Subgroups — C₃×#20495 #10639102

Order 768.

1130 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×C₃×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#405	C₂	1	2	yes	maximal, complemented
4	C₃×#2293	C₂	1	1	yes	maximal, characteristic
5	C₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1753	C₂	1	2	yes	maximal, complemented
9	C₃×#1752	C₂	1	2	yes	maximal, complemented
10	C₃×#1750	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	#20495	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
14	C₂³×C₃×C₈	C₂²	1	2	yes	—
15	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×#117	C₂²	1	2	yes	—
17	C₃×#436	C₄	1	8	yes	complemented
18	C₃×C₈×D₄	C₄	1	8	yes	complemented
19	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₃×#405	—	2	8	no	—
24	C₂×C₃×#97	C₂²	1	2	yes	—
25	C₂×C₃×#97	C₂²	1	1	yes	characteristic
26	C₂×C₃×#97	C₂²	1	1	yes	characteristic
27	C₂×C₃×#97	C₂²	1	1	yes	characteristic
28	C₂×C₃×#97	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
30	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
31	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
33	C₃×#390	C₄	1	2	yes	—
34	C₃×#389	C₄	1	2	yes	—
35	C₃×#388	C₄	1	4	yes	—
36	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₃×C₄³	C₂²	1	1	yes	characteristic
39	C₃×#336	C₂²	1	2	yes	—
40	C₃×#336	C₂²	1	2	yes	—
41	C₃×#336	C₂²	1	2	yes	—
42	C₂×#436	C₂×C₃	1	1	yes	characteristic
43	C₂×C₈×D₄	C₂×C₃	1	1	yes	characteristic
44	C₂×#405	C₂×C₃	1	2	yes	complemented
45	#2293	C₂×C₃	1	1	yes	characteristic
46	#1770	C₂×C₃	1	1	yes	characteristic, complemented
47	C₈×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₄×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
49	#1753	C₂×C₃	1	2	yes	complemented
50	#1752	C₂×C₃	1	2	yes	complemented
51	#1750	C₂×C₃	1	2	yes	complemented
52	C₄×#97	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₃×C₄	C₂³	1	2	yes	—
55	C₂×C₃×M₁₆	—	2	4	no	—
56	C₂×C₃×M₁₆	—	2	4	no	—
57	C₂×C₃×M₁₆	C₂×C₄	1	8	yes	—
58	C₂²×C₃×C₈	—	2	4	no	—
59	C₂²×C₃×C₈	—	2	4	no	—
60	C₂²×C₃×C₈	C₂×C₄	1	8	yes	—
61	C₂²×C₃×C₈	C₂³	1	2	yes	—
62	C₂²×C₃×C₈	C₂³	1	2	yes	—
63	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₄×D₄	C₂×C₄	1	4	yes	—
68	C₃×C₄×D₄	C₂×C₄	1	4	yes	—
69	C₃×#117	—	2	4	no	—
70	C₃×#117	—	2	4	no	—
71	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
73	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
75	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
76	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
78	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
79	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄²	C₂³	1	2	yes	—
81	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
83	C₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
84	C₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
85	C₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
86	C₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
87	C₃×#97	—	2	4	no	—
88	C₃×#97	—	2	2	no	—
89	C₃×#97	—	2	2	no	—
90	C₃×#97	—	2	2	no	—
91	C₃×#97	D₄	1	4	yes	complemented
92	C₃×C₄×C₈	—	2	4	no	—
93	C₃×C₄×C₈	—	2	4	no	—
94	C₃×C₄×C₈	C₂×C₄	1	4	yes	—
95	C₃×C₄×C₈	C₂×C₄	1	4	yes	—
96	C₃×#95	C₂×C₄	1	4	yes	—
97	C₃×#95	C₂×C₄	1	2	yes	—
98	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
99	C₂³×C₈	C₂²×C₃	1	2	yes	—
100	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×#117	C₂²×C₃	1	2	yes	—
102	#436	C₃×C₄	1	8	yes	complemented
103	C₈×D₄	C₃×C₄	1	8	yes	complemented
104	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
107	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
108	#405	—	2	8	no	—
109	C₂×#97	C₂²×C₃	1	2	yes	—
110	C₂×#97	C₂²×C₃	1	1	yes	characteristic
111	C₂×#97	C₂²×C₃	1	1	yes	characteristic
112	C₂×#97	C₂²×C₃	1	1	yes	characteristic
113	C₂×#97	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
115	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
116	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
118	#390	C₃×C₄	1	2	yes	—
119	#389	C₃×C₄	1	2	yes	—
120	#388	C₃×C₄	1	4	yes	—
121	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
123	C₄³	C₂²×C₃	1	1	yes	characteristic
124	#336	C₂²×C₃	1	2	yes	—
125	#336	C₂²×C₃	1	2	yes	—
126	#336	C₂²×C₃	1	2	yes	—
127	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
128	C₂×C₃×D₄	—	2	4	no	—
129	C₂×C₃×D₄	C₄²	1	4	yes	—
130	C₂²×C₃×C₄	—	2	2	no	—
131	C₂²×C₃×C₄	—	2	2	no	—
132	C₂²×C₃×C₄	—	2	2	no	—
133	C₂²×C₃×C₄	—	2	2	no	—
134	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
135	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
136	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
138	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
139	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
140	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
141	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
143	C₃×M₁₆	—	2	16	no	—
144	C₂×C₃×C₈	—	2	2	no	—
145	C₂×C₃×C₈	—	2	2	no	—
146	C₂×C₃×C₈	—	2	1	no	—
147	C₂×C₃×C₈	—	2	1	no	—
148	C₂×C₃×C₈	—	2	1	no	—
149	C₂×C₃×C₈	—	2	1	no	—
150	C₂×C₃×C₈	—	2	2	no	—
151	C₂×C₃×C₈	—	2	2	no	—
152	C₂×C₃×C₈	—	2	16	no	—
153	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
155	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
156	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
157	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
158	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
159	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
160	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₈	#41	1	2	yes	—
162	C₂×C₃×C₈	#41	1	2	yes	—
163	C₃×C₄⋊C₄	—	2	8	no	—
164	C₃×C₄⋊C₄	—	2	4	no	—
165	C₃×C₄⋊C₄	C₄²	1	4	yes	—
166	C₃×C₂²⋊C₄	—	2	8	no	—
167	C₃×C₂²⋊C₄	—	4	4	no	—
168	C₃×C₂²⋊C₄	C₄²	1	8	yes	—
169	C₃×C₄²	—	2	4	no	—
170	C₃×C₄²	—	2	2	no	—
171	C₃×C₄²	—	2	1	no	—
172	C₃×C₄²	—	2	1	no	—
173	C₃×C₄²	—	2	2	no	—
174	C₃×C₄²	—	4	2	no	—
175	C₃×C₄²	C₂²×C₄	1	2	yes	—
176	C₃×C₄²	C₂²×C₄	1	2	yes	—
177	C₃×C₄²	C₂×D₄	1	2	yes	—
178	C₃×C₄²	#41	1	2	yes	—
179	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
180	C₂³×C₄	C₂³×C₃	1	2	yes	—
181	C₂×M₁₆	—	2	4	no	—
182	C₂×M₁₆	—	2	4	no	—
183	C₂×M₁₆	C₂×C₃×C₄	1	8	yes	—
184	C₂²×C₈	—	2	4	no	—
185	C₂²×C₈	—	2	4	no	—
186	C₂²×C₈	C₂×C₃×C₄	1	8	yes	—
187	C₂²×C₈	C₂³×C₃	1	2	yes	—
188	C₂²×C₈	C₂³×C₃	1	2	yes	—
189	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
192	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
193	C₄×D₄	C₂×C₃×C₄	1	4	yes	—
194	C₄×D₄	C₂×C₃×C₄	1	4	yes	—
195	#117	—	2	4	no	—
196	#117	—	2	4	no	—
197	C₂×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
198	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
199	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
200	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
201	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
202	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
203	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
204	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
205	C₂×C₄²	C₂³×C₃	1	2	yes	—
206	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
208	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
209	C₄⋊C₈	C₂×C₃×C₄	1	4	yes	—
210	C₄⋊C₈	C₂×C₃×C₄	1	4	yes	—
211	C₂²⋊C₈	C₂×C₃×C₄	1	8	yes	—
212	C₂²⋊C₈	C₂×C₃×C₄	1	8	yes	—
213	#97	—	2	4	no	—
214	#97	—	2	2	no	—
215	#97	—	2	2	no	—
216	#97	—	2	2	no	—
217	#97	C₃×D₄	1	4	yes	complemented
218	C₄×C₈	—	2	4	no	—
219	C₄×C₈	—	2	4	no	—
220	C₄×C₈	C₂×C₃×C₄	1	4	yes	—
221	C₄×C₈	C₂×C₃×C₄	1	4	yes	—
222	#95	C₂×C₃×C₄	1	4	yes	—
223	#95	C₂×C₃×C₄	1	2	yes	—
224	C₂³×C₃	—	2	2	no	—
225	C₂³×C₃	—	2	2	no	—
226	C₂³×C₃	—	2	4	no	—
227	C₂³×C₃	—	2	4	no	—
228	C₂³×C₃	C₂×C₄²	1	4	yes	—
229	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
230	C₃×D₄	—	2	8	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	C₂×C₄²	1	2	yes	—
247	C₂×C₃×C₄	C₂×C₄²	1	4	yes	—
248	C₂×C₃×C₄	C₂×C₄²	1	2	yes	—
249	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
250	C₂×C₃×C₄	#131	1	4	yes	—
251	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
257	C₃×C₈	—	2	4	no	—
258	C₃×C₈	—	2	4	no	—
259	C₃×C₈	—	2	2	no	—
260	C₃×C₈	—	2	2	no	—
261	C₃×C₈	C₄×D₄	1	4	yes	—
262	C₃×C₈	C₄×D₄	1	4	yes	—
263	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	C₃×C₄²	1	4	yes	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
271	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
272	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
274	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
275	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
276	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
277	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
278	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
279	M₁₆	—	2	16	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	16	no	—
289	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
290	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
291	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
292	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
293	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
294	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
295	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
296	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
297	C₂×C₈	C₃×#41	1	2	yes	—
298	C₂×C₈	C₃×#41	1	2	yes	—
299	C₄⋊C₄	—	2	8	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	C₃×C₄²	1	4	yes	—
302	C₂²⋊C₄	—	2	8	no	—
303	C₂²⋊C₄	—	4	4	no	—
304	C₂²⋊C₄	C₃×C₄²	1	8	yes	—
305	C₄²	—	2	4	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	4	2	no	—
311	C₄²	C₂²×C₃×C₄	1	2	yes	—
312	C₄²	C₂²×C₃×C₄	1	2	yes	—
313	C₄²	C₂×C₃×D₄	1	2	yes	—
314	C₄²	C₃×#41	1	2	yes	—
315	C₂²×C₃	—	2	4	no	—
316	C₂²×C₃	—	2	4	no	—
317	C₂²×C₃	—	2	4	no	—
318	C₂²×C₃	—	4	4	no	—
319	C₂²×C₃	—	4	4	no	—
320	C₂²×C₃	C₂²×C₄²	1	1	yes	characteristic
321	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
322	C₂²×C₃	C₄×#41	1	1	yes	characteristic
323	C₂²×C₃	C₂×#131	1	2	yes	—
324	C₂²×C₃	#568	1	2	yes	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	—	2	4	no	—
327	C₃×C₄	—	2	4	no	—
328	C₃×C₄	—	4	4	no	—
329	C₃×C₄	—	4	2	no	—
330	C₃×C₄	#405	1	4	yes	complemented
331	C₃×C₄	C₂×C₄×D₄	1	1	yes	characteristic
332	C₃×C₄	C₂×C₄×D₄	1	1	yes	characteristic
333	C₃×C₄	C₄×#41	1	1	yes	characteristic
334	C₃×C₄	C₄×#41	1	1	yes	characteristic
335	C₂³	—	2	4	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	C₂×C₃×C₄²	1	4	yes	—
340	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
341	D₄	—	2	8	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	C₂×C₃×C₄²	1	2	yes	—
358	C₂×C₄	C₂×C₃×C₄²	1	4	yes	—
359	C₂×C₄	C₂×C₃×C₄²	1	2	yes	—
360	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
361	C₂×C₄	C₃×#131	1	4	yes	—
362	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
363	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
365	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
366	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
367	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
368	C₈	—	2	4	no	—
369	C₈	—	2	4	no	—
370	C₈	—	2	2	no	—
371	C₈	—	2	2	no	—
372	C₈	C₃×C₄×D₄	1	4	yes	—
373	C₈	C₃×C₄×D₄	1	4	yes	—
374	C₂×C₃	—	4	4	no	—
375	C₂×C₃	C₄²×D₄	1	1	yes	characteristic
376	C₂×C₃	C₂×#405	1	1	yes	characteristic
377	C₂×C₃	#2875	1	1	yes	characteristic
378	C₂×C₃	#2935	1	2	yes	—
379	C₂×C₃	#2969	1	2	yes	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	C₂²×C₃×C₄²	1	1	yes	characteristic
386	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
387	C₂²	C₃×C₄×#41	1	1	yes	characteristic
388	C₂²	C₂×C₃×#131	1	2	yes	—
389	C₂²	C₃×#568	1	2	yes	—
390	C₄	—	2	2	no	—
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	2	no	—
395	C₄	C₃×#405	1	4	yes	complemented
396	C₄	C₂×C₃×C₄×D₄	1	1	yes	characteristic
397	C₄	C₂×C₃×C₄×D₄	1	1	yes	characteristic
398	C₄	C₃×C₄×#41	1	1	yes	characteristic
399	C₄	C₃×C₄×#41	1	1	yes	characteristic
400	C₃	#20495	1	1	yes	characteristic, direct product factor, Sylow
401	C₂	—	4	4	no	—
402	C₂	C₃×C₄²×D₄	1	1	yes	characteristic
403	C₂	C₂×C₃×#405	1	1	yes	characteristic
404	C₂	C₃×#2875	1	1	yes	characteristic
405	C₂	C₃×#2935	1	2	yes	—
406	C₂	C₃×#2969	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂⁴
commutator	C₂²	C₂²×C₃×C₄²
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂³×C₄
prime radical	C₂²×C₃×D₄	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×#405	C₂	semidirect
5. C₃×#1770	C₂	semidirect
6. C₃×C₈×C₄⋊C₄	C₂	semidirect
7. C₃×C₄×C₄⋊C₈	C₂	semidirect
8. C₃×#1753	C₂	semidirect
9. C₃×#1752	C₂	semidirect
10. C₃×#1750	C₂	semidirect
11. C₃×C₄×#97	C₂	semidirect
12. #20495	C₃	direct (N × H)
17. C₃×#436	C₄	semidirect
18. C₃×C₈×D₄	C₄	semidirect
44. C₂×#405	C₂×C₃	semidirect
46. #1770	C₂×C₃	semidirect
47. C₈×C₄⋊C₄	C₂×C₃	semidirect
48. C₄×C₄⋊C₈	C₂×C₃	semidirect
49. #1753	C₂×C₃	semidirect
50. #1752	C₂×C₃	semidirect
51. #1750	C₂×C₃	semidirect
52. C₄×#97	C₂×C₃	semidirect
91. C₃×#97	D₄	semidirect
102. #436	C₃×C₄	semidirect
103. C₈×D₄	C₃×C₄	semidirect
217. #97	C₃×D₄	semidirect
330. C₃×C₄	#405	semidirect
395. C₄	C₃×#405	semidirect
400. C₃	#20495	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×#436	2
C₂×C₃×C₈×D₄	2
C₂×C₃×#405	2
C₃×#2293	2
C₃×#1770	2
C₃×C₈×C₄⋊C₄	2
C₃×C₄×C₄⋊C₈	2
C₃×#1753	2
C₃×#1752	2
C₃×#1750	2
C₃×C₄×#97	2
#20495	3

Subgroups — C3×#20495 #10639102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#20495 #10639102