Subgroups — C₃×#35982 #10654589

Order 768.

2568 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2633	C₂	1	2	yes	maximal, complemented
4	C₃×#2625	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2598	C₂	1	2	yes	maximal, complemented
6	C₃×#2562	C₂	1	2	yes	maximal, complemented
7	C₃×#2480	C₂	1	4	yes	maximal, complemented
8	C₃×#2454	C₂	1	2	yes	maximal, complemented
9	C₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2427	C₂	1	2	yes	maximal, complemented
11	C₃×#2418	C₂	1	4	yes	maximal, complemented
12	C₃×#2408	C₂	1	1	yes	maximal, characteristic
13	C₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2392	C₂	1	2	yes	maximal, complemented
15	C₃×#2367	C₂	1	2	yes	maximal, complemented
16	C₃×#2361	C₂	1	2	yes	maximal, complemented
17	C₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
18	#35982	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
20	C₃×#552	—	2	8	no	—
21	C₂×C₃×#126	C₂²	1	2	yes	—
22	C₂×C₃×#125	C₂²	1	2	yes	complemented
23	C₂×C₃×#125	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#124	C₂²	1	2	yes	—
25	C₂×C₃×#123	C₂²	1	2	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#121	C₂²	1	2	yes	—
29	C₂×C₃×#120	C₂²	1	2	yes	—
30	C₃×#518	—	2	8	no	—
31	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
33	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
34	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
35	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
36	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
38	C₂×C₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₃×#117	C₂²	1	1	yes	characteristic
40	C₂×C₃×#117	C₂²	1	2	yes	complemented
41	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	—
43	C₃×#400	C₂²	1	2	yes	complemented
44	C₃×#400	C₂²	1	1	yes	characteristic, complemented
45	C₃×#399	C₂²	1	4	yes	complemented
46	C₃×#399	C₂²	1	1	yes	characteristic, complemented
47	C₃×#398	C₂²	1	2	yes	complemented
48	C₃×#398	C₂²	1	1	yes	characteristic, complemented
49	C₃×#397	C₂²	1	4	yes	—
50	C₃×#397	C₂²	1	2	yes	—
51	C₃×#397	C₂²	1	4	yes	complemented
52	C₃×#397	C₂²	1	1	yes	characteristic, complemented
53	C₃×#396	C₂²	1	4	yes	complemented
54	C₃×#394	C₂²	1	2	yes	—
55	C₃×#394	C₂²	1	2	yes	—
56	C₃×#394	C₂²	1	2	yes	—
57	C₃×#394	C₂²	1	2	yes	—
58	C₃×#394	C₂²	1	4	yes	complemented
59	C₃×#392	C₂²	1	2	yes	—
60	C₃×#391	C₂²	1	2	yes	complemented
61	C₃×#390	C₂²	1	2	yes	—
62	C₃×#390	C₂²	1	2	yes	—
63	C₃×#389	C₂²	1	2	yes	complemented
64	C₃×#389	C₂²	1	2	yes	complemented
65	C₃×#388	C₂²	1	4	yes	—
66	C₃×#388	C₂²	1	4	yes	complemented
67	C₃×#388	C₂²	1	4	yes	complemented
68	C₃×#388	C₂²	1	4	yes	complemented
69	C₃×#386	C₂²	1	4	yes	complemented
70	C₃×#386	C₂²	1	4	yes	complemented
71	C₃×#385	C₂²	1	4	yes	complemented
72	C₃×#385	C₂²	1	4	yes	complemented
73	C₃×#385	C₂²	1	4	yes	complemented
74	C₃×#383	C₂²	1	2	yes	complemented
75	C₃×#380	C₂²	1	1	yes	characteristic
76	C₃×#380	C₂²	1	4	yes	complemented
77	C₃×#380	C₂²	1	4	yes	complemented
78	C₃×#379	C₂²	1	2	yes	—
79	C₃×#379	C₂²	1	4	yes	—
80	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
82	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
83	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
84	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
85	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
86	C₂×#552	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×#518	C₂×C₃	1	1	yes	characteristic, complemented
88	#2633	C₂×C₃	1	2	yes	complemented
89	#2625	C₂×C₃	1	1	yes	characteristic, complemented
90	#2598	C₂×C₃	1	2	yes	complemented
91	#2562	C₂×C₃	1	2	yes	complemented
92	#2480	C₂×C₃	1	4	yes	complemented
93	#2454	C₂×C₃	1	2	yes	complemented
94	#2435	C₂×C₃	1	1	yes	characteristic, complemented
95	#2427	C₂×C₃	1	2	yes	complemented
96	#2418	C₂×C₃	1	4	yes	complemented
97	#2408	C₂×C₃	1	1	yes	characteristic
98	#2395	C₂×C₃	1	1	yes	characteristic, complemented
99	#2392	C₂×C₃	1	2	yes	complemented
100	#2367	C₂×C₃	1	2	yes	complemented
101	#2361	C₂×C₃	1	2	yes	complemented
102	#2347	C₂×C₃	1	1	yes	characteristic, complemented
103	C₂⁵×C₃	C₂³	1	2	yes	—
104	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
105	C₂²×C₃×D₄	—	2	8	no	—
106	C₂²×C₃×D₄	—	2	4	no	—
107	C₂²×C₃×D₄	C₂³	1	2	yes	—
108	C₂²×C₃×D₄	C₂³	1	4	yes	—
109	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
110	C₂²×C₃×D₄	C₂³	1	2	yes	—
111	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
112	C₂³×C₃×C₄	C₂³	1	2	yes	—
113	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
114	C₂³×C₃×C₄	C₂³	1	4	yes	—
115	C₂³×C₃×C₄	C₂³	1	4	yes	—
116	C₃×#126	—	2	8	no	—
117	C₃×#125	—	2	4	no	—
118	C₃×#125	—	2	8	no	—
119	C₃×#124	—	2	8	no	—
120	C₃×#123	—	2	8	no	—
121	C₃×C₂²⋊Q₈	—	2	4	no	—
122	C₃×C₂²⋊Q₈	—	2	4	no	—
123	C₃×#121	—	2	8	no	—
124	C₃×#120	—	4	4	no	—
125	C₃×C₄×Q₈	—	2	4	no	—
126	C₃×C₄×D₄	—	2	4	no	—
127	C₃×C₄×D₄	—	2	8	no	—
128	C₃×C₄×D₄	—	2	8	no	—
129	C₃×C₄×D₄	—	2	8	no	—
130	C₃×C₄×D₄	—	2	8	no	—
131	C₃×C₄×D₄	—	4	8	no	—
132	C₃×#117	—	2	4	no	—
133	C₃×#117	—	2	8	no	—
134	C₃×#117	D₄	1	8	yes	complemented
135	C₂×C₃×C₄⋊C₄	—	2	4	no	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₂²⋊C₄	—	2	16	no	—
154	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₄²	C₂³	1	2	yes	—
174	C₂×C₃×C₄²	C₂³	1	2	yes	—
175	C₂×C₃×C₄²	C₂³	1	2	yes	—
176	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄²	C₂³	1	4	yes	—
178	C₂×C₃×C₄²	C₂³	1	2	yes	—
179	C₃×#95	C₂³	1	1	yes	characteristic
180	C₃×#95	C₂³	1	1	yes	characteristic
181	C₃×#95	C₂³	1	2	yes	—
182	C₃×#95	C₂³	1	2	yes	—
183	C₃×#95	C₂³	1	2	yes	—
184	C₃×#95	C₂³	1	4	yes	—
185	C₃×#95	C₂³	1	2	yes	—
186	C₃×#95	C₂³	1	2	yes	—
187	C₃×#95	C₂³	1	4	yes	—
188	C₃×#95	C₂³	1	4	yes	—
189	C₃×#95	C₂³	1	4	yes	—
190	C₃×#95	C₂³	1	4	yes	—
191	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
192	#552	—	2	8	no	—
193	C₂×#126	C₂²×C₃	1	2	yes	—
194	C₂×#125	C₂²×C₃	1	2	yes	complemented
195	C₂×#125	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₂×#124	C₂²×C₃	1	2	yes	—
197	C₂×#123	C₂²×C₃	1	2	yes	—
198	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
199	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
200	C₂×#121	C₂²×C₃	1	2	yes	—
201	C₂×#120	C₂²×C₃	1	2	yes	—
202	#518	—	2	8	no	—
203	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
204	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
205	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
206	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
207	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
209	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
210	C₂×#117	C₂²×C₃	1	1	yes	characteristic
211	C₂×#117	C₂²×C₃	1	1	yes	characteristic
212	C₂×#117	C₂²×C₃	1	2	yes	complemented
213	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
214	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
215	#400	C₂²×C₃	1	1	yes	characteristic, complemented
216	#400	C₂²×C₃	1	2	yes	complemented
217	#399	C₂²×C₃	1	1	yes	characteristic, complemented
218	#399	C₂²×C₃	1	4	yes	complemented
219	#398	C₂²×C₃	1	2	yes	complemented
220	#398	C₂²×C₃	1	1	yes	characteristic, complemented
221	#397	C₂²×C₃	1	4	yes	—
222	#397	C₂²×C₃	1	2	yes	—
223	#397	C₂²×C₃	1	4	yes	complemented
224	#397	C₂²×C₃	1	1	yes	characteristic, complemented
225	#396	C₂²×C₃	1	4	yes	complemented
226	#394	C₂²×C₃	1	2	yes	—
227	#394	C₂²×C₃	1	2	yes	—
228	#394	C₂²×C₃	1	2	yes	—
229	#394	C₂²×C₃	1	2	yes	—
230	#394	C₂²×C₃	1	4	yes	complemented
231	#392	C₂²×C₃	1	2	yes	—
232	#391	C₂²×C₃	1	2	yes	complemented
233	#390	C₂²×C₃	1	2	yes	—
234	#390	C₂²×C₃	1	2	yes	—
235	#389	C₂²×C₃	1	2	yes	complemented
236	#389	C₂²×C₃	1	2	yes	complemented
237	#388	C₂²×C₃	1	4	yes	—
238	#388	C₂²×C₃	1	4	yes	complemented
239	#388	C₂²×C₃	1	4	yes	complemented
240	#388	C₂²×C₃	1	4	yes	complemented
241	#386	C₂²×C₃	1	4	yes	complemented
242	#386	C₂²×C₃	1	4	yes	complemented
243	#385	C₂²×C₃	1	4	yes	complemented
244	#385	C₂²×C₃	1	4	yes	complemented
245	#385	C₂²×C₃	1	4	yes	complemented
246	#383	C₂²×C₃	1	2	yes	complemented
247	#380	C₂²×C₃	1	1	yes	characteristic
248	#380	C₂²×C₃	1	4	yes	complemented
249	#380	C₂²×C₃	1	4	yes	complemented
250	#379	C₂²×C₃	1	2	yes	—
251	#379	C₂²×C₃	1	4	yes	—
252	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
253	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
254	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
255	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
256	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
257	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
258	C₂⁴×C₃	—	2	4	no	—
259	C₂⁴×C₃	—	2	8	no	—
260	C₂⁴×C₃	—	4	2	no	—
261	C₂⁴×C₃	—	4	4	no	—
262	C₂⁴×C₃	—	4	2	no	—
263	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₃	C₂⁴	1	4	yes	—
265	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
266	C₂×C₃×Q₈	—	2	2	no	—
267	C₂×C₃×Q₈	—	2	4	no	—
268	C₂×C₃×D₄	—	2	32	no	—
269	C₂×C₃×D₄	—	2	8	no	—
270	C₂×C₃×D₄	—	2	2	no	—
271	C₂×C₃×D₄	—	2	8	no	—
272	C₂×C₃×D₄	—	2	8	no	—
273	C₂×C₃×D₄	—	2	2	no	—
274	C₂×C₃×D₄	—	2	4	no	—
275	C₂×C₃×D₄	—	2	4	no	—
276	C₂×C₃×D₄	—	2	4	no	—
277	C₂×C₃×D₄	—	4	4	no	—
278	C₂×C₃×D₄	—	4	1	no	—
279	C₂×C₃×D₄	#41	1	8	yes	—
280	C₂²×C₃×C₄	—	2	4	no	—
281	C₂²×C₃×C₄	—	2	4	no	—
282	C₂²×C₃×C₄	—	2	4	no	—
283	C₂²×C₃×C₄	—	2	2	no	—
284	C₂²×C₃×C₄	—	2	4	no	—
285	C₂²×C₃×C₄	—	2	8	no	—
286	C₂²×C₃×C₄	—	2	8	no	—
287	C₂²×C₃×C₄	—	4	2	no	—
288	C₂²×C₃×C₄	—	4	4	no	—
289	C₂²×C₃×C₄	—	4	4	no	—
290	C₂²×C₃×C₄	—	4	4	no	—
291	C₂²×C₃×C₄	—	4	4	no	—
292	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
293	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
294	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
295	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
296	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
297	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
298	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
299	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
300	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
301	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
302	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
303	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
304	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
305	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
306	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
307	C₃×C₄⋊C₄	—	2	2	no	—
308	C₃×C₄⋊C₄	—	2	4	no	—
309	C₃×C₄⋊C₄	—	2	2	no	—
310	C₃×C₄⋊C₄	—	2	2	no	—
311	C₃×C₄⋊C₄	—	2	4	no	—
312	C₃×C₄⋊C₄	—	2	4	no	—
313	C₃×C₄⋊C₄	—	2	2	no	—
314	C₃×C₄⋊C₄	—	2	4	no	—
315	C₃×C₄⋊C₄	—	2	4	no	—
316	C₃×C₄⋊C₄	—	2	4	no	—
317	C₃×C₄⋊C₄	—	2	4	no	—
318	C₃×C₄⋊C₄	—	4	4	no	—
319	C₃×C₄⋊C₄	—	4	2	no	—
320	C₃×C₄⋊C₄	—	4	2	no	—
321	C₃×C₄⋊C₄	—	4	4	no	—
322	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
323	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
324	C₃×C₂²⋊C₄	—	2	4	no	—
325	C₃×C₂²⋊C₄	—	2	2	no	—
326	C₃×C₂²⋊C₄	—	2	4	no	—
327	C₃×C₂²⋊C₄	—	2	8	no	—
328	C₃×C₂²⋊C₄	—	2	8	no	—
329	C₃×C₂²⋊C₄	—	2	8	no	—
330	C₃×C₂²⋊C₄	—	2	4	no	—
331	C₃×C₂²⋊C₄	—	2	8	no	—
332	C₃×C₂²⋊C₄	—	2	8	no	—
333	C₃×C₂²⋊C₄	—	2	2	no	—
334	C₃×C₂²⋊C₄	—	2	4	no	—
335	C₃×C₂²⋊C₄	—	4	4	no	—
336	C₃×C₂²⋊C₄	—	4	2	no	—
337	C₃×C₂²⋊C₄	—	4	4	no	—
338	C₃×C₂²⋊C₄	—	4	2	no	—
339	C₃×C₂²⋊C₄	—	4	4	no	—
340	C₃×C₂²⋊C₄	—	4	2	no	—
341	C₃×C₂²⋊C₄	—	4	4	no	—
342	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
343	C₃×C₄²	—	2	4	no	—
344	C₃×C₄²	—	2	4	no	—
345	C₃×C₄²	—	2	2	no	—
346	C₃×C₄²	—	2	4	no	—
347	C₃×C₄²	—	4	4	no	—
348	C₃×C₄²	C₂×D₄	1	8	yes	—
349	C₂⁵	C₂³×C₃	1	2	yes	—
350	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
351	C₂²×D₄	—	2	8	no	—
352	C₂²×D₄	—	2	4	no	—
353	C₂²×D₄	C₂³×C₃	1	2	yes	—
354	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
355	C₂²×D₄	C₂³×C₃	1	4	yes	—
356	C₂²×D₄	C₂³×C₃	1	2	yes	—
357	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₃	1	2	yes	—
359	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₃	1	4	yes	—
361	C₂³×C₄	C₂³×C₃	1	4	yes	—
362	#126	—	2	8	no	—
363	#125	—	2	4	no	—
364	#125	—	2	8	no	—
365	#124	—	2	8	no	—
366	#123	—	2	8	no	—
367	C₂²⋊Q₈	—	2	4	no	—
368	C₂²⋊Q₈	—	2	4	no	—
369	#121	—	2	8	no	—
370	#120	—	4	4	no	—
371	C₄×Q₈	—	2	4	no	—
372	C₄×D₄	—	2	4	no	—
373	C₄×D₄	—	2	8	no	—
374	C₄×D₄	—	2	8	no	—
375	C₄×D₄	—	2	8	no	—
376	C₄×D₄	—	2	8	no	—
377	C₄×D₄	—	4	8	no	—
378	#117	—	2	4	no	—
379	#117	—	2	8	no	—
380	#117	C₃×D₄	1	8	yes	complemented
381	C₂×C₄⋊C₄	—	2	4	no	—
382	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	—	2	16	no	—
400	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₄²	C₂³×C₃	1	2	yes	—
420	C₂×C₄²	C₂³×C₃	1	2	yes	—
421	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₃	1	2	yes	—
423	C₂×C₄²	C₂³×C₃	1	4	yes	—
424	C₂×C₄²	C₂³×C₃	1	2	yes	—
425	#95	C₂³×C₃	1	1	yes	characteristic
426	#95	C₂³×C₃	1	1	yes	characteristic
427	#95	C₂³×C₃	1	2	yes	—
428	#95	C₂³×C₃	1	2	yes	—
429	#95	C₂³×C₃	1	2	yes	—
430	#95	C₂³×C₃	1	4	yes	—
431	#95	C₂³×C₃	1	2	yes	—
432	#95	C₂³×C₃	1	2	yes	—
433	#95	C₂³×C₃	1	4	yes	—
434	#95	C₂³×C₃	1	4	yes	—
435	#95	C₂³×C₃	1	4	yes	—
436	#95	C₂³×C₃	1	4	yes	—
437	C₂³×C₃	—	2	16	no	—
438	C₂³×C₃	—	2	1	no	—
439	C₂³×C₃	—	2	4	no	—
440	C₂³×C₃	—	2	2	no	—
441	C₂³×C₃	—	2	2	no	—
442	C₂³×C₃	—	2	4	no	—
443	C₂³×C₃	—	2	4	no	—
444	C₂³×C₃	—	2	1	no	—
445	C₂³×C₃	—	2	4	no	—
446	C₂³×C₃	—	2	4	no	—
447	C₂³×C₃	—	2	2	no	—
448	C₂³×C₃	—	2	2	no	—
449	C₂³×C₃	—	2	1	no	—
450	C₂³×C₃	—	2	4	no	—
451	C₂³×C₃	—	2	1	no	—
452	C₂³×C₃	—	8	4	no	—
453	C₂³×C₃	—	8	4	no	—
454	C₂³×C₃	—	8	8	no	—
455	C₂³×C₃	—	8	8	no	—
456	C₂³×C₃	C₂²×D₄	1	2	yes	—
457	C₂³×C₃	C₂×#41	1	8	yes	—
458	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
459	C₂³×C₃	C₂⁵	1	1	yes	characteristic
460	C₃×Q₈	—	4	4	no	—
461	C₃×D₄	—	2	16	no	—
462	C₃×D₄	—	2	16	no	—
463	C₃×D₄	—	4	4	no	—
464	C₃×D₄	—	4	16	no	—
465	C₂×C₃×C₄	—	2	2	no	—
466	C₂×C₃×C₄	—	2	2	no	—
467	C₂×C₃×C₄	—	2	4	no	—
468	C₂×C₃×C₄	—	2	2	no	—
469	C₂×C₃×C₄	—	2	8	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	2	no	—
472	C₂×C₃×C₄	—	2	2	no	—
473	C₂×C₃×C₄	—	2	2	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	2	no	—
477	C₂×C₃×C₄	—	2	2	no	—
478	C₂×C₃×C₄	—	2	2	no	—
479	C₂×C₃×C₄	—	2	2	no	—
480	C₂×C₃×C₄	—	2	4	no	—
481	C₂×C₃×C₄	—	2	4	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	2	4	no	—
484	C₂×C₃×C₄	—	2	2	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	2	no	—
487	C₂×C₃×C₄	—	2	2	no	—
488	C₂×C₃×C₄	—	2	2	no	—
489	C₂×C₃×C₄	—	2	2	no	—
490	C₂×C₃×C₄	—	2	2	no	—
491	C₂×C₃×C₄	—	2	2	no	—
492	C₂×C₃×C₄	—	2	4	no	—
493	C₂×C₃×C₄	—	2	2	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	2	no	—
497	C₂×C₃×C₄	—	4	8	no	—
498	C₂×C₃×C₄	—	4	4	no	—
499	C₂×C₃×C₄	—	8	8	no	—
500	C₂×C₃×C₄	—	8	8	no	—
501	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
502	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
503	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
504	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
505	C₂×C₃×C₄	C₂×#41	1	4	yes	—
506	C₂⁴	—	2	4	no	—
507	C₂⁴	—	2	8	no	—
508	C₂⁴	—	4	2	no	—
509	C₂⁴	—	4	2	no	—
510	C₂⁴	—	4	4	no	—
511	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
512	C₂⁴	C₂⁴×C₃	1	4	yes	—
513	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	2	4	no	—
516	C₂×D₄	—	2	32	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	8	no	—
520	C₂×D₄	—	2	8	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	4	4	no	—
526	C₂×D₄	—	4	1	no	—
527	C₂×D₄	C₃×#41	1	8	yes	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	8	no	—
534	C₂²×C₄	—	2	8	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	4	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	4	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	4	4	no	—
567	C₄⋊C₄	—	4	4	no	—
568	C₄⋊C₄	—	4	2	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
571	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	8	no	—
576	C₂²⋊C₄	—	2	8	no	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	2	8	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	4	no	—
586	C₂²⋊C₄	—	4	4	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	4	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
591	C₄²	—	2	4	no	—
592	C₄²	—	2	4	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	4	no	—
595	C₄²	—	4	4	no	—
596	C₄²	C₂×C₃×D₄	1	8	yes	—
597	C₂²×C₃	—	2	2	no	—
598	C₂²×C₃	—	2	8	no	—
599	C₂²×C₃	—	2	2	no	—
600	C₂²×C₃	—	2	2	no	—
601	C₂²×C₃	—	2	2	no	—
602	C₂²×C₃	—	2	4	no	—
603	C₂²×C₃	—	2	8	no	—
604	C₂²×C₃	—	2	8	no	—
605	C₂²×C₃	—	4	1	no	—
606	C₂²×C₃	—	4	4	no	—
607	C₂²×C₃	—	4	4	no	—
608	C₂²×C₃	—	4	1	no	—
609	C₂²×C₃	—	4	4	no	—
610	C₂²×C₃	—	4	2	no	—
611	C₂²×C₃	—	4	2	no	—
612	C₂²×C₃	—	4	4	no	—
613	C₂²×C₃	—	4	2	no	—
614	C₂²×C₃	—	8	16	no	—
615	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
616	C₂²×C₃	C₂²×#41	1	2	yes	—
617	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
618	C₂²×C₃	#585	1	1	yes	characteristic
619	C₂²×C₃	#585	1	2	yes	—
620	C₃×C₄	—	2	2	no	—
621	C₃×C₄	—	2	4	no	—
622	C₃×C₄	—	2	4	no	—
623	C₃×C₄	—	4	1	no	—
624	C₃×C₄	—	4	2	no	—
625	C₃×C₄	—	4	2	no	—
626	C₃×C₄	—	4	2	no	—
627	C₃×C₄	—	4	1	no	—
628	C₃×C₄	—	4	1	no	—
629	C₃×C₄	—	4	2	no	—
630	C₃×C₄	—	4	2	no	—
631	C₃×C₄	—	4	4	no	—
632	C₃×C₄	—	4	2	no	—
633	C₃×C₄	#525	1	4	yes	—
634	C₂³	—	2	16	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	4	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	4	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	4	no	—
643	C₂³	—	2	4	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	8	4	no	—
650	C₂³	—	8	4	no	—
651	C₂³	—	8	8	no	—
652	C₂³	—	8	8	no	—
653	C₂³	C₂²×C₃×D₄	1	2	yes	—
654	C₂³	C₂×C₃×#41	1	8	yes	—
655	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
656	C₂³	C₂⁵×C₃	1	1	yes	characteristic
657	Q₈	—	4	4	no	—
658	D₄	—	2	16	no	—
659	D₄	—	2	16	no	—
660	D₄	—	4	4	no	—
661	D₄	—	4	16	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	8	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	4	8	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	8	8	no	—
697	C₂×C₄	—	8	8	no	—
698	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
699	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
700	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
701	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
702	C₂×C₄	C₂×C₃×#41	1	4	yes	—
703	C₂×C₃	—	4	2	no	—
704	C₂×C₃	—	4	8	no	—
705	C₂×C₃	—	4	2	no	—
706	C₂×C₃	C₂×#525	1	1	yes	characteristic
707	C₂×C₃	#3488	1	1	yes	characteristic
708	C₂×C₃	#3500	1	1	yes	characteristic
709	C₂×C₃	#3513	1	2	yes	—
710	C₂×C₃	#3521	1	2	yes	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	8	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	2	8	no	—
718	C₂²	—	2	8	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	8	16	no	—
729	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
730	C₂²	C₂²×C₃×#41	1	2	yes	—
731	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
732	C₂²	C₃×#585	1	1	yes	characteristic
733	C₂²	C₃×#585	1	2	yes	—
734	C₄	—	2	2	no	—
735	C₄	—	2	4	no	—
736	C₄	—	2	4	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	4	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	C₃×#525	1	4	yes	—
748	C₃	#35982	1	1	yes	characteristic, direct product factor, Sylow
749	C₂	—	4	2	no	—
750	C₂	—	4	8	no	—
751	C₂	—	4	2	no	—
752	C₂	C₂×C₃×#525	1	1	yes	characteristic
753	C₂	C₃×#3488	1	1	yes	characteristic
754	C₂	C₃×#3500	1	1	yes	characteristic
755	C₂	C₃×#3513	1	2	yes	—
756	C₂	C₃×#3521	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2408	C₂
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×#552	C₂	semidirect
2. C₂×C₃×#518	C₂	semidirect
3. C₃×#2633	C₂	semidirect
4. C₃×#2625	C₂	semidirect
5. C₃×#2598	C₂	semidirect
6. C₃×#2562	C₂	semidirect
7. C₃×#2480	C₂	semidirect
8. C₃×#2454	C₂	semidirect
9. C₃×#2435	C₂	semidirect
10. C₃×#2427	C₂	semidirect
11. C₃×#2418	C₂	semidirect
13. C₃×#2395	C₂	semidirect
14. C₃×#2392	C₂	semidirect
15. C₃×#2367	C₂	semidirect
16. C₃×#2361	C₂	semidirect
17. C₃×#2347	C₂	semidirect
18. #35982	C₃	direct (N × H)
22. C₂×C₃×#125	C₂²	semidirect
23. C₂×C₃×#125	C₂²	semidirect
27. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₃×C₄×Q₈	C₂²	semidirect
37. C₂×C₃×C₄×D₄	C₂²	semidirect
40. C₂×C₃×#117	C₂²	semidirect
41. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
43. C₃×#400	C₂²	semidirect
44. C₃×#400	C₂²	semidirect
45. C₃×#399	C₂²	semidirect
46. C₃×#399	C₂²	semidirect
47. C₃×#398	C₂²	semidirect
48. C₃×#398	C₂²	semidirect
51. C₃×#397	C₂²	semidirect
52. C₃×#397	C₂²	semidirect
53. C₃×#396	C₂²	semidirect
58. C₃×#394	C₂²	semidirect
60. C₃×#391	C₂²	semidirect
63. C₃×#389	C₂²	semidirect
64. C₃×#389	C₂²	semidirect
66. C₃×#388	C₂²	semidirect
67. C₃×#388	C₂²	semidirect
68. C₃×#388	C₂²	semidirect
69. C₃×#386	C₂²	semidirect
70. C₃×#386	C₂²	semidirect
71. C₃×#385	C₂²	semidirect
72. C₃×#385	C₂²	semidirect
73. C₃×#385	C₂²	semidirect
74. C₃×#383	C₂²	semidirect
76. C₃×#380	C₂²	semidirect
77. C₃×#380	C₂²	semidirect
80. C₃×C₄×C₄⋊C₄	C₂²	semidirect
81. C₃×C₄×C₄⋊C₄	C₂²	semidirect
82. C₃×C₄×C₄⋊C₄	C₂²	semidirect
84. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
85. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
86. C₂×#552	C₂×C₃	semidirect
87. C₂×#518	C₂×C₃	semidirect
88. #2633	C₂×C₃	semidirect
89. #2625	C₂×C₃	semidirect
90. #2598	C₂×C₃	semidirect
91. #2562	C₂×C₃	semidirect
92. #2480	C₂×C₃	semidirect
93. #2454	C₂×C₃	semidirect
94. #2435	C₂×C₃	semidirect
95. #2427	C₂×C₃	semidirect
96. #2418	C₂×C₃	semidirect
98. #2395	C₂×C₃	semidirect
99. #2392	C₂×C₃	semidirect
100. #2367	C₂×C₃	semidirect
101. #2361	C₂×C₃	semidirect
102. #2347	C₂×C₃	semidirect
134. C₃×#117	D₄	semidirect
194. C₂×#125	C₂²×C₃	semidirect
195. C₂×#125	C₂²×C₃	semidirect
199. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
203. C₂×C₄×Q₈	C₂²×C₃	semidirect
209. C₂×C₄×D₄	C₂²×C₃	semidirect
212. C₂×#117	C₂²×C₃	semidirect
213. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
215. #400	C₂²×C₃	semidirect
216. #400	C₂²×C₃	semidirect
217. #399	C₂²×C₃	semidirect
218. #399	C₂²×C₃	semidirect
219. #398	C₂²×C₃	semidirect
220. #398	C₂²×C₃	semidirect
223. #397	C₂²×C₃	semidirect
224. #397	C₂²×C₃	semidirect
225. #396	C₂²×C₃	semidirect
230. #394	C₂²×C₃	semidirect
232. #391	C₂²×C₃	semidirect
235. #389	C₂²×C₃	semidirect
236. #389	C₂²×C₃	semidirect
238. #388	C₂²×C₃	semidirect
239. #388	C₂²×C₃	semidirect
240. #388	C₂²×C₃	semidirect
241. #386	C₂²×C₃	semidirect
242. #386	C₂²×C₃	semidirect
243. #385	C₂²×C₃	semidirect
244. #385	C₂²×C₃	semidirect
245. #385	C₂²×C₃	semidirect
246. #383	C₂²×C₃	semidirect
248. #380	C₂²×C₃	semidirect
249. #380	C₂²×C₃	semidirect
252. C₄×C₄⋊C₄	C₂²×C₃	semidirect
253. C₄×C₄⋊C₄	C₂²×C₃	semidirect
254. C₄×C₄⋊C₄	C₂²×C₃	semidirect
256. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
257. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
380. #117	C₃×D₄	semidirect
748. C₃	#35982	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×#552	2
C₂×C₃×#518	2
C₃×#2633	2
C₃×#2625	2
C₃×#2598	2
C₃×#2562	2
C₃×#2480	2
C₃×#2454	2
C₃×#2435	2
C₃×#2427	2
C₃×#2418	2
C₃×#2408	2
C₃×#2395	2
C₃×#2392	2
C₃×#2367	2
C₃×#2361	2
C₃×#2347	2
#35982	3

Subgroups — C3×#35982 #10654589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35982 #10654589