Subgroups — C₃×#20504 #10639111

Order 768.

1130 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#440	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2275	C₂	1	1	yes	maximal, characteristic
5	C₃×#1776	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#107	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1762	C₂	1	1	yes	maximal, characteristic
9	C₃×C₄×#103	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×#102	C₂	1	2	yes	maximal
11	C₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	#20504	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
15	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
17	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
18	C₃×#440	C₄	1	16	yes	complemented
19	C₃×C₄×SD₁₆	C₄	1	8	yes	complemented
20	C₂×C₃×#107	C₂²	1	2	yes	—
21	C₂×C₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₃×#103	C₂²	1	1	yes	characteristic
23	C₂×C₃×#103	C₂²	1	2	yes	—
24	C₂×C₃×#102	C₂²	1	1	yes	characteristic
25	C₂×C₃×#102	C₂²	1	2	yes	—
26	C₂×C₃×#97	C₂²	1	1	yes	characteristic
27	C₂×C₃×#97	C₂²	1	2	yes	—
28	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
29	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₄⋊C₄	—	2	1	no	—
31	C₃×C₄×C₄⋊C₄	—	2	2	no	—
32	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
33	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
34	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₂²⋊C₄	—	2	1	no	—
37	C₃×C₄×C₂²⋊C₄	—	2	2	no	—
38	C₃×#376	—	2	1	no	—
39	C₃×#376	C₂²	1	1	yes	characteristic
40	C₂×C₃×#95	—	2	1	no	—
41	C₃×#340	C₂²	1	2	yes	—
42	C₃×#340	C₂²	1	2	yes	—
43	C₃×#340	C₂²	1	2	yes	—
44	C₂×#440	C₂×C₃	1	2	yes	—
45	C₂×C₄×SD₁₆	C₂×C₃	1	1	yes	characteristic
46	#2276	C₂×C₃	1	1	yes	characteristic, complemented
47	#2275	C₂×C₃	1	1	yes	characteristic
48	#1776	C₂×C₃	1	2	yes	complemented
49	C₄×#107	C₂×C₃	1	1	yes	characteristic, complemented
50	#1763	C₂×C₃	1	1	yes	characteristic, complemented
51	#1762	C₂×C₃	1	1	yes	characteristic
52	C₄×#103	C₂×C₃	1	2	yes	complemented
53	C₄×#102	C₂×C₃	1	2	yes	—
54	#1726	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
56	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
57	C₂³×C₃×C₄	—	2	1	no	—
58	C₂³×C₃×C₄	—	2	2	no	—
59	C₂×C₃×SD₁₆	C₂×C₄	1	4	yes	—
60	C₂×C₃×SD₁₆	C₂×C₄	1	8	yes	—
61	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₈	C₂³	1	2	yes	—
63	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
64	C₃×C₄×Q₈	—	2	4	no	—
65	C₃×C₄×Q₈	—	2	2	no	—
66	C₃×C₄×Q₈	C₂×C₄	1	4	yes	complemented
67	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
68	C₃×C₄×D₄	—	2	4	no	—
69	C₃×C₄×D₄	—	2	2	no	—
70	C₃×C₄×D₄	C₂×C₄	1	4	yes	—
71	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
72	C₂×C₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₃×C₄²	—	2	1	no	—
81	C₂×C₃×C₄²	—	2	2	no	—
82	C₂×C₃×C₄²	—	2	2	no	—
83	C₂×C₃×C₄²	—	2	1	no	—
84	C₂×C₃×C₄²	—	2	2	no	—
85	C₂×C₃×C₄²	—	2	1	no	—
86	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄²	C₂³	1	2	yes	—
88	C₃×#107	C₂×C₄	1	8	yes	complemented
89	C₃×#106	C₂×C₄	1	4	yes	complemented
90	C₃×#103	C₂×C₄	1	4	yes	complemented
91	C₃×#103	C₂×C₄	1	8	yes	complemented
92	C₃×#102	C₂×C₄	1	4	yes	—
93	C₃×#102	C₂×C₄	1	8	yes	—
94	C₃×#97	—	2	2	no	—
95	C₃×#97	C₂×C₄	1	8	yes	complemented
96	C₃×C₄×C₈	—	2	4	no	—
97	C₃×C₄×C₈	C₂×C₄	1	4	yes	complemented
98	C₃×#95	—	2	1	no	—
99	C₃×#95	—	2	2	no	—
100	C₃×#95	—	2	1	no	—
101	C₃×#95	—	2	2	no	—
102	C₃×#95	D₄	1	1	yes	characteristic
103	C₃×#95	D₄	1	1	yes	characteristic
104	C₃×#95	D₄	1	2	yes	—
105	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
108	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
110	#440	C₃×C₄	1	16	yes	complemented
111	C₄×SD₁₆	C₃×C₄	1	8	yes	complemented
112	C₂×#107	C₂²×C₃	1	2	yes	—
113	C₂×#106	C₂²×C₃	1	1	yes	characteristic
114	C₂×#103	C₂²×C₃	1	1	yes	characteristic
115	C₂×#103	C₂²×C₃	1	2	yes	—
116	C₂×#102	C₂²×C₃	1	1	yes	characteristic
117	C₂×#102	C₂²×C₃	1	2	yes	—
118	C₂×#97	C₂²×C₃	1	1	yes	characteristic
119	C₂×#97	C₂²×C₃	1	2	yes	—
120	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
121	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
122	C₄×C₄⋊C₄	—	2	1	no	—
123	C₄×C₄⋊C₄	—	2	2	no	—
124	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
125	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
126	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₄×C₂²⋊C₄	—	2	1	no	—
129	C₄×C₂²⋊C₄	—	2	2	no	—
130	#376	—	2	1	no	—
131	#376	C₂²×C₃	1	1	yes	characteristic
132	C₂×#95	—	2	1	no	—
133	#340	C₂²×C₃	1	2	yes	—
134	#340	C₂²×C₃	1	2	yes	—
135	#340	C₂²×C₃	1	2	yes	—
136	C₂⁴×C₃	—	2	1	no	—
137	C₂×C₃×Q₈	—	2	2	no	—
138	C₂×C₃×Q₈	—	2	1	no	—
139	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
140	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
141	C₂×C₃×D₄	—	2	2	no	—
142	C₂×C₃×D₄	—	2	1	no	—
143	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
144	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
145	C₂²×C₃×C₄	—	2	1	no	—
146	C₂²×C₃×C₄	—	2	2	no	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	—	2	1	no	—
150	C₂²×C₃×C₄	—	2	4	no	—
151	C₂²×C₃×C₄	—	2	8	no	—
152	C₂²×C₃×C₄	—	8	2	no	—
153	C₂²×C₃×C₄	—	8	2	no	—
154	C₂²×C₃×C₄	—	8	2	no	—
155	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
157	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
158	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
160	C₃×SD₁₆	C₄²	1	16	yes	complemented
161	C₂×C₃×C₈	—	2	2	no	—
162	C₂×C₃×C₈	—	2	2	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
165	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
166	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	8	no	—
170	C₃×C₄⋊C₄	—	2	1	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
175	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
176	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
177	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
178	C₃×C₂²⋊C₄	—	2	8	no	—
179	C₃×C₂²⋊C₄	—	2	4	no	—
180	C₃×C₄²	—	2	8	no	—
181	C₃×C₄²	—	2	4	no	—
182	C₃×C₄²	—	8	1	no	—
183	C₃×C₄²	—	8	1	no	—
184	C₃×C₄²	—	8	2	no	—
185	C₃×C₄²	—	8	2	no	—
186	C₃×C₄²	C₂²×C₄	1	2	yes	—
187	C₃×C₄²	C₂²×C₄	1	4	yes	—
188	C₃×C₄²	#41	1	4	yes	—
189	C₃×C₄²	#41	1	2	yes	—
190	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
191	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
192	C₂³×C₄	—	2	1	no	—
193	C₂³×C₄	—	2	2	no	—
194	C₂×SD₁₆	C₂×C₃×C₄	1	4	yes	—
195	C₂×SD₁₆	C₂×C₃×C₄	1	8	yes	—
196	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
197	C₂²×C₈	C₂³×C₃	1	2	yes	—
198	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
199	C₄×Q₈	—	2	4	no	—
200	C₄×Q₈	—	2	2	no	—
201	C₄×Q₈	C₂×C₃×C₄	1	4	yes	complemented
202	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
203	C₄×D₄	—	2	4	no	—
204	C₄×D₄	—	2	2	no	—
205	C₄×D₄	C₂×C₃×C₄	1	4	yes	—
206	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
207	C₂×C₄⋊C₄	—	2	2	no	—
208	C₂×C₄⋊C₄	—	2	1	no	—
209	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
211	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
212	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
213	C₂×C₂²⋊C₄	—	2	2	no	—
214	C₂×C₂²⋊C₄	—	2	1	no	—
215	C₂×C₄²	—	2	1	no	—
216	C₂×C₄²	—	2	2	no	—
217	C₂×C₄²	—	2	2	no	—
218	C₂×C₄²	—	2	1	no	—
219	C₂×C₄²	—	2	2	no	—
220	C₂×C₄²	—	2	1	no	—
221	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₃	1	2	yes	—
223	#107	C₂×C₃×C₄	1	8	yes	complemented
224	#106	C₂×C₃×C₄	1	4	yes	complemented
225	#103	C₂×C₃×C₄	1	4	yes	complemented
226	#103	C₂×C₃×C₄	1	8	yes	complemented
227	#102	C₂×C₃×C₄	1	4	yes	—
228	#102	C₂×C₃×C₄	1	8	yes	—
229	#97	—	2	2	no	—
230	#97	C₂×C₃×C₄	1	8	yes	complemented
231	C₄×C₈	—	2	4	no	—
232	C₄×C₈	C₂×C₃×C₄	1	4	yes	complemented
233	#95	—	2	1	no	—
234	#95	—	2	2	no	—
235	#95	—	2	1	no	—
236	#95	—	2	2	no	—
237	#95	C₃×D₄	1	1	yes	characteristic
238	#95	C₃×D₄	1	1	yes	characteristic
239	#95	C₃×D₄	1	2	yes	—
240	C₂³×C₃	—	2	4	no	—
241	C₂³×C₃	—	2	2	no	—
242	C₂³×C₃	—	4	1	no	—
243	C₂³×C₃	—	4	2	no	—
244	C₂³×C₃	—	4	1	no	—
245	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
246	C₃×Q₈	—	2	2	no	—
247	C₃×Q₈	—	2	4	no	—
248	C₃×Q₈	C₂×C₄²	1	4	yes	—
249	C₃×D₄	—	2	2	no	—
250	C₃×D₄	—	2	4	no	—
251	C₃×D₄	C₂×C₄²	1	4	yes	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	1	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	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	4	2	no	—
266	C₂×C₃×C₄	—	4	1	no	—
267	C₂×C₃×C₄	—	4	2	no	—
268	C₂×C₃×C₄	—	4	2	no	—
269	C₂×C₃×C₄	—	4	2	no	—
270	C₂×C₃×C₄	—	4	2	no	—
271	C₂×C₃×C₄	—	4	1	no	—
272	C₂×C₃×C₄	—	8	8	no	—
273	C₂×C₃×C₄	—	8	4	no	—
274	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
275	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
276	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
277	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
278	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
279	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×#41	1	2	yes	—
281	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
282	C₃×C₈	—	2	2	no	—
283	C₃×C₈	—	2	4	no	—
284	C₃×C₈	C₂×C₄²	1	4	yes	—
285	C₂⁴	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
289	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
293	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	8	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	—	8	2	no	—
304	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
306	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
307	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
308	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
309	SD₁₆	C₃×C₄²	1	16	yes	complemented
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
314	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
315	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
316	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
324	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
325	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
326	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₄²	—	2	8	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	8	1	no	—
332	C₄²	—	8	1	no	—
333	C₄²	—	8	2	no	—
334	C₄²	—	8	2	no	—
335	C₄²	C₂²×C₃×C₄	1	2	yes	—
336	C₄²	C₂²×C₃×C₄	1	4	yes	—
337	C₄²	C₃×#41	1	4	yes	—
338	C₄²	C₃×#41	1	2	yes	—
339	C₂²×C₃	—	2	4	no	—
340	C₂²×C₃	—	4	4	no	—
341	C₂²×C₃	—	4	4	no	—
342	C₂²×C₃	—	4	2	no	—
343	C₂²×C₃	—	4	2	no	—
344	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
345	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
346	C₂²×C₃	#576	1	1	yes	characteristic
347	C₂²×C₃	#577	1	2	yes	—
348	C₂²×C₃	#578	1	1	yes	characteristic
349	C₃×C₄	—	2	4	no	—
350	C₃×C₄	—	2	4	no	—
351	C₃×C₄	—	2	2	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	2	4	no	—
354	C₃×C₄	—	4	4	no	—
355	C₃×C₄	—	4	4	no	—
356	C₃×C₄	—	4	2	no	—
357	C₃×C₄	—	4	2	no	—
358	C₃×C₄	C₂²×C₄²	1	1	yes	characteristic
359	C₃×C₄	C₄×#41	1	1	yes	characteristic
360	C₃×C₄	C₄×#41	1	2	yes	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	1	no	—
366	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	2	4	no	—
369	Q₈	C₂×C₃×C₄²	1	4	yes	—
370	D₄	—	2	2	no	—
371	D₄	—	2	4	no	—
372	D₄	C₂×C₃×C₄²	1	4	yes	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	8	8	no	—
394	C₂×C₄	—	8	4	no	—
395	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
396	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
397	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
398	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
399	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
400	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
401	C₂×C₄	C₂×C₃×#41	1	2	yes	—
402	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	2	4	no	—
405	C₈	C₂×C₃×C₄²	1	4	yes	—
406	C₂×C₃	—	4	4	no	—
407	C₂×C₃	C₄²×D₄	1	1	yes	characteristic
408	C₂×C₃	#2946	1	2	yes	—
409	C₂×C₃	#2947	1	2	yes	—
410	C₂×C₃	#2949	1	1	yes	characteristic
411	C₂×C₃	#2951	1	1	yes	characteristic
412	C₂²	—	2	4	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
418	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
419	C₂²	C₃×#576	1	1	yes	characteristic
420	C₂²	C₃×#577	1	2	yes	—
421	C₂²	C₃×#578	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	4	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	C₂²×C₃×C₄²	1	1	yes	characteristic
432	C₄	C₃×C₄×#41	1	1	yes	characteristic
433	C₄	C₃×C₄×#41	1	2	yes	—
434	C₃	#20504	1	1	yes	characteristic, direct product factor, Sylow
435	C₂	—	4	4	no	—
436	C₂	C₃×C₄²×D₄	1	1	yes	characteristic
437	C₂	C₃×#2946	1	2	yes	—
438	C₂	C₃×#2947	1	2	yes	—
439	C₂	C₃×#2949	1	1	yes	characteristic
440	C₂	C₃×#2951	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator	C₄	C₂²×C₃×C₄²
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#2276	C₂	semidirect
5. C₃×#1776	C₂	semidirect
6. C₃×C₄×#107	C₂	semidirect
7. C₃×#1763	C₂	semidirect
9. C₃×C₄×#103	C₂	semidirect
11. C₃×#1726	C₂	semidirect
12. #20504	C₃	direct (N × H)
18. C₃×#440	C₄	semidirect
19. C₃×C₄×SD₁₆	C₄	semidirect
46. #2276	C₂×C₃	semidirect
48. #1776	C₂×C₃	semidirect
49. C₄×#107	C₂×C₃	semidirect
50. #1763	C₂×C₃	semidirect
52. C₄×#103	C₂×C₃	semidirect
54. #1726	C₂×C₃	semidirect
66. C₃×C₄×Q₈	C₂×C₄	semidirect
67. C₃×C₄×Q₈	C₂×C₄	semidirect
88. C₃×#107	C₂×C₄	semidirect
89. C₃×#106	C₂×C₄	semidirect
90. C₃×#103	C₂×C₄	semidirect
91. C₃×#103	C₂×C₄	semidirect
95. C₃×#97	C₂×C₄	semidirect
97. C₃×C₄×C₈	C₂×C₄	semidirect
110. #440	C₃×C₄	semidirect
111. C₄×SD₁₆	C₃×C₄	semidirect
160. C₃×SD₁₆	C₄²	semidirect
201. C₄×Q₈	C₂×C₃×C₄	semidirect
202. C₄×Q₈	C₂×C₃×C₄	semidirect
223. #107	C₂×C₃×C₄	semidirect
224. #106	C₂×C₃×C₄	semidirect
225. #103	C₂×C₃×C₄	semidirect
226. #103	C₂×C₃×C₄	semidirect
230. #97	C₂×C₃×C₄	semidirect
232. C₄×C₈	C₂×C₃×C₄	semidirect
309. SD₁₆	C₃×C₄²	semidirect
434. C₃	#20504	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×#440	2
C₂×C₃×C₄×SD₁₆	2
C₃×#2276	2
C₃×#2275	2
C₃×#1776	2
C₃×C₄×#107	2
C₃×#1763	2
C₃×#1762	2
C₃×C₄×#103	2
C₃×C₄×#102	2
C₃×#1726	2
#20504	3

Subgroups — C3×#20504 #10639111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#20504 #10639111