Subgroups — C₇×#22817 #13200033

Order 1792.

886 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic
2	C₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1972	C₂	1	1	yes	maximal, characteristic
5	C₇×#1970	C₂	1	1	yes	maximal, characteristic
6	C₇×#1926	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1925	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1847	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1802	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₇×#117	—	2	1	no	—
20	C₇×#442	C₄	1	8	yes	complemented
21	C₂×C₇×#107	C₂²	1	1	yes	characteristic
22	C₂×C₇×#107	C₂²	1	1	yes	characteristic
23	C₂×C₇×#106	C₂²	1	1	yes	characteristic
24	C₂×C₇×#106	C₂²	1	1	yes	characteristic
25	C₂×C₇×#106	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₇×#102	C₂²	1	1	yes	characteristic
29	C₂×C₇×#102	C₂²	1	1	yes	characteristic
30	C₂×C₇×#102	C₂²	1	1	yes	characteristic
31	C₂×C₇×#102	C₂²	1	1	yes	characteristic
32	C₂×C₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₇×#97	C₂²	1	1	yes	characteristic
34	C₂×C₇×#97	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
36	C₇×#390	C₂²	1	1	yes	characteristic
37	C₇×#390	C₂²	1	1	yes	characteristic
38	C₇×#390	C₂²	1	1	yes	characteristic
39	C₇×#390	C₂²	1	1	yes	characteristic
40	C₇×#388	—	2	1	no	—
41	C₇×#388	—	2	1	no	—
42	C₇×#388	—	2	1	no	—
43	C₇×#388	—	2	1	no	—
44	C₇×#384	C₂²	1	1	yes	characteristic
45	C₇×#382	C₂²	1	1	yes	characteristic
46	C₇×#381	—	2	1	no	—
47	C₇×#380	—	2	1	no	—
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
54	C₇×#340	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	C₇×#336	C₂²	1	1	yes	characteristic
60	#22817	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
62	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₇	—	2	1	no	—
64	C₂³×C₄×C₇	—	2	1	no	—
65	C₂×C₇×D₈	—	2	2	no	—
66	C₂×C₇×D₈	—	2	2	no	—
67	C₂×C₇×D₈	C₂×C₄	1	4	yes	—
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	C₄×C₇×D₄	—	2	2	no	—
73	C₄×C₇×D₄	—	2	2	no	—
74	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
75	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
76	C₇×#117	—	4	4	no	—
77	C₂×C₇×C₄⋊C₄	—	2	1	no	—
78	C₂×C₇×C₄⋊C₄	—	2	1	no	—
79	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₄²×C₇	—	2	1	no	—
98	C₂×C₄²×C₇	—	2	1	no	—
99	C₂×C₄²×C₇	—	2	1	no	—
100	C₂×C₄²×C₇	—	2	1	no	—
101	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
104	C₇×#107	—	2	2	no	—
105	C₇×#107	—	4	1	no	—
106	C₇×#106	—	2	2	no	—
107	C₇×#106	—	4	1	no	—
108	C₇×#106	C₂×C₄	1	4	yes	—
109	C₇×C₄⋊C₈	—	2	2	no	—
110	C₇×#102	—	4	1	no	—
111	C₇×#102	—	4	1	no	—
112	C₇×#102	—	4	1	no	—
113	C₇×#102	—	4	1	no	—
114	C₇×#102	C₂×C₄	1	4	yes	—
115	C₇×#102	C₂×C₄	1	4	yes	—
116	C₇×#97	—	2	2	no	—
117	C₇×#97	C₂×C₄	1	4	yes	—
118	C₄×C₇×C₈	—	2	2	no	—
119	C₇×#95	—	2	1	no	—
120	C₇×#95	—	2	1	no	—
121	C₇×#95	—	2	1	no	—
122	C₇×#95	—	2	1	no	—
123	C₇×#95	—	2	1	no	—
124	C₇×#95	—	2	1	no	—
125	C₇×#95	D₄	1	1	yes	characteristic
126	C₇×#95	D₄	1	1	yes	characteristic
127	C₂×#442	C₂×C₇	1	1	yes	characteristic
128	#2357	C₂×C₇	1	1	yes	characteristic, complemented
129	#2354	C₂×C₇	1	1	yes	characteristic, complemented
130	#1972	C₂×C₇	1	1	yes	characteristic
131	#1970	C₂×C₇	1	1	yes	characteristic
132	#1926	C₂×C₇	1	1	yes	characteristic, complemented
133	#1926	C₂×C₇	1	1	yes	characteristic, complemented
134	#1925	C₂×C₇	1	1	yes	characteristic, complemented
135	#1925	C₂×C₇	1	1	yes	characteristic, complemented
136	#1847	C₂×C₇	1	1	yes	characteristic, complemented
137	#1804	C₂×C₇	1	1	yes	characteristic, complemented
138	#1802	C₂×C₇	1	1	yes	characteristic, complemented
139	#1776	C₂×C₇	1	1	yes	characteristic, complemented
140	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
141	#1771	C₂×C₇	1	1	yes	characteristic, complemented
142	C₂⁴×C₇	—	2	1	no	—
143	C₂⁴×C₇	—	2	1	no	—
144	C₂×C₇×D₄	—	2	1	no	—
145	C₂×C₇×D₄	—	2	1	no	—
146	C₂×C₇×D₄	—	2	1	no	—
147	C₂×C₇×D₄	—	2	1	no	—
148	C₂×C₇×D₄	—	2	1	no	—
149	C₂×C₇×D₄	—	2	1	no	—
150	C₂×C₇×D₄	—	2	1	no	—
151	C₂×C₇×D₄	—	2	1	no	—
152	C₂×C₇×D₄	—	2	1	no	—
153	C₂×C₇×D₄	—	2	1	no	—
154	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
155	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₇	—	2	1	no	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	4	no	—
159	C₂²×C₄×C₇	—	2	4	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	—	2	1	no	—
164	C₂²×C₄×C₇	—	4	2	no	—
165	C₂²×C₄×C₇	—	4	2	no	—
166	C₂²×C₄×C₇	—	8	1	no	—
167	C₂²×C₄×C₇	—	8	1	no	—
168	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
175	C₇×D₈	—	2	8	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	C₂²×C₄	1	2	yes	—
185	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
186	C₂×C₇×C₈	#41	1	2	yes	—
187	C₂×C₇×C₈	#41	1	2	yes	—
188	C₇×C₄⋊C₄	—	2	2	no	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	—	2	1	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	—	2	1	no	—
194	C₇×C₄⋊C₄	—	2	1	no	—
195	C₇×C₄⋊C₄	—	2	1	no	—
196	C₇×C₄⋊C₄	—	2	1	no	—
197	C₇×C₄⋊C₄	—	2	1	no	—
198	C₇×C₄⋊C₄	—	2	1	no	—
199	C₇×C₄⋊C₄	—	4	1	no	—
200	C₇×C₄⋊C₄	—	4	2	no	—
201	C₇×C₄⋊C₄	—	8	1	no	—
202	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
203	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
204	C₇×C₂²⋊C₄	—	2	4	no	—
205	C₇×C₂²⋊C₄	—	2	4	no	—
206	C₇×C₂²⋊C₄	—	4	2	no	—
207	C₇×C₂²⋊C₄	—	4	2	no	—
208	C₇×C₂²⋊C₄	—	4	2	no	—
209	C₇×C₂²⋊C₄	—	4	2	no	—
210	C₇×C₂²⋊C₄	—	8	1	no	—
211	C₇×C₂²⋊C₄	—	8	1	no	—
212	C₇×C₂²⋊C₄	—	8	1	no	—
213	C₇×C₂²⋊C₄	—	8	1	no	—
214	C₄²×C₇	—	2	1	no	—
215	C₄²×C₇	—	2	1	no	—
216	C₄²×C₇	—	2	1	no	—
217	C₄²×C₇	—	2	1	no	—
218	C₄²×C₇	—	4	2	no	—
219	C₄²×C₇	—	4	2	no	—
220	C₄²×C₇	—	8	1	no	—
221	C₄²×C₇	—	8	1	no	—
222	C₄²×C₇	C₂²×C₄	1	2	yes	—
223	C₄²×C₇	#41	1	2	yes	—
224	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
227	C₂×#117	—	2	1	no	—
228	#442	C₄×C₇	1	8	yes	complemented
229	C₂×#107	C₂²×C₇	1	1	yes	characteristic
230	C₂×#107	C₂²×C₇	1	1	yes	characteristic
231	C₂×#106	C₂²×C₇	1	1	yes	characteristic
232	C₂×#106	C₂²×C₇	1	1	yes	characteristic
233	C₂×#106	C₂²×C₇	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
235	C₂×#102	C₂²×C₇	1	1	yes	characteristic
236	C₂×#102	C₂²×C₇	1	1	yes	characteristic
237	C₂×#102	C₂²×C₇	1	1	yes	characteristic
238	C₂×#102	C₂²×C₇	1	1	yes	characteristic
239	C₂×#102	C₂²×C₇	1	1	yes	characteristic
240	C₂×#102	C₂²×C₇	1	1	yes	characteristic
241	C₂×#97	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	#390	C₂²×C₇	1	1	yes	characteristic
245	#390	C₂²×C₇	1	1	yes	characteristic
246	#390	C₂²×C₇	1	1	yes	characteristic
247	#390	C₂²×C₇	1	1	yes	characteristic
248	#388	—	2	1	no	—
249	#388	—	2	1	no	—
250	#388	—	2	1	no	—
251	#388	—	2	1	no	—
252	#384	C₂²×C₇	1	1	yes	characteristic
253	#382	C₂²×C₇	1	1	yes	characteristic
254	#381	—	2	1	no	—
255	#380	—	2	1	no	—
256	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
257	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
258	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
259	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
261	C₄×C₂²⋊C₄	—	2	1	no	—
262	#340	C₂²×C₇	1	1	yes	characteristic
263	#340	C₂²×C₇	1	1	yes	characteristic
264	#340	C₂²×C₇	1	1	yes	characteristic
265	#340	C₂²×C₇	1	1	yes	characteristic
266	#336	C₂²×C₇	1	1	yes	characteristic
267	#336	C₂²×C₇	1	1	yes	characteristic
268	C₂³×C₇	—	2	2	no	—
269	C₂³×C₇	—	2	2	no	—
270	C₂³×C₇	—	4	1	no	—
271	C₂³×C₇	—	4	1	no	—
272	C₂³×C₇	—	4	1	no	—
273	C₂³×C₇	—	4	1	no	—
274	C₂³×C₇	—	4	1	no	—
275	C₂³×C₇	—	4	1	no	—
276	C₂³×C₇	—	4	1	no	—
277	C₂³×C₇	—	4	1	no	—
278	C₂³×C₇	—	4	1	no	—
279	C₂³×C₇	—	4	1	no	—
280	C₂³×C₇	—	4	1	no	—
281	C₂³×C₇	—	4	1	no	—
282	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
283	C₇×D₄	—	2	2	no	—
284	C₇×D₄	—	2	2	no	—
285	C₇×D₄	—	2	2	no	—
286	C₇×D₄	—	2	2	no	—
287	C₇×D₄	—	4	1	no	—
288	C₇×D₄	—	4	1	no	—
289	C₇×D₄	—	4	1	no	—
290	C₇×D₄	—	4	1	no	—
291	C₂×C₄×C₇	—	2	1	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	2	no	—
298	C₂×C₄×C₇	—	2	2	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	—	4	8	no	—
309	C₂×C₄×C₇	—	4	1	no	—
310	C₂×C₄×C₇	—	4	1	no	—
311	C₂×C₄×C₇	—	4	1	no	—
312	C₂×C₄×C₇	—	4	1	no	—
313	C₂×C₄×C₇	—	4	1	no	—
314	C₂×C₄×C₇	—	4	1	no	—
315	C₂×C₄×C₇	—	4	1	no	—
316	C₂×C₄×C₇	—	4	1	no	—
317	C₂×C₄×C₇	—	4	1	no	—
318	C₂×C₄×C₇	—	4	1	no	—
319	C₂×C₄×C₇	—	4	1	no	—
320	C₂×C₄×C₇	—	4	1	no	—
321	C₂×C₄×C₇	—	4	1	no	—
322	C₂×C₄×C₇	—	4	1	no	—
323	C₂×C₄×C₇	—	4	1	no	—
324	C₂×C₄×C₇	—	4	1	no	—
325	C₂×C₄×C₇	—	8	4	no	—
326	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
327	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
328	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
329	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
330	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
335	C₇×C₈	—	2	2	no	—
336	C₇×C₈	—	4	1	no	—
337	C₇×C₈	—	4	1	no	—
338	C₇×C₈	#117	1	4	yes	complemented
339	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
340	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
341	C₂³×C₄	—	2	1	no	—
342	C₂³×C₄	—	2	1	no	—
343	C₂×D₈	—	2	2	no	—
344	C₂×D₈	—	2	2	no	—
345	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
346	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
353	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
354	#117	—	4	4	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
382	#107	—	2	2	no	—
383	#107	—	4	1	no	—
384	#106	—	2	2	no	—
385	#106	—	4	1	no	—
386	#106	C₂×C₄×C₇	1	4	yes	—
387	C₄⋊C₈	—	2	2	no	—
388	#102	—	4	1	no	—
389	#102	—	4	1	no	—
390	#102	—	4	1	no	—
391	#102	—	4	1	no	—
392	#102	C₂×C₄×C₇	1	4	yes	—
393	#102	C₂×C₄×C₇	1	4	yes	—
394	#97	—	2	2	no	—
395	#97	C₂×C₄×C₇	1	4	yes	—
396	C₄×C₈	—	2	2	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	C₇×D₄	1	1	yes	characteristic
404	#95	C₇×D₄	1	1	yes	characteristic
405	C₂²×C₇	—	4	2	no	—
406	C₂²×C₇	—	4	2	no	—
407	C₂²×C₇	—	4	2	no	—
408	C₂²×C₇	—	4	2	no	—
409	C₂²×C₇	—	4	2	no	—
410	C₂²×C₇	—	4	2	no	—
411	C₂²×C₇	—	8	1	no	—
412	C₂²×C₇	—	8	1	no	—
413	C₂²×C₇	—	8	1	no	—
414	C₂²×C₇	—	8	1	no	—
415	C₂²×C₇	—	8	1	no	—
416	C₂²×C₇	—	8	1	no	—
417	C₂²×C₇	—	8	1	no	—
418	C₂²×C₇	—	8	1	no	—
419	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
420	C₂²×C₇	#547	1	1	yes	characteristic
421	C₂²×C₇	#550	1	1	yes	characteristic
422	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂²×C₇	#575	1	1	yes	characteristic
424	C₂²×C₇	#576	1	1	yes	characteristic
425	C₂²×C₇	#577	1	1	yes	characteristic
426	C₄×C₇	—	2	2	no	—
427	C₄×C₇	—	2	2	no	—
428	C₄×C₇	—	2	2	no	—
429	C₄×C₇	—	4	1	no	—
430	C₄×C₇	—	4	1	no	—
431	C₄×C₇	—	4	1	no	—
432	C₄×C₇	—	4	2	no	—
433	C₄×C₇	—	4	2	no	—
434	C₄×C₇	—	8	1	no	—
435	C₄×C₇	—	8	1	no	—
436	C₄×C₇	—	8	1	no	—
437	C₄×C₇	—	8	1	no	—
438	C₄×C₇	C₂×#117	1	1	yes	characteristic
439	C₄×C₇	#520	1	1	yes	characteristic
440	C₄×C₇	#555	1	1	yes	characteristic
441	C₄×C₇	#556	1	1	yes	characteristic
442	C₂⁴	—	2	1	no	—
443	C₂⁴	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
455	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	8	1	no	—
467	C₂²×C₄	—	8	1	no	—
468	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
475	D₈	—	2	8	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
485	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
486	C₂×C₈	C₇×#41	1	2	yes	—
487	C₂×C₈	C₇×#41	1	2	yes	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	8	1	no	—
502	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
503	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	4	2	no	—
507	C₂²⋊C₄	—	4	2	no	—
508	C₂²⋊C₄	—	4	2	no	—
509	C₂²⋊C₄	—	4	2	no	—
510	C₂²⋊C₄	—	8	1	no	—
511	C₂²⋊C₄	—	8	1	no	—
512	C₂²⋊C₄	—	8	1	no	—
513	C₂²⋊C₄	—	8	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	4	2	no	—
519	C₄²	—	4	2	no	—
520	C₄²	—	8	1	no	—
521	C₄²	—	8	1	no	—
522	C₄²	C₂²×C₄×C₇	1	2	yes	—
523	C₄²	C₇×#41	1	2	yes	—
524	C₂×C₇	—	8	2	no	—
525	C₂×C₇	—	8	2	no	—
526	C₂×C₇	#2354	1	1	yes	characteristic
527	C₂×C₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
528	C₂×C₇	#2946	1	1	yes	characteristic
529	C₂×C₇	#3345	1	1	yes	characteristic
530	C₂×C₇	#3347	1	1	yes	characteristic
531	C₂×C₇	#3399	1	1	yes	characteristic
532	C₂×C₇	#3401	1	1	yes	characteristic
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	2	2	no	—
552	D₄	—	4	1	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	4	8	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	8	4	no	—
591	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
592	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
593	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
594	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
595	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
596	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
597	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
598	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
599	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
600	C₈	—	2	2	no	—
601	C₈	—	4	1	no	—
602	C₈	—	4	1	no	—
603	C₈	C₇×#117	1	4	yes	complemented
604	C₇	#22817	1	1	yes	characteristic, direct product factor, Sylow
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
620	C₂²	C₇×#547	1	1	yes	characteristic
621	C₂²	C₇×#550	1	1	yes	characteristic
622	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
623	C₂²	C₇×#575	1	1	yes	characteristic
624	C₂²	C₇×#576	1	1	yes	characteristic
625	C₂²	C₇×#577	1	1	yes	characteristic
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	8	1	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	1	no	—
638	C₄	C₂×C₇×#117	1	1	yes	characteristic
639	C₄	C₇×#520	1	1	yes	characteristic
640	C₄	C₇×#555	1	1	yes	characteristic
641	C₄	C₇×#556	1	1	yes	characteristic
642	C₂	—	8	2	no	—
643	C₂	—	8	2	no	—
644	C₂	C₇×#2354	1	1	yes	characteristic
645	C₂	C₄×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
646	C₂	C₇×#2946	1	1	yes	characteristic
647	C₂	C₇×#3345	1	1	yes	characteristic
648	C₂	C₇×#3347	1	1	yes	characteristic
649	C₂	C₇×#3399	1	1	yes	characteristic
650	C₂	C₇×#3401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2357	C₂	semidirect
3. C₇×#2354	C₂	semidirect
6. C₇×#1926	C₂	semidirect
7. C₇×#1926	C₂	semidirect
8. C₇×#1925	C₂	semidirect
9. C₇×#1925	C₂	semidirect
10. C₇×#1847	C₂	semidirect
11. C₇×#1804	C₂	semidirect
12. C₇×#1802	C₂	semidirect
13. C₇×#1776	C₂	semidirect
14. C₄×C₇×#106	C₂	semidirect
15. C₇×#1771	C₂	semidirect
20. C₇×#442	C₄	semidirect
60. #22817	C₇	direct (N × H)
128. #2357	C₂×C₇	semidirect
129. #2354	C₂×C₇	semidirect
132. #1926	C₂×C₇	semidirect
133. #1926	C₂×C₇	semidirect
134. #1925	C₂×C₇	semidirect
135. #1925	C₂×C₇	semidirect
136. #1847	C₂×C₇	semidirect
137. #1804	C₂×C₇	semidirect
138. #1802	C₂×C₇	semidirect
139. #1776	C₂×C₇	semidirect
140. C₄×#106	C₂×C₇	semidirect
141. #1771	C₂×C₇	semidirect
228. #442	C₄×C₇	semidirect
338. C₇×C₈	#117	semidirect
603. C₈	C₇×#117	semidirect
604. C₇	#22817	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×#442	2
C₇×#2357	2
C₇×#2354	2
C₇×#1972	2
C₇×#1970	2
C₇×#1926	2
C₇×#1925	2
C₇×#1847	2
C₇×#1804	2
C₇×#1802	2
C₇×#1776	2
C₄×C₇×#106	2
C₇×#1771	2
#22817	7

Subgroups — C7×#22817 #13200033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22817 #13200033