Subgroups — C₇×#60708 #13237924

Order 1792.

1860 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	2	yes	maximal, complemented
2	C₇×#3181	C₂	1	4	yes	maximal, complemented
3	C₇×#3178	C₂	1	4	yes	maximal, complemented
4	C₇×#3177	C₂	1	2	yes	maximal, complemented
5	C₇×#3175	C₂	1	2	yes	maximal, complemented
6	C₇×#3170	C₂	1	2	yes	maximal, complemented
7	C₇×#3168	C₂	1	2	yes	maximal, complemented
8	C₇×#3164	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×#3056	C₂	1	2	yes	maximal, complemented
12	C₇×#3050	C₂	1	1	yes	maximal, characteristic
13	C₂×C₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2947	C₂	1	2	yes	maximal, complemented
17	C₂×C₇×#405	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	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₇×#556	—	2	2	no	—
24	C₇×#554	—	2	2	no	—
25	C₇×#552	—	2	4	no	—
26	C₇×#552	—	2	2	no	—
27	C₇×#552	—	2	2	no	—
28	C₇×#551	—	2	4	no	—
29	C₇×#544	C₂²	1	2	yes	—
30	C₇×#542	C₂²	1	4	yes	—
31	C₇×#541	C₂²	1	4	yes	—
32	C₇×#536	C₂²	1	2	yes	—
33	C₇×#533	C₂²	1	4	yes	—
34	C₇×#529	C₂²	1	4	yes	—
35	C₇×#525	C₂²	1	2	yes	—
36	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₇×#520	C₂²	1	2	yes	—
38	C₇×#519	C₂²	1	2	yes	—
39	C₂×C₇×#117	C₂²	1	1	yes	characteristic
40	C₇×#501	C₂²	1	4	yes	complemented
41	C₇×#500	C₂²	1	2	yes	complemented
42	C₇×#499	C₂²	1	2	yes	complemented
43	C₇×#497	C₂²	1	4	yes	complemented
44	C₇×#495	C₂²	1	2	yes	complemented
45	C₇×#494	C₂²	1	2	yes	complemented
46	C₇×#491	C₂²	1	4	yes	complemented
47	C₇×#489	C₂²	1	4	yes	complemented
48	C₇×#488	C₂²	1	4	yes	complemented
49	C₇×#487	C₂²	1	4	yes	complemented
50	C₇×#470	C₂²	1	4	yes	—
51	C₇×#468	C₂²	1	4	yes	—
52	C₇×#467	C₂²	1	2	yes	—
53	C₇×#467	C₂²	1	1	yes	characteristic
54	C₇×#467	C₂²	1	4	yes	—
55	C₇×#467	C₂²	1	2	yes	—
56	C₇×#467	C₂²	1	1	yes	characteristic
57	C₇×#467	C₂²	1	2	yes	—
58	C₇×#467	C₂²	1	2	yes	—
59	C₇×#466	C₂²	1	1	yes	characteristic
60	C₇×#466	C₂²	1	1	yes	characteristic
61	C₇×#465	C₂²	1	4	yes	—
62	C₇×#465	C₂²	1	2	yes	—
63	C₇×#465	C₂²	1	2	yes	—
64	C₇×#441	C₂²	1	4	yes	complemented
65	C₇×#441	C₂²	1	4	yes	complemented
66	C₇×#440	C₂²	1	4	yes	complemented
67	C₇×#440	C₂²	1	4	yes	complemented
68	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
69	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
70	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
71	C₄×C₇×Q₁₆	C₂²	1	4	yes	complemented
72	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
73	C₄×C₇×D₈	C₂²	1	2	yes	complemented
74	C₇×#428	C₂²	1	2	yes	—
75	C₇×#427	C₂²	1	1	yes	characteristic
76	C₂×C₇×#107	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	C₇×#405	C₂²	1	1	yes	characteristic
86	C₇×#405	C₂²	1	1	yes	characteristic
87	C₂×C₇×#97	C₂²	1	2	yes	—
88	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
89	#60708	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	C₂³	1	2	yes	—
91	C₂²×C₇×Q₈	C₂³	1	2	yes	—
92	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
97	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
98	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
99	C₂×C₇×Q₁₆	C₂³	1	4	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	C₂×C₇×M₁₆	—	2	4	no	—
104	C₂×C₇×M₁₆	C₂³	1	2	yes	—
105	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
106	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
107	C₂²×C₇×C₈	—	2	4	no	—
108	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
115	C₇×C₄⋊Q₈	—	2	2	no	—
116	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₇×#126	—	2	4	no	—
119	C₇×#126	—	2	4	no	—
120	C₇×#126	—	2	4	no	—
121	C₇×#126	—	2	4	no	—
122	C₇×#125	—	2	4	no	—
123	C₇×#125	—	2	4	no	—
124	C₇×#125	—	2	2	no	—
125	C₇×#125	—	2	4	no	—
126	C₇×#125	C₂³	1	4	yes	—
127	C₇×#124	—	2	4	no	—
128	C₇×#124	C₂³	1	4	yes	—
129	C₇×#123	—	2	2	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	2	no	—
135	C₇×C₂²⋊Q₈	—	2	4	no	—
136	C₇×C₂²⋊Q₈	—	2	2	no	—
137	C₇×C₂²⋊Q₈	—	2	2	no	—
138	C₇×C₂²⋊Q₈	—	2	4	no	—
139	C₇×C₂²⋊Q₈	—	2	4	no	—
140	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₇×#121	C₂³	1	2	yes	—
145	C₇×#121	C₂³	1	2	yes	—
146	C₇×#120	—	2	2	no	—
147	C₄×C₇×Q₈	—	2	2	no	—
148	C₄×C₇×Q₈	—	2	2	no	—
149	C₄×C₇×Q₈	—	2	4	no	—
150	C₄×C₇×Q₈	C₂³	1	4	yes	—
151	C₄×C₇×Q₈	C₂³	1	4	yes	—
152	C₄×C₇×Q₈	C₂³	1	4	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	—	2	4	no	—
157	C₄×C₇×D₄	C₂³	1	4	yes	—
158	C₇×#117	—	2	4	no	—
159	C₇×#117	—	2	2	no	—
160	C₇×#117	—	2	4	no	—
161	C₇×#117	—	2	4	no	—
162	C₇×#117	D₄	1	1	yes	characteristic
163	C₇×#117	D₄	1	2	yes	—
164	C₇×#117	D₄	1	1	yes	characteristic
165	C₇×#117	C₂³	1	2	yes	—
166	C₇×#117	C₂³	1	1	yes	characteristic
167	C₇×#117	C₂³	1	1	yes	characteristic
168	C₇×#117	C₂³	1	2	yes	—
169	C₂×C₇×C₄⋊C₄	—	2	2	no	—
170	C₂×C₇×C₄⋊C₄	—	2	2	no	—
171	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
172	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
175	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
176	C₂×C₄²×C₇	C₂³	1	2	yes	—
177	C₇×#107	C₂³	1	1	yes	characteristic
178	C₇×#107	C₂³	1	1	yes	characteristic
179	C₇×#107	C₂³	1	2	yes	—
180	C₇×#107	C₂³	1	2	yes	—
181	C₇×#107	C₂³	1	4	yes	—
182	C₇×#106	C₂³	1	4	yes	—
183	C₇×#106	C₂³	1	2	yes	—
184	C₇×#103	C₂³	1	4	yes	—
185	C₇×#103	C₂³	1	4	yes	—
186	C₇×#103	C₂³	1	4	yes	—
187	C₇×#103	C₂³	1	4	yes	—
188	C₇×#103	C₂³	1	2	yes	—
189	C₇×#103	C₂³	1	2	yes	—
190	C₇×#103	C₂³	1	4	yes	—
191	C₇×#102	C₂³	1	2	yes	—
192	C₇×#102	C₂³	1	2	yes	—
193	C₇×#102	C₂³	1	4	yes	—
194	C₇×#97	C₂³	1	2	yes	—
195	C₇×#97	C₂³	1	2	yes	—
196	C₇×#97	C₂³	1	2	yes	—
197	C₇×#97	C₂³	1	2	yes	—
198	C₄×C₇×C₈	C₂³	1	2	yes	—
199	C₄×C₇×C₈	C₂³	1	2	yes	—
200	C₄×C₇×C₈	C₂³	1	2	yes	—
201	C₄×C₇×C₈	C₂³	1	2	yes	—
202	#3495	C₂×C₇	1	2	yes	complemented
203	#3181	C₂×C₇	1	4	yes	complemented
204	#3178	C₂×C₇	1	4	yes	complemented
205	#3177	C₂×C₇	1	2	yes	complemented
206	#3175	C₂×C₇	1	2	yes	complemented
207	#3170	C₂×C₇	1	2	yes	complemented
208	#3168	C₂×C₇	1	2	yes	complemented
209	#3164	C₂×C₇	1	1	yes	characteristic, complemented
210	#3156	C₂×C₇	1	1	yes	characteristic, complemented
211	#3137	C₂×C₇	1	2	yes	complemented
212	#3056	C₂×C₇	1	2	yes	complemented
213	#3050	C₂×C₇	1	1	yes	characteristic
214	C₂×#467	C₂×C₇	1	1	yes	characteristic, complemented
215	#2951	C₂×C₇	1	1	yes	characteristic, complemented
216	#2950	C₂×C₇	1	1	yes	characteristic, complemented
217	#2947	C₂×C₇	1	2	yes	complemented
218	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
219	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
220	C₇×#41	—	2	4	no	—
221	C₇×#41	—	2	4	no	—
222	C₂×C₇×Q₈	—	2	2	no	—
223	C₂×C₇×Q₈	—	2	4	no	—
224	C₂×C₇×Q₈	—	2	4	no	—
225	C₂×C₇×Q₈	—	2	4	no	—
226	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
227	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
228	C₂×C₇×D₄	—	2	2	no	—
229	C₂×C₇×D₄	—	2	2	no	—
230	C₂×C₇×D₄	—	2	2	no	—
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	—	2	4	no	—
238	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
239	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
246	C₇×Q₁₆	—	2	4	no	—
247	C₇×Q₁₆	—	2	4	no	—
248	C₇×Q₁₆	—	2	2	no	—
249	C₇×Q₁₆	—	2	8	no	—
250	C₇×SD₁₆	—	2	4	no	—
251	C₇×SD₁₆	—	2	8	no	—
252	C₇×D₈	—	2	2	no	—
253	C₇×M₁₆	—	2	2	no	—
254	C₇×M₁₆	—	2	4	no	—
255	C₇×M₁₆	#41	1	4	yes	—
256	C₂×C₇×C₈	—	2	2	no	—
257	C₂×C₇×C₈	—	2	2	no	—
258	C₂×C₇×C₈	—	2	2	no	—
259	C₂×C₇×C₈	—	2	2	no	—
260	C₂×C₇×C₈	—	2	2	no	—
261	C₂×C₇×C₈	—	2	4	no	—
262	C₂×C₇×C₈	#41	1	4	yes	—
263	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
264	C₂×C₇×C₈	C₂⁴	1	2	yes	—
265	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
266	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
267	C₂×C₇×C₈	C₂⁴	1	2	yes	—
268	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
269	C₇×C₄⋊C₄	—	2	2	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	—	2	4	no	—
276	C₇×C₄⋊C₄	—	2	4	no	—
277	C₇×C₄⋊C₄	—	2	4	no	—
278	C₇×C₄⋊C₄	—	2	2	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	2	2	no	—
281	C₇×C₄⋊C₄	—	2	4	no	—
282	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
283	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
284	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
285	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
286	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
287	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
288	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
291	C₇×C₂²⋊C₄	—	2	4	no	—
292	C₇×C₂²⋊C₄	—	2	4	no	—
293	C₇×C₂²⋊C₄	—	2	2	no	—
294	C₇×C₂²⋊C₄	—	2	2	no	—
295	C₇×C₂²⋊C₄	—	2	2	no	—
296	C₇×C₂²⋊C₄	—	2	2	no	—
297	C₇×C₂²⋊C₄	—	2	4	no	—
298	C₇×C₂²⋊C₄	—	2	4	no	—
299	C₇×C₂²⋊C₄	—	2	2	no	—
300	C₇×C₂²⋊C₄	—	2	4	no	—
301	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
302	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
303	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
304	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
305	C₄²×C₇	—	2	4	no	—
306	C₄²×C₇	—	2	4	no	—
307	C₄²×C₇	—	2	4	no	—
308	C₄²×C₇	—	2	2	no	—
309	C₄²×C₇	C₂×D₄	1	2	yes	—
310	C₄²×C₇	C₂×D₄	1	2	yes	—
311	C₄²×C₇	C₂⁴	1	2	yes	—
312	C₄²×C₇	C₂⁴	1	2	yes	—
313	C₂×#137	C₂²×C₇	1	2	yes	—
314	C₂×#135	C₂²×C₇	1	1	yes	characteristic
315	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
316	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
317	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
318	#556	—	2	2	no	—
319	#554	—	2	2	no	—
320	#552	—	2	4	no	—
321	#552	—	2	2	no	—
322	#552	—	2	2	no	—
323	#551	—	2	4	no	—
324	#544	C₂²×C₇	1	2	yes	—
325	#542	C₂²×C₇	1	4	yes	—
326	#541	C₂²×C₇	1	4	yes	—
327	#536	C₂²×C₇	1	2	yes	—
328	#533	C₂²×C₇	1	4	yes	—
329	#529	C₂²×C₇	1	4	yes	—
330	#525	C₂²×C₇	1	2	yes	—
331	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
332	#520	C₂²×C₇	1	2	yes	—
333	#519	C₂²×C₇	1	2	yes	—
334	C₂×#117	C₂²×C₇	1	1	yes	characteristic
335	#501	C₂²×C₇	1	4	yes	complemented
336	#500	C₂²×C₇	1	2	yes	complemented
337	#499	C₂²×C₇	1	2	yes	complemented
338	#497	C₂²×C₇	1	4	yes	complemented
339	#495	C₂²×C₇	1	2	yes	complemented
340	#494	C₂²×C₇	1	2	yes	complemented
341	#491	C₂²×C₇	1	4	yes	complemented
342	#489	C₂²×C₇	1	4	yes	complemented
343	#488	C₂²×C₇	1	4	yes	complemented
344	#487	C₂²×C₇	1	4	yes	complemented
345	#470	C₂²×C₇	1	4	yes	—
346	#468	C₂²×C₇	1	4	yes	—
347	#467	C₂²×C₇	1	2	yes	—
348	#467	C₂²×C₇	1	1	yes	characteristic
349	#467	C₂²×C₇	1	4	yes	—
350	#467	C₂²×C₇	1	2	yes	—
351	#467	C₂²×C₇	1	1	yes	characteristic
352	#467	C₂²×C₇	1	2	yes	—
353	#467	C₂²×C₇	1	2	yes	—
354	#466	C₂²×C₇	1	1	yes	characteristic
355	#466	C₂²×C₇	1	1	yes	characteristic
356	#465	C₂²×C₇	1	4	yes	—
357	#465	C₂²×C₇	1	2	yes	—
358	#465	C₂²×C₇	1	2	yes	—
359	#441	C₂²×C₇	1	4	yes	complemented
360	#441	C₂²×C₇	1	4	yes	complemented
361	#440	C₂²×C₇	1	4	yes	complemented
362	#440	C₂²×C₇	1	4	yes	complemented
363	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
364	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
365	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
366	C₄×Q₁₆	C₂²×C₇	1	4	yes	complemented
367	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
368	C₄×D₈	C₂²×C₇	1	2	yes	complemented
369	#428	C₂²×C₇	1	2	yes	—
370	#427	C₂²×C₇	1	1	yes	characteristic
371	C₂×#107	C₂²×C₇	1	1	yes	characteristic
372	#419	C₂²×C₇	1	2	yes	—
373	#417	C₂²×C₇	1	2	yes	—
374	#416	C₂²×C₇	1	2	yes	—
375	C₂×#103	C₂²×C₇	1	2	yes	—
376	#405	C₂²×C₇	1	1	yes	characteristic
377	#405	C₂²×C₇	1	1	yes	characteristic
378	#405	C₂²×C₇	1	2	yes	—
379	#405	C₂²×C₇	1	2	yes	—
380	#405	C₂²×C₇	1	1	yes	characteristic
381	#405	C₂²×C₇	1	1	yes	characteristic
382	C₂×#97	C₂²×C₇	1	2	yes	—
383	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
384	C₂³×C₇	—	2	2	no	—
385	C₂³×C₇	—	2	2	no	—
386	C₂³×C₇	—	2	2	no	—
387	C₂³×C₇	—	4	1	no	—
388	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
389	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
390	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
391	C₇×Q₈	—	2	4	no	—
392	C₇×Q₈	—	2	2	no	—
393	C₇×Q₈	—	2	4	no	—
394	C₇×Q₈	—	2	2	no	—
395	C₇×Q₈	—	4	4	no	—
396	C₇×Q₈	—	8	4	no	—
397	C₇×D₄	—	2	2	no	—
398	C₇×D₄	—	2	2	no	—
399	C₇×D₄	—	4	4	no	—
400	C₇×D₄	—	4	4	no	—
401	C₇×D₄	—	8	2	no	—
402	C₂×C₄×C₇	—	2	2	no	—
403	C₂×C₄×C₇	—	2	4	no	—
404	C₂×C₄×C₇	—	2	2	no	—
405	C₂×C₄×C₇	—	2	2	no	—
406	C₂×C₄×C₇	—	2	1	no	—
407	C₂×C₄×C₇	—	2	1	no	—
408	C₂×C₄×C₇	—	2	1	no	—
409	C₂×C₄×C₇	—	2	1	no	—
410	C₂×C₄×C₇	—	2	2	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	4	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	4	no	—
415	C₂×C₄×C₇	—	4	2	no	—
416	C₂×C₄×C₇	—	4	4	no	—
417	C₂×C₄×C₇	—	4	4	no	—
418	C₂×C₄×C₇	—	8	4	no	—
419	C₂×C₄×C₇	—	8	2	no	—
420	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₇	C₂×#41	1	2	yes	—
428	C₂×C₄×C₇	C₂×#41	1	2	yes	—
429	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
430	C₇×C₈	—	2	1	no	—
431	C₇×C₈	—	2	1	no	—
432	C₇×C₈	—	2	2	no	—
433	C₇×C₈	C₂×#41	1	2	yes	—
434	C₇×C₈	C₂×#41	1	2	yes	—
435	C₇×C₈	C₂×#41	1	4	yes	—
436	C₂×#41	C₂³×C₇	1	2	yes	—
437	C₂²×Q₈	C₂³×C₇	1	2	yes	—
438	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
439	#137	—	2	8	no	—
440	#135	—	2	4	no	—
441	C₂×Q₁₆	—	2	4	no	—
442	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
443	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
444	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
445	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
446	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
447	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
448	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
449	C₂×M₁₆	—	2	4	no	—
450	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
451	C₂×M₁₆	C₂³×C₇	1	2	yes	—
452	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
453	C₂²×C₈	—	2	4	no	—
454	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₇	1	2	yes	—
460	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
463	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
464	#126	—	2	4	no	—
465	#126	—	2	4	no	—
466	#126	—	2	4	no	—
467	#126	—	2	4	no	—
468	#125	—	2	4	no	—
469	#125	—	2	4	no	—
470	#125	—	2	2	no	—
471	#125	—	2	4	no	—
472	#125	C₂³×C₇	1	4	yes	—
473	#124	—	2	4	no	—
474	#124	C₂³×C₇	1	4	yes	—
475	#123	—	2	2	no	—
476	#123	—	2	4	no	—
477	#123	—	2	4	no	—
478	#123	—	2	4	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	4	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
487	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
488	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
489	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
490	#121	C₂³×C₇	1	2	yes	—
491	#121	C₂³×C₇	1	2	yes	—
492	#120	—	2	2	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	4	no	—
496	C₄×Q₈	C₂³×C₇	1	4	yes	—
497	C₄×Q₈	C₂³×C₇	1	4	yes	—
498	C₄×Q₈	C₂³×C₇	1	4	yes	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	4	no	—
502	C₄×D₄	—	2	4	no	—
503	C₄×D₄	C₂³×C₇	1	4	yes	—
504	#117	—	2	4	no	—
505	#117	—	2	2	no	—
506	#117	—	2	4	no	—
507	#117	—	2	4	no	—
508	#117	C₇×D₄	1	1	yes	characteristic
509	#117	C₇×D₄	1	2	yes	—
510	#117	C₇×D₄	1	1	yes	characteristic
511	#117	C₂³×C₇	1	2	yes	—
512	#117	C₂³×C₇	1	1	yes	characteristic
513	#117	C₂³×C₇	1	1	yes	characteristic
514	#117	C₂³×C₇	1	2	yes	—
515	C₂×C₄⋊C₄	—	2	2	no	—
516	C₂×C₄⋊C₄	—	2	2	no	—
517	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
520	C₂×C₂²⋊C₄	—	2	2	no	—
521	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
522	C₂×C₄²	C₂³×C₇	1	2	yes	—
523	#107	C₂³×C₇	1	2	yes	—
524	#107	C₂³×C₇	1	2	yes	—
525	#107	C₂³×C₇	1	1	yes	characteristic
526	#107	C₂³×C₇	1	1	yes	characteristic
527	#107	C₂³×C₇	1	4	yes	—
528	#106	C₂³×C₇	1	2	yes	—
529	#106	C₂³×C₇	1	4	yes	—
530	#103	C₂³×C₇	1	4	yes	—
531	#103	C₂³×C₇	1	4	yes	—
532	#103	C₂³×C₇	1	2	yes	—
533	#103	C₂³×C₇	1	2	yes	—
534	#103	C₂³×C₇	1	4	yes	—
535	#103	C₂³×C₇	1	4	yes	—
536	#103	C₂³×C₇	1	4	yes	—
537	#102	C₂³×C₇	1	2	yes	—
538	#102	C₂³×C₇	1	2	yes	—
539	#102	C₂³×C₇	1	4	yes	—
540	#97	C₂³×C₇	1	2	yes	—
541	#97	C₂³×C₇	1	2	yes	—
542	#97	C₂³×C₇	1	2	yes	—
543	#97	C₂³×C₇	1	2	yes	—
544	C₄×C₈	C₂³×C₇	1	2	yes	—
545	C₄×C₈	C₂³×C₇	1	2	yes	—
546	C₄×C₈	C₂³×C₇	1	2	yes	—
547	C₄×C₈	C₂³×C₇	1	2	yes	—
548	C₂²×C₇	—	2	1	no	—
549	C₂²×C₇	—	2	1	no	—
550	C₂²×C₇	—	2	1	no	—
551	C₂²×C₇	—	2	1	no	—
552	C₂²×C₇	—	2	1	no	—
553	C₂²×C₇	—	2	1	no	—
554	C₂²×C₇	—	2	1	no	—
555	C₂²×C₇	—	4	4	no	—
556	C₂²×C₇	—	4	2	no	—
557	C₂²×C₇	—	4	2	no	—
558	C₂²×C₇	—	4	2	no	—
559	C₂²×C₇	#532	1	2	yes	—
560	C₂²×C₇	#578	1	2	yes	—
561	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₇	—	2	2	no	—
563	C₄×C₇	—	2	2	no	—
564	C₄×C₇	—	2	1	no	—
565	C₄×C₇	—	2	1	no	—
566	C₄×C₇	—	2	2	no	—
567	C₄×C₇	—	2	2	no	—
568	C₄×C₇	—	4	4	no	—
569	C₄×C₇	—	4	2	no	—
570	C₄×C₇	—	4	2	no	—
571	C₄×C₇	—	4	4	no	—
572	C₄×C₇	—	4	2	no	—
573	C₄×C₇	#532	1	2	yes	—
574	C₄×C₇	C₂²×#41	1	1	yes	characteristic
575	C₄×C₇	C₂²×#41	1	1	yes	characteristic
576	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
577	#41	—	2	4	no	—
578	#41	—	2	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
584	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	C₂⁴×C₇	1	2	yes	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
596	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
597	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
598	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
599	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
603	Q₁₆	—	2	4	no	—
604	Q₁₆	—	2	4	no	—
605	Q₁₆	—	2	2	no	—
606	Q₁₆	—	2	8	no	—
607	SD₁₆	—	2	4	no	—
608	SD₁₆	—	2	8	no	—
609	D₈	—	2	2	no	—
610	M₁₆	—	2	2	no	—
611	M₁₆	—	2	4	no	—
612	M₁₆	C₇×#41	1	4	yes	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	—	2	2	no	—
617	C₂×C₈	—	2	2	no	—
618	C₂×C₈	—	2	4	no	—
619	C₂×C₈	C₇×#41	1	4	yes	—
620	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₇	1	2	yes	—
622	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
623	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
624	C₂×C₈	C₂⁴×C₇	1	2	yes	—
625	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
640	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
641	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
642	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
643	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
644	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
647	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
659	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
660	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
661	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
662	C₄²	—	2	4	no	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	4	no	—
665	C₄²	—	2	2	no	—
666	C₄²	C₂×C₇×D₄	1	2	yes	—
667	C₄²	C₂×C₇×D₄	1	2	yes	—
668	C₄²	C₂⁴×C₇	1	2	yes	—
669	C₄²	C₂⁴×C₇	1	2	yes	—
670	C₂×C₇	—	2	2	no	—
671	C₂×C₇	—	2	2	no	—
672	C₂×C₇	—	4	1	no	—
673	C₂×C₇	—	8	2	no	—
674	C₂×C₇	C₂×#532	1	1	yes	characteristic
675	C₂×C₇	C₂×#578	1	1	yes	characteristic
676	C₂×C₇	#3584	1	1	yes	characteristic
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	4	1	no	—
681	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
682	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
683	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
684	Q₈	—	2	4	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	2	4	no	—
687	Q₈	—	2	2	no	—
688	Q₈	—	4	4	no	—
689	Q₈	—	8	4	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	4	4	no	—
693	D₄	—	4	4	no	—
694	D₄	—	8	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	8	4	no	—
712	C₂×C₄	—	8	2	no	—
713	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
714	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
715	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
716	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
717	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
718	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
719	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
720	C₂×C₄	C₂×C₇×#41	1	2	yes	—
721	C₂×C₄	C₂×C₇×#41	1	2	yes	—
722	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
723	C₈	—	2	1	no	—
724	C₈	—	2	1	no	—
725	C₈	—	2	2	no	—
726	C₈	C₂×C₇×#41	1	2	yes	—
727	C₈	C₂×C₇×#41	1	2	yes	—
728	C₈	C₂×C₇×#41	1	4	yes	—
729	C₇	#60708	1	1	yes	characteristic, direct product factor, Sylow
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	C₇×#532	1	2	yes	—
742	C₂²	C₇×#578	1	2	yes	—
743	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	4	no	—
755	C₄	C₇×#532	1	2	yes	—
756	C₄	C₂²×C₇×#41	1	1	yes	characteristic
757	C₄	C₂²×C₇×#41	1	1	yes	characteristic
758	C₂	—	2	2	no	—
759	C₂	—	2	2	no	—
760	C₂	—	4	1	no	—
761	C₂	—	8	2	no	—
762	C₂	C₂×C₇×#532	1	1	yes	characteristic
763	C₂	C₂×C₇×#578	1	1	yes	characteristic
764	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3495	C₂	semidirect
2. C₇×#3181	C₂	semidirect
3. C₇×#3178	C₂	semidirect
4. C₇×#3177	C₂	semidirect
5. C₇×#3175	C₂	semidirect
6. C₇×#3170	C₂	semidirect
7. C₇×#3168	C₂	semidirect
8. C₇×#3164	C₂	semidirect
9. C₇×#3156	C₂	semidirect
10. C₇×#3137	C₂	semidirect
11. C₇×#3056	C₂	semidirect
13. C₂×C₇×#467	C₂	semidirect
14. C₇×#2951	C₂	semidirect
15. C₇×#2950	C₂	semidirect
16. C₇×#2947	C₂	semidirect
17. C₂×C₇×#405	C₂	semidirect
40. C₇×#501	C₂²	semidirect
41. C₇×#500	C₂²	semidirect
42. C₇×#499	C₂²	semidirect
43. C₇×#497	C₂²	semidirect
44. C₇×#495	C₂²	semidirect
45. C₇×#494	C₂²	semidirect
46. C₇×#491	C₂²	semidirect
47. C₇×#489	C₂²	semidirect
48. C₇×#488	C₂²	semidirect
49. C₇×#487	C₂²	semidirect
64. C₇×#441	C₂²	semidirect
65. C₇×#441	C₂²	semidirect
66. C₇×#440	C₂²	semidirect
67. C₇×#440	C₂²	semidirect
68. C₄×C₇×Q₁₆	C₂²	semidirect
69. C₄×C₇×Q₁₆	C₂²	semidirect
70. C₄×C₇×Q₁₆	C₂²	semidirect
71. C₄×C₇×Q₁₆	C₂²	semidirect
72. C₄×C₇×SD₁₆	C₂²	semidirect
73. C₄×C₇×D₈	C₂²	semidirect
89. #60708	C₇	direct (N × H)
202. #3495	C₂×C₇	semidirect
203. #3181	C₂×C₇	semidirect
204. #3178	C₂×C₇	semidirect
205. #3177	C₂×C₇	semidirect
206. #3175	C₂×C₇	semidirect
207. #3170	C₂×C₇	semidirect
208. #3168	C₂×C₇	semidirect
209. #3164	C₂×C₇	semidirect
210. #3156	C₂×C₇	semidirect
211. #3137	C₂×C₇	semidirect
212. #3056	C₂×C₇	semidirect
214. C₂×#467	C₂×C₇	semidirect
215. #2951	C₂×C₇	semidirect
216. #2950	C₂×C₇	semidirect
217. #2947	C₂×C₇	semidirect
218. C₂×#405	C₂×C₇	semidirect
335. #501	C₂²×C₇	semidirect
336. #500	C₂²×C₇	semidirect
337. #499	C₂²×C₇	semidirect
338. #497	C₂²×C₇	semidirect
339. #495	C₂²×C₇	semidirect
340. #494	C₂²×C₇	semidirect
341. #491	C₂²×C₇	semidirect
342. #489	C₂²×C₇	semidirect
343. #488	C₂²×C₇	semidirect
344. #487	C₂²×C₇	semidirect
359. #441	C₂²×C₇	semidirect
360. #441	C₂²×C₇	semidirect
361. #440	C₂²×C₇	semidirect
362. #440	C₂²×C₇	semidirect
363. C₄×Q₁₆	C₂²×C₇	semidirect
364. C₄×Q₁₆	C₂²×C₇	semidirect
365. C₄×Q₁₆	C₂²×C₇	semidirect
366. C₄×Q₁₆	C₂²×C₇	semidirect
367. C₄×SD₁₆	C₂²×C₇	semidirect
368. C₄×D₈	C₂²×C₇	semidirect
729. C₇	#60708	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×#3495	2
C₇×#3181	2
C₇×#3178	2
C₇×#3177	2
C₇×#3175	2
C₇×#3170	2
C₇×#3168	2
C₇×#3164	2
C₇×#3156	2
C₇×#3137	2
C₇×#3056	2
C₇×#3050	2
C₂×C₇×#467	2
C₇×#2951	2
C₇×#2950	2
C₇×#2947	2
C₂×C₇×#405	2
#60708	7

Subgroups — C7×#60708 #13237924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60708 #13237924