Finite Group Databasebeta

← #11782669

Subgroups — #11782669

Order 1152.

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

normal subgroups only

This group has 330 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×#486C211yesmaximal, characteristic, complemented
2#10588770C211yesmaximal, characteristic, complemented
3#10588760C211yesmaximal, characteristic, complemented
4#10588755C211yesmaximal, characteristic
5#10588750C211yesmaximal, characteristic, complemented
6#10588375C211yesmaximal, characteristic, complemented
7#10588131C211yesmaximal, characteristic, complemented
8#71185—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C9×#127C2211yescharacteristic
11C2×#3675—22no—
12C2×#3673—22no—
13C2×#3664—22no—
14#63436C2211yescharacteristic
15#63431C2211yescharacteristic
16C9×#102—22no—
17C4×C8×C9C2211yescharacteristic
18#63392—22no—
19#63367—22no—
20C4×C9⋊C8C2211yescharacteristic
21C4×C9⋊C8C2211yescharacteristic
22C3×#486D311yescharacteristic
23#5085—31no—
24#5080—31no—
25#5073—31no—
26#5070—31no—
27#4693—31no—
28#4454—31no—
29C2×Q8×C9—21no—
30C2×D4×C9—21no—
31C2×D4×C9—21no—
32C2×D4×C9—21no—
33C2×D36—21no—
34C2×D36—21no—
35C2×D36—21no—
36C2×Dic18—21no—
37C2×C8×C9D412yes—
38C9×C4⋊C4—21no—
39C9×C4⋊C4—21no—
40C42×C9C2311yescharacteristic
41#3675—44no—
42#3673—44no—
43C4⋊Dic9—21no—
44C4⋊Dic9—21no—
45C2×C9⋊C8D412yes—
46C2×C9⋊C8D412yes—
47#3664—44no—
48#1715—91noSylow
49C3×C4⋊Q8C2×D311yescharacteristic
50C3×#127C2×D311yescharacteristic
51C2×#215—62no—
52C2×#213—62no—
53C2×#204—62no—
54#874—31no—
55#869—31no—
56C3×#102—22no—
57C3×C4×C8C2×D311yescharacteristic
58#832—62no—
59#808—62no—
60C4×C3⋊C8—31no—
61C4×C3⋊C8—31no—
62C23×C9—41no—
63C22×D9—41no—
64Q8×C9—42no—
65D4×C9—42no—
66D4×C9—42no—
67D4×C9—42no—
68C2×C4×C9—41no—
69C2×C4×C9C2×D411yescharacteristic
70C2×C4×C9C2×D411yescharacteristic
71C2×C4×C9C2×D411yescharacteristic
72C2×Dic9—41no—
73D36—42no—
74D36—42no—
75D36—42no—
76Dic18—42no—
77C8×C9—22no—
78C9⋊C8—22no—
79C9⋊C8SD1614yescomplemented
80#498—91no—
81#493—91no—
82#492—91no—
83#492—91no—
84#486—91no—
85#486D911yescharacteristic, complemented
86#322—91no—
87C2×C3×Q8—21no—
88C2×C3×D4—21no—
89C2×C3×D4—21no—
90C2×C3×D4—21no—
91C2×D12—61no—
92C2×D12—61no—
93C2×D12—61no—
94C2×Dic6—61no—
95C2×C3×C8#6712yes—
96C3×C4⋊C4—21no—
97C3×C4⋊C4—21no—
98C3×C42C22×D311yescharacteristic
99#215—124no—
100#213—124no—
101C4⋊Dic3—61no—
102C4⋊Dic3—61no—
103C2×C3⋊C8—32no—
104C2×C3⋊C8—32no—
105#204—124no—
106C22×C9—81no—
107C22×C9—81no—
108C22×C9—81no—
109C22×C9#12711yescharacteristic
110C2×D9—81no—
111C2×D9—81no—
112C2×D9—81no—
113C4×C9—81no—
114C4×C9C2×SD1612yes—
115C4×C9AGL(1,ℤ/8)12yes—
116C4×C9AGL(1,ℤ/8)12yes—
117Dic9—81no—
118C2×SD16—182no—
119C2×SD16—182no—
120C2×D8—182no—
121C4⋊Q8—91no—
122C4⋊Q8C2×D911yescharacteristic
123#127—91no—
124#127C2×D911yescharacteristic
125#106—182no—
126#102—22no—
127#102—182no—
128C4×C8—91no—
129C4×C8—91no—
130C4×C8C2×D911yescharacteristic
131C23×C3—41no—
132C22×D3—121no—
133C3×Q8—42no—
134C3×D4—42no—
135C3×D4—42no—
136C3×D4—42no—
137C2×C3×C4—41no—
138C2×C3×C4D3×D411yescharacteristic
139C2×C3×C4D3×D411yescharacteristic
140C2×C3×C4C2×#6711yescharacteristic
141C2×Dic3—121no—
142D12—122no—
143D12—122no—
144D12—122no—
145Dic6—122no—
146C3×C8—22no—
147C3⋊C8—34no—
148C3⋊C8—62no—
149C2×C9—161no—
150C2×C9#49211yescharacteristic
151C2×C9#49611yescharacteristic
152C2×C9#49611yescharacteristic
153D9—161no—
154C2×Q8—21no—
155C2×Q8—181no—
156C2×D4—21no—
157C2×D4—21no—
158C2×D4—21no—
159C2×D4—181no—
160C2×D4—181no—
161C2×D4—181no—
162SD16—364no—
163SD16—364no—
164D8—364no—
165C2×C8—92no—
166C2×C8—92no—
167C2×C8#61112yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—181no—
171C4⋊C4—181no—
172C42C22×D911yescharacteristic
173C22×C3—81no—
174C22×C3—81no—
175C22×C3—81no—
176C22×C3#94011yescharacteristic
177C2×D3—241no—
178C2×D3—241no—
179C2×D3—241no—
180C3×C4—81no—
181C3×C4#91112yes—
182C3×C4D3×SD1612yes—
183C3×C4#94912yes—
184Dic3—241no—
185C9#171511yescharacteristic, complemented, Sylow
186C23—41no—
187C23—361no—
188Q8—42no—
189Q8—362no—
190D4—42no—
191D4—42no—
192D4—42no—
193D4—362no—
194D4—362no—
195D4—362no—
196C2×C4—41no—
197C2×C4—361no—
198C2×C4D4×D911yescharacteristic
199C2×C4D4×D911yescharacteristic
200C2×C4C2×#61111yescharacteristic
201C8—22no—
202C8—94no—
203C8—182no—
204C2×C3—161no—
205C2×C3#505811yescharacteristic
206C2×C3#515411yescharacteristic
207C2×C3#517511yescharacteristic
208D3—481no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—721no—
213C22—721no—
214C22—721no—
215C22#6350211yescharacteristic
216C4—81no—
217C4—721no—
218C4#6347312yes—
219C4SD16×D912yes—
220C4#6351212yes—
221C3#7118511yescharacteristic
222C2—161no—
223C2—1441no—
224C2#1058873911yescharacteristic
225C2#1058883411yescharacteristic
226C2#1058885511yescharacteristic
subgroupG/H
centerC22#63502
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#486C2
socleC22×C3#940
prime radical#10588755C2
hypercenter#486D9
hypocenterC9#1715
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. C9×#486C2semidirect
2. #10588770C2semidirect
3. #10588760C2semidirect
5. #10588750C2semidirect
6. #10588375C2semidirect
7. #10588131C2semidirect
79. C9⋊C8SD16semidirect
85. #486D9semidirect
185. C9#1715semidirect

Maximal subgroups

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

subgroupindex
C9×#4862
#105887702
#105887602
#105887552
#105887502
#105883752
#105881312
#711853