Finite Group Databasebeta

← #11782626

Subgroups — #11782626

Order 1152.

297 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 297 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C9×#487C211yesmaximal, characteristic, complemented
2#10588773C211yesmaximal, characteristic
3#10588770C211yesmaximal, characteristic
4#10588760C211yesmaximal, characteristic, complemented
5#10588758C211yesmaximal, characteristic, complemented
6#10588375C211yesmaximal, characteristic
7#10588131C211yesmaximal, characteristic, complemented
8#71216—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C9×C4⋊Q8C2211yescharacteristic
11C2×#3675—22no—
12C2×#3664—22no—
13#63436C2211yescharacteristic
14#63431C2211yescharacteristic
15C9×#103—22no—
16C4×C8×C9C2211yescharacteristic
17#63369—22no—
18#63367—22no—
19#63366—22no—
20C4×C9⋊C8C2211yescharacteristic
21C4×C9⋊C8C2211yescharacteristic
22C3×#487D311yescharacteristic
23#5088—31no—
24#5085—31no—
25#5080—31no—
26#5078—31no—
27#4693—31no—
28#4454—31no—
29C2×Q8×C9—21no—
30C2×Q8×C9—21no—
31C2×D36—21no—
32C2×D36—21no—
33C2×D36—21no—
34C2×Dic18—21no—
35C2×C8×C9D412yes—
36C9×C4⋊C4—21no—
37C9×C4⋊C4—21no—
38C9×C4⋊C4—21no—
39C9×C4⋊C4—21no—
40C42×C9C2311yescharacteristic
41#3675—44no—
42C4⋊Dic9—21no—
43C4⋊Dic9—21no—
44C2×C9⋊C8D412yes—
45C2×C9⋊C8D412yes—
46#3664—44no—
47#1714—91noSylow
48C3×C4⋊Q8C2×D311yescharacteristic
49C3×C4⋊Q8C2×D311yescharacteristic
50C2×#215—62no—
51C2×#204—62no—
52#874—31no—
53#869—31no—
54C3×#103—22no—
55C3×C4×C8C2×D311yescharacteristic
56#809—62no—
57#808—62no—
58#807—62no—
59C4×C3⋊C8—31no—
60C4×C3⋊C8—31no—
61C22×D9—41no—
62Q8×C9—42no—
63Q8×C9—42no—
64C2×C4×C9—41no—
65C2×C4×C9—41no—
66C2×C4×C9C2×D411yescharacteristic
67C2×C4×C9C2×D411yescharacteristic
68C2×C4×C9C2×D411yescharacteristic
69C2×Dic9—41no—
70D36—42no—
71D36—42no—
72D36—42no—
73Dic18—42no—
74C8×C9—22no—
75C9⋊C8—22no—
76C9⋊C8SD1614yescomplemented
77#500—91no—
78#498—91no—
79#492—91no—
80#492—91no—
81#487D911yescharacteristic, complemented
82#486—91no—
83#322—91no—
84C2×C3×Q8—21no—
85C2×C3×Q8—21no—
86C2×D12—61no—
87C2×D12—61no—
88C2×D12—61no—
89C2×Dic6—61no—
90C2×C3×C8#6712yes—
91C3×C4⋊C4—21no—
92C3×C4⋊C4—21no—
93C3×C4⋊C4—21no—
94C3×C4⋊C4—21no—
95C3×C42C22×D311yescharacteristic
96#215—124no—
97C4⋊Dic3—61no—
98C4⋊Dic3—61no—
99C2×C3⋊C8—32no—
100C2×C3⋊C8—32no—
101#204—124no—
102C22×C9#12711yescharacteristic
103C2×D9—81no—
104C2×D9—81no—
105C2×D9—81no—
106C4×C9—81no—
107C4×C9—81no—
108C4×C9C2×SD1612yes—
109C4×C9AGL(1,ℤ/8)12yes—
110C4×C9#13712yes—
111Dic9—81no—
112C2×SD16—182no—
113C2×SD16—182no—
114C4⋊Q8—91no—
115C4⋊Q8C2×D911yescharacteristic
116C4⋊Q8C2×D911yescharacteristic
117#127—91no—
118#107—182no—
119#106—182no—
120#103—22no—
121#102—182no—
122C4×C8—91no—
123C4×C8—91no—
124C4×C8C2×D911yescharacteristic
125C22×D3—121no—
126C3×Q8—42no—
127C3×Q8—42no—
128C2×C3×C4—41no—
129C2×C3×C4—41no—
130C2×C3×C4D3×D411yescharacteristic
131C2×C3×C4D3×D411yescharacteristic
132C2×C3×C4C2×#6711yescharacteristic
133C2×Dic3—121no—
134D12—122no—
135D12—122no—
136D12—122no—
137Dic6—122no—
138C3×C8—22no—
139C3⋊C8—34no—
140C3⋊C8—62no—
141C2×C9#49211yescharacteristic
142C2×C9#49611yescharacteristic
143C2×C9#49711yescharacteristic
144D9—161no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—181no—
148C2×D4—181no—
149C2×D4—181no—
150C2×D4—181no—
151SD16—364no—
152SD16—364no—
153C2×C8—92no—
154C2×C8—92no—
155C2×C8#61112yes—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—181no—
161C4⋊C4—181no—
162C42C22×D911yescharacteristic
163C22×C3#94011yescharacteristic
164C2×D3—241no—
165C2×D3—241no—
166C2×D3—241no—
167C3×C4—81no—
168C3×C4—81no—
169C3×C4D3×SD1612yes—
170C3×C4#91812yes—
171C3×C4#94912yes—
172Dic3—241no—
173C9#171411yescharacteristic, complemented, Sylow
174C23—361no—
175Q8—42no—
176Q8—42no—
177Q8—362no—
178D4—362no—
179D4—362no—
180D4—362no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—361no—
184C2×C4D4×D911yescharacteristic
185C2×C4D4×D911yescharacteristic
186C2×C4C2×#61111yescharacteristic
187C8—22no—
188C8—94no—
189C8—182no—
190C2×C3#505811yescharacteristic
191C2×C3#517511yescharacteristic
192C2×C3#519011yescharacteristic
193D3—481no—
194C22—721no—
195C22—721no—
196C22—721no—
197C22#6350211yescharacteristic
198C4—81no—
199C4—81no—
200C4—721no—
201C4SD16×D912yes—
202C4#6348012yes—
203C4#6351212yes—
204C3#7121611yescharacteristic
205C2—1441no—
206C2#1058873911yescharacteristic
207C2#1058885511yescharacteristic
208C2#1058887011yescharacteristic
subgroupG/H
centerC22#63502
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#487C2
socleC22×C3#940
prime radical#63436C22
hypercenter#487D9
hypocenterC9#1714
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. C9×#487C2semidirect
4. #10588760C2semidirect
5. #10588758C2semidirect
7. #10588131C2semidirect
76. C9⋊C8SD16semidirect
81. #487D9semidirect
173. C9#1714semidirect

Maximal subgroups

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

subgroupindex
C9×#4872
#105887732
#105887702
#105887602
#105887582
#105883752
#105881312
#712163