Subgroups — C₇×#60182 #13237398

Order 1792.

2628 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#568	C₂	1	2	yes	maximal, complemented
3	C₇×#2957	C₂	1	8	yes	maximal, complemented
4	C₇×#2956	C₂	1	8	yes	maximal, complemented
5	C₇×#2955	C₂	1	8	yes	maximal, complemented
6	C₂×C₇×#430	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#421	C₂	1	2	yes	maximal, complemented
8	C₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#41	C₂²	1	2	yes	—
10	C₇×#575	C₄	1	8	yes	complemented
11	C₇×#575	C₂²	1	4	yes	—
12	C₇×#575	C₂²	1	4	yes	—
13	C₂×C₇×#137	C₄	1	4	yes	complemented
14	C₂×C₇×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
15	C₂×C₇×#135	C₂²	1	4	yes	—
16	C₇×#568	—	2	4	no	—
17	C₇×#568	—	2	4	no	—
18	C₇×#568	C₂²	1	8	yes	complemented
19	C₇×#568	C₂²	1	8	yes	complemented
20	C₂×C₇×#131	—	2	4	no	—
21	C₂×C₇×#131	C₂²	1	8	yes	complemented
22	C₂²×C₇×M₁₆	—	2	4	no	—
23	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
24	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₇×#117	C₂²	1	1	yes	characteristic
27	C₇×#444	C₂²	1	32	yes	complemented
28	C₇×#443	C₂²	1	32	yes	complemented
29	C₇×#430	C₂²	1	4	yes	complemented
30	C₇×#430	C₂²	1	4	yes	complemented
31	C₂×C₇×#108	C₂²	1	4	yes	complemented
32	C₇×#421	C₂²	1	8	yes	complemented
33	C₇×#421	C₂²	1	8	yes	complemented
34	C₂×C₇×#104	C₂²	1	8	yes	complemented
35	C₇×#405	C₂²	1	4	yes	complemented
36	C₇×#405	C₂²	1	4	yes	complemented
37	C₄×C₇×M₁₆	C₂²	1	4	yes	complemented
38	#60182	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₇×#41	—	2	2	no	—
40	C₂×C₇×#41	—	2	2	no	—
41	C₂×C₇×#41	—	2	2	no	—
42	C₂×C₇×#41	—	2	2	no	—
43	C₂×C₇×#41	—	2	2	no	—
44	C₂×C₇×#41	—	2	2	no	—
45	C₂×C₇×#41	C₂×C₄	1	4	yes	—
46	C₂×C₇×#41	C₂×C₄	1	4	yes	—
47	C₂×C₇×#41	C₂×C₄	1	4	yes	—
48	C₂×C₇×#41	C₂³	1	4	yes	—
49	C₂×C₇×#41	C₂³	1	4	yes	—
50	C₂×C₇×#41	C₂³	1	4	yes	—
51	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
52	C₂²×C₇×D₄	—	2	2	no	—
53	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
54	C₂³×C₄×C₇	—	2	2	no	—
55	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
56	C₇×#137	C₂×C₄	1	16	yes	—
57	C₇×#137	C₂×C₄	1	16	yes	complemented
58	C₇×AGL(1,ℤ/8)	C₂×C₄	1	16	yes	—
59	C₇×AGL(1,ℤ/8)	C₂×C₄	1	16	yes	complemented
60	C₇×#135	C₂×C₄	1	16	yes	complemented
61	C₇×#135	C₂³	1	16	yes	—
62	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	complemented
63	C₂×C₇×SD₁₆	C₂×C₄	1	8	yes	complemented
64	C₂×C₇×D₈	C₂×C₄	1	4	yes	complemented
65	C₇×#131	—	2	16	no	—
66	C₇×#131	—	2	16	no	—
67	C₇×#131	—	2	16	no	—
68	C₇×#131	C₂³	1	32	yes	complemented
69	C₂×C₇×M₁₆	—	2	2	no	—
70	C₂×C₇×M₁₆	—	2	2	no	—
71	C₂×C₇×M₁₆	—	2	2	no	—
72	C₂×C₇×M₁₆	—	2	16	no	—
73	C₂×C₇×M₁₆	—	2	16	no	—
74	C₂×C₇×M₁₆	—	2	8	no	—
75	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
76	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
77	C₂×C₇×M₁₆	D₄	1	4	yes	—
78	C₂×C₇×M₁₆	D₄	1	4	yes	—
79	C₂×C₇×M₁₆	C₂³	1	4	yes	—
80	C₂×C₇×M₁₆	C₂³	1	4	yes	—
81	C₂×C₇×M₁₆	C₂³	1	4	yes	—
82	C₂×C₇×M₁₆	C₂³	1	2	yes	—
83	C₂×C₇×M₁₆	C₂³	1	2	yes	—
84	C₂×C₇×M₁₆	C₂³	1	2	yes	—
85	C₂×C₇×M₁₆	C₂³	1	2	yes	—
86	C₂²×C₇×C₈	—	2	2	no	—
87	C₂²×C₇×C₈	—	2	8	no	—
88	C₂²×C₇×C₈	C₂³	1	2	yes	—
89	C₂²×C₇×C₈	C₂³	1	2	yes	—
90	C₇×#117	—	2	1	no	—
91	C₇×#117	—	2	1	no	—
92	C₇×#117	C₂³	1	2	yes	—
93	C₇×#117	C₂³	1	2	yes	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₄²×C₇	C₂³	1	2	yes	—
97	C₇×#108	C₂³	1	16	yes	complemented
98	C₇×#104	C₂³	1	32	yes	complemented
99	C₇×#97	C₂³	1	8	yes	complemented
100	C₄×C₇×C₈	C₂³	1	8	yes	complemented
101	C₂×#575	C₂×C₇	1	1	yes	characteristic
102	C₂×#568	C₂×C₇	1	2	yes	complemented
103	#2957	C₂×C₇	1	8	yes	complemented
104	#2956	C₂×C₇	1	8	yes	complemented
105	#2955	C₂×C₇	1	8	yes	complemented
106	C₂×#430	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂×#421	C₂×C₇	1	2	yes	complemented
108	#2873	C₂×C₇	1	1	yes	characteristic, complemented
109	C₂⁴×C₇	—	2	2	no	—
110	C₂⁴×C₇	#41	1	1	yes	characteristic
111	C₇×#41	—	2	4	no	—
112	C₇×#41	—	2	4	no	—
113	C₇×#41	—	2	4	no	—
114	C₇×#41	—	2	4	no	—
115	C₇×#41	—	2	4	no	—
116	C₇×#41	—	2	4	no	—
117	C₇×#41	—	2	4	no	—
118	C₇×#41	—	2	4	no	—
119	C₇×#41	—	2	4	no	—
120	C₇×#41	—	2	4	no	—
121	C₇×#41	—	2	4	no	—
122	C₇×#41	—	2	4	no	—
123	C₇×#41	C₂²×C₄	1	8	yes	—
124	C₇×#41	C₂²×C₄	1	8	yes	—
125	C₇×#41	C₂²×C₄	1	8	yes	—
126	C₇×#41	C₂⁴	1	8	yes	—
127	C₂×C₇×Q₈	—	2	2	no	—
128	C₂×C₇×Q₈	—	2	2	no	—
129	C₂×C₇×Q₈	—	2	2	no	—
130	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
131	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
132	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
133	C₂×C₇×D₄	—	2	4	no	—
134	C₂×C₇×D₄	—	2	4	no	—
135	C₂×C₇×D₄	—	2	4	no	—
136	C₂×C₇×D₄	—	2	4	no	—
137	C₂×C₇×D₄	—	2	4	no	—
138	C₂×C₇×D₄	—	2	4	no	—
139	C₂×C₇×D₄	—	2	2	no	—
140	C₂×C₇×D₄	—	2	2	no	—
141	C₂×C₇×D₄	—	2	2	no	—
142	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
143	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
144	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₇	—	2	2	no	—
146	C₂²×C₄×C₇	—	2	4	no	—
147	C₂²×C₄×C₇	—	2	4	no	—
148	C₂²×C₄×C₇	—	2	4	no	—
149	C₂²×C₄×C₇	—	2	4	no	—
150	C₂²×C₄×C₇	—	2	4	no	—
151	C₂²×C₄×C₇	—	2	4	no	—
152	C₂²×C₄×C₇	—	2	2	no	—
153	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₇	#41	1	1	yes	characteristic
158	C₂²×C₄×C₇	#41	1	1	yes	characteristic
159	C₂²×C₄×C₇	#41	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
163	C₇×Q₁₆	C₂²×C₄	1	16	yes	—
164	C₇×SD₁₆	C₂²×C₄	1	32	yes	—
165	C₇×D₈	C₂²×C₄	1	16	yes	—
166	C₇×M₁₆	—	2	4	no	—
167	C₇×M₁₆	—	2	4	no	—
168	C₇×M₁₆	—	2	4	no	—
169	C₇×M₁₆	—	2	32	no	—
170	C₇×M₁₆	C₂²×C₄	1	8	yes	—
171	C₇×M₁₆	C₂²×C₄	1	8	yes	—
172	C₇×M₁₆	C₂×D₄	1	4	yes	—
173	C₇×M₁₆	C₂×D₄	1	8	yes	—
174	C₇×M₁₆	C₂×D₄	1	4	yes	—
175	C₇×M₁₆	C₂⁴	1	8	yes	—
176	C₂×C₇×C₈	—	2	4	no	—
177	C₂×C₇×C₈	—	2	4	no	—
178	C₂×C₇×C₈	—	2	4	no	—
179	C₂×C₇×C₈	—	2	32	no	—
180	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
181	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
182	C₂×C₇×C₈	C₂×D₄	1	8	yes	—
183	C₂×C₇×C₈	C₂⁴	1	4	yes	—
184	C₂×C₇×C₈	C₂⁴	1	4	yes	—
185	C₇×C₄⋊C₄	—	2	2	no	—
186	C₇×C₄⋊C₄	—	2	2	no	—
187	C₇×C₂²⋊C₄	—	2	2	no	—
188	C₇×C₂²⋊C₄	—	2	2	no	—
189	C₄²×C₇	—	2	2	no	—
190	C₄²×C₇	C₂⁴	1	4	yes	—
191	C₂²×#41	C₂²×C₇	1	2	yes	—
192	#575	C₄×C₇	1	8	yes	complemented
193	#575	C₂²×C₇	1	4	yes	—
194	#575	C₂²×C₇	1	4	yes	—
195	C₂×#137	C₄×C₇	1	4	yes	complemented
196	C₂×AGL(1,ℤ/8)	C₄×C₇	1	4	yes	complemented
197	C₂×#135	C₂²×C₇	1	4	yes	—
198	#568	—	2	4	no	—
199	#568	—	2	4	no	—
200	#568	C₂²×C₇	1	8	yes	complemented
201	#568	C₂²×C₇	1	8	yes	complemented
202	C₂×#131	—	2	4	no	—
203	C₂×#131	C₂²×C₇	1	8	yes	complemented
204	C₂²×M₁₆	—	2	4	no	—
205	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
206	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
207	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
208	C₂×#117	C₂²×C₇	1	1	yes	characteristic
209	#444	C₂²×C₇	1	32	yes	complemented
210	#443	C₂²×C₇	1	32	yes	complemented
211	#430	C₂²×C₇	1	4	yes	complemented
212	#430	C₂²×C₇	1	4	yes	complemented
213	C₂×#108	C₂²×C₇	1	4	yes	complemented
214	#421	C₂²×C₇	1	8	yes	complemented
215	#421	C₂²×C₇	1	8	yes	complemented
216	C₂×#104	C₂²×C₇	1	8	yes	complemented
217	#405	C₂²×C₇	1	4	yes	complemented
218	#405	C₂²×C₇	1	4	yes	complemented
219	C₄×M₁₆	C₂²×C₇	1	4	yes	complemented
220	C₂³×C₇	—	2	4	no	—
221	C₂³×C₇	—	2	4	no	—
222	C₂³×C₇	—	2	4	no	—
223	C₂³×C₇	—	8	1	no	—
224	C₂³×C₇	—	8	4	no	—
225	C₂³×C₇	C₄×D₄	1	2	yes	—
226	C₂³×C₇	C₄×D₄	1	2	yes	—
227	C₂³×C₇	C₂×#41	1	1	yes	characteristic
228	C₂³×C₇	C₂×#41	1	1	yes	characteristic
229	C₂³×C₇	C₂×#41	1	1	yes	characteristic
230	C₇×Q₈	—	2	4	no	—
231	C₇×Q₈	—	2	4	no	—
232	C₇×Q₈	—	2	4	no	—
233	C₇×Q₈	C₂³×C₄	1	8	yes	—
234	C₇×D₄	—	2	8	no	—
235	C₇×D₄	—	2	8	no	—
236	C₇×D₄	—	2	8	no	—
237	C₇×D₄	—	2	8	no	—
238	C₇×D₄	—	2	4	no	—
239	C₇×D₄	—	2	4	no	—
240	C₇×D₄	—	2	4	no	—
241	C₇×D₄	C₂³×C₄	1	8	yes	—
242	C₂×C₄×C₇	—	2	4	no	—
243	C₂×C₄×C₇	—	2	4	no	—
244	C₂×C₄×C₇	—	2	4	no	—
245	C₂×C₄×C₇	—	2	8	no	—
246	C₂×C₄×C₇	—	2	8	no	—
247	C₂×C₄×C₇	—	2	8	no	—
248	C₂×C₄×C₇	—	2	8	no	—
249	C₂×C₄×C₇	—	2	4	no	—
250	C₂×C₄×C₇	—	8	2	no	—
251	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
252	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
255	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
256	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
260	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
261	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
269	C₇×C₈	—	2	8	no	—
270	C₇×C₈	C₂³×C₄	1	8	yes	—
271	C₇×C₈	C₂²×D₄	1	8	yes	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	C₂×C₄×C₇	1	4	yes	—
279	C₂×#41	C₂×C₄×C₇	1	4	yes	—
280	C₂×#41	C₂×C₄×C₇	1	4	yes	—
281	C₂×#41	C₂³×C₇	1	4	yes	—
282	C₂×#41	C₂³×C₇	1	4	yes	—
283	C₂×#41	C₂³×C₇	1	4	yes	—
284	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
285	C₂²×D₄	—	2	2	no	—
286	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
287	C₂³×C₄	—	2	2	no	—
288	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
289	#137	C₂×C₄×C₇	1	16	yes	—
290	#137	C₂×C₄×C₇	1	16	yes	complemented
291	AGL(1,ℤ/8)	C₂×C₄×C₇	1	16	yes	—
292	AGL(1,ℤ/8)	C₂×C₄×C₇	1	16	yes	complemented
293	#135	C₂×C₄×C₇	1	16	yes	complemented
294	#135	C₂³×C₇	1	16	yes	—
295	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
296	C₂×SD₁₆	C₂×C₄×C₇	1	8	yes	complemented
297	C₂×D₈	C₂×C₄×C₇	1	4	yes	complemented
298	#131	—	2	16	no	—
299	#131	—	2	16	no	—
300	#131	—	2	16	no	—
301	#131	C₂³×C₇	1	32	yes	complemented
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	16	no	—
306	C₂×M₁₆	—	2	16	no	—
307	C₂×M₁₆	—	2	8	no	—
308	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
309	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
310	C₂×M₁₆	C₇×D₄	1	4	yes	—
311	C₂×M₁₆	C₇×D₄	1	4	yes	—
312	C₂×M₁₆	C₂³×C₇	1	4	yes	—
313	C₂×M₁₆	C₂³×C₇	1	4	yes	—
314	C₂×M₁₆	C₂³×C₇	1	4	yes	—
315	C₂×M₁₆	C₂³×C₇	1	2	yes	—
316	C₂×M₁₆	C₂³×C₇	1	2	yes	—
317	C₂×M₁₆	C₂³×C₇	1	2	yes	—
318	C₂×M₁₆	C₂³×C₇	1	2	yes	—
319	C₂²×C₈	—	2	2	no	—
320	C₂²×C₈	—	2	8	no	—
321	C₂²×C₈	C₂³×C₇	1	2	yes	—
322	C₂²×C₈	C₂³×C₇	1	2	yes	—
323	#117	—	2	1	no	—
324	#117	—	2	1	no	—
325	#117	C₂³×C₇	1	2	yes	—
326	#117	C₂³×C₇	1	2	yes	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₄²	C₂³×C₇	1	2	yes	—
330	#108	C₂³×C₇	1	16	yes	complemented
331	#104	C₂³×C₇	1	32	yes	complemented
332	#97	C₂³×C₇	1	8	yes	complemented
333	C₄×C₈	C₂³×C₇	1	8	yes	complemented
334	C₂²×C₇	—	2	8	no	—
335	C₂²×C₇	—	4	1	no	—
336	C₂²×C₇	—	4	2	no	—
337	C₂²×C₇	—	4	2	no	—
338	C₂²×C₇	—	4	1	no	—
339	C₂²×C₇	—	4	1	no	—
340	C₂²×C₇	—	4	8	no	—
341	C₂²×C₇	—	8	4	no	—
342	C₂²×C₇	—	8	4	no	—
343	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
344	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
345	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
346	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
347	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
348	C₄×C₇	—	2	8	no	—
349	C₄×C₇	—	4	4	no	—
350	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
351	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
352	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
353	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
354	C₄×C₇	C₂⁴×C₄	1	1	yes	characteristic
355	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
356	C₂⁴	—	2	2	no	—
357	C₂⁴	C₇×#41	1	1	yes	characteristic
358	#41	—	2	4	no	—
359	#41	—	2	4	no	—
360	#41	—	2	4	no	—
361	#41	—	2	4	no	—
362	#41	—	2	4	no	—
363	#41	—	2	4	no	—
364	#41	—	2	4	no	—
365	#41	—	2	4	no	—
366	#41	—	2	4	no	—
367	#41	—	2	4	no	—
368	#41	—	2	4	no	—
369	#41	—	2	4	no	—
370	#41	C₂²×C₄×C₇	1	8	yes	—
371	#41	C₂²×C₄×C₇	1	8	yes	—
372	#41	C₂²×C₄×C₇	1	8	yes	—
373	#41	C₂⁴×C₇	1	8	yes	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
378	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
379	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
390	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
391	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
401	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
402	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
403	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
404	C₂²×C₄	C₇×#41	1	1	yes	characteristic
405	C₂²×C₄	C₇×#41	1	1	yes	characteristic
406	C₂²×C₄	C₇×#41	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
410	Q₁₆	C₂²×C₄×C₇	1	16	yes	—
411	SD₁₆	C₂²×C₄×C₇	1	32	yes	—
412	D₈	C₂²×C₄×C₇	1	16	yes	—
413	M₁₆	—	2	4	no	—
414	M₁₆	—	2	4	no	—
415	M₁₆	—	2	4	no	—
416	M₁₆	—	2	32	no	—
417	M₁₆	C₂²×C₄×C₇	1	8	yes	—
418	M₁₆	C₂²×C₄×C₇	1	8	yes	—
419	M₁₆	C₂×C₇×D₄	1	4	yes	—
420	M₁₆	C₂×C₇×D₄	1	8	yes	—
421	M₁₆	C₂×C₇×D₄	1	4	yes	—
422	M₁₆	C₂⁴×C₇	1	8	yes	—
423	C₂×C₈	—	2	4	no	—
424	C₂×C₈	—	2	4	no	—
425	C₂×C₈	—	2	4	no	—
426	C₂×C₈	—	2	32	no	—
427	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
428	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
429	C₂×C₈	C₂×C₇×D₄	1	8	yes	—
430	C₂×C₈	C₂⁴×C₇	1	4	yes	—
431	C₂×C₈	C₂⁴×C₇	1	4	yes	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	C₂⁴×C₇	1	4	yes	—
438	C₂×C₇	—	2	1	no	—
439	C₂×C₇	—	2	2	no	—
440	C₂×C₇	—	2	1	no	—
441	C₂×C₇	—	2	2	no	—
442	C₂×C₇	—	2	1	no	—
443	C₂×C₇	—	4	8	no	—
444	C₂×C₇	C₂²×C₄×D₄	1	1	yes	characteristic
445	C₂³	—	2	4	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	8	1	no	—
449	C₂³	—	8	4	no	—
450	C₂³	C₄×C₇×D₄	1	2	yes	—
451	C₂³	C₄×C₇×D₄	1	2	yes	—
452	C₂³	C₂×C₇×#41	1	1	yes	characteristic
453	C₂³	C₂×C₇×#41	1	1	yes	characteristic
454	C₂³	C₂×C₇×#41	1	1	yes	characteristic
455	Q₈	—	2	4	no	—
456	Q₈	—	2	4	no	—
457	Q₈	—	2	4	no	—
458	Q₈	C₂³×C₄×C₇	1	8	yes	—
459	D₄	—	2	8	no	—
460	D₄	—	2	8	no	—
461	D₄	—	2	8	no	—
462	D₄	—	2	8	no	—
463	D₄	—	2	4	no	—
464	D₄	—	2	4	no	—
465	D₄	—	2	4	no	—
466	D₄	C₂³×C₄×C₇	1	8	yes	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	8	2	no	—
476	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
477	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
478	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
479	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
480	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
481	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
482	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
483	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
484	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
485	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
486	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
488	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
489	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
490	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
491	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
492	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
493	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
494	C₈	—	2	8	no	—
495	C₈	C₂³×C₄×C₇	1	8	yes	—
496	C₈	C₂²×C₇×D₄	1	8	yes	—
497	C₇	#60182	1	1	yes	characteristic, direct product factor, Sylow
498	C₂²	—	2	8	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	8	no	—
505	C₂²	—	8	4	no	—
506	C₂²	—	8	4	no	—
507	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
508	C₂²	C₂×C₄×C₇×D₄	1	2	yes	—
509	C₂²	C₂×C₄×C₇×D₄	1	2	yes	—
510	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
511	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
512	C₄	—	2	8	no	—
513	C₄	—	4	4	no	—
514	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
515	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
516	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
517	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
518	C₄	C₂⁴×C₄×C₇	1	1	yes	characteristic
519	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
520	C₂	—	2	1	no	—
521	C₂	—	2	2	no	—
522	C₂	—	2	1	no	—
523	C₂	—	2	2	no	—
524	C₂	—	2	1	no	—
525	C₂	—	4	8	no	—
526	C₂	C₂²×C₄×C₇×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂×C₇	C₂²×C₄×D₄
prime radical	C₂×C₇×#575	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇ ◁ C₂²×C₇×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#568	C₂	semidirect
3. C₇×#2957	C₂	semidirect
4. C₇×#2956	C₂	semidirect
5. C₇×#2955	C₂	semidirect
6. C₂×C₇×#430	C₂	semidirect
7. C₂×C₇×#421	C₂	semidirect
8. C₇×#2873	C₂	semidirect
10. C₇×#575	C₄	semidirect
13. C₂×C₇×#137	C₄	semidirect
14. C₂×C₇×AGL(1,ℤ/8)	C₄	semidirect
18. C₇×#568	C₂²	semidirect
19. C₇×#568	C₂²	semidirect
21. C₂×C₇×#131	C₂²	semidirect
27. C₇×#444	C₂²	semidirect
28. C₇×#443	C₂²	semidirect
29. C₇×#430	C₂²	semidirect
30. C₇×#430	C₂²	semidirect
31. C₂×C₇×#108	C₂²	semidirect
32. C₇×#421	C₂²	semidirect
33. C₇×#421	C₂²	semidirect
34. C₂×C₇×#104	C₂²	semidirect
35. C₇×#405	C₂²	semidirect
36. C₇×#405	C₂²	semidirect
37. C₄×C₇×M₁₆	C₂²	semidirect
38. #60182	C₇	direct (N × H)
57. C₇×#137	C₂×C₄	semidirect
59. C₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
60. C₇×#135	C₂×C₄	semidirect
62. C₂×C₇×Q₁₆	C₂×C₄	semidirect
63. C₂×C₇×SD₁₆	C₂×C₄	semidirect
64. C₂×C₇×D₈	C₂×C₄	semidirect
68. C₇×#131	C₂³	semidirect
97. C₇×#108	C₂³	semidirect
98. C₇×#104	C₂³	semidirect
99. C₇×#97	C₂³	semidirect
100. C₄×C₇×C₈	C₂³	semidirect
102. C₂×#568	C₂×C₇	semidirect
103. #2957	C₂×C₇	semidirect
104. #2956	C₂×C₇	semidirect
105. #2955	C₂×C₇	semidirect
106. C₂×#430	C₂×C₇	semidirect
107. C₂×#421	C₂×C₇	semidirect
108. #2873	C₂×C₇	semidirect
192. #575	C₄×C₇	semidirect
195. C₂×#137	C₄×C₇	semidirect
196. C₂×AGL(1,ℤ/8)	C₄×C₇	semidirect
200. #568	C₂²×C₇	semidirect
201. #568	C₂²×C₇	semidirect
203. C₂×#131	C₂²×C₇	semidirect
209. #444	C₂²×C₇	semidirect
210. #443	C₂²×C₇	semidirect
211. #430	C₂²×C₇	semidirect
212. #430	C₂²×C₇	semidirect
213. C₂×#108	C₂²×C₇	semidirect
214. #421	C₂²×C₇	semidirect
215. #421	C₂²×C₇	semidirect
216. C₂×#104	C₂²×C₇	semidirect
217. #405	C₂²×C₇	semidirect
218. #405	C₂²×C₇	semidirect
219. C₄×M₁₆	C₂²×C₇	semidirect
290. #137	C₂×C₄×C₇	semidirect
292. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
293. #135	C₂×C₄×C₇	semidirect
295. C₂×Q₁₆	C₂×C₄×C₇	semidirect
296. C₂×SD₁₆	C₂×C₄×C₇	semidirect
297. C₂×D₈	C₂×C₄×C₇	semidirect
301. #131	C₂³×C₇	semidirect
330. #108	C₂³×C₇	semidirect
331. #104	C₂³×C₇	semidirect
332. #97	C₂³×C₇	semidirect
333. C₄×C₈	C₂³×C₇	semidirect
497. C₇	#60182	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×#575	2
C₂×C₇×#568	2
C₇×#2957	2
C₇×#2956	2
C₇×#2955	2
C₂×C₇×#430	2
C₂×C₇×#421	2
C₇×#2873	2
#60182	7

Subgroups — C7×#60182 #13237398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60182 #13237398