Subgroups — C₇×#34123 #13211339

Order 1792.

2598 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic
2	C₇×#2356	C₂	1	2	yes	maximal, complemented
3	C₇×#2353	C₂	1	4	yes	maximal, complemented
4	C₇×#2349	C₂	1	2	yes	maximal, complemented
5	C₇×#2346	C₂	1	2	yes	maximal, complemented
6	C₇×#2343	C₂	1	4	yes	maximal, complemented
7	C₇×#2339	C₂	1	2	yes	maximal
8	C₇×#2295	C₂	1	2	yes	maximal, complemented
9	C₇×#2290	C₂	1	4	yes	maximal, complemented
10	C₇×#2283	C₂	1	2	yes	maximal, complemented
11	C₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄²×C₇×D₄	C₂	1	2	yes	maximal, complemented
13	C₄×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#376	C₂	1	2	yes	maximal, complemented
15	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
16	C₄×C₇×#41	C₄	1	16	yes	complemented
17	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
20	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
23	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
24	C₂×C₇×#117	C₂²	1	2	yes	—
25	C₂×C₇×#117	C₂²	1	2	yes	—
26	C₂×C₇×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₇	C₂²	1	4	yes	—
28	C₂²×C₄²×C₇	C₂²	1	2	yes	—
29	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
30	C₇×#391	C₂²	1	4	yes	—
31	C₇×#389	C₂²	1	4	yes	—
32	C₇×#388	C₂²	1	8	yes	—
33	C₇×#387	C₂²	1	8	yes	—
34	C₇×#387	C₂²	1	8	yes	—
35	C₇×#386	C₂²	1	8	yes	—
36	C₇×#385	C₂²	1	8	yes	—
37	C₇×#383	C₂²	1	2	yes	—
38	C₇×#383	C₂²	1	4	yes	—
39	C₇×#382	C₂²	1	4	yes	—
40	C₇×#382	C₂²	1	2	yes	—
41	C₇×#381	C₂²	1	4	yes	—
42	C₇×#381	C₂²	1	2	yes	—
43	C₇×#380	C₂²	1	2	yes	—
44	C₇×#380	C₂²	1	4	yes	—
45	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
46	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
47	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
48	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
49	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
50	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
51	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
52	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
53	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
54	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
55	C₇×#376	C₂²	1	1	yes	characteristic
56	C₇×#376	C₂²	1	2	yes	—
57	C₇×#376	C₂²	1	4	yes	—
58	C₇×#376	C₂²	1	4	yes	—
59	C₇×#376	C₂²	1	4	yes	—
60	C₇×#376	C₂²	1	1	yes	characteristic
61	C₂×C₇×#95	C₂²	1	4	yes	—
62	C₂×C₇×#95	C₂²	1	4	yes	—
63	C₄³×C₇	C₂²	1	2	yes	—
64	#34123	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂×C₇×#41	—	2	8	no	—
66	C₂×C₇×#41	C₂×C₄	1	8	yes	—
67	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×D₄	C₂³	1	2	yes	—
69	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₇	C₂³	1	8	yes	—
71	C₂³×C₄×C₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇	C₂³	1	2	yes	—
74	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
77	C₄×C₇×Q₈	C₂×C₄	1	8	yes	complemented
78	C₄×C₇×Q₈	C₂×C₄	1	8	yes	complemented
79	C₄×C₇×D₄	—	2	16	no	—
80	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
81	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
82	C₄×C₇×D₄	C₂×C₄	1	16	yes	complemented
83	C₄×C₇×D₄	C₂×C₄	1	16	yes	complemented
84	C₇×#117	—	2	8	no	—
85	C₇×#117	C₂×C₄	1	16	yes	complemented
86	C₇×#117	C₂×C₄	1	8	yes	complemented
87	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
90	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
98	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
99	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
100	C₂×C₄²×C₇	—	2	16	no	—
101	C₂×C₄²×C₇	C₂×C₄	1	8	yes	complemented
102	C₂×C₄²×C₇	C₂×C₄	1	16	yes	complemented
103	C₂×C₄²×C₇	C₂³	1	4	yes	—
104	C₂×C₄²×C₇	C₂³	1	8	yes	—
105	C₂×C₄²×C₇	C₂³	1	2	yes	—
106	C₂×C₄²×C₇	C₂³	1	4	yes	—
107	C₂×C₄²×C₇	C₂³	1	4	yes	—
108	C₂×C₄²×C₇	C₂³	1	2	yes	—
109	C₂×C₄²×C₇	C₂³	1	2	yes	—
110	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₇	C₂³	1	2	yes	—
115	C₂×C₄²×C₇	C₂³	1	2	yes	—
116	C₇×#95	C₂³	1	2	yes	—
117	C₇×#95	C₂³	1	2	yes	—
118	C₇×#95	C₂³	1	4	yes	—
119	C₇×#95	C₂³	1	4	yes	—
120	C₇×#95	C₂³	1	8	yes	—
121	C₇×#95	C₂³	1	8	yes	—
122	C₇×#95	C₂³	1	2	yes	—
123	C₇×#95	C₂³	1	2	yes	—
124	C₇×#95	C₂³	1	4	yes	—
125	C₇×#95	C₂³	1	8	yes	—
126	C₇×#95	C₂³	1	4	yes	—
127	C₇×#95	C₂³	1	8	yes	—
128	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic
129	#2356	C₂×C₇	1	2	yes	complemented
130	#2353	C₂×C₇	1	4	yes	complemented
131	#2349	C₂×C₇	1	2	yes	complemented
132	#2346	C₂×C₇	1	2	yes	complemented
133	#2343	C₂×C₇	1	4	yes	complemented
134	#2339	C₂×C₇	1	2	yes	—
135	#2295	C₂×C₇	1	2	yes	complemented
136	#2290	C₂×C₇	1	4	yes	complemented
137	#2283	C₂×C₇	1	1	yes	characteristic, complemented
138	#2283	C₂×C₇	1	2	yes	complemented
139	C₄²×D₄	C₂×C₇	1	2	yes	complemented
140	C₄×#117	C₂×C₇	1	1	yes	characteristic, complemented
141	C₂×#376	C₂×C₇	1	2	yes	complemented
142	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
143	C₂⁴×C₇	C₂⁴	1	2	yes	—
144	C₇×#41	—	2	32	no	—
145	C₂×C₇×Q₈	—	2	4	no	—
146	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
147	C₂×C₇×D₄	—	2	8	no	—
148	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
149	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
150	C₂×C₇×D₄	#41	1	8	yes	—
151	C₂²×C₄×C₇	—	2	8	no	—
152	C₂²×C₄×C₇	—	2	8	no	—
153	C₂²×C₄×C₇	—	2	4	no	—
154	C₂²×C₄×C₇	—	2	4	no	—
155	C₂²×C₄×C₇	—	2	16	no	—
156	C₂²×C₄×C₇	—	2	16	no	—
157	C₂²×C₄×C₇	—	4	2	no	—
158	C₂²×C₄×C₇	—	4	8	no	—
159	C₂²×C₄×C₇	—	4	4	no	—
160	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
161	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
162	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
163	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
164	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
165	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
166	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
167	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
178	C₇×C₄⋊C₄	—	2	8	no	—
179	C₇×C₄⋊C₄	—	2	8	no	—
180	C₇×C₄⋊C₄	—	4	8	no	—
181	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
182	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
183	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
184	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
185	C₇×C₂²⋊C₄	—	2	16	no	—
186	C₇×C₂²⋊C₄	—	2	8	no	—
187	C₇×C₂²⋊C₄	—	4	4	no	—
188	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
189	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
190	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
191	C₄²×C₇	—	2	16	no	—
192	C₄²×C₇	—	2	8	no	—
193	C₄²×C₇	—	2	4	no	—
194	C₄²×C₇	—	2	8	no	—
195	C₄²×C₇	—	4	4	no	—
196	C₄²×C₇	C₂²×C₄	1	4	yes	—
197	C₄²×C₇	C₂²×C₄	1	8	yes	—
198	C₄²×C₇	C₂²×C₄	1	4	yes	—
199	C₄²×C₇	C₂²×C₄	1	4	yes	—
200	C₄²×C₇	C₂²×C₄	1	4	yes	—
201	C₄²×C₇	C₂²×C₄	1	8	yes	—
202	C₄²×C₇	C₂²×C₄	1	8	yes	—
203	C₄²×C₇	#41	1	8	yes	complemented
204	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
205	C₄×#41	C₄×C₇	1	16	yes	complemented
206	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
209	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
210	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
212	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
213	C₂×#117	C₂²×C₇	1	2	yes	—
214	C₂×#117	C₂²×C₇	1	2	yes	—
215	C₂×#117	C₂²×C₇	1	1	yes	characteristic
216	C₂²×C₄²	C₂²×C₇	1	4	yes	—
217	C₂²×C₄²	C₂²×C₇	1	2	yes	—
218	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
219	#391	C₂²×C₇	1	4	yes	—
220	#389	C₂²×C₇	1	4	yes	—
221	#388	C₂²×C₇	1	8	yes	—
222	#387	C₂²×C₇	1	8	yes	—
223	#387	C₂²×C₇	1	8	yes	—
224	#386	C₂²×C₇	1	8	yes	—
225	#385	C₂²×C₇	1	8	yes	—
226	#383	C₂²×C₇	1	2	yes	—
227	#383	C₂²×C₇	1	4	yes	—
228	#382	C₂²×C₇	1	4	yes	—
229	#382	C₂²×C₇	1	2	yes	—
230	#381	C₂²×C₇	1	4	yes	—
231	#381	C₂²×C₇	1	2	yes	—
232	#380	C₂²×C₇	1	2	yes	—
233	#380	C₂²×C₇	1	4	yes	—
234	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
235	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
236	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
237	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
238	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
239	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
241	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
242	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
243	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
244	#376	C₂²×C₇	1	4	yes	—
245	#376	C₂²×C₇	1	4	yes	—
246	#376	C₂²×C₇	1	1	yes	characteristic
247	#376	C₂²×C₇	1	2	yes	—
248	#376	C₂²×C₇	1	4	yes	—
249	#376	C₂²×C₇	1	1	yes	characteristic
250	C₂×#95	C₂²×C₇	1	4	yes	—
251	C₂×#95	C₂²×C₇	1	4	yes	—
252	C₄³	C₂²×C₇	1	2	yes	—
253	C₂³×C₇	—	2	4	no	—
254	C₂³×C₇	—	2	4	no	—
255	C₂³×C₇	—	2	2	no	—
256	C₂³×C₇	—	2	2	no	—
257	C₂³×C₇	—	2	2	no	—
258	C₂³×C₇	C₂³×C₄	1	2	yes	—
259	C₂³×C₇	C₂³×C₄	1	4	yes	—
260	C₂³×C₇	C₂×#41	1	8	yes	—
261	C₂³×C₇	C₂⁵	1	1	yes	characteristic
262	C₇×Q₈	—	2	8	no	—
263	C₇×D₄	—	2	16	no	—
264	C₇×D₄	#117	1	16	yes	complemented
265	C₂×C₄×C₇	—	2	16	no	—
266	C₂×C₄×C₇	—	2	4	no	—
267	C₂×C₄×C₇	—	2	4	no	—
268	C₂×C₄×C₇	—	2	2	no	—
269	C₂×C₄×C₇	—	2	2	no	—
270	C₂×C₄×C₇	—	2	4	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	4	no	—
273	C₂×C₄×C₇	—	2	4	no	—
274	C₂×C₄×C₇	—	2	2	no	—
275	C₂×C₄×C₇	—	2	8	no	—
276	C₂×C₄×C₇	—	2	16	no	—
277	C₂×C₄×C₇	—	2	8	no	—
278	C₂×C₄×C₇	—	2	8	no	—
279	C₂×C₄×C₇	—	2	4	no	—
280	C₂×C₄×C₇	—	2	4	no	—
281	C₂×C₄×C₇	—	2	8	no	—
282	C₂×C₄×C₇	—	2	4	no	—
283	C₂×C₄×C₇	—	2	8	no	—
284	C₂×C₄×C₇	—	4	8	no	—
285	C₂×C₄×C₇	—	4	4	no	—
286	C₂×C₄×C₇	—	4	32	no	—
287	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
291	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
296	C₂×C₄×C₇	C₂×#41	1	8	yes	—
297	C₂×C₄×C₇	C₂×#41	1	4	yes	—
298	C₂×C₄×C₇	C₂×#41	1	4	yes	—
299	C₂×#41	—	2	8	no	—
300	C₂×#41	C₂×C₄×C₇	1	8	yes	—
301	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
302	C₂²×D₄	C₂³×C₇	1	2	yes	—
303	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₇	1	8	yes	—
305	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₇	1	2	yes	—
307	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₇	1	2	yes	—
309	C₂³×C₄	C₂³×C₇	1	2	yes	—
310	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
311	C₄×Q₈	C₂×C₄×C₇	1	8	yes	complemented
312	C₄×Q₈	C₂×C₄×C₇	1	8	yes	complemented
313	C₄×D₄	—	2	16	no	—
314	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
315	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
316	C₄×D₄	C₂×C₄×C₇	1	16	yes	complemented
317	C₄×D₄	C₂×C₄×C₇	1	16	yes	complemented
318	#117	—	2	8	no	—
319	#117	C₂×C₄×C₇	1	16	yes	complemented
320	#117	C₂×C₄×C₇	1	8	yes	complemented
321	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
324	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
334	C₂×C₄²	—	2	16	no	—
335	C₂×C₄²	C₂×C₄×C₇	1	8	yes	complemented
336	C₂×C₄²	C₂×C₄×C₇	1	16	yes	complemented
337	C₂×C₄²	C₂³×C₇	1	2	yes	—
338	C₂×C₄²	C₂³×C₇	1	4	yes	—
339	C₂×C₄²	C₂³×C₇	1	4	yes	—
340	C₂×C₄²	C₂³×C₇	1	8	yes	—
341	C₂×C₄²	C₂³×C₇	1	4	yes	—
342	C₂×C₄²	C₂³×C₇	1	2	yes	—
343	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₇	1	2	yes	—
346	C₂×C₄²	C₂³×C₇	1	2	yes	—
347	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₇	1	2	yes	—
350	#95	C₂³×C₇	1	2	yes	—
351	#95	C₂³×C₇	1	2	yes	—
352	#95	C₂³×C₇	1	4	yes	—
353	#95	C₂³×C₇	1	4	yes	—
354	#95	C₂³×C₇	1	8	yes	—
355	#95	C₂³×C₇	1	8	yes	—
356	#95	C₂³×C₇	1	2	yes	—
357	#95	C₂³×C₇	1	2	yes	—
358	#95	C₂³×C₇	1	4	yes	—
359	#95	C₂³×C₇	1	8	yes	—
360	#95	C₂³×C₇	1	4	yes	—
361	#95	C₂³×C₇	1	8	yes	—
362	C₂²×C₇	—	2	4	no	—
363	C₂²×C₇	—	2	4	no	—
364	C₂²×C₇	—	2	16	no	—
365	C₂²×C₇	—	2	2	no	—
366	C₂²×C₇	—	2	2	no	—
367	C₂²×C₇	—	2	2	no	—
368	C₂²×C₇	—	4	4	no	—
369	C₂²×C₇	C₂×#117	1	8	yes	—
370	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
371	C₂²×C₇	C₂²×#41	1	2	yes	—
372	C₂²×C₇	C₂²×#41	1	2	yes	—
373	C₂²×C₇	#585	1	2	yes	—
374	C₄×C₇	—	2	2	no	—
375	C₄×C₇	—	2	4	no	—
376	C₄×C₇	—	2	4	no	—
377	C₄×C₇	—	2	2	no	—
378	C₄×C₇	—	2	2	no	—
379	C₄×C₇	—	2	2	no	—
380	C₄×C₇	—	2	4	no	—
381	C₄×C₇	—	2	8	no	—
382	C₄×C₇	—	4	4	no	—
383	C₄×C₇	—	4	8	no	—
384	C₄×C₇	C₂×#117	1	4	yes	—
385	C₄×C₇	C₄×#41	1	4	yes	—
386	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
387	C₂⁴	C₂⁴×C₇	1	2	yes	—
388	#41	—	2	32	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
393	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
394	C₂×D₄	C₇×#41	1	8	yes	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	2	8	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	16	no	—
400	C₂²×C₄	—	2	16	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	8	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
405	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
406	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
407	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
408	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
409	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
411	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
420	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	2	8	no	—
424	C₄⋊C₄	—	4	8	no	—
425	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
426	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
427	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
428	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
429	C₂²⋊C₄	—	2	16	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	4	4	no	—
432	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
433	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
434	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
435	C₄²	—	2	16	no	—
436	C₄²	—	2	8	no	—
437	C₄²	—	2	4	no	—
438	C₄²	—	2	8	no	—
439	C₄²	—	4	4	no	—
440	C₄²	C₂²×C₄×C₇	1	4	yes	—
441	C₄²	C₂²×C₄×C₇	1	8	yes	—
442	C₄²	C₂²×C₄×C₇	1	4	yes	—
443	C₄²	C₂²×C₄×C₇	1	4	yes	—
444	C₄²	C₂²×C₄×C₇	1	4	yes	—
445	C₄²	C₂²×C₄×C₇	1	8	yes	—
446	C₄²	C₂²×C₄×C₇	1	8	yes	—
447	C₄²	C₇×#41	1	8	yes	complemented
448	C₂×C₇	—	2	8	no	—
449	C₂×C₇	—	4	2	no	—
450	C₂×C₇	C₂²×#117	1	1	yes	characteristic
451	C₂×C₇	C₂×C₄×#41	1	1	yes	characteristic
452	C₂×C₇	#3428	1	1	yes	characteristic
453	C₂×C₇	#3475	1	4	yes	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	C₂³×C₄×C₇	1	2	yes	—
460	C₂³	C₂³×C₄×C₇	1	4	yes	—
461	C₂³	C₂×C₇×#41	1	8	yes	—
462	C₂³	C₂⁵×C₇	1	1	yes	characteristic
463	Q₈	—	2	8	no	—
464	D₄	—	2	16	no	—
465	D₄	C₇×#117	1	16	yes	complemented
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	16	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	16	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	32	no	—
488	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
489	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
490	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
491	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
492	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
493	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
494	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
495	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
496	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
497	C₂×C₄	C₂×C₇×#41	1	8	yes	—
498	C₂×C₄	C₂×C₇×#41	1	4	yes	—
499	C₂×C₄	C₂×C₇×#41	1	4	yes	—
500	C₇	#34123	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	16	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	4	no	—
508	C₂²	C₂×C₇×#117	1	8	yes	—
509	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
510	C₂²	C₂²×C₇×#41	1	2	yes	—
511	C₂²	C₂²×C₇×#41	1	2	yes	—
512	C₂²	C₇×#585	1	2	yes	—
513	C₄	—	2	2	no	—
514	C₄	—	2	4	no	—
515	C₄	—	2	4	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	4	no	—
520	C₄	—	2	8	no	—
521	C₄	—	4	8	no	—
522	C₄	—	4	4	no	—
523	C₄	C₂×C₇×#117	1	4	yes	—
524	C₄	C₄×C₇×#41	1	4	yes	—
525	C₂	—	2	8	no	—
526	C₂	—	4	2	no	—
527	C₂	C₂²×C₇×#117	1	1	yes	characteristic
528	C₂	C₂×C₄×C₇×#41	1	1	yes	characteristic
529	C₂	C₇×#3428	1	1	yes	characteristic
530	C₂	C₇×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₂²×C₇×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2356	C₂	semidirect
3. C₇×#2353	C₂	semidirect
4. C₇×#2349	C₂	semidirect
5. C₇×#2346	C₂	semidirect
6. C₇×#2343	C₂	semidirect
8. C₇×#2295	C₂	semidirect
9. C₇×#2290	C₂	semidirect
10. C₇×#2283	C₂	semidirect
11. C₇×#2283	C₂	semidirect
12. C₄²×C₇×D₄	C₂	semidirect
13. C₄×C₇×#117	C₂	semidirect
14. C₂×C₇×#376	C₂	semidirect
16. C₄×C₇×#41	C₄	semidirect
64. #34123	C₇	direct (N × H)
77. C₄×C₇×Q₈	C₂×C₄	semidirect
78. C₄×C₇×Q₈	C₂×C₄	semidirect
82. C₄×C₇×D₄	C₂×C₄	semidirect
83. C₄×C₇×D₄	C₂×C₄	semidirect
85. C₇×#117	C₂×C₄	semidirect
86. C₇×#117	C₂×C₄	semidirect
101. C₂×C₄²×C₇	C₂×C₄	semidirect
102. C₂×C₄²×C₇	C₂×C₄	semidirect
129. #2356	C₂×C₇	semidirect
130. #2353	C₂×C₇	semidirect
131. #2349	C₂×C₇	semidirect
132. #2346	C₂×C₇	semidirect
133. #2343	C₂×C₇	semidirect
135. #2295	C₂×C₇	semidirect
136. #2290	C₂×C₇	semidirect
137. #2283	C₂×C₇	semidirect
138. #2283	C₂×C₇	semidirect
139. C₄²×D₄	C₂×C₇	semidirect
140. C₄×#117	C₂×C₇	semidirect
141. C₂×#376	C₂×C₇	semidirect
203. C₄²×C₇	#41	semidirect
205. C₄×#41	C₄×C₇	semidirect
264. C₇×D₄	#117	semidirect
311. C₄×Q₈	C₂×C₄×C₇	semidirect
312. C₄×Q₈	C₂×C₄×C₇	semidirect
316. C₄×D₄	C₂×C₄×C₇	semidirect
317. C₄×D₄	C₂×C₄×C₇	semidirect
319. #117	C₂×C₄×C₇	semidirect
320. #117	C₂×C₄×C₇	semidirect
335. C₂×C₄²	C₂×C₄×C₇	semidirect
336. C₂×C₄²	C₂×C₄×C₇	semidirect
447. C₄²	C₇×#41	semidirect
465. D₄	C₇×#117	semidirect
500. C₇	#34123	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₇×#41	2
C₇×#2356	2
C₇×#2353	2
C₇×#2349	2
C₇×#2346	2
C₇×#2343	2
C₇×#2339	2
C₇×#2295	2
C₇×#2290	2
C₇×#2283	2
C₄²×C₇×D₄	2
C₄×C₇×#117	2
C₂×C₇×#376	2
#34123	7

Subgroups — C7×#34123 #13211339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34123 #13211339