Finite Group Databasebeta

← #11795309

Subgroups — #11795309

Order 1152.

409 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 409 conjugacy classes of subgroups — too many to draw. Only its 118 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#10592698C211yesmaximal, characteristic
2C3×#4995C212yesmaximal
3C2×#63576C211yesmaximal, characteristic
4#10589167C212yesmaximal
5#10589165C211yesmaximal, characteristic
6#70670—32nomaximal
7C32×#117C2211yescharacteristic
8C2×#3748C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×#208C2212yes—
12C4⋊(C3⋊(C3⋊C8))—22no—
13C3×#808—22no—
14C3×#807—22no—
15#63576—22no—
16C3×#428—32no—
17#4999—32no—
18#4999—61no—
19#4995D312yes—
20C2×#807—32no—
21#4558—32no—
22#4554—32no—
23#4530—32no—
24C22×C32×C4C2311yescharacteristic
25C22×C3×Dic3—22no—
26C32×C4⋊C4D411yescharacteristic
27C32×C4⋊C4D411yescharacteristic
28C32×C22⋊C4—21no—
29C32×C42—21no—
30#3748—22no—
31C2×C3⋊(C3⋊C8)—22no—
32C2×C3⋊(C3⋊C8)—21no—
33C2×C3⋊(C3⋊C8)D412yes—
34C3×C4⋊Dic3—22no—
35C3×C4⋊Dic3—22no—
36C3×#208—22no—
37C3×#208Q814yes—
38C2×C3×C3⋊C8—22no—
39#2089—91noSylow
40C2×C3×M16—32no—
41C3×#117—21no—
42C3×#117C2×D312yes—
43C2×C3×C4⋊C4—32no—
44C2×C4⋊Dic3C2×D312yes—
45C2×#208—32no—
46C2×#208—61no—
47C2×#208C2×D312yes—
48C22×C3⋊C8—32no—
49C22×C3⋊C8—61no—
50C3×#107—62no—
51C3×#106—62no—
52#808—22no—
53#807—22no—
54#807—64no—
55C4⋊(C3⋊C8)—64no—
56C4⋊(C3⋊C8)—64no—
57C23×C32#4111yescharacteristic
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4C2×D411yescharacteristic
61C2×C32×C4C2×D411yescharacteristic
62C2×C32×C4C2×Q812yes—
63C2×C32×C4#4112yes—
64C2×C3×Dic3—42no—
65C2×C3×Dic3—82no—
66C3⋊(C3⋊C8)—22no—
67C3⋊(C3⋊C8)—41no—
68C3×C3⋊C8—24no—
69#428—32no—
70C2×#107—91no—
71#424—91no—
72#343—92no—
73#341—91no—
74C22×C3×C4—21no—
75C22×C3×C4—62no—
76C22×C3×C4C22×D312yes—
77C22×Dic3—22no—
78C3×M16—34no—
79C3×M16—62no—
80C2×C3×C8—62no—
81C3×C4⋊C4—21no—
82C3×C4⋊C4—21no—
83C3×C4⋊C4—62no—
84C3×C4⋊C4—62no—
85C3×C4⋊C4#6712yes—
86C3×C4⋊C4#6712yes—
87C3×C22⋊C4—22no—
88C3×C22⋊C4—22no—
89C3×C42—22no—
90C3×C42—22no—
91C4⋊Dic3—22no—
92C4⋊Dic3—22no—
93#208—22no—
94#208—62no—
95#208—62no—
96#208—122no—
97#208Dic614yes—
98C2×C3⋊C8—22no—
99C2×C3⋊C8—34no—
100C2×C3⋊C8—62no—
101C2×C3⋊C8—62no—
102C2×C3⋊C8—62no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8—62no—
105C2×C3⋊C8—122no—
106C22×C32—21no—
107C22×C32—21no—
108C22×C32#12111yescharacteristic
109C22×C32#12512yes—
110C32×C4—41no—
111C32×C4—41no—
112C32×C4C22⋊Q812yes—
113C32×C4#12311yescharacteristic
114C32×C4C4⋊Q811yescharacteristic
115C3×Dic3—82no—
116C2×M16—32no—
117C2×M16—91no—
118C22×C8—91no—
119#117D3211yescharacteristic
120C2×C4⋊C4—32no—
121#107—62no—
122#107—182no—
123#106—62no—
124C4⋊C8—182no—
125C23×C3—21no—
126C23×C3#23712yes—
127C2×C3×C4—22no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×C3×C4—22no—
131C2×C3×C4—22no—
132C2×C3×C4—22no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—122no—
136C2×C3×C4—242no—
137C2×C3×C4C2×Dic612yes—
138C2×C3×C4#23512yes—
139C2×C3×C4D3×D412yes—
140C2×C3×C4D3×Q812yes—
141C2×C3×C4#23912yes—
142C2×C3×C4C2×#6712yes—
143C2×Dic3—42no—
144C2×Dic3—82no—
145C3×C8—64no—
146C3⋊C8—24no—
147C3⋊C8—64no—
148C3⋊C8—122no—
149C3⋊C8—122no—
150C3⋊C8—122no—
151C2×C32—22no—
152C2×C32#39811yescharacteristic
153C2×C32#47211yescharacteristic
154C2×C32#47311yescharacteristic
155C22×C4—62no—
156C22×C4C2×D3211yescharacteristic
157M16—34no—
158M16—62no—
159M16—182no—
160C2×C8—62no—
161C2×C8—92no—
162C2×C8—182no—
163C2×C8—181no—
164C4⋊C4—62no—
165C4⋊C4—62no—
166C4⋊C4#62511yescharacteristic
167C4⋊C4#62511yescharacteristic
168C22⋊C4—21no—
169C42—21no—
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—22no—
173C22×C3—21no—
174C22×C3—41no—
175C22×C3—41no—
176C22×C3#88912yes—
177C22×C3#89012yes—
178C22×C3#93912yes—
179C3×C4—21no—
180C3×C4—22no—
181C3×C4—21no—
182C3×C4—42no—
183C3×C4—42no—
184C3×C4—42no—
185C3×C4—42no—
186C3×C4—242no—
187C3×C4#88812yes—
188C3×C4#89412yes—
189C3×C4#92412yes—
190C3×C4#94612yes—
191Dic3—82no—
192C32#208911yescharacteristic, complemented, Sylow
193C23#380511yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—122no—
197C2×C4—242no—
198C2×C4D3×Dic612yes—
199C2×C4#379912yes—
200C2×C4C2×#62511yescharacteristic
201C2×C4#381111yescharacteristic
202C8—64no—
203C8—182no—
204C8—361no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—42no—
211C2×C3#498212yes—
212C2×C3#519912yes—
213C2×C3#520412yes—
214C22—21no—
215C22—21no—
216C22#6384512yes—
217C22#6398011yescharacteristic
218C4—41no—
219C4—41no—
220C4—242no—
221C4#6384011yescharacteristic
222C4#6385612yes—
223C4#6389711yescharacteristic
224C3—21no—
225C3#7067012yescomplemented
226C2—22no—
227C2#1059121511yescharacteristic
228C2#1059167811yescharacteristic
229C2#1059168311yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#121
prime radicalC23×C32#41
hypercenter#117D32
hypocenterC32#2089
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
192. C32#2089semidirect
225. C3#70670semidirect

Maximal subgroups

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

subgroupindex
#105926982
C3×#49952
C2×#635762
#105891672
#105891652
#706703