Finite Group Databasebeta

← C9×#1932 #11766653

Subgroups — C9×#1932 #11766653

Order 1152.

324 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#430C211yesmaximal, characteristic, complemented
2C9×#421C211yesmaximal, characteristic
3C2×C9×#104C211yesmaximal, characteristic
4C9×#413C211yesmaximal, characteristic
5C4×C9×M16C211yesmaximal, characteristic, complemented
6C9×#344C211yesmaximal, characteristic, complemented
7C9×#339C211yesmaximal, characteristic, complemented
8C3×#1932C311yesmaximal, characteristic
9C2×C9×#41C2211yescharacteristic
10C2×C9×M16C2211yescharacteristic
11C2×C9×M16C2211yescharacteristic
12C2×C9×M16C2211yescharacteristic
13C2×C9×M16C2211yescharacteristic
14C9×#117C2211yescharacteristic
15C2×C42×C9C2211yescharacteristic
16C9×#108—22no—
17C9×#104—22no—
18C9×#104—21no—
19C9×#104—21no—
20C9×#101C412yescomplemented
21C9×#100C412yescomplemented
22C9×#97—21no—
23C4×C8×C9—21no—
24C3×#430C2×C311yescharacteristic
25C3×#421C2×C311yescharacteristic
26C2×C3×#104C2×C311yescharacteristic
27C3×#413C2×C311yescharacteristic
28C3×C4×M16C2×C311yescharacteristic
29C3×#344C2×C311yescharacteristic
30C3×#339C2×C311yescharacteristic
31C9×#41—21no—
32C9×#41—21no—
33C9×#41—21no—
34C9×#41—21no—
35C2×Q8×C9C2×C411yescharacteristic
36C2×D4×C9—21no—
37C2×D4×C9C2×C411yescharacteristic
38C22×C4×C9—21no—
39C22×C4×C9—21no—
40C22×C4×C9C2311yescharacteristic
41C9×M16—21no—
42C9×M16—21no—
43C9×M16—21no—
44C9×M16—21no—
45C9×M16—21no—
46C9×M16C2×C412yes—
47C9×M16C2×C412yes—
48C9×M16D412yes—
49C2×C8×C9—21no—
50C2×C8×C9—21no—
51C2×C8×C9—21no—
52C2×C8×C9—21no—
53C9×C4⋊C4—21no—
54C9×C22⋊C4—21no—
55C42×C9—21no—
56C42×C9—21no—
57C42×C9D411yescharacteristic
58C42×C9D411yescharacteristic
59#1932C911yescharacteristic, direct product factor, Sylow
60C2×C3×#41C22×C311yescharacteristic
61C2×C3×M16C22×C311yescharacteristic
62C2×C3×M16C22×C311yescharacteristic
63C2×C3×M16C22×C311yescharacteristic
64C2×C3×M16C22×C311yescharacteristic
65C3×#117C22×C311yescharacteristic
66C2×C3×C42C22×C311yescharacteristic
67C3×#108—22no—
68C3×#104—22no—
69C3×#104—21no—
70C3×#104—21no—
71C3×#101C3×C412yes—
72C3×#100C3×C412yes—
73C3×#97—21no—
74C3×C4×C8—21no—
75C23×C9—21no—
76C23×C9#4111yescharacteristic
77Q8×C9—21no—
78Q8×C9—21no—
79D4×C9—21no—
80D4×C9—21no—
81D4×C9—41no—
82D4×C9—41no—
83C2×C4×C9—21no—
84C2×C4×C9—21no—
85C2×C4×C9—21no—
86C2×C4×C9—42no—
87C2×C4×C9—41no—
88C2×C4×C9—41no—
89C2×C4×C9—41no—
90C2×C4×C9C22×C411yescharacteristic
91C2×C4×C9C2×D411yescharacteristic
92C2×C4×C9C2×D411yescharacteristic
93C2×C4×C9#4111yescharacteristic
94C2×C4×C9#4111yescharacteristic
95C2×C4×C9#4111yescharacteristic
96C8×C9—22no—
97C8×C9—22no—
98C8×C9—22no—
99C8×C9—41no—
100#430C2×C911yescharacteristic, complemented
101#421C2×C911yescharacteristic
102C2×#104C2×C911yescharacteristic
103#413C2×C911yescharacteristic
104C4×M16C2×C911yescharacteristic, complemented
105#344C2×C911yescharacteristic, complemented
106#339C2×C911yescharacteristic, complemented
107C3×#41—21no—
108C3×#41—21no—
109C3×#41—21no—
110C3×#41—21no—
111C2×C3×Q8C2×C3×C411yescharacteristic
112C2×C3×D4—21no—
113C2×C3×D4C2×C3×C411yescharacteristic
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4C23×C311yescharacteristic
117C3×M16—21no—
118C3×M16—21no—
119C3×M16—21no—
120C3×M16—21no—
121C3×M16—21no—
122C3×M16C2×C3×C412yes—
123C3×M16C2×C3×C412yes—
124C3×M16C3×D412yes—
125C2×C3×C8—21no—
126C2×C3×C8—21no—
127C2×C3×C8—21no—
128C2×C3×C8—21no—
129C3×C4⋊C4—21no—
130C3×C22⋊C4—21no—
131C3×C42—21no—
132C3×C42—21no—
133C3×C42C3×D411yescharacteristic
134C3×C42C3×D411yescharacteristic
135C22×C9—41no—
136C22×C9—41no—
137C22×C9—81no—
138C22×C9#11711yescharacteristic
139C22×C9#12311yescharacteristic
140C22×C9#12411yescharacteristic
141C4×C9—22no—
142C4×C9—41no—
143C4×C9—41no—
144C4×C9—81no—
145C4×C9C4×D411yescharacteristic
146C4×C9C4×D411yescharacteristic
147C4×C9#12111yescharacteristic
148C4×C9#12611yescharacteristic
149C2×#41C22×C911yescharacteristic
150C2×M16C22×C911yescharacteristic
151C2×M16C22×C911yescharacteristic
152C2×M16C22×C911yescharacteristic
153C2×M16C22×C911yescharacteristic
154#117C22×C911yescharacteristic
155C2×C42C22×C911yescharacteristic
156#108—22no—
157#104—22no—
158#104—21no—
159#104—21no—
160#101C4×C912yescomplemented
161#100C4×C912yescomplemented
162#97—21no—
163C4×C8—21no—
164C23×C3—21no—
165C23×C3C3×#4111yescharacteristic
166C3×Q8—21no—
167C3×Q8—21no—
168C3×D4—21no—
169C3×D4—21no—
170C3×D4—41no—
171C3×D4—41no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—42no—
176C2×C3×C4—41no—
177C2×C3×C4—41no—
178C2×C3×C4—41no—
179C2×C3×C4C22×C3×C411yescharacteristic
180C2×C3×C4C2×C3×D411yescharacteristic
181C2×C3×C4C2×C3×D411yescharacteristic
182C2×C3×C4C3×#4111yescharacteristic
183C2×C3×C4C3×#4111yescharacteristic
184C2×C3×C4C3×#4111yescharacteristic
185C3×C8—22no—
186C3×C8—22no—
187C3×C8—22no—
188C3×C8—41no—
189C2×C9—21no—
190C2×C9—21no—
191C2×C9—21no—
192C2×C9—81no—
193C2×C9#38811yescharacteristic
194#41—21no—
195#41—21no—
196#41—21no—
197#41—21no—
198C2×Q8C2×C4×C911yescharacteristic
199C2×D4—21no—
200C2×D4C2×C4×C911yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4C23×C911yescharacteristic
204M16—21no—
205M16—21no—
206M16—21no—
207M16—21no—
208M16—21no—
209M16C2×C4×C912yes—
210M16C2×C4×C912yes—
211M16D4×C912yes—
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—21no—
216C4⋊C4—21no—
217C22⋊C4—21no—
218C42—21no—
219C42—21no—
220C42D4×C911yescharacteristic
221C42D4×C911yescharacteristic
222C22×C3—41no—
223C22×C3—41no—
224C22×C3—81no—
225C22×C3C3×#11711yescharacteristic
226C22×C3C3×#12311yescharacteristic
227C22×C3C3×#12411yescharacteristic
228C3×C4—22no—
229C3×C4—41no—
230C3×C4—41no—
231C3×C4—81no—
232C3×C4C3×C4×D411yescharacteristic
233C3×C4C3×C4×D411yescharacteristic
234C3×C4C3×#12111yescharacteristic
235C3×C4C3×#12611yescharacteristic
236C9#193211yescharacteristic, direct product factor, Sylow
237C23—21no—
238C23C9×#4111yescharacteristic
239Q8—21no—
240Q8—21no—
241D4—21no—
242D4—21no—
243D4—41no—
244D4—41no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4C22×C4×C911yescharacteristic
253C2×C4C2×D4×C911yescharacteristic
254C2×C4C2×D4×C911yescharacteristic
255C2×C4C9×#4111yescharacteristic
256C2×C4C9×#4111yescharacteristic
257C2×C4C9×#4111yescharacteristic
258C8—22no—
259C8—22no—
260C8—22no—
261C8—41no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—81no—
266C2×C3C3×#38811yescharacteristic
267C22—41no—
268C22—41no—
269C22—81no—
270C22C9×#11711yescharacteristic
271C22C9×#12311yescharacteristic
272C22C9×#12411yescharacteristic
273C4—22no—
274C4—41no—
275C4—41no—
276C4—81no—
277C4C4×D4×C911yescharacteristic
278C4C4×D4×C911yescharacteristic
279C4C9×#12111yescharacteristic
280C4C9×#12611yescharacteristic
281C3C3×#193211yescharacteristic
282C2—21no—
283C2—21no—
284C2—21no—
285C2—81no—
286C2C9×#38811yescharacteristic
subgroupG/H
centerC4×C9#121
commutatorC2×C4C22×C4×C9
Frattini, cosocleC22×C3×C4C23×C3
socleC2×C3C3×#388
prime radicalC2×C3×#41C22×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C9 ◁ C22×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#430C2semidirect
5. C4×C9×M16C2semidirect
6. C9×#344C2semidirect
7. C9×#339C2semidirect
20. C9×#101C4semidirect
21. C9×#100C4semidirect
59. #1932C9direct (N × H)
100. #430C2×C9semidirect
104. C4×M16C2×C9semidirect
105. #344C2×C9semidirect
106. #339C2×C9semidirect
160. #101C4×C9semidirect
161. #100C4×C9semidirect
236. C9#1932direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#4302
C9×#4212
C2×C9×#1042
C9×#4132
C4×C9×M162
C9×#3442
C9×#3392
C3×#19323