Subgroups — C₇×#62852 #13240068

Order 1792.

11618 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3500	C₂	1	8	yes	maximal, complemented
4	C₇×#3498	C₂	1	8	yes	maximal, complemented
5	C₇×#3488	C₂	1	16	yes	maximal, complemented
6	C₇×#3487	C₂	1	4	yes	maximal, complemented
7	C₇×#3484	C₂	1	12	yes	maximal, complemented
8	C₇×#3449	C₂	1	6	yes	maximal, complemented
9	C₂×C₇×#535	C₂	1	6	yes	maximal, complemented
10	C₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#585	—	2	16	no	—
12	C₂×C₇×2₋¹⁺⁴	C₂²	1	2	yes	complemented
13	C₂×C₇×2₋¹⁺⁴	C₂²	1	4	yes	complemented
14	C₂×C₇×H(5,𝔽₂)	—	2	16	no	—
15	C₂×C₇×H(5,𝔽₂)	C₂²	1	8	yes	complemented
16	C₂×C₇×H(5,𝔽₂)	C₂²	1	8	yes	complemented
17	C₂×C₇×H(5,𝔽₂)	C₂²	1	6	yes	complemented
18	C₂×C₇×H(5,𝔽₂)	C₂²	1	4	yes	complemented
19	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₇×#41	C₂²	1	3	yes	complemented
21	C₂²×C₇×#41	C₂²	1	2	yes	complemented
22	C₂²×C₇×#41	C₂²	1	6	yes	complemented
23	C₂²×C₇×#41	C₂²	1	8	yes	complemented
24	C₂³×C₇×D₄	C₂²	1	3	yes	complemented
25	C₂³×C₇×D₄	C₂²	1	6	yes	complemented
26	C₇×#550	C₂²	1	32	yes	complemented
27	C₇×#548	C₂²	1	32	yes	complemented
28	C₇×#546	C₂²	1	96	yes	complemented
29	C₇×D₄²	C₂²	1	96	yes	complemented
30	C₇×#537	C₂²	1	24	yes	complemented
31	C₇×#536	C₂²	1	4	yes	complemented
32	C₇×#536	C₂²	1	12	yes	complemented
33	C₇×#535	C₂²	1	12	yes	complemented
34	C₇×#535	C₂²	1	24	yes	complemented
35	C₇×#535	C₂²	1	24	yes	complemented
36	C₇×#535	C₂²	1	24	yes	complemented
37	C₇×#535	C₂²	1	12	yes	complemented
38	C₇×#534	C₂²	1	24	yes	complemented
39	C₇×#532	C₂²	1	24	yes	complemented
40	C₂×C₇×#127	C₂²	1	12	yes	complemented
41	C₂×C₇×#124	C₂²	1	12	yes	complemented
42	C₇×#525	C₂²	1	24	yes	complemented
43	C₇×#525	C₂²	1	24	yes	complemented
44	C₂×C₇×#121	C₂²	1	24	yes	complemented
45	C₂×C₇×#120	C₂²	1	24	yes	complemented
46	C₇×#520	C₂²	1	8	yes	complemented
47	C₇×#519	C₂²	1	2	yes	complemented
48	C₇×#518	C₂²	1	6	yes	complemented
49	C₄×C₇×#41	C₂²	1	8	yes	complemented
50	C₂×C₇×#117	C₂²	1	6	yes	complemented
51	#62852	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂⁵×C₇	C₂³	1	6	yes	—
53	C₇×2₋¹⁺⁴	—	2	32	no	—
54	C₇×2₋¹⁺⁴	—	2	16	no	—
55	C₇×H(5,𝔽₂)	—	2	64	no	—
56	C₇×H(5,𝔽₂)	—	2	64	no	—
57	C₇×H(5,𝔽₂)	—	2	32	no	—
58	C₇×H(5,𝔽₂)	—	2	48	no	—
59	C₂×C₇×#41	—	2	64	no	—
60	C₂×C₇×#41	—	2	16	no	—
61	C₂×C₇×#41	—	2	24	no	—
62	C₂×C₇×#41	—	2	48	no	—
63	C₂×C₇×#41	D₄	1	16	yes	complemented
64	C₂×C₇×#41	C₂³	1	4	yes	—
65	C₂×C₇×#41	C₂³	1	12	yes	—
66	C₂×C₇×#41	C₂³	1	12	yes	—
67	C₂×C₇×#41	C₂³	1	16	yes	—
68	C₂×C₇×#41	C₂³	1	12	yes	—
69	C₂×C₇×#41	C₂³	1	4	yes	—
70	C₂×C₇×#41	C₂³	1	4	yes	—
71	C₂×C₇×#41	C₂³	1	12	yes	complemented
72	C₂×C₇×#41	C₂³	1	12	yes	complemented
73	C₂×C₇×#41	C₂³	1	24	yes	complemented
74	C₂×C₇×#41	C₂³	1	8	yes	complemented
75	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×Q₈	C₂³	1	6	yes	complemented
78	C₂²×C₇×Q₈	C₂³	1	8	yes	complemented
79	C₂²×C₇×D₄	—	2	48	no	—
80	C₂²×C₇×D₄	—	2	24	no	—
81	C₂²×C₇×D₄	C₂³	1	6	yes	—
82	C₂²×C₇×D₄	C₂³	1	3	yes	—
83	C₂²×C₇×D₄	C₂³	1	6	yes	—
84	C₂²×C₇×D₄	C₂³	1	12	yes	—
85	C₂²×C₇×D₄	C₂³	1	12	yes	—
86	C₂²×C₇×D₄	C₂³	1	48	yes	—
87	C₂²×C₇×D₄	C₂³	1	12	yes	—
88	C₂²×C₇×D₄	C₂³	1	3	yes	—
89	C₂²×C₇×D₄	C₂³	1	6	yes	complemented
90	C₂²×C₇×D₄	C₂³	1	24	yes	complemented
91	C₂²×C₇×D₄	C₂³	1	48	yes	complemented
92	C₂³×C₄×C₇	C₂³	1	6	yes	—
93	C₂³×C₄×C₇	C₂³	1	3	yes	—
94	C₂³×C₄×C₇	C₂³	1	12	yes	complemented
95	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
96	C₇×#127	C₂³	1	24	yes	complemented
97	C₇×#127	C₂³	1	48	yes	complemented
98	C₇×#124	C₂³	1	24	yes	complemented
99	C₇×#124	C₂³	1	48	yes	complemented
100	C₇×#124	C₂³	1	8	yes	complemented
101	C₇×#123	C₂³	1	16	yes	—
102	C₇×#123	C₂³	1	48	yes	complemented
103	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
104	C₇×C₂²⋊Q₈	C₂³	1	48	yes	complemented
105	C₇×#121	C₂³	1	48	yes	complemented
106	C₇×#121	C₂³	1	96	yes	complemented
107	C₇×#121	C₂³	1	48	yes	complemented
108	C₇×#121	C₂³	1	96	yes	complemented
109	C₇×#120	C₂³	1	48	yes	—
110	C₇×#120	C₂³	1	96	yes	complemented
111	C₇×#120	C₂³	1	48	yes	complemented
112	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
113	C₄×C₇×D₄	C₂³	1	48	yes	complemented
114	C₄×C₇×D₄	C₂³	1	96	yes	complemented
115	C₇×#117	C₂³	1	4	yes	—
116	C₇×#117	C₂³	1	12	yes	—
117	C₇×#117	C₂³	1	12	yes	complemented
118	C₇×#117	C₂³	1	12	yes	complemented
119	C₂×C₇×C₄⋊C₄	C₂³	1	12	yes	complemented
120	C₂×C₇×C₂²⋊C₄	C₂³	1	12	yes	—
121	C₂×C₇×C₂²⋊C₄	C₂³	1	48	yes	complemented
122	C₂×C₄²×C₇	C₂³	1	12	yes	complemented
123	C₂×#585	C₂×C₇	1	1	yes	characteristic, complemented
124	C₂²×H(5,𝔽₂)	C₂×C₇	1	1	yes	characteristic, complemented
125	#3500	C₂×C₇	1	8	yes	complemented
126	#3498	C₂×C₇	1	8	yes	complemented
127	#3488	C₂×C₇	1	16	yes	complemented
128	#3487	C₂×C₇	1	4	yes	complemented
129	#3484	C₂×C₇	1	12	yes	complemented
130	#3449	C₂×C₇	1	6	yes	complemented
131	C₂×#535	C₂×C₇	1	6	yes	complemented
132	#3428	C₂×C₇	1	1	yes	characteristic, complemented
133	C₂⁴×C₇	—	2	24	no	—
134	C₂⁴×C₇	—	8	12	no	—
135	C₂⁴×C₇	C₂⁴	1	24	yes	—
136	C₂⁴×C₇	C₂⁴	1	6	yes	—
137	C₂⁴×C₇	C₂⁴	1	12	yes	—
138	C₂⁴×C₇	C₂⁴	1	3	yes	—
139	C₇×#41	—	2	64	no	—
140	C₇×#41	—	2	32	no	—
141	C₇×#41	—	2	96	no	—
142	C₇×#41	—	2	16	no	—
143	C₇×#41	—	2	48	no	—
144	C₇×#41	—	2	48	no	—
145	C₇×#41	—	2	48	no	—
146	C₇×#41	—	2	48	no	—
147	C₇×#41	—	2	48	no	—
148	C₇×#41	C₂×D₄	1	32	yes	complemented
149	C₇×#41	C₂×D₄	1	32	yes	complemented
150	C₂×C₇×Q₈	—	2	32	no	—
151	C₂×C₇×Q₈	—	2	4	no	—
152	C₂×C₇×Q₈	—	2	24	no	—
153	C₂×C₇×Q₈	C₂×D₄	1	8	yes	complemented
154	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
155	C₂×C₇×Q₈	C₂⁴	1	12	yes	—
156	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
157	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
158	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
159	C₂×C₇×D₄	—	2	24	no	—
160	C₂×C₇×D₄	—	2	48	no	—
161	C₂×C₇×D₄	—	2	192	no	—
162	C₂×C₇×D₄	—	2	96	no	—
163	C₂×C₇×D₄	—	2	24	no	—
164	C₂×C₇×D₄	—	2	12	no	—
165	C₂×C₇×D₄	—	2	48	no	—
166	C₂×C₇×D₄	—	2	48	no	—
167	C₂×C₇×D₄	—	2	24	no	—
168	C₂×C₇×D₄	—	8	48	no	—
169	C₂×C₇×D₄	C₂×D₄	1	24	yes	complemented
170	C₂×C₇×D₄	C₂⁴	1	8	yes	—
171	C₂×C₇×D₄	C₂⁴	1	24	yes	—
172	C₂×C₇×D₄	C₂⁴	1	24	yes	—
173	C₂×C₇×D₄	C₂⁴	1	6	yes	—
174	C₂×C₇×D₄	C₂⁴	1	24	yes	—
175	C₂×C₇×D₄	C₂⁴	1	12	yes	—
176	C₂×C₇×D₄	C₂⁴	1	6	yes	—
177	C₂×C₇×D₄	C₂⁴	1	4	yes	—
178	C₂×C₇×D₄	C₂⁴	1	96	yes	—
179	C₂×C₇×D₄	C₂⁴	1	12	yes	—
180	C₂²×C₄×C₇	—	2	24	no	—
181	C₂²×C₄×C₇	—	2	48	no	—
182	C₂²×C₄×C₇	C₂×D₄	1	24	yes	complemented
183	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
184	C₂²×C₄×C₇	C₂⁴	1	24	yes	—
185	C₂²×C₄×C₇	C₂⁴	1	24	yes	—
186	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
187	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₇	C₂⁴	1	24	yes	—
189	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
190	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
191	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
192	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
193	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
194	C₇×C₄⋊C₄	C₂⁴	1	24	yes	—
195	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
196	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
197	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
198	C₇×C₂²⋊C₄	C₂⁴	1	96	yes	—
199	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
200	C₄²×C₇	C₂⁴	1	8	yes	—
201	C₄²×C₇	C₂⁴	1	24	yes	—
202	#585	—	2	16	no	—
203	C₂×2₋¹⁺⁴	C₂²×C₇	1	2	yes	complemented
204	C₂×2₋¹⁺⁴	C₂²×C₇	1	4	yes	complemented
205	C₂×H(5,𝔽₂)	—	2	16	no	—
206	C₂×H(5,𝔽₂)	C₂²×C₇	1	8	yes	complemented
207	C₂×H(5,𝔽₂)	C₂²×C₇	1	8	yes	complemented
208	C₂×H(5,𝔽₂)	C₂²×C₇	1	6	yes	complemented
209	C₂×H(5,𝔽₂)	C₂²×C₇	1	4	yes	complemented
210	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
211	C₂²×#41	C₂²×C₇	1	3	yes	complemented
212	C₂²×#41	C₂²×C₇	1	2	yes	complemented
213	C₂²×#41	C₂²×C₇	1	6	yes	complemented
214	C₂²×#41	C₂²×C₇	1	8	yes	complemented
215	C₂³×D₄	C₂²×C₇	1	3	yes	complemented
216	C₂³×D₄	C₂²×C₇	1	6	yes	complemented
217	#550	C₂²×C₇	1	32	yes	complemented
218	#548	C₂²×C₇	1	32	yes	complemented
219	#546	C₂²×C₇	1	96	yes	complemented
220	D₄²	C₂²×C₇	1	96	yes	complemented
221	#537	C₂²×C₇	1	24	yes	complemented
222	#536	C₂²×C₇	1	4	yes	complemented
223	#536	C₂²×C₇	1	12	yes	complemented
224	#535	C₂²×C₇	1	12	yes	complemented
225	#535	C₂²×C₇	1	24	yes	complemented
226	#535	C₂²×C₇	1	24	yes	complemented
227	#535	C₂²×C₇	1	24	yes	complemented
228	#535	C₂²×C₇	1	12	yes	complemented
229	#534	C₂²×C₇	1	24	yes	complemented
230	#532	C₂²×C₇	1	24	yes	complemented
231	C₂×#127	C₂²×C₇	1	12	yes	complemented
232	C₂×#124	C₂²×C₇	1	12	yes	complemented
233	#525	C₂²×C₇	1	24	yes	complemented
234	#525	C₂²×C₇	1	24	yes	complemented
235	C₂×#121	C₂²×C₇	1	24	yes	complemented
236	C₂×#120	C₂²×C₇	1	24	yes	complemented
237	#520	C₂²×C₇	1	8	yes	complemented
238	#519	C₂²×C₇	1	2	yes	complemented
239	#518	C₂²×C₇	1	6	yes	complemented
240	C₄×#41	C₂²×C₇	1	8	yes	complemented
241	C₂×#117	C₂²×C₇	1	6	yes	complemented
242	C₂³×C₇	—	2	12	no	—
243	C₂³×C₇	—	2	24	no	—
244	C₂³×C₇	—	2	48	no	—
245	C₂³×C₇	—	4	6	no	—
246	C₂³×C₇	—	4	12	no	—
247	C₂³×C₇	—	4	24	no	—
248	C₂³×C₇	—	4	48	no	—
249	C₂³×C₇	—	8	48	no	—
250	C₂³×C₇	C₂²×D₄	1	12	yes	—
251	C₂³×C₇	C₂⁵	1	12	yes	—
252	C₂³×C₇	C₂⁵	1	8	yes	—
253	C₂³×C₇	C₂⁵	1	1	yes	characteristic
254	C₂³×C₇	C₂⁵	1	6	yes	—
255	C₇×Q₈	—	2	24	no	—
256	C₇×Q₈	—	2	8	no	—
257	C₇×Q₈	—	2	4	no	—
258	C₇×Q₈	—	2	4	no	—
259	C₇×Q₈	C₂²×D₄	1	16	yes	—
260	C₇×D₄	—	2	48	no	—
261	C₇×D₄	—	2	16	no	—
262	C₇×D₄	—	2	48	no	—
263	C₇×D₄	—	2	12	no	—
264	C₇×D₄	—	2	48	no	—
265	C₇×D₄	—	2	12	no	—
266	C₇×D₄	—	2	24	no	—
267	C₇×D₄	—	2	8	no	—
268	C₇×D₄	—	4	96	no	—
269	C₇×D₄	C₂²×D₄	1	48	yes	—
270	C₂×C₄×C₇	—	2	4	no	—
271	C₂×C₄×C₇	—	2	24	no	—
272	C₂×C₄×C₇	—	2	16	no	—
273	C₂×C₄×C₇	—	2	48	no	—
274	C₂×C₄×C₇	—	2	48	no	—
275	C₂×C₄×C₇	—	4	24	no	—
276	C₂×C₄×C₇	C₂²×D₄	1	12	yes	—
277	C₂×C₄×C₇	C₂²×D₄	1	24	yes	—
278	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₇	C₂²×D₄	1	24	yes	—
280	C₂×C₄×C₇	C₂⁵	1	16	yes	—
281	C₂×C₄×C₇	C₂⁵	1	8	yes	—
282	C₂×C₄×C₇	C₂⁵	1	4	yes	—
283	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
284	C₂×C₄×C₇	C₂⁵	1	6	yes	—
285	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
286	C₂⁵	C₂³×C₇	1	6	yes	—
287	2₋¹⁺⁴	—	2	32	no	—
288	2₋¹⁺⁴	—	2	16	no	—
289	H(5,𝔽₂)	—	2	64	no	—
290	H(5,𝔽₂)	—	2	64	no	—
291	H(5,𝔽₂)	—	2	32	no	—
292	H(5,𝔽₂)	—	2	48	no	—
293	C₂×#41	—	2	64	no	—
294	C₂×#41	—	2	16	no	—
295	C₂×#41	—	2	24	no	—
296	C₂×#41	—	2	48	no	—
297	C₂×#41	C₇×D₄	1	16	yes	complemented
298	C₂×#41	C₂³×C₇	1	12	yes	—
299	C₂×#41	C₂³×C₇	1	12	yes	—
300	C₂×#41	C₂³×C₇	1	12	yes	—
301	C₂×#41	C₂³×C₇	1	4	yes	—
302	C₂×#41	C₂³×C₇	1	16	yes	—
303	C₂×#41	C₂³×C₇	1	4	yes	—
304	C₂×#41	C₂³×C₇	1	4	yes	—
305	C₂×#41	C₂³×C₇	1	12	yes	complemented
306	C₂×#41	C₂³×C₇	1	12	yes	complemented
307	C₂×#41	C₂³×C₇	1	24	yes	complemented
308	C₂×#41	C₂³×C₇	1	8	yes	complemented
309	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
311	C₂²×Q₈	C₂³×C₇	1	6	yes	complemented
312	C₂²×Q₈	C₂³×C₇	1	8	yes	complemented
313	C₂²×D₄	—	2	48	no	—
314	C₂²×D₄	—	2	24	no	—
315	C₂²×D₄	C₂³×C₇	1	12	yes	—
316	C₂²×D₄	C₂³×C₇	1	12	yes	—
317	C₂²×D₄	C₂³×C₇	1	12	yes	—
318	C₂²×D₄	C₂³×C₇	1	6	yes	—
319	C₂²×D₄	C₂³×C₇	1	3	yes	—
320	C₂²×D₄	C₂³×C₇	1	6	yes	—
321	C₂²×D₄	C₂³×C₇	1	48	yes	—
322	C₂²×D₄	C₂³×C₇	1	3	yes	—
323	C₂²×D₄	C₂³×C₇	1	6	yes	complemented
324	C₂²×D₄	C₂³×C₇	1	24	yes	complemented
325	C₂²×D₄	C₂³×C₇	1	48	yes	complemented
326	C₂³×C₄	C₂³×C₇	1	6	yes	—
327	C₂³×C₄	C₂³×C₇	1	3	yes	—
328	C₂³×C₄	C₂³×C₇	1	12	yes	complemented
329	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
330	#127	C₂³×C₇	1	24	yes	complemented
331	#127	C₂³×C₇	1	48	yes	complemented
332	#124	C₂³×C₇	1	24	yes	complemented
333	#124	C₂³×C₇	1	48	yes	complemented
334	#124	C₂³×C₇	1	8	yes	complemented
335	#123	C₂³×C₇	1	16	yes	—
336	#123	C₂³×C₇	1	48	yes	complemented
337	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
338	C₂²⋊Q₈	C₂³×C₇	1	48	yes	complemented
339	#121	C₂³×C₇	1	48	yes	complemented
340	#121	C₂³×C₇	1	96	yes	complemented
341	#121	C₂³×C₇	1	48	yes	complemented
342	#121	C₂³×C₇	1	96	yes	complemented
343	#120	C₂³×C₇	1	48	yes	—
344	#120	C₂³×C₇	1	96	yes	complemented
345	#120	C₂³×C₇	1	48	yes	complemented
346	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
347	C₄×D₄	C₂³×C₇	1	48	yes	complemented
348	C₄×D₄	C₂³×C₇	1	96	yes	complemented
349	#117	C₂³×C₇	1	4	yes	—
350	#117	C₂³×C₇	1	12	yes	—
351	#117	C₂³×C₇	1	12	yes	complemented
352	#117	C₂³×C₇	1	12	yes	complemented
353	C₂×C₄⋊C₄	C₂³×C₇	1	12	yes	complemented
354	C₂×C₂²⋊C₄	C₂³×C₇	1	12	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₇	1	48	yes	complemented
356	C₂×C₄²	C₂³×C₇	1	12	yes	complemented
357	C₂²×C₇	—	2	12	no	—
358	C₂²×C₇	—	2	2	no	—
359	C₂²×C₇	—	2	8	no	—
360	C₂²×C₇	—	2	12	no	—
361	C₂²×C₇	—	2	16	no	—
362	C₂²×C₇	—	2	24	no	—
363	C₂²×C₇	—	4	12	no	—
364	C₂²×C₇	—	4	24	no	—
365	C₂²×C₇	—	8	24	no	—
366	C₂²×C₇	—	8	48	no	—
367	C₂²×C₇	C₂³×D₄	1	2	yes	—
368	C₂²×C₇	C₂³×D₄	1	12	yes	—
369	C₂²×C₇	C₂⁶	1	1	yes	characteristic
370	C₄×C₇	—	2	4	no	—
371	C₄×C₇	—	2	8	no	—
372	C₄×C₇	—	2	16	no	—
373	C₄×C₇	C₂³×D₄	1	2	yes	—
374	C₄×C₇	C₂³×D₄	1	12	yes	—
375	C₄×C₇	C₂³×D₄	1	2	yes	—
376	C₂⁴	—	2	24	no	—
377	C₂⁴	—	8	12	no	—
378	C₂⁴	C₂⁴×C₇	1	24	yes	—
379	C₂⁴	C₂⁴×C₇	1	6	yes	—
380	C₂⁴	C₂⁴×C₇	1	12	yes	—
381	C₂⁴	C₂⁴×C₇	1	3	yes	—
382	#41	—	2	64	no	—
383	#41	—	2	32	no	—
384	#41	—	2	96	no	—
385	#41	—	2	16	no	—
386	#41	—	2	48	no	—
387	#41	—	2	48	no	—
388	#41	—	2	48	no	—
389	#41	—	2	48	no	—
390	#41	—	2	48	no	—
391	#41	C₂×C₇×D₄	1	32	yes	complemented
392	#41	C₂×C₇×D₄	1	32	yes	complemented
393	C₂×Q₈	—	2	32	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	24	no	—
396	C₂×Q₈	C₂×C₇×D₄	1	8	yes	complemented
397	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
398	C₂×Q₈	C₂⁴×C₇	1	12	yes	—
399	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
400	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
401	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
402	C₂×D₄	—	2	24	no	—
403	C₂×D₄	—	2	48	no	—
404	C₂×D₄	—	2	192	no	—
405	C₂×D₄	—	2	96	no	—
406	C₂×D₄	—	2	24	no	—
407	C₂×D₄	—	2	12	no	—
408	C₂×D₄	—	2	48	no	—
409	C₂×D₄	—	2	48	no	—
410	C₂×D₄	—	2	24	no	—
411	C₂×D₄	—	8	48	no	—
412	C₂×D₄	C₂×C₇×D₄	1	24	yes	complemented
413	C₂×D₄	C₂⁴×C₇	1	8	yes	—
414	C₂×D₄	C₂⁴×C₇	1	24	yes	—
415	C₂×D₄	C₂⁴×C₇	1	24	yes	—
416	C₂×D₄	C₂⁴×C₇	1	6	yes	—
417	C₂×D₄	C₂⁴×C₇	1	24	yes	—
418	C₂×D₄	C₂⁴×C₇	1	12	yes	—
419	C₂×D₄	C₂⁴×C₇	1	6	yes	—
420	C₂×D₄	C₂⁴×C₇	1	4	yes	—
421	C₂×D₄	C₂⁴×C₇	1	96	yes	—
422	C₂×D₄	C₂⁴×C₇	1	12	yes	—
423	C₂²×C₄	—	2	24	no	—
424	C₂²×C₄	—	2	48	no	—
425	C₂²×C₄	C₂×C₇×D₄	1	24	yes	complemented
426	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
427	C₂²×C₄	C₂⁴×C₇	1	24	yes	—
428	C₂²×C₄	C₂⁴×C₇	1	24	yes	—
429	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
430	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₇	1	24	yes	—
432	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
433	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
434	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
435	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
436	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
437	C₄⋊C₄	C₂⁴×C₇	1	24	yes	—
438	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
439	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
440	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
441	C₂²⋊C₄	C₂⁴×C₇	1	96	yes	—
442	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
443	C₄²	C₂⁴×C₇	1	8	yes	—
444	C₄²	C₂⁴×C₇	1	24	yes	—
445	C₂×C₇	—	2	2	no	—
446	C₂×C₇	—	2	12	no	—
447	C₂×C₇	—	4	12	no	—
448	C₂×C₇	—	4	8	no	—
449	C₂×C₇	C₂⁴×D₄	1	1	yes	characteristic
450	C₂×C₇	H(7,𝔽₂)	1	2	yes	—
451	C₂³	—	2	12	no	—
452	C₂³	—	2	24	no	—
453	C₂³	—	2	48	no	—
454	C₂³	—	4	6	no	—
455	C₂³	—	4	12	no	—
456	C₂³	—	4	24	no	—
457	C₂³	—	4	48	no	—
458	C₂³	—	8	48	no	—
459	C₂³	C₂²×C₇×D₄	1	12	yes	—
460	C₂³	C₂⁵×C₇	1	12	yes	—
461	C₂³	C₂⁵×C₇	1	8	yes	—
462	C₂³	C₂⁵×C₇	1	1	yes	characteristic
463	C₂³	C₂⁵×C₇	1	6	yes	—
464	Q₈	—	2	24	no	—
465	Q₈	—	2	8	no	—
466	Q₈	—	2	4	no	—
467	Q₈	—	2	4	no	—
468	Q₈	C₂²×C₇×D₄	1	16	yes	—
469	D₄	—	2	48	no	—
470	D₄	—	2	16	no	—
471	D₄	—	2	48	no	—
472	D₄	—	2	12	no	—
473	D₄	—	2	48	no	—
474	D₄	—	2	12	no	—
475	D₄	—	2	24	no	—
476	D₄	—	2	8	no	—
477	D₄	—	4	96	no	—
478	D₄	C₂²×C₇×D₄	1	48	yes	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	24	no	—
481	C₂×C₄	—	2	16	no	—
482	C₂×C₄	—	2	48	no	—
483	C₂×C₄	—	2	48	no	—
484	C₂×C₄	—	4	24	no	—
485	C₂×C₄	C₂²×C₇×D₄	1	12	yes	—
486	C₂×C₄	C₂²×C₇×D₄	1	24	yes	—
487	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
488	C₂×C₄	C₂²×C₇×D₄	1	24	yes	—
489	C₂×C₄	C₂⁵×C₇	1	16	yes	—
490	C₂×C₄	C₂⁵×C₇	1	8	yes	—
491	C₂×C₄	C₂⁵×C₇	1	4	yes	—
492	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
493	C₂×C₄	C₂⁵×C₇	1	6	yes	—
494	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
495	C₇	#62852	1	1	yes	characteristic, direct product factor, Sylow
496	C₂²	—	2	12	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	8	no	—
499	C₂²	—	2	12	no	—
500	C₂²	—	2	16	no	—
501	C₂²	—	2	24	no	—
502	C₂²	—	4	12	no	—
503	C₂²	—	4	24	no	—
504	C₂²	—	8	48	no	—
505	C₂²	—	8	24	no	—
506	C₂²	C₂³×C₇×D₄	1	2	yes	—
507	C₂²	C₂³×C₇×D₄	1	12	yes	—
508	C₂²	C₂⁶×C₇	1	1	yes	characteristic
509	C₄	—	2	4	no	—
510	C₄	—	2	8	no	—
511	C₄	—	2	16	no	—
512	C₄	C₂³×C₇×D₄	1	2	yes	—
513	C₄	C₂³×C₇×D₄	1	12	yes	—
514	C₄	C₂³×C₇×D₄	1	2	yes	—
515	C₂	—	2	2	no	—
516	C₂	—	2	12	no	—
517	C₂	—	4	12	no	—
518	C₂	—	4	8	no	—
519	C₂	C₂⁴×C₇×D₄	1	1	yes	characteristic
520	C₂	C₇×H(7,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#585	C₂	semidirect
2. C₂²×C₇×H(5,𝔽₂)	C₂	semidirect
3. C₇×#3500	C₂	semidirect
4. C₇×#3498	C₂	semidirect
5. C₇×#3488	C₂	semidirect
6. C₇×#3487	C₂	semidirect
7. C₇×#3484	C₂	semidirect
8. C₇×#3449	C₂	semidirect
9. C₂×C₇×#535	C₂	semidirect
10. C₇×#3428	C₂	semidirect
12. C₂×C₇×2₋¹⁺⁴	C₂²	semidirect
13. C₂×C₇×2₋¹⁺⁴	C₂²	semidirect
15. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
16. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
18. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
20. C₂²×C₇×#41	C₂²	semidirect
21. C₂²×C₇×#41	C₂²	semidirect
22. C₂²×C₇×#41	C₂²	semidirect
23. C₂²×C₇×#41	C₂²	semidirect
24. C₂³×C₇×D₄	C₂²	semidirect
25. C₂³×C₇×D₄	C₂²	semidirect
26. C₇×#550	C₂²	semidirect
27. C₇×#548	C₂²	semidirect
28. C₇×#546	C₂²	semidirect
29. C₇×D₄²	C₂²	semidirect
30. C₇×#537	C₂²	semidirect
31. C₇×#536	C₂²	semidirect
32. C₇×#536	C₂²	semidirect
33. C₇×#535	C₂²	semidirect
34. C₇×#535	C₂²	semidirect
35. C₇×#535	C₂²	semidirect
36. C₇×#535	C₂²	semidirect
37. C₇×#535	C₂²	semidirect
38. C₇×#534	C₂²	semidirect
39. C₇×#532	C₂²	semidirect
40. C₂×C₇×#127	C₂²	semidirect
41. C₂×C₇×#124	C₂²	semidirect
42. C₇×#525	C₂²	semidirect
43. C₇×#525	C₂²	semidirect
44. C₂×C₇×#121	C₂²	semidirect
45. C₂×C₇×#120	C₂²	semidirect
46. C₇×#520	C₂²	semidirect
47. C₇×#519	C₂²	semidirect
48. C₇×#518	C₂²	semidirect
49. C₄×C₇×#41	C₂²	semidirect
50. C₂×C₇×#117	C₂²	semidirect
51. #62852	C₇	direct (N × H)
63. C₂×C₇×#41	D₄	semidirect
71. C₂×C₇×#41	C₂³	semidirect
72. C₂×C₇×#41	C₂³	semidirect
73. C₂×C₇×#41	C₂³	semidirect
74. C₂×C₇×#41	C₂³	semidirect
77. C₂²×C₇×Q₈	C₂³	semidirect
78. C₂²×C₇×Q₈	C₂³	semidirect
89. C₂²×C₇×D₄	C₂³	semidirect
90. C₂²×C₇×D₄	C₂³	semidirect
91. C₂²×C₇×D₄	C₂³	semidirect
94. C₂³×C₄×C₇	C₂³	semidirect
95. C₇×C₄⋊Q₈	C₂³	semidirect
96. C₇×#127	C₂³	semidirect
97. C₇×#127	C₂³	semidirect
98. C₇×#124	C₂³	semidirect
99. C₇×#124	C₂³	semidirect
100. C₇×#124	C₂³	semidirect
102. C₇×#123	C₂³	semidirect
103. C₇×C₂²⋊Q₈	C₂³	semidirect
104. C₇×C₂²⋊Q₈	C₂³	semidirect
105. C₇×#121	C₂³	semidirect
106. C₇×#121	C₂³	semidirect
107. C₇×#121	C₂³	semidirect
108. C₇×#121	C₂³	semidirect
110. C₇×#120	C₂³	semidirect
111. C₇×#120	C₂³	semidirect
112. C₄×C₇×Q₈	C₂³	semidirect
113. C₄×C₇×D₄	C₂³	semidirect
114. C₄×C₇×D₄	C₂³	semidirect
117. C₇×#117	C₂³	semidirect
118. C₇×#117	C₂³	semidirect
119. C₂×C₇×C₄⋊C₄	C₂³	semidirect
121. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
122. C₂×C₄²×C₇	C₂³	semidirect
123. C₂×#585	C₂×C₇	semidirect
124. C₂²×H(5,𝔽₂)	C₂×C₇	semidirect
125. #3500	C₂×C₇	semidirect
126. #3498	C₂×C₇	semidirect
127. #3488	C₂×C₇	semidirect
128. #3487	C₂×C₇	semidirect
129. #3484	C₂×C₇	semidirect
130. #3449	C₂×C₇	semidirect
131. C₂×#535	C₂×C₇	semidirect
132. #3428	C₂×C₇	semidirect
148. C₇×#41	C₂×D₄	semidirect
149. C₇×#41	C₂×D₄	semidirect
153. C₂×C₇×Q₈	C₂×D₄	semidirect
169. C₂×C₇×D₄	C₂×D₄	semidirect
182. C₂²×C₄×C₇	C₂×D₄	semidirect
203. C₂×2₋¹⁺⁴	C₂²×C₇	semidirect
204. C₂×2₋¹⁺⁴	C₂²×C₇	semidirect
206. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
207. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
208. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
209. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
211. C₂²×#41	C₂²×C₇	semidirect
212. C₂²×#41	C₂²×C₇	semidirect
213. C₂²×#41	C₂²×C₇	semidirect
214. C₂²×#41	C₂²×C₇	semidirect
215. C₂³×D₄	C₂²×C₇	semidirect
216. C₂³×D₄	C₂²×C₇	semidirect
217. #550	C₂²×C₇	semidirect
218. #548	C₂²×C₇	semidirect
219. #546	C₂²×C₇	semidirect
220. D₄²	C₂²×C₇	semidirect
221. #537	C₂²×C₇	semidirect
222. #536	C₂²×C₇	semidirect
223. #536	C₂²×C₇	semidirect
224. #535	C₂²×C₇	semidirect
225. #535	C₂²×C₇	semidirect
226. #535	C₂²×C₇	semidirect
227. #535	C₂²×C₇	semidirect
228. #535	C₂²×C₇	semidirect
229. #534	C₂²×C₇	semidirect
230. #532	C₂²×C₇	semidirect
231. C₂×#127	C₂²×C₇	semidirect
232. C₂×#124	C₂²×C₇	semidirect
233. #525	C₂²×C₇	semidirect
234. #525	C₂²×C₇	semidirect
235. C₂×#121	C₂²×C₇	semidirect
236. C₂×#120	C₂²×C₇	semidirect
237. #520	C₂²×C₇	semidirect
238. #519	C₂²×C₇	semidirect
239. #518	C₂²×C₇	semidirect
240. C₄×#41	C₂²×C₇	semidirect
241. C₂×#117	C₂²×C₇	semidirect
297. C₂×#41	C₇×D₄	semidirect
305. C₂×#41	C₂³×C₇	semidirect
306. C₂×#41	C₂³×C₇	semidirect
307. C₂×#41	C₂³×C₇	semidirect
308. C₂×#41	C₂³×C₇	semidirect
311. C₂²×Q₈	C₂³×C₇	semidirect
312. C₂²×Q₈	C₂³×C₇	semidirect
323. C₂²×D₄	C₂³×C₇	semidirect
324. C₂²×D₄	C₂³×C₇	semidirect
325. C₂²×D₄	C₂³×C₇	semidirect
328. C₂³×C₄	C₂³×C₇	semidirect
329. C₄⋊Q₈	C₂³×C₇	semidirect
330. #127	C₂³×C₇	semidirect
331. #127	C₂³×C₇	semidirect
332. #124	C₂³×C₇	semidirect
333. #124	C₂³×C₇	semidirect
334. #124	C₂³×C₇	semidirect
336. #123	C₂³×C₇	semidirect
337. C₂²⋊Q₈	C₂³×C₇	semidirect
338. C₂²⋊Q₈	C₂³×C₇	semidirect
339. #121	C₂³×C₇	semidirect
340. #121	C₂³×C₇	semidirect
341. #121	C₂³×C₇	semidirect
342. #121	C₂³×C₇	semidirect
344. #120	C₂³×C₇	semidirect
345. #120	C₂³×C₇	semidirect
346. C₄×Q₈	C₂³×C₇	semidirect
347. C₄×D₄	C₂³×C₇	semidirect
348. C₄×D₄	C₂³×C₇	semidirect
351. #117	C₂³×C₇	semidirect
352. #117	C₂³×C₇	semidirect
353. C₂×C₄⋊C₄	C₂³×C₇	semidirect
355. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
356. C₂×C₄²	C₂³×C₇	semidirect
391. #41	C₂×C₇×D₄	semidirect
392. #41	C₂×C₇×D₄	semidirect
396. C₂×Q₈	C₂×C₇×D₄	semidirect
412. C₂×D₄	C₂×C₇×D₄	semidirect
425. C₂²×C₄	C₂×C₇×D₄	semidirect
495. C₇	#62852	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×#585	2
C₂²×C₇×H(5,𝔽₂)	2
C₇×#3500	2
C₇×#3498	2
C₇×#3488	2
C₇×#3487	2
C₇×#3484	2
C₇×#3449	2
C₂×C₇×#535	2
C₇×#3428	2
#62852	7

Subgroups — C7×#62852 #13240068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62852 #13240068