Subgroups — C₇×#22663 #13199879

Order 1792.

1022 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
3	C₇×#2354	C₂	1	1	yes	maximal, characteristic
4	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1854	C₂	1	2	yes	maximal, complemented
8	C₇×#1853	C₂	1	2	yes	maximal, complemented
9	C₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1809	C₂	1	2	yes	maximal, complemented
11	C₄×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₂×C₄×C₇×D₄	—	2	1	no	—
14	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₇×#117	C₂²	1	2	yes	—
16	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
17	C₇×#436	C₄	1	8	yes	complemented
18	C₇×#428	—	2	8	no	—
19	C₂×C₇×#107	C₂²	1	2	yes	—
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#107	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	2	yes	—
23	C₂×C₇×#106	C₂²	1	2	yes	—
24	C₂×C₇×#106	C₂²	1	2	yes	—
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₇×#390	—	2	1	no	—
29	C₇×#389	—	2	1	no	—
30	C₇×#388	—	2	2	no	—
31	C₇×#385	—	2	2	no	—
32	C₇×#384	C₂²	1	1	yes	characteristic
33	C₇×#384	C₂²	1	1	yes	characteristic
34	C₇×#380	C₂²	1	2	yes	—
35	C₇×#380	C₂²	1	2	yes	—
36	C₄×C₇×C₄⋊C₄	—	2	1	no	—
37	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₇×#340	C₂²	1	1	yes	characteristic
40	C₇×#340	C₂²	1	1	yes	characteristic
41	C₇×#340	C₂²	1	2	yes	—
42	C₇×#340	C₂²	1	2	yes	—
43	#22663	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₇	—	2	2	no	—
46	C₂³×C₄×C₇	C₂³	1	2	yes	—
47	C₂×C₇×M₁₆	—	2	4	no	—
48	C₂×C₇×M₁₆	—	2	4	no	—
49	C₂×C₇×M₁₆	C₂×C₄	1	8	yes	complemented
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	2	yes	—
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₄×C₇×D₄	—	4	4	no	—
54	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
55	C₄×C₇×D₄	Q₈	1	4	yes	—
56	C₇×#117	—	2	4	no	—
57	C₇×#117	—	4	2	no	—
58	C₂×C₇×C₄⋊C₄	—	2	4	no	—
59	C₂×C₇×C₄⋊C₄	—	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	—	4	2	no	—
65	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
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	C₂³	1	1	yes	characteristic
80	C₇×#107	—	2	2	no	—
81	C₇×#107	—	2	4	no	—
82	C₇×#107	D₄	1	4	yes	complemented
83	C₇×#106	—	2	4	no	—
84	C₇×#106	—	2	4	no	—
85	C₇×#106	—	4	2	no	—
86	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
87	C₇×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
88	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
89	C₇×#95	—	2	2	no	—
90	C₇×#95	—	2	1	no	—
91	C₇×#95	—	2	1	no	—
92	C₇×#95	—	2	2	no	—
93	C₂×#436	C₂×C₇	1	1	yes	characteristic
94	C₂×#428	C₂×C₇	1	2	yes	complemented
95	#2354	C₂×C₇	1	1	yes	characteristic
96	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
97	#1948	C₂×C₇	1	1	yes	characteristic, complemented
98	#1947	C₂×C₇	1	1	yes	characteristic, complemented
99	#1854	C₂×C₇	1	2	yes	complemented
100	#1853	C₂×C₇	1	2	yes	complemented
101	#1844	C₂×C₇	1	1	yes	characteristic, complemented
102	#1809	C₂×C₇	1	2	yes	complemented
103	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
104	C₂⁴×C₇	C₂×D₄	1	2	yes	—
105	C₂×C₇×D₄	—	2	2	no	—
106	C₂×C₇×D₄	—	2	2	no	—
107	C₂×C₇×D₄	C₄⋊C₄	1	4	yes	—
108	C₂²×C₄×C₇	—	2	2	no	—
109	C₂²×C₄×C₇	—	2	2	no	—
110	C₂²×C₄×C₇	—	2	2	no	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	1	no	—
115	C₂²×C₄×C₇	—	2	1	no	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	4	4	no	—
119	C₂²×C₄×C₇	—	4	4	no	—
120	C₂²×C₄×C₇	—	8	2	no	—
121	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
126	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
127	C₇×M₁₆	—	2	16	no	—
128	C₂×C₇×C₈	—	2	2	no	—
129	C₂×C₇×C₈	—	2	2	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
134	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
136	C₂×C₇×C₈	#41	1	2	yes	—
137	C₇×C₄⋊C₄	—	2	1	no	—
138	C₇×C₄⋊C₄	—	2	1	no	—
139	C₇×C₄⋊C₄	—	2	2	no	—
140	C₇×C₄⋊C₄	—	2	2	no	—
141	C₇×C₄⋊C₄	—	2	1	no	—
142	C₇×C₄⋊C₄	—	2	1	no	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	1	no	—
146	C₇×C₄⋊C₄	—	2	1	no	—
147	C₇×C₄⋊C₄	—	4	4	no	—
148	C₇×C₄⋊C₄	—	4	2	no	—
149	C₇×C₄⋊C₄	—	4	2	no	—
150	C₇×C₄⋊C₄	—	8	1	no	—
151	C₇×C₄⋊C₄	—	8	1	no	—
152	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
153	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
155	C₇×C₂²⋊C₄	—	4	4	no	—
156	C₇×C₂²⋊C₄	—	4	4	no	—
157	C₇×C₂²⋊C₄	—	8	2	no	—
158	C₇×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
159	C₄²×C₇	—	4	4	no	—
160	C₄²×C₇	—	4	2	no	—
161	C₄²×C₇	—	4	2	no	—
162	C₄²×C₇	C₂²×C₄	1	2	yes	—
163	C₄²×C₇	C₂×Q₈	1	2	yes	—
164	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
165	C₂×C₄×D₄	—	2	1	no	—
166	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
167	C₂×#117	C₂²×C₇	1	2	yes	—
168	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
169	#436	C₄×C₇	1	8	yes	complemented
170	#428	—	2	8	no	—
171	C₂×#107	C₂²×C₇	1	1	yes	characteristic
172	C₂×#107	C₂²×C₇	1	2	yes	—
173	C₂×#107	C₂²×C₇	1	1	yes	characteristic
174	C₂×#106	C₂²×C₇	1	2	yes	—
175	C₂×#106	C₂²×C₇	1	2	yes	—
176	C₂×#106	C₂²×C₇	1	2	yes	—
177	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
178	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
179	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
180	#390	—	2	1	no	—
181	#389	—	2	1	no	—
182	#388	—	2	2	no	—
183	#385	—	2	2	no	—
184	#384	C₂²×C₇	1	1	yes	characteristic
185	#384	C₂²×C₇	1	1	yes	characteristic
186	#380	C₂²×C₇	1	2	yes	—
187	#380	C₂²×C₇	1	2	yes	—
188	C₄×C₄⋊C₄	—	2	1	no	—
189	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
190	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
191	#340	C₂²×C₇	1	2	yes	—
192	#340	C₂²×C₇	1	2	yes	—
193	#340	C₂²×C₇	1	1	yes	characteristic
194	#340	C₂²×C₇	1	1	yes	characteristic
195	C₂³×C₇	—	2	2	no	—
196	C₂³×C₇	—	2	2	no	—
197	C₂³×C₇	—	2	2	no	—
198	C₂³×C₇	—	2	2	no	—
199	C₂³×C₇	—	2	2	no	—
200	C₂³×C₇	—	2	2	no	—
201	C₂³×C₇	C₂×C₄⋊C₄	1	4	yes	—
202	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
203	C₇×D₄	—	2	8	no	—
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	4	no	—
209	C₂×C₄×C₇	—	2	4	no	—
210	C₂×C₄×C₇	—	2	4	no	—
211	C₂×C₄×C₇	—	2	4	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	4	1	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	1	no	—
217	C₂×C₄×C₇	—	4	1	no	—
218	C₂×C₄×C₇	—	4	2	no	—
219	C₂×C₄×C₇	—	4	2	no	—
220	C₂×C₄×C₇	—	4	1	no	—
221	C₂×C₄×C₇	—	4	1	no	—
222	C₂×C₄×C₇	—	4	1	no	—
223	C₂×C₄×C₇	—	4	1	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	4	2	no	—
226	C₂×C₄×C₇	—	4	1	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	4	2	no	—
229	C₂×C₄×C₇	—	4	1	no	—
230	C₂×C₄×C₇	—	8	8	no	—
231	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
232	C₂×C₄×C₇	C₂×C₄⋊C₄	1	4	yes	—
233	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
234	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
235	C₂×C₄×C₇	#137	1	2	yes	—
236	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
242	C₇×C₈	—	2	4	no	—
243	C₇×C₈	—	2	2	no	—
244	C₇×C₈	C₄×D₄	1	4	yes	complemented
245	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
246	C₂³×C₄	—	2	2	no	—
247	C₂³×C₄	C₂³×C₇	1	2	yes	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	—	2	4	no	—
250	C₂×M₁₆	C₂×C₄×C₇	1	8	yes	complemented
251	C₂²×C₈	C₂³×C₇	1	2	yes	—
252	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
254	C₄×D₄	—	4	4	no	—
255	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
256	C₄×D₄	C₇×Q₈	1	4	yes	—
257	#117	—	2	4	no	—
258	#117	—	4	2	no	—
259	C₂×C₄⋊C₄	—	2	4	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	4	2	no	—
266	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
281	#107	—	2	2	no	—
282	#107	—	2	4	no	—
283	#107	C₇×D₄	1	4	yes	complemented
284	#106	—	2	4	no	—
285	#106	—	2	4	no	—
286	#106	—	4	2	no	—
287	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
288	C₂²⋊C₈	C₂×C₄×C₇	1	8	yes	complemented
289	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
290	#95	—	2	2	no	—
291	#95	—	2	1	no	—
292	#95	—	2	1	no	—
293	#95	—	2	2	no	—
294	C₂²×C₇	—	2	4	no	—
295	C₂²×C₇	—	2	4	no	—
296	C₂²×C₇	—	2	4	no	—
297	C₂²×C₇	—	4	2	no	—
298	C₂²×C₇	—	4	2	no	—
299	C₂²×C₇	—	4	2	no	—
300	C₂²×C₇	—	4	2	no	—
301	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
302	C₂²×C₇	D₄²	1	1	yes	characteristic
303	C₂²×C₇	#547	1	1	yes	characteristic
304	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
305	C₂²×C₇	C₂×#137	1	1	yes	characteristic
306	C₂²×C₇	#577	1	1	yes	characteristic
307	C₂²×C₇	#577	1	1	yes	characteristic
308	C₄×C₇	—	2	4	no	—
309	C₄×C₇	—	2	2	no	—
310	C₄×C₇	—	4	2	no	—
311	C₄×C₇	—	4	2	no	—
312	C₄×C₇	—	8	1	no	—
313	C₄×C₇	—	8	1	no	—
314	C₄×C₇	—	8	2	no	—
315	C₄×C₇	—	8	2	no	—
316	C₄×C₇	#428	1	4	yes	complemented
317	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
318	C₄×C₇	#520	1	1	yes	characteristic
319	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
320	C₄×C₇	#554	1	1	yes	characteristic
321	C₂⁴	C₂×C₇×D₄	1	2	yes	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	C₇×C₄⋊C₄	1	4	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
339	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
340	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
343	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
344	M₁₆	—	2	16	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
350	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
351	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
352	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
353	C₂×C₈	C₇×#41	1	2	yes	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	8	1	no	—
368	C₄⋊C₄	—	8	1	no	—
369	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
370	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
371	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	8	2	no	—
375	C₂²⋊C₄	C₇×C₄⋊C₄	1	8	yes	—
376	C₄²	—	4	4	no	—
377	C₄²	—	4	2	no	—
378	C₄²	—	4	2	no	—
379	C₄²	C₂²×C₄×C₇	1	2	yes	—
380	C₄²	C₂×C₇×Q₈	1	2	yes	—
381	C₂×C₇	—	4	4	no	—
382	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
383	C₂×C₇	C₂×#428	1	1	yes	characteristic
384	C₂×C₇	#2912	1	1	yes	characteristic
385	C₂×C₇	#3272	1	1	yes	characteristic
386	C₂×C₇	#3278	1	1	yes	characteristic
387	C₂×C₇	#3354	1	1	yes	characteristic
388	C₂×C₇	#3356	1	1	yes	characteristic
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	C₂×C₇×C₄⋊C₄	1	4	yes	—
396	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
397	D₄	—	2	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	8	8	no	—
425	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
426	C₂×C₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
427	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
428	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
429	C₂×C₄	C₇×#137	1	2	yes	—
430	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
431	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
432	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
433	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
434	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
436	C₈	—	2	4	no	—
437	C₈	—	2	2	no	—
438	C₈	C₄×C₇×D₄	1	4	yes	complemented
439	C₇	#22663	1	1	yes	characteristic, direct product factor, Sylow
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
448	C₂²	C₇×D₄²	1	1	yes	characteristic
449	C₂²	C₇×#547	1	1	yes	characteristic
450	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂²	C₂×C₇×#137	1	1	yes	characteristic
452	C₂²	C₇×#577	1	1	yes	characteristic
453	C₂²	C₇×#577	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	4	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	C₇×#428	1	4	yes	complemented
463	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
464	C₄	C₇×#520	1	1	yes	characteristic
465	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
466	C₄	C₇×#554	1	1	yes	characteristic
467	C₂	—	4	4	no	—
468	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
469	C₂	C₂×C₇×#428	1	1	yes	characteristic
470	C₂	C₇×#2912	1	1	yes	characteristic
471	C₂	C₇×#3272	1	1	yes	characteristic
472	C₂	C₇×#3278	1	1	yes	characteristic
473	C₂	C₇×#3354	1	1	yes	characteristic
474	C₂	C₇×#3356	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	C₂²×C₇×D₄	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#428	C₂	semidirect
5. C₇×#1948	C₂	semidirect
6. C₇×#1947	C₂	semidirect
7. C₇×#1854	C₂	semidirect
8. C₇×#1853	C₂	semidirect
9. C₇×#1844	C₂	semidirect
10. C₇×#1809	C₂	semidirect
11. C₄×C₇×#107	C₂	semidirect
17. C₇×#436	C₄	semidirect
43. #22663	C₇	direct (N × H)
49. C₂×C₇×M₁₆	C₂×C₄	semidirect
82. C₇×#107	D₄	semidirect
86. C₇×C₄⋊C₈	C₂×C₄	semidirect
87. C₇×C₂²⋊C₈	C₂×C₄	semidirect
88. C₄×C₇×C₈	C₂×C₄	semidirect
94. C₂×#428	C₂×C₇	semidirect
97. #1948	C₂×C₇	semidirect
98. #1947	C₂×C₇	semidirect
99. #1854	C₂×C₇	semidirect
100. #1853	C₂×C₇	semidirect
101. #1844	C₂×C₇	semidirect
102. #1809	C₂×C₇	semidirect
103. C₄×#107	C₂×C₇	semidirect
169. #436	C₄×C₇	semidirect
244. C₇×C₈	C₄×D₄	semidirect
250. C₂×M₁₆	C₂×C₄×C₇	semidirect
283. #107	C₇×D₄	semidirect
287. C₄⋊C₈	C₂×C₄×C₇	semidirect
288. C₂²⋊C₈	C₂×C₄×C₇	semidirect
289. C₄×C₈	C₂×C₄×C₇	semidirect
316. C₄×C₇	#428	semidirect
438. C₈	C₄×C₇×D₄	semidirect
439. C₇	#22663	direct (N × H)
462. C₄	C₇×#428	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#436	2
C₂×C₇×#428	2
C₇×#2354	2
C₇×D₄×C₄⋊C₄	2
C₇×#1948	2
C₇×#1947	2
C₇×#1854	2
C₇×#1853	2
C₇×#1844	2
C₇×#1809	2
C₄×C₇×#107	2
#22663	7

Subgroups — C7×#22663 #13199879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22663 #13199879