Subgroups — C₇×#23787 #13201003

Order 1792.

712 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2331	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2319	C₂	1	1	yes	maximal, characteristic
3	C₇×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2092	C₂	1	1	yes	maximal, characteristic
5	C₇×#2088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2087	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2067	C₂	1	1	yes	maximal, characteristic
8	C₇×#2067	C₂	1	1	yes	maximal, characteristic
9	C₇×#2057	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2023	C₂	1	1	yes	maximal, characteristic
11	C₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1762	C₂	1	1	yes	maximal, characteristic
15	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic
16	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₇×#107	C₂²	1	1	yes	characteristic
19	C₂×C₇×#107	C₂²	1	1	yes	characteristic
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#102	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×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₇×#391	—	2	1	no	—
31	C₇×#391	—	2	1	no	—
32	C₇×#390	C₂²	1	1	yes	characteristic
33	C₇×#390	C₂²	1	1	yes	characteristic
34	C₇×#389	C₂²	1	1	yes	characteristic
35	C₇×#389	C₂²	1	1	yes	characteristic
36	C₇×#389	C₂²	1	1	yes	characteristic
37	C₇×#389	C₂²	1	1	yes	characteristic
38	C₇×#388	—	2	1	no	—
39	C₇×#388	—	2	1	no	—
40	C₇×#387	—	2	1	no	—
41	C₇×#387	—	2	1	no	—
42	C₇×#382	C₂²	1	1	yes	characteristic
43	C₇×#381	—	2	1	no	—
44	C₇×#380	—	2	1	no	—
45	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₇×#376	C₂²	1	1	yes	characteristic
49	C₇×#340	C₂²	1	1	yes	characteristic
50	C₇×#340	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	#23787	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₇×Q₈	—	2	1	no	—
61	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	—	2	1	no	—
63	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₇×C₄⋊Q₈	—	2	2	no	—
68	C₇×C₄⋊Q₈	—	2	2	no	—
69	C₄×C₇×D₄	—	2	2	no	—
70	C₄×C₇×D₄	Q₈	1	4	yes	complemented
71	C₂×C₇×C₄⋊C₄	—	2	1	no	—
72	C₂×C₇×C₄⋊C₄	—	2	1	no	—
73	C₂×C₇×C₄⋊C₄	—	2	1	no	—
74	C₂×C₇×C₄⋊C₄	—	2	1	no	—
75	C₂×C₇×C₄⋊C₄	—	2	1	no	—
76	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₇	—	2	1	no	—
89	C₂×C₄²×C₇	—	2	1	no	—
90	C₂×C₄²×C₇	—	2	1	no	—
91	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
94	C₇×#107	—	2	2	no	—
95	C₇×#107	—	2	2	no	—
96	C₇×#107	—	2	2	no	—
97	C₇×#106	—	2	2	no	—
98	C₇×C₄⋊C₈	—	2	2	no	—
99	C₇×C₄⋊C₈	—	2	2	no	—
100	C₇×#102	—	2	2	no	—
101	C₇×#102	—	2	2	no	—
102	C₇×#102	—	2	2	no	—
103	C₇×#102	—	2	2	no	—
104	C₇×#97	—	2	2	no	—
105	C₄×C₇×C₈	—	2	2	no	—
106	C₇×#95	—	2	1	no	—
107	C₇×#95	—	2	1	no	—
108	C₇×#95	—	2	1	no	—
109	C₇×#95	—	2	1	no	—
110	C₇×#95	—	2	1	no	—
111	C₇×#95	—	2	1	no	—
112	C₇×#95	—	2	1	no	—
113	C₇×#95	—	2	1	no	—
114	C₇×#95	—	2	1	no	—
115	C₇×#95	D₄	1	1	yes	characteristic
116	C₇×#95	D₄	1	1	yes	characteristic
117	C₇×#95	D₄	1	1	yes	characteristic
118	C₇×#95	D₄	1	1	yes	characteristic
119	#2331	C₂×C₇	1	1	yes	characteristic, complemented
120	#2319	C₂×C₇	1	1	yes	characteristic
121	#2101	C₂×C₇	1	1	yes	characteristic, complemented
122	#2092	C₂×C₇	1	1	yes	characteristic
123	#2088	C₂×C₇	1	1	yes	characteristic, complemented
124	#2087	C₂×C₇	1	1	yes	characteristic, complemented
125	#2067	C₂×C₇	1	1	yes	characteristic
126	#2067	C₂×C₇	1	1	yes	characteristic
127	#2057	C₂×C₇	1	1	yes	characteristic, complemented
128	#2023	C₂×C₇	1	1	yes	characteristic
129	#1776	C₂×C₇	1	1	yes	characteristic, complemented
130	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
131	#1768	C₂×C₇	1	1	yes	characteristic, complemented
132	#1762	C₂×C₇	1	1	yes	characteristic
133	C₄×#102	C₂×C₇	1	1	yes	characteristic
134	C₂⁴×C₇	—	2	1	no	—
135	C₂×C₇×Q₈	—	2	4	no	—
136	C₂×C₇×Q₈	—	8	1	no	—
137	C₂×C₇×Q₈	—	8	1	no	—
138	C₂×C₇×D₄	—	2	1	no	—
139	C₂×C₇×D₄	—	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	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₇	—	2	1	no	—
145	C₂²×C₄×C₇	—	2	1	no	—
146	C₂²×C₄×C₇	—	2	1	no	—
147	C₂²×C₄×C₇	—	2	4	no	—
148	C₂²×C₄×C₇	—	2	1	no	—
149	C₂²×C₄×C₇	—	2	1	no	—
150	C₂²×C₄×C₇	—	2	1	no	—
151	C₂²×C₄×C₇	—	2	1	no	—
152	C₂²×C₄×C₇	—	8	1	no	—
153	C₂²×C₄×C₇	—	8	1	no	—
154	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
161	C₂×C₇×C₈	—	2	1	no	—
162	C₂×C₇×C₈	—	2	1	no	—
163	C₂×C₇×C₈	—	2	1	no	—
164	C₂×C₇×C₈	—	2	1	no	—
165	C₂×C₇×C₈	—	2	1	no	—
166	C₂×C₇×C₈	—	2	1	no	—
167	C₂×C₇×C₈	—	2	1	no	—
168	C₂×C₇×C₈	—	2	1	no	—
169	C₂×C₇×C₈	—	2	1	no	—
170	C₂×C₇×C₈	—	2	1	no	—
171	C₂×C₇×C₈	#41	1	2	yes	—
172	C₂×C₇×C₈	#41	1	2	yes	—
173	C₇×C₄⋊C₄	—	2	4	no	—
174	C₇×C₄⋊C₄	—	2	1	no	—
175	C₇×C₄⋊C₄	—	2	1	no	—
176	C₇×C₄⋊C₄	—	2	1	no	—
177	C₇×C₄⋊C₄	—	2	1	no	—
178	C₇×C₄⋊C₄	—	2	1	no	—
179	C₇×C₄⋊C₄	—	2	1	no	—
180	C₇×C₄⋊C₄	—	2	1	no	—
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	—	8	1	no	—
186	C₇×C₄⋊C₄	—	8	1	no	—
187	C₇×C₄⋊C₄	—	8	1	no	—
188	C₇×C₄⋊C₄	—	8	1	no	—
189	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
190	C₇×C₄⋊C₄	#41	1	2	yes	—
191	C₇×C₄⋊C₄	#41	1	2	yes	—
192	C₇×C₂²⋊C₄	—	2	4	no	—
193	C₇×C₂²⋊C₄	—	8	1	no	—
194	C₇×C₂²⋊C₄	—	8	1	no	—
195	C₇×C₂²⋊C₄	—	8	1	no	—
196	C₇×C₂²⋊C₄	—	8	1	no	—
197	C₄²×C₇	—	2	1	no	—
198	C₄²×C₇	—	2	1	no	—
199	C₄²×C₇	—	2	1	no	—
200	C₄²×C₇	—	2	1	no	—
201	C₄²×C₇	—	8	1	no	—
202	C₄²×C₇	—	8	1	no	—
203	C₄²×C₇	—	8	1	no	—
204	C₄²×C₇	C₂×Q₈	1	2	yes	—
205	C₄²×C₇	#41	1	2	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
207	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
208	C₂×#107	C₂²×C₇	1	1	yes	characteristic
209	C₂×#107	C₂²×C₇	1	1	yes	characteristic
210	C₂×#107	C₂²×C₇	1	1	yes	characteristic
211	C₂×#106	C₂²×C₇	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
214	C₂×#102	C₂²×C₇	1	1	yes	characteristic
215	C₂×#102	C₂²×C₇	1	1	yes	characteristic
216	C₂×#102	C₂²×C₇	1	1	yes	characteristic
217	C₂×#102	C₂²×C₇	1	1	yes	characteristic
218	C₂×#97	C₂²×C₇	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
220	#391	—	2	1	no	—
221	#391	—	2	1	no	—
222	#390	C₂²×C₇	1	1	yes	characteristic
223	#390	C₂²×C₇	1	1	yes	characteristic
224	#389	C₂²×C₇	1	1	yes	characteristic
225	#389	C₂²×C₇	1	1	yes	characteristic
226	#389	C₂²×C₇	1	1	yes	characteristic
227	#389	C₂²×C₇	1	1	yes	characteristic
228	#388	—	2	1	no	—
229	#388	—	2	1	no	—
230	#387	—	2	1	no	—
231	#387	—	2	1	no	—
232	#382	C₂²×C₇	1	1	yes	characteristic
233	#381	—	2	1	no	—
234	#380	—	2	1	no	—
235	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
236	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
238	#376	C₂²×C₇	1	1	yes	characteristic
239	#340	C₂²×C₇	1	1	yes	characteristic
240	#340	C₂²×C₇	1	1	yes	characteristic
241	#340	C₂²×C₇	1	1	yes	characteristic
242	#340	C₂²×C₇	1	1	yes	characteristic
243	#340	C₂²×C₇	1	1	yes	characteristic
244	#340	C₂²×C₇	1	1	yes	characteristic
245	#340	C₂²×C₇	1	1	yes	characteristic
246	#340	C₂²×C₇	1	1	yes	characteristic
247	#336	C₂²×C₇	1	1	yes	characteristic
248	#336	C₂²×C₇	1	1	yes	characteristic
249	C₂³×C₇	—	2	2	no	—
250	C₂³×C₇	—	4	1	no	—
251	C₂³×C₇	—	4	1	no	—
252	C₂³×C₇	—	4	1	no	—
253	C₂³×C₇	—	4	1	no	—
254	C₂³×C₇	—	4	1	no	—
255	C₂³×C₇	—	4	1	no	—
256	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
257	C₇×Q₈	—	8	4	no	—
258	C₇×D₄	—	2	2	no	—
259	C₇×D₄	—	2	2	no	—
260	C₇×D₄	—	4	1	no	—
261	C₇×D₄	—	4	1	no	—
262	C₂×C₄×C₇	—	2	1	no	—
263	C₂×C₄×C₇	—	2	1	no	—
264	C₂×C₄×C₇	—	2	1	no	—
265	C₂×C₄×C₇	—	2	1	no	—
266	C₂×C₄×C₇	—	2	2	no	—
267	C₂×C₄×C₇	—	2	1	no	—
268	C₂×C₄×C₇	—	2	1	no	—
269	C₂×C₄×C₇	—	2	2	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	2	1	no	—
272	C₂×C₄×C₇	—	2	1	no	—
273	C₂×C₄×C₇	—	2	1	no	—
274	C₂×C₄×C₇	—	2	1	no	—
275	C₂×C₄×C₇	—	2	1	no	—
276	C₂×C₄×C₇	—	2	1	no	—
277	C₂×C₄×C₇	—	2	1	no	—
278	C₂×C₄×C₇	—	2	1	no	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	2	1	no	—
281	C₂×C₄×C₇	—	4	1	no	—
282	C₂×C₄×C₇	—	4	1	no	—
283	C₂×C₄×C₇	—	4	1	no	—
284	C₂×C₄×C₇	—	4	1	no	—
285	C₂×C₄×C₇	—	4	1	no	—
286	C₂×C₄×C₇	—	4	1	no	—
287	C₂×C₄×C₇	—	4	1	no	—
288	C₂×C₄×C₇	—	4	1	no	—
289	C₂×C₄×C₇	—	4	1	no	—
290	C₂×C₄×C₇	—	4	1	no	—
291	C₂×C₄×C₇	—	4	1	no	—
292	C₂×C₄×C₇	—	4	1	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	—	4	1	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	—	4	1	no	—
297	C₂×C₄×C₇	—	4	1	no	—
298	C₂×C₄×C₇	—	4	1	no	—
299	C₂×C₄×C₇	—	8	4	no	—
300	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
301	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
302	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
303	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
308	C₇×C₈	—	2	2	no	—
309	C₇×C₈	—	2	2	no	—
310	C₇×C₈	—	4	1	no	—
311	C₇×C₈	—	4	1	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
314	C₂³×C₄	—	2	1	no	—
315	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
319	C₄⋊Q₈	—	2	2	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	C₇×Q₈	1	4	yes	complemented
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
346	#107	—	2	2	no	—
347	#107	—	2	2	no	—
348	#107	—	2	2	no	—
349	#106	—	2	2	no	—
350	C₄⋊C₈	—	2	2	no	—
351	C₄⋊C₈	—	2	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	#102	—	2	2	no	—
356	#97	—	2	2	no	—
357	C₄×C₈	—	2	2	no	—
358	#95	—	2	1	no	—
359	#95	—	2	1	no	—
360	#95	—	2	1	no	—
361	#95	—	2	1	no	—
362	#95	—	2	1	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	#95	C₇×D₄	1	1	yes	characteristic
368	#95	C₇×D₄	1	1	yes	characteristic
369	#95	C₇×D₄	1	1	yes	characteristic
370	#95	C₇×D₄	1	1	yes	characteristic
371	C₂²×C₇	—	4	2	no	—
372	C₂²×C₇	—	4	2	no	—
373	C₂²×C₇	—	4	2	no	—
374	C₂²×C₇	—	8	1	no	—
375	C₂²×C₇	—	8	1	no	—
376	C₂²×C₇	—	8	1	no	—
377	C₂²×C₇	—	8	1	no	—
378	C₂²×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
379	C₂²×C₇	#525	1	1	yes	characteristic
380	C₂²×C₇	#532	1	1	yes	characteristic
381	C₂²×C₇	#576	1	1	yes	characteristic
382	C₂²×C₇	#576	1	1	yes	characteristic
383	C₂²×C₇	#577	1	1	yes	characteristic
384	C₂²×C₇	#578	1	1	yes	characteristic
385	C₄×C₇	—	2	2	no	—
386	C₄×C₇	—	2	2	no	—
387	C₄×C₇	—	4	2	no	—
388	C₄×C₇	—	4	1	no	—
389	C₄×C₇	—	4	1	no	—
390	C₄×C₇	—	4	2	no	—
391	C₄×C₇	—	4	2	no	—
392	C₄×C₇	—	4	1	no	—
393	C₄×C₇	—	4	1	no	—
394	C₄×C₇	—	8	1	no	—
395	C₄×C₇	—	8	1	no	—
396	C₄×C₇	—	8	1	no	—
397	C₄×C₇	—	8	1	no	—
398	C₄×C₇	#529	1	1	yes	characteristic
399	C₄×C₇	#529	1	1	yes	characteristic
400	C₄×C₇	#533	1	1	yes	characteristic
401	C₄×C₇	#533	1	1	yes	characteristic
402	C₂⁴	—	2	1	no	—
403	C₂×Q₈	—	2	4	no	—
404	C₂×Q₈	—	8	1	no	—
405	C₂×Q₈	—	8	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	8	1	no	—
421	C₂²×C₄	—	8	1	no	—
422	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
423	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	C₇×#41	1	2	yes	—
440	C₂×C₈	C₇×#41	1	2	yes	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	8	1	no	—
454	C₄⋊C₄	—	8	1	no	—
455	C₄⋊C₄	—	8	1	no	—
456	C₄⋊C₄	—	8	1	no	—
457	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
458	C₄⋊C₄	C₇×#41	1	2	yes	—
459	C₄⋊C₄	C₇×#41	1	2	yes	—
460	C₂²⋊C₄	—	2	4	no	—
461	C₂²⋊C₄	—	8	1	no	—
462	C₂²⋊C₄	—	8	1	no	—
463	C₂²⋊C₄	—	8	1	no	—
464	C₂²⋊C₄	—	8	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	8	1	no	—
470	C₄²	—	8	1	no	—
471	C₄²	—	8	1	no	—
472	C₄²	C₂×C₇×Q₈	1	2	yes	—
473	C₄²	C₇×#41	1	2	yes	—
474	C₂×C₇	—	8	2	no	—
475	C₂×C₇	#2396	1	1	yes	characteristic
476	C₂×C₇	#3081	1	1	yes	characteristic
477	C₂×C₇	#3083	1	1	yes	characteristic
478	C₂×C₇	#3121	1	1	yes	characteristic
479	C₂×C₇	#3122	1	1	yes	characteristic
480	C₂×C₇	#3175	1	1	yes	characteristic
481	C₂×C₇	#3179	1	1	yes	characteristic
482	C₂³	—	2	2	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
490	Q₈	—	8	4	no	—
491	D₄	—	2	2	no	—
492	D₄	—	2	2	no	—
493	D₄	—	4	1	no	—
494	D₄	—	4	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	8	4	no	—
533	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
534	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
535	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
536	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
537	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
538	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
539	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
540	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
541	C₈	—	2	2	no	—
542	C₈	—	2	2	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₇	#23787	1	1	yes	characteristic, direct product factor, Sylow
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	—	8	1	no	—
553	C₂²	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
554	C₂²	C₇×#525	1	1	yes	characteristic
555	C₂²	C₇×#532	1	1	yes	characteristic
556	C₂²	C₇×#576	1	1	yes	characteristic
557	C₂²	C₇×#576	1	1	yes	characteristic
558	C₂²	C₇×#577	1	1	yes	characteristic
559	C₂²	C₇×#578	1	1	yes	characteristic
560	C₄	—	2	2	no	—
561	C₄	—	2	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	C₇×#529	1	1	yes	characteristic
574	C₄	C₇×#529	1	1	yes	characteristic
575	C₄	C₇×#533	1	1	yes	characteristic
576	C₄	C₇×#533	1	1	yes	characteristic
577	C₂	—	8	2	no	—
578	C₂	C₇×#2396	1	1	yes	characteristic
579	C₂	C₇×#3081	1	1	yes	characteristic
580	C₂	C₇×#3083	1	1	yes	characteristic
581	C₂	C₇×#3121	1	1	yes	characteristic
582	C₂	C₇×#3122	1	1	yes	characteristic
583	C₂	C₇×#3175	1	1	yes	characteristic
584	C₂	C₇×#3179	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2331	C₂	semidirect
3. C₇×#2101	C₂	semidirect
5. C₇×#2088	C₂	semidirect
6. C₇×#2087	C₂	semidirect
9. C₇×#2057	C₂	semidirect
11. C₇×#1776	C₂	semidirect
12. C₄×C₇×#107	C₂	semidirect
13. C₇×#1768	C₂	semidirect
59. #23787	C₇	direct (N × H)
70. C₄×C₇×D₄	Q₈	semidirect
119. #2331	C₂×C₇	semidirect
121. #2101	C₂×C₇	semidirect
123. #2088	C₂×C₇	semidirect
124. #2087	C₂×C₇	semidirect
127. #2057	C₂×C₇	semidirect
129. #1776	C₂×C₇	semidirect
130. C₄×#107	C₂×C₇	semidirect
131. #1768	C₂×C₇	semidirect
322. C₄×D₄	C₇×Q₈	semidirect
545. C₇	#23787	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×#2331	2
C₇×#2319	2
C₇×#2101	2
C₇×#2092	2
C₇×#2088	2
C₇×#2087	2
C₇×#2067	2
C₇×#2057	2
C₇×#2023	2
C₇×#1776	2
C₄×C₇×#107	2
C₇×#1768	2
C₇×#1762	2
C₄×C₇×#102	2
#23787	7

Subgroups — C7×#23787 #13201003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23787 #13201003