Finite Group Databasebeta

← C9×#1345 #11766066

Subgroups — C9×#1345 #11766066

Order 1152.

252 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 60 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×#394C211yesmaximal, characteristic
2C9×#343C211yesmaximal, characteristic, complemented
3C9×#324C211yesmaximal, characteristic, complemented
4C3×#1345C311yesmaximal, characteristic
5C22×D4×C9C411yescharacteristic
6C2×C9×M16—21no—
7C2×C9×C4⋊C4C2211yescharacteristic
8C2×C9×C22⋊C4—21no—
9C2×C9×C22⋊C4—21no—
10C9×C22⋊C8—21no—
11C9×#95C411yescharacteristic
12C3×#394C2×C311yescharacteristic
13C3×#343C2×C311yescharacteristic
14C3×#324C2×C311yescharacteristic
15C24×C9—21no—
16C2×D4×C9—41no—
17C2×D4×C9—42no—
18C22×C4×C9—21no—
19C22×C4×C9C2×C411yescharacteristic
20C22×C4×C9D411yescharacteristic
21C22×C4×C9D411yescharacteristic
22C9×M16—22no—
23C9×M16—41no—
24C2×C8×C9—41no—
25C2×C8×C9—41no—
26C9×C4⋊C4—41no—
27C9×C22⋊C4—42no—
28C9×C22⋊C4—41no—
29C9×C22⋊C4—41no—
30#1345C911yescharacteristic, direct product factor, Sylow
31C22×C3×D4C3×C411yescharacteristic
32C2×C3×M16—21no—
33C2×C3×C4⋊C4C22×C311yescharacteristic
34C2×C3×C22⋊C4—21no—
35C2×C3×C22⋊C4—21no—
36C3×C22⋊C8—21no—
37C3×#95C3×C411yescharacteristic
38C23×C9—22no—
39C23×C9—41no—
40C23×C9—41no—
41C23×C9—41no—
42C23×C9—41no—
43C23×C9—41no—
44C23×C9—41no—
45C23×C9C22⋊C411yescharacteristic
46D4×C9—42no—
47D4×C9—42no—
48C2×C4×C9—21no—
49C2×C4×C9—21no—
50C2×C4×C9—21no—
51C2×C4×C9—21no—
52C2×C4×C9—41no—
53C2×C4×C9—41no—
54C2×C4×C9—41no—
55C2×C4×C9—41no—
56C2×C4×C9—41no—
57C2×C4×C9D811yescharacteristic
58C2×C4×C9SD1611yescharacteristic
59C8×C9—42no—
60C8×C9—81no—
61#394C2×C911yescharacteristic
62#343C2×C911yescharacteristic, complemented
63#324C2×C911yescharacteristic, complemented
64C24×C3—21no—
65C2×C3×D4—41no—
66C2×C3×D4—42no—
67C22×C3×C4—21no—
68C22×C3×C4C2×C3×C411yescharacteristic
69C22×C3×C4C3×D411yescharacteristic
70C22×C3×C4C3×D411yescharacteristic
71C3×M16—22no—
72C3×M16—41no—
73C2×C3×C8—41no—
74C2×C3×C8—41no—
75C3×C4⋊C4—41no—
76C3×C22⋊C4—42no—
77C3×C22⋊C4—41no—
78C3×C22⋊C4—41no—
79C22×C9—21no—
80C22×C9—21no—
81C22×C9—42no—
82C22×C9—42no—
83C22×C9—42no—
84C22×C9—81no—
85C22×C9—81no—
86C22×C9—81no—
87C22×C9—81no—
88C22×C9#9911yescharacteristic
89C22×C9#10211yescharacteristic
90C22×C9#10411yescharacteristic
91C4×C9—21no—
92C4×C9—21no—
93C4×C9—41no—
94C4×C9—41no—
95C4×C9—81no—
96C22×D4C4×C911yescharacteristic
97C2×M16—21no—
98C2×C4⋊C4C22×C911yescharacteristic
99C2×C22⋊C4—21no—
100C2×C22⋊C4—21no—
101C22⋊C8—21no—
102#95C4×C911yescharacteristic
103C23×C3—22no—
104C23×C3—41no—
105C23×C3—41no—
106C23×C3—41no—
107C23×C3—41no—
108C23×C3—41no—
109C23×C3—41no—
110C23×C3C3×C22⋊C411yescharacteristic
111C3×D4—42no—
112C3×D4—42no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—41no—
118C2×C3×C4—41no—
119C2×C3×C4—41no—
120C2×C3×C4—41no—
121C2×C3×C4—41no—
122C2×C3×C4C3×D811yescharacteristic
123C2×C3×C4C3×SD1611yescharacteristic
124C3×C8—42no—
125C3×C8—81no—
126C2×C9—21no—
127C2×C9—21no—
128C2×C9—82no—
129C2×C9#32711yescharacteristic
130C2×C9AΣL(1,𝔽16)11yescharacteristic
131C2×C9#35511yescharacteristic
132C24—21no—
133C2×D4—41no—
134C2×D4—42no—
135C22×C4—21no—
136C22×C4C2×C4×C911yescharacteristic
137C22×C4D4×C911yescharacteristic
138C22×C4D4×C911yescharacteristic
139M16—22no—
140M16—41no—
141C2×C8—41no—
142C2×C8—41no—
143C4⋊C4—41no—
144C22⋊C4—42no—
145C22⋊C4—41no—
146C22⋊C4—41no—
147C22×C3—21no—
148C22×C3—21no—
149C22×C3—42no—
150C22×C3—42no—
151C22×C3—42no—
152C22×C3—81no—
153C22×C3—81no—
154C22×C3—81no—
155C22×C3—81no—
156C22×C3C3×#9911yescharacteristic
157C22×C3C3×#10211yescharacteristic
158C22×C3C3×#10411yescharacteristic
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—41no—
162C3×C4—41no—
163C3×C4—81no—
164C9#134511yescharacteristic, direct product factor, Sylow
165C23—22no—
166C23—41no—
167C23—41no—
168C23—41no—
169C23—41no—
170C23—41no—
171C23—41no—
172C23C9×C22⋊C411yescharacteristic
173D4—42no—
174D4—42no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4C9×D811yescharacteristic
185C2×C4C9×SD1611yescharacteristic
186C8—42no—
187C8—81no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—82no—
191C2×C3C3×#32711yescharacteristic
192C2×C3C3×AΣL(1,𝔽16)11yescharacteristic
193C2×C3C3×#35511yescharacteristic
194C22—21no—
195C22—21no—
196C22—42no—
197C22—42no—
198C22—42no—
199C22—81no—
200C22—81no—
201C22—81no—
202C22—81no—
203C22C9×#9911yescharacteristic
204C22C9×#10211yescharacteristic
205C22C9×#10411yescharacteristic
206C4—21no—
207C4—21no—
208C4—41no—
209C4—41no—
210C4—81no—
211C3C3×#134511yescharacteristic
212C2—21no—
213C2—21no—
214C2—82no—
215C2C9×#32711yescharacteristic
216C2C9×AΣL(1,𝔽16)11yescharacteristic
217C2C9×#35511yescharacteristic
subgroupG/H
centerC22×C9#99
commutatorC22×C4C2×C4×C9
Frattini, cosocleC2×C3×C4⋊C4C22×C3
socleC22×C3C3×#99
prime radicalC22×C3×D4C3×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C9 ◁ C23×C9 ◁ C2×C9×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C9×#343C2semidirect
3. C9×#324C2semidirect
30. #1345C9direct (N × H)
62. #343C2×C9semidirect
63. #324C2×C9semidirect
164. C9#1345direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#3942
C9×#3432
C9×#3242
C3×#13453