Subgroups — C₃×D₃×D₄×D₇ #72246594

Order 2016.

998 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×D₇	C₂	1	2	yes	maximal, complemented
2	C₃×D₄×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#66694	C₂	1	2	yes	maximal, complemented
6	C₃×D₃×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
7	C₃×D₇×#67	C₂	1	2	yes	maximal, complemented
8	C₃×#66681	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₃×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₇×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×D₄×D₇	—	3	1	no	maximal
13	D₃×D₄×D₇	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃×D₂₁	C₂²	1	2	yes	complemented
15	C₂²×C₃×D₃×C₇	C₂²	1	2	yes	complemented
16	C₂²×C₃²×D₇	C₂²	1	2	yes	complemented
17	C₂×C₃×D₃×D₇	—	2	8	no	—
18	C₂×C₃×D₃×D₇	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₃×D₇	C₂²	1	2	yes	complemented
20	C₂×C₃×D₃×D₇	C₂²	1	2	yes	complemented
21	C₂×C₃×D₃×D₇	C₂²	1	2	yes	complemented
22	C₃²×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
23	C₃×#4268	C₂²	1	2	yes	complemented
24	C₃×D₈₄	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×D₂₁	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₇×#67	C₂²	1	2	yes	complemented
27	C₃×C₇×D₁₂	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₄×D₃×C₇	C₂²	1	1	yes	characteristic, complemented
29	C₃²×C₂²⋊D₇	C₂²	1	2	yes	complemented
30	C₃²×D₂₈	C₂²	1	1	yes	characteristic, complemented
31	C₃²×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
32	C₃×#4247	C₂²	1	2	yes	complemented
33	C₃×#4246	C₂²	1	2	yes	complemented
34	C₃×#4245	C₂²	1	2	yes	complemented
35	C₃×D₂₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₃×D₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
37	C₃×Dic₃×D₇	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₃×D₇	—	3	2	no	—
39	C₂²×D₃×D₇	C₂×C₃	1	2	yes	complemented
40	C₂×C₃×C₇×D₄	—	3	1	no	—
41	D₄×D₂₁	C₂×C₃	1	1	yes	characteristic, complemented
42	D₃×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₃×C₂²⋊D₇	—	3	2	no	—
44	C₃×D₄×D₇	—	2	1	no	—
45	C₃×D₄×D₇	—	3	2	no	—
46	C₃×D₄×D₇	—	3	1	no	—
47	C₃×D₄×D₇	—	3	2	no	—
48	C₃×D₄×D₇	—	3	1	no	—
49	C₃×D₄×D₇	—	3	1	no	—
50	C₃×D₄×D₇	D₃	1	1	yes	characteristic, direct product factor
51	C₃×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×C₃×D₂₈	—	3	1	no	—
53	C₂×C₃×C₄×D₇	—	3	1	no	—
54	#66694	C₂×C₃	1	2	yes	complemented
55	D₃×C₂²⋊D₇	C₂×C₃	1	2	yes	complemented
56	D₇×#67	C₂×C₃	1	2	yes	complemented
57	#66681	C₂×C₃	1	1	yes	characteristic, complemented
58	D₃×D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
59	D₇×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
60	C₄×D₃×D₇	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂×C₃×D₃×D₄	—	7	1	no	maximal, Hall
62	C₂²×C₃²×C₇	C₂³	1	2	yes	complemented
63	C₂×C₃×D₂₁	—	2	4	no	—
64	C₂×C₃×D₂₁	C₂³	1	1	yes	characteristic
65	C₂×C₃×D₂₁	C₂³	1	2	yes	complemented
66	C₂×C₃×D₃×C₇	—	2	4	no	—
67	C₂×C₃×D₃×C₇	C₂³	1	1	yes	characteristic
68	C₂×C₃×D₃×C₇	C₂³	1	2	yes	complemented
69	C₂×C₃²×D₇	—	2	4	no	—
70	C₂×C₃²×D₇	C₂³	1	1	yes	characteristic
71	C₂×C₃²×D₇	C₂³	1	2	yes	complemented
72	C₃×D₃×D₇	—	2	4	no	—
73	C₃×D₃×D₇	—	2	4	no	—
74	C₃×D₃×D₇	—	2	4	no	—
75	C₃×D₃×D₇	D₄	1	4	yes	direct product factor
76	C₃²×C₄×C₇	C₂³	1	1	yes	characteristic, complemented
77	C₃×Dic₂₁	C₂³	1	1	yes	characteristic, complemented
78	C₃×C₇×Dic₃	C₂³	1	1	yes	characteristic, complemented
79	C₃²×Dic₇	C₂³	1	1	yes	characteristic, complemented
80	C₂×D₄×D₇	—	3	1	no	Hall
81	C₂³×C₃×C₇	—	3	2	no	—
82	C₂²×D₂₁	C₂²×C₃	1	2	yes	complemented
83	C₂²×D₃×C₇	C₂²×C₃	1	2	yes	complemented
84	C₂²×C₃×D₇	—	2	2	no	—
85	C₂²×C₃×D₇	—	3	1	no	—
86	C₂²×C₃×D₇	—	3	2	no	—
87	C₂²×C₃×D₇	—	3	2	no	—
88	C₂²×C₃×D₇	—	3	2	no	—
89	C₂²×C₃×D₇	—	3	2	no	—
90	C₂²×C₃×D₇	—	6	8	no	—
91	C₂²×C₃×D₇	C₂×D₃	1	2	yes	complemented
92	C₂²×C₃×D₇	C₂²×C₃	1	2	yes	complemented
93	C₂×D₃×D₇	—	2	8	no	—
94	C₂×D₃×D₇	C₂²×C₃	1	1	yes	characteristic
95	C₂×D₃×D₇	C₂²×C₃	1	2	yes	complemented
96	C₂×D₃×D₇	C₂²×C₃	1	2	yes	complemented
97	C₂×D₃×D₇	C₂²×C₃	1	2	yes	complemented
98	C₃×C₇×D₄	—	2	1	no	—
99	C₃×C₇×D₄	—	3	2	no	—
100	C₃×C₇×D₄	—	3	1	no	—
101	C₃×C₇×D₄	C₂×D₃	1	1	yes	characteristic, complemented
102	C₃×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
103	C₂×C₃×C₄×C₇	—	3	1	no	—
104	#4268	C₂²×C₃	1	2	yes	complemented
105	D₈₄	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₄×D₂₁	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₇×#67	C₂²×C₃	1	2	yes	complemented
108	C₇×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
109	C₄×D₃×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₃×C₂²⋊D₇	—	2	2	no	—
111	C₃×C₂²⋊D₇	—	3	2	no	—
112	C₃×C₂²⋊D₇	—	3	2	no	—
113	C₃×C₂²⋊D₇	—	3	2	no	—
114	C₃×C₂²⋊D₇	C₂×D₃	1	2	yes	complemented
115	C₃×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
116	C₂×C₃×Dic₇	—	3	1	no	—
117	C₃×D₂₈	—	2	1	no	—
118	C₃×D₂₈	—	3	2	no	—
119	C₃×D₂₈	—	3	1	no	—
120	C₃×D₂₈	C₂×D₃	1	1	yes	characteristic, complemented
121	C₃×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₃×C₄×D₇	—	2	1	no	—
123	C₃×C₄×D₇	—	3	1	no	—
124	C₃×C₄×D₇	—	3	1	no	—
125	C₃×C₄×D₇	—	3	1	no	—
126	C₃×C₄×D₇	C₂×D₃	1	1	yes	characteristic, complemented
127	C₃×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
128	#4247	C₂²×C₃	1	2	yes	complemented
129	#4246	C₂²×C₃	1	2	yes	complemented
130	#4245	C₂²×C₃	1	2	yes	complemented
131	D₂₁⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
132	D₃×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
133	Dic₃×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
134	C₂³×C₃×D₃	—	7	2	no	—
135	C₂×C₃²×D₄	—	7	1	no	—
136	C₂×C₃×#67	—	7	2	no	—
137	C₃×D₃×D₄	—	7	2	no	—
138	C₃×D₃×D₄	—	7	1	no	—
139	C₃×D₃×D₄	—	7	2	no	—
140	C₃×D₃×D₄	—	7	1	no	—
141	C₃×D₃×D₄	—	7	1	no	—
142	C₃×D₃×D₄	D₇	1	1	yes	characteristic, direct product factor
143	C₂×C₃×D₁₂	—	7	1	no	—
144	C₂×C₃×C₄×D₃	—	7	1	no	—
145	C₂×C₃²×C₇	—	2	2	no	—
146	C₂×C₃²×C₇	C₂⁴	1	1	yes	characteristic
147	C₃×D₂₁	—	2	2	no	—
148	C₃×D₂₁	C₂×D₄	1	2	yes	complemented
149	C₃×D₃×C₇	—	2	2	no	—
150	C₃×D₃×C₇	C₂×D₄	1	2	yes	complemented
151	C₃²×D₇	—	2	2	no	—
152	C₃²×D₇	C₂×D₄	1	2	yes	complemented
153	C₂³×D₇	—	3	2	no	—
154	C₂×C₇×D₄	—	3	1	no	—
155	C₂×C₂²⋊D₇	—	3	2	no	—
156	D₄×D₇	—	3	2	no	—
157	D₄×D₇	—	3	1	no	—
158	D₄×D₇	—	3	2	no	—
159	D₄×D₇	—	3	1	no	—
160	D₄×D₇	—	3	1	no	—
161	D₄×D₇	C₃×D₃	1	1	yes	characteristic, direct product factor
162	C₂×D₂₈	—	3	1	no	—
163	C₂×C₄×D₇	—	3	1	no	—
164	C₂²×C₃×D₄	—	21	1	no	—
165	C₂×D₃×D₄	—	7	1	no	—
166	C₂²×C₃×C₇	—	2	2	no	—
167	C₂²×C₃×C₇	—	3	1	no	—
168	C₂²×C₃×C₇	—	3	2	no	—
169	C₂²×C₃×C₇	—	6	4	no	—
170	C₂²×C₃×C₇	C₂²×D₃	1	2	yes	complemented
171	C₂²×C₃×C₇	C₂³×C₃	1	2	yes	complemented
172	C₂×D₂₁	—	2	4	no	—
173	C₂×D₂₁	C₂³×C₃	1	1	yes	characteristic
174	C₂×D₂₁	C₂³×C₃	1	2	yes	complemented
175	C₂×D₃×C₇	—	2	4	no	—
176	C₂×D₃×C₇	C₂³×C₃	1	1	yes	characteristic
177	C₂×D₃×C₇	C₂³×C₃	1	2	yes	complemented
178	C₂×C₃×D₇	—	2	4	no	—
179	C₂×C₃×D₇	—	2	4	no	—
180	C₂×C₃×D₇	—	2	1	no	—
181	C₂×C₃×D₇	—	2	2	no	—
182	C₂×C₃×D₇	—	3	1	no	—
183	C₂×C₃×D₇	—	3	4	no	—
184	C₂×C₃×D₇	—	3	2	no	—
185	C₂×C₃×D₇	—	4	4	no	—
186	C₂×C₃×D₇	—	6	4	no	—
187	C₂×C₃×D₇	—	6	4	no	—
188	C₂×C₃×D₇	—	6	4	no	—
189	C₂×C₃×D₇	—	6	4	no	—
190	C₂×C₃×D₇	C₂²×D₃	1	1	yes	characteristic
191	C₂×C₃×D₇	C₂²×D₃	1	2	yes	complemented
192	C₂×C₃×D₇	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₃×D₇	C₂³×C₃	1	2	yes	complemented
194	D₃×D₇	—	2	4	no	—
195	D₃×D₇	—	2	4	no	—
196	D₃×D₇	—	2	4	no	—
197	D₃×D₇	C₃×D₄	1	4	yes	direct product factor
198	C₃×C₄×C₇	—	2	1	no	—
199	C₃×C₄×C₇	—	3	1	no	—
200	C₃×C₄×C₇	C₂²×D₃	1	1	yes	characteristic, complemented
201	C₃×C₄×C₇	C₂³×C₃	1	1	yes	characteristic, complemented
202	Dic₂₁	C₂³×C₃	1	1	yes	characteristic, complemented
203	C₃×Dic₇	—	2	1	no	—
204	C₃×Dic₇	—	3	1	no	—
205	C₃×Dic₇	C₂²×D₃	1	1	yes	characteristic, complemented
206	C₃×Dic₇	C₂³×C₃	1	1	yes	characteristic, complemented
207	C₇×Dic₃	C₂³×C₃	1	1	yes	characteristic, complemented
208	C₂³×C₃²	—	7	2	no	—
209	C₂²×C₃×D₃	—	7	1	no	—
210	C₂²×C₃×D₃	—	7	2	no	—
211	C₂²×C₃×D₃	—	7	2	no	—
212	C₂²×C₃×D₃	—	7	2	no	—
213	C₂²×C₃×D₃	—	7	2	no	—
214	C₂²×C₃×D₃	—	14	8	no	—
215	C₂²×C₃×D₃	C₂×D₇	1	2	yes	complemented
216	C₃²×D₄	—	7	2	no	—
217	C₃²×D₄	—	7	1	no	—
218	C₃²×D₄	C₂×D₇	1	1	yes	characteristic, complemented
219	C₂×C₃²×C₄	—	7	1	no	—
220	C₃×#67	—	7	2	no	—
221	C₃×#67	—	7	2	no	—
222	C₃×#67	—	7	2	no	—
223	C₃×#67	C₂×D₇	1	2	yes	complemented
224	C₂×C₃×Dic₃	—	7	1	no	—
225	C₃×D₁₂	—	7	2	no	—
226	C₃×D₁₂	—	7	1	no	—
227	C₃×D₁₂	C₂×D₇	1	1	yes	characteristic, complemented
228	C₃×C₄×D₃	—	7	1	no	—
229	C₃×C₄×D₃	—	7	1	no	—
230	C₃×C₄×D₃	—	7	1	no	—
231	C₃×C₄×D₃	C₂×D₇	1	1	yes	characteristic, complemented
232	C₃²×C₇	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
233	C₂³×C₇	—	3	2	no	—
234	C₂²×D₇	—	3	1	no	—
235	C₂²×D₇	—	3	2	no	—
236	C₂²×D₇	—	3	2	no	—
237	C₂²×D₇	—	3	2	no	—
238	C₂²×D₇	—	3	2	no	—
239	C₂²×D₇	—	6	8	no	—
240	C₂²×D₇	C₂×C₃×D₃	1	2	yes	complemented
241	C₇×D₄	—	3	2	no	—
242	C₇×D₄	—	3	1	no	—
243	C₇×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
244	C₂×C₄×C₇	—	3	1	no	—
245	C₂²⋊D₇	—	3	2	no	—
246	C₂²⋊D₇	—	3	2	no	—
247	C₂²⋊D₇	—	3	2	no	—
248	C₂²⋊D₇	C₂×C₃×D₃	1	2	yes	complemented
249	C₂×Dic₇	—	3	1	no	—
250	D₂₈	—	3	2	no	—
251	D₂₈	—	3	1	no	—
252	D₂₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
253	C₄×D₇	—	3	1	no	—
254	C₄×D₇	—	3	1	no	—
255	C₄×D₇	—	3	1	no	—
256	C₄×D₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented
257	C₂⁴×C₃	—	21	2	no	—
258	C₂³×D₃	—	7	2	no	—
259	C₂×C₃×D₄	—	3	1	no	—
260	C₂×C₃×D₄	—	7	1	no	—
261	C₂×C₃×D₄	—	7	1	no	—
262	C₂×C₃×D₄	—	14	1	no	—
263	C₂×C₃×D₄	—	21	1	no	—
264	C₂×C₃×D₄	—	21	1	no	—
265	C₂×C₃×D₄	—	21	2	no	—
266	C₂×C₃×D₄	—	21	1	no	—
267	C₂×C₃×D₄	—	21	2	no	—
268	C₂×C₃×D₄	—	21	2	no	—
269	C₂×C₃×D₄	—	21	1	no	—
270	C₂²×C₃×C₄	—	21	1	no	—
271	C₂×#67	—	7	2	no	—
272	D₃×D₄	—	7	2	no	—
273	D₃×D₄	—	7	1	no	—
274	D₃×D₄	—	7	2	no	—
275	D₃×D₄	—	7	1	no	—
276	D₃×D₄	—	7	1	no	—
277	D₃×D₄	C₃×D₇	1	1	yes	characteristic, direct product factor
278	C₂×D₁₂	—	7	1	no	—
279	C₂×C₄×D₃	—	7	1	no	—
280	C₂×C₃×C₇	—	2	2	no	—
281	C₂×C₃×C₇	—	2	2	no	—
282	C₂×C₃×C₇	—	2	1	no	—
283	C₂×C₃×C₇	—	3	2	no	—
284	C₂×C₃×C₇	—	4	2	no	—
285	C₂×C₃×C₇	—	6	2	no	—
286	C₂×C₃×C₇	C₂³×D₃	1	1	yes	characteristic
287	C₂×C₃×C₇	C₂⁴×C₃	1	1	yes	characteristic
288	D₂₁	—	2	2	no	—
289	D₂₁	C₂×C₃×D₄	1	2	yes	complemented
290	C₃×D₇	—	2	2	no	—
291	C₃×D₇	—	2	2	no	—
292	C₃×D₇	—	2	2	no	—
293	C₃×D₇	—	3	2	no	—
294	C₃×D₇	—	4	2	no	—
295	C₃×D₇	—	6	2	no	—
296	C₃×D₇	D₃×D₄	1	2	yes	direct product factor
297	C₃×D₇	C₂×C₃×D₄	1	2	yes	complemented
298	D₃×C₇	—	2	2	no	—
299	D₃×C₇	C₂×C₃×D₄	1	2	yes	complemented
300	C₂²×C₃²	—	7	1	no	—
301	C₂²×C₃²	—	7	2	no	—
302	C₂²×C₃²	—	14	4	no	—
303	C₂²×C₃²	C₂²×D₇	1	2	yes	complemented
304	C₂×C₃×D₃	—	2	4	no	—
305	C₂×C₃×D₃	—	7	1	no	—
306	C₂×C₃×D₃	—	7	4	no	—
307	C₂×C₃×D₃	—	7	2	no	—
308	C₂×C₃×D₃	—	14	4	no	—
309	C₂×C₃×D₃	—	14	4	no	—
310	C₂×C₃×D₃	—	14	4	no	—
311	C₂×C₃×D₃	—	14	4	no	—
312	C₂×C₃×D₃	C₂²×D₇	1	1	yes	characteristic
313	C₂×C₃×D₃	C₂²×D₇	1	2	yes	complemented
314	C₃²×C₄	—	7	1	no	—
315	C₃²×C₄	C₂²×D₇	1	1	yes	characteristic, complemented
316	C₃×Dic₃	—	7	1	no	—
317	C₃×Dic₃	C₂²×D₇	1	1	yes	characteristic, complemented
318	C₂²×D₄	—	21	1	no	Sylow
319	C₂²×C₇	—	3	1	no	—
320	C₂²×C₇	—	3	2	no	—
321	C₂²×C₇	—	6	4	no	—
322	C₂²×C₇	C₂²×C₃×D₃	1	2	yes	complemented
323	C₂×D₇	—	2	4	no	—
324	C₂×D₇	—	3	1	no	—
325	C₂×D₇	—	3	4	no	—
326	C₂×D₇	—	3	2	no	—
327	C₂×D₇	—	6	4	no	—
328	C₂×D₇	—	6	4	no	—
329	C₂×D₇	—	6	4	no	—
330	C₂×D₇	—	6	4	no	—
331	C₂×D₇	C₂²×C₃×D₃	1	1	yes	characteristic
332	C₂×D₇	C₂²×C₃×D₃	1	2	yes	complemented
333	C₄×C₇	—	3	1	no	—
334	C₄×C₇	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
335	Dic₇	—	3	1	no	—
336	Dic₇	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
337	C₂³×C₃	—	3	2	no	—
338	C₂³×C₃	—	7	2	no	—
339	C₂³×C₃	—	7	2	no	—
340	C₂³×C₃	—	14	2	no	—
341	C₂³×C₃	—	21	1	no	—
342	C₂³×C₃	—	21	2	no	—
343	C₂³×C₃	—	21	2	no	—
344	C₂³×C₃	—	21	2	no	—
345	C₂³×C₃	—	21	2	no	—
346	C₂³×C₃	—	42	8	no	—
347	C₂²×D₃	—	7	1	no	—
348	C₂²×D₃	—	7	2	no	—
349	C₂²×D₃	—	7	2	no	—
350	C₂²×D₃	—	7	2	no	—
351	C₂²×D₃	—	7	2	no	—
352	C₂²×D₃	—	14	8	no	—
353	C₂²×D₃	C₂×C₃×D₇	1	2	yes	complemented
354	C₃×D₄	—	2	1	no	—
355	C₃×D₄	—	3	2	no	—
356	C₃×D₄	—	3	1	no	—
357	C₃×D₄	—	7	2	no	—
358	C₃×D₄	—	7	2	no	—
359	C₃×D₄	—	7	1	no	—
360	C₃×D₄	—	7	1	no	—
361	C₃×D₄	—	14	1	no	—
362	C₃×D₄	—	14	2	no	—
363	C₃×D₄	—	21	2	no	—
364	C₃×D₄	—	21	2	no	—
365	C₃×D₄	—	21	2	no	—
366	C₃×D₄	—	21	2	no	—
367	C₃×D₄	—	21	1	no	—
368	C₃×D₄	D₃×D₇	1	1	yes	characteristic, direct product factor
369	C₃×D₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
370	C₂×C₃×C₄	—	3	1	no	—
371	C₂×C₃×C₄	—	7	1	no	—
372	C₂×C₃×C₄	—	7	1	no	—
373	C₂×C₃×C₄	—	14	1	no	—
374	C₂×C₃×C₄	—	21	1	no	—
375	C₂×C₃×C₄	—	21	1	no	—
376	C₂×C₃×C₄	—	21	1	no	—
377	C₂×C₃×C₄	—	21	1	no	—
378	#67	—	7	2	no	—
379	#67	—	7	2	no	—
380	#67	—	7	2	no	—
381	#67	C₂×C₃×D₇	1	2	yes	complemented
382	C₂×Dic₃	—	7	1	no	—
383	D₁₂	—	7	2	no	—
384	D₁₂	—	7	1	no	—
385	D₁₂	C₂×C₃×D₇	1	1	yes	characteristic, complemented
386	C₄×D₃	—	7	1	no	—
387	C₄×D₃	—	7	1	no	—
388	C₄×D₃	—	7	1	no	—
389	C₄×D₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
390	C₃×C₇	—	2	1	no	—
391	C₃×C₇	C₂×D₃×D₄	1	1	yes	characteristic, complemented
392	C₃×C₇	C₂²×C₃×D₄	1	1	yes	characteristic, complemented
393	C₂×C₃²	—	2	2	no	—
394	C₂×C₃²	—	7	2	no	—
395	C₂×C₃²	—	14	2	no	—
396	C₂×C₃²	C₂³×D₇	1	1	yes	characteristic
397	C₃×D₃	—	2	2	no	—
398	C₃×D₃	—	7	2	no	—
399	C₃×D₃	—	14	2	no	—
400	C₃×D₃	D₄×D₇	1	2	yes	direct product factor
401	C₂⁴	—	21	2	no	—
402	C₂×D₄	—	3	1	no	—
403	C₂×D₄	—	7	1	no	—
404	C₂×D₄	—	21	1	no	—
405	C₂×D₄	—	21	1	no	—
406	C₂×D₄	—	21	2	no	—
407	C₂×D₄	—	21	1	no	—
408	C₂×D₄	—	21	2	no	—
409	C₂×D₄	—	21	2	no	—
410	C₂×D₄	—	21	1	no	—
411	C₂²×C₄	—	21	1	no	—
412	C₂×C₇	—	2	2	no	—
413	C₂×C₇	—	3	2	no	—
414	C₂×C₇	—	6	2	no	—
415	C₂×C₇	C₂³×C₃×D₃	1	1	yes	characteristic
416	D₇	—	2	2	no	—
417	D₇	—	3	2	no	—
418	D₇	—	6	2	no	—
419	D₇	C₃×D₃×D₄	1	2	yes	direct product factor
420	C₂²×C₃	—	2	2	no	—
421	C₂²×C₃	—	3	1	no	—
422	C₂²×C₃	—	3	2	no	—
423	C₂²×C₃	—	6	4	no	—
424	C₂²×C₃	—	7	1	no	—
425	C₂²×C₃	—	7	1	no	—
426	C₂²×C₃	—	7	2	no	—
427	C₂²×C₃	—	7	2	no	—
428	C₂²×C₃	—	14	1	no	—
429	C₂²×C₃	—	14	2	no	—
430	C₂²×C₃	—	14	4	no	—
431	C₂²×C₃	—	14	4	no	—
432	C₂²×C₃	—	21	4	no	—
433	C₂²×C₃	—	21	1	no	—
434	C₂²×C₃	—	21	2	no	—
435	C₂²×C₃	—	28	4	no	—
436	C₂²×C₃	—	42	4	no	—
437	C₂²×C₃	—	42	4	no	—
438	C₂²×C₃	—	42	4	no	—
439	C₂²×C₃	—	42	4	no	—
440	C₂²×C₃	C₂×D₃×D₇	1	2	yes	complemented
441	C₂²×C₃	C₂²×C₃×D₇	1	2	yes	complemented
442	C₂×D₃	—	2	4	no	—
443	C₂×D₃	—	7	1	no	—
444	C₂×D₃	—	7	4	no	—
445	C₂×D₃	—	7	2	no	—
446	C₂×D₃	—	14	4	no	—
447	C₂×D₃	—	14	4	no	—
448	C₂×D₃	—	14	4	no	—
449	C₂×D₃	—	14	4	no	—
450	C₂×D₃	C₂²×C₃×D₇	1	1	yes	characteristic
451	C₂×D₃	C₂²×C₃×D₇	1	2	yes	complemented
452	C₃×C₄	—	2	1	no	—
453	C₃×C₄	—	3	1	no	—
454	C₃×C₄	—	7	1	no	—
455	C₃×C₄	—	7	1	no	—
456	C₃×C₄	—	14	1	no	—
457	C₃×C₄	—	21	1	no	—
458	C₃×C₄	C₂×D₃×D₇	1	1	yes	characteristic, complemented
459	C₃×C₄	C₂²×C₃×D₇	1	1	yes	characteristic, complemented
460	Dic₃	—	7	1	no	—
461	Dic₃	C₂²×C₃×D₇	1	1	yes	characteristic, complemented
462	C₃²	C₂×D₄×D₇	1	1	yes	characteristic, complemented, Sylow
463	C₂³	—	3	2	no	—
464	C₂³	—	7	2	no	—
465	C₂³	—	21	1	no	—
466	C₂³	—	21	2	no	—
467	C₂³	—	21	2	no	—
468	C₂³	—	21	2	no	—
469	C₂³	—	21	2	no	—
470	C₂³	—	42	8	no	—
471	D₄	—	3	2	no	—
472	D₄	—	3	1	no	—
473	D₄	—	7	2	no	—
474	D₄	—	7	1	no	—
475	D₄	—	21	2	no	—
476	D₄	—	21	2	no	—
477	D₄	—	21	2	no	—
478	D₄	—	21	2	no	—
479	D₄	—	21	1	no	—
480	D₄	C₃×D₃×D₇	1	1	yes	characteristic, direct product factor
481	C₂×C₄	—	3	1	no	—
482	C₂×C₄	—	7	1	no	—
483	C₂×C₄	—	21	1	no	—
484	C₂×C₄	—	21	1	no	—
485	C₂×C₄	—	21	1	no	—
486	C₂×C₄	—	21	1	no	—
487	C₇	C₂×C₃×D₃×D₄	1	1	yes	characteristic, complemented, Sylow
488	C₂×C₃	—	2	2	no	—
489	C₂×C₃	—	2	2	no	—
490	C₂×C₃	—	2	1	no	—
491	C₂×C₃	—	3	2	no	—
492	C₂×C₃	—	4	2	no	—
493	C₂×C₃	—	6	2	no	—
494	C₂×C₃	—	7	2	no	—
495	C₂×C₃	—	7	2	no	—
496	C₂×C₃	—	14	2	no	—
497	C₂×C₃	—	14	2	no	—
498	C₂×C₃	—	14	2	no	—
499	C₂×C₃	—	21	2	no	—
500	C₂×C₃	—	28	2	no	—
501	C₂×C₃	—	42	2	no	—
502	C₂×C₃	C₂²×D₃×D₇	1	1	yes	characteristic
503	C₂×C₃	C₂³×C₃×D₇	1	1	yes	characteristic
504	D₃	—	2	2	no	—
505	D₃	—	7	2	no	—
506	D₃	—	14	2	no	—
507	D₃	C₃×D₄×D₇	1	2	yes	direct product factor
508	C₂²	—	3	1	no	—
509	C₂²	—	3	2	no	—
510	C₂²	—	6	4	no	—
511	C₂²	—	7	1	no	—
512	C₂²	—	7	2	no	—
513	C₂²	—	14	4	no	—
514	C₂²	—	21	4	no	—
515	C₂²	—	21	1	no	—
516	C₂²	—	21	2	no	—
517	C₂²	—	42	4	no	—
518	C₂²	—	42	4	no	—
519	C₂²	—	42	4	no	—
520	C₂²	—	42	4	no	—
521	C₂²	C₂×C₃×D₃×D₇	1	2	yes	complemented
522	C₄	—	3	1	no	—
523	C₄	—	7	1	no	—
524	C₄	—	21	1	no	—
525	C₄	C₂×C₃×D₃×D₇	1	1	yes	characteristic, complemented
526	C₃	—	2	1	no	—
527	C₃	D₃×D₄×D₇	1	1	yes	characteristic, direct product factor
528	C₃	C₂×C₃×D₄×D₇	1	1	yes	characteristic, complemented
529	C₂	—	2	2	no	—
530	C₂	—	3	2	no	—
531	C₂	—	6	2	no	—
532	C₂	—	7	2	no	—
533	C₂	—	14	2	no	—
534	C₂	—	21	2	no	—
535	C₂	—	42	2	no	—
536	C₂	C₂²×C₃×D₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₃×D₇
commutator, cosocle	C₂×C₃×C₇	C₂⁴×C₃
Frattini	C₂	C₂²×C₃×D₃×D₇
Fitting	C₃²×C₇×D₄	C₂²
socle	C₂×C₃²×C₇	C₂⁴
hypercenter	C₃×D₄	D₃×D₇
hypocenter	C₃×C₇	C₂²×C₃×D₄
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₃×D₇	C₂	semidirect
2. C₃×D₄×D₂₁	C₂	semidirect
3. C₃×D₃×C₇×D₄	C₂	semidirect
4. C₃²×D₄×D₇	C₂	semidirect
5. C₃×#66694	C₂	semidirect
6. C₃×D₃×C₂²⋊D₇	C₂	semidirect
7. C₃×D₇×#67	C₂	semidirect
8. C₃×#66681	C₂	semidirect
9. C₃×D₃×D₂₈	C₂	semidirect
10. C₃×D₇×D₁₂	C₂	semidirect
11. C₃×C₄×D₃×D₇	C₂	semidirect
13. D₃×D₄×D₇	C₃	direct (N × H)
14. C₂²×C₃×D₂₁	C₂²	semidirect
15. C₂²×C₃×D₃×C₇	C₂²	semidirect
16. C₂²×C₃²×D₇	C₂²	semidirect
19. C₂×C₃×D₃×D₇	C₂²	semidirect
20. C₂×C₃×D₃×D₇	C₂²	semidirect
21. C₂×C₃×D₃×D₇	C₂²	semidirect
22. C₃²×C₇×D₄	C₂²	semidirect
23. C₃×#4268	C₂²	semidirect
24. C₃×D₈₄	C₂²	semidirect
25. C₃×C₄×D₂₁	C₂²	semidirect
26. C₃×C₇×#67	C₂²	semidirect
27. C₃×C₇×D₁₂	C₂²	semidirect
28. C₃×C₄×D₃×C₇	C₂²	semidirect
29. C₃²×C₂²⋊D₇	C₂²	semidirect
30. C₃²×D₂₈	C₂²	semidirect
31. C₃²×C₄×D₇	C₂²	semidirect
32. C₃×#4247	C₂²	semidirect
33. C₃×#4246	C₂²	semidirect
34. C₃×#4245	C₂²	semidirect
35. C₃×D₂₁⋊C₄	C₂²	semidirect
36. C₃×D₃×Dic₇	C₂²	semidirect
37. C₃×Dic₃×D₇	C₂²	semidirect
39. C₂²×D₃×D₇	C₂×C₃	semidirect
41. D₄×D₂₁	C₂×C₃	semidirect
42. D₃×C₇×D₄	C₂×C₃	semidirect
50. C₃×D₄×D₇	D₃	direct (N × H)
51. C₃×D₄×D₇	C₂×C₃	semidirect
54. #66694	C₂×C₃	semidirect
55. D₃×C₂²⋊D₇	C₂×C₃	semidirect
56. D₇×#67	C₂×C₃	semidirect
57. #66681	C₂×C₃	semidirect
58. D₃×D₂₈	C₂×C₃	semidirect
59. D₇×D₁₂	C₂×C₃	semidirect
60. C₄×D₃×D₇	C₂×C₃	semidirect
62. C₂²×C₃²×C₇	C₂³	semidirect
65. C₂×C₃×D₂₁	C₂³	semidirect
68. C₂×C₃×D₃×C₇	C₂³	semidirect
71. C₂×C₃²×D₇	C₂³	semidirect
75. C₃×D₃×D₇	D₄	direct (N × H)
76. C₃²×C₄×C₇	C₂³	semidirect
77. C₃×Dic₂₁	C₂³	semidirect
78. C₃×C₇×Dic₃	C₂³	semidirect
79. C₃²×Dic₇	C₂³	semidirect
82. C₂²×D₂₁	C₂²×C₃	semidirect
83. C₂²×D₃×C₇	C₂²×C₃	semidirect
91. C₂²×C₃×D₇	C₂×D₃	semidirect
92. C₂²×C₃×D₇	C₂²×C₃	semidirect
95. C₂×D₃×D₇	C₂²×C₃	semidirect
96. C₂×D₃×D₇	C₂²×C₃	semidirect
97. C₂×D₃×D₇	C₂²×C₃	semidirect
101. C₃×C₇×D₄	C₂×D₃	semidirect
102. C₃×C₇×D₄	C₂²×C₃	semidirect
104. #4268	C₂²×C₃	semidirect
105. D₈₄	C₂²×C₃	semidirect
106. C₄×D₂₁	C₂²×C₃	semidirect
107. C₇×#67	C₂²×C₃	semidirect
108. C₇×D₁₂	C₂²×C₃	semidirect
109. C₄×D₃×C₇	C₂²×C₃	semidirect
114. C₃×C₂²⋊D₇	C₂×D₃	semidirect
115. C₃×C₂²⋊D₇	C₂²×C₃	semidirect
120. C₃×D₂₈	C₂×D₃	semidirect
121. C₃×D₂₈	C₂²×C₃	semidirect
126. C₃×C₄×D₇	C₂×D₃	semidirect
127. C₃×C₄×D₇	C₂²×C₃	semidirect
128. #4247	C₂²×C₃	semidirect
129. #4246	C₂²×C₃	semidirect
130. #4245	C₂²×C₃	semidirect
131. D₂₁⋊C₄	C₂²×C₃	semidirect
132. D₃×Dic₇	C₂²×C₃	semidirect
133. Dic₃×D₇	C₂²×C₃	semidirect
142. C₃×D₃×D₄	D₇	direct (N × H)
148. C₃×D₂₁	C₂×D₄	semidirect
150. C₃×D₃×C₇	C₂×D₄	semidirect
152. C₃²×D₇	C₂×D₄	semidirect
161. D₄×D₇	C₃×D₃	direct (N × H)
170. C₂²×C₃×C₇	C₂²×D₃	semidirect
171. C₂²×C₃×C₇	C₂³×C₃	semidirect
174. C₂×D₂₁	C₂³×C₃	semidirect
177. C₂×D₃×C₇	C₂³×C₃	semidirect
191. C₂×C₃×D₇	C₂²×D₃	semidirect
193. C₂×C₃×D₇	C₂³×C₃	semidirect
197. D₃×D₇	C₃×D₄	direct (N × H)
200. C₃×C₄×C₇	C₂²×D₃	semidirect
201. C₃×C₄×C₇	C₂³×C₃	semidirect
202. Dic₂₁	C₂³×C₃	semidirect
205. C₃×Dic₇	C₂²×D₃	semidirect
206. C₃×Dic₇	C₂³×C₃	semidirect
207. C₇×Dic₃	C₂³×C₃	semidirect
215. C₂²×C₃×D₃	C₂×D₇	semidirect
218. C₃²×D₄	C₂×D₇	semidirect
223. C₃×#67	C₂×D₇	semidirect
227. C₃×D₁₂	C₂×D₇	semidirect
231. C₃×C₄×D₃	C₂×D₇	semidirect
232. C₃²×C₇	C₂²×D₄	semidirect
240. C₂²×D₇	C₂×C₃×D₃	semidirect
243. C₇×D₄	C₂×C₃×D₃	semidirect
248. C₂²⋊D₇	C₂×C₃×D₃	semidirect
252. D₂₈	C₂×C₃×D₃	semidirect
256. C₄×D₇	C₂×C₃×D₃	semidirect
277. D₃×D₄	C₃×D₇	direct (N × H)
289. D₂₁	C₂×C₃×D₄	semidirect
296. C₃×D₇	D₃×D₄	direct (N × H)
297. C₃×D₇	C₂×C₃×D₄	semidirect
299. D₃×C₇	C₂×C₃×D₄	semidirect
303. C₂²×C₃²	C₂²×D₇	semidirect
313. C₂×C₃×D₃	C₂²×D₇	semidirect
315. C₃²×C₄	C₂²×D₇	semidirect
317. C₃×Dic₃	C₂²×D₇	semidirect
322. C₂²×C₇	C₂²×C₃×D₃	semidirect
332. C₂×D₇	C₂²×C₃×D₃	semidirect
334. C₄×C₇	C₂²×C₃×D₃	semidirect
336. Dic₇	C₂²×C₃×D₃	semidirect
353. C₂²×D₃	C₂×C₃×D₇	semidirect
368. C₃×D₄	D₃×D₇	direct (N × H)
369. C₃×D₄	C₂×C₃×D₇	semidirect
381. #67	C₂×C₃×D₇	semidirect
385. D₁₂	C₂×C₃×D₇	semidirect
389. C₄×D₃	C₂×C₃×D₇	semidirect
391. C₃×C₇	C₂×D₃×D₄	semidirect
392. C₃×C₇	C₂²×C₃×D₄	semidirect
400. C₃×D₃	D₄×D₇	direct (N × H)
419. D₇	C₃×D₃×D₄	direct (N × H)
440. C₂²×C₃	C₂×D₃×D₇	semidirect
441. C₂²×C₃	C₂²×C₃×D₇	semidirect
451. C₂×D₃	C₂²×C₃×D₇	semidirect
458. C₃×C₄	C₂×D₃×D₇	semidirect
459. C₃×C₄	C₂²×C₃×D₇	semidirect
461. Dic₃	C₂²×C₃×D₇	semidirect
462. C₃²	C₂×D₄×D₇	semidirect
480. D₄	C₃×D₃×D₇	direct (N × H)
487. C₇	C₂×C₃×D₃×D₄	semidirect
507. D₃	C₃×D₄×D₇	direct (N × H)
521. C₂²	C₂×C₃×D₃×D₇	semidirect
525. C₄	C₂×C₃×D₃×D₇	semidirect
527. C₃	D₃×D₄×D₇	direct (N × H)
528. C₃	C₂×C₃×D₄×D₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃×D₇	2
C₃×D₄×D₂₁	2
C₃×D₃×C₇×D₄	2
C₃²×D₄×D₇	2
C₃×#66694	2
C₃×D₃×C₂²⋊D₇	2
C₃×D₇×#67	2
C₃×#66681	2
C₃×D₃×D₂₈	2
C₃×D₇×D₁₂	2
C₃×C₄×D₃×D₇	2
C₂×C₃×D₄×D₇	3
D₃×D₄×D₇	3
C₂×C₃×D₃×D₄	7

Subgroups — C3×D3×D4×D7 #72246594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×D₄×D₇ #72246594