Subgroups — D₃×C₇×#1157 #72254263

Order 4704.

818 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#66675	C₂	1	2	yes	maximal, complemented
2	C₇×#66683	C₂	1	2	yes	maximal, complemented
3	C₇×#66669	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#66728	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#66673	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₇×#1157	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×C₇×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₃×C₇×D₇	C₂	1	2	yes	maximal, complemented
9	D₃×C₇×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×D₃×C₇²	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×C₇×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#1157	—	3	1	no	maximal, Hall
13	C₂²×D₃×C₇²	C₂²	1	1	yes	characteristic
14	C₂×D₃×C₇×D₇	C₂²	1	2	yes	—
15	C₂×C₃×C₄×C₇²	C₂²	1	1	yes	characteristic, complemented
16	C₇×#4268	C₂²	1	2	yes	complemented
17	C₇×D₈₄	C₂²	1	1	yes	characteristic, complemented
18	C₄×C₇×D₂₁	C₂²	1	2	yes	complemented
19	C₇×Dic₄₂	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₇²×Dic₃	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₃×C₇²	C₂²	1	1	yes	characteristic
22	C₄×D₃×C₇²	C₂²	1	1	yes	characteristic
23	C₄×D₃×C₇²	C₂²	1	1	yes	characteristic, complemented
24	C₄×D₃×C₇²	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₇×C₂²⋊D₇	C₂²	1	2	yes	complemented
26	C₃×C₇×D₂₈	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₄×C₇×D₇	C₂²	1	2	yes	complemented
28	C₃×C₇×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
29	C₇×#4248	C₂²	1	2	yes	complemented
30	C₇×#4247	C₂²	1	2	yes	complemented
31	C₇×#4246	C₂²	1	2	yes	complemented
32	C₇×#4245	C₂²	1	2	yes	complemented
33	C₇×D₂₁⋊C₄	C₂²	1	2	yes	complemented
34	D₃×C₇×Dic₇	C₂²	1	2	yes	—
35	C₇×Dic₃×D₇	C₂²	1	2	yes	complemented
36	C₂²×C₄×C₇²	—	3	1	no	—
37	C₂×C₇×C₂²⋊D₇	—	3	2	no	—
38	C₇×#1157	—	3	1	no	—
39	C₇×#1157	—	3	2	no	—
40	C₇×#1157	—	3	1	no	—
41	C₇×#1157	—	3	2	no	—
42	C₇×#1157	—	3	1	no	—
43	C₇×#1157	D₃	1	1	yes	characteristic, direct product factor
44	C₂×C₇×D₂₈	—	3	1	no	—
45	C₂×C₄×C₇×D₇	—	3	2	no	—
46	C₂×C₇×Dic₁₄	—	3	1	no	—
47	D₃×C₇×#41	—	7	1	no	maximal
48	D₃×#1157	C₇	1	1	yes	maximal, characteristic, direct product factor
49	C₂²×C₃×C₇²	C₂³	1	1	yes	characteristic
50	C₂×C₇×D₂₁	C₂³	1	2	yes	—
51	C₂×D₃×C₇²	—	2	2	no	—
52	C₂×D₃×C₇²	C₂³	1	1	yes	characteristic
53	C₂×D₃×C₇²	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₇×D₇	C₂³	1	2	yes	—
55	D₃×C₇×D₇	—	2	4	no	—
56	C₃×C₄×C₇²	C₂³	1	1	yes	characteristic
57	C₃×C₄×C₇²	C₂³	1	1	yes	characteristic
58	C₇×Dic₂₁	C₂³	1	2	yes	—
59	C₇²×Dic₃	C₂³	1	1	yes	characteristic
60	C₇²×Dic₃	C₂³	1	1	yes	characteristic
61	C₃×C₇×Dic₇	C₂³	1	2	yes	—
62	C₂³×C₇²	—	3	1	no	—
63	C₂²×C₇×D₇	—	3	2	no	—
64	C₂×C₄×C₇²	—	3	1	no	—
65	C₂×C₄×C₇²	—	3	1	no	—
66	C₂×C₄×C₇²	—	3	1	no	—
67	C₂×C₄×C₇²	—	3	1	no	—
68	C₂×C₄×C₇²	—	3	1	no	—
69	C₂×C₄×C₇²	C₂×D₃	1	1	yes	characteristic, complemented
70	C₇×C₂²⋊D₇	—	3	2	no	—
71	C₇×C₂²⋊D₇	—	3	2	no	—
72	C₇×C₂²⋊D₇	—	3	2	no	—
73	C₇×C₂²⋊D₇	C₂×D₃	1	2	yes	complemented
74	C₂×C₇×Dic₇	—	3	2	no	—
75	C₇×D₂₈	—	3	2	no	—
76	C₇×D₂₈	—	3	1	no	—
77	C₇×D₂₈	C₂×D₃	1	1	yes	characteristic, complemented
78	C₄×C₇×D₇	—	3	2	no	—
79	C₄×C₇×D₇	—	3	2	no	—
80	C₄×C₇×D₇	—	3	2	no	—
81	C₄×C₇×D₇	C₂×D₃	1	2	yes	complemented
82	C₇×Dic₁₄	—	3	1	no	—
83	C₇×Dic₁₄	—	3	2	no	—
84	C₇×Dic₁₄	C₂×D₃	1	1	yes	characteristic, complemented
85	C₃×C₇×#41	—	7	1	no	—
86	#66728	C₂×C₇	1	1	yes	characteristic, complemented
87	C₇×#239	—	7	1	no	—
88	D₃×C₇×Q₈	—	7	1	no	—
89	C₇×#237	—	7	2	no	—
90	C₇×#237	—	7	1	no	—
91	D₃×C₇×D₄	—	7	2	no	—
92	D₃×C₇×D₄	—	7	1	no	—
93	C₇×#235	—	7	1	no	—
94	C₇×#235	—	7	2	no	—
95	C₂×C₄×D₃×C₇	—	2	3	no	—
96	C₂×C₄×D₃×C₇	—	7	2	no	—
97	C₂×C₄×D₃×C₇	D₇	1	1	yes	characteristic, complemented
98	C₂×C₄×D₃×C₇	C₂×C₇	1	1	yes	characteristic, complemented
99	C₃×#1157	C₂×C₇	1	1	yes	characteristic, complemented
100	D₃×C₂²⋊D₇	C₂×C₇	1	2	yes	complemented
101	#66683	C₂×C₇	1	2	yes	complemented
102	D₃×D₂₈	C₂×C₇	1	1	yes	characteristic, complemented
103	C₄×D₃×D₇	C₂×C₇	1	2	yes	complemented
104	#66675	C₂×C₇	1	2	yes	complemented
105	#66673	C₂×C₇	1	1	yes	characteristic, complemented
106	D₃×Dic₁₄	C₂×C₇	1	1	yes	characteristic, complemented
107	#66669	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂×C₃×C₇²	—	2	1	no	—
109	C₂×C₃×C₇²	C₂⁴	1	1	yes	characteristic
110	C₇×D₂₁	—	2	2	no	—
111	D₃×C₇²	—	2	1	no	—
112	D₃×C₇²	#41	1	2	yes	complemented
113	C₃×C₇×D₇	—	2	2	no	—
114	C₂×C₇×#41	—	21	1	no	—
115	C₂×#1157	—	3	1	no	—
116	C₂²×C₇²	—	3	1	no	—
117	C₂²×C₇²	—	3	1	no	—
118	C₂²×C₇²	—	6	2	no	—
119	C₂²×C₇²	C₂²×D₃	1	1	yes	characteristic
120	C₂×C₇×D₇	—	3	2	no	—
121	C₂×C₇×D₇	—	6	4	no	—
122	C₂×C₇×D₇	C₂²×D₃	1	2	yes	—
123	C₄×C₇²	—	3	1	no	—
124	C₄×C₇²	—	3	1	no	—
125	C₄×C₇²	C₂²×D₃	1	1	yes	characteristic
126	C₄×C₇²	C₂²×D₃	1	1	yes	characteristic
127	C₇×Dic₇	—	3	2	no	—
128	C₇×Dic₇	C₂²×D₃	1	2	yes	—
129	C₂²×D₃×C₇	—	2	3	no	—
130	C₂²×D₃×C₇	—	7	2	no	—
131	C₂²×D₃×C₇	C₂×D₇	1	1	yes	characteristic
132	C₂²×D₃×C₇	C₂²×C₇	1	1	yes	characteristic
133	C₂×D₃×D₇	C₂²×C₇	1	2	yes	—
134	C₃×C₇×Q₈	—	7	1	no	—
135	C₃×C₇×D₄	—	7	2	no	—
136	C₃×C₇×D₄	—	7	1	no	—
137	C₂×C₃×C₄×C₇	—	2	3	no	—
138	C₂×C₃×C₄×C₇	—	7	2	no	—
139	C₂×C₃×C₄×C₇	C₂×D₇	1	1	yes	characteristic, complemented
140	C₂×C₃×C₄×C₇	C₂²×C₇	1	1	yes	characteristic, complemented
141	#4268	C₂²×C₇	1	2	yes	complemented
142	D₈₄	C₂²×C₇	1	1	yes	characteristic, complemented
143	C₄×D₂₁	C₂²×C₇	1	2	yes	complemented
144	Dic₄₂	C₂²×C₇	1	1	yes	characteristic, complemented
145	C₇×#67	—	7	2	no	—
146	C₇×#67	—	7	2	no	—
147	C₇×#67	—	7	2	no	—
148	C₂×C₇×Dic₃	—	2	3	no	—
149	C₂×C₇×Dic₃	—	7	2	no	—
150	C₂×C₇×Dic₃	C₂×D₇	1	1	yes	characteristic, complemented
151	C₂×C₇×Dic₃	C₂²×C₇	1	1	yes	characteristic, complemented
152	C₇×D₁₂	—	7	2	no	—
153	C₇×D₁₂	—	7	1	no	—
154	C₄×D₃×C₇	—	2	3	no	—
155	C₄×D₃×C₇	—	2	3	no	—
156	C₄×D₃×C₇	—	2	3	no	—
157	C₄×D₃×C₇	—	2	3	no	—
158	C₄×D₃×C₇	—	7	2	no	—
159	C₄×D₃×C₇	—	7	2	no	—
160	C₄×D₃×C₇	—	7	2	no	—
161	C₄×D₃×C₇	C₂×D₇	1	1	yes	characteristic
162	C₄×D₃×C₇	C₂×D₇	1	1	yes	characteristic
163	C₄×D₃×C₇	C₂×D₇	1	1	yes	characteristic, complemented
164	C₄×D₃×C₇	C₂×D₇	1	1	yes	characteristic, complemented
165	C₄×D₃×C₇	C₂²×C₇	1	1	yes	characteristic
166	C₄×D₃×C₇	C₂²×C₇	1	1	yes	characteristic
167	C₄×D₃×C₇	C₂²×C₇	1	1	yes	characteristic, complemented
168	C₄×D₃×C₇	C₂²×C₇	1	1	yes	characteristic, complemented
169	C₇×Dic₆	—	7	1	no	—
170	C₇×Dic₆	—	7	2	no	—
171	C₃×C₂²⋊D₇	C₂²×C₇	1	2	yes	complemented
172	C₃×D₂₈	C₂²×C₇	1	1	yes	characteristic, complemented
173	C₃×C₄×D₇	C₂²×C₇	1	2	yes	complemented
174	C₃×Dic₁₄	C₂²×C₇	1	1	yes	characteristic, complemented
175	#4248	C₂²×C₇	1	2	yes	complemented
176	#4247	C₂²×C₇	1	2	yes	complemented
177	#4246	C₂²×C₇	1	2	yes	complemented
178	#4245	C₂²×C₇	1	2	yes	complemented
179	D₂₁⋊C₄	C₂²×C₇	1	2	yes	complemented
180	D₃×Dic₇	C₂²×C₇	1	2	yes	—
181	Dic₃×D₇	C₂²×C₇	1	2	yes	complemented
182	C₃×C₇²	C₂×#41	1	1	yes	characteristic, complemented, Hall
183	C₇×#41	—	7	1	no	—
184	C₇×#41	—	21	2	no	—
185	C₇×#41	—	21	2	no	—
186	C₇×#41	—	21	1	no	—
187	C₇×#41	—	21	1	no	—
188	C₇×#41	—	21	1	no	—
189	C₂×C₇×Q₈	—	21	1	no	—
190	C₂×C₇×D₄	—	21	1	no	—
191	C₂×C₇×D₄	—	21	2	no	—
192	C₂²×C₄×C₇	—	3	1	no	—
193	C₂²×C₄×C₇	—	3	1	no	—
194	C₂²×C₄×C₇	—	6	3	no	—
195	C₂²×C₄×C₇	—	21	2	no	—
196	C₂×C₂²⋊D₇	—	3	2	no	—
197	#1157	—	3	1	no	—
198	#1157	—	3	2	no	—
199	#1157	—	3	1	no	—
200	#1157	—	3	2	no	—
201	#1157	—	3	1	no	—
202	#1157	D₃×C₇	1	1	yes	characteristic, direct product factor
203	C₂×D₂₈	—	3	1	no	—
204	C₂×C₄×D₇	—	3	2	no	—
205	C₂×Dic₁₄	—	3	1	no	—
206	C₂×C₇²	—	2	1	no	—
207	C₂×C₇²	—	3	2	no	—
208	C₂×C₇²	—	6	1	no	—
209	C₂×C₇²	C₂³×D₃	1	1	yes	characteristic
210	C₇×D₇	—	2	2	no	—
211	C₇×D₇	—	6	2	no	—
212	D₃×#41	—	7	1	no	Hall
213	C₂²×C₃×C₇	—	2	3	no	—
214	C₂²×C₃×C₇	—	7	2	no	—
215	C₂²×C₃×C₇	C₂²×D₇	1	1	yes	characteristic
216	C₂²×C₃×C₇	C₂³×C₇	1	1	yes	characteristic
217	C₂×D₂₁	C₂³×C₇	1	2	yes	—
218	C₂×D₃×C₇	—	2	12	no	—
219	C₂×D₃×C₇	—	2	2	no	—
220	C₂×D₃×C₇	—	2	2	no	—
221	C₂×D₃×C₇	—	2	3	no	—
222	C₂×D₃×C₇	—	2	3	no	—
223	C₂×D₃×C₇	—	7	2	no	—
224	C₂×D₃×C₇	—	14	4	no	—
225	C₂×D₃×C₇	C₂²×D₇	1	1	yes	characteristic
226	C₂×D₃×C₇	C₂²×D₇	1	1	yes	characteristic
227	C₂×D₃×C₇	C₂³×C₇	1	1	yes	characteristic
228	C₂×D₃×C₇	C₂³×C₇	1	1	yes	characteristic
229	C₂×C₃×D₇	C₂³×C₇	1	2	yes	—
230	D₃×D₇	—	2	4	no	—
231	C₃×C₄×C₇	—	2	3	no	—
232	C₃×C₄×C₇	—	2	3	no	—
233	C₃×C₄×C₇	—	7	2	no	—
234	C₃×C₄×C₇	C₂²×D₇	1	1	yes	characteristic
235	C₃×C₄×C₇	C₂²×D₇	1	1	yes	characteristic
236	C₃×C₄×C₇	C₂³×C₇	1	1	yes	characteristic
237	C₃×C₄×C₇	C₂³×C₇	1	1	yes	characteristic
238	Dic₂₁	C₂³×C₇	1	2	yes	—
239	C₃×Dic₇	C₂³×C₇	1	2	yes	—
240	C₇×Dic₃	—	2	3	no	—
241	C₇×Dic₃	—	2	3	no	—
242	C₇×Dic₃	—	7	2	no	—
243	C₇×Dic₃	C₂²×D₇	1	1	yes	characteristic
244	C₇×Dic₃	C₂²×D₇	1	1	yes	characteristic
245	C₇×Dic₃	C₂³×C₇	1	1	yes	characteristic
246	C₇×Dic₃	C₂³×C₇	1	1	yes	characteristic
247	C₂³×C₇	—	3	1	no	—
248	C₂³×C₇	—	3	1	no	—
249	C₂³×C₇	—	6	3	no	—
250	C₂³×C₇	—	21	2	no	—
251	C₂²×D₇	—	3	2	no	—
252	C₇×Q₈	—	7	1	no	—
253	C₇×Q₈	—	21	2	no	—
254	C₇×Q₈	—	21	1	no	—
255	C₇×D₄	—	7	2	no	—
256	C₇×D₄	—	7	1	no	—
257	C₇×D₄	—	21	2	no	—
258	C₇×D₄	—	21	2	no	—
259	C₇×D₄	—	21	2	no	—
260	C₇×D₄	—	21	2	no	—
261	C₇×D₄	—	21	1	no	—
262	C₂×C₄×C₇	—	2	3	no	—
263	C₂×C₄×C₇	—	3	1	no	—
264	C₂×C₄×C₇	—	3	1	no	—
265	C₂×C₄×C₇	—	3	1	no	—
266	C₂×C₄×C₇	—	3	1	no	—
267	C₂×C₄×C₇	—	3	1	no	—
268	C₂×C₄×C₇	—	3	1	no	—
269	C₂×C₄×C₇	—	3	1	no	—
270	C₂×C₄×C₇	—	3	1	no	—
271	C₂×C₄×C₇	—	3	1	no	—
272	C₂×C₄×C₇	—	3	1	no	—
273	C₂×C₄×C₇	—	6	3	no	—
274	C₂×C₄×C₇	—	6	3	no	—
275	C₂×C₄×C₇	—	6	3	no	—
276	C₂×C₄×C₇	—	6	3	no	—
277	C₂×C₄×C₇	—	6	3	no	—
278	C₂×C₄×C₇	—	7	2	no	—
279	C₂×C₄×C₇	—	21	2	no	—
280	C₂×C₄×C₇	—	21	2	no	—
281	C₂×C₄×C₇	—	21	2	no	—
282	C₂×C₄×C₇	—	21	2	no	—
283	C₂×C₄×C₇	D₃×D₇	1	1	yes	characteristic, complemented
284	C₂×C₄×C₇	C₂×D₃×C₇	1	1	yes	characteristic, complemented
285	C₂²⋊D₇	—	3	2	no	—
286	C₂²⋊D₇	—	3	2	no	—
287	C₂²⋊D₇	—	3	2	no	—
288	C₂²⋊D₇	C₂×D₃×C₇	1	2	yes	complemented
289	C₂×Dic₇	—	3	2	no	—
290	D₂₈	—	3	2	no	—
291	D₂₈	—	3	1	no	—
292	D₂₈	C₂×D₃×C₇	1	1	yes	characteristic, complemented
293	C₄×D₇	—	3	2	no	—
294	C₄×D₇	—	3	2	no	—
295	C₄×D₇	—	3	2	no	—
296	C₄×D₇	C₂×D₃×C₇	1	2	yes	complemented
297	Dic₁₄	—	3	1	no	—
298	Dic₁₄	—	3	2	no	—
299	Dic₁₄	C₂×D₃×C₇	1	1	yes	characteristic, complemented
300	C₇²	D₃×#41	1	1	yes	characteristic, complemented, Sylow
301	C₃×#41	—	7	1	no	—
302	#239	—	7	1	no	—
303	D₃×Q₈	—	7	1	no	—
304	#237	—	7	2	no	—
305	#237	—	7	1	no	—
306	D₃×D₄	—	7	2	no	—
307	D₃×D₄	—	7	1	no	—
308	#235	—	7	1	no	—
309	#235	—	7	2	no	—
310	C₂×C₄×D₃	—	7	2	no	—
311	C₂×C₄×D₃	C₇×D₇	1	1	yes	characteristic, complemented
312	C₂×C₃×C₇	—	2	6	no	—
313	C₂×C₃×C₇	—	2	1	no	—
314	C₂×C₃×C₇	—	2	1	no	—
315	C₂×C₃×C₇	—	2	3	no	—
316	C₂×C₃×C₇	—	14	2	no	—
317	C₂×C₃×C₇	C₂³×D₇	1	1	yes	characteristic
318	C₂×C₃×C₇	C₂⁴×C₇	1	1	yes	characteristic
319	D₂₁	—	2	2	no	—
320	C₃×D₇	—	2	2	no	—
321	D₃×C₇	—	2	6	no	—
322	D₃×C₇	—	2	1	no	—
323	D₃×C₇	—	2	1	no	—
324	D₃×C₇	—	2	6	no	—
325	D₃×C₇	—	14	2	no	—
326	D₃×C₇	#1157	1	2	yes	direct product factor
327	D₃×C₇	C₇×#41	1	2	yes	complemented
328	C₂×#41	—	21	1	no	Sylow
329	C₂²×C₇	—	2	3	no	—
330	C₂²×C₇	—	3	1	no	—
331	C₂²×C₇	—	3	1	no	—
332	C₂²×C₇	—	3	1	no	—
333	C₂²×C₇	—	3	1	no	—
334	C₂²×C₇	—	6	3	no	—
335	C₂²×C₇	—	6	3	no	—
336	C₂²×C₇	—	6	2	no	—
337	C₂²×C₇	—	6	2	no	—
338	C₂²×C₇	—	6	12	no	—
339	C₂²×C₇	—	7	2	no	—
340	C₂²×C₇	—	21	2	no	—
341	C₂²×C₇	—	42	4	no	—
342	C₂²×C₇	C₂×D₃×D₇	1	1	yes	characteristic
343	C₂²×C₇	C₂²×D₃×C₇	1	1	yes	characteristic
344	C₂×D₇	—	3	2	no	—
345	C₂×D₇	—	6	4	no	—
346	C₂×D₇	C₂²×D₃×C₇	1	2	yes	—
347	C₄×C₇	—	2	3	no	—
348	C₄×C₇	—	2	3	no	—
349	C₄×C₇	—	3	1	no	—
350	C₄×C₇	—	3	1	no	—
351	C₄×C₇	—	3	1	no	—
352	C₄×C₇	—	3	1	no	—
353	C₄×C₇	—	6	3	no	—
354	C₄×C₇	—	6	3	no	—
355	C₄×C₇	—	7	2	no	—
356	C₄×C₇	—	21	2	no	—
357	C₄×C₇	C₂×D₃×D₇	1	1	yes	characteristic
358	C₄×C₇	C₂×D₃×D₇	1	1	yes	characteristic
359	C₄×C₇	C₂²×D₃×C₇	1	1	yes	characteristic
360	C₄×C₇	C₂²×D₃×C₇	1	1	yes	characteristic
361	Dic₇	—	3	2	no	—
362	Dic₇	C₂²×D₃×C₇	1	2	yes	—
363	C₂²×D₃	—	7	2	no	—
364	C₂²×D₃	C₂×C₇×D₇	1	1	yes	characteristic
365	C₃×Q₈	—	7	1	no	—
366	C₃×D₄	—	7	2	no	—
367	C₃×D₄	—	7	1	no	—
368	C₂×C₃×C₄	—	7	2	no	—
369	C₂×C₃×C₄	C₂×C₇×D₇	1	1	yes	characteristic, complemented
370	#67	—	7	2	no	—
371	#67	—	7	2	no	—
372	#67	—	7	2	no	—
373	C₂×Dic₃	—	7	2	no	—
374	C₂×Dic₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented
375	D₁₂	—	7	2	no	—
376	D₁₂	—	7	1	no	—
377	C₄×D₃	—	7	2	no	—
378	C₄×D₃	—	7	2	no	—
379	C₄×D₃	—	7	2	no	—
380	C₄×D₃	C₂×C₇×D₇	1	1	yes	characteristic
381	C₄×D₃	C₂×C₇×D₇	1	1	yes	characteristic
382	C₄×D₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented
383	C₄×D₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented
384	Dic₆	—	7	1	no	—
385	Dic₆	—	7	2	no	—
386	C₃×C₇	—	2	3	no	—
387	C₃×C₇	C₂×#1157	1	1	yes	characteristic, complemented
388	C₃×C₇	C₂×C₇×#41	1	1	yes	characteristic, complemented
389	#41	—	7	1	no	—
390	#41	—	21	2	no	—
391	#41	—	21	2	no	—
392	#41	—	21	1	no	—
393	#41	—	21	1	no	—
394	#41	—	21	1	no	—
395	C₂×Q₈	—	21	1	no	—
396	C₂×D₄	—	21	1	no	—
397	C₂×D₄	—	21	2	no	—
398	C₂²×C₄	—	3	1	no	—
399	C₂²×C₄	—	21	2	no	—
400	C₂×C₇	—	2	6	no	—
401	C₂×C₇	—	2	1	no	—
402	C₂×C₇	—	2	1	no	—
403	C₂×C₇	—	2	3	no	—
404	C₂×C₇	—	3	2	no	—
405	C₂×C₇	—	3	2	no	—
406	C₂×C₇	—	6	6	no	—
407	C₂×C₇	—	6	6	no	—
408	C₂×C₇	—	6	1	no	—
409	C₂×C₇	—	6	1	no	—
410	C₂×C₇	—	14	2	no	—
411	C₂×C₇	—	42	2	no	—
412	C₂×C₇	C₂²×D₃×D₇	1	1	yes	characteristic
413	C₂×C₇	C₂³×D₃×C₇	1	1	yes	characteristic
414	D₇	—	2	2	no	—
415	D₇	—	6	2	no	—
416	C₂²×C₃	—	7	2	no	—
417	C₂²×C₃	C₂²×C₇×D₇	1	1	yes	characteristic
418	C₂×D₃	—	2	2	no	—
419	C₂×D₃	—	7	2	no	—
420	C₂×D₃	—	14	4	no	—
421	C₂×D₃	C₂²×C₇×D₇	1	1	yes	characteristic
422	C₂×D₃	C₂²×C₇×D₇	1	1	yes	characteristic
423	C₃×C₄	—	7	2	no	—
424	C₃×C₄	C₂²×C₇×D₇	1	1	yes	characteristic
425	C₃×C₄	C₂²×C₇×D₇	1	1	yes	characteristic
426	Dic₃	—	7	2	no	—
427	Dic₃	C₂²×C₇×D₇	1	1	yes	characteristic
428	Dic₃	C₂²×C₇×D₇	1	1	yes	characteristic
429	C₂³	—	3	1	no	—
430	C₂³	—	21	2	no	—
431	Q₈	—	7	1	no	—
432	Q₈	—	21	2	no	—
433	Q₈	—	21	1	no	—
434	D₄	—	7	2	no	—
435	D₄	—	7	1	no	—
436	D₄	—	21	2	no	—
437	D₄	—	21	2	no	—
438	D₄	—	21	2	no	—
439	D₄	—	21	2	no	—
440	D₄	—	21	1	no	—
441	C₂×C₄	—	3	1	no	—
442	C₂×C₄	—	3	1	no	—
443	C₂×C₄	—	3	1	no	—
444	C₂×C₄	—	3	1	no	—
445	C₂×C₄	—	3	1	no	—
446	C₂×C₄	—	7	2	no	—
447	C₂×C₄	—	21	2	no	—
448	C₂×C₄	—	21	2	no	—
449	C₂×C₄	—	21	2	no	—
450	C₂×C₄	—	21	2	no	—
451	C₂×C₄	D₃×C₇×D₇	1	1	yes	characteristic, complemented
452	C₇	—	2	3	no	—
453	C₇	D₃×#1157	1	1	yes	characteristic, direct product factor
454	C₇	D₃×C₇×#41	1	1	yes	characteristic, complemented
455	C₂×C₃	—	2	1	no	—
456	C₂×C₃	—	14	2	no	—
457	C₂×C₃	C₂³×C₇×D₇	1	1	yes	characteristic
458	D₃	—	2	1	no	—
459	D₃	—	14	2	no	—
460	D₃	C₇×#1157	1	2	yes	direct product factor
461	C₂²	—	3	1	no	—
462	C₂²	—	3	1	no	—
463	C₂²	—	6	2	no	—
464	C₂²	—	7	2	no	—
465	C₂²	—	21	2	no	—
466	C₂²	—	42	4	no	—
467	C₂²	C₂×D₃×C₇×D₇	1	1	yes	characteristic
468	C₄	—	3	1	no	—
469	C₄	—	3	1	no	—
470	C₄	—	7	2	no	—
471	C₄	—	21	2	no	—
472	C₄	C₂×D₃×C₇×D₇	1	1	yes	characteristic
473	C₄	C₂×D₃×C₇×D₇	1	1	yes	characteristic
474	C₃	C₂×C₇×#1157	1	1	yes	characteristic, complemented, Sylow
475	C₂	—	2	1	no	—
476	C₂	—	3	2	no	—
477	C₂	—	6	1	no	—
478	C₂	—	14	2	no	—
479	C₂	—	42	2	no	—
480	C₂	C₂²×D₃×C₇×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇	C₂×D₃×D₇
commutator, cosocle	C₂×C₃×C₇	C₂⁴×C₇
Frattini	C₂	C₂²×D₃×C₇×D₇
Fitting	C₂×C₃×C₄×C₇²	C₂²
socle	C₂×C₃×C₇²	C₂⁴
hypercenter	C₂×C₄×C₇	D₃×D₇
hypocenter	C₃×C₇	C₂×C₇×#41
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₄×C₇ ◁ C₂×C₄×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×#66675	C₂	semidirect
2. C₇×#66683	C₂	semidirect
3. C₇×#66669	C₂	semidirect
4. C₇×#66728	C₂	semidirect
5. C₇×#66673	C₂	semidirect
6. C₃×C₇×#1157	C₂	semidirect
7. D₃×C₇×Dic₁₄	C₂	semidirect
8. C₄×D₃×C₇×D₇	C₂	semidirect
9. D₃×C₇×D₂₈	C₂	semidirect
10. C₂×C₄×D₃×C₇²	C₂	semidirect
11. D₃×C₇×C₂²⋊D₇	C₂	semidirect
15. C₂×C₃×C₄×C₇²	C₂²	semidirect
16. C₇×#4268	C₂²	semidirect
17. C₇×D₈₄	C₂²	semidirect
18. C₄×C₇×D₂₁	C₂²	semidirect
19. C₇×Dic₄₂	C₂²	semidirect
20. C₂×C₇²×Dic₃	C₂²	semidirect
23. C₄×D₃×C₇²	C₂²	semidirect
24. C₄×D₃×C₇²	C₂²	semidirect
25. C₃×C₇×C₂²⋊D₇	C₂²	semidirect
26. C₃×C₇×D₂₈	C₂²	semidirect
27. C₃×C₄×C₇×D₇	C₂²	semidirect
28. C₃×C₇×Dic₁₄	C₂²	semidirect
29. C₇×#4248	C₂²	semidirect
30. C₇×#4247	C₂²	semidirect
31. C₇×#4246	C₂²	semidirect
32. C₇×#4245	C₂²	semidirect
33. C₇×D₂₁⋊C₄	C₂²	semidirect
35. C₇×Dic₃×D₇	C₂²	semidirect
43. C₇×#1157	D₃	direct (N × H)
48. D₃×#1157	C₇	direct (N × H)
69. C₂×C₄×C₇²	C₂×D₃	semidirect
73. C₇×C₂²⋊D₇	C₂×D₃	semidirect
77. C₇×D₂₈	C₂×D₃	semidirect
81. C₄×C₇×D₇	C₂×D₃	semidirect
84. C₇×Dic₁₄	C₂×D₃	semidirect
86. #66728	C₂×C₇	semidirect
97. C₂×C₄×D₃×C₇	D₇	semidirect
98. C₂×C₄×D₃×C₇	C₂×C₇	semidirect
99. C₃×#1157	C₂×C₇	semidirect
100. D₃×C₂²⋊D₇	C₂×C₇	semidirect
101. #66683	C₂×C₇	semidirect
102. D₃×D₂₈	C₂×C₇	semidirect
103. C₄×D₃×D₇	C₂×C₇	semidirect
104. #66675	C₂×C₇	semidirect
105. #66673	C₂×C₇	semidirect
106. D₃×Dic₁₄	C₂×C₇	semidirect
107. #66669	C₂×C₇	semidirect
112. D₃×C₇²	#41	semidirect
139. C₂×C₃×C₄×C₇	C₂×D₇	semidirect
140. C₂×C₃×C₄×C₇	C₂²×C₇	semidirect
141. #4268	C₂²×C₇	semidirect
142. D₈₄	C₂²×C₇	semidirect
143. C₄×D₂₁	C₂²×C₇	semidirect
144. Dic₄₂	C₂²×C₇	semidirect
150. C₂×C₇×Dic₃	C₂×D₇	semidirect
151. C₂×C₇×Dic₃	C₂²×C₇	semidirect
163. C₄×D₃×C₇	C₂×D₇	semidirect
164. C₄×D₃×C₇	C₂×D₇	semidirect
167. C₄×D₃×C₇	C₂²×C₇	semidirect
168. C₄×D₃×C₇	C₂²×C₇	semidirect
171. C₃×C₂²⋊D₇	C₂²×C₇	semidirect
172. C₃×D₂₈	C₂²×C₇	semidirect
173. C₃×C₄×D₇	C₂²×C₇	semidirect
174. C₃×Dic₁₄	C₂²×C₇	semidirect
175. #4248	C₂²×C₇	semidirect
176. #4247	C₂²×C₇	semidirect
177. #4246	C₂²×C₇	semidirect
178. #4245	C₂²×C₇	semidirect
179. D₂₁⋊C₄	C₂²×C₇	semidirect
181. Dic₃×D₇	C₂²×C₇	semidirect
182. C₃×C₇²	C₂×#41	semidirect
202. #1157	D₃×C₇	direct (N × H)
283. C₂×C₄×C₇	D₃×D₇	semidirect
284. C₂×C₄×C₇	C₂×D₃×C₇	semidirect
288. C₂²⋊D₇	C₂×D₃×C₇	semidirect
292. D₂₈	C₂×D₃×C₇	semidirect
296. C₄×D₇	C₂×D₃×C₇	semidirect
299. Dic₁₄	C₂×D₃×C₇	semidirect
300. C₇²	D₃×#41	semidirect
311. C₂×C₄×D₃	C₇×D₇	semidirect
326. D₃×C₇	#1157	direct (N × H)
327. D₃×C₇	C₇×#41	semidirect
369. C₂×C₃×C₄	C₂×C₇×D₇	semidirect
374. C₂×Dic₃	C₂×C₇×D₇	semidirect
382. C₄×D₃	C₂×C₇×D₇	semidirect
383. C₄×D₃	C₂×C₇×D₇	semidirect
387. C₃×C₇	C₂×#1157	semidirect
388. C₃×C₇	C₂×C₇×#41	semidirect
451. C₂×C₄	D₃×C₇×D₇	semidirect
453. C₇	D₃×#1157	direct (N × H)
454. C₇	D₃×C₇×#41	semidirect
460. D₃	C₇×#1157	direct (N × H)
474. C₃	C₂×C₇×#1157	semidirect

Maximal subgroups

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

subgroup	index
C₇×#66675	2
C₇×#66683	2
C₇×#66669	2
C₇×#66728	2
C₇×#66673	2
C₃×C₇×#1157	2
D₃×C₇×Dic₁₄	2
C₄×D₃×C₇×D₇	2
D₃×C₇×D₂₈	2
C₂×C₄×D₃×C₇²	2
D₃×C₇×C₂²⋊D₇	2
C₂×C₇×#1157	3
D₃×C₇×#41	7
D₃×#1157	7

Subgroups — D3×C7×#1157 #72254263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×#1157 #72254263