Finite Group Databasebeta

← C3×D32×#261 #72277178

Subgroups — C3×D32×#261 #72277178

Order 5616.

540 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C3⋊#261C212yesmaximal, complemented
2C3×(C3⋊#261)⋊D3C211yesmaximal, characteristic, complemented
3C3×D32×D13C211yesmaximal, characteristic
4C32×D3×#261C212yesmaximal, complemented
5C3×C3⋊D3×#261C211yesmaximal, characteristic, complemented
6C2×C3×D3×#261—32nomaximal
7D32×#261C311yesmaximal, characteristic, direct product factor
8C3×(C3⋊D3)⋊D13C411yescharacteristic, complemented
9C3×D3×D39C412yescomplemented
10C3×D32×C13C411yescharacteristic, complemented
11C3×C3⋊D3×D13C2211yescharacteristic
12C32×D3×D13C2212yes—
13C3×C3⋊(C3⋊#261)C2211yescharacteristic, complemented
14C32×C3⋊#261C2212yescomplemented
15C33×#261C2211yescharacteristic, complemented
16C2×C3×D3×D13—32no—
17C2×C3×C3⋊#261—32no—
18C2×C32×#261—32no—
19D32×D13C2×C311yescharacteristic
20(C3⋊#261)⋊D3C2×C311yescharacteristic, complemented
21D3×C3⋊#261C2×C312yescomplemented
22C3⋊D3×#261C2×C311yescharacteristic, complemented
23C3×D3×#261—22no—
24C3×D3×#261—32no—
25C3×D3×#261—32no—
26C3×D3×#261—32no—
27C3×D3×#261—61no—
28C3×D3×#261D312yesdirect product factor
29C3×D3×#261C2×C312yescomplemented
30C3×C3⋊D39C2×C411yescharacteristic, complemented
31C3×C13×C3⋊D3C2×C411yescharacteristic, complemented
32C32×D39C2×C412yescomplemented
33C32×D3×C13C2×C412yescomplemented
34C33×D13C2311yescharacteristic
35C22×C3×#261—91no—
36C2×D3×#261—32no—
37C2×C3×D39—32no—
38C2×C3×D3×C13—32no—
39C2×C32×D13—32no—
40(C3⋊D3)⋊D13C3×C411yescharacteristic, complemented
41D3×D39C3×C412yescomplemented
42D32×C13C3×C411yescharacteristic, complemented
43C3⋊D3×D13C22×C311yescharacteristic
44C3×D3×D13—22no—
45C3×D3×D13—32no—
46C3×D3×D13—32no—
47C3×D3×D13—32no—
48C3×D3×D13—61no—
49C3×D3×D13C2×D312yes—
50C3×D3×D13C22×C312yes—
51C3⋊(C3⋊#261)C22×C311yescharacteristic, complemented
52C3×C3⋊#261—22no—
53C3×C3⋊#261—32no—
54C3×C3⋊#261—61no—
55C3×C3⋊#261C2×D312yescomplemented
56C3×C3⋊#261C22×C312yescomplemented
57C32×#261—21no—
58C32×#261—22no—
59C32×#261—32no—
60C32×#261—41no—
61C32×#261C2×D312yescomplemented
62C32×#261C22×C311yescharacteristic, complemented
63C3×C4×D32—131nomaximal, Hall
64C33×C13C22×C411yescharacteristic, complemented, Hall
65C22×C3×D13—91no—
66C2×D3×D13—32no—
67C2×C3⋊#261—32no—
68C2×C3×#261—32no—
69C2×C3×#261—32no—
70C2×C3×#261—62no—
71C2×C3×#261—91no—
72C2×C3×#261—92no—
73C2×C3×#261—91no—
74D3×#261—32no—
75D3×#261—32no—
76D3×#261—32no—
77D3×#261—61no—
78D3×#261C3×D312yesdirect product factor
79C2×C32×C13—32no—
80C3⋊D39C2×C3×C411yescharacteristic, complemented
81C13×C3⋊D3C2×C3×C411yescharacteristic, complemented
82C3×D39—22no—
83C3×D39—32no—
84C3×D39—61no—
85C3×D39C4×D312yescomplemented
86C3×D39C2×C3×C412yescomplemented
87C3×D3×C13—22no—
88C3×D3×C13—32no—
89C3×D3×C13—61no—
90C3×D3×C13C4×D312yescomplemented
91C3×D3×C13C2×C3×C412yescomplemented
92C32×D13—21no—
93C32×D13—22no—
94C32×D13—32no—
95C32×D13—41no—
96C32×D13C22×D312yes—
97C32×D13C23×C311yescharacteristic
98C2×C3×D32—131no—
99C3×C4×C3⋊D3—131no—
100C32×C4×D3—132no—
101C3×#624—131no—
102C3×D3×Dic3—132no—
103C22×#261—91noHall
104C22×C3×C13—91no—
105C2×D39—32no—
106C2×D3×C13—32no—
107C2×C3×D13—32no—
108C2×C3×D13—32no—
109C2×C3×D13—62no—
110C2×C3×D13—91no—
111C2×C3×D13—92no—
112C2×C3×D13—91no—
113D3×D13—32no—
114D3×D13—32no—
115D3×D13—32no—
116D3×D13—61no—
117D3×D13C2×C3×D312yes—
118C3⋊#261—32no—
119C3⋊#261—61no—
120C3⋊#261C2×C3×D312yescomplemented
121C3×#261—21no—
122C3×#261—22no—
123C3×#261—32no—
124C3×#261—32no—
125C3×#261—41no—
126C3×#261—62no—
127C3×#261—91no—
128C3×#261D3211yescharacteristic, direct product factor
129C3×#261C2×C3×D312yescomplemented
130C2×C3×C4×D3—392no—
131C4×D32—131no—
132C32×C13—21no—
133C32×C13—22no—
134C32×C13—41no—
135C32×C13C2×C4×D312yescomplemented
136C32×C13C22×C3×C411yescharacteristic, complemented
137C2×C3×C3⋊D3—131no—
138C2×C32×D3—132no—
139C3×D32—131no—
140C3×D32—132no—
141C3×D32#26111yescharacteristic, direct product factor
142C33×C4—131no—
143C3×C3⋊Dic3—131no—
144C32×Dic3—132no—
145C22×D13—91no—
146C2×#261—32no—
147C2×#261—91no—
148C2×#261—92no—
149C2×#261—91no—
150C2×C3×C13—32no—
151C2×C3×C13—32no—
152C2×C3×C13—62no—
153C2×C3×C13—91no—
154D39—32no—
155D39—61no—
156D39C3×C4×D312yescomplemented
157C3×D13—22no—
158C3×D13—21no—
159C3×D13—32no—
160C3×D13—32no—
161C3×D13—41no—
162C3×D13—62no—
163C3×D13—91no—
164C3×D13C2×D3211yescharacteristic
165C3×D13C22×C3×D312yes—
166D3×C13—32no—
167D3×C13—61no—
168D3×C13C3×C4×D312yescomplemented
169C22×C3×D3—392no—
170C2×D32—131no—
171C2×C32×C4—392no—
172C4×C3⋊D3—131no—
173C2×C3×Dic3—392no—
174C3×C4×D3—132no—
175C3×C4×D3—132no—
176C3×C4×D3—262no—
177C3×C4×D3—392no—
178C3×C4×D3—392no—
179C3×C4×D3—392no—
180C3×C4×D3—781no—
181#624—131no—
182D3×Dic3—132no—
183C2×C33—131no—
184C3×C3⋊D3—131no—
185C3×C3⋊D3C2×#26111yescharacteristic, complemented
186C32×D3—132no—
187C32×D3C2×#26112yescomplemented
188C22×C13—91no—
189C2×D13—32no—
190C2×D13—91no—
191C2×D13—92no—
192C2×D13—91no—
193#261—32no—
194#261—91no—
195#261C3×D3211yescharacteristic, direct product factor
196C22×C3×C4—1171no—
197C2×C4×D3—392no—
198C3×C13—21no—
199C3×C13—22no—
200C3×C13—41no—
201C3×C13C4×D3211yescharacteristic, complemented
202C3×C13C2×C3×C4×D312yescomplemented
203C22×C32—392no—
204C2×C3⋊D3—131no—
205C2×C3×D3—32no—
206C2×C3×D3—132no—
207C2×C3×D3—132no—
208C2×C3×D3—262no—
209C2×C3×D3—392no—
210C2×C3×D3—392no—
211C2×C3×D3—392no—
212C2×C3×D3—392no—
213C2×C3×D3—781no—
214D32—131no—
215D32—132no—
216D32C3×#26111yescharacteristic, direct product factor
217C32×C4—131no—
218C32×C4—132no—
219C32×C4—262no—
220C32×C4—261no—
221C32×C4—392no—
222C32×C4—521no—
223C3⋊Dic3—131no—
224C3×Dic3—132no—
225C3×Dic3—132no—
226C3×Dic3—262no—
227C3×Dic3—392no—
228C3×Dic3—781no—
229C33C22×#26111yescharacteristic, complemented, Sylow
230C2×C13—32no—
231C2×C13—91no—
232D13—32no—
233D13—91no—
234D13C2×C3×D3211yescharacteristic
235C23×C3—1171no—
236C22×D3—392no—
237C2×C3×C4—392no—
238C2×C3×C4—392no—
239C2×C3×C4—782no—
240C2×C3×C4—1171no—
241C2×C3×C4—1171no—
242C2×C3×C4—1172no—
243C2×Dic3—392no—
244C4×D3—132no—
245C4×D3—392no—
246C4×D3—392no—
247C4×D3—392no—
248C4×D3—781no—
249C2×C32—32no—
250C2×C32—132no—
251C2×C32—131no—
252C2×C32—262no—
253C2×C32—261no—
254C2×C32—392no—
255C2×C32—521no—
256C3⋊D3—131no—
257C3⋊D3C2×C3×#26111yescharacteristic, complemented
258C3×D3—22no—
259C3×D3—32no—
260C3×D3—61no—
261C3×D3—132no—
262C3×D3—132no—
263C3×D3—262no—
264C3×D3—392no—
265C3×D3—781no—
266C3×D3D3×#26112yesdirect product factor
267C3×D3C2×C3×#26112yescomplemented
268C22×C4—1171noSylow
269C13C3×C4×D3211yescharacteristic, complemented, Sylow
270C22×C3—91no—
271C22×C3—392no—
272C22×C3—392no—
273C22×C3—782no—
274C22×C3—1172no—
275C22×C3—1171no—
276C22×C3—1171no—
277C2×D3—32no—
278C2×D3—132no—
279C2×D3—392no—
280C2×D3—392no—
281C2×D3—392no—
282C2×D3—392no—
283C2×D3—781no—
284C3×C4—132no—
285C3×C4—131no—
286C3×C4—261no—
287C3×C4—262no—
288C3×C4—392no—
289C3×C4—392no—
290C3×C4—521no—
291C3×C4—782no—
292C3×C4—1171no—
293Dic3—132no—
294Dic3—392no—
295Dic3—781no—
296C32—21no—
297C32—22no—
298C32—41no—
299C32C2×D3×#26112yescomplemented
300C32C22×C3×#26111yescharacteristic, complemented
301C23—1171no—
302C2×C4—392no—
303C2×C4—1171no—
304C2×C4—1171no—
305C2×C4—1172no—
306C2×C3—32no—
307C2×C3—32no—
308C2×C3—62no—
309C2×C3—91no—
310C2×C3—131no—
311C2×C3—132no—
312C2×C3—261no—
313C2×C3—262no—
314C2×C3—392no—
315C2×C3—392no—
316C2×C3—521no—
317C2×C3—782no—
318C2×C3—1171no—
319D3—32no—
320D3—61no—
321D3—132no—
322D3—392no—
323D3—781no—
324D3C3×D3×#26112yesdirect product factor
325C22—91no—
326C22—392no—
327C22—1172no—
328C22—1171no—
329C22—1171no—
330C4—131no—
331C4—392no—
332C4—1171no—
333C3—21no—
334C3—22no—
335C3—41no—
336C3D32×#26111yescharacteristic, direct product factor
337C3C2×C3×D3×#26112yescomplemented
338C2—32no—
339C2—91no—
340C2—131no—
341C2—392no—
342C2—1171no—
subgroupG/H
center, hypercenterC3D32×#261
commutator, hypocenterC32×C13C22×C3×C4
FrattiniC1G
Fitting, socleC33×C13C22×C4
prime radicalC3×D32×D13C2
cosocleC32×D13C23×C3
LCSG ▷ C32×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×D3×C3⋊#261C2semidirect
2. C3×(C3⋊#261)⋊D3C2semidirect
4. C32×D3×#261C2semidirect
5. C3×C3⋊D3×#261C2semidirect
7. D32×#261C3direct (N × H)
8. C3×(C3⋊D3)⋊D13C4semidirect
9. C3×D3×D39C4semidirect
10. C3×D32×C13C4semidirect
13. C3×C3⋊(C3⋊#261)C22semidirect
14. C32×C3⋊#261C22semidirect
15. C33×#261C22semidirect
20. (C3⋊#261)⋊D3C2×C3semidirect
21. D3×C3⋊#261C2×C3semidirect
22. C3⋊D3×#261C2×C3semidirect
28. C3×D3×#261D3direct (N × H)
29. C3×D3×#261C2×C3semidirect
30. C3×C3⋊D39C2×C4semidirect
31. C3×C13×C3⋊D3C2×C4semidirect
32. C32×D39C2×C4semidirect
33. C32×D3×C13C2×C4semidirect
40. (C3⋊D3)⋊D13C3×C4semidirect
41. D3×D39C3×C4semidirect
42. D32×C13C3×C4semidirect
51. C3⋊(C3⋊#261)C22×C3semidirect
55. C3×C3⋊#261C2×D3semidirect
56. C3×C3⋊#261C22×C3semidirect
61. C32×#261C2×D3semidirect
62. C32×#261C22×C3semidirect
64. C33×C13C22×C4semidirect
78. D3×#261C3×D3direct (N × H)
80. C3⋊D39C2×C3×C4semidirect
81. C13×C3⋊D3C2×C3×C4semidirect
85. C3×D39C4×D3semidirect
86. C3×D39C2×C3×C4semidirect
90. C3×D3×C13C4×D3semidirect
91. C3×D3×C13C2×C3×C4semidirect
120. C3⋊#261C2×C3×D3semidirect
128. C3×#261D32direct (N × H)
129. C3×#261C2×C3×D3semidirect
135. C32×C13C2×C4×D3semidirect
136. C32×C13C22×C3×C4semidirect
141. C3×D32#261direct (N × H)
156. D39C3×C4×D3semidirect
168. D3×C13C3×C4×D3semidirect
185. C3×C3⋊D3C2×#261semidirect
187. C32×D3C2×#261semidirect
195. #261C3×D32direct (N × H)
201. C3×C13C4×D32semidirect
202. C3×C13C2×C3×C4×D3semidirect
216. D32C3×#261direct (N × H)
229. C33C22×#261semidirect
257. C3⋊D3C2×C3×#261semidirect
266. C3×D3D3×#261direct (N × H)
267. C3×D3C2×C3×#261semidirect
269. C13C3×C4×D32semidirect
299. C32C2×D3×#261semidirect
300. C32C22×C3×#261semidirect
324. D3C3×D3×#261direct (N × H)
336. C3D32×#261direct (N × H)
337. C3C2×C3×D3×#261semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C3⋊#2612
C3×(C3⋊#261)⋊D32
C3×D32×D132
C32×D3×#2612
C3×C3⋊D3×#2612
C2×C3×D3×#2613
D32×#2613
C3×C4×D3213