Subgroups — C₇×#60237 #13237453

Order 1792.

2168 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic
2	C₇×#2981	C₂	1	4	yes	maximal, complemented
3	C₇×#2980	C₂	1	4	yes	maximal, complemented
4	C₇×#2974	C₂	1	4	yes	maximal, complemented
5	C₇×#2973	C₂	1	4	yes	maximal, complemented
6	C₇×#2935	C₂	1	4	yes	maximal, complemented
7	C₇×#2932	C₂	1	4	yes	maximal, complemented
8	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2880	C₂	1	4	yes	maximal, complemented
11	C₂²×C₇×#41	C₂²	1	2	yes	—
12	C₂×C₇×#131	C₂²	1	8	yes	complemented
13	C₇×#532	C₄	1	2	yes	—
14	C₇×#532	C₄	1	2	yes	—
15	C₇×#532	C₄	1	2	yes	—
16	C₇×#532	C₄	1	2	yes	—
17	C₇×#532	C₂²	1	2	yes	—
18	C₇×#532	C₂²	1	2	yes	—
19	C₇×#532	C₂²	1	2	yes	—
20	C₇×#532	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊Q₈	C₄	1	1	yes	characteristic
22	C₂×C₇×#127	C₄	1	1	yes	characteristic
23	C₂×C₇×#124	C₄	1	2	yes	—
24	C₂×C₇×#121	C₄	1	2	yes	—
25	C₂×C₇×#121	C₄	1	2	yes	—
26	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
27	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
28	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
29	C₇×#436	C₂²	1	8	yes	complemented
30	C₇×#435	C₂²	1	16	yes	complemented
31	C₇×#435	C₂²	1	16	yes	complemented
32	C₇×#435	C₂²	1	16	yes	complemented
33	C₇×C₈×D₄	C₂²	1	8	yes	complemented
34	C₇×#432	C₂²	1	2	yes	—
35	C₇×#432	C₂²	1	2	yes	—
36	C₇×#432	C₂²	1	2	yes	—
37	C₇×#432	C₂²	1	2	yes	complemented
38	C₇×#432	C₂²	1	2	yes	complemented
39	C₇×#432	C₂²	1	2	yes	complemented
40	C₇×#431	C₂²	1	2	yes	—
41	C₇×#431	C₂²	1	2	yes	complemented
42	C₇×#423	C₂²	1	2	yes	complemented
43	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
44	C₇×#408	C₂²	1	8	yes	complemented
45	C₇×#408	C₂²	1	16	yes	complemented
46	C₇×#407	C₂²	1	2	yes	—
47	C₇×#407	C₂²	1	8	yes	—
48	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
49	C₂×C₇×C₂²⋊C₈	C₂²	1	8	yes	—
50	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
51	C₂×C₇×#97	C₂²	1	2	yes	complemented
52	#60237	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂×C₇×#41	—	4	8	no	—
54	C₂×C₇×#41	C₂×C₄	1	4	yes	—
55	C₂×C₇×#41	C₂×C₄	1	4	yes	—
56	C₂×C₇×#41	C₂³	1	4	yes	—
57	C₂×C₇×#41	C₂³	1	4	yes	—
58	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
59	C₂²×C₇×D₄	C₂×C₄	1	4	yes	—
60	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
61	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
62	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
63	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₇	C₂³	1	4	yes	—
67	C₇×#131	—	4	16	no	—
68	C₂×C₇×M₁₆	C₂³	1	4	yes	—
69	C₂×C₇×M₁₆	C₂³	1	16	yes	—
70	C₂²×C₇×C₈	C₂³	1	4	yes	—
71	C₂²×C₇×C₈	C₂³	1	16	yes	—
72	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
73	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
74	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
75	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
76	C₇×#127	C₂×C₄	1	2	yes	—
77	C₇×#127	C₂×C₄	1	2	yes	—
78	C₇×#127	C₂×C₄	1	2	yes	—
79	C₇×#127	C₂×C₄	1	2	yes	—
80	C₇×#124	C₂×C₄	1	4	yes	—
81	C₇×#124	C₂×C₄	1	4	yes	—
82	C₇×#124	C₂×C₄	1	4	yes	—
83	C₇×#124	C₂×C₄	1	4	yes	—
84	C₇×#121	C₂×C₄	1	4	yes	—
85	C₇×#121	C₂×C₄	1	4	yes	—
86	C₇×#121	C₂×C₄	1	4	yes	—
87	C₇×#121	C₂×C₄	1	4	yes	—
88	C₇×#121	C₂×C₄	1	4	yes	—
89	C₇×#121	C₂×C₄	1	4	yes	—
90	C₇×#121	C₂×C₄	1	4	yes	—
91	C₇×#121	C₂×C₄	1	4	yes	—
92	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
93	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
94	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
95	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
96	C₄×C₇×D₄	C₂³	1	4	yes	—
97	C₄×C₇×D₄	C₂³	1	4	yes	—
98	C₄×C₇×D₄	C₂³	1	4	yes	—
99	C₄×C₇×D₄	C₂³	1	4	yes	—
100	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
101	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
102	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	4	yes	—
103	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	4	yes	—
104	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
115	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
116	C₇×C₄⋊C₈	C₂³	1	4	yes	—
117	C₇×C₄⋊C₈	C₂³	1	4	yes	—
118	C₇×C₄⋊C₈	C₂³	1	4	yes	—
119	C₇×C₄⋊C₈	C₂³	1	4	yes	—
120	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
121	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
122	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
123	C₇×C₂²⋊C₈	C₂³	1	16	yes	—
124	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
125	C₇×C₂²⋊C₈	C₂³	1	16	yes	—
126	C₇×#97	C₂³	1	4	yes	—
127	C₇×#97	C₂³	1	4	yes	—
128	C₇×#97	C₂³	1	4	yes	—
129	C₄×C₇×C₈	C₂³	1	4	yes	—
130	C₂×#532	C₂×C₇	1	1	yes	characteristic
131	#2981	C₂×C₇	1	4	yes	complemented
132	#2980	C₂×C₇	1	4	yes	complemented
133	#2974	C₂×C₇	1	4	yes	complemented
134	#2973	C₂×C₇	1	4	yes	complemented
135	#2935	C₂×C₇	1	4	yes	complemented
136	#2932	C₂×C₇	1	4	yes	complemented
137	#2920	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
139	#2880	C₂×C₇	1	4	yes	complemented
140	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
141	C₂⁴×C₇	C₂²×C₄	1	4	yes	—
142	C₇×#41	—	2	16	no	—
143	C₇×#41	—	4	8	no	—
144	C₇×#41	—	4	8	no	—
145	C₇×#41	—	4	8	no	—
146	C₂×C₇×Q₈	—	4	4	no	—
147	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
148	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
149	C₂×C₇×D₄	—	4	4	no	—
150	C₂×C₇×D₄	—	4	4	no	—
151	C₂×C₇×D₄	—	4	4	no	—
152	C₂×C₇×D₄	—	4	8	no	—
153	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
154	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
155	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
156	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
157	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
158	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
159	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
160	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
161	C₂²×C₄×C₇	—	2	4	no	—
162	C₂²×C₄×C₇	—	4	2	no	—
163	C₂²×C₄×C₇	—	4	8	no	—
164	C₂²×C₄×C₇	—	4	2	no	—
165	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
181	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
182	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
185	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
186	C₇×M₁₆	—	2	8	no	—
187	C₇×M₁₆	—	4	16	no	—
188	C₂×C₇×C₈	—	2	8	no	—
189	C₂×C₇×C₈	—	4	16	no	—
190	C₂×C₇×C₈	C₂⁴	1	8	yes	—
191	C₂×C₇×C₈	C₂⁴	1	8	yes	—
192	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
193	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
194	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
195	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
196	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
197	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
198	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
199	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
200	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
204	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₇	C₂⁴	1	1	yes	characteristic
213	C₄²×C₇	C₂⁴	1	1	yes	characteristic
214	C₄²×C₇	C₂⁴	1	1	yes	characteristic
215	C₄²×C₇	C₂⁴	1	1	yes	characteristic
216	C₂²×#41	C₂²×C₇	1	2	yes	—
217	C₂×#131	C₂²×C₇	1	8	yes	complemented
218	#532	C₄×C₇	1	2	yes	—
219	#532	C₄×C₇	1	2	yes	—
220	#532	C₄×C₇	1	2	yes	—
221	#532	C₄×C₇	1	2	yes	—
222	#532	C₂²×C₇	1	2	yes	—
223	#532	C₂²×C₇	1	2	yes	—
224	#532	C₂²×C₇	1	2	yes	—
225	#532	C₂²×C₇	1	2	yes	—
226	C₂×C₄⋊Q₈	C₄×C₇	1	1	yes	characteristic
227	C₂×#127	C₄×C₇	1	1	yes	characteristic
228	C₂×#124	C₄×C₇	1	2	yes	—
229	C₂×#121	C₄×C₇	1	2	yes	—
230	C₂×#121	C₄×C₇	1	2	yes	—
231	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
232	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
233	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
234	#436	C₂²×C₇	1	8	yes	complemented
235	#435	C₂²×C₇	1	16	yes	complemented
236	#435	C₂²×C₇	1	16	yes	complemented
237	#435	C₂²×C₇	1	16	yes	complemented
238	C₈×D₄	C₂²×C₇	1	8	yes	complemented
239	#432	C₂²×C₇	1	2	yes	—
240	#432	C₂²×C₇	1	2	yes	—
241	#432	C₂²×C₇	1	2	yes	—
242	#432	C₂²×C₇	1	2	yes	complemented
243	#432	C₂²×C₇	1	2	yes	complemented
244	#432	C₂²×C₇	1	2	yes	complemented
245	#431	C₂²×C₇	1	2	yes	—
246	#431	C₂²×C₇	1	2	yes	complemented
247	#423	C₂²×C₇	1	2	yes	complemented
248	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
249	#408	C₂²×C₇	1	8	yes	complemented
250	#408	C₂²×C₇	1	16	yes	complemented
251	#407	C₂²×C₇	1	2	yes	—
252	#407	C₂²×C₇	1	8	yes	—
253	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₇	1	8	yes	—
255	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
256	C₂×#97	C₂²×C₇	1	2	yes	complemented
257	C₂³×C₇	—	2	2	no	—
258	C₂³×C₇	—	2	2	no	—
259	C₂³×C₇	—	2	8	no	—
260	C₂³×C₇	—	4	1	no	—
261	C₂³×C₇	—	4	4	no	—
262	C₂³×C₇	—	4	4	no	—
263	C₂³×C₇	C₂³×C₄	1	8	yes	—
264	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
265	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
266	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
267	C₇×Q₈	—	2	8	no	—
268	C₇×Q₈	—	4	4	no	—
269	C₇×D₄	—	2	16	no	—
270	C₇×D₄	—	2	8	no	—
271	C₇×D₄	—	2	8	no	—
272	C₇×D₄	—	4	4	no	—
273	C₇×D₄	—	4	4	no	—
274	C₇×D₄	—	4	4	no	—
275	C₇×D₄	—	4	4	no	—
276	C₇×D₄	—	4	8	no	—
277	C₂×C₄×C₇	—	2	2	no	—
278	C₂×C₄×C₇	—	2	2	no	—
279	C₂×C₄×C₇	—	2	2	no	—
280	C₂×C₄×C₇	—	2	2	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	2	no	—
283	C₂×C₄×C₇	—	2	2	no	—
284	C₂×C₄×C₇	—	2	2	no	—
285	C₂×C₄×C₇	—	2	16	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	4	1	no	—
289	C₂×C₄×C₇	—	4	1	no	—
290	C₂×C₄×C₇	—	4	1	no	—
291	C₂×C₄×C₇	—	4	1	no	—
292	C₂×C₄×C₇	—	4	1	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	—	4	1	no	—
295	C₂×C₄×C₇	—	4	4	no	—
296	C₂×C₄×C₇	—	4	8	no	—
297	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
299	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
301	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
302	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
303	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂³×C₄	1	8	yes	—
307	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
308	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
309	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
310	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
311	C₇×C₈	—	2	8	no	—
312	C₇×C₈	—	2	8	no	—
313	C₂×#41	—	4	8	no	—
314	C₂×#41	C₂×C₄×C₇	1	4	yes	—
315	C₂×#41	C₂×C₄×C₇	1	4	yes	—
316	C₂×#41	C₂³×C₇	1	4	yes	—
317	C₂×#41	C₂³×C₇	1	4	yes	—
318	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
319	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
320	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
321	C₂²×D₄	C₂×C₄×C₇	1	4	yes	—
322	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
323	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
324	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₇	1	4	yes	—
327	#131	—	4	16	no	—
328	C₂×M₁₆	C₂³×C₇	1	4	yes	—
329	C₂×M₁₆	C₂³×C₇	1	16	yes	—
330	C₂²×C₈	C₂³×C₇	1	4	yes	—
331	C₂²×C₈	C₂³×C₇	1	16	yes	—
332	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
333	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
334	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
335	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
336	#127	C₂×C₄×C₇	1	2	yes	—
337	#127	C₂×C₄×C₇	1	2	yes	—
338	#127	C₂×C₄×C₇	1	2	yes	—
339	#127	C₂×C₄×C₇	1	2	yes	—
340	#124	C₂×C₄×C₇	1	4	yes	—
341	#124	C₂×C₄×C₇	1	4	yes	—
342	#124	C₂×C₄×C₇	1	4	yes	—
343	#124	C₂×C₄×C₇	1	4	yes	—
344	#121	C₂×C₄×C₇	1	4	yes	—
345	#121	C₂×C₄×C₇	1	4	yes	—
346	#121	C₂×C₄×C₇	1	4	yes	—
347	#121	C₂×C₄×C₇	1	4	yes	—
348	#121	C₂×C₄×C₇	1	4	yes	—
349	#121	C₂×C₄×C₇	1	4	yes	—
350	#121	C₂×C₄×C₇	1	4	yes	—
351	#121	C₂×C₄×C₇	1	4	yes	—
352	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
353	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
354	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
355	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
356	C₄×D₄	C₂³×C₇	1	4	yes	—
357	C₄×D₄	C₂³×C₇	1	4	yes	—
358	C₄×D₄	C₂³×C₇	1	4	yes	—
359	C₄×D₄	C₂³×C₇	1	4	yes	—
360	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
361	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
362	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	4	yes	—
363	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	4	yes	—
364	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
365	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
366	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
367	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
368	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
369	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
376	C₄⋊C₈	C₂³×C₇	1	4	yes	—
377	C₄⋊C₈	C₂³×C₇	1	4	yes	—
378	C₄⋊C₈	C₂³×C₇	1	4	yes	—
379	C₄⋊C₈	C₂³×C₇	1	4	yes	—
380	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
381	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
382	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
383	C₂²⋊C₈	C₂³×C₇	1	16	yes	—
384	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
385	C₂²⋊C₈	C₂³×C₇	1	16	yes	—
386	#97	C₂³×C₇	1	4	yes	—
387	#97	C₂³×C₇	1	4	yes	—
388	#97	C₂³×C₇	1	4	yes	—
389	C₄×C₈	C₂³×C₇	1	4	yes	—
390	C₂²×C₇	—	2	1	no	—
391	C₂²×C₇	—	2	1	no	—
392	C₂²×C₇	—	2	1	no	—
393	C₂²×C₇	—	2	1	no	—
394	C₂²×C₇	—	2	1	no	—
395	C₂²×C₇	—	2	8	no	—
396	C₂²×C₇	—	2	1	no	—
397	C₂²×C₇	—	2	1	no	—
398	C₂²×C₇	—	2	8	no	—
399	C₂²×C₇	—	2	8	no	—
400	C₂²×C₇	—	4	4	no	—
401	C₂²×C₇	—	8	8	no	—
402	C₂²×C₇	#518	1	2	yes	—
403	C₂²×C₇	#568	1	2	yes	—
404	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
405	C₄×C₇	—	2	1	no	—
406	C₄×C₇	—	2	1	no	—
407	C₄×C₇	—	2	8	no	—
408	C₄×C₇	—	2	1	no	—
409	C₄×C₇	—	2	1	no	—
410	C₄×C₇	—	2	1	no	—
411	C₄×C₇	—	2	1	no	—
412	C₄×C₇	—	2	1	no	—
413	C₄×C₇	—	2	1	no	—
414	C₄×C₇	—	2	1	no	—
415	C₄×C₇	#518	1	2	yes	—
416	C₄×C₇	#568	1	2	yes	—
417	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
418	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
419	C₂⁴	C₂²×C₄×C₇	1	4	yes	—
420	#41	—	2	16	no	—
421	#41	—	4	8	no	—
422	#41	—	4	8	no	—
423	#41	—	4	8	no	—
424	C₂×Q₈	—	4	4	no	—
425	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
426	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
427	C₂×D₄	—	4	4	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	8	no	—
431	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
432	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
433	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
434	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
435	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
436	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
437	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
438	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	8	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
444	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
445	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
446	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
447	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
448	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
449	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
451	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
452	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
453	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
455	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
456	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
457	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
458	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
459	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
460	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
463	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
464	M₁₆	—	2	8	no	—
465	M₁₆	—	4	16	no	—
466	C₂×C₈	—	2	8	no	—
467	C₂×C₈	—	4	16	no	—
468	C₂×C₈	C₂⁴×C₇	1	8	yes	—
469	C₂×C₈	C₂⁴×C₇	1	8	yes	—
470	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
471	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
472	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
473	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
474	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
475	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
476	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
477	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
478	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
479	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
480	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
481	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
482	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
483	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
484	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
485	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
486	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
487	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
488	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
489	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
490	C₄²	C₂⁴×C₇	1	1	yes	characteristic
491	C₄²	C₂⁴×C₇	1	1	yes	characteristic
492	C₄²	C₂⁴×C₇	1	1	yes	characteristic
493	C₄²	C₂⁴×C₇	1	1	yes	characteristic
494	C₂×C₇	—	2	2	no	—
495	C₂×C₇	—	2	2	no	—
496	C₂×C₇	—	4	1	no	—
497	C₂×C₇	—	4	8	no	—
498	C₂×C₇	C₂×#518	1	1	yes	characteristic
499	C₂×C₇	C₂×#568	1	1	yes	characteristic
500	C₂×C₇	C₂×#568	1	1	yes	characteristic
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	8	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	4	no	—
506	C₂³	—	4	4	no	—
507	C₂³	C₂³×C₄×C₇	1	8	yes	—
508	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
509	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
510	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
511	Q₈	—	2	8	no	—
512	Q₈	—	4	4	no	—
513	D₄	—	2	16	no	—
514	D₄	—	2	8	no	—
515	D₄	—	2	8	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	4	no	—
518	D₄	—	4	4	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	8	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	16	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	8	no	—
541	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
542	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
543	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
544	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
545	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
546	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
547	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
548	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
549	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
550	C₂×C₄	C₂³×C₄×C₇	1	8	yes	—
551	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
552	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
553	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
554	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
555	C₈	—	2	8	no	—
556	C₈	—	2	8	no	—
557	C₇	#60237	1	1	yes	characteristic, direct product factor, Sylow
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	8	no	—
565	C₂²	—	2	8	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	8	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	8	8	no	—
570	C₂²	C₇×#518	1	2	yes	—
571	C₂²	C₇×#568	1	2	yes	—
572	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	8	no	—
583	C₄	C₇×#518	1	2	yes	—
584	C₄	C₇×#568	1	2	yes	—
585	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
586	C₂	—	2	2	no	—
587	C₂	—	2	2	no	—
588	C₂	—	4	1	no	—
589	C₂	—	4	8	no	—
590	C₂	C₂×C₇×#518	1	1	yes	characteristic
591	C₂	C₂×C₇×#568	1	1	yes	characteristic
592	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	C₂×C₇×#532	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×#2981	C₂	semidirect
3. C₇×#2980	C₂	semidirect
4. C₇×#2974	C₂	semidirect
5. C₇×#2973	C₂	semidirect
6. C₇×#2935	C₂	semidirect
7. C₇×#2932	C₂	semidirect
8. C₇×#2920	C₂	semidirect
9. C₂×C₇×#432	C₂	semidirect
10. C₇×#2880	C₂	semidirect
12. C₂×C₇×#131	C₂²	semidirect
29. C₇×#436	C₂²	semidirect
30. C₇×#435	C₂²	semidirect
31. C₇×#435	C₂²	semidirect
32. C₇×#435	C₂²	semidirect
33. C₇×C₈×D₄	C₂²	semidirect
37. C₇×#432	C₂²	semidirect
38. C₇×#432	C₂²	semidirect
39. C₇×#432	C₂²	semidirect
41. C₇×#431	C₂²	semidirect
42. C₇×#423	C₂²	semidirect
43. C₂×C₇×C₄⋊C₈	C₂²	semidirect
44. C₇×#408	C₂²	semidirect
45. C₇×#408	C₂²	semidirect
50. C₄×C₇×M₁₆	C₂²	semidirect
51. C₂×C₇×#97	C₂²	semidirect
52. #60237	C₇	direct (N × H)
131. #2981	C₂×C₇	semidirect
132. #2980	C₂×C₇	semidirect
133. #2974	C₂×C₇	semidirect
134. #2973	C₂×C₇	semidirect
135. #2935	C₂×C₇	semidirect
136. #2932	C₂×C₇	semidirect
137. #2920	C₂×C₇	semidirect
138. C₂×#432	C₂×C₇	semidirect
139. #2880	C₂×C₇	semidirect
217. C₂×#131	C₂²×C₇	semidirect
234. #436	C₂²×C₇	semidirect
235. #435	C₂²×C₇	semidirect
236. #435	C₂²×C₇	semidirect
237. #435	C₂²×C₇	semidirect
238. C₈×D₄	C₂²×C₇	semidirect
242. #432	C₂²×C₇	semidirect
243. #432	C₂²×C₇	semidirect
244. #432	C₂²×C₇	semidirect
246. #431	C₂²×C₇	semidirect
247. #423	C₂²×C₇	semidirect
248. C₂×C₄⋊C₈	C₂²×C₇	semidirect
249. #408	C₂²×C₇	semidirect
250. #408	C₂²×C₇	semidirect
255. C₄×M₁₆	C₂²×C₇	semidirect
256. C₂×#97	C₂²×C₇	semidirect
557. C₇	#60237	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×C₇×#532	2
C₇×#2981	2
C₇×#2980	2
C₇×#2974	2
C₇×#2973	2
C₇×#2935	2
C₇×#2932	2
C₇×#2920	2
C₂×C₇×#432	2
C₇×#2880	2
#60237	7

Subgroups — C7×#60237 #13237453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60237 #13237453