Finite Group Databasebeta

← #11795340

Subgroups — #11795340

Order 1152.

417 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 417 conjugacy classes of subgroups — too many to draw. Only its 120 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×#63644C211yesmaximal, characteristic
2C3×#5102C211yesmaximal, characteristic
3#10591131C212yesmaximal
4C3×#4552C211yesmaximal, characteristic
5#10589168C212yesmaximal
6#70533—31nomaximal
7#68924—31nomaximal
8C22×C32×C8C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2212yes—
10C3×#926C2211yescharacteristic
11C2×C3×#208C2211yescharacteristic
12C2×C3×#208C2212yes—
13#63644—22no—
14C3×Dic3⋊C8—22no—
15#63575—22no—
16#63573—22no—
17C3×#424—31no—
18#5121—32no—
19C2×#817—31no—
20C2×#817—31no—
21C2×#817—61no—
22#5102D311yescharacteristic
23#4995—32no—
24C3×#341—31no—
25#4554—32no—
26#4554—32no—
27#4552D311yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3—22no—
30C2×C32×C8—22no—
31C2×C32×C8D412yes—
32C4⋊(C3⋊Dic3)—22no—
33C4⋊(C3⋊Dic3)—22no—
34C3×#217—21no—
35C3×C4⋊Dic3D412yes—
36C3×C4×Dic3—21no—
37C3×#208—22no—
38C3×#208—22no—
39C3×#208Q814yes—
40C2×C3×C3⋊C8—22no—
41C2×C3×C3⋊C8—21no—
42#2090—91noSylow
43C2×C3×M16—32no—
44C2×C3×M16—31no—
45C22×C3×C8—21no—
46C22×C3×C8C2×D311yescharacteristic
47C22×C3×C8C2×D311yescharacteristic
48C3×#117—31no—
49#926C2×D311yescharacteristic
50C2×C4⋊Dic3—32no—
51C2×C4⋊Dic3—32no—
52C2×C4⋊Dic3—62no—
53C2×#208C2×D311yescharacteristic
54C2×#208C2×D312yes—
55C3×C4⋊C8—62no—
56#818—62no—
57#817—64no—
58#817—62no—
59#817—62no—
60#817—62no—
61Dic3⋊C8—22no—
62#808—62no—
63#807—62no—
64C23×C32#4111yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×Q812yes—
68C2×C32×C4#4112yes—
69C2×C3⋊Dic3—42no—
70C2×C3⋊Dic3—82no—
71C2×C3×Dic3—22no—
72C32×C8—22no—
73C3×C3⋊C8—24no—
74C3×C3⋊C8—41no—
75#428—92no—
76C2×#106—91no—
77#424—31no—
78#343—92no—
79#341—31no—
80C22×C3×C4—21no—
81C22×C3×C4C22×D311yescharacteristic
82C22×C3×C4C22×D311yescharacteristic
83C22×Dic3—62no—
84C22×Dic3—62no—
85C22×Dic3—122no—
86C3×M16—34no—
87C3×M16—62no—
88C3×M16—62no—
89C2×C3×C8—24no—
90C2×C3×C8—22no—
91C2×C3×C8—22no—
92C2×C3×C8—22no—
93C2×C3×C8—62no—
94C2×C3×C8—61no—
95C2×C3×C8D1212yes—
96C2×C3×C8#6712yes—
97C3×C4⋊C4—32no—
98C3×C22⋊C4—61no—
99C3×C42—61no—
100#217—21no—
101C4⋊Dic3—64no—
102C4⋊Dic3—62no—
103C4⋊Dic3—62no—
104C4⋊Dic3—62no—
105C4⋊Dic3—62no—
106C4⋊Dic3—122no—
107C4⋊Dic3D1212yes—
108C4×Dic3—21no—
109#208—22no—
110#208—22no—
111#208Dic614yes—
112C2×C3⋊C8—22no—
113C2×C3⋊C8—21no—
114C22×C32—22no—
115C22×C32#12111yescharacteristic
116C22×C32#12512yes—
117C32×C4C22⋊Q812yes—
118C32×C4#12311yescharacteristic
119C32×C4C4⋊Q811yescharacteristic
120C3⋊Dic3—82no—
121C3×Dic3—42no—
122C2×M16—32no—
123C2×M16—31no—
124C22×C8D3211yescharacteristic
125#117—31no—
126C2×C4⋊C4—92no—
127#107—182no—
128#106—182no—
129#106—182no—
130C4⋊C8—62no—
131C23×C3—21no—
132C23×C3#23511yescharacteristic
133C23×C3#23911yescharacteristic
134C2×C3×C4—22no—
135C2×C3×C4—21no—
136C2×C3×C4—22no—
137C2×C3×C4—21no—
138C2×C3×C4—62no—
139C2×C3×C4C2×Dic612yes—
140C2×C3×C4C2×D1211yescharacteristic
141C2×C3×C4C2×D1211yescharacteristic
142C2×C3×C4D3×D411yescharacteristic
143C2×C3×C4#23712yes—
144C2×C3×C4#23712yes—
145C2×C3×C4D3×Q812yes—
146C2×C3×C4C2×#6711yescharacteristic
147C2×Dic3—22no—
148C2×Dic3—124no—
149C2×Dic3—122no—
150C2×Dic3—122no—
151C2×Dic3—244no—
152C2×Dic3—242no—
153C2×Dic3—242no—
154C3×C8—24no—
155C3×C8—22no—
156C3×C8—22no—
157C3×C8—64no—
158C3×C8—121no—
159C3⋊C8—24no—
160C3⋊C8—41no—
161C2×C32—22no—
162C2×C32#39811yescharacteristic
163C2×C32#47112yes—
164C22×C4—182no—
165C22×C4C2×D3211yescharacteristic
166M16—34no—
167M16—62no—
168M16—62no—
169C2×C8—22no—
170C2×C8—62no—
171C2×C8—61no—
172C2×C8#62612yes—
173C4⋊C4—32no—
174C4⋊C4—182no—
175C4⋊C4—182no—
176C22⋊C4—61no—
177C42—61no—
178C22×C3—24no—
179C22×C3—22no—
180C22×C3—22no—
181C22×C3—22no—
182C22×C3—21no—
183C22×C3#88912yes—
184C22×C3#89012yes—
185C22×C3#89511yescharacteristic
186C22×C3#93011yescharacteristic
187C3×C4—21no—
188C3×C4—22no—
189C3×C4—21no—
190C3×C4—122no—
191C3×C4#86911yescharacteristic
192C3×C4#87812yes—
193C3×C4#88611yescharacteristic
194C3×C4#89712yes—
195C3×C4#93511yescharacteristic
196C3×C4#94411yescharacteristic
197Dic3—42no—
198Dic3—244no—
199Dic3—242no—
200Dic3—242no—
201C32#209011yescharacteristic, complemented, Sylow
202C23#379911yescharacteristic
203C2×C4—62no—
204C2×C4—362no—
205C2×C4—722no—
206C2×C4D3×Dic612yes—
207C2×C4D3×D1211yescharacteristic
208C2×C4#380512yes—
209C2×C4C2×#62611yescharacteristic
210C8—22no—
211C8—64no—
212C8—121no—
213C2×C3—24no—
214C2×C3—22no—
215C2×C3—22no—
216C2×C3—21no—
217C2×C3—22no—
218C2×C3#466111yescharacteristic
219C2×C3#489812yes—
220C2×C3#498111yescharacteristic
221C2×C3#514112yes—
222C22—22no—
223C22#6384512yes—
224C22#6390911yescharacteristic
225C4—122no—
226C4—722no—
227C4#6386611yescharacteristic
228C4#6389312yes—
229C4#6396211yescharacteristic
230C3—21no—
231C3#6892411yescharacteristic, complemented
232C3#7053311yescharacteristic, complemented
233C2—22no—
234C2#1059093112yes—
235C2#1059135311yescharacteristic
subgroupG/H
centerC22#63909
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
201. C32#2090semidirect
231. C3#68924semidirect
232. C3#70533semidirect

Maximal subgroups

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

subgroupindex
C2×#636442
C3×#51022
#105911312
C3×#45522
#105891682
#705333
#689243