Finite Group Databasebeta

← #10589722

Subgroups — #10589722

Order 576.

378 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#121C211yesmaximal, characteristic, complemented
2#63502C211yesmaximal, characteristic, complemented
3#63501C211yesmaximal, characteristic, complemented
4#63501C211yesmaximal, characteristic, complemented
5#63500C211yesmaximal, characteristic, complemented
6#63499C211yesmaximal, characteristic, complemented
7#63499C211yesmaximal, characteristic, complemented
8#63492C211yesmaximal, characteristic, complemented
9#63491C211yesmaximal, characteristic, complemented
10#63460C211yesmaximal, characteristic, complemented
11#63456C211yesmaximal, characteristic, complemented
12#63448C211yesmaximal, characteristic, complemented
13#63446C211yesmaximal, characteristic, complemented
14#63444C211yesmaximal, characteristic, complemented
15#63441C211yesmaximal, characteristic, complemented
16#5620—31nomaximal
17C23×D9C2211yescharacteristic
18C2×D4×C9C2211yescharacteristic
19C2×D4×C9C2211yescharacteristic
20C2×D4×C9C2211yescharacteristic, complemented
21C22×C4×C9C2211yescharacteristic, complemented
22C2×#611C2211yescharacteristic
23C2×#611C2211yescharacteristic
24C2×#611C2211yescharacteristic
25C2×#611C2211yescharacteristic
26C2×#611C2211yescharacteristic
27C2×#611C2211yescharacteristic, complemented
28C2×#611C2211yescharacteristic, complemented
29C22×Dic9C2211yescharacteristic, complemented
30C2×D36C2211yescharacteristic
31C2×D36C2211yescharacteristic
32C2×C4×D9C2211yescharacteristic, complemented
33C9×C4⋊C4C2211yescharacteristic, complemented
34C9×C22⋊C4C2211yescharacteristic
35C9×C22⋊C4C2211yescharacteristic, complemented
36#3676C2211yescharacteristic
37#3676C2211yescharacteristic
38#3676C2211yescharacteristic, complemented
39(C2×D9)⋊C4C2211yescharacteristic
40(C2×D9)⋊C4C2211yescharacteristic
41(C2×D9)⋊C4C2211yescharacteristic
42(C2×D9)⋊C4C2211yescharacteristic
43(C2×D9)⋊C4C2211yescharacteristic
44(C2×D9)⋊C4C2211yescharacteristic
45(C2×D9)⋊C4C2211yescharacteristic, complemented
46C4⋊Dic9C2211yescharacteristic, complemented
47C4⋊Dic9C2211yescharacteristic, complemented
48Dic9⋊C4C2211yescharacteristic, complemented
49Dic9⋊C4C2211yescharacteristic, complemented
50Dic9⋊C4C2211yescharacteristic, complemented
51C4×Dic9C2211yescharacteristic, complemented
52C3×#121D311yescharacteristic
53#940—31no—
54#939—31no—
55#939—31no—
56#938—31no—
57#937—31no—
58#937—31no—
59#930—31no—
60#929—31no—
61#898—31no—
62#894—31no—
63#886—31no—
64#884—31no—
65#882—31no—
66#879—31no—
67C23×C9C2311yescharacteristic
68C23×C9C2311yescharacteristic
69C23×C9C2311yescharacteristic
70C22×D9—41no—
71C22×D9—41no—
72C22×D9—41no—
73C22×D9C2311yescharacteristic
74C22×D9C2311yescharacteristic
75C22×D9C2311yescharacteristic
76D4×C9—41no—
77D4×C9—41no—
78D4×C9—41no—
79C2×C4×C9—41no—
80C2×C4×C9C2311yescharacteristic
81C2×C4×C9C2311yescharacteristic
82C2×C4×C9C2311yescharacteristic
83C2×C4×C9C2311yescharacteristic
84#611—41no—
85#611—41no—
86#611—41no—
87#611—41no—
88#611—41no—
89#611—41no—
90#611—41no—
91C2×Dic9—41no—
92C2×Dic9C2311yescharacteristic
93C2×Dic9C2311yescharacteristic
94C2×Dic9C2311yescharacteristic
95C2×Dic9C2311yescharacteristic
96C2×Dic9C2311yescharacteristic
97D36—41no—
98D36—41no—
99C4×D9—41no—
100#560—91noSylow
101C23×D3—31no—
102C2×C3×D4C2×D311yescharacteristic
103C2×C3×D4C2×D311yescharacteristic
104C2×C3×D4C2×D311yescharacteristic
105C22×C3×C4C2×D311yescharacteristic
106C2×#67—31no—
107C2×#67—31no—
108C2×#67—31no—
109C2×#67—31no—
110C2×#67—31no—
111C2×#67—31no—
112C2×#67—31no—
113C22×Dic3—31no—
114C2×D12—31no—
115C2×D12—31no—
116C2×C4×D3—31no—
117C3×C4⋊C4C2×D311yescharacteristic
118C3×C22⋊C4C2×D311yescharacteristic
119C3×C22⋊C4C2×D311yescharacteristic
120#217—31no—
121#217—31no—
122#217—31no—
123(C2×D3)⋊C4—31no—
124(C2×D3)⋊C4—31no—
125(C2×D3)⋊C4—31no—
126(C2×D3)⋊C4—31no—
127(C2×D3)⋊C4—31no—
128(C2×D3)⋊C4—31no—
129(C2×D3)⋊C4—31no—
130C4⋊Dic3—31no—
131C4⋊Dic3—31no—
132Dic3⋊C4—31no—
133Dic3⋊C4—31no—
134Dic3⋊C4—31no—
135C4×Dic3—31no—
136C22×C9—21no—
137C22×C9—21no—
138C22×C9—21no—
139C22×C9—21no—
140C22×C9—21no—
141C22×C9—21no—
142C22×C9—21no—
143C22×C9—21no—
144C22×C9—21no—
145C22×C9C2411yescharacteristic
146C2×D9—21no—
147C2×D9—21no—
148C2×D9—21no—
149C2×D9—21no—
150C2×D9—21no—
151C2×D9—21no—
152C2×D9—21no—
153C2×D9—21no—
154C2×D9—21no—
155C2×D9—44no—
156C4×C9—21no—
157C4×C9—21no—
158C4×C9—21no—
159C4×C9—21no—
160Dic9—21no—
161Dic9—21no—
162Dic9—21no—
163Dic9—21no—
164Dic9—21no—
165#127—91no—
166#126—91no—
167#126—91no—
168#123—91no—
169#123—91no—
170#123—91no—
171#121—91no—
172#121—91no—
173#121—91no—
174#121—91no—
175#121—91no—
176#121D911yescharacteristic, complemented
177#120—91no—
178#120—91no—
179#120—91no—
180C23×C3C22×D311yescharacteristic
181C23×C3C22×D311yescharacteristic
182C23×C3C22×D311yescharacteristic
183C22×D3—31no—
184C22×D3—31no—
185C22×D3—31no—
186C22×D3—121no—
187C22×D3—121no—
188C22×D3—121no—
189C3×D4—41no—
190C3×D4—41no—
191C3×D4—41no—
192C2×C3×C4—41no—
193C2×C3×C4C22×D311yescharacteristic
194C2×C3×C4C22×D311yescharacteristic
195C2×C3×C4C22×D311yescharacteristic
196C2×C3×C4C22×D311yescharacteristic
197#67—121no—
198#67—121no—
199#67—121no—
200#67—121no—
201#67—121no—
202#67—121no—
203#67—121no—
204C2×Dic3—31no—
205C2×Dic3—31no—
206C2×Dic3—31no—
207C2×Dic3—31no—
208C2×Dic3—31no—
209C2×Dic3—121no—
210D12—121no—
211D12—121no—
212C4×D3—121no—
213C2×C9—41no—
214C2×C9—41no—
215C2×C9—41no—
216C2×C9H(5,𝔽2)11yescharacteristic
217C2×C9H(5,𝔽2)11yescharacteristic
218C2×C9H(5,𝔽2)11yescharacteristic
219D9—41no—
220D9—41no—
221D9—41no—
222C24—91no—
223C2×D4—91no—
224C2×D4—91no—
225C2×D4—91no—
226C2×D4—91no—
227C2×D4—91no—
228C2×D4—91no—
229C2×D4—91no—
230C2×D4—91no—
231C2×D4—91no—
232C2×D4C2×D911yescharacteristic
233C2×D4C2×D911yescharacteristic
234C2×D4C2×D911yescharacteristic, complemented
235C22×C4—91no—
236C22×C4—91no—
237C22×C4C2×D911yescharacteristic, complemented
238C4⋊C4—91no—
239C4⋊C4—91no—
240C4⋊C4—91no—
241C4⋊C4—91no—
242C4⋊C4—91no—
243C4⋊C4C2×D911yescharacteristic, complemented
244C22⋊C4—91no—
245C22⋊C4—91no—
246C22⋊C4—91no—
247C22⋊C4—91no—
248C22⋊C4—91no—
249C22⋊C4—91no—
250C22⋊C4—91no—
251C22⋊C4—91no—
252C22⋊C4—91no—
253C22⋊C4—91no—
254C22⋊C4C2×D911yescharacteristic
255C22⋊C4C2×D911yescharacteristic, complemented
256C42—91no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3C23×D311yescharacteristic
267C2×D3—61no—
268C2×D3—61no—
269C2×D3—61no—
270C2×D3—61no—
271C2×D3—61no—
272C2×D3—61no—
273C2×D3—61no—
274C2×D3—61no—
275C2×D3—61no—
276C2×D3—124no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281Dic3—61no—
282Dic3—61no—
283Dic3—61no—
284Dic3—61no—
285Dic3—61no—
286C9#56011yescharacteristic, complemented, Sylow
287C23—91no—
288C23—91no—
289C23—91no—
290C23—361no—
291C23—361no—
292C23—361no—
293C23C22×D911yescharacteristic
294C23C22×D911yescharacteristic
295C23C22×D911yescharacteristic
296D4—41no—
297D4—41no—
298D4—41no—
299D4—361no—
300D4—361no—
301D4—361no—
302D4—361no—
303D4—361no—
304D4—361no—
305D4—361no—
306D4—361no—
307D4—361no—
308C2×C4—41no—
309C2×C4—91no—
310C2×C4—91no—
311C2×C4—91no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—361no—
315C2×C4—361no—
316C2×C4C22×D911yescharacteristic
317C2×C4C22×D911yescharacteristic
318C2×C4C22×D911yescharacteristic
319C2×C4C22×D911yescharacteristic
320C2×C3—41no—
321C2×C3—41no—
322C2×C3—41no—
323C2×C3#100411yescharacteristic
324C2×C3#100411yescharacteristic
325C2×C3#100911yescharacteristic
326D3—121no—
327D3—121no—
328D3—121no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—181no—
339C22—181no—
340C22—181no—
341C22—181no—
342C22—181no—
343C22—181no—
344C22—181no—
345C22—181no—
346C22—181no—
347C22—364no—
348C22C23×D911yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—181no—
354C4—181no—
355C4—181no—
356C4—181no—
357C4—181no—
358C3#562011yescharacteristic
359C2—41no—
360C2—41no—
361C2—41no—
362C2—361no—
363C2—361no—
364C2—361no—
365C2#6371011yescharacteristic
366C2#6371011yescharacteristic
367C2#6371511yescharacteristic
subgroupG/H
centerC22C23×D9
commutator, cosocleC22×C9C24
Frattini, socleC22×C3C23×D3
FittingC9×#121C2
hypercenter#121D9
hypocenterC9#560
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C9×#121C2semidirect
2. #63502C2semidirect
3. #63501C2semidirect
4. #63501C2semidirect
5. #63500C2semidirect
6. #63499C2semidirect
7. #63499C2semidirect
8. #63492C2semidirect
9. #63491C2semidirect
10. #63460C2semidirect
11. #63456C2semidirect
12. #63448C2semidirect
13. #63446C2semidirect
14. #63444C2semidirect
15. #63441C2semidirect
20. C2×D4×C9C22semidirect
21. C22×C4×C9C22semidirect
27. C2×#611C22semidirect
28. C2×#611C22semidirect
29. C22×Dic9C22semidirect
32. C2×C4×D9C22semidirect
33. C9×C4⋊C4C22semidirect
35. C9×C22⋊C4C22semidirect
38. #3676C22semidirect
45. (C2×D9)⋊C4C22semidirect
46. C4⋊Dic9C22semidirect
47. C4⋊Dic9C22semidirect
48. Dic9⋊C4C22semidirect
49. Dic9⋊C4C22semidirect
50. Dic9⋊C4C22semidirect
51. C4×Dic9C22semidirect
176. #121D9semidirect
234. C2×D4C2×D9semidirect
237. C22×C4C2×D9semidirect
243. C4⋊C4C2×D9semidirect
255. C22⋊C4C2×D9semidirect
286. C9#560semidirect

Maximal subgroups

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

subgroupindex
C9×#1212
#635022
#635012
#635002
#634992
#634922
#634912
#634602
#634562
#634482
#634462
#634442
#634412
#56203