Finite Group Databasebeta

← C9×#2077 #11766798

Subgroups — C9×#2077 #11766798

Order 1152.

384 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#106C211yesmaximal, characteristic, complemented
2C2×C9×C22⋊C8C211yesmaximal, characteristic
3C9×#380C211yesmaximal, characteristic
4C9×#380C211yesmaximal, characteristic
5C9×#340C211yesmaximal, characteristic, complemented
6C9×#340C211yesmaximal, characteristic, complemented
7C9×#340C211yesmaximal, characteristic, complemented
8C3×#2077C311yesmaximal, characteristic
9C23×C4×C9C2211yescharacteristic
10C22×C8×C9C2211yescharacteristic
11C22×C8×C9C2211yescharacteristic
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×C9×C4⋊C4C2211yescharacteristic
14C2×C9×C4⋊C4C2211yescharacteristic
15C2×C9×C4⋊C4C2211yescharacteristic
16C2×C9×C22⋊C4—21no—
17C2×C9×C22⋊C4—21no—
18C9×#106—22no—
19C9×C22⋊C8—22no—
20C9×#95—21no—
21C9×#95—21no—
22C2×C3×#106C2×C311yescharacteristic
23C2×C3×C22⋊C8C2×C311yescharacteristic
24C3×#380C2×C311yescharacteristic
25C3×#380C2×C311yescharacteristic
26C3×#340C2×C311yescharacteristic
27C3×#340C2×C311yescharacteristic
28C3×#340C2×C311yescharacteristic
29C24×C9D411yescharacteristic
30C22×C4×C9—21no—
31C22×C4×C9—21no—
32C22×C4×C9—21no—
33C22×C4×C9—21no—
34C22×C4×C9—21no—
35C22×C4×C9—21no—
36C22×C4×C9—21no—
37C22×C4×C9—21no—
38C22×C4×C9—21no—
39C22×C4×C9—21no—
40C22×C4×C9D411yescharacteristic
41C22×C4×C9C2311yescharacteristic
42C2×C8×C9—21no—
43C2×C8×C9—21no—
44C2×C8×C9—21no—
45C2×C8×C9—21no—
46C2×C8×C9—21no—
47C2×C8×C9D412yes—
48C9×C4⋊C4—21no—
49C9×C4⋊C4—21no—
50C9×C4⋊C4—21no—
51C9×C4⋊C4—21no—
52C9×C4⋊C4—21no—
53C9×C4⋊C4—21no—
54C9×C4⋊C4—21no—
55C9×C4⋊C4—21no—
56C9×C22⋊C4—42no—
57C9×C22⋊C4—42no—
58#2077C911yescharacteristic, direct product factor, Sylow
59C23×C3×C4C22×C311yescharacteristic
60C22×C3×C8C22×C311yescharacteristic
61C22×C3×C8C22×C311yescharacteristic
62C2×C3×C4⋊C4C22×C311yescharacteristic
63C2×C3×C4⋊C4C22×C311yescharacteristic
64C2×C3×C4⋊C4C22×C311yescharacteristic
65C2×C3×C4⋊C4C22×C311yescharacteristic
66C2×C3×C22⋊C4—21no—
67C2×C3×C22⋊C4—21no—
68C3×#106—22no—
69C3×C22⋊C8—22no—
70C3×#95—21no—
71C3×#95—21no—
72C23×C9—21no—
73C23×C9—21no—
74C23×C9—21no—
75C23×C9—21no—
76C23×C9—21no—
77C23×C9—21no—
78C23×C9SD1612yes—
79C23×C9C2×D411yescharacteristic
80C2×C4×C9—21no—
81C2×C4×C9—21no—
82C2×C4×C9—21no—
83C2×C4×C9—41no—
84C2×C4×C9—41no—
85C2×C4×C9—41no—
86C2×C4×C9—41no—
87C2×C4×C9—41no—
88C2×C4×C9—41no—
89C2×C4×C9—41no—
90C2×C4×C9—41no—
91C2×C4×C9—41no—
92C2×C4×C9—41no—
93C2×C4×C9—41no—
94C2×C4×C9—41no—
95C2×C4×C9—41no—
96C2×C4×C9—41no—
97C2×C4×C9—41no—
98C2×C4×C9—41no—
99C2×C4×C9C2×D411yescharacteristic
100C2×C4×C9#4111yescharacteristic
101C2×C4×C9#4111yescharacteristic
102C2×C4×C9#4111yescharacteristic
103C2×C4×C9#4111yescharacteristic
104C2×C4×C9#4111yescharacteristic
105C8×C9—22no—
106C8×C9—41no—
107C2×#106C2×C911yescharacteristic, complemented
108C2×C22⋊C8C2×C911yescharacteristic
109#380C2×C911yescharacteristic
110#380C2×C911yescharacteristic
111#340C2×C911yescharacteristic, complemented
112#340C2×C911yescharacteristic, complemented
113#340C2×C911yescharacteristic, complemented
114C24×C3C3×D411yescharacteristic
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4C3×D411yescharacteristic
126C22×C3×C4C23×C311yescharacteristic
127C2×C3×C8—21no—
128C2×C3×C8—21no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8C3×D412yes—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C22⋊C4—42no—
142C3×C22⋊C4—42no—
143C22×C9—22no—
144C22×C9—22no—
145C22×C9—22no—
146C22×C9—41no—
147C22×C9—41no—
148C22×C9—41no—
149C22×C9—41no—
150C22×C9#12111yescharacteristic
151C22×C9#12311yescharacteristic
152C22×C9#12311yescharacteristic
153C22×C9C2×SD1611yescharacteristic
154C22×C9#13511yescharacteristic
155C22×C9AGL(1,ℤ/8)11yescharacteristic
156C22×C9#13711yescharacteristic
157C4×C9—41no—
158C4×C9—81no—
159C4×C9—81no—
160C4×C9—81no—
161C4×C9—81no—
162C4×C9#12311yescharacteristic
163C4×C9#12411yescharacteristic
164C4×C9#12611yescharacteristic
165C4×C9#12611yescharacteristic
166C23×C4C22×C911yescharacteristic
167C22×C8C22×C911yescharacteristic
168C22×C8C22×C911yescharacteristic
169C2×C4⋊C4C22×C911yescharacteristic
170C2×C4⋊C4C22×C911yescharacteristic
171C2×C4⋊C4C22×C911yescharacteristic
172C2×C4⋊C4C22×C911yescharacteristic
173C2×C22⋊C4—21no—
174C2×C22⋊C4—21no—
175#106—22no—
176C22⋊C8—22no—
177#95—21no—
178#95—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3C3×SD1612yes—
186C23×C3C2×C3×D411yescharacteristic
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4—41no—
197C2×C3×C4—41no—
198C2×C3×C4—41no—
199C2×C3×C4—41no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4C2×C3×D411yescharacteristic
207C2×C3×C4C3×#4111yescharacteristic
208C2×C3×C4C3×#4111yescharacteristic
209C2×C3×C4C3×#4111yescharacteristic
210C2×C3×C4C3×#4111yescharacteristic
211C2×C3×C4C3×#4111yescharacteristic
212C3×C8—22no—
213C3×C8—41no—
214C2×C9—42no—
215C2×C9#39711yescharacteristic
216C2×C9#46511yescharacteristic
217C2×C9#46811yescharacteristic
218C2×C9#48111yescharacteristic
219C2×C9#48211yescharacteristic
220C2×C9#48311yescharacteristic
221C2×C9#48511yescharacteristic
222C24D4×C911yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4D4×C911yescharacteristic
234C22×C4C23×C911yescharacteristic
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8D4×C912yes—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22×C3—22no—
252C22×C3—22no—
253C22×C3—22no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3—41no—
257C22×C3—41no—
258C22×C3C3×#12111yescharacteristic
259C22×C3C3×#12311yescharacteristic
260C22×C3C3×#12311yescharacteristic
261C22×C3C2×C3×SD1611yescharacteristic
262C22×C3C3×#13511yescharacteristic
263C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
264C22×C3C3×#13711yescharacteristic
265C3×C4—41no—
266C3×C4—81no—
267C3×C4—81no—
268C3×C4—81no—
269C3×C4—81no—
270C3×C4C3×#12311yescharacteristic
271C3×C4C3×#12411yescharacteristic
272C3×C4C3×#12611yescharacteristic
273C3×C4C3×#12611yescharacteristic
274C9#207711yescharacteristic, direct product factor, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23C9×SD1612yes—
282C23C2×D4×C911yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4C2×D4×C911yescharacteristic
303C2×C4C9×#4111yescharacteristic
304C2×C4C9×#4111yescharacteristic
305C2×C4C9×#4111yescharacteristic
306C2×C4C9×#4111yescharacteristic
307C2×C4C9×#4111yescharacteristic
308C8—22no—
309C8—41no—
310C2×C3—42no—
311C2×C3C3×#39711yescharacteristic
312C2×C3C3×#46511yescharacteristic
313C2×C3C3×#46811yescharacteristic
314C2×C3C3×#48111yescharacteristic
315C2×C3C3×#48211yescharacteristic
316C2×C3C3×#48311yescharacteristic
317C2×C3C3×#48511yescharacteristic
318C22—22no—
319C22—22no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22C9×#12111yescharacteristic
326C22C9×#12311yescharacteristic
327C22C9×#12311yescharacteristic
328C22C2×C9×SD1611yescharacteristic
329C22C9×#13511yescharacteristic
330C22C9×AGL(1,ℤ/8)11yescharacteristic
331C22C9×#13711yescharacteristic
332C4—41no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4C9×#12311yescharacteristic
338C4C9×#12411yescharacteristic
339C4C9×#12611yescharacteristic
340C4C9×#12611yescharacteristic
341C3C3×#207711yescharacteristic
342C2—42no—
343C2C9×#39711yescharacteristic
344C2C9×#46511yescharacteristic
345C2C9×#46811yescharacteristic
346C2C9×#48111yescharacteristic
347C2C9×#48211yescharacteristic
348C2C9×#48311yescharacteristic
349C2C9×#48511yescharacteristic
subgroupG/H
centerC23×C9C2×D4
commutatorC22×C4C23×C9
Frattini, cosocleC22×C3×C4C23×C3
socleC23×C3C2×C3×D4
prime radicalC24×C3C3×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C9 ◁ C23×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C9×#106C2semidirect
5. C9×#340C2semidirect
6. C9×#340C2semidirect
7. C9×#340C2semidirect
58. #2077C9direct (N × H)
107. C2×#106C2×C9semidirect
111. #340C2×C9semidirect
112. #340C2×C9semidirect
113. #340C2×C9semidirect
274. C9#2077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1062
C2×C9×C22⋊C82
C9×#3802
C9×#3402
C3×#20773