Subgroups — C₇×#23758 #13200974

Order 1792.

836 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic
2	C₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2092	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2076	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2073	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2034	C₂	1	1	yes	maximal, characteristic
10	C₇×#2033	C₂	1	1	yes	maximal, characteristic
11	C₄×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×D₄	—	2	1	no	—
18	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#107	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
23	C₂×C₇×#106	C₂²	1	1	yes	characteristic
24	C₂×C₇×#102	C₂²	1	1	yes	characteristic
25	C₂×C₇×#102	C₂²	1	1	yes	characteristic
26	C₂×C₇×#102	C₂²	1	1	yes	characteristic
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₇×#390	C₂²	1	1	yes	characteristic
33	C₇×#389	C₂²	1	1	yes	characteristic
34	C₇×#388	—	2	1	no	—
35	C₇×#386	—	2	1	no	—
36	C₇×#383	—	2	1	no	—
37	C₇×#382	C₂²	1	1	yes	characteristic
38	C₇×#382	C₂²	1	1	yes	characteristic
39	C₇×#381	—	2	1	no	—
40	C₇×#380	C₂²	1	1	yes	characteristic
41	C₇×#380	C₂²	1	1	yes	characteristic
42	C₇×#380	C₂²	1	1	yes	characteristic
43	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
47	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
48	C₇×#376	—	2	1	no	—
49	C₇×#340	C₂²	1	1	yes	characteristic
50	C₇×#340	C₂²	1	1	yes	characteristic
51	C₇×#340	C₂²	1	1	yes	characteristic
52	C₇×#340	C₂²	1	1	yes	characteristic
53	C₇×#340	C₂²	1	1	yes	characteristic
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×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	#23758	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₇×D₄	—	2	1	no	—
61	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	—	2	1	no	—
63	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₇×#121	—	2	2	no	—
71	C₇×#121	—	2	2	no	—
72	C₄×C₇×D₄	—	2	2	no	—
73	C₄×C₇×D₄	—	2	2	no	—
74	C₄×C₇×D₄	—	4	4	no	—
75	C₂×C₇×C₄⋊C₄	—	2	1	no	—
76	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₇×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₇	—	2	2	no	—
91	C₂×C₄²×C₇	—	2	2	no	—
92	C₂×C₄²×C₇	—	2	1	no	—
93	C₂×C₄²×C₇	—	2	1	no	—
94	C₂×C₄²×C₇	—	2	1	no	—
95	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
99	C₇×#107	—	2	2	no	—
100	C₇×#107	—	2	2	no	—
101	C₇×#106	—	2	2	no	—
102	C₇×#106	—	2	2	no	—
103	C₇×#102	—	2	2	no	—
104	C₇×#102	—	2	2	no	—
105	C₇×#102	—	2	2	no	—
106	C₇×#102	—	2	2	no	—
107	C₇×C₂²⋊C₈	—	2	2	no	—
108	C₇×C₂²⋊C₈	—	2	2	no	—
109	C₄×C₇×C₈	—	2	2	no	—
110	C₄×C₇×C₈	—	2	2	no	—
111	C₇×#95	—	2	1	no	—
112	C₇×#95	—	2	1	no	—
113	C₇×#95	—	2	1	no	—
114	C₇×#95	—	2	1	no	—
115	C₇×#95	—	2	1	no	—
116	C₇×#95	—	2	1	no	—
117	C₇×#95	—	2	1	no	—
118	C₇×#95	—	2	1	no	—
119	C₇×#95	—	2	1	no	—
120	C₇×#95	—	2	1	no	—
121	C₇×#95	—	2	1	no	—
122	C₄×#121	C₂×C₇	1	1	yes	characteristic
123	#2283	C₂×C₇	1	1	yes	characteristic, complemented
124	#2101	C₂×C₇	1	1	yes	characteristic, complemented
125	#2092	C₂×C₇	1	1	yes	characteristic, complemented
126	#2085	C₂×C₇	1	1	yes	characteristic, complemented
127	#2077	C₂×C₇	1	1	yes	characteristic, complemented
128	#2076	C₂×C₇	1	1	yes	characteristic, complemented
129	#2073	C₂×C₇	1	1	yes	characteristic, complemented
130	#2034	C₂×C₇	1	1	yes	characteristic
131	#2033	C₂×C₇	1	1	yes	characteristic
132	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
133	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
134	C₄×#102	C₂×C₇	1	1	yes	characteristic, complemented
135	C₄×#102	C₂×C₇	1	1	yes	characteristic, complemented
136	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂⁴×C₇	—	2	1	no	—
138	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₇×D₄	—	2	4	no	—
140	C₂×C₇×D₄	—	2	1	no	—
141	C₂×C₇×D₄	—	2	1	no	—
142	C₂×C₇×D₄	—	2	1	no	—
143	C₂×C₇×D₄	—	2	1	no	—
144	C₂×C₇×D₄	—	2	1	no	—
145	C₂×C₇×D₄	—	4	2	no	—
146	C₂×C₇×D₄	—	4	2	no	—
147	C₂×C₇×D₄	#41	1	2	yes	—
148	C₂²×C₄×C₇	—	2	2	no	—
149	C₂²×C₄×C₇	—	2	1	no	—
150	C₂²×C₄×C₇	—	2	2	no	—
151	C₂²×C₄×C₇	—	2	2	no	—
152	C₂²×C₄×C₇	—	2	2	no	—
153	C₂²×C₄×C₇	—	2	2	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	—	2	1	no	—
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	4	1	no	—
167	C₂²×C₄×C₇	—	4	2	no	—
168	C₂²×C₄×C₇	—	4	2	no	—
169	C₂²×C₄×C₇	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	#41	1	2	yes	—
187	C₂×C₇×C₈	#41	1	2	yes	—
188	C₇×C₄⋊C₄	—	2	1	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	—	2	1	no	—
200	C₇×C₄⋊C₄	—	2	1	no	—
201	C₇×C₄⋊C₄	—	4	2	no	—
202	C₇×C₄⋊C₄	#41	1	2	yes	—
203	C₇×C₂²⋊C₄	—	2	4	no	—
204	C₇×C₂²⋊C₄	—	4	2	no	—
205	C₇×C₂²⋊C₄	—	4	2	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	C₄²×C₇	—	2	2	no	—
211	C₄²×C₇	—	2	2	no	—
212	C₄²×C₇	—	2	1	no	—
213	C₄²×C₇	—	2	1	no	—
214	C₄²×C₇	—	4	2	no	—
215	C₄²×C₇	—	4	2	no	—
216	C₄²×C₇	—	4	2	no	—
217	C₄²×C₇	#41	1	2	yes	—
218	C₄²×C₇	#41	1	2	yes	—
219	C₂×#121	C₂²×C₇	1	1	yes	characteristic
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
222	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
223	C₂×#107	C₂²×C₇	1	1	yes	characteristic
224	C₂×#107	C₂²×C₇	1	1	yes	characteristic
225	C₂×#106	C₂²×C₇	1	1	yes	characteristic
226	C₂×#106	C₂²×C₇	1	1	yes	characteristic
227	C₂×#102	C₂²×C₇	1	1	yes	characteristic
228	C₂×#102	C₂²×C₇	1	1	yes	characteristic
229	C₂×#102	C₂²×C₇	1	1	yes	characteristic
230	C₂×#102	C₂²×C₇	1	1	yes	characteristic
231	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
232	C₂×C₂²⋊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	#390	C₂²×C₇	1	1	yes	characteristic
236	#389	C₂²×C₇	1	1	yes	characteristic
237	#388	—	2	1	no	—
238	#386	—	2	1	no	—
239	#383	—	2	1	no	—
240	#382	C₂²×C₇	1	1	yes	characteristic
241	#382	C₂²×C₇	1	1	yes	characteristic
242	#381	—	2	1	no	—
243	#380	C₂²×C₇	1	1	yes	characteristic
244	#380	C₂²×C₇	1	1	yes	characteristic
245	#380	C₂²×C₇	1	1	yes	characteristic
246	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
247	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
248	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
249	C₄×C₂²⋊C₄	—	2	1	no	—
250	C₄×C₂²⋊C₄	—	2	1	no	—
251	#376	—	2	1	no	—
252	#340	C₂²×C₇	1	1	yes	characteristic
253	#340	C₂²×C₇	1	1	yes	characteristic
254	#340	C₂²×C₇	1	1	yes	characteristic
255	#340	C₂²×C₇	1	1	yes	characteristic
256	#340	C₂²×C₇	1	1	yes	characteristic
257	#340	C₂²×C₇	1	1	yes	characteristic
258	#340	C₂²×C₇	1	1	yes	characteristic
259	#340	C₂²×C₇	1	1	yes	characteristic
260	#336	C₂²×C₇	1	1	yes	characteristic
261	#336	C₂²×C₇	1	1	yes	characteristic
262	C₂³×C₇	—	2	1	no	—
263	C₂³×C₇	—	2	1	no	—
264	C₂³×C₇	—	2	1	no	—
265	C₂³×C₇	—	2	1	no	—
266	C₂³×C₇	—	2	1	no	—
267	C₂³×C₇	—	2	1	no	—
268	C₂³×C₇	—	2	2	no	—
269	C₂³×C₇	—	4	1	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	#135	1	2	yes	—
276	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
277	C₇×D₄	—	2	2	no	—
278	C₇×D₄	—	2	2	no	—
279	C₇×D₄	—	4	8	no	—
280	C₇×D₄	—	4	1	no	—
281	C₇×D₄	—	4	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	1	no	—
290	C₂×C₄×C₇	—	2	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	—	4	4	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	—	4	1	no	—
297	C₂×C₄×C₇	—	4	1	no	—
298	C₂×C₄×C₇	—	4	1	no	—
299	C₂×C₄×C₇	—	4	1	no	—
300	C₂×C₄×C₇	—	4	1	no	—
301	C₂×C₄×C₇	—	4	4	no	—
302	C₂×C₄×C₇	—	4	1	no	—
303	C₂×C₄×C₇	—	4	1	no	—
304	C₂×C₄×C₇	—	4	1	no	—
305	C₂×C₄×C₇	—	4	1	no	—
306	C₂×C₄×C₇	—	4	1	no	—
307	C₂×C₄×C₇	—	4	1	no	—
308	C₂×C₄×C₇	—	4	1	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	—	8	4	no	—
321	C₂×C₄×C₇	#123	1	2	yes	—
322	C₂×C₄×C₇	#123	1	2	yes	—
323	C₂×C₄×C₇	#135	1	2	yes	—
324	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
325	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
331	C₇×C₈	—	2	2	no	—
332	C₇×C₈	—	2	2	no	—
333	C₇×C₈	—	4	1	no	—
334	C₇×C₈	—	4	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
339	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
340	C₂³×C₄	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	#121	—	2	2	no	—
346	#121	—	2	2	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	4	4	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
371	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
374	#107	—	2	2	no	—
375	#107	—	2	2	no	—
376	#106	—	2	2	no	—
377	#106	—	2	2	no	—
378	#102	—	2	2	no	—
379	#102	—	2	2	no	—
380	#102	—	2	2	no	—
381	#102	—	2	2	no	—
382	C₂²⋊C₈	—	2	2	no	—
383	C₂²⋊C₈	—	2	2	no	—
384	C₄×C₈	—	2	2	no	—
385	C₄×C₈	—	2	2	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	C₂²×C₇	—	2	2	no	—
398	C₂²×C₇	—	2	2	no	—
399	C₂²×C₇	—	2	2	no	—
400	C₂²×C₇	—	4	1	no	—
401	C₂²×C₇	—	4	1	no	—
402	C₂²×C₇	—	4	1	no	—
403	C₂²×C₇	—	4	1	no	—
404	C₂²×C₇	—	4	2	no	—
405	C₂²×C₇	—	4	2	no	—
406	C₂²×C₇	—	4	2	no	—
407	C₂²×C₇	—	8	1	no	—
408	C₂²×C₇	—	8	1	no	—
409	C₂²×C₇	—	8	1	no	—
410	C₂²×C₇	—	8	1	no	—
411	C₂²×C₇	C₂×#123	1	1	yes	characteristic
412	C₂²×C₇	#525	1	1	yes	characteristic
413	C₂²×C₇	#532	1	1	yes	characteristic
414	C₂²×C₇	C₂×#135	1	1	yes	characteristic
415	C₂²×C₇	C₂×#135	1	1	yes	characteristic
416	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
417	C₂²×C₇	#575	1	1	yes	characteristic
418	C₄×C₇	—	2	2	no	—
419	C₄×C₇	—	4	1	no	—
420	C₄×C₇	—	4	1	no	—
421	C₄×C₇	—	4	2	no	—
422	C₄×C₇	—	4	1	no	—
423	C₄×C₇	—	8	1	no	—
424	C₄×C₇	—	8	1	no	—
425	C₄×C₇	—	8	1	no	—
426	C₄×C₇	—	8	1	no	—
427	C₄×C₇	—	8	1	no	—
428	C₄×C₇	—	8	1	no	—
429	C₄×C₇	#482	1	4	yes	—
430	C₄×C₇	#529	1	1	yes	characteristic
431	C₄×C₇	#529	1	1	yes	characteristic
432	C₄×C₇	#529	1	1	yes	characteristic
433	C₄×C₇	#529	1	1	yes	characteristic
434	C₂⁴	—	2	1	no	—
435	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	—	4	2	no	—
444	C₂×D₄	C₇×#41	1	2	yes	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
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	C₂⁴×C₇	1	1	yes	characteristic
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	—	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	C₇×#41	1	2	yes	—
484	C₂×C₈	C₇×#41	1	2	yes	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	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	—	4	2	no	—
499	C₄⋊C₄	C₇×#41	1	2	yes	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₂²⋊C₄	—	4	2	no	—
503	C₂²⋊C₄	—	4	2	no	—
504	C₂²⋊C₄	—	4	2	no	—
505	C₂²⋊C₄	—	4	2	no	—
506	C₂²⋊C₄	—	4	2	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	4	2	no	—
512	C₄²	—	4	2	no	—
513	C₄²	—	4	2	no	—
514	C₄²	C₇×#41	1	2	yes	—
515	C₄²	C₇×#41	1	2	yes	—
516	C₂×C₇	—	4	2	no	—
517	C₂×C₇	—	8	2	no	—
518	C₂×C₇	#2395	1	1	yes	characteristic
519	C₂×C₇	C₂×#482	1	1	yes	characteristic
520	C₂×C₇	#3091	1	1	yes	characteristic
521	C₂×C₇	#3102	1	1	yes	characteristic
522	C₂×C₇	#3105	1	1	yes	characteristic
523	C₂×C₇	#3168	1	1	yes	characteristic
524	C₂×C₇	#3171	1	1	yes	characteristic
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	C₇×#135	1	2	yes	—
539	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
540	D₄	—	2	2	no	—
541	D₄	—	2	2	no	—
542	D₄	—	4	8	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	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	2	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	—	4	4	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	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	—	8	4	no	—
584	C₂×C₄	C₇×#123	1	2	yes	—
585	C₂×C₄	C₇×#123	1	2	yes	—
586	C₂×C₄	C₇×#135	1	2	yes	—
587	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
588	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
589	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
590	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
591	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
592	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
593	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	2	2	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₇	#23758	1	1	yes	characteristic, direct product factor, Sylow
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	C₂×C₇×#123	1	1	yes	characteristic
614	C₂²	C₇×#525	1	1	yes	characteristic
615	C₂²	C₇×#532	1	1	yes	characteristic
616	C₂²	C₂×C₇×#135	1	1	yes	characteristic
617	C₂²	C₂×C₇×#135	1	1	yes	characteristic
618	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
619	C₂²	C₇×#575	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	—	8	1	no	—
628	C₄	—	8	1	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	C₇×#482	1	4	yes	—
632	C₄	C₇×#529	1	1	yes	characteristic
633	C₄	C₇×#529	1	1	yes	characteristic
634	C₄	C₇×#529	1	1	yes	characteristic
635	C₄	C₇×#529	1	1	yes	characteristic
636	C₂	—	4	2	no	—
637	C₂	—	8	2	no	—
638	C₂	C₇×#2395	1	1	yes	characteristic
639	C₂	C₂×C₇×#482	1	1	yes	characteristic
640	C₂	C₇×#3091	1	1	yes	characteristic
641	C₂	C₇×#3102	1	1	yes	characteristic
642	C₂	C₇×#3105	1	1	yes	characteristic
643	C₂	C₇×#3168	1	1	yes	characteristic
644	C₂	C₇×#3171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂²×D₄
prime radical	C₂×C₇×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2283	C₂	semidirect
3. C₇×#2101	C₂	semidirect
4. C₇×#2092	C₂	semidirect
5. C₇×#2085	C₂	semidirect
6. C₇×#2077	C₂	semidirect
7. C₇×#2076	C₂	semidirect
8. C₇×#2073	C₂	semidirect
11. C₄×C₇×#107	C₂	semidirect
12. C₄×C₇×#106	C₂	semidirect
13. C₄×C₇×#102	C₂	semidirect
14. C₄×C₇×#102	C₂	semidirect
15. C₄×C₇×C₂²⋊C₈	C₂	semidirect
59. #23758	C₇	direct (N × H)
123. #2283	C₂×C₇	semidirect
124. #2101	C₂×C₇	semidirect
125. #2092	C₂×C₇	semidirect
126. #2085	C₂×C₇	semidirect
127. #2077	C₂×C₇	semidirect
128. #2076	C₂×C₇	semidirect
129. #2073	C₂×C₇	semidirect
132. C₄×#107	C₂×C₇	semidirect
133. C₄×#106	C₂×C₇	semidirect
134. C₄×#102	C₂×C₇	semidirect
135. C₄×#102	C₂×C₇	semidirect
136. C₄×C₂²⋊C₈	C₂×C₇	semidirect
598. C₇	#23758	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₇×#121	2
C₇×#2283	2
C₇×#2101	2
C₇×#2092	2
C₇×#2085	2
C₇×#2077	2
C₇×#2076	2
C₇×#2073	2
C₇×#2034	2
C₇×#2033	2
C₄×C₇×#107	2
C₄×C₇×#106	2
C₄×C₇×#102	2
C₄×C₇×C₂²⋊C₈	2
#23758	7

Subgroups — C7×#23758 #13200974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23758 #13200974