Subgroups — C₃×#86979 #11903463

Order 1152.

2370 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5728	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5726	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5706	C₂	1	4	yes	maximal, complemented
5	C₃×#5705	C₂	1	4	yes	maximal, complemented
6	C₃×#5680	C₂	1	2	yes	maximal, complemented
7	C₃×#5676	C₂	1	2	yes	maximal, complemented
8	C₃×#5639	C₂	1	2	yes	maximal, complemented
9	C₃×#5627	C₂	1	2	yes	maximal, complemented
10	C₃×#5581	C₂	1	2	yes	maximal, complemented
11	C₃×#5579	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×#239	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₄×#239	C₂	1	2	yes	maximal, complemented
14	C₃×#5563	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5530	C₂	1	2	yes	maximal, complemented
17	C₃×D₃×#117	C₂	1	2	yes	maximal, complemented
18	C₃×#3475	—	3	1	no	maximal
19	#86979	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×C₃×#239	C₂²	1	1	yes	characteristic
21	C₂×C₃×#239	C₂²	1	2	yes	—
22	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
24	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃²×#126	C₂²	1	4	yes	complemented
26	C₃²×#124	C₂²	1	2	yes	—
27	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
30	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
31	C₃²×#117	C₂²	1	2	yes	complemented
32	C₃×#946	C₂²	1	2	yes	—
33	C₃×#946	C₂²	1	2	yes	complemented
34	C₃×#946	C₂²	1	2	yes	complemented
35	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
37	C₃×#938	C₂²	1	2	yes	—
38	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×#930	C₂²	1	2	yes	complemented
40	C₃×C₄×#67	C₂²	1	2	yes	—
41	C₃×#926	C₂²	1	2	yes	complemented
42	C₃×#897	C₂²	1	2	yes	—
43	C₃×#896	C₂²	1	4	yes	complemented
44	C₃×#895	C₂²	1	2	yes	complemented
45	C₃×#894	C₂²	1	4	yes	—
46	C₃×#894	C₂²	1	4	yes	complemented
47	C₃×#893	C₂²	1	1	yes	characteristic
48	C₃×#893	C₂²	1	2	yes	—
49	C₃×#893	C₂²	1	1	yes	characteristic, complemented
50	C₃×#893	C₂²	1	4	yes	complemented
51	C₃×#892	C₂²	1	1	yes	characteristic
52	C₃×#892	C₂²	1	2	yes	—
53	C₃×#892	C₂²	1	2	yes	complemented
54	C₃×#892	C₂²	1	4	yes	complemented
55	C₃×#892	C₂²	1	2	yes	complemented
56	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
58	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
59	C₃×#890	C₂²	1	2	yes	complemented
60	C₃×#889	C₂²	1	4	yes	complemented
61	C₃×#887	C₂²	1	2	yes	complemented
62	C₃×#885	C₂²	1	4	yes	complemented
63	C₃×#884	C₂²	1	4	yes	—
64	C₃×#883	C₂²	1	4	yes	—
65	C₃×#883	C₂²	1	4	yes	complemented
66	C₃×#882	C₂²	1	4	yes	—
67	C₃×#67⋊C₄	C₂²	1	2	yes	—
68	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
69	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
70	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₃×#879	C₂²	1	4	yes	complemented
72	C₃×#877	C₂²	1	4	yes	complemented
73	C₃×#876	C₂²	1	4	yes	complemented
74	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
75	C₃×C₄×D₁₂	C₂²	1	2	yes	—
76	C₃×C₄×D₁₂	C₂²	1	2	yes	—
77	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
78	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
79	C₃×#872	C₂²	1	4	yes	—
80	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
81	C₃×C₄²×D₃	C₂²	1	4	yes	complemented
82	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
83	C₃×#870	C₂²	1	2	yes	complemented
84	C₃×#869	C₂²	1	1	yes	characteristic, complemented
85	C₃×#556	—	2	1	no	—
86	C₃×#556	D₃	1	1	yes	characteristic, complemented
87	C₃×#556	C₂×C₃	1	1	yes	characteristic, complemented
88	C₃×#555	—	3	1	no	—
89	C₃×#554	—	3	1	no	—
90	C₃×#553	—	3	2	no	—
91	C₃×#552	—	3	2	no	—
92	C₃×#552	—	3	2	no	—
93	C₃×#551	—	3	4	no	—
94	C₃×#547	—	3	1	no	—
95	C₃×#546	—	3	2	no	—
96	C₃×#533	—	3	1	no	—
97	C₃×#529	—	3	4	no	—
98	C₃×#529	—	3	2	no	—
99	C₃×#525	—	3	2	no	—
100	C₃×C₄×#41	—	3	2	no	—
101	C₃×C₄×#41	—	3	1	no	—
102	C₂×C₃×C₄×D₄	—	3	1	no	—
103	C₂×C₃×#117	—	3	2	no	—
104	#5728	C₂×C₃	1	1	yes	characteristic, complemented
105	#5726	C₂×C₃	1	1	yes	characteristic, complemented
106	#5706	C₂×C₃	1	4	yes	complemented
107	#5705	C₂×C₃	1	4	yes	complemented
108	#5680	C₂×C₃	1	2	yes	complemented
109	#5676	C₂×C₃	1	2	yes	complemented
110	#5639	C₂×C₃	1	2	yes	complemented
111	#5627	C₂×C₃	1	2	yes	complemented
112	#5581	C₂×C₃	1	2	yes	complemented
113	#5579	C₂×C₃	1	1	yes	characteristic, complemented
114	C₄×#239	C₂×C₃	1	1	yes	characteristic, complemented
115	C₄×#239	C₂×C₃	1	2	yes	complemented
116	#5563	C₂×C₃	1	1	yes	characteristic, complemented
117	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
118	#5530	C₂×C₃	1	2	yes	complemented
119	D₃×#117	C₂×C₃	1	2	yes	complemented
120	C₂³×C₃×D₃	C₂³	1	2	yes	—
121	C₂×C₃²×Q₈	C₂³	1	2	yes	—
122	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
123	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
124	C₂²×C₃²×C₄	C₂³	1	2	yes	—
125	C₂×C₃×#67	C₂³	1	2	yes	—
126	C₂×C₃×#67	C₂³	1	4	yes	—
127	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
128	C₃×#239	—	2	8	no	—
129	C₃×#239	—	2	4	no	—
130	C₃×D₃×D₄	—	2	4	no	—
131	C₂×C₃×D₁₂	C₂³	1	2	yes	—
132	C₂×C₃×D₁₂	C₂³	1	4	yes	—
133	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
134	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₄×D₃	—	2	8	no	—
136	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
137	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
138	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
139	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
140	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
141	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
142	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
143	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
145	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
146	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
147	C₂×C₃×Dic₆	C₂³	1	2	yes	—
148	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
149	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
150	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
151	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
154	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₃²×C₄²	C₂³	1	4	yes	—
158	C₃²×C₄²	C₂³	1	1	yes	characteristic
159	C₃²×C₄²	C₂³	1	2	yes	—
160	C₃×#217	C₂³	1	4	yes	—
161	C₃×#217	C₂³	1	2	yes	—
162	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
163	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
164	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
165	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
166	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
167	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
168	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
169	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
170	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
171	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
172	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
173	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
174	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
175	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
176	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
177	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
178	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
179	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
180	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
181	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
182	C₃×C₄×Dic₃	C₂³	1	2	yes	—
183	C₃×C₄×Dic₃	C₂³	1	4	yes	—
184	C₃×C₄×Dic₃	C₂³	1	2	yes	—
185	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
186	C₃×C₄×Dic₃	C₂³	1	4	yes	—
187	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
188	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
189	#3475	—	3	1	no	Sylow
190	C₂×C₃×#41	—	3	1	no	—
191	C₂×C₃×#41	—	3	2	no	—
192	C₂²×C₃×D₄	—	3	1	no	—
193	C₂³×C₃×C₄	—	3	2	no	—
194	C₂×#239	C₂²×C₃	1	2	yes	—
195	C₂×#239	C₂²×C₃	1	1	yes	characteristic
196	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
197	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
198	C₃×C₄⋊Q₈	—	2	1	no	—
199	C₃×C₄⋊Q₈	—	3	1	no	—
200	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
201	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
202	C₃×#126	—	2	4	no	—
203	C₃×#126	—	3	4	no	—
204	C₃×#126	—	3	4	no	—
205	C₃×#126	C₂×D₃	1	4	yes	complemented
206	C₃×#126	C₂²×C₃	1	4	yes	complemented
207	C₃×#125	—	3	4	no	—
208	C₃×#125	—	3	2	no	—
209	C₃×#125	—	3	2	no	—
210	C₃×#124	—	2	2	no	—
211	C₃×#124	—	3	4	no	—
212	C₃×#124	C₂×D₃	1	2	yes	—
213	C₃×#124	C₂²×C₃	1	2	yes	—
214	C₃×#123	—	3	4	no	—
215	C₃×#123	—	3	4	no	—
216	C₃×#123	—	3	4	no	—
217	C₃×#123	—	3	4	no	—
218	C₃×C₂²⋊Q₈	—	2	2	no	—
219	C₃×C₂²⋊Q₈	—	3	2	no	—
220	C₃×C₂²⋊Q₈	—	3	2	no	—
221	C₃×C₂²⋊Q₈	—	3	2	no	—
222	C₃×C₂²⋊Q₈	—	3	4	no	—
223	C₃×C₂²⋊Q₈	—	3	2	no	—
224	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
225	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
226	C₃×#121	—	3	2	no	—
227	C₃×#121	—	3	2	no	—
228	C₃×#121	—	3	2	no	—
229	C₃×#121	—	3	4	no	—
230	C₃×#120	—	3	4	no	—
231	C₃×C₄×Q₈	—	2	2	no	—
232	C₃×C₄×Q₈	—	2	1	no	—
233	C₃×C₄×Q₈	—	3	2	no	—
234	C₃×C₄×Q₈	—	3	1	no	—
235	C₃×C₄×Q₈	—	3	2	no	—
236	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
237	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
238	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
239	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
240	C₃×C₄×D₄	—	2	1	no	—
241	C₃×C₄×D₄	—	3	1	no	—
242	C₃×C₄×D₄	—	3	2	no	—
243	C₃×C₄×D₄	—	3	1	no	—
244	C₃×C₄×D₄	—	3	2	no	—
245	C₃×C₄×D₄	—	3	4	no	—
246	C₃×C₄×D₄	—	3	1	no	—
247	C₃×C₄×D₄	—	3	2	no	—
248	C₃×C₄×D₄	—	3	4	no	—
249	C₃×C₄×D₄	—	3	1	no	—
250	C₃×C₄×D₄	—	3	2	no	—
251	C₃×C₄×D₄	—	3	2	no	—
252	C₃×C₄×D₄	—	3	1	no	—
253	C₃×C₄×D₄	—	3	4	no	—
254	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
255	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
256	C₃×#117	—	2	2	no	—
257	C₃×#117	—	3	2	no	—
258	C₃×#117	—	3	1	no	—
259	C₃×#117	—	3	2	no	—
260	C₃×#117	—	3	2	no	—
261	C₃×#117	—	3	4	no	—
262	C₃×#117	—	3	2	no	—
263	C₃×#117	—	3	4	no	—
264	C₃×#117	—	3	4	no	—
265	C₃×#117	C₂×D₃	1	2	yes	complemented
266	C₃×#117	C₂²×C₃	1	2	yes	complemented
267	C₂×C₃×C₄⋊C₄	—	3	1	no	—
268	C₂×C₃×C₄⋊C₄	—	3	2	no	—
269	C₂×C₃×C₄⋊C₄	—	3	2	no	—
270	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
271	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
272	C₂×C₃×C₄²	—	3	4	no	—
273	C₂×C₃×C₄²	—	3	1	no	—
274	C₂×C₃×C₄²	—	3	2	no	—
275	#946	C₂²×C₃	1	2	yes	—
276	#946	C₂²×C₃	1	2	yes	complemented
277	#946	C₂²×C₃	1	2	yes	complemented
278	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
279	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
280	#938	C₂²×C₃	1	2	yes	—
281	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
282	#930	C₂²×C₃	1	2	yes	complemented
283	C₄×#67	C₂²×C₃	1	2	yes	—
284	#926	C₂²×C₃	1	2	yes	complemented
285	#897	C₂²×C₃	1	2	yes	—
286	#896	C₂²×C₃	1	4	yes	complemented
287	#895	C₂²×C₃	1	2	yes	complemented
288	#894	C₂²×C₃	1	4	yes	—
289	#894	C₂²×C₃	1	4	yes	complemented
290	#893	C₂²×C₃	1	2	yes	—
291	#893	C₂²×C₃	1	1	yes	characteristic
292	#893	C₂²×C₃	1	4	yes	complemented
293	#893	C₂²×C₃	1	1	yes	characteristic, complemented
294	#892	C₂²×C₃	1	2	yes	—
295	#892	C₂²×C₃	1	1	yes	characteristic
296	#892	C₂²×C₃	1	4	yes	complemented
297	#892	C₂²×C₃	1	2	yes	complemented
298	#892	C₂²×C₃	1	2	yes	complemented
299	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
300	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
301	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
302	#890	C₂²×C₃	1	2	yes	complemented
303	#889	C₂²×C₃	1	4	yes	complemented
304	#887	C₂²×C₃	1	2	yes	complemented
305	#885	C₂²×C₃	1	4	yes	complemented
306	#884	C₂²×C₃	1	4	yes	—
307	#883	C₂²×C₃	1	4	yes	—
308	#883	C₂²×C₃	1	4	yes	complemented
309	#882	C₂²×C₃	1	4	yes	—
310	#67⋊C₄	C₂²×C₃	1	2	yes	—
311	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
312	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
313	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
314	#879	C₂²×C₃	1	4	yes	complemented
315	#877	C₂²×C₃	1	4	yes	complemented
316	#876	C₂²×C₃	1	4	yes	complemented
317	C₄×D₁₂	C₂²×C₃	1	2	yes	—
318	C₄×D₁₂	C₂²×C₃	1	2	yes	—
319	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
320	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
321	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
322	#872	C₂²×C₃	1	4	yes	—
323	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
324	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
325	C₄²×D₃	C₂²×C₃	1	4	yes	complemented
326	#870	C₂²×C₃	1	2	yes	complemented
327	#869	C₂²×C₃	1	1	yes	characteristic, complemented
328	C₂³×C₃²	C₂⁴	1	2	yes	—
329	C₂²×C₃×D₃	—	2	4	no	—
330	C₂²×C₃×D₃	—	2	4	no	—
331	C₂²×C₃×D₃	—	4	2	no	—
332	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
333	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
335	C₃²×Q₈	—	2	4	no	—
336	C₃²×Q₈	—	2	2	no	—
337	C₃²×D₄	—	2	2	no	—
338	C₂×C₃²×C₄	—	2	4	no	—
339	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
340	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
341	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
342	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
343	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
344	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
345	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
346	C₃×#67	—	2	4	no	—
347	C₃×#67	—	4	4	no	—
348	C₂×C₃×Dic₃	—	2	4	no	—
349	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
350	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
353	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
354	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
355	C₃×D₁₂	—	2	4	no	—
356	C₃×D₁₂	—	2	8	no	—
357	C₃×D₁₂	—	2	2	no	—
358	C₃×D₁₂	#41	1	4	yes	complemented
359	C₃×C₄×D₃	—	2	4	no	—
360	C₃×C₄×D₃	—	2	8	no	—
361	C₃×C₄×D₃	—	2	4	no	—
362	C₃×C₄×D₃	—	2	2	no	—
363	C₃×C₄×D₃	—	2	4	no	—
364	C₃×C₄×D₃	—	2	4	no	—
365	C₃×C₄×D₃	—	2	4	no	—
366	C₃×C₄×D₃	—	4	4	no	—
367	C₃×C₄×D₃	—	4	1	no	—
368	C₃×C₄×D₃	—	4	2	no	—
369	C₃×C₄×D₃	#41	1	4	yes	complemented
370	C₃×Dic₆	—	4	2	no	—
371	#556	C₃×D₃	1	1	yes	characteristic, complemented
372	#555	—	3	1	no	—
373	#554	—	3	1	no	—
374	#553	—	3	2	no	—
375	#552	—	3	2	no	—
376	#552	—	3	2	no	—
377	#551	—	3	4	no	—
378	#547	—	3	1	no	—
379	#546	—	3	2	no	—
380	#533	—	3	1	no	—
381	#529	—	3	4	no	—
382	#529	—	3	2	no	—
383	#525	—	3	2	no	—
384	C₄×#41	—	3	2	no	—
385	C₄×#41	—	3	1	no	—
386	C₂×C₄×D₄	—	3	1	no	—
387	C₂×#117	—	3	2	no	—
388	C₂⁴×C₃	—	3	2	no	—
389	C₂³×D₃	C₂³×C₃	1	2	yes	—
390	C₃×#41	—	6	4	no	—
391	C₃×#41	—	6	8	no	—
392	C₂×C₃×Q₈	—	2	1	no	—
393	C₂×C₃×Q₈	—	2	2	no	—
394	C₂×C₃×Q₈	—	3	2	no	—
395	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
396	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
397	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
398	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
399	C₂×C₃×D₄	—	2	1	no	—
400	C₂×C₃×D₄	—	3	2	no	—
401	C₂×C₃×D₄	—	3	4	no	—
402	C₂×C₃×D₄	—	3	1	no	—
403	C₂×C₃×D₄	—	3	2	no	—
404	C₂×C₃×D₄	—	3	4	no	—
405	C₂×C₃×D₄	—	3	1	no	—
406	C₂×C₃×D₄	—	6	4	no	—
407	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
408	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
409	C₂²×C₃×C₄	—	2	2	no	—
410	C₂²×C₃×C₄	—	3	1	no	—
411	C₂²×C₃×C₄	—	3	2	no	—
412	C₂²×C₃×C₄	—	3	2	no	—
413	C₂²×C₃×C₄	—	3	4	no	—
414	C₂²×C₃×C₄	—	3	1	no	—
415	C₂²×C₃×C₄	—	3	2	no	—
416	C₂²×C₃×C₄	—	3	2	no	—
417	C₂²×C₃×C₄	—	3	2	no	—
418	C₂²×C₃×C₄	—	3	2	no	—
419	C₂²×C₃×C₄	—	3	1	no	—
420	C₂²×C₃×C₄	—	3	4	no	—
421	C₂²×C₃×C₄	—	3	2	no	—
422	C₂²×C₃×C₄	—	6	8	no	—
423	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
424	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
425	C₂×#67	C₂³×C₃	1	2	yes	—
426	C₂×#67	C₂³×C₃	1	4	yes	—
427	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
428	#239	—	2	8	no	—
429	#239	—	2	4	no	—
430	D₃×D₄	—	2	4	no	—
431	C₂×D₁₂	C₂³×C₃	1	2	yes	—
432	C₂×D₁₂	C₂³×C₃	1	4	yes	—
433	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
434	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
435	C₂×C₄×D₃	—	2	8	no	—
436	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
437	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
438	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
439	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
440	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
441	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
442	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
443	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
444	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
445	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
446	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
447	C₂×Dic₆	C₂³×C₃	1	2	yes	—
448	C₃×C₄⋊C₄	—	2	1	no	—
449	C₃×C₄⋊C₄	—	2	2	no	—
450	C₃×C₄⋊C₄	—	2	1	no	—
451	C₃×C₄⋊C₄	—	2	4	no	—
452	C₃×C₄⋊C₄	—	2	2	no	—
453	C₃×C₄⋊C₄	—	2	2	no	—
454	C₃×C₄⋊C₄	—	3	4	no	—
455	C₃×C₄⋊C₄	—	3	4	no	—
456	C₃×C₄⋊C₄	—	3	2	no	—
457	C₃×C₄⋊C₄	—	3	4	no	—
458	C₃×C₄⋊C₄	—	3	4	no	—
459	C₃×C₄⋊C₄	—	3	1	no	—
460	C₃×C₄⋊C₄	—	3	2	no	—
461	C₃×C₄⋊C₄	—	3	1	no	—
462	C₃×C₄⋊C₄	—	3	2	no	—
463	C₃×C₄⋊C₄	—	3	4	no	—
464	C₃×C₄⋊C₄	—	3	2	no	—
465	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
466	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
467	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
468	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
469	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
470	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
471	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
472	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
473	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
474	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
475	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
476	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
477	C₃×C₂²⋊C₄	—	2	4	no	—
478	C₃×C₂²⋊C₄	—	2	2	no	—
479	C₃×C₂²⋊C₄	—	2	4	no	—
480	C₃×C₂²⋊C₄	—	3	4	no	—
481	C₃×C₂²⋊C₄	—	3	2	no	—
482	C₃×C₂²⋊C₄	—	3	2	no	—
483	C₃×C₂²⋊C₄	—	3	2	no	—
484	C₃×C₂²⋊C₄	—	3	4	no	—
485	C₃×C₂²⋊C₄	—	3	2	no	—
486	C₃×C₂²⋊C₄	—	3	4	no	—
487	C₃×C₂²⋊C₄	—	3	2	no	—
488	C₃×C₂²⋊C₄	—	3	4	no	—
489	C₃×C₂²⋊C₄	—	3	2	no	—
490	C₃×C₂²⋊C₄	—	3	4	no	—
491	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
492	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
493	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
494	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
495	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
496	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
497	C₃×C₄²	—	2	4	no	—
498	C₃×C₄²	—	2	1	no	—
499	C₃×C₄²	—	2	2	no	—
500	C₃×C₄²	—	3	2	no	—
501	C₃×C₄²	—	3	1	no	—
502	C₃×C₄²	—	3	4	no	—
503	C₃×C₄²	—	3	4	no	—
504	C₃×C₄²	—	3	1	no	—
505	C₃×C₄²	—	3	2	no	—
506	C₃×C₄²	—	3	1	no	—
507	C₃×C₄²	C₂²×D₃	1	4	yes	—
508	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
509	C₃×C₄²	C₂²×D₃	1	2	yes	—
510	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
511	C₃×C₄²	C₂³×C₃	1	2	yes	—
512	C₃×C₄²	C₂³×C₃	1	4	yes	—
513	#217	C₂³×C₃	1	4	yes	—
514	#217	C₂³×C₃	1	2	yes	—
515	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
516	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
517	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
518	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
519	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
520	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
521	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
522	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
523	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
524	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
525	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
526	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
527	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
528	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
529	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
530	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
531	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
532	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
533	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
534	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
535	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
536	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
537	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
538	C₄×Dic₃	C₂³×C₃	1	2	yes	—
539	C₄×Dic₃	C₂³×C₃	1	4	yes	—
540	C₄×Dic₃	C₂³×C₃	1	4	yes	—
541	C₄×Dic₃	C₂³×C₃	1	2	yes	—
542	C₂²×C₃²	—	2	2	no	—
543	C₂²×C₃²	—	2	2	no	—
544	C₂²×C₃²	—	2	2	no	—
545	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
546	C₂×C₃×D₃	—	2	2	no	—
547	C₂×C₃×D₃	—	2	1	no	—
548	C₂×C₃×D₃	—	2	2	no	—
549	C₂×C₃×D₃	—	2	1	no	—
550	C₂×C₃×D₃	—	2	2	no	—
551	C₂×C₃×D₃	—	2	2	no	—
552	C₂×C₃×D₃	—	2	2	no	—
553	C₂×C₃×D₃	—	4	8	no	—
554	C₂×C₃×D₃	C₂×#41	1	2	yes	—
555	C₂×C₃×D₃	C₂×#41	1	4	yes	—
556	C₃²×C₄	—	2	2	no	—
557	C₃²×C₄	—	2	4	no	—
558	C₃²×C₄	—	2	2	no	—
559	C₃²×C₄	—	2	1	no	—
560	C₃²×C₄	—	2	2	no	—
561	C₃²×C₄	C₂×#41	1	2	yes	—
562	C₃²×C₄	C₂×#41	1	2	yes	—
563	C₃×Dic₃	—	2	2	no	—
564	C₃×Dic₃	—	2	2	no	—
565	C₃×Dic₃	—	2	1	no	—
566	C₃×Dic₃	—	2	4	no	—
567	C₃×Dic₃	—	2	1	no	—
568	C₃×Dic₃	C₂×#41	1	2	yes	—
569	C₂×#41	—	3	1	no	—
570	C₂×#41	—	3	2	no	—
571	C₂²×D₄	—	3	1	no	—
572	C₂³×C₄	—	3	2	no	—
573	C₄⋊Q₈	—	3	1	no	—
574	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
575	#126	—	3	4	no	—
576	#126	—	3	4	no	—
577	#126	C₂×C₃×D₃	1	4	yes	complemented
578	#125	—	3	4	no	—
579	#125	—	3	2	no	—
580	#125	—	3	2	no	—
581	#124	—	3	4	no	—
582	#124	C₂×C₃×D₃	1	2	yes	—
583	#123	—	3	4	no	—
584	#123	—	3	4	no	—
585	#123	—	3	4	no	—
586	#123	—	3	4	no	—
587	C₂²⋊Q₈	—	3	2	no	—
588	C₂²⋊Q₈	—	3	2	no	—
589	C₂²⋊Q₈	—	3	2	no	—
590	C₂²⋊Q₈	—	3	4	no	—
591	C₂²⋊Q₈	—	3	2	no	—
592	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
593	#121	—	3	2	no	—
594	#121	—	3	2	no	—
595	#121	—	3	2	no	—
596	#121	—	3	4	no	—
597	#120	—	3	4	no	—
598	C₄×Q₈	—	3	2	no	—
599	C₄×Q₈	—	3	1	no	—
600	C₄×Q₈	—	3	2	no	—
601	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
602	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
603	C₄×D₄	—	3	1	no	—
604	C₄×D₄	—	3	2	no	—
605	C₄×D₄	—	3	1	no	—
606	C₄×D₄	—	3	4	no	—
607	C₄×D₄	—	3	2	no	—
608	C₄×D₄	—	3	1	no	—
609	C₄×D₄	—	3	2	no	—
610	C₄×D₄	—	3	4	no	—
611	C₄×D₄	—	3	1	no	—
612	C₄×D₄	—	3	2	no	—
613	C₄×D₄	—	3	2	no	—
614	C₄×D₄	—	3	1	no	—
615	C₄×D₄	—	3	4	no	—
616	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
617	#117	—	3	2	no	—
618	#117	—	3	1	no	—
619	#117	—	3	2	no	—
620	#117	—	3	2	no	—
621	#117	—	3	4	no	—
622	#117	—	3	2	no	—
623	#117	—	3	4	no	—
624	#117	—	3	4	no	—
625	#117	C₂×C₃×D₃	1	2	yes	complemented
626	C₂×C₄⋊C₄	—	3	2	no	—
627	C₂×C₄⋊C₄	—	3	2	no	—
628	C₂×C₄⋊C₄	—	3	1	no	—
629	C₂×C₂²⋊C₄	—	3	4	no	—
630	C₂×C₂²⋊C₄	—	3	2	no	—
631	C₂×C₄²	—	3	4	no	—
632	C₂×C₄²	—	3	1	no	—
633	C₂×C₄²	—	3	2	no	—
634	C₂³×C₃	—	2	2	no	—
635	C₂³×C₃	—	3	1	no	—
636	C₂³×C₃	—	3	2	no	—
637	C₂³×C₃	—	3	2	no	—
638	C₂³×C₃	—	6	4	no	—
639	C₂³×C₃	—	6	4	no	—
640	C₂³×C₃	—	12	2	no	—
641	C₂³×C₃	C₂³×D₃	1	2	yes	—
642	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
643	C₂²×D₃	—	2	4	no	—
644	C₂²×D₃	—	2	4	no	—
645	C₂²×D₃	—	4	2	no	—
646	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
647	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
648	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
649	C₃×Q₈	—	2	2	no	—
650	C₃×Q₈	—	2	4	no	—
651	C₃×Q₈	—	2	4	no	—
652	C₃×Q₈	—	2	2	no	—
653	C₃×Q₈	—	4	2	no	—
654	C₃×Q₈	—	4	4	no	—
655	C₃×Q₈	—	12	2	no	—
656	C₃×D₄	—	2	2	no	—
657	C₃×D₄	—	2	2	no	—
658	C₃×D₄	—	3	4	no	—
659	C₃×D₄	—	4	2	no	—
660	C₃×D₄	—	6	4	no	—
661	C₃×D₄	—	6	8	no	—
662	C₃×D₄	—	6	4	no	—
663	C₃×D₄	—	6	2	no	—
664	C₃×D₄	—	12	4	no	—
665	C₂×C₃×C₄	—	2	4	no	—
666	C₂×C₃×C₄	—	2	4	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	2	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	4	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	3	1	no	—
675	C₂×C₃×C₄	—	3	4	no	—
676	C₂×C₃×C₄	—	3	2	no	—
677	C₂×C₃×C₄	—	3	1	no	—
678	C₂×C₃×C₄	—	3	4	no	—
679	C₂×C₃×C₄	—	3	1	no	—
680	C₂×C₃×C₄	—	3	2	no	—
681	C₂×C₃×C₄	—	4	4	no	—
682	C₂×C₃×C₄	—	6	4	no	—
683	C₂×C₃×C₄	—	6	4	no	—
684	C₂×C₃×C₄	—	6	4	no	—
685	C₂×C₃×C₄	—	6	8	no	—
686	C₂×C₃×C₄	—	6	4	no	—
687	C₂×C₃×C₄	—	6	4	no	—
688	C₂×C₃×C₄	—	6	2	no	—
689	C₂×C₃×C₄	—	6	4	no	—
690	C₂×C₃×C₄	—	12	2	no	—
691	C₂×C₃×C₄	—	12	4	no	—
692	C₂×C₃×C₄	—	12	1	no	—
693	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
694	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
695	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
696	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
697	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
698	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
699	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
700	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
701	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
702	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
703	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
704	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
705	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
706	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
707	#67	—	2	4	no	—
708	#67	—	4	4	no	—
709	C₂×Dic₃	—	2	4	no	—
710	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
711	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
712	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
713	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
714	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
715	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
716	D₁₂	—	2	4	no	—
717	D₁₂	—	2	8	no	—
718	D₁₂	—	2	2	no	—
719	D₁₂	C₃×#41	1	4	yes	complemented
720	C₄×D₃	—	2	4	no	—
721	C₄×D₃	—	2	8	no	—
722	C₄×D₃	—	2	4	no	—
723	C₄×D₃	—	2	2	no	—
724	C₄×D₃	—	2	4	no	—
725	C₄×D₃	—	2	4	no	—
726	C₄×D₃	—	2	4	no	—
727	C₄×D₃	—	4	4	no	—
728	C₄×D₃	—	4	1	no	—
729	C₄×D₃	—	4	2	no	—
730	C₄×D₃	C₃×#41	1	4	yes	complemented
731	Dic₆	—	4	2	no	—
732	C₂×C₃²	—	4	2	no	—
733	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
734	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
735	C₂×C₃²	#585	1	1	yes	characteristic
736	C₃×D₃	—	2	2	no	—
737	C₃×D₃	—	2	4	no	—
738	C₃×D₃	—	4	2	no	—
739	C₂⁴	—	3	2	no	—
740	#41	—	6	4	no	—
741	#41	—	6	8	no	—
742	C₂×Q₈	—	3	2	no	—
743	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
744	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
745	C₂×D₄	—	3	2	no	—
746	C₂×D₄	—	3	4	no	—
747	C₂×D₄	—	3	1	no	—
748	C₂×D₄	—	3	2	no	—
749	C₂×D₄	—	3	4	no	—
750	C₂×D₄	—	3	1	no	—
751	C₂×D₄	—	6	4	no	—
752	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
753	C₂²×C₄	—	3	1	no	—
754	C₂²×C₄	—	3	2	no	—
755	C₂²×C₄	—	3	2	no	—
756	C₂²×C₄	—	3	4	no	—
757	C₂²×C₄	—	3	1	no	—
758	C₂²×C₄	—	3	2	no	—
759	C₂²×C₄	—	3	2	no	—
760	C₂²×C₄	—	3	2	no	—
761	C₂²×C₄	—	3	2	no	—
762	C₂²×C₄	—	3	1	no	—
763	C₂²×C₄	—	3	4	no	—
764	C₂²×C₄	—	3	2	no	—
765	C₂²×C₄	—	6	8	no	—
766	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
767	C₄⋊C₄	—	3	1	no	—
768	C₄⋊C₄	—	3	2	no	—
769	C₄⋊C₄	—	3	4	no	—
770	C₄⋊C₄	—	3	4	no	—
771	C₄⋊C₄	—	3	1	no	—
772	C₄⋊C₄	—	3	2	no	—
773	C₄⋊C₄	—	3	2	no	—
774	C₄⋊C₄	—	3	4	no	—
775	C₄⋊C₄	—	3	2	no	—
776	C₄⋊C₄	—	3	4	no	—
777	C₄⋊C₄	—	3	4	no	—
778	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
781	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
782	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
783	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
784	C₂²⋊C₄	—	3	4	no	—
785	C₂²⋊C₄	—	3	2	no	—
786	C₂²⋊C₄	—	3	2	no	—
787	C₂²⋊C₄	—	3	2	no	—
788	C₂²⋊C₄	—	3	4	no	—
789	C₂²⋊C₄	—	3	2	no	—
790	C₂²⋊C₄	—	3	4	no	—
791	C₂²⋊C₄	—	3	2	no	—
792	C₂²⋊C₄	—	3	4	no	—
793	C₂²⋊C₄	—	3	2	no	—
794	C₂²⋊C₄	—	3	4	no	—
795	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
796	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
797	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
798	C₄²	—	3	2	no	—
799	C₄²	—	3	1	no	—
800	C₄²	—	3	4	no	—
801	C₄²	—	3	4	no	—
802	C₄²	—	3	1	no	—
803	C₄²	—	3	2	no	—
804	C₄²	—	3	1	no	—
805	C₄²	C₂²×C₃×D₃	1	4	yes	—
806	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
807	C₄²	C₂²×C₃×D₃	1	2	yes	—
808	C₂²×C₃	—	2	2	no	—
809	C₂²×C₃	—	2	2	no	—
810	C₂²×C₃	—	2	2	no	—
811	C₂²×C₃	—	2	2	no	—
812	C₂²×C₃	—	2	2	no	—
813	C₂²×C₃	—	2	2	no	—
814	C₂²×C₃	—	2	1	no	—
815	C₂²×C₃	—	3	2	no	—
816	C₂²×C₃	—	3	4	no	—
817	C₂²×C₃	—	4	2	no	—
818	C₂²×C₃	—	4	2	no	—
819	C₂²×C₃	—	4	2	no	—
820	C₂²×C₃	—	6	2	no	—
821	C₂²×C₃	—	6	1	no	—
822	C₂²×C₃	—	6	2	no	—
823	C₂²×C₃	—	6	1	no	—
824	C₂²×C₃	—	6	2	no	—
825	C₂²×C₃	—	6	2	no	—
826	C₂²×C₃	—	6	2	no	—
827	C₂²×C₃	—	12	8	no	—
828	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
829	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
830	C₂×D₃	—	2	2	no	—
831	C₂×D₃	—	2	1	no	—
832	C₂×D₃	—	2	2	no	—
833	C₂×D₃	—	2	1	no	—
834	C₂×D₃	—	2	2	no	—
835	C₂×D₃	—	2	2	no	—
836	C₂×D₃	—	2	2	no	—
837	C₂×D₃	—	4	8	no	—
838	C₂×D₃	C₂×C₃×#41	1	2	yes	—
839	C₂×D₃	C₂×C₃×#41	1	4	yes	—
840	C₃×C₄	—	2	2	no	—
841	C₃×C₄	—	2	2	no	—
842	C₃×C₄	—	2	4	no	—
843	C₃×C₄	—	2	2	no	—
844	C₃×C₄	—	2	1	no	—
845	C₃×C₄	—	2	2	no	—
846	C₃×C₄	—	2	4	no	—
847	C₃×C₄	—	2	2	no	—
848	C₃×C₄	—	2	1	no	—
849	C₃×C₄	—	2	2	no	—
850	C₃×C₄	—	2	2	no	—
851	C₃×C₄	—	2	2	no	—
852	C₃×C₄	—	3	2	no	—
853	C₃×C₄	—	4	2	no	—
854	C₃×C₄	—	4	2	no	—
855	C₃×C₄	—	4	4	no	—
856	C₃×C₄	—	4	2	no	—
857	C₃×C₄	—	4	1	no	—
858	C₃×C₄	—	6	2	no	—
859	C₃×C₄	—	6	2	no	—
860	C₃×C₄	—	6	1	no	—
861	C₃×C₄	—	6	1	no	—
862	C₃×C₄	—	6	4	no	—
863	C₃×C₄	D₃×#41	1	2	yes	—
864	C₃×C₄	D₃×#41	1	2	yes	—
865	C₃×C₄	C₂×C₃×#41	1	2	yes	—
866	C₃×C₄	C₂×C₃×#41	1	2	yes	—
867	Dic₃	—	2	2	no	—
868	Dic₃	—	2	2	no	—
869	Dic₃	—	2	1	no	—
870	Dic₃	—	2	4	no	—
871	Dic₃	—	2	1	no	—
872	Dic₃	C₂×C₃×#41	1	2	yes	—
873	C₃²	#3475	1	1	yes	characteristic, complemented, Sylow
874	C₂³	—	3	1	no	—
875	C₂³	—	3	2	no	—
876	C₂³	—	3	2	no	—
877	C₂³	—	6	4	no	—
878	C₂³	—	6	4	no	—
879	C₂³	—	12	2	no	—
880	C₂³	C₂³×C₃×D₃	1	2	yes	—
881	Q₈	—	2	2	no	—
882	Q₈	—	2	4	no	—
883	Q₈	—	12	2	no	—
884	D₄	—	2	2	no	—
885	D₄	—	3	4	no	—
886	D₄	—	6	4	no	—
887	D₄	—	6	8	no	—
888	D₄	—	6	4	no	—
889	D₄	—	6	2	no	—
890	D₄	—	12	4	no	—
891	C₂×C₄	—	2	4	no	—
892	C₂×C₄	—	3	1	no	—
893	C₂×C₄	—	3	4	no	—
894	C₂×C₄	—	3	2	no	—
895	C₂×C₄	—	3	1	no	—
896	C₂×C₄	—	3	4	no	—
897	C₂×C₄	—	3	1	no	—
898	C₂×C₄	—	3	2	no	—
899	C₂×C₄	—	6	4	no	—
900	C₂×C₄	—	6	4	no	—
901	C₂×C₄	—	6	4	no	—
902	C₂×C₄	—	6	8	no	—
903	C₂×C₄	—	6	4	no	—
904	C₂×C₄	—	6	4	no	—
905	C₂×C₄	—	6	2	no	—
906	C₂×C₄	—	6	4	no	—
907	C₂×C₄	—	12	2	no	—
908	C₂×C₄	—	12	4	no	—
909	C₂×C₄	—	12	1	no	—
910	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
911	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
912	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
913	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
914	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
915	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
916	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
917	C₂×C₃	—	2	1	no	—
918	C₂×C₃	—	2	1	no	—
919	C₂×C₃	—	2	1	no	—
920	C₂×C₃	—	4	2	no	—
921	C₂×C₃	—	4	2	no	—
922	C₂×C₃	—	6	2	no	—
923	C₂×C₃	—	6	4	no	—
924	C₂×C₃	—	8	2	no	—
925	C₂×C₃	—	12	2	no	—
926	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
927	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
928	C₂×C₃	#5968	1	1	yes	characteristic
929	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
930	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
931	C₂×C₃	C₃×#585	1	1	yes	characteristic
932	D₃	—	2	2	no	—
933	D₃	—	2	4	no	—
934	D₃	—	4	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	3	2	no	—
939	C₂²	—	3	4	no	—
940	C₂²	—	6	2	no	—
941	C₂²	—	6	1	no	—
942	C₂²	—	6	2	no	—
943	C₂²	—	6	1	no	—
944	C₂²	—	6	2	no	—
945	C₂²	—	6	2	no	—
946	C₂²	—	6	2	no	—
947	C₂²	—	12	8	no	—
948	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	4	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	1	no	—
954	C₄	—	3	2	no	—
955	C₄	—	6	2	no	—
956	C₄	—	6	2	no	—
957	C₄	—	6	1	no	—
958	C₄	—	6	1	no	—
959	C₄	—	6	4	no	—
960	C₄	C₃×D₃×#41	1	2	yes	—
961	C₄	C₃×D₃×#41	1	2	yes	—
962	C₃	—	2	1	no	—
963	C₃	#86979	1	1	yes	characteristic, direct product factor
964	C₃	C₃×#3475	1	1	yes	characteristic, complemented
965	C₂	—	4	2	no	—
966	C₂	—	6	2	no	—
967	C₂	—	6	4	no	—
968	C₂	—	12	2	no	—
969	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
970	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
971	C₂	C₃×#5968	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#556	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#556	D₃
hypocenter	C₃	C₃×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#556

Complements

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

N	H ≅ G/N	type
1. C₃²×#556	C₂	semidirect
2. C₃×#5728	C₂	semidirect
3. C₃×#5726	C₂	semidirect
4. C₃×#5706	C₂	semidirect
5. C₃×#5705	C₂	semidirect
6. C₃×#5680	C₂	semidirect
7. C₃×#5676	C₂	semidirect
8. C₃×#5639	C₂	semidirect
9. C₃×#5627	C₂	semidirect
10. C₃×#5581	C₂	semidirect
11. C₃×#5579	C₂	semidirect
12. C₃×C₄×#239	C₂	semidirect
13. C₃×C₄×#239	C₂	semidirect
14. C₃×#5563	C₂	semidirect
15. C₃×C₄×D₃×D₄	C₂	semidirect
16. C₃×#5530	C₂	semidirect
17. C₃×D₃×#117	C₂	semidirect
19. #86979	C₃	direct (N × H)
24. C₃²×C₄⋊Q₈	C₂²	semidirect
25. C₃²×#126	C₂²	semidirect
27. C₃²×C₂²⋊Q₈	C₂²	semidirect
28. C₃²×C₄×Q₈	C₂²	semidirect
29. C₃²×C₄×Q₈	C₂²	semidirect
31. C₃²×#117	C₂²	semidirect
33. C₃×#946	C₂²	semidirect
34. C₃×#946	C₂²	semidirect
35. C₃×Q₈×Dic₃	C₂²	semidirect
36. C₃×Q₈×Dic₃	C₂²	semidirect
39. C₃×#930	C₂²	semidirect
41. C₃×#926	C₂²	semidirect
43. C₃×#896	C₂²	semidirect
44. C₃×#895	C₂²	semidirect
46. C₃×#894	C₂²	semidirect
49. C₃×#893	C₂²	semidirect
50. C₃×#893	C₂²	semidirect
53. C₃×#892	C₂²	semidirect
54. C₃×#892	C₂²	semidirect
55. C₃×#892	C₂²	semidirect
57. C₃×D₃×C₄⋊C₄	C₂²	semidirect
58. C₃×D₃×C₄⋊C₄	C₂²	semidirect
59. C₃×#890	C₂²	semidirect
60. C₃×#889	C₂²	semidirect
61. C₃×#887	C₂²	semidirect
62. C₃×#885	C₂²	semidirect
65. C₃×#883	C₂²	semidirect
68. C₃×#67⋊C₄	C₂²	semidirect
71. C₃×#879	C₂²	semidirect
72. C₃×#877	C₂²	semidirect
73. C₃×#876	C₂²	semidirect
77. C₃×C₄×D₁₂	C₂²	semidirect
78. C₃×C₄×D₁₂	C₂²	semidirect
81. C₃×C₄²×D₃	C₂²	semidirect
82. C₃×C₄²×D₃	C₂²	semidirect
83. C₃×#870	C₂²	semidirect
84. C₃×#869	C₂²	semidirect
86. C₃×#556	D₃	semidirect
87. C₃×#556	C₂×C₃	semidirect
104. #5728	C₂×C₃	semidirect
105. #5726	C₂×C₃	semidirect
106. #5706	C₂×C₃	semidirect
107. #5705	C₂×C₃	semidirect
108. #5680	C₂×C₃	semidirect
109. #5676	C₂×C₃	semidirect
110. #5639	C₂×C₃	semidirect
111. #5627	C₂×C₃	semidirect
112. #5581	C₂×C₃	semidirect
113. #5579	C₂×C₃	semidirect
114. C₄×#239	C₂×C₃	semidirect
115. C₄×#239	C₂×C₃	semidirect
116. #5563	C₂×C₃	semidirect
117. C₄×D₃×D₄	C₂×C₃	semidirect
118. #5530	C₂×C₃	semidirect
119. D₃×#117	C₂×C₃	semidirect
200. C₃×C₄⋊Q₈	C₂×D₃	semidirect
201. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
205. C₃×#126	C₂×D₃	semidirect
206. C₃×#126	C₂²×C₃	semidirect
224. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
225. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
236. C₃×C₄×Q₈	C₂×D₃	semidirect
237. C₃×C₄×Q₈	C₂×D₃	semidirect
238. C₃×C₄×Q₈	C₂²×C₃	semidirect
239. C₃×C₄×Q₈	C₂²×C₃	semidirect
265. C₃×#117	C₂×D₃	semidirect
266. C₃×#117	C₂²×C₃	semidirect
276. #946	C₂²×C₃	semidirect
277. #946	C₂²×C₃	semidirect
278. Q₈×Dic₃	C₂²×C₃	semidirect
279. Q₈×Dic₃	C₂²×C₃	semidirect
282. #930	C₂²×C₃	semidirect
284. #926	C₂²×C₃	semidirect
286. #896	C₂²×C₃	semidirect
287. #895	C₂²×C₃	semidirect
289. #894	C₂²×C₃	semidirect
292. #893	C₂²×C₃	semidirect
293. #893	C₂²×C₃	semidirect
296. #892	C₂²×C₃	semidirect
297. #892	C₂²×C₃	semidirect
298. #892	C₂²×C₃	semidirect
300. D₃×C₄⋊C₄	C₂²×C₃	semidirect
301. D₃×C₄⋊C₄	C₂²×C₃	semidirect
302. #890	C₂²×C₃	semidirect
303. #889	C₂²×C₃	semidirect
304. #887	C₂²×C₃	semidirect
305. #885	C₂²×C₃	semidirect
308. #883	C₂²×C₃	semidirect
311. #67⋊C₄	C₂²×C₃	semidirect
314. #879	C₂²×C₃	semidirect
315. #877	C₂²×C₃	semidirect
316. #876	C₂²×C₃	semidirect
320. C₄×D₁₂	C₂²×C₃	semidirect
321. C₄×D₁₂	C₂²×C₃	semidirect
324. C₄²×D₃	C₂²×C₃	semidirect
325. C₄²×D₃	C₂²×C₃	semidirect
326. #870	C₂²×C₃	semidirect
327. #869	C₂²×C₃	semidirect
358. C₃×D₁₂	#41	semidirect
369. C₃×C₄×D₃	#41	semidirect
371. #556	C₃×D₃	semidirect
574. C₄⋊Q₈	C₂×C₃×D₃	semidirect
577. #126	C₂×C₃×D₃	semidirect
592. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
601. C₄×Q₈	C₂×C₃×D₃	semidirect
602. C₄×Q₈	C₂×C₃×D₃	semidirect
625. #117	C₂×C₃×D₃	semidirect
719. D₁₂	C₃×#41	semidirect
730. C₄×D₃	C₃×#41	semidirect
873. C₃²	#3475	semidirect
963. C₃	#86979	direct (N × H)
964. C₃	C₃×#3475	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#556	2
C₃×#5728	2
C₃×#5726	2
C₃×#5706	2
C₃×#5705	2
C₃×#5680	2
C₃×#5676	2
C₃×#5639	2
C₃×#5627	2
C₃×#5581	2
C₃×#5579	2
C₃×C₄×#239	2
C₃×#5563	2
C₃×C₄×D₃×D₄	2
C₃×#5530	2
C₃×D₃×#117	2
C₃×#3475	3
#86979	3

Subgroups — C3×#86979 #11903463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86979 #11903463