Finite Group Databasebeta

← #11795341

Subgroups — #11795341

Order 1152.

397 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 397 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C2×C3×#817C211yesmaximal, characteristic
2C3×#5102C211yesmaximal, characteristic
3#10591139C212yesmaximal
4#10589418C211yesmaximal, characteristic
5#10589167C212yesmaximal
6#70573—31nomaximal
7#70533—31nomaximal
8C22×C32×C8C2211yescharacteristic
9C2×#3748C2212yes—
10C3×#926C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×#208C2211yescharacteristic
13C3×#817—22no—
14C3×Dic3⋊C8—22no—
15#63576—22no—
16#63574—22no—
17C2×C3×#106—31no—
18C3×#424—31no—
19C2×#817D311yescharacteristic
20#5102D311yescharacteristic
21#4995—32no—
22#4964—32no—
23#4554—32no—
24#4552—31no—
25#4552—31no—
26#4552—61no—
27#4530—32no—
28C22×C32×C4C2311yescharacteristic
29C22×C3×Dic3—22no—
30C2×C32×C8—22no—
31C2×C32×C8D412yes—
32#3748—22no—
33#3748Q814yes—
34C2×C3⋊(C3⋊C8)—22no—
35C3×#217—21no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C3×C4⋊Dic3D412yes—
39C3×C4×Dic3—21no—
40C3×#208—22no—
41C2×C3×C3⋊C8—21no—
42#2090—91noSylow
43C2×C3×M16—31no—
44C22×C3×C8—21no—
45C22×C3×C8C2×D311yescharacteristic
46C22×C3×C8C2×D311yescharacteristic
47C3×#117—31no—
48C2×C3×C4⋊C4—32no—
49#926C2×D311yescharacteristic
50C2×C4⋊Dic3C2×D312yes—
51C2×#208—32no—
52C2×#208—32no—
53C2×#208—62no—
54C2×#208C2×D311yescharacteristic
55C3×#106—62no—
56C3×C4⋊C8—62no—
57#817—22no—
58Dic3⋊C8—22no—
59#808—62no—
60#808—62no—
61#807—62no—
62#807—62no—
63C23×C32#4111yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4C2×Q812yes—
67C2×C32×C4#4112yes—
68C2×C3×Dic3—22no—
69C2×C3×Dic3—42no—
70C2×C3×Dic3—82no—
71C32×C8—22no—
72C3⋊(C3⋊C8)—24no—
73C3×C3⋊C8—41no—
74#428—92no—
75C2×#106—31no—
76#424—31no—
77#343—92no—
78#341—91no—
79C22×C3×C4—21no—
80C22×C3×C4—62no—
81C22×C3×C4C22×D311yescharacteristic
82C22×C3×C4C22×D311yescharacteristic
83C22×Dic3—22no—
84C3×M16—62no—
85C2×C3×C8—22no—
86C2×C3×C8—22no—
87C2×C3×C8—22no—
88C2×C3×C8—42no—
89C2×C3×C8—61no—
90C2×C3×C8#6712yes—
91C2×C3×C8#6712yes—
92C3×C4⋊C4—32no—
93C3×C4⋊C4—62no—
94C3×C4⋊C4—62no—
95C3×C22⋊C4—61no—
96C3×C42—61no—
97#217—21no—
98C4⋊Dic3—22no—
99C4⋊Dic3—22no—
100C4⋊Dic3D1212yes—
101C4×Dic3—21no—
102#208—22no—
103#208—34no—
104#208—34no—
105#208—64no—
106#208—62no—
107#208—62no—
108#208—122no—
109C2×C3⋊C8—21no—
110C2×C3⋊C8—62no—
111C2×C3⋊C8—62no—
112C2×C3⋊C8—122no—
113C22×C32—22no—
114C22×C32#12111yescharacteristic
115C22×C32#12512yes—
116C32×C4C22⋊Q812yes—
117C32×C4#12311yescharacteristic
118C32×C4C4⋊Q811yescharacteristic
119C3×Dic3—42no—
120C3×Dic3—82no—
121C2×M16—31no—
122C2×M16—92no—
123C22×C8D3211yescharacteristic
124#117—31no—
125C2×C4⋊C4—32no—
126#107—182no—
127#106—62no—
128#106—182no—
129C4⋊C8—62no—
130C23×C3—21no—
131C23×C3#23511yescharacteristic
132C23×C3#23711yescharacteristic
133C2×C3×C4—22no—
134C2×C3×C4—21no—
135C2×C3×C4—22no—
136C2×C3×C4—21no—
137C2×C3×C4—62no—
138C2×C3×C4—122no—
139C2×C3×C4—242no—
140C2×C3×C4C2×D1211yescharacteristic
141C2×C3×C4#23512yes—
142C2×C3×C4D3×D411yescharacteristic
143C2×C3×C4#23712yes—
144C2×C3×C4D3×Q812yes—
145C2×C3×C4D3×Q812yes—
146C2×C3×C4C2×#6711yescharacteristic
147C2×C3×C4C2×#6711yescharacteristic
148C2×Dic3—22no—
149C2×Dic3—42no—
150C2×Dic3—82no—
151C3×C8—22no—
152C3×C8—22no—
153C3×C8—42no—
154C3×C8—121no—
155C3⋊C8—41no—
156C3⋊C8—64no—
157C3⋊C8—64no—
158C3⋊C8—124no—
159C2×C32—22no—
160C2×C32#39811yescharacteristic
161C2×C32#47112yes—
162C22×C4—62no—
163C22×C4C2×D3211yescharacteristic
164M16—62no—
165M16—94no—
166M16—182no—
167C2×C8—22no—
168C2×C8—61no—
169C2×C8—182no—
170C2×C8#62512yes—
171C4⋊C4—32no—
172C4⋊C4—62no—
173C4⋊C4—62no—
174C22⋊C4—61no—
175C42—61no—
176C22×C3—22no—
177C22×C3—22no—
178C22×C3—22no—
179C22×C3—21no—
180C22×C3—42no—
181C22×C3#88912yes—
182C22×C3#88912yes—
183C22×C3#93011yescharacteristic
184C22×C3#93811yescharacteristic
185C3×C4—21no—
186C3×C4—22no—
187C3×C4—21no—
188C3×C4—122no—
189C3×C4—242no—
190C3×C4#89612yes—
191C3×C4#89712yes—
192C3×C4#92911yescharacteristic
193C3×C4#93511yescharacteristic
194C3×C4#94411yescharacteristic
195C3×C4#94411yescharacteristic
196Dic3—42no—
197Dic3—82no—
198C32#209011yescharacteristic, complemented, Sylow
199C23#379511yescharacteristic
200C2×C4—62no—
201C2×C4—122no—
202C2×C4—242no—
203C2×C4#379712yes—
204C2×C4D3×D1211yescharacteristic
205C2×C4#380412yes—
206C2×C4C2×#62511yescharacteristic
207C8—22no—
208C8—121no—
209C8—184no—
210C2×C3—22no—
211C2×C3—22no—
212C2×C3—22no—
213C2×C3—21no—
214C2×C3—42no—
215C2×C3#498111yescharacteristic
216C2×C3#498311yescharacteristic
217C2×C3#514112yes—
218C2×C3#517712yes—
219C22—22no—
220C22#6384712yes—
221C22#6390811yescharacteristic
222C4—122no—
223C4—242no—
224C4#6387311yescharacteristic
225C4#6389512yes—
226C4#6396111yescharacteristic
227C3—21no—
228C3#7053311yescharacteristic, complemented
229C3#7057311yescharacteristic, complemented
230C2—22no—
231C2#1059092512yes—
232C2#1059121411yescharacteristic
subgroupG/H
centerC22#63908
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32#121
prime radicalC23×C32#41
hypercenterC22×C8D32
hypocenterC32#2090
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
198. C32#2090semidirect
228. C3#70533semidirect
229. C3#70573semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8172
C3×#51022
#105911392
#105894182
#105891672
#705733
#705333