Subgroups — C₃×#35987 #10654594

Order 768.

2752 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2624	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2623	C₂	1	2	yes	maximal, complemented
5	C₃×#2501	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2498	C₂	1	2	yes	maximal, complemented
7	C₃×#2487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2482	C₂	1	2	yes	maximal, complemented
9	C₃×#2448	C₂	1	2	yes	maximal, complemented
10	C₃×#2443	C₂	1	4	yes	maximal, complemented
11	C₃×#2423	C₂	1	2	yes	maximal, complemented
12	C₃×#2418	C₂	1	4	yes	maximal, complemented
13	C₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#399	C₂	1	2	yes	maximal, complemented
15	C₃×D₄×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
16	C₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
18	#35987	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
21	C₃×#546	—	2	8	no	—
22	C₂×C₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₃×#123	C₂²	1	2	yes	—
24	C₂×C₃×#123	C₂²	1	4	yes	complemented
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₃×#121	C₂²	1	2	yes	—
28	C₂×C₃×#120	C₂²	1	2	yes	—
29	C₃×#520	—	2	8	no	—
30	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
31	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
35	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
36	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×#117	C₂²	1	2	yes	complemented
38	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
39	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₃×C₄⋊C₄	C₂²	1	4	yes	complemented
41	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	—
43	C₃×#400	C₂²	1	1	yes	characteristic, complemented
44	C₃×#400	C₂²	1	2	yes	complemented
45	C₃×#399	C₂²	1	1	yes	characteristic
46	C₃×#399	C₂²	1	4	yes	—
47	C₃×#399	C₂²	1	2	yes	—
48	C₃×#399	C₂²	1	2	yes	complemented
49	C₃×#399	C₂²	1	2	yes	complemented
50	C₃×#399	C₂²	1	4	yes	complemented
51	C₃×#399	C₂²	1	2	yes	complemented
52	C₃×#398	C₂²	1	4	yes	complemented
53	C₃×#398	C₂²	1	1	yes	characteristic, complemented
54	C₃×#397	C₂²	1	1	yes	characteristic
55	C₃×#397	C₂²	1	4	yes	complemented
56	C₃×#397	C₂²	1	2	yes	complemented
57	C₃×#397	C₂²	1	2	yes	complemented
58	C₃×#394	C₂²	1	2	yes	—
59	C₃×#394	C₂²	1	4	yes	complemented
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×#387	C₂²	1	4	yes	complemented
69	C₃×#386	C₂²	1	4	yes	—
70	C₃×#386	C₂²	1	2	yes	—
71	C₃×#386	C₂²	1	4	yes	—
72	C₃×#386	C₂²	1	4	yes	complemented
73	C₃×#385	C₂²	1	4	yes	complemented
74	C₃×#385	C₂²	1	2	yes	complemented
75	C₃×#385	C₂²	1	4	yes	complemented
76	C₃×#384	C₂²	1	2	yes	complemented
77	C₃×#381	C₂²	1	2	yes	complemented
78	C₃×#380	C₂²	1	2	yes	—
79	C₃×#380	C₂²	1	1	yes	characteristic, complemented
80	C₃×#380	C₂²	1	4	yes	complemented
81	C₃×#379	C₂²	1	4	yes	—
82	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
83	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
84	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₃×#95	C₂²	1	2	yes	complemented
86	C₂×#546	C₂×C₃	1	1	yes	characteristic
87	C₂×#520	C₂×C₃	1	1	yes	characteristic, complemented
88	#2624	C₂×C₃	1	1	yes	characteristic, complemented
89	#2623	C₂×C₃	1	2	yes	complemented
90	#2501	C₂×C₃	1	1	yes	characteristic, complemented
91	#2498	C₂×C₃	1	2	yes	complemented
92	#2487	C₂×C₃	1	1	yes	characteristic, complemented
93	#2482	C₂×C₃	1	2	yes	complemented
94	#2448	C₂×C₃	1	2	yes	complemented
95	#2443	C₂×C₃	1	4	yes	complemented
96	#2423	C₂×C₃	1	2	yes	complemented
97	#2418	C₂×C₃	1	4	yes	complemented
98	#2395	C₂×C₃	1	1	yes	characteristic, complemented
99	C₂×#399	C₂×C₃	1	2	yes	complemented
100	D₄×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
101	#2339	C₂×C₃	1	1	yes	characteristic, complemented
102	D₄×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
103	C₂⁵×C₃	C₂³	1	2	yes	—
104	C₂×C₃×#41	—	2	8	no	—
105	C₂×C₃×#41	D₄	1	8	yes	—
106	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
107	C₂²×C₃×D₄	—	2	4	no	—
108	C₂²×C₃×D₄	—	2	8	no	—
109	C₂²×C₃×D₄	C₂³	1	2	yes	—
110	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
111	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
112	C₂²×C₃×D₄	C₂³	1	2	yes	—
113	C₂²×C₃×D₄	C₂³	1	2	yes	—
114	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
115	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
116	C₂³×C₃×C₄	C₂³	1	4	yes	—
117	C₂³×C₃×C₄	C₂³	1	2	yes	—
118	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
119	C₂³×C₃×C₄	C₂³	1	2	yes	—
120	C₂³×C₃×C₄	C₂³	1	4	yes	—
121	C₂³×C₃×C₄	C₂³	1	2	yes	—
122	C₃×#124	—	2	4	no	—
123	C₃×#123	—	2	8	no	—
124	C₃×#123	—	4	8	no	—
125	C₃×C₂²⋊Q₈	—	2	4	no	—
126	C₃×#121	—	2	8	no	—
127	C₃×#121	—	2	4	no	—
128	C₃×#120	—	2	8	no	—
129	C₃×C₄×Q₈	—	2	8	no	—
130	C₃×C₄×D₄	—	2	8	no	—
131	C₃×C₄×D₄	—	2	4	no	—
132	C₃×C₄×D₄	—	2	16	no	—
133	C₃×C₄×D₄	—	2	8	no	—
134	C₃×C₄×D₄	—	2	4	no	—
135	C₃×#117	—	2	8	no	—
136	C₃×#117	—	2	4	no	—
137	C₂×C₃×C₄⋊C₄	—	2	8	no	—
138	C₂×C₃×C₄⋊C₄	—	2	4	no	—
139	C₂×C₃×C₄⋊C₄	—	4	8	no	—
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	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
149	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
155	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
156	C₂×C₃×C₂²⋊C₄	—	4	8	no	—
157	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	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	1	yes	characteristic
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
176	C₂×C₃×C₄²	C₂³	1	2	yes	—
177	C₂×C₃×C₄²	C₂³	1	2	yes	—
178	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄²	C₂³	1	4	yes	—
180	C₃×#95	C₂³	1	1	yes	characteristic
181	C₃×#95	C₂³	1	2	yes	—
182	C₃×#95	C₂³	1	4	yes	—
183	C₃×#95	C₂³	1	2	yes	—
184	C₃×#95	C₂³	1	2	yes	—
185	C₃×#95	C₂³	1	1	yes	characteristic
186	C₃×#95	C₂³	1	2	yes	—
187	C₃×#95	C₂³	1	2	yes	—
188	C₃×#95	C₂³	1	4	yes	—
189	C₃×#95	C₂³	1	4	yes	—
190	C₃×#95	C₂³	1	4	yes	—
191	C₃×#95	C₂³	1	4	yes	—
192	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
193	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
194	#546	—	2	8	no	—
195	C₂×#124	C₂²×C₃	1	1	yes	characteristic
196	C₂×#123	C₂²×C₃	1	2	yes	—
197	C₂×#123	C₂²×C₃	1	4	yes	complemented
198	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
199	C₂×#121	C₂²×C₃	1	1	yes	characteristic
200	C₂×#121	C₂²×C₃	1	2	yes	—
201	C₂×#120	C₂²×C₃	1	2	yes	—
202	#520	—	2	8	no	—
203	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	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	1	yes	characteristic
207	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
209	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
210	C₂×#117	C₂²×C₃	1	2	yes	complemented
211	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
212	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
213	C₂²×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
214	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
215	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
216	#400	C₂²×C₃	1	1	yes	characteristic, complemented
217	#400	C₂²×C₃	1	2	yes	complemented
218	#399	C₂²×C₃	1	1	yes	characteristic
219	#399	C₂²×C₃	1	4	yes	—
220	#399	C₂²×C₃	1	2	yes	—
221	#399	C₂²×C₃	1	2	yes	complemented
222	#399	C₂²×C₃	1	2	yes	complemented
223	#399	C₂²×C₃	1	4	yes	complemented
224	#399	C₂²×C₃	1	2	yes	complemented
225	#398	C₂²×C₃	1	4	yes	complemented
226	#398	C₂²×C₃	1	1	yes	characteristic, complemented
227	#397	C₂²×C₃	1	1	yes	characteristic
228	#397	C₂²×C₃	1	4	yes	complemented
229	#397	C₂²×C₃	1	2	yes	complemented
230	#397	C₂²×C₃	1	2	yes	complemented
231	#394	C₂²×C₃	1	2	yes	—
232	#394	C₂²×C₃	1	4	yes	complemented
233	#391	C₂²×C₃	1	2	yes	complemented
234	#390	C₂²×C₃	1	2	yes	—
235	#390	C₂²×C₃	1	2	yes	—
236	#389	C₂²×C₃	1	2	yes	complemented
237	#389	C₂²×C₃	1	2	yes	complemented
238	#388	C₂²×C₃	1	4	yes	—
239	#388	C₂²×C₃	1	4	yes	complemented
240	#388	C₂²×C₃	1	4	yes	complemented
241	#387	C₂²×C₃	1	4	yes	complemented
242	#386	C₂²×C₃	1	4	yes	—
243	#386	C₂²×C₃	1	4	yes	—
244	#386	C₂²×C₃	1	2	yes	—
245	#386	C₂²×C₃	1	4	yes	complemented
246	#385	C₂²×C₃	1	4	yes	complemented
247	#385	C₂²×C₃	1	4	yes	complemented
248	#385	C₂²×C₃	1	2	yes	complemented
249	#384	C₂²×C₃	1	2	yes	complemented
250	#381	C₂²×C₃	1	2	yes	complemented
251	#380	C₂²×C₃	1	2	yes	—
252	#380	C₂²×C₃	1	1	yes	characteristic, complemented
253	#380	C₂²×C₃	1	4	yes	complemented
254	#379	C₂²×C₃	1	4	yes	—
255	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
256	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
257	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
258	C₂×#95	C₂²×C₃	1	2	yes	complemented
259	C₂⁴×C₃	—	2	4	no	—
260	C₂⁴×C₃	—	2	4	no	—
261	C₂⁴×C₃	—	2	8	no	—
262	C₂⁴×C₃	—	4	2	no	—
263	C₂⁴×C₃	—	4	4	no	—
264	C₂⁴×C₃	C₂⁴	1	2	yes	—
265	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
266	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₃	C₂⁴	1	2	yes	—
268	C₃×#41	—	2	32	no	—
269	C₂×C₃×Q₈	—	2	4	no	—
270	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
271	C₂×C₃×D₄	—	2	8	no	—
272	C₂×C₃×D₄	—	2	2	no	—
273	C₂×C₃×D₄	—	2	4	no	—
274	C₂×C₃×D₄	—	2	8	no	—
275	C₂×C₃×D₄	—	2	2	no	—
276	C₂×C₃×D₄	—	2	4	no	—
277	C₂×C₃×D₄	—	2	2	no	—
278	C₂×C₃×D₄	—	2	4	no	—
279	C₂×C₃×D₄	—	4	1	no	—
280	C₂×C₃×D₄	—	4	4	no	—
281	C₂×C₃×D₄	—	4	16	no	—
282	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
283	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
284	C₂×C₃×D₄	#41	1	8	yes	—
285	C₂²×C₃×C₄	—	2	8	no	—
286	C₂²×C₃×C₄	—	2	4	no	—
287	C₂²×C₃×C₄	—	2	8	no	—
288	C₂²×C₃×C₄	—	2	4	no	—
289	C₂²×C₃×C₄	—	2	4	no	—
290	C₂²×C₃×C₄	—	2	8	no	—
291	C₂²×C₃×C₄	—	2	2	no	—
292	C₂²×C₃×C₄	—	2	4	no	—
293	C₂²×C₃×C₄	—	2	8	no	—
294	C₂²×C₃×C₄	—	4	4	no	—
295	C₂²×C₃×C₄	—	4	4	no	—
296	C₂²×C₃×C₄	—	4	4	no	—
297	C₂²×C₃×C₄	—	4	4	no	—
298	C₂²×C₃×C₄	—	4	4	no	—
299	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
300	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
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	4	yes	—
305	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
306	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
307	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
308	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
309	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
310	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
311	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
313	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
314	C₃×C₄⋊C₄	—	2	2	no	—
315	C₃×C₄⋊C₄	—	2	4	no	—
316	C₃×C₄⋊C₄	—	2	8	no	—
317	C₃×C₄⋊C₄	—	2	4	no	—
318	C₃×C₄⋊C₄	—	2	2	no	—
319	C₃×C₄⋊C₄	—	2	2	no	—
320	C₃×C₄⋊C₄	—	2	2	no	—
321	C₃×C₄⋊C₄	—	2	4	no	—
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	2	8	no	—
325	C₃×C₄⋊C₄	—	4	4	no	—
326	C₃×C₄⋊C₄	—	4	4	no	—
327	C₃×C₄⋊C₄	—	4	2	no	—
328	C₃×C₄⋊C₄	—	4	4	no	—
329	C₃×C₂²⋊C₄	—	2	4	no	—
330	C₃×C₂²⋊C₄	—	2	8	no	—
331	C₃×C₂²⋊C₄	—	2	4	no	—
332	C₃×C₂²⋊C₄	—	2	2	no	—
333	C₃×C₂²⋊C₄	—	2	8	no	—
334	C₃×C₂²⋊C₄	—	2	4	no	—
335	C₃×C₂²⋊C₄	—	2	2	no	—
336	C₃×C₂²⋊C₄	—	2	4	no	—
337	C₃×C₂²⋊C₄	—	2	4	no	—
338	C₃×C₂²⋊C₄	—	2	4	no	—
339	C₃×C₂²⋊C₄	—	2	4	no	—
340	C₃×C₂²⋊C₄	—	2	4	no	—
341	C₃×C₂²⋊C₄	—	2	8	no	—
342	C₃×C₂²⋊C₄	—	2	4	no	—
343	C₃×C₂²⋊C₄	—	4	4	no	—
344	C₃×C₂²⋊C₄	—	4	4	no	—
345	C₃×C₂²⋊C₄	—	4	4	no	—
346	C₃×C₂²⋊C₄	—	4	2	no	—
347	C₃×C₂²⋊C₄	—	4	4	no	—
348	C₃×C₄²	—	2	8	no	—
349	C₃×C₄²	—	2	4	no	—
350	C₃×C₄²	—	2	2	no	—
351	C₃×C₄²	—	2	4	no	—
352	C₂⁵	C₂³×C₃	1	2	yes	—
353	C₂×#41	—	2	8	no	—
354	C₂×#41	C₃×D₄	1	8	yes	—
355	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
356	C₂²×D₄	—	2	4	no	—
357	C₂²×D₄	—	2	8	no	—
358	C₂²×D₄	C₂³×C₃	1	2	yes	—
359	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
360	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
361	C₂²×D₄	C₂³×C₃	1	2	yes	—
362	C₂²×D₄	C₂³×C₃	1	2	yes	—
363	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
364	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₃	1	4	yes	—
366	C₂³×C₄	C₂³×C₃	1	2	yes	—
367	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₃	1	4	yes	—
369	C₂³×C₄	C₂³×C₃	1	2	yes	—
370	C₂³×C₄	C₂³×C₃	1	2	yes	—
371	#124	—	2	4	no	—
372	#123	—	2	8	no	—
373	#123	—	4	8	no	—
374	C₂²⋊Q₈	—	2	4	no	—
375	#121	—	2	8	no	—
376	#121	—	2	4	no	—
377	#120	—	2	8	no	—
378	C₄×Q₈	—	2	8	no	—
379	C₄×D₄	—	2	8	no	—
380	C₄×D₄	—	2	4	no	—
381	C₄×D₄	—	2	16	no	—
382	C₄×D₄	—	2	8	no	—
383	C₄×D₄	—	2	4	no	—
384	#117	—	2	8	no	—
385	#117	—	2	4	no	—
386	C₂×C₄⋊C₄	—	2	8	no	—
387	C₂×C₄⋊C₄	—	2	4	no	—
388	C₂×C₄⋊C₄	—	4	8	no	—
389	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
404	C₂×C₂²⋊C₄	—	2	8	no	—
405	C₂×C₂²⋊C₄	—	4	8	no	—
406	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
425	C₂×C₄²	C₂³×C₃	1	2	yes	—
426	C₂×C₄²	C₂³×C₃	1	4	yes	—
427	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₃	1	2	yes	—
429	#95	C₂³×C₃	1	1	yes	characteristic
430	#95	C₂³×C₃	1	2	yes	—
431	#95	C₂³×C₃	1	4	yes	—
432	#95	C₂³×C₃	1	2	yes	—
433	#95	C₂³×C₃	1	2	yes	—
434	#95	C₂³×C₃	1	1	yes	characteristic
435	#95	C₂³×C₃	1	2	yes	—
436	#95	C₂³×C₃	1	2	yes	—
437	#95	C₂³×C₃	1	4	yes	—
438	#95	C₂³×C₃	1	4	yes	—
439	#95	C₂³×C₃	1	4	yes	—
440	#95	C₂³×C₃	1	4	yes	—
441	C₂³×C₃	—	2	4	no	—
442	C₂³×C₃	—	2	2	no	—
443	C₂³×C₃	—	2	2	no	—
444	C₂³×C₃	—	2	1	no	—
445	C₂³×C₃	—	2	2	no	—
446	C₂³×C₃	—	2	2	no	—
447	C₂³×C₃	—	2	2	no	—
448	C₂³×C₃	—	2	2	no	—
449	C₂³×C₃	—	2	1	no	—
450	C₂³×C₃	—	2	1	no	—
451	C₂³×C₃	—	2	1	no	—
452	C₂³×C₃	—	2	2	no	—
453	C₂³×C₃	—	2	4	no	—
454	C₂³×C₃	—	2	4	no	—
455	C₂³×C₃	—	2	2	no	—
456	C₂³×C₃	—	2	2	no	—
457	C₂³×C₃	—	4	8	no	—
458	C₂³×C₃	—	4	16	no	—
459	C₂³×C₃	—	4	8	no	—
460	C₂³×C₃	—	8	4	no	—
461	C₂³×C₃	—	8	8	no	—
462	C₂³×C₃	C₂²×D₄	1	2	yes	—
463	C₂³×C₃	C₂²×D₄	1	4	yes	—
464	C₂³×C₃	C₂×#41	1	8	yes	—
465	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
466	C₂³×C₃	C₂⁵	1	1	yes	characteristic
467	C₃×Q₈	—	2	8	no	—
468	C₃×D₄	—	2	16	no	—
469	C₃×D₄	—	4	4	no	—
470	C₃×D₄	—	4	8	no	—
471	C₃×D₄	—	4	4	no	—
472	C₃×D₄	—	8	4	no	—
473	C₃×D₄	#123	1	16	yes	complemented
474	C₂×C₃×C₄	—	2	16	no	—
475	C₂×C₃×C₄	—	2	2	no	—
476	C₂×C₃×C₄	—	2	2	no	—
477	C₂×C₃×C₄	—	2	4	no	—
478	C₂×C₃×C₄	—	2	2	no	—
479	C₂×C₃×C₄	—	2	8	no	—
480	C₂×C₃×C₄	—	2	2	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	2	no	—
484	C₂×C₃×C₄	—	2	4	no	—
485	C₂×C₃×C₄	—	2	2	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	2	no	—
488	C₂×C₃×C₄	—	2	4	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	4	no	—
494	C₂×C₃×C₄	—	2	4	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	2	no	—
497	C₂×C₃×C₄	—	2	4	no	—
498	C₂×C₃×C₄	—	2	2	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	2	2	no	—
502	C₂×C₃×C₄	—	2	4	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	4	16	no	—
505	C₂×C₃×C₄	—	4	4	no	—
506	C₂×C₃×C₄	—	8	8	no	—
507	C₂×C₃×C₄	—	8	4	no	—
508	C₂×C₃×C₄	—	8	4	no	—
509	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
510	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
511	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
512	C₂×C₃×C₄	C₂×#41	1	4	yes	—
513	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
514	C₂⁴	—	2	4	no	—
515	C₂⁴	—	2	4	no	—
516	C₂⁴	—	2	8	no	—
517	C₂⁴	—	4	4	no	—
518	C₂⁴	—	4	2	no	—
519	C₂⁴	C₂⁴×C₃	1	2	yes	—
520	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
521	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
522	C₂⁴	C₂⁴×C₃	1	2	yes	—
523	#41	—	2	32	no	—
524	C₂×Q₈	—	2	4	no	—
525	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	8	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	4	1	no	—
535	C₂×D₄	—	4	4	no	—
536	C₂×D₄	—	4	16	no	—
537	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
538	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
539	C₂×D₄	C₃×#41	1	8	yes	—
540	C₂²×C₄	—	2	8	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	8	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	8	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	8	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	—	4	4	no	—
552	C₂²×C₄	—	4	4	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
555	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
556	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
564	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	8	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	8	no	—
580	C₄⋊C₄	—	4	4	no	—
581	C₄⋊C₄	—	4	4	no	—
582	C₄⋊C₄	—	4	4	no	—
583	C₄⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	8	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	4	4	no	—
599	C₂²⋊C₄	—	4	4	no	—
600	C₂²⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	—	4	4	no	—
602	C₂²⋊C₄	—	4	2	no	—
603	C₄²	—	2	8	no	—
604	C₄²	—	2	4	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	4	no	—
607	C₂²×C₃	—	2	4	no	—
608	C₂²×C₃	—	2	4	no	—
609	C₂²×C₃	—	2	8	no	—
610	C₂²×C₃	—	2	8	no	—
611	C₂²×C₃	—	2	2	no	—
612	C₂²×C₃	—	2	2	no	—
613	C₂²×C₃	—	2	2	no	—
614	C₂²×C₃	—	2	2	no	—
615	C₂²×C₃	—	2	4	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	—	4	2	no	—
619	C₂²×C₃	—	4	2	no	—
620	C₂²×C₃	—	4	2	no	—
621	C₂²×C₃	—	4	2	no	—
622	C₂²×C₃	—	4	2	no	—
623	C₂²×C₃	—	4	2	no	—
624	C₂²×C₃	—	4	4	no	—
625	C₂²×C₃	—	4	4	no	—
626	C₂²×C₃	—	8	16	no	—
627	C₂²×C₃	C₂×#123	1	8	yes	—
628	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
629	C₂²×C₃	C₂²×#41	1	2	yes	—
630	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
631	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
632	C₂²×C₃	#585	1	1	yes	characteristic
633	C₃×C₄	—	2	2	no	—
634	C₃×C₄	—	2	4	no	—
635	C₃×C₄	—	2	4	no	—
636	C₃×C₄	—	4	1	no	—
637	C₃×C₄	—	4	2	no	—
638	C₃×C₄	—	4	1	no	—
639	C₃×C₄	—	4	1	no	—
640	C₃×C₄	—	4	2	no	—
641	C₃×C₄	—	4	4	no	—
642	C₃×C₄	—	4	2	no	—
643	C₃×C₄	—	4	4	no	—
644	C₃×C₄	—	4	2	no	—
645	C₃×C₄	C₂×#123	1	4	yes	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	4	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	4	8	no	—
663	C₂³	—	4	16	no	—
664	C₂³	—	4	8	no	—
665	C₂³	—	8	4	no	—
666	C₂³	—	8	8	no	—
667	C₂³	C₂²×C₃×D₄	1	2	yes	—
668	C₂³	C₂²×C₃×D₄	1	4	yes	—
669	C₂³	C₂×C₃×#41	1	8	yes	—
670	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
671	C₂³	C₂⁵×C₃	1	1	yes	characteristic
672	Q₈	—	2	8	no	—
673	D₄	—	2	16	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	8	no	—
676	D₄	—	4	4	no	—
677	D₄	—	8	4	no	—
678	D₄	C₃×#123	1	16	yes	complemented
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	16	no	—
684	C₂×C₄	—	2	8	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	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	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	4	16	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	8	8	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
715	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
716	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
717	C₂×C₄	C₂×C₃×#41	1	4	yes	—
718	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
719	C₂×C₃	—	2	8	no	—
720	C₂×C₃	—	4	2	no	—
721	C₂×C₃	—	4	2	no	—
722	C₂×C₃	—	8	2	no	—
723	C₂×C₃	C₂²×#123	1	1	yes	characteristic
724	C₂×C₃	#3489	1	1	yes	characteristic
725	C₂×C₃	#3498	1	1	yes	characteristic
726	C₂×C₃	#3513	1	2	yes	—
727	C₂×C₃	#3520	1	2	yes	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	8	no	—
731	C₂²	—	2	8	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	4	4	no	—
747	C₂²	—	8	16	no	—
748	C₂²	C₂×C₃×#123	1	8	yes	—
749	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
750	C₂²	C₂²×C₃×#41	1	2	yes	—
751	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
752	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
753	C₂²	C₃×#585	1	1	yes	characteristic
754	C₄	—	2	2	no	—
755	C₄	—	2	4	no	—
756	C₄	—	2	4	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	4	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	4	no	—
765	C₄	—	4	2	no	—
766	C₄	C₂×C₃×#123	1	4	yes	—
767	C₃	#35987	1	1	yes	characteristic, direct product factor, Sylow
768	C₂	—	2	8	no	—
769	C₂	—	4	2	no	—
770	C₂	—	4	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂²×C₃×#123	1	1	yes	characteristic
773	C₂	C₃×#3489	1	1	yes	characteristic
774	C₂	C₃×#3498	1	1	yes	characteristic
775	C₂	C₃×#3513	1	2	yes	—
776	C₂	C₃×#3520	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#546	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
2. C₂×C₃×#520	C₂	semidirect
3. C₃×#2624	C₂	semidirect
4. C₃×#2623	C₂	semidirect
5. C₃×#2501	C₂	semidirect
6. C₃×#2498	C₂	semidirect
7. C₃×#2487	C₂	semidirect
8. C₃×#2482	C₂	semidirect
9. C₃×#2448	C₂	semidirect
10. C₃×#2443	C₂	semidirect
11. C₃×#2423	C₂	semidirect
12. C₃×#2418	C₂	semidirect
13. C₃×#2395	C₂	semidirect
14. C₂×C₃×#399	C₂	semidirect
15. C₃×D₄×C₄⋊C₄	C₂	semidirect
16. C₃×#2339	C₂	semidirect
17. C₃×D₄×C₂²⋊C₄	C₂	semidirect
18. #35987	C₃	direct (N × H)
24. C₂×C₃×#123	C₂²	semidirect
30. C₂×C₃×C₄×Q₈	C₂²	semidirect
35. C₂×C₃×C₄×D₄	C₂²	semidirect
36. C₂×C₃×#117	C₂²	semidirect
37. C₂×C₃×#117	C₂²	semidirect
38. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
39. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
40. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
43. C₃×#400	C₂²	semidirect
44. C₃×#400	C₂²	semidirect
48. C₃×#399	C₂²	semidirect
49. C₃×#399	C₂²	semidirect
50. C₃×#399	C₂²	semidirect
51. C₃×#399	C₂²	semidirect
52. C₃×#398	C₂²	semidirect
53. C₃×#398	C₂²	semidirect
55. C₃×#397	C₂²	semidirect
56. C₃×#397	C₂²	semidirect
57. C₃×#397	C₂²	semidirect
59. 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×#387	C₂²	semidirect
72. C₃×#386	C₂²	semidirect
73. C₃×#385	C₂²	semidirect
74. C₃×#385	C₂²	semidirect
75. C₃×#385	C₂²	semidirect
76. C₃×#384	C₂²	semidirect
77. C₃×#381	C₂²	semidirect
79. C₃×#380	C₂²	semidirect
80. C₃×#380	C₂²	semidirect
82. C₃×C₄×C₄⋊C₄	C₂²	semidirect
84. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
85. C₂×C₃×#95	C₂²	semidirect
87. C₂×#520	C₂×C₃	semidirect
88. #2624	C₂×C₃	semidirect
89. #2623	C₂×C₃	semidirect
90. #2501	C₂×C₃	semidirect
91. #2498	C₂×C₃	semidirect
92. #2487	C₂×C₃	semidirect
93. #2482	C₂×C₃	semidirect
94. #2448	C₂×C₃	semidirect
95. #2443	C₂×C₃	semidirect
96. #2423	C₂×C₃	semidirect
97. #2418	C₂×C₃	semidirect
98. #2395	C₂×C₃	semidirect
99. C₂×#399	C₂×C₃	semidirect
100. D₄×C₄⋊C₄	C₂×C₃	semidirect
101. #2339	C₂×C₃	semidirect
102. D₄×C₂²⋊C₄	C₂×C₃	semidirect
197. C₂×#123	C₂²×C₃	semidirect
203. C₂×C₄×Q₈	C₂²×C₃	semidirect
208. C₂×C₄×D₄	C₂²×C₃	semidirect
209. C₂×#117	C₂²×C₃	semidirect
210. C₂×#117	C₂²×C₃	semidirect
211. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
212. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
213. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
216. #400	C₂²×C₃	semidirect
217. #400	C₂²×C₃	semidirect
221. #399	C₂²×C₃	semidirect
222. #399	C₂²×C₃	semidirect
223. #399	C₂²×C₃	semidirect
224. #399	C₂²×C₃	semidirect
225. #398	C₂²×C₃	semidirect
226. #398	C₂²×C₃	semidirect
228. #397	C₂²×C₃	semidirect
229. #397	C₂²×C₃	semidirect
230. #397	C₂²×C₃	semidirect
232. #394	C₂²×C₃	semidirect
233. #391	C₂²×C₃	semidirect
236. #389	C₂²×C₃	semidirect
237. #389	C₂²×C₃	semidirect
239. #388	C₂²×C₃	semidirect
240. #388	C₂²×C₃	semidirect
241. #387	C₂²×C₃	semidirect
245. #386	C₂²×C₃	semidirect
246. #385	C₂²×C₃	semidirect
247. #385	C₂²×C₃	semidirect
248. #385	C₂²×C₃	semidirect
249. #384	C₂²×C₃	semidirect
250. #381	C₂²×C₃	semidirect
252. #380	C₂²×C₃	semidirect
253. #380	C₂²×C₃	semidirect
255. C₄×C₄⋊C₄	C₂²×C₃	semidirect
257. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
258. C₂×#95	C₂²×C₃	semidirect
473. C₃×D₄	#123	semidirect
678. D₄	C₃×#123	semidirect
767. C₃	#35987	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×#546	2
C₂×C₃×#520	2
C₃×#2624	2
C₃×#2623	2
C₃×#2501	2
C₃×#2498	2
C₃×#2487	2
C₃×#2482	2
C₃×#2448	2
C₃×#2443	2
C₃×#2423	2
C₃×#2418	2
C₃×#2395	2
C₂×C₃×#399	2
C₃×D₄×C₄⋊C₄	2
C₃×#2339	2
C₃×D₄×C₂²⋊C₄	2
#35987	3

Subgroups — C3×#35987 #10654594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35987 #10654594