Subgroups — C₇×#21536 #13198752

Order 1792.

1066 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2324	C₂	1	2	yes	maximal, complemented
5	C₇×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1934	C₂	1	2	yes	maximal, complemented
8	C₇×#1893	C₂	1	2	yes	maximal, complemented
9	C₇×#1809	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1762	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
13	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×#121	C₂²	1	2	yes	—
16	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
17	C₂×C₇×#117	C₂²	1	1	yes	characteristic
18	C₇×#469	C₄	1	8	yes	complemented
19	C₄×C₇×D₈	—	2	4	no	—
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
23	C₂×C₇×#102	C₂²	1	2	yes	—
24	C₂×C₇×#102	C₂²	1	2	yes	—
25	C₂×C₇×#102	C₂²	1	2	yes	—
26	C₇×#405	—	2	4	no	—
27	C₂×C₇×#97	C₂²	1	1	yes	characteristic
28	C₂×C₇×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₇×#390	—	2	2	no	—
32	C₇×#390	C₂²	1	2	yes	—
33	C₇×#389	C₂²	1	2	yes	—
34	C₇×#388	—	2	2	no	—
35	C₇×#386	—	2	2	no	—
36	C₇×#385	—	2	2	no	—
37	C₇×#380	C₂²	1	2	yes	—
38	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#340	C₂²	1	2	yes	—
42	#21536	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×D₄	—	2	2	no	—
44	C₂²×C₇×D₄	C₂³	1	2	yes	—
45	C₂³×C₄×C₇	—	2	2	no	—
46	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
47	C₂×C₇×D₈	—	2	2	no	—
48	C₂×C₇×D₈	—	2	2	no	—
49	C₂×C₇×D₈	C₂×C₄	1	4	yes	—
50	C₂×C₇×M₁₆	—	2	2	no	—
51	C₂×C₇×M₁₆	—	2	2	no	—
52	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	complemented
53	C₂²×C₇×C₈	—	2	2	no	—
54	C₂²×C₇×C₈	—	2	2	no	—
55	C₂²×C₇×C₈	—	2	2	no	—
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
60	C₇×#121	—	2	4	no	—
61	C₇×#121	C₂×C₄	1	8	yes	complemented
62	C₄×C₇×D₄	—	2	4	no	—
63	C₄×C₇×D₄	—	2	4	no	—
64	C₇×#117	—	2	2	no	—
65	C₇×#117	—	2	2	no	—
66	C₂×C₇×C₄⋊C₄	—	2	2	no	—
67	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
78	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₇	—	2	2	no	—
80	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₇×#107	—	2	2	no	—
83	C₇×#106	—	2	2	no	—
84	C₇×#106	C₂×C₄	1	4	yes	complemented
85	C₇×#102	—	2	4	no	—
86	C₇×#102	—	2	4	no	—
87	C₇×#102	C₂×C₄	1	8	yes	complemented
88	C₇×#97	—	2	2	no	—
89	C₇×#97	—	2	2	no	—
90	C₄×C₇×C₈	—	2	2	no	—
91	C₄×C₇×C₈	D₄	1	4	yes	complemented
92	C₇×#95	—	2	2	no	—
93	C₇×#95	—	2	2	no	—
94	C₇×#95	—	2	2	no	—
95	C₂×#469	C₂×C₇	1	1	yes	characteristic
96	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
97	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
98	#2324	C₂×C₇	1	2	yes	complemented
99	#1972	C₂×C₇	1	1	yes	characteristic, complemented
100	#1944	C₂×C₇	1	1	yes	characteristic, complemented
101	#1934	C₂×C₇	1	2	yes	complemented
102	#1893	C₂×C₇	1	2	yes	complemented
103	#1809	C₂×C₇	1	1	yes	characteristic, complemented
104	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
105	#1762	C₂×C₇	1	2	yes	complemented
106	C₂⁴×C₇	—	2	2	no	—
107	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
108	C₂×C₇×D₄	—	2	8	no	—
109	C₂×C₇×D₄	—	2	2	no	—
110	C₂×C₇×D₄	—	2	2	no	—
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	2	2	no	—
113	C₂×C₇×D₄	—	2	2	no	—
114	C₂×C₇×D₄	—	8	2	no	—
115	C₂×C₇×D₄	—	8	2	no	—
116	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
117	C₂²×C₄×C₇	—	2	1	no	—
118	C₂²×C₄×C₇	—	2	1	no	—
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	—	2	1	no	—
121	C₂²×C₄×C₇	—	2	2	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	4	4	no	—
125	C₂²×C₄×C₇	—	8	2	no	—
126	C₂²×C₄×C₇	—	8	2	no	—
127	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	#41	1	2	yes	—
134	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
135	C₇×D₈	—	2	8	no	—
136	C₇×M₁₆	—	2	8	no	—
137	C₂×C₇×C₈	—	2	8	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	1	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	—	2	1	no	—
144	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
147	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
148	C₂×C₇×C₈	#41	1	2	yes	—
149	C₂×C₇×C₈	#41	1	2	yes	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	2	2	no	—
156	C₇×C₄⋊C₄	—	2	2	no	—
157	C₇×C₄⋊C₄	—	8	2	no	—
158	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
159	C₇×C₂²⋊C₄	—	2	8	no	—
160	C₇×C₂²⋊C₄	—	2	2	no	—
161	C₇×C₂²⋊C₄	—	2	2	no	—
162	C₇×C₂²⋊C₄	—	4	4	no	—
163	C₇×C₂²⋊C₄	—	8	2	no	—
164	C₇×C₂²⋊C₄	—	8	2	no	—
165	C₇×C₂²⋊C₄	—	8	2	no	—
166	C₄²×C₇	—	2	1	no	—
167	C₄²×C₇	—	2	1	no	—
168	C₄²×C₇	—	8	2	no	—
169	C₄²×C₇	C₂×D₄	1	2	yes	—
170	C₄²×C₇	#41	1	2	yes	—
171	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
172	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
173	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
174	C₂×#121	C₂²×C₇	1	2	yes	—
175	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
176	C₂×#117	C₂²×C₇	1	1	yes	characteristic
177	#469	C₄×C₇	1	8	yes	complemented
178	C₄×D₈	—	2	4	no	—
179	C₂×#107	C₂²×C₇	1	1	yes	characteristic
180	C₂×#106	C₂²×C₇	1	1	yes	characteristic
181	C₂×#106	C₂²×C₇	1	1	yes	characteristic
182	C₂×#102	C₂²×C₇	1	2	yes	—
183	C₂×#102	C₂²×C₇	1	2	yes	—
184	C₂×#102	C₂²×C₇	1	2	yes	—
185	#405	—	2	4	no	—
186	C₂×#97	C₂²×C₇	1	1	yes	characteristic
187	C₂×#97	C₂²×C₇	1	1	yes	characteristic
188	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
189	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
190	#390	—	2	2	no	—
191	#390	C₂²×C₇	1	2	yes	—
192	#389	C₂²×C₇	1	2	yes	—
193	#388	—	2	2	no	—
194	#386	—	2	2	no	—
195	#385	—	2	2	no	—
196	#380	C₂²×C₇	1	2	yes	—
197	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
198	#340	C₂²×C₇	1	2	yes	—
199	#340	C₂²×C₇	1	2	yes	—
200	#340	C₂²×C₇	1	2	yes	—
201	C₂³×C₇	—	2	1	no	—
202	C₂³×C₇	—	2	1	no	—
203	C₂³×C₇	—	2	2	no	—
204	C₂³×C₇	—	2	2	no	—
205	C₂³×C₇	—	2	4	no	—
206	C₂³×C₇	—	4	2	no	—
207	C₂³×C₇	—	4	2	no	—
208	C₂³×C₇	—	4	2	no	—
209	C₂³×C₇	—	4	2	no	—
210	C₂³×C₇	—	4	2	no	—
211	C₂³×C₇	—	4	2	no	—
212	C₂³×C₇	C₄×D₄	1	2	yes	—
213	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
214	C₇×D₄	—	2	4	no	—
215	C₇×D₄	—	2	4	no	—
216	C₇×D₄	—	4	2	no	—
217	C₇×D₄	—	4	2	no	—
218	C₇×D₄	—	8	8	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	2	2	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	2	no	—
226	C₂×C₄×C₇	—	2	2	no	—
227	C₂×C₄×C₇	—	2	4	no	—
228	C₂×C₄×C₇	—	2	1	no	—
229	C₂×C₄×C₇	—	2	1	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	4	2	no	—
233	C₂×C₄×C₇	—	4	2	no	—
234	C₂×C₄×C₇	—	4	2	no	—
235	C₂×C₄×C₇	—	4	2	no	—
236	C₂×C₄×C₇	—	4	2	no	—
237	C₂×C₄×C₇	—	4	2	no	—
238	C₂×C₄×C₇	—	4	2	no	—
239	C₂×C₄×C₇	—	4	2	no	—
240	C₂×C₄×C₇	—	8	8	no	—
241	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₇	#121	1	2	yes	—
243	C₂×C₄×C₇	#121	1	2	yes	—
244	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
250	C₇×C₈	—	2	2	no	—
251	C₇×C₈	—	2	2	no	—
252	C₇×C₈	—	2	2	no	—
253	C₇×C₈	C₄×D₄	1	4	yes	—
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	C₂³×C₇	1	2	yes	—
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
258	C₂×D₈	—	2	2	no	—
259	C₂×D₈	—	2	2	no	—
260	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	complemented
264	C₂²×C₈	—	2	2	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
271	#121	—	2	4	no	—
272	#121	C₂×C₄×C₇	1	8	yes	complemented
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	#117	—	2	2	no	—
276	#117	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	#106	—	2	2	no	—
295	#106	C₂×C₄×C₇	1	4	yes	complemented
296	#102	—	2	4	no	—
297	#102	—	2	4	no	—
298	#102	C₂×C₄×C₇	1	8	yes	complemented
299	#97	—	2	2	no	—
300	#97	—	2	2	no	—
301	C₄×C₈	—	2	2	no	—
302	C₄×C₈	C₇×D₄	1	4	yes	complemented
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	C₂²×C₇	—	2	4	no	—
307	C₂²×C₇	—	2	2	no	—
308	C₂²×C₇	—	4	2	no	—
309	C₂²×C₇	—	4	1	no	—
310	C₂²×C₇	—	4	1	no	—
311	C₂²×C₇	—	4	4	no	—
312	C₂²×C₇	—	4	4	no	—
313	C₂²×C₇	—	4	4	no	—
314	C₂²×C₇	—	8	2	no	—
315	C₂²×C₇	—	8	2	no	—
316	C₂²×C₇	—	8	2	no	—
317	C₂²×C₇	—	8	2	no	—
318	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
319	C₂²×C₇	C₂×#121	1	1	yes	characteristic
320	C₂²×C₇	#532	1	1	yes	characteristic
321	C₂²×C₇	#576	1	2	yes	—
322	C₂²×C₇	#577	1	2	yes	—
323	C₄×C₇	—	2	2	no	—
324	C₄×C₇	—	2	2	no	—
325	C₄×C₇	—	2	2	no	—
326	C₄×C₇	—	4	4	no	—
327	C₄×C₇	—	4	1	no	—
328	C₄×C₇	—	4	1	no	—
329	C₄×C₇	—	8	2	no	—
330	C₄×C₇	—	8	2	no	—
331	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
332	C₄×C₇	C₄×#41	1	1	yes	characteristic
333	C₄×C₇	#525	1	1	yes	characteristic
334	C₄×C₇	#529	1	1	yes	characteristic
335	C₂⁴	—	2	2	no	—
336	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	8	2	no	—
344	C₂×D₄	—	8	2	no	—
345	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	8	2	no	—
355	C₂²×C₄	—	8	2	no	—
356	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
357	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₇×#41	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
364	D₈	—	2	8	no	—
365	M₁₆	—	2	8	no	—
366	C₂×C₈	—	2	8	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
374	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
375	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
376	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
377	C₂×C₈	C₇×#41	1	2	yes	—
378	C₂×C₈	C₇×#41	1	2	yes	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	8	2	no	—
387	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	8	2	no	—
393	C₂²⋊C₄	—	8	2	no	—
394	C₂²⋊C₄	—	8	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	8	2	no	—
398	C₄²	C₂×C₇×D₄	1	2	yes	—
399	C₄²	C₇×#41	1	2	yes	—
400	C₂×C₇	—	4	2	no	—
401	C₂×C₇	—	8	4	no	—
402	C₂×C₇	C₄×#121	1	1	yes	characteristic
403	C₂×C₇	#2946	1	2	yes	—
404	C₂×C₇	#3058	1	1	yes	characteristic
405	C₂×C₇	#3060	1	1	yes	characteristic
406	C₂×C₇	#3179	1	2	yes	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	C₄×C₇×D₄	1	2	yes	—
419	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
420	D₄	—	2	4	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	8	8	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	8	no	—
447	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
448	C₂×C₄	C₇×#121	1	2	yes	—
449	C₂×C₄	C₇×#121	1	2	yes	—
450	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
452	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
453	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
454	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
455	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	C₄×C₇×D₄	1	4	yes	—
460	C₇	#21536	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²	—	2	4	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
474	C₂²	C₂×C₇×#121	1	1	yes	characteristic
475	C₂²	C₇×#532	1	1	yes	characteristic
476	C₂²	C₇×#576	1	2	yes	—
477	C₂²	C₇×#577	1	2	yes	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	4	4	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	8	2	no	—
485	C₄	—	8	2	no	—
486	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
487	C₄	C₄×C₇×#41	1	1	yes	characteristic
488	C₄	C₇×#525	1	1	yes	characteristic
489	C₄	C₇×#529	1	1	yes	characteristic
490	C₂	—	4	2	no	—
491	C₂	—	8	4	no	—
492	C₂	C₄×C₇×#121	1	1	yes	characteristic
493	C₂	C₇×#2946	1	2	yes	—
494	C₂	C₇×#3058	1	1	yes	characteristic
495	C₂	C₇×#3060	1	1	yes	characteristic
496	C₂	C₇×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₇×D₈	C₂	semidirect
3. C₂×C₇×#405	C₂	semidirect
4. C₇×#2324	C₂	semidirect
5. C₇×#1972	C₂	semidirect
6. C₇×#1944	C₂	semidirect
7. C₇×#1934	C₂	semidirect
8. C₇×#1893	C₂	semidirect
9. C₇×#1809	C₂	semidirect
10. C₄×C₇×#106	C₂	semidirect
11. C₇×#1762	C₂	semidirect
18. C₇×#469	C₄	semidirect
42. #21536	C₇	direct (N × H)
52. C₂×C₇×M₁₆	C₂×C₄	semidirect
61. C₇×#121	C₂×C₄	semidirect
84. C₇×#106	C₂×C₄	semidirect
87. C₇×#102	C₂×C₄	semidirect
91. C₄×C₇×C₈	D₄	semidirect
96. C₂×C₄×D₈	C₂×C₇	semidirect
97. C₂×#405	C₂×C₇	semidirect
98. #2324	C₂×C₇	semidirect
99. #1972	C₂×C₇	semidirect
100. #1944	C₂×C₇	semidirect
101. #1934	C₂×C₇	semidirect
102. #1893	C₂×C₇	semidirect
103. #1809	C₂×C₇	semidirect
104. C₄×#106	C₂×C₇	semidirect
105. #1762	C₂×C₇	semidirect
177. #469	C₄×C₇	semidirect
263. C₂×M₁₆	C₂×C₄×C₇	semidirect
272. #121	C₂×C₄×C₇	semidirect
295. #106	C₂×C₄×C₇	semidirect
298. #102	C₂×C₄×C₇	semidirect
302. C₄×C₈	C₇×D₄	semidirect
460. C₇	#21536	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×#469	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#405	2
C₇×#2324	2
C₇×#1972	2
C₇×#1944	2
C₇×#1934	2
C₇×#1893	2
C₇×#1809	2
C₄×C₇×#106	2
C₇×#1762	2
#21536	7

Subgroups — C7×#21536 #13198752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21536 #13198752