Subgroups — C₃×D₇×#1004 #72246728

Order 4032.

3828 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10621596	C₂	1	4	yes	maximal, complemented
2	C₃×#10621657	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#10621564	C₂	1	2	yes	maximal, complemented
4	C₃×#10621573	C₂	1	4	yes	maximal, complemented
5	C₃×#10621572	C₂	1	4	yes	maximal, complemented
6	C₃×C₇×#1004	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₃×D₄×D₇	C₂	1	4	yes	maximal, complemented
8	C₃×D₇×#237	C₂	1	4	yes	maximal, complemented
9	C₂×C₃×D₇×#67	C₂	1	4	yes	maximal, complemented
10	C₃×D₇×#235	C₂	1	2	yes	maximal, complemented
11	C₂×C₃²×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₇×H(5,𝔽₂)	—	3	1	no	maximal
13	D₇×#1004	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂³×C₃²×D₇	C₂²	1	2	yes	complemented
15	C₂²×C₃×D₃×D₇	C₂²	1	4	yes	complemented
16	C₂×C₃²×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×#4268	C₂²	1	4	yes	complemented
18	C₃×#66730	C₂²	1	4	yes	complemented
19	C₃×D₄×D₂₁	C₂²	1	4	yes	complemented
20	C₃×#66728	C₂²	1	2	yes	complemented
21	C₂×C₃×C₇×#67	C₂²	1	4	yes	complemented
22	C₃×C₇×#237	C₂²	1	4	yes	complemented
23	C₃×D₃×C₇×D₄	C₂²	1	4	yes	complemented
24	C₃×C₇×#235	C₂²	1	2	yes	complemented
25	C₂×C₃²×C₂²⋊D₇	C₂²	1	2	yes	complemented
26	C₃²×D₄×D₇	C₂²	1	4	yes	complemented
27	C₃²×D₄×D₇	C₂²	1	4	yes	complemented
28	C₂×C₃²×D₂₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃²×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
30	C₃×#66694	C₂²	1	8	yes	complemented
31	C₃×D₃×C₂²⋊D₇	C₂²	1	8	yes	complemented
32	C₃×D₇×#67	C₂²	1	8	yes	complemented
33	C₃×D₇×#67	C₂²	1	4	yes	complemented
34	C₃×D₇×#67	C₂²	1	8	yes	complemented
35	C₃×D₇×#67	C₂²	1	8	yes	complemented
36	C₂×C₃×#4246	C₂²	1	4	yes	complemented
37	C₂×C₃×#4245	C₂²	1	4	yes	complemented
38	C₃×#66686	C₂²	1	4	yes	complemented
39	C₃×#66684	C₂²	1	8	yes	complemented
40	C₃×#66683	C₂²	1	8	yes	complemented
41	C₂×C₃×Dic₃×D₇	C₂²	1	4	yes	complemented
42	C₃×#66681	C₂²	1	4	yes	complemented
43	C₃×D₃×D₂₈	C₂²	1	4	yes	complemented
44	C₃×D₇×D₁₂	C₂²	1	2	yes	complemented
45	C₃×C₄×D₃×D₇	C₂²	1	4	yes	complemented
46	C₃×#66677	C₂²	1	2	yes	complemented
47	C₃×#66676	C₂²	1	2	yes	complemented
48	C₃×#66675	C₂²	1	4	yes	complemented
49	C₃×#66670	C₂²	1	4	yes	complemented
50	C₃×#66669	C₂²	1	4	yes	complemented
51	C₃×D₇×Dic₆	C₂²	1	2	yes	complemented
52	C₃×C₇×H(5,𝔽₂)	—	3	1	no	—
53	#10621657	C₂×C₃	1	1	yes	characteristic, complemented
54	C₇×#1004	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×#6553	—	3	4	no	—
56	C₃×#6553	—	3	2	no	—
57	C₃×D₇×#41	—	3	4	no	—
58	C₃×D₇×#41	—	3	2	no	—
59	C₃×#6548	—	3	1	no	—
60	C₃×#6548	—	3	4	no	—
61	C₃×#6548	—	3	4	no	—
62	C₂×C₃×D₄×D₇	—	2	1	no	—
63	C₂×C₃×D₄×D₇	—	3	4	no	—
64	C₂×C₃×D₄×D₇	—	3	4	no	—
65	C₂×C₃×D₄×D₇	D₃	1	1	yes	characteristic, complemented
66	C₂×C₃×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
67	#10621596	C₂×C₃	1	4	yes	complemented
68	C₂×D₇×#67	C₂×C₃	1	4	yes	complemented
69	#10621573	C₂×C₃	1	4	yes	complemented
70	#10621572	C₂×C₃	1	4	yes	complemented
71	D₇×#237	C₂×C₃	1	4	yes	complemented
72	D₃×D₄×D₇	C₂×C₃	1	4	yes	complemented
73	#10621564	C₂×C₃	1	2	yes	complemented
74	D₇×#235	C₂×C₃	1	2	yes	complemented
75	C₂×C₃×#1004	—	7	1	no	maximal, Hall
76	C₂³×C₃²×C₇	C₂³	1	2	yes	complemented
77	C₂²×C₃×D₂₁	C₂³	1	4	yes	complemented
78	C₂²×C₃×D₃×C₇	C₂³	1	4	yes	complemented
79	C₂²×C₃²×D₇	—	4	4	no	—
80	C₂²×C₃²×D₇	C₂³	1	1	yes	characteristic
81	C₂²×C₃²×D₇	C₂³	1	4	yes	—
82	C₂²×C₃²×D₇	C₂³	1	2	yes	complemented
83	C₂²×C₃²×D₇	C₂³	1	4	yes	complemented
84	C₂×C₃×D₃×D₇	—	4	8	no	—
85	C₂×C₃×D₃×D₇	C₂³	1	4	yes	—
86	C₂×C₃×D₃×D₇	C₂³	1	8	yes	complemented
87	C₃²×C₇×D₄	C₂³	1	4	yes	complemented
88	C₂×C₃²×C₄×C₇	C₂³	1	1	yes	characteristic, complemented
89	C₃×#4268	C₂³	1	4	yes	complemented
90	C₃×#4268	C₂³	1	8	yes	complemented
91	C₂×C₃×Dic₂₁	C₂³	1	4	yes	complemented
92	C₃×D₈₄	C₂³	1	2	yes	complemented
93	C₃×C₄×D₂₁	C₂³	1	4	yes	complemented
94	C₃×Dic₄₂	C₂³	1	2	yes	complemented
95	C₃×C₇×#67	C₂³	1	4	yes	complemented
96	C₃×C₇×#67	C₂³	1	8	yes	complemented
97	C₂×C₃×C₇×Dic₃	C₂³	1	4	yes	complemented
98	C₃×C₇×D₁₂	C₂³	1	2	yes	complemented
99	C₃×C₄×D₃×C₇	C₂³	1	4	yes	complemented
100	C₃×C₇×Dic₆	C₂³	1	2	yes	complemented
101	C₃²×C₂²⋊D₇	C₂³	1	8	yes	complemented
102	C₂×C₃²×Dic₇	C₂³	1	1	yes	characteristic, complemented
103	C₃²×D₂₈	C₂³	1	4	yes	complemented
104	C₃²×C₄×D₇	C₂³	1	2	yes	—
105	C₃²×C₄×D₇	C₂³	1	2	yes	complemented
106	C₃×#4248	C₂³	1	4	yes	complemented
107	C₃×#4247	C₂³	1	4	yes	complemented
108	C₃×#4246	C₂³	1	8	yes	complemented
109	C₃×#4246	C₂³	1	4	yes	complemented
110	C₃×#4245	C₂³	1	8	yes	complemented
111	C₃×#4245	C₂³	1	4	yes	complemented
112	C₃×D₂₁⋊C₄	C₂³	1	4	yes	complemented
113	C₃×D₃×Dic₇	C₂³	1	4	yes	complemented
114	C₃×Dic₃×D₇	C₂³	1	4	yes	—
115	C₃×Dic₃×D₇	C₂³	1	8	yes	complemented
116	D₇×H(5,𝔽₂)	—	3	1	no	Hall
117	C₂³×C₃×D₇	—	2	2	no	—
118	C₂³×C₃×D₇	—	3	4	no	—
119	C₂³×C₃×D₇	C₂×D₃	1	2	yes	complemented
120	C₂³×C₃×D₇	C₂²×C₃	1	2	yes	complemented
121	C₂²×D₃×D₇	C₂²×C₃	1	4	yes	complemented
122	C₃×C₇×#41	—	3	4	no	—
123	C₃×C₇×#41	—	3	2	no	—
124	C₂×C₃×C₇×D₄	—	2	1	no	—
125	C₂×C₃×C₇×D₄	—	3	4	no	—
126	C₂×C₃×C₇×D₄	—	3	4	no	—
127	C₂×C₃×C₇×D₄	C₂×D₃	1	1	yes	characteristic, complemented
128	C₂×C₃×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂×#4268	C₂²×C₃	1	4	yes	complemented
130	#66730	C₂²×C₃	1	4	yes	complemented
131	D₄×D₂₁	C₂²×C₃	1	4	yes	complemented
132	#66728	C₂²×C₃	1	2	yes	complemented
133	C₂×C₇×#67	C₂²×C₃	1	4	yes	complemented
134	C₇×#237	C₂²×C₃	1	4	yes	complemented
135	D₃×C₇×D₄	C₂²×C₃	1	4	yes	complemented
136	C₇×#235	C₂²×C₃	1	2	yes	complemented
137	C₂×C₃×C₂²⋊D₇	—	2	2	no	—
138	C₂×C₃×C₂²⋊D₇	—	3	4	no	—
139	C₂×C₃×C₂²⋊D₇	—	3	4	no	—
140	C₂×C₃×C₂²⋊D₇	—	3	8	no	—
141	C₂×C₃×C₂²⋊D₇	C₂×D₃	1	2	yes	complemented
142	C₂×C₃×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
143	C₃×#1161	—	3	4	no	—
144	C₃×#1161	—	3	2	no	—
145	C₃×Q₈×D₇	—	3	2	no	—
146	C₃×#1159	—	3	4	no	—
147	C₃×#1159	—	3	8	no	—
148	C₃×#1159	—	3	4	no	—
149	C₃×#1159	—	3	2	no	—
150	C₃×D₄×D₇	—	2	4	no	—
151	C₃×D₄×D₇	—	2	4	no	—
152	C₃×D₄×D₇	—	3	8	no	—
153	C₃×D₄×D₇	—	3	4	no	—
154	C₃×D₄×D₇	—	3	8	no	—
155	C₃×D₄×D₇	—	3	8	no	—
156	C₃×D₄×D₇	—	3	4	no	—
157	C₃×D₄×D₇	—	3	8	no	—
158	C₃×D₄×D₇	—	3	4	no	—
159	C₃×D₄×D₇	—	3	2	no	—
160	C₃×D₄×D₇	C₂×D₃	1	4	yes	complemented
161	C₃×D₄×D₇	C₂×D₃	1	4	yes	complemented
162	C₃×D₄×D₇	C₂²×C₃	1	4	yes	complemented
163	C₃×D₄×D₇	C₂²×C₃	1	4	yes	complemented
164	C₃×#1157	—	3	2	no	—
165	C₃×#1157	—	3	8	no	—
166	C₃×#1157	—	3	4	no	—
167	C₃×#1157	—	3	4	no	—
168	C₂×C₃×D₂₈	—	2	1	no	—
169	C₂×C₃×D₂₈	—	3	4	no	—
170	C₂×C₃×D₂₈	—	3	4	no	—
171	C₂×C₃×D₂₈	C₂×D₃	1	1	yes	characteristic, complemented
172	C₂×C₃×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₂×C₃×C₄×D₇	—	2	1	no	—
174	C₂×C₃×C₄×D₇	—	3	4	no	—
175	C₂×C₃×C₄×D₇	—	3	4	no	—
176	C₂×C₃×C₄×D₇	C₂×D₃	1	1	yes	characteristic, complemented
177	C₂×C₃×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
178	#66694	C₂²×C₃	1	8	yes	complemented
179	D₃×C₂²⋊D₇	C₂²×C₃	1	8	yes	complemented
180	D₇×#67	C₂²×C₃	1	4	yes	complemented
181	D₇×#67	C₂²×C₃	1	8	yes	complemented
182	D₇×#67	C₂²×C₃	1	8	yes	complemented
183	D₇×#67	C₂²×C₃	1	8	yes	complemented
184	C₂×#4246	C₂²×C₃	1	4	yes	complemented
185	C₂×#4245	C₂²×C₃	1	4	yes	complemented
186	#66686	C₂²×C₃	1	4	yes	complemented
187	#66684	C₂²×C₃	1	8	yes	complemented
188	#66683	C₂²×C₃	1	8	yes	complemented
189	C₂×Dic₃×D₇	C₂²×C₃	1	4	yes	complemented
190	#66681	C₂²×C₃	1	4	yes	complemented
191	D₃×D₂₈	C₂²×C₃	1	4	yes	complemented
192	D₇×D₁₂	C₂²×C₃	1	2	yes	complemented
193	C₄×D₃×D₇	C₂²×C₃	1	4	yes	complemented
194	#66677	C₂²×C₃	1	2	yes	complemented
195	#66676	C₂²×C₃	1	2	yes	complemented
196	#66675	C₂²×C₃	1	4	yes	complemented
197	#66670	C₂²×C₃	1	4	yes	complemented
198	#66669	C₂²×C₃	1	4	yes	complemented
199	D₇×Dic₆	C₂²×C₃	1	2	yes	complemented
200	C₂²×C₃²×D₄	—	7	1	no	—
201	C₂²×C₃×#67	—	7	4	no	—
202	C₃×#1004	—	7	1	no	—
203	C₃×#1004	—	7	4	no	—
204	C₃×#1004	—	7	4	no	—
205	C₃×#1004	—	7	4	no	—
206	C₃×#1004	—	7	2	no	—
207	C₃×#1004	D₇	1	1	yes	characteristic, direct product factor
208	C₂×C₃×#237	—	7	4	no	—
209	C₂×C₃×D₃×D₄	—	7	4	no	—
210	C₂×C₃×#235	—	7	2	no	—
211	C₂²×C₃²×C₇	—	4	2	no	—
212	C₂²×C₃²×C₇	C₂⁴	1	1	yes	characteristic
213	C₂²×C₃²×C₇	C₂⁴	1	4	yes	—
214	C₂×C₃×D₂₁	—	4	4	no	—
215	C₂×C₃×D₂₁	C₂⁴	1	4	yes	—
216	C₂×C₃×D₃×C₇	—	4	4	no	—
217	C₂×C₃×D₃×C₇	C₂⁴	1	4	yes	—
218	C₂×C₃²×D₇	—	2	2	no	—
219	C₂×C₃²×D₇	—	2	8	no	—
220	C₂×C₃²×D₇	—	4	4	no	—
221	C₂×C₃²×D₇	—	4	2	no	—
222	C₂×C₃²×D₇	C₂⁴	1	1	yes	characteristic
223	C₂×C₃²×D₇	C₂⁴	1	4	yes	—
224	C₂×C₃²×D₇	C₂⁴	1	1	yes	characteristic
225	C₃×D₃×D₇	—	2	8	no	—
226	C₃×D₃×D₇	—	4	8	no	—
227	C₃²×C₄×C₇	C₂⁴	1	2	yes	—
228	C₃×Dic₂₁	C₂⁴	1	4	yes	—
229	C₃×C₇×Dic₃	C₂⁴	1	4	yes	—
230	C₃²×Dic₇	C₂⁴	1	2	yes	—
231	C₇×H(5,𝔽₂)	—	3	1	no	—
232	#6553	—	3	4	no	—
233	#6553	—	3	2	no	—
234	D₇×#41	—	3	4	no	—
235	D₇×#41	—	3	2	no	—
236	#6548	—	3	1	no	—
237	#6548	—	3	4	no	—
238	#6548	—	3	4	no	—
239	C₂×D₄×D₇	—	3	4	no	—
240	C₂×D₄×D₇	—	3	4	no	—
241	C₂×D₄×D₇	C₃×D₃	1	1	yes	characteristic, complemented
242	C₂×C₃×H(5,𝔽₂)	—	21	1	no	—
243	C₂×#1004	—	7	1	no	—
244	C₂³×C₃×C₇	—	2	2	no	—
245	C₂³×C₃×C₇	—	3	4	no	—
246	C₂³×C₃×C₇	C₂²×D₃	1	2	yes	complemented
247	C₂³×C₃×C₇	C₂³×C₃	1	2	yes	complemented
248	C₂²×D₂₁	C₂³×C₃	1	4	yes	complemented
249	C₂²×D₃×C₇	C₂³×C₃	1	4	yes	complemented
250	C₂²×C₃×D₇	—	2	1	no	—
251	C₂²×C₃×D₇	—	2	4	no	—
252	C₂²×C₃×D₇	—	2	2	no	—
253	C₂²×C₃×D₇	—	2	4	no	—
254	C₂²×C₃×D₇	—	3	4	no	—
255	C₂²×C₃×D₇	—	3	4	no	—
256	C₂²×C₃×D₇	—	3	8	no	—
257	C₂²×C₃×D₇	—	4	4	no	—
258	C₂²×C₃×D₇	—	4	4	no	—
259	C₂²×C₃×D₇	—	4	4	no	—
260	C₂²×C₃×D₇	—	4	4	no	—
261	C₂²×C₃×D₇	—	12	8	no	—
262	C₂²×C₃×D₇	C₂²×D₃	1	4	yes	—
263	C₂²×C₃×D₇	C₂²×D₃	1	1	yes	characteristic
264	C₂²×C₃×D₇	C₂²×D₃	1	4	yes	complemented
265	C₂²×C₃×D₇	C₂²×D₃	1	2	yes	complemented
266	C₂²×C₃×D₇	C₂³×C₃	1	4	yes	—
267	C₂²×C₃×D₇	C₂³×C₃	1	1	yes	characteristic
268	C₂²×C₃×D₇	C₂³×C₃	1	4	yes	complemented
269	C₂²×C₃×D₇	C₂³×C₃	1	2	yes	complemented
270	C₂×D₃×D₇	—	4	8	no	—
271	C₂×D₃×D₇	C₂³×C₃	1	4	yes	—
272	C₂×D₃×D₇	C₂³×C₃	1	8	yes	complemented
273	C₃×C₇×Q₈	—	3	2	no	—
274	C₃×C₇×D₄	—	2	4	no	—
275	C₃×C₇×D₄	—	3	8	no	—
276	C₃×C₇×D₄	—	3	4	no	—
277	C₃×C₇×D₄	—	3	2	no	—
278	C₃×C₇×D₄	C₂²×D₃	1	4	yes	complemented
279	C₃×C₇×D₄	C₂³×C₃	1	4	yes	complemented
280	C₂×C₃×C₄×C₇	—	2	1	no	—
281	C₂×C₃×C₄×C₇	—	3	4	no	—
282	C₂×C₃×C₄×C₇	—	3	4	no	—
283	C₂×C₃×C₄×C₇	C₂²×D₃	1	1	yes	characteristic, complemented
284	C₂×C₃×C₄×C₇	C₂³×C₃	1	1	yes	characteristic, complemented
285	#4268	C₂³×C₃	1	8	yes	complemented
286	#4268	C₂³×C₃	1	4	yes	complemented
287	C₂×Dic₂₁	C₂³×C₃	1	4	yes	complemented
288	D₈₄	C₂³×C₃	1	2	yes	complemented
289	C₄×D₂₁	C₂³×C₃	1	4	yes	complemented
290	Dic₄₂	C₂³×C₃	1	2	yes	complemented
291	C₇×#67	C₂³×C₃	1	8	yes	complemented
292	C₇×#67	C₂³×C₃	1	4	yes	complemented
293	C₂×C₇×Dic₃	C₂³×C₃	1	4	yes	complemented
294	C₇×D₁₂	C₂³×C₃	1	2	yes	complemented
295	C₄×D₃×C₇	C₂³×C₃	1	4	yes	complemented
296	C₇×Dic₆	C₂³×C₃	1	2	yes	complemented
297	C₃×C₂²⋊D₇	—	2	8	no	—
298	C₃×C₂²⋊D₇	—	3	8	no	—
299	C₃×C₂²⋊D₇	—	3	4	no	—
300	C₃×C₂²⋊D₇	—	3	8	no	—
301	C₃×C₂²⋊D₇	—	3	4	no	—
302	C₃×C₂²⋊D₇	—	3	4	no	—
303	C₃×C₂²⋊D₇	C₂²×D₃	1	8	yes	complemented
304	C₃×C₂²⋊D₇	C₂³×C₃	1	8	yes	complemented
305	C₂×C₃×Dic₇	—	2	1	no	—
306	C₂×C₃×Dic₇	—	3	4	no	—
307	C₂×C₃×Dic₇	—	3	4	no	—
308	C₂×C₃×Dic₇	C₂²×D₃	1	1	yes	characteristic, complemented
309	C₂×C₃×Dic₇	C₂³×C₃	1	1	yes	characteristic, complemented
310	C₃×D₂₈	—	2	4	no	—
311	C₃×D₂₈	—	3	8	no	—
312	C₃×D₂₈	—	3	4	no	—
313	C₃×D₂₈	—	3	2	no	—
314	C₃×D₂₈	C₂²×D₃	1	4	yes	complemented
315	C₃×D₂₈	C₂³×C₃	1	4	yes	complemented
316	C₃×C₄×D₇	—	2	2	no	—
317	C₃×C₄×D₇	—	2	2	no	—
318	C₃×C₄×D₇	—	3	4	no	—
319	C₃×C₄×D₇	—	3	8	no	—
320	C₃×C₄×D₇	—	3	4	no	—
321	C₃×C₄×D₇	—	3	4	no	—
322	C₃×C₄×D₇	C₂²×D₃	1	2	yes	—
323	C₃×C₄×D₇	C₂²×D₃	1	2	yes	complemented
324	C₃×C₄×D₇	C₂³×C₃	1	2	yes	—
325	C₃×C₄×D₇	C₂³×C₃	1	2	yes	complemented
326	C₃×Dic₁₄	—	3	2	no	—
327	C₃×Dic₁₄	—	3	4	no	—
328	#4248	C₂³×C₃	1	4	yes	complemented
329	#4247	C₂³×C₃	1	4	yes	complemented
330	#4246	C₂³×C₃	1	8	yes	complemented
331	#4246	C₂³×C₃	1	4	yes	complemented
332	#4245	C₂³×C₃	1	8	yes	complemented
333	#4245	C₂³×C₃	1	4	yes	complemented
334	D₂₁⋊C₄	C₂³×C₃	1	4	yes	complemented
335	D₃×Dic₇	C₂³×C₃	1	4	yes	complemented
336	Dic₃×D₇	C₂³×C₃	1	4	yes	—
337	Dic₃×D₇	C₂³×C₃	1	8	yes	complemented
338	C₂⁴×C₃²	—	7	2	no	—
339	C₂³×C₃×D₃	—	7	4	no	—
340	C₂×C₃²×D₄	—	7	2	no	—
341	C₂×C₃²×D₄	—	7	4	no	—
342	C₂×C₃²×D₄	—	7	4	no	—
343	C₂×C₃²×D₄	—	7	1	no	—
344	C₂×C₃²×D₄	C₂×D₇	1	1	yes	characteristic, complemented
345	C₂²×C₃²×C₄	—	7	1	no	—
346	C₂×C₃×#67	—	7	4	no	—
347	C₂×C₃×#67	—	7	4	no	—
348	C₂×C₃×#67	—	7	4	no	—
349	C₂×C₃×#67	—	7	8	no	—
350	C₂×C₃×#67	—	7	8	no	—
351	C₂×C₃×#67	—	7	8	no	—
352	C₂×C₃×#67	—	7	4	no	—
353	C₂×C₃×#67	C₂×D₇	1	4	yes	complemented
354	C₂²×C₃×Dic₃	—	7	4	no	—
355	C₃×#237	—	7	4	no	—
356	C₃×#237	—	7	8	no	—
357	C₃×#237	—	7	8	no	—
358	C₃×#237	—	7	4	no	—
359	C₃×#237	—	7	4	no	—
360	C₃×#237	C₂×D₇	1	4	yes	complemented
361	C₃×D₃×D₄	—	7	8	no	—
362	C₃×D₃×D₄	—	7	4	no	—
363	C₃×D₃×D₄	—	7	8	no	—
364	C₃×D₃×D₄	—	7	4	no	—
365	C₃×D₃×D₄	—	7	4	no	—
366	C₃×D₃×D₄	C₂×D₇	1	4	yes	complemented
367	C₃×#235	—	7	2	no	—
368	C₃×#235	—	7	4	no	—
369	C₃×#235	—	7	2	no	—
370	C₃×#235	—	7	4	no	—
371	C₃×#235	—	7	2	no	—
372	C₃×#235	C₂×D₇	1	2	yes	complemented
373	C₂×C₃×D₁₂	—	7	2	no	—
374	C₂×C₃×C₄×D₃	—	7	4	no	—
375	C₂×C₃×Dic₆	—	7	2	no	—
376	C₂×C₃²×C₇	—	2	1	no	—
377	C₂×C₃²×C₇	—	2	4	no	—
378	C₂×C₃²×C₇	C₂⁵	1	1	yes	characteristic
379	C₃×D₂₁	—	2	4	no	—
380	C₃×D₃×C₇	—	2	4	no	—
381	C₃²×D₇	—	2	1	no	—
382	C₃²×D₇	—	2	4	no	—
383	C₃²×D₇	H(5,𝔽₂)	1	2	yes	complemented
384	C₂³×D₇	—	3	4	no	—
385	C₂³×D₇	C₂×C₃×D₃	1	2	yes	complemented
386	C₇×#41	—	3	4	no	—
387	C₇×#41	—	3	2	no	—
388	C₂×C₇×D₄	—	3	4	no	—
389	C₂×C₇×D₄	—	3	4	no	—
390	C₂×C₇×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
391	C₂×C₂²⋊D₇	—	3	4	no	—
392	C₂×C₂²⋊D₇	—	3	4	no	—
393	C₂×C₂²⋊D₇	—	3	8	no	—
394	C₂×C₂²⋊D₇	C₂×C₃×D₃	1	2	yes	complemented
395	#1161	—	3	4	no	—
396	#1161	—	3	2	no	—
397	Q₈×D₇	—	3	2	no	—
398	#1159	—	3	4	no	—
399	#1159	—	3	8	no	—
400	#1159	—	3	4	no	—
401	#1159	—	3	2	no	—
402	D₄×D₇	—	3	8	no	—
403	D₄×D₇	—	3	4	no	—
404	D₄×D₇	—	3	8	no	—
405	D₄×D₇	—	3	8	no	—
406	D₄×D₇	—	3	4	no	—
407	D₄×D₇	—	3	8	no	—
408	D₄×D₇	—	3	4	no	—
409	D₄×D₇	—	3	2	no	—
410	D₄×D₇	C₂×C₃×D₃	1	4	yes	complemented
411	D₄×D₇	C₂×C₃×D₃	1	4	yes	complemented
412	#1157	—	3	2	no	—
413	#1157	—	3	8	no	—
414	#1157	—	3	4	no	—
415	#1157	—	3	4	no	—
416	C₂×D₂₈	—	3	4	no	—
417	C₂×D₂₈	—	3	4	no	—
418	C₂×D₂₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
419	C₂×C₄×D₇	—	3	4	no	—
420	C₂×C₄×D₇	—	3	4	no	—
421	C₂×C₄×D₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented
422	C₃×H(5,𝔽₂)	—	3	1	no	—
423	C₃×H(5,𝔽₂)	—	21	4	no	—
424	C₃×H(5,𝔽₂)	—	21	4	no	—
425	C₃×H(5,𝔽₂)	—	21	4	no	—
426	C₃×H(5,𝔽₂)	—	21	2	no	—
427	C₃×H(5,𝔽₂)	—	21	1	no	—
428	C₂×C₃×#41	—	21	2	no	—
429	C₂×C₃×#41	—	21	4	no	—
430	C₂²×C₃×D₄	—	7	1	no	—
431	C₂²×C₃×D₄	—	7	1	no	—
432	C₂²×C₃×D₄	—	14	1	no	—
433	C₂²×C₃×D₄	—	21	4	no	—
434	C₂²×C₃×D₄	—	21	4	no	—
435	C₂²×#67	—	7	4	no	—
436	#1004	—	7	1	no	—
437	#1004	—	7	4	no	—
438	#1004	—	7	4	no	—
439	#1004	—	7	4	no	—
440	#1004	—	7	2	no	—
441	#1004	C₃×D₇	1	1	yes	characteristic, direct product factor
442	C₂×#237	—	7	4	no	—
443	C₂×D₃×D₄	—	7	4	no	—
444	C₂×#235	—	7	2	no	—
445	C₂²×C₃×C₇	—	2	1	no	—
446	C₂²×C₃×C₇	—	2	4	no	—
447	C₂²×C₃×C₇	—	3	4	no	—
448	C₂²×C₃×C₇	—	4	2	no	—
449	C₂²×C₃×C₇	—	4	2	no	—
450	C₂²×C₃×C₇	—	4	2	no	—
451	C₂²×C₃×C₇	—	4	2	no	—
452	C₂²×C₃×C₇	—	12	4	no	—
453	C₂²×C₃×C₇	C₂³×D₃	1	4	yes	—
454	C₂²×C₃×C₇	C₂³×D₃	1	1	yes	characteristic
455	C₂²×C₃×C₇	C₂⁴×C₃	1	1	yes	characteristic
456	C₂²×C₃×C₇	C₂⁴×C₃	1	4	yes	—
457	C₂×D₂₁	—	4	4	no	—
458	C₂×D₂₁	C₂⁴×C₃	1	4	yes	—
459	C₂×D₃×C₇	—	4	4	no	—
460	C₂×D₃×C₇	C₂⁴×C₃	1	4	yes	—
461	C₂×C₃×D₇	—	2	2	no	—
462	C₂×C₃×D₇	—	2	2	no	—
463	C₂×C₃×D₇	—	2	2	no	—
464	C₂×C₃×D₇	—	2	8	no	—
465	C₂×C₃×D₇	—	2	8	no	—
466	C₂×C₃×D₇	—	2	2	no	—
467	C₂×C₃×D₇	—	2	1	no	—
468	C₂×C₃×D₇	—	2	1	no	—
469	C₂×C₃×D₇	—	2	4	no	—
470	C₂×C₃×D₇	—	3	4	no	—
471	C₂×C₃×D₇	—	4	8	no	—
472	C₂×C₃×D₇	—	4	4	no	—
473	C₂×C₃×D₇	—	4	2	no	—
474	C₂×C₃×D₇	—	4	2	no	—
475	C₂×C₃×D₇	—	4	4	no	—
476	C₂×C₃×D₇	—	4	4	no	—
477	C₂×C₃×D₇	—	4	4	no	—
478	C₂×C₃×D₇	—	4	2	no	—
479	C₂×C₃×D₇	—	4	2	no	—
480	C₂×C₃×D₇	—	6	8	no	—
481	C₂×C₃×D₇	—	12	8	no	—
482	C₂×C₃×D₇	—	12	4	no	—
483	C₂×C₃×D₇	C₂³×D₃	1	4	yes	—
484	C₂×C₃×D₇	C₂³×D₃	1	1	yes	characteristic
485	C₂×C₃×D₇	C₂³×D₃	1	1	yes	characteristic
486	C₂×C₃×D₇	C₂⁴×C₃	1	4	yes	—
487	C₂×C₃×D₇	C₂⁴×C₃	1	1	yes	characteristic
488	C₂×C₃×D₇	C₂⁴×C₃	1	1	yes	characteristic
489	D₃×D₇	—	2	8	no	—
490	D₃×D₇	—	4	8	no	—
491	C₃×C₄×C₇	—	2	2	no	—
492	C₃×C₄×C₇	—	3	4	no	—
493	C₃×C₄×C₇	C₂³×D₃	1	2	yes	—
494	C₃×C₄×C₇	C₂⁴×C₃	1	2	yes	—
495	Dic₂₁	C₂⁴×C₃	1	4	yes	—
496	C₃×Dic₇	—	2	2	no	—
497	C₃×Dic₇	—	3	4	no	—
498	C₃×Dic₇	C₂³×D₃	1	2	yes	—
499	C₃×Dic₇	C₂⁴×C₃	1	2	yes	—
500	C₇×Dic₃	C₂⁴×C₃	1	4	yes	—
501	C₂³×C₃²	—	7	4	no	—
502	C₂³×C₃²	—	7	1	no	—
503	C₂³×C₃²	—	7	2	no	—
504	C₂³×C₃²	—	7	4	no	—
505	C₂³×C₃²	—	28	4	no	—
506	C₂³×C₃²	C₂²×D₇	1	2	yes	complemented
507	C₂²×C₃×D₃	—	7	4	no	—
508	C₂²×C₃×D₃	—	7	4	no	—
509	C₂²×C₃×D₃	—	7	8	no	—
510	C₂²×C₃×D₃	—	28	8	no	—
511	C₂²×C₃×D₃	C₂²×D₇	1	4	yes	complemented
512	C₃²×D₄	—	7	8	no	—
513	C₃²×D₄	—	7	4	no	—
514	C₃²×D₄	C₂²×D₇	1	4	yes	complemented
515	C₂×C₃²×C₄	—	7	1	no	—
516	C₂×C₃²×C₄	—	7	2	no	—
517	C₂×C₃²×C₄	—	7	2	no	—
518	C₂×C₃²×C₄	C₂²×D₇	1	1	yes	characteristic, complemented
519	C₃×#67	—	7	4	no	—
520	C₃×#67	—	7	8	no	—
521	C₃×#67	—	7	4	no	—
522	C₃×#67	—	7	8	no	—
523	C₃×#67	—	7	4	no	—
524	C₃×#67	—	7	8	no	—
525	C₃×#67	C₂²×D₇	1	4	yes	complemented
526	C₃×#67	C₂²×D₇	1	8	yes	complemented
527	C₂×C₃×Dic₃	—	7	4	no	—
528	C₂×C₃×Dic₃	—	7	4	no	—
529	C₂×C₃×Dic₃	—	7	8	no	—
530	C₂×C₃×Dic₃	C₂²×D₇	1	4	yes	complemented
531	C₃×D₁₂	—	7	4	no	—
532	C₃×D₁₂	—	7	2	no	—
533	C₃×D₁₂	C₂²×D₇	1	2	yes	complemented
534	C₃×C₄×D₃	—	7	4	no	—
535	C₃×C₄×D₃	—	7	4	no	—
536	C₃×C₄×D₃	—	7	4	no	—
537	C₃×C₄×D₃	C₂²×D₇	1	4	yes	complemented
538	C₃×Dic₆	—	7	2	no	—
539	C₃×Dic₆	—	7	4	no	—
540	C₃×Dic₆	C₂²×D₇	1	2	yes	complemented
541	C₂×H(5,𝔽₂)	—	21	1	no	Sylow
542	C₃²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
543	C₂³×C₇	—	3	4	no	—
544	C₂³×C₇	C₂²×C₃×D₃	1	2	yes	complemented
545	C₂²×D₇	—	3	4	no	—
546	C₂²×D₇	—	3	4	no	—
547	C₂²×D₇	—	3	8	no	—
548	C₂²×D₇	—	4	4	no	—
549	C₂²×D₇	—	12	8	no	—
550	C₂²×D₇	C₂²×C₃×D₃	1	4	yes	—
551	C₂²×D₇	C₂²×C₃×D₃	1	1	yes	characteristic
552	C₂²×D₇	C₂²×C₃×D₃	1	4	yes	complemented
553	C₂²×D₇	C₂²×C₃×D₃	1	2	yes	complemented
554	C₇×Q₈	—	3	2	no	—
555	C₇×D₄	—	3	8	no	—
556	C₇×D₄	—	3	4	no	—
557	C₇×D₄	—	3	2	no	—
558	C₇×D₄	C₂²×C₃×D₃	1	4	yes	complemented
559	C₂×C₄×C₇	—	3	4	no	—
560	C₂×C₄×C₇	—	3	4	no	—
561	C₂×C₄×C₇	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
562	C₂²⋊D₇	—	3	8	no	—
563	C₂²⋊D₇	—	3	4	no	—
564	C₂²⋊D₇	—	3	8	no	—
565	C₂²⋊D₇	—	3	4	no	—
566	C₂²⋊D₇	—	3	4	no	—
567	C₂²⋊D₇	C₂²×C₃×D₃	1	8	yes	complemented
568	C₂×Dic₇	—	3	4	no	—
569	C₂×Dic₇	—	3	4	no	—
570	C₂×Dic₇	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
571	D₂₈	—	3	8	no	—
572	D₂₈	—	3	4	no	—
573	D₂₈	—	3	2	no	—
574	D₂₈	C₂²×C₃×D₃	1	4	yes	complemented
575	C₄×D₇	—	3	4	no	—
576	C₄×D₇	—	3	8	no	—
577	C₄×D₇	—	3	4	no	—
578	C₄×D₇	—	3	4	no	—
579	C₄×D₇	C₂²×C₃×D₃	1	2	yes	—
580	C₄×D₇	C₂²×C₃×D₃	1	2	yes	complemented
581	Dic₁₄	—	3	2	no	—
582	Dic₁₄	—	3	4	no	—
583	C₂⁴×C₃	—	7	2	no	—
584	C₂⁴×C₃	—	7	2	no	—
585	C₂⁴×C₃	—	14	2	no	—
586	C₂⁴×C₃	—	21	4	no	—
587	C₂³×D₃	—	7	4	no	—
588	C₃×#41	—	3	4	no	—
589	C₃×#41	—	3	2	no	—
590	C₃×#41	—	21	4	no	—
591	C₃×#41	—	21	8	no	—
592	C₃×#41	—	21	4	no	—
593	C₃×#41	—	21	4	no	—
594	C₃×#41	—	21	2	no	—
595	C₃×#41	—	21	2	no	—
596	C₃×#41	—	21	8	no	—
597	C₃×#41	—	21	4	no	—
598	C₃×#41	—	21	4	no	—
599	C₃×#41	—	21	2	no	—
600	C₂×C₃×Q₈	—	21	2	no	—
601	C₂×C₃×D₄	—	2	1	no	—
602	C₂×C₃×D₄	—	3	4	no	—
603	C₂×C₃×D₄	—	3	4	no	—
604	C₂×C₃×D₄	—	7	2	no	—
605	C₂×C₃×D₄	—	7	2	no	—
606	C₂×C₃×D₄	—	7	4	no	—
607	C₂×C₃×D₄	—	7	4	no	—
608	C₂×C₃×D₄	—	7	4	no	—
609	C₂×C₃×D₄	—	7	4	no	—
610	C₂×C₃×D₄	—	7	1	no	—
611	C₂×C₃×D₄	—	7	1	no	—
612	C₂×C₃×D₄	—	14	1	no	—
613	C₂×C₃×D₄	—	14	4	no	—
614	C₂×C₃×D₄	—	14	4	no	—
615	C₂×C₃×D₄	—	14	2	no	—
616	C₂×C₃×D₄	—	21	4	no	—
617	C₂×C₃×D₄	—	21	4	no	—
618	C₂×C₃×D₄	—	21	2	no	—
619	C₂×C₃×D₄	—	21	8	no	—
620	C₂×C₃×D₄	—	21	4	no	—
621	C₂×C₃×D₄	—	21	4	no	—
622	C₂×C₃×D₄	—	21	8	no	—
623	C₂×C₃×D₄	—	21	8	no	—
624	C₂×C₃×D₄	—	21	8	no	—
625	C₂×C₃×D₄	—	21	8	no	—
626	C₂×C₃×D₄	—	21	4	no	—
627	C₂×C₃×D₄	—	21	4	no	—
628	C₂×C₃×D₄	—	21	4	no	—
629	C₂×C₃×D₄	D₃×D₇	1	1	yes	characteristic, complemented
630	C₂×C₃×D₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
631	C₂²×C₃×C₄	—	7	1	no	—
632	C₂²×C₃×C₄	—	7	1	no	—
633	C₂²×C₃×C₄	—	14	1	no	—
634	C₂²×C₃×C₄	—	21	4	no	—
635	C₂²×C₃×C₄	—	21	4	no	—
636	C₂×#67	—	7	4	no	—
637	C₂×#67	—	7	4	no	—
638	C₂×#67	—	7	4	no	—
639	C₂×#67	—	7	8	no	—
640	C₂×#67	—	7	8	no	—
641	C₂×#67	—	7	8	no	—
642	C₂×#67	—	7	4	no	—
643	C₂×#67	C₂×C₃×D₇	1	4	yes	complemented
644	C₂²×Dic₃	—	7	4	no	—
645	#237	—	7	4	no	—
646	#237	—	7	8	no	—
647	#237	—	7	8	no	—
648	#237	—	7	4	no	—
649	#237	—	7	4	no	—
650	#237	C₂×C₃×D₇	1	4	yes	complemented
651	D₃×D₄	—	7	8	no	—
652	D₃×D₄	—	7	4	no	—
653	D₃×D₄	—	7	8	no	—
654	D₃×D₄	—	7	4	no	—
655	D₃×D₄	—	7	4	no	—
656	D₃×D₄	C₂×C₃×D₇	1	4	yes	complemented
657	#235	—	7	2	no	—
658	#235	—	7	4	no	—
659	#235	—	7	2	no	—
660	#235	—	7	4	no	—
661	#235	—	7	2	no	—
662	#235	C₂×C₃×D₇	1	2	yes	complemented
663	C₂×D₁₂	—	7	2	no	—
664	C₂×C₄×D₃	—	7	4	no	—
665	C₂×Dic₆	—	7	2	no	—
666	C₂×C₃×C₇	—	2	1	no	—
667	C₂×C₃×C₇	—	2	1	no	—
668	C₂×C₃×C₇	—	2	1	no	—
669	C₂×C₃×C₇	—	2	4	no	—
670	C₂×C₃×C₇	—	2	1	no	—
671	C₂×C₃×C₇	—	2	4	no	—
672	C₂×C₃×C₇	—	2	1	no	—
673	C₂×C₃×C₇	—	4	4	no	—
674	C₂×C₃×C₇	—	6	4	no	—
675	C₂×C₃×C₇	C₂⁴×D₃	1	1	yes	characteristic
676	C₂×C₃×C₇	C₂⁵×C₃	1	1	yes	characteristic
677	D₂₁	—	2	4	no	—
678	C₃×D₇	—	2	1	no	—
679	C₃×D₇	—	2	1	no	—
680	C₃×D₇	—	2	1	no	—
681	C₃×D₇	—	2	4	no	—
682	C₃×D₇	—	2	4	no	—
683	C₃×D₇	—	2	1	no	—
684	C₃×D₇	—	2	2	no	—
685	C₃×D₇	—	4	4	no	—
686	C₃×D₇	—	6	4	no	—
687	C₃×D₇	#1004	1	2	yes	direct product factor
688	C₃×D₇	C₃×H(5,𝔽₂)	1	2	yes	complemented
689	D₃×C₇	—	2	4	no	—
690	C₂²×C₃²	—	4	2	no	—
691	C₂²×C₃²	—	7	1	no	—
692	C₂²×C₃²	—	7	4	no	—
693	C₂²×C₃²	—	7	1	no	—
694	C₂²×C₃²	—	14	2	no	—
695	C₂²×C₃²	—	14	8	no	—
696	C₂²×C₃²	—	28	2	no	—
697	C₂²×C₃²	—	28	4	no	—
698	C₂²×C₃²	C₂³×D₇	1	4	yes	—
699	C₂²×C₃²	C₂³×D₇	1	1	yes	characteristic
700	C₂×C₃×D₃	—	4	4	no	—
701	C₂×C₃×D₃	—	7	4	no	—
702	C₂×C₃×D₃	—	14	8	no	—
703	C₂×C₃×D₃	—	28	8	no	—
704	C₂×C₃×D₃	—	28	4	no	—
705	C₂×C₃×D₃	C₂³×D₇	1	4	yes	—
706	C₃²×C₄	—	7	2	no	—
707	C₃²×C₄	C₂³×D₇	1	2	yes	—
708	C₃×Dic₃	—	7	4	no	—
709	C₃×Dic₃	C₂³×D₇	1	4	yes	—
710	H(5,𝔽₂)	—	3	1	no	—
711	H(5,𝔽₂)	—	21	4	no	—
712	H(5,𝔽₂)	—	21	4	no	—
713	H(5,𝔽₂)	—	21	4	no	—
714	H(5,𝔽₂)	—	21	2	no	—
715	H(5,𝔽₂)	—	21	1	no	—
716	C₂×#41	—	21	2	no	—
717	C₂×#41	—	21	4	no	—
718	C₂²×D₄	—	7	1	no	—
719	C₂²×D₄	—	21	4	no	—
720	C₂²×D₄	—	21	4	no	—
721	C₂²×C₇	—	3	4	no	—
722	C₂²×C₇	—	4	2	no	—
723	C₂²×C₇	—	12	4	no	—
724	C₂²×C₇	C₂³×C₃×D₃	1	4	yes	—
725	C₂²×C₇	C₂³×C₃×D₃	1	1	yes	characteristic
726	C₂×D₇	—	2	2	no	—
727	C₂×D₇	—	2	8	no	—
728	C₂×D₇	—	3	4	no	—
729	C₂×D₇	—	4	4	no	—
730	C₂×D₇	—	4	2	no	—
731	C₂×D₇	—	6	8	no	—
732	C₂×D₇	—	12	8	no	—
733	C₂×D₇	—	12	4	no	—
734	C₂×D₇	C₂³×C₃×D₃	1	4	yes	—
735	C₂×D₇	C₂³×C₃×D₃	1	1	yes	characteristic
736	C₂×D₇	C₂³×C₃×D₃	1	1	yes	characteristic
737	C₄×C₇	—	3	4	no	—
738	C₄×C₇	C₂³×C₃×D₃	1	2	yes	—
739	Dic₇	—	3	4	no	—
740	Dic₇	C₂³×C₃×D₃	1	2	yes	—
741	C₂³×C₃	—	2	2	no	—
742	C₂³×C₃	—	3	4	no	—
743	C₂³×C₃	—	7	1	no	—
744	C₂³×C₃	—	7	4	no	—
745	C₂³×C₃	—	7	4	no	—
746	C₂³×C₃	—	7	1	no	—
747	C₂³×C₃	—	7	4	no	—
748	C₂³×C₃	—	7	2	no	—
749	C₂³×C₃	—	7	2	no	—
750	C₂³×C₃	—	7	4	no	—
751	C₂³×C₃	—	14	1	no	—
752	C₂³×C₃	—	14	2	no	—
753	C₂³×C₃	—	14	4	no	—
754	C₂³×C₃	—	14	4	no	—
755	C₂³×C₃	—	21	4	no	—
756	C₂³×C₃	—	21	8	no	—
757	C₂³×C₃	—	21	4	no	—
758	C₂³×C₃	—	28	4	no	—
759	C₂³×C₃	—	28	4	no	—
760	C₂³×C₃	—	28	4	no	—
761	C₂³×C₃	—	28	4	no	—
762	C₂³×C₃	—	84	8	no	—
763	C₂³×C₃	C₂×D₃×D₇	1	2	yes	complemented
764	C₂³×C₃	C₂²×C₃×D₇	1	2	yes	complemented
765	C₂²×D₃	—	7	4	no	—
766	C₂²×D₃	—	7	4	no	—
767	C₂²×D₃	—	7	8	no	—
768	C₂²×D₃	—	28	8	no	—
769	C₂²×D₃	C₂²×C₃×D₇	1	4	yes	complemented
770	C₃×Q₈	—	3	2	no	—
771	C₃×Q₈	—	21	4	no	—
772	C₃×Q₈	—	21	2	no	—
773	C₃×D₄	—	2	4	no	—
774	C₃×D₄	—	3	8	no	—
775	C₃×D₄	—	3	4	no	—
776	C₃×D₄	—	3	2	no	—
777	C₃×D₄	—	7	8	no	—
778	C₃×D₄	—	7	8	no	—
779	C₃×D₄	—	7	4	no	—
780	C₃×D₄	—	7	4	no	—
781	C₃×D₄	—	14	4	no	—
782	C₃×D₄	—	14	8	no	—
783	C₃×D₄	—	21	4	no	—
784	C₃×D₄	—	21	8	no	—
785	C₃×D₄	—	21	4	no	—
786	C₃×D₄	—	21	4	no	—
787	C₃×D₄	—	21	8	no	—
788	C₃×D₄	—	21	8	no	—
789	C₃×D₄	—	21	4	no	—
790	C₃×D₄	—	21	2	no	—
791	C₃×D₄	C₂×D₃×D₇	1	4	yes	complemented
792	C₃×D₄	C₂²×C₃×D₇	1	4	yes	complemented
793	C₂×C₃×C₄	—	2	1	no	—
794	C₂×C₃×C₄	—	3	4	no	—
795	C₂×C₃×C₄	—	3	4	no	—
796	C₂×C₃×C₄	—	7	1	no	—
797	C₂×C₃×C₄	—	7	1	no	—
798	C₂×C₃×C₄	—	7	2	no	—
799	C₂×C₃×C₄	—	7	2	no	—
800	C₂×C₃×C₄	—	7	2	no	—
801	C₂×C₃×C₄	—	7	2	no	—
802	C₂×C₃×C₄	—	14	2	no	—
803	C₂×C₃×C₄	—	14	2	no	—
804	C₂×C₃×C₄	—	14	1	no	—
805	C₂×C₃×C₄	—	21	4	no	—
806	C₂×C₃×C₄	—	21	4	no	—
807	C₂×C₃×C₄	—	21	8	no	—
808	C₂×C₃×C₄	—	21	4	no	—
809	C₂×C₃×C₄	—	21	4	no	—
810	C₂×C₃×C₄	—	21	4	no	—
811	C₂×C₃×C₄	C₂×D₃×D₇	1	1	yes	characteristic, complemented
812	C₂×C₃×C₄	C₂²×C₃×D₇	1	1	yes	characteristic, complemented
813	#67	—	7	4	no	—
814	#67	—	7	8	no	—
815	#67	—	7	4	no	—
816	#67	—	7	8	no	—
817	#67	—	7	4	no	—
818	#67	—	7	8	no	—
819	#67	C₂²×C₃×D₇	1	4	yes	complemented
820	#67	C₂²×C₃×D₇	1	8	yes	complemented
821	C₂×Dic₃	—	7	4	no	—
822	C₂×Dic₃	—	7	4	no	—
823	C₂×Dic₃	—	7	8	no	—
824	C₂×Dic₃	C₂²×C₃×D₇	1	4	yes	complemented
825	D₁₂	—	7	4	no	—
826	D₁₂	—	7	2	no	—
827	D₁₂	C₂²×C₃×D₇	1	2	yes	complemented
828	C₄×D₃	—	7	4	no	—
829	C₄×D₃	—	7	4	no	—
830	C₄×D₃	—	7	4	no	—
831	C₄×D₃	C₂²×C₃×D₇	1	4	yes	complemented
832	Dic₆	—	7	2	no	—
833	Dic₆	—	7	4	no	—
834	Dic₆	C₂²×C₃×D₇	1	2	yes	complemented
835	C₃×C₇	—	2	1	no	—
836	C₃×C₇	C₂×#1004	1	1	yes	characteristic, complemented
837	C₃×C₇	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented
838	C₂×C₃²	—	2	1	no	—
839	C₂×C₃²	—	2	4	no	—
840	C₂×C₃²	—	7	2	no	—
841	C₂×C₃²	—	14	1	no	—
842	C₂×C₃²	—	14	4	no	—
843	C₂×C₃²	C₂⁴×D₇	1	1	yes	characteristic
844	C₃×D₃	—	2	4	no	—
845	C₃×D₃	—	14	4	no	—
846	C₂⁴	—	7	2	no	—
847	C₂⁴	—	21	4	no	—
848	#41	—	3	4	no	—
849	#41	—	3	2	no	—
850	#41	—	21	4	no	—
851	#41	—	21	8	no	—
852	#41	—	21	4	no	—
853	#41	—	21	4	no	—
854	#41	—	21	2	no	—
855	#41	—	21	2	no	—
856	#41	—	21	8	no	—
857	#41	—	21	4	no	—
858	#41	—	21	4	no	—
859	#41	—	21	2	no	—
860	C₂×Q₈	—	21	2	no	—
861	C₂×D₄	—	3	4	no	—
862	C₂×D₄	—	3	4	no	—
863	C₂×D₄	—	7	2	no	—
864	C₂×D₄	—	7	4	no	—
865	C₂×D₄	—	7	4	no	—
866	C₂×D₄	—	7	1	no	—
867	C₂×D₄	—	21	4	no	—
868	C₂×D₄	—	21	4	no	—
869	C₂×D₄	—	21	2	no	—
870	C₂×D₄	—	21	8	no	—
871	C₂×D₄	—	21	4	no	—
872	C₂×D₄	—	21	4	no	—
873	C₂×D₄	—	21	8	no	—
874	C₂×D₄	—	21	8	no	—
875	C₂×D₄	—	21	8	no	—
876	C₂×D₄	—	21	8	no	—
877	C₂×D₄	—	21	4	no	—
878	C₂×D₄	—	21	4	no	—
879	C₂×D₄	—	21	4	no	—
880	C₂×D₄	C₃×D₃×D₇	1	1	yes	characteristic, complemented
881	C₂²×C₄	—	7	1	no	—
882	C₂²×C₄	—	21	4	no	—
883	C₂²×C₄	—	21	4	no	—
884	C₂×C₇	—	2	1	no	—
885	C₂×C₇	—	2	4	no	—
886	C₂×C₇	—	6	4	no	—
887	C₂×C₇	C₂⁴×C₃×D₃	1	1	yes	characteristic
888	D₇	—	2	1	no	—
889	D₇	—	2	4	no	—
890	D₇	—	6	4	no	—
891	D₇	C₃×#1004	1	2	yes	direct product factor
892	C₂²×C₃	—	2	1	no	—
893	C₂²×C₃	—	2	4	no	—
894	C₂²×C₃	—	3	4	no	—
895	C₂²×C₃	—	4	2	no	—
896	C₂²×C₃	—	4	2	no	—
897	C₂²×C₃	—	4	2	no	—
898	C₂²×C₃	—	4	2	no	—
899	C₂²×C₃	—	7	1	no	—
900	C₂²×C₃	—	7	1	no	—
901	C₂²×C₃	—	7	1	no	—
902	C₂²×C₃	—	7	4	no	—
903	C₂²×C₃	—	7	4	no	—
904	C₂²×C₃	—	7	1	no	—
905	C₂²×C₃	—	12	4	no	—
906	C₂²×C₃	—	14	1	no	—
907	C₂²×C₃	—	14	1	no	—
908	C₂²×C₃	—	14	4	no	—
909	C₂²×C₃	—	14	8	no	—
910	C₂²×C₃	—	14	2	no	—
911	C₂²×C₃	—	14	2	no	—
912	C₂²×C₃	—	14	8	no	—
913	C₂²×C₃	—	14	2	no	—
914	C₂²×C₃	—	14	2	no	—
915	C₂²×C₃	—	21	4	no	—
916	C₂²×C₃	—	28	8	no	—
917	C₂²×C₃	—	28	2	no	—
918	C₂²×C₃	—	28	4	no	—
919	C₂²×C₃	—	28	4	no	—
920	C₂²×C₃	—	28	2	no	—
921	C₂²×C₃	—	28	2	no	—
922	C₂²×C₃	—	28	2	no	—
923	C₂²×C₃	—	28	4	no	—
924	C₂²×C₃	—	28	4	no	—
925	C₂²×C₃	—	42	8	no	—
926	C₂²×C₃	—	84	4	no	—
927	C₂²×C₃	—	84	8	no	—
928	C₂²×C₃	C₂²×D₃×D₇	1	4	yes	—
929	C₂²×C₃	C₂²×D₃×D₇	1	1	yes	characteristic
930	C₂²×C₃	C₂³×C₃×D₇	1	4	yes	—
931	C₂²×C₃	C₂³×C₃×D₇	1	1	yes	characteristic
932	C₂×D₃	—	4	4	no	—
933	C₂×D₃	—	7	4	no	—
934	C₂×D₃	—	14	8	no	—
935	C₂×D₃	—	28	8	no	—
936	C₂×D₃	—	28	4	no	—
937	C₂×D₃	C₂³×C₃×D₇	1	4	yes	—
938	C₃×C₄	—	2	2	no	—
939	C₃×C₄	—	3	4	no	—
940	C₃×C₄	—	7	2	no	—
941	C₃×C₄	—	7	2	no	—
942	C₃×C₄	—	14	2	no	—
943	C₃×C₄	—	21	4	no	—
944	C₃×C₄	C₂²×D₃×D₇	1	2	yes	—
945	C₃×C₄	C₂³×C₃×D₇	1	2	yes	—
946	Dic₃	—	7	4	no	—
947	Dic₃	C₂³×C₃×D₇	1	4	yes	—
948	C₃²	D₇×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
949	C₂³	—	3	4	no	—
950	C₂³	—	7	1	no	—
951	C₂³	—	7	4	no	—
952	C₂³	—	7	4	no	—
953	C₂³	—	7	2	no	—
954	C₂³	—	21	4	no	—
955	C₂³	—	21	8	no	—
956	C₂³	—	21	4	no	—
957	C₂³	—	28	4	no	—
958	C₂³	—	84	8	no	—
959	C₂³	C₂×C₃×D₃×D₇	1	2	yes	complemented
960	Q₈	—	3	2	no	—
961	Q₈	—	21	4	no	—
962	Q₈	—	21	2	no	—
963	D₄	—	3	8	no	—
964	D₄	—	3	4	no	—
965	D₄	—	3	2	no	—
966	D₄	—	7	8	no	—
967	D₄	—	7	4	no	—
968	D₄	—	21	4	no	—
969	D₄	—	21	8	no	—
970	D₄	—	21	4	no	—
971	D₄	—	21	4	no	—
972	D₄	—	21	8	no	—
973	D₄	—	21	8	no	—
974	D₄	—	21	4	no	—
975	D₄	—	21	2	no	—
976	D₄	C₂×C₃×D₃×D₇	1	4	yes	complemented
977	C₂×C₄	—	3	4	no	—
978	C₂×C₄	—	3	4	no	—
979	C₂×C₄	—	7	1	no	—
980	C₂×C₄	—	7	2	no	—
981	C₂×C₄	—	7	2	no	—
982	C₂×C₄	—	21	4	no	—
983	C₂×C₄	—	21	4	no	—
984	C₂×C₄	—	21	8	no	—
985	C₂×C₄	—	21	4	no	—
986	C₂×C₄	—	21	4	no	—
987	C₂×C₄	—	21	4	no	—
988	C₂×C₄	C₂×C₃×D₃×D₇	1	1	yes	characteristic, complemented
989	C₇	C₂×C₃×#1004	1	1	yes	characteristic, complemented, Sylow
990	C₂×C₃	—	2	1	no	—
991	C₂×C₃	—	2	1	no	—
992	C₂×C₃	—	2	1	no	—
993	C₂×C₃	—	2	4	no	—
994	C₂×C₃	—	2	4	no	—
995	C₂×C₃	—	2	1	no	—
996	C₂×C₃	—	2	1	no	—
997	C₂×C₃	—	4	4	no	—
998	C₂×C₃	—	6	4	no	—
999	C₂×C₃	—	7	2	no	—
1000	C₂×C₃	—	7	2	no	—
1001	C₂×C₃	—	14	2	no	—
1002	C₂×C₃	—	14	1	no	—
1003	C₂×C₃	—	14	1	no	—
1004	C₂×C₃	—	14	1	no	—
1005	C₂×C₃	—	14	4	no	—
1006	C₂×C₃	—	14	4	no	—
1007	C₂×C₃	—	14	1	no	—
1008	C₂×C₃	—	28	4	no	—
1009	C₂×C₃	—	42	4	no	—
1010	C₂×C₃	C₂³×D₃×D₇	1	1	yes	characteristic
1011	C₂×C₃	C₂⁴×C₃×D₇	1	1	yes	characteristic
1012	D₃	—	2	4	no	—
1013	D₃	—	14	4	no	—
1014	C₂²	—	3	4	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	7	1	no	—
1017	C₂²	—	7	1	no	—
1018	C₂²	—	7	4	no	—
1019	C₂²	—	12	4	no	—
1020	C₂²	—	14	2	no	—
1021	C₂²	—	14	8	no	—
1022	C₂²	—	21	4	no	—
1023	C₂²	—	28	2	no	—
1024	C₂²	—	28	4	no	—
1025	C₂²	—	42	8	no	—
1026	C₂²	—	84	4	no	—
1027	C₂²	—	84	8	no	—
1028	C₂²	C₂²×C₃×D₃×D₇	1	4	yes	—
1029	C₂²	C₂²×C₃×D₃×D₇	1	1	yes	characteristic
1030	C₄	—	3	4	no	—
1031	C₄	—	7	2	no	—
1032	C₄	—	21	4	no	—
1033	C₄	C₂²×C₃×D₃×D₇	1	2	yes	—
1034	C₃	—	2	1	no	—
1035	C₃	D₇×#1004	1	1	yes	characteristic, direct product factor
1036	C₃	C₃×D₇×H(5,𝔽₂)	1	1	yes	characteristic, complemented
1037	C₂	—	2	1	no	—
1038	C₂	—	2	4	no	—
1039	C₂	—	6	4	no	—
1040	C₂	—	7	2	no	—
1041	C₂	—	14	1	no	—
1042	C₂	—	14	4	no	—
1043	C₂	—	42	4	no	—
1044	C₂	C₂³×C₃×D₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂³×D₃×D₇
commutator, cosocle	C₂×C₃×C₇	C₂⁵×C₃
Frattini	C₂	C₂³×C₃×D₃×D₇
Fitting	C₂×C₃²×C₇×D₄	C₂²
socle	C₂×C₃²×C₇	C₂⁵
hypercenter	C₂×C₃×D₄	D₃×D₇
hypocenter	C₃×C₇	C₂×C₃×H(5,𝔽₂)
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×#10621596	C₂	semidirect
2. C₃×#10621657	C₂	semidirect
3. C₃×#10621564	C₂	semidirect
4. C₃×#10621573	C₂	semidirect
5. C₃×#10621572	C₂	semidirect
6. C₃×C₇×#1004	C₂	semidirect
7. C₃×D₃×D₄×D₇	C₂	semidirect
8. C₃×D₇×#237	C₂	semidirect
9. C₂×C₃×D₇×#67	C₂	semidirect
10. C₃×D₇×#235	C₂	semidirect
11. C₂×C₃²×D₄×D₇	C₂	semidirect
13. D₇×#1004	C₃	direct (N × H)
14. C₂³×C₃²×D₇	C₂²	semidirect
15. C₂²×C₃×D₃×D₇	C₂²	semidirect
16. C₂×C₃²×C₇×D₄	C₂²	semidirect
17. C₂×C₃×#4268	C₂²	semidirect
18. C₃×#66730	C₂²	semidirect
19. C₃×D₄×D₂₁	C₂²	semidirect
20. C₃×#66728	C₂²	semidirect
21. C₂×C₃×C₇×#67	C₂²	semidirect
22. C₃×C₇×#237	C₂²	semidirect
23. C₃×D₃×C₇×D₄	C₂²	semidirect
24. C₃×C₇×#235	C₂²	semidirect
25. C₂×C₃²×C₂²⋊D₇	C₂²	semidirect
26. C₃²×D₄×D₇	C₂²	semidirect
27. C₃²×D₄×D₇	C₂²	semidirect
28. C₂×C₃²×D₂₈	C₂²	semidirect
29. C₂×C₃²×C₄×D₇	C₂²	semidirect
30. C₃×#66694	C₂²	semidirect
31. C₃×D₃×C₂²⋊D₇	C₂²	semidirect
32. C₃×D₇×#67	C₂²	semidirect
33. C₃×D₇×#67	C₂²	semidirect
34. C₃×D₇×#67	C₂²	semidirect
35. C₃×D₇×#67	C₂²	semidirect
36. C₂×C₃×#4246	C₂²	semidirect
37. C₂×C₃×#4245	C₂²	semidirect
38. C₃×#66686	C₂²	semidirect
39. C₃×#66684	C₂²	semidirect
40. C₃×#66683	C₂²	semidirect
41. C₂×C₃×Dic₃×D₇	C₂²	semidirect
42. C₃×#66681	C₂²	semidirect
43. C₃×D₃×D₂₈	C₂²	semidirect
44. C₃×D₇×D₁₂	C₂²	semidirect
45. C₃×C₄×D₃×D₇	C₂²	semidirect
46. C₃×#66677	C₂²	semidirect
47. C₃×#66676	C₂²	semidirect
48. C₃×#66675	C₂²	semidirect
49. C₃×#66670	C₂²	semidirect
50. C₃×#66669	C₂²	semidirect
51. C₃×D₇×Dic₆	C₂²	semidirect
53. #10621657	C₂×C₃	semidirect
54. C₇×#1004	C₂×C₃	semidirect
65. C₂×C₃×D₄×D₇	D₃	semidirect
66. C₂×C₃×D₄×D₇	C₂×C₃	semidirect
67. #10621596	C₂×C₃	semidirect
68. C₂×D₇×#67	C₂×C₃	semidirect
69. #10621573	C₂×C₃	semidirect
70. #10621572	C₂×C₃	semidirect
71. D₇×#237	C₂×C₃	semidirect
72. D₃×D₄×D₇	C₂×C₃	semidirect
73. #10621564	C₂×C₃	semidirect
74. D₇×#235	C₂×C₃	semidirect
76. C₂³×C₃²×C₇	C₂³	semidirect
77. C₂²×C₃×D₂₁	C₂³	semidirect
78. C₂²×C₃×D₃×C₇	C₂³	semidirect
82. C₂²×C₃²×D₇	C₂³	semidirect
83. C₂²×C₃²×D₇	C₂³	semidirect
86. C₂×C₃×D₃×D₇	C₂³	semidirect
87. C₃²×C₇×D₄	C₂³	semidirect
88. C₂×C₃²×C₄×C₇	C₂³	semidirect
89. C₃×#4268	C₂³	semidirect
90. C₃×#4268	C₂³	semidirect
91. C₂×C₃×Dic₂₁	C₂³	semidirect
92. C₃×D₈₄	C₂³	semidirect
93. C₃×C₄×D₂₁	C₂³	semidirect
94. C₃×Dic₄₂	C₂³	semidirect
95. C₃×C₇×#67	C₂³	semidirect
96. C₃×C₇×#67	C₂³	semidirect
97. C₂×C₃×C₇×Dic₃	C₂³	semidirect
98. C₃×C₇×D₁₂	C₂³	semidirect
99. C₃×C₄×D₃×C₇	C₂³	semidirect
100. C₃×C₇×Dic₆	C₂³	semidirect
101. C₃²×C₂²⋊D₇	C₂³	semidirect
102. C₂×C₃²×Dic₇	C₂³	semidirect
103. C₃²×D₂₈	C₂³	semidirect
105. C₃²×C₄×D₇	C₂³	semidirect
106. C₃×#4248	C₂³	semidirect
107. C₃×#4247	C₂³	semidirect
108. C₃×#4246	C₂³	semidirect
109. C₃×#4246	C₂³	semidirect
110. C₃×#4245	C₂³	semidirect
111. C₃×#4245	C₂³	semidirect
112. C₃×D₂₁⋊C₄	C₂³	semidirect
113. C₃×D₃×Dic₇	C₂³	semidirect
115. C₃×Dic₃×D₇	C₂³	semidirect
119. C₂³×C₃×D₇	C₂×D₃	semidirect
120. C₂³×C₃×D₇	C₂²×C₃	semidirect
121. C₂²×D₃×D₇	C₂²×C₃	semidirect
127. C₂×C₃×C₇×D₄	C₂×D₃	semidirect
128. C₂×C₃×C₇×D₄	C₂²×C₃	semidirect
129. C₂×#4268	C₂²×C₃	semidirect
130. #66730	C₂²×C₃	semidirect
131. D₄×D₂₁	C₂²×C₃	semidirect
132. #66728	C₂²×C₃	semidirect
133. C₂×C₇×#67	C₂²×C₃	semidirect
134. C₇×#237	C₂²×C₃	semidirect
135. D₃×C₇×D₄	C₂²×C₃	semidirect
136. C₇×#235	C₂²×C₃	semidirect
141. C₂×C₃×C₂²⋊D₇	C₂×D₃	semidirect
142. C₂×C₃×C₂²⋊D₇	C₂²×C₃	semidirect
160. C₃×D₄×D₇	C₂×D₃	semidirect
161. C₃×D₄×D₇	C₂×D₃	semidirect
162. C₃×D₄×D₇	C₂²×C₃	semidirect
163. C₃×D₄×D₇	C₂²×C₃	semidirect
171. C₂×C₃×D₂₈	C₂×D₃	semidirect
172. C₂×C₃×D₂₈	C₂²×C₃	semidirect
176. C₂×C₃×C₄×D₇	C₂×D₃	semidirect
177. C₂×C₃×C₄×D₇	C₂²×C₃	semidirect
178. #66694	C₂²×C₃	semidirect
179. D₃×C₂²⋊D₇	C₂²×C₃	semidirect
180. D₇×#67	C₂²×C₃	semidirect
181. D₇×#67	C₂²×C₃	semidirect
182. D₇×#67	C₂²×C₃	semidirect
183. D₇×#67	C₂²×C₃	semidirect
184. C₂×#4246	C₂²×C₃	semidirect
185. C₂×#4245	C₂²×C₃	semidirect
186. #66686	C₂²×C₃	semidirect
187. #66684	C₂²×C₃	semidirect
188. #66683	C₂²×C₃	semidirect
189. C₂×Dic₃×D₇	C₂²×C₃	semidirect
190. #66681	C₂²×C₃	semidirect
191. D₃×D₂₈	C₂²×C₃	semidirect
192. D₇×D₁₂	C₂²×C₃	semidirect
193. C₄×D₃×D₇	C₂²×C₃	semidirect
194. #66677	C₂²×C₃	semidirect
195. #66676	C₂²×C₃	semidirect
196. #66675	C₂²×C₃	semidirect
197. #66670	C₂²×C₃	semidirect
198. #66669	C₂²×C₃	semidirect
199. D₇×Dic₆	C₂²×C₃	semidirect
207. C₃×#1004	D₇	direct (N × H)
241. C₂×D₄×D₇	C₃×D₃	semidirect
246. C₂³×C₃×C₇	C₂²×D₃	semidirect
247. C₂³×C₃×C₇	C₂³×C₃	semidirect
248. C₂²×D₂₁	C₂³×C₃	semidirect
249. C₂²×D₃×C₇	C₂³×C₃	semidirect
264. C₂²×C₃×D₇	C₂²×D₃	semidirect
265. C₂²×C₃×D₇	C₂²×D₃	semidirect
268. C₂²×C₃×D₇	C₂³×C₃	semidirect
269. C₂²×C₃×D₇	C₂³×C₃	semidirect
272. C₂×D₃×D₇	C₂³×C₃	semidirect
278. C₃×C₇×D₄	C₂²×D₃	semidirect
279. C₃×C₇×D₄	C₂³×C₃	semidirect
283. C₂×C₃×C₄×C₇	C₂²×D₃	semidirect
284. C₂×C₃×C₄×C₇	C₂³×C₃	semidirect
285. #4268	C₂³×C₃	semidirect
286. #4268	C₂³×C₃	semidirect
287. C₂×Dic₂₁	C₂³×C₃	semidirect
288. D₈₄	C₂³×C₃	semidirect
289. C₄×D₂₁	C₂³×C₃	semidirect
290. Dic₄₂	C₂³×C₃	semidirect
291. C₇×#67	C₂³×C₃	semidirect
292. C₇×#67	C₂³×C₃	semidirect
293. C₂×C₇×Dic₃	C₂³×C₃	semidirect
294. C₇×D₁₂	C₂³×C₃	semidirect
295. C₄×D₃×C₇	C₂³×C₃	semidirect
296. C₇×Dic₆	C₂³×C₃	semidirect
303. C₃×C₂²⋊D₇	C₂²×D₃	semidirect
304. C₃×C₂²⋊D₇	C₂³×C₃	semidirect
308. C₂×C₃×Dic₇	C₂²×D₃	semidirect
309. C₂×C₃×Dic₇	C₂³×C₃	semidirect
314. C₃×D₂₈	C₂²×D₃	semidirect
315. C₃×D₂₈	C₂³×C₃	semidirect
323. C₃×C₄×D₇	C₂²×D₃	semidirect
325. C₃×C₄×D₇	C₂³×C₃	semidirect
328. #4248	C₂³×C₃	semidirect
329. #4247	C₂³×C₃	semidirect
330. #4246	C₂³×C₃	semidirect
331. #4246	C₂³×C₃	semidirect
332. #4245	C₂³×C₃	semidirect
333. #4245	C₂³×C₃	semidirect
334. D₂₁⋊C₄	C₂³×C₃	semidirect
335. D₃×Dic₇	C₂³×C₃	semidirect
337. Dic₃×D₇	C₂³×C₃	semidirect
344. C₂×C₃²×D₄	C₂×D₇	semidirect
353. C₂×C₃×#67	C₂×D₇	semidirect
360. C₃×#237	C₂×D₇	semidirect
366. C₃×D₃×D₄	C₂×D₇	semidirect
372. C₃×#235	C₂×D₇	semidirect
383. C₃²×D₇	H(5,𝔽₂)	semidirect
385. C₂³×D₇	C₂×C₃×D₃	semidirect
390. C₂×C₇×D₄	C₂×C₃×D₃	semidirect
394. C₂×C₂²⋊D₇	C₂×C₃×D₃	semidirect
410. D₄×D₇	C₂×C₃×D₃	semidirect
411. D₄×D₇	C₂×C₃×D₃	semidirect
418. C₂×D₂₈	C₂×C₃×D₃	semidirect
421. C₂×C₄×D₇	C₂×C₃×D₃	semidirect
441. #1004	C₃×D₇	direct (N × H)
506. C₂³×C₃²	C₂²×D₇	semidirect
511. C₂²×C₃×D₃	C₂²×D₇	semidirect
514. C₃²×D₄	C₂²×D₇	semidirect
518. C₂×C₃²×C₄	C₂²×D₇	semidirect
525. C₃×#67	C₂²×D₇	semidirect
526. C₃×#67	C₂²×D₇	semidirect
530. C₂×C₃×Dic₃	C₂²×D₇	semidirect
533. C₃×D₁₂	C₂²×D₇	semidirect
537. C₃×C₄×D₃	C₂²×D₇	semidirect
540. C₃×Dic₆	C₂²×D₇	semidirect
542. C₃²×C₇	C₂×H(5,𝔽₂)	semidirect
544. C₂³×C₇	C₂²×C₃×D₃	semidirect
552. C₂²×D₇	C₂²×C₃×D₃	semidirect
553. C₂²×D₇	C₂²×C₃×D₃	semidirect
558. C₇×D₄	C₂²×C₃×D₃	semidirect
561. C₂×C₄×C₇	C₂²×C₃×D₃	semidirect
567. C₂²⋊D₇	C₂²×C₃×D₃	semidirect
570. C₂×Dic₇	C₂²×C₃×D₃	semidirect
574. D₂₈	C₂²×C₃×D₃	semidirect
580. C₄×D₇	C₂²×C₃×D₃	semidirect
629. C₂×C₃×D₄	D₃×D₇	semidirect
630. C₂×C₃×D₄	C₂×C₃×D₇	semidirect
643. C₂×#67	C₂×C₃×D₇	semidirect
650. #237	C₂×C₃×D₇	semidirect
656. D₃×D₄	C₂×C₃×D₇	semidirect
662. #235	C₂×C₃×D₇	semidirect
687. C₃×D₇	#1004	direct (N × H)
688. C₃×D₇	C₃×H(5,𝔽₂)	semidirect
763. C₂³×C₃	C₂×D₃×D₇	semidirect
764. C₂³×C₃	C₂²×C₃×D₇	semidirect
769. C₂²×D₃	C₂²×C₃×D₇	semidirect
791. C₃×D₄	C₂×D₃×D₇	semidirect
792. C₃×D₄	C₂²×C₃×D₇	semidirect
811. C₂×C₃×C₄	C₂×D₃×D₇	semidirect
812. C₂×C₃×C₄	C₂²×C₃×D₇	semidirect
819. #67	C₂²×C₃×D₇	semidirect
820. #67	C₂²×C₃×D₇	semidirect
824. C₂×Dic₃	C₂²×C₃×D₇	semidirect
827. D₁₂	C₂²×C₃×D₇	semidirect
831. C₄×D₃	C₂²×C₃×D₇	semidirect
834. Dic₆	C₂²×C₃×D₇	semidirect
836. C₃×C₇	C₂×#1004	semidirect
837. C₃×C₇	C₂×C₃×H(5,𝔽₂)	semidirect
880. C₂×D₄	C₃×D₃×D₇	semidirect
891. D₇	C₃×#1004	direct (N × H)
948. C₃²	D₇×H(5,𝔽₂)	semidirect
959. C₂³	C₂×C₃×D₃×D₇	semidirect
976. D₄	C₂×C₃×D₃×D₇	semidirect
988. C₂×C₄	C₂×C₃×D₃×D₇	semidirect
989. C₇	C₂×C₃×#1004	semidirect
1035. C₃	D₇×#1004	direct (N × H)
1036. C₃	C₃×D₇×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₃×#10621596	2
C₃×#10621657	2
C₃×#10621564	2
C₃×#10621573	2
C₃×#10621572	2
C₃×C₇×#1004	2
C₃×D₃×D₄×D₇	2
C₃×D₇×#237	2
C₂×C₃×D₇×#67	2
C₃×D₇×#235	2
C₂×C₃²×D₄×D₇	2
C₃×D₇×H(5,𝔽₂)	3
D₇×#1004	3
C₂×C₃×#1004	7

Subgroups — C3×D7×#1004 #72246728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×#1004 #72246728