Subgroups — C₇×#21980 #13199196

Order 1792.

774 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic
3	C₇×#2298	C₂	1	1	yes	maximal, characteristic
4	C₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1851	C₂	1	1	yes	maximal, characteristic
9	C₇×#1851	C₂	1	1	yes	maximal, characteristic
10	C₇×#1850	C₂	1	1	yes	maximal, characteristic
11	C₇×#1850	C₂	1	1	yes	maximal, characteristic
12	C₇×#1843	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1832	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×#117	C₂²	1	1	yes	characteristic
19	C₇×#433	—	2	4	no	—
20	C₇×#424	—	2	4	no	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₇×#388	C₄	1	1	yes	characteristic
40	C₇×#388	C₄	1	1	yes	characteristic
41	C₇×#388	C₄	1	1	yes	characteristic
42	C₇×#388	C₄	1	1	yes	characteristic
43	C₇×#387	C₄	1	1	yes	characteristic
44	C₇×#387	C₄	1	1	yes	characteristic
45	C₇×#387	C₄	1	1	yes	characteristic
46	C₇×#387	C₄	1	1	yes	characteristic
47	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₇×#376	C₂²	1	1	yes	characteristic
52	C₄³×C₇	C₂²	1	1	yes	characteristic
53	C₇×#336	C₂²	1	1	yes	characteristic
54	C₇×#336	C₂²	1	1	yes	characteristic
55	C₇×#336	C₂²	1	1	yes	characteristic
56	C₇×#336	C₂²	1	1	yes	characteristic
57	C₇×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	C₇×#336	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	#21980	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂×C₇×M₁₆	—	2	2	no	—
64	C₂×C₇×M₁₆	—	4	1	no	—
65	C₂×C₇×M₁₆	—	4	1	no	—
66	C₂²×C₇×C₈	—	2	2	no	—
67	C₂²×C₇×C₈	—	4	1	no	—
68	C₂²×C₇×C₈	—	4	1	no	—
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₇×#117	D₄	1	4	yes	—
78	C₇×#117	Q₈	1	4	yes	—
79	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
101	C₇×C₄⋊C₈	—	2	2	no	—
102	C₇×C₄⋊C₈	—	2	2	no	—
103	C₇×C₄⋊C₈	—	2	2	no	—
104	C₇×C₄⋊C₈	—	2	2	no	—
105	C₇×C₄⋊C₈	—	2	2	no	—
106	C₇×C₄⋊C₈	—	2	2	no	—
107	C₇×C₄⋊C₈	—	4	1	no	—
108	C₇×C₄⋊C₈	—	4	1	no	—
109	C₇×C₄⋊C₈	—	4	1	no	—
110	C₇×C₄⋊C₈	—	4	1	no	—
111	C₇×C₄⋊C₈	—	4	1	no	—
112	C₇×C₄⋊C₈	—	4	1	no	—
113	C₇×C₄⋊C₈	—	4	1	no	—
114	C₇×C₄⋊C₈	—	4	1	no	—
115	C₇×C₂²⋊C₈	—	2	2	no	—
116	C₇×C₂²⋊C₈	—	2	2	no	—
117	C₇×#97	—	2	2	no	—
118	C₄×C₇×C₈	—	2	2	no	—
119	C₇×#95	C₂×C₄	1	1	yes	characteristic
120	C₇×#95	C₂×C₄	1	1	yes	characteristic
121	C₇×#95	C₂×C₄	1	1	yes	characteristic
122	C₇×#95	C₂×C₄	1	1	yes	characteristic
123	C₇×#95	C₂×C₄	1	1	yes	characteristic
124	C₇×#95	C₂×C₄	1	1	yes	characteristic
125	C₇×#95	C₂×C₄	1	1	yes	characteristic
126	C₇×#95	C₂×C₄	1	1	yes	characteristic
127	C₇×#95	C₂×C₄	1	1	yes	characteristic
128	C₇×#95	C₂×C₄	1	1	yes	characteristic
129	C₇×#95	C₂×C₄	1	1	yes	characteristic
130	C₇×#95	C₂×C₄	1	1	yes	characteristic
131	C₂×#433	C₂×C₇	1	1	yes	characteristic
132	C₂×#424	C₂×C₇	1	1	yes	characteristic
133	#2298	C₂×C₇	1	1	yes	characteristic
134	#1940	C₂×C₇	1	1	yes	characteristic, complemented
135	#1940	C₂×C₇	1	1	yes	characteristic, complemented
136	#1939	C₂×C₇	1	1	yes	characteristic, complemented
137	#1939	C₂×C₇	1	1	yes	characteristic, complemented
138	#1851	C₂×C₇	1	1	yes	characteristic
139	#1851	C₂×C₇	1	1	yes	characteristic
140	#1850	C₂×C₇	1	1	yes	characteristic
141	#1850	C₂×C₇	1	1	yes	characteristic
142	#1843	C₂×C₇	1	1	yes	characteristic, complemented
143	#1842	C₂×C₇	1	1	yes	characteristic, complemented
144	#1832	C₂×C₇	1	1	yes	characteristic, complemented
145	#1831	C₂×C₇	1	1	yes	characteristic, complemented
146	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₇	—	2	1	no	—
148	C₂²×C₄×C₇	—	2	1	no	—
149	C₂²×C₄×C₇	—	2	1	no	—
150	C₂²×C₄×C₇	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
166	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
167	C₇×M₁₆	—	4	4	no	—
168	C₂×C₇×C₈	—	2	1	no	—
169	C₂×C₇×C₈	—	2	1	no	—
170	C₂×C₇×C₈	—	2	1	no	—
171	C₂×C₇×C₈	—	2	1	no	—
172	C₂×C₇×C₈	—	2	1	no	—
173	C₂×C₇×C₈	—	2	1	no	—
174	C₂×C₇×C₈	—	2	1	no	—
175	C₂×C₇×C₈	—	2	1	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	—	2	1	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	—	2	1	no	—
185	C₂×C₇×C₈	—	2	1	no	—
186	C₂×C₇×C₈	—	2	1	no	—
187	C₂×C₇×C₈	—	2	1	no	—
188	C₂×C₇×C₈	—	2	1	no	—
189	C₂×C₇×C₈	—	2	1	no	—
190	C₂×C₇×C₈	—	2	1	no	—
191	C₂×C₇×C₈	—	2	1	no	—
192	C₂×C₇×C₈	—	4	4	no	—
193	C₇×C₄⋊C₄	—	2	2	no	—
194	C₇×C₄⋊C₄	—	2	2	no	—
195	C₇×C₄⋊C₄	—	4	1	no	—
196	C₇×C₄⋊C₄	—	4	1	no	—
197	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
198	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
199	C₇×C₂²⋊C₄	—	2	2	no	—
200	C₇×C₂²⋊C₄	—	2	2	no	—
201	C₇×C₂²⋊C₄	—	4	1	no	—
202	C₇×C₂²⋊C₄	—	4	1	no	—
203	C₇×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
204	C₇×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
205	C₄²×C₇	—	2	2	no	—
206	C₄²×C₇	—	2	2	no	—
207	C₄²×C₇	—	2	1	no	—
208	C₄²×C₇	—	2	1	no	—
209	C₄²×C₇	—	2	1	no	—
210	C₄²×C₇	—	2	1	no	—
211	C₄²×C₇	—	2	1	no	—
212	C₄²×C₇	—	2	1	no	—
213	C₄²×C₇	—	2	1	no	—
214	C₄²×C₇	—	2	1	no	—
215	C₄²×C₇	—	4	1	no	—
216	C₄²×C₇	—	4	1	no	—
217	C₄²×C₇	C₂×D₄	1	2	yes	—
218	C₄²×C₇	C₂×D₄	1	2	yes	—
219	C₄²×C₇	C₂×Q₈	1	2	yes	—
220	C₄²×C₇	C₂×Q₈	1	2	yes	—
221	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
222	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×#117	C₂²×C₇	1	1	yes	characteristic
224	#433	—	2	4	no	—
225	#424	—	2	4	no	—
226	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
240	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
241	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
242	C₂×#97	C₂²×C₇	1	1	yes	characteristic
243	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
244	#388	C₄×C₇	1	1	yes	characteristic
245	#388	C₄×C₇	1	1	yes	characteristic
246	#388	C₄×C₇	1	1	yes	characteristic
247	#388	C₄×C₇	1	1	yes	characteristic
248	#387	C₄×C₇	1	1	yes	characteristic
249	#387	C₄×C₇	1	1	yes	characteristic
250	#387	C₄×C₇	1	1	yes	characteristic
251	#387	C₄×C₇	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
254	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
255	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
256	#376	C₂²×C₇	1	1	yes	characteristic
257	C₄³	C₂²×C₇	1	1	yes	characteristic
258	#336	C₂²×C₇	1	1	yes	characteristic
259	#336	C₂²×C₇	1	1	yes	characteristic
260	#336	C₂²×C₇	1	1	yes	characteristic
261	#336	C₂²×C₇	1	1	yes	characteristic
262	#336	C₂²×C₇	1	1	yes	characteristic
263	#336	C₂²×C₇	1	1	yes	characteristic
264	#336	C₂²×C₇	1	1	yes	characteristic
265	#336	C₂²×C₇	1	1	yes	characteristic
266	C₂³×C₇	—	2	1	no	—
267	C₂³×C₇	—	2	1	no	—
268	C₂³×C₇	—	2	1	no	—
269	C₂³×C₇	—	2	1	no	—
270	C₂³×C₇	—	2	1	no	—
271	C₂³×C₇	—	2	1	no	—
272	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
273	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
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	—	2	1	no	—
281	C₂×C₄×C₇	—	2	1	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	2	2	no	—
289	C₂×C₄×C₇	—	2	2	no	—
290	C₂×C₄×C₇	—	2	2	no	—
291	C₂×C₄×C₇	—	2	2	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	2	1	no	—
299	C₂×C₄×C₇	—	2	1	no	—
300	C₂×C₄×C₇	—	2	1	no	—
301	C₂×C₄×C₇	—	2	1	no	—
302	C₂×C₄×C₇	—	2	1	no	—
303	C₂×C₄×C₇	—	2	1	no	—
304	C₂×C₄×C₇	—	2	1	no	—
305	C₂×C₄×C₇	—	2	1	no	—
306	C₂×C₄×C₇	—	2	1	no	—
307	C₂×C₄×C₇	—	2	1	no	—
308	C₂×C₄×C₇	—	2	1	no	—
309	C₂×C₄×C₇	—	2	1	no	—
310	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
311	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
312	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
313	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
314	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
315	C₂×C₄×C₇	#131	1	2	yes	—
316	C₂×C₄×C₇	#131	1	2	yes	—
317	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
319	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
320	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
321	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
322	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
323	C₇×C₈	—	4	1	no	—
324	C₇×C₈	—	4	1	no	—
325	C₇×C₈	—	4	1	no	—
326	C₇×C₈	—	4	1	no	—
327	C₇×C₈	—	4	1	no	—
328	C₇×C₈	—	4	1	no	—
329	C₇×C₈	—	4	1	no	—
330	C₇×C₈	—	4	1	no	—
331	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	4	1	no	—
334	C₂×M₁₆	—	4	1	no	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	4	1	no	—
337	C₂²×C₈	—	4	1	no	—
338	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
346	#117	C₇×D₄	1	4	yes	—
347	#117	C₇×Q₈	1	4	yes	—
348	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
360	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
361	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
362	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
363	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
370	C₄⋊C₈	—	2	2	no	—
371	C₄⋊C₈	—	2	2	no	—
372	C₄⋊C₈	—	2	2	no	—
373	C₄⋊C₈	—	2	2	no	—
374	C₄⋊C₈	—	2	2	no	—
375	C₄⋊C₈	—	2	2	no	—
376	C₄⋊C₈	—	4	1	no	—
377	C₄⋊C₈	—	4	1	no	—
378	C₄⋊C₈	—	4	1	no	—
379	C₄⋊C₈	—	4	1	no	—
380	C₄⋊C₈	—	4	1	no	—
381	C₄⋊C₈	—	4	1	no	—
382	C₄⋊C₈	—	4	1	no	—
383	C₄⋊C₈	—	4	1	no	—
384	C₂²⋊C₈	—	2	2	no	—
385	C₂²⋊C₈	—	2	2	no	—
386	#97	—	2	2	no	—
387	C₄×C₈	—	2	2	no	—
388	#95	C₂×C₄×C₇	1	1	yes	characteristic
389	#95	C₂×C₄×C₇	1	1	yes	characteristic
390	#95	C₂×C₄×C₇	1	1	yes	characteristic
391	#95	C₂×C₄×C₇	1	1	yes	characteristic
392	#95	C₂×C₄×C₇	1	1	yes	characteristic
393	#95	C₂×C₄×C₇	1	1	yes	characteristic
394	#95	C₂×C₄×C₇	1	1	yes	characteristic
395	#95	C₂×C₄×C₇	1	1	yes	characteristic
396	#95	C₂×C₄×C₇	1	1	yes	characteristic
397	#95	C₂×C₄×C₇	1	1	yes	characteristic
398	#95	C₂×C₄×C₇	1	1	yes	characteristic
399	#95	C₂×C₄×C₇	1	1	yes	characteristic
400	C₂²×C₇	—	2	2	no	—
401	C₂²×C₇	—	2	2	no	—
402	C₂²×C₇	—	2	2	no	—
403	C₂²×C₇	—	4	1	no	—
404	C₂²×C₇	—	4	1	no	—
405	C₂²×C₇	—	4	1	no	—
406	C₂²×C₇	—	4	1	no	—
407	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
408	C₂²×C₇	#520	1	1	yes	characteristic
409	C₂²×C₇	#520	1	1	yes	characteristic
410	C₂²×C₇	C₂×#131	1	1	yes	characteristic
411	C₂²×C₇	C₂×#131	1	1	yes	characteristic
412	C₂²×C₇	#568	1	1	yes	characteristic
413	C₂²×C₇	#568	1	1	yes	characteristic
414	C₄×C₇	—	2	2	no	—
415	C₄×C₇	—	2	2	no	—
416	C₄×C₇	—	2	2	no	—
417	C₄×C₇	—	2	2	no	—
418	C₄×C₇	—	2	2	no	—
419	C₄×C₇	—	2	2	no	—
420	C₄×C₇	—	2	2	no	—
421	C₄×C₇	—	4	1	no	—
422	C₄×C₇	—	4	1	no	—
423	C₄×C₇	—	4	1	no	—
424	C₄×C₇	—	4	1	no	—
425	C₄×C₇	—	4	1	no	—
426	C₄×C₇	—	4	1	no	—
427	C₄×C₇	#535	1	1	yes	characteristic
428	C₄×C₇	#536	1	1	yes	characteristic
429	C₄×C₇	#544	1	1	yes	characteristic
430	C₄×C₇	#544	1	1	yes	characteristic
431	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
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	C₂²×C₄×C₇	1	1	yes	characteristic
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	C₂×C₇×D₄	1	2	yes	—
450	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
452	M₁₆	—	4	4	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	4	4	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
483	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
489	C₂²⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	4	1	no	—
501	C₄²	—	4	1	no	—
502	C₄²	C₂×C₇×D₄	1	2	yes	—
503	C₄²	C₂×C₇×D₄	1	2	yes	—
504	C₄²	C₂×C₇×Q₈	1	2	yes	—
505	C₄²	C₂×C₇×Q₈	1	2	yes	—
506	C₂×C₇	—	4	2	no	—
507	C₂×C₇	#2317	1	1	yes	characteristic
508	C₂×C₇	#2906	1	1	yes	characteristic
509	C₂×C₇	#2906	1	1	yes	characteristic
510	C₂×C₇	#2992	1	1	yes	characteristic
511	C₂×C₇	#2993	1	1	yes	characteristic
512	C₂×C₇	#2994	1	1	yes	characteristic
513	C₂×C₇	#2995	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
521	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	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	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
559	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
560	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
561	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
562	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
563	C₂×C₄	C₇×#131	1	2	yes	—
564	C₂×C₄	C₇×#131	1	2	yes	—
565	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
567	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
570	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₈	—	4	1	no	—
579	C₇	#21980	1	1	yes	characteristic, direct product factor, Sylow
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
588	C₂²	C₇×#520	1	1	yes	characteristic
589	C₂²	C₇×#520	1	1	yes	characteristic
590	C₂²	C₂×C₇×#131	1	1	yes	characteristic
591	C₂²	C₂×C₇×#131	1	1	yes	characteristic
592	C₂²	C₇×#568	1	1	yes	characteristic
593	C₂²	C₇×#568	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	C₇×#535	1	1	yes	characteristic
608	C₄	C₇×#536	1	1	yes	characteristic
609	C₄	C₇×#544	1	1	yes	characteristic
610	C₄	C₇×#544	1	1	yes	characteristic
611	C₂	—	4	2	no	—
612	C₂	C₇×#2317	1	1	yes	characteristic
613	C₂	C₇×#2906	1	1	yes	characteristic
614	C₂	C₇×#2906	1	1	yes	characteristic
615	C₂	C₇×#2992	1	1	yes	characteristic
616	C₂	C₇×#2993	1	1	yes	characteristic
617	C₂	C₇×#2994	1	1	yes	characteristic
618	C₂	C₇×#2995	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	C₂⁴×C₇	C₂²×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
4. C₇×#1940	C₂	semidirect
5. C₇×#1940	C₂	semidirect
6. C₇×#1939	C₂	semidirect
7. C₇×#1939	C₂	semidirect
12. C₇×#1843	C₂	semidirect
13. C₇×#1842	C₂	semidirect
14. C₇×#1832	C₂	semidirect
15. C₇×#1831	C₂	semidirect
61. #21980	C₇	direct (N × H)
134. #1940	C₂×C₇	semidirect
135. #1940	C₂×C₇	semidirect
136. #1939	C₂×C₇	semidirect
137. #1939	C₂×C₇	semidirect
142. #1843	C₂×C₇	semidirect
143. #1842	C₂×C₇	semidirect
144. #1832	C₂×C₇	semidirect
145. #1831	C₂×C₇	semidirect
579. C₇	#21980	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×#433	2
C₂×C₇×#424	2
C₇×#2298	2
C₇×#1940	2
C₇×#1939	2
C₇×#1851	2
C₇×#1850	2
C₇×#1843	2
C₇×#1842	2
C₇×#1832	2
C₇×#1831	2
#21980	7

Subgroups — C7×#21980 #13199196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21980 #13199196