Subgroups — C₇×#21997 #13199213

Order 1792.

800 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2290	C₂	1	1	yes	maximal, characteristic
2	C₇×#1923	C₂	1	2	yes	maximal, complemented
3	C₇×#1916	C₂	1	2	yes	maximal, complemented
4	C₇×#1869	C₂	1	2	yes	maximal
5	C₇×#1850	C₂	1	2	yes	maximal, complemented
6	C₇×#1840	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1832	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1818	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#336	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₇×C₈	C₂²	1	2	yes	—
13	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₇×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
22	C₇×#388	C₄	1	2	yes	—
23	C₇×#387	C₄	1	2	yes	—
24	C₇×#386	C₄	1	2	yes	—
25	C₇×#385	C₄	1	2	yes	—
26	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₇×#376	C₂²	1	1	yes	characteristic
30	C₇×#336	C₂²	1	1	yes	characteristic
31	C₇×#336	C₂²	1	1	yes	characteristic
32	C₇×#336	C₂²	1	2	yes	—
33	C₇×#336	C₂²	1	1	yes	characteristic
34	C₇×#336	C₂²	1	1	yes	characteristic
35	C₇×#336	C₂²	1	2	yes	—
36	C₇×#336	C₂²	1	2	yes	—
37	C₇×#336	C₂²	1	2	yes	—
38	C₇×#336	C₂²	1	2	yes	—
39	#21997	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
44	C₂²×C₇×C₈	—	2	4	no	—
45	C₂²×C₇×C₈	—	4	2	no	—
46	C₂²×C₇×C₈	—	4	2	no	—
47	C₂²×C₇×C₈	C₂³	1	2	yes	—
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₂²×C₇×C₈	C₂³	1	2	yes	—
50	C₂²×C₇×C₈	C₂³	1	2	yes	—
51	C₄×C₇×D₄	—	2	4	no	—
52	C₇×#117	—	4	2	no	—
53	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₇	—	4	2	no	—
62	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
68	C₇×C₄⋊C₈	—	4	2	no	—
69	C₇×C₄⋊C₈	—	4	2	no	—
70	C₇×C₂²⋊C₈	—	2	4	no	—
71	C₇×C₂²⋊C₈	—	4	2	no	—
72	C₇×C₂²⋊C₈	—	4	2	no	—
73	C₄×C₇×C₈	—	4	2	no	—
74	C₇×#95	C₂×C₄	1	2	yes	—
75	C₇×#95	C₂×C₄	1	2	yes	—
76	C₇×#95	C₂×C₄	1	2	yes	—
77	C₇×#95	C₂×C₄	1	2	yes	—
78	C₇×#95	C₂×C₄	1	2	yes	—
79	#2290	C₂×C₇	1	1	yes	characteristic
80	#1923	C₂×C₇	1	2	yes	complemented
81	#1916	C₂×C₇	1	2	yes	complemented
82	#1869	C₂×C₇	1	2	yes	—
83	#1850	C₂×C₇	1	2	yes	complemented
84	#1840	C₂×C₇	1	1	yes	characteristic, complemented
85	#1832	C₂×C₇	1	1	yes	characteristic, complemented
86	#1818	C₂×C₇	1	1	yes	characteristic, complemented
87	#1798	C₂×C₇	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
89	C₂×#336	C₂×C₇	1	1	yes	characteristic, complemented
90	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
91	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₇×D₄	—	2	2	no	—
93	C₂×C₇×D₄	—	2	4	no	—
94	C₂²×C₄×C₇	—	2	2	no	—
95	C₂²×C₄×C₇	—	2	1	no	—
96	C₂²×C₄×C₇	—	2	1	no	—
97	C₂²×C₄×C₇	—	2	4	no	—
98	C₂²×C₄×C₇	—	2	4	no	—
99	C₂²×C₄×C₇	—	2	2	no	—
100	C₂²×C₄×C₇	—	2	1	no	—
101	C₂²×C₄×C₇	—	2	2	no	—
102	C₂²×C₄×C₇	—	2	1	no	—
103	C₂²×C₄×C₇	—	4	2	no	—
104	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₇	#41	1	4	yes	—
113	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	—	2	2	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	—	2	2	no	—
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	2	2	no	—
123	C₂×C₇×C₈	—	2	2	no	—
124	C₂×C₇×C₈	—	2	2	no	—
125	C₂×C₇×C₈	—	2	2	no	—
126	C₂×C₇×C₈	—	4	8	no	—
127	C₇×C₄⋊C₄	—	2	2	no	—
128	C₇×C₄⋊C₄	—	2	4	no	—
129	C₇×C₄⋊C₄	—	4	2	no	—
130	C₇×C₂²⋊C₄	—	2	2	no	—
131	C₇×C₂²⋊C₄	—	2	4	no	—
132	C₇×C₂²⋊C₄	—	2	2	no	—
133	C₇×C₂²⋊C₄	—	2	4	no	—
134	C₇×C₂²⋊C₄	—	4	2	no	—
135	C₄²×C₇	—	2	2	no	—
136	C₄²×C₇	—	2	2	no	—
137	C₄²×C₇	—	2	1	no	—
138	C₄²×C₇	—	2	2	no	—
139	C₄²×C₇	—	2	2	no	—
140	C₄²×C₇	—	2	1	no	—
141	C₄²×C₇	—	4	2	no	—
142	C₂³×C₈	C₂²×C₇	1	2	yes	—
143	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
144	C₂×#117	C₂²×C₇	1	1	yes	characteristic
145	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
146	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
147	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
148	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
149	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
150	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
151	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
152	#388	C₄×C₇	1	2	yes	—
153	#387	C₄×C₇	1	2	yes	—
154	#386	C₄×C₇	1	2	yes	—
155	#385	C₄×C₇	1	2	yes	—
156	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
157	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
158	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
159	#376	C₂²×C₇	1	1	yes	characteristic
160	#336	C₂²×C₇	1	1	yes	characteristic
161	#336	C₂²×C₇	1	1	yes	characteristic
162	#336	C₂²×C₇	1	1	yes	characteristic
163	#336	C₂²×C₇	1	1	yes	characteristic
164	#336	C₂²×C₇	1	2	yes	—
165	#336	C₂²×C₇	1	2	yes	—
166	#336	C₂²×C₇	1	2	yes	—
167	#336	C₂²×C₇	1	2	yes	—
168	#336	C₂²×C₇	1	2	yes	—
169	C₂³×C₇	—	2	1	no	—
170	C₂³×C₇	—	2	1	no	—
171	C₂³×C₇	—	2	2	no	—
172	C₂³×C₇	—	2	1	no	—
173	C₂³×C₇	—	2	1	no	—
174	C₂³×C₇	—	2	1	no	—
175	C₂³×C₇	—	2	2	no	—
176	C₂³×C₇	—	2	2	no	—
177	C₂³×C₇	#117	1	2	yes	—
178	C₂³×C₇	#131	1	4	yes	—
179	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
180	C₇×D₄	—	4	4	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	2	1	no	—
183	C₂×C₄×C₇	—	2	1	no	—
184	C₂×C₄×C₇	—	2	2	no	—
185	C₂×C₄×C₇	—	2	4	no	—
186	C₂×C₄×C₇	—	2	4	no	—
187	C₂×C₄×C₇	—	2	1	no	—
188	C₂×C₄×C₇	—	2	1	no	—
189	C₂×C₄×C₇	—	2	1	no	—
190	C₂×C₄×C₇	—	2	2	no	—
191	C₂×C₄×C₇	—	2	2	no	—
192	C₂×C₄×C₇	—	2	1	no	—
193	C₂×C₄×C₇	—	2	2	no	—
194	C₂×C₄×C₇	—	2	1	no	—
195	C₂×C₄×C₇	—	2	2	no	—
196	C₂×C₄×C₇	—	2	2	no	—
197	C₂×C₄×C₇	—	2	2	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	2	2	no	—
200	C₂×C₄×C₇	—	2	2	no	—
201	C₂×C₄×C₇	—	2	2	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	4	8	no	—
204	C₂×C₄×C₇	—	4	2	no	—
205	C₂×C₄×C₇	—	4	2	no	—
206	C₂×C₄×C₇	#117	1	2	yes	—
207	C₂×C₄×C₇	#131	1	4	yes	—
208	C₂×C₄×C₇	C₂×#41	1	2	yes	—
209	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
211	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
212	C₇×C₈	—	4	2	no	—
213	C₇×C₈	—	4	2	no	—
214	C₇×C₈	—	4	2	no	—
215	C₇×C₈	—	4	2	no	—
216	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
217	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
218	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	4	2	no	—
222	C₂²×C₈	—	4	2	no	—
223	C₂²×C₈	C₂³×C₇	1	2	yes	—
224	C₂²×C₈	C₂³×C₇	1	2	yes	—
225	C₂²×C₈	C₂³×C₇	1	2	yes	—
226	C₂²×C₈	C₂³×C₇	1	2	yes	—
227	C₄×D₄	—	2	4	no	—
228	#117	—	4	2	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
232	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
236	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
237	C₂×C₄²	—	4	2	no	—
238	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
239	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
244	C₄⋊C₈	—	4	2	no	—
245	C₄⋊C₈	—	4	2	no	—
246	C₂²⋊C₈	—	2	4	no	—
247	C₂²⋊C₈	—	4	2	no	—
248	C₂²⋊C₈	—	4	2	no	—
249	C₄×C₈	—	4	2	no	—
250	#95	C₂×C₄×C₇	1	2	yes	—
251	#95	C₂×C₄×C₇	1	2	yes	—
252	#95	C₂×C₄×C₇	1	2	yes	—
253	#95	C₂×C₄×C₇	1	2	yes	—
254	#95	C₂×C₄×C₇	1	2	yes	—
255	C₂²×C₇	—	2	2	no	—
256	C₂²×C₇	—	2	2	no	—
257	C₂²×C₇	—	2	4	no	—
258	C₂²×C₇	—	2	4	no	—
259	C₂²×C₇	—	4	1	no	—
260	C₂²×C₇	—	4	1	no	—
261	C₂²×C₇	—	4	1	no	—
262	C₂²×C₇	—	4	2	no	—
263	C₂²×C₇	—	4	2	no	—
264	C₂²×C₇	#433	1	4	yes	—
265	C₂²×C₇	C₂×#117	1	1	yes	characteristic
266	C₂²×C₇	#518	1	1	yes	characteristic
267	C₂²×C₇	#520	1	1	yes	characteristic
268	C₂²×C₇	C₂×#131	1	2	yes	—
269	C₂²×C₇	C₂×#131	1	2	yes	—
270	C₄×C₇	—	2	2	no	—
271	C₄×C₇	—	2	4	no	—
272	C₄×C₇	—	4	1	no	—
273	C₄×C₇	—	4	1	no	—
274	C₄×C₇	—	4	1	no	—
275	C₄×C₇	—	4	2	no	—
276	C₄×C₇	—	4	2	no	—
277	C₄×C₇	—	4	2	no	—
278	C₄×C₇	#538	1	2	yes	—
279	C₄×C₇	#539	1	2	yes	—
280	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
281	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
302	C₂²×C₄	C₇×#41	1	4	yes	—
303	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	8	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	4	2	no	—
332	C₂×C₇	—	2	4	no	—
333	C₂×C₇	—	8	1	no	—
334	C₂×C₇	#2318	1	1	yes	characteristic
335	C₂×C₇	C₂×#433	1	1	yes	characteristic
336	C₂×C₇	#2922	1	1	yes	characteristic
337	C₂×C₇	#2977	1	2	yes	—
338	C₂×C₇	#2994	1	2	yes	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	C₇×#117	1	2	yes	—
348	C₂³	C₇×#131	1	4	yes	—
349	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	8	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	C₇×#117	1	2	yes	—
377	C₂×C₄	C₇×#131	1	4	yes	—
378	C₂×C₄	C₂×C₇×#41	1	2	yes	—
379	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
381	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₇	#21997	1	1	yes	characteristic, direct product factor, Sylow
387	C₂²	—	2	2	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	C₇×#433	1	4	yes	—
397	C₂²	C₂×C₇×#117	1	1	yes	characteristic
398	C₂²	C₇×#518	1	1	yes	characteristic
399	C₂²	C₇×#520	1	1	yes	characteristic
400	C₂²	C₂×C₇×#131	1	2	yes	—
401	C₂²	C₂×C₇×#131	1	2	yes	—
402	C₄	—	2	4	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	1	no	—
410	C₄	C₇×#538	1	2	yes	—
411	C₄	C₇×#539	1	2	yes	—
412	C₂	—	2	4	no	—
413	C₂	—	8	1	no	—
414	C₂	C₇×#2318	1	1	yes	characteristic
415	C₂	C₂×C₇×#433	1	1	yes	characteristic
416	C₂	C₇×#2922	1	1	yes	characteristic
417	C₂	C₇×#2977	1	2	yes	—
418	C₂	C₇×#2994	1	2	yes	—

	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	C₂²×C₇×D₄	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
2. C₇×#1923	C₂	semidirect
3. C₇×#1916	C₂	semidirect
5. C₇×#1850	C₂	semidirect
6. C₇×#1840	C₂	semidirect
7. C₇×#1832	C₂	semidirect
8. C₇×#1818	C₂	semidirect
9. C₇×#1798	C₂	semidirect
10. C₄×C₇×C₂²⋊C₈	C₂	semidirect
11. C₂×C₇×#336	C₂	semidirect
39. #21997	C₇	direct (N × H)
80. #1923	C₂×C₇	semidirect
81. #1916	C₂×C₇	semidirect
83. #1850	C₂×C₇	semidirect
84. #1840	C₂×C₇	semidirect
85. #1832	C₂×C₇	semidirect
86. #1818	C₂×C₇	semidirect
87. #1798	C₂×C₇	semidirect
88. C₄×C₂²⋊C₈	C₂×C₇	semidirect
89. C₂×#336	C₂×C₇	semidirect
386. C₇	#21997	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2290	2
C₇×#1923	2
C₇×#1916	2
C₇×#1869	2
C₇×#1850	2
C₇×#1840	2
C₇×#1832	2
C₇×#1818	2
C₇×#1798	2
C₄×C₇×C₂²⋊C₈	2
C₂×C₇×#336	2
#21997	7

Subgroups — C7×#21997 #13199213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21997 #13199213