Subgroups — C₇×#22172 #13199388

Order 1792.

1004 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic
4	C₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#336	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×#121	C₄	1	1	yes	characteristic
21	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
25	C₇×#435	—	2	4	no	—
26	C₇×C₈×D₄	—	2	4	no	—
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₇×#390	C₄	1	1	yes	characteristic
42	C₇×#389	C₄	1	1	yes	characteristic
43	C₇×#388	C₄	1	1	yes	characteristic
44	C₇×#388	C₄	1	1	yes	characteristic
45	C₇×#386	C₄	1	1	yes	characteristic
46	C₇×#386	C₄	1	1	yes	characteristic
47	C₇×#380	C₄	1	1	yes	characteristic
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₇×#336	C₂²	1	1	yes	characteristic
52	C₇×#336	C₂²	1	1	yes	characteristic
53	C₇×#336	C₂²	1	1	yes	characteristic
54	C₇×#336	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	C₇×#336	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	#22172	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₇×M₁₆	—	2	2	no	—
71	C₂×C₇×M₁₆	—	4	1	no	—
72	C₂×C₇×M₁₆	—	4	1	no	—
73	C₂²×C₇×C₈	—	2	2	no	—
74	C₂²×C₇×C₈	—	2	2	no	—
75	C₂²×C₇×C₈	—	4	1	no	—
76	C₂²×C₇×C₈	—	4	1	no	—
77	C₂²×C₇×C₈	—	4	1	no	—
78	C₂²×C₇×C₈	—	4	1	no	—
79	C₂²×C₇×C₈	—	4	1	no	—
80	C₂²×C₇×C₈	—	4	1	no	—
81	C₂²×C₇×C₈	D₄	1	4	yes	complemented
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₇×#121	—	2	4	no	—
91	C₄×C₇×D₄	—	2	2	no	—
92	C₄×C₇×D₄	—	2	2	no	—
93	C₄×C₇×D₄	—	2	2	no	—
94	C₄×C₇×D₄	—	2	2	no	—
95	C₄×C₇×D₄	—	4	1	no	—
96	C₄×C₇×D₄	—	4	1	no	—
97	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₇	—	4	1	no	—
113	C₂×C₄²×C₇	—	4	1	no	—
114	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
120	C₇×C₄⋊C₈	—	2	2	no	—
121	C₇×C₄⋊C₈	—	2	2	no	—
122	C₇×C₄⋊C₈	—	4	1	no	—
123	C₇×C₄⋊C₈	—	4	1	no	—
124	C₇×C₂²⋊C₈	—	2	2	no	—
125	C₇×C₂²⋊C₈	—	2	2	no	—
126	C₇×C₂²⋊C₈	—	2	2	no	—
127	C₇×C₂²⋊C₈	—	2	2	no	—
128	C₇×C₂²⋊C₈	—	4	1	no	—
129	C₇×C₂²⋊C₈	—	4	1	no	—
130	C₇×C₂²⋊C₈	—	4	1	no	—
131	C₇×C₂²⋊C₈	—	4	1	no	—
132	C₇×#97	—	2	2	no	—
133	C₄×C₇×C₈	—	2	2	no	—
134	C₇×#95	C₂×C₄	1	1	yes	characteristic
135	C₇×#95	C₂×C₄	1	1	yes	characteristic
136	C₇×#95	C₂×C₄	1	1	yes	characteristic
137	C₇×#95	C₂×C₄	1	1	yes	characteristic
138	C₇×#95	C₂×C₄	1	1	yes	characteristic
139	C₇×#95	C₂×C₄	1	1	yes	characteristic
140	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
141	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
142	C₄×#121	C₂×C₇	1	1	yes	characteristic
143	#1924	C₂×C₇	1	1	yes	characteristic, complemented
144	#1923	C₂×C₇	1	1	yes	characteristic, complemented
145	#1917	C₂×C₇	1	1	yes	characteristic, complemented
146	#1916	C₂×C₇	1	1	yes	characteristic, complemented
147	#1870	C₂×C₇	1	1	yes	characteristic, complemented
148	#1869	C₂×C₇	1	1	yes	characteristic, complemented
149	#1869	C₂×C₇	1	1	yes	characteristic, complemented
150	#1869	C₂×C₇	1	1	yes	characteristic, complemented
151	#1851	C₂×C₇	1	1	yes	characteristic, complemented
152	#1850	C₂×C₇	1	1	yes	characteristic, complemented
153	#1797	C₂×C₇	1	1	yes	characteristic, complemented
154	C₂×#336	C₂×C₇	1	1	yes	characteristic, complemented
155	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
156	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
157	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₇×D₄	—	2	2	no	—
159	C₂×C₇×D₄	—	2	2	no	—
160	C₂×C₇×D₄	—	2	2	no	—
161	C₂×C₇×D₄	—	2	2	no	—
162	C₂×C₇×D₄	—	2	2	no	—
163	C₂×C₇×D₄	—	2	2	no	—
164	C₂×C₇×D₄	—	2	2	no	—
165	C₂×C₇×D₄	—	4	1	no	—
166	C₂×C₇×D₄	M₁₆	1	4	yes	complemented
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	1	no	—
171	C₂²×C₄×C₇	—	2	2	no	—
172	C₂²×C₄×C₇	—	2	2	no	—
173	C₂²×C₄×C₇	—	2	2	no	—
174	C₂²×C₄×C₇	—	2	2	no	—
175	C₂²×C₄×C₇	—	2	1	no	—
176	C₂²×C₄×C₇	—	2	1	no	—
177	C₂²×C₄×C₇	—	2	1	no	—
178	C₂²×C₄×C₇	—	2	1	no	—
179	C₂²×C₄×C₇	—	2	1	no	—
180	C₂²×C₄×C₇	—	2	1	no	—
181	C₂²×C₄×C₇	—	2	1	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	4	1	no	—
188	C₂²×C₄×C₇	—	4	1	no	—
189	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₇	#41	1	2	yes	—
202	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
203	C₇×M₁₆	—	4	4	no	—
204	C₂×C₇×C₈	—	2	1	no	—
205	C₂×C₇×C₈	—	2	1	no	—
206	C₂×C₇×C₈	—	2	1	no	—
207	C₂×C₇×C₈	—	2	1	no	—
208	C₂×C₇×C₈	—	2	1	no	—
209	C₂×C₇×C₈	—	2	1	no	—
210	C₂×C₇×C₈	—	2	1	no	—
211	C₂×C₇×C₈	—	2	1	no	—
212	C₂×C₇×C₈	—	2	1	no	—
213	C₂×C₇×C₈	—	2	1	no	—
214	C₂×C₇×C₈	—	2	1	no	—
215	C₂×C₇×C₈	—	2	1	no	—
216	C₂×C₇×C₈	—	2	1	no	—
217	C₂×C₇×C₈	—	2	1	no	—
218	C₂×C₇×C₈	—	2	1	no	—
219	C₂×C₇×C₈	—	2	1	no	—
220	C₂×C₇×C₈	—	2	1	no	—
221	C₂×C₇×C₈	—	2	1	no	—
222	C₂×C₇×C₈	—	2	1	no	—
223	C₂×C₇×C₈	—	2	1	no	—
224	C₂×C₇×C₈	—	2	1	no	—
225	C₂×C₇×C₈	—	2	1	no	—
226	C₂×C₇×C₈	—	4	4	no	—
227	C₂×C₇×C₈	—	4	4	no	—
228	C₂×C₇×C₈	—	4	4	no	—
229	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
230	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
231	C₇×C₄⋊C₄	—	2	2	no	—
232	C₇×C₄⋊C₄	—	2	2	no	—
233	C₇×C₄⋊C₄	—	2	2	no	—
234	C₇×C₄⋊C₄	—	2	2	no	—
235	C₇×C₄⋊C₄	—	4	1	no	—
236	C₇×C₂²⋊C₄	—	2	2	no	—
237	C₇×C₂²⋊C₄	—	2	2	no	—
238	C₇×C₂²⋊C₄	—	2	2	no	—
239	C₇×C₂²⋊C₄	—	2	2	no	—
240	C₇×C₂²⋊C₄	—	2	2	no	—
241	C₇×C₂²⋊C₄	—	2	2	no	—
242	C₇×C₂²⋊C₄	—	2	2	no	—
243	C₇×C₂²⋊C₄	—	2	2	no	—
244	C₇×C₂²⋊C₄	—	4	1	no	—
245	C₇×C₂²⋊C₄	—	4	1	no	—
246	C₄²×C₇	—	2	1	no	—
247	C₄²×C₇	—	2	1	no	—
248	C₄²×C₇	—	2	1	no	—
249	C₄²×C₇	—	2	1	no	—
250	C₄²×C₇	—	2	1	no	—
251	C₄²×C₇	—	2	1	no	—
252	C₄²×C₇	—	2	1	no	—
253	C₄²×C₇	—	2	1	no	—
254	C₄²×C₇	—	4	1	no	—
255	C₄²×C₇	—	4	1	no	—
256	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
257	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
258	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
259	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
260	C₂×#121	C₄×C₇	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
264	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
265	#435	—	2	4	no	—
266	C₈×D₄	—	2	4	no	—
267	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
271	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
274	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
279	C₂×#97	C₂²×C₇	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
281	#390	C₄×C₇	1	1	yes	characteristic
282	#389	C₄×C₇	1	1	yes	characteristic
283	#388	C₄×C₇	1	1	yes	characteristic
284	#388	C₄×C₇	1	1	yes	characteristic
285	#386	C₄×C₇	1	1	yes	characteristic
286	#386	C₄×C₇	1	1	yes	characteristic
287	#380	C₄×C₇	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
289	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
290	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
291	#336	C₂²×C₇	1	1	yes	characteristic
292	#336	C₂²×C₇	1	1	yes	characteristic
293	#336	C₂²×C₇	1	1	yes	characteristic
294	#336	C₂²×C₇	1	1	yes	characteristic
295	#336	C₂²×C₇	1	1	yes	characteristic
296	#336	C₂²×C₇	1	1	yes	characteristic
297	#336	C₂²×C₇	1	1	yes	characteristic
298	#336	C₂²×C₇	1	1	yes	characteristic
299	#336	C₂²×C₇	1	1	yes	characteristic
300	#336	C₂²×C₇	1	1	yes	characteristic
301	C₂³×C₇	—	2	1	no	—
302	C₂³×C₇	—	2	1	no	—
303	C₂³×C₇	—	2	1	no	—
304	C₂³×C₇	—	2	1	no	—
305	C₂³×C₇	—	2	1	no	—
306	C₂³×C₇	—	2	1	no	—
307	C₂³×C₇	—	2	1	no	—
308	C₂³×C₇	—	2	1	no	—
309	C₂³×C₇	—	2	1	no	—
310	C₂³×C₇	—	2	1	no	—
311	C₂³×C₇	—	2	1	no	—
312	C₂³×C₇	—	2	1	no	—
313	C₂³×C₇	—	2	1	no	—
314	C₂³×C₇	—	2	1	no	—
315	C₂³×C₇	—	2	1	no	—
316	C₂³×C₇	—	2	1	no	—
317	C₂³×C₇	—	2	1	no	—
318	C₂³×C₇	C₄×D₄	1	2	yes	—
319	C₂³×C₇	C₂×M₁₆	1	2	yes	—
320	C₂³×C₇	C₂×M₁₆	1	2	yes	—
321	C₂³×C₇	#131	1	2	yes	—
322	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
323	C₇×D₄	—	2	8	no	—
324	C₇×D₄	—	4	4	no	—
325	C₇×D₄	—	4	4	no	—
326	C₂×C₄×C₇	—	2	1	no	—
327	C₂×C₄×C₇	—	2	1	no	—
328	C₂×C₄×C₇	—	2	1	no	—
329	C₂×C₄×C₇	—	2	1	no	—
330	C₂×C₄×C₇	—	2	1	no	—
331	C₂×C₄×C₇	—	2	1	no	—
332	C₂×C₄×C₇	—	2	1	no	—
333	C₂×C₄×C₇	—	2	1	no	—
334	C₂×C₄×C₇	—	2	2	no	—
335	C₂×C₄×C₇	—	2	2	no	—
336	C₂×C₄×C₇	—	2	2	no	—
337	C₂×C₄×C₇	—	2	2	no	—
338	C₂×C₄×C₇	—	2	1	no	—
339	C₂×C₄×C₇	—	2	1	no	—
340	C₂×C₄×C₇	—	2	1	no	—
341	C₂×C₄×C₇	—	2	1	no	—
342	C₂×C₄×C₇	—	2	1	no	—
343	C₂×C₄×C₇	—	2	1	no	—
344	C₂×C₄×C₇	—	2	1	no	—
345	C₂×C₄×C₇	—	2	1	no	—
346	C₂×C₄×C₇	—	2	1	no	—
347	C₂×C₄×C₇	—	2	1	no	—
348	C₂×C₄×C₇	—	2	1	no	—
349	C₂×C₄×C₇	—	2	1	no	—
350	C₂×C₄×C₇	—	2	1	no	—
351	C₂×C₄×C₇	—	2	1	no	—
352	C₂×C₄×C₇	—	2	1	no	—
353	C₂×C₄×C₇	—	2	1	no	—
354	C₂×C₄×C₇	—	2	1	no	—
355	C₂×C₄×C₇	—	2	1	no	—
356	C₂×C₄×C₇	—	2	1	no	—
357	C₂×C₄×C₇	—	2	1	no	—
358	C₂×C₄×C₇	—	2	1	no	—
359	C₂×C₄×C₇	—	4	4	no	—
360	C₂×C₄×C₇	—	4	4	no	—
361	C₂×C₄×C₇	—	4	1	no	—
362	C₂×C₄×C₇	—	4	1	no	—
363	C₂×C₄×C₇	—	4	1	no	—
364	C₂×C₄×C₇	—	4	1	no	—
365	C₂×C₄×C₇	—	4	1	no	—
366	C₂×C₄×C₇	—	4	1	no	—
367	C₂×C₄×C₇	—	4	1	no	—
368	C₂×C₄×C₇	—	4	1	no	—
369	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
370	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
371	C₂×C₄×C₇	#131	1	2	yes	—
372	C₂×C₄×C₇	#131	1	2	yes	—
373	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
375	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
376	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
377	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
379	C₇×C₈	—	2	2	no	—
380	C₇×C₈	—	2	2	no	—
381	C₇×C₈	—	4	1	no	—
382	C₇×C₈	—	4	1	no	—
383	C₇×C₈	—	4	1	no	—
384	C₇×C₈	—	4	1	no	—
385	C₇×C₈	—	4	1	no	—
386	C₇×C₈	—	4	1	no	—
387	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
388	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
389	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
390	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
391	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	—	4	1	no	—
397	C₂×M₁₆	—	4	1	no	—
398	C₂²×C₈	—	2	2	no	—
399	C₂²×C₈	—	2	2	no	—
400	C₂²×C₈	—	4	1	no	—
401	C₂²×C₈	—	4	1	no	—
402	C₂²×C₈	—	4	1	no	—
403	C₂²×C₈	—	4	1	no	—
404	C₂²×C₈	—	4	1	no	—
405	C₂²×C₈	—	4	1	no	—
406	C₂²×C₈	C₇×D₄	1	4	yes	complemented
407	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
415	#121	—	2	4	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	4	1	no	—
421	C₄×D₄	—	4	1	no	—
422	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
437	C₂×C₄²	—	4	1	no	—
438	C₂×C₄²	—	4	1	no	—
439	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
440	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
445	C₄⋊C₈	—	2	2	no	—
446	C₄⋊C₈	—	2	2	no	—
447	C₄⋊C₈	—	4	1	no	—
448	C₄⋊C₈	—	4	1	no	—
449	C₂²⋊C₈	—	2	2	no	—
450	C₂²⋊C₈	—	2	2	no	—
451	C₂²⋊C₈	—	2	2	no	—
452	C₂²⋊C₈	—	2	2	no	—
453	C₂²⋊C₈	—	4	1	no	—
454	C₂²⋊C₈	—	4	1	no	—
455	C₂²⋊C₈	—	4	1	no	—
456	C₂²⋊C₈	—	4	1	no	—
457	#97	—	2	2	no	—
458	C₄×C₈	—	2	2	no	—
459	#95	C₂×C₄×C₇	1	1	yes	characteristic
460	#95	C₂×C₄×C₇	1	1	yes	characteristic
461	#95	C₂×C₄×C₇	1	1	yes	characteristic
462	#95	C₂×C₄×C₇	1	1	yes	characteristic
463	#95	C₂×C₄×C₇	1	1	yes	characteristic
464	#95	C₂×C₄×C₇	1	1	yes	characteristic
465	C₂²×C₇	—	2	2	no	—
466	C₂²×C₇	—	2	2	no	—
467	C₂²×C₇	—	2	2	no	—
468	C₂²×C₇	—	2	2	no	—
469	C₂²×C₇	—	2	2	no	—
470	C₂²×C₇	—	2	2	no	—
471	C₂²×C₇	—	2	2	no	—
472	C₂²×C₇	—	2	2	no	—
473	C₂²×C₇	—	2	2	no	—
474	C₂²×C₇	—	4	1	no	—
475	C₂²×C₇	—	4	1	no	—
476	C₂²×C₇	—	4	1	no	—
477	C₂²×C₇	—	4	1	no	—
478	C₂²×C₇	—	4	1	no	—
479	C₂²×C₇	—	4	1	no	—
480	C₂²×C₇	—	4	1	no	—
481	C₂²×C₇	—	4	1	no	—
482	C₂²×C₇	—	4	1	no	—
483	C₂²×C₇	—	4	1	no	—
484	C₂²×C₇	—	4	1	no	—
485	C₂²×C₇	#435	1	4	yes	—
486	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
487	C₂²×C₇	#518	1	1	yes	characteristic
488	C₂²×C₇	#520	1	1	yes	characteristic
489	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
490	C₂²×C₇	C₂×#131	1	1	yes	characteristic
491	C₂²×C₇	C₂×#131	1	1	yes	characteristic
492	C₂²×C₇	C₂×#131	1	1	yes	characteristic
493	C₄×C₇	—	2	2	no	—
494	C₄×C₇	—	2	2	no	—
495	C₄×C₇	—	2	2	no	—
496	C₄×C₇	—	2	2	no	—
497	C₄×C₇	—	4	1	no	—
498	C₄×C₇	—	4	1	no	—
499	C₄×C₇	—	4	1	no	—
500	C₄×C₇	—	4	1	no	—
501	C₄×C₇	—	4	1	no	—
502	C₄×C₇	—	4	1	no	—
503	C₄×C₇	—	4	1	no	—
504	C₄×C₇	#534	1	1	yes	characteristic
505	C₄×C₇	#537	1	1	yes	characteristic
506	C₄×C₇	#538	1	1	yes	characteristic
507	C₄×C₇	#539	1	1	yes	characteristic
508	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
509	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
510	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	4	1	no	—
519	C₂×D₄	C₇×M₁₆	1	4	yes	complemented
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	4	1	no	—
541	C₂²×C₄	—	4	1	no	—
542	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
549	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
550	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
551	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
552	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
553	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
554	C₂²×C₄	C₇×#41	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
556	M₁₆	—	4	4	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	4	4	no	—
580	C₂×C₈	—	4	4	no	—
581	C₂×C₈	—	4	4	no	—
582	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
583	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	4	1	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	4	1	no	—
598	C₂²⋊C₄	—	4	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	—	4	1	no	—
608	C₄²	—	4	1	no	—
609	C₂×C₇	—	2	4	no	—
610	C₂×C₇	—	4	2	no	—
611	C₂×C₇	—	8	1	no	—
612	C₂×C₇	#2325	1	1	yes	characteristic
613	C₂×C₇	C₂×#435	1	1	yes	characteristic
614	C₂×C₇	#2931	1	1	yes	characteristic
615	C₂×C₇	#2974	1	1	yes	characteristic
616	C₂×C₇	#2977	1	1	yes	characteristic
617	C₂×C₇	#2990	1	1	yes	characteristic
618	C₂×C₇	#2994	1	1	yes	characteristic
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	C₄×C₇×D₄	1	2	yes	—
637	C₂³	C₂×C₇×M₁₆	1	2	yes	—
638	C₂³	C₂×C₇×M₁₆	1	2	yes	—
639	C₂³	C₇×#131	1	2	yes	—
640	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
641	D₄	—	2	8	no	—
642	D₄	—	4	4	no	—
643	D₄	—	4	4	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
688	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
689	C₂×C₄	C₇×#131	1	2	yes	—
690	C₂×C₄	C₇×#131	1	2	yes	—
691	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
692	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
693	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
694	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
695	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
697	C₈	—	2	2	no	—
698	C₈	—	2	2	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₈	—	4	1	no	—
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₈	—	4	1	no	—
705	C₇	#22172	1	1	yes	characteristic, direct product factor, Sylow
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	C₇×#435	1	4	yes	—
727	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
728	C₂²	C₇×#518	1	1	yes	characteristic
729	C₂²	C₇×#520	1	1	yes	characteristic
730	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
731	C₂²	C₂×C₇×#131	1	1	yes	characteristic
732	C₂²	C₂×C₇×#131	1	1	yes	characteristic
733	C₂²	C₂×C₇×#131	1	1	yes	characteristic
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	2	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	C₇×#534	1	1	yes	characteristic
746	C₄	C₇×#537	1	1	yes	characteristic
747	C₄	C₇×#538	1	1	yes	characteristic
748	C₄	C₇×#539	1	1	yes	characteristic
749	C₂	—	2	4	no	—
750	C₂	—	4	2	no	—
751	C₂	—	8	1	no	—
752	C₂	C₇×#2325	1	1	yes	characteristic
753	C₂	C₂×C₇×#435	1	1	yes	characteristic
754	C₂	C₇×#2931	1	1	yes	characteristic
755	C₂	C₇×#2974	1	1	yes	characteristic
756	C₂	C₇×#2977	1	1	yes	characteristic
757	C₂	C₇×#2990	1	1	yes	characteristic
758	C₂	C₇×#2994	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂×C₇×#121	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#435	C₂	semidirect
2. C₂×C₇×C₈×D₄	C₂	semidirect
4. C₇×#1924	C₂	semidirect
5. C₇×#1923	C₂	semidirect
6. C₇×#1917	C₂	semidirect
7. C₇×#1916	C₂	semidirect
8. C₇×#1870	C₂	semidirect
9. C₇×#1869	C₂	semidirect
10. C₇×#1869	C₂	semidirect
11. C₇×#1869	C₂	semidirect
12. C₇×#1851	C₂	semidirect
13. C₇×#1850	C₂	semidirect
14. C₇×#1797	C₂	semidirect
15. C₂×C₇×#336	C₂	semidirect
61. #22172	C₇	direct (N × H)
81. C₂²×C₇×C₈	D₄	semidirect
140. C₂×#435	C₂×C₇	semidirect
141. C₂×C₈×D₄	C₂×C₇	semidirect
143. #1924	C₂×C₇	semidirect
144. #1923	C₂×C₇	semidirect
145. #1917	C₂×C₇	semidirect
146. #1916	C₂×C₇	semidirect
147. #1870	C₂×C₇	semidirect
148. #1869	C₂×C₇	semidirect
149. #1869	C₂×C₇	semidirect
150. #1869	C₂×C₇	semidirect
151. #1851	C₂×C₇	semidirect
152. #1850	C₂×C₇	semidirect
153. #1797	C₂×C₇	semidirect
154. C₂×#336	C₂×C₇	semidirect
166. C₂×C₇×D₄	M₁₆	semidirect
406. C₂²×C₈	C₇×D₄	semidirect
519. C₂×D₄	C₇×M₁₆	semidirect
705. C₇	#22172	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×#435	2
C₂×C₇×C₈×D₄	2
C₄×C₇×#121	2
C₇×#1924	2
C₇×#1923	2
C₇×#1917	2
C₇×#1916	2
C₇×#1870	2
C₇×#1869	2
C₇×#1851	2
C₇×#1850	2
C₇×#1797	2
C₂×C₇×#336	2
#22172	7

Subgroups — C7×#22172 #13199388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22172 #13199388