Subgroups — C₇×#22548 #13199764

Order 1792.

1054 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1983	C₂	1	1	yes	maximal, characteristic
5	C₇×#1983	C₂	1	1	yes	maximal, characteristic
6	C₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1960	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1959	C₂	1	1	yes	maximal, characteristic
9	C₇×#1958	C₂	1	1	yes	maximal, characteristic
10	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1804	C₂	1	1	yes	maximal, characteristic
12	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1762	C₂	1	1	yes	maximal, characteristic
15	C₄×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#556	—	2	4	no	—
17	C₇×#556	C₄	1	8	yes	complemented
18	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×#126	—	2	1	no	—
20	C₂×C₇×#126	—	2	1	no	—
21	C₂×C₇×#124	C₂²	1	1	yes	characteristic
22	C₂×C₇×#124	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₇×#117	—	2	1	no	—
29	C₇×#446	—	2	4	no	—
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×#103	C₂²	1	1	yes	characteristic
34	C₂×C₇×#103	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₇×#103	C₂²	1	1	yes	characteristic
39	C₂×C₇×#103	C₂²	1	1	yes	characteristic
40	C₂×C₇×#103	C₂²	1	1	yes	characteristic
41	C₂×C₇×#102	C₂²	1	1	yes	characteristic
42	C₂×C₇×#102	C₂²	1	1	yes	characteristic
43	C₂×C₇×#102	C₂²	1	1	yes	characteristic
44	C₂×C₇×#102	C₂²	1	1	yes	characteristic
45	C₂×C₇×#97	C₂²	1	1	yes	characteristic
46	C₂×C₇×#97	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
48	C₇×#391	—	2	1	no	—
49	C₇×#387	—	2	1	no	—
50	C₇×#387	—	2	1	no	—
51	C₇×#384	C₂²	1	1	yes	characteristic
52	C₇×#382	C₂²	1	1	yes	characteristic
53	C₇×#382	C₂²	1	1	yes	characteristic
54	C₄×C₇×C₄⋊C₄	—	2	1	no	—
55	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
56	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
58	C₇×#340	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#340	C₂²	1	1	yes	characteristic
61	C₇×#340	C₂²	1	1	yes	characteristic
62	#22548	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	—	2	1	no	—
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₇×C₄⋊Q₈	—	2	2	no	—
73	C₇×C₄⋊Q₈	C₂×C₄	1	4	yes	—
74	C₇×#126	—	2	8	no	—
75	C₇×#126	—	2	8	no	—
76	C₇×#124	—	2	2	no	—
77	C₇×#124	—	2	2	no	—
78	C₇×#124	C₂×C₄	1	4	yes	—
79	C₇×#124	C₂×C₄	1	4	yes	—
80	C₇×C₂²⋊Q₈	—	2	8	no	—
81	C₄×C₇×Q₈	—	2	2	no	—
82	C₄×C₇×Q₈	—	2	2	no	—
83	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
84	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
85	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
86	C₄×C₇×Q₈	D₄	1	4	yes	—
87	C₄×C₇×D₄	—	2	2	no	—
88	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
89	C₇×#117	—	2	8	no	—
90	C₂×C₇×C₄⋊C₄	—	2	1	no	—
91	C₂×C₇×C₄⋊C₄	—	2	1	no	—
92	C₂×C₇×C₄⋊C₄	—	2	1	no	—
93	C₂×C₇×C₄⋊C₄	—	2	1	no	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₄⋊C₄	—	2	1	no	—
96	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
97	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
98	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
99	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₄²×C₇	—	2	1	no	—
110	C₂×C₄²×C₇	—	2	1	no	—
111	C₂×C₄²×C₇	—	2	1	no	—
112	C₂×C₄²×C₇	—	2	1	no	—
113	C₂×C₄²×C₇	—	2	1	no	—
114	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊C₈	—	2	2	no	—
118	C₇×C₄⋊C₈	—	2	2	no	—
119	C₇×C₄⋊C₈	—	2	2	no	—
120	C₇×#103	—	2	2	no	—
121	C₇×#103	—	2	2	no	—
122	C₇×#103	—	2	2	no	—
123	C₇×#103	—	2	2	no	—
124	C₇×#103	—	4	1	no	—
125	C₇×#103	—	4	1	no	—
126	C₇×#103	—	4	1	no	—
127	C₇×#103	—	4	1	no	—
128	C₇×#102	—	2	2	no	—
129	C₇×#102	—	2	2	no	—
130	C₇×#102	—	4	1	no	—
131	C₇×#102	—	4	1	no	—
132	C₇×#97	—	2	2	no	—
133	C₇×#97	—	2	2	no	—
134	C₄×C₇×C₈	—	2	2	no	—
135	C₇×#95	—	2	1	no	—
136	C₇×#95	—	2	1	no	—
137	C₇×#95	—	2	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₇×#95	—	2	1	no	—
140	C₇×#95	—	2	1	no	—
141	C₇×#95	—	2	1	no	—
142	C₂×#556	C₂×C₇	1	1	yes	characteristic
143	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
144	#2355	C₂×C₇	1	1	yes	characteristic, complemented
145	#1983	C₂×C₇	1	1	yes	characteristic
146	#1983	C₂×C₇	1	1	yes	characteristic
147	#1981	C₂×C₇	1	1	yes	characteristic, complemented
148	#1960	C₂×C₇	1	1	yes	characteristic, complemented
149	#1959	C₂×C₇	1	1	yes	characteristic
150	#1958	C₂×C₇	1	1	yes	characteristic
151	#1805	C₂×C₇	1	1	yes	characteristic, complemented
152	#1804	C₂×C₇	1	1	yes	characteristic
153	#1803	C₂×C₇	1	1	yes	characteristic, complemented
154	#1763	C₂×C₇	1	1	yes	characteristic, complemented
155	#1762	C₂×C₇	1	1	yes	characteristic
156	C₄×#103	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂⁴×C₇	—	2	1	no	—
158	C₂×C₇×Q₈	—	2	1	no	—
159	C₂×C₇×Q₈	—	2	1	no	—
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	—	2	1	no	—
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	2	1	no	—
165	C₂×C₇×Q₈	—	2	1	no	—
166	C₂×C₇×Q₈	—	2	1	no	—
167	C₂×C₇×Q₈	—	2	1	no	—
168	C₂×C₇×Q₈	—	4	1	no	—
169	C₂×C₇×Q₈	—	4	1	no	—
170	C₂×C₇×Q₈	C₂²⋊C₄	1	4	yes	—
171	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
172	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
173	C₂×C₇×D₄	—	2	1	no	—
174	C₂×C₇×D₄	—	2	1	no	—
175	C₂×C₇×D₄	—	2	1	no	—
176	C₂×C₇×D₄	—	2	1	no	—
177	C₂×C₇×D₄	—	2	1	no	—
178	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
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	4	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	4	2	no	—
188	C₂²×C₄×C₇	—	4	2	no	—
189	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
196	C₂×C₇×C₈	—	2	1	no	—
197	C₂×C₇×C₈	—	2	1	no	—
198	C₂×C₇×C₈	—	2	1	no	—
199	C₂×C₇×C₈	—	2	1	no	—
200	C₂×C₇×C₈	—	2	1	no	—
201	C₂×C₇×C₈	—	2	1	no	—
202	C₂×C₇×C₈	—	2	1	no	—
203	C₂×C₇×C₈	—	2	1	no	—
204	C₂×C₇×C₈	—	2	1	no	—
205	C₂×C₇×C₈	—	2	1	no	—
206	C₂×C₇×C₈	—	2	1	no	—
207	C₂×C₇×C₈	#41	1	2	yes	—
208	C₇×C₄⋊C₄	—	2	4	no	—
209	C₇×C₄⋊C₄	—	2	4	no	—
210	C₇×C₄⋊C₄	—	2	4	no	—
211	C₇×C₄⋊C₄	—	2	4	no	—
212	C₇×C₄⋊C₄	—	2	1	no	—
213	C₇×C₄⋊C₄	—	2	1	no	—
214	C₇×C₄⋊C₄	—	2	1	no	—
215	C₇×C₄⋊C₄	—	2	1	no	—
216	C₇×C₄⋊C₄	—	2	1	no	—
217	C₇×C₄⋊C₄	—	2	1	no	—
218	C₇×C₄⋊C₄	—	2	1	no	—
219	C₇×C₄⋊C₄	—	2	1	no	—
220	C₇×C₄⋊C₄	—	4	2	no	—
221	C₇×C₄⋊C₄	—	8	1	no	—
222	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
223	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
224	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
225	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
226	C₇×C₄⋊C₄	#41	1	2	yes	—
227	C₇×C₂²⋊C₄	—	2	4	no	—
228	C₇×C₂²⋊C₄	—	2	4	no	—
229	C₇×C₂²⋊C₄	—	2	4	no	—
230	C₇×C₂²⋊C₄	—	2	4	no	—
231	C₇×C₂²⋊C₄	—	2	4	no	—
232	C₄²×C₇	—	2	4	no	—
233	C₄²×C₇	—	2	4	no	—
234	C₄²×C₇	—	4	2	no	—
235	C₄²×C₇	—	8	1	no	—
236	C₄²×C₇	—	8	1	no	—
237	C₄²×C₇	C₂²×C₄	1	2	yes	—
238	C₄²×C₇	C₂²×C₄	1	2	yes	—
239	C₄²×C₇	C₂²×C₄	1	2	yes	—
240	C₄²×C₇	C₂×D₄	1	2	yes	—
241	C₄²×C₇	C₂×D₄	1	2	yes	—
242	C₄²×C₇	C₂×D₄	1	2	yes	—
243	#556	—	2	4	no	—
244	#556	C₄×C₇	1	8	yes	complemented
245	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
246	C₂×#126	—	2	1	no	—
247	C₂×#126	—	2	1	no	—
248	C₂×#124	C₂²×C₇	1	1	yes	characteristic
249	C₂×#124	C₂²×C₇	1	1	yes	characteristic
250	C₂×C₂²⋊Q₈	—	2	1	no	—
251	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
255	C₂×#117	—	2	1	no	—
256	#446	—	2	4	no	—
257	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
260	C₂×#103	C₂²×C₇	1	1	yes	characteristic
261	C₂×#103	C₂²×C₇	1	1	yes	characteristic
262	C₂×#103	C₂²×C₇	1	1	yes	characteristic
263	C₂×#103	C₂²×C₇	1	1	yes	characteristic
264	C₂×#103	C₂²×C₇	1	1	yes	characteristic
265	C₂×#103	C₂²×C₇	1	1	yes	characteristic
266	C₂×#103	C₂²×C₇	1	1	yes	characteristic
267	C₂×#103	C₂²×C₇	1	1	yes	characteristic
268	C₂×#102	C₂²×C₇	1	1	yes	characteristic
269	C₂×#102	C₂²×C₇	1	1	yes	characteristic
270	C₂×#102	C₂²×C₇	1	1	yes	characteristic
271	C₂×#102	C₂²×C₇	1	1	yes	characteristic
272	C₂×#97	C₂²×C₇	1	1	yes	characteristic
273	C₂×#97	C₂²×C₇	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
275	#391	—	2	1	no	—
276	#387	—	2	1	no	—
277	#387	—	2	1	no	—
278	#384	C₂²×C₇	1	1	yes	characteristic
279	#382	C₂²×C₇	1	1	yes	characteristic
280	#382	C₂²×C₇	1	1	yes	characteristic
281	C₄×C₄⋊C₄	—	2	1	no	—
282	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
284	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
285	#340	C₂²×C₇	1	1	yes	characteristic
286	#340	C₂²×C₇	1	1	yes	characteristic
287	#340	C₂²×C₇	1	1	yes	characteristic
288	#340	C₂²×C₇	1	1	yes	characteristic
289	C₂³×C₇	—	2	2	no	—
290	C₂³×C₇	—	4	1	no	—
291	C₂³×C₇	—	4	1	no	—
292	C₂³×C₇	—	4	1	no	—
293	C₂³×C₇	—	4	1	no	—
294	C₂³×C₇	—	4	1	no	—
295	C₂³×C₇	—	4	1	no	—
296	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
297	C₇×Q₈	—	2	2	no	—
298	C₇×Q₈	—	2	2	no	—
299	C₇×Q₈	—	2	2	no	—
300	C₇×Q₈	—	2	2	no	—
301	C₇×Q₈	—	4	4	no	—
302	C₇×Q₈	—	4	1	no	—
303	C₇×Q₈	—	4	1	no	—
304	C₇×Q₈	—	4	1	no	—
305	C₇×Q₈	—	4	1	no	—
306	C₇×D₄	—	2	2	no	—
307	C₇×D₄	—	2	2	no	—
308	C₇×D₄	—	4	1	no	—
309	C₇×D₄	—	4	1	no	—
310	C₂×C₄×C₇	—	2	1	no	—
311	C₂×C₄×C₇	—	2	1	no	—
312	C₂×C₄×C₇	—	2	1	no	—
313	C₂×C₄×C₇	—	2	1	no	—
314	C₂×C₄×C₇	—	2	1	no	—
315	C₂×C₄×C₇	—	2	1	no	—
316	C₂×C₄×C₇	—	2	1	no	—
317	C₂×C₄×C₇	—	2	1	no	—
318	C₂×C₄×C₇	—	2	1	no	—
319	C₂×C₄×C₇	—	2	1	no	—
320	C₂×C₄×C₇	—	2	1	no	—
321	C₂×C₄×C₇	—	2	1	no	—
322	C₂×C₄×C₇	—	2	2	no	—
323	C₂×C₄×C₇	—	2	2	no	—
324	C₂×C₄×C₇	—	2	2	no	—
325	C₂×C₄×C₇	—	2	2	no	—
326	C₂×C₄×C₇	—	4	8	no	—
327	C₂×C₄×C₇	—	4	1	no	—
328	C₂×C₄×C₇	—	4	1	no	—
329	C₂×C₄×C₇	—	4	1	no	—
330	C₂×C₄×C₇	—	4	1	no	—
331	C₂×C₄×C₇	—	4	1	no	—
332	C₂×C₄×C₇	—	4	1	no	—
333	C₂×C₄×C₇	—	4	1	no	—
334	C₂×C₄×C₇	—	4	1	no	—
335	C₂×C₄×C₇	—	4	1	no	—
336	C₂×C₄×C₇	—	4	1	no	—
337	C₂×C₄×C₇	—	4	1	no	—
338	C₂×C₄×C₇	—	4	1	no	—
339	C₂×C₄×C₇	—	4	1	no	—
340	C₂×C₄×C₇	—	4	1	no	—
341	C₂×C₄×C₇	—	4	1	no	—
342	C₂×C₄×C₇	—	4	1	no	—
343	C₂×C₄×C₇	—	4	1	no	—
344	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
345	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
346	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
347	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
348	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
349	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
351	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
353	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
354	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
356	C₇×C₈	—	2	2	no	—
357	C₇×C₈	—	4	1	no	—
358	C₇×C₈	—	4	1	no	—
359	C₇×C₈	—	4	1	no	—
360	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
361	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
362	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
363	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
364	C₂³×C₄	—	2	1	no	—
365	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
369	C₄⋊Q₈	—	2	2	no	—
370	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	—
371	#126	—	2	8	no	—
372	#126	—	2	8	no	—
373	#124	—	2	2	no	—
374	#124	—	2	2	no	—
375	#124	C₂×C₄×C₇	1	4	yes	—
376	#124	C₂×C₄×C₇	1	4	yes	—
377	C₂²⋊Q₈	—	2	8	no	—
378	C₄×Q₈	—	2	2	no	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
381	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
382	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
383	C₄×Q₈	C₇×D₄	1	4	yes	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
386	#117	—	2	8	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
414	C₄⋊C₈	—	2	2	no	—
415	C₄⋊C₈	—	2	2	no	—
416	C₄⋊C₈	—	2	2	no	—
417	#103	—	2	2	no	—
418	#103	—	2	2	no	—
419	#103	—	2	2	no	—
420	#103	—	2	2	no	—
421	#103	—	4	1	no	—
422	#103	—	4	1	no	—
423	#103	—	4	1	no	—
424	#103	—	4	1	no	—
425	#102	—	2	2	no	—
426	#102	—	2	2	no	—
427	#102	—	4	1	no	—
428	#102	—	4	1	no	—
429	#97	—	2	2	no	—
430	#97	—	2	2	no	—
431	C₄×C₈	—	2	2	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	C₂²×C₇	—	4	2	no	—
440	C₂²×C₇	—	4	2	no	—
441	C₂²×C₇	—	4	2	no	—
442	C₂²×C₇	—	8	1	no	—
443	C₂²×C₇	—	8	1	no	—
444	C₂²×C₇	—	8	1	no	—
445	C₂²×C₇	—	8	1	no	—
446	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
447	C₂²×C₇	#548	1	1	yes	characteristic
448	C₂²×C₇	#550	1	1	yes	characteristic
449	C₂²×C₇	#575	1	1	yes	characteristic
450	C₂²×C₇	#575	1	1	yes	characteristic
451	C₂²×C₇	#577	1	1	yes	characteristic
452	C₂²×C₇	#578	1	1	yes	characteristic
453	C₄×C₇	—	2	2	no	—
454	C₄×C₇	—	2	2	no	—
455	C₄×C₇	—	2	2	no	—
456	C₄×C₇	—	2	2	no	—
457	C₄×C₇	—	2	2	no	—
458	C₄×C₇	—	2	2	no	—
459	C₄×C₇	—	4	2	no	—
460	C₄×C₇	—	4	2	no	—
461	C₄×C₇	—	4	2	no	—
462	C₄×C₇	—	4	2	no	—
463	C₄×C₇	—	8	1	no	—
464	C₄×C₇	—	8	1	no	—
465	C₄×C₇	—	8	1	no	—
466	C₄×C₇	C₄×#41	1	1	yes	characteristic
467	C₄×C₇	#520	1	1	yes	characteristic
468	C₄×C₇	#548	1	1	yes	characteristic
469	C₄×C₇	#550	1	1	yes	characteristic
470	C₂⁴	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	4	1	no	—
482	C₂×Q₈	—	4	1	no	—
483	C₂×Q₈	C₇×C₂²⋊C₄	1	4	yes	—
484	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
485	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
506	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
507	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	C₇×#41	1	2	yes	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	4	2	no	—
534	C₄⋊C₄	—	8	1	no	—
535	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
536	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
537	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
538	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
539	C₄⋊C₄	C₇×#41	1	2	yes	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₄²	—	2	4	no	—
546	C₄²	—	2	4	no	—
547	C₄²	—	4	2	no	—
548	C₄²	—	8	1	no	—
549	C₄²	—	8	1	no	—
550	C₄²	C₂²×C₄×C₇	1	2	yes	—
551	C₄²	C₂²×C₄×C₇	1	2	yes	—
552	C₄²	C₂²×C₄×C₇	1	2	yes	—
553	C₄²	C₂×C₇×D₄	1	2	yes	—
554	C₄²	C₂×C₇×D₄	1	2	yes	—
555	C₄²	C₂×C₇×D₄	1	2	yes	—
556	C₂×C₇	—	8	2	no	—
557	C₂×C₇	#2341	1	1	yes	characteristic
558	C₂×C₇	#2896	1	1	yes	characteristic
559	C₂×C₇	#2898	1	1	yes	characteristic
560	C₂×C₇	#3376	1	1	yes	characteristic
561	C₂×C₇	#3377	1	1	yes	characteristic
562	C₂×C₇	#3401	1	1	yes	characteristic
563	C₂×C₇	#3402	1	1	yes	characteristic
564	C₂³	—	2	2	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
572	Q₈	—	2	2	no	—
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	4	4	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	4	1	no	—
579	Q₈	—	4	1	no	—
580	Q₈	—	4	1	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	4	8	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
620	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
621	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
622	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
623	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
624	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
625	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
626	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
627	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
628	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
629	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
630	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
631	C₈	—	2	2	no	—
632	C₈	—	4	1	no	—
633	C₈	—	4	1	no	—
634	C₈	—	4	1	no	—
635	C₇	#22548	1	1	yes	characteristic, direct product factor, Sylow
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	8	1	no	—
640	C₂²	—	8	1	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
644	C₂²	C₇×#548	1	1	yes	characteristic
645	C₂²	C₇×#550	1	1	yes	characteristic
646	C₂²	C₇×#575	1	1	yes	characteristic
647	C₂²	C₇×#575	1	1	yes	characteristic
648	C₂²	C₇×#577	1	1	yes	characteristic
649	C₂²	C₇×#578	1	1	yes	characteristic
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	2	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	C₄×C₇×#41	1	1	yes	characteristic
664	C₄	C₇×#520	1	1	yes	characteristic
665	C₄	C₇×#548	1	1	yes	characteristic
666	C₄	C₇×#550	1	1	yes	characteristic
667	C₂	—	8	2	no	—
668	C₂	C₇×#2341	1	1	yes	characteristic
669	C₂	C₇×#2896	1	1	yes	characteristic
670	C₂	C₇×#2898	1	1	yes	characteristic
671	C₂	C₇×#3376	1	1	yes	characteristic
672	C₂	C₇×#3377	1	1	yes	characteristic
673	C₂	C₇×#3401	1	1	yes	characteristic
674	C₂	C₇×#3402	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#446	C₂	semidirect
3. C₇×#2355	C₂	semidirect
6. C₇×#1981	C₂	semidirect
7. C₇×#1960	C₂	semidirect
10. C₇×#1805	C₂	semidirect
12. C₇×#1803	C₂	semidirect
13. C₇×#1763	C₂	semidirect
15. C₄×C₇×#103	C₂	semidirect
17. C₇×#556	C₄	semidirect
62. #22548	C₇	direct (N × H)
143. C₂×#446	C₂×C₇	semidirect
144. #2355	C₂×C₇	semidirect
147. #1981	C₂×C₇	semidirect
148. #1960	C₂×C₇	semidirect
151. #1805	C₂×C₇	semidirect
153. #1803	C₂×C₇	semidirect
154. #1763	C₂×C₇	semidirect
156. C₄×#103	C₂×C₇	semidirect
244. #556	C₄×C₇	semidirect
635. C₇	#22548	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×#556	2
C₂×C₇×#446	2
C₇×#2355	2
C₇×#1983	2
C₇×#1981	2
C₇×#1960	2
C₇×#1959	2
C₇×#1958	2
C₇×#1805	2
C₇×#1804	2
C₇×#1803	2
C₇×#1763	2
C₇×#1762	2
C₄×C₇×#103	2
#22548	7

Subgroups — C7×#22548 #13199764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22548 #13199764