Subgroups — C₃×#10596005 #13179285

Order 1728.

1600 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64139	C₂	1	1	yes	maximal, characteristic
3	C₃×#64133	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64107	C₂	1	2	yes	maximal, complemented
5	C₃×#64105	C₂	1	2	yes	maximal, complemented
6	C₃×#64094	C₂	1	2	yes	maximal, complemented
7	C₃×#64092	C₂	1	2	yes	maximal, complemented
8	C₃×#64084	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#64078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596005	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×#5534	—	3	4	no	maximal
14	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×#638	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
18	C₂×C₃×#634	C₂²	1	1	yes	characteristic
19	C₂×C₃×#634	C₂²	1	2	yes	—
20	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₃³×C₄²	C₂²	1	1	yes	characteristic
25	C₃³×C₄²	C₂²	1	1	yes	characteristic
26	C₃×#3757	C₂²	1	2	yes	—
27	C₃×#3752	C₂²	1	2	yes	—
28	C₃×#3752	C₂²	1	2	yes	—
29	C₃×#3752	C₂²	1	2	yes	—
30	C₃×#3752	C₂²	1	2	yes	—
31	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
32	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
33	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
34	C₃×#3750	C₂²	1	2	yes	—
35	C₃×#3750	C₂²	1	2	yes	—
36	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
37	C₃²×#117	—	2	4	no	—
38	C₃²×#117	D₃	1	4	yes	complemented
39	C₃²×#117	C₂×C₃	1	1	yes	characteristic, complemented
40	#64139	C₂×C₃	1	1	yes	characteristic
41	#64133	C₂×C₃	1	1	yes	characteristic, complemented
42	#64107	C₂×C₃	1	2	yes	complemented
43	#64105	C₂×C₃	1	2	yes	complemented
44	#64094	C₂×C₃	1	2	yes	complemented
45	#64092	C₂×C₃	1	2	yes	complemented
46	#64084	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
48	#64078	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃×#930	—	3	4	no	—
51	C₃×#924	—	3	4	no	—
52	C₃×#898	—	3	8	no	—
53	C₃×#896	—	3	8	no	—
54	C₃×#885	—	3	8	no	—
55	C₃×#883	—	3	8	no	—
56	C₃×#875	—	3	4	no	—
57	C₃×C₄×D₁₂	—	3	4	no	—
58	C₃×#869	—	3	4	no	—
59	C₃×C₄×Dic₆	—	3	4	no	—
60	C₂³×C₃³	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
62	C₂×C₃³×C₄	—	2	2	no	—
63	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
64	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
65	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
66	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
68	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
69	C₃×#638	—	4	2	no	—
70	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
71	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
72	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
73	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
74	C₃×C₄×C₃⋊D₃	—	4	2	no	—
75	C₃×#634	—	2	2	no	—
76	C₃×#634	—	4	2	no	—
77	C₃×#542	—	9	1	no	—
78	#5534	—	3	4	no	—
79	C₂²×C₃²×C₄	—	2	4	no	—
80	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
81	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×#638	C₂²×C₃	1	2	yes	—
83	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
85	C₂×#634	C₂²×C₃	1	1	yes	characteristic
86	C₂×#634	C₂²×C₃	1	2	yes	—
87	C₂×C₃×#67	—	3	8	no	—
88	C₂×C₃×D₁₂	—	3	4	no	—
89	C₂×C₃×C₄×D₃	—	3	8	no	—
90	C₂×C₃×Dic₆	—	3	4	no	—
91	C₂×C₃×Dic₆	—	3	8	no	—
92	C₃²×C₄⋊C₄	—	2	4	no	—
93	C₃²×C₄⋊C₄	—	2	4	no	—
94	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
95	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
96	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₃²×C₂²⋊C₄	—	2	4	no	—
99	C₃²×C₂²⋊C₄	—	2	4	no	—
100	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
101	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
102	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₃²×C₄²	—	2	4	no	—
105	C₃²×C₄²	—	2	4	no	—
106	C₃²×C₄²	C₂×D₃	1	4	yes	—
107	C₃²×C₄²	C₂×D₃	1	4	yes	—
108	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
109	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
110	#3757	C₂²×C₃	1	2	yes	—
111	#3752	C₂²×C₃	1	2	yes	—
112	#3752	C₂²×C₃	1	2	yes	—
113	#3752	C₂²×C₃	1	2	yes	—
114	#3752	C₂²×C₃	1	2	yes	—
115	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
116	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
117	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
118	#3750	C₂²×C₃	1	2	yes	—
119	#3750	C₂²×C₃	1	2	yes	—
120	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
121	C₃×#217	—	3	8	no	—
122	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
123	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
124	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
125	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
126	C₃×C₄⋊Dic₃	—	3	8	no	—
127	C₃×C₄⋊Dic₃	—	3	4	no	—
128	C₃×C₄⋊Dic₃	—	3	4	no	—
129	C₃×Dic₃⋊C₄	—	3	8	no	—
130	C₃×Dic₃⋊C₄	—	3	8	no	—
131	C₃×C₄×Dic₃	—	3	8	no	—
132	C₂²×C₃³	—	2	1	no	—
133	C₂²×C₃³	—	2	1	no	—
134	C₂²×C₃³	—	2	1	no	—
135	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
136	C₂×C₃×C₃⋊D₃	—	2	2	no	—
137	C₂×C₃×C₃⋊D₃	—	2	2	no	—
138	C₂×C₃×C₃⋊D₃	—	2	2	no	—
139	C₃³×C₄	—	2	1	no	—
140	C₃³×C₄	—	2	1	no	—
141	C₃³×C₄	—	2	1	no	—
142	C₃³×C₄	—	2	1	no	—
143	C₃³×C₄	—	2	1	no	—
144	C₃³×C₄	#41	1	2	yes	—
145	C₃×C₃⋊Dic₃	—	2	2	no	—
146	C₃×C₃⋊Dic₃	—	2	2	no	—
147	C₃×C₃⋊Dic₃	—	2	2	no	—
148	C₃×C₄⋊Q₈	—	9	1	no	—
149	C₃×#126	—	9	2	no	—
150	C₃×#124	—	9	2	no	—
151	C₃×#124	—	9	1	no	—
152	C₃×#123	—	9	2	no	—
153	C₃×C₂²⋊Q₈	—	9	1	no	—
154	C₃×C₂²⋊Q₈	—	9	2	no	—
155	C₃×#121	—	9	1	no	—
156	C₃×C₄×Q₈	—	9	1	no	—
157	C₃×C₄×D₄	—	9	1	no	—
158	C₃×#117	—	2	4	no	—
159	C₃×#117	C₃×D₃	1	4	yes	complemented
160	C₃×#117	C₃⋊D₃	1	1	yes	characteristic, complemented
161	#930	—	3	4	no	—
162	#924	—	3	4	no	—
163	#898	—	3	8	no	—
164	#896	—	3	8	no	—
165	#885	—	3	8	no	—
166	#883	—	3	8	no	—
167	#875	—	3	4	no	—
168	C₄×D₁₂	—	3	4	no	—
169	#869	—	3	4	no	—
170	C₄×Dic₆	—	3	4	no	—
171	C₂³×C₃²	—	2	4	no	—
172	C₂³×C₃²	C₂²×D₃	1	4	yes	—
173	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
175	C₂²×C₃×D₃	—	3	8	no	—
176	C₂×C₃²×C₄	—	2	16	no	—
177	C₂×C₃²×C₄	—	2	8	no	—
178	C₂×C₃²×C₄	—	2	2	no	—
179	C₂×C₃²×C₄	—	2	4	no	—
180	C₂×C₃²×C₄	—	2	4	no	—
181	C₂×C₃²×C₄	—	2	4	no	—
182	C₂×C₃²×C₄	—	2	4	no	—
183	C₂×C₃²×C₄	—	2	4	no	—
184	C₂×C₃²×C₄	—	2	4	no	—
185	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
186	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
187	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
188	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
189	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
190	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
191	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
197	#638	—	4	2	no	—
198	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
199	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
200	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
201	C₄⋊(C₃⋊D₃)	—	2	2	no	—
202	C₄×C₃⋊D₃	—	4	2	no	—
203	#634	—	2	2	no	—
204	#634	—	4	2	no	—
205	C₃×#67	—	12	8	no	—
206	C₂×C₃×Dic₃	—	3	8	no	—
207	C₂×C₃×Dic₃	—	3	8	no	—
208	C₂×C₃×Dic₃	—	3	8	no	—
209	C₃×D₁₂	—	6	8	no	—
210	C₃×C₄×D₃	—	12	8	no	—
211	C₃×Dic₆	—	6	8	no	—
212	C₃×Dic₆	—	12	8	no	—
213	#542	—	9	1	no	Sylow
214	C₂×C₃³	—	4	1	no	—
215	C₂×C₃³	C₂×#41	1	1	yes	characteristic
216	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
218	C₃×C₃⋊D₃	—	4	2	no	—
219	C₂×C₃×Q₈	—	9	1	no	—
220	C₂×C₃×Q₈	—	9	2	no	—
221	C₂×C₃×D₄	—	9	2	no	—
222	C₂×C₃×D₄	—	9	1	no	—
223	C₂²×C₃×C₄	—	2	4	no	—
224	C₂²×C₃×C₄	—	9	2	no	—
225	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
226	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
227	C₂×#67	—	3	8	no	—
228	C₂×D₁₂	—	3	4	no	—
229	C₂×C₄×D₃	—	3	8	no	—
230	C₂×Dic₆	—	3	4	no	—
231	C₂×Dic₆	—	3	8	no	—
232	C₃×C₄⋊C₄	—	2	4	no	—
233	C₃×C₄⋊C₄	—	2	4	no	—
234	C₃×C₄⋊C₄	—	9	2	no	—
235	C₃×C₄⋊C₄	—	9	2	no	—
236	C₃×C₄⋊C₄	—	9	1	no	—
237	C₃×C₄⋊C₄	—	9	1	no	—
238	C₃×C₄⋊C₄	—	9	2	no	—
239	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
240	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
241	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
242	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
243	C₃×C₂²⋊C₄	—	2	4	no	—
244	C₃×C₂²⋊C₄	—	2	4	no	—
245	C₃×C₂²⋊C₄	—	9	2	no	—
246	C₃×C₂²⋊C₄	—	9	2	no	—
247	C₃×C₂²⋊C₄	—	9	2	no	—
248	C₃×C₂²⋊C₄	—	9	2	no	—
249	C₃×C₂²⋊C₄	—	9	2	no	—
250	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
251	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
252	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
253	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
254	C₃×C₄²	—	2	4	no	—
255	C₃×C₄²	—	2	4	no	—
256	C₃×C₄²	—	9	2	no	—
257	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
258	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
259	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
260	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
261	#217	—	3	8	no	—
262	(C₂×D₃)⋊C₄	—	3	8	no	—
263	(C₂×D₃)⋊C₄	—	3	8	no	—
264	(C₂×D₃)⋊C₄	—	3	8	no	—
265	(C₂×D₃)⋊C₄	—	3	8	no	—
266	C₄⋊Dic₃	—	3	4	no	—
267	C₄⋊Dic₃	—	3	4	no	—
268	C₄⋊Dic₃	—	3	8	no	—
269	Dic₃⋊C₄	—	3	8	no	—
270	Dic₃⋊C₄	—	3	8	no	—
271	C₄×Dic₃	—	3	8	no	—
272	C₂²×C₃²	—	2	8	no	—
273	C₂²×C₃²	—	2	4	no	—
274	C₂²×C₃²	—	2	1	no	—
275	C₂²×C₃²	—	2	1	no	—
276	C₂²×C₃²	—	2	1	no	—
277	C₂²×C₃²	—	2	4	no	—
278	C₂²×C₃²	—	2	4	no	—
279	C₂²×C₃²	—	2	4	no	—
280	C₂²×C₃²	—	4	4	no	—
281	C₂²×C₃²	—	4	4	no	—
282	C₂²×C₃²	C₂³×D₃	1	4	yes	—
283	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
284	C₂×C₃⋊D₃	—	2	2	no	—
285	C₂×C₃⋊D₃	—	2	2	no	—
286	C₂×C₃⋊D₃	—	2	2	no	—
287	C₂×C₃×D₃	—	6	8	no	—
288	C₂×C₃×D₃	—	6	8	no	—
289	C₂×C₃×D₃	—	6	8	no	—
290	C₃²×C₄	—	2	8	no	—
291	C₃²×C₄	—	2	4	no	—
292	C₃²×C₄	—	2	1	no	—
293	C₃²×C₄	—	2	1	no	—
294	C₃²×C₄	—	2	1	no	—
295	C₃²×C₄	—	2	1	no	—
296	C₃²×C₄	—	2	1	no	—
297	C₃²×C₄	—	2	8	no	—
298	C₃²×C₄	—	2	4	no	—
299	C₃²×C₄	—	2	4	no	—
300	C₃²×C₄	—	2	4	no	—
301	C₃²×C₄	—	2	4	no	—
302	C₃²×C₄	—	4	4	no	—
303	C₃²×C₄	—	4	4	no	—
304	C₃²×C₄	—	4	4	no	—
305	C₃²×C₄	—	4	4	no	—
306	C₃²×C₄	#235	1	8	yes	—
307	C₃²×C₄	C₃×#41	1	2	yes	—
308	C₃⋊Dic₃	—	2	2	no	—
309	C₃⋊Dic₃	—	2	2	no	—
310	C₃⋊Dic₃	—	2	2	no	—
311	C₃×Dic₃	—	6	8	no	—
312	C₃×Dic₃	—	6	8	no	—
313	C₃×Dic₃	—	6	8	no	—
314	C₄⋊Q₈	—	9	1	no	—
315	#126	—	9	2	no	—
316	#124	—	9	2	no	—
317	#124	—	9	1	no	—
318	#123	—	9	2	no	—
319	C₂²⋊Q₈	—	9	1	no	—
320	C₂²⋊Q₈	—	9	2	no	—
321	#121	—	9	1	no	—
322	C₄×Q₈	—	9	1	no	—
323	C₄×D₄	—	9	1	no	—
324	#117	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
325	C₃³	#542	1	1	yes	characteristic, complemented, Sylow
326	C₂³×C₃	—	2	4	no	—
327	C₂³×C₃	—	9	2	no	—
328	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
329	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
330	C₂²×D₃	—	3	8	no	—
331	C₃×Q₈	—	18	2	no	—
332	C₃×Q₈	—	36	2	no	—
333	C₃×D₄	—	18	2	no	—
334	C₃×D₄	—	36	2	no	—
335	C₂×C₃×C₄	—	2	16	no	—
336	C₂×C₃×C₄	—	2	8	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	4	no	—
339	C₂×C₃×C₄	—	2	4	no	—
340	C₂×C₃×C₄	—	2	4	no	—
341	C₂×C₃×C₄	—	2	4	no	—
342	C₂×C₃×C₄	—	2	4	no	—
343	C₂×C₃×C₄	—	2	4	no	—
344	C₂×C₃×C₄	—	9	2	no	—
345	C₂×C₃×C₄	—	9	2	no	—
346	C₂×C₃×C₄	—	9	2	no	—
347	C₂×C₃×C₄	—	36	2	no	—
348	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
349	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
350	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
351	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
352	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
353	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
354	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
360	#67	—	12	8	no	—
361	C₂×Dic₃	—	3	8	no	—
362	C₂×Dic₃	—	3	8	no	—
363	C₂×Dic₃	—	3	8	no	—
364	D₁₂	—	6	8	no	—
365	C₄×D₃	—	12	8	no	—
366	Dic₆	—	6	8	no	—
367	Dic₆	—	12	8	no	—
368	C₂×C₃²	—	2	4	no	—
369	C₂×C₃²	—	2	4	no	—
370	C₂×C₃²	—	2	4	no	—
371	C₂×C₃²	—	4	8	no	—
372	C₂×C₃²	—	4	4	no	—
373	C₂×C₃²	—	4	1	no	—
374	C₂×C₃²	C₂×#235	1	4	yes	—
375	C₂×C₃²	#1009	1	4	yes	—
376	C₂×C₃²	#1010	1	4	yes	—
377	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
378	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
380	C₃⋊D₃	—	4	2	no	—
381	C₃×D₃	—	12	8	no	—
382	C₂×Q₈	—	9	1	no	—
383	C₂×Q₈	—	9	2	no	—
384	C₂×D₄	—	9	2	no	—
385	C₂×D₄	—	9	1	no	—
386	C₂²×C₄	—	9	2	no	—
387	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
388	C₄⋊C₄	—	9	1	no	—
389	C₄⋊C₄	—	9	1	no	—
390	C₄⋊C₄	—	9	2	no	—
391	C₄⋊C₄	—	9	2	no	—
392	C₄⋊C₄	—	9	2	no	—
393	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
394	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
395	C₂²⋊C₄	—	9	2	no	—
396	C₂²⋊C₄	—	9	2	no	—
397	C₂²⋊C₄	—	9	2	no	—
398	C₂²⋊C₄	—	9	2	no	—
399	C₂²⋊C₄	—	9	2	no	—
400	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
401	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
402	C₄²	—	9	2	no	—
403	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
404	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
405	C₂²×C₃	—	2	8	no	—
406	C₂²×C₃	—	2	4	no	—
407	C₂²×C₃	—	2	4	no	—
408	C₂²×C₃	—	2	4	no	—
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	2	1	no	—
411	C₂²×C₃	—	2	1	no	—
412	C₂²×C₃	—	2	4	no	—
413	C₂²×C₃	—	4	4	no	—
414	C₂²×C₃	—	4	4	no	—
415	C₂²×C₃	—	18	2	no	—
416	C₂²×C₃	—	18	2	no	—
417	C₂²×C₃	—	18	2	no	—
418	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
419	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
420	C₂×D₃	—	6	8	no	—
421	C₂×D₃	—	6	8	no	—
422	C₂×D₃	—	6	8	no	—
423	C₃×C₄	—	2	8	no	—
424	C₃×C₄	—	2	4	no	—
425	C₃×C₄	—	2	4	no	—
426	C₃×C₄	—	2	4	no	—
427	C₃×C₄	—	2	4	no	—
428	C₃×C₄	—	2	4	no	—
429	C₃×C₄	—	2	1	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	1	no	—
434	C₃×C₄	—	2	8	no	—
435	C₃×C₄	—	4	4	no	—
436	C₃×C₄	—	4	4	no	—
437	C₃×C₄	—	4	4	no	—
438	C₃×C₄	—	4	4	no	—
439	C₃×C₄	—	18	2	no	—
440	C₃×C₄	—	18	2	no	—
441	C₃×C₄	—	18	2	no	—
442	C₃×C₄	C₃×#235	1	8	yes	—
443	C₃×C₄	#3828	1	2	yes	—
444	Dic₃	—	6	8	no	—
445	Dic₃	—	6	8	no	—
446	Dic₃	—	6	8	no	—
447	C₃²	—	2	4	no	—
448	C₃²	#5534	1	4	yes	complemented
449	C₃²	C₃×#542	1	1	yes	characteristic, complemented
450	C₂³	—	9	2	no	—
451	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
452	Q₈	—	18	2	no	—
453	Q₈	—	36	2	no	—
454	D₄	—	18	2	no	—
455	D₄	—	36	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	9	2	no	—
458	C₂×C₄	—	9	2	no	—
459	C₂×C₄	—	9	2	no	—
460	C₂×C₄	—	36	2	no	—
461	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
463	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
464	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
467	C₂×C₃	—	2	4	no	—
468	C₂×C₃	—	2	4	no	—
469	C₂×C₃	—	2	4	no	—
470	C₂×C₃	—	4	8	no	—
471	C₂×C₃	—	4	4	no	—
472	C₂×C₃	—	4	1	no	—
473	C₂×C₃	—	36	2	no	—
474	C₂×C₃	C₂×C₃×#235	1	4	yes	—
475	C₂×C₃	C₃×#1009	1	4	yes	—
476	C₂×C₃	C₃×#1010	1	4	yes	—
477	C₂×C₃	C₂×#3828	1	1	yes	characteristic
478	C₂×C₃	#64366	1	1	yes	characteristic
479	C₂×C₃	#64367	1	1	yes	characteristic
480	D₃	—	12	8	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	18	2	no	—
485	C₂²	—	18	2	no	—
486	C₂²	—	18	2	no	—
487	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	18	2	no	—
494	C₄	—	18	2	no	—
495	C₄	—	18	2	no	—
496	C₄	C₃×#3828	1	2	yes	—
497	C₃	—	2	4	no	—
498	C₃	C₃×#5534	1	4	yes	complemented
499	C₃	#10596005	1	1	yes	characteristic, direct product factor
500	C₂	—	4	1	no	—
501	C₂	—	36	2	no	—
502	C₂	C₂×C₃×#3828	1	1	yes	characteristic
503	C₂	C₃×#64366	1	1	yes	characteristic
504	C₂	C₃×#64367	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#117	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₃×#64139	C₂
hypercenter	C₃×#117	C₃⋊D₃
hypocenter	C₃²	C₃×#542
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₃³×#117	C₂	semidirect
3. C₃×#64133	C₂	semidirect
4. C₃×#64107	C₂	semidirect
5. C₃×#64105	C₂	semidirect
6. C₃×#64094	C₂	semidirect
7. C₃×#64092	C₂	semidirect
8. C₃×#64084	C₂	semidirect
9. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	semidirect
10. C₃×#64078	C₂	semidirect
11. C₃×C₄×#634	C₂	semidirect
12. #10596005	C₃	direct (N × H)
38. C₃²×#117	D₃	semidirect
39. C₃²×#117	C₂×C₃	semidirect
41. #64133	C₂×C₃	semidirect
42. #64107	C₂×C₃	semidirect
43. #64105	C₂×C₃	semidirect
44. #64094	C₂×C₃	semidirect
45. #64092	C₂×C₃	semidirect
46. #64084	C₂×C₃	semidirect
47. C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
48. #64078	C₂×C₃	semidirect
49. C₄×#634	C₂×C₃	semidirect
159. C₃×#117	C₃×D₃	semidirect
160. C₃×#117	C₃⋊D₃	semidirect
324. #117	C₃×C₃⋊D₃	semidirect
325. C₃³	#542	semidirect
448. C₃²	#5534	semidirect
449. C₃²	C₃×#542	semidirect
498. C₃	C₃×#5534	semidirect
499. C₃	#10596005	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×#117	2
C₃×#64139	2
C₃×#64133	2
C₃×#64107	2
C₃×#64105	2
C₃×#64094	2
C₃×#64092	2
C₃×#64084	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
C₃×#64078	2
C₃×C₄×#634	2
#10596005	3
C₃×#5534	3

Subgroups — C3×#10596005 #13179285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596005 #13179285