Subgroups — C₇×#60682 #13237898

Order 1792.

1878 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3455	C₂	1	2	yes	maximal, complemented
2	C₇×#3177	C₂	1	2	yes	maximal, complemented
3	C₇×#3176	C₂	1	2	yes	maximal, complemented
4	C₇×#3175	C₂	1	4	yes	maximal, complemented
5	C₇×#3174	C₂	1	4	yes	maximal, complemented
6	C₇×#3173	C₂	1	4	yes	maximal, complemented
7	C₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3135	C₂	1	2	yes	maximal, complemented
10	C₇×#3054	C₂	1	2	yes	maximal, complemented
11	C₇×#3050	C₂	1	2	yes	maximal, complemented
12	C₇×#2943	C₂	1	2	yes	maximal, complemented
13	C₄×C₇×#135	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#135	C₂²	1	2	yes	—
16	C₂×C₇×#135	C₂²	1	2	yes	—
17	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
19	C₇×#542	C₂²	1	8	yes	—
20	C₇×#541	C₂²	1	4	yes	—
21	C₇×#540	C₂²	1	4	yes	—
22	C₇×#539	—	2	4	no	—
23	C₇×#538	—	2	4	no	—
24	C₇×#533	C₂²	1	2	yes	—
25	C₇×#532	C₂²	1	2	yes	—
26	C₇×#529	—	2	8	no	—
27	C₇×#525	C₂²	1	4	yes	—
28	C₄×C₇×#41	C₂²	1	4	yes	—
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₇×#500	C₂²	1	2	yes	complemented
31	C₇×#499	C₂²	1	2	yes	complemented
32	C₇×#499	C₂²	1	2	yes	complemented
33	C₇×#498	C₂²	1	2	yes	complemented
34	C₇×#495	C₂²	1	2	yes	complemented
35	C₇×#495	C₂²	1	2	yes	complemented
36	C₇×#494	C₂²	1	1	yes	characteristic, complemented
37	C₇×#493	C₂²	1	1	yes	characteristic, complemented
38	C₇×#492	C₂²	1	2	yes	complemented
39	C₇×#491	C₂²	1	4	yes	complemented
40	C₇×#490	C₂²	1	4	yes	complemented
41	C₇×#489	C₂²	1	8	yes	complemented
42	C₇×#470	C₂²	1	4	yes	—
43	C₇×#469	C₂²	1	4	yes	—
44	C₇×#468	C₂²	1	8	yes	—
45	C₇×#467	C₂²	1	4	yes	—
46	C₇×#466	C₂²	1	4	yes	—
47	C₇×#465	C₂²	1	8	yes	—
48	C₇×#442	C₂²	1	4	yes	complemented
49	C₇×#441	C₂²	1	4	yes	complemented
50	C₇×#440	C₂²	1	8	yes	complemented
51	C₄×C₇×Q₁₆	C₂²	1	4	yes	complemented
52	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
53	C₄×C₇×D₈	C₂²	1	4	yes	complemented
54	C₇×#427	C₂²	1	2	yes	—
55	C₇×#427	C₂²	1	2	yes	—
56	C₇×#416	C₂²	1	4	yes	—
57	C₇×#416	C₂²	1	4	yes	—
58	C₇×#405	C₂²	1	2	yes	—
59	C₇×#405	C₂²	1	2	yes	—
60	C₇×#405	C₂²	1	2	yes	—
61	C₇×#405	C₂²	1	2	yes	—
62	C₂×C₇×#97	C₂²	1	1	yes	characteristic
63	C₂×C₇×#97	C₂²	1	1	yes	characteristic
64	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
65	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
66	#60682	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂×C₇×#41	C₂³	1	4	yes	—
68	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
69	C₇×#135	—	2	8	no	—
70	C₇×#135	—	2	8	no	—
71	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
72	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
73	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
74	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
75	C₂×C₇×D₈	C₂³	1	2	yes	—
76	C₂×C₇×D₈	C₂³	1	2	yes	—
77	C₂×C₇×M₁₆	—	2	4	no	—
78	C₂×C₇×M₁₆	C₂³	1	2	yes	—
79	C₂×C₇×M₁₆	C₂³	1	2	yes	—
80	C₂²×C₇×C₈	—	2	4	no	—
81	C₂²×C₇×C₈	C₂³	1	2	yes	—
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₇×C₈	C₂³	1	2	yes	—
85	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
88	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
89	C₇×#127	C₂³	1	2	yes	—
90	C₇×#126	—	2	8	no	—
91	C₇×#126	—	2	8	no	—
92	C₇×#125	—	2	8	no	—
93	C₇×#125	C₂³	1	4	yes	—
94	C₇×#124	—	2	8	no	—
95	C₇×#124	C₂³	1	4	yes	—
96	C₇×#123	—	2	4	no	—
97	C₇×#123	—	2	8	no	—
98	C₇×#123	—	2	8	no	—
99	C₇×C₂²⋊Q₈	—	2	4	no	—
100	C₇×C₂²⋊Q₈	—	2	8	no	—
101	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
102	C₇×#121	—	2	4	no	—
103	C₇×#121	—	2	8	no	—
104	C₇×#121	C₂³	1	8	yes	—
105	C₇×#120	—	2	4	no	—
106	C₄×C₇×Q₈	—	2	4	no	—
107	C₄×C₇×Q₈	C₂³	1	8	yes	—
108	C₄×C₇×D₄	—	2	8	no	—
109	C₄×C₇×D₄	—	2	8	no	—
110	C₄×C₇×D₄	—	2	4	no	—
111	C₄×C₇×D₄	C₂³	1	8	yes	—
112	C₇×#117	—	2	4	no	—
113	C₇×#117	D₄	1	4	yes	—
114	C₇×#117	C₂³	1	4	yes	—
115	C₇×#117	C₂³	1	2	yes	—
116	C₇×#117	C₂³	1	2	yes	—
117	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
118	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
119	C₂×C₄²×C₇	—	2	4	no	—
120	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
122	C₇×#107	C₂³	1	4	yes	—
123	C₇×#107	C₂³	1	4	yes	—
124	C₇×#106	C₂³	1	4	yes	—
125	C₇×#106	C₂³	1	4	yes	—
126	C₇×#103	C₂³	1	8	yes	—
127	C₇×#103	C₂³	1	8	yes	—
128	C₇×#102	C₂³	1	8	yes	—
129	C₇×#102	C₂³	1	8	yes	—
130	C₇×#97	C₂³	1	2	yes	—
131	C₇×#97	C₂³	1	2	yes	—
132	C₇×#97	C₂³	1	2	yes	—
133	C₇×#97	C₂³	1	2	yes	—
134	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
135	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
136	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
137	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
138	C₄×C₇×C₈	C₂³	1	2	yes	—
139	C₄×C₇×C₈	C₂³	1	2	yes	—
140	#3455	C₂×C₇	1	2	yes	complemented
141	#3177	C₂×C₇	1	2	yes	complemented
142	#3176	C₂×C₇	1	2	yes	complemented
143	#3175	C₂×C₇	1	4	yes	complemented
144	#3174	C₂×C₇	1	4	yes	complemented
145	#3173	C₂×C₇	1	4	yes	complemented
146	#3160	C₂×C₇	1	1	yes	characteristic, complemented
147	#3147	C₂×C₇	1	1	yes	characteristic, complemented
148	#3135	C₂×C₇	1	2	yes	complemented
149	#3054	C₂×C₇	1	2	yes	complemented
150	#3050	C₂×C₇	1	2	yes	complemented
151	#2943	C₂×C₇	1	2	yes	complemented
152	C₄×#135	C₂×C₇	1	2	yes	complemented
153	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
154	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
155	C₇×#41	—	2	8	no	—
156	C₇×#41	—	2	8	no	—
157	C₂×C₇×Q₈	—	2	4	no	—
158	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
159	C₂×C₇×D₄	—	2	4	no	—
160	C₂×C₇×D₄	—	2	8	no	—
161	C₂×C₇×D₄	—	2	4	no	—
162	C₂×C₇×D₄	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₇	—	2	2	no	—
164	C₂²×C₄×C₇	—	2	2	no	—
165	C₂²×C₄×C₇	—	2	4	no	—
166	C₂²×C₄×C₇	—	2	8	no	—
167	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
173	C₇×Q₁₆	—	2	4	no	—
174	C₇×Q₁₆	—	2	4	no	—
175	C₇×SD₁₆	—	2	8	no	—
176	C₇×SD₁₆	—	2	8	no	—
177	C₇×D₈	—	2	4	no	—
178	C₇×D₈	—	2	4	no	—
179	C₇×M₁₆	—	2	4	no	—
180	C₇×M₁₆	—	2	4	no	—
181	C₂×C₇×C₈	—	2	2	no	—
182	C₂×C₇×C₈	—	2	2	no	—
183	C₂×C₇×C₈	—	2	4	no	—
184	C₂×C₇×C₈	—	2	4	no	—
185	C₂×C₇×C₈	#41	1	4	yes	—
186	C₂×C₇×C₈	#41	1	4	yes	—
187	C₂×C₇×C₈	C₂⁴	1	2	yes	—
188	C₂×C₇×C₈	C₂⁴	1	2	yes	—
189	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
190	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
191	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
192	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
193	C₇×C₄⋊C₄	—	2	8	no	—
194	C₇×C₄⋊C₄	—	2	4	no	—
195	C₇×C₄⋊C₄	—	2	8	no	—
196	C₇×C₄⋊C₄	—	2	8	no	—
197	C₇×C₄⋊C₄	—	2	4	no	—
198	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
199	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
200	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
201	C₇×C₂²⋊C₄	—	2	4	no	—
202	C₇×C₂²⋊C₄	—	2	8	no	—
203	C₇×C₂²⋊C₄	—	2	8	no	—
204	C₇×C₂²⋊C₄	—	2	8	no	—
205	C₇×C₂²⋊C₄	—	2	8	no	—
206	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
207	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
208	C₄²×C₇	—	2	8	no	—
209	C₄²×C₇	—	2	4	no	—
210	C₄²×C₇	C₂×D₄	1	2	yes	—
211	C₄²×C₇	C₂×D₄	1	2	yes	—
212	C₄²×C₇	C₂⁴	1	2	yes	—
213	C₄²×C₇	C₂⁴	1	1	yes	characteristic
214	C₄²×C₇	C₂⁴	1	1	yes	characteristic
215	C₂×#135	C₂²×C₇	1	2	yes	—
216	C₂×#135	C₂²×C₇	1	2	yes	—
217	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
218	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
219	#542	C₂²×C₇	1	8	yes	—
220	#541	C₂²×C₇	1	4	yes	—
221	#540	C₂²×C₇	1	4	yes	—
222	#539	—	2	4	no	—
223	#538	—	2	4	no	—
224	#533	C₂²×C₇	1	2	yes	—
225	#532	C₂²×C₇	1	2	yes	—
226	#529	—	2	8	no	—
227	#525	C₂²×C₇	1	4	yes	—
228	C₄×#41	C₂²×C₇	1	4	yes	—
229	C₂×#117	C₂²×C₇	1	1	yes	characteristic
230	#500	C₂²×C₇	1	2	yes	complemented
231	#499	C₂²×C₇	1	2	yes	complemented
232	#499	C₂²×C₇	1	2	yes	complemented
233	#498	C₂²×C₇	1	2	yes	complemented
234	#495	C₂²×C₇	1	2	yes	complemented
235	#495	C₂²×C₇	1	2	yes	complemented
236	#494	C₂²×C₇	1	1	yes	characteristic, complemented
237	#493	C₂²×C₇	1	1	yes	characteristic, complemented
238	#492	C₂²×C₇	1	2	yes	complemented
239	#491	C₂²×C₇	1	4	yes	complemented
240	#490	C₂²×C₇	1	4	yes	complemented
241	#489	C₂²×C₇	1	8	yes	complemented
242	#470	C₂²×C₇	1	4	yes	—
243	#469	C₂²×C₇	1	4	yes	—
244	#468	C₂²×C₇	1	8	yes	—
245	#467	C₂²×C₇	1	4	yes	—
246	#466	C₂²×C₇	1	4	yes	—
247	#465	C₂²×C₇	1	8	yes	—
248	#442	C₂²×C₇	1	4	yes	complemented
249	#441	C₂²×C₇	1	4	yes	complemented
250	#440	C₂²×C₇	1	8	yes	complemented
251	C₄×Q₁₆	C₂²×C₇	1	4	yes	complemented
252	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
253	C₄×D₈	C₂²×C₇	1	4	yes	complemented
254	#427	C₂²×C₇	1	2	yes	—
255	#427	C₂²×C₇	1	2	yes	—
256	#416	C₂²×C₇	1	4	yes	—
257	#416	C₂²×C₇	1	4	yes	—
258	#405	C₂²×C₇	1	2	yes	—
259	#405	C₂²×C₇	1	2	yes	—
260	#405	C₂²×C₇	1	2	yes	—
261	#405	C₂²×C₇	1	2	yes	—
262	C₂×#97	C₂²×C₇	1	1	yes	characteristic
263	C₂×#97	C₂²×C₇	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
266	C₂³×C₇	—	2	2	no	—
267	C₂³×C₇	—	2	4	no	—
268	C₂³×C₇	—	4	2	no	—
269	C₂³×C₇	C₂²×D₄	1	2	yes	—
270	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
271	C₇×Q₈	—	2	4	no	—
272	C₇×Q₈	—	2	4	no	—
273	C₇×Q₈	—	8	4	no	—
274	C₇×D₄	—	2	4	no	—
275	C₇×D₄	—	2	4	no	—
276	C₇×D₄	—	4	8	no	—
277	C₇×D₄	—	8	4	no	—
278	C₇×D₄	—	8	8	no	—
279	C₂×C₄×C₇	—	2	2	no	—
280	C₂×C₄×C₇	—	2	4	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	2	no	—
283	C₂×C₄×C₇	—	2	4	no	—
284	C₂×C₄×C₇	—	2	8	no	—
285	C₂×C₄×C₇	—	4	2	no	—
286	C₂×C₄×C₇	—	4	2	no	—
287	C₂×C₄×C₇	—	4	8	no	—
288	C₂×C₄×C₇	—	8	8	no	—
289	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
290	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₇	C₂×#41	1	2	yes	—
295	C₂×C₄×C₇	C₂×#41	1	2	yes	—
296	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
297	C₇×C₈	—	2	2	no	—
298	C₇×C₈	—	2	2	no	—
299	C₇×C₈	C₂×#41	1	2	yes	—
300	C₇×C₈	C₂×#41	1	2	yes	—
301	C₇×C₈	C₂×#41	1	2	yes	—
302	C₇×C₈	C₂×#41	1	2	yes	—
303	C₂×#41	C₂³×C₇	1	4	yes	—
304	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
305	#135	—	2	8	no	—
306	#135	—	2	8	no	—
307	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
308	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
309	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
310	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
311	C₂×D₈	C₂³×C₇	1	2	yes	—
312	C₂×D₈	C₂³×C₇	1	2	yes	—
313	C₂×M₁₆	—	2	4	no	—
314	C₂×M₁₆	C₂³×C₇	1	2	yes	—
315	C₂×M₁₆	C₂³×C₇	1	2	yes	—
316	C₂²×C₈	—	2	4	no	—
317	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₇	1	2	yes	—
319	C₂²×C₈	C₂³×C₇	1	2	yes	—
320	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
324	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
325	#127	C₂³×C₇	1	2	yes	—
326	#126	—	2	8	no	—
327	#126	—	2	8	no	—
328	#125	—	2	8	no	—
329	#125	C₂³×C₇	1	4	yes	—
330	#124	—	2	8	no	—
331	#124	C₂³×C₇	1	4	yes	—
332	#123	—	2	4	no	—
333	#123	—	2	8	no	—
334	#123	—	2	8	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	—	2	8	no	—
337	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
338	#121	—	2	4	no	—
339	#121	—	2	8	no	—
340	#121	C₂³×C₇	1	8	yes	—
341	#120	—	2	4	no	—
342	C₄×Q₈	—	2	4	no	—
343	C₄×Q₈	C₂³×C₇	1	8	yes	—
344	C₄×D₄	—	2	8	no	—
345	C₄×D₄	—	2	8	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	C₂³×C₇	1	8	yes	—
348	#117	—	2	4	no	—
349	#117	C₇×D₄	1	4	yes	—
350	#117	C₂³×C₇	1	4	yes	—
351	#117	C₂³×C₇	1	2	yes	—
352	#117	C₂³×C₇	1	2	yes	—
353	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
354	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
355	C₂×C₄²	—	2	4	no	—
356	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
358	#107	C₂³×C₇	1	4	yes	—
359	#107	C₂³×C₇	1	4	yes	—
360	#106	C₂³×C₇	1	4	yes	—
361	#106	C₂³×C₇	1	4	yes	—
362	#103	C₂³×C₇	1	8	yes	—
363	#103	C₂³×C₇	1	8	yes	—
364	#102	C₂³×C₇	1	8	yes	—
365	#102	C₂³×C₇	1	8	yes	—
366	#97	C₂³×C₇	1	2	yes	—
367	#97	C₂³×C₇	1	2	yes	—
368	#97	C₂³×C₇	1	2	yes	—
369	#97	C₂³×C₇	1	2	yes	—
370	C₄×C₈	C₂³×C₇	1	2	yes	—
371	C₄×C₈	C₂³×C₇	1	2	yes	—
372	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
373	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
374	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
375	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
376	C₂²×C₇	—	2	2	no	—
377	C₂²×C₇	—	2	4	no	—
378	C₂²×C₇	—	2	2	no	—
379	C₂²×C₇	—	4	4	no	—
380	C₂²×C₇	—	4	8	no	—
381	C₂²×C₇	—	4	4	no	—
382	C₂²×C₇	#532	1	2	yes	—
383	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
384	C₄×C₇	—	2	4	no	—
385	C₄×C₇	—	2	2	no	—
386	C₄×C₇	—	2	2	no	—
387	C₄×C₇	—	2	2	no	—
388	C₄×C₇	—	4	8	no	—
389	C₄×C₇	—	4	4	no	—
390	C₄×C₇	#532	1	2	yes	—
391	C₄×C₇	C₂²×#41	1	1	yes	characteristic
392	C₄×C₇	C₂²×#41	1	1	yes	characteristic
393	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
394	#41	—	2	8	no	—
395	#41	—	2	8	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	8	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	C₂⁴×C₇	1	4	yes	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	8	no	—
406	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
407	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
408	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
409	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
412	Q₁₆	—	2	4	no	—
413	Q₁₆	—	2	4	no	—
414	SD₁₆	—	2	8	no	—
415	SD₁₆	—	2	8	no	—
416	D₈	—	2	4	no	—
417	D₈	—	2	4	no	—
418	M₁₆	—	2	4	no	—
419	M₁₆	—	2	4	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	4	no	—
423	C₂×C₈	—	2	4	no	—
424	C₂×C₈	C₇×#41	1	4	yes	—
425	C₂×C₈	C₇×#41	1	4	yes	—
426	C₂×C₈	C₂⁴×C₇	1	2	yes	—
427	C₂×C₈	C₂⁴×C₇	1	2	yes	—
428	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
429	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
430	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
431	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
438	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
439	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
446	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
447	C₄²	—	2	4	no	—
448	C₄²	—	2	8	no	—
449	C₄²	C₂×C₇×D₄	1	2	yes	—
450	C₄²	C₂×C₇×D₄	1	2	yes	—
451	C₄²	C₂⁴×C₇	1	2	yes	—
452	C₄²	C₂⁴×C₇	1	1	yes	characteristic
453	C₄²	C₂⁴×C₇	1	1	yes	characteristic
454	C₂×C₇	—	2	2	no	—
455	C₂×C₇	—	4	2	no	—
456	C₂×C₇	—	8	4	no	—
457	C₂×C₇	C₂×#532	1	1	yes	characteristic
458	C₂×C₇	#3584	1	2	yes	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	4	2	no	—
462	C₂³	C₂²×C₇×D₄	1	2	yes	—
463	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
464	Q₈	—	2	4	no	—
465	Q₈	—	2	4	no	—
466	Q₈	—	8	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	2	4	no	—
469	D₄	—	4	8	no	—
470	D₄	—	8	4	no	—
471	D₄	—	8	8	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	8	no	—
481	C₂×C₄	—	8	8	no	—
482	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
483	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
484	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
485	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
486	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
487	C₂×C₄	C₂×C₇×#41	1	2	yes	—
488	C₂×C₄	C₂×C₇×#41	1	2	yes	—
489	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	C₂×C₇×#41	1	2	yes	—
493	C₈	C₂×C₇×#41	1	2	yes	—
494	C₈	C₂×C₇×#41	1	2	yes	—
495	C₈	C₂×C₇×#41	1	2	yes	—
496	C₇	#60682	1	1	yes	characteristic, direct product factor, Sylow
497	C₂²	—	2	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	8	no	—
502	C₂²	—	4	4	no	—
503	C₂²	C₇×#532	1	2	yes	—
504	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
505	C₄	—	2	4	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	8	no	—
510	C₄	—	4	4	no	—
511	C₄	C₇×#532	1	2	yes	—
512	C₄	C₂²×C₇×#41	1	1	yes	characteristic
513	C₄	C₂²×C₇×#41	1	1	yes	characteristic
514	C₂	—	2	2	no	—
515	C₂	—	4	2	no	—
516	C₂	—	8	4	no	—
517	C₂	C₂×C₇×#532	1	1	yes	characteristic
518	C₂	C₇×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3455	C₂	semidirect
2. C₇×#3177	C₂	semidirect
3. C₇×#3176	C₂	semidirect
4. C₇×#3175	C₂	semidirect
5. C₇×#3174	C₂	semidirect
6. C₇×#3173	C₂	semidirect
7. C₇×#3160	C₂	semidirect
8. C₇×#3147	C₂	semidirect
9. C₇×#3135	C₂	semidirect
10. C₇×#3054	C₂	semidirect
11. C₇×#3050	C₂	semidirect
12. C₇×#2943	C₂	semidirect
13. C₄×C₇×#135	C₂	semidirect
14. C₂×C₇×#405	C₂	semidirect
30. C₇×#500	C₂²	semidirect
31. C₇×#499	C₂²	semidirect
32. C₇×#499	C₂²	semidirect
33. C₇×#498	C₂²	semidirect
34. C₇×#495	C₂²	semidirect
35. C₇×#495	C₂²	semidirect
36. C₇×#494	C₂²	semidirect
37. C₇×#493	C₂²	semidirect
38. C₇×#492	C₂²	semidirect
39. C₇×#491	C₂²	semidirect
40. C₇×#490	C₂²	semidirect
41. C₇×#489	C₂²	semidirect
48. C₇×#442	C₂²	semidirect
49. C₇×#441	C₂²	semidirect
50. C₇×#440	C₂²	semidirect
51. C₄×C₇×Q₁₆	C₂²	semidirect
52. C₄×C₇×SD₁₆	C₂²	semidirect
53. C₄×C₇×D₈	C₂²	semidirect
66. #60682	C₇	direct (N × H)
140. #3455	C₂×C₇	semidirect
141. #3177	C₂×C₇	semidirect
142. #3176	C₂×C₇	semidirect
143. #3175	C₂×C₇	semidirect
144. #3174	C₂×C₇	semidirect
145. #3173	C₂×C₇	semidirect
146. #3160	C₂×C₇	semidirect
147. #3147	C₂×C₇	semidirect
148. #3135	C₂×C₇	semidirect
149. #3054	C₂×C₇	semidirect
150. #3050	C₂×C₇	semidirect
151. #2943	C₂×C₇	semidirect
152. C₄×#135	C₂×C₇	semidirect
153. C₂×#405	C₂×C₇	semidirect
230. #500	C₂²×C₇	semidirect
231. #499	C₂²×C₇	semidirect
232. #499	C₂²×C₇	semidirect
233. #498	C₂²×C₇	semidirect
234. #495	C₂²×C₇	semidirect
235. #495	C₂²×C₇	semidirect
236. #494	C₂²×C₇	semidirect
237. #493	C₂²×C₇	semidirect
238. #492	C₂²×C₇	semidirect
239. #491	C₂²×C₇	semidirect
240. #490	C₂²×C₇	semidirect
241. #489	C₂²×C₇	semidirect
248. #442	C₂²×C₇	semidirect
249. #441	C₂²×C₇	semidirect
250. #440	C₂²×C₇	semidirect
251. C₄×Q₁₆	C₂²×C₇	semidirect
252. C₄×SD₁₆	C₂²×C₇	semidirect
253. C₄×D₈	C₂²×C₇	semidirect
496. C₇	#60682	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3455	2
C₇×#3177	2
C₇×#3176	2
C₇×#3175	2
C₇×#3174	2
C₇×#3173	2
C₇×#3160	2
C₇×#3147	2
C₇×#3135	2
C₇×#3054	2
C₇×#3050	2
C₇×#2943	2
C₄×C₇×#135	2
C₂×C₇×#405	2
#60682	7

Subgroups — C7×#60682 #13237898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60682 #13237898