Subgroups — C₃×#10596024 #13179289

Order 1728.

2248 conjugacy classes of subgroups.

The subgroup lattice has 424 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×#64149	C₂	1	2	yes	maximal, complemented
4	C₃×#64139	C₂	1	2	yes	maximal, complemented
5	C₃×#64102	C₂	1	2	yes	maximal, complemented
6	C₃×#64093	C₂	1	4	yes	maximal, complemented
7	C₃×#64083	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596024	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5553	—	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	C₂×C₃×#638	C₂²	1	4	yes	—
15	C₃×#3828	—	2	8	no	—
16	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
18	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
19	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	4	yes	—
20	C₂×C₃×#634	C₂²	1	1	yes	characteristic
21	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃³×C₄²	C₂²	1	1	yes	characteristic
24	C₃×#3752	C₂²	1	4	yes	—
25	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
26	C₃×#3750	C₂²	1	2	yes	—
27	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	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	#64149	C₂×C₃	1	2	yes	complemented
34	#64139	C₂×C₃	1	2	yes	complemented
35	#64102	C₂×C₃	1	2	yes	complemented
36	#64093	C₂×C₃	1	4	yes	complemented
37	#64083	C₂×C₃	1	1	yes	characteristic, complemented
38	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×#940	—	3	8	no	—
40	C₃×#930	—	3	8	no	—
41	C₃×#893	—	3	8	no	—
42	C₃×#884	—	3	16	no	—
43	C₃×#874	—	3	4	no	—
44	C₃×C₄×Dic₆	—	3	4	no	—
45	C₂³×C₃³	C₂³	1	2	yes	—
46	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	—
47	C₃³×D₄	—	2	2	no	—
48	C₂×C₃³×C₄	—	2	4	no	—
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃³×C₄	C₂³	1	2	yes	—
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	C₃×#638	—	4	4	no	—
55	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
56	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
57	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
58	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
59	C₃×C₄⋊(C₃⋊D₃)	—	4	2	no	—
60	C₃×C₄×C₃⋊D₃	—	2	8	no	—
61	C₃×#634	D₄	1	4	yes	complemented
62	C₃×#550	—	9	1	no	—
63	#5553	—	3	4	no	—
64	C₂×C₃²×D₄	—	2	4	no	—
65	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
66	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₃²×C₄	—	2	8	no	—
68	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
69	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
70	C₂×#638	C₂²×C₃	1	4	yes	—
71	C₂×#638	C₂²×C₃	1	4	yes	—
72	#3828	—	2	8	no	—
73	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
74	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
75	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
76	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	4	yes	—
77	C₂×#634	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×#67	—	3	16	no	—
79	C₂×C₃×#67	—	3	16	no	—
80	C₃×#235	—	6	32	no	—
81	C₂×C₃×D₁₂	—	3	8	no	—
82	C₂×C₃×D₁₂	—	3	8	no	—
83	C₂×C₃×D₁₂	—	3	8	no	—
84	C₂×C₃×C₄×D₃	—	3	16	no	—
85	C₂×C₃×Dic₆	—	3	4	no	—
86	C₃²×C₄⋊C₄	—	2	4	no	—
87	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
88	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₃²×C₂²⋊C₄	—	2	8	no	—
90	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
91	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃²×C₄²	—	2	4	no	—
93	C₃²×C₄²	C₂×D₃	1	4	yes	—
94	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
95	#3752	C₂²×C₃	1	4	yes	—
96	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
97	#3750	C₂²×C₃	1	2	yes	—
98	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
99	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
100	C₃×C₄⋊Dic₃	—	3	4	no	—
101	C₃×Dic₃⋊C₄	—	3	8	no	—
102	C₃×C₄×Dic₃	—	3	8	no	—
103	C₂²×C₃³	—	2	2	no	—
104	C₂²×C₃³	—	2	2	no	—
105	C₂²×C₃³	—	2	2	no	—
106	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
107	C₂×C₃×C₃⋊D₃	—	2	4	no	—
108	C₂×C₃×C₃⋊D₃	—	2	4	no	—
109	C₂×C₃×C₃⋊D₃	—	2	4	no	—
110	C₃³×C₄	—	2	2	no	—
111	C₃³×C₄	—	2	1	no	—
112	C₃³×C₄	C₂×D₄	1	2	yes	—
113	C₃³×C₄	#41	1	2	yes	complemented
114	C₃×C₃⋊Dic₃	—	2	2	no	—
115	C₃×C₃⋊Dic₃	C₂×D₄	1	4	yes	—
116	C₂×C₃×#41	—	9	2	no	—
117	C₂×#235	—	3	8	no	—
118	C₃×#127	—	9	2	no	—
119	C₃×#127	—	9	1	no	—
120	C₃×#121	—	9	2	no	—
121	C₃×#121	—	9	4	no	—
122	C₃×C₄×Q₈	—	9	1	no	—
123	C₃×C₄×D₄	—	2	4	no	—
124	C₃×C₄×D₄	—	9	2	no	—
125	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
126	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
127	#940	—	3	8	no	—
128	#930	—	3	8	no	—
129	#893	—	3	8	no	—
130	#884	—	3	16	no	—
131	#874	—	3	4	no	—
132	C₄×Dic₆	—	3	4	no	—
133	C₂³×C₃²	—	2	8	no	—
134	C₂³×C₃²	C₂²×D₃	1	8	yes	—
135	C₂³×C₃²	C₂³×C₃	1	2	yes	—
136	C₂²×C₃⋊D₃	C₂³×C₃	1	4	yes	—
137	C₂²×C₃×D₃	—	3	16	no	—
138	C₃²×D₄	—	2	16	no	—
139	C₃²×D₄	—	2	8	no	—
140	C₃²×D₄	—	2	2	no	—
141	C₂×C₃²×C₄	—	2	4	no	—
142	C₂×C₃²×C₄	—	2	4	no	—
143	C₂×C₃²×C₄	—	2	4	no	—
144	C₂×C₃²×C₄	—	2	4	no	—
145	C₂×C₃²×C₄	—	2	8	no	—
146	C₂×C₃²×C₄	—	2	16	no	—
147	C₂×C₃²×C₄	—	4	16	no	—
148	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
149	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
150	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
151	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
152	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
153	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
154	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
155	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
156	#638	—	2	8	no	—
157	#638	—	4	4	no	—
158	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
159	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
160	C₄⋊(C₃⋊D₃)	—	2	4	no	—
161	C₄⋊(C₃⋊D₃)	—	2	4	no	—
162	C₄⋊(C₃⋊D₃)	—	4	2	no	—
163	C₄×C₃⋊D₃	—	2	8	no	—
164	#634	C₃×D₄	1	4	yes	complemented
165	C₃×#67	—	6	32	no	—
166	C₃×#67	—	12	16	no	—
167	C₂×C₃×Dic₃	—	3	8	no	—
168	C₂×C₃×Dic₃	—	3	8	no	—
169	C₃×D₁₂	—	6	16	no	—
170	C₃×D₁₂	—	6	16	no	—
171	C₃×D₁₂	—	12	8	no	—
172	C₃×C₄×D₃	—	6	32	no	—
173	C₃×Dic₆	—	3	16	no	—
174	#550	—	9	1	no	Sylow
175	C₂×C₃³	—	4	2	no	—
176	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₃³	C₂×#41	1	1	yes	characteristic
178	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
179	C₃×C₃⋊D₃	—	4	4	no	—
180	C₃×#41	—	18	8	no	—
181	C₂×C₃×Q₈	—	9	1	no	—
182	C₂×C₃×D₄	—	2	4	no	—
183	C₂×C₃×D₄	—	9	4	no	—
184	C₂×C₃×D₄	—	9	4	no	—
185	C₂×C₃×D₄	—	9	2	no	—
186	C₂×C₃×D₄	—	9	2	no	—
187	C₂×C₃×D₄	—	9	2	no	—
188	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
189	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
190	C₂²×C₃×C₄	—	2	8	no	—
191	C₂²×C₃×C₄	—	9	4	no	—
192	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
193	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
194	C₂×#67	—	3	16	no	—
195	C₂×#67	—	3	16	no	—
196	#235	—	6	32	no	—
197	C₂×D₁₂	—	3	8	no	—
198	C₂×D₁₂	—	3	8	no	—
199	C₂×D₁₂	—	3	8	no	—
200	C₂×C₄×D₃	—	3	16	no	—
201	C₂×Dic₆	—	3	4	no	—
202	C₃×C₄⋊C₄	—	2	4	no	—
203	C₃×C₄⋊C₄	—	9	2	no	—
204	C₃×C₄⋊C₄	—	9	1	no	—
205	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
206	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
207	C₃×C₂²⋊C₄	—	2	8	no	—
208	C₃×C₂²⋊C₄	—	9	4	no	—
209	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
210	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
211	C₃×C₄²	—	2	4	no	—
212	C₃×C₄²	—	9	2	no	—
213	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
214	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	—	3	16	no	—
216	C₄⋊Dic₃	—	3	4	no	—
217	Dic₃⋊C₄	—	3	8	no	—
218	C₄×Dic₃	—	3	8	no	—
219	C₂²×C₃²	—	2	16	no	—
220	C₂²×C₃²	—	2	8	no	—
221	C₂²×C₃²	—	2	2	no	—
222	C₂²×C₃²	—	2	2	no	—
223	C₂²×C₃²	—	2	2	no	—
224	C₂²×C₃²	—	2	4	no	—
225	C₂²×C₃²	—	2	8	no	—
226	C₂²×C₃²	—	2	8	no	—
227	C₂²×C₃²	—	4	8	no	—
228	C₂²×C₃²	—	4	8	no	—
229	C₂²×C₃²	C₂³×D₃	1	4	yes	—
230	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
231	C₂×C₃⋊D₃	—	2	4	no	—
232	C₂×C₃⋊D₃	—	2	4	no	—
233	C₂×C₃⋊D₃	—	2	4	no	—
234	C₂×C₃×D₃	—	6	16	no	—
235	C₂×C₃×D₃	—	6	16	no	—
236	C₂×C₃×D₃	—	6	16	no	—
237	C₃²×C₄	—	2	2	no	—
238	C₃²×C₄	—	2	1	no	—
239	C₃²×C₄	—	2	8	no	—
240	C₃²×C₄	—	2	8	no	—
241	C₃²×C₄	—	2	8	no	—
242	C₃²×C₄	—	2	4	no	—
243	C₃²×C₄	—	4	4	no	—
244	C₃²×C₄	—	4	8	no	—
245	C₃²×C₄	#235	1	8	yes	complemented
246	C₃²×C₄	D₃×D₄	1	8	yes	—
247	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
248	C₃²×C₄	C₃×#41	1	2	yes	complemented
249	C₃⋊Dic₃	—	2	2	no	—
250	C₃⋊Dic₃	C₂×C₃×D₄	1	4	yes	—
251	C₃×Dic₃	—	3	16	no	—
252	C₃×Dic₃	—	6	8	no	—
253	C₂×#41	—	9	2	no	—
254	#127	—	9	2	no	—
255	#127	—	9	1	no	—
256	#121	—	9	2	no	—
257	#121	—	9	4	no	—
258	C₄×Q₈	—	9	1	no	—
259	C₄×D₄	—	9	2	no	—
260	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
261	C₃³	#550	1	1	yes	characteristic, complemented, Sylow
262	C₂³×C₃	—	2	8	no	—
263	C₂³×C₃	—	9	4	no	—
264	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
265	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
266	C₂²×D₃	—	3	16	no	—
267	C₃×Q₈	—	9	4	no	—
268	C₃×D₄	—	2	16	no	—
269	C₃×D₄	—	2	8	no	—
270	C₃×D₄	—	2	2	no	—
271	C₃×D₄	—	18	8	no	—
272	C₃×D₄	—	18	4	no	—
273	C₃×D₄	—	18	4	no	—
274	C₃×D₄	—	36	2	no	—
275	C₃×D₄	—	36	4	no	—
276	C₂×C₃×C₄	—	2	16	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	8	no	—
282	C₂×C₃×C₄	—	4	16	no	—
283	C₂×C₃×C₄	—	9	2	no	—
284	C₂×C₃×C₄	—	9	2	no	—
285	C₂×C₃×C₄	—	18	8	no	—
286	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
287	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
288	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
289	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
290	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
292	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
294	#67	—	6	32	no	—
295	#67	—	12	16	no	—
296	C₂×Dic₃	—	3	8	no	—
297	C₂×Dic₃	—	3	8	no	—
298	D₁₂	—	6	16	no	—
299	D₁₂	—	6	16	no	—
300	D₁₂	—	12	8	no	—
301	C₄×D₃	—	6	32	no	—
302	Dic₆	—	3	16	no	—
303	C₂×C₃²	—	2	4	no	—
304	C₂×C₃²	—	2	4	no	—
305	C₂×C₃²	—	2	4	no	—
306	C₂×C₃²	—	4	16	no	—
307	C₂×C₃²	—	4	8	no	—
308	C₂×C₃²	—	4	2	no	—
309	C₂×C₃²	C₂×#235	1	4	yes	—
310	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
311	C₂×C₃²	#1009	1	4	yes	—
312	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
313	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
314	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
315	C₃⋊D₃	—	4	4	no	—
316	C₃×D₃	—	12	16	no	—
317	#41	—	18	8	no	—
318	C₂×Q₈	—	9	1	no	—
319	C₂×D₄	—	9	4	no	—
320	C₂×D₄	—	9	4	no	—
321	C₂×D₄	—	9	2	no	—
322	C₂×D₄	—	9	2	no	—
323	C₂×D₄	—	9	2	no	—
324	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
325	C₂²×C₄	—	9	4	no	—
326	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
327	C₄⋊C₄	—	9	2	no	—
328	C₄⋊C₄	—	9	1	no	—
329	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
330	C₂²⋊C₄	—	9	4	no	—
331	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
332	C₄²	—	9	2	no	—
333	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
334	C₂²×C₃	—	2	16	no	—
335	C₂²×C₃	—	2	8	no	—
336	C₂²×C₃	—	2	8	no	—
337	C₂²×C₃	—	2	8	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	4	8	no	—
343	C₂²×C₃	—	4	8	no	—
344	C₂²×C₃	—	18	4	no	—
345	C₂²×C₃	—	18	4	no	—
346	C₂²×C₃	—	18	4	no	—
347	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
348	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
349	C₂×D₃	—	6	16	no	—
350	C₂×D₃	—	6	16	no	—
351	C₂×D₃	—	6	16	no	—
352	C₃×C₄	—	2	8	no	—
353	C₃×C₄	—	2	4	no	—
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	8	no	—
357	C₃×C₄	—	2	8	no	—
358	C₃×C₄	—	4	8	no	—
359	C₃×C₄	—	4	4	no	—
360	C₃×C₄	—	9	4	no	—
361	C₃×C₄	—	18	2	no	—
362	C₃×C₄	C₃×#235	1	8	yes	complemented
363	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
364	C₃×C₄	#3828	1	2	yes	complemented
365	C₃×C₄	D₄×C₃⋊D₃	1	2	yes	—
366	Dic₃	—	3	16	no	—
367	Dic₃	—	6	8	no	—
368	C₃²	—	2	4	no	—
369	C₃²	#5553	1	4	yes	complemented
370	C₃²	C₃×#550	1	1	yes	characteristic, complemented
371	C₂³	—	9	4	no	—
372	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
373	Q₈	—	9	4	no	—
374	D₄	—	2	2	no	—
375	D₄	—	18	8	no	—
376	D₄	—	18	4	no	—
377	D₄	—	18	4	no	—
378	D₄	—	36	2	no	—
379	D₄	—	36	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	9	2	no	—
382	C₂×C₄	—	9	2	no	—
383	C₂×C₄	—	18	8	no	—
384	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
386	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
387	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
388	C₂×C₃	—	2	4	no	—
389	C₂×C₃	—	2	4	no	—
390	C₂×C₃	—	2	4	no	—
391	C₂×C₃	—	4	16	no	—
392	C₂×C₃	—	4	8	no	—
393	C₂×C₃	—	4	2	no	—
394	C₂×C₃	—	36	4	no	—
395	C₂×C₃	C₂×C₃×#235	1	4	yes	—
396	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
397	C₂×C₃	C₃×#1009	1	4	yes	—
398	C₂×C₃	C₂×#3828	1	1	yes	characteristic
399	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
400	C₂×C₃	#64366	1	1	yes	characteristic
401	D₃	—	12	16	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	18	4	no	—
406	C₂²	—	18	4	no	—
407	C₂²	—	18	4	no	—
408	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	1	no	—
411	C₄	—	9	4	no	—
412	C₄	—	18	2	no	—
413	C₄	C₃×#3828	1	2	yes	complemented
414	C₄	C₃×D₄×C₃⋊D₃	1	2	yes	—
415	C₃	—	2	4	no	—
416	C₃	C₃×#5553	1	4	yes	complemented
417	C₃	#10596024	1	1	yes	characteristic, direct product factor
418	C₂	—	4	2	no	—
419	C₂	—	36	4	no	—
420	C₂	C₂×C₃×#3828	1	1	yes	characteristic
421	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
422	C₂	C₃×#64366	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×#550
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×#64149	C₂	semidirect
4. C₃×#64139	C₂	semidirect
5. C₃×#64102	C₂	semidirect
6. C₃×#64093	C₂	semidirect
7. C₃×#64083	C₂	semidirect
8. C₃×C₄×#634	C₂	semidirect
9. #10596024	C₃	direct (N × H)
28. C₂×#3828	C₂×C₃	semidirect
31. C₃²×C₄×D₄	D₃	semidirect
32. C₃²×C₄×D₄	C₂×C₃	semidirect
33. #64149	C₂×C₃	semidirect
34. #64139	C₂×C₃	semidirect
35. #64102	C₂×C₃	semidirect
36. #64093	C₂×C₃	semidirect
37. #64083	C₂×C₃	semidirect
38. C₄×#634	C₂×C₃	semidirect
61. C₃×#634	D₄	semidirect
113. C₃³×C₄	#41	semidirect
125. C₃×C₄×D₄	C₃×D₃	semidirect
126. C₃×C₄×D₄	C₃⋊D₃	semidirect
164. #634	C₃×D₄	semidirect
245. C₃²×C₄	#235	semidirect
248. C₃²×C₄	C₃×#41	semidirect
260. C₄×D₄	C₃×C₃⋊D₃	semidirect
261. C₃³	#550	semidirect
362. C₃×C₄	C₃×#235	semidirect
364. C₃×C₄	#3828	semidirect
369. C₃²	#5553	semidirect
370. C₃²	C₃×#550	semidirect
413. C₄	C₃×#3828	semidirect
416. C₃	C₃×#5553	semidirect
417. C₃	#10596024	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×#64149	2
C₃×#64139	2
C₃×#64102	2
C₃×#64093	2
C₃×#64083	2
C₃×C₄×#634	2
#10596024	3
C₃×#5553	3

Subgroups — C3×#10596024 #13179289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596024 #13179289