Subgroups — C₇×#22749 #13199965

Order 1792.

984 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#1924	C₂	1	2	yes	maximal, complemented
5	C₇×#1916	C₂	1	2	yes	maximal, complemented
6	C₇×#1870	C₂	1	2	yes	maximal
7	C₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1753	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₂×C₄×C₇×D₄	C₄	1	1	yes	characteristic
14	C₂×C₄×C₇×D₄	C₄	1	1	yes	characteristic
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
18	C₇×#431	—	2	4	no	—
19	C₇×#423	—	2	4	no	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₇×#97	C₂²	1	2	yes	—
29	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
30	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
31	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
32	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₇×C₂²⋊C₄	C₄	1	1	yes	characteristic
34	C₄×C₇×C₂²⋊C₄	C₄	1	1	yes	characteristic
35	C₄×C₇×C₂²⋊C₄	C₄	1	1	yes	characteristic
36	C₄×C₇×C₂²⋊C₄	C₄	1	1	yes	characteristic
37	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₄³×C₇	C₂²	1	1	yes	characteristic
40	C₇×#336	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	C₇×#336	C₂²	1	2	yes	—
44	C₇×#336	C₂²	1	2	yes	—
45	#22749	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
53	C₂×C₇×M₁₆	—	2	4	no	—
54	C₂×C₇×M₁₆	—	2	4	no	—
55	C₂×C₇×M₁₆	—	4	2	no	—
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	2	yes	—
58	C₂²×C₇×C₈	C₂³	1	2	yes	—
59	C₂²×C₇×C₈	C₂³	1	2	yes	—
60	C₄×C₇×D₄	—	2	4	no	—
61	C₄×C₇×D₄	—	2	2	no	—
62	C₄×C₇×D₄	—	2	2	no	—
63	C₄×C₇×D₄	—	2	4	no	—
64	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₇	—	2	2	no	—
74	C₂×C₄²×C₇	—	2	2	no	—
75	C₂×C₄²×C₇	—	2	2	no	—
76	C₂×C₄²×C₇	—	2	2	no	—
77	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
90	C₇×C₄⋊C₈	—	2	4	no	—
91	C₇×C₄⋊C₈	—	2	2	no	—
92	C₇×C₄⋊C₈	—	2	2	no	—
93	C₇×C₄⋊C₈	—	2	2	no	—
94	C₇×C₄⋊C₈	D₄	1	4	yes	complemented
95	C₇×C₂²⋊C₈	—	2	4	no	—
96	C₇×C₂²⋊C₈	—	2	4	no	—
97	C₇×C₂²⋊C₈	—	4	2	no	—
98	C₇×#97	—	4	2	no	—
99	C₄×C₇×C₈	—	2	4	no	—
100	C₇×#95	C₂×C₄	1	1	yes	characteristic
101	C₇×#95	C₂×C₄	1	1	yes	characteristic
102	C₇×#95	C₂×C₄	1	1	yes	characteristic
103	C₇×#95	C₂×C₄	1	1	yes	characteristic
104	C₇×#95	C₂×C₄	1	1	yes	characteristic
105	C₇×#95	C₂×C₄	1	1	yes	characteristic
106	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂×#423	C₂×C₇	1	1	yes	characteristic, complemented
108	C₄²×D₄	C₂×C₇	1	1	yes	characteristic
109	#1924	C₂×C₇	1	2	yes	complemented
110	#1916	C₂×C₇	1	2	yes	complemented
111	#1870	C₂×C₇	1	2	yes	—
112	#1831	C₂×C₇	1	1	yes	characteristic, complemented
113	#1797	C₂×C₇	1	1	yes	characteristic, complemented
114	#1797	C₂×C₇	1	1	yes	characteristic, complemented
115	#1767	C₂×C₇	1	1	yes	characteristic, complemented
116	#1753	C₂×C₇	1	2	yes	complemented
117	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
118	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₇×D₄	—	2	2	no	—
120	C₂×C₇×D₄	—	2	2	no	—
121	C₂×C₇×D₄	—	2	2	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	1	no	—
125	C₂²×C₄×C₇	—	2	1	no	—
126	C₂²×C₄×C₇	—	2	1	no	—
127	C₂²×C₄×C₇	—	2	1	no	—
128	C₂²×C₄×C₇	—	2	2	no	—
129	C₂²×C₄×C₇	—	2	2	no	—
130	C₂²×C₄×C₇	—	2	2	no	—
131	C₂²×C₄×C₇	—	2	2	no	—
132	C₂²×C₄×C₇	—	2	2	no	—
133	C₂²×C₄×C₇	—	2	2	no	—
134	C₂²×C₄×C₇	—	2	2	no	—
135	C₂²×C₄×C₇	—	2	1	no	—
136	C₂²×C₄×C₇	—	2	1	no	—
137	C₂²×C₄×C₇	—	2	1	no	—
138	C₂²×C₄×C₇	—	2	1	no	—
139	C₂²×C₄×C₇	—	2	1	no	—
140	C₂²×C₄×C₇	—	2	1	no	—
141	C₂²×C₄×C₇	—	4	1	no	—
142	C₂²×C₄×C₇	—	4	1	no	—
143	C₂²×C₄×C₇	M₁₆	1	4	yes	complemented
144	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₇	#41	1	2	yes	—
157	C₂²×C₄×C₇	#41	1	2	yes	—
158	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
159	C₇×M₁₆	—	4	8	no	—
160	C₂×C₇×C₈	—	2	2	no	—
161	C₂×C₇×C₈	—	2	2	no	—
162	C₂×C₇×C₈	—	2	2	no	—
163	C₂×C₇×C₈	—	2	2	no	—
164	C₂×C₇×C₈	—	2	2	no	—
165	C₂×C₇×C₈	—	2	2	no	—
166	C₂×C₇×C₈	—	2	2	no	—
167	C₂×C₇×C₈	—	2	2	no	—
168	C₂×C₇×C₈	—	2	2	no	—
169	C₂×C₇×C₈	—	2	2	no	—
170	C₂×C₇×C₈	—	2	2	no	—
171	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
172	C₇×C₄⋊C₄	—	2	2	no	—
173	C₇×C₄⋊C₄	—	2	2	no	—
174	C₇×C₄⋊C₄	M₁₆	1	4	yes	complemented
175	C₇×C₂²⋊C₄	—	2	2	no	—
176	C₇×C₂²⋊C₄	—	2	2	no	—
177	C₇×C₂²⋊C₄	—	2	2	no	—
178	C₇×C₂²⋊C₄	—	2	2	no	—
179	C₇×C₂²⋊C₄	—	2	2	no	—
180	C₇×C₂²⋊C₄	—	2	2	no	—
181	C₄²×C₇	—	2	2	no	—
182	C₄²×C₇	—	2	2	no	—
183	C₄²×C₇	—	2	2	no	—
184	C₄²×C₇	—	2	2	no	—
185	C₄²×C₇	—	2	2	no	—
186	C₄²×C₇	—	2	2	no	—
187	C₄²×C₇	—	2	2	no	—
188	C₄²×C₇	—	2	1	no	—
189	C₄²×C₇	—	2	1	no	—
190	C₄²×C₇	—	2	1	no	—
191	C₄²×C₇	—	2	1	no	—
192	C₄²×C₇	—	2	1	no	—
193	C₄²×C₇	—	2	1	no	—
194	C₄²×C₇	—	2	1	no	—
195	C₄²×C₇	—	2	1	no	—
196	C₄²×C₇	—	4	1	no	—
197	C₄²×C₇	C₂×D₄	1	2	yes	—
198	C₄²×C₇	#41	1	2	yes	—
199	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
200	C₂×C₄×D₄	C₄×C₇	1	1	yes	characteristic
201	C₂×C₄×D₄	C₄×C₇	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
203	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
204	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
205	#431	—	2	4	no	—
206	#423	—	2	4	no	—
207	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
209	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
211	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
212	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
213	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
215	C₂×#97	C₂²×C₇	1	2	yes	—
216	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
217	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
218	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
219	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
220	C₄×C₂²⋊C₄	C₄×C₇	1	1	yes	characteristic
221	C₄×C₂²⋊C₄	C₄×C₇	1	1	yes	characteristic
222	C₄×C₂²⋊C₄	C₄×C₇	1	1	yes	characteristic
223	C₄×C₂²⋊C₄	C₄×C₇	1	1	yes	characteristic
224	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
225	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
226	C₄³	C₂²×C₇	1	1	yes	characteristic
227	#336	C₂²×C₇	1	2	yes	—
228	#336	C₂²×C₇	1	2	yes	—
229	#336	C₂²×C₇	1	2	yes	—
230	#336	C₂²×C₇	1	2	yes	—
231	#336	C₂²×C₇	1	2	yes	—
232	C₂³×C₇	—	2	1	no	—
233	C₂³×C₇	—	2	1	no	—
234	C₂³×C₇	—	2	1	no	—
235	C₂³×C₇	—	2	1	no	—
236	C₂³×C₇	—	2	1	no	—
237	C₂³×C₇	—	2	1	no	—
238	C₂³×C₇	—	2	1	no	—
239	C₂³×C₇	—	2	1	no	—
240	C₂³×C₇	—	2	1	no	—
241	C₂³×C₇	—	2	1	no	—
242	C₂³×C₇	—	2	1	no	—
243	C₂³×C₇	—	2	1	no	—
244	C₂³×C₇	#117	1	2	yes	—
245	C₂³×C₇	C₂×M₁₆	1	2	yes	—
246	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
247	C₇×D₄	—	2	8	no	—
248	C₂×C₄×C₇	—	2	1	no	—
249	C₂×C₄×C₇	—	2	1	no	—
250	C₂×C₄×C₇	—	2	1	no	—
251	C₂×C₄×C₇	—	2	1	no	—
252	C₂×C₄×C₇	—	2	1	no	—
253	C₂×C₄×C₇	—	2	1	no	—
254	C₂×C₄×C₇	—	2	1	no	—
255	C₂×C₄×C₇	—	2	1	no	—
256	C₂×C₄×C₇	—	2	1	no	—
257	C₂×C₄×C₇	—	2	1	no	—
258	C₂×C₄×C₇	—	2	1	no	—
259	C₂×C₄×C₇	—	2	1	no	—
260	C₂×C₄×C₇	—	2	2	no	—
261	C₂×C₄×C₇	—	2	2	no	—
262	C₂×C₄×C₇	—	2	2	no	—
263	C₂×C₄×C₇	—	2	2	no	—
264	C₂×C₄×C₇	—	2	8	no	—
265	C₂×C₄×C₇	—	2	1	no	—
266	C₂×C₄×C₇	—	2	1	no	—
267	C₂×C₄×C₇	—	2	1	no	—
268	C₂×C₄×C₇	—	2	1	no	—
269	C₂×C₄×C₇	—	2	1	no	—
270	C₂×C₄×C₇	—	2	1	no	—
271	C₂×C₄×C₇	—	2	1	no	—
272	C₂×C₄×C₇	—	2	1	no	—
273	C₂×C₄×C₇	—	2	1	no	—
274	C₂×C₄×C₇	—	2	1	no	—
275	C₂×C₄×C₇	—	2	1	no	—
276	C₂×C₄×C₇	—	2	1	no	—
277	C₂×C₄×C₇	—	2	1	no	—
278	C₂×C₄×C₇	—	2	1	no	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	4	4	no	—
281	C₂×C₄×C₇	—	4	4	no	—
282	C₂×C₄×C₇	—	4	1	no	—
283	C₂×C₄×C₇	—	4	1	no	—
284	C₂×C₄×C₇	—	4	1	no	—
285	C₂×C₄×C₇	—	4	1	no	—
286	C₂×C₄×C₇	—	4	4	no	—
287	C₂×C₄×C₇	#117	1	2	yes	—
288	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
289	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
290	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
291	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
292	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
293	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
294	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
295	C₂×C₄×C₇	#131	1	2	yes	—
296	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
301	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
302	C₇×C₈	—	2	4	no	—
303	C₇×C₈	—	4	2	no	—
304	C₇×C₈	—	4	2	no	—
305	C₇×C₈	—	4	2	no	—
306	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
307	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
308	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
309	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
310	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
313	C₂×M₁₆	—	2	4	no	—
314	C₂×M₁₆	—	2	4	no	—
315	C₂×M₁₆	—	4	2	no	—
316	C₂²×C₈	C₂³×C₇	1	2	yes	—
317	C₂²×C₈	C₂³×C₇	1	2	yes	—
318	C₂²×C₈	C₂³×C₇	1	2	yes	—
319	C₂²×C₈	C₂³×C₇	1	2	yes	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	4	no	—
324	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
333	C₂×C₄²	—	2	2	no	—
334	C₂×C₄²	—	2	2	no	—
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
338	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
339	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
340	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
341	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
342	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
343	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
344	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
350	C₄⋊C₈	—	2	4	no	—
351	C₄⋊C₈	—	2	2	no	—
352	C₄⋊C₈	—	2	2	no	—
353	C₄⋊C₈	—	2	2	no	—
354	C₄⋊C₈	C₇×D₄	1	4	yes	complemented
355	C₂²⋊C₈	—	2	4	no	—
356	C₂²⋊C₈	—	2	4	no	—
357	C₂²⋊C₈	—	4	2	no	—
358	#97	—	4	2	no	—
359	C₄×C₈	—	2	4	no	—
360	#95	C₂×C₄×C₇	1	1	yes	characteristic
361	#95	C₂×C₄×C₇	1	1	yes	characteristic
362	#95	C₂×C₄×C₇	1	1	yes	characteristic
363	#95	C₂×C₄×C₇	1	1	yes	characteristic
364	#95	C₂×C₄×C₇	1	1	yes	characteristic
365	#95	C₂×C₄×C₇	1	1	yes	characteristic
366	C₂²×C₇	—	2	2	no	—
367	C₂²×C₇	—	2	2	no	—
368	C₂²×C₇	—	2	2	no	—
369	C₂²×C₇	—	2	2	no	—
370	C₂²×C₇	—	2	2	no	—
371	C₂²×C₇	—	2	2	no	—
372	C₂²×C₇	—	4	1	no	—
373	C₂²×C₇	—	4	1	no	—
374	C₂²×C₇	—	4	1	no	—
375	C₂²×C₇	—	4	1	no	—
376	C₂²×C₇	—	4	1	no	—
377	C₂²×C₇	—	4	1	no	—
378	C₂²×C₇	—	4	1	no	—
379	C₂²×C₇	—	4	1	no	—
380	C₂²×C₇	C₂×#117	1	1	yes	characteristic
381	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
382	C₂²×C₇	#520	1	1	yes	characteristic
383	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
384	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
385	C₂²×C₇	C₂×#131	1	1	yes	characteristic
386	C₂²×C₇	#568	1	1	yes	characteristic
387	C₄×C₇	—	2	2	no	—
388	C₄×C₇	—	2	2	no	—
389	C₄×C₇	—	2	2	no	—
390	C₄×C₇	—	2	2	no	—
391	C₄×C₇	—	2	2	no	—
392	C₄×C₇	—	2	2	no	—
393	C₄×C₇	—	4	1	no	—
394	C₄×C₇	—	4	1	no	—
395	C₄×C₇	—	4	1	no	—
396	C₄×C₇	—	4	1	no	—
397	C₄×C₇	—	4	1	no	—
398	C₄×C₇	#435	1	4	yes	—
399	C₄×C₇	#546	1	1	yes	characteristic
400	C₄×C₇	#548	1	1	yes	characteristic
401	C₄×C₇	#552	1	1	yes	characteristic
402	C₄×C₇	#553	1	1	yes	characteristic
403	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
404	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	C₇×M₁₆	1	4	yes	complemented
430	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
431	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
432	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
433	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
440	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
441	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
442	C₂²×C₄	C₇×#41	1	2	yes	—
443	C₂²×C₄	C₇×#41	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
445	M₁₆	—	4	8	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	C₇×M₁₆	1	4	yes	complemented
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	4	1	no	—
483	C₄²	C₂×C₇×D₄	1	2	yes	—
484	C₄²	C₇×#41	1	2	yes	—
485	C₂×C₇	—	4	2	no	—
486	C₂×C₇	—	4	2	no	—
487	C₂×C₇	#2352	1	1	yes	characteristic
488	C₂×C₇	#2920	1	1	yes	characteristic
489	C₂×C₇	#2925	1	1	yes	characteristic
490	C₂×C₇	C₂×#435	1	1	yes	characteristic
491	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
492	C₂×C₇	#2989	1	1	yes	characteristic
493	C₂×C₇	#2991	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	C₇×#117	1	2	yes	—
507	C₂³	C₂×C₇×M₁₆	1	2	yes	—
508	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
509	D₄	—	2	8	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	8	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	C₇×#117	1	2	yes	—
550	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
551	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
552	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
553	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
554	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
555	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
556	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
557	C₂×C₄	C₇×#131	1	2	yes	—
558	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
559	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
560	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
561	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
562	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
564	C₈	—	2	4	no	—
565	C₈	—	4	2	no	—
566	C₈	—	4	2	no	—
567	C₈	—	4	2	no	—
568	C₇	#22749	1	1	yes	characteristic, direct product factor, Sylow
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	C₂×C₇×#117	1	1	yes	characteristic
584	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
585	C₂²	C₇×#520	1	1	yes	characteristic
586	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
587	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
588	C₂²	C₂×C₇×#131	1	1	yes	characteristic
589	C₂²	C₇×#568	1	1	yes	characteristic
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	C₇×#435	1	4	yes	—
602	C₄	C₇×#546	1	1	yes	characteristic
603	C₄	C₇×#548	1	1	yes	characteristic
604	C₄	C₇×#552	1	1	yes	characteristic
605	C₄	C₇×#553	1	1	yes	characteristic
606	C₂	—	4	2	no	—
607	C₂	—	4	2	no	—
608	C₂	C₇×#2352	1	1	yes	characteristic
609	C₂	C₇×#2920	1	1	yes	characteristic
610	C₂	C₇×#2925	1	1	yes	characteristic
611	C₂	C₂×C₇×#435	1	1	yes	characteristic
612	C₂	C₇×D₄×M₁₆	1	1	yes	characteristic
613	C₂	C₇×#2989	1	1	yes	characteristic
614	C₂	C₇×#2991	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂²×C₇×D₄	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#431	C₂	semidirect
2. C₂×C₇×#423	C₂	semidirect
4. C₇×#1924	C₂	semidirect
5. C₇×#1916	C₂	semidirect
7. C₇×#1831	C₂	semidirect
8. C₇×#1797	C₂	semidirect
9. C₇×#1797	C₂	semidirect
10. C₇×#1767	C₂	semidirect
11. C₇×#1753	C₂	semidirect
45. #22749	C₇	direct (N × H)
94. C₇×C₄⋊C₈	D₄	semidirect
106. C₂×#431	C₂×C₇	semidirect
107. C₂×#423	C₂×C₇	semidirect
109. #1924	C₂×C₇	semidirect
110. #1916	C₂×C₇	semidirect
112. #1831	C₂×C₇	semidirect
113. #1797	C₂×C₇	semidirect
114. #1797	C₂×C₇	semidirect
115. #1767	C₂×C₇	semidirect
116. #1753	C₂×C₇	semidirect
143. C₂²×C₄×C₇	M₁₆	semidirect
174. C₇×C₄⋊C₄	M₁₆	semidirect
354. C₄⋊C₈	C₇×D₄	semidirect
429. C₂²×C₄	C₇×M₁₆	semidirect
460. C₄⋊C₄	C₇×M₁₆	semidirect
568. C₇	#22749	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×#431	2
C₂×C₇×#423	2
C₄²×C₇×D₄	2
C₇×#1924	2
C₇×#1916	2
C₇×#1870	2
C₇×#1831	2
C₇×#1797	2
C₇×#1767	2
C₇×#1753	2
#22749	7

Subgroups — C7×#22749 #13199965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22749 #13199965