Subgroups — C₄×C₇×#471 #13198768

Order 1792.

914 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#471	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1977	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1951	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1931	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1930	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1908	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1907	C₂	1	1	yes	maximal, characteristic
12	C₇×#1815	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₇×#100	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#137	C₂²	1	1	yes	characteristic
17	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×#131	C₂²	1	1	yes	characteristic
20	C₂×C₇×#131	C₂²	1	1	yes	characteristic
21	C₄×C₇×#41	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₇×#471	C₄	1	8	yes	direct product factor
25	C₇×#442	—	2	1	no	—
26	C₇×#441	—	2	1	no	—
27	C₇×#440	—	2	1	no	—
28	C₇×#440	—	2	1	no	—
29	C₄×C₇×Q₁₆	—	2	1	no	—
30	C₄×C₇×SD₁₆	—	2	1	no	—
31	C₄×C₇×SD₁₆	—	2	1	no	—
32	C₄×C₇×SD₁₆	—	2	1	no	—
33	C₄×C₇×SD₁₆	—	2	1	no	—
34	C₄×C₇×SD₁₆	—	2	1	no	—
35	C₄×C₇×SD₁₆	—	2	1	no	—
36	C₄×C₇×D₈	—	2	1	no	—
37	C₂×C₇×#108	C₂²	1	1	yes	characteristic
38	C₂×C₇×#108	C₂²	1	1	yes	characteristic
39	C₇×#428	C₂²	1	1	yes	characteristic
40	C₇×#428	C₂²	1	1	yes	characteristic
41	C₂×C₇×#106	C₂²	1	1	yes	characteristic
42	C₇×#419	C₂²	1	1	yes	characteristic
43	C₇×#418	C₂²	1	1	yes	characteristic
44	C₇×#417	C₂²	1	1	yes	characteristic
45	C₇×#417	C₂²	1	1	yes	characteristic
46	C₂×C₇×#103	C₂²	1	1	yes	characteristic
47	C₂×C₇×#102	C₂²	1	1	yes	characteristic
48	C₂×C₇×#101	C₂²	1	1	yes	characteristic
49	C₂×C₇×#101	C₂²	1	1	yes	characteristic
50	C₂×C₇×#100	C₂²	1	1	yes	characteristic
51	C₂×C₇×#100	C₂²	1	1	yes	characteristic
52	C₇×#405	—	2	1	no	—
53	C₇×#405	—	2	1	no	—
54	C₇×#405	C₂²	1	1	yes	characteristic
55	C₇×#405	C₂²	1	1	yes	characteristic
56	C₄×C₇×M₁₆	—	2	1	no	—
57	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
58	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
59	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
60	C₂×C₄×C₇×C₈	—	2	1	no	—
61	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
62	C₇×#343	C₂²	1	1	yes	characteristic
63	C₇×#343	C₂²	1	1	yes	characteristic
64	C₇×#343	C₂²	1	1	yes	characteristic
65	C₇×#343	C₂²	1	1	yes	characteristic
66	C₇×#341	C₂²	1	1	yes	characteristic
67	C₇×#341	C₂²	1	1	yes	characteristic
68	C₄×#471	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂×C₇×#41	C₂³	1	1	yes	characteristic
70	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₇×#137	—	2	2	no	—
74	C₇×#137	C₂×C₄	1	4	yes	complemented
75	C₇×AGL(1,ℤ/8)	—	2	2	no	—
76	C₇×AGL(1,ℤ/8)	C₂×C₄	1	4	yes	—
77	C₂×C₇×Q₁₆	—	2	1	no	—
78	C₂×C₇×SD₁₆	—	2	1	no	—
79	C₂×C₇×SD₁₆	—	2	1	no	—
80	C₂×C₇×SD₁₆	—	2	1	no	—
81	C₂×C₇×SD₁₆	—	2	1	no	—
82	C₂×C₇×SD₁₆	—	2	2	no	—
83	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	complemented
84	C₂×C₇×D₈	—	2	1	no	—
85	C₇×#131	—	2	2	no	—
86	C₇×#131	—	2	2	no	—
87	C₇×#131	—	2	2	no	—
88	C₇×#131	C₂×C₄	1	4	yes	complemented
89	C₂×C₇×M₁₆	—	2	1	no	—
90	C₂×C₇×M₁₆	—	2	1	no	—
91	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
92	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
97	C₂²×C₇×C₈	—	2	1	no	—
98	C₂²×C₇×C₈	—	2	1	no	—
99	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
100	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
101	C₄×C₇×Q₈	—	2	1	no	—
102	C₄×C₇×Q₈	—	2	1	no	—
103	C₄×C₇×Q₈	—	2	1	no	—
104	C₄×C₇×Q₈	—	2	1	no	—
105	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
106	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
107	C₄×C₇×D₄	—	2	1	no	—
108	C₄×C₇×D₄	—	2	1	no	—
109	C₄×C₇×D₄	—	2	1	no	—
110	C₄×C₇×D₄	—	2	1	no	—
111	C₄×C₇×D₄	—	2	1	no	—
112	C₄×C₇×D₄	—	2	1	no	—
113	C₄×C₇×D₄	D₄	1	1	yes	characteristic
114	C₄×C₇×D₄	D₄	1	1	yes	characteristic
115	C₇×#117	—	2	1	no	—
116	C₇×#117	C₂³	1	1	yes	characteristic
117	C₂×C₇×C₄⋊C₄	—	2	1	no	—
118	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₄²×C₇	—	2	1	no	—
122	C₂×C₄²×C₇	—	2	1	no	—
123	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
124	C₇×#108	—	2	2	no	—
125	C₇×#108	C₂×C₄	1	4	yes	complemented
126	C₇×#107	—	2	1	no	—
127	C₇×#107	—	2	1	no	—
128	C₇×#106	—	2	1	no	—
129	C₇×#106	—	2	1	no	—
130	C₇×#106	—	2	1	no	—
131	C₇×#106	—	2	1	no	—
132	C₇×#103	—	2	1	no	—
133	C₇×#103	—	2	1	no	—
134	C₇×#103	—	2	1	no	—
135	C₇×#103	—	2	1	no	—
136	C₇×#103	—	2	1	no	—
137	C₇×#103	—	2	1	no	—
138	C₇×#102	—	2	1	no	—
139	C₇×#102	—	2	1	no	—
140	C₇×#102	—	2	1	no	—
141	C₇×#102	—	2	1	no	—
142	C₇×#102	—	2	1	no	—
143	C₇×#102	—	2	1	no	—
144	C₇×#101	—	2	2	no	—
145	C₇×#101	C₂×C₄	1	4	yes	complemented
146	C₇×#100	—	2	2	no	—
147	C₇×#100	C₂×C₄	1	4	yes	complemented
148	C₇×#97	—	2	1	no	—
149	C₇×#97	—	2	1	no	—
150	C₇×#97	—	2	1	no	—
151	C₇×#97	—	2	1	no	—
152	C₇×#97	—	2	1	no	—
153	C₄×C₇×C₈	—	2	1	no	—
154	C₄×C₇×C₈	—	2	1	no	—
155	C₄×C₇×C₈	—	2	1	no	—
156	C₄×C₇×C₈	—	2	1	no	—
157	C₄×C₇×C₈	—	2	1	no	—
158	C₄×C₇×C₈	D₄	1	1	yes	characteristic
159	C₄×C₇×C₈	D₄	1	1	yes	characteristic
160	C₄×C₇×C₈	D₄	1	1	yes	characteristic
161	C₄×C₇×C₈	D₄	1	1	yes	characteristic
162	C₂×#471	C₂×C₇	1	1	yes	characteristic
163	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
164	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic
165	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
166	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
167	#1977	C₂×C₇	1	1	yes	characteristic, complemented
168	#1951	C₂×C₇	1	1	yes	characteristic, complemented
169	#1931	C₂×C₇	1	1	yes	characteristic, complemented
170	#1930	C₂×C₇	1	1	yes	characteristic, complemented
171	#1908	C₂×C₇	1	1	yes	characteristic, complemented
172	#1907	C₂×C₇	1	1	yes	characteristic
173	#1815	C₂×C₇	1	1	yes	characteristic, complemented
174	C₄×#108	C₂×C₇	1	1	yes	characteristic, complemented
175	C₄×#101	C₂×C₇	1	1	yes	characteristic, complemented
176	C₄×#100	C₂×C₇	1	1	yes	characteristic, complemented
177	C₂⁴×C₇	—	2	1	no	—
178	C₇×#41	—	2	1	no	—
179	C₇×#41	—	2	1	no	—
180	C₇×#41	C₂²×C₄	1	2	yes	—
181	C₇×#41	#41	1	2	yes	—
182	C₂×C₇×Q₈	—	2	1	no	—
183	C₂×C₇×Q₈	—	2	1	no	—
184	C₂×C₇×Q₈	—	2	1	no	—
185	C₂×C₇×Q₈	—	2	1	no	—
186	C₂×C₇×Q₈	—	2	1	no	—
187	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
188	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
189	C₂×C₇×D₄	—	2	1	no	—
190	C₂×C₇×D₄	—	2	1	no	—
191	C₂×C₇×D₄	—	2	1	no	—
192	C₂×C₇×D₄	—	2	1	no	—
193	C₂×C₇×D₄	—	2	1	no	—
194	C₂×C₇×D₄	—	2	1	no	—
195	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
196	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	—	2	1	no	—
198	C₂²×C₄×C₇	—	2	1	no	—
199	C₂²×C₄×C₇	—	2	1	no	—
200	C₂²×C₄×C₇	—	2	1	no	—
201	C₂²×C₄×C₇	—	2	1	no	—
202	C₂²×C₄×C₇	—	2	1	no	—
203	C₂²×C₄×C₇	—	4	1	no	—
204	C₂²×C₄×C₇	—	4	1	no	—
205	C₂²×C₄×C₇	—	8	2	no	—
206	C₂²×C₄×C₇	#41	1	1	yes	characteristic
207	C₂²×C₄×C₇	#41	1	1	yes	characteristic
208	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
209	C₇×Q₁₆	—	2	4	no	—
210	C₇×SD₁₆	—	2	4	no	—
211	C₇×SD₁₆	—	2	4	no	—
212	C₇×SD₁₆	—	2	4	no	—
213	C₇×SD₁₆	—	2	4	no	—
214	C₇×D₈	—	2	4	no	—
215	C₇×M₁₆	—	2	4	no	—
216	C₇×M₁₆	—	2	1	no	—
217	C₇×M₁₆	—	2	1	no	—
218	C₇×M₁₆	—	2	1	no	—
219	C₇×M₁₆	—	2	1	no	—
220	C₇×M₁₆	—	2	4	no	—
221	C₇×M₁₆	—	2	1	no	—
222	C₇×M₁₆	—	2	1	no	—
223	C₇×M₁₆	—	2	1	no	—
224	C₇×M₁₆	—	2	1	no	—
225	C₇×M₁₆	C₂²×C₄	1	2	yes	—
226	C₇×M₁₆	C₂²×C₄	1	2	yes	—
227	C₇×M₁₆	C₂²×C₄	1	2	yes	—
228	C₇×M₁₆	#41	1	2	yes	—
229	C₂×C₇×C₈	—	2	4	no	—
230	C₂×C₇×C₈	—	2	1	no	—
231	C₂×C₇×C₈	—	2	1	no	—
232	C₂×C₇×C₈	—	2	1	no	—
233	C₂×C₇×C₈	—	2	1	no	—
234	C₂×C₇×C₈	—	2	1	no	—
235	C₂×C₇×C₈	—	2	1	no	—
236	C₂×C₇×C₈	—	2	4	no	—
237	C₂×C₇×C₈	—	2	1	no	—
238	C₂×C₇×C₈	—	2	1	no	—
239	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
240	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
241	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
242	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
243	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
244	C₂×C₇×C₈	#41	1	2	yes	—
245	C₇×C₄⋊C₄	—	2	1	no	—
246	C₇×C₄⋊C₄	—	2	1	no	—
247	C₇×C₄⋊C₄	—	2	1	no	—
248	C₇×C₄⋊C₄	—	2	1	no	—
249	C₇×C₄⋊C₄	—	2	1	no	—
250	C₇×C₄⋊C₄	—	2	1	no	—
251	C₇×C₄⋊C₄	—	4	1	no	—
252	C₇×C₄⋊C₄	—	4	1	no	—
253	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
254	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
255	C₇×C₂²⋊C₄	—	2	1	no	—
256	C₇×C₂²⋊C₄	—	2	1	no	—
257	C₇×C₂²⋊C₄	—	2	1	no	—
258	C₇×C₂²⋊C₄	—	4	1	no	—
259	C₇×C₂²⋊C₄	—	4	1	no	—
260	C₄²×C₇	—	2	1	no	—
261	C₄²×C₇	—	2	1	no	—
262	C₄²×C₇	—	2	1	no	—
263	C₄²×C₇	—	4	1	no	—
264	C₄²×C₇	—	4	1	no	—
265	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
269	C₂×#137	C₂²×C₇	1	1	yes	characteristic
270	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
271	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
272	C₂×#131	C₂²×C₇	1	1	yes	characteristic
273	C₂×#131	C₂²×C₇	1	1	yes	characteristic
274	C₄×#41	C₂²×C₇	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
277	#471	C₄×C₇	1	8	yes	direct product factor
278	#442	—	2	1	no	—
279	#441	—	2	1	no	—
280	#440	—	2	1	no	—
281	#440	—	2	1	no	—
282	C₄×Q₁₆	—	2	1	no	—
283	C₄×SD₁₆	—	2	1	no	—
284	C₄×SD₁₆	—	2	1	no	—
285	C₄×SD₁₆	—	2	1	no	—
286	C₄×SD₁₆	—	2	1	no	—
287	C₄×SD₁₆	—	2	1	no	—
288	C₄×SD₁₆	—	2	1	no	—
289	C₄×D₈	—	2	1	no	—
290	C₂×#108	C₂²×C₇	1	1	yes	characteristic
291	C₂×#108	C₂²×C₇	1	1	yes	characteristic
292	#428	C₂²×C₇	1	1	yes	characteristic
293	#428	C₂²×C₇	1	1	yes	characteristic
294	C₂×#106	C₂²×C₇	1	1	yes	characteristic
295	#419	C₂²×C₇	1	1	yes	characteristic
296	#418	C₂²×C₇	1	1	yes	characteristic
297	#417	C₂²×C₇	1	1	yes	characteristic
298	#417	C₂²×C₇	1	1	yes	characteristic
299	C₂×#103	C₂²×C₇	1	1	yes	characteristic
300	C₂×#102	C₂²×C₇	1	1	yes	characteristic
301	C₂×#101	C₂²×C₇	1	1	yes	characteristic
302	C₂×#101	C₂²×C₇	1	1	yes	characteristic
303	C₂×#100	C₂²×C₇	1	1	yes	characteristic
304	C₂×#100	C₂²×C₇	1	1	yes	characteristic
305	#405	—	2	1	no	—
306	#405	—	2	1	no	—
307	#405	C₂²×C₇	1	1	yes	characteristic
308	#405	C₂²×C₇	1	1	yes	characteristic
309	C₄×M₁₆	—	2	1	no	—
310	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
311	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
312	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
313	C₂×C₄×C₈	—	2	1	no	—
314	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
315	#343	C₂²×C₇	1	1	yes	characteristic
316	#343	C₂²×C₇	1	1	yes	characteristic
317	#343	C₂²×C₇	1	1	yes	characteristic
318	#343	C₂²×C₇	1	1	yes	characteristic
319	#341	C₂²×C₇	1	1	yes	characteristic
320	#341	C₂²×C₇	1	1	yes	characteristic
321	C₂³×C₇	—	2	1	no	—
322	C₂³×C₇	—	2	2	no	—
323	C₂³×C₇	—	4	1	no	—
324	C₂³×C₇	—	4	1	no	—
325	C₂³×C₇	—	8	1	no	—
326	C₂³×C₇	—	8	1	no	—
327	C₂³×C₇	C₂×#41	1	1	yes	characteristic
328	C₇×Q₈	—	2	1	no	—
329	C₇×Q₈	—	2	2	no	—
330	C₇×Q₈	—	2	2	no	—
331	C₇×Q₈	—	4	1	no	—
332	C₇×Q₈	—	4	1	no	—
333	C₇×Q₈	C₄×D₄	1	2	yes	—
334	C₇×D₄	—	2	2	no	—
335	C₇×D₄	—	2	2	no	—
336	C₇×D₄	—	2	2	no	—
337	C₇×D₄	—	2	2	no	—
338	C₇×D₄	—	2	1	no	—
339	C₇×D₄	—	4	1	no	—
340	C₇×D₄	—	4	1	no	—
341	C₇×D₄	C₄×D₄	1	2	yes	—
342	C₂×C₄×C₇	—	2	1	no	—
343	C₂×C₄×C₇	—	2	2	no	—
344	C₂×C₄×C₇	—	2	2	no	—
345	C₂×C₄×C₇	—	2	2	no	—
346	C₂×C₄×C₇	—	2	2	no	—
347	C₂×C₄×C₇	—	2	1	no	—
348	C₂×C₄×C₇	—	2	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	4	2	no	—
351	C₂×C₄×C₇	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	—	4	2	no	—
354	C₂×C₄×C₇	—	4	1	no	—
355	C₂×C₄×C₇	—	4	1	no	—
356	C₂×C₄×C₇	—	8	2	no	—
357	C₂×C₄×C₇	—	8	2	no	—
358	C₂×C₄×C₇	—	8	1	no	—
359	C₂×C₄×C₇	—	8	1	no	—
360	C₂×C₄×C₇	#121	1	1	yes	characteristic
361	C₂×C₄×C₇	#121	1	1	yes	characteristic
362	C₂×C₄×C₇	#121	1	1	yes	characteristic
363	C₂×C₄×C₇	#121	1	1	yes	characteristic
364	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
365	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
368	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
369	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
370	C₇×C₈	—	2	2	no	—
371	C₇×C₈	—	2	2	no	—
372	C₇×C₈	—	2	2	no	—
373	C₇×C₈	—	2	1	no	—
374	C₇×C₈	—	2	2	no	—
375	C₇×C₈	—	2	1	no	—
376	C₇×C₈	—	4	1	no	—
377	C₇×C₈	—	4	1	no	—
378	C₇×C₈	C₄×D₄	1	2	yes	—
379	C₇×C₈	C₄×D₄	1	2	yes	—
380	C₂×#41	C₂³×C₇	1	1	yes	characteristic
381	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
382	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
383	C₂³×C₄	—	2	1	no	—
384	#137	—	2	2	no	—
385	#137	C₂×C₄×C₇	1	4	yes	complemented
386	AGL(1,ℤ/8)	—	2	2	no	—
387	AGL(1,ℤ/8)	C₂×C₄×C₇	1	4	yes	—
388	C₂×Q₁₆	—	2	1	no	—
389	C₂×SD₁₆	—	2	1	no	—
390	C₂×SD₁₆	—	2	1	no	—
391	C₂×SD₁₆	—	2	1	no	—
392	C₂×SD₁₆	—	2	1	no	—
393	C₂×SD₁₆	—	2	2	no	—
394	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	complemented
395	C₂×D₈	—	2	1	no	—
396	#131	—	2	2	no	—
397	#131	—	2	2	no	—
398	#131	—	2	2	no	—
399	#131	C₂×C₄×C₇	1	4	yes	complemented
400	C₂×M₁₆	—	2	1	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
403	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
404	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
405	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
406	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
407	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
408	C₂²×C₈	—	2	1	no	—
409	C₂²×C₈	—	2	1	no	—
410	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	—	2	1	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
417	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	C₇×D₄	1	1	yes	characteristic
425	C₄×D₄	C₇×D₄	1	1	yes	characteristic
426	#117	—	2	1	no	—
427	#117	C₂³×C₇	1	1	yes	characteristic
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₄²	—	2	1	no	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
435	#108	—	2	2	no	—
436	#108	C₂×C₄×C₇	1	4	yes	complemented
437	#107	—	2	1	no	—
438	#107	—	2	1	no	—
439	#106	—	2	1	no	—
440	#106	—	2	1	no	—
441	#106	—	2	1	no	—
442	#106	—	2	1	no	—
443	#103	—	2	1	no	—
444	#103	—	2	1	no	—
445	#103	—	2	1	no	—
446	#103	—	2	1	no	—
447	#103	—	2	1	no	—
448	#103	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	—	2	1	no	—
455	#101	—	2	2	no	—
456	#101	C₂×C₄×C₇	1	4	yes	complemented
457	#100	—	2	2	no	—
458	#100	C₂×C₄×C₇	1	4	yes	complemented
459	#97	—	2	1	no	—
460	#97	—	2	1	no	—
461	#97	—	2	1	no	—
462	#97	—	2	1	no	—
463	#97	—	2	1	no	—
464	C₄×C₈	—	2	1	no	—
465	C₄×C₈	—	2	1	no	—
466	C₄×C₈	—	2	1	no	—
467	C₄×C₈	—	2	1	no	—
468	C₄×C₈	—	2	1	no	—
469	C₄×C₈	C₇×D₄	1	1	yes	characteristic
470	C₄×C₈	C₇×D₄	1	1	yes	characteristic
471	C₄×C₈	C₇×D₄	1	1	yes	characteristic
472	C₄×C₈	C₇×D₄	1	1	yes	characteristic
473	C₂²×C₇	—	2	1	no	—
474	C₂²×C₇	—	2	1	no	—
475	C₂²×C₇	—	2	2	no	—
476	C₂²×C₇	—	4	1	no	—
477	C₂²×C₇	—	4	1	no	—
478	C₂²×C₇	—	4	2	no	—
479	C₂²×C₇	—	8	2	no	—
480	C₂²×C₇	—	8	2	no	—
481	C₂²×C₇	—	8	1	no	—
482	C₂²×C₇	—	8	1	no	—
483	C₂²×C₇	C₄×#41	1	1	yes	characteristic
484	C₂²×C₇	C₂×#121	1	1	yes	characteristic
485	C₂²×C₇	#529	1	1	yes	characteristic
486	C₄×C₇	—	2	1	no	—
487	C₄×C₇	—	2	1	no	—
488	C₄×C₇	—	2	1	no	—
489	C₄×C₇	—	2	2	no	—
490	C₄×C₇	—	4	1	no	—
491	C₄×C₇	—	4	1	no	—
492	C₄×C₇	—	4	2	no	—
493	C₄×C₇	—	8	1	no	—
494	C₄×C₇	—	8	1	no	—
495	C₄×C₇	#471	1	2	yes	direct product factor
496	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
497	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
498	C₄×C₇	#525	1	1	yes	characteristic
499	C₄×C₇	#532	1	1	yes	characteristic
500	C₂⁴	—	2	1	no	—
501	#41	—	2	1	no	—
502	#41	—	2	1	no	—
503	#41	C₂²×C₄×C₇	1	2	yes	—
504	#41	C₇×#41	1	2	yes	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
511	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
519	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	4	1	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	—	8	2	no	—
529	C₂²×C₄	C₇×#41	1	1	yes	characteristic
530	C₂²×C₄	C₇×#41	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
532	Q₁₆	—	2	4	no	—
533	SD₁₆	—	2	4	no	—
534	SD₁₆	—	2	4	no	—
535	SD₁₆	—	2	4	no	—
536	SD₁₆	—	2	4	no	—
537	D₈	—	2	4	no	—
538	M₁₆	—	2	4	no	—
539	M₁₆	—	2	1	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	—	2	1	no	—
542	M₁₆	—	2	1	no	—
543	M₁₆	—	2	4	no	—
544	M₁₆	—	2	1	no	—
545	M₁₆	—	2	1	no	—
546	M₁₆	—	2	1	no	—
547	M₁₆	—	2	1	no	—
548	M₁₆	C₂²×C₄×C₇	1	2	yes	—
549	M₁₆	C₂²×C₄×C₇	1	2	yes	—
550	M₁₆	C₂²×C₄×C₇	1	2	yes	—
551	M₁₆	C₇×#41	1	2	yes	—
552	C₂×C₈	—	2	4	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	4	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
563	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
564	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
565	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
566	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
567	C₂×C₈	C₇×#41	1	2	yes	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	4	1	no	—
575	C₄⋊C₄	—	4	1	no	—
576	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
577	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
578	C₂²⋊C₄	—	2	1	no	—
579	C₂²⋊C₄	—	2	1	no	—
580	C₂²⋊C₄	—	2	1	no	—
581	C₂²⋊C₄	—	4	1	no	—
582	C₂²⋊C₄	—	4	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	4	1	no	—
587	C₄²	—	4	1	no	—
588	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
589	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
590	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
591	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
592	C₂×C₇	—	2	1	no	—
593	C₂×C₇	—	2	1	no	—
594	C₂×C₇	—	4	2	no	—
595	C₂×C₇	—	8	2	no	—
596	C₂×C₇	C₄×#121	1	1	yes	characteristic
597	C₂×C₇	C₂×#471	1	1	yes	characteristic
598	C₂×C₇	#3067	1	1	yes	characteristic
599	C₂³	—	2	1	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	8	1	no	—
604	C₂³	—	8	1	no	—
605	C₂³	C₂×C₇×#41	1	1	yes	characteristic
606	Q₈	—	2	1	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	2	2	no	—
609	Q₈	—	4	1	no	—
610	Q₈	—	4	1	no	—
611	Q₈	C₄×C₇×D₄	1	2	yes	—
612	D₄	—	2	2	no	—
613	D₄	—	2	2	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	1	no	—
617	D₄	—	4	1	no	—
618	D₄	—	4	1	no	—
619	D₄	C₄×C₇×D₄	1	2	yes	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	8	2	no	—
635	C₂×C₄	—	8	2	no	—
636	C₂×C₄	—	8	1	no	—
637	C₂×C₄	—	8	1	no	—
638	C₂×C₄	C₇×#121	1	1	yes	characteristic
639	C₂×C₄	C₇×#121	1	1	yes	characteristic
640	C₂×C₄	C₇×#121	1	1	yes	characteristic
641	C₂×C₄	C₇×#121	1	1	yes	characteristic
642	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
643	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
644	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
645	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
646	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
647	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
648	C₈	—	2	2	no	—
649	C₈	—	2	2	no	—
650	C₈	—	2	2	no	—
651	C₈	—	2	1	no	—
652	C₈	—	2	2	no	—
653	C₈	—	2	1	no	—
654	C₈	—	4	1	no	—
655	C₈	—	4	1	no	—
656	C₈	C₄×C₇×D₄	1	2	yes	—
657	C₈	C₄×C₇×D₄	1	2	yes	—
658	C₇	C₄×#471	1	1	yes	characteristic, direct product factor, Sylow
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	8	2	no	—
666	C₂²	—	8	2	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	C₄×C₇×#41	1	1	yes	characteristic
670	C₂²	C₂×C₇×#121	1	1	yes	characteristic
671	C₂²	C₇×#529	1	1	yes	characteristic
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	2	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	2	no	—
679	C₄	—	8	1	no	—
680	C₄	—	8	1	no	—
681	C₄	C₇×#471	1	2	yes	direct product factor
682	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
683	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
684	C₄	C₇×#525	1	1	yes	characteristic
685	C₄	C₇×#532	1	1	yes	characteristic
686	C₂	—	2	1	no	—
687	C₂	—	2	1	no	—
688	C₂	—	4	2	no	—
689	C₂	—	8	2	no	—
690	C₂	C₄×C₇×#121	1	1	yes	characteristic
691	C₂	C₂×C₇×#471	1	1	yes	characteristic
692	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×AGL(1,ℤ/8)	C₂²
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×#137	C₂	semidirect
4. C₂×C₄×C₇×SD₁₆	C₂	semidirect
5. C₄×C₇×#131	C₂	semidirect
6. C₇×#1977	C₂	semidirect
7. C₇×#1951	C₂	semidirect
8. C₇×#1931	C₂	semidirect
9. C₇×#1930	C₂	semidirect
10. C₇×#1908	C₂	semidirect
12. C₇×#1815	C₂	semidirect
13. C₄×C₇×#108	C₂	semidirect
14. C₄×C₇×#101	C₂	semidirect
15. C₄×C₇×#100	C₂	semidirect
24. C₇×#471	C₄	direct (N × H)
68. C₄×#471	C₇	direct (N × H)
74. C₇×#137	C₂×C₄	semidirect
83. C₂×C₇×SD₁₆	C₂×C₄	semidirect
88. C₇×#131	C₂×C₄	semidirect
125. C₇×#108	C₂×C₄	semidirect
145. C₇×#101	C₂×C₄	semidirect
147. C₇×#100	C₂×C₄	semidirect
163. C₄×#137	C₂×C₇	semidirect
165. C₂×C₄×SD₁₆	C₂×C₇	semidirect
166. C₄×#131	C₂×C₇	semidirect
167. #1977	C₂×C₇	semidirect
168. #1951	C₂×C₇	semidirect
169. #1931	C₂×C₇	semidirect
170. #1930	C₂×C₇	semidirect
171. #1908	C₂×C₇	semidirect
173. #1815	C₂×C₇	semidirect
174. C₄×#108	C₂×C₇	semidirect
175. C₄×#101	C₂×C₇	semidirect
176. C₄×#100	C₂×C₇	semidirect
277. #471	C₄×C₇	direct (N × H)
385. #137	C₂×C₄×C₇	semidirect
394. C₂×SD₁₆	C₂×C₄×C₇	semidirect
399. #131	C₂×C₄×C₇	semidirect
436. #108	C₂×C₄×C₇	semidirect
456. #101	C₂×C₄×C₇	semidirect
458. #100	C₂×C₄×C₇	semidirect
495. C₄×C₇	#471	direct (N × H)
658. C₇	C₄×#471	direct (N × H)
681. C₄	C₇×#471	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×#471	2
C₄×C₇×#137	2
C₄×C₇×AGL(1,ℤ/8)	2
C₂×C₄×C₇×SD₁₆	2
C₄×C₇×#131	2
C₇×#1977	2
C₇×#1951	2
C₇×#1931	2
C₇×#1930	2
C₇×#1908	2
C₇×#1907	2
C₇×#1815	2
C₄×C₇×#108	2
C₄×C₇×#101	2
C₄×C₇×#100	2
C₄×#471	7

Subgroups — C4×C7×#471 #13198768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×#471 #13198768