Subgroups — C₇×#18745 #13195961

Order 1792.

818 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×#3555	C₂	1	1	yes	maximal, characteristic
2	C₇×#3249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3233	C₂	1	1	yes	maximal, characteristic
4	C₇×#3185	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1652	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1645	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1644	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1638	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1636	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1633	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1485	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1483	C₂	1	1	yes	maximal, characteristic
16	C₇×#563	—	2	2	no	—
17	C₇×Q₈²	C₂²	1	1	yes	characteristic
18	C₇×#557	—	2	1	no	—
19	C₇×#557	C₂²	1	1	yes	characteristic
20	C₇×#556	—	2	1	no	—
21	C₇×#556	—	2	1	no	—
22	C₇×#556	C₂²	1	1	yes	characteristic
23	C₇×#554	C₂²	1	1	yes	characteristic
24	C₇×#552	—	2	1	no	—
25	C₇×#544	—	2	1	no	—
26	C₇×#542	—	2	1	no	—
27	C₇×#541	—	2	1	no	—
28	C₇×#541	—	2	1	no	—
29	C₇×#541	—	2	2	no	—
30	C₇×#533	C₂²	1	1	yes	characteristic
31	C₇×#533	C₂²	1	1	yes	characteristic
32	C₇×#533	C₂²	1	1	yes	characteristic
33	C₇×#529	C₂²	1	1	yes	characteristic
34	C₇×#499	—	2	1	no	—
35	C₇×#498	C₂²	1	1	yes	characteristic
36	C₇×#494	C₂²	1	1	yes	characteristic
37	C₇×#488	—	2	1	no	—
38	C₇×#487	C₂²	1	1	yes	characteristic
39	C₇×#487	C₂²	1	1	yes	characteristic
40	C₇×#485	—	2	1	no	—
41	C₇×#482	—	2	1	no	—
42	C₇×#477	—	2	1	no	—
43	C₇×#477	C₂²	1	1	yes	characteristic
44	C₇×#477	C₂²	1	1	yes	characteristic
45	C₇×#477	C₂²	1	1	yes	characteristic
46	C₇×#476	C₂²	1	1	yes	characteristic
47	C₇×#475	C₂²	1	1	yes	characteristic
48	C₇×#474	C₂²	1	1	yes	characteristic
49	C₇×#470	—	2	2	no	—
50	C₇×#467	—	2	1	no	—
51	C₇×#467	—	2	1	no	—
52	C₇×#462	—	2	1	no	—
53	C₇×#462	C₂²	1	1	yes	characteristic
54	C₇×#462	C₂²	1	1	yes	characteristic
55	C₇×#441	—	2	2	no	—
56	C₇×#431	C₂²	1	1	yes	characteristic
57	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
59	C₇×#333	C₂²	1	1	yes	characteristic
60	C₇×#333	C₂²	1	1	yes	characteristic
61	C₇×#332	C₂²	1	1	yes	characteristic
62	C₇×#332	C₂²	1	1	yes	characteristic
63	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
69	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	#18745	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₇×Q₁₆	—	2	2	no	—
73	C₂×C₇×Q₁₆	—	2	1	no	—
74	C₂×C₇×Q₁₆	—	2	1	no	—
75	C₂×C₇×M₁₆	—	2	1	no	—
76	C₂²×C₇×C₈	—	2	1	no	—
77	C₇×C₄⋊Q₈	—	2	2	no	—
78	C₇×C₄⋊Q₈	—	2	1	no	—
79	C₇×C₄⋊Q₈	—	2	2	no	—
80	C₇×C₄⋊Q₈	—	2	1	no	—
81	C₇×C₄⋊Q₈	—	2	1	no	—
82	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
83	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
84	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₇×#126	—	2	2	no	—
89	C₇×#126	—	2	2	no	—
90	C₇×#126	—	2	2	no	—
91	C₇×#126	—	2	2	no	—
92	C₇×#126	—	2	2	no	—
93	C₇×#126	—	2	2	no	—
94	C₇×#126	—	2	1	no	—
95	C₇×#125	—	2	2	no	—
96	C₇×#125	—	2	2	no	—
97	C₇×#125	—	2	2	no	—
98	C₇×#125	—	2	2	no	—
99	C₇×#125	—	2	1	no	—
100	C₇×#125	—	2	2	no	—
101	C₇×#125	—	2	1	no	—
102	C₇×#125	—	2	1	no	—
103	C₇×#125	—	2	1	no	—
104	C₇×#125	—	2	1	no	—
105	C₇×#125	D₄	1	1	yes	characteristic
106	C₇×#124	—	2	2	no	—
107	C₇×#124	—	2	1	no	—
108	C₇×#124	D₄	1	1	yes	characteristic
109	C₇×#123	—	2	2	no	—
110	C₇×#123	—	2	1	no	—
111	C₇×C₂²⋊Q₈	—	2	2	no	—
112	C₇×C₂²⋊Q₈	—	2	2	no	—
113	C₇×C₂²⋊Q₈	—	2	1	no	—
114	C₇×C₂²⋊Q₈	—	2	1	no	—
115	C₇×C₂²⋊Q₈	—	2	2	no	—
116	C₇×C₂²⋊Q₈	—	2	1	no	—
117	C₇×C₂²⋊Q₈	—	2	1	no	—
118	C₇×C₂²⋊Q₈	—	2	1	no	—
119	C₇×C₂²⋊Q₈	—	2	1	no	—
120	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
121	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
122	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
123	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
124	C₇×#121	D₄	1	1	yes	characteristic
125	C₄×C₇×Q₈	—	2	2	no	—
126	C₄×C₇×Q₈	—	2	1	no	—
127	C₄×C₇×Q₈	—	2	1	no	—
128	C₄×C₇×Q₈	—	2	1	no	—
129	C₄×C₇×Q₈	—	2	1	no	—
130	C₄×C₇×Q₈	—	2	1	no	—
131	C₄×C₇×Q₈	—	2	1	no	—
132	C₄×C₇×Q₈	—	2	1	no	—
133	C₄×C₇×Q₈	—	2	1	no	—
134	C₄×C₇×Q₈	—	2	1	no	—
135	C₄×C₇×Q₈	D₄	1	2	yes	—
136	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
137	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
138	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
139	C₄×C₇×D₄	—	2	1	no	—
140	C₄×C₇×D₄	—	2	1	no	—
141	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
142	C₇×#117	—	2	2	no	—
143	C₇×#117	—	2	1	no	—
144	C₇×#117	—	2	1	no	—
145	C₇×#117	—	2	1	no	—
146	C₇×#117	—	2	1	no	—
147	C₇×#117	—	2	1	no	—
148	C₂×C₇×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
150	C₇×#107	—	2	1	no	—
151	C₇×#107	—	2	1	no	—
152	C₇×#107	—	2	1	no	—
153	C₇×#107	—	2	1	no	—
154	C₇×#106	—	2	2	no	—
155	C₇×#106	—	2	1	no	—
156	C₇×#106	—	2	1	no	—
157	C₇×C₄⋊C₈	—	2	1	no	—
158	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₇×#103	—	2	1	no	—
163	C₇×#103	—	2	1	no	—
164	C₇×#103	—	2	2	no	—
165	C₇×#103	—	2	1	no	—
166	C₇×#103	—	2	1	no	—
167	C₇×#103	—	2	1	no	—
168	C₇×#103	—	2	1	no	—
169	C₇×#103	—	2	2	no	—
170	C₇×#102	—	2	1	no	—
171	C₇×#102	—	2	1	no	—
172	C₇×C₂²⋊C₈	—	2	1	no	—
173	C₇×#97	—	2	1	no	—
174	C₄×C₇×C₈	—	2	1	no	—
175	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
176	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
177	#3555	C₂×C₇	1	1	yes	characteristic
178	#3249	C₂×C₇	1	1	yes	characteristic, complemented
179	#3233	C₂×C₇	1	1	yes	characteristic
180	#3185	C₂×C₇	1	1	yes	characteristic, complemented
181	#1653	C₂×C₇	1	1	yes	characteristic, complemented
182	#1652	C₂×C₇	1	1	yes	characteristic, complemented
183	#1645	C₂×C₇	1	1	yes	characteristic, complemented
184	#1644	C₂×C₇	1	1	yes	characteristic, complemented
185	#1638	C₂×C₇	1	1	yes	characteristic, complemented
186	#1636	C₂×C₇	1	1	yes	characteristic, complemented
187	#1633	C₂×C₇	1	1	yes	characteristic, complemented
188	#1632	C₂×C₇	1	1	yes	characteristic, complemented
189	#1542	C₂×C₇	1	1	yes	characteristic, complemented
190	#1485	C₂×C₇	1	1	yes	characteristic, complemented
191	#1483	C₂×C₇	1	1	yes	characteristic
192	C₂×C₇×Q₈	—	2	2	no	—
193	C₂×C₇×Q₈	—	2	1	no	—
194	C₂×C₇×Q₈	—	2	1	no	—
195	C₂×C₇×Q₈	—	2	1	no	—
196	C₂×C₇×Q₈	—	2	1	no	—
197	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
198	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
199	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
200	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
201	C₂×C₇×D₄	—	2	1	no	—
202	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₇	—	2	2	no	—
204	C₂²×C₄×C₇	—	2	1	no	—
205	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
208	C₇×Q₁₆	—	4	4	no	—
209	C₇×Q₁₆	—	8	1	no	—
210	C₇×Q₁₆	—	8	1	no	—
211	C₇×M₁₆	—	4	2	no	—
212	C₂×C₇×C₈	—	2	1	no	—
213	C₂×C₇×C₈	—	2	1	no	—
214	C₂×C₇×C₈	—	2	1	no	—
215	C₂×C₇×C₈	—	2	1	no	—
216	C₂×C₇×C₈	—	2	1	no	—
217	C₂×C₇×C₈	—	2	1	no	—
218	C₂×C₇×C₈	—	8	1	no	—
219	C₇×C₄⋊C₄	—	2	2	no	—
220	C₇×C₄⋊C₄	—	2	2	no	—
221	C₇×C₄⋊C₄	—	2	2	no	—
222	C₇×C₄⋊C₄	—	2	2	no	—
223	C₇×C₄⋊C₄	—	2	2	no	—
224	C₇×C₄⋊C₄	—	2	2	no	—
225	C₇×C₄⋊C₄	—	2	2	no	—
226	C₇×C₄⋊C₄	—	2	2	no	—
227	C₇×C₄⋊C₄	—	2	1	no	—
228	C₇×C₄⋊C₄	—	2	1	no	—
229	C₇×C₄⋊C₄	—	2	1	no	—
230	C₇×C₄⋊C₄	—	2	1	no	—
231	C₇×C₄⋊C₄	—	2	1	no	—
232	C₇×C₄⋊C₄	—	2	1	no	—
233	C₇×C₄⋊C₄	—	2	1	no	—
234	C₇×C₄⋊C₄	—	2	2	no	—
235	C₇×C₄⋊C₄	—	2	1	no	—
236	C₇×C₄⋊C₄	—	2	2	no	—
237	C₇×C₄⋊C₄	—	2	1	no	—
238	C₇×C₄⋊C₄	—	2	1	no	—
239	C₇×C₄⋊C₄	—	2	1	no	—
240	C₇×C₄⋊C₄	—	2	1	no	—
241	C₇×C₄⋊C₄	—	2	1	no	—
242	C₇×C₄⋊C₄	—	2	1	no	—
243	C₇×C₄⋊C₄	—	2	1	no	—
244	C₇×C₄⋊C₄	—	2	1	no	—
245	C₇×C₄⋊C₄	—	2	1	no	—
246	C₇×C₄⋊C₄	—	2	1	no	—
247	C₇×C₄⋊C₄	—	4	1	no	—
248	C₇×C₄⋊C₄	—	4	1	no	—
249	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
250	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
251	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
252	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
253	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
254	C₇×C₂²⋊C₄	—	2	2	no	—
255	C₇×C₂²⋊C₄	—	2	2	no	—
256	C₇×C₂²⋊C₄	—	2	2	no	—
257	C₇×C₂²⋊C₄	—	2	1	no	—
258	C₇×C₂²⋊C₄	—	2	2	no	—
259	C₇×C₂²⋊C₄	—	2	1	no	—
260	C₇×C₂²⋊C₄	—	2	1	no	—
261	C₇×C₂²⋊C₄	—	2	1	no	—
262	C₇×C₂²⋊C₄	—	2	1	no	—
263	C₇×C₂²⋊C₄	—	2	1	no	—
264	C₇×C₂²⋊C₄	—	2	1	no	—
265	C₇×C₂²⋊C₄	—	4	1	no	—
266	C₄²×C₇	—	2	2	no	—
267	C₄²×C₇	—	2	2	no	—
268	C₄²×C₇	—	2	2	no	—
269	C₄²×C₇	—	2	2	no	—
270	C₄²×C₇	—	2	1	no	—
271	C₄²×C₇	—	2	1	no	—
272	C₄²×C₇	—	2	1	no	—
273	C₄²×C₇	—	4	1	no	—
274	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₇	C₂⁴	1	1	yes	characteristic
278	#563	—	2	2	no	—
279	Q₈²	C₂²×C₇	1	1	yes	characteristic
280	#557	—	2	1	no	—
281	#557	C₂²×C₇	1	1	yes	characteristic
282	#556	—	2	1	no	—
283	#556	—	2	1	no	—
284	#556	C₂²×C₇	1	1	yes	characteristic
285	#554	C₂²×C₇	1	1	yes	characteristic
286	#552	—	2	1	no	—
287	#544	—	2	1	no	—
288	#542	—	2	1	no	—
289	#541	—	2	1	no	—
290	#541	—	2	1	no	—
291	#541	—	2	2	no	—
292	#533	C₂²×C₇	1	1	yes	characteristic
293	#533	C₂²×C₇	1	1	yes	characteristic
294	#533	C₂²×C₇	1	1	yes	characteristic
295	#529	C₂²×C₇	1	1	yes	characteristic
296	#499	—	2	1	no	—
297	#498	C₂²×C₇	1	1	yes	characteristic
298	#494	C₂²×C₇	1	1	yes	characteristic
299	#488	—	2	1	no	—
300	#487	C₂²×C₇	1	1	yes	characteristic
301	#487	C₂²×C₇	1	1	yes	characteristic
302	#485	—	2	1	no	—
303	#482	—	2	1	no	—
304	#477	—	2	1	no	—
305	#477	C₂²×C₇	1	1	yes	characteristic
306	#477	C₂²×C₇	1	1	yes	characteristic
307	#477	C₂²×C₇	1	1	yes	characteristic
308	#476	C₂²×C₇	1	1	yes	characteristic
309	#475	C₂²×C₇	1	1	yes	characteristic
310	#474	C₂²×C₇	1	1	yes	characteristic
311	#470	—	2	2	no	—
312	#467	—	2	1	no	—
313	#467	—	2	1	no	—
314	#462	—	2	1	no	—
315	#462	C₂²×C₇	1	1	yes	characteristic
316	#462	C₂²×C₇	1	1	yes	characteristic
317	#441	—	2	2	no	—
318	#431	C₂²×C₇	1	1	yes	characteristic
319	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
320	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
321	#333	C₂²×C₇	1	1	yes	characteristic
322	#333	C₂²×C₇	1	1	yes	characteristic
323	#332	C₂²×C₇	1	1	yes	characteristic
324	#332	C₂²×C₇	1	1	yes	characteristic
325	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
326	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
327	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
328	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
329	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
330	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
331	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
332	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
333	C₂³×C₇	—	2	1	no	—
334	C₂³×C₇	#120	1	1	yes	characteristic
335	C₇×Q₈	—	2	1	no	—
336	C₇×Q₈	—	2	1	no	—
337	C₇×Q₈	—	2	1	no	—
338	C₇×Q₈	—	2	1	no	—
339	C₇×Q₈	—	2	1	no	—
340	C₇×Q₈	—	2	1	no	—
341	C₇×Q₈	—	4	2	no	—
342	C₇×Q₈	—	4	2	no	—
343	C₇×Q₈	—	4	1	no	—
344	C₇×Q₈	—	4	1	no	—
345	C₇×Q₈	—	4	1	no	—
346	C₇×Q₈	—	4	1	no	—
347	C₇×Q₈	—	8	1	no	—
348	C₇×Q₈	—	8	2	no	—
349	C₇×D₄	—	2	1	no	—
350	C₇×D₄	—	2	1	no	—
351	C₇×D₄	—	8	1	no	—
352	C₂×C₄×C₇	—	2	1	no	—
353	C₂×C₄×C₇	—	2	1	no	—
354	C₂×C₄×C₇	—	2	1	no	—
355	C₂×C₄×C₇	—	2	1	no	—
356	C₂×C₄×C₇	—	2	1	no	—
357	C₂×C₄×C₇	—	2	1	no	—
358	C₂×C₄×C₇	—	2	1	no	—
359	C₂×C₄×C₇	—	2	2	no	—
360	C₂×C₄×C₇	—	2	1	no	—
361	C₂×C₄×C₇	—	2	1	no	—
362	C₂×C₄×C₇	—	2	1	no	—
363	C₂×C₄×C₇	—	2	2	no	—
364	C₂×C₄×C₇	—	2	1	no	—
365	C₂×C₄×C₇	—	4	1	no	—
366	C₂×C₄×C₇	—	4	1	no	—
367	C₂×C₄×C₇	—	4	1	no	—
368	C₂×C₄×C₇	—	4	1	no	—
369	C₂×C₄×C₇	—	4	1	no	—
370	C₂×C₄×C₇	—	8	2	no	—
371	C₂×C₄×C₇	#120	1	1	yes	characteristic
372	C₂×C₄×C₇	#120	1	1	yes	characteristic
373	C₂×C₄×C₇	#120	1	1	yes	characteristic
374	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
377	C₇×C₈	—	2	2	no	—
378	C₇×C₈	—	4	1	no	—
379	C₇×C₈	—	4	1	no	—
380	C₇×C₈	—	4	1	no	—
381	C₇×C₈	—	4	1	no	—
382	C₇×C₈	—	4	1	no	—
383	C₂×Q₁₆	—	2	2	no	—
384	C₂×Q₁₆	—	2	1	no	—
385	C₂×Q₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₂²×C₈	—	2	1	no	—
388	C₄⋊Q₈	—	2	2	no	—
389	C₄⋊Q₈	—	2	1	no	—
390	C₄⋊Q₈	—	2	2	no	—
391	C₄⋊Q₈	—	2	1	no	—
392	C₄⋊Q₈	—	2	1	no	—
393	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
394	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
395	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
396	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
397	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
398	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
399	#126	—	2	2	no	—
400	#126	—	2	2	no	—
401	#126	—	2	2	no	—
402	#126	—	2	2	no	—
403	#126	—	2	2	no	—
404	#126	—	2	2	no	—
405	#126	—	2	1	no	—
406	#125	—	2	2	no	—
407	#125	—	2	2	no	—
408	#125	—	2	2	no	—
409	#125	—	2	2	no	—
410	#125	—	2	1	no	—
411	#125	—	2	2	no	—
412	#125	—	2	1	no	—
413	#125	—	2	1	no	—
414	#125	—	2	1	no	—
415	#125	—	2	1	no	—
416	#125	C₇×D₄	1	1	yes	characteristic
417	#124	—	2	2	no	—
418	#124	—	2	1	no	—
419	#124	C₇×D₄	1	1	yes	characteristic
420	#123	—	2	2	no	—
421	#123	—	2	1	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	2	no	—
424	C₂²⋊Q₈	—	2	1	no	—
425	C₂²⋊Q₈	—	2	1	no	—
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	—	2	1	no	—
428	C₂²⋊Q₈	—	2	1	no	—
429	C₂²⋊Q₈	—	2	1	no	—
430	C₂²⋊Q₈	—	2	1	no	—
431	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
432	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
433	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
434	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
435	#121	C₇×D₄	1	1	yes	characteristic
436	C₄×Q₈	—	2	2	no	—
437	C₄×Q₈	—	2	1	no	—
438	C₄×Q₈	—	2	1	no	—
439	C₄×Q₈	—	2	1	no	—
440	C₄×Q₈	—	2	1	no	—
441	C₄×Q₈	—	2	1	no	—
442	C₄×Q₈	—	2	1	no	—
443	C₄×Q₈	—	2	1	no	—
444	C₄×Q₈	—	2	1	no	—
445	C₄×Q₈	—	2	1	no	—
446	C₄×Q₈	C₇×D₄	1	2	yes	—
447	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
448	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
449	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	2	1	no	—
452	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
453	#117	—	2	2	no	—
454	#117	—	2	1	no	—
455	#117	—	2	1	no	—
456	#117	—	2	1	no	—
457	#117	—	2	1	no	—
458	#117	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
461	#107	—	2	1	no	—
462	#107	—	2	1	no	—
463	#107	—	2	1	no	—
464	#107	—	2	1	no	—
465	#106	—	2	2	no	—
466	#106	—	2	1	no	—
467	#106	—	2	1	no	—
468	C₄⋊C₈	—	2	1	no	—
469	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
470	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
471	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
472	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
473	#103	—	2	2	no	—
474	#103	—	2	1	no	—
475	#103	—	2	1	no	—
476	#103	—	2	1	no	—
477	#103	—	2	1	no	—
478	#103	—	2	2	no	—
479	#103	—	2	1	no	—
480	#103	—	2	1	no	—
481	#102	—	2	1	no	—
482	#102	—	2	1	no	—
483	C₂²⋊C₈	—	2	1	no	—
484	#97	—	2	1	no	—
485	C₄×C₈	—	2	1	no	—
486	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
487	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
488	C₂²×C₇	—	2	1	no	—
489	C₂²×C₇	—	2	1	no	—
490	C₂²×C₇	—	2	1	no	—
491	C₂²×C₇	—	4	1	no	—
492	C₂²×C₇	—	4	1	no	—
493	C₂²×C₇	—	4	1	no	—
494	C₂²×C₇	C₂×#120	1	1	yes	characteristic
495	C₄×C₇	—	2	1	no	—
496	C₄×C₇	—	2	1	no	—
497	C₄×C₇	—	2	1	no	—
498	C₄×C₇	—	2	1	no	—
499	C₄×C₇	—	4	1	no	—
500	C₄×C₇	—	4	2	no	—
501	C₄×C₇	—	4	1	no	—
502	C₄×C₇	—	4	1	no	—
503	C₄×C₇	—	4	1	no	—
504	C₄×C₇	—	4	1	no	—
505	C₄×C₇	—	4	2	no	—
506	C₄×C₇	—	4	1	no	—
507	C₄×C₇	—	4	1	no	—
508	C₄×C₇	—	8	1	no	—
509	C₄×C₇	—	8	1	no	—
510	C₄×C₇	#577	1	1	yes	characteristic
511	C₄×C₇	#578	1	1	yes	characteristic
512	C₄×C₇	#578	1	1	yes	characteristic
513	C₄×C₇	#578	1	1	yes	characteristic
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
520	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
521	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
522	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
528	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
529	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
530	Q₁₆	—	4	4	no	—
531	Q₁₆	—	8	1	no	—
532	Q₁₆	—	8	1	no	—
533	M₁₆	—	4	2	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	8	1	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	4	1	no	—
570	C₄⋊C₄	—	4	1	no	—
571	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
572	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
573	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
574	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
575	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	1	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	1	no	—
582	C₂²⋊C₄	—	2	1	no	—
583	C₂²⋊C₄	—	2	1	no	—
584	C₂²⋊C₄	—	2	1	no	—
585	C₂²⋊C₄	—	2	1	no	—
586	C₂²⋊C₄	—	2	1	no	—
587	C₂²⋊C₄	—	4	1	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	4	1	no	—
596	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
597	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
598	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
599	C₄²	C₂⁴×C₇	1	1	yes	characteristic
600	C₂×C₇	—	4	1	no	—
601	C₂×C₇	—	8	1	no	—
602	C₂×C₇	#3011	1	1	yes	characteristic
603	C₂×C₇	#3013	1	1	yes	characteristic
604	C₂×C₇	#3018	1	1	yes	characteristic
605	C₂³	—	2	1	no	—
606	C₂³	C₇×#120	1	1	yes	characteristic
607	Q₈	—	2	1	no	—
608	Q₈	—	2	1	no	—
609	Q₈	—	2	1	no	—
610	Q₈	—	2	1	no	—
611	Q₈	—	2	1	no	—
612	Q₈	—	2	1	no	—
613	Q₈	—	4	2	no	—
614	Q₈	—	4	2	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	4	1	no	—
619	Q₈	—	8	1	no	—
620	Q₈	—	8	2	no	—
621	D₄	—	2	1	no	—
622	D₄	—	2	1	no	—
623	D₄	—	8	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	8	2	no	—
643	C₂×C₄	C₇×#120	1	1	yes	characteristic
644	C₂×C₄	C₇×#120	1	1	yes	characteristic
645	C₂×C₄	C₇×#120	1	1	yes	characteristic
646	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
647	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
648	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
649	C₈	—	2	2	no	—
650	C₈	—	4	1	no	—
651	C₈	—	4	1	no	—
652	C₈	—	4	1	no	—
653	C₈	—	4	1	no	—
654	C₈	—	4	1	no	—
655	C₇	#18745	1	1	yes	characteristic, direct product factor, Sylow
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	C₂×C₇×#120	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	1	no	—
678	C₄	C₇×#577	1	1	yes	characteristic
679	C₄	C₇×#578	1	1	yes	characteristic
680	C₄	C₇×#578	1	1	yes	characteristic
681	C₄	C₇×#578	1	1	yes	characteristic
682	C₂	—	4	1	no	—
683	C₂	—	8	1	no	—
684	C₂	C₇×#3011	1	1	yes	characteristic
685	C₂	C₇×#3013	1	1	yes	characteristic
686	C₂	C₇×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#121	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3249	C₂	semidirect
4. C₇×#3185	C₂	semidirect
5. C₇×#1653	C₂	semidirect
6. C₇×#1652	C₂	semidirect
7. C₇×#1645	C₂	semidirect
8. C₇×#1644	C₂	semidirect
9. C₇×#1638	C₂	semidirect
10. C₇×#1636	C₂	semidirect
11. C₇×#1633	C₂	semidirect
12. C₇×#1632	C₂	semidirect
13. C₇×#1542	C₂	semidirect
14. C₇×#1485	C₂	semidirect
71. #18745	C₇	direct (N × H)
178. #3249	C₂×C₇	semidirect
180. #3185	C₂×C₇	semidirect
181. #1653	C₂×C₇	semidirect
182. #1652	C₂×C₇	semidirect
183. #1645	C₂×C₇	semidirect
184. #1644	C₂×C₇	semidirect
185. #1638	C₂×C₇	semidirect
186. #1636	C₂×C₇	semidirect
187. #1633	C₂×C₇	semidirect
188. #1632	C₂×C₇	semidirect
189. #1542	C₂×C₇	semidirect
190. #1485	C₂×C₇	semidirect
655. C₇	#18745	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×#3555	2
C₇×#3249	2
C₇×#3233	2
C₇×#3185	2
C₇×#1653	2
C₇×#1652	2
C₇×#1645	2
C₇×#1644	2
C₇×#1638	2
C₇×#1636	2
C₇×#1633	2
C₇×#1632	2
C₇×#1542	2
C₇×#1485	2
C₇×#1483	2
#18745	7

Subgroups — C7×#18745 #13195961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#18745 #13195961