Subgroups — C₄×C₇×#575 #13237374

Order 1792.

2842 conjugacy classes of subgroups.

The subgroup lattice has 482 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×C₄×C₇×#41	C₂	1	2	yes	maximal, complemented
3	C₄×C₇×#137	C₂	1	8	yes	maximal, complemented
4	C₄×C₇×AGL(1,ℤ/8)	C₂	1	8	yes	maximal, complemented
5	C₇×#2943	C₂	1	4	yes	maximal, complemented
6	C₄×C₇×#135	C₂	1	4	yes	maximal, complemented
7	C₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2896	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₇×#41	C₂²	1	2	yes	—
11	C₇×#575	C₄	1	16	yes	direct product factor
12	C₂×C₇×#137	C₂²	1	4	yes	—
13	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	4	yes	—
14	C₂×C₇×#135	C₂²	1	4	yes	—
15	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₄×C₇×#41	—	2	4	no	—
18	C₄×C₇×#41	—	2	2	no	—
19	C₄×C₇×#41	—	2	2	no	—
20	C₄×C₇×#41	C₂²	1	8	yes	—
21	C₄×C₇×#41	C₂²	1	4	yes	complemented
22	C₄×C₇×#41	C₂²	1	4	yes	complemented
23	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
24	C₂×C₄×C₇×D₄	—	2	4	no	—
25	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
26	C₂×C₇×#117	—	2	2	no	—
27	C₂×C₇×#117	C₂²	1	2	yes	—
28	C₂²×C₄²×C₇	—	2	2	no	—
29	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
30	C₇×#442	C₂²	1	8	yes	complemented
31	C₇×#441	C₂²	1	8	yes	complemented
32	C₇×#440	C₂²	1	16	yes	complemented
33	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
34	C₄×C₇×SD₁₆	C₂²	1	16	yes	complemented
35	C₄×C₇×D₈	C₂²	1	8	yes	complemented
36	C₇×#428	C₂²	1	8	yes	complemented
37	C₇×#427	C₂²	1	4	yes	complemented
38	C₇×#419	C₂²	1	4	yes	complemented
39	C₇×#418	C₂²	1	4	yes	complemented
40	C₇×#417	C₂²	1	8	yes	—
41	C₇×#416	C₂²	1	8	yes	complemented
42	C₄×C₇×M₁₆	C₂²	1	8	yes	complemented
43	C₂×C₇×#97	C₂²	1	2	yes	complemented
44	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
45	C₄×#575	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₇×#41	—	2	2	no	—
47	C₂×C₇×#41	—	2	2	no	—
48	C₂×C₇×#41	—	2	8	no	—
49	C₂×C₇×#41	C₂×C₄	1	16	yes	complemented
50	C₂×C₇×#41	C₂³	1	4	yes	—
51	C₂×C₇×#41	C₂³	1	4	yes	—
52	C₂²×C₇×Q₈	C₂³	1	2	yes	—
53	C₂²×C₇×D₄	—	2	2	no	—
54	C₂²×C₇×D₄	C₂³	1	2	yes	—
55	C₂³×C₄×C₇	—	2	2	no	—
56	C₂³×C₄×C₇	—	2	4	no	—
57	C₂³×C₄×C₇	D₄	1	2	yes	—
58	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₇×#137	C₂×C₄	1	32	yes	complemented
60	C₇×AGL(1,ℤ/8)	C₂×C₄	1	32	yes	complemented
61	C₇×#135	C₂×C₄	1	32	yes	complemented
62	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
63	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
64	C₂×C₇×D₈	C₂³	1	4	yes	—
65	C₂×C₇×M₁₆	—	2	4	no	—
66	C₂×C₇×M₁₆	C₂×C₄	1	8	yes	complemented
67	C₂×C₇×M₁₆	C₂³	1	4	yes	—
68	C₂×C₇×M₁₆	C₂³	1	4	yes	—
69	C₂²×C₇×C₈	C₂³	1	2	yes	—
70	C₂²×C₇×C₈	C₂³	1	2	yes	—
71	C₄×C₇×Q₈	—	2	4	no	—
72	C₄×C₇×Q₈	—	2	4	no	—
73	C₄×C₇×Q₈	C₂³	1	8	yes	—
74	C₄×C₇×Q₈	C₂³	1	8	yes	—
75	C₄×C₇×D₄	—	2	8	no	—
76	C₄×C₇×D₄	—	2	8	no	—
77	C₄×C₇×D₄	—	2	8	no	—
78	C₄×C₇×D₄	—	2	8	no	—
79	C₄×C₇×D₄	—	2	4	no	—
80	C₄×C₇×D₄	—	2	4	no	—
81	C₄×C₇×D₄	C₂³	1	8	yes	—
82	C₄×C₇×D₄	C₂³	1	8	yes	—
83	C₇×#117	—	2	2	no	—
84	C₇×#117	—	2	2	no	—
85	C₇×#117	—	2	8	no	—
86	C₇×#117	—	2	4	no	—
87	C₇×#117	—	2	4	no	—
88	C₇×#117	C₂³	1	4	yes	—
89	C₇×#117	C₂³	1	4	yes	—
90	C₂×C₇×C₄⋊C₄	—	2	4	no	—
91	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
94	C₂×C₄²×C₇	—	2	2	no	—
95	C₂×C₄²×C₇	—	2	4	no	—
96	C₂×C₄²×C₇	—	2	8	no	—
97	C₂×C₄²×C₇	—	2	4	no	—
98	C₂×C₄²×C₇	—	2	4	no	—
99	C₂×C₄²×C₇	D₄	1	2	yes	—
100	C₂×C₄²×C₇	D₄	1	2	yes	—
101	C₂×C₄²×C₇	D₄	1	2	yes	—
102	C₂×C₄²×C₇	C₂³	1	4	yes	—
103	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
105	C₇×#107	C₂³	1	8	yes	—
106	C₇×#106	C₂³	1	8	yes	—
107	C₇×#103	C₂³	1	16	yes	—
108	C₇×#102	C₂³	1	16	yes	—
109	C₇×#97	C₂³	1	8	yes	—
110	C₄×C₇×C₈	C₂³	1	8	yes	—
111	C₂×#575	C₂×C₇	1	1	yes	characteristic
112	C₂×C₄×#41	C₂×C₇	1	2	yes	complemented
113	C₄×#137	C₂×C₇	1	8	yes	complemented
114	C₄×AGL(1,ℤ/8)	C₂×C₇	1	8	yes	complemented
115	#2943	C₂×C₇	1	4	yes	complemented
116	C₄×#135	C₂×C₇	1	4	yes	complemented
117	#2911	C₂×C₇	1	1	yes	characteristic, complemented
118	#2896	C₂×C₇	1	2	yes	complemented
119	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
120	C₂⁴×C₇	—	2	2	no	—
121	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
122	C₇×#41	—	2	16	no	—
123	C₇×#41	—	2	16	no	—
124	C₇×#41	—	2	8	no	—
125	C₇×#41	—	2	8	no	—
126	C₇×#41	C₂²×C₄	1	16	yes	—
127	C₇×#41	C₂²×C₄	1	16	yes	complemented
128	C₂×C₇×Q₈	—	2	2	no	—
129	C₂×C₇×Q₈	—	2	4	no	—
130	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	complemented
131	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
132	C₂×C₇×D₄	—	2	16	no	—
133	C₂×C₇×D₄	—	2	4	no	—
134	C₂×C₇×D₄	—	2	4	no	—
135	C₂×C₇×D₄	—	2	2	no	—
136	C₂×C₇×D₄	—	2	4	no	—
137	C₂×C₇×D₄	C₂²×C₄	1	8	yes	complemented
138	C₂×C₇×D₄	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₇	—	2	2	no	—
140	C₂²×C₄×C₇	—	2	16	no	—
141	C₂²×C₄×C₇	—	2	4	no	—
142	C₂²×C₄×C₇	—	2	4	no	—
143	C₂²×C₄×C₇	—	2	4	no	—
144	C₂²×C₄×C₇	—	2	8	no	—
145	C₂²×C₄×C₇	—	2	8	no	—
146	C₂²×C₄×C₇	—	4	4	no	—
147	C₂²×C₄×C₇	—	4	16	no	—
148	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
149	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₇	#41	1	4	yes	—
156	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
158	C₇×Q₁₆	C₂²×C₄	1	16	yes	complemented
159	C₇×SD₁₆	C₂²×C₄	1	32	yes	complemented
160	C₇×D₈	C₂²×C₄	1	16	yes	complemented
161	C₇×M₁₆	—	2	8	no	—
162	C₇×M₁₆	C₂²×C₄	1	16	yes	complemented
163	C₂×C₇×C₈	—	2	4	no	—
164	C₂×C₇×C₈	C₂²×C₄	1	8	yes	complemented
165	C₂×C₇×C₈	C₂⁴	1	4	yes	—
166	C₂×C₇×C₈	C₂⁴	1	4	yes	—
167	C₇×C₄⋊C₄	—	2	8	no	—
168	C₇×C₄⋊C₄	—	2	8	no	—
169	C₇×C₄⋊C₄	—	2	4	no	—
170	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
171	C₇×C₂²⋊C₄	—	2	4	no	—
172	C₇×C₂²⋊C₄	—	2	4	no	—
173	C₇×C₂²⋊C₄	—	2	8	no	—
174	C₇×C₂²⋊C₄	—	2	8	no	—
175	C₄²×C₇	—	2	4	no	—
176	C₄²×C₇	—	2	4	no	—
177	C₄²×C₇	—	2	8	no	—
178	C₄²×C₇	—	2	8	no	—
179	C₄²×C₇	C₂×D₄	1	2	yes	—
180	C₄²×C₇	C₂×D₄	1	4	yes	—
181	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₇	C₂×D₄	1	4	yes	—
183	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₇	C₂⁴	1	2	yes	—
185	C₄²×C₇	C₂⁴	1	2	yes	—
186	C₂²×#41	C₂²×C₇	1	2	yes	—
187	#575	C₄×C₇	1	16	yes	direct product factor
188	C₂×#137	C₂²×C₇	1	4	yes	—
189	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	4	yes	—
190	C₂×#135	C₂²×C₇	1	4	yes	—
191	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
192	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
193	C₄×#41	—	2	4	no	—
194	C₄×#41	—	2	2	no	—
195	C₄×#41	—	2	2	no	—
196	C₄×#41	C₂²×C₇	1	8	yes	—
197	C₄×#41	C₂²×C₇	1	4	yes	complemented
198	C₄×#41	C₂²×C₇	1	4	yes	complemented
199	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
200	C₂×C₄×D₄	—	2	4	no	—
201	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
202	C₂×#117	—	2	2	no	—
203	C₂×#117	C₂²×C₇	1	2	yes	—
204	C₂²×C₄²	—	2	2	no	—
205	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
206	#442	C₂²×C₇	1	8	yes	complemented
207	#441	C₂²×C₇	1	8	yes	complemented
208	#440	C₂²×C₇	1	16	yes	complemented
209	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
210	C₄×SD₁₆	C₂²×C₇	1	16	yes	complemented
211	C₄×D₈	C₂²×C₇	1	8	yes	complemented
212	#428	C₂²×C₇	1	8	yes	complemented
213	#427	C₂²×C₇	1	4	yes	complemented
214	#419	C₂²×C₇	1	4	yes	complemented
215	#418	C₂²×C₇	1	4	yes	complemented
216	#417	C₂²×C₇	1	8	yes	—
217	#416	C₂²×C₇	1	8	yes	complemented
218	C₄×M₁₆	C₂²×C₇	1	8	yes	complemented
219	C₂×#97	C₂²×C₇	1	2	yes	complemented
220	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
221	C₂³×C₇	—	2	8	no	—
222	C₂³×C₇	—	2	4	no	—
223	C₂³×C₇	—	4	2	no	—
224	C₂³×C₇	—	4	8	no	—
225	C₂³×C₇	C₄×D₄	1	4	yes	—
226	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
227	C₂³×C₇	C₂²×D₄	1	2	yes	—
228	C₇×Q₈	—	2	8	no	—
229	C₇×Q₈	—	2	4	no	—
230	C₇×Q₈	C₂³×C₄	1	8	yes	—
231	C₇×D₄	—	2	16	no	—
232	C₇×D₄	—	2	16	no	—
233	C₇×D₄	—	2	8	no	—
234	C₇×D₄	—	2	4	no	—
235	C₇×D₄	C₂³×C₄	1	8	yes	—
236	C₂×C₄×C₇	—	2	8	no	—
237	C₂×C₄×C₇	—	2	4	no	—
238	C₂×C₄×C₇	—	2	16	no	—
239	C₂×C₄×C₇	—	2	16	no	—
240	C₂×C₄×C₇	—	2	8	no	—
241	C₂×C₄×C₇	—	2	4	no	—
242	C₂×C₄×C₇	—	2	8	no	—
243	C₂×C₄×C₇	—	4	2	no	—
244	C₂×C₄×C₇	—	4	4	no	—
245	C₂×C₄×C₇	—	4	16	no	—
246	C₂×C₄×C₇	—	4	8	no	—
247	C₂×C₄×C₇	—	4	16	no	—
248	C₂×C₄×C₇	C₄×D₄	1	8	yes	—
249	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
250	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
251	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
252	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
253	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₇	C₂×#41	1	2	yes	—
258	C₂×C₄×C₇	C₂×#41	1	4	yes	—
259	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
260	C₇×C₈	—	2	4	no	—
261	C₇×C₈	C₂³×C₄	1	8	yes	—
262	C₂×#41	—	2	2	no	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	—	2	8	no	—
265	C₂×#41	C₂×C₄×C₇	1	16	yes	complemented
266	C₂×#41	C₂³×C₇	1	4	yes	—
267	C₂×#41	C₂³×C₇	1	4	yes	—
268	C₂²×Q₈	C₂³×C₇	1	2	yes	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	C₂³×C₇	1	2	yes	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	—	2	4	no	—
273	C₂³×C₄	C₇×D₄	1	2	yes	—
274	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
275	#137	C₂×C₄×C₇	1	32	yes	complemented
276	AGL(1,ℤ/8)	C₂×C₄×C₇	1	32	yes	complemented
277	#135	C₂×C₄×C₇	1	32	yes	complemented
278	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
279	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
280	C₂×D₈	C₂³×C₇	1	4	yes	—
281	C₂×M₁₆	—	2	4	no	—
282	C₂×M₁₆	C₂×C₄×C₇	1	8	yes	complemented
283	C₂×M₁₆	C₂³×C₇	1	4	yes	—
284	C₂×M₁₆	C₂³×C₇	1	4	yes	—
285	C₂²×C₈	C₂³×C₇	1	2	yes	—
286	C₂²×C₈	C₂³×C₇	1	2	yes	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	2	4	no	—
289	C₄×Q₈	C₂³×C₇	1	8	yes	—
290	C₄×Q₈	C₂³×C₇	1	8	yes	—
291	C₄×D₄	—	2	8	no	—
292	C₄×D₄	—	2	8	no	—
293	C₄×D₄	—	2	8	no	—
294	C₄×D₄	—	2	8	no	—
295	C₄×D₄	—	2	4	no	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	C₂³×C₇	1	8	yes	—
298	C₄×D₄	C₂³×C₇	1	8	yes	—
299	#117	—	2	2	no	—
300	#117	—	2	2	no	—
301	#117	—	2	8	no	—
302	#117	—	2	4	no	—
303	#117	—	2	4	no	—
304	#117	C₂³×C₇	1	4	yes	—
305	#117	C₂³×C₇	1	4	yes	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	4	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	4	no	—
312	C₂×C₄²	—	2	8	no	—
313	C₂×C₄²	—	2	4	no	—
314	C₂×C₄²	—	2	4	no	—
315	C₂×C₄²	C₇×D₄	1	2	yes	—
316	C₂×C₄²	C₇×D₄	1	2	yes	—
317	C₂×C₄²	C₇×D₄	1	2	yes	—
318	C₂×C₄²	C₂³×C₇	1	4	yes	—
319	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
321	#107	C₂³×C₇	1	8	yes	—
322	#106	C₂³×C₇	1	8	yes	—
323	#103	C₂³×C₇	1	16	yes	—
324	#102	C₂³×C₇	1	16	yes	—
325	#97	C₂³×C₇	1	8	yes	—
326	C₄×C₈	C₂³×C₇	1	8	yes	—
327	C₂²×C₇	—	2	4	no	—
328	C₂²×C₇	—	2	2	no	—
329	C₂²×C₇	—	2	8	no	—
330	C₂²×C₇	—	4	4	no	—
331	C₂²×C₇	—	4	16	no	—
332	C₂²×C₇	—	4	8	no	—
333	C₂²×C₇	C₂×C₄×D₄	1	4	yes	—
334	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
335	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
336	C₄×C₇	—	2	8	no	—
337	C₄×C₇	—	2	4	no	—
338	C₄×C₇	—	2	2	no	—
339	C₄×C₇	—	4	8	no	—
340	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
341	C₄×C₇	C₂×C₄×D₄	1	4	yes	—
342	C₄×C₇	#575	1	4	yes	direct product factor
343	C₄×C₇	C₂⁴×C₄	1	1	yes	characteristic
344	C₄×C₇	C₂²×#41	1	1	yes	characteristic
345	C₂⁴	—	2	2	no	—
346	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
347	#41	—	2	16	no	—
348	#41	—	2	16	no	—
349	#41	—	2	8	no	—
350	#41	—	2	8	no	—
351	#41	C₂²×C₄×C₇	1	16	yes	—
352	#41	C₂²×C₄×C₇	1	16	yes	complemented
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	complemented
356	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
357	C₂×D₄	—	2	16	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	C₂²×C₄×C₇	1	8	yes	complemented
363	C₂×D₄	C₂⁴×C₇	1	4	yes	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	16	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	16	no	—
373	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
374	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
375	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
376	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
377	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
378	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
379	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
380	C₂²×C₄	C₇×#41	1	4	yes	—
381	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
383	Q₁₆	C₂²×C₄×C₇	1	16	yes	complemented
384	SD₁₆	C₂²×C₄×C₇	1	32	yes	complemented
385	D₈	C₂²×C₄×C₇	1	16	yes	complemented
386	M₁₆	—	2	8	no	—
387	M₁₆	C₂²×C₄×C₇	1	16	yes	complemented
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	C₂²×C₄×C₇	1	8	yes	complemented
390	C₂×C₈	C₂⁴×C₇	1	4	yes	—
391	C₂×C₈	C₂⁴×C₇	1	4	yes	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	2	8	no	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	2	4	no	—
402	C₄²	—	2	8	no	—
403	C₄²	—	2	8	no	—
404	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
405	C₄²	C₂×C₇×D₄	1	2	yes	—
406	C₄²	C₂×C₇×D₄	1	4	yes	—
407	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
408	C₄²	C₂×C₇×D₄	1	4	yes	—
409	C₄²	C₂⁴×C₇	1	2	yes	—
410	C₄²	C₂⁴×C₇	1	2	yes	—
411	C₂×C₇	—	2	4	no	—
412	C₂×C₇	—	2	2	no	—
413	C₂×C₇	—	4	8	no	—
414	C₂×C₇	C₂²×C₄×D₄	1	1	yes	characteristic
415	C₂×C₇	C₂×#575	1	2	yes	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	8	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	8	no	—
420	C₂³	C₄×C₇×D₄	1	4	yes	—
421	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
422	C₂³	C₂²×C₇×D₄	1	2	yes	—
423	Q₈	—	2	4	no	—
424	Q₈	—	2	8	no	—
425	Q₈	C₂³×C₄×C₇	1	8	yes	—
426	D₄	—	2	16	no	—
427	D₄	—	2	16	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	8	no	—
430	D₄	C₂³×C₄×C₇	1	8	yes	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	16	no	—
434	C₂×C₄	—	2	16	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	16	no	—
441	C₂×C₄	—	4	8	no	—
442	C₂×C₄	—	4	16	no	—
443	C₂×C₄	C₄×C₇×D₄	1	8	yes	—
444	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
445	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
446	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
447	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
448	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
449	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
451	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
452	C₂×C₄	C₂×C₇×#41	1	2	yes	—
453	C₂×C₄	C₂×C₇×#41	1	4	yes	—
454	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	C₂³×C₄×C₇	1	8	yes	—
457	C₇	C₄×#575	1	1	yes	characteristic, direct product factor, Sylow
458	C₂²	—	2	4	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	8	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	16	no	—
463	C₂²	—	4	8	no	—
464	C₂²	C₂×C₄×C₇×D₄	1	4	yes	—
465	C₂²	C₂×C₄×C₇×D₄	1	2	yes	—
466	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	8	no	—
470	C₄	—	4	8	no	—
471	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
472	C₄	C₂×C₄×C₇×D₄	1	4	yes	—
473	C₄	C₇×#575	1	4	yes	direct product factor
474	C₄	C₂⁴×C₄×C₇	1	1	yes	characteristic
475	C₄	C₂²×C₇×#41	1	1	yes	characteristic
476	C₂	—	2	4	no	—
477	C₂	—	2	2	no	—
478	C₂	—	4	8	no	—
479	C₂	C₂²×C₄×C₇×D₄	1	1	yes	characteristic
480	C₂	C₂×C₇×#575	1	2	yes	—

	subgroup	G/H
center	C₄²×C₇	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
prime radical	C₂×C₇×#575	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₇×#41	C₂	semidirect
3. C₄×C₇×#137	C₂	semidirect
4. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
5. C₇×#2943	C₂	semidirect
6. C₄×C₇×#135	C₂	semidirect
7. C₇×#2911	C₂	semidirect
8. C₇×#2896	C₂	semidirect
9. C₂×C₄×C₇×M₁₆	C₂	semidirect
11. C₇×#575	C₄	direct (N × H)
21. C₄×C₇×#41	C₂²	semidirect
22. C₄×C₇×#41	C₂²	semidirect
23. C₂×C₄×C₇×Q₈	C₂²	semidirect
25. C₂×C₄×C₇×D₄	C₂²	semidirect
30. C₇×#442	C₂²	semidirect
31. C₇×#441	C₂²	semidirect
32. C₇×#440	C₂²	semidirect
33. C₄×C₇×Q₁₆	C₂²	semidirect
34. C₄×C₇×SD₁₆	C₂²	semidirect
35. C₄×C₇×D₈	C₂²	semidirect
36. C₇×#428	C₂²	semidirect
37. C₇×#427	C₂²	semidirect
38. C₇×#419	C₂²	semidirect
39. C₇×#418	C₂²	semidirect
41. C₇×#416	C₂²	semidirect
42. C₄×C₇×M₁₆	C₂²	semidirect
43. C₂×C₇×#97	C₂²	semidirect
44. C₂×C₄×C₇×C₈	C₂²	semidirect
45. C₄×#575	C₇	direct (N × H)
49. C₂×C₇×#41	C₂×C₄	semidirect
59. C₇×#137	C₂×C₄	semidirect
60. C₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
61. C₇×#135	C₂×C₄	semidirect
66. C₂×C₇×M₁₆	C₂×C₄	semidirect
112. C₂×C₄×#41	C₂×C₇	semidirect
113. C₄×#137	C₂×C₇	semidirect
114. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
115. #2943	C₂×C₇	semidirect
116. C₄×#135	C₂×C₇	semidirect
117. #2911	C₂×C₇	semidirect
118. #2896	C₂×C₇	semidirect
119. C₂×C₄×M₁₆	C₂×C₇	semidirect
127. C₇×#41	C₂²×C₄	semidirect
130. C₂×C₇×Q₈	C₂²×C₄	semidirect
137. C₂×C₇×D₄	C₂²×C₄	semidirect
158. C₇×Q₁₆	C₂²×C₄	semidirect
159. C₇×SD₁₆	C₂²×C₄	semidirect
160. C₇×D₈	C₂²×C₄	semidirect
162. C₇×M₁₆	C₂²×C₄	semidirect
164. C₂×C₇×C₈	C₂²×C₄	semidirect
187. #575	C₄×C₇	direct (N × H)
197. C₄×#41	C₂²×C₇	semidirect
198. C₄×#41	C₂²×C₇	semidirect
199. C₂×C₄×Q₈	C₂²×C₇	semidirect
201. C₂×C₄×D₄	C₂²×C₇	semidirect
206. #442	C₂²×C₇	semidirect
207. #441	C₂²×C₇	semidirect
208. #440	C₂²×C₇	semidirect
209. C₄×Q₁₆	C₂²×C₇	semidirect
210. C₄×SD₁₆	C₂²×C₇	semidirect
211. C₄×D₈	C₂²×C₇	semidirect
212. #428	C₂²×C₇	semidirect
213. #427	C₂²×C₇	semidirect
214. #419	C₂²×C₇	semidirect
215. #418	C₂²×C₇	semidirect
217. #416	C₂²×C₇	semidirect
218. C₄×M₁₆	C₂²×C₇	semidirect
219. C₂×#97	C₂²×C₇	semidirect
220. C₂×C₄×C₈	C₂²×C₇	semidirect
265. C₂×#41	C₂×C₄×C₇	semidirect
275. #137	C₂×C₄×C₇	semidirect
276. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
277. #135	C₂×C₄×C₇	semidirect
282. C₂×M₁₆	C₂×C₄×C₇	semidirect
342. C₄×C₇	#575	direct (N × H)
352. #41	C₂²×C₄×C₇	semidirect
355. C₂×Q₈	C₂²×C₄×C₇	semidirect
362. C₂×D₄	C₂²×C₄×C₇	semidirect
383. Q₁₆	C₂²×C₄×C₇	semidirect
384. SD₁₆	C₂²×C₄×C₇	semidirect
385. D₈	C₂²×C₄×C₇	semidirect
387. M₁₆	C₂²×C₄×C₇	semidirect
389. C₂×C₈	C₂²×C₄×C₇	semidirect
457. C₇	C₄×#575	direct (N × H)
473. C₄	C₇×#575	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×C₄×C₇×#41	2
C₄×C₇×#137	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×#2943	2
C₄×C₇×#135	2
C₇×#2911	2
C₇×#2896	2
C₂×C₄×C₇×M₁₆	2
C₄×#575	7

Subgroups — C4×C7×#575 #13237374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×#575 #13237374