Subgroups — C₄×C₇×#472 #13198769

Order 1792.

946 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#472	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1978	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1931	C₂	1	2	yes	maximal, complemented
8	C₇×#1907	C₂	1	2	yes	maximal, complemented
9	C₇×#1816	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#100	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×#131	C₂²	1	1	yes	characteristic
15	C₂×C₇×#131	C₂²	1	1	yes	characteristic
16	C₄×C₇×#41	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
18	C₇×#472	C₄	1	8	yes	direct product factor
19	C₇×#442	—	2	2	no	—
20	C₇×#440	—	2	2	no	—
21	C₄×C₇×SD₁₆	—	2	2	no	—
22	C₄×C₇×D₈	—	2	2	no	—
23	C₄×C₇×D₈	—	2	1	no	—
24	C₄×C₇×D₈	—	2	1	no	—
25	C₄×C₇×D₈	—	2	1	no	—
26	C₄×C₇×D₈	—	2	1	no	—
27	C₂×C₇×#108	C₂²	1	1	yes	characteristic
28	C₂×C₇×#108	C₂²	1	1	yes	characteristic
29	C₇×#428	C₂²	1	2	yes	—
30	C₂×C₇×#107	C₂²	1	1	yes	characteristic
31	C₇×#418	C₂²	1	2	yes	—
32	C₇×#417	C₂²	1	2	yes	—
33	C₂×C₇×#102	C₂²	1	2	yes	—
34	C₂×C₇×#100	C₂²	1	2	yes	—
35	C₂×C₇×#100	C₂²	1	2	yes	—
36	C₇×#405	—	2	1	no	—
37	C₇×#405	—	2	1	no	—
38	C₇×#405	C₂²	1	1	yes	characteristic
39	C₇×#405	C₂²	1	1	yes	characteristic
40	C₄×C₇×M₁₆	—	2	1	no	—
41	C₄×C₇×M₁₆	C₂²	1	2	yes	—
42	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×C₈	—	2	1	no	—
44	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
45	C₇×#343	C₂²	1	2	yes	—
46	C₇×#343	C₂²	1	2	yes	—
47	C₇×#341	C₂²	1	2	yes	—
48	C₄×#472	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂×C₇×#41	C₂³	1	1	yes	characteristic
50	C₂²×C₇×D₄	C₂³	1	2	yes	—
51	C₂³×C₄×C₇	—	2	2	no	—
52	C₇×AGL(1,ℤ/8)	—	2	4	no	—
53	C₇×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
54	C₂×C₇×SD₁₆	—	2	2	no	—
55	C₂×C₇×D₈	—	2	2	no	—
56	C₂×C₇×D₈	—	2	1	no	—
57	C₂×C₇×D₈	—	2	1	no	—
58	C₂×C₇×D₈	—	2	2	no	—
59	C₂×C₇×D₈	C₂×C₄	1	4	yes	complemented
60	C₇×#131	—	2	2	no	—
61	C₇×#131	—	2	2	no	—
62	C₇×#131	—	2	2	no	—
63	C₇×#131	C₂×C₄	1	4	yes	complemented
64	C₂×C₇×M₁₆	—	2	1	no	—
65	C₂×C₇×M₁₆	—	2	1	no	—
66	C₂×C₇×M₁₆	C₂³	1	2	yes	—
67	C₂×C₇×M₁₆	C₂³	1	2	yes	—
68	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	—	2	1	no	—
71	C₂²×C₇×C₈	—	2	1	no	—
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
75	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
76	C₄×C₇×D₄	—	2	1	no	—
77	C₄×C₇×D₄	—	2	1	no	—
78	C₄×C₇×D₄	—	2	2	no	—
79	C₄×C₇×D₄	—	2	2	no	—
80	C₄×C₇×D₄	—	2	2	no	—
81	C₄×C₇×D₄	—	2	2	no	—
82	C₄×C₇×D₄	D₄	1	1	yes	characteristic
83	C₄×C₇×D₄	D₄	1	1	yes	characteristic
84	C₇×#117	—	2	1	no	—
85	C₇×#117	C₂³	1	1	yes	characteristic
86	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₄²×C₇	—	2	1	no	—
89	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
90	C₇×#108	—	2	2	no	—
91	C₇×#108	C₂×C₄	1	4	yes	complemented
92	C₇×#107	—	2	1	no	—
93	C₇×#107	—	2	1	no	—
94	C₇×#107	—	2	2	no	—
95	C₇×#106	—	2	2	no	—
96	C₇×#103	—	2	2	no	—
97	C₇×#102	—	2	2	no	—
98	C₇×#102	—	2	2	no	—
99	C₇×#102	—	2	2	no	—
100	C₇×#102	—	2	2	no	—
101	C₇×#102	—	2	2	no	—
102	C₇×#100	—	2	4	no	—
103	C₇×#100	C₂×C₄	1	8	yes	complemented
104	C₇×#97	—	2	1	no	—
105	C₇×#97	—	2	1	no	—
106	C₇×#97	—	2	1	no	—
107	C₇×#97	—	2	2	no	—
108	C₄×C₇×C₈	—	2	1	no	—
109	C₄×C₇×C₈	—	2	1	no	—
110	C₄×C₇×C₈	—	2	1	no	—
111	C₄×C₇×C₈	—	2	2	no	—
112	C₄×C₇×C₈	D₄	1	1	yes	characteristic
113	C₄×C₇×C₈	D₄	1	1	yes	characteristic
114	C₄×C₇×C₈	D₄	1	1	yes	characteristic
115	C₄×C₇×C₈	D₄	1	1	yes	characteristic
116	C₂×#472	C₂×C₇	1	1	yes	characteristic
117	C₄×AGL(1,ℤ/8)	C₂×C₇	1	2	yes	complemented
118	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
119	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
120	#1978	C₂×C₇	1	1	yes	characteristic, complemented
121	#1952	C₂×C₇	1	1	yes	characteristic, complemented
122	#1931	C₂×C₇	1	2	yes	complemented
123	#1907	C₂×C₇	1	2	yes	complemented
124	#1816	C₂×C₇	1	1	yes	characteristic, complemented
125	C₄×#108	C₂×C₇	1	1	yes	characteristic, complemented
126	C₄×#100	C₂×C₇	1	2	yes	complemented
127	C₂⁴×C₇	—	2	2	no	—
128	C₇×#41	—	2	1	no	—
129	C₇×#41	—	2	1	no	—
130	C₇×#41	C₂²×C₄	1	2	yes	—
131	C₇×#41	#41	1	2	yes	—
132	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₇×D₄	—	2	1	no	—
134	C₂×C₇×D₄	—	2	2	no	—
135	C₂×C₇×D₄	—	2	2	no	—
136	C₂×C₇×D₄	—	2	2	no	—
137	C₂×C₇×D₄	—	2	2	no	—
138	C₂×C₇×D₄	—	2	2	no	—
139	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
140	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	—	2	1	no	—
142	C₂²×C₄×C₇	—	2	1	no	—
143	C₂²×C₄×C₇	—	2	1	no	—
144	C₂²×C₄×C₇	—	2	2	no	—
145	C₂²×C₄×C₇	—	4	2	no	—
146	C₂²×C₄×C₇	—	4	2	no	—
147	C₂²×C₄×C₇	—	8	4	no	—
148	C₂²×C₄×C₇	#41	1	1	yes	characteristic
149	C₂²×C₄×C₇	#41	1	1	yes	characteristic
150	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
151	C₇×SD₁₆	—	2	8	no	—
152	C₇×D₈	—	2	8	no	—
153	C₇×D₈	—	2	4	no	—
154	C₇×D₈	—	2	4	no	—
155	C₇×M₁₆	—	2	4	no	—
156	C₇×M₁₆	—	2	1	no	—
157	C₇×M₁₆	—	2	1	no	—
158	C₇×M₁₆	—	2	2	no	—
159	C₇×M₁₆	—	2	4	no	—
160	C₇×M₁₆	—	2	2	no	—
161	C₇×M₁₆	—	2	2	no	—
162	C₇×M₁₆	C₂²×C₄	1	2	yes	—
163	C₇×M₁₆	C₂²×C₄	1	4	yes	—
164	C₇×M₁₆	#41	1	2	yes	—
165	C₂×C₇×C₈	—	2	4	no	—
166	C₂×C₇×C₈	—	2	1	no	—
167	C₂×C₇×C₈	—	2	1	no	—
168	C₂×C₇×C₈	—	2	2	no	—
169	C₂×C₇×C₈	—	2	1	no	—
170	C₂×C₇×C₈	—	2	1	no	—
171	C₂×C₇×C₈	—	2	4	no	—
172	C₂×C₇×C₈	—	2	2	no	—
173	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
174	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
176	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
177	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
178	C₂×C₇×C₈	#41	1	2	yes	—
179	C₇×C₄⋊C₄	—	2	1	no	—
180	C₇×C₄⋊C₄	—	2	1	no	—
181	C₇×C₄⋊C₄	—	2	2	no	—
182	C₇×C₄⋊C₄	—	2	2	no	—
183	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
184	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
185	C₇×C₂²⋊C₄	—	2	1	no	—
186	C₇×C₂²⋊C₄	—	2	1	no	—
187	C₇×C₂²⋊C₄	—	2	1	no	—
188	C₇×C₂²⋊C₄	—	4	2	no	—
189	C₇×C₂²⋊C₄	—	4	2	no	—
190	C₄²×C₇	—	2	1	no	—
191	C₄²×C₇	—	2	1	no	—
192	C₄²×C₇	—	2	1	no	—
193	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
197	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
198	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
199	C₂×#131	C₂²×C₇	1	1	yes	characteristic
200	C₂×#131	C₂²×C₇	1	1	yes	characteristic
201	C₄×#41	C₂²×C₇	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
203	#472	C₄×C₇	1	8	yes	direct product factor
204	#442	—	2	2	no	—
205	#440	—	2	2	no	—
206	C₄×SD₁₆	—	2	2	no	—
207	C₄×D₈	—	2	2	no	—
208	C₄×D₈	—	2	1	no	—
209	C₄×D₈	—	2	1	no	—
210	C₄×D₈	—	2	1	no	—
211	C₄×D₈	—	2	1	no	—
212	C₂×#108	C₂²×C₇	1	1	yes	characteristic
213	C₂×#108	C₂²×C₇	1	1	yes	characteristic
214	#428	C₂²×C₇	1	2	yes	—
215	C₂×#107	C₂²×C₇	1	1	yes	characteristic
216	#418	C₂²×C₇	1	2	yes	—
217	#417	C₂²×C₇	1	2	yes	—
218	C₂×#102	C₂²×C₇	1	2	yes	—
219	C₂×#100	C₂²×C₇	1	2	yes	—
220	C₂×#100	C₂²×C₇	1	2	yes	—
221	#405	—	2	1	no	—
222	#405	—	2	1	no	—
223	#405	C₂²×C₇	1	1	yes	characteristic
224	#405	C₂²×C₇	1	1	yes	characteristic
225	C₄×M₁₆	—	2	1	no	—
226	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
227	C₄×M₁₆	C₂²×C₇	1	2	yes	—
228	C₂×C₄×C₈	—	2	1	no	—
229	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
230	#343	C₂²×C₇	1	2	yes	—
231	#343	C₂²×C₇	1	2	yes	—
232	#341	C₂²×C₇	1	2	yes	—
233	C₂³×C₇	—	2	1	no	—
234	C₂³×C₇	—	2	4	no	—
235	C₂³×C₇	—	4	2	no	—
236	C₂³×C₇	—	4	2	no	—
237	C₂³×C₇	—	8	2	no	—
238	C₂³×C₇	—	8	2	no	—
239	C₂³×C₇	C₂×#41	1	1	yes	characteristic
240	C₇×Q₈	—	2	1	no	—
241	C₇×Q₈	C₄×D₄	1	2	yes	—
242	C₇×D₄	—	2	2	no	—
243	C₇×D₄	—	2	2	no	—
244	C₇×D₄	—	2	4	no	—
245	C₇×D₄	—	2	4	no	—
246	C₇×D₄	—	2	1	no	—
247	C₇×D₄	—	4	2	no	—
248	C₇×D₄	—	4	2	no	—
249	C₇×D₄	C₄×D₄	1	2	yes	—
250	C₂×C₄×C₇	—	2	1	no	—
251	C₂×C₄×C₇	—	2	2	no	—
252	C₂×C₄×C₇	—	2	2	no	—
253	C₂×C₄×C₇	—	2	2	no	—
254	C₂×C₄×C₇	—	2	1	no	—
255	C₂×C₄×C₇	—	2	1	no	—
256	C₂×C₄×C₇	—	4	1	no	—
257	C₂×C₄×C₇	—	4	2	no	—
258	C₂×C₄×C₇	—	4	2	no	—
259	C₂×C₄×C₇	—	4	2	no	—
260	C₂×C₄×C₇	—	8	4	no	—
261	C₂×C₄×C₇	—	8	4	no	—
262	C₂×C₄×C₇	—	8	2	no	—
263	C₂×C₄×C₇	#121	1	1	yes	characteristic
264	C₂×C₄×C₇	#121	1	1	yes	characteristic
265	C₂×C₄×C₇	#121	1	1	yes	characteristic
266	C₂×C₄×C₇	#121	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
273	C₇×C₈	—	2	2	no	—
274	C₇×C₈	—	2	4	no	—
275	C₇×C₈	—	2	1	no	—
276	C₇×C₈	—	2	2	no	—
277	C₇×C₈	—	2	1	no	—
278	C₇×C₈	—	4	2	no	—
279	C₇×C₈	C₄×D₄	1	2	yes	—
280	C₇×C₈	C₄×D₄	1	2	yes	—
281	C₂×#41	C₂³×C₇	1	1	yes	characteristic
282	C₂²×D₄	C₂³×C₇	1	2	yes	—
283	C₂³×C₄	—	2	2	no	—
284	AGL(1,ℤ/8)	—	2	4	no	—
285	AGL(1,ℤ/8)	C₂×C₄×C₇	1	8	yes	complemented
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×D₈	—	2	1	no	—
289	C₂×D₈	—	2	1	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂×D₈	C₂×C₄×C₇	1	4	yes	complemented
292	#131	—	2	2	no	—
293	#131	—	2	2	no	—
294	#131	—	2	2	no	—
295	#131	C₂×C₄×C₇	1	4	yes	complemented
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂×M₁₆	C₂³×C₇	1	2	yes	—
299	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
300	C₂×M₁₆	C₂³×C₇	1	2	yes	—
301	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
306	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
307	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	C₇×D₄	1	1	yes	characteristic
315	C₄×D₄	C₇×D₄	1	1	yes	characteristic
316	#117	—	2	1	no	—
317	#117	C₂³×C₇	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
322	#108	—	2	2	no	—
323	#108	C₂×C₄×C₇	1	4	yes	complemented
324	#107	—	2	1	no	—
325	#107	—	2	1	no	—
326	#107	—	2	2	no	—
327	#106	—	2	2	no	—
328	#103	—	2	2	no	—
329	#102	—	2	2	no	—
330	#102	—	2	2	no	—
331	#102	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	2	2	no	—
334	#100	—	2	4	no	—
335	#100	C₂×C₄×C₇	1	8	yes	complemented
336	#97	—	2	1	no	—
337	#97	—	2	1	no	—
338	#97	—	2	1	no	—
339	#97	—	2	2	no	—
340	C₄×C₈	—	2	1	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	—	2	2	no	—
344	C₄×C₈	C₇×D₄	1	1	yes	characteristic
345	C₄×C₈	C₇×D₄	1	1	yes	characteristic
346	C₄×C₈	C₇×D₄	1	1	yes	characteristic
347	C₄×C₈	C₇×D₄	1	1	yes	characteristic
348	C₂²×C₇	—	2	1	no	—
349	C₂²×C₇	—	2	1	no	—
350	C₂²×C₇	—	2	2	no	—
351	C₂²×C₇	—	4	1	no	—
352	C₂²×C₇	—	4	1	no	—
353	C₂²×C₇	—	4	4	no	—
354	C₂²×C₇	—	8	4	no	—
355	C₂²×C₇	—	8	4	no	—
356	C₂²×C₇	—	8	2	no	—
357	C₂²×C₇	—	8	2	no	—
358	C₂²×C₇	C₄×#41	1	1	yes	characteristic
359	C₂²×C₇	C₂×#121	1	1	yes	characteristic
360	C₂²×C₇	#529	1	1	yes	characteristic
361	C₄×C₇	—	2	1	no	—
362	C₄×C₇	—	2	1	no	—
363	C₄×C₇	—	2	1	no	—
364	C₄×C₇	—	2	2	no	—
365	C₄×C₇	—	4	1	no	—
366	C₄×C₇	—	4	1	no	—
367	C₄×C₇	—	8	2	no	—
368	C₄×C₇	#472	1	2	yes	direct product factor
369	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
370	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
371	C₄×C₇	#525	1	1	yes	characteristic
372	C₄×C₇	#532	1	1	yes	characteristic
373	C₂⁴	—	2	2	no	—
374	#41	—	2	1	no	—
375	#41	—	2	1	no	—
376	#41	C₂²×C₄×C₇	1	2	yes	—
377	#41	C₇×#41	1	2	yes	—
378	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
386	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	8	4	no	—
394	C₂²×C₄	C₇×#41	1	1	yes	characteristic
395	C₂²×C₄	C₇×#41	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
397	SD₁₆	—	2	8	no	—
398	D₈	—	2	8	no	—
399	D₈	—	2	4	no	—
400	D₈	—	2	4	no	—
401	M₁₆	—	2	4	no	—
402	M₁₆	—	2	1	no	—
403	M₁₆	—	2	1	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	2	4	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	C₂²×C₄×C₇	1	2	yes	—
409	M₁₆	C₂²×C₄×C₇	1	4	yes	—
410	M₁₆	C₇×#41	1	2	yes	—
411	C₂×C₈	—	2	4	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	4	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
420	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
421	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
422	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
423	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
424	C₂×C₈	C₇×#41	1	2	yes	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
430	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	4	2	no	—
435	C₂²⋊C₄	—	4	2	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
440	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
441	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
442	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
443	C₂×C₇	—	2	1	no	—
444	C₂×C₇	—	2	1	no	—
445	C₂×C₇	—	4	2	no	—
446	C₂×C₇	—	8	4	no	—
447	C₂×C₇	C₄×#121	1	1	yes	characteristic
448	C₂×C₇	C₂×#472	1	1	yes	characteristic
449	C₂×C₇	#3067	1	1	yes	characteristic
450	C₂³	—	2	1	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	C₂×C₇×#41	1	1	yes	characteristic
457	Q₈	—	2	1	no	—
458	Q₈	C₄×C₇×D₄	1	2	yes	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	4	no	—
462	D₄	—	2	4	no	—
463	D₄	—	2	1	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	2	no	—
466	D₄	C₄×C₇×D₄	1	2	yes	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	8	4	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	C₇×#121	1	1	yes	characteristic
481	C₂×C₄	C₇×#121	1	1	yes	characteristic
482	C₂×C₄	C₇×#121	1	1	yes	characteristic
483	C₂×C₄	C₇×#121	1	1	yes	characteristic
484	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
487	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
488	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
489	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
490	C₈	—	2	2	no	—
491	C₈	—	2	4	no	—
492	C₈	—	2	1	no	—
493	C₈	—	2	2	no	—
494	C₈	—	2	1	no	—
495	C₈	—	4	2	no	—
496	C₈	C₄×C₇×D₄	1	2	yes	—
497	C₈	C₄×C₇×D₄	1	2	yes	—
498	C₇	C₄×#472	1	1	yes	characteristic, direct product factor, Sylow
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	8	4	no	—
506	C₂²	—	8	4	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	C₄×C₇×#41	1	1	yes	characteristic
510	C₂²	C₂×C₇×#121	1	1	yes	characteristic
511	C₂²	C₇×#529	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	8	2	no	—
519	C₄	C₇×#472	1	2	yes	direct product factor
520	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
521	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
522	C₄	C₇×#525	1	1	yes	characteristic
523	C₄	C₇×#532	1	1	yes	characteristic
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	4	no	—
528	C₂	C₄×C₇×#121	1	1	yes	characteristic
529	C₂	C₂×C₇×#472	1	1	yes	characteristic
530	C₂	C₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	#121
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×#121
prime radical	C₂×C₇×#472	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₄×C₇×D₈	C₂	semidirect
4. C₄×C₇×#131	C₂	semidirect
5. C₇×#1978	C₂	semidirect
6. C₇×#1952	C₂	semidirect
7. C₇×#1931	C₂	semidirect
8. C₇×#1907	C₂	semidirect
9. C₇×#1816	C₂	semidirect
10. C₄×C₇×#108	C₂	semidirect
11. C₄×C₇×#100	C₂	semidirect
18. C₇×#472	C₄	direct (N × H)
48. C₄×#472	C₇	direct (N × H)
53. C₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
59. C₂×C₇×D₈	C₂×C₄	semidirect
63. C₇×#131	C₂×C₄	semidirect
91. C₇×#108	C₂×C₄	semidirect
103. C₇×#100	C₂×C₄	semidirect
117. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
118. C₂×C₄×D₈	C₂×C₇	semidirect
119. C₄×#131	C₂×C₇	semidirect
120. #1978	C₂×C₇	semidirect
121. #1952	C₂×C₇	semidirect
122. #1931	C₂×C₇	semidirect
123. #1907	C₂×C₇	semidirect
124. #1816	C₂×C₇	semidirect
125. C₄×#108	C₂×C₇	semidirect
126. C₄×#100	C₂×C₇	semidirect
203. #472	C₄×C₇	direct (N × H)
285. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
291. C₂×D₈	C₂×C₄×C₇	semidirect
295. #131	C₂×C₄×C₇	semidirect
323. #108	C₂×C₄×C₇	semidirect
335. #100	C₂×C₄×C₇	semidirect
368. C₄×C₇	#472	direct (N × H)
498. C₇	C₄×#472	direct (N × H)
519. C₄	C₇×#472	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×#472	2
C₄×C₇×AGL(1,ℤ/8)	2
C₂×C₄×C₇×D₈	2
C₄×C₇×#131	2
C₇×#1978	2
C₇×#1952	2
C₇×#1931	2
C₇×#1907	2
C₇×#1816	2
C₄×C₇×#108	2
C₄×C₇×#100	2
C₄×#472	7

Subgroups — C4×C7×#472 #13198769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×#472 #13198769