Subgroups — C₇×#21540 #13198756

Order 1792.

1086 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#468	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic
6	C₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1934	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1895	C₂	1	1	yes	maximal, characteristic
11	C₇×#1894	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1809	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	—	2	1	no	—
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
25	C₇×#468	C₄	1	8	yes	complemented
26	C₇×#440	—	2	4	no	—
27	C₂×C₇×#107	C₂²	1	1	yes	characteristic
28	C₂×C₇×#107	C₂²	1	1	yes	characteristic
29	C₂×C₇×#106	C₂²	1	1	yes	characteristic
30	C₂×C₇×#103	C₂²	1	1	yes	characteristic
31	C₂×C₇×#103	C₂²	1	1	yes	characteristic
32	C₂×C₇×#103	C₂²	1	1	yes	characteristic
33	C₂×C₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₇×#102	C₂²	1	1	yes	characteristic
35	C₂×C₇×#102	C₂²	1	1	yes	characteristic
36	C₄×C₇×M₁₆	—	2	4	no	—
37	C₂×C₇×#97	C₂²	1	1	yes	characteristic
38	C₂×C₇×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₇×#391	C₂²	1	1	yes	characteristic
42	C₇×#390	C₂²	1	1	yes	characteristic
43	C₇×#389	C₂²	1	1	yes	characteristic
44	C₇×#389	C₂²	1	1	yes	characteristic
45	C₇×#388	—	2	1	no	—
46	C₇×#387	—	2	1	no	—
47	C₇×#386	—	2	1	no	—
48	C₇×#385	—	2	1	no	—
49	C₇×#380	C₂²	1	1	yes	characteristic
50	C₇×#380	C₂²	1	1	yes	characteristic
51	C₄×C₇×C₄⋊C₄	—	2	1	no	—
52	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
55	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	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	#21540	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×D₄	—	2	1	no	—
65	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₇	—	2	1	no	—
67	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₇×SD₁₆	—	2	2	no	—
71	C₂×C₇×SD₁₆	—	2	2	no	—
72	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	complemented
73	C₂×C₇×M₁₆	—	2	2	no	—
74	C₂×C₇×M₁₆	—	2	2	no	—
75	C₂×C₇×M₁₆	—	2	2	no	—
76	C₂×C₇×M₁₆	—	2	2	no	—
77	C₂×C₇×M₁₆	—	2	2	no	—
78	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	complemented
79	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₇×C₂²⋊Q₈	—	2	2	no	—
84	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
85	C₇×#121	—	2	2	no	—
86	C₇×#121	C₂×C₄	1	4	yes	—
87	C₄×C₇×Q₈	—	2	2	no	—
88	C₄×C₇×Q₈	—	2	2	no	—
89	C₄×C₇×D₄	—	2	2	no	—
90	C₄×C₇×D₄	—	2	2	no	—
91	C₄×C₇×D₄	—	4	4	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	C₂³	1	1	yes	characteristic
97	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₇×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
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	2	no	—
110	C₂×C₄²×C₇	—	2	2	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	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
118	C₇×#107	—	2	2	no	—
119	C₇×#107	C₂×C₄	1	4	yes	complemented
120	C₇×#106	—	2	2	no	—
121	C₇×#103	—	2	2	no	—
122	C₇×#103	—	2	2	no	—
123	C₇×#103	C₂×C₄	1	4	yes	complemented
124	C₇×#102	—	2	2	no	—
125	C₇×#102	—	2	2	no	—
126	C₇×#102	C₂×C₄	1	4	yes	complemented
127	C₇×#97	—	2	2	no	—
128	C₇×#97	D₄	1	4	yes	complemented
129	C₄×C₇×C₈	—	2	2	no	—
130	C₄×C₇×C₈	—	2	2	no	—
131	C₇×#95	—	2	1	no	—
132	C₇×#95	—	2	1	no	—
133	C₇×#95	—	2	1	no	—
134	C₇×#95	—	2	1	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	C₂×#468	C₂×C₇	1	1	yes	characteristic
140	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
141	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
142	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
143	C₄×#121	C₂×C₇	1	1	yes	characteristic
144	#1968	C₂×C₇	1	1	yes	characteristic, complemented
145	#1942	C₂×C₇	1	1	yes	characteristic, complemented
146	#1934	C₂×C₇	1	1	yes	characteristic, complemented
147	#1933	C₂×C₇	1	1	yes	characteristic, complemented
148	#1895	C₂×C₇	1	1	yes	characteristic
149	#1894	C₂×C₇	1	1	yes	characteristic, complemented
150	#1809	C₂×C₇	1	1	yes	characteristic, complemented
151	#1776	C₂×C₇	1	1	yes	characteristic, complemented
152	#1763	C₂×C₇	1	1	yes	characteristic, complemented
153	#1762	C₂×C₇	1	1	yes	characteristic, complemented
154	C₂⁴×C₇	—	2	1	no	—
155	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
156	C₂×C₇×Q₈	—	2	1	no	—
157	C₂×C₇×Q₈	—	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	C₂²×C₄	1	2	yes	—
162	C₂×C₇×D₄	—	2	4	no	—
163	C₂×C₇×D₄	—	2	1	no	—
164	C₂×C₇×D₄	—	2	1	no	—
165	C₂×C₇×D₄	—	2	1	no	—
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	—	2	1	no	—
168	C₂×C₇×D₄	—	4	2	no	—
169	C₂×C₇×D₄	—	4	2	no	—
170	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₇	—	2	1	no	—
172	C₂²×C₄×C₇	—	2	1	no	—
173	C₂²×C₄×C₇	—	2	1	no	—
174	C₂²×C₄×C₇	—	2	1	no	—
175	C₂²×C₄×C₇	—	2	1	no	—
176	C₂²×C₄×C₇	—	2	1	no	—
177	C₂²×C₄×C₇	—	2	1	no	—
178	C₂²×C₄×C₇	—	2	2	no	—
179	C₂²×C₄×C₇	—	2	2	no	—
180	C₂²×C₄×C₇	—	2	2	no	—
181	C₂²×C₄×C₇	—	2	2	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	4	1	no	—
187	C₂²×C₄×C₇	—	4	1	no	—
188	C₂²×C₄×C₇	—	4	2	no	—
189	C₂²×C₄×C₇	—	4	2	no	—
190	C₂²×C₄×C₇	—	4	2	no	—
191	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	#41	1	2	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
199	C₇×SD₁₆	—	2	8	no	—
200	C₇×M₁₆	—	2	8	no	—
201	C₇×M₁₆	—	2	8	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	—	2	1	no	—
208	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
209	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
210	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
211	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
212	C₂×C₇×C₈	#41	1	2	yes	—
213	C₂×C₇×C₈	#41	1	2	yes	—
214	C₇×C₄⋊C₄	—	2	4	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	—	2	1	no	—
221	C₇×C₄⋊C₄	—	2	1	no	—
222	C₇×C₄⋊C₄	—	2	1	no	—
223	C₇×C₄⋊C₄	—	2	1	no	—
224	C₇×C₄⋊C₄	—	2	1	no	—
225	C₇×C₄⋊C₄	—	4	2	no	—
226	C₇×C₄⋊C₄	—	4	2	no	—
227	C₇×C₄⋊C₄	—	4	2	no	—
228	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
229	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
230	C₇×C₂²⋊C₄	—	2	4	no	—
231	C₇×C₂²⋊C₄	—	2	4	no	—
232	C₇×C₂²⋊C₄	—	4	2	no	—
233	C₇×C₂²⋊C₄	—	4	2	no	—
234	C₇×C₂²⋊C₄	—	4	2	no	—
235	C₇×C₂²⋊C₄	—	4	2	no	—
236	C₇×C₂²⋊C₄	—	4	2	no	—
237	C₄²×C₇	—	2	2	no	—
238	C₄²×C₇	—	2	2	no	—
239	C₄²×C₇	—	2	1	no	—
240	C₄²×C₇	—	2	1	no	—
241	C₄²×C₇	—	4	2	no	—
242	C₄²×C₇	—	4	2	no	—
243	C₄²×C₇	—	4	2	no	—
244	C₄²×C₇	C₂×D₄	1	2	yes	—
245	C₄²×C₇	#41	1	2	yes	—
246	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
249	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
250	C₂×#121	C₂²×C₇	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
252	C₂×C₄×D₄	—	2	1	no	—
253	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
254	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
255	#468	C₄×C₇	1	8	yes	complemented
256	#440	—	2	4	no	—
257	C₂×#107	C₂²×C₇	1	1	yes	characteristic
258	C₂×#107	C₂²×C₇	1	1	yes	characteristic
259	C₂×#106	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×#102	C₂²×C₇	1	1	yes	characteristic
264	C₂×#102	C₂²×C₇	1	1	yes	characteristic
265	C₂×#102	C₂²×C₇	1	1	yes	characteristic
266	C₄×M₁₆	—	2	4	no	—
267	C₂×#97	C₂²×C₇	1	1	yes	characteristic
268	C₂×#97	C₂²×C₇	1	1	yes	characteristic
269	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
271	#391	C₂²×C₇	1	1	yes	characteristic
272	#390	C₂²×C₇	1	1	yes	characteristic
273	#389	C₂²×C₇	1	1	yes	characteristic
274	#389	C₂²×C₇	1	1	yes	characteristic
275	#388	—	2	1	no	—
276	#387	—	2	1	no	—
277	#386	—	2	1	no	—
278	#385	—	2	1	no	—
279	#380	C₂²×C₇	1	1	yes	characteristic
280	#380	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×C₂²⋊C₄	—	2	1	no	—
285	C₄×C₂²⋊C₄	—	2	1	no	—
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	#340	C₂²×C₇	1	1	yes	characteristic
290	#340	C₂²×C₇	1	1	yes	characteristic
291	#340	C₂²×C₇	1	1	yes	characteristic
292	C₂³×C₇	—	2	1	no	—
293	C₂³×C₇	—	2	1	no	—
294	C₂³×C₇	—	2	1	no	—
295	C₂³×C₇	—	2	1	no	—
296	C₂³×C₇	—	2	1	no	—
297	C₂³×C₇	—	2	1	no	—
298	C₂³×C₇	—	2	2	no	—
299	C₂³×C₇	—	4	1	no	—
300	C₂³×C₇	—	4	1	no	—
301	C₂³×C₇	—	4	1	no	—
302	C₂³×C₇	—	4	1	no	—
303	C₂³×C₇	—	4	1	no	—
304	C₂³×C₇	—	4	1	no	—
305	C₂³×C₇	C₄×D₄	1	2	yes	—
306	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
307	C₇×Q₈	—	2	2	no	—
308	C₇×Q₈	—	2	2	no	—
309	C₇×Q₈	—	4	1	no	—
310	C₇×Q₈	—	4	1	no	—
311	C₇×D₄	—	2	2	no	—
312	C₇×D₄	—	2	2	no	—
313	C₇×D₄	—	4	8	no	—
314	C₇×D₄	—	4	1	no	—
315	C₇×D₄	—	4	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	1	no	—
323	C₂×C₄×C₇	—	2	1	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	2	1	no	—
326	C₂×C₄×C₇	—	2	2	no	—
327	C₂×C₄×C₇	—	2	2	no	—
328	C₂×C₄×C₇	—	2	2	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	2	no	—
331	C₂×C₄×C₇	—	2	2	no	—
332	C₂×C₄×C₇	—	2	2	no	—
333	C₂×C₄×C₇	—	4	4	no	—
334	C₂×C₄×C₇	—	4	4	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	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	1	no	—
347	C₂×C₄×C₇	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	4	1	no	—
351	C₂×C₄×C₇	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	—	8	4	no	—
354	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
355	C₂×C₄×C₇	#121	1	2	yes	—
356	C₂×C₄×C₇	#121	1	2	yes	—
357	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
358	C₂×C₄×C₇	#137	1	2	yes	—
359	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
360	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
363	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
364	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
365	C₇×C₈	—	2	2	no	—
366	C₇×C₈	—	2	2	no	—
367	C₇×C₈	—	2	2	no	—
368	C₇×C₈	C₄×D₄	1	4	yes	complemented
369	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
370	C₂²×D₄	—	2	1	no	—
371	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
374	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
376	C₂×SD₁₆	—	2	2	no	—
377	C₂×SD₁₆	—	2	2	no	—
378	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	complemented
379	C₂×M₁₆	—	2	2	no	—
380	C₂×M₁₆	—	2	2	no	—
381	C₂×M₁₆	—	2	2	no	—
382	C₂×M₁₆	—	2	2	no	—
383	C₂×M₁₆	—	2	2	no	—
384	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	complemented
385	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
386	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	complemented
391	#121	—	2	2	no	—
392	#121	C₂×C₄×C₇	1	4	yes	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	4	4	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₄²	—	2	2	no	—
416	C₂×C₄²	—	2	2	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
421	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
424	#107	—	2	2	no	—
425	#107	C₂×C₄×C₇	1	4	yes	complemented
426	#106	—	2	2	no	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#103	C₂×C₄×C₇	1	4	yes	complemented
430	#102	—	2	2	no	—
431	#102	—	2	2	no	—
432	#102	C₂×C₄×C₇	1	4	yes	complemented
433	#97	—	2	2	no	—
434	#97	C₇×D₄	1	4	yes	complemented
435	C₄×C₈	—	2	2	no	—
436	C₄×C₈	—	2	2	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	C₂²×C₇	—	2	2	no	—
446	C₂²×C₇	—	2	2	no	—
447	C₂²×C₇	—	2	2	no	—
448	C₂²×C₇	—	4	1	no	—
449	C₂²×C₇	—	4	1	no	—
450	C₂²×C₇	—	4	1	no	—
451	C₂²×C₇	—	4	1	no	—
452	C₂²×C₇	—	4	2	no	—
453	C₂²×C₇	—	4	2	no	—
454	C₂²×C₇	—	4	2	no	—
455	C₂²×C₇	—	8	1	no	—
456	C₂²×C₇	—	8	1	no	—
457	C₂²×C₇	—	8	1	no	—
458	C₂²×C₇	—	8	1	no	—
459	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
460	C₂²×C₇	C₂×#121	1	1	yes	characteristic
461	C₂²×C₇	#532	1	1	yes	characteristic
462	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
463	C₂²×C₇	C₂×#137	1	1	yes	characteristic
464	C₂²×C₇	#575	1	1	yes	characteristic
465	C₂²×C₇	#575	1	1	yes	characteristic
466	C₄×C₇	—	2	2	no	—
467	C₄×C₇	—	2	2	no	—
468	C₄×C₇	—	2	2	no	—
469	C₄×C₇	—	2	2	no	—
470	C₄×C₇	—	2	2	no	—
471	C₄×C₇	—	4	2	no	—
472	C₄×C₇	—	4	2	no	—
473	C₄×C₇	—	4	2	no	—
474	C₄×C₇	—	8	1	no	—
475	C₄×C₇	—	8	1	no	—
476	C₄×C₇	—	8	1	no	—
477	C₄×C₇	—	8	1	no	—
478	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
479	C₄×C₇	C₄×#41	1	1	yes	characteristic
480	C₄×C₇	#525	1	1	yes	characteristic
481	C₄×C₇	#529	1	1	yes	characteristic
482	C₂⁴	—	2	1	no	—
483	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	4	2	no	—
497	C₂×D₄	—	4	2	no	—
498	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	4	1	no	—
515	C₂²×C₄	—	4	1	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
520	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
522	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
525	C₂²×C₄	C₇×#41	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
527	SD₁₆	—	2	8	no	—
528	M₁₆	—	2	8	no	—
529	M₁₆	—	2	8	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
537	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
538	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
539	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
540	C₂×C₈	C₇×#41	1	2	yes	—
541	C₂×C₈	C₇×#41	1	2	yes	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
557	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	4	2	no	—
570	C₄²	—	4	2	no	—
571	C₄²	—	4	2	no	—
572	C₄²	C₂×C₇×D₄	1	2	yes	—
573	C₄²	C₇×#41	1	2	yes	—
574	C₂×C₇	—	4	2	no	—
575	C₂×C₇	—	8	2	no	—
576	C₂×C₇	C₄×#121	1	1	yes	characteristic
577	C₂×C₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
578	C₂×C₇	C₄×#137	1	1	yes	characteristic
579	C₂×C₇	#3055	1	1	yes	characteristic
580	C₂×C₇	#3056	1	1	yes	characteristic
581	C₂×C₇	#3182	1	1	yes	characteristic
582	C₂×C₇	#3183	1	1	yes	characteristic
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	C₄×C₇×D₄	1	2	yes	—
597	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	4	1	no	—
601	Q₈	—	4	1	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	8	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	8	4	no	—
645	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
646	C₂×C₄	C₇×#121	1	2	yes	—
647	C₂×C₄	C₇×#121	1	2	yes	—
648	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
649	C₂×C₄	C₇×#137	1	2	yes	—
650	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
651	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
652	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
653	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
654	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
655	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
656	C₈	—	2	2	no	—
657	C₈	—	2	2	no	—
658	C₈	—	2	2	no	—
659	C₈	C₄×C₇×D₄	1	4	yes	complemented
660	C₇	#21540	1	1	yes	characteristic, direct product factor, Sylow
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	8	1	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
676	C₂²	C₂×C₇×#121	1	1	yes	characteristic
677	C₂²	C₇×#532	1	1	yes	characteristic
678	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
679	C₂²	C₂×C₇×#137	1	1	yes	characteristic
680	C₂²	C₇×#575	1	1	yes	characteristic
681	C₂²	C₇×#575	1	1	yes	characteristic
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	8	1	no	—
691	C₄	—	8	1	no	—
692	C₄	—	8	1	no	—
693	C₄	—	8	1	no	—
694	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
695	C₄	C₄×C₇×#41	1	1	yes	characteristic
696	C₄	C₇×#525	1	1	yes	characteristic
697	C₄	C₇×#529	1	1	yes	characteristic
698	C₂	—	4	2	no	—
699	C₂	—	8	2	no	—
700	C₂	C₄×C₇×#121	1	1	yes	characteristic
701	C₂	C₄×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
702	C₂	C₄×C₇×#137	1	1	yes	characteristic
703	C₂	C₇×#3055	1	1	yes	characteristic
704	C₂	C₇×#3056	1	1	yes	characteristic
705	C₂	C₇×#3182	1	1	yes	characteristic
706	C₂	C₇×#3183	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	C₂×C₇×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#440	C₂	semidirect
3. C₂×C₄×C₇×M₁₆	C₂	semidirect
4. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
6. C₇×#1968	C₂	semidirect
7. C₇×#1942	C₂	semidirect
8. C₇×#1934	C₂	semidirect
9. C₇×#1933	C₂	semidirect
11. C₇×#1894	C₂	semidirect
12. C₇×#1809	C₂	semidirect
13. C₇×#1776	C₂	semidirect
14. C₇×#1763	C₂	semidirect
15. C₇×#1762	C₂	semidirect
25. C₇×#468	C₄	semidirect
62. #21540	C₇	direct (N × H)
72. C₂×C₇×SD₁₆	C₂×C₄	semidirect
78. C₂×C₇×M₁₆	C₂×C₄	semidirect
84. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
119. C₇×#107	C₂×C₄	semidirect
123. C₇×#103	C₂×C₄	semidirect
126. C₇×#102	C₂×C₄	semidirect
128. C₇×#97	D₄	semidirect
140. C₂×#440	C₂×C₇	semidirect
141. C₂×C₄×M₁₆	C₂×C₇	semidirect
142. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
144. #1968	C₂×C₇	semidirect
145. #1942	C₂×C₇	semidirect
146. #1934	C₂×C₇	semidirect
147. #1933	C₂×C₇	semidirect
149. #1894	C₂×C₇	semidirect
150. #1809	C₂×C₇	semidirect
151. #1776	C₂×C₇	semidirect
152. #1763	C₂×C₇	semidirect
153. #1762	C₂×C₇	semidirect
255. #468	C₄×C₇	semidirect
368. C₇×C₈	C₄×D₄	semidirect
378. C₂×SD₁₆	C₂×C₄×C₇	semidirect
384. C₂×M₁₆	C₂×C₄×C₇	semidirect
390. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
425. #107	C₂×C₄×C₇	semidirect
429. #103	C₂×C₄×C₇	semidirect
432. #102	C₂×C₄×C₇	semidirect
434. #97	C₇×D₄	semidirect
659. C₈	C₄×C₇×D₄	semidirect
660. C₇	#21540	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×#468	2
C₂×C₇×#440	2
C₂×C₄×C₇×M₁₆	2
C₄×C₇×C₂²⋊Q₈	2
C₄×C₇×#121	2
C₇×#1968	2
C₇×#1942	2
C₇×#1934	2
C₇×#1933	2
C₇×#1895	2
C₇×#1894	2
C₇×#1809	2
C₇×#1776	2
C₇×#1763	2
C₇×#1762	2
#21540	7

Subgroups — C7×#21540 #13198756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21540 #13198756