Subgroups — D₇×#4095 #72218500

Order 2240.

596 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₇×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	#11765279	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#4095	C₂	1	1	yes	maximal, characteristic, complemented
5	#11764950	C₂	1	2	yes	maximal, complemented
6	D₇×#688	C₂	1	2	yes	maximal, complemented
7	#11764926	C₂	1	2	yes	maximal, complemented
8	D₇×#686	C₂	1	2	yes	maximal, complemented
9	#11764800	C₂	1	1	yes	maximal, characteristic, complemented
10	#11764798	C₂	1	1	yes	maximal, characteristic, complemented
11	D₇×#681	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₅×D₇	—	2	1	no	—
13	C₅×C₇×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂×D₁₄₀	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₇×D₂₀	C₂²	1	1	yes	characteristic, complemented
16	C₅×#1161	C₂²	1	1	yes	characteristic, complemented
17	C₅×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
18	C₅×#1159	—	2	1	no	—
19	C₅×#1159	C₂²	1	1	yes	characteristic, complemented
20	C₅×D₄×D₇	—	2	1	no	—
21	C₅×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
22	C₅×#1157	—	2	1	no	—
23	C₅×#1157	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×C₅×D₇	—	2	1	no	—
25	C₂×C₄×C₅×D₇	C₂²	1	1	yes	characteristic
26	C₂×#63307	—	2	1	no	—
27	D₇×D₂₀	—	2	1	no	—
28	D₇×D₂₀	—	2	1	no	—
29	D₇×D₂₀	C₂²	1	2	yes	—
30	D₇×D₂₀	C₂²	1	2	yes	complemented
31	#10587905	C₂²	1	2	yes	complemented
32	#10587903	C₂²	1	2	yes	complemented
33	#10587898	C₂²	1	1	yes	characteristic, complemented
34	C₇×#688	C₂²	1	2	yes	complemented
35	C₇×#686	C₂²	1	2	yes	complemented
36	C₇×#681	C₂²	1	1	yes	characteristic, complemented
37	#10587847	C₂²	1	2	yes	complemented
38	#10587845	C₂²	1	2	yes	complemented
39	#10587842	C₂²	1	2	yes	complemented
40	#10587841	C₂²	1	2	yes	complemented
41	#10587838	C₂²	1	2	yes	complemented
42	D₇×#168	C₂²	1	2	yes	complemented
43	D₇×AGL(1,ℤ/8)	—	5	1	no	maximal, Hall
44	C₂×#4095	—	7	1	no	maximal, Hall
45	C₂²×D₃₅	—	2	1	no	—
46	C₂²×C₇×D₅	—	2	1	no	—
47	C₂²×C₅×D₇	—	2	1	no	—
48	C₂²×C₅×D₇	D₄	1	1	yes	characteristic
49	C₂×D₅×D₇	—	2	2	no	—
50	C₂×D₅×D₇	—	2	2	no	—
51	C₂×D₅×D₇	—	4	4	no	—
52	C₅×C₇×Q₈	C₂³	1	1	yes	characteristic, complemented
53	C₅×C₇×D₄	—	2	1	no	—
54	C₅×C₇×D₄	C₂³	1	1	yes	characteristic, complemented
55	C₂×C₄×C₅×C₇	—	2	1	no	—
56	C₂×C₄×C₅×C₇	C₂³	1	1	yes	characteristic
57	D₁₄₀	—	2	1	no	—
58	D₁₄₀	C₂³	1	2	yes	—
59	C₇×D₂₀	—	2	1	no	—
60	C₇×D₂₀	C₂³	1	2	yes	—
61	C₅×C₂²⋊D₇	—	2	1	no	—
62	C₅×C₂²⋊D₇	—	2	1	no	—
63	C₅×C₂²⋊D₇	—	2	1	no	—
64	C₂×C₅×Dic₇	—	2	1	no	—
65	C₂×C₅×Dic₇	D₄	1	1	yes	characteristic
66	C₅×D₂₈	—	2	1	no	—
67	C₅×D₂₈	C₂³	1	1	yes	characteristic, complemented
68	C₄×C₅×D₇	—	2	1	no	—
69	C₄×C₅×D₇	—	2	1	no	—
70	C₄×C₅×D₇	—	2	1	no	—
71	C₄×C₅×D₇	D₄	1	1	yes	characteristic
72	C₄×C₅×D₇	D₄	1	1	yes	characteristic
73	C₄×C₅×D₇	C₂³	1	1	yes	characteristic
74	C₄×C₅×D₇	C₂³	1	1	yes	characteristic
75	C₅×Dic₁₄	—	2	1	no	—
76	C₅×Dic₁₄	C₂³	1	1	yes	characteristic, complemented
77	#63307	—	2	2	no	—
78	#63307	—	2	2	no	—
79	C₇⋊#168	C₂³	1	2	yes	complemented
80	C₇×#168	C₂³	1	2	yes	complemented
81	D₇×#41	D₅	1	1	yes	characteristic, complemented
82	C₂×D₄×D₇	—	5	1	no	—
83	C₇×AGL(1,ℤ/8)	—	5	1	no	—
84	#6512	—	5	1	no	—
85	#6495	—	5	1	no	—
86	#6477	—	5	2	no	—
87	D₇×SD₁₆	—	5	2	no	—
88	#6474	—	5	2	no	—
89	D₇×D₈	—	5	2	no	—
90	#6471	—	5	1	no	—
91	D₇×M₁₆	—	5	1	no	—
92	C₂×C₅×#41	—	7	1	no	—
93	C₂²×D₂₀	—	7	1	no	—
94	#4095	—	7	1	no	—
95	#4095	—	7	1	no	—
96	#4095	—	7	2	no	—
97	#4095	—	7	2	no	—
98	#4095	—	7	1	no	—
99	#4095	D₇	1	1	yes	characteristic, direct product factor
100	C₂×#688	—	7	2	no	—
101	C₂×#686	—	7	2	no	—
102	C₂×#681	—	7	1	no	—
103	C₂²×C₅×C₇	—	2	1	no	—
104	C₂²×C₅×C₇	C₂×D₄	1	1	yes	characteristic
105	C₂×D₃₅	—	2	2	no	—
106	C₂×D₃₅	—	4	2	no	—
107	C₂×C₇×D₅	—	2	2	no	—
108	C₂×C₇×D₅	—	4	2	no	—
109	C₂×C₅×D₇	—	2	2	no	—
110	C₂×C₅×D₇	—	2	1	no	—
111	C₂×C₅×D₇	—	4	2	no	—
112	C₂×C₅×D₇	C₂×D₄	1	1	yes	characteristic
113	C₂×C₅×D₇	C₂×D₄	1	1	yes	characteristic
114	D₅×D₇	—	4	4	no	—
115	D₅×D₇	—	4	4	no	—
116	C₄×C₅×C₇	—	2	1	no	—
117	C₄×C₅×C₇	C₂×D₄	1	1	yes	characteristic
118	C₄×C₅×C₇	C₂⁴	1	1	yes	characteristic
119	C₅×Dic₇	—	2	1	no	—
120	C₅×Dic₇	C₂×D₄	1	1	yes	characteristic
121	C₅×Dic₇	C₂×D₄	1	1	yes	characteristic
122	C₂³×D₇	—	10	1	no	—
123	C₇×#41	C₂×D₅	1	1	yes	characteristic, complemented
124	C₂×C₇×D₄	—	5	1	no	—
125	C₂×C₂²⋊D₇	—	10	1	no	—
126	#1161	C₂×D₅	1	1	yes	characteristic, complemented
127	Q₈×D₇	C₂×D₅	1	1	yes	characteristic, complemented
128	#1159	—	2	1	no	—
129	#1159	C₂×D₅	1	1	yes	characteristic, complemented
130	D₄×D₇	—	2	1	no	—
131	D₄×D₇	—	5	2	no	—
132	D₄×D₇	—	5	2	no	—
133	D₄×D₇	—	10	1	no	—
134	D₄×D₇	—	10	1	no	—
135	D₄×D₇	C₂×D₅	1	1	yes	characteristic, complemented
136	#1157	—	2	1	no	—
137	#1157	C₂×D₅	1	1	yes	characteristic, complemented
138	C₂×D₂₈	—	5	1	no	—
139	C₂×C₄×D₇	—	2	1	no	—
140	C₂×C₄×D₇	C₂×D₅	1	1	yes	characteristic
141	C₇×SD₁₆	—	5	2	no	—
142	C₇×D₈	—	5	2	no	—
143	C₇×M₁₆	—	5	1	no	—
144	#1143	—	5	2	no	—
145	#1142	—	5	2	no	—
146	#1141	—	5	2	no	—
147	#1141	—	5	2	no	—
148	#1136	—	5	1	no	—
149	D₅₆	—	5	2	no	—
150	#1132	—	5	2	no	—
151	#1131	—	5	2	no	—
152	C₈×D₇	—	5	2	no	—
153	C₂³×D₅	—	14	1	no	—
154	C₅×#41	—	7	1	no	—
155	C₅×#41	—	7	1	no	—
156	C₅×#41	—	7	1	no	—
157	C₅×#41	—	14	1	no	—
158	C₅×#41	—	14	1	no	—
159	C₅×#41	C₂×D₇	1	1	yes	characteristic, complemented
160	C₂×C₅×Q₈	—	7	1	no	—
161	C₂×C₅×D₄	—	7	1	no	—
162	C₂×C₅×D₄	—	14	1	no	—
163	C₂²×C₄×C₅	—	7	1	no	—
164	C₂²×C₄×C₅	—	14	1	no	—
165	C₂×D₂₀	—	7	1	no	—
166	C₂×D₂₀	—	7	2	no	—
167	C₂×D₂₀	—	7	2	no	—
168	C₂×D₂₀	—	14	1	no	—
169	C₂×D₂₀	—	14	1	no	—
170	C₂×D₂₀	—	14	1	no	—
171	C₂×D₂₀	C₂×D₇	1	1	yes	characteristic, complemented
172	#688	—	7	2	no	—
173	#688	—	7	2	no	—
174	#688	—	7	2	no	—
175	#688	C₂×D₇	1	2	yes	complemented
176	#686	—	7	2	no	—
177	#686	—	7	2	no	—
178	#686	—	7	2	no	—
179	#686	C₂×D₇	1	2	yes	complemented
180	#681	—	7	1	no	—
181	#681	—	7	2	no	—
182	#681	C₂×D₇	1	1	yes	characteristic, complemented
183	C₂×#168	—	7	2	no	—
184	C₂×C₅×C₇	—	2	1	no	—
185	C₂×C₅×C₇	—	4	1	no	—
186	C₂×C₅×C₇	C₂²×D₄	1	1	yes	characteristic
187	D₃₅	—	4	2	no	—
188	C₅×D₇	—	2	1	no	—
189	C₅×D₇	—	4	1	no	—
190	C₅×D₇	AGL(1,ℤ/8)	1	2	yes	complemented
191	C₇×D₅	—	4	2	no	—
192	C₂×AGL(1,ℤ/8)	—	35	1	no	Sylow
193	C₂³×C₇	—	10	1	no	—
194	C₂²×D₇	—	2	1	no	—
195	C₂²×D₇	—	10	1	no	—
196	C₂²×D₇	—	10	2	no	—
197	C₂²×D₇	—	10	2	no	—
198	C₂²×D₇	—	20	4	no	—
199	C₂²×D₇	C₂²⋊D₅	1	1	yes	characteristic
200	C₇×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
201	C₇×D₄	—	2	1	no	—
202	C₇×D₄	—	5	2	no	—
203	C₇×D₄	—	10	1	no	—
204	C₇×D₄	C₂²×D₅	1	1	yes	characteristic, complemented
205	C₂×C₄×C₇	—	2	1	no	—
206	C₂×C₄×C₇	C₂²×D₅	1	1	yes	characteristic
207	C₂²⋊D₇	—	2	1	no	—
208	C₂²⋊D₇	—	2	1	no	—
209	C₂²⋊D₇	—	2	1	no	—
210	C₂²⋊D₇	—	10	2	no	—
211	C₂²⋊D₇	—	10	2	no	—
212	C₂×Dic₇	—	2	1	no	—
213	C₂×Dic₇	C₂²⋊D₅	1	1	yes	characteristic
214	D₂₈	—	2	1	no	—
215	D₂₈	—	5	2	no	—
216	D₂₈	—	10	1	no	—
217	D₂₈	C₂²×D₅	1	1	yes	characteristic, complemented
218	C₄×D₇	—	2	1	no	—
219	C₄×D₇	—	2	1	no	—
220	C₄×D₇	—	2	1	no	—
221	C₄×D₇	C₂²⋊D₅	1	1	yes	characteristic
222	C₄×D₇	C₂²⋊D₅	1	1	yes	characteristic
223	C₄×D₇	C₂²×D₅	1	1	yes	characteristic
224	C₄×D₇	C₂²×D₅	1	1	yes	characteristic
225	Dic₁₄	—	2	1	no	—
226	Dic₁₄	C₂²×D₅	1	1	yes	characteristic, complemented
227	C₇×C₈	—	5	2	no	—
228	C₇⋊C₈	—	5	2	no	—
229	C₂³×C₅	—	7	1	no	—
230	C₂³×C₅	—	14	1	no	—
231	C₂²×D₅	—	2	1	no	—
232	C₂²×D₅	—	14	2	no	—
233	C₂²×D₅	—	14	2	no	—
234	C₂²×D₅	—	14	1	no	—
235	C₂²×D₅	—	28	4	no	—
236	C₅×Q₈	—	7	1	no	—
237	C₅×Q₈	—	14	1	no	—
238	C₅×Q₈	C₂²×D₇	1	1	yes	characteristic, complemented
239	C₅×D₄	—	2	1	no	—
240	C₅×D₄	—	7	1	no	—
241	C₅×D₄	—	14	1	no	—
242	C₅×D₄	—	14	1	no	—
243	C₅×D₄	—	14	1	no	—
244	C₅×D₄	—	14	1	no	—
245	C₅×D₄	C₂²×D₇	1	1	yes	characteristic, complemented
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	7	1	no	—
248	C₂×C₄×C₅	—	7	1	no	—
249	C₂×C₄×C₅	—	7	1	no	—
250	C₂×C₄×C₅	—	7	1	no	—
251	C₂×C₄×C₅	—	7	1	no	—
252	C₂×C₄×C₅	—	14	1	no	—
253	C₂×C₄×C₅	—	14	1	no	—
254	C₂×C₄×C₅	—	14	1	no	—
255	C₂×C₄×C₅	—	14	1	no	—
256	C₂×C₄×C₅	C₂²×D₇	1	1	yes	characteristic
257	D₂₀	—	2	1	no	—
258	D₂₀	—	7	2	no	—
259	D₂₀	—	14	2	no	—
260	D₂₀	—	14	2	no	—
261	D₂₀	—	14	1	no	—
262	D₂₀	C₂²×D₇	1	2	yes	—
263	#168	—	7	2	no	—
264	#168	C₂²×D₇	1	2	yes	complemented
265	C₅×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
266	C₂×#41	—	7	1	no	—
267	C₂²×D₄	—	35	1	no	—
268	AGL(1,ℤ/8)	—	5	1	no	—
269	AGL(1,ℤ/8)	—	35	1	no	—
270	AGL(1,ℤ/8)	—	35	2	no	—
271	AGL(1,ℤ/8)	—	35	2	no	—
272	AGL(1,ℤ/8)	—	35	1	no	—
273	AGL(1,ℤ/8)	—	35	1	no	—
274	C₂×SD₁₆	—	35	2	no	—
275	C₂×D₈	—	35	2	no	—
276	C₂×M₁₆	—	35	1	no	—
277	C₂²×C₇	—	2	1	no	—
278	C₂²×C₇	—	10	2	no	—
279	C₂²×C₇	—	20	2	no	—
280	C₂²×C₇	C₂×C₂²⋊D₅	1	1	yes	characteristic
281	C₂×D₇	—	2	2	no	—
282	C₂×D₇	—	2	1	no	—
283	C₂×D₇	—	4	2	no	—
284	C₂×D₇	—	10	2	no	—
285	C₂×D₇	—	20	4	no	—
286	C₂×D₇	—	20	2	no	—
287	C₂×D₇	—	20	4	no	—
288	C₂×D₇	C₂×C₂²⋊D₅	1	1	yes	characteristic
289	C₂×D₇	C₂×C₂²⋊D₅	1	1	yes	characteristic
290	C₄×C₇	—	2	1	no	—
291	C₄×C₇	C₂×C₂²⋊D₅	1	1	yes	characteristic
292	C₄×C₇	C₂³×D₅	1	1	yes	characteristic
293	Dic₇	—	2	1	no	—
294	Dic₇	C₂×C₂²⋊D₅	1	1	yes	characteristic
295	Dic₇	C₂×C₂²⋊D₅	1	1	yes	characteristic
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	—	7	1	no	—
298	C₂²×C₅	—	7	1	no	—
299	C₂²×C₅	—	14	2	no	—
300	C₂²×C₅	—	14	1	no	—
301	C₂²×C₅	—	28	2	no	—
302	C₂²×C₅	D₄×D₇	1	1	yes	characteristic
303	C₂×D₅	—	2	2	no	—
304	C₂×D₅	—	4	2	no	—
305	C₂×D₅	—	14	2	no	—
306	C₂×D₅	—	28	4	no	—
307	C₂×D₅	—	28	4	no	—
308	C₂×D₅	—	28	2	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	7	1	no	—
311	C₄×C₅	—	7	1	no	—
312	C₄×C₅	—	14	1	no	—
313	C₄×C₅	D₄×D₇	1	1	yes	characteristic
314	C₄×C₅	C₂³×D₇	1	1	yes	characteristic
315	C₂⁴	—	70	1	no	—
316	#41	—	7	1	no	—
317	#41	—	7	1	no	—
318	#41	—	7	1	no	—
319	#41	—	14	1	no	—
320	#41	—	14	1	no	—
321	#41	D₅×D₇	1	1	yes	characteristic, complemented
322	C₂×Q₈	—	7	1	no	—
323	C₂×D₄	—	5	1	no	—
324	C₂×D₄	—	7	1	no	—
325	C₂×D₄	—	14	1	no	—
326	C₂×D₄	—	35	2	no	—
327	C₂×D₄	—	35	2	no	—
328	C₂×D₄	—	35	1	no	—
329	C₂×D₄	—	70	1	no	—
330	C₂×D₄	—	70	1	no	—
331	C₂×D₄	—	70	1	no	—
332	C₂²×C₄	—	7	1	no	—
333	C₂²×C₄	—	14	1	no	—
334	SD₁₆	—	5	2	no	—
335	SD₁₆	—	35	2	no	—
336	SD₁₆	—	35	2	no	—
337	SD₁₆	—	35	2	no	—
338	D₈	—	5	2	no	—
339	D₈	—	35	2	no	—
340	D₈	—	35	2	no	—
341	D₈	—	35	2	no	—
342	M₁₆	—	5	1	no	—
343	M₁₆	—	35	2	no	—
344	M₁₆	—	35	1	no	—
345	C₂×C₈	—	35	2	no	—
346	C₂×C₇	—	2	1	no	—
347	C₂×C₇	—	4	1	no	—
348	C₂×C₇	—	20	2	no	—
349	C₂×C₇	C₂²×C₂²⋊D₅	1	1	yes	characteristic
350	D₇	—	2	1	no	—
351	D₇	—	4	1	no	—
352	D₇	—	20	2	no	—
353	D₇	#4095	1	2	yes	direct product factor
354	C₂×C₅	—	2	1	no	—
355	C₂×C₅	—	4	1	no	—
356	C₂×C₅	—	7	2	no	—
357	C₂×C₅	—	14	1	no	—
358	C₂×C₅	—	28	1	no	—
359	C₂×C₅	C₂×D₄×D₇	1	1	yes	characteristic
360	D₅	—	4	2	no	—
361	D₅	—	28	2	no	—
362	C₂³	—	7	1	no	—
363	C₂³	—	10	1	no	—
364	C₂³	—	14	1	no	—
365	C₂³	—	70	2	no	—
366	C₂³	—	70	2	no	—
367	C₂³	—	70	1	no	—
368	C₂³	—	140	4	no	—
369	Q₈	—	7	1	no	—
370	Q₈	—	14	1	no	—
371	Q₈	C₂×D₅×D₇	1	1	yes	characteristic, complemented
372	D₄	—	2	1	no	—
373	D₄	—	5	2	no	—
374	D₄	—	7	1	no	—
375	D₄	—	10	1	no	—
376	D₄	—	14	1	no	—
377	D₄	—	14	1	no	—
378	D₄	—	14	1	no	—
379	D₄	—	14	1	no	—
380	D₄	—	35	2	no	—
381	D₄	—	70	2	no	—
382	D₄	—	70	2	no	—
383	D₄	—	70	1	no	—
384	D₄	C₂×D₅×D₇	1	1	yes	characteristic, complemented
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	7	1	no	—
387	C₂×C₄	—	7	1	no	—
388	C₂×C₄	—	7	1	no	—
389	C₂×C₄	—	7	1	no	—
390	C₂×C₄	—	7	1	no	—
391	C₂×C₄	—	14	1	no	—
392	C₂×C₄	—	14	1	no	—
393	C₂×C₄	—	14	1	no	—
394	C₂×C₄	—	14	1	no	—
395	C₂×C₄	C₂×D₅×D₇	1	1	yes	characteristic
396	C₈	—	5	2	no	—
397	C₈	—	35	2	no	—
398	C₇	C₂×#4095	1	1	yes	characteristic, complemented, Sylow
399	C₅	D₇×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
400	C₂²	—	2	1	no	—
401	C₂²	—	7	1	no	—
402	C₂²	—	7	1	no	—
403	C₂²	—	10	2	no	—
404	C₂²	—	14	2	no	—
405	C₂²	—	14	1	no	—
406	C₂²	—	20	2	no	—
407	C₂²	—	28	2	no	—
408	C₂²	—	70	2	no	—
409	C₂²	—	140	2	no	—
410	C₂²	—	140	4	no	—
411	C₂²	—	140	4	no	—
412	C₂²	D₇×C₂²⋊D₅	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	7	1	no	—
415	C₄	—	7	1	no	—
416	C₄	—	14	1	no	—
417	C₄	D₇×C₂²⋊D₅	1	1	yes	characteristic
418	C₄	C₂²×D₅×D₇	1	1	yes	characteristic
419	C₂	—	2	1	no	—
420	C₂	—	4	1	no	—
421	C₂	—	7	2	no	—
422	C₂	—	14	1	no	—
423	C₂	—	20	2	no	—
424	C₂	—	28	1	no	—
425	C₂	—	140	2	no	—
426	C₂	C₂×D₇×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₇×C₂²⋊D₅
commutator, cosocle	C₄×C₅×C₇	C₂⁴
Frattini	C₄	C₂²×D₅×D₇
Fitting	C₅×C₇×#41	C₂²
socle	C₂×C₅×C₇	C₂²×D₄
hypercenter	#41	D₅×D₇
hypocenter	C₅×C₇	C₂×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. C₅×D₇×#41	C₂	semidirect
2. C₂×D₇×D₂₀	C₂	semidirect
3. #11765279	C₂	semidirect
4. C₇×#4095	C₂	semidirect
5. #11764950	C₂	semidirect
6. D₇×#688	C₂	semidirect
7. #11764926	C₂	semidirect
8. D₇×#686	C₂	semidirect
9. #11764800	C₂	semidirect
10. #11764798	C₂	semidirect
11. D₇×#681	C₂	semidirect
13. C₅×C₇×#41	C₂²	semidirect
14. C₂×D₁₄₀	C₂²	semidirect
15. C₂×C₇×D₂₀	C₂²	semidirect
16. C₅×#1161	C₂²	semidirect
17. C₅×Q₈×D₇	C₂²	semidirect
19. C₅×#1159	C₂²	semidirect
21. C₅×D₄×D₇	C₂²	semidirect
23. C₅×#1157	C₂²	semidirect
30. D₇×D₂₀	C₂²	semidirect
31. #10587905	C₂²	semidirect
32. #10587903	C₂²	semidirect
33. #10587898	C₂²	semidirect
34. C₇×#688	C₂²	semidirect
35. C₇×#686	C₂²	semidirect
36. C₇×#681	C₂²	semidirect
37. #10587847	C₂²	semidirect
38. #10587845	C₂²	semidirect
39. #10587842	C₂²	semidirect
40. #10587841	C₂²	semidirect
41. #10587838	C₂²	semidirect
42. D₇×#168	C₂²	semidirect
52. C₅×C₇×Q₈	C₂³	semidirect
54. C₅×C₇×D₄	C₂³	semidirect
67. C₅×D₂₈	C₂³	semidirect
76. C₅×Dic₁₄	C₂³	semidirect
79. C₇⋊#168	C₂³	semidirect
80. C₇×#168	C₂³	semidirect
81. D₇×#41	D₅	semidirect
99. #4095	D₇	direct (N × H)
123. C₇×#41	C₂×D₅	semidirect
126. #1161	C₂×D₅	semidirect
127. Q₈×D₇	C₂×D₅	semidirect
129. #1159	C₂×D₅	semidirect
135. D₄×D₇	C₂×D₅	semidirect
137. #1157	C₂×D₅	semidirect
159. C₅×#41	C₂×D₇	semidirect
171. C₂×D₂₀	C₂×D₇	semidirect
175. #688	C₂×D₇	semidirect
179. #686	C₂×D₇	semidirect
182. #681	C₂×D₇	semidirect
190. C₅×D₇	AGL(1,ℤ/8)	semidirect
200. C₇×Q₈	C₂²×D₅	semidirect
204. C₇×D₄	C₂²×D₅	semidirect
217. D₂₈	C₂²×D₅	semidirect
226. Dic₁₄	C₂²×D₅	semidirect
238. C₅×Q₈	C₂²×D₇	semidirect
245. C₅×D₄	C₂²×D₇	semidirect
264. #168	C₂²×D₇	semidirect
265. C₅×C₇	C₂×AGL(1,ℤ/8)	semidirect
321. #41	D₅×D₇	semidirect
353. D₇	#4095	direct (N × H)
371. Q₈	C₂×D₅×D₇	semidirect
384. D₄	C₂×D₅×D₇	semidirect
398. C₇	C₂×#4095	semidirect
399. C₅	D₇×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₇×#41	2
C₂×D₇×D₂₀	2
#11765279	2
C₇×#4095	2
#11764950	2
D₇×#688	2
#11764926	2
D₇×#686	2
#11764800	2
#11764798	2
D₇×#681	2
D₇×AGL(1,ℤ/8)	5
C₂×#4095	7

Subgroups — D7×#4095 #72218500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#4095 #72218500