Subgroups — C₇×#8079 #13185295

Order 1792.

634 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic
4	C₇×#1301	C₂	1	4	yes	maximal, complemented
5	C₂²×C₇×M₁₆	—	2	1	no	—
6	C₂²×C₇×M₁₆	—	2	1	no	—
7	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
8	C₇×#431	—	2	1	no	—
9	C₇×#431	—	2	1	no	—
10	C₇×#431	C₄	1	2	yes	—
11	C₇×#431	C₂²	1	2	yes	—
12	C₇×#423	—	2	1	no	—
13	C₇×#423	—	2	1	no	—
14	C₇×#423	—	2	1	no	—
15	C₇×#423	—	2	1	no	—
16	C₇×#423	C₄	1	2	yes	—
17	C₇×#423	C₄	1	2	yes	—
18	C₇×#423	C₄	1	2	yes	—
19	C₇×#423	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊C₈	—	2	1	no	—
21	C₂×C₇×C₄⋊C₈	—	2	1	no	—
22	C₂×C₇×C₄⋊C₈	—	2	1	no	—
23	C₂×C₇×C₄⋊C₈	C₄	1	2	yes	—
24	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊C₈	C₄	1	2	yes	—
26	C₂×C₄×C₇×C₈	—	2	1	no	—
27	#8079	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₇	Q₈	1	1	yes	characteristic
31	C₂×C₇×M₁₆	—	2	2	no	—
32	C₂×C₇×M₁₆	—	2	2	no	—
33	C₂×C₇×M₁₆	—	2	2	no	—
34	C₂×C₇×M₁₆	—	2	2	no	—
35	C₂×C₇×M₁₆	—	4	2	no	—
36	C₂×C₇×M₁₆	—	4	2	no	—
37	C₂×C₇×M₁₆	—	4	2	no	—
38	C₂×C₇×M₁₆	—	4	2	no	—
39	C₂²×C₇×C₈	—	2	2	no	—
40	C₂²×C₇×C₈	—	2	2	no	—
41	C₂²×C₇×C₈	—	2	2	no	—
42	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₇	Q₈	1	1	yes	characteristic
53	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
54	C₇×C₄⋊C₈	—	2	2	no	—
55	C₇×C₄⋊C₈	—	2	2	no	—
56	C₇×C₄⋊C₈	—	2	2	no	—
57	C₇×C₄⋊C₈	—	2	2	no	—
58	C₇×C₄⋊C₈	—	2	2	no	—
59	C₇×C₄⋊C₈	—	2	2	no	—
60	C₇×C₄⋊C₈	—	2	2	no	—
61	C₇×C₄⋊C₈	—	2	2	no	—
62	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
64	C₇×C₂²⋊C₈	—	2	2	no	—
65	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
66	C₄×C₇×C₈	—	2	2	no	—
67	C₄×C₇×C₈	—	2	2	no	—
68	C₂×#431	C₂×C₇	1	1	yes	characteristic
69	C₂×#423	C₂×C₇	1	1	yes	characteristic
70	C₂×#423	C₂×C₇	1	1	yes	characteristic
71	#1301	C₂×C₇	1	4	yes	complemented
72	C₂⁴×C₇	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇	—	4	2	no	—
74	C₂²×C₄×C₇	—	4	2	no	—
75	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₇	D₈	1	2	yes	—
91	C₂²×C₄×C₇	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₇	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₇	Q₁₆	1	2	yes	—
94	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
97	C₇×M₁₆	—	4	4	no	—
98	C₇×M₁₆	—	4	4	no	—
99	C₇×M₁₆	—	4	4	no	—
100	C₇×M₁₆	—	4	2	no	—
101	C₇×M₁₆	—	4	2	no	—
102	C₂×C₇×C₈	—	2	4	no	—
103	C₂×C₇×C₈	—	2	4	no	—
104	C₂×C₇×C₈	—	2	4	no	—
105	C₂×C₇×C₈	—	4	4	no	—
106	C₂×C₇×C₈	—	4	4	no	—
107	C₂×C₇×C₈	—	4	2	no	—
108	C₂×C₇×C₈	—	4	2	no	—
109	C₄²×C₇	C₄²	1	1	yes	characteristic
110	C₄²×C₇	C₄²	1	1	yes	characteristic
111	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
113	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
114	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
115	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
116	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
117	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
119	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
121	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×M₁₆	—	2	1	no	—
126	C₂²×M₁₆	—	2	1	no	—
127	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
128	#431	—	2	1	no	—
129	#431	—	2	1	no	—
130	#431	C₄×C₇	1	2	yes	—
131	#431	C₂²×C₇	1	2	yes	—
132	#423	—	2	1	no	—
133	#423	—	2	1	no	—
134	#423	—	2	1	no	—
135	#423	—	2	1	no	—
136	#423	C₄×C₇	1	2	yes	—
137	#423	C₄×C₇	1	2	yes	—
138	#423	C₄×C₇	1	2	yes	—
139	#423	C₂²×C₇	1	2	yes	—
140	C₂×C₄⋊C₈	—	2	1	no	—
141	C₂×C₄⋊C₈	—	2	1	no	—
142	C₂×C₄⋊C₈	—	2	1	no	—
143	C₂×C₄⋊C₈	C₄×C₇	1	2	yes	—
144	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
145	C₂×C₂²⋊C₈	C₄×C₇	1	2	yes	—
146	C₂×C₄×C₈	—	2	1	no	—
147	C₂³×C₇	—	4	1	no	—
148	C₂³×C₇	—	4	1	no	—
149	C₂³×C₇	#95	1	1	yes	characteristic
150	C₂³×C₇	#95	1	1	yes	characteristic
151	C₂³×C₇	#106	1	2	yes	—
152	C₂³×C₇	#107	1	2	yes	—
153	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₇	—	2	2	no	—
155	C₂×C₄×C₇	—	2	2	no	—
156	C₂×C₄×C₇	—	2	2	no	—
157	C₂×C₄×C₇	—	2	2	no	—
158	C₂×C₄×C₇	—	2	2	no	—
159	C₂×C₄×C₇	—	2	2	no	—
160	C₂×C₄×C₇	—	4	1	no	—
161	C₂×C₄×C₇	—	4	1	no	—
162	C₂×C₄×C₇	—	4	1	no	—
163	C₂×C₄×C₇	—	4	1	no	—
164	C₂×C₄×C₇	—	4	1	no	—
165	C₂×C₄×C₇	—	4	1	no	—
166	C₂×C₄×C₇	#95	1	1	yes	characteristic
167	C₂×C₄×C₇	#95	1	1	yes	characteristic
168	C₂×C₄×C₇	#95	1	1	yes	characteristic
169	C₂×C₄×C₇	#95	1	1	yes	characteristic
170	C₂×C₄×C₇	#95	1	1	yes	characteristic
171	C₂×C₄×C₇	#95	1	1	yes	characteristic
172	C₂×C₄×C₇	#102	1	2	yes	—
173	C₂×C₄×C₇	#102	1	2	yes	—
174	C₂×C₄×C₇	#102	1	2	yes	—
175	C₂×C₄×C₇	#102	1	2	yes	—
176	C₂×C₄×C₇	#103	1	2	yes	—
177	C₂×C₄×C₇	#103	1	2	yes	—
178	C₂×C₄×C₇	#103	1	2	yes	—
179	C₂×C₄×C₇	#103	1	2	yes	—
180	C₂×C₄×C₇	#106	1	2	yes	—
181	C₂×C₄×C₇	#107	1	2	yes	—
182	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₇	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₇	C₂×SD₁₆	1	1	yes	characteristic
190	C₂×C₄×C₇	C₂×SD₁₆	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂×Q₁₆	1	1	yes	characteristic
192	C₇×C₈	—	4	4	no	—
193	C₇×C₈	—	4	4	no	—
194	C₇×C₈	—	4	4	no	—
195	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
196	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
197	C₂³×C₄	C₇×Q₈	1	1	yes	characteristic
198	C₂×M₁₆	—	2	2	no	—
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	2	2	no	—
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	—	4	2	no	—
203	C₂×M₁₆	—	4	2	no	—
204	C₂×M₁₆	—	4	2	no	—
205	C₂×M₁₆	—	4	2	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	—	2	2	no	—
208	C₂²×C₈	—	2	2	no	—
209	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
211	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
212	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
213	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
214	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
215	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
216	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
217	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
218	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
219	C₂×C₄²	C₇×Q₈	1	1	yes	characteristic
220	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	2	no	—
224	C₄⋊C₈	—	2	2	no	—
225	C₄⋊C₈	—	2	2	no	—
226	C₄⋊C₈	—	2	2	no	—
227	C₄⋊C₈	—	2	2	no	—
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
230	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
231	C₂²⋊C₈	—	2	2	no	—
232	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
233	C₄×C₈	—	2	2	no	—
234	C₄×C₈	—	2	2	no	—
235	C₂²×C₇	—	2	1	no	—
236	C₂²×C₇	—	2	1	no	—
237	C₂²×C₇	—	2	1	no	—
238	C₂²×C₇	—	2	1	no	—
239	C₂²×C₇	—	2	1	no	—
240	C₂²×C₇	—	2	1	no	—
241	C₂²×C₇	—	4	2	no	—
242	C₂²×C₇	—	4	2	no	—
243	C₂²×C₇	#340	1	2	yes	—
244	C₂²×C₇	#340	1	2	yes	—
245	C₂²×C₇	C₂×#95	1	1	yes	characteristic
246	C₂²×C₇	C₂×#106	1	1	yes	characteristic
247	C₂²×C₇	C₂×#107	1	1	yes	characteristic
248	C₄×C₇	—	2	1	no	—
249	C₄×C₇	—	2	1	no	—
250	C₄×C₇	—	2	1	no	—
251	C₄×C₇	—	2	1	no	—
252	C₄×C₇	—	2	1	no	—
253	C₄×C₇	—	2	1	no	—
254	C₄×C₇	#340	1	2	yes	—
255	C₄×C₇	#340	1	2	yes	—
256	C₄×C₇	#344	1	2	yes	—
257	C₄×C₇	C₂×#102	1	1	yes	characteristic
258	C₄×C₇	C₂×#102	1	1	yes	characteristic
259	C₄×C₇	C₂×#103	1	1	yes	characteristic
260	C₄×C₇	C₂×#103	1	1	yes	characteristic
261	C₄×C₇	#430	1	2	yes	—
262	C₂⁴	C₇×C₄⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	C₄²×C₇	1	1	yes	characteristic
266	C₂²×C₄	C₄²×C₇	1	1	yes	characteristic
267	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	C₇×D₈	1	2	yes	—
281	C₂²×C₄	C₇×SD₁₆	1	2	yes	—
282	C₂²×C₄	C₇×SD₁₆	1	2	yes	—
283	C₂²×C₄	C₇×Q₁₆	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
287	M₁₆	—	4	4	no	—
288	M₁₆	—	4	4	no	—
289	M₁₆	—	4	4	no	—
290	M₁₆	—	4	2	no	—
291	M₁₆	—	4	2	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	4	4	no	—
296	C₂×C₈	—	4	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₄²	C₄²×C₇	1	1	yes	characteristic
300	C₄²	C₄²×C₇	1	1	yes	characteristic
301	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
302	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
303	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
304	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
305	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
306	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
307	C₄²	C₇×C₄⋊C₄	1	1	yes	characteristic
308	C₄²	C₇×C₄⋊C₄	1	1	yes	characteristic
309	C₄²	C₇×C₄⋊C₄	1	1	yes	characteristic
310	C₄²	C₇×C₄⋊C₄	1	1	yes	characteristic
311	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
312	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
313	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
314	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
315	C₂×C₇	—	2	2	no	—
316	C₂×C₇	—	2	2	no	—
317	C₂×C₇	—	2	1	no	—
318	C₂×C₇	—	2	1	no	—
319	C₂×C₇	C₂×#340	1	1	yes	characteristic
320	C₂×C₇	#1738	1	1	yes	characteristic
321	C₂×C₇	C₂×#344	1	1	yes	characteristic
322	C₂³	—	4	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	C₇×#95	1	1	yes	characteristic
325	C₂³	C₇×#95	1	1	yes	characteristic
326	C₂³	C₇×#106	1	2	yes	—
327	C₂³	C₇×#107	1	2	yes	—
328	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	C₇×#95	1	1	yes	characteristic
342	C₂×C₄	C₇×#95	1	1	yes	characteristic
343	C₂×C₄	C₇×#95	1	1	yes	characteristic
344	C₂×C₄	C₇×#95	1	1	yes	characteristic
345	C₂×C₄	C₇×#95	1	1	yes	characteristic
346	C₂×C₄	C₇×#95	1	1	yes	characteristic
347	C₂×C₄	C₇×#102	1	2	yes	—
348	C₂×C₄	C₇×#102	1	2	yes	—
349	C₂×C₄	C₇×#102	1	2	yes	—
350	C₂×C₄	C₇×#102	1	2	yes	—
351	C₂×C₄	C₇×#103	1	2	yes	—
352	C₂×C₄	C₇×#103	1	2	yes	—
353	C₂×C₄	C₇×#103	1	2	yes	—
354	C₂×C₄	C₇×#103	1	2	yes	—
355	C₂×C₄	C₇×#106	1	2	yes	—
356	C₂×C₄	C₇×#107	1	2	yes	—
357	C₂×C₄	C₂×C₄²×C₇	1	1	yes	characteristic
358	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
359	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
361	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
362	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
363	C₂×C₄	C₂×C₇×D₈	1	1	yes	characteristic
364	C₂×C₄	C₂×C₇×SD₁₆	1	1	yes	characteristic
365	C₂×C₄	C₂×C₇×SD₁₆	1	1	yes	characteristic
366	C₂×C₄	C₂×C₇×Q₁₆	1	1	yes	characteristic
367	C₈	—	4	4	no	—
368	C₈	—	4	4	no	—
369	C₈	—	4	4	no	—
370	C₇	#8079	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	C₇×#340	1	2	yes	—
380	C₂²	C₇×#340	1	2	yes	—
381	C₂²	C₂×C₇×#95	1	1	yes	characteristic
382	C₂²	C₂×C₇×#106	1	1	yes	characteristic
383	C₂²	C₂×C₇×#107	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	C₇×#340	1	2	yes	—
391	C₄	C₇×#340	1	2	yes	—
392	C₄	C₇×#344	1	2	yes	—
393	C₄	C₂×C₇×#102	1	1	yes	characteristic
394	C₄	C₂×C₇×#102	1	1	yes	characteristic
395	C₄	C₂×C₇×#103	1	1	yes	characteristic
396	C₄	C₂×C₇×#103	1	1	yes	characteristic
397	C₄	C₇×#430	1	2	yes	—
398	C₂	—	2	2	no	—
399	C₂	—	2	2	no	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	C₂×C₇×#340	1	1	yes	characteristic
403	C₂	C₇×#1738	1	1	yes	characteristic
404	C₂	C₂×C₇×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₇
Frattini, cosocle	C₂×C₄²	C₂³×C₇
socle	C₂²×C₇	C₂×#95
prime radical	C₂⁴×C₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇×#1301	C₂	semidirect
27. #8079	C₇	direct (N × H)
71. #1301	C₂×C₇	semidirect
370. C₇	#8079	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×#431	2
C₂×C₇×#423	2
C₇×#1301	2
#8079	7

Subgroups — C7×#8079 #13185295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#8079 #13185295