922
#105891332
#692363