Subgroups — C₃×#10592469 #13162807

Order 1728.

1340 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3743	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃³×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63659	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63648	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63636	C₂	1	1	yes	maximal, characteristic, complemented
8	#10592469	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃×#4770	—	3	4	no	maximal
10	C₂³×C₃×C₃⋊D₃	—	2	1	no	—
11	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×#638	—	2	1	no	—
13	C₃×D₄×C₃⋊D₃	—	2	2	no	—
14	C₃×D₄×C₃⋊D₃	C₄	1	4	yes	complemented
15	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
17	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
18	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
19	C₃×#3752	—	2	1	no	—
20	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₄×C₃⋊Dic₃	—	2	1	no	—
22	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
23	C₃×#3743	—	2	2	no	—
24	C₂×D₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×D₃×D₄	—	3	4	no	—
26	C₂×#3743	C₂×C₃	1	1	yes	characteristic, complemented
27	#64101	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	4	no	—
29	C₃×#892	—	3	4	no	—
30	C₃²×#102	—	2	4	no	—
31	C₃²×#102	D₃	1	4	yes	complemented
32	C₃²×#102	C₂×C₃	1	1	yes	characteristic, complemented
33	#63659	C₂×C₃	1	1	yes	characteristic, complemented
34	#63648	C₂×C₃	1	1	yes	characteristic, complemented
35	#63636	C₂×C₃	1	1	yes	characteristic, complemented
36	C₃×#832	—	3	4	no	—
37	C₃×#821	—	3	4	no	—
38	C₃×#809	—	3	4	no	—
39	C₂³×C₃³	—	2	1	no	—
40	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
41	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
42	C₂²×C₃×C₃⋊D₃	—	4	2	no	—
43	C₂²×C₃×C₃⋊D₃	—	4	2	no	—
44	C₂²×C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
45	C₃³×D₄	—	2	1	no	—
46	C₃³×D₄	C₂×C₄	1	2	yes	—
47	C₂×C₃³×C₄	—	2	1	no	—
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₃×#638	—	2	4	no	—
50	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
51	C₂×C₃×C₃⋊Dic₃	D₄	1	1	yes	characteristic
52	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
53	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	2	yes	—
54	C₃×C₄×C₃⋊D₃	C₂×C₄	1	2	yes	—
55	C₃×C₄×C₃⋊D₃	D₄	1	2	yes	—
56	C₃³×C₈	—	2	1	no	—
57	C₃×C₃⋊(C₃⋊C₈)	—	2	1	no	—
58	C₃×#418	—	9	1	no	—
59	#4770	—	3	4	no	—
60	C₂³×C₃⋊D₃	—	2	1	no	—
61	C₂³×C₃×D₃	—	6	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	C₂×#638	—	2	1	no	—
66	D₄×C₃⋊D₃	—	2	2	no	—
67	D₄×C₃⋊D₃	C₃×C₄	1	4	yes	complemented
68	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₃×#67	—	6	4	no	—
71	C₃×D₃×D₄	—	3	16	no	—
72	C₃×D₃×D₄	—	6	8	no	—
73	C₂×C₃×D₁₂	—	3	4	no	—
74	C₂×C₃×C₄×D₃	—	3	4	no	—
75	C₂×C₃²×C₈	—	2	4	no	—
76	C₂×C₃²×C₈	C₂×D₃	1	4	yes	complemented
77	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
78	C₃²×C₄⋊C₄	—	2	4	no	—
79	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
80	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
81	#3752	—	2	1	no	—
82	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic, complemented
83	C₄×C₃⋊Dic₃	—	2	1	no	—
84	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
85	#3743	—	2	2	no	—
86	C₃×(C₂×D₃)⋊C₄	—	6	4	no	—
87	C₃×C₄⋊Dic₃	—	3	4	no	—
88	C₃×C₄×Dic₃	—	6	4	no	—
89	C₂×C₃×C₃⋊C₈	—	3	4	no	—
90	C₃×ΓL(1,𝔽₂₅)	—	6	8	no	—
91	C₂²×C₃³	—	2	2	no	—
92	C₂²×C₃³	—	4	1	no	—
93	C₂²×C₃³	—	4	1	no	—
94	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₃⋊D₃	—	2	1	no	—
96	C₂×C₃×C₃⋊D₃	—	2	1	no	—
97	C₂×C₃×C₃⋊D₃	—	2	2	no	—
98	C₂×C₃×C₃⋊D₃	—	4	8	no	—
99	C₂×C₃×C₃⋊D₃	—	4	1	no	—
100	C₂×C₃×C₃⋊D₃	—	4	1	no	—
101	C₂×C₃×C₃⋊D₃	C₂²⋊C₄	1	2	yes	—
102	C₃³×C₄	—	4	1	no	—
103	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
104	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
105	C₃×C₃⋊Dic₃	—	4	1	no	—
106	C₃×C₃⋊Dic₃	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₃×D₄	—	9	1	no	—
108	C₂×D₃×D₄	—	3	4	no	—
109	C₂×C₃×M₁₆	—	9	1	no	—
110	C₃×#117	—	9	1	no	—
111	C₂×ΓL(1,𝔽₂₅)	—	3	4	no	—
112	#892	—	3	4	no	—
113	C₃×#102	—	2	4	no	—
114	C₃×#102	—	9	1	no	—
115	C₃×#102	—	9	1	no	—
116	C₃×#102	—	9	1	no	—
117	C₃×#102	C₃×D₃	1	4	yes	complemented
118	C₃×#102	C₃⋊D₃	1	1	yes	characteristic, complemented
119	#832	—	3	4	no	—
120	#821	—	3	4	no	—
121	#809	—	3	4	no	—
122	C₂³×C₃²	—	2	1	no	—
123	C₂³×C₃²	—	2	4	no	—
124	C₂³×C₃²	—	4	4	no	—
125	C₂²×C₃⋊D₃	—	2	1	no	—
126	C₂²×C₃⋊D₃	—	2	4	no	—
127	C₂²×C₃⋊D₃	—	4	2	no	—
128	C₂²×C₃⋊D₃	—	4	2	no	—
129	C₂²×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
130	C₂²×C₃×D₃	—	3	4	no	—
131	C₂²×C₃×D₃	—	6	16	no	—
132	C₂²×C₃×D₃	—	6	4	no	—
133	C₂²×C₃×D₃	—	12	8	no	—
134	C₂²×C₃×D₃	—	12	8	no	—
135	C₃²×D₄	—	2	1	no	—
136	C₃²×D₄	—	2	8	no	—
137	C₃²×D₄	—	2	4	no	—
138	C₃²×D₄	—	4	4	no	—
139	C₃²×D₄	C₄×D₃	1	8	yes	—
140	C₃²×D₄	C₂×C₃×C₄	1	2	yes	—
141	C₂×C₃²×C₄	—	2	1	no	—
142	C₂×C₃²×C₄	—	2	4	no	—
143	C₂×C₃²×C₄	—	2	4	no	—
144	C₂×C₃²×C₄	—	4	4	no	—
145	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
146	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
147	#638	—	2	4	no	—
148	C₂×C₃⋊Dic₃	—	2	1	no	—
149	C₂×C₃⋊Dic₃	C₃×D₄	1	1	yes	characteristic
150	C₄⋊(C₃⋊D₃)	—	2	1	no	—
151	C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	1	2	yes	—
152	C₄×C₃⋊D₃	C₂×C₃×C₄	1	2	yes	—
153	C₄×C₃⋊D₃	C₃×D₄	1	2	yes	—
154	C₃×#67	—	6	16	no	—
155	C₂×C₃×Dic₃	—	3	4	no	—
156	C₂×C₃×Dic₃	—	6	4	no	—
157	C₃×D₁₂	—	3	8	no	—
158	C₃×D₁₂	—	6	4	no	—
159	C₃×C₄×D₃	—	3	8	no	—
160	C₃×C₄×D₃	—	3	8	no	—
161	C₃²×C₈	—	2	1	no	—
162	C₃²×C₈	—	2	4	no	—
163	C₃²×C₈	—	4	4	no	—
164	C₃⋊(C₃⋊C₈)	—	2	1	no	—
165	C₃×C₃⋊C₈	—	6	4	no	—
166	#418	—	9	1	no	Sylow
167	C₂×C₃³	—	4	2	no	—
168	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₃³	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₃³	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₃×C₃⋊D₃	—	2	2	no	—
172	C₃×C₃⋊D₃	—	4	2	no	—
173	C₂⁴×C₃	—	18	1	no	—
174	C₂³×D₃	—	6	4	no	—
175	C₂×C₃×D₄	—	2	4	no	—
176	C₂×C₃×D₄	—	9	4	no	—
177	C₂×C₃×D₄	—	9	1	no	—
178	C₂×C₃×D₄	—	18	2	no	—
179	C₂×C₃×D₄	—	18	1	no	—
180	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
181	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
182	C₂²×C₃×C₄	—	9	1	no	—
183	C₂×#67	—	6	4	no	—
184	D₃×D₄	—	3	16	no	—
185	D₃×D₄	—	6	8	no	—
186	C₂×D₁₂	—	3	4	no	—
187	C₂×C₄×D₃	—	3	4	no	—
188	C₃×M₁₆	—	18	2	no	—
189	C₂×C₃×C₈	—	2	4	no	—
190	C₂×C₃×C₈	—	9	1	no	—
191	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	complemented
192	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
193	C₃×C₄⋊C₄	—	2	4	no	—
194	C₃×C₄⋊C₄	—	9	1	no	—
195	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
196	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
197	C₃×C₂²⋊C₄	—	18	1	no	—
198	C₃×C₄²	—	18	1	no	—
199	(C₂×D₃)⋊C₄	—	6	4	no	—
200	C₄⋊Dic₃	—	3	4	no	—
201	C₄×Dic₃	—	6	4	no	—
202	C₂×C₃⋊C₈	—	3	4	no	—
203	ΓL(1,𝔽₂₅)	—	6	8	no	—
204	C₂²×C₃²	—	2	2	no	—
205	C₂²×C₃²	—	2	4	no	—
206	C₂²×C₃²	—	2	8	no	—
207	C₂²×C₃²	—	4	8	no	—
208	C₂²×C₃²	—	4	1	no	—
209	C₂²×C₃²	—	4	1	no	—
210	C₂²×C₃²	—	4	4	no	—
211	C₂²×C₃²	—	4	4	no	—
212	C₂²×C₃²	—	8	4	no	—
213	C₂²×C₃²	—	8	4	no	—
214	C₂²×C₃²	D₃×D₄	1	4	yes	—
215	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
216	C₂×C₃⋊D₃	—	2	1	no	—
217	C₂×C₃⋊D₃	—	2	1	no	—
218	C₂×C₃⋊D₃	—	2	2	no	—
219	C₂×C₃⋊D₃	—	4	8	no	—
220	C₂×C₃⋊D₃	—	4	1	no	—
221	C₂×C₃⋊D₃	—	4	1	no	—
222	C₂×C₃⋊D₃	C₃×C₂²⋊C₄	1	2	yes	—
223	C₂×C₃×D₃	—	3	8	no	—
224	C₂×C₃×D₃	—	6	4	no	—
225	C₂×C₃×D₃	—	6	4	no	—
226	C₂×C₃×D₃	—	6	8	no	—
227	C₂×C₃×D₃	—	12	32	no	—
228	C₂×C₃×D₃	—	12	4	no	—
229	C₂×C₃×D₃	—	12	4	no	—
230	C₃²×C₄	—	2	4	no	—
231	C₃²×C₄	—	2	4	no	—
232	C₃²×C₄	—	4	1	no	—
233	C₃²×C₄	—	4	4	no	—
234	C₃²×C₄	—	8	4	no	—
235	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
236	C₃²×C₄	D₃×D₄	1	4	yes	—
237	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
238	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
239	C₃⋊Dic₃	—	4	1	no	—
240	C₃⋊Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
241	C₃×Dic₃	—	3	8	no	—
242	C₃×Dic₃	—	12	4	no	—
243	C₂²×D₄	—	9	1	no	—
244	C₂×M₁₆	—	9	1	no	—
245	#117	—	9	1	no	—
246	#102	—	9	1	no	—
247	#102	—	9	1	no	—
248	#102	—	9	1	no	—
249	#102	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
250	C₃³	#418	1	1	yes	characteristic, complemented, Sylow
251	C₂³×C₃	—	2	4	no	—
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	—	4	4	no	—
254	C₂³×C₃	—	9	1	no	—
255	C₂³×C₃	—	18	4	no	—
256	C₂³×C₃	—	18	1	no	—
257	C₂³×C₃	—	36	2	no	—
258	C₂³×C₃	—	36	2	no	—
259	C₂²×D₃	—	3	4	no	—
260	C₂²×D₃	—	6	16	no	—
261	C₂²×D₃	—	6	4	no	—
262	C₂²×D₃	—	12	8	no	—
263	C₂²×D₃	—	12	8	no	—
264	C₃×D₄	—	2	4	no	—
265	C₃×D₄	—	2	1	no	—
266	C₃×D₄	—	2	8	no	—
267	C₃×D₄	—	4	4	no	—
268	C₃×D₄	—	9	2	no	—
269	C₃×D₄	—	18	4	no	—
270	C₃×D₄	—	18	1	no	—
271	C₃×D₄	C₃×C₄×D₃	1	8	yes	—
272	C₃×D₄	C₄×C₃⋊D₃	1	2	yes	—
273	C₂×C₃×C₄	—	2	4	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	4	no	—
276	C₂×C₃×C₄	—	4	4	no	—
277	C₂×C₃×C₄	—	9	1	no	—
278	C₂×C₃×C₄	—	9	2	no	—
279	C₂×C₃×C₄	—	9	2	no	—
280	C₂×C₃×C₄	—	18	1	no	—
281	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
282	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
283	#67	—	6	16	no	—
284	C₂×Dic₃	—	3	4	no	—
285	C₂×Dic₃	—	6	4	no	—
286	D₁₂	—	3	8	no	—
287	D₁₂	—	6	4	no	—
288	C₄×D₃	—	3	8	no	—
289	C₄×D₃	—	3	8	no	—
290	C₃×C₈	—	2	4	no	—
291	C₃×C₈	—	2	1	no	—
292	C₃×C₈	—	4	4	no	—
293	C₃×C₈	—	18	1	no	—
294	C₃⋊C₈	—	6	4	no	—
295	C₂×C₃²	—	2	4	no	—
296	C₂×C₃²	—	2	4	no	—
297	C₂×C₃²	—	2	4	no	—
298	C₂×C₃²	—	4	2	no	—
299	C₂×C₃²	—	4	8	no	—
300	C₂×C₃²	—	8	8	no	—
301	C₂×C₃²	D₃×C₂²⋊C₄	1	4	yes	—
302	C₂×C₃²	#911	1	4	yes	—
303	C₂×C₃²	#914	1	4	yes	—
304	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
307	C₃⋊D₃	—	2	2	no	—
308	C₃⋊D₃	—	4	2	no	—
309	C₃×D₃	—	6	8	no	—
310	C₃×D₃	—	12	8	no	—
311	C₂⁴	—	18	1	no	—
312	C₂×D₄	—	9	4	no	—
313	C₂×D₄	—	9	1	no	—
314	C₂×D₄	—	18	2	no	—
315	C₂×D₄	—	18	1	no	—
316	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
317	C₂²×C₄	—	9	1	no	—
318	M₁₆	—	18	2	no	—
319	C₂×C₈	—	9	1	no	—
320	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
321	C₄⋊C₄	—	9	1	no	—
322	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
323	C₂²⋊C₄	—	18	1	no	—
324	C₄²	—	18	1	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	4	no	—
328	C₂²×C₃	—	4	8	no	—
329	C₂²×C₃	—	4	4	no	—
330	C₂²×C₃	—	4	4	no	—
331	C₂²×C₃	—	4	1	no	—
332	C₂²×C₃	—	4	1	no	—
333	C₂²×C₃	—	8	4	no	—
334	C₂²×C₃	—	8	4	no	—
335	C₂²×C₃	—	9	2	no	—
336	C₂²×C₃	—	18	1	no	—
337	C₂²×C₃	—	18	1	no	—
338	C₂²×C₃	—	18	2	no	—
339	C₂²×C₃	—	36	8	no	—
340	C₂²×C₃	—	36	1	no	—
341	C₂²×C₃	—	36	1	no	—
342	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
343	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
344	C₂×D₃	—	3	8	no	—
345	C₂×D₃	—	6	4	no	—
346	C₂×D₃	—	6	4	no	—
347	C₂×D₃	—	6	8	no	—
348	C₂×D₃	—	12	32	no	—
349	C₂×D₃	—	12	4	no	—
350	C₂×D₃	—	12	4	no	—
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	4	no	—
353	C₃×C₄	—	4	4	no	—
354	C₃×C₄	—	4	1	no	—
355	C₃×C₄	—	8	4	no	—
356	C₃×C₄	—	9	2	no	—
357	C₃×C₄	—	36	1	no	—
358	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
359	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
360	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
361	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
362	Dic₃	—	3	8	no	—
363	Dic₃	—	12	4	no	—
364	C₃²	—	2	4	no	—
365	C₃²	#4770	1	4	yes	complemented
366	C₃²	C₃×#418	1	1	yes	characteristic, complemented
367	C₂³	—	2	1	no	—
368	C₂³	—	9	1	no	—
369	C₂³	—	18	4	no	—
370	C₂³	—	18	1	no	—
371	C₂³	—	36	2	no	—
372	C₂³	—	36	2	no	—
373	D₄	—	2	1	no	—
374	D₄	—	9	2	no	—
375	D₄	—	18	4	no	—
376	D₄	—	18	1	no	—
377	D₄	C₃×C₄×C₃⋊D₃	1	2	yes	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	9	1	no	—
380	C₂×C₄	—	9	2	no	—
381	C₂×C₄	—	9	2	no	—
382	C₂×C₄	—	18	1	no	—
383	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
384	C₈	—	2	1	no	—
385	C₈	—	18	1	no	—
386	C₂×C₃	—	2	4	no	—
387	C₂×C₃	—	2	4	no	—
388	C₂×C₃	—	2	4	no	—
389	C₂×C₃	—	4	8	no	—
390	C₂×C₃	—	4	2	no	—
391	C₂×C₃	—	8	8	no	—
392	C₂×C₃	—	18	2	no	—
393	C₂×C₃	—	36	2	no	—
394	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	4	yes	—
395	C₂×C₃	C₃×#911	1	4	yes	—
396	C₂×C₃	C₃×#914	1	4	yes	—
397	C₂×C₃	C₂²⋊C₄×C₃⋊D₃	1	1	yes	characteristic
398	C₂×C₃	#64120	1	1	yes	characteristic
399	C₂×C₃	#64123	1	1	yes	characteristic
400	D₃	—	6	8	no	—
401	D₃	—	12	8	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	9	2	no	—
406	C₂²	—	18	1	no	—
407	C₂²	—	18	1	no	—
408	C₂²	—	18	2	no	—
409	C₂²	—	36	8	no	—
410	C₂²	—	36	1	no	—
411	C₂²	—	36	1	no	—
412	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
413	C₄	—	4	1	no	—
414	C₄	—	9	2	no	—
415	C₄	—	36	1	no	—
416	C₄	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
417	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
418	C₃	—	2	4	no	—
419	C₃	C₃×#4770	1	4	yes	complemented
420	C₃	#10592469	1	1	yes	characteristic, direct product factor
421	C₂	—	4	2	no	—
422	C₂	—	18	2	no	—
423	C₂	—	36	2	no	—
424	C₂	C₃×C₂²⋊C₄×C₃⋊D₃	1	1	yes	characteristic
425	C₂	C₃×#64120	1	1	yes	characteristic
426	C₂	C₃×#64123	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₄×C₃⋊D₃
commutator	C₃²×C₄	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₃³×#102	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃×D₄×C₃⋊D₃	C₂
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₃×#102	C₃⋊D₃
hypocenter	C₃²	C₃×#418
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#102

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#3743	C₂	semidirect
3. C₃×#64101	C₂	semidirect
4. C₃³×#102	C₂	semidirect
5. C₃×#63659	C₂	semidirect
6. C₃×#63648	C₂	semidirect
7. C₃×#63636	C₂	semidirect
8. #10592469	C₃	direct (N × H)
14. C₃×D₄×C₃⋊D₃	C₄	semidirect
17. C₂×C₃³×C₈	C₂²	semidirect
18. C₃³×C₄⋊C₄	C₂²	semidirect
20. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
22. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
26. C₂×#3743	C₂×C₃	semidirect
27. #64101	C₂×C₃	semidirect
31. C₃²×#102	D₃	semidirect
32. C₃²×#102	C₂×C₃	semidirect
33. #63659	C₂×C₃	semidirect
34. #63648	C₂×C₃	semidirect
35. #63636	C₂×C₃	semidirect
67. D₄×C₃⋊D₃	C₃×C₄	semidirect
76. C₂×C₃²×C₈	C₂×D₃	semidirect
77. C₂×C₃²×C₈	C₂²×C₃	semidirect
79. C₃²×C₄⋊C₄	C₂×D₃	semidirect
80. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
82. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
84. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
117. C₃×#102	C₃×D₃	semidirect
118. C₃×#102	C₃⋊D₃	semidirect
191. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
192. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
195. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
196. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
249. #102	C₃×C₃⋊D₃	semidirect
250. C₃³	#418	semidirect
320. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
322. C₄⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
365. C₃²	#4770	semidirect
366. C₃²	C₃×#418	semidirect
419. C₃	C₃×#4770	semidirect
420. C₃	#10592469	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×D₄×C₃⋊D₃	2
C₂×C₃×#3743	2
C₃×#64101	2
C₃³×#102	2
C₃×#63659	2
C₃×#63648	2
C₃×#63636	2
#10592469	3
C₃×#4770	3

Subgroups — C3×#10592469 #13162807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10592469 #13162807