Finite Group Databasebeta

← #11799100

Subgroups — #11799100

Order 1152.

255 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 255 conjugacy classes of subgroups — too many to draw. Only its 56 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, complemented
2#10588827C211yesmaximal, characteristic, complemented
3#10588588C211yesmaximal, characteristic, complemented
4#10588575C211yesmaximal, characteristic, complemented
5C9×#361C211yesmaximal, characteristic, complemented
6#10588188C211yesmaximal, characteristic, complemented
7#10588172C211yesmaximal, characteristic, complemented
8#69263—31nomaximal
9C2×C9×D8C2211yescharacteristic
10#63502—21no—
11C2×#3673—21no—
12#63469—21no—
13#63467C2211yescharacteristic
14C2×D72C2211yescharacteristic
15C9×M32C2211yescharacteristic
16C9×#108C2211yescharacteristic
17#63386—21no—
18#63385—21no—
19#63384—21no—
20C8×Dic9C2211yescharacteristic
21#63371C2211yescharacteristic
22#63359—21no—
23D144—21no—
24#5151—31no—
25#5147—31no—
26#4908—31no—
27#4895—31no—
28C3×#361D311yescharacteristic
29#4511—31no—
30#4495—31no—
31C2×D4×C9—21no—
32C2×#611—42no—
33#3697—21no—
34C2×D36—21no—
35C9×D8—21no—
36C9×D8—21no—
37C9×M16—21no—
38C2×C8×C9C2311yescharacteristic
39#3673—41no—
40#3673—41no—
41C4×Dic9D411yescharacteristic
42C2×C9⋊C8D411yescharacteristic
43D72—21no—
44D72—21no—
45D72D411yescharacteristic, complemented
46#3664—21no—
47#3663—41no—
48C8×D9—41no—
49Dic36D411yescharacteristic, complemented
50C9×C16—21no—
51C9⋊C16—21no—
52#2213—91noSylow
53C2×C3×D8C2×D311yescharacteristic
54#940—61no—
55C2×#213—61no—
56#907—61no—
57#904—31no—
58C2×D24—31no—
59C3×M32C2×D311yescharacteristic
60C3×#108C2×D311yescharacteristic
61#827—61no—
62#826—61no—
63#825—61no—
64C8×Dic3—31no—
65#812—31no—
66#800—61no—
67D48—61no—
68C23×C9—41no—
69C22×D9—41no—
70D4×C9—41no—
71D4×C9—41no—
72C2×C4×C9C2×D411yescharacteristic
73#611—41no—
74#611—84no—
75C2×Dic9—21no—
76D36—21no—
77D36—41no—
78D36—41no—
79C4×D9—41no—
80Dic18—21no—
81C8×C9—41no—
82C8×C9C2×D411yescharacteristic
83C8×C9#4111yescharacteristic
84C9⋊C8D811yescharacteristic
85C9⋊C8D811yescharacteristic
86#509—91no—
87#509—91no—
88#493—91no—
89#443—91no—
90#364—91no—
91#361—91no—
92#361D911yescharacteristic, complemented
93C2×C3×D4—21no—
94C2×#67—122no—
95#235—61no—
96C2×D12—61no—
97C3×D8—21no—
98C3×D8—21no—
99C3×M16—21no—
100C2×C3×C8C22×D311yescharacteristic
101#213—121no—
102#213—121no—
103C4×Dic3—31no—
104C2×C3⋊C8—31no—
105Dic12—31no—
106D24—31no—
107D24—61no—
108D24—61no—
109#204—61no—
110ΓL(1,𝔽25)—121no—
111D3×C8—121no—
112C3×C16—21no—
113C3⋊C16—61no—
114C22×C9—82no—
115C22×C9—81no—
116C22×C9AGL(1,ℤ/8)11yescharacteristic
117C2×D9—41no—
118C2×D9—82no—
119C2×D9—81no—
120C4×C9#12111yescharacteristic
121C4×C9C2×D811yescharacteristic
122Dic9—22no—
123Dic9—41no—
124#135—91no—
125C2×D8—91no—
126C2×D8—181no—
127C2×D8C2×D911yescharacteristic
128#131—181no—
129#127—181no—
130SD32—181no—
131SD32—181no—
132D16—181no—
133D16—181no—
134M32—91no—
135M32C2×D911yescharacteristic
136#108C2×D911yescharacteristic
137#104—181no—
138C4×C8—91no—
139C23×C3—41no—
140C22×D3—121no—
141C3×D4—41no—
142C3×D4—41no—
143C2×C3×C4D3×D411yescharacteristic
144#67—121no—
145#67—244no—
146C2×Dic3—61no—
147D12—61no—
148D12—121no—
149D12—121no—
150C4×D3—121no—
151Dic6—61no—
152C3×C8—41no—
153C3×C8#23511yescharacteristic
154C3×C8D3×D411yescharacteristic
155C3⋊C8—31no—
156C3⋊C8—31no—
157C2×C9—21no—
158C2×C9—161no—
159C2×C9#45911yescharacteristic
160D9—81no—
161D9—161no—
162#41—181no—
163C2×D4—21no—
164C2×D4—181no—
165C2×D4—362no—
166Q16—91no—
167SD16—181no—
168D8—21no—
169D8—21no—
170D8—91no—
171D8—181no—
172D8—181no—
173D8—361no—
174D8—361no—
175M16—21no—
176M16—361no—
177C2×C8—91no—
178C2×C8—361no—
179C2×C8C22×D911yescharacteristic
180C42—91no—
181C16—21no—
182C16—181no—
183C22×C3—82no—
184C22×C3—81no—
185C22×C3#91411yescharacteristic
186C2×D3—121no—
187C2×D3—242no—
188C2×D3—241no—
189C3×C4#88411yescharacteristic
190C3×C4D3×D811yescharacteristic
191Dic3—62no—
192Dic3—121no—
193C9#221311yescharacteristic, complemented, Sylow
194C23—41no—
195C23—361no—
196Q8—181no—
197D4—41no—
198D4—41no—
199D4—181no—
200D4—361no—
201D4—361no—
202D4—361no—
203D4—724no—
204C2×C4—181no—
205C2×C4—361no—
206C2×C4D4×D911yescharacteristic
207C8—41no—
208C8—91no—
209C8—91no—
210C8#369711yescharacteristic
211C8D4×D911yescharacteristic
212C2×C3—21no—
213C2×C3—161no—
214C2×C3#478611yescharacteristic
215D3—241no—
216D3—481no—
217C22—82no—
218C22—81no—
219C22—361no—
220C22—722no—
221C22—721no—
222C22#6347611yescharacteristic
223C4—182no—
224C4—361no—
225C4#6344611yescharacteristic
226C4D8×D911yescharacteristic
227C3#6926311yescharacteristic
228C2—21no—
229C2—161no—
230C2—721no—
231C2—1441no—
232C2#1058846611yescharacteristic
subgroupG/H
centerC2#10588466
commutator, cosocleC2×C8×C9C23
FrattiniC2×C3×C8C22×D3
FittingC9×#361C2
socleC2×C3#4786
hypercenter#361D9
hypocenterC9#2213
LCSG ▷ C2×C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #10588831C2semidirect
2. #10588827C2semidirect
3. #10588588C2semidirect
4. #10588575C2semidirect
5. C9×#361C2semidirect
6. #10588188C2semidirect
7. #10588172C2semidirect
45. D72D4semidirect
49. Dic36D4semidirect
92. #361D9semidirect
193. C9#2213semidirect

Maximal subgroups

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

subgroupindex
#105888312
#105888272
#105885882
#105885752
C9×#3612
#105881882
#105881722
#692633