Finite Group Databasebeta

← C9×#4477 #13135358

Subgroups — C9×#4477 #13135358

Order 1728.

230 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 63 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×#947C211yesmaximal, characteristic
2C3×C9×#101C211yesmaximal, characteristic, complemented
3C9×#836C211yesmaximal, characteristic, complemented
4C3×#4477C311yesmaximal, characteristic
5C9×#355—31nomaximal
6C2×C3×Q8×C9C2211yescharacteristic
7C2×C9×D12C411yescharacteristic
8C3×C9×M16—21no—
9C9×(C2×D3)⋊C4—21no—
10C9×(C2×D3)⋊C4—21no—
11C4×C9×Dic3C411yescharacteristic
12C9×#208—21no—
13C3×#947C2×C311yescharacteristic
14C32×#101C2×C311yescharacteristic
15C3×#836C2×C311yescharacteristic
16C9×#124—31no—
17C9×#101—21no—
18C9×#101—31no—
19C9×#101D311yescharacteristic, complemented
20C22×D3×C9—21no—
21C3×Q8×C9—41no—
22C2×C3×C4×C9C2×C411yescharacteristic
23C2×C3×C4×C9D411yescharacteristic
24C2×C3×C4×C9D411yescharacteristic
25C2×C9×Dic3—21no—
26C9×D12—41no—
27C3×C8×C9—41no—
28C9×C3⋊C8—41no—
29C3×#355—31no—
30#4477C911yescharacteristic, direct product factor
31C2×C32×Q8C22×C311yescharacteristic
32C2×C3×D12C3×C411yescharacteristic
33C32×M16—21no—
34C3×(C2×D3)⋊C4—21no—
35C3×(C2×D3)⋊C4—21no—
36C3×C4×Dic3C3×C411yescharacteristic
37C3×#208—21no—
38C2×Q8×C9—21no—
39C2×Q8×C9C2×D311yescharacteristic
40C2×D4×C9—31no—
41C9×M16—22no—
42C9×M16—21no—
43C9×M16—61no—
44C9×C22⋊C4—61no—
45C9×C22⋊C4—61no—
46C42×C9—31no—
47C22×C3×C9C22⋊C411yescharacteristic
48C2×D3×C9—42no—
49C2×D3×C9—41no—
50C3×C4×C9—21no—
51C3×C4×C9—21no—
52C3×C4×C9—21no—
53C9×Dic3—41no—
54C3×#124—31no—
55#947C2×C911yescharacteristic
56C3×#101—21no—
57C3×#101—31no—
58C3×#101C2×C911yescharacteristic, complemented
59C3×#101C3×D311yescharacteristic
60#836C2×C911yescharacteristic, complemented
61C22×C3×D3—21no—
62C32×Q8—41no—
63C2×C32×C4C2×C3×C411yescharacteristic
64C2×C32×C4C3×D411yescharacteristic
65C2×C32×C4C3×D411yescharacteristic
66C2×C3×Dic3—21no—
67C3×D12—41no—
68C23×C9—61no—
69C32×C8—41no—
70C3×C3⋊C8—41no—
71Q8×C9—41no—
72Q8×C9—42no—
73D4×C9—121no—
74C2×C4×C9—21no—
75C2×C4×C9—21no—
76C2×C4×C9—21no—
77C2×C4×C9—61no—
78C2×C4×C9C4×D311yescharacteristic
79C2×C4×C9D1211yescharacteristic
80C2×C4×C9#6711yescharacteristic
81C8×C9—42no—
82C8×C9—41no—
83C8×C9—121no—
84#355—31noSylow
85C2×C3×C9—21no—
86C2×C3×C9#9911yescharacteristic
87D3×C9—81no—
88C2×C3×Q8—21no—
89C2×C3×Q8C22×C911yescharacteristic
90C2×C3×Q8C2×C3×D311yescharacteristic
91C2×C3×D4—31no—
92C2×D12C4×C911yescharacteristic
93C3×M16—22no—
94C3×M16—21no—
95C3×M16—21no—
96C3×M16—61no—
97C3×C22⋊C4—61no—
98C3×C22⋊C4—61no—
99C3×C42—31no—
100(C2×D3)⋊C4—21no—
101(C2×D3)⋊C4—21no—
102C4×Dic3C4×C911yescharacteristic
103#208—21no—
104C22×C32C3×C22⋊C411yescharacteristic
105C2×C3×D3—42no—
106C2×C3×D3—41no—
107C32×C4—21no—
108C32×C4—21no—
109C32×C4—21no—
110C3×Dic3—41no—
111C22×C9—21no—
112C22×C9—122no—
113C22×C9—121no—
114C22×C9(C2×D3)⋊C411yescharacteristic
115C4×C9—22no—
116C4×C9—21no—
117C4×C9—21no—
118C4×C9—21no—
119C4×C9—41no—
120C4×C9—41no—
121C4×C9—121no—
122#124—31no—
123#101—31no—
124#101D3×C911yescharacteristic, complemented
125C3×C9#35511yescharacteristic, complemented, Sylow
126C23×C3—61no—
127C22×D3—21no—
128C3×Q8—41no—
129C3×Q8—41no—
130C3×Q8—42no—
131C3×D4—121no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—61no—
136C2×C3×C4C2×C4×C911yescharacteristic
137C2×C3×C4D4×C911yescharacteristic
138C2×C3×C4D4×C911yescharacteristic
139C2×C3×C4C3×C4×D311yescharacteristic
140C2×C3×C4C3×D1211yescharacteristic
141C2×C3×C4C3×#6711yescharacteristic
142C2×Dic3—21no—
143D12—41no—
144C3×C8—41no—
145C3×C8—42no—
146C3×C8—41no—
147C3×C8—121no—
148C3⋊C8—41no—
149C2×C32—21no—
150C2×C32C3×#9911yescharacteristic
151C3×D3—81no—
152C2×C9—21no—
153C2×C9—21no—
154C2×C9—41no—
155C2×C9—241no—
156C2×C9#80611yescharacteristic
157C2×Q8C2×D3×C911yescharacteristic
158C2×D4—31no—
159M16—21no—
160M16—61no—
161C22⋊C4—61no—
162C22⋊C4—61no—
163C42—31no—
164C22×C3—21no—
165C22×C3—122no—
166C22×C3—121no—
167C22×C3C9×C22⋊C411yescharacteristic
168C22×C3C3×(C2×D3)⋊C411yescharacteristic
169C2×D3—42no—
170C2×D3—41no—
171C3×C4—22no—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—21no—
178C3×C4—41no—
179C3×C4—41no—
180C3×C4—121no—
181Dic3—41no—
182C32C3×#35511yescharacteristic
183C9—21no—
184C9#447711yescharacteristic, direct product factor
185C23—61no—
186Q8—41no—
187D4—121no—
188C2×C4—61no—
189C2×C4C4×D3×C911yescharacteristic
190C2×C4C9×D1211yescharacteristic
191C2×C4C9×#6711yescharacteristic
192C8—41no—
193C8—121no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3—41no—
198C2×C3—241no—
199C2×C3C9×#9911yescharacteristic
200C2×C3C3×#80611yescharacteristic
201D3—81no—
202C22—122no—
203C22—121no—
204C22C9×(C2×D3)⋊C411yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—121no—
209C3—21no—
210C3C9×#35511yescharacteristic, complemented
211C3C3×#447711yescharacteristic
212C2—21no—
213C2—241no—
214C2C9×#80611yescharacteristic
subgroupG/H
centerC2×C9#806
commutatorC2×C3×C4C2×C4×C9
FrattiniC2×C3×Q8C2×C3×D3
FittingC3×C9×#101C2
socleC2×C32C3×#99
prime radicalC2×C3×D12C3×C4
cosocleC2×C32×Q8C22×C3
hypercenterC9×#101D3
hypocenterC3C9×#355
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C9 ◁ C22×C9 ◁ C2×Q8×C9 ◁ C9×#101

Complements

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

NH ≅ G/Ntype
2. C3×C9×#101C2semidirect
3. C9×#836C2semidirect
19. C9×#101D3semidirect
30. #4477C9direct (N × H)
58. C3×#101C2×C9semidirect
60. #836C2×C9semidirect
124. #101D3×C9semidirect
125. C3×C9#355semidirect
184. C9#4477direct (N × H)
210. C3C9×#355semidirect

Maximal subgroups

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

subgroupindex
C9×#9472
C3×C9×#1012
C9×#8362
C3×#44773
C9×#3553