Finite Group Databasebeta

← #11799736

Subgroups — #11799736

Order 1152.

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

normal subgroups only

This group has 180 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#10588575C211yesmaximal, characteristic
2#10588538C211yesmaximal, characteristic, complemented
3C9×#365C211yesmaximal, characteristic, complemented
4#10588194C211yesmaximal, characteristic
5#10588188C211yesmaximal, characteristic, complemented
6#10588171C211yesmaximal, characteristic, complemented
7#10588165C211yesmaximal, characteristic
8#69316—31nomaximal
9#63469—21no—
10#63467C2211yescharacteristic
11#63452—21no—
12C9×M32C2211yescharacteristic
13C9×#108C2211yescharacteristic
14C9×#106C2211yescharacteristic
15#63384—21no—
16#63377C2211yescharacteristic
17C8×Dic9C2211yescharacteristic
18#63371C2211yescharacteristic
19#63366—21no—
20#4895—31no—
21#4858—31no—
22C3×#365D311yescharacteristic
23#4518—31no—
24#4511—31no—
25#4494—31no—
26#4488—31no—
27#3697—21no—
28C9×M16—21no—
29C2×C8×C9C2311yescharacteristic
30C9×C4⋊C4—21no—
31C4⋊Dic9—21no—
32C4⋊Dic9—41no—
33Dic9⋊C4—41no—
34C4×Dic9D411yescharacteristic
35C2×C9⋊C8D411yescharacteristic
36D72Q811yescharacteristic
37#3664—21no—
38#3663—41no—
39C8×D9—41no—
40Dic36Q811yescharacteristic
41C9×C16—21no—
42C9⋊C16—21no—
43#2231—91noSylow
44#907—61no—
45#904—31no—
46#890—61no—
47C3×M32C2×D311yescharacteristic
48C3×#108C2×D311yescharacteristic
49C3×#106C2×D311yescharacteristic
50#825—61no—
51#817—31no—
52C8×Dic3—31no—
53#812—31no—
54#807—61no—
55C2×C4×C9—41no—
56C2×C4×C9C2×D411yescharacteristic
57#611—41no—
58C2×Dic9—21no—
59C2×Dic9—41no—
60D36—21no—
61C4×D9—41no—
62Dic18—21no—
63C8×C9—41no—
64C8×C9C2×Q811yescharacteristic
65C8×C9#4111yescharacteristic
66C9⋊C8SD1611yescharacteristic
67C9⋊C8SD1611yescharacteristic
68#499—91no—
69#443—91no—
70#365—91no—
71#365D911yescharacteristic, complemented
72#364—91no—
73#360—91no—
74#360—91no—
75#235—61no—
76C3×M16—21no—
77C2×C3×C8C22×D311yescharacteristic
78C3×C4⋊C4—21no—
79C4⋊Dic3—61no—
80C4⋊Dic3—121no—
81Dic3⋊C4—121no—
82C4×Dic3—31no—
83C2×C3⋊C8—31no—
84Dic12—31no—
85D24—31no—
86#204—61no—
87ΓL(1,𝔽25)—121no—
88D3×C8—121no—
89C3×C16—21no—
90C3⋊C16—61no—
91C22×C9AGL(1,ℤ/8)11yescharacteristic
92C2×D9—41no—
93C4×C9—81no—
94C4×C9C22⋊Q811yescharacteristic
95C4×C9C2×SD1611yescharacteristic
96Dic9—41no—
97Dic9—41no—
98Dic9—81no—
99#135—91no—
100#131—181no—
101#125—181no—
102M32—91no—
103M32C2×D911yescharacteristic
104#108C2×D911yescharacteristic
105#107—181no—
106#106—91no—
107#106C2×D911yescharacteristic
108#104—181no—
109C4×C8—91no—
110C2×C3×C4—41no—
111C2×C3×C4D3×D411yescharacteristic
112#67—121no—
113C2×Dic3—61no—
114C2×Dic3—121no—
115D12—61no—
116C4×D3—121no—
117Dic6—61no—
118C3×C8—41no—
119C3×C8#23511yescharacteristic
120C3×C8D3×Q811yescharacteristic
121C3⋊C8—31no—
122C3⋊C8—31no—
123C2×C9—21no—
124C2×C9#47611yescharacteristic
125D9—81no—
126#41—181no—
127Q16—91no—
128SD16—181no—
129D8—91no—
130M16—21no—
131M16—361no—
132C2×C8—91no—
133C2×C8—361no—
134C2×C8C22×D911yescharacteristic
135C4⋊C4—21no—
136C4⋊C4—181no—
137C4⋊C4—361no—
138C4⋊C4—361no—
139C42—91no—
140C16—21no—
141C16—181no—
142C22×C3#91411yescharacteristic
143C2×D3—121no—
144C3×C4—81no—
145C3×C4#89611yescharacteristic
146C3×C4D3×SD1611yescharacteristic
147Dic3—121no—
148Dic3—121no—
149Dic3—241no—
150C9#223111yescharacteristic, complemented, Sylow
151Q8—181no—
152D4—181no—
153D4—361no—
154C2×C4—41no—
155C2×C4—181no—
156C2×C4—361no—
157C2×C4—361no—
158C2×C4D4×D911yescharacteristic
159C8—41no—
160C8—91no—
161C8—91no—
162C8#369711yescharacteristic
163C8Q8×D911yescharacteristic
164C2×C3—21no—
165C2×C3#487011yescharacteristic
166D3—241no—
167C22—361no—
168C22#6347611yescharacteristic
169C4—81no—
170C4—361no—
171C4—361no—
172C4—721no—
173C4#6345811yescharacteristic
174C4SD16×D911yescharacteristic
175C3#6931611yescharacteristic
176C2—21no—
177C2—721no—
178C2#1058855011yescharacteristic
subgroupG/H
centerC2#10588550
commutator, cosocleC2×C8×C9C23
FrattiniC2×C3×C8C22×D3
FittingC9×#365C2
socleC2×C3#4870
prime radical#63467C22
hypercenter#365D9
hypocenterC9#2231
LCSG ▷ C2×C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
2. #10588538C2semidirect
3. C9×#365C2semidirect
5. #10588188C2semidirect
6. #10588171C2semidirect
71. #365D9semidirect
150. C9#2231semidirect

Maximal subgroups

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

subgroupindex
#105885752
#105885382
C9×#3652
#105881942
#105881882
#105881712
#105881652
#693163