Subgroups — C₇×#60285 #13237501

Order 1792.

1762 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₇×#2995	C₂	1	4	yes	maximal, complemented
3	C₇×#2994	C₂	1	4	yes	maximal, complemented
4	C₇×#2985	C₂	1	2	yes	maximal, complemented
5	C₇×#2981	C₂	1	2	yes	maximal, complemented
6	C₇×#2976	C₂	1	4	yes	maximal, complemented
7	C₇×#2971	C₂	1	2	yes	maximal, complemented
8	C₇×#2970	C₂	1	4	yes	maximal, complemented
9	C₇×#2970	C₂	1	2	yes	maximal, complemented
10	C₇×#2923	C₂	1	4	yes	maximal, complemented
11	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#533	C₄	1	1	yes	characteristic
14	C₇×#533	C₄	1	1	yes	characteristic
15	C₇×#533	C₂²	1	1	yes	characteristic
16	C₇×#532	C₄	1	1	yes	characteristic
17	C₇×#532	C₄	1	1	yes	characteristic
18	C₇×#532	C₂²	1	1	yes	characteristic
19	C₇×#529	C₄	1	2	yes	—
20	C₇×#529	C₄	1	2	yes	—
21	C₇×#529	C₄	1	2	yes	—
22	C₇×#529	C₄	1	2	yes	—
23	C₇×#529	C₂²	1	2	yes	—
24	C₇×#529	C₂²	1	2	yes	—
25	C₇×#525	C₄	1	2	yes	—
26	C₇×#525	C₄	1	2	yes	—
27	C₇×#525	C₂²	1	2	yes	—
28	C₄×C₇×#41	C₂²	1	2	yes	—
29	C₄×C₇×#41	C₂²	1	2	yes	—
30	C₄×C₇×#41	C₂²	1	2	yes	—
31	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
32	C₇×#446	C₂²	1	4	yes	complemented
33	C₇×#446	C₂²	1	8	yes	complemented
34	C₇×C₈×Q₈	C₂²	1	4	yes	complemented
35	C₇×#436	C₂²	1	8	yes	—
36	C₇×#436	C₂²	1	4	yes	complemented
37	C₇×#435	C₂²	1	8	yes	—
38	C₇×#435	C₂²	1	8	yes	—
39	C₇×#435	C₂²	1	8	yes	complemented
40	C₇×C₈×D₄	C₂²	1	8	yes	—
41	C₇×C₈×D₄	C₂²	1	4	yes	complemented
42	C₇×#433	C₂²	1	8	yes	—
43	C₇×#433	C₂²	1	8	yes	complemented
44	C₇×#432	C₂²	1	2	yes	—
45	C₇×#432	C₂²	1	2	yes	—
46	C₇×#432	C₂²	1	2	yes	—
47	C₇×#432	C₂²	1	2	yes	—
48	C₇×#432	C₂²	1	2	yes	—
49	C₇×#432	C₂²	1	2	yes	—
50	C₇×#432	C₂²	1	4	yes	complemented
51	C₇×#432	C₂²	1	4	yes	complemented
52	C₇×#431	C₂²	1	2	yes	—
53	C₇×#431	C₂²	1	2	yes	—
54	C₇×#424	C₂²	1	8	yes	complemented
55	C₇×#423	C₂²	1	2	yes	—
56	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
57	C₇×#408	C₂²	1	8	yes	—
58	C₇×#407	C₂²	1	2	yes	—
59	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
60	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
61	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
62	C₄×C₇×M₁₆	C₂²	1	4	yes	complemented
63	C₂×C₇×#97	C₂²	1	2	yes	—
64	C₂×C₇×#97	C₂²	1	4	yes	complemented
65	#60285	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂×C₇×#41	C₂×C₄	1	2	yes	—
67	C₂×C₇×#41	C₂×C₄	1	2	yes	—
68	C₂×C₇×#41	C₂³	1	2	yes	—
69	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂×C₇×M₁₆	C₂³	1	2	yes	—
73	C₂×C₇×M₁₆	C₂³	1	2	yes	—
74	C₂×C₇×M₁₆	C₂³	1	8	yes	—
75	C₂²×C₇×C₈	C₂³	1	4	yes	—
76	C₂²×C₇×C₈	C₂³	1	8	yes	—
77	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
79	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
80	C₇×#127	C₂×C₄	1	1	yes	characteristic
81	C₇×#126	C₂×C₄	1	4	yes	—
82	C₇×#126	C₂×C₄	1	4	yes	—
83	C₇×#125	C₂×C₄	1	2	yes	—
84	C₇×#125	C₂×C₄	1	2	yes	—
85	C₇×#125	C₂×C₄	1	2	yes	—
86	C₇×#124	C₂×C₄	1	2	yes	—
87	C₇×#124	C₂×C₄	1	2	yes	—
88	C₇×#124	C₂×C₄	1	2	yes	—
89	C₇×#123	C₂×C₄	1	4	yes	—
90	C₇×#123	C₂×C₄	1	4	yes	—
91	C₇×#123	C₂×C₄	1	4	yes	—
92	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
93	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
94	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
95	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
96	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
97	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
98	C₇×#121	C₂×C₄	1	2	yes	—
99	C₇×#121	C₂×C₄	1	2	yes	—
100	C₇×#121	C₂×C₄	1	2	yes	—
101	C₇×#121	C₂×C₄	1	2	yes	—
102	C₇×#121	C₂×C₄	1	2	yes	—
103	C₇×#121	C₂×C₄	1	2	yes	—
104	C₇×#120	C₂×C₄	1	4	yes	—
105	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
106	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
107	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
108	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
109	C₄×C₇×Q₈	C₂³	1	2	yes	—
110	C₄×C₇×Q₈	C₂³	1	2	yes	—
111	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
112	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
113	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
114	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
115	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
116	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
117	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
118	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
119	C₄×C₇×D₄	C₂³	1	4	yes	—
120	C₄×C₇×D₄	C₂³	1	4	yes	—
121	C₄×C₇×D₄	C₂³	1	2	yes	—
122	C₄×C₇×D₄	C₂³	1	2	yes	—
123	C₇×#117	C₂×C₄	1	2	yes	—
124	C₇×#117	C₂×C₄	1	2	yes	—
125	C₇×#117	C₂×C₄	1	4	yes	—
126	C₇×#117	C₂×C₄	1	4	yes	—
127	C₇×#117	C₂³	1	2	yes	—
128	C₇×#117	C₂³	1	4	yes	—
129	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₇	C₂³	1	4	yes	—
142	C₇×C₄⋊C₈	C₂³	1	4	yes	—
143	C₇×C₄⋊C₈	C₂³	1	4	yes	—
144	C₇×C₄⋊C₈	C₂³	1	4	yes	—
145	C₇×C₄⋊C₈	C₂³	1	4	yes	—
146	C₇×C₄⋊C₈	C₂³	1	8	yes	—
147	C₇×C₄⋊C₈	C₂³	1	8	yes	—
148	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
149	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
150	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
151	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
152	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
153	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
154	C₇×#97	C₂³	1	4	yes	—
155	C₇×#97	C₂³	1	4	yes	—
156	C₇×#97	C₂³	1	2	yes	—
157	C₇×#97	C₂³	1	8	yes	—
158	C₇×#97	C₂³	1	2	yes	—
159	C₄×C₇×C₈	C₂³	1	2	yes	—
160	C₄×C₇×C₈	C₂³	1	2	yes	—
161	C₄×C₇×C₈	C₂³	1	8	yes	—
162	#3444	C₂×C₇	1	1	yes	characteristic
163	#2995	C₂×C₇	1	4	yes	complemented
164	#2994	C₂×C₇	1	4	yes	complemented
165	#2985	C₂×C₇	1	2	yes	complemented
166	#2981	C₂×C₇	1	2	yes	complemented
167	#2976	C₂×C₇	1	4	yes	complemented
168	#2971	C₂×C₇	1	2	yes	complemented
169	#2970	C₂×C₇	1	4	yes	complemented
170	#2970	C₂×C₇	1	2	yes	complemented
171	#2923	C₂×C₇	1	4	yes	complemented
172	#2920	C₂×C₇	1	1	yes	characteristic, complemented
173	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
174	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
175	C₇×#41	—	4	4	no	—
176	C₇×#41	—	4	4	no	—
177	C₇×#41	—	4	4	no	—
178	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
179	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
180	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
181	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
182	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
183	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
184	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
185	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
186	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
187	C₂²×C₄×C₇	—	4	2	no	—
188	C₂²×C₄×C₇	—	4	2	no	—
189	C₂²×C₄×C₇	—	4	2	no	—
190	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
206	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
207	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
211	C₇×M₁₆	—	4	2	no	—
212	C₇×M₁₆	—	4	8	no	—
213	C₇×M₁₆	—	4	2	no	—
214	C₂×C₇×C₈	—	4	4	no	—
215	C₂×C₇×C₈	—	4	8	no	—
216	C₂×C₇×C₈	C₂⁴	1	4	yes	—
217	C₂×C₇×C₈	C₂⁴	1	4	yes	—
218	C₂×C₇×C₈	C₂⁴	1	8	yes	—
219	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
220	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
221	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
222	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
223	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
224	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
225	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
226	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
227	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
228	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
229	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
230	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
231	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
232	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
233	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
234	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
235	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
236	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
237	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
238	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
239	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
240	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
241	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
242	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
243	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
244	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
245	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
246	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
249	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
250	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
251	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
252	C₄²×C₇	C₂²×C₄	1	4	yes	—
253	C₄²×C₇	C₂²×C₄	1	4	yes	—
254	C₄²×C₇	C₂⁴	1	1	yes	characteristic
255	C₄²×C₇	C₂⁴	1	4	yes	—
256	C₄²×C₇	C₂⁴	1	1	yes	characteristic
257	C₄²×C₇	C₂⁴	1	1	yes	characteristic
258	C₄²×C₇	C₂⁴	1	1	yes	characteristic
259	#533	C₄×C₇	1	1	yes	characteristic
260	#533	C₄×C₇	1	1	yes	characteristic
261	#533	C₂²×C₇	1	1	yes	characteristic
262	#532	C₄×C₇	1	1	yes	characteristic
263	#532	C₄×C₇	1	1	yes	characteristic
264	#532	C₂²×C₇	1	1	yes	characteristic
265	#529	C₄×C₇	1	2	yes	—
266	#529	C₄×C₇	1	2	yes	—
267	#529	C₄×C₇	1	2	yes	—
268	#529	C₄×C₇	1	2	yes	—
269	#529	C₂²×C₇	1	2	yes	—
270	#529	C₂²×C₇	1	2	yes	—
271	#525	C₄×C₇	1	2	yes	—
272	#525	C₄×C₇	1	2	yes	—
273	#525	C₂²×C₇	1	2	yes	—
274	C₄×#41	C₂²×C₇	1	2	yes	—
275	C₄×#41	C₂²×C₇	1	2	yes	—
276	C₄×#41	C₂²×C₇	1	2	yes	—
277	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
278	#446	C₂²×C₇	1	4	yes	complemented
279	#446	C₂²×C₇	1	8	yes	complemented
280	C₈×Q₈	C₂²×C₇	1	4	yes	complemented
281	#436	C₂²×C₇	1	8	yes	—
282	#436	C₂²×C₇	1	4	yes	complemented
283	#435	C₂²×C₇	1	8	yes	—
284	#435	C₂²×C₇	1	8	yes	—
285	#435	C₂²×C₇	1	8	yes	complemented
286	C₈×D₄	C₂²×C₇	1	8	yes	—
287	C₈×D₄	C₂²×C₇	1	4	yes	complemented
288	#433	C₂²×C₇	1	8	yes	—
289	#433	C₂²×C₇	1	8	yes	complemented
290	#432	C₂²×C₇	1	2	yes	—
291	#432	C₂²×C₇	1	2	yes	—
292	#432	C₂²×C₇	1	2	yes	—
293	#432	C₂²×C₇	1	2	yes	—
294	#432	C₂²×C₇	1	2	yes	—
295	#432	C₂²×C₇	1	2	yes	—
296	#432	C₂²×C₇	1	4	yes	complemented
297	#432	C₂²×C₇	1	4	yes	complemented
298	#431	C₂²×C₇	1	2	yes	—
299	#431	C₂²×C₇	1	2	yes	—
300	#424	C₂²×C₇	1	8	yes	complemented
301	#423	C₂²×C₇	1	2	yes	—
302	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
303	#408	C₂²×C₇	1	8	yes	—
304	#407	C₂²×C₇	1	2	yes	—
305	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
306	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
307	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
308	C₄×M₁₆	C₂²×C₇	1	4	yes	complemented
309	C₂×#97	C₂²×C₇	1	2	yes	—
310	C₂×#97	C₂²×C₇	1	4	yes	complemented
311	C₂³×C₇	—	2	2	no	—
312	C₂³×C₇	—	4	1	no	—
313	C₂³×C₇	—	4	1	no	—
314	C₂³×C₇	C₂³×C₄	1	4	yes	—
315	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
316	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
317	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
318	C₇×Q₈	—	2	4	no	—
319	C₇×Q₈	—	4	2	no	—
320	C₇×Q₈	—	4	2	no	—
321	C₇×D₄	—	2	8	no	—
322	C₇×D₄	—	2	4	no	—
323	C₇×D₄	—	4	2	no	—
324	C₇×D₄	—	4	4	no	—
325	C₇×D₄	—	4	2	no	—
326	C₇×D₄	—	4	4	no	—
327	C₂×C₄×C₇	—	2	2	no	—
328	C₂×C₄×C₇	—	2	2	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	2	no	—
331	C₂×C₄×C₇	—	2	2	no	—
332	C₂×C₄×C₇	—	2	2	no	—
333	C₂×C₄×C₇	—	2	8	no	—
334	C₂×C₄×C₇	—	2	2	no	—
335	C₂×C₄×C₇	—	2	2	no	—
336	C₂×C₄×C₇	—	4	1	no	—
337	C₂×C₄×C₇	—	4	1	no	—
338	C₂×C₄×C₇	—	4	1	no	—
339	C₂×C₄×C₇	—	4	1	no	—
340	C₂×C₄×C₇	—	4	1	no	—
341	C₂×C₄×C₇	—	4	1	no	—
342	C₂×C₄×C₇	—	4	1	no	—
343	C₂×C₄×C₇	—	4	1	no	—
344	C₂×C₄×C₇	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	4	no	—
347	C₂×C₄×C₇	—	4	4	no	—
348	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
349	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
350	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
351	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
352	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
353	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
354	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
355	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
356	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
357	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
358	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
359	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
360	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
361	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
362	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
363	C₇×C₈	—	2	8	no	—
364	C₇×C₈	—	2	4	no	—
365	C₇×C₈	—	2	4	no	—
366	C₂×#41	C₂×C₄×C₇	1	2	yes	—
367	C₂×#41	C₂×C₄×C₇	1	2	yes	—
368	C₂×#41	C₂³×C₇	1	2	yes	—
369	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
370	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
372	C₂×M₁₆	C₂³×C₇	1	2	yes	—
373	C₂×M₁₆	C₂³×C₇	1	2	yes	—
374	C₂×M₁₆	C₂³×C₇	1	8	yes	—
375	C₂²×C₈	C₂³×C₇	1	4	yes	—
376	C₂²×C₈	C₂³×C₇	1	8	yes	—
377	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
378	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
379	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
380	#127	C₂×C₄×C₇	1	1	yes	characteristic
381	#126	C₂×C₄×C₇	1	4	yes	—
382	#126	C₂×C₄×C₇	1	4	yes	—
383	#125	C₂×C₄×C₇	1	2	yes	—
384	#125	C₂×C₄×C₇	1	2	yes	—
385	#125	C₂×C₄×C₇	1	2	yes	—
386	#124	C₂×C₄×C₇	1	2	yes	—
387	#124	C₂×C₄×C₇	1	2	yes	—
388	#124	C₂×C₄×C₇	1	2	yes	—
389	#123	C₂×C₄×C₇	1	4	yes	—
390	#123	C₂×C₄×C₇	1	4	yes	—
391	#123	C₂×C₄×C₇	1	4	yes	—
392	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
393	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
394	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
395	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
396	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
397	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
398	#121	C₂×C₄×C₇	1	2	yes	—
399	#121	C₂×C₄×C₇	1	2	yes	—
400	#121	C₂×C₄×C₇	1	2	yes	—
401	#121	C₂×C₄×C₇	1	2	yes	—
402	#121	C₂×C₄×C₇	1	2	yes	—
403	#121	C₂×C₄×C₇	1	2	yes	—
404	#120	C₂×C₄×C₇	1	4	yes	—
405	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
406	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
407	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
408	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
409	C₄×Q₈	C₂³×C₇	1	2	yes	—
410	C₄×Q₈	C₂³×C₇	1	2	yes	—
411	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
412	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
413	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
414	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
415	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
416	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
417	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
418	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
419	C₄×D₄	C₂³×C₇	1	4	yes	—
420	C₄×D₄	C₂³×C₇	1	4	yes	—
421	C₄×D₄	C₂³×C₇	1	2	yes	—
422	C₄×D₄	C₂³×C₇	1	2	yes	—
423	#117	C₂×C₄×C₇	1	2	yes	—
424	#117	C₂×C₄×C₇	1	2	yes	—
425	#117	C₂×C₄×C₇	1	4	yes	—
426	#117	C₂×C₄×C₇	1	4	yes	—
427	#117	C₂³×C₇	1	2	yes	—
428	#117	C₂³×C₇	1	4	yes	—
429	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
430	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
431	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
432	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
433	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
434	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₇	1	4	yes	—
436	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
442	C₄⋊C₈	C₂³×C₇	1	4	yes	—
443	C₄⋊C₈	C₂³×C₇	1	4	yes	—
444	C₄⋊C₈	C₂³×C₇	1	4	yes	—
445	C₄⋊C₈	C₂³×C₇	1	4	yes	—
446	C₄⋊C₈	C₂³×C₇	1	8	yes	—
447	C₄⋊C₈	C₂³×C₇	1	8	yes	—
448	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
449	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
450	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
451	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
452	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
453	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
454	#97	C₂³×C₇	1	4	yes	—
455	#97	C₂³×C₇	1	4	yes	—
456	#97	C₂³×C₇	1	2	yes	—
457	#97	C₂³×C₇	1	8	yes	—
458	#97	C₂³×C₇	1	2	yes	—
459	C₄×C₈	C₂³×C₇	1	2	yes	—
460	C₄×C₈	C₂³×C₇	1	2	yes	—
461	C₄×C₈	C₂³×C₇	1	8	yes	—
462	C₂²×C₇	—	2	1	no	—
463	C₂²×C₇	—	2	1	no	—
464	C₂²×C₇	—	2	1	no	—
465	C₂²×C₇	—	2	1	no	—
466	C₂²×C₇	—	2	4	no	—
467	C₂²×C₇	—	2	1	no	—
468	C₂²×C₇	—	2	1	no	—
469	C₂²×C₇	—	2	1	no	—
470	C₂²×C₇	—	2	1	no	—
471	C₂²×C₇	—	2	4	no	—
472	C₂²×C₇	—	2	4	no	—
473	C₂²×C₇	—	4	4	no	—
474	C₂²×C₇	#568	1	2	yes	—
475	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
476	C₄×C₇	—	2	1	no	—
477	C₄×C₇	—	2	1	no	—
478	C₄×C₇	—	2	1	no	—
479	C₄×C₇	—	2	4	no	—
480	C₄×C₇	—	2	1	no	—
481	C₄×C₇	—	2	1	no	—
482	C₄×C₇	—	2	1	no	—
483	C₄×C₇	—	2	1	no	—
484	C₄×C₇	—	2	1	no	—
485	C₄×C₇	—	2	1	no	—
486	C₄×C₇	—	2	1	no	—
487	C₄×C₇	—	2	4	no	—
488	C₄×C₇	—	2	4	no	—
489	C₄×C₇	#568	1	2	yes	—
490	C₄×C₇	#585	1	2	yes	—
491	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
492	#41	—	4	4	no	—
493	#41	—	4	4	no	—
494	#41	—	4	4	no	—
495	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
496	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
497	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
498	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
499	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
500	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
501	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
502	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
503	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
508	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
509	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
510	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
511	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
512	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
513	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
514	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
515	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
516	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
517	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
518	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
519	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
520	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
521	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
522	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
523	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
524	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
528	M₁₆	—	4	2	no	—
529	M₁₆	—	4	8	no	—
530	M₁₆	—	4	2	no	—
531	C₂×C₈	—	4	4	no	—
532	C₂×C₈	—	4	8	no	—
533	C₂×C₈	C₂⁴×C₇	1	4	yes	—
534	C₂×C₈	C₂⁴×C₇	1	4	yes	—
535	C₂×C₈	C₂⁴×C₇	1	8	yes	—
536	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
537	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
538	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
539	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
540	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
541	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
542	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
543	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
544	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
545	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
546	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
547	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
548	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
549	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
550	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
551	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
552	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
553	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
554	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
555	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
556	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
557	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
558	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
559	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
560	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
561	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
562	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
563	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
564	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
565	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
566	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
567	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
568	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
569	C₄²	C₂²×C₄×C₇	1	4	yes	—
570	C₄²	C₂²×C₄×C₇	1	4	yes	—
571	C₄²	C₂⁴×C₇	1	1	yes	characteristic
572	C₄²	C₂⁴×C₇	1	4	yes	—
573	C₄²	C₂⁴×C₇	1	1	yes	characteristic
574	C₄²	C₂⁴×C₇	1	1	yes	characteristic
575	C₄²	C₂⁴×C₇	1	1	yes	characteristic
576	C₂×C₇	—	2	2	no	—
577	C₂×C₇	—	4	4	no	—
578	C₂×C₇	—	4	1	no	—
579	C₂×C₇	—	4	1	no	—
580	C₂×C₇	#3428	1	1	yes	characteristic
581	C₂×C₇	C₂×#568	1	1	yes	characteristic
582	C₂×C₇	C₂×#568	1	1	yes	characteristic
583	C₂³	—	2	2	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	C₂³×C₄×C₇	1	4	yes	—
587	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
588	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
589	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
590	Q₈	—	2	4	no	—
591	Q₈	—	4	2	no	—
592	Q₈	—	4	2	no	—
593	D₄	—	2	8	no	—
594	D₄	—	2	4	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	4	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	8	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
621	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
622	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
623	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
626	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
627	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
628	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
629	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
630	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
631	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
632	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
633	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
634	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
635	C₈	—	2	8	no	—
636	C₈	—	2	4	no	—
637	C₈	—	2	4	no	—
638	C₇	#60285	1	1	yes	characteristic, direct product factor, Sylow
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	4	4	no	—
651	C₂²	C₇×#568	1	2	yes	—
652	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	4	no	—
661	C₄	—	2	4	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	4	no	—
666	C₄	C₇×#568	1	2	yes	—
667	C₄	C₇×#585	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	4	1	no	—
670	C₂	—	4	1	no	—
671	C₂	—	4	4	no	—
672	C₂	C₇×#3428	1	1	yes	characteristic
673	C₂	C₂×C₇×#568	1	1	yes	characteristic
674	C₂	C₂×C₇×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂⁴×C₄
prime radical	C₇×#3444	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2995	C₂	semidirect
3. C₇×#2994	C₂	semidirect
4. C₇×#2985	C₂	semidirect
5. C₇×#2981	C₂	semidirect
6. C₇×#2976	C₂	semidirect
7. C₇×#2971	C₂	semidirect
8. C₇×#2970	C₂	semidirect
9. C₇×#2970	C₂	semidirect
10. C₇×#2923	C₂	semidirect
11. C₇×#2920	C₂	semidirect
12. C₂×C₇×#432	C₂	semidirect
32. C₇×#446	C₂²	semidirect
33. C₇×#446	C₂²	semidirect
34. C₇×C₈×Q₈	C₂²	semidirect
36. C₇×#436	C₂²	semidirect
39. C₇×#435	C₂²	semidirect
41. C₇×C₈×D₄	C₂²	semidirect
43. C₇×#433	C₂²	semidirect
50. C₇×#432	C₂²	semidirect
51. C₇×#432	C₂²	semidirect
54. C₇×#424	C₂²	semidirect
62. C₄×C₇×M₁₆	C₂²	semidirect
64. C₂×C₇×#97	C₂²	semidirect
65. #60285	C₇	direct (N × H)
163. #2995	C₂×C₇	semidirect
164. #2994	C₂×C₇	semidirect
165. #2985	C₂×C₇	semidirect
166. #2981	C₂×C₇	semidirect
167. #2976	C₂×C₇	semidirect
168. #2971	C₂×C₇	semidirect
169. #2970	C₂×C₇	semidirect
170. #2970	C₂×C₇	semidirect
171. #2923	C₂×C₇	semidirect
172. #2920	C₂×C₇	semidirect
173. C₂×#432	C₂×C₇	semidirect
278. #446	C₂²×C₇	semidirect
279. #446	C₂²×C₇	semidirect
280. C₈×Q₈	C₂²×C₇	semidirect
282. #436	C₂²×C₇	semidirect
285. #435	C₂²×C₇	semidirect
287. C₈×D₄	C₂²×C₇	semidirect
289. #433	C₂²×C₇	semidirect
296. #432	C₂²×C₇	semidirect
297. #432	C₂²×C₇	semidirect
300. #424	C₂²×C₇	semidirect
308. C₄×M₁₆	C₂²×C₇	semidirect
310. C₂×#97	C₂²×C₇	semidirect
638. C₇	#60285	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3444	2
C₇×#2995	2
C₇×#2994	2
C₇×#2985	2
C₇×#2981	2
C₇×#2976	2
C₇×#2971	2
C₇×#2970	2
C₇×#2923	2
C₇×#2920	2
C₂×C₇×#432	2
#60285	7

Subgroups — C7×#60285 #13237501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60285 #13237501