Subgroups — C₇×#27136 #13204352

Order 1792.

642 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2513	C₂	1	1	yes	maximal, characteristic
2	C₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2065	C₂	1	1	yes	maximal, characteristic
5	C₇×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2025	C₂	1	1	yes	maximal, characteristic
7	C₇×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1934	C₂	1	1	yes	maximal, characteristic
9	C₇×#1926	C₂	1	1	yes	maximal, characteristic
10	C₇×#1925	C₂	1	1	yes	maximal, characteristic
11	C₇×#1925	C₂	1	1	yes	maximal, characteristic
12	C₇×#1921	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1918	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#125	C₂²	1	1	yes	characteristic
17	C₂×C₇×#107	C₂²	1	1	yes	characteristic
18	C₂×C₇×#107	C₂²	1	1	yes	characteristic
19	C₂×C₇×#106	C₂²	1	1	yes	characteristic
20	C₂×C₇×#106	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×#102	C₂²	1	1	yes	characteristic
23	C₂×C₇×#102	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×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₇×#397	—	2	1	no	—
28	C₇×#397	—	2	1	no	—
29	C₇×#390	C₂²	1	1	yes	characteristic
30	C₇×#390	C₂²	1	1	yes	characteristic
31	C₇×#390	C₂²	1	1	yes	characteristic
32	C₇×#389	—	2	1	no	—
33	C₇×#389	C₂²	1	1	yes	characteristic
34	C₇×#389	C₂²	1	1	yes	characteristic
35	C₇×#389	C₂²	1	1	yes	characteristic
36	C₇×#388	—	2	1	no	—
37	C₇×#388	—	2	1	no	—
38	C₇×#387	—	2	1	no	—
39	C₇×#387	—	2	1	no	—
40	C₇×#382	C₂²	1	1	yes	characteristic
41	C₄×C₇×C₄⋊C₄	—	2	1	no	—
42	C₄×C₇×C₄⋊C₄	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×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₇×#340	C₂²	1	1	yes	characteristic
48	C₇×#340	C₂²	1	1	yes	characteristic
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×#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	#27136	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₇×#125	—	2	2	no	—
66	C₇×#125	—	2	2	no	—
67	C₂×C₇×C₄⋊C₄	—	2	1	no	—
68	C₂×C₇×C₄⋊C₄	—	2	1	no	—
69	C₂×C₇×C₄⋊C₄	—	2	1	no	—
70	C₂×C₇×C₄⋊C₄	—	2	1	no	—
71	C₂×C₇×C₄⋊C₄	—	2	1	no	—
72	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₇	—	2	1	no	—
88	C₂×C₄²×C₇	—	2	1	no	—
89	C₂×C₄²×C₇	—	2	1	no	—
90	C₂×C₄²×C₇	—	2	1	no	—
91	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
94	C₇×#107	—	2	2	no	—
95	C₇×#107	—	2	2	no	—
96	C₇×#106	—	2	2	no	—
97	C₇×#106	—	2	2	no	—
98	C₇×C₄⋊C₈	—	2	2	no	—
99	C₇×#102	—	2	2	no	—
100	C₇×#102	—	2	2	no	—
101	C₇×#102	—	2	2	no	—
102	C₇×#102	—	2	2	no	—
103	C₄×C₇×C₈	—	2	2	no	—
104	C₇×#95	—	2	1	no	—
105	C₇×#95	—	2	1	no	—
106	C₇×#95	—	2	1	no	—
107	C₇×#95	—	2	1	no	—
108	C₇×#95	—	2	1	no	—
109	C₇×#95	—	2	1	no	—
110	C₇×#95	—	2	1	no	—
111	C₇×#95	—	2	1	no	—
112	C₇×#95	—	2	1	no	—
113	C₇×#95	D₄	1	1	yes	characteristic
114	C₇×#95	D₄	1	1	yes	characteristic
115	#2513	C₂×C₇	1	1	yes	characteristic
116	#2370	C₂×C₇	1	1	yes	characteristic, complemented
117	#2101	C₂×C₇	1	1	yes	characteristic, complemented
118	#2065	C₂×C₇	1	1	yes	characteristic
119	#2059	C₂×C₇	1	1	yes	characteristic, complemented
120	#2025	C₂×C₇	1	1	yes	characteristic
121	#1949	C₂×C₇	1	1	yes	characteristic, complemented
122	#1934	C₂×C₇	1	1	yes	characteristic
123	#1926	C₂×C₇	1	1	yes	characteristic
124	#1925	C₂×C₇	1	1	yes	characteristic
125	#1925	C₂×C₇	1	1	yes	characteristic
126	#1921	C₂×C₇	1	1	yes	characteristic, complemented
127	#1918	C₂×C₇	1	1	yes	characteristic, complemented
128	#1916	C₂×C₇	1	1	yes	characteristic, complemented
129	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂⁴×C₇	—	2	1	no	—
131	C₂×C₇×D₄	—	2	1	no	—
132	C₂×C₇×D₄	—	2	1	no	—
133	C₂×C₇×D₄	—	2	1	no	—
134	C₂×C₇×D₄	—	2	1	no	—
135	C₂×C₇×D₄	—	2	1	no	—
136	C₂×C₇×D₄	—	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	—	2	1	no	—
142	C₂²×C₄×C₇	—	2	1	no	—
143	C₂²×C₄×C₇	—	2	1	no	—
144	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
151	C₂×C₇×C₈	—	2	1	no	—
152	C₂×C₇×C₈	—	2	1	no	—
153	C₂×C₇×C₈	—	2	1	no	—
154	C₂×C₇×C₈	—	2	1	no	—
155	C₂×C₇×C₈	—	2	1	no	—
156	C₂×C₇×C₈	—	2	1	no	—
157	C₂×C₇×C₈	—	2	1	no	—
158	C₂×C₇×C₈	—	2	1	no	—
159	C₂×C₇×C₈	—	2	1	no	—
160	C₂×C₇×C₈	—	2	1	no	—
161	C₂×C₇×C₈	—	2	1	no	—
162	C₂×C₇×C₈	#41	1	2	yes	—
163	C₇×C₄⋊C₄	—	2	4	no	—
164	C₇×C₄⋊C₄	—	2	4	no	—
165	C₇×C₄⋊C₄	—	2	2	no	—
166	C₇×C₄⋊C₄	—	2	1	no	—
167	C₇×C₄⋊C₄	—	2	1	no	—
168	C₇×C₄⋊C₄	—	2	1	no	—
169	C₇×C₄⋊C₄	—	2	1	no	—
170	C₇×C₄⋊C₄	—	2	1	no	—
171	C₇×C₄⋊C₄	—	2	1	no	—
172	C₇×C₄⋊C₄	—	2	1	no	—
173	C₇×C₄⋊C₄	—	2	1	no	—
174	C₇×C₄⋊C₄	—	2	1	no	—
175	C₇×C₄⋊C₄	—	2	1	no	—
176	C₇×C₄⋊C₄	—	2	1	no	—
177	C₇×C₄⋊C₄	—	4	1	no	—
178	C₇×C₄⋊C₄	—	4	2	no	—
179	C₇×C₄⋊C₄	—	8	1	no	—
180	C₇×C₄⋊C₄	—	8	1	no	—
181	C₇×C₄⋊C₄	#41	1	2	yes	—
182	C₇×C₄⋊C₄	#41	1	2	yes	—
183	C₇×C₄⋊C₄	#41	1	2	yes	—
184	C₇×C₂²⋊C₄	—	4	2	no	—
185	C₇×C₂²⋊C₄	—	4	2	no	—
186	C₇×C₂²⋊C₄	—	8	1	no	—
187	C₇×C₂²⋊C₄	—	8	1	no	—
188	C₇×C₂²⋊C₄	—	8	1	no	—
189	C₇×C₂²⋊C₄	—	8	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	2	no	—
197	C₄²×C₇	—	8	1	no	—
198	C₄²×C₇	—	8	1	no	—
199	C₄²×C₇	—	8	1	no	—
200	C₂×#125	C₂²×C₇	1	1	yes	characteristic
201	C₂×#107	C₂²×C₇	1	1	yes	characteristic
202	C₂×#107	C₂²×C₇	1	1	yes	characteristic
203	C₂×#106	C₂²×C₇	1	1	yes	characteristic
204	C₂×#106	C₂²×C₇	1	1	yes	characteristic
205	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
206	C₂×#102	C₂²×C₇	1	1	yes	characteristic
207	C₂×#102	C₂²×C₇	1	1	yes	characteristic
208	C₂×#102	C₂²×C₇	1	1	yes	characteristic
209	C₂×#102	C₂²×C₇	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
211	#397	—	2	1	no	—
212	#397	—	2	1	no	—
213	#390	C₂²×C₇	1	1	yes	characteristic
214	#390	C₂²×C₇	1	1	yes	characteristic
215	#390	C₂²×C₇	1	1	yes	characteristic
216	#389	—	2	1	no	—
217	#389	C₂²×C₇	1	1	yes	characteristic
218	#389	C₂²×C₇	1	1	yes	characteristic
219	#389	C₂²×C₇	1	1	yes	characteristic
220	#388	—	2	1	no	—
221	#388	—	2	1	no	—
222	#387	—	2	1	no	—
223	#387	—	2	1	no	—
224	#382	C₂²×C₇	1	1	yes	characteristic
225	C₄×C₄⋊C₄	—	2	1	no	—
226	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
227	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
229	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
230	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
231	#340	C₂²×C₇	1	1	yes	characteristic
232	#340	C₂²×C₇	1	1	yes	characteristic
233	#340	C₂²×C₇	1	1	yes	characteristic
234	#340	C₂²×C₇	1	1	yes	characteristic
235	#340	C₂²×C₇	1	1	yes	characteristic
236	#340	C₂²×C₇	1	1	yes	characteristic
237	#340	C₂²×C₇	1	1	yes	characteristic
238	#340	C₂²×C₇	1	1	yes	characteristic
239	#336	C₂²×C₇	1	1	yes	characteristic
240	#336	C₂²×C₇	1	1	yes	characteristic
241	#336	C₂²×C₇	1	1	yes	characteristic
242	#336	C₂²×C₇	1	1	yes	characteristic
243	C₂³×C₇	—	4	1	no	—
244	C₂³×C₇	—	4	1	no	—
245	C₂³×C₇	—	4	1	no	—
246	C₂³×C₇	—	4	1	no	—
247	C₂³×C₇	—	4	1	no	—
248	C₂³×C₇	—	4	1	no	—
249	C₂³×C₇	—	4	1	no	—
250	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
251	C₇×D₄	—	4	1	no	—
252	C₇×D₄	—	4	1	no	—
253	C₇×D₄	—	4	1	no	—
254	C₇×D₄	—	4	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	2	no	—
260	C₂×C₄×C₇	—	2	2	no	—
261	C₂×C₄×C₇	—	2	1	no	—
262	C₂×C₄×C₇	—	2	1	no	—
263	C₂×C₄×C₇	—	2	1	no	—
264	C₂×C₄×C₇	—	2	2	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	—	4	1	no	—
276	C₂×C₄×C₇	—	4	1	no	—
277	C₂×C₄×C₇	—	4	1	no	—
278	C₂×C₄×C₇	—	4	1	no	—
279	C₂×C₄×C₇	—	4	1	no	—
280	C₂×C₄×C₇	—	4	1	no	—
281	C₂×C₄×C₇	—	4	1	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	1	no	—
287	C₂×C₄×C₇	—	4	1	no	—
288	C₂×C₄×C₇	—	4	1	no	—
289	C₂×C₄×C₇	—	4	1	no	—
290	C₂×C₄×C₇	—	4	1	no	—
291	C₂×C₄×C₇	—	4	1	no	—
292	C₂×C₄×C₇	—	4	1	no	—
293	C₂×C₄×C₇	#135	1	2	yes	—
294	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
299	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
300	C₇×C₈	—	2	2	no	—
301	C₇×C₈	—	4	1	no	—
302	C₇×C₈	—	4	1	no	—
303	C₇×C₈	—	4	1	no	—
304	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
309	#125	—	2	2	no	—
310	#125	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
338	#107	—	2	2	no	—
339	#107	—	2	2	no	—
340	#106	—	2	2	no	—
341	#106	—	2	2	no	—
342	C₄⋊C₈	—	2	2	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#102	—	2	2	no	—
346	#102	—	2	2	no	—
347	C₄×C₈	—	2	2	no	—
348	#95	—	2	1	no	—
349	#95	—	2	1	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	1	no	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	#95	C₇×D₄	1	1	yes	characteristic
358	#95	C₇×D₄	1	1	yes	characteristic
359	C₂²×C₇	—	8	1	no	—
360	C₂²×C₇	—	8	1	no	—
361	C₂²×C₇	—	8	1	no	—
362	C₂²×C₇	—	8	1	no	—
363	C₂²×C₇	—	8	1	no	—
364	C₂²×C₇	—	8	1	no	—
365	C₂²×C₇	—	8	1	no	—
366	C₂²×C₇	#525	1	1	yes	characteristic
367	C₂²×C₇	#547	1	1	yes	characteristic
368	C₂²×C₇	#548	1	1	yes	characteristic
369	C₂²×C₇	C₂×#135	1	1	yes	characteristic
370	C₂²×C₇	#575	1	1	yes	characteristic
371	C₂²×C₇	#576	1	1	yes	characteristic
372	C₂²×C₇	#577	1	1	yes	characteristic
373	C₄×C₇	—	2	2	no	—
374	C₄×C₇	—	4	1	no	—
375	C₄×C₇	—	4	1	no	—
376	C₄×C₇	—	4	1	no	—
377	C₄×C₇	—	4	1	no	—
378	C₄×C₇	—	4	2	no	—
379	C₄×C₇	—	4	2	no	—
380	C₄×C₇	—	4	1	no	—
381	C₄×C₇	—	4	2	no	—
382	C₄×C₇	—	8	1	no	—
383	C₄×C₇	—	8	1	no	—
384	C₄×C₇	—	8	1	no	—
385	C₄×C₇	—	8	1	no	—
386	C₄×C₇	#529	1	1	yes	characteristic
387	C₄×C₇	#541	1	1	yes	characteristic
388	C₄×C₇	#556	1	1	yes	characteristic
389	C₄×C₇	#556	1	1	yes	characteristic
390	C₂⁴	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
407	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
408	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	C₇×#41	1	2	yes	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	4	1	no	—
438	C₄⋊C₄	—	4	2	no	—
439	C₄⋊C₄	—	8	1	no	—
440	C₄⋊C₄	—	8	1	no	—
441	C₄⋊C₄	C₇×#41	1	2	yes	—
442	C₄⋊C₄	C₇×#41	1	2	yes	—
443	C₄⋊C₄	C₇×#41	1	2	yes	—
444	C₂²⋊C₄	—	4	2	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	8	1	no	—
447	C₂²⋊C₄	—	8	1	no	—
448	C₂²⋊C₄	—	8	1	no	—
449	C₂²⋊C₄	—	8	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	4	2	no	—
457	C₄²	—	8	1	no	—
458	C₄²	—	8	1	no	—
459	C₄²	—	8	1	no	—
460	C₂×C₇	—	16	1	no	—
461	C₂×C₇	#2469	1	1	yes	characteristic
462	C₂×C₇	#3102	1	1	yes	characteristic
463	C₂×C₇	#3119	1	1	yes	characteristic
464	C₂×C₇	#3337	1	1	yes	characteristic
465	C₂×C₇	#3347	1	1	yes	characteristic
466	C₂×C₇	#3361	1	1	yes	characteristic
467	C₂×C₇	#3371	1	1	yes	characteristic
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	1	no	—
475	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
476	D₄	—	4	1	no	—
477	D₄	—	4	1	no	—
478	D₄	—	4	1	no	—
479	D₄	—	4	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	C₇×#135	1	2	yes	—
519	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
520	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
521	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
522	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
523	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
524	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₇	#27136	1	1	yes	characteristic, direct product factor, Sylow
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	C₇×#525	1	1	yes	characteristic
538	C₂²	C₇×#547	1	1	yes	characteristic
539	C₂²	C₇×#548	1	1	yes	characteristic
540	C₂²	C₂×C₇×#135	1	1	yes	characteristic
541	C₂²	C₇×#575	1	1	yes	characteristic
542	C₂²	C₇×#576	1	1	yes	characteristic
543	C₂²	C₇×#577	1	1	yes	characteristic
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	C₇×#529	1	1	yes	characteristic
558	C₄	C₇×#541	1	1	yes	characteristic
559	C₄	C₇×#556	1	1	yes	characteristic
560	C₄	C₇×#556	1	1	yes	characteristic
561	C₂	—	16	1	no	—
562	C₂	C₇×#2469	1	1	yes	characteristic
563	C₂	C₇×#3102	1	1	yes	characteristic
564	C₂	C₇×#3119	1	1	yes	characteristic
565	C₂	C₇×#3337	1	1	yes	characteristic
566	C₂	C₇×#3347	1	1	yes	characteristic
567	C₂	C₇×#3361	1	1	yes	characteristic
568	C₂	C₇×#3371	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂²×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×#2370	C₂	semidirect
3. C₇×#2101	C₂	semidirect
5. C₇×#2059	C₂	semidirect
7. C₇×#1949	C₂	semidirect
12. C₇×#1921	C₂	semidirect
13. C₇×#1918	C₂	semidirect
14. C₇×#1916	C₂	semidirect
15. C₄×C₇×#106	C₂	semidirect
59. #27136	C₇	direct (N × H)
116. #2370	C₂×C₇	semidirect
117. #2101	C₂×C₇	semidirect
119. #2059	C₂×C₇	semidirect
121. #1949	C₂×C₇	semidirect
126. #1921	C₂×C₇	semidirect
127. #1918	C₂×C₇	semidirect
128. #1916	C₂×C₇	semidirect
129. C₄×#106	C₂×C₇	semidirect
529. C₇	#27136	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2513	2
C₇×#2370	2
C₇×#2101	2
C₇×#2065	2
C₇×#2059	2
C₇×#2025	2
C₇×#1949	2
C₇×#1934	2
C₇×#1926	2
C₇×#1925	2
C₇×#1921	2
C₇×#1918	2
C₇×#1916	2
C₄×C₇×#106	2
#27136	7

Subgroups — C7×#27136 #13204352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#27136 #13204352