Subgroups — C₇×#60650 #13237866

Order 1792.

3274 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#577	C₂	1	2	yes	maximal, complemented
2	C₂×C₇×#576	C₂	1	2	yes	maximal, complemented
3	C₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3155	C₂	1	6	yes	maximal, complemented
6	C₇×#3154	C₂	1	6	yes	maximal, complemented
7	C₇×#3153	C₂	1	3	yes	maximal, complemented
8	C₇×#3151	C₂	1	3	yes	maximal, complemented
9	C₇×#3150	C₂	1	3	yes	maximal, complemented
10	C₂×C₇×#496	C₂	1	3	yes	maximal, complemented
11	C₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
13	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
14	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
15	C₇×#577	—	2	16	no	—
16	C₇×#576	—	2	16	no	—
17	C₂×C₇×#137	C₂²	1	6	yes	complemented
18	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
19	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
20	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
21	C₂×C₇×#135	C₂²	1	6	yes	complemented
22	C₂×C₇×#135	C₂²	1	6	yes	complemented
23	C₂²×C₇×SD₁₆	C₂²	1	6	yes	complemented
24	C₂²×C₇×D₈	C₂²	1	6	yes	complemented
25	C₂×C₇×#131	C₂²	1	2	yes	—
26	C₇×#550	—	2	2	no	—
27	C₇×#548	—	2	2	no	—
28	C₇×#546	—	2	6	no	—
29	C₇×D₄²	—	2	6	no	—
30	C₇×#536	C₂²	1	3	yes	complemented
31	C₇×#535	C₂²	1	3	yes	complemented
32	C₇×#535	C₂²	1	6	yes	complemented
33	C₇×#532	C₂²	1	3	yes	complemented
34	C₇×#532	C₂²	1	3	yes	complemented
35	C₂×C₇×#127	C₂²	1	3	yes	complemented
36	C₂×C₇×#124	C₂²	1	3	yes	complemented
37	C₄×C₇×#41	C₂²	1	1	yes	characteristic
38	C₇×#497	C₂²	1	1	yes	characteristic, complemented
39	C₇×#497	C₂²	1	3	yes	complemented
40	C₇×#497	C₂²	1	6	yes	complemented
41	C₇×#496	C₂²	1	6	yes	complemented
42	C₇×#496	C₂²	1	12	yes	complemented
43	C₇×#496	C₂²	1	3	yes	complemented
44	C₇×#496	C₂²	1	6	yes	complemented
45	C₇×#496	C₂²	1	3	yes	complemented
46	C₇×#495	C₂²	1	12	yes	complemented
47	C₇×#493	C₂²	1	6	yes	complemented
48	C₇×#492	C₂²	1	6	yes	complemented
49	C₇×#405	C₂²	1	6	yes	complemented
50	C₄×C₇×M₁₆	C₂²	1	3	yes	complemented
51	C₂×C₇×#97	C₂²	1	3	yes	complemented
52	#60650	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₇×2₋¹⁺⁴	—	2	8	no	—
54	C₇×H(5,𝔽₂)	—	2	8	no	—
55	C₇×H(5,𝔽₂)	—	2	8	no	—
56	C₇×H(5,𝔽₂)	—	2	8	no	—
57	C₂×C₇×#41	—	2	1	no	—
58	C₂×C₇×#41	—	2	2	no	—
59	C₂×C₇×#41	—	2	3	no	—
60	C₂×C₇×#41	C₂³	1	6	yes	—
61	C₂×C₇×#41	C₂³	1	3	yes	—
62	C₂×C₇×#41	C₂³	1	3	yes	—
63	C₂×C₇×#41	C₂³	1	1	yes	characteristic
64	C₂²×C₇×Q₈	—	2	1	no	—
65	C₂²×C₇×Q₈	C₂³	1	3	yes	—
66	C₂²×C₇×D₄	—	2	6	no	—
67	C₂²×C₇×D₄	—	2	3	no	—
68	C₂²×C₇×D₄	—	2	6	no	—
69	C₂²×C₇×D₄	C₂³	1	3	yes	—
70	C₂²×C₇×D₄	C₂³	1	6	yes	—
71	C₇×#137	—	2	24	no	—
72	C₇×AGL(1,ℤ/8)	—	2	24	no	—
73	C₇×AGL(1,ℤ/8)	—	2	24	no	—
74	C₇×AGL(1,ℤ/8)	—	2	24	no	—
75	C₇×#135	—	2	24	no	—
76	C₇×#135	—	2	24	no	—
77	C₂×C₇×Q₁₆	C₂³	1	6	yes	—
78	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
79	C₂×C₇×SD₁₆	—	2	24	no	—
80	C₂×C₇×SD₁₆	C₂³	1	6	yes	—
81	C₂×C₇×SD₁₆	C₂³	1	12	yes	—
82	C₂×C₇×SD₁₆	C₂³	1	6	yes	—
83	C₂×C₇×SD₁₆	C₂³	1	6	yes	—
84	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
85	C₂×C₇×D₈	—	2	24	no	—
86	C₂×C₇×D₈	C₂³	1	6	yes	—
87	C₂×C₇×D₈	C₂³	1	12	yes	—
88	C₂×C₇×D₈	C₂³	1	6	yes	—
89	C₇×#131	D₄	1	16	yes	complemented
90	C₂×C₇×M₁₆	C₂³	1	6	yes	—
91	C₂²×C₇×C₈	C₂³	1	6	yes	—
92	C₇×C₄⋊Q₈	C₂³	1	3	yes	—
93	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₇×#127	—	2	6	no	—
95	C₇×#127	C₂³	1	6	yes	—
96	C₇×#127	C₂³	1	3	yes	—
97	C₇×#127	C₂³	1	3	yes	—
98	C₇×#124	—	2	6	no	—
99	C₇×#124	C₂³	1	6	yes	—
100	C₇×#124	C₂³	1	6	yes	—
101	C₇×#124	C₂³	1	3	yes	—
102	C₇×#124	C₂³	1	1	yes	characteristic
103	C₇×#123	—	2	6	no	—
104	C₇×C₂²⋊Q₈	—	2	6	no	—
105	C₇×#121	—	2	6	no	—
106	C₇×#121	—	2	6	no	—
107	C₇×#121	—	2	12	no	—
108	C₇×#121	—	2	6	no	—
109	C₇×#120	—	2	12	no	—
110	C₇×#120	—	2	6	no	—
111	C₄×C₇×Q₈	D₄	1	2	yes	—
112	C₄×C₇×D₄	—	2	6	no	—
113	C₄×C₇×D₄	—	2	6	no	—
114	C₄×C₇×D₄	D₄	1	6	yes	—
115	C₇×#117	C₂³	1	3	yes	—
116	C₂×C₇×C₂²⋊C₄	—	2	6	no	—
117	C₂×C₄²×C₇	C₂³	1	3	yes	—
118	C₇×#97	C₂³	1	1	yes	characteristic
119	C₇×#97	C₂³	1	3	yes	—
120	C₇×#97	C₂³	1	6	yes	—
121	C₄×C₇×C₈	C₂³	1	6	yes	—
122	C₂×#577	C₂×C₇	1	2	yes	complemented
123	C₂×#576	C₂×C₇	1	2	yes	complemented
124	#3500	C₂×C₇	1	1	yes	characteristic, complemented
125	#3498	C₂×C₇	1	1	yes	characteristic, complemented
126	#3155	C₂×C₇	1	6	yes	complemented
127	#3154	C₂×C₇	1	6	yes	complemented
128	#3153	C₂×C₇	1	3	yes	complemented
129	#3151	C₂×C₇	1	3	yes	complemented
130	#3150	C₂×C₇	1	3	yes	complemented
131	C₂×#496	C₂×C₇	1	3	yes	complemented
132	#2875	C₂×C₇	1	1	yes	characteristic, complemented
133	C₂⁴×C₇	—	2	3	no	—
134	C₂⁴×C₇	—	2	6	no	—
135	C₇×#41	—	2	12	no	—
136	C₇×#41	—	2	12	no	—
137	C₇×#41	—	2	12	no	—
138	C₇×#41	—	2	12	no	—
139	C₇×#41	—	4	4	no	—
140	C₇×#41	—	4	8	no	—
141	C₇×#41	—	4	12	no	—
142	C₇×#41	C₂×D₄	1	8	yes	—
143	C₂×C₇×Q₈	—	2	3	no	—
144	C₂×C₇×Q₈	—	2	12	no	—
145	C₂×C₇×Q₈	—	4	4	no	—
146	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₇×Q₈	C₂⁴	1	3	yes	—
148	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
149	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
150	C₂×C₇×D₄	—	2	6	no	—
151	C₂×C₇×D₄	—	2	3	no	—
152	C₂×C₇×D₄	—	2	3	no	—
153	C₂×C₇×D₄	—	2	12	no	—
154	C₂×C₇×D₄	—	2	12	no	—
155	C₂×C₇×D₄	—	2	12	no	—
156	C₂×C₇×D₄	—	2	6	no	—
157	C₂×C₇×D₄	—	2	3	no	—
158	C₂×C₇×D₄	—	2	6	no	—
159	C₂×C₇×D₄	—	2	6	no	—
160	C₂×C₇×D₄	—	2	12	no	—
161	C₂×C₇×D₄	—	4	24	no	—
162	C₂×C₇×D₄	—	4	12	no	—
163	C₂×C₇×D₄	—	8	12	no	—
164	C₂×C₇×D₄	C₂×D₄	1	3	yes	—
165	C₂×C₇×D₄	C₂⁴	1	3	yes	—
166	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
167	C₂×C₇×D₄	C₂⁴	1	6	yes	—
168	C₂²×C₄×C₇	—	2	3	no	—
169	C₂²×C₄×C₇	—	2	6	no	—
170	C₂²×C₄×C₇	—	2	3	no	—
171	C₂²×C₄×C₇	—	2	3	no	—
172	C₂²×C₄×C₇	C₂×D₄	1	6	yes	—
173	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
174	C₇×Q₁₆	—	2	4	no	—
175	C₇×Q₁₆	—	2	12	no	—
176	C₇×SD₁₆	—	2	12	no	—
177	C₇×SD₁₆	—	2	24	no	—
178	C₇×SD₁₆	—	2	4	no	—
179	C₇×SD₁₆	—	2	12	no	—
180	C₇×SD₁₆	—	2	12	no	—
181	C₇×D₈	—	2	12	no	—
182	C₇×D₈	—	2	24	no	—
183	C₇×D₈	—	2	12	no	—
184	C₇×M₁₆	C₂×D₄	1	24	yes	complemented
185	C₂×C₇×C₈	C₂×D₄	1	24	yes	complemented
186	C₂×C₇×C₈	C₂⁴	1	6	yes	—
187	C₂×C₇×C₈	C₂⁴	1	2	yes	—
188	C₇×C₄⋊C₄	—	2	2	no	—
189	C₇×C₄⋊C₄	—	2	6	no	—
190	C₇×C₄⋊C₄	C₂×D₄	1	6	yes	—
191	C₇×C₂²⋊C₄	—	2	6	no	—
192	C₇×C₂²⋊C₄	—	2	12	no	—
193	C₇×C₂²⋊C₄	—	2	2	no	—
194	C₇×C₂²⋊C₄	—	2	12	no	—
195	C₇×C₂²⋊C₄	C₂×D₄	1	6	yes	—
196	C₄²×C₇	C₂×D₄	1	6	yes	—
197	C₄²×C₇	C₂⁴	1	3	yes	—
198	C₄²×C₇	C₂⁴	1	1	yes	characteristic
199	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
200	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
201	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
202	#577	—	2	16	no	—
203	#576	—	2	16	no	—
204	C₂×#137	C₂²×C₇	1	6	yes	complemented
205	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	6	yes	complemented
206	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	6	yes	complemented
207	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	6	yes	complemented
208	C₂×#135	C₂²×C₇	1	6	yes	complemented
209	C₂×#135	C₂²×C₇	1	6	yes	complemented
210	C₂²×SD₁₆	C₂²×C₇	1	6	yes	complemented
211	C₂²×D₈	C₂²×C₇	1	6	yes	complemented
212	C₂×#131	C₂²×C₇	1	2	yes	—
213	#550	—	2	2	no	—
214	#548	—	2	2	no	—
215	#546	—	2	6	no	—
216	D₄²	—	2	6	no	—
217	#536	C₂²×C₇	1	3	yes	complemented
218	#535	C₂²×C₇	1	6	yes	complemented
219	#535	C₂²×C₇	1	3	yes	complemented
220	#532	C₂²×C₇	1	3	yes	complemented
221	#532	C₂²×C₇	1	3	yes	complemented
222	C₂×#127	C₂²×C₇	1	3	yes	complemented
223	C₂×#124	C₂²×C₇	1	3	yes	complemented
224	C₄×#41	C₂²×C₇	1	1	yes	characteristic
225	#497	C₂²×C₇	1	1	yes	characteristic, complemented
226	#497	C₂²×C₇	1	3	yes	complemented
227	#497	C₂²×C₇	1	6	yes	complemented
228	#496	C₂²×C₇	1	3	yes	complemented
229	#496	C₂²×C₇	1	6	yes	complemented
230	#496	C₂²×C₇	1	12	yes	complemented
231	#496	C₂²×C₇	1	3	yes	complemented
232	#496	C₂²×C₇	1	6	yes	complemented
233	#495	C₂²×C₇	1	12	yes	complemented
234	#493	C₂²×C₇	1	6	yes	complemented
235	#492	C₂²×C₇	1	6	yes	complemented
236	#405	C₂²×C₇	1	6	yes	complemented
237	C₄×M₁₆	C₂²×C₇	1	3	yes	complemented
238	C₂×#97	C₂²×C₇	1	3	yes	complemented
239	C₂³×C₇	—	2	3	no	—
240	C₂³×C₇	—	2	1	no	—
241	C₂³×C₇	—	2	6	no	—
242	C₂³×C₇	—	4	6	no	—
243	C₂³×C₇	—	4	12	no	—
244	C₂³×C₇	—	8	12	no	—
245	C₂³×C₇	—	8	6	no	—
246	C₂³×C₇	C₂²×D₄	1	3	yes	—
247	C₇×Q₈	—	2	6	no	—
248	C₇×Q₈	—	2	2	no	—
249	C₇×Q₈	—	2	2	no	—
250	C₇×Q₈	—	2	2	no	—
251	C₇×Q₈	—	4	6	no	—
252	C₇×Q₈	#127	1	4	yes	—
253	C₇×D₄	—	2	6	no	—
254	C₇×D₄	—	2	6	no	—
255	C₇×D₄	—	2	2	no	—
256	C₇×D₄	—	2	6	no	—
257	C₇×D₄	—	4	12	no	—
258	C₇×D₄	—	4	12	no	—
259	C₇×D₄	—	4	6	no	—
260	C₇×D₄	—	4	6	no	—
261	C₇×D₄	—	4	6	no	—
262	C₇×D₄	—	4	12	no	—
263	C₇×D₄	—	8	6	no	—
264	C₇×D₄	—	8	12	no	—
265	C₇×D₄	#127	1	12	yes	—
266	C₂×C₄×C₇	—	2	2	no	—
267	C₂×C₄×C₇	—	2	3	no	—
268	C₂×C₄×C₇	—	2	1	no	—
269	C₂×C₄×C₇	—	4	6	no	—
270	C₂×C₄×C₇	—	4	6	no	—
271	C₂×C₄×C₇	—	4	12	no	—
272	C₂×C₄×C₇	—	4	6	no	—
273	C₂×C₄×C₇	—	4	6	no	—
274	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₇	C₂²×D₄	1	6	yes	—
276	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
277	C₂×C₄×C₇	C₂²×D₄	1	12	yes	—
278	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
279	C₇×C₈	C₂²×D₄	1	4	yes	—
280	C₇×C₈	C₂²×D₄	1	12	yes	—
281	2₋¹⁺⁴	—	2	8	no	—
282	H(5,𝔽₂)	—	2	8	no	—
283	H(5,𝔽₂)	—	2	8	no	—
284	H(5,𝔽₂)	—	2	8	no	—
285	C₂×#41	—	2	1	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	3	no	—
288	C₂×#41	C₂³×C₇	1	3	yes	—
289	C₂×#41	C₂³×C₇	1	6	yes	—
290	C₂×#41	C₂³×C₇	1	3	yes	—
291	C₂×#41	C₂³×C₇	1	1	yes	characteristic
292	C₂²×Q₈	—	2	1	no	—
293	C₂²×Q₈	C₂³×C₇	1	3	yes	—
294	C₂²×D₄	—	2	6	no	—
295	C₂²×D₄	—	2	3	no	—
296	C₂²×D₄	—	2	6	no	—
297	C₂²×D₄	C₂³×C₇	1	3	yes	—
298	C₂²×D₄	C₂³×C₇	1	6	yes	—
299	#137	—	2	24	no	—
300	AGL(1,ℤ/8)	—	2	24	no	—
301	AGL(1,ℤ/8)	—	2	24	no	—
302	AGL(1,ℤ/8)	—	2	24	no	—
303	#135	—	2	24	no	—
304	#135	—	2	24	no	—
305	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
306	C₂×Q₁₆	C₂³×C₇	1	6	yes	—
307	C₂×SD₁₆	—	2	24	no	—
308	C₂×SD₁₆	C₂³×C₇	1	6	yes	—
309	C₂×SD₁₆	C₂³×C₇	1	12	yes	—
310	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
311	C₂×SD₁₆	C₂³×C₇	1	6	yes	—
312	C₂×SD₁₆	C₂³×C₇	1	6	yes	—
313	C₂×D₈	—	2	24	no	—
314	C₂×D₈	C₂³×C₇	1	6	yes	—
315	C₂×D₈	C₂³×C₇	1	12	yes	—
316	C₂×D₈	C₂³×C₇	1	6	yes	—
317	#131	C₇×D₄	1	16	yes	complemented
318	C₂×M₁₆	C₂³×C₇	1	6	yes	—
319	C₂²×C₈	C₂³×C₇	1	6	yes	—
320	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
321	C₄⋊Q₈	C₂³×C₇	1	3	yes	—
322	#127	—	2	6	no	—
323	#127	C₂³×C₇	1	3	yes	—
324	#127	C₂³×C₇	1	6	yes	—
325	#127	C₂³×C₇	1	3	yes	—
326	#124	—	2	6	no	—
327	#124	C₂³×C₇	1	3	yes	—
328	#124	C₂³×C₇	1	6	yes	—
329	#124	C₂³×C₇	1	1	yes	characteristic
330	#124	C₂³×C₇	1	6	yes	—
331	#123	—	2	6	no	—
332	C₂²⋊Q₈	—	2	6	no	—
333	#121	—	2	6	no	—
334	#121	—	2	6	no	—
335	#121	—	2	12	no	—
336	#121	—	2	6	no	—
337	#120	—	2	12	no	—
338	#120	—	2	6	no	—
339	C₄×Q₈	C₇×D₄	1	2	yes	—
340	C₄×D₄	—	2	6	no	—
341	C₄×D₄	—	2	6	no	—
342	C₄×D₄	C₇×D₄	1	6	yes	—
343	#117	C₂³×C₇	1	3	yes	—
344	C₂×C₂²⋊C₄	—	2	6	no	—
345	C₂×C₄²	C₂³×C₇	1	3	yes	—
346	#97	C₂³×C₇	1	1	yes	characteristic
347	#97	C₂³×C₇	1	3	yes	—
348	#97	C₂³×C₇	1	6	yes	—
349	C₄×C₈	C₂³×C₇	1	6	yes	—
350	C₂²×C₇	—	2	6	no	—
351	C₂²×C₇	—	4	12	no	—
352	C₂²×C₇	—	4	2	no	—
353	C₂²×C₇	—	4	6	no	—
354	C₂²×C₇	—	4	1	no	—
355	C₂²×C₇	—	4	3	no	—
356	C₂²×C₇	—	4	6	no	—
357	C₂²×C₇	—	16	12	no	—
358	C₂²×C₇	—	16	6	no	—
359	C₂²×C₇	C₂×#127	1	6	yes	—
360	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₇	—	2	2	no	—
362	C₄×C₇	—	2	6	no	—
363	C₄×C₇	—	4	2	no	—
364	C₄×C₇	—	4	1	no	—
365	C₄×C₇	—	4	3	no	—
366	C₄×C₇	C₂×#127	1	6	yes	—
367	C₄×C₇	C₂³×D₄	1	2	yes	—
368	C₂⁴	—	2	3	no	—
369	C₂⁴	—	2	6	no	—
370	#41	—	2	12	no	—
371	#41	—	2	12	no	—
372	#41	—	2	12	no	—
373	#41	—	2	12	no	—
374	#41	—	4	4	no	—
375	#41	—	4	8	no	—
376	#41	—	4	12	no	—
377	#41	C₂×C₇×D₄	1	8	yes	—
378	C₂×Q₈	—	2	3	no	—
379	C₂×Q₈	—	2	12	no	—
380	C₂×Q₈	—	4	4	no	—
381	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
382	C₂×Q₈	C₂⁴×C₇	1	3	yes	—
383	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
384	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
385	C₂×D₄	—	2	6	no	—
386	C₂×D₄	—	2	3	no	—
387	C₂×D₄	—	2	3	no	—
388	C₂×D₄	—	2	12	no	—
389	C₂×D₄	—	2	12	no	—
390	C₂×D₄	—	2	12	no	—
391	C₂×D₄	—	2	6	no	—
392	C₂×D₄	—	2	3	no	—
393	C₂×D₄	—	2	6	no	—
394	C₂×D₄	—	2	6	no	—
395	C₂×D₄	—	2	12	no	—
396	C₂×D₄	—	4	24	no	—
397	C₂×D₄	—	4	12	no	—
398	C₂×D₄	—	8	12	no	—
399	C₂×D₄	C₂×C₇×D₄	1	3	yes	—
400	C₂×D₄	C₂⁴×C₇	1	3	yes	—
401	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
402	C₂×D₄	C₂⁴×C₇	1	6	yes	—
403	C₂²×C₄	—	2	3	no	—
404	C₂²×C₄	—	2	6	no	—
405	C₂²×C₄	—	2	3	no	—
406	C₂²×C₄	—	2	3	no	—
407	C₂²×C₄	C₂×C₇×D₄	1	6	yes	—
408	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
409	Q₁₆	—	2	4	no	—
410	Q₁₆	—	2	12	no	—
411	SD₁₆	—	2	12	no	—
412	SD₁₆	—	2	24	no	—
413	SD₁₆	—	2	4	no	—
414	SD₁₆	—	2	12	no	—
415	SD₁₆	—	2	12	no	—
416	D₈	—	2	12	no	—
417	D₈	—	2	24	no	—
418	D₈	—	2	12	no	—
419	M₁₆	C₂×C₇×D₄	1	24	yes	complemented
420	C₂×C₈	C₂×C₇×D₄	1	24	yes	complemented
421	C₂×C₈	C₂⁴×C₇	1	6	yes	—
422	C₂×C₈	C₂⁴×C₇	1	2	yes	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	6	no	—
425	C₄⋊C₄	C₂×C₇×D₄	1	6	yes	—
426	C₂²⋊C₄	—	2	6	no	—
427	C₂²⋊C₄	—	2	12	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	12	no	—
430	C₂²⋊C₄	C₂×C₇×D₄	1	6	yes	—
431	C₄²	C₂×C₇×D₄	1	6	yes	—
432	C₄²	C₂⁴×C₇	1	3	yes	—
433	C₄²	C₂⁴×C₇	1	1	yes	characteristic
434	C₂×C₇	—	2	6	no	—
435	C₂×C₇	—	8	1	no	—
436	C₂×C₇	—	8	6	no	—
437	C₂×C₇	—	8	3	no	—
438	C₂×C₇	C₂²×#127	1	1	yes	characteristic
439	C₂×C₇	#3585	1	2	yes	—
440	C₂³	—	2	3	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	6	no	—
443	C₂³	—	4	6	no	—
444	C₂³	—	4	12	no	—
445	C₂³	—	8	12	no	—
446	C₂³	—	8	6	no	—
447	C₂³	C₂²×C₇×D₄	1	3	yes	—
448	Q₈	—	2	6	no	—
449	Q₈	—	2	2	no	—
450	Q₈	—	2	2	no	—
451	Q₈	—	2	2	no	—
452	Q₈	—	4	6	no	—
453	Q₈	C₇×#127	1	4	yes	—
454	D₄	—	2	6	no	—
455	D₄	—	2	6	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	6	no	—
458	D₄	—	4	12	no	—
459	D₄	—	4	12	no	—
460	D₄	—	4	6	no	—
461	D₄	—	4	6	no	—
462	D₄	—	4	6	no	—
463	D₄	—	4	12	no	—
464	D₄	—	8	6	no	—
465	D₄	—	8	12	no	—
466	D₄	C₇×#127	1	12	yes	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	3	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	4	6	no	—
471	C₂×C₄	—	4	6	no	—
472	C₂×C₄	—	4	12	no	—
473	C₂×C₄	—	4	6	no	—
474	C₂×C₄	—	4	6	no	—
475	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
476	C₂×C₄	C₂²×C₇×D₄	1	6	yes	—
477	C₂×C₄	C₂²×C₇×D₄	1	12	yes	—
478	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
479	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
480	C₈	C₂²×C₇×D₄	1	4	yes	—
481	C₈	C₂²×C₇×D₄	1	12	yes	—
482	C₇	#60650	1	1	yes	characteristic, direct product factor, Sylow
483	C₂²	—	2	6	no	—
484	C₂²	—	4	12	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	6	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	3	no	—
489	C₂²	—	4	6	no	—
490	C₂²	—	16	12	no	—
491	C₂²	—	16	6	no	—
492	C₂²	C₂×C₇×#127	1	6	yes	—
493	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	6	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	3	no	—
499	C₄	C₂×C₇×#127	1	6	yes	—
500	C₄	C₂³×C₇×D₄	1	2	yes	—
501	C₂	—	2	6	no	—
502	C₂	—	8	6	no	—
503	C₂	—	8	3	no	—
504	C₂	—	8	1	no	—
505	C₂	C₂²×C₇×#127	1	1	yes	characteristic
506	C₂	C₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#577	C₂	semidirect
2. C₂×C₇×#576	C₂	semidirect
3. C₇×#3500	C₂	semidirect
4. C₇×#3498	C₂	semidirect
5. C₇×#3155	C₂	semidirect
6. C₇×#3154	C₂	semidirect
7. C₇×#3153	C₂	semidirect
8. C₇×#3151	C₂	semidirect
9. C₇×#3150	C₂	semidirect
10. C₂×C₇×#496	C₂	semidirect
11. C₇×#2875	C₂	semidirect
17. C₂×C₇×#137	C₂²	semidirect
18. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₇×#135	C₂²	semidirect
22. C₂×C₇×#135	C₂²	semidirect
23. C₂²×C₇×SD₁₆	C₂²	semidirect
24. C₂²×C₇×D₈	C₂²	semidirect
30. C₇×#536	C₂²	semidirect
31. C₇×#535	C₂²	semidirect
32. C₇×#535	C₂²	semidirect
33. C₇×#532	C₂²	semidirect
34. C₇×#532	C₂²	semidirect
35. C₂×C₇×#127	C₂²	semidirect
36. C₂×C₇×#124	C₂²	semidirect
38. C₇×#497	C₂²	semidirect
39. C₇×#497	C₂²	semidirect
40. C₇×#497	C₂²	semidirect
41. C₇×#496	C₂²	semidirect
42. C₇×#496	C₂²	semidirect
43. C₇×#496	C₂²	semidirect
44. C₇×#496	C₂²	semidirect
45. C₇×#496	C₂²	semidirect
46. C₇×#495	C₂²	semidirect
47. C₇×#493	C₂²	semidirect
48. C₇×#492	C₂²	semidirect
49. C₇×#405	C₂²	semidirect
50. C₄×C₇×M₁₆	C₂²	semidirect
51. C₂×C₇×#97	C₂²	semidirect
52. #60650	C₇	direct (N × H)
89. C₇×#131	D₄	semidirect
122. C₂×#577	C₂×C₇	semidirect
123. C₂×#576	C₂×C₇	semidirect
124. #3500	C₂×C₇	semidirect
125. #3498	C₂×C₇	semidirect
126. #3155	C₂×C₇	semidirect
127. #3154	C₂×C₇	semidirect
128. #3153	C₂×C₇	semidirect
129. #3151	C₂×C₇	semidirect
130. #3150	C₂×C₇	semidirect
131. C₂×#496	C₂×C₇	semidirect
132. #2875	C₂×C₇	semidirect
184. C₇×M₁₆	C₂×D₄	semidirect
185. C₂×C₇×C₈	C₂×D₄	semidirect
204. C₂×#137	C₂²×C₇	semidirect
205. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
206. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
207. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
208. C₂×#135	C₂²×C₇	semidirect
209. C₂×#135	C₂²×C₇	semidirect
210. C₂²×SD₁₆	C₂²×C₇	semidirect
211. C₂²×D₈	C₂²×C₇	semidirect
217. #536	C₂²×C₇	semidirect
218. #535	C₂²×C₇	semidirect
219. #535	C₂²×C₇	semidirect
220. #532	C₂²×C₇	semidirect
221. #532	C₂²×C₇	semidirect
222. C₂×#127	C₂²×C₇	semidirect
223. C₂×#124	C₂²×C₇	semidirect
225. #497	C₂²×C₇	semidirect
226. #497	C₂²×C₇	semidirect
227. #497	C₂²×C₇	semidirect
228. #496	C₂²×C₇	semidirect
229. #496	C₂²×C₇	semidirect
230. #496	C₂²×C₇	semidirect
231. #496	C₂²×C₇	semidirect
232. #496	C₂²×C₇	semidirect
233. #495	C₂²×C₇	semidirect
234. #493	C₂²×C₇	semidirect
235. #492	C₂²×C₇	semidirect
236. #405	C₂²×C₇	semidirect
237. C₄×M₁₆	C₂²×C₇	semidirect
238. C₂×#97	C₂²×C₇	semidirect
317. #131	C₇×D₄	semidirect
419. M₁₆	C₂×C₇×D₄	semidirect
420. C₂×C₈	C₂×C₇×D₄	semidirect
482. C₇	#60650	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×#577	2
C₂×C₇×#576	2
C₇×#3500	2
C₇×#3498	2
C₇×#3155	2
C₇×#3154	2
C₇×#3153	2
C₇×#3151	2
C₇×#3150	2
C₂×C₇×#496	2
C₇×#2875	2
#60650	7

Subgroups — C7×#60650 #13237866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60650 #13237866