Subgroups — C₇×#61259 #13238475

Order 1792.

1866 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3492	C₂	1	2	yes	maximal, complemented
2	C₇×#3345	C₂	1	4	yes	maximal, complemented
3	C₇×#3344	C₂	1	4	yes	maximal, complemented
4	C₇×#3337	C₂	1	4	yes	maximal, complemented
5	C₇×#3335	C₂	1	4	yes	maximal, complemented
6	C₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3099	C₂	1	2	yes	maximal, complemented
8	C₇×#3092	C₂	1	2	yes	maximal, complemented
9	C₇×#3084	C₂	1	2	yes	maximal, complemented
10	C₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2952	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2912	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#135	C₂²	1	1	yes	characteristic
17	C₂×C₇×#131	C₂²	1	1	yes	characteristic
18	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
19	C₇×#554	—	2	2	no	—
20	C₇×#554	C₂²	1	4	yes	—
21	C₇×#553	—	2	2	no	—
22	C₇×#553	C₂²	1	4	yes	—
23	C₇×#552	—	2	2	no	—
24	C₇×#552	C₂²	1	4	yes	—
25	C₇×#547	—	2	2	no	—
26	C₇×#547	C₂²	1	4	yes	—
27	C₇×#544	C₂²	1	2	yes	—
28	C₇×#539	—	2	4	no	—
29	C₇×#537	C₂²	1	2	yes	—
30	C₇×#525	—	2	4	no	—
31	C₇×#525	C₂²	1	2	yes	—
32	C₇×#525	C₂²	1	1	yes	characteristic
33	C₇×#520	C₂²	1	2	yes	—
34	C₇×#520	C₂²	1	2	yes	—
35	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
36	C₇×#501	C₂²	1	4	yes	complemented
37	C₇×#499	C₂²	1	2	yes	complemented
38	C₇×#498	C₂²	1	2	yes	complemented
39	C₇×#485	C₂²	1	4	yes	complemented
40	C₇×#484	C₂²	1	4	yes	—
41	C₇×#483	C₂²	1	4	yes	—
42	C₇×#483	C₂²	1	4	yes	complemented
43	C₇×#482	C₂²	1	4	yes	complemented
44	C₇×#481	C₂²	1	4	yes	—
45	C₇×#481	C₂²	1	4	yes	complemented
46	C₇×#480	C₂²	1	4	yes	—
47	C₇×#479	C₂²	1	4	yes	complemented
48	C₇×#478	C₂²	1	4	yes	complemented
49	C₇×#476	C₂²	1	4	yes	complemented
50	C₇×#475	C₂²	1	4	yes	complemented
51	C₇×#470	C₂²	1	2	yes	complemented
52	C₇×#469	C₂²	1	2	yes	complemented
53	C₇×#467	C₂²	1	2	yes	—
54	C₇×#466	C₂²	1	2	yes	—
55	C₇×#465	C₂²	1	2	yes	—
56	C₇×#465	C₂²	1	2	yes	—
57	C₇×#465	C₂²	1	4	yes	complemented
58	C₇×#442	C₂²	1	2	yes	complemented
59	C₇×#441	C₂²	1	2	yes	complemented
60	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
61	C₇×#435	C₂²	1	4	yes	—
62	C₇×C₈×D₄	C₂²	1	4	yes	—
63	C₇×#428	C₂²	1	2	yes	—
64	C₇×#428	C₂²	1	2	yes	—
65	C₇×#428	C₂²	1	4	yes	complemented
66	C₇×#427	C₂²	1	1	yes	characteristic
67	C₇×#427	C₂²	1	2	yes	complemented
68	C₂×C₇×#106	C₂²	1	1	yes	characteristic
69	C₂×C₇×#106	C₂²	1	1	yes	characteristic
70	C₂×C₇×#106	C₂²	1	4	yes	—
71	C₂×C₇×#106	C₂²	1	2	yes	—
72	C₂×C₇×#106	C₂²	1	4	yes	—
73	C₂×C₇×#106	C₂²	1	2	yes	complemented
74	C₇×#424	C₂²	1	1	yes	characteristic
75	C₇×#417	C₂²	1	2	yes	—
76	C₇×#417	C₂²	1	2	yes	—
77	C₇×#416	C₂²	1	2	yes	—
78	C₇×#408	C₂²	1	1	yes	characteristic
79	C₇×#407	C₂²	1	1	yes	characteristic
80	C₇×#405	C₂²	1	1	yes	characteristic
81	#61259	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂×C₇×#41	—	2	4	no	—
83	C₂×C₇×#41	C₂³	1	2	yes	—
84	C₂×C₇×#41	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₇	—	2	2	no	—
86	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
87	C₇×#135	—	2	4	no	—
88	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
89	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
90	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
91	C₇×#131	—	2	4	no	—
92	C₂×C₇×M₁₆	C₂³	1	2	yes	—
93	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
95	C₂²×C₇×C₈	—	2	4	no	—
96	C₂²×C₇×C₈	C₂³	1	2	yes	—
97	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
98	C₂²×C₇×C₈	C₂³	1	2	yes	—
99	C₂²×C₇×C₈	C₂³	1	2	yes	—
100	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
101	C₇×C₄⋊Q₈	—	2	2	no	—
102	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
103	C₇×#126	—	2	4	no	—
104	C₇×#126	—	2	4	no	—
105	C₇×#125	—	2	4	no	—
106	C₇×#125	—	2	4	no	—
107	C₇×#125	—	2	2	no	—
108	C₇×#125	C₂³	1	4	yes	—
109	C₇×#123	—	2	4	no	—
110	C₇×#123	—	2	2	no	—
111	C₇×#123	—	2	4	no	—
112	C₇×#123	—	2	4	no	—
113	C₇×#123	—	2	4	no	—
114	C₇×#123	D₄	1	2	yes	—
115	C₇×C₂²⋊Q₈	—	2	2	no	—
116	C₇×C₂²⋊Q₈	—	2	4	no	—
117	C₇×C₂²⋊Q₈	—	2	4	no	—
118	C₇×C₂²⋊Q₈	—	2	4	no	—
119	C₇×C₂²⋊Q₈	—	2	4	no	—
120	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
121	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
122	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
123	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
124	C₇×#121	—	2	4	no	—
125	C₇×#121	—	2	4	no	—
126	C₇×#121	—	2	2	no	—
127	C₇×#121	D₄	1	2	yes	—
128	C₇×#121	C₂³	1	2	yes	—
129	C₇×#121	C₂³	1	2	yes	—
130	C₇×#121	C₂³	1	4	yes	—
131	C₇×#120	—	2	2	no	—
132	C₇×#120	D₄	1	2	yes	—
133	C₄×C₇×Q₈	—	2	2	no	—
134	C₄×C₇×Q₈	C₂³	1	4	yes	—
135	C₄×C₇×D₄	—	2	4	no	—
136	C₄×C₇×D₄	—	2	2	no	—
137	C₄×C₇×D₄	—	2	4	no	—
138	C₄×C₇×D₄	—	2	2	no	—
139	C₄×C₇×D₄	—	2	2	no	—
140	C₄×C₇×D₄	—	2	4	no	—
141	C₄×C₇×D₄	—	2	4	no	—
142	C₄×C₇×D₄	C₂³	1	4	yes	—
143	C₄×C₇×D₄	C₂³	1	4	yes	—
144	C₇×#117	—	2	2	no	—
145	C₇×#117	—	2	4	no	—
146	C₇×#117	C₂³	1	4	yes	—
147	C₇×#117	C₂³	1	2	yes	—
148	C₇×#117	C₂³	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	—	2	2	no	—
150	C₂×C₇×C₄⋊C₄	—	2	2	no	—
151	C₂×C₇×C₄⋊C₄	—	2	2	no	—
152	C₂×C₇×C₄⋊C₄	—	2	2	no	—
153	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
155	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
156	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
158	C₇×#107	C₂³	1	2	yes	—
159	C₇×#107	C₂³	1	4	yes	—
160	C₇×#107	C₂³	1	4	yes	—
161	C₇×#106	C₂³	1	2	yes	—
162	C₇×#106	C₂³	1	4	yes	—
163	C₇×#106	C₂³	1	4	yes	—
164	C₇×#106	C₂³	1	4	yes	—
165	C₇×#106	C₂³	1	4	yes	—
166	C₇×#106	C₂³	1	1	yes	characteristic
167	C₇×#106	C₂³	1	2	yes	—
168	C₇×#106	C₂³	1	1	yes	characteristic
169	C₇×#106	C₂³	1	2	yes	—
170	C₇×#106	C₂³	1	2	yes	—
171	C₇×C₄⋊C₈	C₂³	1	4	yes	—
172	C₇×#103	C₂³	1	2	yes	—
173	C₇×#103	C₂³	1	2	yes	—
174	C₇×#103	C₂³	1	4	yes	—
175	C₇×#103	C₂³	1	4	yes	—
176	C₇×#102	C₂³	1	2	yes	—
177	C₇×#102	C₂³	1	2	yes	—
178	C₇×#102	C₂³	1	4	yes	—
179	C₇×#102	C₂³	1	4	yes	—
180	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
181	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
182	C₇×#97	C₂³	1	2	yes	—
183	C₄×C₇×C₈	C₂³	1	2	yes	—
184	#3492	C₂×C₇	1	2	yes	complemented
185	#3345	C₂×C₇	1	4	yes	complemented
186	#3344	C₂×C₇	1	4	yes	complemented
187	#3337	C₂×C₇	1	4	yes	complemented
188	#3335	C₂×C₇	1	4	yes	complemented
189	#3163	C₂×C₇	1	1	yes	characteristic, complemented
190	#3099	C₂×C₇	1	2	yes	complemented
191	#3092	C₂×C₇	1	2	yes	complemented
192	#3084	C₂×C₇	1	2	yes	complemented
193	#3060	C₂×C₇	1	1	yes	characteristic, complemented
194	#3050	C₂×C₇	1	1	yes	characteristic, complemented
195	#2952	C₂×C₇	1	1	yes	characteristic, complemented
196	#2929	C₂×C₇	1	1	yes	characteristic, complemented
197	#2912	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂²×#106	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
200	C₇×#41	—	2	2	no	—
201	C₇×#41	—	2	2	no	—
202	C₇×#41	—	2	4	no	—
203	C₇×#41	—	2	4	no	—
204	C₇×#41	—	8	8	no	—
205	C₂×C₇×Q₈	—	2	4	no	—
206	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
208	C₂×C₇×D₄	—	2	2	no	—
209	C₂×C₇×D₄	—	2	2	no	—
210	C₂×C₇×D₄	—	2	2	no	—
211	C₂×C₇×D₄	—	2	4	no	—
212	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
213	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
214	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
215	C₂×C₇×D₄	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₇	—	2	2	no	—
217	C₂²×C₄×C₇	—	2	2	no	—
218	C₂²×C₄×C₇	—	2	4	no	—
219	C₂²×C₄×C₇	—	2	2	no	—
220	C₂²×C₄×C₇	—	2	4	no	—
221	C₂²×C₄×C₇	—	2	2	no	—
222	C₂²×C₄×C₇	—	2	4	no	—
223	C₂²×C₄×C₇	—	2	2	no	—
224	C₂²×C₄×C₇	—	2	4	no	—
225	C₂²×C₄×C₇	—	8	4	no	—
226	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
231	C₇×Q₁₆	—	2	2	no	—
232	C₇×SD₁₆	—	2	4	no	—
233	C₇×D₈	—	2	2	no	—
234	C₇×M₁₆	—	2	2	no	—
235	C₇×M₁₆	—	2	2	no	—
236	C₇×M₁₆	—	2	4	no	—
237	C₂×C₇×C₈	—	2	2	no	—
238	C₂×C₇×C₈	—	2	4	no	—
239	C₂×C₇×C₈	—	2	4	no	—
240	C₂×C₇×C₈	—	2	4	no	—
241	C₂×C₇×C₈	#41	1	4	yes	complemented
242	C₂×C₇×C₈	C₂⁴	1	2	yes	—
243	C₂×C₇×C₈	C₂⁴	1	2	yes	—
244	C₂×C₇×C₈	C₂⁴	1	2	yes	—
245	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
246	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
247	C₇×C₄⋊C₄	—	2	2	no	—
248	C₇×C₄⋊C₄	—	2	2	no	—
249	C₇×C₄⋊C₄	—	2	4	no	—
250	C₇×C₄⋊C₄	—	2	4	no	—
251	C₇×C₄⋊C₄	—	2	4	no	—
252	C₇×C₄⋊C₄	—	2	4	no	—
253	C₇×C₄⋊C₄	—	2	4	no	—
254	C₇×C₄⋊C₄	—	2	4	no	—
255	C₇×C₄⋊C₄	—	2	2	no	—
256	C₇×C₄⋊C₄	—	2	4	no	—
257	C₇×C₄⋊C₄	—	2	4	no	—
258	C₇×C₄⋊C₄	—	2	2	no	—
259	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
260	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
261	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
262	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
263	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
264	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
265	C₇×C₂²⋊C₄	—	2	2	no	—
266	C₇×C₂²⋊C₄	—	2	2	no	—
267	C₇×C₂²⋊C₄	—	2	4	no	—
268	C₇×C₂²⋊C₄	—	2	2	no	—
269	C₇×C₂²⋊C₄	—	2	4	no	—
270	C₇×C₂²⋊C₄	—	2	4	no	—
271	C₇×C₂²⋊C₄	—	2	4	no	—
272	C₇×C₂²⋊C₄	—	2	2	no	—
273	C₇×C₂²⋊C₄	—	2	2	no	—
274	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
275	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
276	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
277	C₄²×C₇	—	2	4	no	—
278	C₄²×C₇	—	2	4	no	—
279	C₄²×C₇	—	2	2	no	—
280	C₄²×C₇	C₂⁴	1	2	yes	—
281	C₂×#135	C₂²×C₇	1	1	yes	characteristic
282	C₂×#131	C₂²×C₇	1	1	yes	characteristic
283	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
284	#554	—	2	2	no	—
285	#554	C₂²×C₇	1	4	yes	—
286	#553	—	2	2	no	—
287	#553	C₂²×C₇	1	4	yes	—
288	#552	—	2	2	no	—
289	#552	C₂²×C₇	1	4	yes	—
290	#547	—	2	2	no	—
291	#547	C₂²×C₇	1	4	yes	—
292	#544	C₂²×C₇	1	2	yes	—
293	#539	—	2	4	no	—
294	#537	C₂²×C₇	1	2	yes	—
295	#525	—	2	4	no	—
296	#525	C₂²×C₇	1	2	yes	—
297	#525	C₂²×C₇	1	1	yes	characteristic
298	#520	C₂²×C₇	1	2	yes	—
299	#520	C₂²×C₇	1	2	yes	—
300	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
301	#501	C₂²×C₇	1	4	yes	complemented
302	#499	C₂²×C₇	1	2	yes	complemented
303	#498	C₂²×C₇	1	2	yes	complemented
304	#485	C₂²×C₇	1	4	yes	complemented
305	#484	C₂²×C₇	1	4	yes	—
306	#483	C₂²×C₇	1	4	yes	—
307	#483	C₂²×C₇	1	4	yes	complemented
308	#482	C₂²×C₇	1	4	yes	complemented
309	#481	C₂²×C₇	1	4	yes	—
310	#481	C₂²×C₇	1	4	yes	complemented
311	#480	C₂²×C₇	1	4	yes	—
312	#479	C₂²×C₇	1	4	yes	complemented
313	#478	C₂²×C₇	1	4	yes	complemented
314	#476	C₂²×C₇	1	4	yes	complemented
315	#475	C₂²×C₇	1	4	yes	complemented
316	#470	C₂²×C₇	1	2	yes	complemented
317	#469	C₂²×C₇	1	2	yes	complemented
318	#467	C₂²×C₇	1	2	yes	—
319	#466	C₂²×C₇	1	2	yes	—
320	#465	C₂²×C₇	1	2	yes	—
321	#465	C₂²×C₇	1	2	yes	—
322	#465	C₂²×C₇	1	4	yes	complemented
323	#442	C₂²×C₇	1	2	yes	complemented
324	#441	C₂²×C₇	1	2	yes	complemented
325	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
326	#435	C₂²×C₇	1	4	yes	—
327	C₈×D₄	C₂²×C₇	1	4	yes	—
328	#428	C₂²×C₇	1	2	yes	—
329	#428	C₂²×C₇	1	2	yes	—
330	#428	C₂²×C₇	1	4	yes	complemented
331	#427	C₂²×C₇	1	1	yes	characteristic
332	#427	C₂²×C₇	1	2	yes	complemented
333	C₂×#106	C₂²×C₇	1	4	yes	—
334	C₂×#106	C₂²×C₇	1	2	yes	—
335	C₂×#106	C₂²×C₇	1	4	yes	—
336	C₂×#106	C₂²×C₇	1	1	yes	characteristic
337	C₂×#106	C₂²×C₇	1	1	yes	characteristic
338	C₂×#106	C₂²×C₇	1	2	yes	complemented
339	#424	C₂²×C₇	1	1	yes	characteristic
340	#417	C₂²×C₇	1	2	yes	—
341	#417	C₂²×C₇	1	2	yes	—
342	#416	C₂²×C₇	1	2	yes	—
343	#408	C₂²×C₇	1	1	yes	characteristic
344	#407	C₂²×C₇	1	1	yes	characteristic
345	#405	C₂²×C₇	1	1	yes	characteristic
346	C₂³×C₇	—	2	2	no	—
347	C₂³×C₇	—	2	4	no	—
348	C₂³×C₇	—	2	2	no	—
349	C₂³×C₇	C₂²×D₄	1	2	yes	—
350	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
351	C₂³×C₇	C₂²×D₄	1	2	yes	—
352	C₇×Q₈	—	2	2	no	—
353	C₇×Q₈	—	2	2	no	—
354	C₇×Q₈	—	2	2	no	—
355	C₇×Q₈	—	8	4	no	—
356	C₇×D₄	—	2	4	no	—
357	C₇×D₄	—	2	8	no	—
358	C₇×D₄	—	2	2	no	—
359	C₇×D₄	—	2	2	no	—
360	C₇×D₄	—	2	2	no	—
361	C₇×D₄	—	4	4	no	—
362	C₇×D₄	—	4	4	no	—
363	C₇×D₄	—	4	4	no	—
364	C₇×D₄	—	8	4	no	—
365	C₂×C₄×C₇	—	2	2	no	—
366	C₂×C₄×C₇	—	2	4	no	—
367	C₂×C₄×C₇	—	2	2	no	—
368	C₂×C₄×C₇	—	2	2	no	—
369	C₂×C₄×C₇	—	2	2	no	—
370	C₂×C₄×C₇	—	2	2	no	—
371	C₂×C₄×C₇	—	2	2	no	—
372	C₂×C₄×C₇	—	2	2	no	—
373	C₂×C₄×C₇	—	2	4	no	—
374	C₂×C₄×C₇	—	2	2	no	—
375	C₂×C₄×C₇	—	2	4	no	—
376	C₂×C₄×C₇	—	4	8	no	—
377	C₂×C₄×C₇	—	4	4	no	—
378	C₂×C₄×C₇	—	8	4	no	—
379	C₂×C₄×C₇	—	8	2	no	—
380	C₂×C₄×C₇	—	8	4	no	—
381	C₂×C₄×C₇	—	8	2	no	—
382	C₂×C₄×C₇	—	8	4	no	—
383	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
385	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₇	C₂×#41	1	2	yes	—
388	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
389	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
390	C₇×C₈	—	2	2	no	—
391	C₇×C₈	—	2	2	no	—
392	C₇×C₈	—	2	2	no	—
393	C₇×C₈	C₂×#41	1	2	yes	—
394	C₇×C₈	C₂×#41	1	2	yes	—
395	C₂×#41	—	2	4	no	—
396	C₂×#41	C₂³×C₇	1	2	yes	—
397	C₂×#41	C₂³×C₇	1	1	yes	characteristic
398	C₂³×C₄	—	2	2	no	—
399	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
400	#135	—	2	4	no	—
401	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
402	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
403	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
404	#131	—	2	4	no	—
405	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
406	C₂×M₁₆	C₂³×C₇	1	2	yes	—
407	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
408	C₂²×C₈	—	2	4	no	—
409	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₇	1	2	yes	—
411	C₂²×C₈	C₂³×C₇	1	2	yes	—
412	C₂²×C₈	C₂³×C₇	1	2	yes	—
413	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
414	C₄⋊Q₈	—	2	2	no	—
415	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
416	#126	—	2	4	no	—
417	#126	—	2	4	no	—
418	#125	—	2	4	no	—
419	#125	—	2	4	no	—
420	#125	—	2	2	no	—
421	#125	C₂³×C₇	1	4	yes	—
422	#123	—	2	4	no	—
423	#123	—	2	2	no	—
424	#123	—	2	4	no	—
425	#123	—	2	4	no	—
426	#123	—	2	4	no	—
427	#123	C₇×D₄	1	2	yes	—
428	C₂²⋊Q₈	—	2	2	no	—
429	C₂²⋊Q₈	—	2	4	no	—
430	C₂²⋊Q₈	—	2	4	no	—
431	C₂²⋊Q₈	—	2	4	no	—
432	C₂²⋊Q₈	—	2	4	no	—
433	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
434	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
435	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
436	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
437	#121	—	2	4	no	—
438	#121	—	2	4	no	—
439	#121	—	2	2	no	—
440	#121	C₇×D₄	1	2	yes	—
441	#121	C₂³×C₇	1	2	yes	—
442	#121	C₂³×C₇	1	2	yes	—
443	#121	C₂³×C₇	1	4	yes	—
444	#120	—	2	2	no	—
445	#120	C₇×D₄	1	2	yes	—
446	C₄×Q₈	—	2	2	no	—
447	C₄×Q₈	C₂³×C₇	1	4	yes	—
448	C₄×D₄	—	2	4	no	—
449	C₄×D₄	—	2	2	no	—
450	C₄×D₄	—	2	4	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	4	no	—
454	C₄×D₄	—	2	4	no	—
455	C₄×D₄	C₂³×C₇	1	4	yes	—
456	C₄×D₄	C₂³×C₇	1	4	yes	—
457	#117	—	2	2	no	—
458	#117	—	2	4	no	—
459	#117	C₂³×C₇	1	2	yes	—
460	#117	C₂³×C₇	1	4	yes	—
461	#117	C₂³×C₇	1	1	yes	characteristic
462	C₂×C₄⋊C₄	—	2	2	no	—
463	C₂×C₄⋊C₄	—	2	2	no	—
464	C₂×C₄⋊C₄	—	2	2	no	—
465	C₂×C₄⋊C₄	—	2	2	no	—
466	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
471	#107	C₂³×C₇	1	2	yes	—
472	#107	C₂³×C₇	1	4	yes	—
473	#107	C₂³×C₇	1	4	yes	—
474	#106	C₂³×C₇	1	2	yes	—
475	#106	C₂³×C₇	1	2	yes	—
476	#106	C₂³×C₇	1	2	yes	—
477	#106	C₂³×C₇	1	2	yes	—
478	#106	C₂³×C₇	1	4	yes	—
479	#106	C₂³×C₇	1	4	yes	—
480	#106	C₂³×C₇	1	1	yes	characteristic
481	#106	C₂³×C₇	1	4	yes	—
482	#106	C₂³×C₇	1	1	yes	characteristic
483	#106	C₂³×C₇	1	4	yes	—
484	C₄⋊C₈	C₂³×C₇	1	4	yes	—
485	#103	C₂³×C₇	1	2	yes	—
486	#103	C₂³×C₇	1	2	yes	—
487	#103	C₂³×C₇	1	4	yes	—
488	#103	C₂³×C₇	1	4	yes	—
489	#102	C₂³×C₇	1	2	yes	—
490	#102	C₂³×C₇	1	2	yes	—
491	#102	C₂³×C₇	1	4	yes	—
492	#102	C₂³×C₇	1	4	yes	—
493	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
494	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
495	#97	C₂³×C₇	1	2	yes	—
496	C₄×C₈	C₂³×C₇	1	2	yes	—
497	C₂²×C₇	—	2	8	no	—
498	C₂²×C₇	—	2	2	no	—
499	C₂²×C₇	—	2	2	no	—
500	C₂²×C₇	—	2	2	no	—
501	C₂²×C₇	—	2	2	no	—
502	C₂²×C₇	—	2	4	no	—
503	C₂²×C₇	—	4	2	no	—
504	C₂²×C₇	—	4	2	no	—
505	C₂²×C₇	—	4	2	no	—
506	C₂²×C₇	#547	1	2	yes	—
507	C₂²×C₇	#577	1	4	yes	—
508	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
509	C₄×C₇	—	2	2	no	—
510	C₄×C₇	—	2	2	no	—
511	C₄×C₇	—	2	4	no	—
512	C₄×C₇	—	4	2	no	—
513	C₄×C₇	—	4	4	no	—
514	C₄×C₇	—	4	4	no	—
515	C₄×C₇	—	4	2	no	—
516	C₄×C₇	—	4	2	no	—
517	C₄×C₇	#547	1	2	yes	—
518	C₄×C₇	C₂²×#41	1	1	yes	characteristic
519	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
521	#41	—	2	2	no	—
522	#41	—	2	2	no	—
523	#41	—	2	4	no	—
524	#41	—	2	4	no	—
525	#41	—	8	8	no	—
526	C₂×Q₈	—	2	4	no	—
527	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
528	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
534	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
535	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
536	C₂×D₄	C₂⁴×C₇	1	2	yes	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	8	4	no	—
547	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
548	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
552	Q₁₆	—	2	2	no	—
553	SD₁₆	—	2	4	no	—
554	D₈	—	2	2	no	—
555	M₁₆	—	2	2	no	—
556	M₁₆	—	2	2	no	—
557	M₁₆	—	2	4	no	—
558	C₂×C₈	—	2	2	no	—
559	C₂×C₈	—	2	4	no	—
560	C₂×C₈	—	2	4	no	—
561	C₂×C₈	—	2	4	no	—
562	C₂×C₈	C₇×#41	1	4	yes	complemented
563	C₂×C₈	C₂⁴×C₇	1	2	yes	—
564	C₂×C₈	C₂⁴×C₇	1	2	yes	—
565	C₂×C₈	C₂⁴×C₇	1	2	yes	—
566	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
567	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
581	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
582	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
583	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
584	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
585	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
596	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
597	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
598	C₄²	—	2	4	no	—
599	C₄²	—	2	4	no	—
600	C₄²	—	2	2	no	—
601	C₄²	C₂⁴×C₇	1	2	yes	—
602	C₂×C₇	—	2	2	no	—
603	C₂×C₇	—	2	4	no	—
604	C₂×C₇	—	4	2	no	—
605	C₂×C₇	—	8	2	no	—
606	C₂×C₇	C₂×#547	1	1	yes	characteristic
607	C₂×C₇	C₂×#577	1	2	yes	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	4	no	—
610	C₂³	—	2	2	no	—
611	C₂³	C₂²×C₇×D₄	1	2	yes	—
612	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
613	C₂³	C₂²×C₇×D₄	1	2	yes	—
614	Q₈	—	2	2	no	—
615	Q₈	—	2	2	no	—
616	Q₈	—	2	2	no	—
617	Q₈	—	8	4	no	—
618	D₄	—	2	4	no	—
619	D₄	—	2	8	no	—
620	D₄	—	2	2	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	2	no	—
623	D₄	—	4	4	no	—
624	D₄	—	4	4	no	—
625	D₄	—	4	4	no	—
626	D₄	—	8	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	4	8	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	8	4	no	—
641	C₂×C₄	—	8	2	no	—
642	C₂×C₄	—	8	4	no	—
643	C₂×C₄	—	8	2	no	—
644	C₂×C₄	—	8	4	no	—
645	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
646	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
647	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
648	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
649	C₂×C₄	C₂×C₇×#41	1	2	yes	—
650	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
651	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
652	C₈	—	2	2	no	—
653	C₈	—	2	2	no	—
654	C₈	—	2	2	no	—
655	C₈	C₂×C₇×#41	1	2	yes	—
656	C₈	C₂×C₇×#41	1	2	yes	—
657	C₇	#61259	1	1	yes	characteristic, direct product factor, Sylow
658	C₂²	—	2	8	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	C₇×#547	1	2	yes	—
668	C₂²	C₇×#577	1	4	yes	—
669	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
670	C₄	—	2	4	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	4	4	no	—
674	C₄	—	4	4	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	2	no	—
678	C₄	C₇×#547	1	2	yes	—
679	C₄	C₂²×C₇×#41	1	1	yes	characteristic
680	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
681	C₂	—	2	2	no	—
682	C₂	—	2	4	no	—
683	C₂	—	4	2	no	—
684	C₂	—	8	2	no	—
685	C₂	C₂×C₇×#547	1	1	yes	characteristic
686	C₂	C₂×C₇×#577	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 ◁ C₇×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3492	C₂	semidirect
2. C₇×#3345	C₂	semidirect
3. C₇×#3344	C₂	semidirect
4. C₇×#3337	C₂	semidirect
5. C₇×#3335	C₂	semidirect
6. C₇×#3163	C₂	semidirect
7. C₇×#3099	C₂	semidirect
8. C₇×#3092	C₂	semidirect
9. C₇×#3084	C₂	semidirect
10. C₇×#3060	C₂	semidirect
11. C₇×#3050	C₂	semidirect
12. C₇×#2952	C₂	semidirect
13. C₇×#2929	C₂	semidirect
14. C₇×#2912	C₂	semidirect
15. C₂²×C₇×#106	C₂	semidirect
36. C₇×#501	C₂²	semidirect
37. C₇×#499	C₂²	semidirect
38. C₇×#498	C₂²	semidirect
39. C₇×#485	C₂²	semidirect
42. C₇×#483	C₂²	semidirect
43. C₇×#482	C₂²	semidirect
45. C₇×#481	C₂²	semidirect
47. C₇×#479	C₂²	semidirect
48. C₇×#478	C₂²	semidirect
49. C₇×#476	C₂²	semidirect
50. C₇×#475	C₂²	semidirect
51. C₇×#470	C₂²	semidirect
52. C₇×#469	C₂²	semidirect
57. C₇×#465	C₂²	semidirect
58. C₇×#442	C₂²	semidirect
59. C₇×#441	C₂²	semidirect
60. C₄×C₇×SD₁₆	C₂²	semidirect
65. C₇×#428	C₂²	semidirect
67. C₇×#427	C₂²	semidirect
73. C₂×C₇×#106	C₂²	semidirect
81. #61259	C₇	direct (N × H)
184. #3492	C₂×C₇	semidirect
185. #3345	C₂×C₇	semidirect
186. #3344	C₂×C₇	semidirect
187. #3337	C₂×C₇	semidirect
188. #3335	C₂×C₇	semidirect
189. #3163	C₂×C₇	semidirect
190. #3099	C₂×C₇	semidirect
191. #3092	C₂×C₇	semidirect
192. #3084	C₂×C₇	semidirect
193. #3060	C₂×C₇	semidirect
194. #3050	C₂×C₇	semidirect
195. #2952	C₂×C₇	semidirect
196. #2929	C₂×C₇	semidirect
197. #2912	C₂×C₇	semidirect
198. C₂²×#106	C₂×C₇	semidirect
241. C₂×C₇×C₈	#41	semidirect
301. #501	C₂²×C₇	semidirect
302. #499	C₂²×C₇	semidirect
303. #498	C₂²×C₇	semidirect
304. #485	C₂²×C₇	semidirect
307. #483	C₂²×C₇	semidirect
308. #482	C₂²×C₇	semidirect
310. #481	C₂²×C₇	semidirect
312. #479	C₂²×C₇	semidirect
313. #478	C₂²×C₇	semidirect
314. #476	C₂²×C₇	semidirect
315. #475	C₂²×C₇	semidirect
316. #470	C₂²×C₇	semidirect
317. #469	C₂²×C₇	semidirect
322. #465	C₂²×C₇	semidirect
323. #442	C₂²×C₇	semidirect
324. #441	C₂²×C₇	semidirect
325. C₄×SD₁₆	C₂²×C₇	semidirect
330. #428	C₂²×C₇	semidirect
332. #427	C₂²×C₇	semidirect
338. C₂×#106	C₂²×C₇	semidirect
562. C₂×C₈	C₇×#41	semidirect
657. C₇	#61259	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×#3492	2
C₇×#3345	2
C₇×#3344	2
C₇×#3337	2
C₇×#3335	2
C₇×#3163	2
C₇×#3099	2
C₇×#3092	2
C₇×#3084	2
C₇×#3060	2
C₇×#3050	2
C₇×#2952	2
C₇×#2929	2
C₇×#2912	2
C₂²×C₇×#106	2
#61259	7

Subgroups — C7×#61259 #13238475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61259 #13238475