Finite Group Databasebeta

← #11799021

Subgroups — #11799021

Order 1152.

237 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 237 conjugacy classes of subgroups — too many to draw. Only its 62 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#10588871C211yesmaximal, characteristic
2C2×#63388C211yesmaximal, characteristic, complemented
3C2×#63359C211yesmaximal, characteristic
4#10588553C211yesmaximal, characteristic, complemented
5C9×#358C211yesmaximal, characteristic, complemented
6Dic9⋊C16C211yesmaximal, characteristic, complemented
7#10588168C211yesmaximal, characteristic
8#69237—31nomaximal
9C2×C9×Q16C2211yescharacteristic
10#63509—21no—
11C2×#3675—21no—
12C2×D72C2211yescharacteristic
13C2×Dic36C2211yescharacteristic
14#63449—21no—
15C2×C9×C16C2211yescharacteristic
16C9×#107C2211yescharacteristic
17#63388—22no—
18C8×Dic9C2211yescharacteristic
19C2×C9⋊C16C2211yescharacteristic
20#63368—21no—
21#63359—22no—
22#5191—31no—
23C2×#829—31no—
24C2×#800—31no—
25#4873—31no—
26C3×#358D311yescharacteristic
27Dic3⋊C16—31no—
28#4491—31no—
29C2×Q8×C9—21no—
30C2×D36—21no—
31C2×Dic18—21no—
32C9×Q16—21no—
33C9×Q16—21no—
34C2×C8×C9C2311yescharacteristic
35C9×C4⋊C4—21no—
36#3675—42no—
37(C2×D9)⋊C4—41no—
38(C2×D9)⋊C4—41no—
39Dic9⋊C4—41no—
40C4×Dic9—41no—
41C4×Dic9D411yescharacteristic
42C2×C9⋊C8D411yescharacteristic
43D72—21no—
44D72—21no—
45Dic36—21no—
46Dic36D412yes—
47C9×C16—21no—
48C9⋊C16—21no—
49#2211—91noSylow
50C2×C3×Q16C2×D311yescharacteristic
51#947—61no—
52C2×#215—61no—
53C2×Dic12—31no—
54C2×D24—31no—
55#887—61no—
56C2×C3×C16C2×D311yescharacteristic
57C3×#107C2×D311yescharacteristic
58#829—62no—
59C8×Dic3—31no—
60C2×C3⋊C16—31no—
61#810—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—41no—
73D36—41no—
74Dic18—22no—
75Dic18—41no—
76C8×C9C2×D411yescharacteristic
77C8×C9#4111yescharacteristic
78C9⋊C8—21no—
79C2×Q32—91no—
80C2×SD32—91no—
81#495—91no—
82C4×Q16—91no—
83C4⋊C16—91no—
84#358D911yescharacteristic, complemented
85#357—91no—
86C2×C3×Q8—21no—
87C2×D12—61no—
88C2×Dic6—61no—
89C3×Q16—21no—
90C3×Q16—21no—
91C2×C3×C8C22×D311yescharacteristic
92C3×C4⋊C4—21no—
93#215—122no—
94(C2×D3)⋊C4—121no—
95(C2×D3)⋊C4—121no—
96Dic3⋊C4—121no—
97C4×Dic3—31no—
98C4×Dic3—121no—
99C2×C3⋊C8—31no—
100Dic12—32no—
101Dic12—61no—
102D24—61no—
103D24—61no—
104C3×C16—21no—
105C3⋊C16—61no—
106C22×C9C2×D811yescharacteristic
107C2×D9—81no—
108C2×D9—81no—
109C2×D9—81no—
110C4×C9—81no—
111C4×C9—81no—
112C4×C9#12111yescharacteristic
113C4×C9AGL(1,ℤ/8)11yescharacteristic
114Dic9—21no—
115Dic9—21no—
116Dic9—42no—
117C2×Q16—91no—
118C2×Q16C2×D911yescharacteristic
119C2×SD16—181no—
120C2×D8—91no—
121#124—181no—
122C4×Q8—181no—
123Q32—182no—
124SD32—182no—
125C2×C16—91no—
126C2×C16C2×D911yescharacteristic
127#107C2×D911yescharacteristic
128#103—181no—
129C4×C8—91no—
130C22×D3—121no—
131C3×Q8—41no—
132C3×Q8—41no—
133C2×C3×C4—41no—
134C2×C3×C4—41no—
135C2×C3×C4D3×D411yescharacteristic
136C2×Dic3—31no—
137C2×Dic3—31no—
138C2×Dic3—121no—
139D12—121no—
140D12—121no—
141Dic6—62no—
142Dic6—121no—
143C3×C8#23511yescharacteristic
144C3×C8D3×D411yescharacteristic
145C3⋊C8—61no—
146C2×C9#45911yescharacteristic
147C2×C9#50811yescharacteristic
148C2×C9#51011yescharacteristic
149D9—161no—
150C2×Q8—21no—
151C2×Q8—181no—
152C2×D4—181no—
153Q16—21no—
154Q16—21no—
155Q16—92no—
156Q16—181no—
157SD16—362no—
158D8—181no—
159D8—181no—
160C2×C8—91no—
161C2×C8C22×D911yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—361no—
164C22⋊C4—361no—
165C22⋊C4—361no—
166C42—91no—
167C42—361no—
168C16—21no—
169C16—181no—
170C22×C3D3×D811yescharacteristic
171C2×D3—241no—
172C2×D3—241no—
173C2×D3—241no—
174C3×C4—81no—
175C3×C4—81no—
176C3×C4#88411yescharacteristic
177C3×C4#91411yescharacteristic
178Dic3—61no—
179Dic3—61no—
180Dic3—122no—
181C9#221111yescharacteristic, complemented, Sylow
182C23—361no—
183Q8—41no—
184Q8—41no—
185Q8—182no—
186Q8—361no—
187D4—361no—
188D4—361no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—361no—
194C2×C4D4×D911yescharacteristic
195C8—181no—
196C8#369711yescharacteristic
197C8D4×D911yescharacteristic
198C2×C3#478611yescharacteristic
199C2×C3#491611yescharacteristic
200C2×C3#491811yescharacteristic
201D3—481no—
202C22—721no—
203C22—721no—
204C22—721no—
205C22D8×D911yescharacteristic
206C4—81no—
207C4—81no—
208C4—181no—
209C4—181no—
210C4—362no—
211C4#6344611yescharacteristic
212C4#6347611yescharacteristic
213C3#6923711yescharacteristic
214C2—1441no—
215C2#1058846611yescharacteristic
216C2#1058859611yescharacteristic
217C2#1058859811yescharacteristic
subgroupG/H
centerC22D8×D9
commutator, cosocleC2×C8×C9C23
FrattiniC2×C3×C8C22×D3
FittingC9×#358C2
socleC22×C3D3×D8
prime radicalC2×D72C22
hypercenter#358D9
hypocenterC9#2211
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
2. C2×#63388C2semidirect
4. #10588553C2semidirect
5. C9×#358C2semidirect
6. Dic9⋊C16C2semidirect
84. #358D9semidirect
181. C9#2211semidirect

Maximal subgroups

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

subgroupindex
#105888712
C2×#633882
C2×#633592
#105885532
C9×#3582
Dic9⋊C162
#105881682
#692373