Subgroups — C₃²×#4839 #13162277

Order 1728.

836 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×D₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃²×#872	C₂	1	1	yes	maximal, characteristic
4	C₃³×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#424	—	3	1	no	maximal
9	C₃×#4839	C₃	1	4	yes	maximal, direct product factor
10	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
13	C₃³×C₄²	C₂²	1	1	yes	characteristic
14	C₃²×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
15	C₃²×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
16	C₃²×Dic₃⋊C₄	C₄	1	1	yes	characteristic
17	C₃²×Dic₃⋊C₄	C₄	1	1	yes	characteristic
18	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₃²×ΓL(1,𝔽₂₅)	—	2	2	no	—
22	C₃²×D₃×C₈	—	2	2	no	—
23	C₂×C₃²×M₁₆	—	3	1	no	—
24	C₂²×C₃²×C₈	—	3	1	no	—
25	C₃²×#117	—	3	1	no	—
26	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	4	yes	—
27	C₂×C₃×D₃×C₈	C₂×C₃	1	4	yes	—
28	C₃×#872	C₂×C₃	1	4	yes	—
29	C₃²×C₄⋊C₈	—	2	4	no	—
30	C₃²×C₄⋊C₈	—	3	1	no	—
31	C₃²×C₄⋊C₈	—	3	1	no	—
32	C₃²×C₄⋊C₈	—	3	1	no	—
33	C₃²×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
34	C₃²×C₄⋊C₈	C₂×C₃	1	4	yes	complemented
35	C₃×Dic₃⋊C₈	C₂×C₃	1	4	yes	complemented
36	C₃×Dic₃⋊C₈	C₂×C₃	1	4	yes	complemented
37	C₃×C₄⋊(C₃⋊C₈)	C₂×C₃	1	4	yes	complemented
38	C₂²×C₃²×D₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
42	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₃²×C₄×D₃	D₄	1	2	yes	—
46	C₃²×C₄×D₃	Q₈	1	2	yes	—
47	C₃³×C₈	—	2	1	no	—
48	C₃³×C₈	—	2	1	no	—
49	C₃²×C₃⋊C₈	—	2	1	no	—
50	C₃²×C₃⋊C₈	—	2	1	no	—
51	C₃×#424	—	3	4	no	—
52	#4839	C₃²	1	1	yes	characteristic, direct product factor
53	C₂²×C₃²×C₄	—	3	1	no	—
54	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
55	C₃²×M₁₆	—	6	2	no	—
56	C₂×C₃²×C₈	—	2	4	no	—
57	C₂×C₃²×C₈	—	2	4	no	—
58	C₂×C₃²×C₈	—	3	1	no	—
59	C₂×C₃²×C₈	—	3	1	no	—
60	C₂×C₃²×C₈	—	6	2	no	—
61	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
62	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
64	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
65	C₃²×C₄⋊C₄	—	3	1	no	—
66	C₃²×C₄⋊C₄	—	3	1	no	—
67	C₃²×C₂²⋊C₄	—	3	1	no	—
68	C₃²×C₂²⋊C₄	—	3	1	no	—
69	C₃²×C₄²	—	2	4	no	—
70	C₃²×C₄²	—	3	1	no	—
71	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
72	C₃²×C₄²	C₂²×C₃	1	4	yes	—
73	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	4	yes	—
74	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	4	yes	—
75	C₃×Dic₃⋊C₄	C₃×C₄	1	4	yes	—
76	C₃×Dic₃⋊C₄	C₃×C₄	1	4	yes	—
77	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
78	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
79	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
80	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
81	C₃×D₃×C₈	—	2	8	no	—
82	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₃²×D₃	—	2	1	no	—
84	C₂×C₃²×D₃	—	2	1	no	—
85	C₂×C₃²×D₃	C₄⋊C₄	1	2	yes	—
86	C₃³×C₄	—	2	1	no	—
87	C₃³×C₄	—	2	1	no	—
88	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
89	C₃³×C₄	C₂×Q₈	1	1	yes	characteristic
90	C₃²×Dic₃	—	2	1	no	—
91	C₃²×Dic₃	—	2	1	no	—
92	C₃²×Dic₃	C₄⋊C₄	1	2	yes	—
93	C₂×C₃×M₁₆	—	3	4	no	—
94	C₂²×C₃×C₈	—	3	4	no	—
95	C₃×#117	—	3	4	no	—
96	C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	1	1	yes	characteristic
97	C₂×D₃×C₈	C₂×C₃²	1	1	yes	characteristic
98	#872	C₂×C₃²	1	1	yes	characteristic
99	C₃×C₄⋊C₈	—	2	4	no	—
100	C₃×C₄⋊C₈	—	3	4	no	—
101	C₃×C₄⋊C₈	—	3	4	no	—
102	C₃×C₄⋊C₈	—	3	4	no	—
103	C₃×C₄⋊C₈	C₃×D₃	1	4	yes	complemented
104	C₃×C₄⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
105	Dic₃⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
106	Dic₃⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
107	C₄⋊(C₃⋊C₈)	C₂×C₃²	1	1	yes	characteristic, complemented
108	C₂³×C₃²	—	3	1	no	—
109	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
110	C₂×C₃²×C₄	—	2	4	no	—
111	C₂×C₃²×C₄	—	2	4	no	—
112	C₂×C₃²×C₄	—	2	4	no	—
113	C₂×C₃²×C₄	—	3	1	no	—
114	C₂×C₃²×C₄	—	3	2	no	—
115	C₂×C₃²×C₄	—	3	2	no	—
116	C₂×C₃²×C₄	—	3	1	no	—
117	C₂×C₃²×C₄	—	3	1	no	—
118	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
120	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
121	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
122	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
124	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
125	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
126	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
127	C₃×C₄×D₃	C₃×D₄	1	8	yes	—
128	C₃×C₄×D₃	C₃×Q₈	1	8	yes	—
129	C₃²×C₈	—	2	1	no	—
130	C₃²×C₈	—	2	1	no	—
131	C₃²×C₈	—	2	4	no	—
132	C₃²×C₈	—	2	4	no	—
133	C₃²×C₈	—	4	4	no	—
134	C₃²×C₈	—	4	4	no	—
135	C₃²×C₈	—	6	1	no	—
136	C₃²×C₈	—	6	1	no	—
137	C₃×C₃⋊C₈	—	2	4	no	—
138	C₃×C₃⋊C₈	—	2	4	no	—
139	#424	—	3	1	no	Sylow
140	C₂×C₃³	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₃³	#131	1	1	yes	characteristic
142	C₂×C₃³	#131	1	1	yes	characteristic
143	C₃²×D₃	—	2	2	no	—
144	C₂²×C₃×C₄	—	3	4	no	—
145	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
146	C₃×M₁₆	—	6	8	no	—
147	C₂×C₃×C₈	—	2	4	no	—
148	C₂×C₃×C₈	—	2	4	no	—
149	C₂×C₃×C₈	—	3	4	no	—
150	C₂×C₃×C₈	—	3	4	no	—
151	C₂×C₃×C₈	—	6	8	no	—
152	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
153	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
154	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
155	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
156	C₃×C₄⋊C₄	—	3	4	no	—
157	C₃×C₄⋊C₄	—	3	4	no	—
158	C₃×C₂²⋊C₄	—	3	4	no	—
159	C₃×C₂²⋊C₄	—	3	4	no	—
160	C₃×C₄²	—	2	4	no	—
161	C₃×C₄²	—	3	4	no	—
162	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
163	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
164	(C₂×D₃)⋊C₄	C₃²×C₄	1	1	yes	characteristic
165	(C₂×D₃)⋊C₄	C₃²×C₄	1	1	yes	characteristic
166	Dic₃⋊C₄	C₃²×C₄	1	1	yes	characteristic
167	Dic₃⋊C₄	C₃²×C₄	1	1	yes	characteristic
168	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
169	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
170	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
171	ΓL(1,𝔽₂₅)	—	2	2	no	—
172	D₃×C₈	—	2	2	no	—
173	C₂²×C₃²	—	2	4	no	—
174	C₂²×C₃²	—	3	2	no	—
175	C₂²×C₃²	—	6	1	no	—
176	C₂²×C₃²	—	6	1	no	—
177	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
178	C₂²×C₃²	C₂²×C₃×C₄	1	4	yes	—
179	C₂×C₃×D₃	—	2	4	no	—
180	C₂×C₃×D₃	—	2	4	no	—
181	C₂×C₃×D₃	C₃×C₄⋊C₄	1	8	yes	—
182	C₃²×C₄	—	2	8	no	—
183	C₃²×C₄	—	2	1	no	—
184	C₃²×C₄	—	2	1	no	—
185	C₃²×C₄	—	2	4	no	—
186	C₃²×C₄	—	2	4	no	—
187	C₃²×C₄	—	2	4	no	—
188	C₃²×C₄	—	2	4	no	—
189	C₃²×C₄	—	3	2	no	—
190	C₃²×C₄	—	4	4	no	—
191	C₃²×C₄	—	6	1	no	—
192	C₃²×C₄	—	6	1	no	—
193	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
194	C₃²×C₄	D₃×Q₈	1	1	yes	characteristic
195	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
196	C₃²×C₄	C₂×C₃×Q₈	1	4	yes	—
197	C₃×Dic₃	—	2	4	no	—
198	C₃×Dic₃	—	2	4	no	—
199	C₃×Dic₃	C₃×C₄⋊C₄	1	8	yes	—
200	C₂×M₁₆	—	3	1	no	—
201	C₂²×C₈	—	3	1	no	—
202	#117	—	3	1	no	—
203	C₄⋊C₈	—	3	1	no	—
204	C₄⋊C₈	—	3	1	no	—
205	C₄⋊C₈	—	3	1	no	—
206	C₄⋊C₈	C₃²×D₃	1	1	yes	characteristic, complemented
207	C₃³	#424	1	1	yes	characteristic, complemented, Sylow
208	C₂³×C₃	—	3	4	no	—
209	C₂²×D₃	C₂×C₃²×C₄	1	1	yes	characteristic
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	4	no	—
213	C₂×C₃×C₄	—	3	4	no	—
214	C₂×C₃×C₄	—	3	8	no	—
215	C₂×C₃×C₄	—	3	8	no	—
216	C₂×C₃×C₄	—	3	4	no	—
217	C₂×C₃×C₄	—	3	4	no	—
218	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
219	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
220	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
221	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
222	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
223	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
224	C₂×Dic₃	C₂×C₃²×C₄	1	1	yes	characteristic
225	C₂×Dic₃	C₂×C₃²×C₄	1	1	yes	characteristic
226	C₂×Dic₃	C₂×C₃²×C₄	1	1	yes	characteristic
227	C₄×D₃	C₃²×D₄	1	2	yes	—
228	C₄×D₃	C₃²×Q₈	1	2	yes	—
229	C₃×C₈	—	2	4	no	—
230	C₃×C₈	—	2	4	no	—
231	C₃×C₈	—	2	1	no	—
232	C₃×C₈	—	2	1	no	—
233	C₃×C₈	—	4	4	no	—
234	C₃×C₈	—	4	4	no	—
235	C₃×C₈	—	6	4	no	—
236	C₃×C₈	—	6	4	no	—
237	C₃⋊C₈	—	2	1	no	—
238	C₃⋊C₈	—	2	1	no	—
239	C₂×C₃²	—	2	4	no	—
240	C₂×C₃²	—	2	4	no	—
241	C₂×C₃²	—	2	4	no	—
242	C₂×C₃²	—	6	2	no	—
243	C₂×C₃²	D₃×C₄⋊C₄	1	1	yes	characteristic
244	C₂×C₃²	#901	1	1	yes	characteristic
245	C₂×C₃²	#907	1	1	yes	characteristic
246	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	4	yes	—
247	C₂×C₃²	C₃×#131	1	4	yes	—
248	C₂×C₃²	C₃×#131	1	4	yes	—
249	C₃×D₃	—	2	8	no	—
250	C₂²×C₄	—	3	1	no	—
251	M₁₆	—	6	2	no	—
252	C₂×C₈	—	3	1	no	—
253	C₂×C₈	—	3	1	no	—
254	C₂×C₈	—	6	2	no	—
255	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
256	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
257	C₄⋊C₄	—	3	1	no	—
258	C₄⋊C₄	—	3	1	no	—
259	C₂²⋊C₄	—	3	1	no	—
260	C₂²⋊C₄	—	3	1	no	—
261	C₄²	—	3	1	no	—
262	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
263	C₂²×C₃	—	2	4	no	—
264	C₂²×C₃	—	3	8	no	—
265	C₂²×C₃	—	6	4	no	—
266	C₂²×C₃	—	6	4	no	—
267	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
268	C₂²×C₃	C₂²×C₃²×C₄	1	1	yes	characteristic
269	C₂×D₃	—	2	1	no	—
270	C₂×D₃	—	2	1	no	—
271	C₂×D₃	C₃²×C₄⋊C₄	1	2	yes	—
272	C₃×C₄	—	2	8	no	—
273	C₃×C₄	—	2	4	no	—
274	C₃×C₄	—	2	4	no	—
275	C₃×C₄	—	2	1	no	—
276	C₃×C₄	—	2	1	no	—
277	C₃×C₄	—	2	4	no	—
278	C₃×C₄	—	2	4	no	—
279	C₃×C₄	—	3	8	no	—
280	C₃×C₄	—	4	4	no	—
281	C₃×C₄	—	6	4	no	—
282	C₃×C₄	—	6	4	no	—
283	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
284	C₃×C₄	C₃×D₃×Q₈	1	4	yes	—
285	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
286	C₃×C₄	C₂×C₃²×Q₈	1	1	yes	characteristic
287	Dic₃	—	2	1	no	—
288	Dic₃	—	2	1	no	—
289	Dic₃	C₃²×C₄⋊C₄	1	2	yes	—
290	C₃²	—	2	4	no	—
291	C₃²	#4839	1	1	yes	characteristic, direct product factor
292	C₃²	C₃×#424	1	4	yes	complemented
293	C₂³	—	3	1	no	—
294	C₂×C₄	—	3	1	no	—
295	C₂×C₄	—	3	2	no	—
296	C₂×C₄	—	3	2	no	—
297	C₂×C₄	—	3	1	no	—
298	C₂×C₄	—	3	1	no	—
299	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
300	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
301	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
302	C₈	—	2	1	no	—
303	C₈	—	2	1	no	—
304	C₈	—	6	1	no	—
305	C₈	—	6	1	no	—
306	C₂×C₃	—	2	4	no	—
307	C₂×C₃	—	2	4	no	—
308	C₂×C₃	—	2	4	no	—
309	C₂×C₃	—	6	8	no	—
310	C₂×C₃	C₃×D₃×C₄⋊C₄	1	4	yes	—
311	C₂×C₃	C₃×#901	1	4	yes	—
312	C₂×C₃	C₃×#907	1	4	yes	—
313	C₂×C₃	C₂×C₃²×C₄⋊C₄	1	1	yes	characteristic
314	C₂×C₃	C₃²×#131	1	1	yes	characteristic
315	C₂×C₃	C₃²×#131	1	1	yes	characteristic
316	D₃	—	2	2	no	—
317	C₂²	—	3	2	no	—
318	C₂²	—	6	1	no	—
319	C₂²	—	6	1	no	—
320	C₂²	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
321	C₄	—	2	1	no	—
322	C₄	—	2	1	no	—
323	C₄	—	3	2	no	—
324	C₄	—	6	1	no	—
325	C₄	—	6	1	no	—
326	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
327	C₄	C₃²×D₃×Q₈	1	1	yes	characteristic
328	C₃	—	2	4	no	—
329	C₃	C₃×#4839	1	4	yes	direct product factor
330	C₃	C₃²×#424	1	1	yes	characteristic, complemented
331	C₂	—	6	2	no	—
332	C₂	C₃²×D₃×C₄⋊C₄	1	1	yes	characteristic
333	C₂	C₃²×#901	1	1	yes	characteristic
334	C₂	C₃²×#907	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₃³×C₄⋊C₈	C₂
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂²×C₃²×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₃²×C₄⋊C₈	D₃
hypocenter	C₃	C₃²×#424
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₃²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₃³×C₄⋊C₈	C₂	semidirect
5. C₃²×Dic₃⋊C₈	C₂	semidirect
6. C₃²×Dic₃⋊C₈	C₂	semidirect
7. C₃²×C₄⋊(C₃⋊C₈)	C₂	semidirect
9. C₃×#4839	C₃	direct (N × H)
33. C₃²×C₄⋊C₈	D₃	semidirect
34. C₃²×C₄⋊C₈	C₂×C₃	semidirect
35. C₃×Dic₃⋊C₈	C₂×C₃	semidirect
36. C₃×Dic₃⋊C₈	C₂×C₃	semidirect
37. C₃×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
52. #4839	C₃²	direct (N × H)
103. C₃×C₄⋊C₈	C₃×D₃	semidirect
104. C₃×C₄⋊C₈	C₂×C₃²	semidirect
105. Dic₃⋊C₈	C₂×C₃²	semidirect
106. Dic₃⋊C₈	C₂×C₃²	semidirect
107. C₄⋊(C₃⋊C₈)	C₂×C₃²	semidirect
206. C₄⋊C₈	C₃²×D₃	semidirect
207. C₃³	#424	semidirect
291. C₃²	#4839	direct (N × H)
292. C₃²	C₃×#424	semidirect
329. C₃	C₃×#4839	direct (N × H)
330. C₃	C₃²×#424	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×ΓL(1,𝔽₂₅)	2
C₂×C₃²×D₃×C₈	2
C₃²×#872	2
C₃³×C₄⋊C₈	2
C₃²×Dic₃⋊C₈	2
C₃²×C₄⋊(C₃⋊C₈)	2
C₃²×#424	3
C₃×#4839	3

Subgroups — C32×#4839 #13162277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#4839 #13162277