Subgroups — C₇×#60695 #13237911

Order 1792.

1978 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3460	C₂	1	2	yes	maximal, complemented
2	C₇×#3179	C₂	1	4	yes	maximal, complemented
3	C₇×#3176	C₂	1	2	yes	maximal, complemented
4	C₇×#3175	C₂	1	2	yes	maximal, complemented
5	C₇×#3171	C₂	1	4	yes	maximal, complemented
6	C₇×#3169	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×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₇×#3062	C₂	1	2	yes	maximal, complemented
12	C₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3058	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₇×#135	C₂²	1	1	yes	characteristic
20	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#131	C₂²	1	1	yes	characteristic
22	C₂×C₇×#131	C₂²	1	1	yes	characteristic
23	C₇×#544	C₂²	1	2	yes	—
24	C₇×#542	—	2	2	no	—
25	C₇×#542	C₂²	1	4	yes	complemented
26	C₇×#540	—	2	2	no	—
27	C₇×#540	C₂²	1	4	yes	complemented
28	C₇×#538	—	2	4	no	—
29	C₇×#537	C₂²	1	2	yes	—
30	C₇×#535	C₂²	1	2	yes	—
31	C₇×#535	C₂²	1	2	yes	—
32	C₇×#532	—	2	2	no	—
33	C₇×#532	C₂²	1	4	yes	complemented
34	C₇×#529	—	2	2	no	—
35	C₇×#529	C₂²	1	4	yes	complemented
36	C₇×#525	—	2	4	no	—
37	C₄×C₇×#41	C₂²	1	2	yes	—
38	C₄×C₇×#41	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
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×#496	C₂²	1	4	yes	—
44	C₇×#495	C₂²	1	2	yes	—
45	C₇×#493	C₂²	1	2	yes	—
46	C₇×#490	C₂²	1	4	yes	complemented
47	C₇×#489	C₂²	1	4	yes	complemented
48	C₇×#488	C₂²	1	4	yes	complemented
49	C₇×#486	C₂²	1	4	yes	complemented
50	C₇×#469	C₂²	1	4	yes	—
51	C₇×#469	C₂²	1	4	yes	complemented
52	C₇×#468	C₂²	1	4	yes	complemented
53	C₇×#468	C₂²	1	4	yes	complemented
54	C₇×#467	C₂²	1	2	yes	complemented
55	C₇×#466	C₂²	1	2	yes	—
56	C₇×#466	C₂²	1	2	yes	—
57	C₇×#466	C₂²	1	2	yes	complemented
58	C₇×#466	C₂²	1	4	yes	complemented
59	C₇×#465	C₂²	1	4	yes	complemented
60	C₇×#442	C₂²	1	4	yes	complemented
61	C₇×#440	C₂²	1	4	yes	complemented
62	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
65	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
66	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
67	C₄×C₇×D₈	C₂²	1	2	yes	—
68	C₄×C₇×D₈	C₂²	1	2	yes	—
69	C₄×C₇×D₈	C₂²	1	2	yes	—
70	C₄×C₇×D₈	C₂²	1	2	yes	—
71	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
72	C₄×C₇×D₈	C₂²	1	4	yes	complemented
73	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, 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×#418	C₂²	1	2	yes	—
78	C₇×#417	C₂²	1	2	yes	—
79	C₇×#416	C₂²	1	2	yes	—
80	C₂×C₇×#102	C₂²	1	2	yes	—
81	C₇×#405	C₂²	1	1	yes	characteristic
82	C₇×#405	C₂²	1	1	yes	characteristic
83	C₇×#405	C₂²	1	2	yes	complemented
84	C₇×#405	C₂²	1	2	yes	complemented
85	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
86	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
87	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
89	#60695	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	—	2	4	no	—
91	C₂×C₇×#41	C₂³	1	2	yes	—
92	C₂×C₇×#41	C₂³	1	1	yes	characteristic
93	C₂²×C₇×D₄	C₂³	1	2	yes	—
94	C₂³×C₄×C₇	—	2	2	no	—
95	C₇×AGL(1,ℤ/8)	—	2	8	no	—
96	C₇×#135	—	2	4	no	—
97	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
99	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₇×D₈	—	2	4	no	—
101	C₂×C₇×D₈	C₂³	1	2	yes	—
102	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
103	C₂×C₇×D₈	C₂³	1	4	yes	—
104	C₂×C₇×D₈	C₂³	1	2	yes	—
105	C₇×#131	—	2	4	no	—
106	C₇×#131	—	2	4	no	—
107	C₂×C₇×M₁₆	C₂³	1	2	yes	—
108	C₂×C₇×M₁₆	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	C₂²×C₇×C₈	C₂³	1	2	yes	—
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×#127	—	2	2	no	—
118	C₇×#127	C₂³	1	4	yes	—
119	C₇×#126	—	2	4	no	—
120	C₇×#126	—	2	4	no	—
121	C₇×#125	—	2	2	no	—
122	C₇×#125	C₂³	1	4	yes	—
123	C₇×#124	—	2	2	no	—
124	C₇×#124	—	2	4	no	—
125	C₇×#124	—	2	4	no	—
126	C₇×#124	C₂³	1	4	yes	—
127	C₇×#123	—	2	4	no	—
128	C₇×#123	—	2	4	no	—
129	C₇×#123	—	2	4	no	—
130	C₇×#123	—	2	4	no	—
131	C₇×C₂²⋊Q₈	—	2	2	no	—
132	C₇×C₂²⋊Q₈	—	2	4	no	—
133	C₇×C₂²⋊Q₈	—	2	4	no	—
134	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₇×#121	—	2	4	no	—
136	C₇×#121	—	2	2	no	—
137	C₇×#121	—	2	4	no	—
138	C₇×#121	—	2	2	no	—
139	C₇×#121	—	2	2	no	—
140	C₇×#121	—	2	4	no	—
141	C₇×#121	—	2	4	no	—
142	C₇×#121	C₂³	1	4	yes	—
143	C₇×#121	C₂³	1	4	yes	—
144	C₇×#121	C₂³	1	4	yes	—
145	C₇×#120	—	2	4	no	—
146	C₇×#120	—	2	4	no	—
147	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
148	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
149	C₄×C₇×Q₈	C₂³	1	2	yes	—
150	C₄×C₇×Q₈	C₂³	1	2	yes	—
151	C₄×C₇×D₄	—	2	2	no	—
152	C₄×C₇×D₄	—	2	2	no	—
153	C₄×C₇×D₄	—	2	4	no	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	—	2	2	no	—
156	C₄×C₇×D₄	—	2	4	no	—
157	C₄×C₇×D₄	D₄	1	2	yes	—
158	C₄×C₇×D₄	D₄	1	1	yes	characteristic
159	C₄×C₇×D₄	D₄	1	2	yes	—
160	C₄×C₇×D₄	D₄	1	1	yes	characteristic
161	C₄×C₇×D₄	C₂³	1	4	yes	—
162	C₄×C₇×D₄	C₂³	1	4	yes	—
163	C₄×C₇×D₄	C₂³	1	2	yes	—
164	C₄×C₇×D₄	C₂³	1	2	yes	—
165	C₇×#117	—	2	2	no	—
166	C₇×#117	—	2	4	no	—
167	C₇×#117	C₂³	1	2	yes	—
168	C₇×#117	C₂³	1	1	yes	characteristic
169	C₇×#117	C₂³	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
172	C₂×C₄²×C₇	—	2	2	no	—
173	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₇	C₂³	1	2	yes	—
175	C₇×#107	C₂³	1	1	yes	characteristic
176	C₇×#107	C₂³	1	1	yes	characteristic
177	C₇×#107	C₂³	1	2	yes	—
178	C₇×#107	C₂³	1	4	yes	—
179	C₇×#107	C₂³	1	2	yes	—
180	C₇×#106	C₂³	1	2	yes	—
181	C₇×#106	C₂³	1	4	yes	—
182	C₇×#103	C₂³	1	4	yes	—
183	C₇×#103	C₂³	1	2	yes	—
184	C₇×#103	C₂³	1	2	yes	—
185	C₇×#102	C₂³	1	4	yes	—
186	C₇×#102	C₂³	1	4	yes	—
187	C₇×#102	C₂³	1	2	yes	—
188	C₇×#102	C₂³	1	4	yes	—
189	C₇×#102	C₂³	1	4	yes	—
190	C₇×#102	C₂³	1	4	yes	—
191	C₇×#102	C₂³	1	2	yes	—
192	C₇×#97	C₂³	1	2	yes	—
193	C₇×#97	C₂³	1	2	yes	—
194	C₇×#97	C₂³	1	2	yes	—
195	C₄×C₇×C₈	C₂³	1	2	yes	—
196	C₄×C₇×C₈	C₂³	1	2	yes	—
197	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
198	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
199	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
200	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
201	C₄×C₇×C₈	C₂³	1	2	yes	—
202	#3460	C₂×C₇	1	2	yes	complemented
203	#3179	C₂×C₇	1	4	yes	complemented
204	#3176	C₂×C₇	1	2	yes	complemented
205	#3175	C₂×C₇	1	2	yes	complemented
206	#3171	C₂×C₇	1	4	yes	complemented
207	#3169	C₂×C₇	1	2	yes	complemented
208	#3168	C₂×C₇	1	2	yes	complemented
209	#3164	C₂×C₇	1	1	yes	characteristic, complemented
210	#3155	C₂×C₇	1	1	yes	characteristic, complemented
211	#3136	C₂×C₇	1	2	yes	complemented
212	#3062	C₂×C₇	1	2	yes	complemented
213	#3061	C₂×C₇	1	1	yes	characteristic, complemented
214	#3058	C₂×C₇	1	1	yes	characteristic, complemented
215	C₄×AGL(1,ℤ/8)	C₂×C₇	1	2	yes	complemented
216	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
217	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
218	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
219	C₂⁴×C₇	—	2	2	no	—
220	C₇×#41	—	2	2	no	—
221	C₇×#41	—	2	2	no	—
222	C₇×#41	—	2	4	no	—
223	C₇×#41	—	2	4	no	—
224	C₇×#41	—	8	8	no	—
225	C₂×C₇×Q₈	—	2	4	no	—
226	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
227	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
228	C₂×C₇×D₄	—	2	2	no	—
229	C₂×C₇×D₄	—	2	4	no	—
230	C₂×C₇×D₄	—	2	4	no	—
231	C₂×C₇×D₄	—	2	4	no	—
232	C₂×C₇×D₄	—	2	2	no	—
233	C₂×C₇×D₄	—	2	4	no	—
234	C₂×C₇×D₄	—	2	4	no	—
235	C₂×C₇×D₄	—	2	4	no	—
236	C₂×C₇×D₄	—	2	4	no	—
237	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
238	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
239	C₂×C₇×D₄	C₂⁴	1	4	yes	—
240	C₂×C₇×D₄	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₇	—	2	2	no	—
242	C₂²×C₄×C₇	—	2	2	no	—
243	C₂²×C₄×C₇	—	2	2	no	—
244	C₂²×C₄×C₇	—	2	4	no	—
245	C₂²×C₄×C₇	—	2	2	no	—
246	C₂²×C₄×C₇	—	2	4	no	—
247	C₂²×C₄×C₇	—	8	4	no	—
248	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
252	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
254	C₇×Q₁₆	—	2	2	no	—
255	C₇×SD₁₆	—	2	4	no	—
256	C₇×SD₁₆	—	2	8	no	—
257	C₇×D₈	—	2	4	no	—
258	C₇×D₈	—	2	4	no	—
259	C₇×D₈	—	2	2	no	—
260	C₇×D₈	—	2	8	no	—
261	C₇×M₁₆	—	2	2	no	—
262	C₇×M₁₆	—	2	4	no	—
263	C₇×M₁₆	—	2	4	no	—
264	C₇×M₁₆	#41	1	4	yes	complemented
265	C₂×C₇×C₈	—	2	2	no	—
266	C₂×C₇×C₈	—	2	4	no	—
267	C₂×C₇×C₈	—	2	4	no	—
268	C₂×C₇×C₈	#41	1	4	yes	complemented
269	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
270	C₂×C₇×C₈	C₂⁴	1	2	yes	—
271	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
272	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
273	C₂×C₇×C₈	C₂⁴	1	2	yes	—
274	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
275	C₇×C₄⋊C₄	—	2	2	no	—
276	C₇×C₄⋊C₄	—	2	2	no	—
277	C₇×C₄⋊C₄	—	2	2	no	—
278	C₇×C₄⋊C₄	—	2	4	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	2	4	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	2	yes	—
286	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
288	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₇×C₂²⋊C₄	—	2	2	no	—
290	C₇×C₂²⋊C₄	—	2	4	no	—
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	4	no	—
296	C₇×C₂²⋊C₄	—	2	4	no	—
297	C₇×C₂²⋊C₄	—	2	4	no	—
298	C₇×C₂²⋊C₄	—	2	4	no	—
299	C₇×C₂²⋊C₄	—	2	4	no	—
300	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
301	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
302	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
303	C₄²×C₇	—	2	2	no	—
304	C₄²×C₇	—	2	2	no	—
305	C₄²×C₇	—	2	2	no	—
306	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₇	C₂×D₄	1	2	yes	—
308	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₇	C₂×D₄	1	2	yes	—
310	C₄²×C₇	C₂⁴	1	1	yes	characteristic
311	C₄²×C₇	C₂⁴	1	2	yes	—
312	C₄²×C₇	C₂⁴	1	1	yes	characteristic
313	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
314	C₂×#135	C₂²×C₇	1	1	yes	characteristic
315	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
316	C₂×#131	C₂²×C₇	1	1	yes	characteristic
317	C₂×#131	C₂²×C₇	1	1	yes	characteristic
318	#544	C₂²×C₇	1	2	yes	—
319	#542	—	2	2	no	—
320	#542	C₂²×C₇	1	4	yes	complemented
321	#540	—	2	2	no	—
322	#540	C₂²×C₇	1	4	yes	complemented
323	#538	—	2	4	no	—
324	#537	C₂²×C₇	1	2	yes	—
325	#535	C₂²×C₇	1	2	yes	—
326	#535	C₂²×C₇	1	2	yes	—
327	#532	—	2	2	no	—
328	#532	C₂²×C₇	1	4	yes	complemented
329	#529	—	2	2	no	—
330	#529	C₂²×C₇	1	4	yes	complemented
331	#525	—	2	4	no	—
332	C₄×#41	C₂²×C₇	1	2	yes	—
333	C₄×#41	C₂²×C₇	1	1	yes	characteristic
334	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
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	#496	C₂²×C₇	1	4	yes	—
339	#495	C₂²×C₇	1	2	yes	—
340	#493	C₂²×C₇	1	2	yes	—
341	#490	C₂²×C₇	1	4	yes	complemented
342	#489	C₂²×C₇	1	4	yes	complemented
343	#488	C₂²×C₇	1	4	yes	complemented
344	#486	C₂²×C₇	1	4	yes	complemented
345	#469	C₂²×C₇	1	4	yes	—
346	#469	C₂²×C₇	1	4	yes	complemented
347	#468	C₂²×C₇	1	4	yes	complemented
348	#468	C₂²×C₇	1	4	yes	complemented
349	#467	C₂²×C₇	1	2	yes	complemented
350	#466	C₂²×C₇	1	2	yes	—
351	#466	C₂²×C₇	1	2	yes	—
352	#466	C₂²×C₇	1	2	yes	complemented
353	#466	C₂²×C₇	1	4	yes	complemented
354	#465	C₂²×C₇	1	4	yes	complemented
355	#442	C₂²×C₇	1	4	yes	complemented
356	#440	C₂²×C₇	1	4	yes	complemented
357	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
358	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
359	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
360	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
361	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
362	C₄×D₈	C₂²×C₇	1	2	yes	—
363	C₄×D₈	C₂²×C₇	1	2	yes	—
364	C₄×D₈	C₂²×C₇	1	2	yes	—
365	C₄×D₈	C₂²×C₇	1	2	yes	—
366	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
367	C₄×D₈	C₂²×C₇	1	4	yes	complemented
368	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, 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	#418	C₂²×C₇	1	2	yes	—
373	#417	C₂²×C₇	1	2	yes	—
374	#416	C₂²×C₇	1	2	yes	—
375	C₂×#102	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	complemented
379	#405	C₂²×C₇	1	2	yes	complemented
380	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
381	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
382	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
383	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
384	C₂³×C₇	—	2	4	no	—
385	C₂³×C₇	—	2	2	no	—
386	C₂³×C₇	—	4	4	no	—
387	C₂³×C₇	—	8	2	no	—
388	C₂³×C₇	—	8	2	no	—
389	C₂³×C₇	C₂²×D₄	1	2	yes	—
390	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
391	C₇×Q₈	—	2	2	no	—
392	C₇×Q₈	—	2	2	no	—
393	C₇×Q₈	—	2	2	no	—
394	C₇×Q₈	—	8	4	no	—
395	C₇×D₄	—	2	4	no	—
396	C₇×D₄	—	2	2	no	—
397	C₇×D₄	—	2	4	no	—
398	C₇×D₄	—	2	2	no	—
399	C₇×D₄	—	2	4	no	—
400	C₇×D₄	—	2	2	no	—
401	C₇×D₄	—	4	4	no	—
402	C₇×D₄	—	4	4	no	—
403	C₇×D₄	—	8	4	no	—
404	C₇×D₄	—	8	4	no	—
405	C₇×D₄	—	8	4	no	—
406	C₇×D₄	—	8	4	no	—
407	C₇×D₄	—	8	4	no	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	4	no	—
410	C₂×C₄×C₇	—	2	2	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	4	no	—
416	C₂×C₄×C₇	—	4	1	no	—
417	C₂×C₄×C₇	—	4	2	no	—
418	C₂×C₄×C₇	—	4	4	no	—
419	C₂×C₄×C₇	—	4	8	no	—
420	C₂×C₄×C₇	—	4	4	no	—
421	C₂×C₄×C₇	—	8	2	no	—
422	C₂×C₄×C₇	—	8	4	no	—
423	C₂×C₄×C₇	—	8	2	no	—
424	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₇	C₂×#41	1	2	yes	—
433	C₂×C₄×C₇	C₂×#41	1	2	yes	—
434	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
435	C₇×C₈	—	2	1	no	—
436	C₇×C₈	—	2	1	no	—
437	C₇×C₈	—	2	2	no	—
438	C₇×C₈	C₂×#41	1	2	yes	—
439	C₇×C₈	C₂×#41	1	4	yes	—
440	C₇×C₈	C₂×#41	1	2	yes	—
441	C₂×#41	—	2	4	no	—
442	C₂×#41	C₂³×C₇	1	2	yes	—
443	C₂×#41	C₂³×C₇	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₇	1	2	yes	—
445	C₂³×C₄	—	2	2	no	—
446	AGL(1,ℤ/8)	—	2	8	no	—
447	#135	—	2	4	no	—
448	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
449	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
450	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
451	C₂×D₈	—	2	4	no	—
452	C₂×D₈	C₂³×C₇	1	2	yes	—
453	C₂×D₈	C₂³×C₇	1	2	yes	—
454	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
455	C₂×D₈	C₂³×C₇	1	4	yes	—
456	#131	—	2	4	no	—
457	#131	—	2	4	no	—
458	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
459	C₂×M₁₆	C₂³×C₇	1	2	yes	—
460	C₂×M₁₆	C₂³×C₇	1	2	yes	—
461	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
463	C₂²×C₈	C₂³×C₇	1	2	yes	—
464	C₂²×C₈	C₂³×C₇	1	2	yes	—
465	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
466	C₄⋊Q₈	—	2	2	no	—
467	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
468	#127	—	2	2	no	—
469	#127	C₂³×C₇	1	4	yes	—
470	#126	—	2	4	no	—
471	#126	—	2	4	no	—
472	#125	—	2	2	no	—
473	#125	C₂³×C₇	1	4	yes	—
474	#124	—	2	2	no	—
475	#124	—	2	4	no	—
476	#124	—	2	4	no	—
477	#124	C₂³×C₇	1	4	yes	—
478	#123	—	2	4	no	—
479	#123	—	2	4	no	—
480	#123	—	2	4	no	—
481	#123	—	2	4	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	4	no	—
484	C₂²⋊Q₈	—	2	4	no	—
485	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
486	#121	—	2	4	no	—
487	#121	—	2	2	no	—
488	#121	—	2	4	no	—
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	—	2	4	no	—
492	#121	—	2	4	no	—
493	#121	C₂³×C₇	1	4	yes	—
494	#121	C₂³×C₇	1	4	yes	—
495	#121	C₂³×C₇	1	4	yes	—
496	#120	—	2	4	no	—
497	#120	—	2	4	no	—
498	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
499	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
500	C₄×Q₈	C₂³×C₇	1	2	yes	—
501	C₄×Q₈	C₂³×C₇	1	2	yes	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	4	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	C₇×D₄	1	2	yes	—
509	C₄×D₄	C₇×D₄	1	1	yes	characteristic
510	C₄×D₄	C₇×D₄	1	2	yes	—
511	C₄×D₄	C₇×D₄	1	1	yes	characteristic
512	C₄×D₄	C₂³×C₇	1	4	yes	—
513	C₄×D₄	C₂³×C₇	1	4	yes	—
514	C₄×D₄	C₂³×C₇	1	2	yes	—
515	C₄×D₄	C₂³×C₇	1	2	yes	—
516	#117	—	2	2	no	—
517	#117	—	2	4	no	—
518	#117	C₂³×C₇	1	2	yes	—
519	#117	C₂³×C₇	1	1	yes	characteristic
520	#117	C₂³×C₇	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
522	C₂×C₂²⋊C₄	—	2	2	no	—
523	C₂×C₄²	—	2	2	no	—
524	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₇	1	2	yes	—
526	#107	C₂³×C₇	1	2	yes	—
527	#107	C₂³×C₇	1	2	yes	—
528	#107	C₂³×C₇	1	1	yes	characteristic
529	#107	C₂³×C₇	1	1	yes	characteristic
530	#107	C₂³×C₇	1	4	yes	—
531	#106	C₂³×C₇	1	2	yes	—
532	#106	C₂³×C₇	1	4	yes	—
533	#103	C₂³×C₇	1	2	yes	—
534	#103	C₂³×C₇	1	2	yes	—
535	#103	C₂³×C₇	1	4	yes	—
536	#102	C₂³×C₇	1	4	yes	—
537	#102	C₂³×C₇	1	4	yes	—
538	#102	C₂³×C₇	1	2	yes	—
539	#102	C₂³×C₇	1	2	yes	—
540	#102	C₂³×C₇	1	4	yes	—
541	#102	C₂³×C₇	1	4	yes	—
542	#102	C₂³×C₇	1	4	yes	—
543	#97	C₂³×C₇	1	2	yes	—
544	#97	C₂³×C₇	1	2	yes	—
545	#97	C₂³×C₇	1	2	yes	—
546	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
547	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
548	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
549	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
550	C₄×C₈	C₂³×C₇	1	2	yes	—
551	C₄×C₈	C₂³×C₇	1	2	yes	—
552	C₄×C₈	C₂³×C₇	1	2	yes	—
553	C₂²×C₇	—	2	1	no	—
554	C₂²×C₇	—	2	1	no	—
555	C₂²×C₇	—	2	2	no	—
556	C₂²×C₇	—	2	2	no	—
557	C₂²×C₇	—	2	2	no	—
558	C₂²×C₇	—	4	2	no	—
559	C₂²×C₇	—	4	4	no	—
560	C₂²×C₇	—	4	2	no	—
561	C₂²×C₇	—	4	4	no	—
562	C₂²×C₇	—	4	4	no	—
563	C₂²×C₇	—	4	2	no	—
564	C₂²×C₇	—	8	8	no	—
565	C₂²×C₇	#532	1	2	yes	—
566	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
567	C₄×C₇	—	2	1	no	—
568	C₄×C₇	—	2	1	no	—
569	C₄×C₇	—	2	2	no	—
570	C₄×C₇	—	2	2	no	—
571	C₄×C₇	—	2	1	no	—
572	C₄×C₇	—	2	2	no	—
573	C₄×C₇	—	4	2	no	—
574	C₄×C₇	—	4	2	no	—
575	C₄×C₇	—	4	4	no	—
576	C₄×C₇	—	4	2	no	—
577	C₄×C₇	#532	1	2	yes	—
578	C₄×C₇	#576	1	2	yes	—
579	C₄×C₇	C₂²×#41	1	1	yes	characteristic
580	C₄×C₇	C₂²×#41	1	1	yes	characteristic
581	C₂⁴	—	2	2	no	—
582	#41	—	2	2	no	—
583	#41	—	2	2	no	—
584	#41	—	2	4	no	—
585	#41	—	2	4	no	—
586	#41	—	8	8	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
589	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
600	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
601	C₂×D₄	C₂⁴×C₇	1	4	yes	—
602	C₂×D₄	C₂⁴×C₇	1	2	yes	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	8	4	no	—
610	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
611	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
612	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
613	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
616	Q₁₆	—	2	2	no	—
617	SD₁₆	—	2	4	no	—
618	SD₁₆	—	2	8	no	—
619	D₈	—	2	4	no	—
620	D₈	—	2	4	no	—
621	D₈	—	2	2	no	—
622	D₈	—	2	8	no	—
623	M₁₆	—	2	2	no	—
624	M₁₆	—	2	4	no	—
625	M₁₆	—	2	4	no	—
626	M₁₆	C₇×#41	1	4	yes	complemented
627	C₂×C₈	—	2	2	no	—
628	C₂×C₈	—	2	4	no	—
629	C₂×C₈	—	2	4	no	—
630	C₂×C₈	C₇×#41	1	4	yes	complemented
631	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
632	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
633	C₂×C₈	C₂⁴×C₇	1	2	yes	—
634	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
635	C₂×C₈	C₂⁴×C₇	1	2	yes	—
636	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
645	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
646	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
647	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
648	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
649	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
650	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
663	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
664	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
665	C₄²	—	2	2	no	—
666	C₄²	—	2	2	no	—
667	C₄²	—	2	2	no	—
668	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
669	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
670	C₄²	C₂×C₇×D₄	1	2	yes	—
671	C₄²	C₂×C₇×D₄	1	2	yes	—
672	C₄²	C₂⁴×C₇	1	1	yes	characteristic
673	C₄²	C₂⁴×C₇	1	1	yes	characteristic
674	C₄²	C₂⁴×C₇	1	2	yes	—
675	C₂×C₇	—	2	2	no	—
676	C₂×C₇	—	4	2	no	—
677	C₂×C₇	—	8	2	no	—
678	C₂×C₇	—	8	4	no	—
679	C₂×C₇	C₂×#532	1	1	yes	characteristic
680	C₂×C₇	C₂×#576	1	1	yes	characteristic
681	C₂×C₇	#3584	1	1	yes	characteristic
682	C₂³	—	2	4	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	4	4	no	—
685	C₂³	—	8	2	no	—
686	C₂³	—	8	2	no	—
687	C₂³	C₂²×C₇×D₄	1	2	yes	—
688	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	8	4	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	4	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	8	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
723	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
724	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
725	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
726	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
727	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
728	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
729	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
730	C₂×C₄	C₂×C₇×#41	1	2	yes	—
731	C₂×C₄	C₂×C₇×#41	1	2	yes	—
732	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
733	C₈	—	2	1	no	—
734	C₈	—	2	1	no	—
735	C₈	—	2	2	no	—
736	C₈	C₂×C₇×#41	1	2	yes	—
737	C₈	C₂×C₇×#41	1	4	yes	—
738	C₈	C₂×C₇×#41	1	2	yes	—
739	C₇	#60695	1	1	yes	characteristic, direct product factor, Sylow
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	8	8	no	—
752	C₂²	C₇×#532	1	2	yes	—
753	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₇×#532	1	2	yes	—
765	C₄	C₇×#576	1	2	yes	—
766	C₄	C₂²×C₇×#41	1	1	yes	characteristic
767	C₄	C₂²×C₇×#41	1	1	yes	characteristic
768	C₂	—	2	2	no	—
769	C₂	—	4	2	no	—
770	C₂	—	8	4	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×C₇×#532	1	1	yes	characteristic
773	C₂	C₂×C₇×#576	1	1	yes	characteristic
774	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3460	C₂	semidirect
2. C₇×#3179	C₂	semidirect
3. C₇×#3176	C₂	semidirect
4. C₇×#3175	C₂	semidirect
5. C₇×#3171	C₂	semidirect
6. C₇×#3169	C₂	semidirect
7. C₇×#3168	C₂	semidirect
8. C₇×#3164	C₂	semidirect
9. C₇×#3155	C₂	semidirect
10. C₇×#3136	C₂	semidirect
11. C₇×#3062	C₂	semidirect
12. C₇×#3061	C₂	semidirect
13. C₇×#3058	C₂	semidirect
14. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
15. C₄×C₇×#135	C₂	semidirect
16. C₂×C₄×C₇×D₈	C₂	semidirect
17. C₄×C₇×#131	C₂	semidirect
25. C₇×#542	C₂²	semidirect
27. C₇×#540	C₂²	semidirect
33. C₇×#532	C₂²	semidirect
35. C₇×#529	C₂²	semidirect
40. C₇×#501	C₂²	semidirect
41. C₇×#500	C₂²	semidirect
42. C₇×#499	C₂²	semidirect
46. C₇×#490	C₂²	semidirect
47. C₇×#489	C₂²	semidirect
48. C₇×#488	C₂²	semidirect
49. C₇×#486	C₂²	semidirect
51. C₇×#469	C₂²	semidirect
52. C₇×#468	C₂²	semidirect
53. C₇×#468	C₂²	semidirect
54. C₇×#467	C₂²	semidirect
57. C₇×#466	C₂²	semidirect
58. C₇×#466	C₂²	semidirect
59. C₇×#465	C₂²	semidirect
60. C₇×#442	C₂²	semidirect
61. C₇×#440	C₂²	semidirect
62. C₄×C₇×Q₁₆	C₂²	semidirect
63. C₄×C₇×Q₁₆	C₂²	semidirect
64. C₄×C₇×SD₁₆	C₂²	semidirect
65. C₄×C₇×SD₁₆	C₂²	semidirect
66. C₄×C₇×SD₁₆	C₂²	semidirect
71. C₄×C₇×D₈	C₂²	semidirect
72. C₄×C₇×D₈	C₂²	semidirect
73. C₄×C₇×D₈	C₂²	semidirect
83. C₇×#405	C₂²	semidirect
84. C₇×#405	C₂²	semidirect
86. C₄×C₇×M₁₆	C₂²	semidirect
88. C₂×C₄×C₇×C₈	C₂²	semidirect
89. #60695	C₇	direct (N × H)
202. #3460	C₂×C₇	semidirect
203. #3179	C₂×C₇	semidirect
204. #3176	C₂×C₇	semidirect
205. #3175	C₂×C₇	semidirect
206. #3171	C₂×C₇	semidirect
207. #3169	C₂×C₇	semidirect
208. #3168	C₂×C₇	semidirect
209. #3164	C₂×C₇	semidirect
210. #3155	C₂×C₇	semidirect
211. #3136	C₂×C₇	semidirect
212. #3062	C₂×C₇	semidirect
213. #3061	C₂×C₇	semidirect
214. #3058	C₂×C₇	semidirect
215. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
216. C₄×#135	C₂×C₇	semidirect
217. C₂×C₄×D₈	C₂×C₇	semidirect
218. C₄×#131	C₂×C₇	semidirect
264. C₇×M₁₆	#41	semidirect
268. C₂×C₇×C₈	#41	semidirect
320. #542	C₂²×C₇	semidirect
322. #540	C₂²×C₇	semidirect
328. #532	C₂²×C₇	semidirect
330. #529	C₂²×C₇	semidirect
335. #501	C₂²×C₇	semidirect
336. #500	C₂²×C₇	semidirect
337. #499	C₂²×C₇	semidirect
341. #490	C₂²×C₇	semidirect
342. #489	C₂²×C₇	semidirect
343. #488	C₂²×C₇	semidirect
344. #486	C₂²×C₇	semidirect
346. #469	C₂²×C₇	semidirect
347. #468	C₂²×C₇	semidirect
348. #468	C₂²×C₇	semidirect
349. #467	C₂²×C₇	semidirect
352. #466	C₂²×C₇	semidirect
353. #466	C₂²×C₇	semidirect
354. #465	C₂²×C₇	semidirect
355. #442	C₂²×C₇	semidirect
356. #440	C₂²×C₇	semidirect
357. C₄×Q₁₆	C₂²×C₇	semidirect
358. C₄×Q₁₆	C₂²×C₇	semidirect
359. C₄×SD₁₆	C₂²×C₇	semidirect
360. C₄×SD₁₆	C₂²×C₇	semidirect
361. C₄×SD₁₆	C₂²×C₇	semidirect
366. C₄×D₈	C₂²×C₇	semidirect
367. C₄×D₈	C₂²×C₇	semidirect
368. C₄×D₈	C₂²×C₇	semidirect
378. #405	C₂²×C₇	semidirect
379. #405	C₂²×C₇	semidirect
381. C₄×M₁₆	C₂²×C₇	semidirect
383. C₂×C₄×C₈	C₂²×C₇	semidirect
626. M₁₆	C₇×#41	semidirect
630. C₂×C₈	C₇×#41	semidirect
739. C₇	#60695	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×#3460	2
C₇×#3179	2
C₇×#3176	2
C₇×#3175	2
C₇×#3171	2
C₇×#3169	2
C₇×#3168	2
C₇×#3164	2
C₇×#3155	2
C₇×#3136	2
C₇×#3062	2
C₇×#3061	2
C₇×#3058	2
C₄×C₇×AGL(1,ℤ/8)	2
C₄×C₇×#135	2
C₂×C₄×C₇×D₈	2
C₄×C₇×#131	2
#60695	7

Subgroups — C7×#60695 #13237911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60695 #13237911