Finite Group Databasebeta

← #11785479

Subgroups — #11785479

Order 1152.

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

normal subgroups only

This group has 390 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×#63510C211yesmaximal, characteristic
2C9×#410C211yesmaximal, characteristic
3#10588920C211yesmaximal, characteristic
4#10588676C212yesmaximal, complemented
5#10588210C212yesmaximal, complemented
6#70041—31nomaximal
7C2×C9×#41C2211yescharacteristic
8C9×#117C2212yes—
9#63510—22no—
10#63510—22no—
11#63488C2212yes—
12C2×#3667C412yescomplemented
13C2×#3667C2211yescharacteristic
14C22×C9⋊C8C412yescomplemented
15C22×C9⋊C8C2211yescharacteristic
16C9×#99—22no—
17#63393—22no—
18#63367—22no—
19#63366—22no—
20C2×#948—31no—
21C3×#410D311yescharacteristic
22#5240—31no—
23#4998—32no—
24#4531—32no—
25C9×#41—22no—
26C9×#41—22no—
27C2×Q8×C9Q811yescharacteristic
28C2×D4×C9D412yes—
29C2×D4×C9Q811yescharacteristic
30C22×C4×C9C2×C412yes—
31C22×C4×C9C2311yescharacteristic
32C9×C4⋊C4—22no—
33C9×C22⋊C4—22no—
34C42×C9—22no—
35#3676—22no—
36C4⋊Dic9—22no—
37C4×Dic9—22no—
38#3667—22no—
39#3667—24no—
40C2×C9⋊C8—22no—
41C2×C9⋊C8—22no—
42C2×C9⋊C8C2×C412yes—
43C2×C9⋊C8C2×C411yescharacteristic
44C2×C9⋊C8C2×C411yescharacteristic
45C2×C9⋊C8D412yes—
46C2×C9⋊C8D412yes—
47#1812—91noSylow
48C2×C3×#41C2×D311yescharacteristic
49C3×#117C2×D312yes—
50#948—62no—
51#948—62no—
52#926—32no—
53C2×#208—32no—
54C2×#208—31no—
55C22×C3⋊C8—31no—
56C22×C3⋊C8—32no—
57C3×#99—22no—
58#834—62no—
59#808—62no—
60#807—62no—
61C23×C9C4⋊C412yes—
62C23×C9C2×D411yescharacteristic
63Q8×C9—22no—
64D4×C9—24no—
65D4×C9—22no—
66C2×C4×C9—22no—
67C2×C4×C9—22no—
68C2×C4×C9—42no—
69C2×C4×C9C4⋊C412yes—
70C2×C4×C9C22×C411yescharacteristic
71C2×C4×C9C2×D412yes—
72C2×C4×C9C2×Q811yescharacteristic
73C2×C4×C9#4112yes—
74C2×Dic9—42no—
75C9⋊C8—22no—
76C9⋊C8C22⋊C411yescharacteristic
77C9⋊C8C22⋊C411yescharacteristic
78C9⋊C8C22⋊C412yes—
79C2×#131—91no—
80#427—92no—
81#410—91no—
82#410D911yescharacteristic
83H(3,ℤ/4)—92no—
84C3×#41—22no—
85C3×#41—22no—
86C2×C3×Q8Dic611yescharacteristic
87C2×C3×D4Dic611yescharacteristic
88C2×C3×D4#6712yes—
89C22×C3×C4C4×D312yes—
90C22×C3×C4C22×D311yescharacteristic
91C3×C4⋊C4—22no—
92C3×C22⋊C4—22no—
93C3×C42—22no—
94#217—62no—
95C4⋊Dic3—62no—
96C4×Dic3—62no—
97#208—64no—
98#208—62no—
99C2×C3⋊C8—31no—
100C2×C3⋊C8—31no—
101C2×C3⋊C8—32no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—32no—
104C2×C3⋊C8—62no—
105C2×C3⋊C8—62no—
106C22×C9—22no—
107C22×C9—41no—
108C22×C9—42no—
109C22×C9C2×C4⋊C411yescharacteristic
110C22×C9#12112yes—
111C4×C9—22no—
112C4×C9—82no—
113C4×C9C2×C22⋊C411yescharacteristic
114C4×C9#11711yescharacteristic
115C4×C9C22⋊Q812yes—
116Dic9—82no—
117C2×#41C2×D911yescharacteristic
118#131—182no—
119#131—182no—
120C2×M16—92no—
121C2×M16—91no—
122C22×C8—91no—
123C22×C8—92no—
124#117—92no—
125#117C2×D912yes—
126#107—182no—
127#106—182no—
128#99—22no—
129#99—182no—
130C23×C3Dic3⋊C412yes—
131C23×C3C2×#6711yescharacteristic
132C3×Q8—22no—
133C3×D4—24no—
134C3×D4—22no—
135C2×C3×C4—22no—
136C2×C3×C4—22no—
137C2×C3×C4—42no—
138C2×C3×C4Dic3⋊C412yes—
139C2×C3×C4C2×Dic611yescharacteristic
140C2×C3×C4C2×C4×D311yescharacteristic
141C2×C3×C4D3×D412yes—
142C2×C3×C4#23712yes—
143C2×Dic3—122no—
144C3⋊C8—31no—
145C3⋊C8—31no—
146C3⋊C8—32no—
147C3⋊C8—62no—
148C2×C9—22no—
149C2×C9—21no—
150C2×C9—42no—
151C2×C9#38011yescharacteristic
152#41—22no—
153#41—22no—
154C2×Q8Dic1811yescharacteristic
155C2×D4Dic1811yescharacteristic
156C2×D4#61112yes—
157C22×C4C4×D912yes—
158C22×C4C22×D911yescharacteristic
159M16—184no—
160M16—182no—
161C2×C8—91no—
162C2×C8—91no—
163C2×C8—92no—
164C2×C8—92no—
165C2×C8—92no—
166C2×C8—182no—
167C2×C8—182no—
168C4⋊C4—22no—
169C4⋊C4—182no—
170C22⋊C4—22no—
171C22⋊C4—182no—
172C42—22no—
173C42—182no—
174C22×C3—22no—
175C22×C3—41no—
176C22×C3—42no—
177C22×C3C2×Dic3⋊C411yescharacteristic
178C22×C3#93912yes—
179C3×C4—22no—
180C3×C4—82no—
181C3×C4#87711yescharacteristic
182C3×C4#87812yes—
183C3×C4D3×C22⋊C411yescharacteristic
184Dic3—242no—
185C9#181211yescharacteristic, complemented, Sylow
186C23Dic9⋊C412yes—
187C23C2×#61111yescharacteristic
188Q8—22no—
189D4—24no—
190D4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—42no—
194C2×C4—362no—
195C2×C4Dic9⋊C412yes—
196C2×C4C2×Dic1811yescharacteristic
197C2×C4C2×C4×D911yescharacteristic
198C2×C4D4×D912yes—
199C2×C4#369912yes—
200C8—91no—
201C8—91no—
202C8—92no—
203C8—182no—
204C2×C3—22no—
205C2×C3—21no—
206C2×C3—42no—
207C2×C3#494211yescharacteristic
208C22—22no—
209C22—41no—
210C22—42no—
211C22C2×Dic9⋊C411yescharacteristic
212C22#6350112yes—
213C4—22no—
214C4—82no—
215C4—722no—
216C4#6343911yescharacteristic
217C4#6344012yes—
218C4C22⋊C4×D911yescharacteristic
219C3#7004111yescharacteristic
220C2—22no—
221C2—21no—
222C2—42no—
223C2#1058862211yescharacteristic
subgroupG/H
centerC4#63439
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#410C2
socleC2×C3#4942
prime radicalC2×C3×#41C2×D3
cosocleC22×C4×C9C23
hypercenter#410D9
hypocenterC9#1812
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
4. #10588676C2semidirect
5. #10588210C2semidirect
12. C2×#3667C4semidirect
14. C22×C9⋊C8C4semidirect
185. C9#1812semidirect

Maximal subgroups

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

subgroupindex
C2×#635102
C9×#4102
#105889202
#105886762
#105882102
#700413