Finite Group Databasebeta

← C9×#2052 #11766773

Subgroups — C9×#2052 #11766773

Order 1152.

393 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#137C211yesmaximal, characteristic
2C2×C9×#108C211yesmaximal, characteristic, complemented
3C9×#417C211yesmaximal, characteristic
4C2×C9×#103C211yesmaximal, characteristic, complemented
5C2×C9×#101C211yesmaximal, characteristic, complemented
6C9×#408C211yesmaximal, characteristic
7C9×#343C211yesmaximal, characteristic, complemented
8C3×#2052C311yesmaximal, characteristic
9C2×C9×#41C2211yescharacteristic
10C22×Q8×C9C2211yescharacteristic
11C9×#137—22no—
12C9×#137—22no—
13C2×C9×Q16—21no—
14C2×C9×SD16—21no—
15C2×C9×M16C2211yescharacteristic
16C2×C9×M16C2211yescharacteristic
17C2×C9×M16C2211yescharacteristic
18C22×C8×C9C2211yescharacteristic
19C2×C9×C4⋊C4C2211yescharacteristic
20C9×#108—22no—
21C9×#103—21no—
22C9×#103—22no—
23C9×#102—21no—
24C9×#101—22no—
25C9×C22⋊C8—22no—
26C2×C3×#137C2×C311yescharacteristic
27C2×C3×#108C2×C311yescharacteristic
28C3×#417C2×C311yescharacteristic
29C2×C3×#103C2×C311yescharacteristic
30C2×C3×#101C2×C311yescharacteristic
31C3×#408C2×C311yescharacteristic
32C3×#343C2×C311yescharacteristic
33C9×#41—21no—
34C9×#41—21no—
35C9×#41—21no—
36C9×#41—21no—
37C2×Q8×C9—21no—
38C2×Q8×C9—21no—
39C2×Q8×C9—21no—
40C2×Q8×C9—21no—
41C2×Q8×C9—21no—
42C2×Q8×C9D411yescharacteristic
43C2×Q8×C9D412yes—
44C2×D4×C9—21no—
45C2×D4×C9D411yescharacteristic
46C22×C4×C9—21no—
47C22×C4×C9—21no—
48C22×C4×C9—21no—
49C22×C4×C9C2311yescharacteristic
50C9×Q16—24no—
51C9×SD16—24no—
52C9×M16—21no—
53C9×M16—21no—
54C9×M16—21no—
55C9×M16—21no—
56C9×M16—21no—
57C9×M16D412yes—
58C2×C8×C9—21no—
59C2×C8×C9—21no—
60C2×C8×C9—21no—
61C2×C8×C9—21no—
62C2×C8×C9—21no—
63C2×C8×C9D412yes—
64C9×C4⋊C4—21no—
65C9×C4⋊C4—21no—
66#2052C911yescharacteristic, direct product factor, Sylow
67C2×C3×#41C22×C311yescharacteristic
68C22×C3×Q8C22×C311yescharacteristic
69C3×#137—22no—
70C3×#137—22no—
71C2×C3×Q16—21no—
72C2×C3×SD16—21no—
73C2×C3×M16C22×C311yescharacteristic
74C2×C3×M16C22×C311yescharacteristic
75C2×C3×M16C22×C311yescharacteristic
76C22×C3×C8C22×C311yescharacteristic
77C2×C3×C4⋊C4C22×C311yescharacteristic
78C3×#108—22no—
79C3×#103—21no—
80C3×#103—22no—
81C3×#102—21no—
82C3×#101—22no—
83C3×C22⋊C8—22no—
84C23×C9—21no—
85C23×C9#4111yescharacteristic
86Q8×C9—22no—
87Q8×C9—21no—
88Q8×C9—22no—
89Q8×C9—21no—
90Q8×C9—41no—
91Q8×C9—41no—
92D4×C9—21no—
93D4×C9—21no—
94D4×C9—41no—
95D4×C9—41no—
96C2×C4×C9—21no—
97C2×C4×C9—22no—
98C2×C4×C9—41no—
99C2×C4×C9—41no—
100C2×C4×C9—41no—
101C2×C4×C9—41no—
102C2×C4×C9—41no—
103C2×C4×C9—81no—
104C2×C4×C9C2×D411yescharacteristic
105C2×C4×C9C2×D411yescharacteristic
106C2×C4×C9C2×D411yescharacteristic
107C2×C4×C9C2×D411yescharacteristic
108C2×C4×C9#4111yescharacteristic
109C2×C4×C9#4111yescharacteristic
110C8×C9—22no—
111C8×C9—22no—
112C8×C9—41no—
113C8×C9—41no—
114C2×#137C2×C911yescharacteristic
115C2×#108C2×C911yescharacteristic, complemented
116#417C2×C911yescharacteristic
117C2×#103C2×C911yescharacteristic, complemented
118C2×#101C2×C911yescharacteristic, complemented
119#408C2×C911yescharacteristic
120#343C2×C911yescharacteristic, complemented
121C3×#41—21no—
122C3×#41—21no—
123C3×#41—21no—
124C3×#41—21no—
125C2×C3×Q8—21no—
126C2×C3×Q8—21no—
127C2×C3×Q8—21no—
128C2×C3×Q8—21no—
129C2×C3×Q8—21no—
130C2×C3×Q8C3×D412yes—
131C2×C3×Q8C3×D411yescharacteristic
132C2×C3×D4—21no—
133C2×C3×D4C3×D411yescharacteristic
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4C23×C311yescharacteristic
138C3×Q16—24no—
139C3×SD16—24no—
140C3×M16—21no—
141C3×M16—21no—
142C3×M16—21no—
143C3×M16—21no—
144C3×M16—21no—
145C3×M16C3×D412yes—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8C3×D412yes—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C22×C9—21no—
155C22×C9—21no—
156C22×C9—41no—
157C22×C9—41no—
158C22×C9—41no—
159C22×C9#12111yescharacteristic
160C22×C9#12311yescharacteristic
161C22×C9#12411yescharacteristic
162C4×C9—41no—
163C4×C9—42no—
164C4×C9—81no—
165C4×C9#12011yescharacteristic
166C4×C9#12111yescharacteristic
167C4×C9#12111yescharacteristic
168C4×C9#12311yescharacteristic
169C2×#41C22×C911yescharacteristic
170C22×Q8C22×C911yescharacteristic
171#137—22no—
172#137—22no—
173C2×Q16—21no—
174C2×SD16—21no—
175C2×M16C22×C911yescharacteristic
176C2×M16C22×C911yescharacteristic
177C2×M16C22×C911yescharacteristic
178C22×C8C22×C911yescharacteristic
179C2×C4⋊C4C22×C911yescharacteristic
180#108—22no—
181#103—21no—
182#103—22no—
183#102—21no—
184#101—22no—
185C22⋊C8—22no—
186C23×C3—21no—
187C23×C3C3×#4111yescharacteristic
188C3×Q8—22no—
189C3×Q8—21no—
190C3×Q8—22no—
191C3×Q8—21no—
192C3×Q8—41no—
193C3×Q8—41no—
194C3×D4—21no—
195C3×D4—21no—
196C3×D4—41no—
197C3×D4—41no—
198C2×C3×C4—21no—
199C2×C3×C4—22no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—81no—
206C2×C3×C4C2×C3×D411yescharacteristic
207C2×C3×C4C2×C3×D411yescharacteristic
208C2×C3×C4C2×C3×D411yescharacteristic
209C2×C3×C4C2×C3×D411yescharacteristic
210C2×C3×C4C3×#4111yescharacteristic
211C2×C3×C4C3×#4111yescharacteristic
212C3×C8—22no—
213C3×C8—22no—
214C3×C8—41no—
215C3×C8—41no—
216C2×C9—21no—
217C2×C9—21no—
218C2×C9—81no—
219C2×C9#39411yescharacteristic
220C2×C9#47111yescharacteristic
221C2×C9#47311yescharacteristic
222#41—21no—
223#41—21no—
224#41—21no—
225#41—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8D4×C912yes—
232C2×Q8D4×C911yescharacteristic
233C2×D4—21no—
234C2×D4D4×C911yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4C23×C911yescharacteristic
239Q16—24no—
240SD16—24no—
241M16—21no—
242M16—21no—
243M16—21no—
244M16—21no—
245M16—21no—
246M16D4×C912yes—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8D4×C912yes—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3C3×#12111yescharacteristic
261C22×C3C3×#12311yescharacteristic
262C22×C3C3×#12411yescharacteristic
263C3×C4—41no—
264C3×C4—42no—
265C3×C4—81no—
266C3×C4C3×#12011yescharacteristic
267C3×C4C3×#12111yescharacteristic
268C3×C4C3×#12111yescharacteristic
269C3×C4C3×#12311yescharacteristic
270C9#205211yescharacteristic, direct product factor, Sylow
271C23—21no—
272C23C9×#4111yescharacteristic
273Q8—22no—
274Q8—21no—
275Q8—22no—
276Q8—21no—
277Q8—41no—
278Q8—41no—
279D4—21no—
280D4—21no—
281D4—41no—
282D4—41no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—81no—
291C2×C4C2×D4×C911yescharacteristic
292C2×C4C2×D4×C911yescharacteristic
293C2×C4C2×D4×C911yescharacteristic
294C2×C4C2×D4×C911yescharacteristic
295C2×C4C9×#4111yescharacteristic
296C2×C4C9×#4111yescharacteristic
297C8—22no—
298C8—22no—
299C8—41no—
300C8—41no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—81no—
304C2×C3C3×#39411yescharacteristic
305C2×C3C3×#47111yescharacteristic
306C2×C3C3×#47311yescharacteristic
307C22—21no—
308C22—21no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22C9×#12111yescharacteristic
313C22C9×#12311yescharacteristic
314C22C9×#12411yescharacteristic
315C4—41no—
316C4—42no—
317C4—81no—
318C4C9×#12011yescharacteristic
319C4C9×#12111yescharacteristic
320C4C9×#12111yescharacteristic
321C4C9×#12311yescharacteristic
322C3C3×#205211yescharacteristic
323C2—21no—
324C2—21no—
325C2—81no—
326C2C9×#39411yescharacteristic
327C2C9×#47111yescharacteristic
328C2C9×#47311yescharacteristic
subgroupG/H
centerC22×C9#121
commutatorC22×C4C23×C9
Frattini, cosocleC22×C3×C4C23×C3
socleC22×C3C3×#121
prime radicalC2×C3×#41C22×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C9 ◁ C22×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C9×#108C2semidirect
4. C2×C9×#103C2semidirect
5. C2×C9×#101C2semidirect
7. C9×#343C2semidirect
66. #2052C9direct (N × H)
115. C2×#108C2×C9semidirect
117. C2×#103C2×C9semidirect
118. C2×#101C2×C9semidirect
120. #343C2×C9semidirect
270. C9#2052direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1372
C2×C9×#1082
C9×#4172
C2×C9×#1032
C2×C9×#1012
C9×#4082
C9×#3432
C3×#20523