Finite Group Databasebeta

← C9×#2031 #11766752

Subgroups — C9×#2031 #11766752

Order 1152.

366 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#533C211yesmaximal, characteristic, complemented
2C9×#421C211yesmaximal, characteristic
3C2×C9×#104C211yesmaximal, characteristic
4C9×#410C211yesmaximal, characteristic
5C9×#344C211yesmaximal, characteristic, complemented
6C9×#339C211yesmaximal, characteristic, complemented
7C9×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C3×#2031C311yesmaximal, characteristic
9C2×C9×#41C2211yescharacteristic
10C2×C9×M16C2211yescharacteristic
11C2×C9×M16C2211yescharacteristic
12C9×C4⋊Q8—21no—
13C9×#125—21no—
14C9×C22⋊Q8—22no—
15C4×Q8×C9—22no—
16C9×#117C2211yescharacteristic
17C9×#117C2211yescharacteristic
18C9×#117C2211yescharacteristic
19C2×C42×C9C2211yescharacteristic
20C9×#104—21no—
21C9×#104—21no—
22C9×#104—22no—
23C9×#99—22no—
24C3×#533C2×C311yescharacteristic
25C3×#421C2×C311yescharacteristic
26C2×C3×#104C2×C311yescharacteristic
27C3×#410C2×C311yescharacteristic
28C3×#344C2×C311yescharacteristic
29C3×#339C2×C311yescharacteristic
30C3×H(3,ℤ/4)C2×C311yescharacteristic
31C9×#41—21no—
32C9×#41—21no—
33C9×#41—21no—
34C9×#41—21no—
35C2×Q8×C9—22no—
36C2×Q8×C9Q811yescharacteristic, complemented
37C2×D4×C9—21no—
38C2×D4×C9Q811yescharacteristic, complemented
39C22×C4×C9—21no—
40C22×C4×C9—21no—
41C22×C4×C9C2311yescharacteristic
42C9×M16—21no—
43C9×M16—21no—
44C9×M16—21no—
45C9×M16—21no—
46C2×C8×C9—21no—
47C2×C8×C9—21no—
48C9×C4⋊C4—24no—
49C9×C4⋊C4—22no—
50C9×C4⋊C4—21no—
51C9×C4⋊C4—21no—
52C9×C4⋊C4—21no—
53C9×C22⋊C4—21no—
54C9×C22⋊C4—21no—
55C9×C22⋊C4D412yes—
56C42×C9—21no—
57C42×C9—21no—
58C42×C9—21no—
59C42×C9D411yescharacteristic
60C42×C9D411yescharacteristic
61C42×C9D412yes—
62#2031C911yescharacteristic, direct product factor, Sylow
63C2×C3×#41C22×C311yescharacteristic
64C2×C3×M16C22×C311yescharacteristic
65C2×C3×M16C22×C311yescharacteristic
66C3×C4⋊Q8—21no—
67C3×#125—21no—
68C3×C22⋊Q8—22no—
69C3×C4×Q8—22no—
70C3×#117C22×C311yescharacteristic
71C3×#117C22×C311yescharacteristic
72C3×#117C22×C311yescharacteristic
73C2×C3×C42C22×C311yescharacteristic
74C3×#104—21no—
75C3×#104—21no—
76C3×#104—22no—
77C3×#99—22no—
78C23×C9—21no—
79C23×C9C2×D411yescharacteristic
80Q8×C9—21no—
81Q8×C9—21no—
82Q8×C9—44no—
83D4×C9—21no—
84D4×C9—21no—
85D4×C9—41no—
86D4×C9—41no—
87C2×C4×C9—21no—
88C2×C4×C9—21no—
89C2×C4×C9—22no—
90C2×C4×C9—22no—
91C2×C4×C9—21no—
92C2×C4×C9—42no—
93C2×C4×C9—41no—
94C2×C4×C9—41no—
95C2×C4×C9—41no—
96C2×C4×C9C2×D411yescharacteristic
97C2×C4×C9C2×D411yescharacteristic
98C2×C4×C9C2×Q811yescharacteristic
99C2×C4×C9#4111yescharacteristic
100C2×C4×C9#4111yescharacteristic
101C2×C4×C9#4111yescharacteristic
102C8×C9—41no—
103C8×C9—41no—
104#533C2×C911yescharacteristic, complemented
105#421C2×C911yescharacteristic
106C2×#104C2×C911yescharacteristic
107#410C2×C911yescharacteristic
108#344C2×C911yescharacteristic, complemented
109#339C2×C911yescharacteristic, complemented
110H(3,ℤ/4)C2×C911yescharacteristic, complemented
111C3×#41—21no—
112C3×#41—21no—
113C3×#41—21no—
114C3×#41—21no—
115C2×C3×Q8—22no—
116C2×C3×Q8C3×Q811yescharacteristic
117C2×C3×D4—21no—
118C2×C3×D4C3×Q811yescharacteristic
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4C23×C311yescharacteristic
122C3×M16—21no—
123C3×M16—21no—
124C3×M16—21no—
125C3×M16—21no—
126C2×C3×C8—21no—
127C2×C3×C8—21no—
128C3×C4⋊C4—24no—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C22⋊C4—21no—
134C3×C22⋊C4—21no—
135C3×C22⋊C4C3×D412yes—
136C3×C42—21no—
137C3×C42—21no—
138C3×C42—21no—
139C3×C42C3×D411yescharacteristic
140C3×C42C3×D411yescharacteristic
141C3×C42C3×D412yes—
142C22×C9—41no—
143C22×C9—41no—
144C22×C9—81no—
145C22×C9#12011yescharacteristic
146C22×C9C22⋊Q811yescharacteristic
147C22×C9#12411yescharacteristic
148C4×C9—22no—
149C4×C9—41no—
150C4×C9—42no—
151C4×C9—42no—
152C4×C9—41no—
153C4×C9—81no—
154C4×C9C22⋊Q811yescharacteristic
155C4×C9C22⋊Q811yescharacteristic
156C4×C9#12411yescharacteristic
157C4×C9#12411yescharacteristic
158C2×#41C22×C911yescharacteristic
159C2×M16C22×C911yescharacteristic
160C2×M16C22×C911yescharacteristic
161C4⋊Q8—21no—
162#125—21no—
163C22⋊Q8—22no—
164C4×Q8—22no—
165#117C22×C911yescharacteristic
166#117C22×C911yescharacteristic
167#117C22×C911yescharacteristic
168C2×C42C22×C911yescharacteristic
169#104—21no—
170#104—21no—
171#104—22no—
172#99—22no—
173C23×C3—21no—
174C23×C3C2×C3×D411yescharacteristic
175C3×Q8—21no—
176C3×Q8—21no—
177C3×Q8—44no—
178C3×D4—21no—
179C3×D4—21no—
180C3×D4—41no—
181C3×D4—41no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—21no—
187C2×C3×C4—42no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4C2×C3×D411yescharacteristic
192C2×C3×C4C2×C3×D411yescharacteristic
193C2×C3×C4C2×C3×Q811yescharacteristic
194C2×C3×C4C3×#4111yescharacteristic
195C2×C3×C4C3×#4111yescharacteristic
196C2×C3×C4C3×#4111yescharacteristic
197C3×C8—41no—
198C3×C8—41no—
199C2×C9—21no—
200C2×C9—21no—
201C2×C9—21no—
202C2×C9—81no—
203C2×C9#39311yescharacteristic
204#41—21no—
205#41—21no—
206#41—21no—
207#41—21no—
208C2×Q8—22no—
209C2×Q8Q8×C911yescharacteristic, complemented
210C2×D4—21no—
211C2×D4Q8×C911yescharacteristic, complemented
212C22×C4—21no—
213C22×C4—21no—
214C22×C4C23×C911yescharacteristic
215M16—21no—
216M16—21no—
217M16—21no—
218M16—21no—
219C2×C8—21no—
220C2×C8—21no—
221C4⋊C4—24no—
222C4⋊C4—22no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4D4×C912yes—
229C42—21no—
230C42—21no—
231C42—21no—
232C42D4×C911yescharacteristic
233C42D4×C911yescharacteristic
234C42D4×C912yes—
235C22×C3—41no—
236C22×C3—41no—
237C22×C3—81no—
238C22×C3C3×#12011yescharacteristic
239C22×C3C3×C22⋊Q811yescharacteristic
240C22×C3C3×#12411yescharacteristic
241C3×C4—22no—
242C3×C4—41no—
243C3×C4—42no—
244C3×C4—42no—
245C3×C4—41no—
246C3×C4—81no—
247C3×C4C3×C22⋊Q811yescharacteristic
248C3×C4C3×C22⋊Q811yescharacteristic
249C3×C4C3×#12411yescharacteristic
250C3×C4C3×#12411yescharacteristic
251C9#203111yescharacteristic, direct product factor, Sylow
252C23—21no—
253C23C2×D4×C911yescharacteristic
254Q8—21no—
255Q8—21no—
256Q8—44no—
257D4—21no—
258D4—21no—
259D4—41no—
260D4—41no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4C2×D4×C911yescharacteristic
271C2×C4C2×D4×C911yescharacteristic
272C2×C4C2×Q8×C911yescharacteristic
273C2×C4C9×#4111yescharacteristic
274C2×C4C9×#4111yescharacteristic
275C2×C4C9×#4111yescharacteristic
276C8—41no—
277C8—41no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—81no—
282C2×C3C3×#39311yescharacteristic
283C22—41no—
284C22—41no—
285C22—81no—
286C22C9×#12011yescharacteristic
287C22C9×C22⋊Q811yescharacteristic
288C22C9×#12411yescharacteristic
289C4—22no—
290C4—41no—
291C4—42no—
292C4—42no—
293C4—41no—
294C4—81no—
295C4C9×C22⋊Q811yescharacteristic
296C4C9×C22⋊Q811yescharacteristic
297C4C9×#12411yescharacteristic
298C4C9×#12411yescharacteristic
299C3C3×#203111yescharacteristic
300C2—21no—
301C2—21no—
302C2—21no—
303C2—81no—
304C2C9×#39311yescharacteristic
subgroupG/H
centerC4×C9#124
commutatorC22×C4C23×C9
Frattini, cosocleC22×C3×C4C23×C3
socleC2×C3C3×#393
prime radicalC2×C3×#41C22×C3
LCSG ▷ C22×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×#533C2semidirect
5. C9×#344C2semidirect
6. C9×#339C2semidirect
7. C9×H(3,ℤ/4)C2semidirect
36. C2×Q8×C9Q8semidirect
38. C2×D4×C9Q8semidirect
62. #2031C9direct (N × H)
104. #533C2×C9semidirect
108. #344C2×C9semidirect
109. #339C2×C9semidirect
110. H(3,ℤ/4)C2×C9semidirect
209. C2×Q8Q8×C9semidirect
211. C2×D4Q8×C9semidirect
251. C9#2031direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5332
C9×#4212
C2×C9×#1042
C9×#4102
C9×#3442
C9×#3392
C9×H(3,ℤ/4)2
C3×#20313