Subgroups — C₇×#60699 #13237915

Order 1792.

1842 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3461	C₂	1	2	yes	maximal, complemented
2	C₇×#3185	C₂	1	2	yes	maximal, complemented
3	C₇×#3183	C₂	1	2	yes	maximal, complemented
4	C₇×#3181	C₂	1	4	yes	maximal, complemented
5	C₇×#3178	C₂	1	4	yes	maximal, complemented
6	C₇×#3177	C₂	1	2	yes	maximal, complemented
7	C₇×#3173	C₂	1	2	yes	maximal, complemented
8	C₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3137	C₂	1	2	yes	maximal, complemented
11	C₇×#3063	C₂	1	2	yes	maximal, complemented
12	C₇×#3060	C₂	1	1	yes	maximal, characteristic
13	C₇×#3059	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#137	C₂	1	2	yes	maximal, complemented
15	C₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#137	C₂²	1	2	yes	—
19	C₂×C₇×#135	C₂²	1	1	yes	characteristic
20	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₇×#131	C₂²	1	1	yes	characteristic
22	C₂×C₇×#131	C₂²	1	1	yes	characteristic
23	C₇×#544	C₂²	1	2	yes	—
24	C₇×#542	—	2	2	no	—
25	C₇×#542	C₂²	1	4	yes	—
26	C₇×#541	—	2	2	no	—
27	C₇×#541	C₂²	1	4	yes	—
28	C₇×#539	—	2	4	no	—
29	C₇×#537	C₂²	1	2	yes	—
30	C₇×#536	C₂²	1	2	yes	—
31	C₇×#536	C₂²	1	2	yes	—
32	C₇×#533	—	2	2	no	—
33	C₇×#533	C₂²	1	4	yes	—
34	C₇×#529	—	2	4	no	—
35	C₇×#529	—	2	2	no	—
36	C₇×#529	C₂²	1	4	yes	—
37	C₄×C₇×#41	C₂²	1	2	yes	—
38	C₄×C₇×#41	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
40	C₇×#501	C₂²	1	4	yes	—
41	C₇×#499	C₂²	1	2	yes	—
42	C₇×#498	C₂²	1	2	yes	—
43	C₇×#497	C₂²	1	4	yes	—
44	C₇×#495	C₂²	1	2	yes	—
45	C₇×#494	C₂²	1	2	yes	—
46	C₇×#491	C₂²	1	4	yes	—
47	C₇×#489	C₂²	1	4	yes	—
48	C₇×#488	C₂²	1	4	yes	—
49	C₇×#487	C₂²	1	4	yes	—
50	C₇×#470	C₂²	1	2	yes	—
51	C₇×#470	C₂²	1	2	yes	—
52	C₇×#470	C₂²	1	2	yes	—
53	C₇×#470	C₂²	1	4	yes	—
54	C₇×#469	C₂²	1	2	yes	—
55	C₇×#468	C₂²	1	4	yes	—
56	C₇×#467	C₂²	1	4	yes	—
57	C₇×#467	C₂²	1	4	yes	—
58	C₇×#465	C₂²	1	4	yes	—
59	C₇×#465	C₂²	1	4	yes	—
60	C₇×#442	C₂²	1	1	yes	characteristic
61	C₇×#442	C₂²	1	1	yes	characteristic
62	C₇×#441	C₂²	1	2	yes	—
63	C₇×#441	C₂²	1	1	yes	characteristic
64	C₇×#441	C₂²	1	2	yes	—
65	C₇×#441	C₂²	1	2	yes	—
66	C₇×#441	C₂²	1	4	yes	—
67	C₇×#441	C₂²	1	2	yes	—
68	C₇×#441	C₂²	1	1	yes	characteristic
69	C₇×#440	C₂²	1	2	yes	—
70	C₇×#440	C₂²	1	2	yes	—
71	C₇×#440	C₂²	1	4	yes	—
72	C₄×C₇×Q₁₆	C₂²	1	4	yes	—
73	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
74	C₇×#428	C₂²	1	2	yes	—
75	C₇×#427	C₂²	1	1	yes	characteristic
76	C₂×C₇×#106	C₂²	1	1	yes	characteristic
77	C₇×#419	C₂²	1	2	yes	—
78	C₇×#417	C₂²	1	2	yes	—
79	C₇×#416	C₂²	1	2	yes	—
80	C₂×C₇×#103	C₂²	1	2	yes	—
81	C₇×#405	C₂²	1	1	yes	characteristic
82	C₇×#405	C₂²	1	2	yes	—
83	C₇×#405	C₂²	1	2	yes	—
84	C₇×#405	C₂²	1	1	yes	characteristic
85	C₄×C₇×M₁₆	C₂²	1	2	yes	—
86	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
87	C₂×C₇×#97	C₂²	1	2	yes	—
88	C₂×C₇×#97	C₂²	1	1	yes	characteristic
89	#60699	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	C₂³	1	2	yes	—
91	C₂×C₇×#41	C₂³	1	1	yes	characteristic
92	C₂²×C₇×Q₈	C₂³	1	2	yes	—
93	C₇×#137	—	2	8	no	—
94	C₇×#135	—	2	4	no	—
95	C₂×C₇×Q₁₆	—	2	4	no	—
96	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
97	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
98	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
100	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
103	C₇×#131	—	2	4	no	—
104	C₇×#131	—	2	4	no	—
105	C₂×C₇×M₁₆	C₂³	1	2	yes	—
106	C₂×C₇×M₁₆	C₂³	1	2	yes	—
107	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	C₂³	1	2	yes	—
110	C₂²×C₇×C₈	C₂³	1	2	yes	—
111	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₇×C₄⋊Q₈	—	2	2	no	—
114	C₇×C₄⋊Q₈	—	2	2	no	—
115	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₇×#126	—	2	4	no	—
118	C₇×#126	—	2	4	no	—
119	C₇×#126	—	2	4	no	—
120	C₇×#126	—	2	4	no	—
121	C₇×#125	—	2	4	no	—
122	C₇×#125	—	2	2	no	—
123	C₇×#125	—	2	4	no	—
124	C₇×#125	—	2	4	no	—
125	C₇×#125	C₂³	1	4	yes	—
126	C₇×#124	—	2	2	no	—
127	C₇×#124	—	2	4	no	—
128	C₇×#124	C₂³	1	4	yes	—
129	C₇×#123	—	2	4	no	—
130	C₇×#123	—	2	4	no	—
131	C₇×#123	—	2	4	no	—
132	C₇×#123	—	2	4	no	—
133	C₇×C₂²⋊Q₈	—	2	2	no	—
134	C₇×C₂²⋊Q₈	—	2	4	no	—
135	C₇×C₂²⋊Q₈	—	2	2	no	—
136	C₇×C₂²⋊Q₈	—	2	2	no	—
137	C₇×C₂²⋊Q₈	—	2	4	no	—
138	C₇×C₂²⋊Q₈	—	2	4	no	—
139	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
142	C₇×#121	—	2	4	no	—
143	C₇×#121	—	2	2	no	—
144	C₇×#121	C₂³	1	4	yes	—
145	C₄×C₇×Q₈	—	2	2	no	—
146	C₄×C₇×Q₈	—	2	2	no	—
147	C₄×C₇×Q₈	—	2	4	no	—
148	C₄×C₇×Q₈	D₄	1	2	yes	—
149	C₄×C₇×Q₈	C₂³	1	4	yes	—
150	C₄×C₇×Q₈	C₂³	1	4	yes	—
151	C₄×C₇×Q₈	C₂³	1	2	yes	—
152	C₄×C₇×Q₈	C₂³	1	2	yes	—
153	C₄×C₇×D₄	—	2	2	no	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	—	2	4	no	—
156	C₄×C₇×D₄	D₄	1	4	yes	—
157	C₄×C₇×D₄	D₄	1	2	yes	—
158	C₄×C₇×D₄	C₂³	1	2	yes	—
159	C₄×C₇×D₄	C₂³	1	2	yes	—
160	C₇×#117	—	2	4	no	—
161	C₇×#117	—	2	2	no	—
162	C₇×#117	—	2	4	no	—
163	C₇×#117	C₂³	1	2	yes	—
164	C₇×#117	C₂³	1	1	yes	characteristic
165	C₇×#117	C₂³	1	2	yes	—
166	C₂×C₇×C₄⋊C₄	—	2	2	no	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₄²×C₇	—	2	2	no	—
169	C₂×C₄²×C₇	—	2	2	no	—
170	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₇	C₂³	1	2	yes	—
172	C₇×#107	C₂³	1	2	yes	—
173	C₇×#107	C₂³	1	4	yes	—
174	C₇×#106	C₂³	1	2	yes	—
175	C₇×#106	C₂³	1	1	yes	characteristic
176	C₇×#106	C₂³	1	1	yes	characteristic
177	C₇×#106	C₂³	1	4	yes	—
178	C₇×#106	C₂³	1	2	yes	—
179	C₇×#103	C₂³	1	2	yes	—
180	C₇×#103	C₂³	1	4	yes	—
181	C₇×#103	C₂³	1	4	yes	—
182	C₇×#103	C₂³	1	4	yes	—
183	C₇×#103	C₂³	1	4	yes	—
184	C₇×#103	C₂³	1	2	yes	—
185	C₇×#103	C₂³	1	4	yes	—
186	C₇×#102	C₂³	1	2	yes	—
187	C₇×#102	C₂³	1	4	yes	—
188	C₇×#102	C₂³	1	2	yes	—
189	C₇×#97	C₂³	1	2	yes	—
190	C₇×#97	C₂³	1	2	yes	—
191	C₇×#97	C₂³	1	1	yes	characteristic
192	C₇×#97	C₂³	1	2	yes	—
193	C₇×#97	C₂³	1	1	yes	characteristic
194	C₇×#97	C₂³	1	1	yes	characteristic
195	C₇×#97	C₂³	1	1	yes	characteristic
196	C₄×C₇×C₈	C₂³	1	2	yes	—
197	C₄×C₇×C₈	C₂³	1	2	yes	—
198	C₄×C₇×C₈	C₂³	1	2	yes	—
199	#3461	C₂×C₇	1	2	yes	complemented
200	#3185	C₂×C₇	1	2	yes	complemented
201	#3183	C₂×C₇	1	2	yes	complemented
202	#3181	C₂×C₇	1	4	yes	complemented
203	#3178	C₂×C₇	1	4	yes	complemented
204	#3177	C₂×C₇	1	2	yes	complemented
205	#3173	C₂×C₇	1	2	yes	complemented
206	#3163	C₂×C₇	1	1	yes	characteristic, complemented
207	#3156	C₂×C₇	1	1	yes	characteristic, complemented
208	#3137	C₂×C₇	1	2	yes	complemented
209	#3063	C₂×C₇	1	2	yes	complemented
210	#3060	C₂×C₇	1	1	yes	characteristic
211	#3059	C₂×C₇	1	1	yes	characteristic, complemented
212	C₄×#137	C₂×C₇	1	2	yes	complemented
213	#2943	C₂×C₇	1	1	yes	characteristic, complemented
214	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
215	#2875	C₂×C₇	1	1	yes	characteristic, complemented
216	C₇×#41	—	2	2	no	—
217	C₇×#41	—	2	2	no	—
218	C₇×#41	—	2	4	no	—
219	C₇×#41	—	2	4	no	—
220	C₂×C₇×Q₈	—	2	2	no	—
221	C₂×C₇×Q₈	—	2	4	no	—
222	C₂×C₇×Q₈	—	2	4	no	—
223	C₂×C₇×Q₈	—	2	4	no	—
224	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
225	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
226	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
227	C₂×C₇×D₄	—	2	2	no	—
228	C₂×C₇×D₄	—	2	4	no	—
229	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
230	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
231	C₂×C₇×D₄	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₇	—	2	2	no	—
233	C₂²×C₄×C₇	—	2	2	no	—
234	C₂²×C₄×C₇	—	2	2	no	—
235	C₂²×C₄×C₇	—	2	2	no	—
236	C₂²×C₄×C₇	—	2	2	no	—
237	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
241	C₇×Q₁₆	—	2	4	no	—
242	C₇×Q₁₆	—	2	4	no	—
243	C₇×Q₁₆	—	2	2	no	—
244	C₇×Q₁₆	—	2	8	no	—
245	C₇×SD₁₆	—	2	4	no	—
246	C₇×SD₁₆	—	2	8	no	—
247	C₇×D₈	—	2	2	no	—
248	C₇×M₁₆	—	2	2	no	—
249	C₇×M₁₆	—	2	4	no	—
250	C₇×M₁₆	—	2	4	no	—
251	C₇×M₁₆	#41	1	4	yes	—
252	C₂×C₇×C₈	—	2	2	no	—
253	C₂×C₇×C₈	—	2	4	no	—
254	C₂×C₇×C₈	—	2	4	no	—
255	C₂×C₇×C₈	#41	1	4	yes	—
256	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
257	C₂×C₇×C₈	C₂⁴	1	2	yes	—
258	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
259	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
260	C₂×C₇×C₈	C₂⁴	1	2	yes	—
261	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
262	C₇×C₄⋊C₄	—	2	4	no	—
263	C₇×C₄⋊C₄	—	2	4	no	—
264	C₇×C₄⋊C₄	—	2	2	no	—
265	C₇×C₄⋊C₄	—	2	2	no	—
266	C₇×C₄⋊C₄	—	2	2	no	—
267	C₇×C₄⋊C₄	—	2	4	no	—
268	C₇×C₄⋊C₄	—	2	4	no	—
269	C₇×C₄⋊C₄	—	2	4	no	—
270	C₇×C₄⋊C₄	—	2	4	no	—
271	C₇×C₄⋊C₄	—	2	4	no	—
272	C₇×C₄⋊C₄	—	2	4	no	—
273	C₇×C₄⋊C₄	—	2	4	no	—
274	C₇×C₄⋊C₄	—	2	4	no	—
275	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
277	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₇×C₂²⋊C₄	—	2	4	no	—
281	C₇×C₂²⋊C₄	—	2	4	no	—
282	C₇×C₂²⋊C₄	—	2	2	no	—
283	C₇×C₂²⋊C₄	—	2	4	no	—
284	C₇×C₂²⋊C₄	—	2	2	no	—
285	C₇×C₂²⋊C₄	—	2	2	no	—
286	C₇×C₂²⋊C₄	—	2	4	no	—
287	C₇×C₂²⋊C₄	—	2	4	no	—
288	C₇×C₂²⋊C₄	—	2	4	no	—
289	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
290	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
291	C₄²×C₇	—	2	4	no	—
292	C₄²×C₇	—	2	2	no	—
293	C₄²×C₇	—	2	2	no	—
294	C₄²×C₇	—	2	2	no	—
295	C₄²×C₇	—	2	4	no	—
296	C₄²×C₇	C₂×D₄	1	2	yes	—
297	C₄²×C₇	C₂×D₄	1	4	yes	—
298	C₄²×C₇	C₂⁴	1	1	yes	characteristic
299	C₄²×C₇	C₂⁴	1	2	yes	—
300	C₄²×C₇	C₂⁴	1	1	yes	characteristic
301	C₂×#137	C₂²×C₇	1	2	yes	—
302	C₂×#135	C₂²×C₇	1	1	yes	characteristic
303	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
304	C₂×#131	C₂²×C₇	1	1	yes	characteristic
305	C₂×#131	C₂²×C₇	1	1	yes	characteristic
306	#544	C₂²×C₇	1	2	yes	—
307	#542	—	2	2	no	—
308	#542	C₂²×C₇	1	4	yes	—
309	#541	—	2	2	no	—
310	#541	C₂²×C₇	1	4	yes	—
311	#539	—	2	4	no	—
312	#537	C₂²×C₇	1	2	yes	—
313	#536	C₂²×C₇	1	2	yes	—
314	#536	C₂²×C₇	1	2	yes	—
315	#533	—	2	2	no	—
316	#533	C₂²×C₇	1	4	yes	—
317	#529	—	2	4	no	—
318	#529	—	2	2	no	—
319	#529	C₂²×C₇	1	4	yes	—
320	C₄×#41	C₂²×C₇	1	2	yes	—
321	C₄×#41	C₂²×C₇	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
323	#501	C₂²×C₇	1	4	yes	—
324	#499	C₂²×C₇	1	2	yes	—
325	#498	C₂²×C₇	1	2	yes	—
326	#497	C₂²×C₇	1	4	yes	—
327	#495	C₂²×C₇	1	2	yes	—
328	#494	C₂²×C₇	1	2	yes	—
329	#491	C₂²×C₇	1	4	yes	—
330	#489	C₂²×C₇	1	4	yes	—
331	#488	C₂²×C₇	1	4	yes	—
332	#487	C₂²×C₇	1	4	yes	—
333	#470	C₂²×C₇	1	2	yes	—
334	#470	C₂²×C₇	1	2	yes	—
335	#470	C₂²×C₇	1	2	yes	—
336	#470	C₂²×C₇	1	4	yes	—
337	#469	C₂²×C₇	1	2	yes	—
338	#468	C₂²×C₇	1	4	yes	—
339	#467	C₂²×C₇	1	4	yes	—
340	#467	C₂²×C₇	1	4	yes	—
341	#465	C₂²×C₇	1	4	yes	—
342	#465	C₂²×C₇	1	4	yes	—
343	#442	C₂²×C₇	1	1	yes	characteristic
344	#442	C₂²×C₇	1	1	yes	characteristic
345	#441	C₂²×C₇	1	2	yes	—
346	#441	C₂²×C₇	1	1	yes	characteristic
347	#441	C₂²×C₇	1	2	yes	—
348	#441	C₂²×C₇	1	2	yes	—
349	#441	C₂²×C₇	1	4	yes	—
350	#441	C₂²×C₇	1	2	yes	—
351	#441	C₂²×C₇	1	1	yes	characteristic
352	#440	C₂²×C₇	1	2	yes	—
353	#440	C₂²×C₇	1	2	yes	—
354	#440	C₂²×C₇	1	4	yes	—
355	C₄×Q₁₆	C₂²×C₇	1	4	yes	—
356	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
357	#428	C₂²×C₇	1	2	yes	—
358	#427	C₂²×C₇	1	1	yes	characteristic
359	C₂×#106	C₂²×C₇	1	1	yes	characteristic
360	#419	C₂²×C₇	1	2	yes	—
361	#417	C₂²×C₇	1	2	yes	—
362	#416	C₂²×C₇	1	2	yes	—
363	C₂×#103	C₂²×C₇	1	2	yes	—
364	#405	C₂²×C₇	1	1	yes	characteristic
365	#405	C₂²×C₇	1	1	yes	characteristic
366	#405	C₂²×C₇	1	2	yes	—
367	#405	C₂²×C₇	1	2	yes	—
368	C₄×M₁₆	C₂²×C₇	1	2	yes	—
369	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
370	C₂×#97	C₂²×C₇	1	2	yes	—
371	C₂×#97	C₂²×C₇	1	1	yes	characteristic
372	C₂³×C₇	—	2	2	no	—
373	C₂³×C₇	C₂²×D₄	1	2	yes	—
374	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
375	C₇×Q₈	—	2	2	no	—
376	C₇×Q₈	—	2	4	no	—
377	C₇×Q₈	—	2	2	no	—
378	C₇×Q₈	—	2	4	no	—
379	C₇×Q₈	—	2	2	no	—
380	C₇×Q₈	—	4	4	no	—
381	C₇×Q₈	—	8	4	no	—
382	C₇×D₄	—	2	4	no	—
383	C₇×D₄	—	2	2	no	—
384	C₇×D₄	—	2	2	no	—
385	C₇×D₄	—	2	2	no	—
386	C₇×D₄	—	4	4	no	—
387	C₇×D₄	—	8	4	no	—
388	C₂×C₄×C₇	—	2	2	no	—
389	C₂×C₄×C₇	—	2	2	no	—
390	C₂×C₄×C₇	—	2	2	no	—
391	C₂×C₄×C₇	—	2	4	no	—
392	C₂×C₄×C₇	—	2	2	no	—
393	C₂×C₄×C₇	—	2	2	no	—
394	C₂×C₄×C₇	—	2	4	no	—
395	C₂×C₄×C₇	—	4	2	no	—
396	C₂×C₄×C₇	—	4	4	no	—
397	C₂×C₄×C₇	—	4	4	no	—
398	C₂×C₄×C₇	—	4	4	no	—
399	C₂×C₄×C₇	—	4	4	no	—
400	C₂×C₄×C₇	—	8	2	no	—
401	C₂×C₄×C₇	—	8	2	no	—
402	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
406	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₇	C₂×#41	1	2	yes	—
408	C₂×C₄×C₇	C₂×#41	1	2	yes	—
409	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
410	C₇×C₈	—	2	1	no	—
411	C₇×C₈	—	2	1	no	—
412	C₇×C₈	—	2	2	no	—
413	C₇×C₈	C₂×#41	1	2	yes	—
414	C₇×C₈	C₂×#41	1	4	yes	—
415	C₇×C₈	C₂×#41	1	2	yes	—
416	C₂×#41	C₂³×C₇	1	2	yes	—
417	C₂×#41	C₂³×C₇	1	1	yes	characteristic
418	C₂²×Q₈	C₂³×C₇	1	2	yes	—
419	#137	—	2	8	no	—
420	#135	—	2	4	no	—
421	C₂×Q₁₆	—	2	4	no	—
422	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
423	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
424	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
425	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
426	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
427	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
428	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
429	#131	—	2	4	no	—
430	#131	—	2	4	no	—
431	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
432	C₂×M₁₆	C₂³×C₇	1	2	yes	—
433	C₂×M₁₆	C₂³×C₇	1	2	yes	—
434	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₇	1	2	yes	—
437	C₂²×C₈	C₂³×C₇	1	2	yes	—
438	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
439	C₄⋊Q₈	—	2	2	no	—
440	C₄⋊Q₈	—	2	2	no	—
441	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
442	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
443	#126	—	2	4	no	—
444	#126	—	2	4	no	—
445	#126	—	2	4	no	—
446	#126	—	2	4	no	—
447	#125	—	2	4	no	—
448	#125	—	2	2	no	—
449	#125	—	2	4	no	—
450	#125	—	2	4	no	—
451	#125	C₂³×C₇	1	4	yes	—
452	#124	—	2	2	no	—
453	#124	—	2	4	no	—
454	#124	C₂³×C₇	1	4	yes	—
455	#123	—	2	4	no	—
456	#123	—	2	4	no	—
457	#123	—	2	4	no	—
458	#123	—	2	4	no	—
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	4	no	—
461	C₂²⋊Q₈	—	2	2	no	—
462	C₂²⋊Q₈	—	2	2	no	—
463	C₂²⋊Q₈	—	2	4	no	—
464	C₂²⋊Q₈	—	2	4	no	—
465	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
466	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
467	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
468	#121	—	2	4	no	—
469	#121	—	2	2	no	—
470	#121	C₂³×C₇	1	4	yes	—
471	C₄×Q₈	—	2	2	no	—
472	C₄×Q₈	—	2	2	no	—
473	C₄×Q₈	—	2	4	no	—
474	C₄×Q₈	C₇×D₄	1	2	yes	—
475	C₄×Q₈	C₂³×C₇	1	4	yes	—
476	C₄×Q₈	C₂³×C₇	1	4	yes	—
477	C₄×Q₈	C₂³×C₇	1	2	yes	—
478	C₄×Q₈	C₂³×C₇	1	2	yes	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	4	no	—
482	C₄×D₄	C₇×D₄	1	4	yes	—
483	C₄×D₄	C₇×D₄	1	2	yes	—
484	C₄×D₄	C₂³×C₇	1	2	yes	—
485	C₄×D₄	C₂³×C₇	1	2	yes	—
486	#117	—	2	4	no	—
487	#117	—	2	2	no	—
488	#117	—	2	4	no	—
489	#117	C₂³×C₇	1	2	yes	—
490	#117	C₂³×C₇	1	1	yes	characteristic
491	#117	C₂³×C₇	1	2	yes	—
492	C₂×C₄⋊C₄	—	2	2	no	—
493	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
494	C₂×C₄²	—	2	2	no	—
495	C₂×C₄²	—	2	2	no	—
496	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₇	1	2	yes	—
498	#107	C₂³×C₇	1	2	yes	—
499	#107	C₂³×C₇	1	4	yes	—
500	#106	C₂³×C₇	1	2	yes	—
501	#106	C₂³×C₇	1	2	yes	—
502	#106	C₂³×C₇	1	1	yes	characteristic
503	#106	C₂³×C₇	1	1	yes	characteristic
504	#106	C₂³×C₇	1	4	yes	—
505	#103	C₂³×C₇	1	4	yes	—
506	#103	C₂³×C₇	1	4	yes	—
507	#103	C₂³×C₇	1	2	yes	—
508	#103	C₂³×C₇	1	2	yes	—
509	#103	C₂³×C₇	1	4	yes	—
510	#103	C₂³×C₇	1	4	yes	—
511	#103	C₂³×C₇	1	4	yes	—
512	#102	C₂³×C₇	1	2	yes	—
513	#102	C₂³×C₇	1	2	yes	—
514	#102	C₂³×C₇	1	4	yes	—
515	#97	C₂³×C₇	1	1	yes	characteristic
516	#97	C₂³×C₇	1	2	yes	—
517	#97	C₂³×C₇	1	1	yes	characteristic
518	#97	C₂³×C₇	1	1	yes	characteristic
519	#97	C₂³×C₇	1	1	yes	characteristic
520	#97	C₂³×C₇	1	2	yes	—
521	#97	C₂³×C₇	1	2	yes	—
522	C₄×C₈	C₂³×C₇	1	2	yes	—
523	C₄×C₈	C₂³×C₇	1	2	yes	—
524	C₄×C₈	C₂³×C₇	1	2	yes	—
525	C₂²×C₇	—	2	2	no	—
526	C₂²×C₇	—	2	4	no	—
527	C₂²×C₇	—	2	2	no	—
528	C₂²×C₇	—	4	2	no	—
529	C₂²×C₇	—	4	2	no	—
530	C₂²×C₇	—	4	2	no	—
531	C₂²×C₇	#532	1	2	yes	—
532	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
533	C₄×C₇	—	2	2	no	—
534	C₄×C₇	—	2	2	no	—
535	C₄×C₇	—	2	4	no	—
536	C₄×C₇	—	2	2	no	—
537	C₄×C₇	—	4	2	no	—
538	C₄×C₇	—	4	4	no	—
539	C₄×C₇	—	4	2	no	—
540	C₄×C₇	—	4	2	no	—
541	C₄×C₇	—	4	4	no	—
542	C₄×C₇	#532	1	2	yes	—
543	C₄×C₇	C₂²×#41	1	1	yes	characteristic
544	C₄×C₇	C₂²×#41	1	1	yes	characteristic
545	#41	—	2	2	no	—
546	#41	—	2	2	no	—
547	#41	—	2	4	no	—
548	#41	—	2	4	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	2	4	no	—
551	C₂×Q₈	—	2	4	no	—
552	C₂×Q₈	—	2	4	no	—
553	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
554	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
555	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
559	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
560	C₂×D₄	C₂⁴×C₇	1	2	yes	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
567	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
568	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
570	Q₁₆	—	2	4	no	—
571	Q₁₆	—	2	4	no	—
572	Q₁₆	—	2	2	no	—
573	Q₁₆	—	2	8	no	—
574	SD₁₆	—	2	4	no	—
575	SD₁₆	—	2	8	no	—
576	D₈	—	2	2	no	—
577	M₁₆	—	2	2	no	—
578	M₁₆	—	2	4	no	—
579	M₁₆	—	2	4	no	—
580	M₁₆	C₇×#41	1	4	yes	—
581	C₂×C₈	—	2	2	no	—
582	C₂×C₈	—	2	4	no	—
583	C₂×C₈	—	2	4	no	—
584	C₂×C₈	C₇×#41	1	4	yes	—
585	C₂×C₈	C₂⁴×C₇	1	2	yes	—
586	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
587	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
588	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
589	C₂×C₈	C₂⁴×C₇	1	2	yes	—
590	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
605	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
606	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
607	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
608	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
619	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	2	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	4	no	—
625	C₄²	C₂×C₇×D₄	1	2	yes	—
626	C₄²	C₂×C₇×D₄	1	4	yes	—
627	C₄²	C₂⁴×C₇	1	1	yes	characteristic
628	C₄²	C₂⁴×C₇	1	2	yes	—
629	C₄²	C₂⁴×C₇	1	1	yes	characteristic
630	C₂×C₇	—	2	2	no	—
631	C₂×C₇	—	4	2	no	—
632	C₂×C₇	—	8	2	no	—
633	C₂×C₇	C₂×#532	1	1	yes	characteristic
634	C₂×C₇	#3586	1	2	yes	—
635	C₂³	—	2	2	no	—
636	C₂³	C₂²×C₇×D₄	1	2	yes	—
637	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
638	Q₈	—	2	2	no	—
639	Q₈	—	2	4	no	—
640	Q₈	—	2	2	no	—
641	Q₈	—	2	4	no	—
642	Q₈	—	2	2	no	—
643	Q₈	—	4	4	no	—
644	Q₈	—	8	4	no	—
645	D₄	—	2	4	no	—
646	D₄	—	2	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	2	no	—
649	D₄	—	4	4	no	—
650	D₄	—	8	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	8	2	no	—
664	C₂×C₄	—	8	2	no	—
665	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
666	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
667	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
668	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
669	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
670	C₂×C₄	C₂×C₇×#41	1	2	yes	—
671	C₂×C₄	C₂×C₇×#41	1	2	yes	—
672	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
673	C₈	—	2	1	no	—
674	C₈	—	2	1	no	—
675	C₈	—	2	2	no	—
676	C₈	C₂×C₇×#41	1	2	yes	—
677	C₈	C₂×C₇×#41	1	4	yes	—
678	C₈	C₂×C₇×#41	1	2	yes	—
679	C₇	#60699	1	1	yes	characteristic, direct product factor, Sylow
680	C₂²	—	2	2	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	C₇×#532	1	2	yes	—
687	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	2	4	no	—
691	C₄	—	2	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	4	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	4	no	—
697	C₄	C₇×#532	1	2	yes	—
698	C₄	C₂²×C₇×#41	1	1	yes	characteristic
699	C₄	C₂²×C₇×#41	1	1	yes	characteristic
700	C₂	—	2	2	no	—
701	C₂	—	4	2	no	—
702	C₂	—	8	2	no	—
703	C₂	C₂×C₇×#532	1	1	yes	characteristic
704	C₂	C₇×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3060	C₂
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. C₇×#3461	C₂	semidirect
2. C₇×#3185	C₂	semidirect
3. C₇×#3183	C₂	semidirect
4. C₇×#3181	C₂	semidirect
5. C₇×#3178	C₂	semidirect
6. C₇×#3177	C₂	semidirect
7. C₇×#3173	C₂	semidirect
8. C₇×#3163	C₂	semidirect
9. C₇×#3156	C₂	semidirect
10. C₇×#3137	C₂	semidirect
11. C₇×#3063	C₂	semidirect
13. C₇×#3059	C₂	semidirect
14. C₄×C₇×#137	C₂	semidirect
15. C₇×#2943	C₂	semidirect
16. C₂×C₇×#441	C₂	semidirect
17. C₇×#2875	C₂	semidirect
89. #60699	C₇	direct (N × H)
199. #3461	C₂×C₇	semidirect
200. #3185	C₂×C₇	semidirect
201. #3183	C₂×C₇	semidirect
202. #3181	C₂×C₇	semidirect
203. #3178	C₂×C₇	semidirect
204. #3177	C₂×C₇	semidirect
205. #3173	C₂×C₇	semidirect
206. #3163	C₂×C₇	semidirect
207. #3156	C₂×C₇	semidirect
208. #3137	C₂×C₇	semidirect
209. #3063	C₂×C₇	semidirect
211. #3059	C₂×C₇	semidirect
212. C₄×#137	C₂×C₇	semidirect
213. #2943	C₂×C₇	semidirect
214. C₂×#441	C₂×C₇	semidirect
215. #2875	C₂×C₇	semidirect
679. C₇	#60699	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×#3461	2
C₇×#3185	2
C₇×#3183	2
C₇×#3181	2
C₇×#3178	2
C₇×#3177	2
C₇×#3173	2
C₇×#3163	2
C₇×#3156	2
C₇×#3137	2
C₇×#3063	2
C₇×#3060	2
C₇×#3059	2
C₄×C₇×#137	2
C₇×#2943	2
C₂×C₇×#441	2
C₇×#2875	2
#60699	7

Subgroups — C7×#60699 #13237915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60699 #13237915