Subgroups — C₇×#22756 #13199972

Order 1792.

858 conjugacy classes of subgroups.

The subgroup lattice has 680 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, complemented
2	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2293	C₂	1	1	yes	maximal, characteristic
4	C₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1870	C₂	1	1	yes	maximal, characteristic
9	C₇×#1869	C₂	1	1	yes	maximal, characteristic
10	C₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×C₈×C₂²⋊C₄	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×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₇×#117	C₂²	1	1	yes	characteristic
20	C₂×C₇×#117	C₂²	1	1	yes	characteristic
21	C₇×#433	—	2	4	no	—
22	C₇×#424	—	2	4	no	—
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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₇×#390	C₄	1	1	yes	characteristic
40	C₇×#390	C₄	1	1	yes	characteristic
41	C₇×#389	C₄	1	1	yes	characteristic
42	C₇×#389	C₄	1	1	yes	characteristic
43	C₇×#388	C₄	1	1	yes	characteristic
44	C₇×#388	C₄	1	1	yes	characteristic
45	C₇×#388	C₄	1	1	yes	characteristic
46	C₇×#388	C₄	1	1	yes	characteristic
47	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₄³×C₇	C₂²	1	1	yes	characteristic
51	C₇×#336	C₂²	1	1	yes	characteristic
52	C₇×#336	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	#22756	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
65	C₂×C₇×M₁₆	—	2	2	no	—
66	C₂×C₇×M₁₆	—	2	2	no	—
67	C₂×C₇×M₁₆	—	4	1	no	—
68	C₂²×C₇×C₈	—	2	2	no	—
69	C₂²×C₇×C₈	—	2	2	no	—
70	C₂²×C₇×C₈	—	4	1	no	—
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	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
79	C₄×C₇×D₄	—	2	2	no	—
80	C₄×C₇×D₄	—	2	2	no	—
81	C₇×#117	—	2	2	no	—
82	C₇×#117	—	2	2	no	—
83	C₇×#117	—	2	2	no	—
84	C₇×#117	—	2	2	no	—
85	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
111	C₇×C₄⋊C₈	—	2	2	no	—
112	C₇×C₄⋊C₈	—	2	2	no	—
113	C₇×C₄⋊C₈	—	2	2	no	—
114	C₇×C₄⋊C₈	—	2	2	no	—
115	C₇×C₄⋊C₈	—	2	2	no	—
116	C₇×C₄⋊C₈	D₄	1	4	yes	complemented
117	C₇×C₂²⋊C₈	—	2	2	no	—
118	C₇×C₂²⋊C₈	—	2	2	no	—
119	C₇×C₂²⋊C₈	—	2	2	no	—
120	C₇×C₂²⋊C₈	—	2	2	no	—
121	C₇×C₂²⋊C₈	—	4	1	no	—
122	C₇×C₂²⋊C₈	—	4	1	no	—
123	C₇×#97	—	2	2	no	—
124	C₄×C₇×C₈	—	2	2	no	—
125	C₄×C₇×C₈	—	4	1	no	—
126	C₄×C₇×C₈	—	4	1	no	—
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	C₇×#95	C₂×C₄	1	1	yes	characteristic
132	C₇×#95	C₂×C₄	1	1	yes	characteristic
133	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#424	C₂×C₇	1	1	yes	characteristic, complemented
135	#2293	C₂×C₇	1	1	yes	characteristic
136	#1923	C₂×C₇	1	1	yes	characteristic, complemented
137	#1923	C₂×C₇	1	1	yes	characteristic, complemented
138	#1917	C₂×C₇	1	1	yes	characteristic, complemented
139	#1916	C₂×C₇	1	1	yes	characteristic, complemented
140	#1870	C₂×C₇	1	1	yes	characteristic
141	#1869	C₂×C₇	1	1	yes	characteristic
142	#1831	C₂×C₇	1	1	yes	characteristic, complemented
143	#1798	C₂×C₇	1	1	yes	characteristic, complemented
144	#1798	C₂×C₇	1	1	yes	characteristic, complemented
145	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
146	#1753	C₂×C₇	1	1	yes	characteristic, complemented
147	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
149	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₇×D₄	—	2	2	no	—
151	C₂×C₇×D₄	—	2	2	no	—
152	C₂×C₇×D₄	—	4	1	no	—
153	C₂²×C₄×C₇	—	2	1	no	—
154	C₂²×C₄×C₇	—	2	1	no	—
155	C₂²×C₄×C₇	—	2	1	no	—
156	C₂²×C₄×C₇	—	2	1	no	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	1	no	—
159	C₂²×C₄×C₇	—	2	1	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	#41	1	2	yes	—
176	C₂²×C₄×C₇	#41	1	2	yes	—
177	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
178	C₇×M₁₆	—	4	4	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	—	2	1	no	—
193	C₂×C₇×C₈	—	2	1	no	—
194	C₂×C₇×C₈	—	2	1	no	—
195	C₂×C₇×C₈	—	2	1	no	—
196	C₂×C₇×C₈	—	2	1	no	—
197	C₂×C₇×C₈	—	2	1	no	—
198	C₂×C₇×C₈	—	2	1	no	—
199	C₂×C₇×C₈	—	2	1	no	—
200	C₂×C₇×C₈	—	2	1	no	—
201	C₂×C₇×C₈	—	4	4	no	—
202	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
203	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
204	C₇×C₄⋊C₄	—	2	2	no	—
205	C₇×C₄⋊C₄	—	2	2	no	—
206	C₇×C₄⋊C₄	—	2	2	no	—
207	C₇×C₄⋊C₄	—	2	2	no	—
208	C₇×C₄⋊C₄	—	2	2	no	—
209	C₇×C₄⋊C₄	—	2	2	no	—
210	C₇×C₄⋊C₄	—	4	1	no	—
211	C₇×C₂²⋊C₄	—	2	2	no	—
212	C₇×C₂²⋊C₄	—	2	2	no	—
213	C₇×C₂²⋊C₄	—	2	2	no	—
214	C₇×C₂²⋊C₄	—	2	2	no	—
215	C₇×C₂²⋊C₄	—	2	2	no	—
216	C₇×C₂²⋊C₄	—	2	2	no	—
217	C₇×C₂²⋊C₄	—	2	2	no	—
218	C₇×C₂²⋊C₄	—	2	2	no	—
219	C₇×C₂²⋊C₄	—	2	2	no	—
220	C₇×C₂²⋊C₄	—	2	2	no	—
221	C₄²×C₇	—	2	2	no	—
222	C₄²×C₇	—	2	2	no	—
223	C₄²×C₇	—	2	2	no	—
224	C₄²×C₇	—	2	1	no	—
225	C₄²×C₇	—	2	1	no	—
226	C₄²×C₇	—	2	1	no	—
227	C₄²×C₇	—	2	1	no	—
228	C₄²×C₇	—	2	1	no	—
229	C₄²×C₇	—	2	1	no	—
230	C₄²×C₇	—	2	1	no	—
231	C₄²×C₇	—	2	1	no	—
232	C₄²×C₇	—	4	1	no	—
233	C₄²×C₇	C₂×D₄	1	2	yes	—
234	C₄²×C₇	#41	1	2	yes	—
235	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
236	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
238	C₂×#117	C₂²×C₇	1	1	yes	characteristic
239	C₂×#117	C₂²×C₇	1	1	yes	characteristic
240	#433	—	2	4	no	—
241	#424	—	2	4	no	—
242	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
248	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
249	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
250	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
252	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
254	C₂×#97	C₂²×C₇	1	1	yes	characteristic
255	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
256	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
258	#390	C₄×C₇	1	1	yes	characteristic
259	#390	C₄×C₇	1	1	yes	characteristic
260	#389	C₄×C₇	1	1	yes	characteristic
261	#389	C₄×C₇	1	1	yes	characteristic
262	#388	C₄×C₇	1	1	yes	characteristic
263	#388	C₄×C₇	1	1	yes	characteristic
264	#388	C₄×C₇	1	1	yes	characteristic
265	#388	C₄×C₇	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
267	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
268	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
269	C₄³	C₂²×C₇	1	1	yes	characteristic
270	#336	C₂²×C₇	1	1	yes	characteristic
271	#336	C₂²×C₇	1	1	yes	characteristic
272	#336	C₂²×C₇	1	1	yes	characteristic
273	#336	C₂²×C₇	1	1	yes	characteristic
274	#336	C₂²×C₇	1	1	yes	characteristic
275	#336	C₂²×C₇	1	1	yes	characteristic
276	#336	C₂²×C₇	1	1	yes	characteristic
277	#336	C₂²×C₇	1	1	yes	characteristic
278	#336	C₂²×C₇	1	1	yes	characteristic
279	#336	C₂²×C₇	1	1	yes	characteristic
280	C₂³×C₇	—	2	1	no	—
281	C₂³×C₇	—	2	1	no	—
282	C₂³×C₇	—	2	1	no	—
283	C₂³×C₇	—	2	1	no	—
284	C₂³×C₇	—	2	1	no	—
285	C₂³×C₇	—	2	1	no	—
286	C₂³×C₇	—	2	1	no	—
287	C₂³×C₇	—	2	1	no	—
288	C₂³×C₇	—	2	1	no	—
289	C₂³×C₇	—	2	1	no	—
290	C₂³×C₇	—	2	1	no	—
291	C₂³×C₇	—	2	1	no	—
292	C₂³×C₇	—	2	1	no	—
293	C₂³×C₇	#117	1	2	yes	—
294	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
295	C₇×D₄	—	4	4	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	2	no	—
309	C₂×C₄×C₇	—	2	2	no	—
310	C₂×C₄×C₇	—	2	2	no	—
311	C₂×C₄×C₇	—	2	2	no	—
312	C₂×C₄×C₇	—	2	1	no	—
313	C₂×C₄×C₇	—	2	1	no	—
314	C₂×C₄×C₇	—	2	1	no	—
315	C₂×C₄×C₇	—	2	1	no	—
316	C₂×C₄×C₇	—	2	1	no	—
317	C₂×C₄×C₇	—	2	1	no	—
318	C₂×C₄×C₇	—	2	1	no	—
319	C₂×C₄×C₇	—	2	1	no	—
320	C₂×C₄×C₇	—	2	1	no	—
321	C₂×C₄×C₇	—	2	1	no	—
322	C₂×C₄×C₇	—	2	1	no	—
323	C₂×C₄×C₇	—	2	1	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	2	1	no	—
326	C₂×C₄×C₇	—	2	1	no	—
327	C₂×C₄×C₇	—	2	1	no	—
328	C₂×C₄×C₇	—	2	1	no	—
329	C₂×C₄×C₇	—	2	1	no	—
330	C₂×C₄×C₇	—	4	1	no	—
331	C₂×C₄×C₇	—	4	1	no	—
332	C₂×C₄×C₇	—	4	1	no	—
333	C₂×C₄×C₇	—	4	1	no	—
334	C₂×C₄×C₇	#117	1	2	yes	—
335	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
336	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
337	C₂×C₄×C₇	#131	1	2	yes	—
338	C₂×C₄×C₇	#131	1	2	yes	—
339	C₂×C₄×C₇	#131	1	2	yes	—
340	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
343	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
344	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
346	C₇×C₈	—	2	2	no	—
347	C₇×C₈	—	2	2	no	—
348	C₇×C₈	—	4	1	no	—
349	C₇×C₈	—	4	1	no	—
350	C₇×C₈	—	4	1	no	—
351	C₇×C₈	—	4	1	no	—
352	C₇×C₈	—	4	1	no	—
353	C₇×C₈	—	4	1	no	—
354	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	4	1	no	—
360	C₂²×C₈	—	2	2	no	—
361	C₂²×C₈	—	2	2	no	—
362	C₂²×C₈	—	4	1	no	—
363	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	#117	—	2	2	no	—
374	#117	—	2	2	no	—
375	#117	—	2	2	no	—
376	#117	—	2	2	no	—
377	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
394	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
395	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
396	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
397	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
403	C₄⋊C₈	—	2	2	no	—
404	C₄⋊C₈	—	2	2	no	—
405	C₄⋊C₈	—	2	2	no	—
406	C₄⋊C₈	—	2	2	no	—
407	C₄⋊C₈	—	2	2	no	—
408	C₄⋊C₈	C₇×D₄	1	4	yes	complemented
409	C₂²⋊C₈	—	2	2	no	—
410	C₂²⋊C₈	—	2	2	no	—
411	C₂²⋊C₈	—	2	2	no	—
412	C₂²⋊C₈	—	2	2	no	—
413	C₂²⋊C₈	—	4	1	no	—
414	C₂²⋊C₈	—	4	1	no	—
415	#97	—	2	2	no	—
416	C₄×C₈	—	2	2	no	—
417	C₄×C₈	—	4	1	no	—
418	C₄×C₈	—	4	1	no	—
419	#95	C₂×C₄×C₇	1	1	yes	characteristic
420	#95	C₂×C₄×C₇	1	1	yes	characteristic
421	#95	C₂×C₄×C₇	1	1	yes	characteristic
422	#95	C₂×C₄×C₇	1	1	yes	characteristic
423	#95	C₂×C₄×C₇	1	1	yes	characteristic
424	#95	C₂×C₄×C₇	1	1	yes	characteristic
425	C₂²×C₇	—	2	2	no	—
426	C₂²×C₇	—	2	2	no	—
427	C₂²×C₇	—	2	2	no	—
428	C₂²×C₇	—	4	1	no	—
429	C₂²×C₇	—	4	1	no	—
430	C₂²×C₇	—	4	1	no	—
431	C₂²×C₇	—	4	1	no	—
432	C₂²×C₇	—	4	1	no	—
433	C₂²×C₇	—	4	1	no	—
434	C₂²×C₇	—	4	1	no	—
435	C₂²×C₇	—	4	1	no	—
436	C₂²×C₇	—	4	1	no	—
437	C₂²×C₇	—	4	1	no	—
438	C₂²×C₇	—	4	1	no	—
439	C₂²×C₇	C₂×#117	1	1	yes	characteristic
440	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
441	C₂²×C₇	#520	1	1	yes	characteristic
442	C₂²×C₇	C₂×#131	1	1	yes	characteristic
443	C₂²×C₇	C₂×#131	1	1	yes	characteristic
444	C₂²×C₇	C₂×#131	1	1	yes	characteristic
445	C₂²×C₇	#568	1	1	yes	characteristic
446	C₄×C₇	—	2	2	no	—
447	C₄×C₇	—	2	2	no	—
448	C₄×C₇	—	2	2	no	—
449	C₄×C₇	—	2	2	no	—
450	C₄×C₇	—	2	2	no	—
451	C₄×C₇	—	2	2	no	—
452	C₄×C₇	—	4	1	no	—
453	C₄×C₇	—	4	1	no	—
454	C₄×C₇	—	4	1	no	—
455	C₄×C₇	—	4	1	no	—
456	C₄×C₇	—	4	1	no	—
457	C₄×C₇	—	4	1	no	—
458	C₄×C₇	#546	1	1	yes	characteristic
459	C₄×C₇	#548	1	1	yes	characteristic
460	C₄×C₇	#552	1	1	yes	characteristic
461	C₄×C₇	#553	1	1	yes	characteristic
462	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
463	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	4	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
479	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
480	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
481	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
483	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
484	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
485	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
486	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
487	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
488	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
489	C₂²×C₄	C₇×#41	1	2	yes	—
490	C₂²×C₄	C₇×#41	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
492	M₁₆	—	4	4	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	4	4	no	—
516	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
517	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	4	1	no	—
547	C₄²	C₂×C₇×D₄	1	2	yes	—
548	C₄²	C₇×#41	1	2	yes	—
549	C₂×C₇	—	4	2	no	—
550	C₂×C₇	—	8	1	no	—
551	C₂×C₇	#2352	1	1	yes	characteristic
552	C₂×C₇	#2922	1	1	yes	characteristic
553	C₂×C₇	#2924	1	1	yes	characteristic
554	C₂×C₇	#2931	1	1	yes	characteristic
555	C₂×C₇	#2935	1	1	yes	characteristic
556	C₂×C₇	#2992	1	1	yes	characteristic
557	C₂×C₇	#2994	1	1	yes	characteristic
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	C₇×#117	1	2	yes	—
572	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
573	D₄	—	4	4	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	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	C₇×#117	1	2	yes	—
613	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
614	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
615	C₂×C₄	C₇×#131	1	2	yes	—
616	C₂×C₄	C₇×#131	1	2	yes	—
617	C₂×C₄	C₇×#131	1	2	yes	—
618	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
619	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
620	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
621	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
622	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
623	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
624	C₈	—	2	2	no	—
625	C₈	—	2	2	no	—
626	C₈	—	4	1	no	—
627	C₈	—	4	1	no	—
628	C₈	—	4	1	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₈	—	4	1	no	—
632	C₇	#22756	1	1	yes	characteristic, direct product factor, Sylow
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	C₂×C₇×#117	1	1	yes	characteristic
648	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
649	C₂²	C₇×#520	1	1	yes	characteristic
650	C₂²	C₂×C₇×#131	1	1	yes	characteristic
651	C₂²	C₂×C₇×#131	1	1	yes	characteristic
652	C₂²	C₂×C₇×#131	1	1	yes	characteristic
653	C₂²	C₇×#568	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	C₇×#546	1	1	yes	characteristic
667	C₄	C₇×#548	1	1	yes	characteristic
668	C₄	C₇×#552	1	1	yes	characteristic
669	C₄	C₇×#553	1	1	yes	characteristic
670	C₂	—	4	2	no	—
671	C₂	—	8	1	no	—
672	C₂	C₇×#2352	1	1	yes	characteristic
673	C₂	C₇×#2922	1	1	yes	characteristic
674	C₂	C₇×#2924	1	1	yes	characteristic
675	C₂	C₇×#2931	1	1	yes	characteristic
676	C₂	C₇×#2935	1	1	yes	characteristic
677	C₂	C₇×#2992	1	1	yes	characteristic
678	C₂	C₇×#2994	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×#433	C₂	semidirect
2. C₂×C₇×#424	C₂	semidirect
4. C₇×#1923	C₂	semidirect
5. C₇×#1923	C₂	semidirect
6. C₇×#1917	C₂	semidirect
7. C₇×#1916	C₂	semidirect
10. C₇×#1831	C₂	semidirect
11. C₇×#1798	C₂	semidirect
12. C₇×#1798	C₂	semidirect
13. C₄×C₇×C₄⋊C₈	C₂	semidirect
14. C₇×#1753	C₂	semidirect
15. C₇×C₈×C₂²⋊C₄	C₂	semidirect
61. #22756	C₇	direct (N × H)
116. C₇×C₄⋊C₈	D₄	semidirect
133. C₂×#433	C₂×C₇	semidirect
134. C₂×#424	C₂×C₇	semidirect
136. #1923	C₂×C₇	semidirect
137. #1923	C₂×C₇	semidirect
138. #1917	C₂×C₇	semidirect
139. #1916	C₂×C₇	semidirect
142. #1831	C₂×C₇	semidirect
143. #1798	C₂×C₇	semidirect
144. #1798	C₂×C₇	semidirect
145. C₄×C₄⋊C₈	C₂×C₇	semidirect
146. #1753	C₂×C₇	semidirect
147. C₈×C₂²⋊C₄	C₂×C₇	semidirect
408. C₄⋊C₈	C₇×D₄	semidirect
632. C₇	#22756	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×#2293	2
C₇×#1923	2
C₇×#1917	2
C₇×#1916	2
C₇×#1870	2
C₇×#1869	2
C₇×#1831	2
C₇×#1798	2
C₄×C₇×C₄⋊C₈	2
C₇×#1753	2
C₇×C₈×C₂²⋊C₄	2
#22756	7

Subgroups — C7×#22756 #13199972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22756 #13199972