Finite Group Databasebeta

← #11795339

Subgroups — #11795339

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#10592801C211yesmaximal, characteristic
2C2×C3×#817C211yesmaximal, characteristic
3#10591130C212yesmaximal
4C3×#4552C211yesmaximal, characteristic
5#10589167C212yesmaximal
6#70573—31nomaximal
7#68924—31nomaximal
8C22×C32×C8C2211yescharacteristic
9#64135C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×#208C2212yes—
13#63641—22no—
14C3×#817—22no—
15#63575—22no—
16#63573—22no—
17C2×C3×#106—31no—
18#5121—32no—
19C2×#817D311yescharacteristic
20#5102—31no—
21#5102—31no—
22#5102—61no—
23#4964—32no—
24C3×#341—31no—
25#4554—32no—
26#4552D311yescharacteristic
27#4530—32no—
28C22×C32×C4C2311yescharacteristic
29C22×C3×Dic3—22no—
30C2×C32×C8—22no—
31C2×C32×C8D412yes—
32#3757—21no—
33C4⋊(C3⋊Dic3)D412yes—
34C4×C3⋊Dic3—21no—
35#3748—22no—
36C2×C3⋊(C3⋊C8)—21no—
37C3×C4⋊Dic3—22no—
38C3×C4⋊Dic3—22no—
39C3×#208—22no—
40C3×#208Q814yes—
41C2×C3×C3⋊C8—22no—
42#2090—91noSylow
43C2×C3×M16—32no—
44C22×C3×C8—21no—
45C22×C3×C8C2×D311yescharacteristic
46C22×C3×C8C2×D311yescharacteristic
47C2×C3×C4⋊C4—32no—
48#926—31no—
49#926—31no—
50#926—61no—
51C2×C4⋊Dic3C2×D312yes—
52C2×#208—31no—
53C2×#208—31no—
54C2×#208—61no—
55C2×#208C2×D312yes—
56C3×#106—62no—
57#818—62no—
58#817—22no—
59#817—62no—
60Dic3⋊C8—64no—
61Dic3⋊C8—62no—
62Dic3⋊C8—62no—
63#808—62no—
64#807—62no—
65C23×C32#4111yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4C2×Q812yes—
69C2×C32×C4#4112yes—
70C2×C3⋊Dic3—22no—
71C2×C3×Dic3—42no—
72C2×C3×Dic3—82no—
73C32×C8—22no—
74C3⋊(C3⋊C8)—41no—
75C3×C3⋊C8—24no—
76#428—92no—
77C2×#106—31no—
78#424—91no—
79#343—92no—
80#341—31no—
81C22×C3×C4—21no—
82C22×C3×C4—62no—
83C22×C3×C4C22×D311yescharacteristic
84C22×C3×C4C22×D311yescharacteristic
85C22×Dic3—22no—
86C3×M16—34no—
87C3×M16—62no—
88C2×C3×C8—22no—
89C2×C3×C8—22no—
90C2×C3×C8—22no—
91C2×C3×C8—42no—
92C2×C3×C8—62no—
93C2×C3×C8D1212yes—
94C2×C3×C8#6712yes—
95C3×C4⋊C4—62no—
96C3×C4⋊C4—62no—
97#217—62no—
98#217—61no—
99#217—61no—
100C4⋊Dic3—22no—
101C4⋊Dic3—22no—
102C4⋊Dic3—32no—
103C4⋊Dic3—32no—
104C4⋊Dic3—62no—
105C4×Dic3—62no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108#208—22no—
109#208—62no—
110#208—62no—
111#208—122no—
112#208Dic614yes—
113C2×C3⋊C8—22no—
114C2×C3⋊C8—62no—
115C2×C3⋊C8—61no—
116C2×C3⋊C8—61no—
117C22×C32—22no—
118C22×C32#12111yescharacteristic
119C22×C32#12512yes—
120C32×C4C22⋊Q812yes—
121C32×C4#12311yescharacteristic
122C32×C4C4⋊Q811yescharacteristic
123C3⋊Dic3—42no—
124C3×Dic3—82no—
125C2×M16—32no—
126C2×M16—91no—
127C22×C8D3211yescharacteristic
128#117—91no—
129C2×C4⋊C4—32no—
130#107—182no—
131#106—62no—
132#106—182no—
133C4⋊C8—182no—
134C23×C3—21no—
135C23×C3#23711yescharacteristic
136C23×C3#23911yescharacteristic
137C2×C3×C4—22no—
138C2×C3×C4—21no—
139C2×C3×C4—22no—
140C2×C3×C4—21no—
141C2×C3×C4—122no—
142C2×C3×C4—242no—
143C2×C3×C4C2×Dic612yes—
144C2×C3×C4C2×D1211yescharacteristic
145C2×C3×C4#23512yes—
146C2×C3×C4D3×D411yescharacteristic
147C2×C3×C4D3×D411yescharacteristic
148C2×C3×C4#23712yes—
149C2×C3×C4D3×Q812yes—
150C2×C3×C4C2×#6711yescharacteristic
151C2×Dic3—42no—
152C2×Dic3—64no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—82no—
156C3×C8—22no—
157C3×C8—22no—
158C3×C8—42no—
159C3×C8—64no—
160C3⋊C8—24no—
161C3⋊C8—122no—
162C3⋊C8—121no—
163C3⋊C8—121no—
164C2×C32—22no—
165C2×C32#39811yescharacteristic
166C2×C32#47112yes—
167C22×C4—62no—
168C22×C4C2×D3211yescharacteristic
169M16—34no—
170M16—62no—
171M16—182no—
172C2×C8—22no—
173C2×C8—62no—
174C2×C8—181no—
175C2×C8#62612yes—
176C4⋊C4—62no—
177C4⋊C4—62no—
178C4⋊C4—92no—
179C22⋊C4—181no—
180C42—181no—
181C22×C3—22no—
182C22×C3—22no—
183C22×C3—22no—
184C22×C3—21no—
185C22×C3—42no—
186C22×C3#88912yes—
187C22×C3#89012yes—
188C22×C3#89511yescharacteristic
189C22×C3#93811yescharacteristic
190C3×C4—21no—
191C3×C4—22no—
192C3×C4—21no—
193C3×C4—242no—
194C3×C4#86911yescharacteristic
195C3×C4#87812yes—
196C3×C4#88611yescharacteristic
197C3×C4#89612yes—
198C3×C4#92911yescharacteristic
199C3×C4#94411yescharacteristic
200Dic3—82no—
201Dic3—124no—
202Dic3—122no—
203Dic3—122no—
204C32#209011yescharacteristic, complemented, Sylow
205C23#379611yescharacteristic
206C2×C4—122no—
207C2×C4—182no—
208C2×C4—242no—
209C2×C4D3×Dic612yes—
210C2×C4#380211yescharacteristic
211C2×C4#380412yes—
212C2×C4C2×#62611yescharacteristic
213C8—22no—
214C8—64no—
215C8—361no—
216C2×C3—22no—
217C2×C3—22no—
218C2×C3—21no—
219C2×C3—22no—
220C2×C3—42no—
221C2×C3#466111yescharacteristic
222C2×C3#489812yes—
223C2×C3#498311yescharacteristic
224C2×C3#517712yes—
225C22—22no—
226C22#6384612yes—
227C22#6391611yescharacteristic
228C4—242no—
229C4—362no—
230C4#6386611yescharacteristic
231C4#6389912yes—
232C4#6396611yescharacteristic
233C3—21no—
234C3#6892411yescharacteristic, complemented
235C3#7057311yescharacteristic, complemented
236C2—22no—
237C2#1059092812yes—
238C2#1059135811yescharacteristic
subgroupG/H
centerC22#63916
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
204. C32#2090semidirect
234. C3#68924semidirect
235. C3#70573semidirect

Maximal subgroups

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

subgroupindex
#105928012
C2×C3×#8172
#105911302
C3×#45522
#105891672
#705733
#689243