Finite Group Databasebeta

← #11799442

Subgroups — #11799442

Order 1152.

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

normal subgroups only

This group has 216 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
2C2×#63386C211yesmaximal, characteristic, complemented
3#10588587C211yesmaximal, characteristic, complemented
4#10588576C211yesmaximal, characteristic, complemented
5C9×#361C211yesmaximal, characteristic, complemented
6#10588195C211yesmaximal, characteristic, complemented
7#10588170C211yesmaximal, characteristic, complemented
8#69261—31nomaximal
9C2×C9×D8C2211yescharacteristic
10#63495—21no—
11#63471—21no—
12#63464C2211yescharacteristic
13C2×Dic36C2211yescharacteristic
14C9×M32C2211yescharacteristic
15C9×#108C2211yescharacteristic
16#63391—21no—
17#63386—21no—
18#63386—21no—
19#63382—21no—
20#63372C2211yescharacteristic
21C2×C9⋊C16C2211yescharacteristic
22#63357—21no—
23C16×D9—21no—
24#5160—31no—
25C2×#827—31no—
26#4907—31no—
27#4896—31no—
28C3×#361D311yescharacteristic
29#4517—31no—
30#4493—31no—
31C2×D4×C9—21no—
32#3697D411yescharacteristic
33C2×Dic18—21no—
34C9×D8—21no—
35C9×D8—21no—
36C9×M16—21no—
37C2×C8×C9C2311yescharacteristic
38#3673—41no—
39#3672—41no—
40#3667—21no—
41#3667D411yescharacteristic
42#3664—41no—
43#3663—21no—
44C8×D9—21no—
45Dic36—21no—
46Dic36—21no—
47Dic36—41no—
48C9×C16—21no—
49C9⋊C16D411yescharacteristic
50C9⋊C16D411yescharacteristic
51#2223—91noSylow
52C2×C3×D8C2×D311yescharacteristic
53#932—61no—
54#909—61no—
55C2×Dic12—31no—
56#901—31no—
57C3×M32C2×D311yescharacteristic
58C3×#108C2×D311yescharacteristic
59#833—61no—
60#827—61no—
61#827—61no—
62#824—61no—
63#819—31no—
64C2×C3⋊C16—31no—
65#798—61no—
66D3×C16—61no—
67C23×C9—41no—
68D4×C9—41no—
69D4×C9—41no—
70C2×C4×C9C2×D411yescharacteristic
71#611—21no—
72C2×Dic9—41no—
73D36D811yescharacteristic
74C4×D9—21no—
75Dic18—41no—
76Dic18—41no—
77Dic18D811yescharacteristic
78C8×C9—41no—
79C8×C9C2×D411yescharacteristic
80C8×C9#4111yescharacteristic
81C9⋊C8—21no—
82C9⋊C8—41no—
83C2×SD32—91no—
84#504—91no—
85#473—91no—
86#472—91no—
87#368—91no—
88#362—91no—
89#361D911yescharacteristic, complemented
90C2×C3×D4—21no—
91#235—31no—
92C2×Dic6—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—
101Dic12—61no—
102Dic12—61no—
103Dic12—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—
114C4×C9#12111yescharacteristic
115C4×C9C2×D811yescharacteristic
116Dic9—21no—
117Dic9—81no—
118#137—181no—
119AGL(1,ℤ/8)—181no—
120C2×Q16—91no—
121C2×D8C2×D911yescharacteristic
122#131—91no—
123SD32—181no—
124SD32—181no—
125M32—181no—
126M32C2×D911yescharacteristic
127C2×C16—91no—
128C2×C16—181no—
129#108—91no—
130#108C2×D911yescharacteristic
131#101—181no—
132#100—181no—
133C23×C3—41no—
134C3×D4—41no—
135C3×D4—41no—
136C2×C3×C4D3×D411yescharacteristic
137#67—61no—
138C2×Dic3—121no—
139D12—31no—
140C4×D3—61no—
141Dic6—31no—
142Dic6—121no—
143Dic6—121no—
144C3×C8—41no—
145C3×C8#23511yescharacteristic
146C3×C8D3×D411yescharacteristic
147C3⋊C8—61no—
148C3⋊C8—121no—
149C2×C9—21no—
150C2×C9—161no—
151C2×C9#46611yescharacteristic
152D9—41no—
153#41—91no—
154C2×Q8—181no—
155C2×D4—21no—
156Q16—181no—
157Q16—181no—
158Q16—361no—
159SD16—361no—
160SD16—361no—
161D8—21no—
162D8—21no—
163D8—361no—
164M16—21no—
165M16—91no—
166M16—181no—
167M16—181no—
168C2×C8—181no—
169C2×C8C22×D911yescharacteristic
170C16—21no—
171C16—91no—
172C16—91no—
173C22×C3—81no—
174C22×C3—161no—
175C22×C3#91611yescharacteristic
176C2×D3—61no—
177C3×C4#88411yescharacteristic
178C3×C4D3×D811yescharacteristic
179Dic3—61no—
180Dic3—241no—
181C9#222311yescharacteristic, complemented, Sylow
182C23—41no—
183Q8—91no—
184Q8—361no—
185Q8—361no—
186D4—41no—
187D4—41no—
188D4—91no—
189D4—181no—
190C2×C4—181no—
191C2×C4—361no—
192C2×C4D4×D911yescharacteristic
193C8—41no—
194C8—181no—
195C8—361no—
196C8#369711yescharacteristic
197C8D4×D911yescharacteristic
198C2×C3—21no—
199C2×C3—161no—
200C2×C3#477511yescharacteristic
201D3—121no—
202C22—81no—
203C22—161no—
204C22—181no—
205C22#6347811yescharacteristic
206C4—181no—
207C4—721no—
208C4#6344611yescharacteristic
209C4D8×D911yescharacteristic
210C3#6926111yescharacteristic
211C2—21no—
212C2—161no—
213C2—361no—
214C2#1058845511yescharacteristic
subgroupG/H
centerC2#10588455
commutator, cosocleC2×C8×C9C23
FrattiniC2×C3×C8C22×D3
FittingC9×#361C2
socleC2×C3#4775
prime radical#10588840C2
hypercenter#361D9
hypocenterC9#2223
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
2. C2×#63386C2semidirect
3. #10588587C2semidirect
4. #10588576C2semidirect
5. C9×#361C2semidirect
6. #10588195C2semidirect
7. #10588170C2semidirect
89. #361D9semidirect
181. C9#2223semidirect

Maximal subgroups

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

subgroupindex
#105888402
C2×#633862
#105885872
#105885762
C9×#3612
#105881952
#105881702
#692613