Finite Group Databasebeta

← #11798871

Subgroups — #11798871

Order 1152.

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

normal subgroups only

This group has 261 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#10588831C211yesmaximal, characteristic
2C2×#63386C211yesmaximal, characteristic, complemented
3C2×#63359C211yesmaximal, characteristic, complemented
4#10588553C211yesmaximal, characteristic, complemented
5C9×#357C211yesmaximal, characteristic, complemented
6Dic9⋊C16C211yesmaximal, characteristic, complemented
7#10588168C211yesmaximal, characteristic, complemented
8#69204—31nomaximal
9C2×C9×D8C2211yescharacteristic
10#63502—21no—
11C2×#3673—21no—
12C2×D72C2211yescharacteristic
13C2×Dic36C2211yescharacteristic
14#63449—21no—
15C2×C9×C16C2211yescharacteristic
16C9×#107C2211yescharacteristic
17#63386—22no—
18C8×Dic9C2211yescharacteristic
19C2×C9⋊C16C2211yescharacteristic
20#63368—21no—
21#63359—22no—
22#5151—31no—
23C2×#827—31no—
24C2×#800—31no—
25#4873—31no—
26C3×#357D311yescharacteristic
27Dic3⋊C16—31no—
28#4491—31no—
29C2×D4×C9—21no—
30C2×#611—41no—
31C2×#611—41no—
32C2×D36—21no—
33C2×Dic18—21no—
34C9×D8—21no—
35C9×D8—21no—
36C2×C8×C9C2311yescharacteristic
37C9×C4⋊C4—21no—
38#3673—42no—
39Dic9⋊C4—41no—
40C4×Dic9—41no—
41C4×Dic9D411yescharacteristic
42C2×C9⋊C8D411yescharacteristic
43D72—21no—
44D72—21no—
45Dic36—21no—
46Dic36D412yescomplemented
47C9×C16—21no—
48C9⋊C16—21no—
49#2207—91noSylow
50C2×C3×D8C2×D311yescharacteristic
51#940—61no—
52C2×#213—61no—
53C2×Dic12—31no—
54C2×D24—31no—
55#887—61no—
56C2×C3×C16C2×D311yescharacteristic
57C3×#107C2×D311yescharacteristic
58#827—62no—
59C8×Dic3—31no—
60C2×C3⋊C16—31no—
61#810—61no—
62#800—62no—
63C23×C9—41no—
64C22×D9—41no—
65D4×C9—41no—
66D4×C9—41no—
67C2×C4×C9—41no—
68C2×C4×C9C2×D411yescharacteristic
69#611—82no—
70#611—82no—
71C2×Dic9—41no—
72C2×Dic9D811yescharacteristic
73C2×Dic9D811yescharacteristic
74D36—41no—
75D36—41no—
76Dic18—22no—
77Dic18—41no—
78C8×C9C2×D411yescharacteristic
79C8×C9#4111yescharacteristic
80C9⋊C8—21no—
81C2×SD32—91no—
82C2×SD32—91no—
83#493—91no—
84C4×Q16—91no—
85C4⋊C16—91no—
86#357—91no—
87#357D911yescharacteristic, complemented
88C2×C3×D4—21no—
89C2×#67—121no—
90C2×#67—121no—
91C2×D12—61no—
92C2×Dic6—61no—
93C3×D8—21no—
94C3×D8—21no—
95C2×C3×C8C22×D311yescharacteristic
96C3×C4⋊C4—21no—
97#213—122no—
98Dic3⋊C4—121no—
99C4×Dic3—31no—
100C4×Dic3—121no—
101C2×C3⋊C8—31no—
102Dic12—32no—
103Dic12—61no—
104D24—61no—
105D24—61no—
106C3×C16—21no—
107C3⋊C16—61no—
108C22×C9—81no—
109C22×C9—81no—
110C22×C9—81no—
111C22×C9C2×D811yescharacteristic
112C2×D9—81no—
113C2×D9—81no—
114C2×D9—81no—
115C4×C9—81no—
116C4×C9#12111yescharacteristic
117C4×C9AGL(1,ℤ/8)11yescharacteristic
118Dic9—21no—
119Dic9—42no—
120Dic9SD3212yescomplemented
121C2×Q16—91no—
122C2×D8—91no—
123C2×D8—181no—
124C2×D8C2×D911yescharacteristic
125#127—181no—
126C4×Q8—181no—
127SD32—182no—
128SD32—182no—
129C2×C16—91no—
130C2×C16C2×D911yescharacteristic
131#107C2×D911yescharacteristic
132#103—181no—
133C4×C8—91no—
134C23×C3—41no—
135C22×D3—121no—
136C3×D4—41no—
137C3×D4—41no—
138C2×C3×C4—41no—
139C2×C3×C4D3×D411yescharacteristic
140#67—242no—
141#67—242no—
142C2×Dic3—31no—
143C2×Dic3—31no—
144C2×Dic3—121no—
145D12—121no—
146D12—121no—
147Dic6—62no—
148Dic6—121no—
149C3×C8#23511yescharacteristic
150C3×C8D3×D411yescharacteristic
151C3⋊C8—61no—
152C2×C9—161no—
153C2×C9#45911yescharacteristic
154C2×C9C2×SD3211yescharacteristic
155C2×C9#50911yescharacteristic
156D9—161no—
157C2×Q8—181no—
158C2×D4—21no—
159C2×D4—181no—
160C2×D4—361no—
161C2×D4—361no—
162Q16—92no—
163Q16—181no—
164D8—21no—
165D8—21no—
166D8—181no—
167D8—181no—
168D8—362no—
169C2×C8—91no—
170C2×C8C22×D911yescharacteristic
171C4⋊C4—21no—
172C4⋊C4—361no—
173C42—91no—
174C42—361no—
175C16—21no—
176C16—181no—
177C22×C3—81no—
178C22×C3—81no—
179C22×C3—81no—
180C22×C3D3×D811yescharacteristic
181C2×D3—241no—
182C2×D3—241no—
183C2×D3—241no—
184C3×C4—81no—
185C3×C4#88411yescharacteristic
186C3×C4#91411yescharacteristic
187Dic3—32no—
188Dic3—61no—
189Dic3—122no—
190C9#220711yescharacteristic, complemented, Sylow
191C23—41no—
192C23—361no—
193Q8—182no—
194Q8—361no—
195D4—41no—
196D4—41no—
197D4—361no—
198D4—361no—
199D4—722no—
200D4—722no—
201C2×C4—41no—
202C2×C4—91no—
203C2×C4—91no—
204C2×C4—361no—
205C2×C4D4×D911yescharacteristic
206C8—181no—
207C8#369711yescharacteristic
208C8D4×D911yescharacteristic
209C2×C3—161no—
210C2×C3#478611yescharacteristic
211C2×C3#491111yescharacteristic
212C2×C3D3×SD3211yescharacteristic
213D3—481no—
214C22—81no—
215C22—81no—
216C22—81no—
217C22—721no—
218C22—721no—
219C22—721no—
220C22D8×D911yescharacteristic
221C4—81no—
222C4—92no—
223C4—181no—
224C4—362no—
225C4#6344611yescharacteristic
226C4#6347611yescharacteristic
227C3#6920411yescharacteristic
228C2—161no—
229C2—1441no—
230C2#1058846611yescharacteristic
231C2#1058859111yescharacteristic
232C2D9×SD3211yescharacteristic
subgroupG/H
centerC22D8×D9
commutator, cosocleC2×C8×C9C23
FrattiniC2×C3×C8C22×D3
FittingC9×#357C2
socleC22×C3D3×D8
prime radical#10588831C2
hypercenter#357D9
hypocenterC9#2207
LCSG ▷ C2×C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C2×#63386C2semidirect
3. C2×#63359C2semidirect
4. #10588553C2semidirect
5. C9×#357C2semidirect
6. Dic9⋊C16C2semidirect
7. #10588168C2semidirect
46. Dic36D4semidirect
87. #357D9semidirect
120. Dic9SD32semidirect
190. C9#2207semidirect

Maximal subgroups

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

subgroupindex
#105888312
C2×#633862
C2×#633592
#105885532
C9×#3572
Dic9⋊C162
#105881682
#692043