Subgroups — C₇×#22559 #13199775

Order 1792.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#407	C₂	1	1	yes	maximal, characteristic
3	C₇×#2280	C₂	1	1	yes	maximal, characteristic
4	C₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1779	C₂	1	1	yes	maximal, characteristic
13	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
17	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×#117	C₂²	1	1	yes	characteristic
20	C₂×C₇×#117	C₂²	1	1	yes	characteristic
21	C₇×#433	—	2	4	no	—
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
26	C₇×#407	—	2	4	no	—
27	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₂²⋊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×#97	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
41	C₇×#381	C₄	1	1	yes	characteristic
42	C₇×#381	C₄	1	1	yes	characteristic
43	C₇×#380	C₄	1	1	yes	characteristic
44	C₇×#380	C₄	1	1	yes	characteristic
45	C₇×#380	C₄	1	1	yes	characteristic
46	C₇×#380	C₄	1	1	yes	characteristic
47	C₇×#379	C₄	1	1	yes	characteristic
48	C₇×#379	C₄	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	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₇×#336	C₂²	1	1	yes	characteristic, complemented
54	C₇×#336	C₂²	1	1	yes	characteristic, complemented
55	C₇×#336	C₂²	1	1	yes	characteristic, complemented
56	C₇×#336	C₂²	1	1	yes	characteristic, complemented
57	C₇×#336	C₂²	1	1	yes	characteristic, complemented
58	C₇×#336	C₂²	1	1	yes	characteristic, complemented
59	C₇×#336	C₂²	1	1	yes	characteristic, complemented
60	C₇×#336	C₂²	1	1	yes	characteristic, complemented
61	#22559	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂⁵×C₇	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₇	—	2	2	no	—
64	C₂³×C₄×C₇	—	2	2	no	—
65	C₂³×C₄×C₇	—	2	2	no	—
66	C₂³×C₄×C₇	—	2	2	no	—
67	C₂³×C₄×C₇	—	4	1	no	—
68	C₂³×C₄×C₇	—	4	1	no	—
69	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₇×M₁₆	—	2	2	no	—
76	C₂×C₇×M₁₆	—	2	2	no	—
77	C₂×C₇×M₁₆	—	2	2	no	—
78	C₂×C₇×M₁₆	—	2	2	no	—
79	C₂×C₇×M₁₆	—	4	1	no	—
80	C₂×C₇×M₁₆	—	4	1	no	—
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	C₇×#117	—	2	2	no	—
90	C₇×#117	—	2	2	no	—
91	C₇×#117	—	4	1	no	—
92	C₇×#117	—	4	1	no	—
93	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₇×C₂²⋊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×C₄²×C₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
113	C₇×C₄⋊C₈	—	2	2	no	—
114	C₇×C₄⋊C₈	—	2	2	no	—
115	C₇×C₄⋊C₈	—	4	1	no	—
116	C₇×C₄⋊C₈	—	4	1	no	—
117	C₇×C₂²⋊C₈	—	2	2	no	—
118	C₇×C₂²⋊C₈	—	2	2	no	—
119	C₇×C₂²⋊C₈	—	2	2	no	—
120	C₇×C₂²⋊C₈	—	2	2	no	—
121	C₇×C₂²⋊C₈	—	2	2	no	—
122	C₇×C₂²⋊C₈	—	2	2	no	—
123	C₇×C₂²⋊C₈	—	2	2	no	—
124	C₇×C₂²⋊C₈	—	4	1	no	—
125	C₇×C₂²⋊C₈	—	4	1	no	—
126	C₇×C₂²⋊C₈	D₄	1	4	yes	—
127	C₇×#97	—	2	2	no	—
128	C₇×#97	—	4	1	no	—
129	C₄×C₇×C₈	—	2	2	no	—
130	C₄×C₇×C₈	—	4	1	no	—
131	C₇×#95	C₂×C₄	1	1	yes	characteristic
132	C₇×#95	C₂×C₄	1	1	yes	characteristic
133	C₇×#95	C₂×C₄	1	1	yes	characteristic
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	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂×#407	C₂×C₇	1	1	yes	characteristic
141	#2280	C₂×C₇	1	1	yes	characteristic
142	#1924	C₂×C₇	1	1	yes	characteristic, complemented
143	#1924	C₂×C₇	1	1	yes	characteristic, complemented
144	#1923	C₂×C₇	1	1	yes	characteristic, complemented
145	#1923	C₂×C₇	1	1	yes	characteristic, complemented
146	#1851	C₂×C₇	1	1	yes	characteristic, complemented
147	#1851	C₂×C₇	1	1	yes	characteristic, complemented
148	#1818	C₂×C₇	1	1	yes	characteristic, complemented
149	#1798	C₂×C₇	1	1	yes	characteristic, complemented
150	#1779	C₂×C₇	1	1	yes	characteristic
151	#1753	C₂×C₇	1	1	yes	characteristic, complemented
152	#1753	C₂×C₇	1	1	yes	characteristic, complemented
153	#1750	C₂×C₇	1	1	yes	characteristic, complemented
154	C₂⁴×C₇	—	2	2	no	—
155	C₂⁴×C₇	—	2	2	no	—
156	C₂⁴×C₇	—	2	2	no	—
157	C₂⁴×C₇	—	4	1	no	—
158	C₂⁴×C₇	—	4	1	no	—
159	C₂⁴×C₇	—	4	1	no	—
160	C₂⁴×C₇	—	4	1	no	—
161	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
162	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
163	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
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	1	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	2	no	—
176	C₂²×C₄×C₇	—	2	2	no	—
177	C₂²×C₄×C₇	—	2	2	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	—	4	1	no	—
185	C₂²×C₄×C₇	—	4	1	no	—
186	C₂²×C₄×C₇	—	4	1	no	—
187	C₂²×C₄×C₇	—	4	4	no	—
188	C₂²×C₄×C₇	—	4	4	no	—
189	C₂²×C₄×C₇	—	4	4	no	—
190	C₂²×C₄×C₇	—	4	4	no	—
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	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₇	#41	1	2	yes	—
204	C₂²×C₄×C₇	#41	1	2	yes	—
205	C₂²×C₄×C₇	#41	1	2	yes	—
206	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
207	C₇×M₁₆	—	4	4	no	—
208	C₇×M₁₆	—	4	4	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	—	2	1	no	—
227	C₂×C₇×C₈	—	2	1	no	—
228	C₂×C₇×C₈	—	2	1	no	—
229	C₂×C₇×C₈	—	2	1	no	—
230	C₂×C₇×C₈	—	2	1	no	—
231	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
232	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
233	C₇×C₄⋊C₄	—	2	2	no	—
234	C₇×C₄⋊C₄	—	2	2	no	—
235	C₇×C₄⋊C₄	—	4	1	no	—
236	C₇×C₄⋊C₄	—	4	1	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	—	4	1	no	—
242	C₇×C₂²⋊C₄	—	4	1	no	—
243	C₇×C₂²⋊C₄	—	4	1	no	—
244	C₇×C₂²⋊C₄	—	4	1	no	—
245	C₇×C₂²⋊C₄	—	4	1	no	—
246	C₇×C₂²⋊C₄	—	4	1	no	—
247	C₇×C₂²⋊C₄	—	4	1	no	—
248	C₇×C₂²⋊C₄	—	4	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	—	2	1	no	—
255	C₄²×C₇	—	2	1	no	—
256	C₄²×C₇	—	2	1	no	—
257	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
258	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
259	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
260	C₂×#117	C₂²×C₇	1	1	yes	characteristic
261	C₂×#117	C₂²×C₇	1	1	yes	characteristic
262	#433	—	2	4	no	—
263	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
264	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
265	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
266	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
267	#407	—	2	4	no	—
268	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
270	C₂×C₂²⋊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×#97	C₂²×C₇	1	1	yes	characteristic, complemented
279	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
280	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
281	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
282	#381	C₄×C₇	1	1	yes	characteristic
283	#381	C₄×C₇	1	1	yes	characteristic
284	#380	C₄×C₇	1	1	yes	characteristic
285	#380	C₄×C₇	1	1	yes	characteristic
286	#380	C₄×C₇	1	1	yes	characteristic
287	#380	C₄×C₇	1	1	yes	characteristic
288	#379	C₄×C₇	1	1	yes	characteristic
289	#379	C₄×C₇	1	1	yes	characteristic
290	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
292	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
293	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
294	#336	C₂²×C₇	1	1	yes	characteristic, complemented
295	#336	C₂²×C₇	1	1	yes	characteristic, complemented
296	#336	C₂²×C₇	1	1	yes	characteristic, complemented
297	#336	C₂²×C₇	1	1	yes	characteristic, complemented
298	#336	C₂²×C₇	1	1	yes	characteristic, complemented
299	#336	C₂²×C₇	1	1	yes	characteristic, complemented
300	#336	C₂²×C₇	1	1	yes	characteristic, complemented
301	#336	C₂²×C₇	1	1	yes	characteristic, complemented
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	—	2	1	no	—
319	C₂³×C₇	—	2	1	no	—
320	C₂³×C₇	—	4	4	no	—
321	C₂³×C₇	—	4	4	no	—
322	C₂³×C₇	—	4	4	no	—
323	C₂³×C₇	—	4	4	no	—
324	C₂³×C₇	—	4	4	no	—
325	C₂³×C₇	—	4	4	no	—
326	C₂³×C₇	—	4	4	no	—
327	C₂³×C₇	#117	1	2	yes	—
328	C₂³×C₇	C₄×D₄	1	2	yes	—
329	C₂³×C₇	#131	1	2	yes	—
330	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
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	1	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	2	no	—
339	C₂×C₄×C₇	—	2	2	no	—
340	C₂×C₄×C₇	—	2	2	no	—
341	C₂×C₄×C₇	—	2	2	no	—
342	C₂×C₄×C₇	—	2	2	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	—	2	1	no	—
360	C₂×C₄×C₇	—	2	1	no	—
361	C₂×C₄×C₇	—	2	1	no	—
362	C₂×C₄×C₇	—	2	1	no	—
363	C₂×C₄×C₇	—	2	1	no	—
364	C₂×C₄×C₇	—	2	1	no	—
365	C₂×C₄×C₇	—	2	1	no	—
366	C₂×C₄×C₇	—	2	1	no	—
367	C₂×C₄×C₇	—	2	1	no	—
368	C₂×C₄×C₇	—	2	1	no	—
369	C₂×C₄×C₇	—	2	1	no	—
370	C₂×C₄×C₇	—	4	4	no	—
371	C₂×C₄×C₇	—	4	4	no	—
372	C₂×C₄×C₇	—	4	4	no	—
373	C₂×C₄×C₇	—	4	1	no	—
374	C₂×C₄×C₇	—	4	1	no	—
375	C₂×C₄×C₇	—	4	1	no	—
376	C₂×C₄×C₇	—	4	1	no	—
377	C₂×C₄×C₇	#117	1	2	yes	—
378	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
379	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
381	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
382	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
383	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
384	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
385	C₇×C₈	—	2	2	no	—
386	C₇×C₈	—	2	2	no	—
387	C₇×C₈	—	4	1	no	—
388	C₇×C₈	—	4	1	no	—
389	C₇×C₈	—	4	1	no	—
390	C₇×C₈	—	4	1	no	—
391	C₇×C₈	—	4	1	no	—
392	C₇×C₈	—	4	1	no	—
393	C₂⁵	C₂×C₄×C₇	1	1	yes	characteristic
394	C₂³×C₄	—	2	2	no	—
395	C₂³×C₄	—	2	2	no	—
396	C₂³×C₄	—	2	2	no	—
397	C₂³×C₄	—	2	2	no	—
398	C₂³×C₄	—	4	1	no	—
399	C₂³×C₄	—	4	1	no	—
400	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
401	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
402	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
406	C₂×M₁₆	—	2	2	no	—
407	C₂×M₁₆	—	2	2	no	—
408	C₂×M₁₆	—	2	2	no	—
409	C₂×M₁₆	—	2	2	no	—
410	C₂×M₁₆	—	4	1	no	—
411	C₂×M₁₆	—	4	1	no	—
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	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
420	#117	—	2	2	no	—
421	#117	—	2	2	no	—
422	#117	—	4	1	no	—
423	#117	—	4	1	no	—
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×C₄⋊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×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
440	C₂×C₄²	C₂³×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	C₄⋊C₈	—	2	2	no	—
445	C₄⋊C₈	—	2	2	no	—
446	C₄⋊C₈	—	4	1	no	—
447	C₄⋊C₈	—	4	1	no	—
448	C₂²⋊C₈	—	2	2	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	—	2	2	no	—
454	C₂²⋊C₈	—	2	2	no	—
455	C₂²⋊C₈	—	4	1	no	—
456	C₂²⋊C₈	—	4	1	no	—
457	C₂²⋊C₈	C₇×D₄	1	4	yes	—
458	#97	—	2	2	no	—
459	#97	—	4	1	no	—
460	C₄×C₈	—	2	2	no	—
461	C₄×C₈	—	4	1	no	—
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	#95	C₂×C₄×C₇	1	1	yes	characteristic
466	#95	C₂×C₄×C₇	1	1	yes	characteristic
467	#95	C₂×C₄×C₇	1	1	yes	characteristic
468	#95	C₂×C₄×C₇	1	1	yes	characteristic
469	#95	C₂×C₄×C₇	1	1	yes	characteristic
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	—	2	2	no	—
475	C₂²×C₇	—	2	2	no	—
476	C₂²×C₇	—	2	2	no	—
477	C₂²×C₇	—	2	2	no	—
478	C₂²×C₇	—	2	2	no	—
479	C₂²×C₇	—	4	16	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	—	4	1	no	—
486	C₂²×C₇	—	4	1	no	—
487	C₂²×C₇	—	4	1	no	—
488	C₂²×C₇	—	4	1	no	—
489	C₂²×C₇	—	4	1	no	—
490	C₂²×C₇	—	4	1	no	—
491	C₂²×C₇	—	4	1	no	—
492	C₂²×C₇	C₂×#117	1	1	yes	characteristic
493	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
494	C₂²×C₇	#518	1	1	yes	characteristic
495	C₂²×C₇	C₂×#131	1	1	yes	characteristic
496	C₂²×C₇	#568	1	1	yes	characteristic
497	C₂²×C₇	#568	1	1	yes	characteristic
498	C₂²×C₇	#568	1	1	yes	characteristic
499	C₄×C₇	—	2	2	no	—
500	C₄×C₇	—	2	2	no	—
501	C₄×C₇	—	4	1	no	—
502	C₄×C₇	—	4	1	no	—
503	C₄×C₇	—	4	1	no	—
504	C₄×C₇	—	4	1	no	—
505	C₄×C₇	—	4	1	no	—
506	C₄×C₇	—	4	1	no	—
507	C₄×C₇	—	4	1	no	—
508	C₄×C₇	—	4	1	no	—
509	C₄×C₇	—	4	1	no	—
510	C₄×C₇	#546	1	1	yes	characteristic
511	C₄×C₇	#546	1	1	yes	characteristic
512	C₄×C₇	#551	1	1	yes	characteristic
513	C₄×C₇	#551	1	1	yes	characteristic
514	C₂⁴	—	2	2	no	—
515	C₂⁴	—	2	2	no	—
516	C₂⁴	—	2	2	no	—
517	C₂⁴	—	4	1	no	—
518	C₂⁴	—	4	1	no	—
519	C₂⁴	—	4	1	no	—
520	C₂⁴	—	4	1	no	—
521	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
522	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
523	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	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	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	4	1	no	—
545	C₂²×C₄	—	4	1	no	—
546	C₂²×C₄	—	4	1	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
552	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
553	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
554	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
555	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
556	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
557	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
558	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
559	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
560	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
561	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
562	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
563	C₂²×C₄	C₇×#41	1	2	yes	—
564	C₂²×C₄	C₇×#41	1	2	yes	—
565	C₂²×C₄	C₇×#41	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
567	M₁₆	—	4	4	no	—
568	M₁₆	—	4	4	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	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
592	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	—	4	1	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	4	1	no	—
602	C₂²⋊C₄	—	4	1	no	—
603	C₂²⋊C₄	—	4	1	no	—
604	C₂²⋊C₄	—	4	1	no	—
605	C₂²⋊C₄	—	4	1	no	—
606	C₂²⋊C₄	—	4	1	no	—
607	C₂²⋊C₄	—	4	1	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₂×C₇	—	4	2	no	—
618	C₂×C₇	—	4	2	no	—
619	C₂×C₇	—	4	2	no	—
620	C₂×C₇	#2342	1	1	yes	characteristic
621	C₂×C₇	#2921	1	1	yes	characteristic
622	C₂×C₇	#2924	1	1	yes	characteristic
623	C₂×C₇	#2930	1	1	yes	characteristic
624	C₂×C₇	#2933	1	1	yes	characteristic
625	C₂×C₇	#2976	1	1	yes	characteristic
626	C₂×C₇	#2978	1	1	yes	characteristic
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	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	4	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	4	4	no	—
650	C₂³	—	4	4	no	—
651	C₂³	—	4	4	no	—
652	C₂³	C₇×#117	1	2	yes	—
653	C₂³	C₄×C₇×D₄	1	2	yes	—
654	C₂³	C₇×#131	1	2	yes	—
655	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
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	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	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	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	C₇×#117	1	2	yes	—
703	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
704	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
705	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
706	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
707	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
708	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
709	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
710	C₈	—	2	2	no	—
711	C₈	—	2	2	no	—
712	C₈	—	4	1	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₈	—	4	1	no	—
717	C₈	—	4	1	no	—
718	C₇	#22559	1	1	yes	characteristic, direct product factor, Sylow
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	4	16	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	C₂×C₇×#117	1	1	yes	characteristic
742	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
743	C₂²	C₇×#518	1	1	yes	characteristic
744	C₂²	C₂×C₇×#131	1	1	yes	characteristic
745	C₂²	C₇×#568	1	1	yes	characteristic
746	C₂²	C₇×#568	1	1	yes	characteristic
747	C₂²	C₇×#568	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	1	no	—
759	C₄	C₇×#546	1	1	yes	characteristic
760	C₄	C₇×#546	1	1	yes	characteristic
761	C₄	C₇×#551	1	1	yes	characteristic
762	C₄	C₇×#551	1	1	yes	characteristic
763	C₂	—	4	2	no	—
764	C₂	—	4	2	no	—
765	C₂	—	4	2	no	—
766	C₂	C₇×#2342	1	1	yes	characteristic
767	C₂	C₇×#2921	1	1	yes	characteristic
768	C₂	C₇×#2924	1	1	yes	characteristic
769	C₂	C₇×#2930	1	1	yes	characteristic
770	C₂	C₇×#2933	1	1	yes	characteristic
771	C₂	C₇×#2976	1	1	yes	characteristic
772	C₂	C₇×#2978	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	C₂⁵×C₇	C₂×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×#433	C₂	semidirect
4. C₇×#1924	C₂	semidirect
5. C₇×#1924	C₂	semidirect
6. C₇×#1923	C₂	semidirect
7. C₇×#1923	C₂	semidirect
8. C₇×#1851	C₂	semidirect
9. C₇×#1851	C₂	semidirect
10. C₇×#1818	C₂	semidirect
11. C₇×#1798	C₂	semidirect
13. C₇×#1753	C₂	semidirect
14. C₇×#1753	C₂	semidirect
15. C₇×#1750	C₂	semidirect
22. C₂×C₇×C₄⋊C₈	C₂²	semidirect
23. C₂×C₇×C₄⋊C₈	C₂²	semidirect
24. C₂×C₇×C₄⋊C₈	C₂²	semidirect
25. C₂×C₇×C₄⋊C₈	C₂²	semidirect
37. C₂×C₇×#97	C₂²	semidirect
38. C₂×C₇×#97	C₂²	semidirect
39. C₂×C₄×C₇×C₈	C₂²	semidirect
40. C₂×C₄×C₇×C₈	C₂²	semidirect
53. C₇×#336	C₂²	semidirect
54. C₇×#336	C₂²	semidirect
55. C₇×#336	C₂²	semidirect
56. C₇×#336	C₂²	semidirect
57. C₇×#336	C₂²	semidirect
58. C₇×#336	C₂²	semidirect
59. C₇×#336	C₂²	semidirect
60. C₇×#336	C₂²	semidirect
61. #22559	C₇	direct (N × H)
139. C₂×#433	C₂×C₇	semidirect
142. #1924	C₂×C₇	semidirect
143. #1924	C₂×C₇	semidirect
144. #1923	C₂×C₇	semidirect
145. #1923	C₂×C₇	semidirect
146. #1851	C₂×C₇	semidirect
147. #1851	C₂×C₇	semidirect
148. #1818	C₂×C₇	semidirect
149. #1798	C₂×C₇	semidirect
151. #1753	C₂×C₇	semidirect
152. #1753	C₂×C₇	semidirect
153. #1750	C₂×C₇	semidirect
263. C₂×C₄⋊C₈	C₂²×C₇	semidirect
264. C₂×C₄⋊C₈	C₂²×C₇	semidirect
265. C₂×C₄⋊C₈	C₂²×C₇	semidirect
266. C₂×C₄⋊C₈	C₂²×C₇	semidirect
278. C₂×#97	C₂²×C₇	semidirect
279. C₂×#97	C₂²×C₇	semidirect
280. C₂×C₄×C₈	C₂²×C₇	semidirect
281. C₂×C₄×C₈	C₂²×C₇	semidirect
294. #336	C₂²×C₇	semidirect
295. #336	C₂²×C₇	semidirect
296. #336	C₂²×C₇	semidirect
297. #336	C₂²×C₇	semidirect
298. #336	C₂²×C₇	semidirect
299. #336	C₂²×C₇	semidirect
300. #336	C₂²×C₇	semidirect
301. #336	C₂²×C₇	semidirect
718. C₇	#22559	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×#433	2
C₂×C₇×#407	2
C₇×#2280	2
C₇×#1924	2
C₇×#1923	2
C₇×#1851	2
C₇×#1818	2
C₇×#1798	2
C₇×#1779	2
C₇×#1753	2
C₇×#1750	2
#22559	7

Subgroups — C7×#22559 #13199775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22559 #13199775