Subgroups — C₃×#10596022 #13179305

Order 1728.

2128 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3828	C₂	1	2	yes	maximal, complemented
2	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64147	C₂	1	2	yes	maximal, complemented
4	C₃×#64133	C₂	1	2	yes	maximal, complemented
5	C₃×C₄⋊C₄×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
6	C₃×#64092	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64078	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596022	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5551	—	3	4	no	maximal
11	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃³×C₄	C₂²	1	2	yes	—
13	C₂×C₃×#638	C₂²	1	4	yes	—
14	C₃×#3828	—	2	8	no	—
15	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
17	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	4	yes	—
18	C₂×C₃×#634	C₂²	1	2	yes	—
19	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₃³×C₄²	C₂²	1	1	yes	characteristic
22	C₃×#3757	C₂²	1	4	yes	—
23	C₃×#3752	C₂²	1	2	yes	—
24	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
25	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
26	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
27	C₃×#3750	C₂²	1	4	yes	—
28	C₂×#3828	C₂×C₃	1	2	yes	complemented
29	C₂×C₃×#235	—	3	8	no	—
30	C₃²×C₄×D₄	—	2	4	no	—
31	C₃²×C₄×D₄	D₃	1	4	yes	complemented
32	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
33	#64147	C₂×C₃	1	2	yes	complemented
34	#64133	C₂×C₃	1	2	yes	complemented
35	C₄⋊C₄×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
36	#64092	C₂×C₃	1	4	yes	complemented
37	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
38	#64078	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×#938	—	3	8	no	—
40	C₃×#924	—	3	8	no	—
41	C₃×D₃×C₄⋊C₄	—	3	8	no	—
42	C₃×#883	—	3	16	no	—
43	C₃×C₄×D₁₂	—	3	4	no	—
44	C₃×#869	—	3	4	no	—
45	C₂³×C₃³	C₂³	1	2	yes	—
46	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
47	C₃³×D₄	—	2	2	no	—
48	C₂×C₃³×C₄	—	2	4	no	—
49	C₂×C₃³×C₄	C₂³	1	2	yes	—
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
52	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
53	C₃×#638	—	2	8	no	—
54	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
55	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
56	C₃×C₄⋊(C₃⋊D₃)	D₄	1	4	yes	complemented
57	C₃×C₄×C₃⋊D₃	—	2	8	no	—
58	C₃×C₄×C₃⋊D₃	—	2	4	no	—
59	C₃×#634	—	2	4	no	—
60	C₃×#547	—	9	1	no	—
61	#5551	—	3	4	no	—
62	C₂×C₃²×D₄	—	2	4	no	—
63	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
64	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₃²×C₄	—	2	8	no	—
66	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
67	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
68	C₂×#638	C₂²×C₃	1	4	yes	—
69	#3828	—	2	8	no	—
70	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
72	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	4	yes	—
73	C₂×#634	C₂²×C₃	1	2	yes	—
74	C₂×C₃×#67	—	3	16	no	—
75	C₃×#235	—	6	32	no	—
76	C₂×C₃×D₁₂	—	3	4	no	—
77	C₂×C₃×C₄×D₃	—	3	16	no	—
78	C₂×C₃×C₄×D₃	—	3	8	no	—
79	C₂×C₃×Dic₆	—	3	8	no	—
80	C₃²×C₄⋊C₄	—	2	4	no	—
81	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
82	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₃²×C₂²⋊C₄	—	2	8	no	—
84	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
85	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
86	C₃²×C₄²	—	2	4	no	—
87	C₃²×C₄²	C₂×D₃	1	4	yes	—
88	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
89	#3757	C₂²×C₃	1	4	yes	—
90	#3752	C₂²×C₃	1	2	yes	—
91	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
92	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
93	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
94	#3750	C₂²×C₃	1	4	yes	—
95	C₃×#217	—	3	16	no	—
96	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
97	C₃×C₄⋊Dic₃	—	3	8	no	—
98	C₃×C₄⋊Dic₃	—	3	8	no	—
99	C₃×C₄⋊Dic₃	—	3	4	no	—
100	C₃×Dic₃⋊C₄	—	3	16	no	—
101	C₂²×C₃³	—	2	2	no	—
102	C₂²×C₃³	—	2	2	no	—
103	C₂²×C₃³	—	2	2	no	—
104	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
105	C₂×C₃×C₃⋊D₃	—	2	2	no	—
106	C₂×C₃×C₃⋊D₃	—	2	2	no	—
107	C₂×C₃×C₃⋊D₃	C₂×D₄	1	4	yes	—
108	C₃³×C₄	—	2	2	no	—
109	C₃³×C₄	—	2	1	no	—
110	C₃³×C₄	C₂×D₄	1	2	yes	—
111	C₃³×C₄	#41	1	2	yes	complemented
112	C₃×C₃⋊Dic₃	—	2	4	no	—
113	C₃×C₃⋊Dic₃	—	2	2	no	—
114	C₂×C₃×#41	—	9	2	no	—
115	C₂×#235	—	3	8	no	—
116	C₃×C₄⋊Q₈	—	9	1	no	—
117	C₃×#123	—	9	4	no	—
118	C₃×C₂²⋊Q₈	—	9	2	no	—
119	C₃×#121	—	9	2	no	—
120	C₃×C₄×D₄	—	2	4	no	—
121	C₃×C₄×D₄	—	9	1	no	—
122	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
123	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
124	C₂×C₃×C₄⋊C₄	—	9	2	no	—
125	#938	—	3	8	no	—
126	#924	—	3	8	no	—
127	D₃×C₄⋊C₄	—	3	8	no	—
128	#883	—	3	16	no	—
129	C₄×D₁₂	—	3	4	no	—
130	#869	—	3	4	no	—
131	C₂³×C₃²	—	2	8	no	—
132	C₂³×C₃²	C₂²×D₃	1	8	yes	—
133	C₂³×C₃²	C₂³×C₃	1	2	yes	—
134	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
135	C₂²×C₃×D₃	—	3	8	no	—
136	C₃²×D₄	—	2	16	no	—
137	C₃²×D₄	—	2	8	no	—
138	C₃²×D₄	—	2	2	no	—
139	C₂×C₃²×C₄	—	2	4	no	—
140	C₂×C₃²×C₄	—	2	4	no	—
141	C₂×C₃²×C₄	—	2	4	no	—
142	C₂×C₃²×C₄	—	2	4	no	—
143	C₂×C₃²×C₄	—	2	8	no	—
144	C₂×C₃²×C₄	—	2	16	no	—
145	C₂×C₃²×C₄	—	4	16	no	—
146	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
147	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
148	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
149	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
150	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
151	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
152	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
153	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
154	#638	—	2	8	no	—
155	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
156	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
157	C₄⋊(C₃⋊D₃)	C₃×D₄	1	4	yes	complemented
158	C₄×C₃⋊D₃	—	2	8	no	—
159	C₄×C₃⋊D₃	—	2	4	no	—
160	#634	—	2	4	no	—
161	C₃×#67	—	6	32	no	—
162	C₂×C₃×Dic₃	—	3	8	no	—
163	C₂×C₃×Dic₃	—	3	16	no	—
164	C₃×D₁₂	—	3	16	no	—
165	C₃×C₄×D₃	—	6	32	no	—
166	C₃×C₄×D₃	—	6	16	no	—
167	C₃×Dic₆	—	6	16	no	—
168	#547	—	9	1	no	Sylow
169	C₂×C₃³	—	4	2	no	—
170	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₃³	C₂×#41	1	1	yes	characteristic
172	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
173	C₃×C₃⋊D₃	—	2	4	no	—
174	C₃×#41	—	18	8	no	—
175	C₂×C₃×Q₈	—	9	2	no	—
176	C₂×C₃×D₄	—	2	4	no	—
177	C₂×C₃×D₄	—	9	4	no	—
178	C₂×C₃×D₄	—	9	1	no	—
179	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
180	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
181	C₂²×C₃×C₄	—	2	8	no	—
182	C₂²×C₃×C₄	—	9	2	no	—
183	C₂²×C₃×C₄	—	9	4	no	—
184	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
185	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
186	C₂×#67	—	3	16	no	—
187	#235	—	6	32	no	—
188	C₂×D₁₂	—	3	4	no	—
189	C₂×C₄×D₃	—	3	8	no	—
190	C₂×C₄×D₃	—	3	16	no	—
191	C₂×Dic₆	—	3	8	no	—
192	C₃×C₄⋊C₄	—	2	4	no	—
193	C₃×C₄⋊C₄	—	9	4	no	—
194	C₃×C₄⋊C₄	—	9	2	no	—
195	C₃×C₄⋊C₄	—	9	1	no	—
196	C₃×C₄⋊C₄	—	9	2	no	—
197	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
198	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	—	2	8	no	—
200	C₃×C₂²⋊C₄	—	9	4	no	—
201	C₃×C₂²⋊C₄	—	9	2	no	—
202	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
203	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
204	C₃×C₄²	—	2	4	no	—
205	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
206	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
207	#217	—	3	16	no	—
208	(C₂×D₃)⋊C₄	—	3	8	no	—
209	C₄⋊Dic₃	—	3	8	no	—
210	C₄⋊Dic₃	—	3	8	no	—
211	C₄⋊Dic₃	—	3	4	no	—
212	Dic₃⋊C₄	—	3	16	no	—
213	C₂²×C₃²	—	2	16	no	—
214	C₂²×C₃²	—	2	8	no	—
215	C₂²×C₃²	—	2	2	no	—
216	C₂²×C₃²	—	2	2	no	—
217	C₂²×C₃²	—	2	2	no	—
218	C₂²×C₃²	—	2	4	no	—
219	C₂²×C₃²	—	2	8	no	—
220	C₂²×C₃²	—	2	8	no	—
221	C₂²×C₃²	—	4	8	no	—
222	C₂²×C₃²	—	4	8	no	—
223	C₂²×C₃²	C₂³×D₃	1	4	yes	—
224	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
225	C₂×C₃⋊D₃	—	2	2	no	—
226	C₂×C₃⋊D₃	—	2	2	no	—
227	C₂×C₃⋊D₃	C₂×C₃×D₄	1	4	yes	—
228	C₂×C₃×D₃	—	3	16	no	—
229	C₂×C₃×D₃	—	6	8	no	—
230	C₂×C₃×D₃	—	6	8	no	—
231	C₃²×C₄	—	2	2	no	—
232	C₃²×C₄	—	2	1	no	—
233	C₃²×C₄	—	2	8	no	—
234	C₃²×C₄	—	2	8	no	—
235	C₃²×C₄	—	2	8	no	—
236	C₃²×C₄	—	2	4	no	—
237	C₃²×C₄	—	4	4	no	—
238	C₃²×C₄	—	4	8	no	—
239	C₃²×C₄	#235	1	8	yes	complemented
240	C₃²×C₄	D₃×D₄	1	8	yes	—
241	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
242	C₃²×C₄	C₃×#41	1	2	yes	complemented
243	C₃⋊Dic₃	—	2	4	no	—
244	C₃⋊Dic₃	—	2	2	no	—
245	C₃×Dic₃	—	6	8	no	—
246	C₃×Dic₃	—	6	16	no	—
247	C₂×#41	—	9	2	no	—
248	C₄⋊Q₈	—	9	1	no	—
249	#123	—	9	4	no	—
250	C₂²⋊Q₈	—	9	2	no	—
251	#121	—	9	2	no	—
252	C₄×D₄	—	9	1	no	—
253	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
254	C₂×C₄⋊C₄	—	9	2	no	—
255	C₃³	#547	1	1	yes	characteristic, complemented, Sylow
256	C₂³×C₃	—	2	8	no	—
257	C₂³×C₃	—	9	2	no	—
258	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
259	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
260	C₂²×D₃	—	3	8	no	—
261	C₃×Q₈	—	18	4	no	—
262	C₃×D₄	—	2	16	no	—
263	C₃×D₄	—	2	8	no	—
264	C₃×D₄	—	2	2	no	—
265	C₃×D₄	—	9	4	no	—
266	C₃×D₄	—	18	8	no	—
267	C₂×C₃×C₄	—	2	16	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	2	8	no	—
273	C₂×C₃×C₄	—	4	16	no	—
274	C₂×C₃×C₄	—	9	2	no	—
275	C₂×C₃×C₄	—	9	4	no	—
276	C₂×C₃×C₄	—	18	8	no	—
277	C₂×C₃×C₄	—	18	4	no	—
278	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
279	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
280	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
281	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
282	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
284	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
286	#67	—	6	32	no	—
287	C₂×Dic₃	—	3	8	no	—
288	C₂×Dic₃	—	3	16	no	—
289	D₁₂	—	3	16	no	—
290	C₄×D₃	—	6	32	no	—
291	C₄×D₃	—	6	16	no	—
292	Dic₆	—	6	16	no	—
293	C₂×C₃²	—	2	4	no	—
294	C₂×C₃²	—	2	4	no	—
295	C₂×C₃²	—	2	4	no	—
296	C₂×C₃²	—	4	16	no	—
297	C₂×C₃²	—	4	8	no	—
298	C₂×C₃²	—	4	2	no	—
299	C₂×C₃²	C₂×#235	1	4	yes	—
300	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
301	C₂×C₃²	#1010	1	4	yes	—
302	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
303	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
304	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
305	C₃⋊D₃	—	2	4	no	—
306	C₃×D₃	—	6	16	no	—
307	#41	—	18	8	no	—
308	C₂×Q₈	—	9	2	no	—
309	C₂×D₄	—	9	4	no	—
310	C₂×D₄	—	9	1	no	—
311	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
312	C₂²×C₄	—	9	2	no	—
313	C₂²×C₄	—	9	4	no	—
314	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
315	C₄⋊C₄	—	9	2	no	—
316	C₄⋊C₄	—	9	4	no	—
317	C₄⋊C₄	—	9	1	no	—
318	C₄⋊C₄	—	9	2	no	—
319	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
320	C₂²⋊C₄	—	9	4	no	—
321	C₂²⋊C₄	—	9	2	no	—
322	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
323	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
324	C₂²×C₃	—	2	16	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	2	8	no	—
327	C₂²×C₃	—	2	8	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	4	no	—
332	C₂²×C₃	—	4	8	no	—
333	C₂²×C₃	—	4	8	no	—
334	C₂²×C₃	—	9	4	no	—
335	C₂²×C₃	—	18	2	no	—
336	C₂²×C₃	—	18	2	no	—
337	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
338	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
339	C₂×D₃	—	3	16	no	—
340	C₂×D₃	—	6	8	no	—
341	C₂×D₃	—	6	8	no	—
342	C₃×C₄	—	2	8	no	—
343	C₃×C₄	—	2	4	no	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	2	8	no	—
347	C₃×C₄	—	2	8	no	—
348	C₃×C₄	—	4	8	no	—
349	C₃×C₄	—	4	4	no	—
350	C₃×C₄	—	18	2	no	—
351	C₃×C₄	—	18	4	no	—
352	C₃×C₄	C₃×#235	1	8	yes	complemented
353	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
354	C₃×C₄	#3828	1	2	yes	complemented
355	C₃×C₄	D₄×C₃⋊D₃	1	2	yes	—
356	Dic₃	—	6	8	no	—
357	Dic₃	—	6	16	no	—
358	C₃²	—	2	4	no	—
359	C₃²	#5551	1	4	yes	complemented
360	C₃²	C₃×#547	1	1	yes	characteristic, complemented
361	C₂³	—	9	2	no	—
362	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
363	Q₈	—	18	4	no	—
364	D₄	—	2	2	no	—
365	D₄	—	9	4	no	—
366	D₄	—	18	8	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	9	2	no	—
369	C₂×C₄	—	9	4	no	—
370	C₂×C₄	—	18	8	no	—
371	C₂×C₄	—	18	4	no	—
372	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
374	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	—	2	4	no	—
378	C₂×C₃	—	2	4	no	—
379	C₂×C₃	—	4	16	no	—
380	C₂×C₃	—	4	8	no	—
381	C₂×C₃	—	4	2	no	—
382	C₂×C₃	—	18	4	no	—
383	C₂×C₃	C₂×C₃×#235	1	4	yes	—
384	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
385	C₂×C₃	C₃×#1010	1	4	yes	—
386	C₂×C₃	C₂×#3828	1	1	yes	characteristic
387	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
388	C₂×C₃	#64367	1	1	yes	characteristic
389	D₃	—	6	16	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	9	4	no	—
394	C₂²	—	18	2	no	—
395	C₂²	—	18	2	no	—
396	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	18	2	no	—
400	C₄	—	18	4	no	—
401	C₄	C₃×#3828	1	2	yes	complemented
402	C₄	C₃×D₄×C₃⋊D₃	1	2	yes	—
403	C₃	—	2	4	no	—
404	C₃	C₃×#5551	1	4	yes	complemented
405	C₃	#10596022	1	1	yes	characteristic, direct product factor
406	C₂	—	4	2	no	—
407	C₂	—	18	4	no	—
408	C₂	C₂×C₃×#3828	1	1	yes	characteristic
409	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
410	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×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×#547
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3828	C₂	semidirect
2. C₃³×C₄×D₄	C₂	semidirect
3. C₃×#64147	C₂	semidirect
4. C₃×#64133	C₂	semidirect
5. C₃×C₄⋊C₄×C₃⋊D₃	C₂	semidirect
6. C₃×#64092	C₂	semidirect
7. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	semidirect
8. C₃×#64078	C₂	semidirect
9. #10596022	C₃	direct (N × H)
28. C₂×#3828	C₂×C₃	semidirect
31. C₃²×C₄×D₄	D₃	semidirect
32. C₃²×C₄×D₄	C₂×C₃	semidirect
33. #64147	C₂×C₃	semidirect
34. #64133	C₂×C₃	semidirect
35. C₄⋊C₄×C₃⋊D₃	C₂×C₃	semidirect
36. #64092	C₂×C₃	semidirect
37. C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
38. #64078	C₂×C₃	semidirect
56. C₃×C₄⋊(C₃⋊D₃)	D₄	semidirect
111. C₃³×C₄	#41	semidirect
122. C₃×C₄×D₄	C₃×D₃	semidirect
123. C₃×C₄×D₄	C₃⋊D₃	semidirect
157. C₄⋊(C₃⋊D₃)	C₃×D₄	semidirect
239. C₃²×C₄	#235	semidirect
242. C₃²×C₄	C₃×#41	semidirect
253. C₄×D₄	C₃×C₃⋊D₃	semidirect
255. C₃³	#547	semidirect
352. C₃×C₄	C₃×#235	semidirect
354. C₃×C₄	#3828	semidirect
359. C₃²	#5551	semidirect
360. C₃²	C₃×#547	semidirect
401. C₄	C₃×#3828	semidirect
404. C₃	C₃×#5551	semidirect
405. C₃	#10596022	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3828	2
C₃³×C₄×D₄	2
C₃×#64147	2
C₃×#64133	2
C₃×C₄⋊C₄×C₃⋊D₃	2
C₃×#64092	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
C₃×#64078	2
#10596022	3
C₃×#5551	3

Subgroups — C3×#10596022 #13179305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596022 #13179305