Subgroups — C₃×#39379 #10657986

Order 768.

1954 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×#541	C₂	1	2	yes	maximal, complemented
2	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2725	C₂	1	8	yes	maximal, complemented
4	C₃×#2629	C₂	1	2	yes	maximal, complemented
5	C₃×#2538	C₂	1	2	yes	maximal
6	C₃×#2512	C₂	1	4	yes	maximal
7	C₃×#2506	C₂	1	4	yes	maximal, complemented
8	C₃×#2421	C₂	1	4	yes	maximal, complemented
9	C₃×Q₈×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2293	C₂	1	1	yes	maximal, characteristic
12	#39379	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×#541	—	2	16	no	—
14	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#126	C₂²	1	8	yes	—
16	C₂×C₃×#125	C₂²	1	2	yes	—
17	C₂×C₃×#125	C₂²	1	8	yes	—
18	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
19	C₂×C₃×C₄×Q₈	C₂²	1	4	yes	—
20	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
21	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×#117	C₂²	1	2	yes	—
23	C₃×#400	C₂²	1	8	yes	—
24	C₃×#398	C₂²	1	8	yes	—
25	C₃×#397	C₂²	1	8	yes	—
26	C₃×#396	C₂²	1	8	yes	—
27	C₃×#396	C₂²	1	8	yes	—
28	C₃×#391	C₂²	1	2	yes	—
29	C₃×#390	C₂²	1	4	yes	—
30	C₃×#390	C₂²	1	2	yes	—
31	C₃×#389	C₂²	1	4	yes	—
32	C₃×#389	C₂²	1	4	yes	—
33	C₃×#389	C₂²	1	4	yes	—
34	C₃×#389	C₂²	1	8	yes	—
35	C₃×#389	C₂²	1	4	yes	—
36	C₃×#389	C₂²	1	2	yes	—
37	C₃×#389	C₂²	1	4	yes	—
38	C₃×#388	C₂²	1	8	yes	—
39	C₃×#388	C₂²	1	4	yes	—
40	C₃×#387	C₂²	1	8	yes	—
41	C₃×#384	C₂²	1	1	yes	characteristic
42	C₃×#384	C₂²	1	4	yes	—
43	C₃×#384	C₂²	1	2	yes	—
44	C₃×#382	C₂²	1	2	yes	—
45	C₃×#380	C₂²	1	4	yes	—
46	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
47	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
48	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	#2859	C₂×C₃	1	1	yes	characteristic, complemented
53	#2725	C₂×C₃	1	8	yes	complemented
54	#2629	C₂×C₃	1	2	yes	complemented
55	#2538	C₂×C₃	1	2	yes	—
56	#2512	C₂×C₃	1	4	yes	—
57	#2506	C₂×C₃	1	4	yes	complemented
58	#2421	C₂×C₃	1	4	yes	complemented
59	Q₈×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
60	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
61	#2293	C₂×C₃	1	1	yes	characteristic
62	C₂²×C₃×Q₈	C₂³	1	2	yes	—
63	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
64	C₂³×C₃×C₄	C₂³	1	2	yes	—
65	C₃×C₄⋊Q₈	D₄	1	8	yes	complemented
66	C₃×#126	—	2	32	no	—
67	C₃×#125	—	2	32	no	—
68	C₃×#125	—	2	8	no	—
69	C₃×C₂²⋊Q₈	—	2	16	no	—
70	C₃×C₄×Q₈	—	2	16	no	—
71	C₃×C₄×Q₈	—	2	8	no	—
72	C₃×C₄×D₄	—	2	4	no	—
73	C₃×#117	—	2	8	no	—
74	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
83	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
84	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
86	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
89	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₄²	C₂³	1	2	yes	—
95	C₂×C₃×C₄²	C₂³	1	2	yes	—
96	C₂×C₃×C₄²	C₂³	1	4	yes	—
97	C₂×C₃×C₄²	C₂³	1	8	yes	—
98	C₂×C₃×C₄²	C₂³	1	2	yes	—
99	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
101	C₃×#95	C₂³	1	4	yes	—
102	C₃×#95	C₂³	1	4	yes	—
103	C₃×#95	C₂³	1	2	yes	—
104	C₃×#95	C₂³	1	4	yes	—
105	C₃×#95	C₂³	1	8	yes	—
106	C₃×#95	C₂³	1	8	yes	—
107	C₃×#95	C₂³	1	8	yes	—
108	#541	—	2	16	no	—
109	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₂×#126	C₂²×C₃	1	8	yes	—
111	C₂×#125	C₂²×C₃	1	2	yes	—
112	C₂×#125	C₂²×C₃	1	8	yes	—
113	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
114	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
115	C₂×C₄×Q₈	C₂²×C₃	1	4	yes	—
116	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×#117	C₂²×C₃	1	2	yes	—
118	#400	C₂²×C₃	1	8	yes	—
119	#398	C₂²×C₃	1	8	yes	—
120	#397	C₂²×C₃	1	8	yes	—
121	#396	C₂²×C₃	1	8	yes	—
122	#396	C₂²×C₃	1	8	yes	—
123	#391	C₂²×C₃	1	2	yes	—
124	#390	C₂²×C₃	1	4	yes	—
125	#390	C₂²×C₃	1	2	yes	—
126	#389	C₂²×C₃	1	4	yes	—
127	#389	C₂²×C₃	1	4	yes	—
128	#389	C₂²×C₃	1	4	yes	—
129	#389	C₂²×C₃	1	4	yes	—
130	#389	C₂²×C₃	1	8	yes	—
131	#389	C₂²×C₃	1	4	yes	—
132	#389	C₂²×C₃	1	2	yes	—
133	#388	C₂²×C₃	1	8	yes	—
134	#388	C₂²×C₃	1	4	yes	—
135	#387	C₂²×C₃	1	8	yes	—
136	#384	C₂²×C₃	1	1	yes	characteristic
137	#384	C₂²×C₃	1	2	yes	—
138	#384	C₂²×C₃	1	4	yes	—
139	#382	C₂²×C₃	1	2	yes	—
140	#380	C₂²×C₃	1	4	yes	—
141	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
142	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
144	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
145	C₄³	C₂²×C₃	1	1	yes	characteristic
146	C₂⁴×C₃	C₂⁴	1	2	yes	—
147	C₂×C₃×Q₈	—	2	4	no	—
148	C₂×C₃×Q₈	—	2	4	no	—
149	C₂×C₃×Q₈	C₂×D₄	1	8	yes	—
150	C₂×C₃×D₄	—	2	2	no	—
151	C₂×C₃×D₄	—	2	4	no	—
152	C₂²×C₃×C₄	—	2	4	no	—
153	C₂²×C₃×C₄	—	2	4	no	—
154	C₂²×C₃×C₄	—	2	4	no	—
155	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
156	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
157	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
158	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
159	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
160	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
161	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
162	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
165	C₃×C₄⋊C₄	—	2	8	no	—
166	C₃×C₄⋊C₄	—	2	8	no	—
167	C₃×C₄⋊C₄	—	2	16	no	—
168	C₃×C₄⋊C₄	—	2	16	no	—
169	C₃×C₄⋊C₄	—	2	16	no	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	8	no	—
172	C₃×C₄⋊C₄	—	2	4	no	—
173	C₃×C₄⋊C₄	—	2	4	no	—
174	C₃×C₄⋊C₄	—	2	8	no	—
175	C₃×C₄⋊C₄	—	4	4	no	—
176	C₃×C₄⋊C₄	—	4	4	no	—
177	C₃×C₄⋊C₄	—	4	8	no	—
178	C₃×C₄⋊C₄	C₂×D₄	1	16	yes	—
179	C₃×C₂²⋊C₄	—	2	8	no	—
180	C₃×C₂²⋊C₄	—	2	16	no	—
181	C₃×C₂²⋊C₄	—	2	4	no	—
182	C₃×C₂²⋊C₄	—	4	4	no	—
183	C₃×C₂²⋊C₄	—	4	8	no	—
184	C₃×C₄²	—	2	4	no	—
185	C₃×C₄²	—	2	16	no	—
186	C₃×C₄²	—	2	8	no	—
187	C₃×C₄²	—	2	4	no	—
188	C₃×C₄²	—	2	2	no	—
189	C₃×C₄²	—	4	2	no	—
190	C₃×C₄²	C₂×D₄	1	4	yes	—
191	C₃×C₄²	#41	1	4	yes	—
192	C₂²×Q₈	C₂³×C₃	1	2	yes	—
193	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
194	C₂³×C₄	C₂³×C₃	1	2	yes	—
195	C₄⋊Q₈	C₃×D₄	1	8	yes	complemented
196	#126	—	2	32	no	—
197	#125	—	2	32	no	—
198	#125	—	2	8	no	—
199	C₂²⋊Q₈	—	2	16	no	—
200	C₄×Q₈	—	2	16	no	—
201	C₄×Q₈	—	2	8	no	—
202	C₄×D₄	—	2	4	no	—
203	#117	—	2	8	no	—
204	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
205	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
207	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
208	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
209	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
210	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
211	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
212	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
213	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
214	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
215	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
216	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
217	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
218	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
219	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
221	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
222	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
223	C₂×C₄²	C₂³×C₃	1	2	yes	—
224	C₂×C₄²	C₂³×C₃	1	8	yes	—
225	C₂×C₄²	C₂³×C₃	1	4	yes	—
226	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₃	1	2	yes	—
228	C₂×C₄²	C₂³×C₃	1	2	yes	—
229	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
231	#95	C₂³×C₃	1	4	yes	—
232	#95	C₂³×C₃	1	4	yes	—
233	#95	C₂³×C₃	1	2	yes	—
234	#95	C₂³×C₃	1	4	yes	—
235	#95	C₂³×C₃	1	8	yes	—
236	#95	C₂³×C₃	1	8	yes	—
237	#95	C₂³×C₃	1	8	yes	—
238	C₂³×C₃	—	2	2	no	—
239	C₂³×C₃	—	2	2	no	—
240	C₂³×C₃	—	2	2	no	—
241	C₂³×C₃	—	2	4	no	—
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	C₂⁵	1	1	yes	characteristic
244	C₃×Q₈	—	2	16	no	—
245	C₃×D₄	—	4	4	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	8	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	8	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	8	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	4	8	no	—
267	C₂×C₃×C₄	C₂²×D₄	1	8	yes	—
268	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
269	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
270	C₂×C₃×C₄	C₂×#41	1	2	yes	—
271	C₂×C₃×C₄	C₂×#41	1	2	yes	—
272	C₂×C₃×C₄	C₂×#41	1	2	yes	—
273	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
274	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
275	C₂⁴	C₂⁴×C₃	1	2	yes	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	C₂×C₃×D₄	1	8	yes	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
285	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
287	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
288	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
289	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
290	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
291	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
292	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
293	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	16	no	—
297	C₄⋊C₄	—	2	16	no	—
298	C₄⋊C₄	—	2	16	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	8	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	8	no	—
304	C₄⋊C₄	—	4	4	no	—
305	C₄⋊C₄	—	4	4	no	—
306	C₄⋊C₄	—	4	8	no	—
307	C₄⋊C₄	C₂×C₃×D₄	1	16	yes	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	2	16	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₂²⋊C₄	—	4	8	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	2	16	no	—
315	C₄²	—	2	8	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	4	2	no	—
319	C₄²	C₂×C₃×D₄	1	4	yes	—
320	C₄²	C₃×#41	1	4	yes	—
321	C₂²×C₃	—	4	2	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	4	4	no	—
324	C₂²×C₃	—	4	2	no	—
325	C₂²×C₃	—	4	4	no	—
326	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
327	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
328	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
329	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
330	C₂²×C₃	#585	1	2	yes	—
331	C₃×C₄	—	2	8	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	4	2	no	—
335	C₃×C₄	—	4	4	no	—
336	C₃×C₄	—	4	8	no	—
337	C₃×C₄	—	4	4	no	—
338	C₃×C₄	—	4	2	no	—
339	C₃×C₄	#541	1	4	yes	complemented
340	C₃×C₄	#547	1	4	yes	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	C₂⁵×C₃	1	1	yes	characteristic
347	Q₈	—	2	16	no	—
348	D₄	—	4	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	C₂²×C₃×D₄	1	8	yes	—
371	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
372	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
373	C₂×C₄	C₂×C₃×#41	1	2	yes	—
374	C₂×C₄	C₂×C₃×#41	1	2	yes	—
375	C₂×C₄	C₂×C₃×#41	1	2	yes	—
376	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
377	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
378	C₂×C₃	—	8	2	no	—
379	C₂×C₃	C₂×#541	1	1	yes	characteristic
380	C₂×C₃	C₂×#547	1	1	yes	characteristic
381	C₂×C₃	#3497	1	2	yes	—
382	C₂×C₃	#3512	1	1	yes	characteristic
383	C₂×C₃	#3555	1	2	yes	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
390	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
391	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
392	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
393	C₂²	C₃×#585	1	2	yes	—
394	C₄	—	2	8	no	—
395	C₄	—	2	4	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	4	8	no	—
400	C₄	—	4	4	no	—
401	C₄	—	4	2	no	—
402	C₄	C₃×#541	1	4	yes	complemented
403	C₄	C₃×#547	1	4	yes	—
404	C₃	#39379	1	1	yes	characteristic, direct product factor, Sylow
405	C₂	—	8	2	no	—
406	C₂	C₂×C₃×#541	1	1	yes	characteristic
407	C₂	C₂×C₃×#547	1	1	yes	characteristic
408	C₂	C₃×#3497	1	2	yes	—
409	C₂	C₃×#3512	1	1	yes	characteristic
410	C₂	C₃×#3555	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×#2859	C₂	semidirect
3. C₃×#2725	C₂	semidirect
4. C₃×#2629	C₂	semidirect
7. C₃×#2506	C₂	semidirect
8. C₃×#2421	C₂	semidirect
9. C₃×Q₈×C₄⋊C₄	C₂	semidirect
10. C₃×C₄×C₄⋊Q₈	C₂	semidirect
12. #39379	C₃	direct (N × H)
51. C₂×#541	C₂×C₃	semidirect
52. #2859	C₂×C₃	semidirect
53. #2725	C₂×C₃	semidirect
54. #2629	C₂×C₃	semidirect
57. #2506	C₂×C₃	semidirect
58. #2421	C₂×C₃	semidirect
59. Q₈×C₄⋊C₄	C₂×C₃	semidirect
60. C₄×C₄⋊Q₈	C₂×C₃	semidirect
65. C₃×C₄⋊Q₈	D₄	semidirect
195. C₄⋊Q₈	C₃×D₄	semidirect
339. C₃×C₄	#541	semidirect
402. C₄	C₃×#541	semidirect
404. C₃	#39379	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×#2859	2
C₃×#2725	2
C₃×#2629	2
C₃×#2538	2
C₃×#2512	2
C₃×#2506	2
C₃×#2421	2
C₃×Q₈×C₄⋊C₄	2
C₃×C₄×C₄⋊Q₈	2
C₃×#2293	2
#39379	3

Subgroups — C3×#39379 #10657986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#39379 #10657986