Subgroups — C₇×#60823 #13238039

Order 1792.

2054 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3223	C₂	1	2	yes	maximal, complemented
4	C₇×#3222	C₂	1	2	yes	maximal, complemented
5	C₇×#3221	C₂	1	2	yes	maximal, complemented
6	C₇×#3220	C₂	1	2	yes	maximal, complemented
7	C₇×#3212	C₂	1	4	yes	maximal, complemented
8	C₇×#3211	C₂	1	4	yes	maximal, complemented
9	C₇×#3153	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#488	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3046	C₂	1	2	yes	maximal, complemented
14	C₇×#3045	C₂	1	2	yes	maximal, complemented
15	C₇×#3013	C₂	1	2	yes	maximal, complemented
16	C₇×#3012	C₂	1	2	yes	maximal, complemented
17	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
19	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	C₂×C₇×#137	C₂²	1	2	yes	complemented
21	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₇×#135	C₂²	1	2	yes	—
23	C₂×C₇×#135	C₂²	1	2	yes	complemented
24	C₇×#553	—	2	4	no	—
25	C₇×#553	—	2	2	no	—
26	C₇×#552	—	2	2	no	—
27	C₇×#548	—	2	2	no	—
28	C₇×#546	—	2	4	no	—
29	C₇×#546	—	2	2	no	—
30	C₇×#541	C₂²	1	2	yes	complemented
31	C₇×#540	C₂²	1	2	yes	complemented
32	C₇×#537	C₂²	1	2	yes	—
33	C₇×#536	C₂²	1	2	yes	—
34	C₇×#536	C₂²	1	1	yes	characteristic
35	C₇×#535	C₂²	1	2	yes	—
36	C₇×#535	C₂²	1	1	yes	characteristic
37	C₇×#532	C₂²	1	2	yes	—
38	C₇×#532	C₂²	1	1	yes	characteristic
39	C₇×#532	C₂²	1	1	yes	characteristic, complemented
40	C₇×#529	C₂²	1	4	yes	complemented
41	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×#124	C₂²	1	2	yes	—
43	C₂×C₇×#124	C₂²	1	1	yes	characteristic
44	C₇×#520	C₂²	1	2	yes	complemented
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₇×#497	C₂²	1	2	yes	complemented
47	C₇×#496	C₂²	1	2	yes	complemented
48	C₇×#495	C₂²	1	2	yes	complemented
49	C₇×#495	C₂²	1	4	yes	complemented
50	C₇×#495	C₂²	1	2	yes	complemented
51	C₇×#494	C₂²	1	1	yes	characteristic, complemented
52	C₇×#493	C₂²	1	1	yes	characteristic, complemented
53	C₇×#492	C₂²	1	1	yes	characteristic, complemented
54	C₇×#492	C₂²	1	1	yes	characteristic, complemented
55	C₇×#491	C₂²	1	2	yes	complemented
56	C₇×#490	C₂²	1	2	yes	complemented
57	C₇×#488	C₂²	1	2	yes	complemented
58	C₇×#488	C₂²	1	4	yes	complemented
59	C₇×#488	C₂²	1	2	yes	complemented
60	C₇×#488	C₂²	1	2	yes	complemented
61	C₇×#488	C₂²	1	2	yes	complemented
62	C₇×#464	C₂²	1	4	yes	complemented
63	C₇×#464	C₂²	1	4	yes	complemented
64	C₇×#463	C₂²	1	4	yes	complemented
65	C₇×#463	C₂²	1	4	yes	complemented
66	C₇×#462	C₂²	1	4	yes	complemented
67	C₇×#461	C₂²	1	4	yes	complemented
68	C₇×#460	C₂²	1	4	yes	complemented
69	C₇×#459	C₂²	1	4	yes	complemented
70	C₇×#452	C₂²	1	4	yes	—
71	C₇×#452	C₂²	1	4	yes	complemented
72	C₇×#451	C₂²	1	4	yes	complemented
73	C₇×#450	C₂²	1	4	yes	—
74	C₇×#449	C₂²	1	4	yes	—
75	C₇×#449	C₂²	1	4	yes	complemented
76	C₇×#448	C₂²	1	4	yes	complemented
77	C₇×#447	C₂²	1	4	yes	—
78	C₇×#433	C₂²	1	2	yes	complemented
79	C₇×#433	C₂²	1	2	yes	complemented
80	C₇×#431	C₂²	1	4	yes	complemented
81	C₇×#424	C₂²	1	2	yes	complemented
82	C₇×#417	C₂²	1	2	yes	—
83	C₇×#417	C₂²	1	2	yes	complemented
84	C₂×C₇×#103	C₂²	1	2	yes	complemented
85	C₂×C₇×#102	C₂²	1	2	yes	—
86	C₇×#408	C₂²	1	2	yes	—
87	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
89	#60823	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₇×2₋¹⁺⁴	—	4	4	no	—
91	C₇×H(5,𝔽₂)	—	4	4	no	—
92	C₂×C₇×#41	—	2	1	no	—
93	C₂×C₇×#41	—	2	1	no	—
94	C₂×C₇×#41	—	2	2	no	—
95	C₂×C₇×#41	C₂³	1	1	yes	characteristic
96	C₂×C₇×#41	C₂³	1	1	yes	characteristic
97	C₂×C₇×#41	C₂³	1	2	yes	—
98	C₂×C₇×#41	C₂³	1	2	yes	—
99	C₂×C₇×#41	C₂³	1	2	yes	—
100	C₂×C₇×#41	C₂³	1	1	yes	characteristic
101	C₂²×C₇×Q₈	—	2	1	no	—
102	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇×Q₈	C₂³	1	2	yes	—
104	C₂²×C₇×D₄	—	2	2	no	—
105	C₂²×C₇×D₄	—	2	1	no	—
106	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
107	C₂²×C₇×D₄	C₂³	1	2	yes	—
108	C₇×#137	—	4	4	no	—
109	C₇×AGL(1,ℤ/8)	—	4	4	no	—
110	C₇×#135	—	4	4	no	—
111	C₇×#135	—	4	4	no	—
112	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
113	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
114	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
115	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
116	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
118	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
119	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
120	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₇×D₈	C₂³	1	2	yes	—
122	C₂×C₇×D₈	C₂³	1	2	yes	—
123	C₂×C₇×D₈	C₂³	1	4	yes	—
124	C₂×C₇×M₁₆	C₂³	1	2	yes	—
125	C₂²×C₇×C₈	C₂³	1	2	yes	—
126	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₇×#127	C₂³	1	1	yes	characteristic
130	C₇×#127	C₂³	1	1	yes	characteristic
131	C₇×#127	C₂³	1	2	yes	—
132	C₇×#126	—	2	4	no	—
133	C₇×#126	—	2	4	no	—
134	C₇×#125	—	2	4	no	—
135	C₇×#125	—	2	2	no	—
136	C₇×#125	C₂³	1	2	yes	—
137	C₇×#125	C₂³	1	2	yes	—
138	C₇×#124	—	2	4	no	—
139	C₇×#124	—	2	2	no	—
140	C₇×#124	C₂³	1	1	yes	characteristic
141	C₇×#124	C₂³	1	2	yes	—
142	C₇×#124	C₂³	1	1	yes	characteristic
143	C₇×#124	C₂³	1	2	yes	—
144	C₇×#124	C₂³	1	2	yes	—
145	C₇×#124	C₂³	1	2	yes	—
146	C₇×#124	C₂³	1	2	yes	—
147	C₇×#123	—	2	4	no	—
148	C₇×#123	—	2	4	no	—
149	C₇×#123	—	2	2	no	—
150	C₇×#123	—	2	4	no	—
151	C₇×C₂²⋊Q₈	—	2	2	no	—
152	C₇×C₂²⋊Q₈	—	2	2	no	—
153	C₇×C₂²⋊Q₈	—	2	4	no	—
154	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₇×#121	—	2	2	no	—
156	C₇×#121	—	2	4	no	—
157	C₇×#121	—	2	2	no	—
158	C₇×#121	—	2	4	no	—
159	C₇×#121	—	2	2	no	—
160	C₇×#121	—	2	2	no	—
161	C₇×#121	—	2	4	no	—
162	C₇×#121	—	2	4	no	—
163	C₇×#121	C₂³	1	4	yes	—
164	C₇×#120	—	2	2	no	—
165	C₇×#120	—	2	4	no	—
166	C₄×C₇×Q₈	D₄	1	2	yes	—
167	C₄×C₇×Q₈	C₂³	1	4	yes	—
168	C₄×C₇×D₄	—	2	4	no	—
169	C₄×C₇×D₄	—	2	4	no	—
170	C₄×C₇×D₄	—	2	4	no	—
171	C₄×C₇×D₄	—	2	2	no	—
172	C₄×C₇×D₄	—	2	2	no	—
173	C₄×C₇×D₄	D₄	1	4	yes	—
174	C₄×C₇×D₄	D₄	1	2	yes	—
175	C₄×C₇×D₄	C₂³	1	4	yes	—
176	C₇×#117	—	2	2	no	—
177	C₇×#117	—	2	4	no	—
178	C₇×#117	C₂³	1	1	yes	characteristic
179	C₇×#117	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	—	2	2	no	—
181	C₂×C₇×C₄⋊C₄	—	2	2	no	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
184	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
185	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇	C₂³	1	2	yes	—
187	C₇×C₄⋊C₈	C₂³	1	4	yes	—
188	C₇×C₄⋊C₈	C₂³	1	4	yes	—
189	C₇×#103	C₂³	1	4	yes	—
190	C₇×#103	C₂³	1	4	yes	—
191	C₇×#103	C₂³	1	4	yes	—
192	C₇×#103	C₂³	1	4	yes	—
193	C₇×#102	C₂³	1	4	yes	—
194	C₇×#102	C₂³	1	4	yes	—
195	C₇×#102	C₂³	1	4	yes	—
196	C₇×#102	C₂³	1	4	yes	—
197	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₇×#97	C₂³	1	2	yes	—
200	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
201	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
202	C₄×C₇×C₈	C₂³	1	2	yes	—
203	C₄×C₇×C₈	C₂³	1	2	yes	—
204	#3512	C₂×C₇	1	1	yes	characteristic, complemented
205	#3500	C₂×C₇	1	1	yes	characteristic, complemented
206	#3223	C₂×C₇	1	2	yes	complemented
207	#3222	C₂×C₇	1	2	yes	complemented
208	#3221	C₂×C₇	1	2	yes	complemented
209	#3220	C₂×C₇	1	2	yes	complemented
210	#3212	C₂×C₇	1	4	yes	complemented
211	#3211	C₂×C₇	1	4	yes	complemented
212	#3153	C₂×C₇	1	1	yes	characteristic, complemented
213	#3147	C₂×C₇	1	1	yes	characteristic, complemented
214	#3142	C₂×C₇	1	1	yes	characteristic, complemented
215	C₂×#488	C₂×C₇	1	1	yes	characteristic, complemented
216	#3046	C₂×C₇	1	2	yes	complemented
217	#3045	C₂×C₇	1	2	yes	complemented
218	#3013	C₂×C₇	1	2	yes	complemented
219	#3012	C₂×C₇	1	2	yes	complemented
220	#2922	C₂×C₇	1	1	yes	characteristic, complemented
221	C₂⁴×C₇	—	2	2	no	—
222	C₂⁴×C₇	—	2	1	no	—
223	C₇×#41	—	2	4	no	—
224	C₇×#41	—	2	4	no	—
225	C₇×#41	—	2	4	no	—
226	C₇×#41	—	2	4	no	—
227	C₇×#41	—	2	4	no	—
228	C₇×#41	—	4	4	no	—
229	C₇×#41	—	4	4	no	—
230	C₇×#41	—	4	8	no	—
231	C₇×#41	—	4	4	no	—
232	C₇×#41	—	4	4	no	—
233	C₂×C₇×Q₈	—	2	2	no	—
234	C₂×C₇×Q₈	—	2	1	no	—
235	C₂×C₇×Q₈	—	2	4	no	—
236	C₂×C₇×Q₈	—	4	4	no	—
237	C₂×C₇×Q₈	—	4	4	no	—
238	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
239	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
240	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
241	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
242	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
243	C₂×C₇×D₄	—	2	2	no	—
244	C₂×C₇×D₄	—	2	2	no	—
245	C₂×C₇×D₄	—	2	1	no	—
246	C₂×C₇×D₄	—	2	2	no	—
247	C₂×C₇×D₄	—	2	1	no	—
248	C₂×C₇×D₄	—	2	4	no	—
249	C₂×C₇×D₄	—	2	2	no	—
250	C₂×C₇×D₄	—	2	1	no	—
251	C₂×C₇×D₄	—	2	4	no	—
252	C₂×C₇×D₄	—	2	2	no	—
253	C₂×C₇×D₄	—	2	2	no	—
254	C₂×C₇×D₄	—	2	4	no	—
255	C₂×C₇×D₄	—	4	4	no	—
256	C₂×C₇×D₄	—	4	8	no	—
257	C₂×C₇×D₄	—	4	4	no	—
258	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
259	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
260	C₂×C₇×D₄	C₂⁴	1	2	yes	—
261	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
262	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
263	C₂×C₇×D₄	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇	—	2	2	no	—
265	C₂²×C₄×C₇	—	2	1	no	—
266	C₂²×C₄×C₇	—	2	2	no	—
267	C₂²×C₄×C₇	—	2	2	no	—
268	C₂²×C₄×C₇	—	2	2	no	—
269	C₂²×C₄×C₇	—	2	1	no	—
270	C₂²×C₄×C₇	—	2	2	no	—
271	C₂²×C₄×C₇	—	2	1	no	—
272	C₂²×C₄×C₇	—	2	4	no	—
273	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
275	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₇×Q₁₆	—	4	2	no	—
278	C₇×Q₁₆	—	4	2	no	—
279	C₇×Q₁₆	—	4	4	no	—
280	C₇×SD₁₆	—	4	2	no	—
281	C₇×SD₁₆	—	4	2	no	—
282	C₇×SD₁₆	—	4	2	no	—
283	C₇×SD₁₆	—	4	2	no	—
284	C₇×SD₁₆	—	4	4	no	—
285	C₇×SD₁₆	—	4	4	no	—
286	C₇×D₈	—	4	2	no	—
287	C₇×D₈	—	4	2	no	—
288	C₇×D₈	—	4	4	no	—
289	C₇×M₁₆	—	2	4	no	—
290	C₂×C₇×C₈	—	2	4	no	—
291	C₂×C₇×C₈	C₂⁴	1	2	yes	—
292	C₂×C₇×C₈	C₂⁴	1	2	yes	—
293	C₂×C₇×C₈	C₂⁴	1	4	yes	—
294	C₇×C₄⋊C₄	—	2	2	no	—
295	C₇×C₄⋊C₄	—	2	4	no	—
296	C₇×C₄⋊C₄	—	2	4	no	—
297	C₇×C₄⋊C₄	—	2	4	no	—
298	C₇×C₄⋊C₄	—	2	4	no	—
299	C₇×C₄⋊C₄	—	2	4	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
304	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
305	C₇×C₂²⋊C₄	—	2	4	no	—
306	C₇×C₂²⋊C₄	—	2	4	no	—
307	C₇×C₂²⋊C₄	—	2	2	no	—
308	C₇×C₂²⋊C₄	—	2	4	no	—
309	C₇×C₂²⋊C₄	—	2	4	no	—
310	C₇×C₂²⋊C₄	—	2	4	no	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	—	2	4	no	—
313	C₇×C₂²⋊C₄	—	2	4	no	—
314	C₇×C₂²⋊C₄	—	2	2	no	—
315	C₇×C₂²⋊C₄	—	2	2	no	—
316	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
317	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
318	C₄²×C₇	—	2	4	no	—
319	C₄²×C₇	C₂×D₄	1	4	yes	—
320	C₄²×C₇	C₂×D₄	1	2	yes	—
321	C₄²×C₇	C₂⁴	1	1	yes	characteristic
322	C₄²×C₇	C₂⁴	1	1	yes	characteristic
323	C₄²×C₇	C₂⁴	1	2	yes	—
324	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
325	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
326	C₂×#137	C₂²×C₇	1	2	yes	complemented
327	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
328	C₂×#135	C₂²×C₇	1	2	yes	—
329	C₂×#135	C₂²×C₇	1	2	yes	complemented
330	#553	—	2	4	no	—
331	#553	—	2	2	no	—
332	#552	—	2	2	no	—
333	#548	—	2	2	no	—
334	#546	—	2	4	no	—
335	#546	—	2	2	no	—
336	#541	C₂²×C₇	1	2	yes	complemented
337	#540	C₂²×C₇	1	2	yes	complemented
338	#537	C₂²×C₇	1	2	yes	—
339	#536	C₂²×C₇	1	2	yes	—
340	#536	C₂²×C₇	1	1	yes	characteristic
341	#535	C₂²×C₇	1	2	yes	—
342	#535	C₂²×C₇	1	1	yes	characteristic
343	#532	C₂²×C₇	1	1	yes	characteristic
344	#532	C₂²×C₇	1	2	yes	—
345	#532	C₂²×C₇	1	1	yes	characteristic, complemented
346	#529	C₂²×C₇	1	4	yes	complemented
347	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
348	C₂×#124	C₂²×C₇	1	1	yes	characteristic
349	C₂×#124	C₂²×C₇	1	2	yes	—
350	#520	C₂²×C₇	1	2	yes	complemented
351	C₄×#41	C₂²×C₇	1	1	yes	characteristic
352	#497	C₂²×C₇	1	2	yes	complemented
353	#496	C₂²×C₇	1	2	yes	complemented
354	#495	C₂²×C₇	1	2	yes	complemented
355	#495	C₂²×C₇	1	2	yes	complemented
356	#495	C₂²×C₇	1	4	yes	complemented
357	#494	C₂²×C₇	1	1	yes	characteristic, complemented
358	#493	C₂²×C₇	1	1	yes	characteristic, complemented
359	#492	C₂²×C₇	1	1	yes	characteristic, complemented
360	#492	C₂²×C₇	1	1	yes	characteristic, complemented
361	#491	C₂²×C₇	1	2	yes	complemented
362	#490	C₂²×C₇	1	2	yes	complemented
363	#488	C₂²×C₇	1	4	yes	complemented
364	#488	C₂²×C₇	1	2	yes	complemented
365	#488	C₂²×C₇	1	2	yes	complemented
366	#488	C₂²×C₇	1	2	yes	complemented
367	#488	C₂²×C₇	1	2	yes	complemented
368	#464	C₂²×C₇	1	4	yes	complemented
369	#464	C₂²×C₇	1	4	yes	complemented
370	#463	C₂²×C₇	1	4	yes	complemented
371	#463	C₂²×C₇	1	4	yes	complemented
372	#462	C₂²×C₇	1	4	yes	complemented
373	#461	C₂²×C₇	1	4	yes	complemented
374	#460	C₂²×C₇	1	4	yes	complemented
375	#459	C₂²×C₇	1	4	yes	complemented
376	#452	C₂²×C₇	1	4	yes	—
377	#452	C₂²×C₇	1	4	yes	complemented
378	#451	C₂²×C₇	1	4	yes	complemented
379	#450	C₂²×C₇	1	4	yes	—
380	#449	C₂²×C₇	1	4	yes	—
381	#449	C₂²×C₇	1	4	yes	complemented
382	#448	C₂²×C₇	1	4	yes	complemented
383	#447	C₂²×C₇	1	4	yes	—
384	#433	C₂²×C₇	1	2	yes	complemented
385	#433	C₂²×C₇	1	2	yes	complemented
386	#431	C₂²×C₇	1	4	yes	complemented
387	#424	C₂²×C₇	1	2	yes	complemented
388	#417	C₂²×C₇	1	2	yes	—
389	#417	C₂²×C₇	1	2	yes	complemented
390	C₂×#103	C₂²×C₇	1	2	yes	complemented
391	C₂×#102	C₂²×C₇	1	2	yes	—
392	#408	C₂²×C₇	1	2	yes	—
393	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
394	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
395	C₂³×C₇	—	2	2	no	—
396	C₂³×C₇	—	2	2	no	—
397	C₂³×C₇	—	2	1	no	—
398	C₂³×C₇	—	2	1	no	—
399	C₂³×C₇	—	4	4	no	—
400	C₂³×C₇	—	4	2	no	—
401	C₂³×C₇	—	8	2	no	—
402	C₂³×C₇	—	8	4	no	—
403	C₂³×C₇	C₂²×D₄	1	2	yes	—
404	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
405	C₇×Q₈	—	2	2	no	—
406	C₇×Q₈	—	2	2	no	—
407	C₇×Q₈	—	2	2	no	—
408	C₇×Q₈	—	2	4	no	—
409	C₇×Q₈	—	2	2	no	—
410	C₇×Q₈	—	2	2	no	—
411	C₇×Q₈	—	4	4	no	—
412	C₇×Q₈	—	4	2	no	—
413	C₇×D₄	—	2	4	no	—
414	C₇×D₄	—	2	2	no	—
415	C₇×D₄	—	2	2	no	—
416	C₇×D₄	—	2	2	no	—
417	C₇×D₄	—	2	4	no	—
418	C₇×D₄	—	2	2	no	—
419	C₇×D₄	—	2	2	no	—
420	C₇×D₄	—	4	4	no	—
421	C₇×D₄	—	4	4	no	—
422	C₇×D₄	—	4	4	no	—
423	C₇×D₄	—	4	2	no	—
424	C₇×D₄	—	4	4	no	—
425	C₇×D₄	—	4	2	no	—
426	C₇×D₄	—	4	2	no	—
427	C₇×D₄	—	8	4	no	—
428	C₇×D₄	—	8	2	no	—
429	C₇×D₄	—	8	2	no	—
430	C₇×D₄	—	8	4	no	—
431	C₂×C₄×C₇	—	2	4	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	4	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	1	no	—
436	C₂×C₄×C₇	—	2	1	no	—
437	C₂×C₄×C₇	—	4	4	no	—
438	C₂×C₄×C₇	—	4	2	no	—
439	C₂×C₄×C₇	—	4	4	no	—
440	C₂×C₄×C₇	—	4	4	no	—
441	C₂×C₄×C₇	—	4	4	no	—
442	C₂×C₄×C₇	—	4	2	no	—
443	C₂×C₄×C₇	—	4	2	no	—
444	C₂×C₄×C₇	—	4	2	no	—
445	C₂×C₄×C₇	—	4	4	no	—
446	C₂×C₄×C₇	—	8	4	no	—
447	C₂×C₄×C₇	—	8	2	no	—
448	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
449	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
454	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
455	C₇×C₈	—	2	2	no	—
456	C₇×C₈	—	2	2	no	—
457	C₇×C₈	—	2	4	no	—
458	2₋¹⁺⁴	—	4	4	no	—
459	H(5,𝔽₂)	—	4	4	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	2	no	—
463	C₂×#41	C₂³×C₇	1	2	yes	—
464	C₂×#41	C₂³×C₇	1	1	yes	characteristic
465	C₂×#41	C₂³×C₇	1	1	yes	characteristic
466	C₂×#41	C₂³×C₇	1	2	yes	—
467	C₂×#41	C₂³×C₇	1	2	yes	—
468	C₂×#41	C₂³×C₇	1	1	yes	characteristic
469	C₂²×Q₈	—	2	1	no	—
470	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₇	1	2	yes	—
472	C₂²×D₄	—	2	2	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₇	1	2	yes	—
476	#137	—	4	4	no	—
477	AGL(1,ℤ/8)	—	4	4	no	—
478	#135	—	4	4	no	—
479	#135	—	4	4	no	—
480	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
481	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
482	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
483	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
484	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
485	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
486	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
487	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
488	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
489	C₂×D₈	C₂³×C₇	1	2	yes	—
490	C₂×D₈	C₂³×C₇	1	2	yes	—
491	C₂×D₈	C₂³×C₇	1	4	yes	—
492	C₂×M₁₆	C₂³×C₇	1	2	yes	—
493	C₂²×C₈	C₂³×C₇	1	2	yes	—
494	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
495	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
496	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
497	#127	C₂³×C₇	1	2	yes	—
498	#127	C₂³×C₇	1	1	yes	characteristic
499	#127	C₂³×C₇	1	1	yes	characteristic
500	#126	—	2	4	no	—
501	#126	—	2	4	no	—
502	#125	—	2	4	no	—
503	#125	—	2	2	no	—
504	#125	C₂³×C₇	1	2	yes	—
505	#125	C₂³×C₇	1	2	yes	—
506	#124	—	2	4	no	—
507	#124	—	2	2	no	—
508	#124	C₂³×C₇	1	2	yes	—
509	#124	C₂³×C₇	1	1	yes	characteristic
510	#124	C₂³×C₇	1	2	yes	—
511	#124	C₂³×C₇	1	2	yes	—
512	#124	C₂³×C₇	1	2	yes	—
513	#124	C₂³×C₇	1	2	yes	—
514	#124	C₂³×C₇	1	1	yes	characteristic
515	#123	—	2	4	no	—
516	#123	—	2	4	no	—
517	#123	—	2	2	no	—
518	#123	—	2	4	no	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	2	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
523	#121	—	2	2	no	—
524	#121	—	2	4	no	—
525	#121	—	2	2	no	—
526	#121	—	2	4	no	—
527	#121	—	2	2	no	—
528	#121	—	2	2	no	—
529	#121	—	2	4	no	—
530	#121	—	2	4	no	—
531	#121	C₂³×C₇	1	4	yes	—
532	#120	—	2	2	no	—
533	#120	—	2	4	no	—
534	C₄×Q₈	C₇×D₄	1	2	yes	—
535	C₄×Q₈	C₂³×C₇	1	4	yes	—
536	C₄×D₄	—	2	4	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	—	2	4	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	C₇×D₄	1	4	yes	—
542	C₄×D₄	C₇×D₄	1	2	yes	—
543	C₄×D₄	C₂³×C₇	1	4	yes	—
544	#117	—	2	2	no	—
545	#117	—	2	4	no	—
546	#117	C₂³×C₇	1	1	yes	characteristic
547	#117	C₂³×C₇	1	2	yes	—
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	—	2	2	no	—
550	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
551	C₂×C₂²⋊C₄	—	2	2	no	—
552	C₂×C₂²⋊C₄	—	2	4	no	—
553	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₇	1	2	yes	—
555	C₄⋊C₈	C₂³×C₇	1	4	yes	—
556	C₄⋊C₈	C₂³×C₇	1	4	yes	—
557	#103	C₂³×C₇	1	4	yes	—
558	#103	C₂³×C₇	1	4	yes	—
559	#103	C₂³×C₇	1	4	yes	—
560	#103	C₂³×C₇	1	4	yes	—
561	#102	C₂³×C₇	1	4	yes	—
562	#102	C₂³×C₇	1	4	yes	—
563	#102	C₂³×C₇	1	4	yes	—
564	#102	C₂³×C₇	1	4	yes	—
565	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
566	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
567	#97	C₂³×C₇	1	2	yes	—
568	C₄×C₈	C₂³×C₇	1	2	yes	—
569	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₇	1	2	yes	—
572	C₂²×C₇	—	2	2	no	—
573	C₂²×C₇	—	2	4	no	—
574	C₂²×C₇	—	2	2	no	—
575	C₂²×C₇	—	4	2	no	—
576	C₂²×C₇	—	4	2	no	—
577	C₂²×C₇	—	4	2	no	—
578	C₂²×C₇	—	4	4	no	—
579	C₂²×C₇	—	4	2	no	—
580	C₂²×C₇	—	4	1	no	—
581	C₂²×C₇	—	4	2	no	—
582	C₂²×C₇	—	4	1	no	—
583	C₂²×C₇	—	4	2	no	—
584	C₂²×C₇	—	16	2	no	—
585	C₂²×C₇	—	16	4	no	—
586	C₂²×C₇	#535	1	2	yes	—
587	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
588	C₄×C₇	—	2	2	no	—
589	C₄×C₇	—	2	4	no	—
590	C₄×C₇	—	2	2	no	—
591	C₄×C₇	—	2	2	no	—
592	C₄×C₇	—	4	4	no	—
593	C₄×C₇	—	4	1	no	—
594	C₄×C₇	—	4	2	no	—
595	C₄×C₇	—	4	1	no	—
596	C₄×C₇	—	4	2	no	—
597	C₄×C₇	#535	1	2	yes	—
598	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
599	C₂⁴	—	2	2	no	—
600	C₂⁴	—	2	1	no	—
601	#41	—	2	4	no	—
602	#41	—	2	4	no	—
603	#41	—	2	4	no	—
604	#41	—	2	4	no	—
605	#41	—	2	4	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	8	no	—
609	#41	—	4	4	no	—
610	#41	—	4	4	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	4	no	—
614	C₂×Q₈	—	4	4	no	—
615	C₂×Q₈	—	4	4	no	—
616	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
617	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
618	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
619	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
620	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	8	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
637	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
638	C₂×D₄	C₂⁴×C₇	1	2	yes	—
639	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
640	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
641	C₂×D₄	C₂⁴×C₇	1	2	yes	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
652	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
653	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
655	Q₁₆	—	4	2	no	—
656	Q₁₆	—	4	2	no	—
657	Q₁₆	—	4	4	no	—
658	SD₁₆	—	4	2	no	—
659	SD₁₆	—	4	2	no	—
660	SD₁₆	—	4	2	no	—
661	SD₁₆	—	4	2	no	—
662	SD₁₆	—	4	4	no	—
663	SD₁₆	—	4	4	no	—
664	D₈	—	4	2	no	—
665	D₈	—	4	2	no	—
666	D₈	—	4	4	no	—
667	M₁₆	—	2	4	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	4	yes	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
681	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
682	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
695	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
696	C₄²	—	2	4	no	—
697	C₄²	C₂×C₇×D₄	1	4	yes	—
698	C₄²	C₂×C₇×D₄	1	2	yes	—
699	C₄²	C₂⁴×C₇	1	1	yes	characteristic
700	C₄²	C₂⁴×C₇	1	1	yes	characteristic
701	C₄²	C₂⁴×C₇	1	2	yes	—
702	C₂×C₇	—	2	2	no	—
703	C₂×C₇	—	4	2	no	—
704	C₂×C₇	—	8	2	no	—
705	C₂×C₇	—	8	1	no	—
706	C₂×C₇	—	8	2	no	—
707	C₂×C₇	—	8	1	no	—
708	C₂×C₇	C₂×#535	1	1	yes	characteristic
709	C₂×C₇	#3584	1	2	yes	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	4	4	no	—
715	C₂³	—	4	2	no	—
716	C₂³	—	8	2	no	—
717	C₂³	—	8	4	no	—
718	C₂³	C₂²×C₇×D₄	1	2	yes	—
719	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
720	Q₈	—	2	2	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	2	2	no	—
723	Q₈	—	2	4	no	—
724	Q₈	—	2	2	no	—
725	Q₈	—	2	2	no	—
726	Q₈	—	4	4	no	—
727	Q₈	—	4	2	no	—
728	D₄	—	2	4	no	—
729	D₄	—	2	2	no	—
730	D₄	—	2	2	no	—
731	D₄	—	2	4	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	4	4	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	2	no	—
739	D₄	—	4	4	no	—
740	D₄	—	4	2	no	—
741	D₄	—	4	2	no	—
742	D₄	—	8	4	no	—
743	D₄	—	8	2	no	—
744	D₄	—	8	2	no	—
745	D₄	—	8	4	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	4	no	—
761	C₂×C₄	—	8	4	no	—
762	C₂×C₄	—	8	2	no	—
763	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
764	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
765	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
766	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
767	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
768	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
769	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₈	—	2	4	no	—
773	C₇	#60823	1	1	yes	characteristic, direct product factor, Sylow
774	C₂²	—	2	2	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	16	2	no	—
787	C₂²	—	16	4	no	—
788	C₂²	C₇×#535	1	2	yes	—
789	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
790	C₄	—	2	2	no	—
791	C₄	—	2	4	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	4	4	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	2	no	—
799	C₄	C₇×#535	1	2	yes	—
800	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
801	C₂	—	2	2	no	—
802	C₂	—	4	2	no	—
803	C₂	—	8	2	no	—
804	C₂	—	8	1	no	—
805	C₂	—	8	2	no	—
806	C₂	—	8	1	no	—
807	C₂	C₂×C₇×#535	1	1	yes	characteristic
808	C₂	C₇×#3584	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 ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3512	C₂	semidirect
2. C₇×#3500	C₂	semidirect
3. C₇×#3223	C₂	semidirect
4. C₇×#3222	C₂	semidirect
5. C₇×#3221	C₂	semidirect
6. C₇×#3220	C₂	semidirect
7. C₇×#3212	C₂	semidirect
8. C₇×#3211	C₂	semidirect
9. C₇×#3153	C₂	semidirect
10. C₇×#3147	C₂	semidirect
11. C₇×#3142	C₂	semidirect
12. C₂×C₇×#488	C₂	semidirect
13. C₇×#3046	C₂	semidirect
14. C₇×#3045	C₂	semidirect
15. C₇×#3013	C₂	semidirect
16. C₇×#3012	C₂	semidirect
17. C₇×#2922	C₂	semidirect
20. C₂×C₇×#137	C₂²	semidirect
23. C₂×C₇×#135	C₂²	semidirect
30. C₇×#541	C₂²	semidirect
31. C₇×#540	C₂²	semidirect
39. C₇×#532	C₂²	semidirect
40. C₇×#529	C₂²	semidirect
41. C₂×C₇×#125	C₂²	semidirect
44. C₇×#520	C₂²	semidirect
46. C₇×#497	C₂²	semidirect
47. C₇×#496	C₂²	semidirect
48. C₇×#495	C₂²	semidirect
49. C₇×#495	C₂²	semidirect
50. C₇×#495	C₂²	semidirect
51. C₇×#494	C₂²	semidirect
52. C₇×#493	C₂²	semidirect
53. C₇×#492	C₂²	semidirect
54. C₇×#492	C₂²	semidirect
55. C₇×#491	C₂²	semidirect
56. C₇×#490	C₂²	semidirect
57. C₇×#488	C₂²	semidirect
58. C₇×#488	C₂²	semidirect
59. C₇×#488	C₂²	semidirect
60. C₇×#488	C₂²	semidirect
61. C₇×#488	C₂²	semidirect
62. C₇×#464	C₂²	semidirect
63. C₇×#464	C₂²	semidirect
64. C₇×#463	C₂²	semidirect
65. C₇×#463	C₂²	semidirect
66. C₇×#462	C₂²	semidirect
67. C₇×#461	C₂²	semidirect
68. C₇×#460	C₂²	semidirect
69. C₇×#459	C₂²	semidirect
71. C₇×#452	C₂²	semidirect
72. C₇×#451	C₂²	semidirect
75. C₇×#449	C₂²	semidirect
76. C₇×#448	C₂²	semidirect
78. C₇×#433	C₂²	semidirect
79. C₇×#433	C₂²	semidirect
80. C₇×#431	C₂²	semidirect
81. C₇×#424	C₂²	semidirect
83. C₇×#417	C₂²	semidirect
84. C₂×C₇×#103	C₂²	semidirect
87. C₄×C₇×M₁₆	C₂²	semidirect
88. C₂×C₄×C₇×C₈	C₂²	semidirect
89. #60823	C₇	direct (N × H)
204. #3512	C₂×C₇	semidirect
205. #3500	C₂×C₇	semidirect
206. #3223	C₂×C₇	semidirect
207. #3222	C₂×C₇	semidirect
208. #3221	C₂×C₇	semidirect
209. #3220	C₂×C₇	semidirect
210. #3212	C₂×C₇	semidirect
211. #3211	C₂×C₇	semidirect
212. #3153	C₂×C₇	semidirect
213. #3147	C₂×C₇	semidirect
214. #3142	C₂×C₇	semidirect
215. C₂×#488	C₂×C₇	semidirect
216. #3046	C₂×C₇	semidirect
217. #3045	C₂×C₇	semidirect
218. #3013	C₂×C₇	semidirect
219. #3012	C₂×C₇	semidirect
220. #2922	C₂×C₇	semidirect
326. C₂×#137	C₂²×C₇	semidirect
329. C₂×#135	C₂²×C₇	semidirect
336. #541	C₂²×C₇	semidirect
337. #540	C₂²×C₇	semidirect
345. #532	C₂²×C₇	semidirect
346. #529	C₂²×C₇	semidirect
347. C₂×#125	C₂²×C₇	semidirect
350. #520	C₂²×C₇	semidirect
352. #497	C₂²×C₇	semidirect
353. #496	C₂²×C₇	semidirect
354. #495	C₂²×C₇	semidirect
355. #495	C₂²×C₇	semidirect
356. #495	C₂²×C₇	semidirect
357. #494	C₂²×C₇	semidirect
358. #493	C₂²×C₇	semidirect
359. #492	C₂²×C₇	semidirect
360. #492	C₂²×C₇	semidirect
361. #491	C₂²×C₇	semidirect
362. #490	C₂²×C₇	semidirect
363. #488	C₂²×C₇	semidirect
364. #488	C₂²×C₇	semidirect
365. #488	C₂²×C₇	semidirect
366. #488	C₂²×C₇	semidirect
367. #488	C₂²×C₇	semidirect
368. #464	C₂²×C₇	semidirect
369. #464	C₂²×C₇	semidirect
370. #463	C₂²×C₇	semidirect
371. #463	C₂²×C₇	semidirect
372. #462	C₂²×C₇	semidirect
373. #461	C₂²×C₇	semidirect
374. #460	C₂²×C₇	semidirect
375. #459	C₂²×C₇	semidirect
377. #452	C₂²×C₇	semidirect
378. #451	C₂²×C₇	semidirect
381. #449	C₂²×C₇	semidirect
382. #448	C₂²×C₇	semidirect
384. #433	C₂²×C₇	semidirect
385. #433	C₂²×C₇	semidirect
386. #431	C₂²×C₇	semidirect
387. #424	C₂²×C₇	semidirect
389. #417	C₂²×C₇	semidirect
390. C₂×#103	C₂²×C₇	semidirect
393. C₄×M₁₆	C₂²×C₇	semidirect
394. C₂×C₄×C₈	C₂²×C₇	semidirect
773. C₇	#60823	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×#3512	2
C₇×#3500	2
C₇×#3223	2
C₇×#3222	2
C₇×#3221	2
C₇×#3220	2
C₇×#3212	2
C₇×#3211	2
C₇×#3153	2
C₇×#3147	2
C₇×#3142	2
C₂×C₇×#488	2
C₇×#3046	2
C₇×#3045	2
C₇×#3013	2
C₇×#3012	2
C₇×#2922	2
#60823	7

Subgroups — C7×#60823 #13238039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60823 #13238039