Subgroups — C₇×#29445 #13206661

Order 1792.

788 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2860	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2067	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2065	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2054	C₂	1	1	yes	maximal, characteristic
7	C₇×#1972	C₂	1	1	yes	maximal, characteristic
8	C₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1936	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1936	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1925	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1879	C₂	1	1	yes	maximal, characteristic
14	C₇×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×#126	—	2	1	no	—
18	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₇×#117	—	2	1	no	—
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#102	C₂²	1	1	yes	characteristic
26	C₂×C₇×#102	C₂²	1	1	yes	characteristic
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₇×#102	C₂²	1	1	yes	characteristic
29	C₂×C₇×#102	C₂²	1	1	yes	characteristic
30	C₂×C₇×#102	C₂²	1	1	yes	characteristic
31	C₂×C₇×#97	C₂²	1	1	yes	characteristic
32	C₂×C₇×#97	C₂²	1	1	yes	characteristic
33	C₇×#390	C₂²	1	1	yes	characteristic
34	C₇×#390	C₂²	1	1	yes	characteristic
35	C₇×#390	C₂²	1	1	yes	characteristic
36	C₇×#390	C₂²	1	1	yes	characteristic
37	C₇×#390	C₂²	1	1	yes	characteristic
38	C₇×#389	C₂²	1	1	yes	characteristic
39	C₇×#389	C₂²	1	1	yes	characteristic
40	C₇×#389	C₂²	1	1	yes	characteristic
41	C₇×#389	C₂²	1	1	yes	characteristic
42	C₇×#389	C₂²	1	1	yes	characteristic
43	C₇×#388	—	2	1	no	—
44	C₇×#388	—	2	1	no	—
45	C₇×#388	—	2	1	no	—
46	C₇×#388	—	2	1	no	—
47	C₇×#388	—	2	1	no	—
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
50	C₄³×C₇	C₂²	1	1	yes	characteristic
51	C₇×#340	C₂²	1	1	yes	characteristic
52	C₇×#340	C₂²	1	1	yes	characteristic
53	C₇×#340	C₂²	1	1	yes	characteristic
54	C₇×#340	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	#29445	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	—	2	1	no	—
63	C₂×C₇×D₈	—	2	2	no	—
64	C₂×C₇×D₈	—	2	2	no	—
65	C₂×C₇×D₈	—	4	1	no	—
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₇×#126	—	4	4	no	—
71	C₄×C₇×D₄	—	2	2	no	—
72	C₄×C₇×D₄	—	2	2	no	—
73	C₇×#117	—	4	4	no	—
74	C₂×C₇×C₄⋊C₄	—	2	1	no	—
75	C₂×C₇×C₄⋊C₄	—	2	1	no	—
76	C₂×C₇×C₄⋊C₄	—	2	1	no	—
77	C₂×C₇×C₄⋊C₄	—	2	1	no	—
78	C₂×C₇×C₄⋊C₄	—	2	1	no	—
79	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₄²×C₇	—	2	1	no	—
97	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
104	C₇×#107	—	4	1	no	—
105	C₇×#106	—	2	2	no	—
106	C₇×#106	—	2	2	no	—
107	C₇×C₄⋊C₈	—	2	2	no	—
108	C₇×C₄⋊C₈	—	2	2	no	—
109	C₇×#102	—	2	2	no	—
110	C₇×#102	—	2	2	no	—
111	C₇×#102	—	2	2	no	—
112	C₇×#102	—	2	2	no	—
113	C₇×#102	—	4	1	no	—
114	C₇×#102	—	4	1	no	—
115	C₇×#97	—	4	1	no	—
116	C₇×#97	—	4	1	no	—
117	C₇×#95	—	2	1	no	—
118	C₇×#95	—	2	1	no	—
119	C₇×#95	—	2	1	no	—
120	C₇×#95	—	2	1	no	—
121	C₇×#95	—	2	1	no	—
122	C₇×#95	—	2	1	no	—
123	#2860	C₂×C₇	1	1	yes	characteristic, complemented
124	#2293	C₂×C₇	1	1	yes	characteristic, complemented
125	#2088	C₂×C₇	1	1	yes	characteristic, complemented
126	#2067	C₂×C₇	1	1	yes	characteristic, complemented
127	#2065	C₂×C₇	1	1	yes	characteristic, complemented
128	#2054	C₂×C₇	1	1	yes	characteristic
129	#1972	C₂×C₇	1	1	yes	characteristic
130	#1944	C₂×C₇	1	1	yes	characteristic, complemented
131	#1936	C₂×C₇	1	1	yes	characteristic, complemented
132	#1936	C₂×C₇	1	1	yes	characteristic, complemented
133	#1925	C₂×C₇	1	1	yes	characteristic, complemented
134	#1920	C₂×C₇	1	1	yes	characteristic, complemented
135	#1879	C₂×C₇	1	1	yes	characteristic
136	#1864	C₂×C₇	1	1	yes	characteristic, complemented
137	#1767	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂⁴×C₇	—	2	1	no	—
139	C₂⁴×C₇	—	2	1	no	—
140	C₂×C₇×D₄	—	2	1	no	—
141	C₂×C₇×D₄	—	2	1	no	—
142	C₂×C₇×D₄	—	2	1	no	—
143	C₂×C₇×D₄	—	2	1	no	—
144	C₂×C₇×D₄	—	2	1	no	—
145	C₂×C₇×D₄	—	2	1	no	—
146	C₂×C₇×D₄	—	2	1	no	—
147	C₂×C₇×D₄	—	2	1	no	—
148	C₂×C₇×D₄	—	2	1	no	—
149	C₂×C₇×D₄	—	2	1	no	—
150	C₂×C₇×D₄	—	2	1	no	—
151	C₂×C₇×D₄	#41	1	2	yes	—
152	C₂²×C₄×C₇	—	2	4	no	—
153	C₂²×C₄×C₇	—	2	1	no	—
154	C₂²×C₄×C₇	—	2	1	no	—
155	C₂²×C₄×C₇	—	2	1	no	—
156	C₂²×C₄×C₇	—	2	1	no	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	1	no	—
159	C₂²×C₄×C₇	—	4	2	no	—
160	C₂²×C₄×C₇	—	4	2	no	—
161	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
168	C₇×D₈	—	4	4	no	—
169	C₂×C₇×C₈	—	2	1	no	—
170	C₂×C₇×C₈	—	2	1	no	—
171	C₂×C₇×C₈	—	2	1	no	—
172	C₂×C₇×C₈	—	2	1	no	—
173	C₂×C₇×C₈	—	2	1	no	—
174	C₂×C₇×C₈	—	2	1	no	—
175	C₂×C₇×C₈	—	2	1	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	#41	1	2	yes	—
180	C₂×C₇×C₈	#41	1	2	yes	—
181	C₇×C₄⋊C₄	—	2	1	no	—
182	C₇×C₄⋊C₄	—	2	1	no	—
183	C₇×C₄⋊C₄	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	1	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	—	2	1	no	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	—	2	1	no	—
192	C₇×C₄⋊C₄	—	4	2	no	—
193	C₇×C₄⋊C₄	—	4	2	no	—
194	C₇×C₄⋊C₄	—	4	2	no	—
195	C₇×C₄⋊C₄	—	4	2	no	—
196	C₇×C₄⋊C₄	—	4	2	no	—
197	C₇×C₄⋊C₄	#41	1	2	yes	—
198	C₇×C₂²⋊C₄	—	2	4	no	—
199	C₇×C₂²⋊C₄	—	4	2	no	—
200	C₇×C₂²⋊C₄	—	4	2	no	—
201	C₇×C₂²⋊C₄	—	4	2	no	—
202	C₇×C₂²⋊C₄	—	4	2	no	—
203	C₇×C₂²⋊C₄	—	4	2	no	—
204	C₇×C₂²⋊C₄	—	4	2	no	—
205	C₇×C₂²⋊C₄	—	4	2	no	—
206	C₇×C₂²⋊C₄	—	4	2	no	—
207	C₇×C₂²⋊C₄	—	4	2	no	—
208	C₇×C₂²⋊C₄	—	4	2	no	—
209	C₄²×C₇	—	2	2	no	—
210	C₄²×C₇	—	2	2	no	—
211	C₄²×C₇	—	2	1	no	—
212	C₄²×C₇	—	2	1	no	—
213	C₄²×C₇	—	2	1	no	—
214	C₄²×C₇	—	2	1	no	—
215	C₄²×C₇	—	2	1	no	—
216	C₄²×C₇	—	2	1	no	—
217	C₄²×C₇	—	4	1	no	—
218	C₄²×C₇	—	4	1	no	—
219	C₄²×C₇	—	4	2	no	—
220	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
221	C₂×#126	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
223	C₂×#117	—	2	1	no	—
224	C₂×#107	C₂²×C₇	1	1	yes	characteristic
225	C₂×#106	C₂²×C₇	1	1	yes	characteristic
226	C₂×#106	C₂²×C₇	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
229	C₂×#102	C₂²×C₇	1	1	yes	characteristic
230	C₂×#102	C₂²×C₇	1	1	yes	characteristic
231	C₂×#102	C₂²×C₇	1	1	yes	characteristic
232	C₂×#102	C₂²×C₇	1	1	yes	characteristic
233	C₂×#102	C₂²×C₇	1	1	yes	characteristic
234	C₂×#102	C₂²×C₇	1	1	yes	characteristic
235	C₂×#97	C₂²×C₇	1	1	yes	characteristic
236	C₂×#97	C₂²×C₇	1	1	yes	characteristic
237	#390	C₂²×C₇	1	1	yes	characteristic
238	#390	C₂²×C₇	1	1	yes	characteristic
239	#390	C₂²×C₇	1	1	yes	characteristic
240	#390	C₂²×C₇	1	1	yes	characteristic
241	#390	C₂²×C₇	1	1	yes	characteristic
242	#389	C₂²×C₇	1	1	yes	characteristic
243	#389	C₂²×C₇	1	1	yes	characteristic
244	#389	C₂²×C₇	1	1	yes	characteristic
245	#389	C₂²×C₇	1	1	yes	characteristic
246	#389	C₂²×C₇	1	1	yes	characteristic
247	#388	—	2	1	no	—
248	#388	—	2	1	no	—
249	#388	—	2	1	no	—
250	#388	—	2	1	no	—
251	#388	—	2	1	no	—
252	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
253	C₄×C₂²⋊C₄	—	2	1	no	—
254	C₄³	C₂²×C₇	1	1	yes	characteristic
255	#340	C₂²×C₇	1	1	yes	characteristic
256	#340	C₂²×C₇	1	1	yes	characteristic
257	#340	C₂²×C₇	1	1	yes	characteristic
258	#340	C₂²×C₇	1	1	yes	characteristic
259	#340	C₂²×C₇	1	1	yes	characteristic
260	#340	C₂²×C₇	1	1	yes	characteristic
261	#336	C₂²×C₇	1	1	yes	characteristic
262	#336	C₂²×C₇	1	1	yes	characteristic
263	C₂³×C₇	—	2	2	no	—
264	C₂³×C₇	—	4	1	no	—
265	C₂³×C₇	—	4	1	no	—
266	C₂³×C₇	—	4	1	no	—
267	C₂³×C₇	—	4	1	no	—
268	C₂³×C₇	—	4	1	no	—
269	C₂³×C₇	—	4	1	no	—
270	C₂³×C₇	—	4	1	no	—
271	C₂³×C₇	—	4	1	no	—
272	C₂³×C₇	—	4	1	no	—
273	C₂³×C₇	—	4	1	no	—
274	C₂³×C₇	—	4	1	no	—
275	C₂³×C₇	—	4	1	no	—
276	C₂³×C₇	—	4	1	no	—
277	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
278	C₇×D₄	—	2	2	no	—
279	C₇×D₄	—	2	2	no	—
280	C₇×D₄	—	4	1	no	—
281	C₇×D₄	—	4	1	no	—
282	C₇×D₄	—	4	1	no	—
283	C₇×D₄	—	4	1	no	—
284	C₇×D₄	—	4	1	no	—
285	C₇×D₄	—	4	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	2	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	2	1	no	—
299	C₂×C₄×C₇	—	2	1	no	—
300	C₂×C₄×C₇	—	2	1	no	—
301	C₂×C₄×C₇	—	2	1	no	—
302	C₂×C₄×C₇	—	2	1	no	—
303	C₂×C₄×C₇	—	4	8	no	—
304	C₂×C₄×C₇	—	4	1	no	—
305	C₂×C₄×C₇	—	4	1	no	—
306	C₂×C₄×C₇	—	4	1	no	—
307	C₂×C₄×C₇	—	4	1	no	—
308	C₂×C₄×C₇	—	4	1	no	—
309	C₂×C₄×C₇	—	4	1	no	—
310	C₂×C₄×C₇	—	4	1	no	—
311	C₂×C₄×C₇	—	4	1	no	—
312	C₂×C₄×C₇	—	4	1	no	—
313	C₂×C₄×C₇	—	4	1	no	—
314	C₂×C₄×C₇	—	4	1	no	—
315	C₂×C₄×C₇	—	4	1	no	—
316	C₂×C₄×C₇	—	4	1	no	—
317	C₂×C₄×C₇	—	4	1	no	—
318	C₂×C₄×C₇	—	4	1	no	—
319	C₂×C₄×C₇	—	4	1	no	—
320	C₂×C₄×C₇	—	4	1	no	—
321	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
322	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
323	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
328	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
329	C₇×C₈	—	2	2	no	—
330	C₇×C₈	—	2	2	no	—
331	C₇×C₈	—	4	1	no	—
332	C₇×C₈	—	4	1	no	—
333	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
334	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
335	C₂³×C₄	—	2	1	no	—
336	C₂×D₈	—	2	2	no	—
337	C₂×D₈	—	2	2	no	—
338	C₂×D₈	—	4	1	no	—
339	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
343	#126	—	4	4	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	#117	—	4	4	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
371	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
372	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
373	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
377	#107	—	4	1	no	—
378	#106	—	2	2	no	—
379	#106	—	2	2	no	—
380	C₄⋊C₈	—	2	2	no	—
381	C₄⋊C₈	—	2	2	no	—
382	#102	—	2	2	no	—
383	#102	—	2	2	no	—
384	#102	—	2	2	no	—
385	#102	—	2	2	no	—
386	#102	—	4	1	no	—
387	#102	—	4	1	no	—
388	#97	—	4	1	no	—
389	#97	—	4	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	C₂²×C₇	—	4	2	no	—
397	C₂²×C₇	—	4	2	no	—
398	C₂²×C₇	—	4	2	no	—
399	C₂²×C₇	—	8	1	no	—
400	C₂²×C₇	—	8	1	no	—
401	C₂²×C₇	—	8	1	no	—
402	C₂²×C₇	—	8	1	no	—
403	C₂²×C₇	—	8	1	no	—
404	C₂²×C₇	—	8	1	no	—
405	C₂²×C₇	—	8	1	no	—
406	C₂²×C₇	—	8	1	no	—
407	C₂²×C₇	—	8	1	no	—
408	C₂²×C₇	—	8	1	no	—
409	C₂²×C₇	—	8	1	no	—
410	C₂²×C₇	#525	1	1	yes	characteristic
411	C₂²×C₇	#532	1	1	yes	characteristic
412	C₂²×C₇	#537	1	1	yes	characteristic
413	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
414	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
415	C₂²×C₇	#575	1	1	yes	characteristic
416	C₂²×C₇	#575	1	1	yes	characteristic
417	C₄×C₇	—	2	2	no	—
418	C₄×C₇	—	2	2	no	—
419	C₄×C₇	—	4	2	no	—
420	C₄×C₇	—	4	1	no	—
421	C₄×C₇	—	4	1	no	—
422	C₄×C₇	—	4	1	no	—
423	C₄×C₇	—	4	1	no	—
424	C₄×C₇	—	8	1	no	—
425	C₄×C₇	—	8	1	no	—
426	C₄×C₇	—	8	1	no	—
427	C₄×C₇	—	8	1	no	—
428	C₄×C₇	—	8	1	no	—
429	C₄×C₇	#551	1	1	yes	characteristic
430	C₄×C₇	#552	1	1	yes	characteristic
431	C₄×C₇	#553	1	1	yes	characteristic
432	C₄×C₇	#556	1	1	yes	characteristic
433	C₂⁴	—	2	1	no	—
434	C₂⁴	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	C₇×#41	1	2	yes	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
463	D₈	—	4	4	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	C₇×#41	1	2	yes	—
475	C₂×C₈	C₇×#41	1	2	yes	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	C₇×#41	1	2	yes	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₂²⋊C₄	—	4	2	no	—
503	C₂²⋊C₄	—	4	2	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	4	1	no	—
513	C₄²	—	4	1	no	—
514	C₄²	—	4	2	no	—
515	C₂×C₇	—	8	2	no	—
516	C₂×C₇	—	16	1	no	—
517	C₂×C₇	#2601	1	1	yes	characteristic
518	C₂×C₇	#3114	1	1	yes	characteristic
519	C₂×C₇	#3115	1	1	yes	characteristic
520	C₂×C₇	#3171	1	1	yes	characteristic
521	C₂×C₇	#3180	1	1	yes	characteristic
522	C₂×C₇	#3253	1	1	yes	characteristic
523	C₂×C₇	#3256	1	1	yes	characteristic
524	C₂³	—	2	2	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	4	8	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
583	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
584	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
585	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
586	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
587	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
588	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
589	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
590	C₈	—	2	2	no	—
591	C₈	—	2	2	no	—
592	C₈	—	4	1	no	—
593	C₈	—	4	1	no	—
594	C₇	#29445	1	1	yes	characteristic, direct product factor, Sylow
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	8	1	no	—
604	C₂²	—	8	1	no	—
605	C₂²	—	8	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	C₇×#525	1	1	yes	characteristic
610	C₂²	C₇×#532	1	1	yes	characteristic
611	C₂²	C₇×#537	1	1	yes	characteristic
612	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
613	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
614	C₂²	C₇×#575	1	1	yes	characteristic
615	C₂²	C₇×#575	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	—	8	1	no	—
628	C₄	C₇×#551	1	1	yes	characteristic
629	C₄	C₇×#552	1	1	yes	characteristic
630	C₄	C₇×#553	1	1	yes	characteristic
631	C₄	C₇×#556	1	1	yes	characteristic
632	C₂	—	8	2	no	—
633	C₂	—	16	1	no	—
634	C₂	C₇×#2601	1	1	yes	characteristic
635	C₂	C₇×#3114	1	1	yes	characteristic
636	C₂	C₇×#3115	1	1	yes	characteristic
637	C₂	C₇×#3171	1	1	yes	characteristic
638	C₂	C₇×#3180	1	1	yes	characteristic
639	C₂	C₇×#3253	1	1	yes	characteristic
640	C₂	C₇×#3256	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2860	C₂	semidirect
2. C₇×#2293	C₂	semidirect
3. C₇×#2088	C₂	semidirect
4. C₇×#2067	C₂	semidirect
5. C₇×#2065	C₂	semidirect
8. C₇×#1944	C₂	semidirect
9. C₇×#1936	C₂	semidirect
10. C₇×#1936	C₂	semidirect
11. C₇×#1925	C₂	semidirect
12. C₇×#1920	C₂	semidirect
14. C₇×#1864	C₂	semidirect
15. C₇×#1767	C₂	semidirect
59. #29445	C₇	direct (N × H)
123. #2860	C₂×C₇	semidirect
124. #2293	C₂×C₇	semidirect
125. #2088	C₂×C₇	semidirect
126. #2067	C₂×C₇	semidirect
127. #2065	C₂×C₇	semidirect
130. #1944	C₂×C₇	semidirect
131. #1936	C₂×C₇	semidirect
132. #1936	C₂×C₇	semidirect
133. #1925	C₂×C₇	semidirect
134. #1920	C₂×C₇	semidirect
136. #1864	C₂×C₇	semidirect
137. #1767	C₂×C₇	semidirect
594. C₇	#29445	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×#2860	2
C₇×#2293	2
C₇×#2088	2
C₇×#2067	2
C₇×#2065	2
C₇×#2054	2
C₇×#1972	2
C₇×#1944	2
C₇×#1936	2
C₇×#1925	2
C₇×#1920	2
C₇×#1879	2
C₇×#1864	2
C₇×#1767	2
#29445	7

Subgroups — C7×#29445 #13206661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#29445 #13206661