Subgroups — C₇×#60170 #13237386

Order 1792.

2742 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#575	C₂	1	1	yes	maximal, characteristic
2	C₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2952	C₂	1	4	yes	maximal, complemented
5	C₇×#2951	C₂	1	4	yes	maximal, complemented
6	C₇×#2947	C₂	1	4	yes	maximal, complemented
7	C₇×#2946	C₂	1	4	yes	maximal, complemented
8	C₄×C₇×#137	C₂	1	4	yes	maximal, complemented
9	C₄×C₇×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
10	C₂×C₇×#428	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#417	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
16	C₇×#575	C₄	1	16	yes	complemented
17	C₂×C₇×#137	C₂²	1	2	yes	—
18	C₂×C₇×#137	C₂²	1	2	yes	—
19	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₇×#135	C₂²	1	4	yes	—
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
24	C₇×#520	—	2	2	no	—
25	C₇×#520	—	2	2	no	—
26	C₇×#520	—	2	1	no	—
27	C₇×#520	—	2	1	no	—
28	C₇×#520	C₂²	1	4	yes	—
29	C₇×#520	C₂²	1	2	yes	complemented
30	C₇×#520	C₂²	1	4	yes	complemented
31	C₇×#520	C₂²	1	2	yes	complemented
32	C₇×#519	C₂²	1	2	yes	complemented
33	C₇×#518	—	2	2	no	—
34	C₇×#518	C₂²	1	2	yes	complemented
35	C₄×C₇×#41	—	2	2	no	—
36	C₄×C₇×#41	C₂²	1	4	yes	—
37	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
38	C₂×C₄×C₇×D₄	—	2	2	no	—
39	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
40	C₂×C₇×#117	—	2	2	no	—
41	C₂×C₇×#117	—	2	1	no	—
42	C₂×C₇×#117	C₂²	1	1	yes	characteristic
43	C₂×C₇×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
45	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₇×#442	C₂²	1	8	yes	complemented
47	C₇×#441	C₂²	1	8	yes	complemented
48	C₇×#440	C₂²	1	8	yes	complemented
49	C₇×#440	C₂²	1	8	yes	complemented
50	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
51	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
52	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
53	C₄×C₇×D₈	C₂²	1	8	yes	complemented
54	C₇×#428	C₂²	1	4	yes	complemented
55	C₇×#428	C₂²	1	4	yes	complemented
56	C₂×C₇×#107	C₂²	1	2	yes	complemented
57	C₂×C₇×#106	C₂²	1	2	yes	complemented
58	C₇×#419	C₂²	1	2	yes	complemented
59	C₇×#418	C₂²	1	2	yes	complemented
60	C₇×#417	C₂²	1	4	yes	—
61	C₇×#417	C₂²	1	2	yes	complemented
62	C₇×#417	C₂²	1	4	yes	complemented
63	C₇×#417	C₂²	1	2	yes	complemented
64	C₇×#416	C₂²	1	4	yes	—
65	C₂×C₇×#103	C₂²	1	2	yes	complemented
66	C₂×C₇×#102	C₂²	1	2	yes	complemented
67	C₇×#405	C₂²	1	4	yes	complemented
68	C₇×#405	C₂²	1	4	yes	complemented
69	C₄×C₇×M₁₆	C₂²	1	4	yes	complemented
70	#60170	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂×C₇×#41	—	2	1	no	—
72	C₂×C₇×#41	—	2	1	no	—
73	C₂×C₇×#41	—	2	1	no	—
74	C₂×C₇×#41	—	2	1	no	—
75	C₂×C₇×#41	—	2	4	no	—
76	C₂×C₇×#41	—	2	4	no	—
77	C₂×C₇×#41	C₂×C₄	1	8	yes	complemented
78	C₂×C₇×#41	C₂×C₄	1	8	yes	complemented
79	C₂×C₇×#41	C₂³	1	2	yes	—
80	C₂×C₇×#41	C₂³	1	2	yes	—
81	C₂×C₇×#41	C₂³	1	2	yes	—
82	C₂×C₇×#41	C₂³	1	2	yes	—
83	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
84	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
85	C₂²×C₇×D₄	—	2	1	no	—
86	C₂²×C₇×D₄	—	2	1	no	—
87	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇	—	2	1	no	—
90	C₂³×C₄×C₇	—	2	1	no	—
91	C₂³×C₄×C₇	—	2	1	no	—
92	C₂³×C₄×C₇	—	2	2	no	—
93	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
94	C₇×#137	C₂×C₄	1	16	yes	complemented
95	C₇×#137	C₂×C₄	1	16	yes	complemented
96	C₇×AGL(1,ℤ/8)	C₂×C₄	1	16	yes	complemented
97	C₇×AGL(1,ℤ/8)	C₂×C₄	1	16	yes	complemented
98	C₇×#135	C₂×C₄	1	32	yes	complemented
99	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
100	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
102	C₂×C₇×D₈	C₂³	1	4	yes	—
103	C₂×C₇×M₁₆	—	2	4	no	—
104	C₂×C₇×M₁₆	C₂×C₄	1	8	yes	complemented
105	C₂×C₇×M₁₆	C₂³	1	2	yes	—
106	C₂×C₇×M₁₆	C₂³	1	2	yes	—
107	C₂×C₇×M₁₆	C₂³	1	2	yes	—
108	C₂×C₇×M₁₆	C₂³	1	2	yes	—
109	C₂²×C₇×C₈	C₂³	1	2	yes	—
110	C₂²×C₇×C₈	C₂³	1	2	yes	—
111	C₄×C₇×Q₈	—	2	2	no	—
112	C₄×C₇×Q₈	—	2	2	no	—
113	C₄×C₇×Q₈	—	2	4	no	—
114	C₄×C₇×Q₈	C₂³	1	8	yes	—
115	C₄×C₇×Q₈	C₂³	1	4	yes	—
116	C₄×C₇×Q₈	C₂³	1	4	yes	—
117	C₄×C₇×D₄	—	2	4	no	—
118	C₄×C₇×D₄	—	2	4	no	—
119	C₄×C₇×D₄	—	2	2	no	—
120	C₄×C₇×D₄	—	2	2	no	—
121	C₄×C₇×D₄	—	2	8	no	—
122	C₄×C₇×D₄	—	2	8	no	—
123	C₄×C₇×D₄	—	2	4	no	—
124	C₄×C₇×D₄	—	2	4	no	—
125	C₄×C₇×D₄	—	2	4	no	—
126	C₄×C₇×D₄	C₂³	1	8	yes	—
127	C₄×C₇×D₄	C₂³	1	4	yes	—
128	C₄×C₇×D₄	C₂³	1	4	yes	—
129	C₇×#117	—	2	1	no	—
130	C₇×#117	—	2	1	no	—
131	C₇×#117	—	2	4	no	—
132	C₇×#117	—	2	4	no	—
133	C₇×#117	—	2	2	no	—
134	C₇×#117	—	2	2	no	—
135	C₇×#117	—	2	4	no	—
136	C₇×#117	—	2	4	no	—
137	C₇×#117	D₄	1	2	yes	—
138	C₇×#117	D₄	1	2	yes	—
139	C₇×#117	C₂³	1	2	yes	—
140	C₇×#117	C₂³	1	2	yes	—
141	C₇×#117	C₂³	1	2	yes	—
142	C₇×#117	C₂³	1	2	yes	—
143	C₂×C₇×C₄⋊C₄	—	2	1	no	—
144	C₂×C₇×C₄⋊C₄	—	2	2	no	—
145	C₂×C₇×C₄⋊C₄	—	2	1	no	—
146	C₂×C₇×C₄⋊C₄	—	2	1	no	—
147	C₂×C₇×C₄⋊C₄	—	2	4	no	—
148	C₂×C₇×C₄⋊C₄	—	2	4	no	—
149	C₂×C₇×C₄⋊C₄	—	2	2	no	—
150	C₂×C₇×C₄⋊C₄	—	2	2	no	—
151	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
152	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
160	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
161	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
162	C₂×C₄²×C₇	—	2	2	no	—
163	C₂×C₄²×C₇	—	2	1	no	—
164	C₂×C₄²×C₇	—	2	4	no	—
165	C₂×C₄²×C₇	C₂³	1	2	yes	—
166	C₇×#107	C₂³	1	8	yes	—
167	C₇×#106	C₂³	1	8	yes	—
168	C₇×#103	C₂³	1	8	yes	—
169	C₇×#103	C₂³	1	4	yes	—
170	C₇×#103	C₂³	1	4	yes	—
171	C₇×#102	C₂³	1	8	yes	—
172	C₇×#102	C₂³	1	4	yes	—
173	C₇×#102	C₂³	1	4	yes	—
174	C₇×#97	C₂³	1	8	yes	—
175	C₄×C₇×C₈	C₂³	1	8	yes	—
176	C₂×#575	C₂×C₇	1	1	yes	characteristic
177	#3428	C₂×C₇	1	1	yes	characteristic, complemented
178	C₂×#520	C₂×C₇	1	1	yes	characteristic, complemented
179	#2952	C₂×C₇	1	4	yes	complemented
180	#2951	C₂×C₇	1	4	yes	complemented
181	#2947	C₂×C₇	1	4	yes	complemented
182	#2946	C₂×C₇	1	4	yes	complemented
183	C₄×#137	C₂×C₇	1	4	yes	complemented
184	C₄×AGL(1,ℤ/8)	C₂×C₇	1	4	yes	complemented
185	C₂×#428	C₂×C₇	1	1	yes	characteristic, complemented
186	#2896	C₂×C₇	1	1	yes	characteristic, complemented
187	C₂×#417	C₂×C₇	1	1	yes	characteristic, complemented
188	#2873	C₂×C₇	1	1	yes	characteristic, complemented
189	C₂⁴×C₇	—	2	1	no	—
190	C₂⁴×C₇	—	2	1	no	—
191	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
192	C₇×#41	—	2	8	no	—
193	C₇×#41	—	2	8	no	—
194	C₇×#41	—	2	8	no	—
195	C₇×#41	—	2	8	no	—
196	C₇×#41	—	2	4	no	—
197	C₇×#41	—	2	4	no	—
198	C₇×#41	—	2	4	no	—
199	C₇×#41	—	2	4	no	—
200	C₇×#41	C₂²×C₄	1	8	yes	—
201	C₇×#41	C₂²×C₄	1	8	yes	—
202	C₇×#41	C₂²×C₄	1	8	yes	—
203	C₇×#41	C₂²×C₄	1	8	yes	complemented
204	C₂×C₇×Q₈	—	2	1	no	—
205	C₂×C₇×Q₈	—	2	1	no	—
206	C₂×C₇×Q₈	—	2	2	no	—
207	C₂×C₇×Q₈	—	2	2	no	—
208	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
209	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	complemented
210	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
211	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
212	C₂×C₇×D₄	—	2	8	no	—
213	C₂×C₇×D₄	—	2	8	no	—
214	C₂×C₇×D₄	—	2	2	no	—
215	C₂×C₇×D₄	—	2	2	no	—
216	C₂×C₇×D₄	—	2	2	no	—
217	C₂×C₇×D₄	—	2	2	no	—
218	C₂×C₇×D₄	—	2	1	no	—
219	C₂×C₇×D₄	—	2	1	no	—
220	C₂×C₇×D₄	—	2	2	no	—
221	C₂×C₇×D₄	—	2	2	no	—
222	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
223	C₂×C₇×D₄	C₂²×C₄	1	4	yes	complemented
224	C₂×C₇×D₄	C₂⁴	1	2	yes	—
225	C₂×C₇×D₄	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₇	—	2	1	no	—
227	C₂²×C₄×C₇	—	2	1	no	—
228	C₂²×C₄×C₇	—	2	8	no	—
229	C₂²×C₄×C₇	—	2	8	no	—
230	C₂²×C₄×C₇	—	2	2	no	—
231	C₂²×C₄×C₇	—	2	2	no	—
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	1	no	—
236	C₂²×C₄×C₇	—	2	1	no	—
237	C₂²×C₄×C₇	—	2	2	no	—
238	C₂²×C₄×C₇	—	2	2	no	—
239	C₂²×C₄×C₇	—	2	4	no	—
240	C₂²×C₄×C₇	—	2	4	no	—
241	C₂²×C₄×C₇	—	2	8	no	—
242	C₂²×C₄×C₇	—	8	4	no	—
243	C₂²×C₄×C₇	—	8	2	no	—
244	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
245	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇	#41	1	4	yes	—
251	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
254	C₇×Q₁₆	C₂²×C₄	1	16	yes	complemented
255	C₇×SD₁₆	C₂²×C₄	1	16	yes	complemented
256	C₇×SD₁₆	C₂²×C₄	1	16	yes	complemented
257	C₇×D₈	C₂²×C₄	1	16	yes	complemented
258	C₇×M₁₆	—	2	4	no	—
259	C₇×M₁₆	—	2	4	no	—
260	C₇×M₁₆	C₂²×C₄	1	8	yes	—
261	C₇×M₁₆	C₂²×C₄	1	8	yes	complemented
262	C₂×C₇×C₈	—	2	4	no	—
263	C₂×C₇×C₈	C₂²×C₄	1	8	yes	complemented
264	C₂×C₇×C₈	C₂⁴	1	4	yes	—
265	C₂×C₇×C₈	C₂⁴	1	4	yes	—
266	C₇×C₄⋊C₄	—	2	2	no	—
267	C₇×C₄⋊C₄	—	2	2	no	—
268	C₇×C₄⋊C₄	—	2	8	no	—
269	C₇×C₄⋊C₄	—	2	1	no	—
270	C₇×C₄⋊C₄	—	2	1	no	—
271	C₇×C₄⋊C₄	—	2	2	no	—
272	C₇×C₄⋊C₄	—	2	4	no	—
273	C₇×C₄⋊C₄	—	2	4	no	—
274	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
275	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
277	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
280	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₇×C₂²⋊C₄	—	2	2	no	—
282	C₇×C₂²⋊C₄	—	2	2	no	—
283	C₇×C₂²⋊C₄	—	2	4	no	—
284	C₇×C₂²⋊C₄	—	2	4	no	—
285	C₇×C₂²⋊C₄	—	2	8	no	—
286	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
287	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
288	C₄²×C₇	—	2	2	no	—
289	C₄²×C₇	—	2	4	no	—
290	C₄²×C₇	—	2	4	no	—
291	C₄²×C₇	—	2	8	no	—
292	C₄²×C₇	—	2	2	no	—
293	C₄²×C₇	C₂×D₄	1	4	yes	—
294	C₄²×C₇	C₂⁴	1	4	yes	—
295	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
296	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
297	#575	C₄×C₇	1	16	yes	complemented
298	C₂×#137	C₂²×C₇	1	2	yes	—
299	C₂×#137	C₂²×C₇	1	2	yes	—
300	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
301	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
302	C₂×#135	C₂²×C₇	1	4	yes	—
303	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
304	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
305	#520	—	2	2	no	—
306	#520	—	2	2	no	—
307	#520	—	2	1	no	—
308	#520	—	2	1	no	—
309	#520	C₂²×C₇	1	4	yes	—
310	#520	C₂²×C₇	1	4	yes	complemented
311	#520	C₂²×C₇	1	2	yes	complemented
312	#520	C₂²×C₇	1	2	yes	complemented
313	#519	C₂²×C₇	1	2	yes	complemented
314	#518	—	2	2	no	—
315	#518	C₂²×C₇	1	2	yes	complemented
316	C₄×#41	—	2	2	no	—
317	C₄×#41	C₂²×C₇	1	4	yes	—
318	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
319	C₂×C₄×D₄	—	2	2	no	—
320	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
321	C₂×#117	—	2	2	no	—
322	C₂×#117	—	2	1	no	—
323	C₂×#117	C₂²×C₇	1	1	yes	characteristic
324	C₂×#117	C₂²×C₇	1	1	yes	characteristic
325	C₂²×C₄⋊C₄	—	2	1	no	—
326	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
327	#442	C₂²×C₇	1	8	yes	complemented
328	#441	C₂²×C₇	1	8	yes	complemented
329	#440	C₂²×C₇	1	8	yes	complemented
330	#440	C₂²×C₇	1	8	yes	complemented
331	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
332	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
333	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
334	C₄×D₈	C₂²×C₇	1	8	yes	complemented
335	#428	C₂²×C₇	1	4	yes	complemented
336	#428	C₂²×C₇	1	4	yes	complemented
337	C₂×#107	C₂²×C₇	1	2	yes	complemented
338	C₂×#106	C₂²×C₇	1	2	yes	complemented
339	#419	C₂²×C₇	1	2	yes	complemented
340	#418	C₂²×C₇	1	2	yes	complemented
341	#417	C₂²×C₇	1	4	yes	—
342	#417	C₂²×C₇	1	4	yes	complemented
343	#417	C₂²×C₇	1	2	yes	complemented
344	#417	C₂²×C₇	1	2	yes	complemented
345	#416	C₂²×C₇	1	4	yes	—
346	C₂×#103	C₂²×C₇	1	2	yes	complemented
347	C₂×#102	C₂²×C₇	1	2	yes	complemented
348	#405	C₂²×C₇	1	4	yes	complemented
349	#405	C₂²×C₇	1	4	yes	complemented
350	C₄×M₁₆	C₂²×C₇	1	4	yes	complemented
351	C₂³×C₇	—	2	4	no	—
352	C₂³×C₇	—	2	2	no	—
353	C₂³×C₇	—	2	2	no	—
354	C₂³×C₇	—	2	4	no	—
355	C₂³×C₇	—	4	1	no	—
356	C₂³×C₇	—	4	1	no	—
357	C₂³×C₇	—	4	2	no	—
358	C₂³×C₇	—	4	2	no	—
359	C₂³×C₇	—	8	1	no	—
360	C₂³×C₇	—	8	1	no	—
361	C₂³×C₇	C₄×D₄	1	4	yes	—
362	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
363	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
364	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
365	C₇×Q₈	—	2	4	no	—
366	C₇×Q₈	—	2	4	no	—
367	C₇×Q₈	—	2	2	no	—
368	C₇×Q₈	—	2	2	no	—
369	C₇×Q₈	C₂³×C₄	1	4	yes	—
370	C₇×Q₈	C₂³×C₄	1	4	yes	—
371	C₇×D₄	—	2	8	no	—
372	C₇×D₄	—	2	8	no	—
373	C₇×D₄	—	2	8	no	—
374	C₇×D₄	—	2	8	no	—
375	C₇×D₄	—	2	4	no	—
376	C₇×D₄	—	2	4	no	—
377	C₇×D₄	—	2	2	no	—
378	C₇×D₄	—	2	2	no	—
379	C₇×D₄	C₂³×C₄	1	4	yes	—
380	C₇×D₄	C₂³×C₄	1	4	yes	—
381	C₂×C₄×C₇	—	2	4	no	—
382	C₂×C₄×C₇	—	2	4	no	—
383	C₂×C₄×C₇	—	2	2	no	—
384	C₂×C₄×C₇	—	2	2	no	—
385	C₂×C₄×C₇	—	2	8	no	—
386	C₂×C₄×C₇	—	2	8	no	—
387	C₂×C₄×C₇	—	2	8	no	—
388	C₂×C₄×C₇	—	2	8	no	—
389	C₂×C₄×C₇	—	2	2	no	—
390	C₂×C₄×C₇	—	2	2	no	—
391	C₂×C₄×C₇	—	2	4	no	—
392	C₂×C₄×C₇	—	4	2	no	—
393	C₂×C₄×C₇	—	4	2	no	—
394	C₂×C₄×C₇	—	4	4	no	—
395	C₂×C₄×C₇	—	8	4	no	—
396	C₂×C₄×C₇	—	8	4	no	—
397	C₂×C₄×C₇	—	8	8	no	—
398	C₂×C₄×C₇	—	8	1	no	—
399	C₂×C₄×C₇	—	8	1	no	—
400	C₂×C₄×C₇	—	8	2	no	—
401	C₂×C₄×C₇	—	8	2	no	—
402	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
403	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
404	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
405	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
406	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
407	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
408	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
409	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
410	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₇	C₂×#41	1	2	yes	—
414	C₂×C₄×C₇	C₂×#41	1	2	yes	—
415	C₂×C₄×C₇	C₂×#41	1	2	yes	—
416	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
417	C₇×C₈	—	2	4	no	—
418	C₇×C₈	C₂³×C₄	1	8	yes	—
419	C₂×#41	—	2	1	no	—
420	C₂×#41	—	2	1	no	—
421	C₂×#41	—	2	1	no	—
422	C₂×#41	—	2	1	no	—
423	C₂×#41	—	2	4	no	—
424	C₂×#41	—	2	4	no	—
425	C₂×#41	C₂×C₄×C₇	1	8	yes	complemented
426	C₂×#41	C₂×C₄×C₇	1	8	yes	complemented
427	C₂×#41	C₂³×C₇	1	2	yes	—
428	C₂×#41	C₂³×C₇	1	2	yes	—
429	C₂×#41	C₂³×C₇	1	2	yes	—
430	C₂×#41	C₂³×C₇	1	2	yes	—
431	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
432	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
433	C₂²×D₄	—	2	1	no	—
434	C₂²×D₄	—	2	1	no	—
435	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
436	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	—	2	1	no	—
440	C₂³×C₄	—	2	2	no	—
441	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
442	#137	C₂×C₄×C₇	1	16	yes	complemented
443	#137	C₂×C₄×C₇	1	16	yes	complemented
444	AGL(1,ℤ/8)	C₂×C₄×C₇	1	16	yes	complemented
445	AGL(1,ℤ/8)	C₂×C₄×C₇	1	16	yes	complemented
446	#135	C₂×C₄×C₇	1	32	yes	complemented
447	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
448	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
449	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
450	C₂×D₈	C₂³×C₇	1	4	yes	—
451	C₂×M₁₆	—	2	4	no	—
452	C₂×M₁₆	C₂×C₄×C₇	1	8	yes	complemented
453	C₂×M₁₆	C₂³×C₇	1	2	yes	—
454	C₂×M₁₆	C₂³×C₇	1	2	yes	—
455	C₂×M₁₆	C₂³×C₇	1	2	yes	—
456	C₂×M₁₆	C₂³×C₇	1	2	yes	—
457	C₂²×C₈	C₂³×C₇	1	2	yes	—
458	C₂²×C₈	C₂³×C₇	1	2	yes	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	—	2	4	no	—
462	C₄×Q₈	C₂³×C₇	1	8	yes	—
463	C₄×Q₈	C₂³×C₇	1	4	yes	—
464	C₄×Q₈	C₂³×C₇	1	4	yes	—
465	C₄×D₄	—	2	4	no	—
466	C₄×D₄	—	2	4	no	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	—	2	2	no	—
469	C₄×D₄	—	2	8	no	—
470	C₄×D₄	—	2	8	no	—
471	C₄×D₄	—	2	4	no	—
472	C₄×D₄	—	2	4	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	C₂³×C₇	1	8	yes	—
475	C₄×D₄	C₂³×C₇	1	4	yes	—
476	C₄×D₄	C₂³×C₇	1	4	yes	—
477	#117	—	2	1	no	—
478	#117	—	2	1	no	—
479	#117	—	2	4	no	—
480	#117	—	2	4	no	—
481	#117	—	2	2	no	—
482	#117	—	2	2	no	—
483	#117	—	2	4	no	—
484	#117	—	2	4	no	—
485	#117	C₇×D₄	1	2	yes	—
486	#117	C₇×D₄	1	2	yes	—
487	#117	C₂³×C₇	1	2	yes	—
488	#117	C₂³×C₇	1	2	yes	—
489	#117	C₂³×C₇	1	2	yes	—
490	#117	C₂³×C₇	1	2	yes	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	2	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	4	no	—
496	C₂×C₄⋊C₄	—	2	4	no	—
497	C₂×C₄⋊C₄	—	2	2	no	—
498	C₂×C₄⋊C₄	—	2	2	no	—
499	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	2	no	—
508	C₂×C₂²⋊C₄	—	2	4	no	—
509	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
510	C₂×C₄²	—	2	2	no	—
511	C₂×C₄²	—	2	1	no	—
512	C₂×C₄²	—	2	4	no	—
513	C₂×C₄²	C₂³×C₇	1	2	yes	—
514	#107	C₂³×C₇	1	8	yes	—
515	#106	C₂³×C₇	1	8	yes	—
516	#103	C₂³×C₇	1	8	yes	—
517	#103	C₂³×C₇	1	4	yes	—
518	#103	C₂³×C₇	1	4	yes	—
519	#102	C₂³×C₇	1	8	yes	—
520	#102	C₂³×C₇	1	4	yes	—
521	#102	C₂³×C₇	1	4	yes	—
522	#97	C₂³×C₇	1	8	yes	—
523	C₄×C₈	C₂³×C₇	1	8	yes	—
524	C₂²×C₇	—	2	1	no	—
525	C₂²×C₇	—	2	1	no	—
526	C₂²×C₇	—	2	1	no	—
527	C₂²×C₇	—	2	1	no	—
528	C₂²×C₇	—	2	1	no	—
529	C₂²×C₇	—	2	1	no	—
530	C₂²×C₇	—	2	4	no	—
531	C₂²×C₇	—	2	4	no	—
532	C₂²×C₇	—	4	4	no	—
533	C₂²×C₇	—	4	8	no	—
534	C₂²×C₇	—	4	2	no	—
535	C₂²×C₇	—	4	2	no	—
536	C₂²×C₇	—	4	2	no	—
537	C₂²×C₇	—	4	2	no	—
538	C₂²×C₇	—	8	4	no	—
539	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
540	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
541	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
542	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
543	C₄×C₇	—	2	4	no	—
544	C₄×C₇	—	2	4	no	—
545	C₄×C₇	—	2	4	no	—
546	C₄×C₇	—	2	4	no	—
547	C₄×C₇	—	4	4	no	—
548	C₄×C₇	—	4	2	no	—
549	C₄×C₇	—	4	2	no	—
550	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
551	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
552	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
553	C₄×C₇	C₂⁴×C₄	1	1	yes	characteristic
554	C₄×C₇	C₂²×#41	1	1	yes	characteristic
555	C₂⁴	—	2	1	no	—
556	C₂⁴	—	2	1	no	—
557	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
558	#41	—	2	8	no	—
559	#41	—	2	8	no	—
560	#41	—	2	8	no	—
561	#41	—	2	8	no	—
562	#41	—	2	4	no	—
563	#41	—	2	4	no	—
564	#41	—	2	4	no	—
565	#41	—	2	4	no	—
566	#41	C₂²×C₄×C₇	1	8	yes	—
567	#41	C₂²×C₄×C₇	1	8	yes	—
568	#41	C₂²×C₄×C₇	1	8	yes	—
569	#41	C₂²×C₄×C₇	1	8	yes	complemented
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
575	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	complemented
576	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
577	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
578	C₂×D₄	—	2	8	no	—
579	C₂×D₄	—	2	8	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
589	C₂×D₄	C₂²×C₄×C₇	1	4	yes	complemented
590	C₂×D₄	C₂⁴×C₇	1	2	yes	—
591	C₂×D₄	C₂⁴×C₇	1	2	yes	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	8	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	8	no	—
608	C₂²×C₄	—	8	4	no	—
609	C₂²×C₄	—	8	2	no	—
610	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
611	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
612	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
613	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
614	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
615	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
616	C₂²×C₄	C₇×#41	1	4	yes	—
617	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
620	Q₁₆	C₂²×C₄×C₇	1	16	yes	complemented
621	SD₁₆	C₂²×C₄×C₇	1	16	yes	complemented
622	SD₁₆	C₂²×C₄×C₇	1	16	yes	complemented
623	D₈	C₂²×C₄×C₇	1	16	yes	complemented
624	M₁₆	—	2	4	no	—
625	M₁₆	—	2	4	no	—
626	M₁₆	C₂²×C₄×C₇	1	8	yes	—
627	M₁₆	C₂²×C₄×C₇	1	8	yes	complemented
628	C₂×C₈	—	2	4	no	—
629	C₂×C₈	C₂²×C₄×C₇	1	8	yes	complemented
630	C₂×C₈	C₂⁴×C₇	1	4	yes	—
631	C₂×C₈	C₂⁴×C₇	1	4	yes	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	8	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
641	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
642	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
643	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
646	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	8	no	—
652	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
653	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	8	no	—
658	C₄²	—	2	2	no	—
659	C₄²	C₂×C₇×D₄	1	4	yes	—
660	C₄²	C₂⁴×C₇	1	4	yes	—
661	C₂×C₇	—	2	2	no	—
662	C₂×C₇	—	2	2	no	—
663	C₂×C₇	—	2	2	no	—
664	C₂×C₇	—	4	4	no	—
665	C₂×C₇	—	4	4	no	—
666	C₂×C₇	C₂²×C₄×D₄	1	1	yes	characteristic
667	C₂×C₇	#3585	1	1	yes	characteristic
668	C₂×C₇	#3586	1	1	yes	characteristic
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	4	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	2	no	—
676	C₂³	—	4	2	no	—
677	C₂³	—	8	1	no	—
678	C₂³	—	8	1	no	—
679	C₂³	C₄×C₇×D₄	1	4	yes	—
680	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
681	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
682	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	4	no	—
686	Q₈	—	2	4	no	—
687	Q₈	C₂³×C₄×C₇	1	4	yes	—
688	Q₈	C₂³×C₄×C₇	1	4	yes	—
689	D₄	—	2	8	no	—
690	D₄	—	2	8	no	—
691	D₄	—	2	8	no	—
692	D₄	—	2	8	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	4	no	—
696	D₄	—	2	4	no	—
697	D₄	C₂³×C₄×C₇	1	4	yes	—
698	D₄	C₂³×C₄×C₇	1	4	yes	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	8	no	—
705	C₂×C₄	—	2	8	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	8	no	—
716	C₂×C₄	—	8	1	no	—
717	C₂×C₄	—	8	1	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
721	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
722	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
723	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
724	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
725	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
726	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
727	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
728	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
729	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
730	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
731	C₂×C₄	C₂×C₇×#41	1	2	yes	—
732	C₂×C₄	C₂×C₇×#41	1	2	yes	—
733	C₂×C₄	C₂×C₇×#41	1	2	yes	—
734	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
735	C₈	—	2	4	no	—
736	C₈	C₂³×C₄×C₇	1	8	yes	—
737	C₇	#60170	1	1	yes	characteristic, direct product factor, Sylow
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	4	4	no	—
747	C₂²	—	4	8	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	8	4	no	—
753	C₂²	C₂×C₄×C₇×D₄	1	2	yes	—
754	C₂²	C₂×C₄×C₇×D₄	1	2	yes	—
755	C₂²	C₂×C₄×C₇×D₄	1	2	yes	—
756	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
757	C₄	—	2	4	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	4	4	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
765	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
766	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
767	C₄	C₂⁴×C₄×C₇	1	1	yes	characteristic
768	C₄	C₂²×C₇×#41	1	1	yes	characteristic
769	C₂	—	2	2	no	—
770	C₂	—	2	2	no	—
771	C₂	—	2	2	no	—
772	C₂	—	4	4	no	—
773	C₂	—	4	4	no	—
774	C₂	C₂²×C₄×C₇×D₄	1	1	yes	characteristic
775	C₂	C₇×#3585	1	1	yes	characteristic
776	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#575	C₂
LCS	G ▷ 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
2. C₇×#3428	C₂	semidirect
3. C₂×C₇×#520	C₂	semidirect
4. C₇×#2952	C₂	semidirect
5. C₇×#2951	C₂	semidirect
6. C₇×#2947	C₂	semidirect
7. C₇×#2946	C₂	semidirect
8. C₄×C₇×#137	C₂	semidirect
9. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
10. C₂×C₇×#428	C₂	semidirect
11. C₇×#2896	C₂	semidirect
12. C₂×C₇×#417	C₂	semidirect
13. C₇×#2873	C₂	semidirect
16. C₇×#575	C₄	semidirect
29. C₇×#520	C₂²	semidirect
30. C₇×#520	C₂²	semidirect
31. C₇×#520	C₂²	semidirect
32. C₇×#519	C₂²	semidirect
34. C₇×#518	C₂²	semidirect
37. C₂×C₄×C₇×Q₈	C₂²	semidirect
39. C₂×C₄×C₇×D₄	C₂²	semidirect
46. C₇×#442	C₂²	semidirect
47. C₇×#441	C₂²	semidirect
48. C₇×#440	C₂²	semidirect
49. C₇×#440	C₂²	semidirect
50. C₄×C₇×Q₁₆	C₂²	semidirect
51. C₄×C₇×SD₁₆	C₂²	semidirect
52. C₄×C₇×SD₁₆	C₂²	semidirect
53. C₄×C₇×D₈	C₂²	semidirect
54. C₇×#428	C₂²	semidirect
55. C₇×#428	C₂²	semidirect
56. C₂×C₇×#107	C₂²	semidirect
57. C₂×C₇×#106	C₂²	semidirect
58. C₇×#419	C₂²	semidirect
59. C₇×#418	C₂²	semidirect
61. C₇×#417	C₂²	semidirect
62. C₇×#417	C₂²	semidirect
63. C₇×#417	C₂²	semidirect
65. C₂×C₇×#103	C₂²	semidirect
66. C₂×C₇×#102	C₂²	semidirect
67. C₇×#405	C₂²	semidirect
68. C₇×#405	C₂²	semidirect
69. C₄×C₇×M₁₆	C₂²	semidirect
70. #60170	C₇	direct (N × H)
77. C₂×C₇×#41	C₂×C₄	semidirect
78. C₂×C₇×#41	C₂×C₄	semidirect
94. C₇×#137	C₂×C₄	semidirect
95. C₇×#137	C₂×C₄	semidirect
96. C₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
97. C₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
98. C₇×#135	C₂×C₄	semidirect
104. C₂×C₇×M₁₆	C₂×C₄	semidirect
177. #3428	C₂×C₇	semidirect
178. C₂×#520	C₂×C₇	semidirect
179. #2952	C₂×C₇	semidirect
180. #2951	C₂×C₇	semidirect
181. #2947	C₂×C₇	semidirect
182. #2946	C₂×C₇	semidirect
183. C₄×#137	C₂×C₇	semidirect
184. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
185. C₂×#428	C₂×C₇	semidirect
186. #2896	C₂×C₇	semidirect
187. C₂×#417	C₂×C₇	semidirect
188. #2873	C₂×C₇	semidirect
203. C₇×#41	C₂²×C₄	semidirect
209. C₂×C₇×Q₈	C₂²×C₄	semidirect
223. C₂×C₇×D₄	C₂²×C₄	semidirect
254. C₇×Q₁₆	C₂²×C₄	semidirect
255. C₇×SD₁₆	C₂²×C₄	semidirect
256. C₇×SD₁₆	C₂²×C₄	semidirect
257. C₇×D₈	C₂²×C₄	semidirect
261. C₇×M₁₆	C₂²×C₄	semidirect
263. C₂×C₇×C₈	C₂²×C₄	semidirect
297. #575	C₄×C₇	semidirect
310. #520	C₂²×C₇	semidirect
311. #520	C₂²×C₇	semidirect
312. #520	C₂²×C₇	semidirect
313. #519	C₂²×C₇	semidirect
315. #518	C₂²×C₇	semidirect
318. C₂×C₄×Q₈	C₂²×C₇	semidirect
320. C₂×C₄×D₄	C₂²×C₇	semidirect
327. #442	C₂²×C₇	semidirect
328. #441	C₂²×C₇	semidirect
329. #440	C₂²×C₇	semidirect
330. #440	C₂²×C₇	semidirect
331. C₄×Q₁₆	C₂²×C₇	semidirect
332. C₄×SD₁₆	C₂²×C₇	semidirect
333. C₄×SD₁₆	C₂²×C₇	semidirect
334. C₄×D₈	C₂²×C₇	semidirect
335. #428	C₂²×C₇	semidirect
336. #428	C₂²×C₇	semidirect
337. C₂×#107	C₂²×C₇	semidirect
338. C₂×#106	C₂²×C₇	semidirect
339. #419	C₂²×C₇	semidirect
340. #418	C₂²×C₇	semidirect
342. #417	C₂²×C₇	semidirect
343. #417	C₂²×C₇	semidirect
344. #417	C₂²×C₇	semidirect
346. C₂×#103	C₂²×C₇	semidirect
347. C₂×#102	C₂²×C₇	semidirect
348. #405	C₂²×C₇	semidirect
349. #405	C₂²×C₇	semidirect
350. C₄×M₁₆	C₂²×C₇	semidirect
425. C₂×#41	C₂×C₄×C₇	semidirect
426. C₂×#41	C₂×C₄×C₇	semidirect
442. #137	C₂×C₄×C₇	semidirect
443. #137	C₂×C₄×C₇	semidirect
444. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
445. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
446. #135	C₂×C₄×C₇	semidirect
452. C₂×M₁₆	C₂×C₄×C₇	semidirect
569. #41	C₂²×C₄×C₇	semidirect
575. C₂×Q₈	C₂²×C₄×C₇	semidirect
589. C₂×D₄	C₂²×C₄×C₇	semidirect
620. Q₁₆	C₂²×C₄×C₇	semidirect
621. SD₁₆	C₂²×C₄×C₇	semidirect
622. SD₁₆	C₂²×C₄×C₇	semidirect
623. D₈	C₂²×C₄×C₇	semidirect
627. M₁₆	C₂²×C₄×C₇	semidirect
629. C₂×C₈	C₂²×C₄×C₇	semidirect
737. C₇	#60170	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#575	2
C₇×#3428	2
C₂×C₇×#520	2
C₇×#2952	2
C₇×#2951	2
C₇×#2947	2
C₇×#2946	2
C₄×C₇×#137	2
C₄×C₇×AGL(1,ℤ/8)	2
C₂×C₇×#428	2
C₇×#2896	2
C₂×C₇×#417	2
C₇×#2873	2
#60170	7

Subgroups — C7×#60170 #13237386

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60170 #13237386