Subgroups — C₃×#39385 #10657992

Order 768.

2030 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#541	C₂	1	2	yes	maximal, complemented
2	C₃×#2868	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2721	C₂	1	8	yes	maximal, complemented
4	C₃×#2621	C₂	1	2	yes	maximal, complemented
5	C₃×#2552	C₂	1	4	yes	maximal, complemented
6	C₃×#2542	C₂	1	2	yes	maximal
7	C₃×#2512	C₂	1	4	yes	maximal
8	C₃×#2429	C₂	1	4	yes	maximal, complemented
9	C₃×#2365	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×#125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2293	C₂	1	1	yes	maximal, characteristic
12	#39385	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×#541	—	2	16	no	—
14	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₃×#126	C₂²	1	8	yes	—
18	C₂×C₃×#125	C₂²	1	8	yes	—
19	C₂×C₃×#125	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₂×C₃×C₄×Q₈	C₂²	1	4	yes	—
23	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×#117	C₂²	1	2	yes	—
25	C₃×#399	C₂²	1	8	yes	—
26	C₃×#398	C₂²	1	8	yes	—
27	C₃×#398	C₂²	1	8	yes	—
28	C₃×#397	C₂²	1	8	yes	—
29	C₃×#396	C₂²	1	8	yes	—
30	C₃×#391	C₂²	1	4	yes	—
31	C₃×#390	C₂²	1	4	yes	—
32	C₃×#390	C₂²	1	2	yes	—
33	C₃×#389	C₂²	1	4	yes	—
34	C₃×#389	C₂²	1	2	yes	—
35	C₃×#389	C₂²	1	8	yes	—
36	C₃×#389	C₂²	1	2	yes	—
37	C₃×#388	C₂²	1	8	yes	—
38	C₃×#388	C₂²	1	4	yes	—
39	C₃×#387	C₂²	1	8	yes	—
40	C₃×#387	C₂²	1	4	yes	—
41	C₃×#384	C₂²	1	4	yes	—
42	C₃×#384	C₂²	1	4	yes	—
43	C₃×#384	C₂²	1	4	yes	—
44	C₃×#382	C₂²	1	1	yes	characteristic
45	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
47	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
48	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
49	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
50	C₃×C₄³	C₂²	1	1	yes	characteristic
51	C₂×#541	C₂×C₃	1	2	yes	complemented
52	#2868	C₂×C₃	1	1	yes	characteristic, complemented
53	#2721	C₂×C₃	1	8	yes	complemented
54	#2621	C₂×C₃	1	2	yes	complemented
55	#2552	C₂×C₃	1	4	yes	complemented
56	#2542	C₂×C₃	1	2	yes	—
57	#2512	C₂×C₃	1	4	yes	—
58	#2429	C₂×C₃	1	4	yes	complemented
59	#2365	C₂×C₃	1	2	yes	complemented
60	C₄×#125	C₂×C₃	1	1	yes	characteristic, complemented
61	#2293	C₂×C₃	1	1	yes	characteristic
62	C₂²×C₃×Q₈	C₂³	1	4	yes	—
63	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
64	C₂³×C₃×C₄	C₂³	1	2	yes	—
65	C₃×C₄⋊Q₈	—	2	8	no	—
66	C₃×C₄⋊Q₈	—	2	8	no	—
67	C₃×C₄⋊Q₈	—	4	4	no	—
68	C₃×#126	—	2	32	no	—
69	C₃×#125	—	2	32	no	—
70	C₃×#125	D₄	1	8	yes	complemented
71	C₃×C₂²⋊Q₈	—	2	16	no	—
72	C₃×C₂²⋊Q₈	—	4	8	no	—
73	C₃×C₄×Q₈	—	2	16	no	—
74	C₃×C₄×D₄	—	2	4	no	—
75	C₃×#117	—	2	8	no	—
76	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
83	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
84	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
85	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
87	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
88	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
92	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₄²	C₂³	1	2	yes	—
97	C₂×C₃×C₄²	C₂³	1	2	yes	—
98	C₂×C₃×C₄²	C₂³	1	2	yes	—
99	C₂×C₃×C₄²	C₂³	1	4	yes	—
100	C₂×C₃×C₄²	C₂³	1	8	yes	—
101	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
103	C₃×#95	C₂³	1	4	yes	—
104	C₃×#95	C₂³	1	4	yes	—
105	C₃×#95	C₂³	1	2	yes	—
106	C₃×#95	C₂³	1	4	yes	—
107	C₃×#95	C₂³	1	4	yes	—
108	C₃×#95	C₂³	1	8	yes	—
109	C₃×#95	C₂³	1	8	yes	—
110	#541	—	2	16	no	—
111	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
112	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
113	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
114	C₂×#126	C₂²×C₃	1	8	yes	—
115	C₂×#125	C₂²×C₃	1	8	yes	—
116	C₂×#125	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
118	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
119	C₂×C₄×Q₈	C₂²×C₃	1	4	yes	—
120	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
121	C₂×#117	C₂²×C₃	1	2	yes	—
122	#399	C₂²×C₃	1	8	yes	—
123	#398	C₂²×C₃	1	8	yes	—
124	#398	C₂²×C₃	1	8	yes	—
125	#397	C₂²×C₃	1	8	yes	—
126	#396	C₂²×C₃	1	8	yes	—
127	#391	C₂²×C₃	1	4	yes	—
128	#390	C₂²×C₃	1	4	yes	—
129	#390	C₂²×C₃	1	2	yes	—
130	#389	C₂²×C₃	1	2	yes	—
131	#389	C₂²×C₃	1	4	yes	—
132	#389	C₂²×C₃	1	8	yes	—
133	#389	C₂²×C₃	1	2	yes	—
134	#388	C₂²×C₃	1	8	yes	—
135	#388	C₂²×C₃	1	4	yes	—
136	#387	C₂²×C₃	1	4	yes	—
137	#387	C₂²×C₃	1	8	yes	—
138	#384	C₂²×C₃	1	4	yes	—
139	#384	C₂²×C₃	1	4	yes	—
140	#384	C₂²×C₃	1	4	yes	—
141	#382	C₂²×C₃	1	1	yes	characteristic
142	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
143	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
144	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
146	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
147	C₄³	C₂²×C₃	1	1	yes	characteristic
148	C₂⁴×C₃	C₂⁴	1	2	yes	—
149	C₂×C₃×Q₈	—	2	8	no	—
150	C₂×C₃×Q₈	—	2	8	no	—
151	C₂×C₃×Q₈	—	2	8	no	—
152	C₂×C₃×D₄	—	2	2	no	—
153	C₂×C₃×D₄	—	2	4	no	—
154	C₂²×C₃×C₄	—	2	4	no	—
155	C₂²×C₃×C₄	—	2	4	no	—
156	C₂²×C₃×C₄	—	2	4	no	—
157	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
158	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
159	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
160	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
161	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
162	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
163	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
165	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
167	C₃×C₄⋊C₄	—	2	8	no	—
168	C₃×C₄⋊C₄	—	2	16	no	—
169	C₃×C₄⋊C₄	—	2	16	no	—
170	C₃×C₄⋊C₄	—	2	16	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	8	no	—
173	C₃×C₄⋊C₄	—	2	8	no	—
174	C₃×C₄⋊C₄	—	2	4	no	—
175	C₃×C₄⋊C₄	—	2	8	no	—
176	C₃×C₄⋊C₄	—	2	4	no	—
177	C₃×C₄⋊C₄	—	4	8	no	—
178	C₃×C₄⋊C₄	—	4	8	no	—
179	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
180	C₃×C₄⋊C₄	C₂×D₄	1	16	yes	—
181	C₃×C₂²⋊C₄	—	2	8	no	—
182	C₃×C₂²⋊C₄	—	2	16	no	—
183	C₃×C₂²⋊C₄	—	2	4	no	—
184	C₃×C₂²⋊C₄	—	2	8	no	—
185	C₃×C₂²⋊C₄	—	4	8	no	—
186	C₃×C₄²	—	2	4	no	—
187	C₃×C₄²	—	2	16	no	—
188	C₃×C₄²	—	2	2	no	—
189	C₃×C₄²	—	2	4	no	—
190	C₃×C₄²	—	2	4	no	—
191	C₃×C₄²	—	2	8	no	—
192	C₃×C₄²	C₂×D₄	1	4	yes	—
193	C₃×C₄²	#41	1	4	yes	—
194	C₂²×Q₈	C₂³×C₃	1	4	yes	—
195	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
196	C₂³×C₄	C₂³×C₃	1	2	yes	—
197	C₄⋊Q₈	—	2	8	no	—
198	C₄⋊Q₈	—	2	8	no	—
199	C₄⋊Q₈	—	4	4	no	—
200	#126	—	2	32	no	—
201	#125	—	2	32	no	—
202	#125	C₃×D₄	1	8	yes	complemented
203	C₂²⋊Q₈	—	2	16	no	—
204	C₂²⋊Q₈	—	4	8	no	—
205	C₄×Q₈	—	2	16	no	—
206	C₄×D₄	—	2	4	no	—
207	#117	—	2	8	no	—
208	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
209	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
211	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
212	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
213	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
214	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
215	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
216	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
217	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
218	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
219	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
220	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
221	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
222	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
223	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
224	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
225	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
226	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
227	C₂×C₄²	C₂³×C₃	1	2	yes	—
228	C₂×C₄²	C₂³×C₃	1	8	yes	—
229	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₃	1	2	yes	—
231	C₂×C₄²	C₂³×C₃	1	2	yes	—
232	C₂×C₄²	C₂³×C₃	1	4	yes	—
233	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
235	#95	C₂³×C₃	1	4	yes	—
236	#95	C₂³×C₃	1	4	yes	—
237	#95	C₂³×C₃	1	2	yes	—
238	#95	C₂³×C₃	1	4	yes	—
239	#95	C₂³×C₃	1	4	yes	—
240	#95	C₂³×C₃	1	8	yes	—
241	#95	C₂³×C₃	1	8	yes	—
242	C₂³×C₃	—	2	2	no	—
243	C₂³×C₃	—	2	2	no	—
244	C₂³×C₃	—	2	2	no	—
245	C₂³×C₃	—	2	4	no	—
246	C₂³×C₃	—	2	4	no	—
247	C₂³×C₃	C₂⁵	1	1	yes	characteristic
248	C₃×Q₈	—	4	16	no	—
249	C₃×D₄	—	4	4	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	8	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	8	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	8	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	4	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	—	4	8	no	—
270	C₂×C₃×C₄	C₂²×D₄	1	8	yes	—
271	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
272	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
273	C₂×C₃×C₄	C₂×#41	1	2	yes	—
274	C₂×C₃×C₄	C₂×#41	1	2	yes	—
275	C₂×C₃×C₄	C₂×#41	1	2	yes	—
276	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
277	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
278	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
279	C₂⁴	C₂⁴×C₃	1	2	yes	—
280	C₂×Q₈	—	2	8	no	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
290	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
291	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
293	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
294	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
298	C₄⋊C₄	—	2	8	no	—
299	C₄⋊C₄	—	2	16	no	—
300	C₄⋊C₄	—	2	16	no	—
301	C₄⋊C₄	—	2	16	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	8	no	—
304	C₄⋊C₄	—	2	8	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	4	8	no	—
309	C₄⋊C₄	—	4	8	no	—
310	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
311	C₄⋊C₄	C₂×C₃×D₄	1	16	yes	—
312	C₂²⋊C₄	—	2	8	no	—
313	C₂²⋊C₄	—	2	16	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	4	8	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	16	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	4	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	8	no	—
323	C₄²	C₂×C₃×D₄	1	4	yes	—
324	C₄²	C₃×#41	1	4	yes	—
325	C₂²×C₃	—	4	2	no	—
326	C₂²×C₃	—	4	2	no	—
327	C₂²×C₃	—	4	4	no	—
328	C₂²×C₃	—	4	2	no	—
329	C₂²×C₃	—	4	4	no	—
330	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
331	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
332	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
333	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
334	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	8	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	—	4	2	no	—
340	C₃×C₄	—	4	8	no	—
341	C₃×C₄	—	4	4	no	—
342	C₃×C₄	—	4	4	no	—
343	C₃×C₄	#541	1	4	yes	complemented
344	C₃×C₄	#550	1	4	yes	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	4	no	—
350	C₂³	C₂⁵×C₃	1	1	yes	characteristic
351	Q₈	—	4	16	no	—
352	D₄	—	4	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	C₂²×C₃×D₄	1	8	yes	—
374	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
375	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
376	C₂×C₄	C₂×C₃×#41	1	2	yes	—
377	C₂×C₄	C₂×C₃×#41	1	2	yes	—
378	C₂×C₄	C₂×C₃×#41	1	2	yes	—
379	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
380	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
381	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
382	C₂×C₃	—	8	2	no	—
383	C₂×C₃	C₂×#541	1	1	yes	characteristic
384	C₂×C₃	C₂×#550	1	1	yes	characteristic
385	C₂×C₃	#3499	1	2	yes	—
386	C₂×C₃	#3509	1	1	yes	characteristic
387	C₂×C₃	#3552	1	2	yes	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
394	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
395	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
397	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	2	8	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	4	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	8	no	—
404	C₄	—	4	4	no	—
405	C₄	—	4	4	no	—
406	C₄	C₃×#541	1	4	yes	complemented
407	C₄	C₃×#550	1	4	yes	—
408	C₃	#39385	1	1	yes	characteristic, direct product factor, Sylow
409	C₂	—	8	2	no	—
410	C₂	C₂×C₃×#541	1	1	yes	characteristic
411	C₂	C₂×C₃×#550	1	1	yes	characteristic
412	C₂	C₃×#3499	1	2	yes	—
413	C₂	C₃×#3509	1	1	yes	characteristic
414	C₂	C₃×#3552	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#541	C₂	semidirect
2. C₃×#2868	C₂	semidirect
3. C₃×#2721	C₂	semidirect
4. C₃×#2621	C₂	semidirect
5. C₃×#2552	C₂	semidirect
8. C₃×#2429	C₂	semidirect
9. C₃×#2365	C₂	semidirect
10. C₃×C₄×#125	C₂	semidirect
12. #39385	C₃	direct (N × H)
51. C₂×#541	C₂×C₃	semidirect
52. #2868	C₂×C₃	semidirect
53. #2721	C₂×C₃	semidirect
54. #2621	C₂×C₃	semidirect
55. #2552	C₂×C₃	semidirect
58. #2429	C₂×C₃	semidirect
59. #2365	C₂×C₃	semidirect
60. C₄×#125	C₂×C₃	semidirect
70. C₃×#125	D₄	semidirect
202. #125	C₃×D₄	semidirect
343. C₃×C₄	#541	semidirect
406. C₄	C₃×#541	semidirect
408. C₃	#39385	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×#541	2
C₃×#2868	2
C₃×#2721	2
C₃×#2621	2
C₃×#2552	2
C₃×#2542	2
C₃×#2512	2
C₃×#2429	2
C₃×#2365	2
C₃×C₄×#125	2
C₃×#2293	2
#39385	3

Subgroups — C3×#39385 #10657992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#39385 #10657992