Subgroups — C₇×#24711 #13201927

Order 1792.

828 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic
3	C₇×#2857	C₂	1	1	yes	maximal, characteristic
4	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
5	C₇×#2075	C₂	1	2	yes	maximal
6	C₇×#2035	C₂	1	2	yes	maximal
7	C₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1944	C₂	1	2	yes	maximal, complemented
10	C₇×#1935	C₂	1	2	yes	maximal, complemented
11	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
17	C₇×#477	—	2	4	no	—
18	C₇×#432	—	2	4	no	—
19	C₂×C₇×#107	C₂²	1	2	yes	—
20	C₂×C₇×#106	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×#103	C₂²	1	2	yes	—
24	C₂×C₇×#103	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₇×#97	C₂²	1	2	yes	—
27	C₇×#391	—	2	1	no	—
28	C₇×#391	C₂²	1	1	yes	characteristic
29	C₇×#389	—	2	1	no	—
30	C₇×#389	C₂²	1	1	yes	characteristic
31	C₇×#389	C₂²	1	2	yes	—
32	C₇×#387	—	2	1	no	—
33	C₇×#385	—	2	1	no	—
34	C₇×#384	C₂²	1	1	yes	characteristic
35	C₇×#380	—	2	1	no	—
36	C₇×#380	C₂²	1	2	yes	—
37	C₇×#380	C₂²	1	1	yes	characteristic
38	C₄×C₇×C₄⋊C₄	—	2	1	no	—
39	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
41	C₇×#340	C₂²	1	2	yes	—
42	C₇×#340	C₂²	1	2	yes	—
43	C₇×#340	C₂²	1	2	yes	—
44	C₇×#340	C₂²	1	2	yes	—
45	#24711	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₇×Q₈	—	2	1	no	—
47	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	2	yes	—
52	C₂²×C₇×C₈	C₂³	1	2	yes	—
53	C₇×C₄⋊Q₈	—	2	2	no	—
54	C₇×C₄⋊Q₈	—	2	2	no	—
55	C₇×C₂²⋊Q₈	—	2	2	no	—
56	C₇×C₂²⋊Q₈	—	2	2	no	—
57	C₇×C₂²⋊Q₈	—	4	4	no	—
58	C₄×C₇×Q₈	—	2	2	no	—
59	C₄×C₇×Q₈	—	2	2	no	—
60	C₂×C₇×C₄⋊C₄	—	2	1	no	—
61	C₂×C₇×C₄⋊C₄	—	2	1	no	—
62	C₂×C₇×C₄⋊C₄	—	2	1	no	—
63	C₂×C₇×C₄⋊C₄	—	2	1	no	—
64	C₂×C₇×C₄⋊C₄	—	2	1	no	—
65	C₂×C₇×C₄⋊C₄	—	2	1	no	—
66	C₂×C₇×C₄⋊C₄	—	2	2	no	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₇×C₄⋊C₄	C₂³	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	1	yes	characteristic
72	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₄²×C₇	—	2	2	no	—
76	C₂×C₄²×C₇	—	2	2	no	—
77	C₂×C₄²×C₇	—	2	1	no	—
78	C₂×C₄²×C₇	—	2	1	no	—
79	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₇×#107	—	2	4	no	—
84	C₇×#106	—	2	4	no	—
85	C₇×C₄⋊C₈	—	2	2	no	—
86	C₇×C₄⋊C₈	D₄	1	4	yes	—
87	C₇×#103	—	2	4	no	—
88	C₇×#103	—	2	4	no	—
89	C₇×C₂²⋊C₈	—	2	4	no	—
90	C₇×#97	—	2	4	no	—
91	C₇×#95	—	2	1	no	—
92	C₇×#95	—	2	1	no	—
93	C₇×#95	—	2	1	no	—
94	C₇×#95	—	2	1	no	—
95	C₇×#95	—	2	1	no	—
96	C₇×#95	—	2	2	no	—
97	C₇×#95	—	2	2	no	—
98	C₂×#477	C₂×C₇	1	1	yes	characteristic, complemented
99	C₂×#432	C₂×C₇	1	1	yes	characteristic
100	#2857	C₂×C₇	1	1	yes	characteristic
101	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
102	#2075	C₂×C₇	1	2	yes	—
103	#2035	C₂×C₇	1	2	yes	—
104	#1987	C₂×C₇	1	1	yes	characteristic, complemented
105	#1948	C₂×C₇	1	1	yes	characteristic, complemented
106	#1944	C₂×C₇	1	2	yes	complemented
107	#1935	C₂×C₇	1	2	yes	complemented
108	#1803	C₂×C₇	1	1	yes	characteristic, complemented
109	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
110	C₂×C₇×Q₈	—	2	1	no	—
111	C₂×C₇×Q₈	—	2	1	no	—
112	C₂×C₇×Q₈	—	2	1	no	—
113	C₂×C₇×Q₈	—	2	1	no	—
114	C₂×C₇×Q₈	—	2	1	no	—
115	C₂×C₇×Q₈	—	4	2	no	—
116	C₂×C₇×Q₈	—	4	2	no	—
117	C₂×C₇×Q₈	—	4	2	no	—
118	C₂×C₇×Q₈	#41	1	2	yes	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	1	no	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	2	1	no	—
127	C₂²×C₄×C₇	—	2	1	no	—
128	C₂²×C₄×C₇	—	2	1	no	—
129	C₂²×C₄×C₇	—	2	1	no	—
130	C₂²×C₄×C₇	—	2	1	no	—
131	C₂²×C₄×C₇	—	2	1	no	—
132	C₂²×C₄×C₇	—	2	1	no	—
133	C₂²×C₄×C₇	—	2	1	no	—
134	C₂²×C₄×C₇	—	2	2	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	4	1	no	—
137	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
143	C₂×C₇×C₈	—	2	2	no	—
144	C₂×C₇×C₈	—	2	2	no	—
145	C₂×C₇×C₈	—	2	2	no	—
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
149	C₇×C₄⋊C₄	—	2	4	no	—
150	C₇×C₄⋊C₄	—	2	1	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	1	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	2	1	no	—
156	C₇×C₄⋊C₄	—	2	2	no	—
157	C₇×C₄⋊C₄	—	2	1	no	—
158	C₇×C₄⋊C₄	—	2	1	no	—
159	C₇×C₄⋊C₄	—	4	2	no	—
160	C₇×C₄⋊C₄	—	4	2	no	—
161	C₇×C₄⋊C₄	—	4	4	no	—
162	C₇×C₄⋊C₄	—	4	2	no	—
163	C₇×C₄⋊C₄	—	4	2	no	—
164	C₇×C₄⋊C₄	—	4	2	no	—
165	C₇×C₄⋊C₄	#41	1	2	yes	—
166	C₇×C₂²⋊C₄	—	2	4	no	—
167	C₇×C₂²⋊C₄	—	4	2	no	—
168	C₇×C₂²⋊C₄	—	4	4	no	—
169	C₄²×C₇	—	2	2	no	—
170	C₄²×C₇	—	2	2	no	—
171	C₄²×C₇	—	2	1	no	—
172	C₄²×C₇	—	2	1	no	—
173	C₄²×C₇	—	4	2	no	—
174	C₄²×C₇	—	4	2	no	—
175	C₄²×C₇	C₂×D₄	1	2	yes	—
176	C₄²×C₇	#41	1	2	yes	—
177	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
178	C₂×C₂²⋊Q₈	—	2	1	no	—
179	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
180	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
181	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
182	#477	—	2	4	no	—
183	#432	—	2	4	no	—
184	C₂×#107	C₂²×C₇	1	2	yes	—
185	C₂×#106	C₂²×C₇	1	2	yes	—
186	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
188	C₂×#103	C₂²×C₇	1	2	yes	—
189	C₂×#103	C₂²×C₇	1	2	yes	—
190	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
191	C₂×#97	C₂²×C₇	1	2	yes	—
192	#391	—	2	1	no	—
193	#391	C₂²×C₇	1	1	yes	characteristic
194	#389	—	2	1	no	—
195	#389	C₂²×C₇	1	2	yes	—
196	#389	C₂²×C₇	1	1	yes	characteristic
197	#387	—	2	1	no	—
198	#385	—	2	1	no	—
199	#384	C₂²×C₇	1	1	yes	characteristic
200	#380	—	2	1	no	—
201	#380	C₂²×C₇	1	1	yes	characteristic
202	#380	C₂²×C₇	1	2	yes	—
203	C₄×C₄⋊C₄	—	2	1	no	—
204	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
205	C₄×C₂²⋊C₄	—	2	1	no	—
206	#340	C₂²×C₇	1	2	yes	—
207	#340	C₂²×C₇	1	2	yes	—
208	#340	C₂²×C₇	1	2	yes	—
209	#340	C₂²×C₇	1	2	yes	—
210	C₂³×C₇	—	2	1	no	—
211	C₂³×C₇	—	2	1	no	—
212	C₂³×C₇	—	2	1	no	—
213	C₂³×C₇	—	2	1	no	—
214	C₂³×C₇	—	2	1	no	—
215	C₂³×C₇	—	2	1	no	—
216	C₂³×C₇	AGL(1,ℤ/8)	1	2	yes	—
217	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
218	C₇×Q₈	—	2	2	no	—
219	C₇×Q₈	—	2	2	no	—
220	C₇×Q₈	—	4	1	no	—
221	C₇×Q₈	—	4	1	no	—
222	C₇×Q₈	—	8	4	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	1	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	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	—	4	4	no	—
237	C₂×C₄×C₇	—	4	1	no	—
238	C₂×C₄×C₇	—	4	1	no	—
239	C₂×C₄×C₇	—	4	1	no	—
240	C₂×C₄×C₇	—	4	1	no	—
241	C₂×C₄×C₇	—	4	1	no	—
242	C₂×C₄×C₇	—	4	1	no	—
243	C₂×C₄×C₇	—	4	1	no	—
244	C₂×C₄×C₇	—	4	1	no	—
245	C₂×C₄×C₇	—	4	4	no	—
246	C₂×C₄×C₇	—	4	1	no	—
247	C₂×C₄×C₇	—	4	2	no	—
248	C₂×C₄×C₇	—	4	2	no	—
249	C₂×C₄×C₇	—	4	1	no	—
250	C₂×C₄×C₇	—	4	2	no	—
251	C₂×C₄×C₇	—	4	2	no	—
252	C₂×C₄×C₇	—	4	1	no	—
253	C₂×C₄×C₇	—	4	1	no	—
254	C₂×C₄×C₇	—	4	1	no	—
255	C₂×C₄×C₇	—	4	2	no	—
256	C₂×C₄×C₇	—	4	1	no	—
257	C₂×C₄×C₇	—	4	2	no	—
258	C₂×C₄×C₇	#121	1	2	yes	—
259	C₂×C₄×C₇	#121	1	2	yes	—
260	C₂×C₄×C₇	#137	1	2	yes	—
261	C₂×C₄×C₇	#137	1	2	yes	—
262	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
267	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
268	C₇×C₈	—	2	4	no	—
269	C₇×C₈	—	4	2	no	—
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
272	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
273	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₇	1	2	yes	—
276	C₂²×C₈	C₂³×C₇	1	2	yes	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₂²⋊Q₈	—	2	2	no	—
280	C₂²⋊Q₈	—	2	2	no	—
281	C₂²⋊Q₈	—	4	4	no	—
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
304	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
307	#107	—	2	4	no	—
308	#106	—	2	4	no	—
309	C₄⋊C₈	—	2	2	no	—
310	C₄⋊C₈	C₇×D₄	1	4	yes	—
311	#103	—	2	4	no	—
312	#103	—	2	4	no	—
313	C₂²⋊C₈	—	2	4	no	—
314	#97	—	2	4	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	1	no	—
319	#95	—	2	1	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	C₂²×C₇	—	2	2	no	—
323	C₂²×C₇	—	2	2	no	—
324	C₂²×C₇	—	2	2	no	—
325	C₂²×C₇	—	4	1	no	—
326	C₂²×C₇	—	4	1	no	—
327	C₂²×C₇	—	4	1	no	—
328	C₂²×C₇	—	4	1	no	—
329	C₂²×C₇	C₂×#121	1	1	yes	characteristic
330	C₂²×C₇	#525	1	1	yes	characteristic
331	C₂²×C₇	#536	1	1	yes	characteristic
332	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
333	C₂²×C₇	C₂×#137	1	1	yes	characteristic
334	C₂²×C₇	C₂×#137	1	1	yes	characteristic
335	C₂²×C₇	#575	1	1	yes	characteristic
336	C₄×C₇	—	2	2	no	—
337	C₄×C₇	—	4	2	no	—
338	C₄×C₇	—	4	1	no	—
339	C₄×C₇	—	4	2	no	—
340	C₄×C₇	—	4	1	no	—
341	C₄×C₇	—	4	1	no	—
342	C₄×C₇	—	8	2	no	—
343	C₄×C₇	—	8	1	no	—
344	C₄×C₇	—	8	1	no	—
345	C₄×C₇	—	8	2	no	—
346	C₄×C₇	#470	1	4	yes	—
347	C₄×C₇	#547	1	1	yes	characteristic
348	C₄×C₇	#548	1	1	yes	characteristic
349	C₄×C₇	#552	1	1	yes	characteristic
350	C₄×C₇	#556	1	1	yes	characteristic
351	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	C₇×#41	1	2	yes	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	C₇×#41	1	2	yes	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	4	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	4	2	no	—
416	C₄²	—	4	2	no	—
417	C₄²	C₂×C₇×D₄	1	2	yes	—
418	C₄²	C₇×#41	1	2	yes	—
419	C₂×C₇	—	4	2	no	—
420	C₂×C₇	#2415	1	1	yes	characteristic
421	C₂×C₇	C₂×#470	1	1	yes	characteristic
422	C₂×C₇	#3055	1	1	yes	characteristic
423	C₂×C₇	#3112	1	1	yes	characteristic
424	C₂×C₇	#3116	1	1	yes	characteristic
425	C₂×C₇	#3237	1	1	yes	characteristic
426	C₂×C₇	#3238	1	1	yes	characteristic
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	C₇×AGL(1,ℤ/8)	1	2	yes	—
434	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	4	1	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	8	4	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	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	C₇×#121	1	2	yes	—
476	C₂×C₄	C₇×#121	1	2	yes	—
477	C₂×C₄	C₇×#137	1	2	yes	—
478	C₂×C₄	C₇×#137	1	2	yes	—
479	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
480	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
481	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
482	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
483	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
484	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
485	C₈	—	2	4	no	—
486	C₈	—	4	2	no	—
487	C₇	#24711	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	C₂×C₇×#121	1	1	yes	characteristic
496	C₂²	C₇×#525	1	1	yes	characteristic
497	C₂²	C₇×#536	1	1	yes	characteristic
498	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
499	C₂²	C₂×C₇×#137	1	1	yes	characteristic
500	C₂²	C₂×C₇×#137	1	1	yes	characteristic
501	C₂²	C₇×#575	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	2	no	—
508	C₄	—	8	1	no	—
509	C₄	—	8	2	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	2	no	—
512	C₄	C₇×#470	1	4	yes	—
513	C₄	C₇×#547	1	1	yes	characteristic
514	C₄	C₇×#548	1	1	yes	characteristic
515	C₄	C₇×#552	1	1	yes	characteristic
516	C₄	C₇×#556	1	1	yes	characteristic
517	C₂	—	4	2	no	—
518	C₂	C₇×#2415	1	1	yes	characteristic
519	C₂	C₂×C₇×#470	1	1	yes	characteristic
520	C₂	C₇×#3055	1	1	yes	characteristic
521	C₂	C₇×#3112	1	1	yes	characteristic
522	C₂	C₇×#3116	1	1	yes	characteristic
523	C₂	C₇×#3237	1	1	yes	characteristic
524	C₂	C₇×#3238	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#477	C₂	semidirect
7. C₇×#1987	C₂	semidirect
8. C₇×#1948	C₂	semidirect
9. C₇×#1944	C₂	semidirect
10. C₇×#1935	C₂	semidirect
11. C₇×#1803	C₂	semidirect
45. #24711	C₇	direct (N × H)
98. C₂×#477	C₂×C₇	semidirect
104. #1987	C₂×C₇	semidirect
105. #1948	C₂×C₇	semidirect
106. #1944	C₂×C₇	semidirect
107. #1935	C₂×C₇	semidirect
108. #1803	C₂×C₇	semidirect
487. C₇	#24711	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×#477	2
C₂×C₇×#432	2
C₇×#2857	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#2075	2
C₇×#2035	2
C₇×#1987	2
C₇×#1948	2
C₇×#1944	2
C₇×#1935	2
C₇×#1803	2
#24711	7

Subgroups — C7×#24711 #13201927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24711 #13201927