Subgroups — C₇×#61347 #13238563

Order 1792.

1846 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3373	C₂	1	4	yes	maximal, complemented
4	C₇×#3371	C₂	1	4	yes	maximal, complemented
5	C₇×#3369	C₂	1	2	yes	maximal, complemented
6	C₇×#3366	C₂	1	2	yes	maximal, complemented
7	C₇×#3362	C₂	1	2	yes	maximal, complemented
8	C₇×#3360	C₂	1	2	yes	maximal, complemented
9	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₇×#3084	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3045	C₂	1	2	yes	maximal, complemented
14	C₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2952	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₇×#135	C₂²	1	2	yes	—
20	C₇×#559	C₂²	1	4	yes	—
21	C₇×Q₈²	C₂²	1	2	yes	complemented
22	C₇×#557	C₂²	1	2	yes	complemented
23	C₇×#556	C₂²	1	2	yes	—
24	C₇×#555	—	2	1	no	—
25	C₇×#554	—	2	2	no	—
26	C₇×#554	C₂²	1	2	yes	complemented
27	C₇×#553	—	2	2	no	—
28	C₇×#550	C₂²	1	2	yes	—
29	C₇×D₄×Q₈	—	2	2	no	—
30	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
31	C₇×#547	—	2	1	no	—
32	C₇×#544	—	2	2	no	—
33	C₇×#544	C₂²	1	2	yes	—
34	C₇×#538	—	2	2	no	—
35	C₇×#535	C₂²	1	2	yes	—
36	C₇×#533	—	2	1	no	—
37	C₇×#533	C₂²	1	1	yes	characteristic
38	C₇×#532	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
40	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₇×#525	—	2	2	no	—
42	C₇×#520	C₂²	1	2	yes	—
43	C₇×#520	C₂²	1	2	yes	—
44	C₄×C₇×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₇×#490	C₂²	1	4	yes	—
47	C₇×#489	C₂²	1	4	yes	—
48	C₇×#489	C₂²	1	4	yes	complemented
49	C₇×#488	C₂²	1	4	yes	—
50	C₇×#487	C₂²	1	2	yes	complemented
51	C₇×#486	C₂²	1	4	yes	—
52	C₇×#486	C₂²	1	2	yes	complemented
53	C₇×#479	C₂²	1	4	yes	complemented
54	C₇×#478	C₂²	1	4	yes	complemented
55	C₇×#476	C₂²	1	2	yes	—
56	C₇×#476	C₂²	1	2	yes	—
57	C₇×#476	C₂²	1	4	yes	—
58	C₇×#476	C₂²	1	4	yes	complemented
59	C₇×#475	C₂²	1	4	yes	complemented
60	C₇×#464	C₂²	1	4	yes	—
61	C₇×#464	C₂²	1	2	yes	complemented
62	C₇×#463	C₂²	1	4	yes	—
63	C₇×#463	C₂²	1	2	yes	complemented
64	C₇×#462	C₂²	1	1	yes	characteristic, complemented
65	C₇×#461	C₂²	1	1	yes	characteristic, complemented
66	C₇×#460	C₂²	1	4	yes	—
67	C₇×#460	C₂²	1	1	yes	characteristic, complemented
68	C₇×#459	C₂²	1	4	yes	—
69	C₇×#459	C₂²	1	1	yes	characteristic, complemented
70	C₇×#446	C₂²	1	2	yes	complemented
71	C₇×#446	C₂²	1	4	yes	complemented
72	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
73	C₇×#442	C₂²	1	2	yes	—
74	C₇×#442	C₂²	1	4	yes	complemented
75	C₇×#441	C₂²	1	4	yes	complemented
76	C₇×#440	C₂²	1	2	yes	—
77	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
78	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
79	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
80	C₄×C₇×D₈	C₂²	1	2	yes	—
81	C₇×#428	C₂²	1	1	yes	characteristic
82	C₂×C₇×#106	C₂²	1	2	yes	—
83	C₇×#424	C₂²	1	2	yes	—
84	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₇×#418	C₂²	1	1	yes	characteristic
86	C₇×#417	C₂²	1	1	yes	characteristic
87	C₇×#417	C₂²	1	2	yes	—
88	C₇×#417	C₂²	1	2	yes	—
89	C₇×#416	C₂²	1	2	yes	—
90	C₂×C₇×#102	C₂²	1	2	yes	—
91	C₇×#405	C₂²	1	2	yes	—
92	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
93	#61347	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂×C₇×#41	—	2	2	no	—
95	C₂×C₇×#41	C₂³	1	2	yes	—
96	C₂×C₇×#41	C₂³	1	1	yes	characteristic
97	C₂²×C₇×Q₈	—	2	2	no	—
98	C₂²×C₇×Q₈	—	2	1	no	—
99	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇	—	2	1	no	—
101	C₇×AGL(1,ℤ/8)	—	2	4	no	—
102	C₇×#135	—	2	8	no	—
103	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
104	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
106	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₇×D₈	C₂³	1	2	yes	—
108	C₂×C₇×D₈	C₂³	1	2	yes	—
109	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
111	C₂²×C₇×C₈	C₂³	1	2	yes	—
112	C₇×C₄⋊Q₈	—	2	2	no	—
113	C₇×C₄⋊Q₈	—	2	2	no	—
114	C₇×C₄⋊Q₈	—	2	2	no	—
115	C₇×C₄⋊Q₈	—	2	4	no	—
116	C₇×C₄⋊Q₈	—	2	1	no	—
117	C₇×C₄⋊Q₈	—	2	1	no	—
118	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
119	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
120	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
122	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₇×#127	C₂³	1	4	yes	—
125	C₇×#127	C₂³	1	1	yes	characteristic
126	C₇×#126	—	2	4	no	—
127	C₇×#125	—	2	2	no	—
128	C₇×#125	—	2	4	no	—
129	C₇×#125	D₄	1	2	yes	—
130	C₇×#125	C₂³	1	4	yes	—
131	C₇×#124	—	2	4	no	—
132	C₇×#124	C₂³	1	4	yes	—
133	C₇×#124	C₂³	1	2	yes	—
134	C₇×#123	—	2	4	no	—
135	C₇×#123	—	2	4	no	—
136	C₇×C₂²⋊Q₈	—	2	2	no	—
137	C₇×C₂²⋊Q₈	—	2	2	no	—
138	C₇×C₂²⋊Q₈	—	2	2	no	—
139	C₇×C₂²⋊Q₈	—	2	4	no	—
140	C₇×C₂²⋊Q₈	—	2	4	no	—
141	C₇×C₂²⋊Q₈	—	2	4	no	—
142	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
143	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
144	C₇×#121	—	2	1	no	—
145	C₇×#121	—	2	1	no	—
146	C₇×#121	—	2	2	no	—
147	C₇×#121	—	2	2	no	—
148	C₇×#121	—	2	2	no	—
149	C₇×#121	—	2	4	no	—
150	C₇×#120	—	2	4	no	—
151	C₄×C₇×Q₈	—	2	2	no	—
152	C₄×C₇×Q₈	—	2	2	no	—
153	C₄×C₇×Q₈	C₂³	1	4	yes	—
154	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
155	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
156	C₄×C₇×Q₈	C₂³	1	4	yes	—
157	C₄×C₇×Q₈	C₂³	1	2	yes	—
158	C₄×C₇×Q₈	C₂³	1	2	yes	—
159	C₄×C₇×D₄	—	2	1	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	—	2	4	no	—
162	C₄×C₇×D₄	—	2	4	no	—
163	C₄×C₇×D₄	—	2	4	no	—
164	C₄×C₇×D₄	—	2	1	no	—
165	C₄×C₇×D₄	—	2	1	no	—
166	C₄×C₇×D₄	—	2	1	no	—
167	C₄×C₇×D₄	—	2	1	no	—
168	C₄×C₇×D₄	C₂³	1	2	yes	—
169	C₄×C₇×D₄	C₂³	1	2	yes	—
170	C₄×C₇×D₄	C₂³	1	4	yes	—
171	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
172	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
173	C₄×C₇×D₄	C₂³	1	4	yes	—
174	C₇×#117	—	2	2	no	—
175	C₇×#117	—	2	2	no	—
176	C₇×#117	—	2	2	no	—
177	C₇×#117	—	2	1	no	—
178	C₇×#117	C₂³	1	1	yes	characteristic
179	C₇×#117	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	—	2	1	no	—
181	C₂×C₇×C₄⋊C₄	—	2	2	no	—
182	C₂×C₇×C₄⋊C₄	—	2	2	no	—
183	C₂×C₇×C₄⋊C₄	—	2	2	no	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₄²×C₇	—	2	1	no	—
188	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₇×#107	C₂³	1	2	yes	—
190	C₇×#106	C₂³	1	2	yes	—
191	C₇×#106	C₂³	1	4	yes	—
192	C₇×#106	C₂³	1	4	yes	—
193	C₇×C₄⋊C₈	C₂³	1	4	yes	—
194	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
195	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
196	C₇×C₄⋊C₈	C₂³	1	2	yes	—
197	C₇×C₄⋊C₈	C₂³	1	4	yes	—
198	C₇×#103	C₂³	1	2	yes	—
199	C₇×#103	C₂³	1	4	yes	—
200	C₇×#103	C₂³	1	2	yes	—
201	C₇×#103	C₂³	1	4	yes	—
202	C₇×#103	C₂³	1	2	yes	—
203	C₇×#102	C₂³	1	4	yes	—
204	C₇×#102	C₂³	1	4	yes	—
205	C₇×#102	C₂³	1	2	yes	—
206	C₇×#102	C₂³	1	4	yes	—
207	C₇×#102	C₂³	1	2	yes	—
208	C₇×#102	C₂³	1	2	yes	—
209	C₇×#102	C₂³	1	4	yes	—
210	C₇×#102	C₂³	1	2	yes	—
211	C₇×#102	C₂³	1	2	yes	—
212	C₇×#97	C₂³	1	4	yes	—
213	C₇×#97	C₂³	1	2	yes	—
214	C₄×C₇×C₈	C₂³	1	4	yes	—
215	C₄×C₇×C₈	C₂³	1	2	yes	—
216	#3506	C₂×C₇	1	1	yes	characteristic, complemented
217	#3503	C₂×C₇	1	1	yes	characteristic, complemented
218	#3373	C₂×C₇	1	4	yes	complemented
219	#3371	C₂×C₇	1	4	yes	complemented
220	#3369	C₂×C₇	1	2	yes	complemented
221	#3366	C₂×C₇	1	2	yes	complemented
222	#3362	C₂×C₇	1	2	yes	complemented
223	#3360	C₂×C₇	1	2	yes	complemented
224	#3141	C₂×C₇	1	1	yes	characteristic, complemented
225	#3136	C₂×C₇	1	2	yes	complemented
226	#3084	C₂×C₇	1	2	yes	complemented
227	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
228	#3045	C₂×C₇	1	2	yes	complemented
229	#3035	C₂×C₇	1	1	yes	characteristic, complemented
230	#2962	C₂×C₇	1	1	yes	characteristic, complemented
231	#2952	C₂×C₇	1	2	yes	complemented
232	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
233	C₂⁴×C₇	—	2	1	no	—
234	C₇×#41	—	2	2	no	—
235	C₇×#41	—	2	4	no	—
236	C₇×#41	—	2	4	no	—
237	C₇×#41	—	8	4	no	—
238	C₇×#41	#41	1	4	yes	complemented
239	C₂×C₇×Q₈	—	2	2	no	—
240	C₂×C₇×Q₈	—	2	4	no	—
241	C₂×C₇×Q₈	—	2	2	no	—
242	C₂×C₇×Q₈	—	8	2	no	—
243	C₂×C₇×Q₈	—	8	4	no	—
244	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
245	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
246	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
247	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
248	C₂×C₇×D₄	—	2	1	no	—
249	C₂×C₇×D₄	—	2	2	no	—
250	C₂×C₇×D₄	—	2	1	no	—
251	C₂×C₇×D₄	—	2	1	no	—
252	C₂×C₇×D₄	—	2	4	no	—
253	C₂×C₇×D₄	—	2	1	no	—
254	C₂×C₇×D₄	—	2	4	no	—
255	C₂×C₇×D₄	—	2	2	no	—
256	C₂×C₇×D₄	—	2	2	no	—
257	C₂×C₇×D₄	C₂⁴	1	2	yes	—
258	C₂×C₇×D₄	C₂⁴	1	2	yes	—
259	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₇	—	2	1	no	—
261	C₂²×C₄×C₇	—	2	1	no	—
262	C₂²×C₄×C₇	—	2	2	no	—
263	C₂²×C₄×C₇	—	2	1	no	—
264	C₂²×C₄×C₇	—	2	1	no	—
265	C₂²×C₄×C₇	—	2	2	no	—
266	C₂²×C₄×C₇	—	2	2	no	—
267	C₂²×C₄×C₇	—	2	4	no	—
268	C₂²×C₄×C₇	—	2	4	no	—
269	C₂²×C₄×C₇	—	2	2	no	—
270	C₂²×C₄×C₇	—	8	2	no	—
271	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₇×Q₁₆	—	2	4	no	—
275	C₇×SD₁₆	—	2	4	no	—
276	C₇×SD₁₆	—	2	4	no	—
277	C₇×SD₁₆	—	2	4	no	—
278	C₇×D₈	—	2	4	no	—
279	C₇×D₈	—	2	4	no	—
280	C₇×M₁₆	—	2	2	no	—
281	C₇×M₁₆	—	2	2	no	—
282	C₂×C₇×C₈	—	2	4	no	—
283	C₂×C₇×C₈	C₂⁴	1	2	yes	—
284	C₂×C₇×C₈	C₂⁴	1	2	yes	—
285	C₂×C₇×C₈	C₂⁴	1	2	yes	—
286	C₂×C₇×C₈	C₂⁴	1	2	yes	—
287	C₇×C₄⋊C₄	—	2	1	no	—
288	C₇×C₄⋊C₄	—	2	2	no	—
289	C₇×C₄⋊C₄	—	2	2	no	—
290	C₇×C₄⋊C₄	—	2	4	no	—
291	C₇×C₄⋊C₄	—	2	4	no	—
292	C₇×C₄⋊C₄	—	2	2	no	—
293	C₇×C₄⋊C₄	—	2	4	no	—
294	C₇×C₄⋊C₄	—	2	1	no	—
295	C₇×C₄⋊C₄	—	2	1	no	—
296	C₇×C₄⋊C₄	—	2	1	no	—
297	C₇×C₄⋊C₄	—	2	1	no	—
298	C₇×C₄⋊C₄	—	2	4	no	—
299	C₇×C₄⋊C₄	—	2	4	no	—
300	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
304	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
306	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
307	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
308	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
309	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
310	C₇×C₂²⋊C₄	—	2	1	no	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	—	2	2	no	—
313	C₇×C₂²⋊C₄	—	2	4	no	—
314	C₇×C₂²⋊C₄	—	2	1	no	—
315	C₇×C₂²⋊C₄	—	2	1	no	—
316	C₇×C₂²⋊C₄	—	2	4	no	—
317	C₇×C₂²⋊C₄	—	2	4	no	—
318	C₇×C₂²⋊C₄	—	2	2	no	—
319	C₇×C₂²⋊C₄	—	2	4	no	—
320	C₇×C₂²⋊C₄	—	2	2	no	—
321	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
322	C₄²×C₇	—	2	1	no	—
323	C₄²×C₇	—	2	1	no	—
324	C₄²×C₇	—	2	1	no	—
325	C₄²×C₇	—	2	4	no	—
326	C₄²×C₇	—	2	4	no	—
327	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₇	C₂⁴	1	1	yes	characteristic
330	C₄²×C₇	C₂⁴	1	4	yes	—
331	C₄²×C₇	C₂⁴	1	1	yes	characteristic
332	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
333	C₂×#135	C₂²×C₇	1	2	yes	—
334	#559	C₂²×C₇	1	4	yes	—
335	Q₈²	C₂²×C₇	1	2	yes	complemented
336	#557	C₂²×C₇	1	2	yes	complemented
337	#556	C₂²×C₇	1	2	yes	—
338	#555	—	2	1	no	—
339	#554	—	2	2	no	—
340	#554	C₂²×C₇	1	2	yes	complemented
341	#553	—	2	2	no	—
342	#550	C₂²×C₇	1	2	yes	—
343	D₄×Q₈	—	2	2	no	—
344	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
345	#547	—	2	1	no	—
346	#544	—	2	2	no	—
347	#544	C₂²×C₇	1	2	yes	—
348	#538	—	2	2	no	—
349	#535	C₂²×C₇	1	2	yes	—
350	#533	—	2	1	no	—
351	#533	C₂²×C₇	1	1	yes	characteristic
352	#532	C₂²×C₇	1	1	yes	characteristic
353	C₂×C₄⋊Q₈	—	2	1	no	—
354	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
355	#525	—	2	2	no	—
356	#520	C₂²×C₇	1	2	yes	—
357	#520	C₂²×C₇	1	2	yes	—
358	C₄×#41	C₂²×C₇	1	1	yes	characteristic
359	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
360	#490	C₂²×C₇	1	4	yes	—
361	#489	C₂²×C₇	1	4	yes	—
362	#489	C₂²×C₇	1	4	yes	complemented
363	#488	C₂²×C₇	1	4	yes	—
364	#487	C₂²×C₇	1	2	yes	complemented
365	#486	C₂²×C₇	1	4	yes	—
366	#486	C₂²×C₇	1	2	yes	complemented
367	#479	C₂²×C₇	1	4	yes	complemented
368	#478	C₂²×C₇	1	4	yes	complemented
369	#476	C₂²×C₇	1	2	yes	—
370	#476	C₂²×C₇	1	2	yes	—
371	#476	C₂²×C₇	1	4	yes	—
372	#476	C₂²×C₇	1	4	yes	complemented
373	#475	C₂²×C₇	1	4	yes	complemented
374	#464	C₂²×C₇	1	4	yes	—
375	#464	C₂²×C₇	1	2	yes	complemented
376	#463	C₂²×C₇	1	4	yes	—
377	#463	C₂²×C₇	1	2	yes	complemented
378	#462	C₂²×C₇	1	1	yes	characteristic, complemented
379	#461	C₂²×C₇	1	1	yes	characteristic, complemented
380	#460	C₂²×C₇	1	4	yes	—
381	#460	C₂²×C₇	1	1	yes	characteristic, complemented
382	#459	C₂²×C₇	1	4	yes	—
383	#459	C₂²×C₇	1	1	yes	characteristic, complemented
384	#446	C₂²×C₇	1	2	yes	complemented
385	#446	C₂²×C₇	1	4	yes	complemented
386	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
387	#442	C₂²×C₇	1	2	yes	—
388	#442	C₂²×C₇	1	4	yes	complemented
389	#441	C₂²×C₇	1	4	yes	complemented
390	#440	C₂²×C₇	1	2	yes	—
391	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
392	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
393	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
394	C₄×D₈	C₂²×C₇	1	2	yes	—
395	#428	C₂²×C₇	1	1	yes	characteristic
396	C₂×#106	C₂²×C₇	1	2	yes	—
397	#424	C₂²×C₇	1	2	yes	—
398	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
399	#418	C₂²×C₇	1	1	yes	characteristic
400	#417	C₂²×C₇	1	2	yes	—
401	#417	C₂²×C₇	1	2	yes	—
402	#417	C₂²×C₇	1	1	yes	characteristic
403	#416	C₂²×C₇	1	2	yes	—
404	C₂×#102	C₂²×C₇	1	2	yes	—
405	#405	C₂²×C₇	1	2	yes	—
406	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
407	C₂³×C₇	—	2	1	no	—
408	C₂³×C₇	—	2	2	no	—
409	C₂³×C₇	—	2	2	no	—
410	C₂³×C₇	—	4	2	no	—
411	C₂³×C₇	—	8	1	no	—
412	C₂³×C₇	—	8	1	no	—
413	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
414	C₇×Q₈	—	2	4	no	—
415	C₇×Q₈	—	2	1	no	—
416	C₇×Q₈	—	2	2	no	—
417	C₇×Q₈	—	2	2	no	—
418	C₇×Q₈	—	4	2	no	—
419	C₇×Q₈	—	4	4	no	—
420	C₇×Q₈	—	8	2	no	—
421	C₇×Q₈	—	8	4	no	—
422	C₇×Q₈	C₂×#41	1	2	yes	—
423	C₇×D₄	—	2	4	no	—
424	C₇×D₄	—	2	2	no	—
425	C₇×D₄	—	2	2	no	—
426	C₇×D₄	—	2	1	no	—
427	C₇×D₄	—	2	2	no	—
428	C₇×D₄	—	2	2	no	—
429	C₇×D₄	—	4	4	no	—
430	C₇×D₄	—	4	2	no	—
431	C₇×D₄	—	4	2	no	—
432	C₇×D₄	—	8	1	no	—
433	C₇×D₄	—	8	4	no	—
434	C₇×D₄	—	8	4	no	—
435	C₇×D₄	C₂×#41	1	2	yes	—
436	C₂×C₄×C₇	—	2	1	no	—
437	C₂×C₄×C₇	—	2	4	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	1	no	—
442	C₂×C₄×C₇	—	2	1	no	—
443	C₂×C₄×C₇	—	2	4	no	—
444	C₂×C₄×C₇	—	4	1	no	—
445	C₂×C₄×C₇	—	4	2	no	—
446	C₂×C₄×C₇	—	4	4	no	—
447	C₂×C₄×C₇	—	4	2	no	—
448	C₂×C₄×C₇	—	4	4	no	—
449	C₂×C₄×C₇	—	8	2	no	—
450	C₂×C₄×C₇	—	8	4	no	—
451	C₂×C₄×C₇	—	8	4	no	—
452	C₂×C₄×C₇	—	8	1	no	—
453	C₂×C₄×C₇	—	8	2	no	—
454	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
456	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
457	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₇	C₂×#41	1	2	yes	—
462	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
463	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
464	C₇×C₈	—	2	2	no	—
465	C₇×C₈	—	2	2	no	—
466	C₇×C₈	—	2	2	no	—
467	C₇×C₈	—	2	2	no	—
468	C₂×#41	—	2	2	no	—
469	C₂×#41	C₂³×C₇	1	2	yes	—
470	C₂×#41	C₂³×C₇	1	1	yes	characteristic
471	C₂²×Q₈	—	2	2	no	—
472	C₂²×Q₈	—	2	1	no	—
473	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
474	C₂³×C₄	—	2	1	no	—
475	AGL(1,ℤ/8)	—	2	4	no	—
476	#135	—	2	8	no	—
477	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
478	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
479	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
480	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
481	C₂×D₈	C₂³×C₇	1	2	yes	—
482	C₂×D₈	C₂³×C₇	1	2	yes	—
483	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
484	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₇	1	2	yes	—
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	—	2	2	no	—
489	C₄⋊Q₈	—	2	4	no	—
490	C₄⋊Q₈	—	2	1	no	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
493	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
495	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
496	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
497	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
498	#127	C₂³×C₇	1	1	yes	characteristic
499	#127	C₂³×C₇	1	4	yes	—
500	#126	—	2	4	no	—
501	#125	—	2	2	no	—
502	#125	—	2	4	no	—
503	#125	C₇×D₄	1	2	yes	—
504	#125	C₂³×C₇	1	4	yes	—
505	#124	—	2	4	no	—
506	#124	C₂³×C₇	1	2	yes	—
507	#124	C₂³×C₇	1	4	yes	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
517	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
518	#121	—	2	1	no	—
519	#121	—	2	1	no	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	4	no	—
524	#120	—	2	4	no	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
528	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
529	C₄×Q₈	C₂³×C₇	1	4	yes	—
530	C₄×Q₈	C₂³×C₇	1	4	yes	—
531	C₄×Q₈	C₂³×C₇	1	2	yes	—
532	C₄×Q₈	C₂³×C₇	1	2	yes	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	—	2	1	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	4	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	—	2	1	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	C₂³×C₇	1	2	yes	—
543	C₄×D₄	C₂³×C₇	1	2	yes	—
544	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
545	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
546	C₄×D₄	C₂³×C₇	1	4	yes	—
547	C₄×D₄	C₂³×C₇	1	4	yes	—
548	#117	—	2	2	no	—
549	#117	—	2	2	no	—
550	#117	—	2	2	no	—
551	#117	—	2	1	no	—
552	#117	C₂³×C₇	1	1	yes	characteristic
553	#117	C₂³×C₇	1	2	yes	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	2	no	—
556	C₂×C₄⋊C₄	—	2	2	no	—
557	C₂×C₄⋊C₄	—	2	2	no	—
558	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₄²	—	2	1	no	—
562	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
563	#107	C₂³×C₇	1	2	yes	—
564	#106	C₂³×C₇	1	4	yes	—
565	#106	C₂³×C₇	1	4	yes	—
566	#106	C₂³×C₇	1	2	yes	—
567	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
568	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
569	C₄⋊C₈	C₂³×C₇	1	2	yes	—
570	C₄⋊C₈	C₂³×C₇	1	4	yes	—
571	C₄⋊C₈	C₂³×C₇	1	4	yes	—
572	#103	C₂³×C₇	1	2	yes	—
573	#103	C₂³×C₇	1	2	yes	—
574	#103	C₂³×C₇	1	2	yes	—
575	#103	C₂³×C₇	1	4	yes	—
576	#103	C₂³×C₇	1	4	yes	—
577	#102	C₂³×C₇	1	4	yes	—
578	#102	C₂³×C₇	1	4	yes	—
579	#102	C₂³×C₇	1	2	yes	—
580	#102	C₂³×C₇	1	2	yes	—
581	#102	C₂³×C₇	1	2	yes	—
582	#102	C₂³×C₇	1	4	yes	—
583	#102	C₂³×C₇	1	4	yes	—
584	#102	C₂³×C₇	1	2	yes	—
585	#102	C₂³×C₇	1	2	yes	—
586	#97	C₂³×C₇	1	2	yes	—
587	#97	C₂³×C₇	1	4	yes	—
588	C₄×C₈	C₂³×C₇	1	2	yes	—
589	C₄×C₈	C₂³×C₇	1	4	yes	—
590	C₂²×C₇	—	2	1	no	—
591	C₂²×C₇	—	2	1	no	—
592	C₂²×C₇	—	2	2	no	—
593	C₂²×C₇	—	4	1	no	—
594	C₂²×C₇	—	4	1	no	—
595	C₂²×C₇	—	4	2	no	—
596	C₂²×C₇	—	4	2	no	—
597	C₂²×C₇	—	4	2	no	—
598	C₂²×C₇	—	4	2	no	—
599	C₂²×C₇	—	4	2	no	—
600	C₂²×C₇	—	4	2	no	—
601	C₂²×C₇	—	8	4	no	—
602	C₂²×C₇	#548	1	2	yes	—
603	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
604	C₄×C₇	—	2	1	no	—
605	C₄×C₇	—	2	1	no	—
606	C₄×C₇	—	2	4	no	—
607	C₄×C₇	—	2	2	no	—
608	C₄×C₇	—	2	1	no	—
609	C₄×C₇	—	2	4	no	—
610	C₄×C₇	—	4	1	no	—
611	C₄×C₇	—	4	4	no	—
612	C₄×C₇	—	4	2	no	—
613	C₄×C₇	—	4	1	no	—
614	C₄×C₇	—	4	2	no	—
615	C₄×C₇	#548	1	2	yes	—
616	C₄×C₇	#577	1	2	yes	—
617	C₄×C₇	C₂²×#41	1	1	yes	characteristic
618	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
619	C₂⁴	—	2	1	no	—
620	#41	—	2	2	no	—
621	#41	—	2	4	no	—
622	#41	—	2	4	no	—
623	#41	—	8	4	no	—
624	#41	C₇×#41	1	4	yes	complemented
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	4	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	8	2	no	—
629	C₂×Q₈	—	8	4	no	—
630	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
631	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
632	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
633	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	C₂⁴×C₇	1	2	yes	—
644	C₂×D₄	C₂⁴×C₇	1	2	yes	—
645	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	8	2	no	—
657	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
658	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
660	Q₁₆	—	2	4	no	—
661	SD₁₆	—	2	4	no	—
662	SD₁₆	—	2	4	no	—
663	SD₁₆	—	2	4	no	—
664	D₈	—	2	4	no	—
665	D₈	—	2	4	no	—
666	M₁₆	—	2	2	no	—
667	M₁₆	—	2	2	no	—
668	C₂×C₈	—	2	4	no	—
669	C₂×C₈	C₂⁴×C₇	1	2	yes	—
670	C₂×C₈	C₂⁴×C₇	1	2	yes	—
671	C₂×C₈	C₂⁴×C₇	1	2	yes	—
672	C₂×C₈	C₂⁴×C₇	1	2	yes	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
687	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
688	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
689	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
690	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
691	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
692	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
693	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
694	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
695	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	1	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
708	C₄²	—	2	1	no	—
709	C₄²	—	2	1	no	—
710	C₄²	—	2	1	no	—
711	C₄²	—	2	4	no	—
712	C₄²	—	2	4	no	—
713	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
714	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
715	C₄²	C₂⁴×C₇	1	1	yes	characteristic
716	C₄²	C₂⁴×C₇	1	4	yes	—
717	C₄²	C₂⁴×C₇	1	1	yes	characteristic
718	C₂×C₇	—	2	2	no	—
719	C₂×C₇	—	4	2	no	—
720	C₂×C₇	—	8	2	no	—
721	C₂×C₇	—	8	2	no	—
722	C₂×C₇	C₂×#548	1	1	yes	characteristic
723	C₂×C₇	C₂×#577	1	1	yes	characteristic
724	C₂×C₇	#3585	1	1	yes	characteristic
725	C₂³	—	2	1	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	4	2	no	—
729	C₂³	—	8	1	no	—
730	C₂³	—	8	1	no	—
731	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
732	Q₈	—	2	1	no	—
733	Q₈	—	2	4	no	—
734	Q₈	—	2	2	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	4	2	no	—
737	Q₈	—	4	4	no	—
738	Q₈	—	8	2	no	—
739	Q₈	—	8	4	no	—
740	Q₈	C₂×C₇×#41	1	2	yes	—
741	D₄	—	2	4	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	1	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	2	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	2	no	—
749	D₄	—	4	2	no	—
750	D₄	—	8	1	no	—
751	D₄	—	8	4	no	—
752	D₄	—	8	4	no	—
753	D₄	C₂×C₇×#41	1	2	yes	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	8	2	no	—
768	C₂×C₄	—	8	4	no	—
769	C₂×C₄	—	8	4	no	—
770	C₂×C₄	—	8	1	no	—
771	C₂×C₄	—	8	2	no	—
772	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
773	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
774	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
775	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
776	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
777	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
778	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
779	C₂×C₄	C₂×C₇×#41	1	2	yes	—
780	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
781	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
782	C₈	—	2	2	no	—
783	C₈	—	2	2	no	—
784	C₈	—	2	2	no	—
785	C₈	—	2	2	no	—
786	C₇	#61347	1	1	yes	characteristic, direct product factor, Sylow
787	C₂²	—	2	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	8	4	no	—
799	C₂²	C₇×#548	1	2	yes	—
800	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
801	C₄	—	2	1	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	4	no	—
806	C₄	—	2	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	4	no	—
811	C₄	—	4	2	no	—
812	C₄	C₇×#548	1	2	yes	—
813	C₄	C₇×#577	1	2	yes	—
814	C₄	C₂²×C₇×#41	1	1	yes	characteristic
815	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
816	C₂	—	2	2	no	—
817	C₂	—	4	2	no	—
818	C₂	—	8	2	no	—
819	C₂	—	8	2	no	—
820	C₂	C₂×C₇×#548	1	1	yes	characteristic
821	C₂	C₂×C₇×#577	1	1	yes	characteristic
822	C₂	C₇×#3585	1	1	yes	characteristic

	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3506	C₂	semidirect
2. C₇×#3503	C₂	semidirect
3. C₇×#3373	C₂	semidirect
4. C₇×#3371	C₂	semidirect
5. C₇×#3369	C₂	semidirect
6. C₇×#3366	C₂	semidirect
7. C₇×#3362	C₂	semidirect
8. C₇×#3360	C₂	semidirect
9. C₇×#3141	C₂	semidirect
10. C₇×#3136	C₂	semidirect
11. C₇×#3084	C₂	semidirect
12. C₂×C₇×#476	C₂	semidirect
13. C₇×#3045	C₂	semidirect
14. C₇×#3035	C₂	semidirect
15. C₇×#2962	C₂	semidirect
16. C₇×#2952	C₂	semidirect
17. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
21. C₇×Q₈²	C₂²	semidirect
22. C₇×#557	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
30. C₇×D₄×Q₈	C₂²	semidirect
48. C₇×#489	C₂²	semidirect
50. C₇×#487	C₂²	semidirect
52. C₇×#486	C₂²	semidirect
53. C₇×#479	C₂²	semidirect
54. C₇×#478	C₂²	semidirect
58. C₇×#476	C₂²	semidirect
59. C₇×#475	C₂²	semidirect
61. C₇×#464	C₂²	semidirect
63. C₇×#463	C₂²	semidirect
64. C₇×#462	C₂²	semidirect
65. C₇×#461	C₂²	semidirect
67. C₇×#460	C₂²	semidirect
69. C₇×#459	C₂²	semidirect
70. C₇×#446	C₂²	semidirect
71. C₇×#446	C₂²	semidirect
72. C₇×C₈×Q₈	C₂²	semidirect
74. C₇×#442	C₂²	semidirect
75. C₇×#441	C₂²	semidirect
78. C₄×C₇×SD₁₆	C₂²	semidirect
79. C₄×C₇×SD₁₆	C₂²	semidirect
93. #61347	C₇	direct (N × H)
216. #3506	C₂×C₇	semidirect
217. #3503	C₂×C₇	semidirect
218. #3373	C₂×C₇	semidirect
219. #3371	C₂×C₇	semidirect
220. #3369	C₂×C₇	semidirect
221. #3366	C₂×C₇	semidirect
222. #3362	C₂×C₇	semidirect
223. #3360	C₂×C₇	semidirect
224. #3141	C₂×C₇	semidirect
225. #3136	C₂×C₇	semidirect
226. #3084	C₂×C₇	semidirect
227. C₂×#476	C₂×C₇	semidirect
228. #3045	C₂×C₇	semidirect
229. #3035	C₂×C₇	semidirect
230. #2962	C₂×C₇	semidirect
231. #2952	C₂×C₇	semidirect
232. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
238. C₇×#41	#41	semidirect
335. Q₈²	C₂²×C₇	semidirect
336. #557	C₂²×C₇	semidirect
340. #554	C₂²×C₇	semidirect
344. D₄×Q₈	C₂²×C₇	semidirect
362. #489	C₂²×C₇	semidirect
364. #487	C₂²×C₇	semidirect
366. #486	C₂²×C₇	semidirect
367. #479	C₂²×C₇	semidirect
368. #478	C₂²×C₇	semidirect
372. #476	C₂²×C₇	semidirect
373. #475	C₂²×C₇	semidirect
375. #464	C₂²×C₇	semidirect
377. #463	C₂²×C₇	semidirect
378. #462	C₂²×C₇	semidirect
379. #461	C₂²×C₇	semidirect
381. #460	C₂²×C₇	semidirect
383. #459	C₂²×C₇	semidirect
384. #446	C₂²×C₇	semidirect
385. #446	C₂²×C₇	semidirect
386. C₈×Q₈	C₂²×C₇	semidirect
388. #442	C₂²×C₇	semidirect
389. #441	C₂²×C₇	semidirect
392. C₄×SD₁₆	C₂²×C₇	semidirect
393. C₄×SD₁₆	C₂²×C₇	semidirect
624. #41	C₇×#41	semidirect
786. C₇	#61347	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×#3506	2
C₇×#3503	2
C₇×#3373	2
C₇×#3371	2
C₇×#3369	2
C₇×#3366	2
C₇×#3362	2
C₇×#3360	2
C₇×#3141	2
C₇×#3136	2
C₇×#3084	2
C₂×C₇×#476	2
C₇×#3045	2
C₇×#3035	2
C₇×#2962	2
C₇×#2952	2
C₄×C₇×AGL(1,ℤ/8)	2
#61347	7

Subgroups — C7×#61347 #13238563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61347 #13238563