Subgroups — C₃×#10596301 #13179580

Order 1728.

2660 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64156	C₂	1	2	yes	maximal, complemented
4	C₃×#64149	C₂	1	2	yes	maximal, complemented
5	C₃×#64146	C₂	1	4	yes	maximal, complemented
6	C₃×#64139	C₂	1	4	yes	maximal, complemented
7	C₃×#64135	C₂	1	1	yes	maximal, characteristic, complemented
8	#10596301	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃×#5830	—	3	4	no	maximal
10	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	—
11	C₃³×#41	—	2	4	no	—
12	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃³×D₄	C₂²	1	2	yes	—
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃³×C₄	C₂²	1	2	yes	complemented
17	C₂×C₃×#638	C₂²	1	8	yes	complemented
18	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
19	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
20	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
21	C₃×#3757	C₂²	1	2	yes	—
22	C₃×#3752	C₂²	1	8	yes	complemented
23	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
24	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	complemented
25	C₂×C₃²×#41	—	2	4	no	—
26	C₂×C₃²×#41	D₃	1	4	yes	complemented
27	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂²×C₃×D₁₂	—	3	4	no	—
30	#64156	C₂×C₃	1	2	yes	complemented
31	#64149	C₂×C₃	1	2	yes	complemented
32	#64146	C₂×C₃	1	4	yes	complemented
33	#64139	C₂×C₃	1	4	yes	complemented
34	#64135	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×#947	—	3	8	no	—
36	C₃×#940	—	3	8	no	—
37	C₃×#937	—	3	16	no	—
38	C₃×#930	—	3	16	no	—
39	C₃×#926	—	3	4	no	—
40	C₂³×C₃³	C₂³	1	2	yes	—
41	C₂³×C₃³	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
43	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
44	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	—
45	C₃³×Q₈	—	2	2	no	—
46	C₃³×D₄	—	2	4	no	—
47	C₃³×D₄	—	2	2	no	—
48	C₂×C₃³×C₄	—	2	4	no	—
49	C₂×C₃³×C₄	D₄	1	4	yes	complemented
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	—	4	8	no	—
54	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
55	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
56	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
57	C₃×#535	—	9	1	no	—
58	#5830	—	3	4	no	—
59	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	—
60	C₂³×C₃×D₃	—	3	8	no	—
61	C₃²×#41	—	2	32	no	—
62	C₃²×#41	—	2	16	no	—
63	C₃²×#41	—	2	4	no	—
64	C₂×C₃²×Q₈	—	2	4	no	—
65	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	complemented
66	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
67	C₂×C₃²×D₄	—	2	8	no	—
68	C₂×C₃²×D₄	—	2	4	no	—
69	C₂×C₃²×D₄	C₂×D₃	1	8	yes	—
70	C₂×C₃²×D₄	C₂×D₃	1	4	yes	complemented
71	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
72	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
73	C₂²×C₃²×C₄	—	2	4	no	—
74	C₂²×C₃²×C₄	—	2	8	no	—
75	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
76	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	complemented
77	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	complemented
79	C₂×#638	C₂²×C₃	1	8	yes	complemented
80	C₂×C₄⋊(C₃⋊D₃)	—	2	4	no	—
81	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
82	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
83	C₂×C₃×#67	—	3	32	no	—
84	C₂×C₃×D₁₂	—	3	8	no	—
85	C₂×C₃×D₁₂	—	3	8	no	—
86	C₂×C₃×D₁₂	—	6	16	no	—
87	#3757	C₂²×C₃	1	2	yes	—
88	#3752	C₂²×C₃	1	8	yes	complemented
89	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	complemented
90	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	complemented
91	C₃×#217	—	3	8	no	—
92	C₃×(C₂×D₃)⋊C₄	—	3	32	no	—
93	C₃×C₄⋊Dic₃	—	3	8	no	—
94	C₃×C₄×Dic₃	—	3	8	no	—
95	C₂²×C₃³	—	2	2	no	—
96	C₂²×C₃³	—	2	2	no	—
97	C₂²×C₃³	—	2	4	no	—
98	C₂²×C₃³	C₂×D₄	1	2	yes	—
99	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×C₃⋊D₃	—	2	4	no	—
101	C₂×C₃×C₃⋊D₃	—	2	8	no	—
102	C₂×C₃×C₃⋊D₃	—	4	8	no	—
103	C₃³×C₄	—	2	2	no	—
104	C₃³×C₄	C₂×D₄	1	2	yes	—
105	C₃³×C₄	C₂×D₄	1	2	yes	—
106	C₃×C₃⋊Dic₃	—	2	4	no	—
107	C₂×C₃×#41	—	2	4	no	—
108	C₂×C₃×#41	C₃×D₃	1	4	yes	complemented
109	C₂×C₃×#41	C₃⋊D₃	1	1	yes	characteristic, complemented
110	C₂²×C₃×D₄	—	9	1	no	—
111	C₂²×D₁₂	—	3	4	no	—
112	C₃×#127	—	9	2	no	—
113	C₃×#124	—	9	2	no	—
114	C₃×#121	—	9	4	no	—
115	C₃×#120	—	9	4	no	—
116	C₃×#117	—	9	1	no	—
117	#947	—	3	8	no	—
118	#940	—	3	8	no	—
119	#937	—	3	16	no	—
120	#930	—	3	16	no	—
121	#926	—	3	4	no	—
122	C₂³×C₃²	—	2	8	no	—
123	C₂³×C₃²	—	2	4	no	—
124	C₂³×C₃²	C₂²×D₃	1	8	yes	—
125	C₂³×C₃²	C₂²×D₃	1	4	yes	—
126	C₂³×C₃²	C₂³×C₃	1	2	yes	—
127	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
128	C₂²×C₃⋊D₃	—	2	4	no	—
129	C₂²×C₃⋊D₃	—	4	4	no	—
130	C₂²×C₃⋊D₃	C₂³×C₃	1	4	yes	—
131	C₂²×C₃×D₃	—	3	16	no	—
132	C₂²×C₃×D₃	—	6	16	no	—
133	C₂²×C₃×D₃	—	12	16	no	—
134	C₃²×Q₈	—	2	16	no	—
135	C₃²×Q₈	—	2	8	no	—
136	C₃²×Q₈	—	2	2	no	—
137	C₃²×D₄	—	2	32	no	—
138	C₃²×D₄	—	2	16	no	—
139	C₃²×D₄	—	2	16	no	—
140	C₃²×D₄	—	2	4	no	—
141	C₃²×D₄	—	2	8	no	—
142	C₃²×D₄	—	2	2	no	—
143	C₂×C₃²×C₄	—	2	32	no	—
144	C₂×C₃²×C₄	—	2	16	no	—
145	C₂×C₃²×C₄	—	2	4	no	—
146	C₂×C₃²×C₄	—	2	16	no	—
147	C₂×C₃²×C₄	—	2	4	no	—
148	C₂×C₃²×C₄	—	2	8	no	—
149	C₂×C₃²×C₄	—	2	4	no	—
150	C₂×C₃²×C₄	#67	1	16	yes	complemented
151	C₂×C₃²×C₄	C₃×D₄	1	4	yes	complemented
152	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
153	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
154	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
155	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
156	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
158	#638	—	4	8	no	—
159	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
160	C₄⋊(C₃⋊D₃)	—	2	4	no	—
161	C₄⋊(C₃⋊D₃)	—	2	4	no	—
162	C₃×#67	—	12	32	no	—
163	C₂×C₃×Dic₃	—	3	16	no	—
164	C₃×D₁₂	—	6	16	no	—
165	C₃×D₁₂	—	6	16	no	—
166	#535	—	9	1	no	Sylow
167	C₂×C₃³	—	2	2	no	—
168	C₂×C₃³	—	4	2	no	—
169	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₃³	H(5,𝔽₂)	1	2	yes	—
171	C₃×C₃⋊D₃	—	4	4	no	—
172	C₂⁴×C₃	—	9	2	no	—
173	C₂³×D₃	—	3	8	no	—
174	C₃×#41	—	2	32	no	—
175	C₃×#41	—	2	16	no	—
176	C₃×#41	—	2	4	no	—
177	C₂×C₃×Q₈	—	2	4	no	—
178	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
179	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
180	C₂×C₃×D₄	—	2	8	no	—
181	C₂×C₃×D₄	—	2	4	no	—
182	C₂×C₃×D₄	—	9	8	no	—
183	C₂×C₃×D₄	—	9	2	no	—
184	C₂×C₃×D₄	—	9	2	no	—
185	C₂×C₃×D₄	—	18	4	no	—
186	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	—
187	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
188	C₂×C₃×D₄	C₂×C₃⋊D₃	1	2	yes	—
189	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
190	C₂²×C₃×C₄	—	2	4	no	—
191	C₂²×C₃×C₄	—	2	8	no	—
192	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
193	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	complemented
194	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	complemented
196	C₂×#67	—	3	32	no	—
197	C₂×D₁₂	—	3	8	no	—
198	C₂×D₁₂	—	3	8	no	—
199	C₂×D₁₂	—	6	16	no	—
200	C₃×C₄⋊C₄	—	9	2	no	—
201	C₃×C₂²⋊C₄	—	9	2	no	—
202	C₃×C₂²⋊C₄	—	9	8	no	—
203	C₃×C₄²	—	9	2	no	—
204	#217	—	3	8	no	—
205	(C₂×D₃)⋊C₄	—	3	32	no	—
206	C₄⋊Dic₃	—	3	8	no	—
207	C₄×Dic₃	—	3	8	no	—
208	C₂²×C₃²	—	2	2	no	—
209	C₂²×C₃²	—	2	16	no	—
210	C₂²×C₃²	—	2	8	no	—
211	C₂²×C₃²	—	2	2	no	—
212	C₂²×C₃²	—	2	4	no	—
213	C₂²×C₃²	—	2	4	no	—
214	C₂²×C₃²	—	2	8	no	—
215	C₂²×C₃²	—	2	8	no	—
216	C₂²×C₃²	—	2	16	no	—
217	C₂²×C₃²	—	4	8	no	—
218	C₂²×C₃²	—	4	16	no	—
219	C₂²×C₃²	C₂×#67	1	8	yes	—
220	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
221	C₂²×C₃²	C₂³×D₃	1	4	yes	—
222	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
223	C₂×C₃⋊D₃	—	2	4	no	—
224	C₂×C₃⋊D₃	—	2	8	no	—
225	C₂×C₃⋊D₃	—	4	8	no	—
226	C₂×C₃×D₃	—	6	32	no	—
227	C₂×C₃×D₃	—	6	16	no	—
228	C₂×C₃×D₃	—	12	32	no	—
229	C₃²×C₄	—	2	16	no	—
230	C₃²×C₄	—	2	8	no	—
231	C₃²×C₄	—	2	2	no	—
232	C₃²×C₄	—	2	8	no	—
233	C₃²×C₄	—	2	8	no	—
234	C₃²×C₄	C₂×#67	1	8	yes	—
235	C₃²×C₄	C₂×#67	1	8	yes	—
236	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
237	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
238	C₃⋊Dic₃	—	2	4	no	—
239	C₃×Dic₃	—	6	16	no	—
240	C₂×#41	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
241	C₂²×D₄	—	9	1	no	—
242	#127	—	9	2	no	—
243	#124	—	9	2	no	—
244	#121	—	9	4	no	—
245	#120	—	9	4	no	—
246	#117	—	9	1	no	—
247	C₃³	#535	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₃	—	2	8	no	—
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	9	4	no	—
251	C₂³×C₃	—	18	4	no	—
252	C₂³×C₃	—	36	4	no	—
253	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
254	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
255	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
256	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
257	C₂²×D₃	—	3	16	no	—
258	C₂²×D₃	—	6	16	no	—
259	C₂²×D₃	—	12	16	no	—
260	C₃×Q₈	—	2	16	no	—
261	C₃×Q₈	—	2	8	no	—
262	C₃×Q₈	—	2	2	no	—
263	C₃×D₄	—	2	32	no	—
264	C₃×D₄	—	2	16	no	—
265	C₃×D₄	—	2	16	no	—
266	C₃×D₄	—	2	4	no	—
267	C₃×D₄	—	2	8	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	18	4	no	—
270	C₃×D₄	—	18	4	no	—
271	C₃×D₄	—	36	8	no	—
272	C₂×C₃×C₄	—	2	32	no	—
273	C₂×C₃×C₄	—	2	16	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	2	16	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	8	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	9	4	no	—
280	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
281	C₂×C₃×C₄	#638	1	4	yes	complemented
282	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
283	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
284	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
285	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
286	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
288	#67	—	12	32	no	—
289	C₂×Dic₃	—	3	16	no	—
290	D₁₂	—	6	16	no	—
291	D₁₂	—	6	16	no	—
292	C₂×C₃²	—	2	2	no	—
293	C₂×C₃²	—	2	8	no	—
294	C₂×C₃²	—	2	4	no	—
295	C₂×C₃²	—	2	8	no	—
296	C₂×C₃²	—	4	8	no	—
297	C₂×C₃²	—	4	16	no	—
298	C₂×C₃²	—	4	8	no	—
299	C₂×C₃²	—	4	2	no	—
300	C₂×C₃²	#1009	1	8	yes	—
301	C₂×C₃²	C₂²×#67	1	4	yes	—
302	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
303	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
304	C₃⋊D₃	—	4	4	no	—
305	C₃×D₃	—	12	16	no	—
306	C₂⁴	—	9	2	no	—
307	#41	—	2	4	no	—
308	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
309	C₂×D₄	—	9	8	no	—
310	C₂×D₄	—	9	2	no	—
311	C₂×D₄	—	9	2	no	—
312	C₂×D₄	—	18	4	no	—
313	C₂×D₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
314	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
315	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
317	C₄⋊C₄	—	9	2	no	—
318	C₂²⋊C₄	—	9	2	no	—
319	C₂²⋊C₄	—	9	8	no	—
320	C₄²	—	9	2	no	—
321	C₂²×C₃	—	2	8	no	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	16	no	—
324	C₂²×C₃	—	2	16	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	2	4	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	—	4	8	no	—
331	C₂²×C₃	—	4	16	no	—
332	C₂²×C₃	—	18	8	no	—
333	C₂²×C₃	—	18	4	no	—
334	C₂²×C₃	—	36	8	no	—
335	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
336	C₂²×C₃	C₂×#638	1	2	yes	—
337	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
338	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
339	C₂×D₃	—	6	32	no	—
340	C₂×D₃	—	6	16	no	—
341	C₂×D₃	—	12	32	no	—
342	C₃×C₄	—	2	16	no	—
343	C₃×C₄	—	2	8	no	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	8	no	—
346	C₃×C₄	—	2	8	no	—
347	C₃×C₄	—	18	4	no	—
348	C₃×C₄	C₂×C₃×#67	1	8	yes	—
349	C₃×C₄	C₂×C₃×#67	1	8	yes	—
350	C₃×C₄	C₂×#638	1	2	yes	—
351	C₃×C₄	C₂×#638	1	2	yes	—
352	Dic₃	—	6	16	no	—
353	C₃²	—	2	4	no	—
354	C₃²	#5830	1	4	yes	complemented
355	C₃²	C₃×#535	1	1	yes	characteristic, complemented
356	C₂³	—	9	4	no	—
357	C₂³	—	18	4	no	—
358	C₂³	—	36	4	no	—
359	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
360	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	18	4	no	—
365	D₄	—	18	4	no	—
366	D₄	—	36	8	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	9	4	no	—
369	C₂×C₄	C₃×#638	1	4	yes	complemented
370	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
371	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
373	C₂×C₃	—	2	8	no	—
374	C₂×C₃	—	2	2	no	—
375	C₂×C₃	—	2	8	no	—
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	—	4	8	no	—
378	C₂×C₃	—	4	16	no	—
379	C₂×C₃	—	4	8	no	—
380	C₂×C₃	—	4	2	no	—
381	C₂×C₃	—	36	4	no	—
382	C₂×C₃	C₃×#1009	1	8	yes	—
383	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
384	C₂×C₃	#64366	1	2	yes	—
385	C₂×C₃	C₂²×#638	1	1	yes	characteristic
386	D₃	—	12	16	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	18	8	no	—
391	C₂²	—	18	4	no	—
392	C₂²	—	36	8	no	—
393	C₂²	C₂×C₃×#638	1	2	yes	—
394	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	18	4	no	—
397	C₄	C₂×C₃×#638	1	2	yes	—
398	C₄	C₂×C₃×#638	1	2	yes	—
399	C₃	—	2	4	no	—
400	C₃	C₃×#5830	1	4	yes	complemented
401	C₃	#10596301	1	1	yes	characteristic, direct product factor
402	C₂	—	2	2	no	—
403	C₂	—	4	2	no	—
404	C₂	—	36	4	no	—
405	C₂	C₃×#64366	1	2	yes	—
406	C₂	C₂²×C₃×#638	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	C₂×C₃³×#41	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂×C₃×#41	C₃⋊D₃
hypocenter	C₃²	C₃×#535
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃³×#41	C₂	semidirect
2. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
3. C₃×#64156	C₂	semidirect
4. C₃×#64149	C₂	semidirect
5. C₃×#64146	C₂	semidirect
6. C₃×#64139	C₂	semidirect
7. C₃×#64135	C₂	semidirect
8. #10596301	C₃	direct (N × H)
12. C₂×C₃³×Q₈	C₂²	semidirect
14. C₂×C₃³×D₄	C₂²	semidirect
16. C₂²×C₃³×C₄	C₂²	semidirect
17. C₂×C₃×#638	C₂²	semidirect
22. C₃×#3752	C₂²	semidirect
23. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
24. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
26. C₂×C₃²×#41	D₃	semidirect
27. C₂×C₃²×#41	C₂×C₃	semidirect
28. C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
30. #64156	C₂×C₃	semidirect
31. #64149	C₂×C₃	semidirect
32. #64146	C₂×C₃	semidirect
33. #64139	C₂×C₃	semidirect
34. #64135	C₂×C₃	semidirect
49. C₂×C₃³×C₄	D₄	semidirect
65. C₂×C₃²×Q₈	C₂×D₃	semidirect
66. C₂×C₃²×Q₈	C₂²×C₃	semidirect
70. C₂×C₃²×D₄	C₂×D₃	semidirect
72. C₂×C₃²×D₄	C₂²×C₃	semidirect
76. C₂²×C₃²×C₄	C₂×D₃	semidirect
78. C₂²×C₃²×C₄	C₂²×C₃	semidirect
79. C₂×#638	C₂²×C₃	semidirect
88. #3752	C₂²×C₃	semidirect
89. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
90. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
108. C₂×C₃×#41	C₃×D₃	semidirect
109. C₂×C₃×#41	C₃⋊D₃	semidirect
150. C₂×C₃²×C₄	#67	semidirect
151. C₂×C₃²×C₄	C₃×D₄	semidirect
178. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
179. C₂×C₃×Q₈	C₂×C₃⋊D₃	semidirect
187. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
189. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
193. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
195. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
240. C₂×#41	C₃×C₃⋊D₃	semidirect
247. C₃³	#535	semidirect
280. C₂×C₃×C₄	C₃×#67	semidirect
281. C₂×C₃×C₄	#638	semidirect
308. C₂×Q₈	C₂×C₃×C₃⋊D₃	semidirect
314. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
316. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
354. C₃²	#5830	semidirect
355. C₃²	C₃×#535	semidirect
369. C₂×C₄	C₃×#638	semidirect
400. C₃	C₃×#5830	semidirect
401. C₃	#10596301	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×C₃³×#41	2
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₃×#64156	2
C₃×#64149	2
C₃×#64146	2
C₃×#64139	2
C₃×#64135	2
#10596301	3
C₃×#5830	3

Subgroups — C3×#10596301 #13179580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596301 #13179580