Finite Group Databasebeta

← #11798902

Subgroups — #11798902

Order 1152.

249 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 249 conjugacy classes of subgroups — too many to draw. Only its 64 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#10588863C211yesmaximal, characteristic, complemented
2C2×#63387C211yesmaximal, characteristic
3C2×#63359C211yesmaximal, characteristic
4#10588552C211yesmaximal, characteristic
5C9×#358C211yesmaximal, characteristic, complemented
6Dic9⋊C16C211yesmaximal, characteristic, complemented
7#10588169C211yesmaximal, characteristic, complemented
8#69234—31nomaximal
9C2×C9×Q16C2211yescharacteristic
10#63506—21no—
11C2×#3674—21no—
12C2×D72C2211yescharacteristic
13C2×Dic36C2211yescharacteristic
14#63455—21no—
15C2×C9×C16C2211yescharacteristic
16C9×#107C2211yescharacteristic
17#63387—22no—
18C8×Dic9C2211yescharacteristic
19C2×C9⋊C16C2211yescharacteristic
20#63369—21no—
21#63359—22no—
22#5183—31no—
23C2×#828—31no—
24C2×#800—31no—
25#4872—31no—
26C3×#358D311yescharacteristic
27Dic3⋊C16—31no—
28#4492—31no—
29C2×Q8×C9—21no—
30C2×D36—21no—
31C2×C4×D9—41no—
32C2×Dic18—21no—
33C9×Q16—21no—
34C9×Q16—21no—
35C2×C8×C9C2311yescharacteristic
36C9×C4⋊C4—21no—
37#3674—42no—
38(C2×D9)⋊C4—41no—
39Dic9⋊C4—41no—
40Dic9⋊C4—41no—
41C4×Dic9D411yescharacteristic
42C2×C9⋊C8D411yescharacteristic
43D72—21no—
44D72D412yes—
45Dic36—21no—
46Dic36—21no—
47C9×C16—21no—
48C9⋊C16—21no—
49#2208—91noSylow
50C2×C3×Q16C2×D311yescharacteristic
51#944—61no—
52C2×#216—61no—
53C2×Dic12—31no—
54C2×D24—31no—
55#893—61no—
56C2×C3×C16C2×D311yescharacteristic
57C3×#107C2×D311yescharacteristic
58#828—62no—
59C8×Dic3—31no—
60C2×C3⋊C16—31no—
61#809—61no—
62#800—62no—
63C22×D9—41no—
64Q8×C9—41no—
65Q8×C9—41no—
66C2×C4×C9—41no—
67C2×C4×C9—41no—
68C2×C4×C9C2×D411yescharacteristic
69C2×Dic9—41no—
70C2×Dic9D811yescharacteristic
71C2×Dic9D811yescharacteristic
72D36—22no—
73D36—41no—
74C4×D9—82no—
75Dic18—41no—
76Dic18—41no—
77C8×C9C2×D411yescharacteristic
78C8×C9#4111yescharacteristic
79C9⋊C8—21no—
80C2×SD32—91no—
81C2×SD32—91no—
82#494—91no—
83C4×D8—91no—
84C4⋊C16—91no—
85#358—91no—
86#358D911yescharacteristic, complemented
87C2×C3×Q8—21no—
88C2×D12—61no—
89C2×C4×D3—121no—
90C2×Dic6—61no—
91C3×Q16—21no—
92C3×Q16—21no—
93C2×C3×C8C22×D311yescharacteristic
94C3×C4⋊C4—21no—
95#216—122no—
96(C2×D3)⋊C4—121no—
97Dic3⋊C4—121no—
98Dic3⋊C4—121no—
99C4×Dic3—31no—
100C2×C3⋊C8—31no—
101Dic12—61no—
102Dic12—61no—
103D24—32no—
104D24—61no—
105C3×C16—21no—
106C3⋊C16—61no—
107C22×C9C2×D811yescharacteristic
108C2×D9—42no—
109C2×D9—81no—
110C2×D9—81no—
111C4×C9—81no—
112C4×C9—81no—
113C4×C9#12111yescharacteristic
114C4×C9AGL(1,ℤ/8)11yescharacteristic
115Dic9—21no—
116Dic9—81no—
117Dic9SD3212yescomplemented
118C2×Q16—91no—
119C2×Q16—181no—
120C2×Q16C2×D911yescharacteristic
121C2×D8—91no—
122C4⋊Q8—181no—
123C4×D4—181no—
124SD32—182no—
125SD32—182no—
126C2×C16—91no—
127C2×C16C2×D911yescharacteristic
128#107C2×D911yescharacteristic
129#102—181no—
130C4×C8—91no—
131C22×D3—121no—
132C3×Q8—41no—
133C3×Q8—41no—
134C2×C3×C4—41no—
135C2×C3×C4—41no—
136C2×C3×C4D3×D411yescharacteristic
137C2×Dic3—31no—
138C2×Dic3—31no—
139C2×Dic3—121no—
140D12—62no—
141D12—121no—
142C4×D3—242no—
143Dic6—121no—
144Dic6—121no—
145C3×C8#23511yescharacteristic
146C3×C8D3×D411yescharacteristic
147C3⋊C8—61no—
148C2×C9#45911yescharacteristic
149C2×C9C2×SD3211yescharacteristic
150C2×C9#51011yescharacteristic
151D9—82no—
152C2×Q8—21no—
153C2×Q8—181no—
154C2×D4—181no—
155C22×C4—361no—
156Q16—21no—
157Q16—21no—
158Q16—181no—
159Q16—181no—
160Q16—362no—
161D8—92no—
162D8—181no—
163C2×C8—91no—
164C2×C8C22×D911yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—361no—
167C4⋊C4—361no—
168C22⋊C4—361no—
169C42—91no—
170C16—21no—
171C16—181no—
172C22×C3D3×D811yescharacteristic
173C2×D3—122no—
174C2×D3—241no—
175C2×D3—241no—
176C3×C4—81no—
177C3×C4—81no—
178C3×C4#88411yescharacteristic
179C3×C4#91411yescharacteristic
180Dic3—32no—
181Dic3—61no—
182Dic3—241no—
183C9#220811yescharacteristic, complemented, Sylow
184C23—361no—
185Q8—41no—
186Q8—41no—
187Q8—361no—
188Q8—361no—
189D4—182no—
190D4—361no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—361no—
196C2×C4—722no—
197C2×C4D4×D911yescharacteristic
198C8—181no—
199C8#369711yescharacteristic
200C8D4×D911yescharacteristic
201C2×C3#478611yescharacteristic
202C2×C3D3×SD3211yescharacteristic
203C2×C3#491811yescharacteristic
204D3—242no—
205C22—362no—
206C22—721no—
207C22—721no—
208C22D8×D911yescharacteristic
209C4—81no—
210C4—81no—
211C4—92no—
212C4—181no—
213C4—721no—
214C4#6344611yescharacteristic
215C4#6347611yescharacteristic
216C3#6923411yescharacteristic
217C2—722no—
218C2#1058846611yescharacteristic
219C2D9×SD3211yescharacteristic
220C2#1058859811yescharacteristic
subgroupG/H
centerC22D8×D9
commutator, cosocleC2×C8×C9C23
FrattiniC2×C3×C8C22×D3
FittingC9×#358C2
socleC22×C3D3×D8
prime radicalC2×D72C22
hypercenter#358D9
hypocenterC9#2208
LCSG ▷ C2×C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. #10588863C2semidirect
5. C9×#358C2semidirect
6. Dic9⋊C16C2semidirect
7. #10588169C2semidirect
86. #358D9semidirect
117. Dic9SD32semidirect
183. C9#2208semidirect

Maximal subgroups

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

subgroupindex
#105888632
C2×#633872
C2×#633592
#105885522
C9×#3582
Dic9⋊C162
#105881692
#692343