Subgroups — C₇×#61267 #13238483

Order 1792.

1870 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3494	C₂	1	2	yes	maximal, complemented
2	C₇×#3355	C₂	1	4	yes	maximal, complemented
3	C₇×#3354	C₂	1	4	yes	maximal, complemented
4	C₇×#3347	C₂	1	4	yes	maximal, complemented
5	C₇×#3345	C₂	1	4	yes	maximal, complemented
6	C₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3096	C₂	1	2	yes	maximal, complemented
8	C₇×#3094	C₂	1	2	yes	maximal, complemented
9	C₇×#3081	C₂	1	2	yes	maximal, complemented
10	C₇×#3058	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2912	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×#131	C₂²	1	1	yes	characteristic
18	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
19	C₇×#555	C₂²	1	4	yes	complemented
20	C₇×#553	C₂²	1	4	yes	complemented
21	C₇×#553	C₂²	1	4	yes	complemented
22	C₇×#551	—	2	4	no	—
23	C₇×#547	C₂²	1	4	yes	complemented
24	C₇×#546	—	2	4	no	—
25	C₇×#544	C₂²	1	2	yes	—
26	C₇×#542	—	2	2	no	—
27	C₇×#540	—	2	2	no	—
28	C₇×#535	C₂²	1	2	yes	—
29	C₇×#532	—	2	2	no	—
30	C₇×#529	—	2	2	no	—
31	C₇×#525	C₂²	1	1	yes	characteristic
32	C₂×C₇×#121	C₂²	1	2	yes	—
33	C₇×#520	C₂²	1	2	yes	—
34	C₇×#518	C₂²	1	2	yes	—
35	C₂×C₇×#117	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×#482	C₂²	1	4	yes	complemented
40	C₇×#482	C₂²	1	4	yes	complemented
41	C₇×#482	C₂²	1	4	yes	complemented
42	C₇×#482	C₂²	1	4	yes	complemented
43	C₇×#481	C₂²	1	4	yes	complemented
44	C₇×#481	C₂²	1	4	yes	complemented
45	C₇×#480	C₂²	1	4	yes	complemented
46	C₇×#480	C₂²	1	4	yes	complemented
47	C₇×#478	C₂²	1	4	yes	complemented
48	C₇×#478	C₂²	1	4	yes	complemented
49	C₇×#476	C₂²	1	4	yes	complemented
50	C₇×#474	C₂²	1	4	yes	complemented
51	C₇×#469	C₂²	1	4	yes	—
52	C₇×#469	C₂²	1	4	yes	—
53	C₇×#469	C₂²	1	2	yes	complemented
54	C₇×#469	C₂²	1	2	yes	complemented
55	C₇×#466	C₂²	1	4	yes	complemented
56	C₇×#442	C₂²	1	2	yes	complemented
57	C₇×#442	C₂²	1	2	yes	complemented
58	C₄×C₇×D₈	C₂²	1	4	yes	complemented
59	C₇×#436	C₂²	1	4	yes	complemented
60	C₇×#435	C₂²	1	4	yes	complemented
61	C₇×#428	C₂²	1	2	yes	—
62	C₇×#428	C₂²	1	2	yes	—
63	C₇×#428	C₂²	1	2	yes	complemented
64	C₇×#428	C₂²	1	2	yes	complemented
65	C₇×#428	C₂²	1	2	yes	complemented
66	C₇×#428	C₂²	1	2	yes	complemented
67	C₇×#428	C₂²	1	4	yes	complemented
68	C₇×#427	C₂²	1	1	yes	characteristic
69	C₇×#427	C₂²	1	1	yes	characteristic
70	C₇×#427	C₂²	1	2	yes	—
71	C₇×#427	C₂²	1	2	yes	complemented
72	C₂×C₇×#106	C₂²	1	1	yes	characteristic
73	C₂×C₇×#106	C₂²	1	2	yes	complemented
74	C₇×#424	C₂²	1	1	yes	characteristic
75	C₇×#418	C₂²	1	2	yes	—
76	C₇×#418	C₂²	1	2	yes	—
77	C₂×C₇×#102	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	#61267	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂×C₇×#41	—	2	4	no	—
83	C₂×C₇×#41	C₂³	1	1	yes	characteristic
84	C₂²×C₇×D₄	—	2	2	no	—
85	C₂²×C₇×D₄	C₂³	1	2	yes	—
86	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₇×D₈	—	2	4	no	—
88	C₂×C₇×D₈	C₂³	1	2	yes	—
89	C₂×C₇×D₈	C₂³	1	2	yes	—
90	C₇×#131	—	2	4	no	—
91	C₂×C₇×M₁₆	—	2	4	no	—
92	C₂×C₇×M₁₆	C₂³	1	2	yes	—
93	C₂×C₇×M₁₆	C₂³	1	2	yes	—
94	C₂×C₇×M₁₆	C₂³	1	2	yes	—
95	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
97	C₂²×C₇×C₈	C₂³	1	2	yes	—
98	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
99	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
100	C₇×C₄⋊Q₈	—	2	2	no	—
101	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₇×#127	—	2	2	no	—
103	C₇×#126	—	2	4	no	—
104	C₇×#126	—	2	4	no	—
105	C₇×#125	—	2	2	no	—
106	C₇×#125	C₂³	1	4	yes	—
107	C₇×#124	—	2	2	no	—
108	C₇×#124	—	2	4	no	—
109	C₇×#124	—	2	4	no	—
110	C₇×#123	—	2	4	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	4	no	—
116	C₇×C₂²⋊Q₈	—	2	4	no	—
117	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
118	C₇×#121	—	2	4	no	—
119	C₇×#121	—	2	4	no	—
120	C₇×#121	—	2	4	no	—
121	C₇×#121	—	2	2	no	—
122	C₇×#121	—	2	2	no	—
123	C₇×#121	D₄	1	2	yes	—
124	C₇×#121	C₂³	1	4	yes	—
125	C₇×#121	C₂³	1	4	yes	—
126	C₇×#121	C₂³	1	4	yes	—
127	C₇×#121	C₂³	1	4	yes	—
128	C₇×#120	—	2	4	no	—
129	C₇×#120	D₄	1	2	yes	—
130	C₄×C₇×Q₈	—	2	2	no	—
131	C₄×C₇×D₄	—	2	2	no	—
132	C₄×C₇×D₄	—	2	4	no	—
133	C₄×C₇×D₄	—	2	2	no	—
134	C₄×C₇×D₄	—	2	2	no	—
135	C₄×C₇×D₄	—	2	4	no	—
136	C₄×C₇×D₄	—	2	4	no	—
137	C₄×C₇×D₄	C₂³	1	4	yes	—
138	C₄×C₇×D₄	C₂³	1	4	yes	—
139	C₄×C₇×D₄	C₂³	1	4	yes	—
140	C₇×#117	—	2	2	no	—
141	C₇×#117	—	2	2	no	—
142	C₇×#117	—	2	4	no	—
143	C₇×#117	C₂³	1	2	yes	—
144	C₇×#117	C₂³	1	2	yes	—
145	C₇×#117	C₂³	1	4	yes	—
146	C₇×#117	C₂³	1	2	yes	—
147	C₇×#117	C₂³	1	2	yes	—
148	C₇×#117	C₂³	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
154	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
155	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
156	C₂×C₄²×C₇	—	2	2	no	—
157	C₇×#107	C₂³	1	2	yes	—
158	C₇×#107	C₂³	1	2	yes	—
159	C₇×#107	C₂³	1	4	yes	—
160	C₇×#107	C₂³	1	2	yes	—
161	C₇×#107	C₂³	1	4	yes	—
162	C₇×#107	C₂³	1	2	yes	—
163	C₇×#106	C₂³	1	2	yes	—
164	C₇×#106	C₂³	1	2	yes	—
165	C₇×#106	C₂³	1	1	yes	characteristic
166	C₇×#106	C₂³	1	1	yes	characteristic
167	C₇×#106	C₂³	1	2	yes	—
168	C₇×#106	C₂³	1	4	yes	—
169	C₇×#106	C₂³	1	2	yes	—
170	C₇×#106	C₂³	1	4	yes	—
171	C₇×#106	C₂³	1	1	yes	characteristic
172	C₇×#106	C₂³	1	1	yes	characteristic
173	C₇×C₄⋊C₈	C₂³	1	4	yes	—
174	C₇×#102	C₂³	1	4	yes	—
175	C₇×#102	C₂³	1	4	yes	—
176	C₇×#102	C₂³	1	4	yes	—
177	C₇×#102	C₂³	1	4	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	#3494	C₂×C₇	1	2	yes	complemented
185	#3355	C₂×C₇	1	4	yes	complemented
186	#3354	C₂×C₇	1	4	yes	complemented
187	#3347	C₂×C₇	1	4	yes	complemented
188	#3345	C₂×C₇	1	4	yes	complemented
189	#3163	C₂×C₇	1	1	yes	characteristic, complemented
190	#3096	C₂×C₇	1	2	yes	complemented
191	#3094	C₂×C₇	1	2	yes	complemented
192	#3081	C₂×C₇	1	2	yes	complemented
193	#3058	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#469	C₂×C₇	1	1	yes	characteristic, complemented
195	#2948	C₂×C₇	1	1	yes	characteristic, complemented
196	#2930	C₂×C₇	1	1	yes	characteristic, complemented
197	#2912	C₂×C₇	1	1	yes	characteristic, complemented
198	#2911	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂⁴×C₇	—	2	2	no	—
200	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
201	C₇×#41	—	2	2	no	—
202	C₇×#41	—	2	2	no	—
203	C₇×#41	—	8	8	no	—
204	C₂×C₇×Q₈	—	2	4	no	—
205	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₇×D₄	—	2	4	no	—
207	C₂×C₇×D₄	—	2	4	no	—
208	C₂×C₇×D₄	—	2	4	no	—
209	C₂×C₇×D₄	—	2	4	no	—
210	C₂×C₇×D₄	—	2	2	no	—
211	C₂×C₇×D₄	—	2	4	no	—
212	C₂×C₇×D₄	—	2	4	no	—
213	C₂×C₇×D₄	—	8	4	no	—
214	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
215	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
216	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
217	C₂×C₇×D₄	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₇	—	2	2	no	—
219	C₂²×C₄×C₇	—	2	2	no	—
220	C₂²×C₄×C₇	—	2	2	no	—
221	C₂²×C₄×C₇	—	2	2	no	—
222	C₂²×C₄×C₇	—	2	2	no	—
223	C₂²×C₄×C₇	—	2	4	no	—
224	C₂²×C₄×C₇	—	2	4	no	—
225	C₂²×C₄×C₇	—	2	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×D₈	—	2	4	no	—
232	C₇×D₈	—	2	4	no	—
233	C₇×M₁₆	—	2	2	no	—
234	C₇×M₁₆	—	2	2	no	—
235	C₇×M₁₆	—	2	4	no	—
236	C₇×M₁₆	—	2	4	no	—
237	C₇×M₁₆	—	2	4	no	—
238	C₂×C₇×C₈	—	2	2	no	—
239	C₂×C₇×C₈	—	2	4	no	—
240	C₂×C₇×C₈	#41	1	4	yes	complemented
241	C₂×C₇×C₈	C₂⁴	1	2	yes	—
242	C₂×C₇×C₈	C₂⁴	1	2	yes	—
243	C₂×C₇×C₈	C₂⁴	1	2	yes	—
244	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
245	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
246	C₇×C₄⋊C₄	—	2	2	no	—
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	C₂×D₄	1	4	yes	—
254	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
255	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
256	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
257	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
258	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
259	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
260	C₇×C₂²⋊C₄	—	2	2	no	—
261	C₇×C₂²⋊C₄	—	2	2	no	—
262	C₇×C₂²⋊C₄	—	2	2	no	—
263	C₇×C₂²⋊C₄	—	2	2	no	—
264	C₇×C₂²⋊C₄	—	2	4	no	—
265	C₇×C₂²⋊C₄	—	2	4	no	—
266	C₇×C₂²⋊C₄	—	2	4	no	—
267	C₇×C₂²⋊C₄	—	2	4	no	—
268	C₇×C₂²⋊C₄	—	2	4	no	—
269	C₇×C₂²⋊C₄	—	2	4	no	—
270	C₇×C₂²⋊C₄	—	2	4	no	—
271	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
272	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
273	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
274	C₄²×C₇	—	2	2	no	—
275	C₄²×C₇	—	2	2	no	—
276	C₄²×C₇	—	2	2	no	—
277	C₄²×C₇	—	2	2	no	—
278	C₄²×C₇	—	2	4	no	—
279	C₄²×C₇	C₂⁴	1	2	yes	—
280	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
281	C₂×#131	C₂²×C₇	1	1	yes	characteristic
282	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
283	#555	C₂²×C₇	1	4	yes	complemented
284	#553	C₂²×C₇	1	4	yes	complemented
285	#553	C₂²×C₇	1	4	yes	complemented
286	#551	—	2	4	no	—
287	#547	C₂²×C₇	1	4	yes	complemented
288	#546	—	2	4	no	—
289	#544	C₂²×C₇	1	2	yes	—
290	#542	—	2	2	no	—
291	#540	—	2	2	no	—
292	#535	C₂²×C₇	1	2	yes	—
293	#532	—	2	2	no	—
294	#529	—	2	2	no	—
295	#525	C₂²×C₇	1	1	yes	characteristic
296	C₂×#121	C₂²×C₇	1	2	yes	—
297	#520	C₂²×C₇	1	2	yes	—
298	#518	C₂²×C₇	1	2	yes	—
299	C₂×#117	C₂²×C₇	1	2	yes	—
300	#501	C₂²×C₇	1	4	yes	complemented
301	#499	C₂²×C₇	1	2	yes	complemented
302	#498	C₂²×C₇	1	2	yes	complemented
303	#482	C₂²×C₇	1	4	yes	complemented
304	#482	C₂²×C₇	1	4	yes	complemented
305	#482	C₂²×C₇	1	4	yes	complemented
306	#482	C₂²×C₇	1	4	yes	complemented
307	#481	C₂²×C₇	1	4	yes	complemented
308	#481	C₂²×C₇	1	4	yes	complemented
309	#480	C₂²×C₇	1	4	yes	complemented
310	#480	C₂²×C₇	1	4	yes	complemented
311	#478	C₂²×C₇	1	4	yes	complemented
312	#478	C₂²×C₇	1	4	yes	complemented
313	#476	C₂²×C₇	1	4	yes	complemented
314	#474	C₂²×C₇	1	4	yes	complemented
315	#469	C₂²×C₇	1	4	yes	—
316	#469	C₂²×C₇	1	4	yes	—
317	#469	C₂²×C₇	1	2	yes	complemented
318	#469	C₂²×C₇	1	2	yes	complemented
319	#466	C₂²×C₇	1	4	yes	complemented
320	#442	C₂²×C₇	1	2	yes	complemented
321	#442	C₂²×C₇	1	2	yes	complemented
322	C₄×D₈	C₂²×C₇	1	4	yes	complemented
323	#436	C₂²×C₇	1	4	yes	complemented
324	#435	C₂²×C₇	1	4	yes	complemented
325	#428	C₂²×C₇	1	2	yes	—
326	#428	C₂²×C₇	1	2	yes	—
327	#428	C₂²×C₇	1	2	yes	complemented
328	#428	C₂²×C₇	1	2	yes	complemented
329	#428	C₂²×C₇	1	2	yes	complemented
330	#428	C₂²×C₇	1	4	yes	complemented
331	#428	C₂²×C₇	1	2	yes	complemented
332	#427	C₂²×C₇	1	2	yes	—
333	#427	C₂²×C₇	1	1	yes	characteristic
334	#427	C₂²×C₇	1	1	yes	characteristic
335	#427	C₂²×C₇	1	2	yes	complemented
336	C₂×#106	C₂²×C₇	1	1	yes	characteristic
337	C₂×#106	C₂²×C₇	1	2	yes	complemented
338	#424	C₂²×C₇	1	1	yes	characteristic
339	#418	C₂²×C₇	1	2	yes	—
340	#418	C₂²×C₇	1	2	yes	—
341	C₂×#102	C₂²×C₇	1	2	yes	—
342	#408	C₂²×C₇	1	1	yes	characteristic
343	#407	C₂²×C₇	1	1	yes	characteristic
344	#405	C₂²×C₇	1	1	yes	characteristic
345	C₂³×C₇	—	2	2	no	—
346	C₂³×C₇	—	2	4	no	—
347	C₂³×C₇	—	4	2	no	—
348	C₂³×C₇	—	4	4	no	—
349	C₂³×C₇	—	8	2	no	—
350	C₂³×C₇	—	8	2	no	—
351	C₂³×C₇	C₂²×D₄	1	2	yes	—
352	C₂³×C₇	C₂²×D₄	1	2	yes	—
353	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
354	C₇×Q₈	—	2	2	no	—
355	C₇×Q₈	—	8	4	no	—
356	C₇×D₄	—	2	4	no	—
357	C₇×D₄	—	2	2	no	—
358	C₇×D₄	—	2	4	no	—
359	C₇×D₄	—	2	4	no	—
360	C₇×D₄	—	4	4	no	—
361	C₇×D₄	—	4	8	no	—
362	C₇×D₄	—	4	4	no	—
363	C₇×D₄	—	8	4	no	—
364	C₇×D₄	—	8	4	no	—
365	C₇×D₄	—	8	4	no	—
366	C₂×C₄×C₇	—	2	2	no	—
367	C₂×C₄×C₇	—	2	4	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	2	no	—
374	C₂×C₄×C₇	—	2	2	no	—
375	C₂×C₄×C₇	—	2	2	no	—
376	C₂×C₄×C₇	—	2	4	no	—
377	C₂×C₄×C₇	—	4	4	no	—
378	C₂×C₄×C₇	—	8	4	no	—
379	C₂×C₄×C₇	—	8	4	no	—
380	C₂×C₄×C₇	—	8	2	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	2	yes	—
385	C₂×C₄×C₇	C₂²×D₄	1	4	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	1	yes	characteristic
397	C₂²×D₄	—	2	2	no	—
398	C₂²×D₄	C₂³×C₇	1	2	yes	—
399	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
400	C₂×D₈	—	2	4	no	—
401	C₂×D₈	C₂³×C₇	1	2	yes	—
402	C₂×D₈	C₂³×C₇	1	2	yes	—
403	#131	—	2	4	no	—
404	C₂×M₁₆	—	2	4	no	—
405	C₂×M₁₆	C₂³×C₇	1	2	yes	—
406	C₂×M₁₆	C₂³×C₇	1	2	yes	—
407	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
408	C₂×M₁₆	C₂³×C₇	1	2	yes	—
409	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₇	1	2	yes	—
412	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
413	C₄⋊Q₈	—	2	2	no	—
414	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
415	#127	—	2	2	no	—
416	#126	—	2	4	no	—
417	#126	—	2	4	no	—
418	#125	—	2	2	no	—
419	#125	C₂³×C₇	1	4	yes	—
420	#124	—	2	2	no	—
421	#124	—	2	4	no	—
422	#124	—	2	4	no	—
423	#123	—	2	4	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	4	no	—
429	C₂²⋊Q₈	—	2	4	no	—
430	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
431	#121	—	2	4	no	—
432	#121	—	2	4	no	—
433	#121	—	2	4	no	—
434	#121	—	2	2	no	—
435	#121	—	2	2	no	—
436	#121	C₇×D₄	1	2	yes	—
437	#121	C₂³×C₇	1	4	yes	—
438	#121	C₂³×C₇	1	4	yes	—
439	#121	C₂³×C₇	1	4	yes	—
440	#121	C₂³×C₇	1	4	yes	—
441	#120	—	2	4	no	—
442	#120	C₇×D₄	1	2	yes	—
443	C₄×Q₈	—	2	2	no	—
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	—	2	4	no	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	2	2	no	—
448	C₄×D₄	—	2	4	no	—
449	C₄×D₄	—	2	4	no	—
450	C₄×D₄	C₂³×C₇	1	4	yes	—
451	C₄×D₄	C₂³×C₇	1	4	yes	—
452	C₄×D₄	C₂³×C₇	1	4	yes	—
453	#117	—	2	2	no	—
454	#117	—	2	2	no	—
455	#117	—	2	4	no	—
456	#117	C₂³×C₇	1	2	yes	—
457	#117	C₂³×C₇	1	2	yes	—
458	#117	C₂³×C₇	1	2	yes	—
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	C₂³×C₇	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
466	C₂×C₂²⋊C₄	—	2	2	no	—
467	C₂×C₂²⋊C₄	—	2	2	no	—
468	C₂×C₂²⋊C₄	—	2	4	no	—
469	C₂×C₄²	—	2	2	no	—
470	#107	C₂³×C₇	1	2	yes	—
471	#107	C₂³×C₇	1	2	yes	—
472	#107	C₂³×C₇	1	2	yes	—
473	#107	C₂³×C₇	1	2	yes	—
474	#107	C₂³×C₇	1	4	yes	—
475	#107	C₂³×C₇	1	4	yes	—
476	#106	C₂³×C₇	1	2	yes	—
477	#106	C₂³×C₇	1	2	yes	—
478	#106	C₂³×C₇	1	1	yes	characteristic
479	#106	C₂³×C₇	1	4	yes	—
480	#106	C₂³×C₇	1	1	yes	characteristic
481	#106	C₂³×C₇	1	1	yes	characteristic
482	#106	C₂³×C₇	1	1	yes	characteristic
483	#106	C₂³×C₇	1	2	yes	—
484	#106	C₂³×C₇	1	2	yes	—
485	#106	C₂³×C₇	1	4	yes	—
486	C₄⋊C₈	C₂³×C₇	1	4	yes	—
487	#102	C₂³×C₇	1	4	yes	—
488	#102	C₂³×C₇	1	4	yes	—
489	#102	C₂³×C₇	1	4	yes	—
490	#102	C₂³×C₇	1	4	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	2	no	—
498	C₂²×C₇	—	2	2	no	—
499	C₂²×C₇	—	2	4	no	—
500	C₂²×C₇	—	2	2	no	—
501	C₂²×C₇	—	2	2	no	—
502	C₂²×C₇	—	2	2	no	—
503	C₂²×C₇	—	4	4	no	—
504	C₂²×C₇	—	4	4	no	—
505	C₂²×C₇	—	4	4	no	—
506	C₂²×C₇	—	8	2	no	—
507	C₂²×C₇	—	16	4	no	—
508	C₂²×C₇	#547	1	2	yes	—
509	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
510	C₄×C₇	—	2	4	no	—
511	C₄×C₇	—	2	2	no	—
512	C₄×C₇	—	2	2	no	—
513	C₄×C₇	—	4	2	no	—
514	C₄×C₇	—	4	2	no	—
515	C₄×C₇	—	4	2	no	—
516	C₄×C₇	—	4	4	no	—
517	C₄×C₇	—	4	2	no	—
518	C₄×C₇	#547	1	2	yes	—
519	C₄×C₇	C₂²×#41	1	1	yes	characteristic
520	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
521	C₂⁴	—	2	2	no	—
522	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	8	8	no	—
526	C₂×Q₈	—	2	4	no	—
527	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	8	4	no	—
536	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
537	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
538	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
539	C₂×D₄	C₂⁴×C₇	1	4	yes	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
549	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
553	D₈	—	2	4	no	—
554	D₈	—	2	4	no	—
555	M₁₆	—	2	2	no	—
556	M₁₆	—	2	2	no	—
557	M₁₆	—	2	4	no	—
558	M₁₆	—	2	4	no	—
559	M₁₆	—	2	4	no	—
560	C₂×C₈	—	2	2	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	2	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	C₂×C₇×D₄	1	4	yes	—
576	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
577	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
578	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
579	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
580	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
581	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
594	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
595	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
596	C₄²	—	2	2	no	—
597	C₄²	—	2	2	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	2	no	—
600	C₄²	—	2	4	no	—
601	C₄²	C₂⁴×C₇	1	2	yes	—
602	C₂×C₇	—	2	2	no	—
603	C₂×C₇	—	4	2	no	—
604	C₂×C₇	—	4	2	no	—
605	C₂×C₇	—	8	4	no	—
606	C₂×C₇	C₂×#547	1	1	yes	characteristic
607	C₂×C₇	#3585	1	2	yes	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	4	no	—
610	C₂³	—	4	2	no	—
611	C₂³	—	4	4	no	—
612	C₂³	—	8	2	no	—
613	C₂³	—	8	2	no	—
614	C₂³	C₂²×C₇×D₄	1	2	yes	—
615	C₂³	C₂²×C₇×D₄	1	2	yes	—
616	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
617	Q₈	—	2	2	no	—
618	Q₈	—	8	4	no	—
619	D₄	—	2	4	no	—
620	D₄	—	2	4	no	—
621	D₄	—	2	4	no	—
622	D₄	—	2	2	no	—
623	D₄	—	4	4	no	—
624	D₄	—	4	8	no	—
625	D₄	—	4	4	no	—
626	D₄	—	8	4	no	—
627	D₄	—	8	4	no	—
628	D₄	—	8	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	8	4	no	—
642	C₂×C₄	—	8	4	no	—
643	C₂×C₄	—	8	2	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	—	8	4	no	—
646	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
647	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
648	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
649	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
650	C₂×C₄	C₂×C₇×#41	1	2	yes	—
651	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
652	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
653	C₈	—	2	2	no	—
654	C₈	—	2	2	no	—
655	C₈	—	2	2	no	—
656	C₈	C₂×C₇×#41	1	2	yes	—
657	C₈	C₂×C₇×#41	1	2	yes	—
658	C₇	#61267	1	1	yes	characteristic, direct product factor, Sylow
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	4	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	8	2	no	—
669	C₂²	—	16	4	no	—
670	C₂²	C₇×#547	1	2	yes	—
671	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
672	C₄	—	2	4	no	—
673	C₄	—	2	2	no	—
674	C₄	—	2	2	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	2	no	—
678	C₄	—	4	4	no	—
679	C₄	—	4	2	no	—
680	C₄	C₇×#547	1	2	yes	—
681	C₄	C₂²×C₇×#41	1	1	yes	characteristic
682	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
683	C₂	—	2	2	no	—
684	C₂	—	4	2	no	—
685	C₂	—	4	2	no	—
686	C₂	—	8	4	no	—
687	C₂	C₂×C₇×#547	1	1	yes	characteristic
688	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 ◁ C₇×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3494	C₂	semidirect
2. C₇×#3355	C₂	semidirect
3. C₇×#3354	C₂	semidirect
4. C₇×#3347	C₂	semidirect
5. C₇×#3345	C₂	semidirect
6. C₇×#3163	C₂	semidirect
7. C₇×#3096	C₂	semidirect
8. C₇×#3094	C₂	semidirect
9. C₇×#3081	C₂	semidirect
10. C₇×#3058	C₂	semidirect
11. C₂×C₇×#469	C₂	semidirect
12. C₇×#2948	C₂	semidirect
13. C₇×#2930	C₂	semidirect
14. C₇×#2912	C₂	semidirect
15. C₇×#2911	C₂	semidirect
19. C₇×#555	C₂²	semidirect
20. C₇×#553	C₂²	semidirect
21. C₇×#553	C₂²	semidirect
23. C₇×#547	C₂²	semidirect
36. C₇×#501	C₂²	semidirect
37. C₇×#499	C₂²	semidirect
38. C₇×#498	C₂²	semidirect
39. C₇×#482	C₂²	semidirect
40. C₇×#482	C₂²	semidirect
41. C₇×#482	C₂²	semidirect
42. C₇×#482	C₂²	semidirect
43. C₇×#481	C₂²	semidirect
44. C₇×#481	C₂²	semidirect
45. C₇×#480	C₂²	semidirect
46. C₇×#480	C₂²	semidirect
47. C₇×#478	C₂²	semidirect
48. C₇×#478	C₂²	semidirect
49. C₇×#476	C₂²	semidirect
50. C₇×#474	C₂²	semidirect
53. C₇×#469	C₂²	semidirect
54. C₇×#469	C₂²	semidirect
55. C₇×#466	C₂²	semidirect
56. C₇×#442	C₂²	semidirect
57. C₇×#442	C₂²	semidirect
58. C₄×C₇×D₈	C₂²	semidirect
59. C₇×#436	C₂²	semidirect
60. C₇×#435	C₂²	semidirect
63. C₇×#428	C₂²	semidirect
64. C₇×#428	C₂²	semidirect
65. C₇×#428	C₂²	semidirect
66. C₇×#428	C₂²	semidirect
67. C₇×#428	C₂²	semidirect
71. C₇×#427	C₂²	semidirect
73. C₂×C₇×#106	C₂²	semidirect
81. #61267	C₇	direct (N × H)
184. #3494	C₂×C₇	semidirect
185. #3355	C₂×C₇	semidirect
186. #3354	C₂×C₇	semidirect
187. #3347	C₂×C₇	semidirect
188. #3345	C₂×C₇	semidirect
189. #3163	C₂×C₇	semidirect
190. #3096	C₂×C₇	semidirect
191. #3094	C₂×C₇	semidirect
192. #3081	C₂×C₇	semidirect
193. #3058	C₂×C₇	semidirect
194. C₂×#469	C₂×C₇	semidirect
195. #2948	C₂×C₇	semidirect
196. #2930	C₂×C₇	semidirect
197. #2912	C₂×C₇	semidirect
198. #2911	C₂×C₇	semidirect
240. C₂×C₇×C₈	#41	semidirect
283. #555	C₂²×C₇	semidirect
284. #553	C₂²×C₇	semidirect
285. #553	C₂²×C₇	semidirect
287. #547	C₂²×C₇	semidirect
300. #501	C₂²×C₇	semidirect
301. #499	C₂²×C₇	semidirect
302. #498	C₂²×C₇	semidirect
303. #482	C₂²×C₇	semidirect
304. #482	C₂²×C₇	semidirect
305. #482	C₂²×C₇	semidirect
306. #482	C₂²×C₇	semidirect
307. #481	C₂²×C₇	semidirect
308. #481	C₂²×C₇	semidirect
309. #480	C₂²×C₇	semidirect
310. #480	C₂²×C₇	semidirect
311. #478	C₂²×C₇	semidirect
312. #478	C₂²×C₇	semidirect
313. #476	C₂²×C₇	semidirect
314. #474	C₂²×C₇	semidirect
317. #469	C₂²×C₇	semidirect
318. #469	C₂²×C₇	semidirect
319. #466	C₂²×C₇	semidirect
320. #442	C₂²×C₇	semidirect
321. #442	C₂²×C₇	semidirect
322. C₄×D₈	C₂²×C₇	semidirect
323. #436	C₂²×C₇	semidirect
324. #435	C₂²×C₇	semidirect
327. #428	C₂²×C₇	semidirect
328. #428	C₂²×C₇	semidirect
329. #428	C₂²×C₇	semidirect
330. #428	C₂²×C₇	semidirect
331. #428	C₂²×C₇	semidirect
335. #427	C₂²×C₇	semidirect
337. C₂×#106	C₂²×C₇	semidirect
562. C₂×C₈	C₇×#41	semidirect
658. C₇	#61267	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×#3494	2
C₇×#3355	2
C₇×#3354	2
C₇×#3347	2
C₇×#3345	2
C₇×#3163	2
C₇×#3096	2
C₇×#3094	2
C₇×#3081	2
C₇×#3058	2
C₂×C₇×#469	2
C₇×#2948	2
C₇×#2930	2
C₇×#2912	2
C₇×#2911	2
#61267	7

Subgroups — C7×#61267 #13238483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61267 #13238483