Subgroups — C₇×#21524 #13198740

Order 1792.

1066 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#466	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×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1936	C₂	1	2	yes	maximal, complemented
8	C₇×#1895	C₂	1	2	yes	maximal, complemented
9	C₇×#1808	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₇×#107	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×#466	C₄	1	8	yes	complemented
19	C₄×C₇×D₈	—	2	4	no	—
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#107	C₂²	1	1	yes	characteristic
22	C₂×C₇×#107	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	#21524	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	—	2	2	no	—
53	C₂²×C₇×C₈	—	2	2	no	—
54	C₂²×C₇×C₈	—	2	2	no	—
55	C₂²×C₇×C₈	C₂×C₄	1	4	yes	complemented
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×#107	—	2	2	no	—
84	C₇×#107	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×#466	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	#1970	C₂×C₇	1	1	yes	characteristic, complemented
100	#1942	C₂×C₇	1	1	yes	characteristic, complemented
101	#1936	C₂×C₇	1	2	yes	complemented
102	#1895	C₂×C₇	1	2	yes	complemented
103	#1808	C₂×C₇	1	1	yes	characteristic, complemented
104	C₄×#107	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	1	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	8	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	#466	C₄×C₇	1	8	yes	complemented
178	C₄×D₈	—	2	4	no	—
179	C₂×#107	C₂²×C₇	1	1	yes	characteristic
180	C₂×#107	C₂²×C₇	1	1	yes	characteristic
181	C₂×#107	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	1	no	—
204	C₂³×C₇	—	2	1	no	—
205	C₂³×C₇	—	2	1	no	—
206	C₂³×C₇	—	2	1	no	—
207	C₂³×C₇	—	2	4	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	—	4	2	no	—
213	C₂³×C₇	—	4	2	no	—
214	C₂³×C₇	C₄×D₄	1	2	yes	—
215	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
216	C₇×D₄	—	2	4	no	—
217	C₇×D₄	—	2	4	no	—
218	C₇×D₄	—	4	2	no	—
219	C₇×D₄	—	4	2	no	—
220	C₇×D₄	—	8	8	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	1	no	—
225	C₂×C₄×C₇	—	2	1	no	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	2	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	4	no	—
232	C₂×C₄×C₇	—	2	1	no	—
233	C₂×C₄×C₇	—	2	1	no	—
234	C₂×C₄×C₇	—	2	1	no	—
235	C₂×C₄×C₇	—	2	1	no	—
236	C₂×C₄×C₇	—	2	1	no	—
237	C₂×C₄×C₇	—	2	1	no	—
238	C₂×C₄×C₇	—	4	2	no	—
239	C₂×C₄×C₇	—	4	2	no	—
240	C₂×C₄×C₇	—	4	2	no	—
241	C₂×C₄×C₇	—	4	2	no	—
242	C₂×C₄×C₇	—	4	2	no	—
243	C₂×C₄×C₇	—	4	2	no	—
244	C₂×C₄×C₇	—	4	2	no	—
245	C₂×C₄×C₇	—	4	2	no	—
246	C₂×C₄×C₇	—	8	8	no	—
247	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
248	C₂×C₄×C₇	#121	1	2	yes	—
249	C₂×C₄×C₇	#121	1	2	yes	—
250	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
256	C₇×C₈	—	2	2	no	—
257	C₇×C₈	—	2	2	no	—
258	C₇×C₈	—	2	2	no	—
259	C₇×C₈	C₄×D₄	1	4	yes	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	C₂³×C₇	1	2	yes	—
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
264	C₂×D₈	—	2	2	no	—
265	C₂×D₈	—	2	2	no	—
266	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	C₂×C₄×C₇	1	4	yes	complemented
273	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
277	#121	—	2	4	no	—
278	#121	C₂×C₄×C₇	1	8	yes	complemented
279	C₄×D₄	—	2	4	no	—
280	C₄×D₄	—	2	4	no	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
299	#107	—	2	2	no	—
300	#107	—	2	2	no	—
301	#107	C₂×C₄×C₇	1	4	yes	complemented
302	#102	—	2	4	no	—
303	#102	—	2	4	no	—
304	#102	C₂×C₄×C₇	1	8	yes	complemented
305	#97	—	2	2	no	—
306	#97	—	2	2	no	—
307	C₄×C₈	—	2	2	no	—
308	C₄×C₈	C₇×D₄	1	4	yes	complemented
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	C₂²×C₇	—	2	2	no	—
313	C₂²×C₇	—	2	2	no	—
314	C₂²×C₇	—	2	2	no	—
315	C₂²×C₇	—	4	1	no	—
316	C₂²×C₇	—	4	1	no	—
317	C₂²×C₇	—	4	1	no	—
318	C₂²×C₇	—	4	1	no	—
319	C₂²×C₇	—	4	4	no	—
320	C₂²×C₇	—	4	4	no	—
321	C₂²×C₇	—	4	4	no	—
322	C₂²×C₇	—	8	2	no	—
323	C₂²×C₇	—	8	2	no	—
324	C₂²×C₇	—	8	2	no	—
325	C₂²×C₇	—	8	2	no	—
326	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
327	C₂²×C₇	C₂×#121	1	1	yes	characteristic
328	C₂²×C₇	#532	1	1	yes	characteristic
329	C₂²×C₇	#576	1	1	yes	characteristic
330	C₂²×C₇	#576	1	1	yes	characteristic
331	C₂²×C₇	#576	1	1	yes	characteristic
332	C₂²×C₇	#578	1	1	yes	characteristic
333	C₄×C₇	—	2	2	no	—
334	C₄×C₇	—	2	2	no	—
335	C₄×C₇	—	2	2	no	—
336	C₄×C₇	—	4	4	no	—
337	C₄×C₇	—	4	1	no	—
338	C₄×C₇	—	4	1	no	—
339	C₄×C₇	—	8	2	no	—
340	C₄×C₇	—	8	2	no	—
341	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
342	C₄×C₇	C₄×#41	1	1	yes	characteristic
343	C₄×C₇	#525	1	1	yes	characteristic
344	C₄×C₇	#529	1	1	yes	characteristic
345	C₂⁴	—	2	2	no	—
346	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	8	2	no	—
354	C₂×D₄	—	8	2	no	—
355	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	8	2	no	—
365	C₂²×C₄	—	8	2	no	—
366	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
367	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
372	C₂²×C₄	C₇×#41	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
374	D₈	—	2	8	no	—
375	M₁₆	—	2	8	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	8	no	—
383	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
384	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
385	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
386	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
387	C₂×C₈	C₇×#41	1	2	yes	—
388	C₂×C₈	C₇×#41	1	2	yes	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	8	2	no	—
397	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
398	C₂²⋊C₄	—	2	8	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₂²⋊C₄	—	8	2	no	—
403	C₂²⋊C₄	—	8	2	no	—
404	C₂²⋊C₄	—	8	2	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	8	2	no	—
408	C₄²	C₂×C₇×D₄	1	2	yes	—
409	C₄²	C₇×#41	1	2	yes	—
410	C₂×C₇	—	4	2	no	—
411	C₂×C₇	—	8	4	no	—
412	C₂×C₇	C₄×#121	1	1	yes	characteristic
413	C₂×C₇	#2948	1	1	yes	characteristic
414	C₂×C₇	#2951	1	1	yes	characteristic
415	C₂×C₇	#3058	1	1	yes	characteristic
416	C₂×C₇	#3061	1	1	yes	characteristic
417	C₂×C₇	#3175	1	1	yes	characteristic
418	C₂×C₇	#3176	1	1	yes	characteristic
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	C₄×C₇×D₄	1	2	yes	—
433	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
434	D₄	—	2	4	no	—
435	D₄	—	2	4	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	2	no	—
438	D₄	—	8	8	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	8	8	no	—
465	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
466	C₂×C₄	C₇×#121	1	2	yes	—
467	C₂×C₄	C₇×#121	1	2	yes	—
468	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
470	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
471	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
472	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
473	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	C₄×C₇×D₄	1	4	yes	—
478	C₇	#21524	1	1	yes	characteristic, direct product factor, Sylow
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
494	C₂²	C₂×C₇×#121	1	1	yes	characteristic
495	C₂²	C₇×#532	1	1	yes	characteristic
496	C₂²	C₇×#576	1	1	yes	characteristic
497	C₂²	C₇×#576	1	1	yes	characteristic
498	C₂²	C₇×#576	1	1	yes	characteristic
499	C₂²	C₇×#578	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	1	no	—
506	C₄	—	8	2	no	—
507	C₄	—	8	2	no	—
508	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
509	C₄	C₄×C₇×#41	1	1	yes	characteristic
510	C₄	C₇×#525	1	1	yes	characteristic
511	C₄	C₇×#529	1	1	yes	characteristic
512	C₂	—	4	2	no	—
513	C₂	—	8	4	no	—
514	C₂	C₄×C₇×#121	1	1	yes	characteristic
515	C₂	C₇×#2948	1	1	yes	characteristic
516	C₂	C₇×#2951	1	1	yes	characteristic
517	C₂	C₇×#3058	1	1	yes	characteristic
518	C₂	C₇×#3061	1	1	yes	characteristic
519	C₂	C₇×#3175	1	1	yes	characteristic
520	C₂	C₇×#3176	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	C₂×C₇×#466	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×#1970	C₂	semidirect
6. C₇×#1942	C₂	semidirect
7. C₇×#1936	C₂	semidirect
8. C₇×#1895	C₂	semidirect
9. C₇×#1808	C₂	semidirect
10. C₄×C₇×#107	C₂	semidirect
11. C₇×#1762	C₂	semidirect
18. C₇×#466	C₄	semidirect
42. #21524	C₇	direct (N × H)
55. C₂²×C₇×C₈	C₂×C₄	semidirect
61. C₇×#121	C₂×C₄	semidirect
84. C₇×#107	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. #1970	C₂×C₇	semidirect
100. #1942	C₂×C₇	semidirect
101. #1936	C₂×C₇	semidirect
102. #1895	C₂×C₇	semidirect
103. #1808	C₂×C₇	semidirect
104. C₄×#107	C₂×C₇	semidirect
105. #1762	C₂×C₇	semidirect
177. #466	C₄×C₇	semidirect
272. C₂²×C₈	C₂×C₄×C₇	semidirect
278. #121	C₂×C₄×C₇	semidirect
301. #107	C₂×C₄×C₇	semidirect
304. #102	C₂×C₄×C₇	semidirect
308. C₄×C₈	C₇×D₄	semidirect
478. C₇	#21524	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×#466	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#405	2
C₇×#2324	2
C₇×#1970	2
C₇×#1942	2
C₇×#1936	2
C₇×#1895	2
C₇×#1808	2
C₄×C₇×#107	2
C₇×#1762	2
#21524	7

Subgroups — C7×#21524 #13198740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21524 #13198740