Subgroups — C₃×#35914 #10654521

Order 768.

2174 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	C₃×#2644	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2643	C₂	1	2	yes	maximal, complemented
3	C₃×#2512	C₂	1	3	yes	maximal, complemented
4	C₃×#2497	C₂	1	3	yes	maximal, complemented
5	C₃×#2481	C₂	1	6	yes	maximal, complemented
6	C₃×#2480	C₂	1	6	yes	maximal, complemented
7	C₃×#2401	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#396	C₂	1	2	yes	maximal, complemented
9	C₃×D₄×C₄⋊C₄	C₂	1	3	yes	maximal, complemented
10	C₃×D₄×C₂²⋊C₄	C₂	1	3	yes	maximal
11	C₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
12	#35914	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×#126	C₂²	1	6	yes	complemented
15	C₂×C₃×C₄×D₄	C₂²	1	3	yes	—
16	C₂×C₃×C₄×D₄	C₂²	1	3	yes	—
17	C₂²×C₃×C₄⋊C₄	C₂²	1	6	yes	complemented
18	C₂²×C₃×C₂²⋊C₄	C₂²	1	6	yes	—
19	C₃×#401	C₂²	1	1	yes	characteristic, complemented
20	C₃×#400	C₂²	1	6	yes	complemented
21	C₃×#400	C₂²	1	3	yes	complemented
22	C₃×#397	C₂²	1	3	yes	—
23	C₃×#397	C₂²	1	6	yes	complemented
24	C₃×#397	C₂²	1	6	yes	complemented
25	C₃×#396	C₂²	1	1	yes	characteristic
26	C₃×#396	C₂²	1	6	yes	—
27	C₃×#396	C₂²	1	2	yes	complemented
28	C₃×#396	C₂²	1	6	yes	complemented
29	C₃×#390	C₂²	1	3	yes	—
30	C₃×#390	C₂²	1	3	yes	—
31	C₃×#389	C₂²	1	3	yes	complemented
32	C₃×#389	C₂²	1	3	yes	complemented
33	C₃×#388	C₂²	1	6	yes	—
34	C₃×#388	C₂²	1	6	yes	complemented
35	C₃×#387	C₂²	1	6	yes	complemented
36	C₃×#386	C₂²	1	6	yes	—
37	C₃×#386	C₂²	1	6	yes	—
38	C₃×#385	C₂²	1	6	yes	complemented
39	C₃×#385	C₂²	1	6	yes	complemented
40	C₃×#384	C₂²	1	3	yes	complemented
41	C₃×#380	C₂²	1	3	yes	—
42	C₃×#380	C₂²	1	6	yes	complemented
43	C₃×#379	C₂²	1	6	yes	—
44	C₃×C₄×C₄⋊C₄	C₂²	1	3	yes	complemented
45	C₃×C₄×C₄⋊C₄	C₂²	1	3	yes	complemented
46	C₃×C₄×C₂²⋊C₄	C₂²	1	3	yes	—
47	C₃×C₄×C₂²⋊C₄	C₂²	1	6	yes	complemented
48	C₃×#376	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×#95	C₂²	1	2	yes	complemented
50	#2644	C₂×C₃	1	1	yes	characteristic, complemented
51	#2643	C₂×C₃	1	2	yes	complemented
52	#2512	C₂×C₃	1	3	yes	complemented
53	#2497	C₂×C₃	1	3	yes	complemented
54	#2481	C₂×C₃	1	6	yes	complemented
55	#2480	C₂×C₃	1	6	yes	complemented
56	#2401	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×#396	C₂×C₃	1	2	yes	complemented
58	D₄×C₄⋊C₄	C₂×C₃	1	3	yes	complemented
59	D₄×C₂²⋊C₄	C₂×C₃	1	3	yes	—
60	#2275	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂⁵×C₃	C₂³	1	2	yes	—
62	C₂²×C₃×D₄	—	2	12	no	—
63	C₂²×C₃×D₄	C₂³	1	2	yes	—
64	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
66	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
67	C₂³×C₃×C₄	C₂³	1	6	yes	—
68	C₂³×C₃×C₄	C₂³	1	6	yes	—
69	C₃×#126	—	4	12	no	—
70	C₃×C₄×D₄	—	2	12	no	—
71	C₃×C₄×D₄	—	2	12	no	—
72	C₂×C₃×C₄⋊C₄	—	4	12	no	—
73	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
74	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
75	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
76	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
77	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
78	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
79	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
80	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
81	C₂×C₃×C₂²⋊C₄	—	4	12	no	—
82	C₂×C₃×C₂²⋊C₄	C₂³	1	3	yes	—
83	C₂×C₃×C₂²⋊C₄	C₂³	1	3	yes	—
84	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
85	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
86	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
87	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
88	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
89	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
90	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
91	C₂×C₃×C₄²	C₂³	1	3	yes	—
92	C₂×C₃×C₄²	C₂³	1	3	yes	—
93	C₂×C₃×C₄²	C₂³	1	6	yes	—
94	C₃×#95	C₂³	1	1	yes	characteristic
95	C₃×#95	C₂³	1	6	yes	—
96	C₃×#95	C₂³	1	3	yes	—
97	C₃×#95	C₂³	1	3	yes	—
98	C₃×#95	C₂³	1	3	yes	—
99	C₃×#95	C₂³	1	3	yes	—
100	C₃×#95	C₂³	1	3	yes	—
101	C₃×#95	C₂³	1	6	yes	—
102	C₃×#95	C₂³	1	6	yes	—
103	C₃×#95	C₂³	1	6	yes	—
104	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
105	C₂×#126	C₂²×C₃	1	6	yes	complemented
106	C₂×C₄×D₄	C₂²×C₃	1	3	yes	—
107	C₂×C₄×D₄	C₂²×C₃	1	3	yes	—
108	C₂²×C₄⋊C₄	C₂²×C₃	1	6	yes	complemented
109	C₂²×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
110	#401	C₂²×C₃	1	1	yes	characteristic, complemented
111	#400	C₂²×C₃	1	6	yes	complemented
112	#400	C₂²×C₃	1	3	yes	complemented
113	#397	C₂²×C₃	1	3	yes	—
114	#397	C₂²×C₃	1	6	yes	complemented
115	#397	C₂²×C₃	1	6	yes	complemented
116	#396	C₂²×C₃	1	1	yes	characteristic
117	#396	C₂²×C₃	1	6	yes	—
118	#396	C₂²×C₃	1	2	yes	complemented
119	#396	C₂²×C₃	1	6	yes	complemented
120	#390	C₂²×C₃	1	3	yes	—
121	#390	C₂²×C₃	1	3	yes	—
122	#389	C₂²×C₃	1	3	yes	complemented
123	#389	C₂²×C₃	1	3	yes	complemented
124	#388	C₂²×C₃	1	6	yes	—
125	#388	C₂²×C₃	1	6	yes	complemented
126	#387	C₂²×C₃	1	6	yes	complemented
127	#386	C₂²×C₃	1	6	yes	—
128	#386	C₂²×C₃	1	6	yes	—
129	#385	C₂²×C₃	1	6	yes	complemented
130	#385	C₂²×C₃	1	6	yes	complemented
131	#384	C₂²×C₃	1	3	yes	complemented
132	#380	C₂²×C₃	1	3	yes	—
133	#380	C₂²×C₃	1	6	yes	complemented
134	#379	C₂²×C₃	1	6	yes	—
135	C₄×C₄⋊C₄	C₂²×C₃	1	3	yes	complemented
136	C₄×C₄⋊C₄	C₂²×C₃	1	3	yes	complemented
137	C₄×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
138	C₄×C₂²⋊C₄	C₂²×C₃	1	6	yes	complemented
139	#376	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₂×#95	C₂²×C₃	1	2	yes	complemented
141	C₂⁴×C₃	—	2	4	no	—
142	C₂⁴×C₃	—	2	12	no	—
143	C₂⁴×C₃	—	4	6	no	—
144	C₂⁴×C₃	C₂⁴	1	2	yes	—
145	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
146	C₂⁴×C₃	C₂⁴	1	2	yes	—
147	C₂×C₃×D₄	—	2	12	no	—
148	C₂×C₃×D₄	—	2	6	no	—
149	C₂×C₃×D₄	—	4	16	no	—
150	C₂×C₃×D₄	#41	1	12	yes	—
151	C₂²×C₃×C₄	—	2	12	no	—
152	C₂²×C₃×C₄	—	2	12	no	—
153	C₂²×C₃×C₄	—	2	6	no	—
154	C₂²×C₃×C₄	—	2	12	no	—
155	C₂²×C₃×C₄	—	4	6	no	—
156	C₂²×C₃×C₄	—	4	6	no	—
157	C₂²×C₃×C₄	—	4	6	no	—
158	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
160	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
161	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
162	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
163	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
164	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
165	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
166	C₃×C₄⋊C₄	—	2	6	no	—
167	C₃×C₄⋊C₄	—	2	6	no	—
168	C₃×C₄⋊C₄	—	2	6	no	—
169	C₃×C₄⋊C₄	—	2	12	no	—
170	C₃×C₄⋊C₄	—	2	6	no	—
171	C₃×C₄⋊C₄	—	4	6	no	—
172	C₃×C₄⋊C₄	—	4	6	no	—
173	C₃×C₄⋊C₄	—	4	6	no	—
174	C₃×C₂²⋊C₄	—	2	12	no	—
175	C₃×C₂²⋊C₄	—	2	12	no	—
176	C₃×C₂²⋊C₄	—	2	6	no	—
177	C₃×C₂²⋊C₄	—	2	6	no	—
178	C₃×C₂²⋊C₄	—	2	12	no	—
179	C₃×C₂²⋊C₄	—	4	6	no	—
180	C₃×C₂²⋊C₄	—	4	6	no	—
181	C₃×C₂²⋊C₄	—	4	6	no	—
182	C₃×C₂²⋊C₄	—	4	6	no	—
183	C₃×C₄²	—	2	6	no	—
184	C₃×C₄²	—	2	6	no	—
185	C₃×C₄²	—	4	6	no	—
186	C₂⁵	C₂³×C₃	1	2	yes	—
187	C₂²×D₄	—	2	12	no	—
188	C₂²×D₄	C₂³×C₃	1	2	yes	—
189	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
190	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
191	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
192	C₂³×C₄	C₂³×C₃	1	6	yes	—
193	C₂³×C₄	C₂³×C₃	1	6	yes	—
194	#126	—	4	12	no	—
195	C₄×D₄	—	2	12	no	—
196	C₄×D₄	—	2	12	no	—
197	C₂×C₄⋊C₄	—	4	12	no	—
198	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
199	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
200	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
201	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
202	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
203	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
204	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
205	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
206	C₂×C₂²⋊C₄	—	4	12	no	—
207	C₂×C₂²⋊C₄	C₂³×C₃	1	3	yes	—
208	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
209	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
210	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
211	C₂×C₂²⋊C₄	C₂³×C₃	1	3	yes	—
212	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
213	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
214	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
215	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
216	C₂×C₄²	C₂³×C₃	1	3	yes	—
217	C₂×C₄²	C₂³×C₃	1	3	yes	—
218	C₂×C₄²	C₂³×C₃	1	6	yes	—
219	#95	C₂³×C₃	1	1	yes	characteristic
220	#95	C₂³×C₃	1	6	yes	—
221	#95	C₂³×C₃	1	3	yes	—
222	#95	C₂³×C₃	1	3	yes	—
223	#95	C₂³×C₃	1	3	yes	—
224	#95	C₂³×C₃	1	3	yes	—
225	#95	C₂³×C₃	1	3	yes	—
226	#95	C₂³×C₃	1	6	yes	—
227	#95	C₂³×C₃	1	6	yes	—
228	#95	C₂³×C₃	1	6	yes	—
229	C₂³×C₃	—	2	6	no	—
230	C₂³×C₃	—	2	2	no	—
231	C₂³×C₃	—	2	3	no	—
232	C₂³×C₃	—	2	3	no	—
233	C₂³×C₃	—	2	6	no	—
234	C₂³×C₃	—	2	6	no	—
235	C₂³×C₃	—	2	2	no	—
236	C₂³×C₃	—	4	24	no	—
237	C₂³×C₃	—	4	8	no	—
238	C₂³×C₃	—	8	12	no	—
239	C₂³×C₃	C₂×#41	1	12	yes	—
240	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
241	C₂³×C₃	C₂⁵	1	1	yes	characteristic
242	C₃×D₄	—	4	8	no	—
243	C₃×D₄	—	4	4	no	—
244	C₃×D₄	#126	1	16	yes	complemented
245	C₂×C₃×C₄	—	2	3	no	—
246	C₂×C₃×C₄	—	2	3	no	—
247	C₂×C₃×C₄	—	2	3	no	—
248	C₂×C₃×C₄	—	2	3	no	—
249	C₂×C₃×C₄	—	2	3	no	—
250	C₂×C₃×C₄	—	2	6	no	—
251	C₂×C₃×C₄	—	2	6	no	—
252	C₂×C₃×C₄	—	2	3	no	—
253	C₂×C₃×C₄	—	2	3	no	—
254	C₂×C₃×C₄	—	2	6	no	—
255	C₂×C₃×C₄	—	2	6	no	—
256	C₂×C₃×C₄	—	2	3	no	—
257	C₂×C₃×C₄	—	2	3	no	—
258	C₂×C₃×C₄	—	2	6	no	—
259	C₂×C₃×C₄	—	2	6	no	—
260	C₂×C₃×C₄	—	2	3	no	—
261	C₂×C₃×C₄	—	2	3	no	—
262	C₂×C₃×C₄	—	2	3	no	—
263	C₂×C₃×C₄	—	4	24	no	—
264	C₂×C₃×C₄	—	4	4	no	—
265	C₂×C₃×C₄	—	8	12	no	—
266	C₂×C₃×C₄	C₂×#41	1	6	yes	—
267	C₂×C₃×C₄	H(5,𝔽₂)	1	6	yes	—
268	C₂⁴	—	2	4	no	—
269	C₂⁴	—	2	12	no	—
270	C₂⁴	—	4	6	no	—
271	C₂⁴	C₂⁴×C₃	1	2	yes	—
272	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
273	C₂⁴	C₂⁴×C₃	1	2	yes	—
274	C₂×D₄	—	2	12	no	—
275	C₂×D₄	—	2	6	no	—
276	C₂×D₄	—	4	16	no	—
277	C₂×D₄	C₃×#41	1	12	yes	—
278	C₂²×C₄	—	2	12	no	—
279	C₂²×C₄	—	2	12	no	—
280	C₂²×C₄	—	2	6	no	—
281	C₂²×C₄	—	2	12	no	—
282	C₂²×C₄	—	4	6	no	—
283	C₂²×C₄	—	4	6	no	—
284	C₂²×C₄	—	4	6	no	—
285	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
286	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
287	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
288	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
289	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
290	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
291	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
292	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
293	C₄⋊C₄	—	2	6	no	—
294	C₄⋊C₄	—	2	6	no	—
295	C₄⋊C₄	—	2	6	no	—
296	C₄⋊C₄	—	2	12	no	—
297	C₄⋊C₄	—	2	6	no	—
298	C₄⋊C₄	—	4	6	no	—
299	C₄⋊C₄	—	4	6	no	—
300	C₄⋊C₄	—	4	6	no	—
301	C₂²⋊C₄	—	2	12	no	—
302	C₂²⋊C₄	—	2	12	no	—
303	C₂²⋊C₄	—	2	6	no	—
304	C₂²⋊C₄	—	2	6	no	—
305	C₂²⋊C₄	—	2	12	no	—
306	C₂²⋊C₄	—	4	6	no	—
307	C₂²⋊C₄	—	4	6	no	—
308	C₂²⋊C₄	—	4	6	no	—
309	C₂²⋊C₄	—	4	6	no	—
310	C₄²	—	2	6	no	—
311	C₄²	—	2	6	no	—
312	C₄²	—	4	6	no	—
313	C₂²×C₃	—	2	12	no	—
314	C₂²×C₃	—	2	12	no	—
315	C₂²×C₃	—	2	6	no	—
316	C₂²×C₃	—	4	1	no	—
317	C₂²×C₃	—	4	3	no	—
318	C₂²×C₃	—	4	2	no	—
319	C₂²×C₃	—	4	6	no	—
320	C₂²×C₃	—	4	6	no	—
321	C₂²×C₃	—	8	16	no	—
322	C₂²×C₃	C₂×#126	1	8	yes	—
323	C₂²×C₃	C₂²×#41	1	3	yes	—
324	C₂²×C₃	C₂×H(5,𝔽₂)	1	3	yes	—
325	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
326	C₃×C₄	—	2	6	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	—	4	6	no	—
329	C₃×C₄	—	4	6	no	—
330	C₃×C₄	—	4	3	no	—
331	C₃×C₄	—	4	3	no	—
332	C₃×C₄	—	4	3	no	—
333	C₃×C₄	C₂×#126	1	4	yes	—
334	C₂³	—	2	6	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	3	no	—
337	C₂³	—	2	3	no	—
338	C₂³	—	2	6	no	—
339	C₂³	—	2	6	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	4	24	no	—
342	C₂³	—	4	8	no	—
343	C₂³	—	8	12	no	—
344	C₂³	C₂×C₃×#41	1	12	yes	—
345	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
346	C₂³	C₂⁵×C₃	1	1	yes	characteristic
347	D₄	—	4	8	no	—
348	D₄	—	4	4	no	—
349	D₄	C₃×#126	1	16	yes	complemented
350	C₂×C₄	—	2	3	no	—
351	C₂×C₄	—	2	3	no	—
352	C₂×C₄	—	2	3	no	—
353	C₂×C₄	—	2	3	no	—
354	C₂×C₄	—	2	3	no	—
355	C₂×C₄	—	2	6	no	—
356	C₂×C₄	—	2	6	no	—
357	C₂×C₄	—	2	3	no	—
358	C₂×C₄	—	2	3	no	—
359	C₂×C₄	—	2	6	no	—
360	C₂×C₄	—	2	6	no	—
361	C₂×C₄	—	2	3	no	—
362	C₂×C₄	—	2	3	no	—
363	C₂×C₄	—	2	6	no	—
364	C₂×C₄	—	2	6	no	—
365	C₂×C₄	—	2	3	no	—
366	C₂×C₄	—	2	3	no	—
367	C₂×C₄	—	2	3	no	—
368	C₂×C₄	—	4	24	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	8	12	no	—
371	C₂×C₄	C₂×C₃×#41	1	6	yes	—
372	C₂×C₄	C₃×H(5,𝔽₂)	1	6	yes	—
373	C₂×C₃	—	2	8	no	—
374	C₂×C₃	—	4	2	no	—
375	C₂×C₃	—	8	2	no	—
376	C₂×C₃	C₂²×#126	1	1	yes	characteristic
377	C₂×C₃	#3519	1	3	yes	—
378	C₂×C₃	#3520	1	3	yes	—
379	C₂²	—	2	12	no	—
380	C₂²	—	2	12	no	—
381	C₂²	—	2	6	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	3	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	6	no	—
386	C₂²	—	4	6	no	—
387	C₂²	—	8	16	no	—
388	C₂²	C₂×C₃×#126	1	8	yes	—
389	C₂²	C₂²×C₃×#41	1	3	yes	—
390	C₂²	C₂×C₃×H(5,𝔽₂)	1	3	yes	—
391	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
392	C₄	—	2	6	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	6	no	—
395	C₄	—	4	3	no	—
396	C₄	—	4	6	no	—
397	C₄	—	4	3	no	—
398	C₄	—	4	3	no	—
399	C₄	C₂×C₃×#126	1	4	yes	—
400	C₃	#35914	1	1	yes	characteristic, direct product factor, Sylow
401	C₂	—	2	8	no	—
402	C₂	—	4	2	no	—
403	C₂	—	8	2	no	—
404	C₂	C₂²×C₃×#126	1	1	yes	characteristic
405	C₂	C₃×#3519	1	3	yes	—
406	C₂	C₃×#3520	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
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. C₃×#2644	C₂	semidirect
2. C₃×#2643	C₂	semidirect
3. C₃×#2512	C₂	semidirect
4. C₃×#2497	C₂	semidirect
5. C₃×#2481	C₂	semidirect
6. C₃×#2480	C₂	semidirect
7. C₃×#2401	C₂	semidirect
8. C₂×C₃×#396	C₂	semidirect
9. C₃×D₄×C₄⋊C₄	C₂	semidirect
11. C₃×#2275	C₂	semidirect
12. #35914	C₃	direct (N × H)
14. C₂×C₃×#126	C₂²	semidirect
17. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
19. C₃×#401	C₂²	semidirect
20. C₃×#400	C₂²	semidirect
21. C₃×#400	C₂²	semidirect
23. C₃×#397	C₂²	semidirect
24. C₃×#397	C₂²	semidirect
27. C₃×#396	C₂²	semidirect
28. C₃×#396	C₂²	semidirect
31. C₃×#389	C₂²	semidirect
32. C₃×#389	C₂²	semidirect
34. C₃×#388	C₂²	semidirect
35. C₃×#387	C₂²	semidirect
38. C₃×#385	C₂²	semidirect
39. C₃×#385	C₂²	semidirect
40. C₃×#384	C₂²	semidirect
42. C₃×#380	C₂²	semidirect
44. C₃×C₄×C₄⋊C₄	C₂²	semidirect
45. C₃×C₄×C₄⋊C₄	C₂²	semidirect
47. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
48. C₃×#376	C₂²	semidirect
49. C₂×C₃×#95	C₂²	semidirect
50. #2644	C₂×C₃	semidirect
51. #2643	C₂×C₃	semidirect
52. #2512	C₂×C₃	semidirect
53. #2497	C₂×C₃	semidirect
54. #2481	C₂×C₃	semidirect
55. #2480	C₂×C₃	semidirect
56. #2401	C₂×C₃	semidirect
57. C₂×#396	C₂×C₃	semidirect
58. D₄×C₄⋊C₄	C₂×C₃	semidirect
60. #2275	C₂×C₃	semidirect
105. C₂×#126	C₂²×C₃	semidirect
108. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
110. #401	C₂²×C₃	semidirect
111. #400	C₂²×C₃	semidirect
112. #400	C₂²×C₃	semidirect
114. #397	C₂²×C₃	semidirect
115. #397	C₂²×C₃	semidirect
118. #396	C₂²×C₃	semidirect
119. #396	C₂²×C₃	semidirect
122. #389	C₂²×C₃	semidirect
123. #389	C₂²×C₃	semidirect
125. #388	C₂²×C₃	semidirect
126. #387	C₂²×C₃	semidirect
129. #385	C₂²×C₃	semidirect
130. #385	C₂²×C₃	semidirect
131. #384	C₂²×C₃	semidirect
133. #380	C₂²×C₃	semidirect
135. C₄×C₄⋊C₄	C₂²×C₃	semidirect
136. C₄×C₄⋊C₄	C₂²×C₃	semidirect
138. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
139. #376	C₂²×C₃	semidirect
140. C₂×#95	C₂²×C₃	semidirect
244. C₃×D₄	#126	semidirect
349. D₄	C₃×#126	semidirect
400. C₃	#35914	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#2644	2
C₃×#2643	2
C₃×#2512	2
C₃×#2497	2
C₃×#2481	2
C₃×#2480	2
C₃×#2401	2
C₂×C₃×#396	2
C₃×D₄×C₄⋊C₄	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2275	2
#35914	3

Subgroups — C3×#35914 #10654521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35914 #10654521