Finite Group Databasebeta

← #11799378

Subgroups — #11799378

Order 1152.

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

normal subgroups only

This group has 222 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#10588840C211yesmaximal, characteristic, complemented
2C2×#63385C211yesmaximal, characteristic, complemented
3#10588587C211yesmaximal, characteristic, complemented
4#10588577C211yesmaximal, characteristic, complemented
5C9×#361C211yesmaximal, characteristic, complemented
6#10588193C211yesmaximal, characteristic, complemented
7#10588170C211yesmaximal, characteristic, complemented
8#69260—31nomaximal
9C2×C9×D8C2211yescharacteristic
10#63495—21no—
11#63470—21no—
12C2×D72C2211yescharacteristic
13#63464C2211yescharacteristic
14C9×M32C2211yescharacteristic
15C9×#108C2211yescharacteristic
16#63391—21no—
17#63385—21no—
18#63385—21no—
19#63383—21no—
20#63372C2211yescharacteristic
21C2×C9⋊C16C2211yescharacteristic
22#63357—21no—
23C16×D9—21no—
24#5160—31no—
25C2×#826—31no—
26#4907—31no—
27#4897—31no—
28C3×#361D311yescharacteristic
29#4516—31no—
30#4493—31no—
31C2×D4×C9—21no—
32#3697D411yescharacteristic
33C2×D36—21no—
34C9×D8—21no—
35C9×D8—21no—
36C9×M16—21no—
37C2×C8×C9C2311yescharacteristic
38#3673—41no—
39#3672—41no—
40#3667—21no—
41#3667D411yescharacteristic
42D72—21no—
43D72—21no—
44D72—41no—
45#3664—41no—
46#3663—21no—
47C8×D9—21no—
48C9×C16—21no—
49C9⋊C16D411yescharacteristic
50C9⋊C16D411yescharacteristic
51#2221—91noSylow
52C2×C3×D8C2×D311yescharacteristic
53#932—61no—
54#908—61no—
55C2×D24—31no—
56#901—31no—
57C3×M32C2×D311yescharacteristic
58C3×#108C2×D311yescharacteristic
59#833—61no—
60#826—61no—
61#826—61no—
62#823—61no—
63#819—31no—
64C2×C3⋊C16—31no—
65#798—61no—
66D3×C16—61no—
67C23×C9—41no—
68C22×D9—41no—
69D4×C9—41no—
70D4×C9—41no—
71C2×C4×C9C2×D411yescharacteristic
72#611—21no—
73D36—41no—
74D36—41no—
75D36D811yescharacteristic
76C4×D9—21no—
77Dic18D811yescharacteristic
78C8×C9—41no—
79C8×C9C2×D411yescharacteristic
80C8×C9#4111yescharacteristic
81C9⋊C8—21no—
82C9⋊C8—41no—
83C2×D16—91no—
84#504—91no—
85#472—91no—
86#472—91no—
87#368—91no—
88#361—91no—
89#361D911yescharacteristic, complemented
90C2×C3×D4—21no—
91#235—31no—
92C2×D12—61no—
93C3×D8—21no—
94C3×D8—21no—
95C3×M16—21no—
96C2×C3×C8C22×D311yescharacteristic
97#214—121no—
98#213—121no—
99#208—31no—
100#208—61no—
101D24—61no—
102D24—61no—
103D24—121no—
104#204—121no—
105ΓL(1,𝔽25)—61no—
106D3×C8—61no—
107C3×C16—21no—
108C3⋊C16—31no—
109C3⋊C16—31no—
110C22×C9—81no—
111C22×C9—161no—
112C22×C9#13511yescharacteristic
113C2×D9—21no—
114C2×D9—81no—
115C2×D9—161no—
116C4×C9#12111yescharacteristic
117C4×C9C2×D811yescharacteristic
118Dic9—21no—
119AGL(1,ℤ/8)—181no—
120AGL(1,ℤ/8)—181no—
121C2×D8—91no—
122C2×D8C2×D911yescharacteristic
123#131—91no—
124D16—181no—
125D16—181no—
126M32—181no—
127M32C2×D911yescharacteristic
128C2×C16—91no—
129C2×C16—181no—
130#108—91no—
131#108C2×D911yescharacteristic
132#100—181no—
133#100—181no—
134C23×C3—41no—
135C22×D3—121no—
136C3×D4—41no—
137C3×D4—41no—
138C2×C3×C4D3×D411yescharacteristic
139#67—61no—
140D12—31no—
141D12—121no—
142D12—121no—
143C4×D3—61no—
144Dic6—31no—
145C3×C8—41no—
146C3×C8#23511yescharacteristic
147C3×C8D3×D411yescharacteristic
148C3⋊C8—61no—
149C3⋊C8—121no—
150C2×C9—21no—
151C2×C9—161no—
152C2×C9#46611yescharacteristic
153D9—41no—
154D9—161no—
155#41—91no—
156C2×D4—21no—
157C2×D4—181no—
158SD16—361no—
159SD16—361no—
160D8—21no—
161D8—21no—
162D8—181no—
163D8—181no—
164D8—361no—
165D8—361no—
166M16—21no—
167M16—91no—
168M16—181no—
169M16—181no—
170C2×C8—181no—
171C2×C8C22×D911yescharacteristic
172C16—21no—
173C16—91no—
174C16—91no—
175C22×C3—81no—
176C22×C3—161no—
177C22×C3#91611yescharacteristic
178C2×D3—61no—
179C2×D3—241no—
180C2×D3—481no—
181C3×C4#88411yescharacteristic
182C3×C4D3×D811yescharacteristic
183Dic3—61no—
184C9#222111yescharacteristic, complemented, Sylow
185C23—41no—
186C23—361no—
187Q8—91no—
188D4—41no—
189D4—41no—
190D4—91no—
191D4—181no—
192D4—361no—
193D4—361no—
194C2×C4—181no—
195C2×C4D4×D911yescharacteristic
196C8—41no—
197C8—181no—
198C8—361no—
199C8#369711yescharacteristic
200C8D4×D911yescharacteristic
201C2×C3—21no—
202C2×C3—161no—
203C2×C3#477511yescharacteristic
204D3—121no—
205D3—481no—
206C22—81no—
207C22—161no—
208C22—181no—
209C22—721no—
210C22—1441no—
211C22#6347811yescharacteristic
212C4—181no—
213C4#6344611yescharacteristic
214C4D8×D911yescharacteristic
215C3#6926011yescharacteristic
216C2—21no—
217C2—161no—
218C2—361no—
219C2—1441no—
220C2#1058845511yescharacteristic
subgroupG/H
centerC2#10588455
commutator, cosocleC2×C8×C9C23
FrattiniC2×C3×C8C22×D3
FittingC9×#361C2
socleC2×C3#4775
hypercenter#361D9
hypocenterC9#2221
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. #10588840C2semidirect
2. C2×#63385C2semidirect
3. #10588587C2semidirect
4. #10588577C2semidirect
5. C9×#361C2semidirect
6. #10588193C2semidirect
7. #10588170C2semidirect
89. #361D9semidirect
184. C9#2221semidirect

Maximal subgroups

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

subgroupindex
#105888402
C2×#633852
#105885872
#105885772
C9×#3612
#105881932
#105881702
#692603