Subgroups — C₃×C₄×D₃×SD₁₆ #11859853

Order 1152.

1165 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃²×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Dic₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄×#215	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×#214	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4852	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4788	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₃×#102	C₂	1	1	yes	maximal, characteristic
13	C₃×#4758	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×#204	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×C₄×SD₁₆	—	3	1	no	maximal
17	C₄×D₃×SD₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×D₃	—	2	1	no	—
21	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
22	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
24	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#215	C₂²	1	1	yes	characteristic
26	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₃×#214	C₂²	1	1	yes	characteristic
28	C₃×C₄×#67	—	2	1	no	—
29	C₃×D₃×SD₁₆	C₄	1	8	yes	direct product factor
30	C₂×C₃×#204	C₂²	1	1	yes	characteristic
31	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
33	C₃×#893	C₂²	1	1	yes	characteristic
34	C₃×D₃×C₄⋊C₄	—	2	1	no	—
35	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×#887	—	2	1	no	—
38	C₃×#887	C₂²	1	1	yes	characteristic, complemented
39	C₃×#67⋊C₄	—	2	1	no	—
40	C₃×D₃×C₂²⋊C₄	—	2	1	no	—
41	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
42	C₃×C₄²×D₃	—	2	1	no	—
43	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
44	C₃×C₄×Dic₆	—	2	1	no	—
45	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
46	C₃²×#106	C₂²	1	1	yes	characteristic, complemented
47	C₃²×#103	C₂²	1	1	yes	characteristic, complemented
48	C₃²×#102	C₂²	1	1	yes	characteristic
49	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
50	C₃×#835	C₂²	1	1	yes	characteristic, complemented
51	C₃×#832	C₂²	1	1	yes	characteristic
52	C₃×#821	C₂²	1	1	yes	characteristic
53	C₃×#817	C₂²	1	1	yes	characteristic, complemented
54	C₃×#816	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
56	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
57	C₃×#810	C₂²	1	1	yes	characteristic, complemented
58	C₃×#809	C₂²	1	1	yes	characteristic
59	C₃×#808	C₂²	1	1	yes	characteristic, complemented
60	C₃×#808	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₂²×C₃×SD₁₆	—	3	1	no	—
63	C₂×C₃×C₄×Q₈	—	3	1	no	—
64	C₂×C₃×C₄×D₄	—	3	1	no	—
65	C₂×D₃×SD₁₆	C₂×C₃	1	1	yes	characteristic
66	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
67	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic
68	C₃×C₄×SD₁₆	—	2	1	no	—
69	C₃×C₄×SD₁₆	—	3	1	no	—
70	C₃×C₄×SD₁₆	—	3	1	no	—
71	C₃×C₄×SD₁₆	—	3	1	no	—
72	C₃×C₄×SD₁₆	—	3	1	no	—
73	C₃×C₄×SD₁₆	—	3	1	no	—
74	C₃×C₄×SD₁₆	—	3	1	no	—
75	C₃×C₄×SD₁₆	—	3	1	no	—
76	C₃×C₄×SD₁₆	D₃	1	1	yes	characteristic, direct product factor
77	C₃×C₄×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂×C₃×#106	—	3	1	no	—
79	C₂×C₃×#103	—	3	1	no	—
80	C₂×C₃×#102	—	3	1	no	—
81	C₂×C₃×C₄×C₈	—	3	1	no	—
82	Dic₃×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
83	C₄×#215	C₂×C₃	1	1	yes	characteristic, complemented
84	C₄×#214	C₂×C₃	1	1	yes	characteristic, complemented
85	D₃×#106	C₂×C₃	1	1	yes	characteristic, complemented
86	#4852	C₂×C₃	1	1	yes	characteristic, complemented
87	D₃×#103	C₂×C₃	1	1	yes	characteristic, complemented
88	#4788	C₂×C₃	1	1	yes	characteristic, complemented
89	D₃×#102	C₂×C₃	1	1	yes	characteristic
90	#4758	C₂×C₃	1	1	yes	characteristic, complemented
91	C₄×#204	C₂×C₃	1	1	yes	characteristic, complemented
92	C₄×D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
93	C₂³×C₃×D₃	—	2	1	no	—
94	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
95	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
96	C₂²×C₃²×C₄	—	2	1	no	—
97	C₂×C₃×#67	—	2	1	no	—
98	C₂²×C₃×Dic₃	—	2	1	no	—
99	C₃×D₃×Q₈	—	2	2	no	—
100	C₃×D₃×Q₈	C₂×C₄	1	4	yes	complemented
101	C₃×D₃×D₄	—	2	2	no	—
102	C₃×D₃×D₄	C₂×C₄	1	4	yes	—
103	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₄×D₃	—	2	1	no	—
105	C₂×C₃×C₄×D₃	—	2	1	no	—
106	C₂×C₃×C₄×D₃	—	2	1	no	—
107	C₂×C₃×C₄×D₃	—	2	1	no	—
108	C₂×C₃×C₄×D₃	—	2	1	no	—
109	C₂×C₃×C₄×D₃	—	4	4	no	—
110	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
113	C₂×C₃×Dic₆	—	2	1	no	—
114	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
115	C₃²×SD₁₆	C₂×C₄	1	4	yes	complemented
116	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
117	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
118	C₃²×C₄⋊C₄	—	2	1	no	—
119	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₃²×C₂²⋊C₄	—	2	1	no	—
122	C₃²×C₄²	—	2	1	no	—
123	C₃²×C₄²	C₂³	1	1	yes	characteristic
124	C₃×#217	—	2	1	no	—
125	C₃×#215	C₂×C₄	1	4	yes	complemented
126	C₃×#214	C₂×C₄	1	4	yes	complemented
127	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
128	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
129	C₃×C₄⋊Dic₃	—	2	1	no	—
130	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
131	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
132	C₃×Dic₃⋊C₄	—	2	1	no	—
133	C₃×Dic₃⋊C₄	—	2	1	no	—
134	C₃×Dic₃⋊C₄	—	2	1	no	—
135	C₃×Dic₃⋊C₄	—	2	1	no	—
136	C₃×C₄×Dic₃	—	2	1	no	—
137	C₃×C₄×Dic₃	—	2	1	no	—
138	C₃×C₄×Dic₃	—	2	1	no	—
139	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
140	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
141	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
142	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
144	C₃×#204	C₂×C₄	1	4	yes	complemented
145	C₃×D₃×C₈	—	2	2	no	—
146	C₃×D₃×C₈	C₂×C₄	1	4	yes	complemented
147	C₂×C₄×SD₁₆	—	3	1	no	Sylow
148	C₂²×C₃×Q₈	—	3	1	no	—
149	C₂²×C₃×D₄	—	3	1	no	—
150	C₂³×C₃×C₄	—	6	1	no	—
151	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
152	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
153	C₂²×C₄×D₃	—	2	1	no	—
154	C₂×C₃×SD₁₆	—	2	1	no	—
155	C₂×C₃×SD₁₆	—	3	1	no	—
156	C₂×C₃×SD₁₆	—	3	1	no	—
157	C₂×C₃×SD₁₆	—	3	8	no	—
158	C₂×C₃×SD₁₆	—	3	1	no	—
159	C₂×C₃×SD₁₆	C₂×D₃	1	1	yes	characteristic
160	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
161	C₂²×C₃×C₈	—	3	1	no	—
162	C₂²×C₃×C₈	—	3	1	no	—
163	C₃×C₄×Q₈	—	2	1	no	—
164	C₃×C₄×Q₈	—	3	1	no	—
165	C₃×C₄×Q₈	—	3	1	no	—
166	C₃×C₄×Q₈	—	3	1	no	—
167	C₃×C₄×Q₈	—	6	1	no	—
168	C₃×C₄×Q₈	—	6	1	no	—
169	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
170	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₃×C₄×D₄	—	2	1	no	—
172	C₃×C₄×D₄	—	3	1	no	—
173	C₃×C₄×D₄	—	3	1	no	—
174	C₃×C₄×D₄	—	3	1	no	—
175	C₃×C₄×D₄	—	6	1	no	—
176	C₃×C₄×D₄	—	6	1	no	—
177	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
178	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
179	C₂×C₃×C₄⋊C₄	—	3	1	no	—
180	C₂×C₃×C₄⋊C₄	—	3	1	no	—
181	C₂×C₃×C₄⋊C₄	—	6	1	no	—
182	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
183	C₂×C₃×C₄²	—	3	1	no	—
184	C₂×C₃×C₄²	—	6	1	no	—
185	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₂×#215	C₂²×C₃	1	1	yes	characteristic
187	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
188	C₂×#214	C₂²×C₃	1	1	yes	characteristic
189	C₄×#67	—	2	1	no	—
190	D₃×SD₁₆	C₃×C₄	1	8	yes	direct product factor
191	C₂×#204	C₂²×C₃	1	1	yes	characteristic
192	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
193	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
194	#893	C₂²×C₃	1	1	yes	characteristic
195	D₃×C₄⋊C₄	—	2	1	no	—
196	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
197	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
198	#887	—	2	1	no	—
199	#887	C₂²×C₃	1	1	yes	characteristic, complemented
200	#67⋊C₄	—	2	1	no	—
201	D₃×C₂²⋊C₄	—	2	1	no	—
202	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
203	C₄²×D₃	—	2	1	no	—
204	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
205	C₄×Dic₆	—	2	1	no	—
206	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
207	C₃×#106	—	2	1	no	—
208	C₃×#106	—	3	1	no	—
209	C₃×#106	—	3	1	no	—
210	C₃×#106	—	3	1	no	—
211	C₃×#106	C₂×D₃	1	1	yes	characteristic, complemented
212	C₃×#106	C₂²×C₃	1	1	yes	characteristic, complemented
213	C₃×#103	—	2	1	no	—
214	C₃×#103	—	3	1	no	—
215	C₃×#103	—	3	1	no	—
216	C₃×#103	—	3	1	no	—
217	C₃×#103	C₂×D₃	1	1	yes	characteristic, complemented
218	C₃×#103	C₂²×C₃	1	1	yes	characteristic, complemented
219	C₃×#102	—	2	1	no	—
220	C₃×#102	—	3	1	no	—
221	C₃×#102	—	3	1	no	—
222	C₃×#102	—	3	1	no	—
223	C₃×#102	C₂×D₃	1	1	yes	characteristic
224	C₃×#102	C₂²×C₃	1	1	yes	characteristic
225	C₃×C₄×C₈	—	2	1	no	—
226	C₃×C₄×C₈	—	3	1	no	—
227	C₃×C₄×C₈	—	3	1	no	—
228	C₃×C₄×C₈	—	3	1	no	—
229	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
230	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
231	#835	C₂²×C₃	1	1	yes	characteristic, complemented
232	#832	C₂²×C₃	1	1	yes	characteristic
233	#821	C₂²×C₃	1	1	yes	characteristic
234	#817	C₂²×C₃	1	1	yes	characteristic, complemented
235	#816	C₂²×C₃	1	1	yes	characteristic, complemented
236	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
237	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
238	#810	C₂²×C₃	1	1	yes	characteristic, complemented
239	#809	C₂²×C₃	1	1	yes	characteristic
240	#808	C₂²×C₃	1	1	yes	characteristic, complemented
241	#808	C₂²×C₃	1	1	yes	characteristic, complemented
242	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
243	C₂³×C₃²	—	2	1	no	—
244	C₂²×C₃×D₃	—	2	1	no	—
245	C₂²×C₃×D₃	—	2	4	no	—
246	C₂²×C₃×D₃	—	4	2	no	—
247	C₂²×C₃×D₃	—	4	2	no	—
248	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
249	C₃²×Q₈	—	2	1	no	—
250	C₃²×Q₈	C₂²×C₄	1	2	yes	complemented
251	C₃²×D₄	—	2	1	no	—
252	C₃²×D₄	C₂²×C₄	1	2	yes	—
253	C₂×C₃²×C₄	—	2	1	no	—
254	C₂×C₃²×C₄	—	2	1	no	—
255	C₂×C₃²×C₄	—	2	1	no	—
256	C₂×C₃²×C₄	—	4	2	no	—
257	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
258	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
259	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
260	C₃×#67	—	2	4	no	—
261	C₂×C₃×Dic₃	—	2	1	no	—
262	C₂×C₃×Dic₃	—	2	1	no	—
263	C₂×C₃×Dic₃	—	2	1	no	—
264	C₂×C₃×Dic₃	—	4	2	no	—
265	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
266	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
267	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
268	C₃×D₁₂	—	2	1	no	—
269	C₃×D₁₂	C₂²×C₄	1	2	yes	—
270	C₃×C₄×D₃	—	2	4	no	—
271	C₃×C₄×D₃	—	2	2	no	—
272	C₃×C₄×D₃	—	4	2	no	—
273	C₃×C₄×D₃	—	4	2	no	—
274	C₃×C₄×D₃	—	4	2	no	—
275	C₃×C₄×D₃	—	4	2	no	—
276	C₃×C₄×D₃	SD₁₆	1	4	yes	direct product factor
277	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
278	C₃×C₄×D₃	#41	1	2	yes	—
279	C₃×Dic₆	—	2	1	no	—
280	C₃×Dic₆	—	2	4	no	—
281	C₃×Dic₆	C₂²×C₄	1	2	yes	complemented
282	C₃²×C₈	—	2	1	no	—
283	C₃²×C₈	C₂²×C₄	1	2	yes	complemented
284	C₃×C₃⋊C₈	—	2	1	no	—
285	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	complemented
286	C₂²×SD₁₆	—	3	1	no	—
287	C₂×C₄×Q₈	—	3	1	no	—
288	C₂×C₄×D₄	—	3	1	no	—
289	C₄×SD₁₆	—	3	1	no	—
290	C₄×SD₁₆	—	3	1	no	—
291	C₄×SD₁₆	—	3	1	no	—
292	C₄×SD₁₆	—	3	1	no	—
293	C₄×SD₁₆	—	3	1	no	—
294	C₄×SD₁₆	—	3	1	no	—
295	C₄×SD₁₆	—	3	1	no	—
296	C₄×SD₁₆	C₃×D₃	1	1	yes	characteristic, direct product factor
297	C₂×#106	—	3	1	no	—
298	C₂×#103	—	3	1	no	—
299	C₂×#102	—	3	1	no	—
300	C₂×C₄×C₈	—	3	1	no	—
301	C₂⁴×C₃	—	6	1	no	—
302	C₂³×D₃	—	2	1	no	—
303	C₂×C₃×Q₈	—	2	1	no	—
304	C₂×C₃×Q₈	—	3	4	no	—
305	C₂×C₃×Q₈	—	3	1	no	—
306	C₂×C₃×Q₈	—	6	1	no	—
307	C₂×C₃×Q₈	—	6	2	no	—
308	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
309	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₃×D₄	—	2	1	no	—
311	C₂×C₃×D₄	—	3	4	no	—
312	C₂×C₃×D₄	—	3	1	no	—
313	C₂×C₃×D₄	—	6	2	no	—
314	C₂×C₃×D₄	—	6	1	no	—
315	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
316	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
317	C₂²×C₃×C₄	—	2	1	no	—
318	C₂²×C₃×C₄	—	2	1	no	—
319	C₂²×C₃×C₄	—	3	1	no	—
320	C₂²×C₃×C₄	—	3	1	no	—
321	C₂²×C₃×C₄	—	3	1	no	—
322	C₂²×C₃×C₄	—	4	1	no	—
323	C₂²×C₃×C₄	—	6	1	no	—
324	C₂²×C₃×C₄	—	6	1	no	—
325	C₂²×C₃×C₄	—	6	1	no	—
326	C₂²×C₃×C₄	—	6	1	no	—
327	C₂²×C₃×C₄	—	6	1	no	—
328	C₂²×C₃×C₄	—	6	1	no	—
329	C₂²×C₃×C₄	—	12	4	no	—
330	C₂×#67	—	2	1	no	—
331	C₂²×Dic₃	—	2	1	no	—
332	D₃×Q₈	—	2	2	no	—
333	D₃×Q₈	C₂×C₃×C₄	1	4	yes	complemented
334	D₃×D₄	—	2	2	no	—
335	D₃×D₄	C₂×C₃×C₄	1	4	yes	—
336	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
337	C₂×C₄×D₃	—	2	1	no	—
338	C₂×C₄×D₃	—	2	1	no	—
339	C₂×C₄×D₃	—	2	1	no	—
340	C₂×C₄×D₃	—	2	1	no	—
341	C₂×C₄×D₃	—	2	1	no	—
342	C₂×C₄×D₃	—	4	4	no	—
343	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
344	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
345	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
346	C₂×Dic₆	—	2	1	no	—
347	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
348	C₃×SD₁₆	—	2	4	no	—
349	C₃×SD₁₆	—	3	4	no	—
350	C₃×SD₁₆	—	3	4	no	—
351	C₃×SD₁₆	—	3	4	no	—
352	C₃×SD₁₆	C₄×D₃	1	4	yes	direct product factor
353	C₃×SD₁₆	C₂×C₃×C₄	1	4	yes	complemented
354	C₂×C₃×C₈	—	2	1	no	—
355	C₂×C₃×C₈	—	2	1	no	—
356	C₂×C₃×C₈	—	3	1	no	—
357	C₂×C₃×C₈	—	3	4	no	—
358	C₂×C₃×C₈	—	3	1	no	—
359	C₂×C₃×C₈	—	6	2	no	—
360	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
361	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
362	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
363	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
364	C₃×C₄⋊C₄	—	2	1	no	—
365	C₃×C₄⋊C₄	—	2	1	no	—
366	C₃×C₄⋊C₄	—	2	1	no	—
367	C₃×C₄⋊C₄	—	2	1	no	—
368	C₃×C₄⋊C₄	—	3	1	no	—
369	C₃×C₄⋊C₄	—	3	1	no	—
370	C₃×C₄⋊C₄	—	4	1	no	—
371	C₃×C₄⋊C₄	—	6	1	no	—
372	C₃×C₄⋊C₄	—	6	1	no	—
373	C₃×C₄⋊C₄	—	6	1	no	—
374	C₃×C₄⋊C₄	—	6	1	no	—
375	C₃×C₄⋊C₄	—	6	1	no	—
376	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
377	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
378	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
379	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
380	C₃×C₂²⋊C₄	—	2	1	no	—
381	C₃×C₂²⋊C₄	—	2	1	no	—
382	C₃×C₂²⋊C₄	—	4	1	no	—
383	C₃×C₂²⋊C₄	—	6	1	no	—
384	C₃×C₂²⋊C₄	—	6	1	no	—
385	C₃×C₂²⋊C₄	—	6	1	no	—
386	C₃×C₄²	—	2	1	no	—
387	C₃×C₄²	—	2	1	no	—
388	C₃×C₄²	—	2	1	no	—
389	C₃×C₄²	—	3	1	no	—
390	C₃×C₄²	—	3	1	no	—
391	C₃×C₄²	—	3	1	no	—
392	C₃×C₄²	—	4	1	no	—
393	C₃×C₄²	—	6	1	no	—
394	C₃×C₄²	—	6	1	no	—
395	C₃×C₄²	—	6	1	no	—
396	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
397	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
398	#217	—	2	1	no	—
399	#215	C₂×C₃×C₄	1	4	yes	complemented
400	#214	C₂×C₃×C₄	1	4	yes	complemented
401	(C₂×D₃)⋊C₄	—	2	1	no	—
402	(C₂×D₃)⋊C₄	—	2	1	no	—
403	C₄⋊Dic₃	—	2	1	no	—
404	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
405	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
406	Dic₃⋊C₄	—	2	1	no	—
407	Dic₃⋊C₄	—	2	1	no	—
408	Dic₃⋊C₄	—	2	1	no	—
409	Dic₃⋊C₄	—	2	1	no	—
410	C₄×Dic₃	—	2	1	no	—
411	C₄×Dic₃	—	2	1	no	—
412	C₄×Dic₃	—	2	1	no	—
413	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
414	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
415	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
416	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
417	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
418	#204	C₂×C₃×C₄	1	4	yes	complemented
419	D₃×C₈	—	2	2	no	—
420	D₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
421	C₂²×C₃²	—	2	2	no	—
422	C₂²×C₃²	—	4	1	no	—
423	C₂²×C₃²	—	4	1	no	—
424	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₃×D₃	—	2	2	no	—
426	C₂×C₃×D₃	—	4	1	no	—
427	C₂×C₃×D₃	—	4	1	no	—
428	C₂×C₃×D₃	—	4	8	no	—
429	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
430	C₂×C₃×D₃	C₂×SD₁₆	1	2	yes	—
431	C₂×C₃×D₃	#135	1	2	yes	—
432	C₃²×C₄	—	2	2	no	—
433	C₃²×C₄	—	2	1	no	—
434	C₃²×C₄	—	4	1	no	—
435	C₃²×C₄	—	4	1	no	—
436	C₃²×C₄	C₂×SD₁₆	1	2	yes	complemented
437	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
438	C₃²×C₄	C₂×#41	1	1	yes	characteristic
439	C₃×Dic₃	—	2	2	no	—
440	C₃×Dic₃	—	2	1	no	—
441	C₃×Dic₃	—	4	1	no	—
442	C₃×Dic₃	—	4	1	no	—
443	C₃×Dic₃	C₄×D₄	1	2	yes	—
444	C₃×Dic₃	C₂×SD₁₆	1	2	yes	complemented
445	C₂²×Q₈	—	3	1	no	—
446	C₂²×D₄	—	3	1	no	—
447	C₂³×C₄	—	6	1	no	—
448	C₂×SD₁₆	—	3	1	no	—
449	C₂×SD₁₆	—	3	1	no	—
450	C₂×SD₁₆	—	3	8	no	—
451	C₂×SD₁₆	—	3	1	no	—
452	C₂×SD₁₆	C₂×C₃×D₃	1	1	yes	characteristic
453	C₂²×C₈	—	3	1	no	—
454	C₂²×C₈	—	3	1	no	—
455	C₄×Q₈	—	3	1	no	—
456	C₄×Q₈	—	3	1	no	—
457	C₄×Q₈	—	3	1	no	—
458	C₄×Q₈	—	6	1	no	—
459	C₄×Q₈	—	6	1	no	—
460	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
461	C₄×D₄	—	3	1	no	—
462	C₄×D₄	—	3	1	no	—
463	C₄×D₄	—	3	1	no	—
464	C₄×D₄	—	6	1	no	—
465	C₄×D₄	—	6	1	no	—
466	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
467	C₂×C₄⋊C₄	—	3	1	no	—
468	C₂×C₄⋊C₄	—	3	1	no	—
469	C₂×C₄⋊C₄	—	6	1	no	—
470	C₂×C₂²⋊C₄	—	6	1	no	—
471	C₂×C₄²	—	3	1	no	—
472	C₂×C₄²	—	6	1	no	—
473	#106	—	3	1	no	—
474	#106	—	3	1	no	—
475	#106	—	3	1	no	—
476	#106	C₂×C₃×D₃	1	1	yes	characteristic, complemented
477	#103	—	3	1	no	—
478	#103	—	3	1	no	—
479	#103	—	3	1	no	—
480	#103	C₂×C₃×D₃	1	1	yes	characteristic, complemented
481	#102	—	3	1	no	—
482	#102	—	3	1	no	—
483	#102	—	3	1	no	—
484	#102	C₂×C₃×D₃	1	1	yes	characteristic
485	C₄×C₈	—	3	1	no	—
486	C₄×C₈	—	3	1	no	—
487	C₄×C₈	—	3	1	no	—
488	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
489	C₂³×C₃	—	2	1	no	—
490	C₂³×C₃	—	2	1	no	—
491	C₂³×C₃	—	3	1	no	—
492	C₂³×C₃	—	4	1	no	—
493	C₂³×C₃	—	6	4	no	—
494	C₂³×C₃	—	6	1	no	—
495	C₂³×C₃	—	12	2	no	—
496	C₂³×C₃	—	12	2	no	—
497	C₂²×D₃	—	2	1	no	—
498	C₂²×D₃	—	2	4	no	—
499	C₂²×D₃	—	4	2	no	—
500	C₂²×D₃	—	4	2	no	—
501	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
502	C₃×Q₈	—	2	1	no	—
503	C₃×Q₈	—	2	1	no	—
504	C₃×Q₈	—	2	2	no	—
505	C₃×Q₈	—	3	2	no	—
506	C₃×Q₈	—	4	1	no	—
507	C₃×Q₈	—	6	4	no	—
508	C₃×Q₈	—	6	1	no	—
509	C₃×Q₈	C₂×C₄×D₃	1	2	yes	complemented
510	C₃×Q₈	C₂²×C₃×C₄	1	2	yes	complemented
511	C₃×D₄	—	2	1	no	—
512	C₃×D₄	—	2	1	no	—
513	C₃×D₄	—	2	2	no	—
514	C₃×D₄	—	3	2	no	—
515	C₃×D₄	—	4	1	no	—
516	C₃×D₄	—	6	4	no	—
517	C₃×D₄	—	6	1	no	—
518	C₃×D₄	C₂×C₄×D₃	1	2	yes	—
519	C₃×D₄	C₂²×C₃×C₄	1	2	yes	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	1	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	3	1	no	—
530	C₂×C₃×C₄	—	3	1	no	—
531	C₂×C₃×C₄	—	3	4	no	—
532	C₂×C₃×C₄	—	3	2	no	—
533	C₂×C₃×C₄	—	3	2	no	—
534	C₂×C₃×C₄	—	3	1	no	—
535	C₂×C₃×C₄	—	4	1	no	—
536	C₂×C₃×C₄	—	4	1	no	—
537	C₂×C₃×C₄	—	4	1	no	—
538	C₂×C₃×C₄	—	4	2	no	—
539	C₂×C₃×C₄	—	4	2	no	—
540	C₂×C₃×C₄	—	6	2	no	—
541	C₂×C₃×C₄	—	6	4	no	—
542	C₂×C₃×C₄	—	6	1	no	—
543	C₂×C₃×C₄	—	6	1	no	—
544	C₂×C₃×C₄	—	6	1	no	—
545	C₂×C₃×C₄	—	8	2	no	—
546	C₂×C₃×C₄	—	12	2	no	—
547	C₂×C₃×C₄	—	12	2	no	—
548	C₂×C₃×C₄	—	12	2	no	—
549	C₂×C₃×C₄	—	12	2	no	—
550	C₂×C₃×C₄	—	12	2	no	—
551	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
552	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
553	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
554	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
555	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
556	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
557	#67	—	2	4	no	—
558	C₂×Dic₃	—	2	1	no	—
559	C₂×Dic₃	—	2	1	no	—
560	C₂×Dic₃	—	2	1	no	—
561	C₂×Dic₃	—	4	2	no	—
562	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
563	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
564	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
565	D₁₂	—	2	1	no	—
566	D₁₂	C₂²×C₃×C₄	1	2	yes	—
567	C₄×D₃	—	2	4	no	—
568	C₄×D₃	—	2	2	no	—
569	C₄×D₃	—	4	2	no	—
570	C₄×D₃	—	4	2	no	—
571	C₄×D₃	—	4	2	no	—
572	C₄×D₃	—	4	2	no	—
573	C₄×D₃	C₃×SD₁₆	1	4	yes	direct product factor
574	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
575	C₄×D₃	C₃×#41	1	2	yes	—
576	Dic₆	—	2	1	no	—
577	Dic₆	—	2	4	no	—
578	Dic₆	C₂²×C₃×C₄	1	2	yes	complemented
579	C₃×C₈	—	2	1	no	—
580	C₃×C₈	—	2	1	no	—
581	C₃×C₈	—	2	2	no	—
582	C₃×C₈	—	3	2	no	—
583	C₃×C₈	—	4	1	no	—
584	C₃×C₈	—	6	1	no	—
585	C₃×C₈	C₂×C₄×D₃	1	2	yes	complemented
586	C₃×C₈	C₂²×C₃×C₄	1	2	yes	complemented
587	C₃⋊C₈	—	2	1	no	—
588	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	complemented
589	C₂×C₃²	—	4	2	no	—
590	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
591	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
592	C₂×C₃²	C₂×#135	1	1	yes	characteristic
593	C₃×D₃	—	4	2	no	—
594	C₃×D₃	C₄×SD₁₆	1	4	yes	direct product factor
595	C₂⁴	—	6	1	no	—
596	C₂×Q₈	—	3	4	no	—
597	C₂×Q₈	—	3	1	no	—
598	C₂×Q₈	—	6	1	no	—
599	C₂×Q₈	—	6	2	no	—
600	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
601	C₂×D₄	—	3	4	no	—
602	C₂×D₄	—	3	1	no	—
603	C₂×D₄	—	6	2	no	—
604	C₂×D₄	—	6	1	no	—
605	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	3	1	no	—
608	C₂²×C₄	—	3	1	no	—
609	C₂²×C₄	—	3	1	no	—
610	C₂²×C₄	—	6	1	no	—
611	C₂²×C₄	—	6	1	no	—
612	C₂²×C₄	—	6	1	no	—
613	C₂²×C₄	—	6	1	no	—
614	C₂²×C₄	—	6	1	no	—
615	C₂²×C₄	—	6	1	no	—
616	C₂²×C₄	—	12	4	no	—
617	SD₁₆	—	3	4	no	—
618	SD₁₆	—	3	4	no	—
619	SD₁₆	—	3	4	no	—
620	SD₁₆	C₃×C₄×D₃	1	4	yes	direct product factor
621	C₂×C₈	—	3	1	no	—
622	C₂×C₈	—	3	4	no	—
623	C₂×C₈	—	3	1	no	—
624	C₂×C₈	—	6	2	no	—
625	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
626	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	3	1	no	—
629	C₄⋊C₄	—	3	1	no	—
630	C₄⋊C₄	—	6	1	no	—
631	C₄⋊C₄	—	6	1	no	—
632	C₄⋊C₄	—	6	1	no	—
633	C₄⋊C₄	—	6	1	no	—
634	C₄⋊C₄	—	6	1	no	—
635	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
636	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	6	1	no	—
639	C₂²⋊C₄	—	6	1	no	—
640	C₂²⋊C₄	—	6	1	no	—
641	C₄²	—	2	1	no	—
642	C₄²	—	3	1	no	—
643	C₄²	—	3	1	no	—
644	C₄²	—	3	1	no	—
645	C₄²	—	6	1	no	—
646	C₄²	—	6	1	no	—
647	C₄²	—	6	1	no	—
648	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
649	C₂²×C₃	—	2	2	no	—
650	C₂²×C₃	—	2	2	no	—
651	C₂²×C₃	—	2	1	no	—
652	C₂²×C₃	—	3	2	no	—
653	C₂²×C₃	—	3	2	no	—
654	C₂²×C₃	—	3	2	no	—
655	C₂²×C₃	—	4	2	no	—
656	C₂²×C₃	—	4	1	no	—
657	C₂²×C₃	—	4	1	no	—
658	C₂²×C₃	—	4	1	no	—
659	C₂²×C₃	—	4	1	no	—
660	C₂²×C₃	—	6	2	no	—
661	C₂²×C₃	—	8	1	no	—
662	C₂²×C₃	—	8	1	no	—
663	C₂²×C₃	—	12	8	no	—
664	C₂²×C₃	—	12	1	no	—
665	C₂²×C₃	—	12	1	no	—
666	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
667	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
668	C₂×D₃	—	2	2	no	—
669	C₂×D₃	—	4	1	no	—
670	C₂×D₃	—	4	1	no	—
671	C₂×D₃	—	4	8	no	—
672	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
673	C₂×D₃	C₂×C₃×SD₁₆	1	2	yes	—
674	C₂×D₃	C₃×#135	1	2	yes	—
675	C₃×C₄	—	2	1	no	—
676	C₃×C₄	—	2	1	no	—
677	C₃×C₄	—	2	2	no	—
678	C₃×C₄	—	2	2	no	—
679	C₃×C₄	—	2	2	no	—
680	C₃×C₄	—	2	1	no	—
681	C₃×C₄	—	2	1	no	—
682	C₃×C₄	—	3	2	no	—
683	C₃×C₄	—	3	2	no	—
684	C₃×C₄	—	4	1	no	—
685	C₃×C₄	—	4	2	no	—
686	C₃×C₄	—	4	1	no	—
687	C₃×C₄	—	4	1	no	—
688	C₃×C₄	—	4	1	no	—
689	C₃×C₄	—	4	1	no	—
690	C₃×C₄	—	6	1	no	—
691	C₃×C₄	—	6	2	no	—
692	C₃×C₄	—	8	1	no	—
693	C₃×C₄	—	8	1	no	—
694	C₃×C₄	—	12	1	no	—
695	C₃×C₄	—	12	1	no	—
696	C₃×C₄	D₃×SD₁₆	1	2	yes	direct product factor
697	C₃×C₄	C₂×C₃×SD₁₆	1	2	yes	complemented
698	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
699	C₃×C₄	D₃×#41	1	1	yes	characteristic
700	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
701	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
702	Dic₃	—	2	1	no	—
703	Dic₃	—	2	2	no	—
704	Dic₃	—	4	1	no	—
705	Dic₃	—	4	1	no	—
706	Dic₃	C₃×C₄×D₄	1	2	yes	—
707	Dic₃	C₂×C₃×SD₁₆	1	2	yes	complemented
708	C₃²	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
709	C₂³	—	2	1	no	—
710	C₂³	—	3	1	no	—
711	C₂³	—	6	4	no	—
712	C₂³	—	6	1	no	—
713	C₂³	—	12	2	no	—
714	C₂³	—	12	2	no	—
715	Q₈	—	2	1	no	—
716	Q₈	—	3	2	no	—
717	Q₈	—	6	4	no	—
718	Q₈	—	6	1	no	—
719	Q₈	C₂×C₃×C₄×D₃	1	2	yes	complemented
720	D₄	—	2	1	no	—
721	D₄	—	3	2	no	—
722	D₄	—	6	4	no	—
723	D₄	—	6	1	no	—
724	D₄	C₂×C₃×C₄×D₃	1	2	yes	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	3	1	no	—
729	C₂×C₄	—	3	1	no	—
730	C₂×C₄	—	3	4	no	—
731	C₂×C₄	—	3	2	no	—
732	C₂×C₄	—	3	2	no	—
733	C₂×C₄	—	3	1	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	6	2	no	—
736	C₂×C₄	—	6	4	no	—
737	C₂×C₄	—	6	1	no	—
738	C₂×C₄	—	6	1	no	—
739	C₂×C₄	—	6	1	no	—
740	C₂×C₄	—	12	2	no	—
741	C₂×C₄	—	12	2	no	—
742	C₂×C₄	—	12	2	no	—
743	C₂×C₄	—	12	2	no	—
744	C₂×C₄	—	12	2	no	—
745	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
746	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
747	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
748	C₈	—	2	1	no	—
749	C₈	—	3	2	no	—
750	C₈	—	6	1	no	—
751	C₈	C₂×C₃×C₄×D₃	1	2	yes	complemented
752	C₂×C₃	—	2	1	no	—
753	C₂×C₃	—	2	1	no	—
754	C₂×C₃	—	2	1	no	—
755	C₂×C₃	—	3	4	no	—
756	C₂×C₃	—	4	2	no	—
757	C₂×C₃	—	4	2	no	—
758	C₂×C₃	—	8	2	no	—
759	C₂×C₃	—	12	2	no	—
760	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
761	C₂×C₃	C₂×D₃×SD₁₆	1	1	yes	characteristic
762	C₂×C₃	D₃×#135	1	1	yes	characteristic
763	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
764	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
765	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
766	D₃	—	4	2	no	—
767	D₃	C₃×C₄×SD₁₆	1	4	yes	direct product factor
768	C₂²	—	2	2	no	—
769	C₂²	—	3	2	no	—
770	C₂²	—	3	2	no	—
771	C₂²	—	3	2	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	6	2	no	—
775	C₂²	—	12	8	no	—
776	C₂²	—	12	1	no	—
777	C₂²	—	12	1	no	—
778	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
779	C₄	—	2	1	no	—
780	C₄	—	2	2	no	—
781	C₄	—	3	2	no	—
782	C₄	—	3	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	6	1	no	—
786	C₄	—	6	2	no	—
787	C₄	—	12	1	no	—
788	C₄	—	12	1	no	—
789	C₄	C₃×D₃×SD₁₆	1	2	yes	direct product factor
790	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
791	C₄	C₃×D₃×#41	1	1	yes	characteristic
792	C₃	—	2	1	no	—
793	C₃	C₄×D₃×SD₁₆	1	1	yes	characteristic, direct product factor
794	C₃	C₂×C₃×C₄×SD₁₆	1	1	yes	characteristic, complemented
795	C₂	—	3	4	no	—
796	C₂	—	4	2	no	—
797	C₂	—	12	2	no	—
798	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
799	C₂	C₂×C₃×D₃×SD₁₆	1	1	yes	characteristic
800	C₂	C₃×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×SD₁₆	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×D₃×D₄	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₄×SD₁₆	D₃
hypocenter	C₃	C₂×C₃×C₄×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×D₃×Q₈	C₂	semidirect
4. C₃²×C₄×SD₁₆	C₂	semidirect
5. C₃×Dic₃×SD₁₆	C₂	semidirect
6. C₃×C₄×#215	C₂	semidirect
7. C₃×C₄×#214	C₂	semidirect
8. C₃×D₃×#106	C₂	semidirect
9. C₃×#4852	C₂	semidirect
10. C₃×D₃×#103	C₂	semidirect
11. C₃×#4788	C₂	semidirect
13. C₃×#4758	C₂	semidirect
14. C₃×C₄×#204	C₂	semidirect
15. C₃×C₄×D₃×C₈	C₂	semidirect
17. C₄×D₃×SD₁₆	C₃	direct (N × H)
22. C₃²×C₄×Q₈	C₂²	semidirect
24. C₃×Q₈×Dic₃	C₂²	semidirect
29. C₃×D₃×SD₁₆	C₄	direct (N × H)
38. C₃×#887	C₂²	semidirect
45. C₃×C₄×Dic₆	C₂²	semidirect
46. C₃²×#106	C₂²	semidirect
47. C₃²×#103	C₂²	semidirect
49. C₃²×C₄×C₈	C₂²	semidirect
50. C₃×#835	C₂²	semidirect
53. C₃×#817	C₂²	semidirect
54. C₃×#816	C₂²	semidirect
55. C₃×C₈×Dic₃	C₂²	semidirect
56. C₃×C₈×Dic₃	C₂²	semidirect
57. C₃×#810	C₂²	semidirect
59. C₃×#808	C₂²	semidirect
60. C₃×#808	C₂²	semidirect
61. C₃×C₄×C₃⋊C₈	C₂²	semidirect
66. C₄×D₃×Q₈	C₂×C₃	semidirect
76. C₃×C₄×SD₁₆	D₃	direct (N × H)
77. C₃×C₄×SD₁₆	C₂×C₃	semidirect
82. Dic₃×SD₁₆	C₂×C₃	semidirect
83. C₄×#215	C₂×C₃	semidirect
84. C₄×#214	C₂×C₃	semidirect
85. D₃×#106	C₂×C₃	semidirect
86. #4852	C₂×C₃	semidirect
87. D₃×#103	C₂×C₃	semidirect
88. #4788	C₂×C₃	semidirect
90. #4758	C₂×C₃	semidirect
91. C₄×#204	C₂×C₃	semidirect
92. C₄×D₃×C₈	C₂×C₃	semidirect
100. C₃×D₃×Q₈	C₂×C₄	semidirect
115. C₃²×SD₁₆	C₂×C₄	semidirect
125. C₃×#215	C₂×C₄	semidirect
126. C₃×#214	C₂×C₄	semidirect
144. C₃×#204	C₂×C₄	semidirect
146. C₃×D₃×C₈	C₂×C₄	semidirect
169. C₃×C₄×Q₈	C₂×D₃	semidirect
170. C₃×C₄×Q₈	C₂²×C₃	semidirect
185. Q₈×Dic₃	C₂²×C₃	semidirect
190. D₃×SD₁₆	C₃×C₄	direct (N × H)
199. #887	C₂²×C₃	semidirect
206. C₄×Dic₆	C₂²×C₃	semidirect
211. C₃×#106	C₂×D₃	semidirect
212. C₃×#106	C₂²×C₃	semidirect
217. C₃×#103	C₂×D₃	semidirect
218. C₃×#103	C₂²×C₃	semidirect
229. C₃×C₄×C₈	C₂×D₃	semidirect
230. C₃×C₄×C₈	C₂²×C₃	semidirect
231. #835	C₂²×C₃	semidirect
234. #817	C₂²×C₃	semidirect
235. #816	C₂²×C₃	semidirect
236. C₈×Dic₃	C₂²×C₃	semidirect
237. C₈×Dic₃	C₂²×C₃	semidirect
238. #810	C₂²×C₃	semidirect
240. #808	C₂²×C₃	semidirect
241. #808	C₂²×C₃	semidirect
242. C₄×C₃⋊C₈	C₂²×C₃	semidirect
250. C₃²×Q₈	C₂²×C₄	semidirect
276. C₃×C₄×D₃	SD₁₆	direct (N × H)
281. C₃×Dic₆	C₂²×C₄	semidirect
283. C₃²×C₈	C₂²×C₄	semidirect
285. C₃×C₃⋊C₈	C₂²×C₄	semidirect
296. C₄×SD₁₆	C₃×D₃	direct (N × H)
333. D₃×Q₈	C₂×C₃×C₄	semidirect
352. C₃×SD₁₆	C₄×D₃	direct (N × H)
353. C₃×SD₁₆	C₂×C₃×C₄	semidirect
399. #215	C₂×C₃×C₄	semidirect
400. #214	C₂×C₃×C₄	semidirect
418. #204	C₂×C₃×C₄	semidirect
420. D₃×C₈	C₂×C₃×C₄	semidirect
436. C₃²×C₄	C₂×SD₁₆	semidirect
444. C₃×Dic₃	C₂×SD₁₆	semidirect
460. C₄×Q₈	C₂×C₃×D₃	semidirect
476. #106	C₂×C₃×D₃	semidirect
480. #103	C₂×C₃×D₃	semidirect
488. C₄×C₈	C₂×C₃×D₃	semidirect
509. C₃×Q₈	C₂×C₄×D₃	semidirect
510. C₃×Q₈	C₂²×C₃×C₄	semidirect
573. C₄×D₃	C₃×SD₁₆	direct (N × H)
578. Dic₆	C₂²×C₃×C₄	semidirect
585. C₃×C₈	C₂×C₄×D₃	semidirect
586. C₃×C₈	C₂²×C₃×C₄	semidirect
588. C₃⋊C₈	C₂²×C₃×C₄	semidirect
594. C₃×D₃	C₄×SD₁₆	direct (N × H)
620. SD₁₆	C₃×C₄×D₃	direct (N × H)
696. C₃×C₄	D₃×SD₁₆	direct (N × H)
697. C₃×C₄	C₂×C₃×SD₁₆	semidirect
707. Dic₃	C₂×C₃×SD₁₆	semidirect
708. C₃²	C₂×C₄×SD₁₆	semidirect
719. Q₈	C₂×C₃×C₄×D₃	semidirect
751. C₈	C₂×C₃×C₄×D₃	semidirect
767. D₃	C₃×C₄×SD₁₆	direct (N × H)
789. C₄	C₃×D₃×SD₁₆	direct (N × H)
793. C₃	C₄×D₃×SD₁₆	direct (N × H)
794. C₃	C₂×C₃×C₄×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×SD₁₆	2
C₃×C₄×D₃×Q₈	2
C₃×C₄×D₃×D₄	2
C₃²×C₄×SD₁₆	2
C₃×Dic₃×SD₁₆	2
C₃×C₄×#215	2
C₃×C₄×#214	2
C₃×D₃×#106	2
C₃×#4852	2
C₃×D₃×#103	2
C₃×#4788	2
C₃×D₃×#102	2
C₃×#4758	2
C₃×C₄×#204	2
C₃×C₄×D₃×C₈	2
C₂×C₃×C₄×SD₁₆	3
C₄×D₃×SD₁₆	3

Subgroups — C3×C4×D3×SD16 #11859853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₃×SD₁₆ #11859853