Subgroups — C₇×#17974 #13195190

Order 1792.

592 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3168	C₂	1	1	yes	maximal, characteristic
2	C₇×#2993	C₂	1	2	yes	maximal, complemented
3	C₇×#1594	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1590	C₂	1	2	yes	maximal, complemented
6	C₇×#1580	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1579	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×C₈×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₇×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1495	C₂	1	2	yes	maximal, complemented
11	C₇×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#529	C₂²	1	2	yes	—
13	C₇×#499	C₄	1	1	yes	characteristic
14	C₇×#495	C₄	1	1	yes	characteristic
15	C₇×#488	C₄	1	2	yes	—
16	C₇×#467	C₄	1	1	yes	characteristic
17	C₇×#466	C₄	1	1	yes	characteristic
18	C₇×#465	C₄	1	2	yes	—
19	C₇×#446	C₂²	1	2	yes	—
20	C₇×C₈×Q₈	C₂²	1	2	yes	—
21	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
23	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
24	C₇×#436	—	2	2	no	—
25	C₇×#436	C₂²	1	2	yes	—
26	C₇×#435	—	2	2	no	—
27	C₇×C₈×D₄	C₂²	1	2	yes	—
28	C₇×#433	—	2	2	no	—
29	C₇×#431	C₂²	1	1	yes	characteristic
30	C₇×#431	C₂²	1	1	yes	characteristic
31	C₇×#424	—	2	2	no	—
32	C₇×#423	C₂²	1	2	yes	—
33	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
34	C₇×#334	C₂²	1	2	yes	—
35	C₇×#334	C₂²	1	1	yes	characteristic
36	C₇×#334	C₂²	1	1	yes	characteristic
37	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₇×D₄⋊C₈	C₂²	1	2	yes	—
40	C₇×D₄⋊C₈	C₂²	1	2	yes	—
41	C₇×#322	C₂²	1	1	yes	characteristic
42	C₇×#322	C₂²	1	1	yes	characteristic
43	C₇×C₈²	C₂²	1	1	yes	characteristic
44	C₇×C₈²	C₂²	1	1	yes	characteristic
45	#17974	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
47	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₇×M₁₆	—	2	2	no	—
50	C₂×C₇×M₁₆	—	2	2	no	—
51	C₂²×C₇×C₈	—	2	2	no	—
52	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
54	C₇×#126	—	2	2	no	—
55	C₇×#125	C₂×C₄	1	2	yes	—
56	C₇×#124	C₂×C₄	1	2	yes	—
57	C₇×#123	—	2	2	no	—
58	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
59	C₇×#121	C₂×C₄	1	2	yes	—
60	C₄×C₇×Q₈	C₂³	1	2	yes	—
61	C₄×C₇×D₄	—	2	2	no	—
62	C₄×C₇×D₄	C₂³	1	2	yes	—
63	C₇×#117	—	2	2	no	—
64	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
65	C₇×#107	C₂×C₄	1	1	yes	characteristic
66	C₇×#107	C₂×C₄	1	1	yes	characteristic
67	C₇×#106	C₂×C₄	1	2	yes	—
68	C₇×C₄⋊C₈	—	2	2	no	—
69	C₇×C₄⋊C₈	—	2	2	no	—
70	C₇×C₄⋊C₈	—	2	2	no	—
71	C₇×C₄⋊C₈	—	2	1	no	—
72	C₇×C₄⋊C₈	D₄	1	2	yes	—
73	C₇×C₄⋊C₈	C₂³	1	2	yes	—
74	C₇×C₄⋊C₈	C₂³	1	2	yes	—
75	C₇×#103	C₂×C₄	1	2	yes	—
76	C₇×#103	C₂×C₄	1	2	yes	—
77	C₇×#102	C₂×C₄	1	2	yes	—
78	C₇×#102	C₂×C₄	1	2	yes	—
79	C₇×C₂²⋊C₈	—	2	1	no	—
80	C₇×C₂²⋊C₈	—	2	2	no	—
81	C₇×C₂²⋊C₈	—	2	2	no	—
82	C₇×C₂²⋊C₈	D₄	1	2	yes	—
83	C₇×#97	—	2	2	no	—
84	C₄×C₇×C₈	—	2	2	no	—
85	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
86	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
87	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
89	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
91	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
93	#3168	C₂×C₇	1	1	yes	characteristic
94	#2993	C₂×C₇	1	2	yes	complemented
95	#1594	C₂×C₇	1	1	yes	characteristic, complemented
96	#1593	C₂×C₇	1	1	yes	characteristic, complemented
97	#1590	C₂×C₇	1	2	yes	complemented
98	#1580	C₂×C₇	1	1	yes	characteristic, complemented
99	#1579	C₂×C₇	1	1	yes	characteristic, complemented
100	C₈×SD₁₆	C₂×C₇	1	2	yes	complemented
101	#1566	C₂×C₇	1	1	yes	characteristic, complemented
102	#1495	C₂×C₇	1	2	yes	complemented
103	#1450	C₂×C₇	1	1	yes	characteristic, complemented
104	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
105	C₂×C₇×D₄	—	2	2	no	—
106	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₇	—	2	2	no	—
108	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	#41	1	1	yes	characteristic
111	C₇×Q₁₆	—	2	2	no	—
112	C₇×SD₁₆	—	2	4	no	—
113	C₇×D₈	—	2	2	no	—
114	C₇×M₁₆	—	8	2	no	—
115	C₇×M₁₆	—	8	2	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	—	2	2	no	—
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	2	1	no	—
121	C₂×C₇×C₈	—	2	1	no	—
122	C₂×C₇×C₈	—	8	2	no	—
123	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
128	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
129	C₇×C₄⋊C₄	—	2	2	no	—
130	C₇×C₄⋊C₄	—	2	2	no	—
131	C₇×C₄⋊C₄	—	2	2	no	—
132	C₇×C₄⋊C₄	—	2	2	no	—
133	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
134	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
135	C₇×C₂²⋊C₄	—	2	2	no	—
136	C₇×C₂²⋊C₄	—	2	2	no	—
137	C₇×C₂²⋊C₄	—	2	2	no	—
138	C₇×C₂²⋊C₄	—	2	2	no	—
139	C₇×C₂²⋊C₄	—	2	2	no	—
140	C₄²×C₇	—	2	2	no	—
141	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₇	#41	1	1	yes	characteristic
144	C₄²×C₇	C₂⁴	1	1	yes	characteristic
145	#529	C₂²×C₇	1	2	yes	—
146	#499	C₄×C₇	1	1	yes	characteristic
147	#495	C₄×C₇	1	1	yes	characteristic
148	#488	C₄×C₇	1	2	yes	—
149	#467	C₄×C₇	1	1	yes	characteristic
150	#466	C₄×C₇	1	1	yes	characteristic
151	#465	C₄×C₇	1	2	yes	—
152	#446	C₂²×C₇	1	2	yes	—
153	C₈×Q₈	C₂²×C₇	1	2	yes	—
154	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
155	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
156	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
157	#436	—	2	2	no	—
158	#436	C₂²×C₇	1	2	yes	—
159	#435	—	2	2	no	—
160	C₈×D₄	C₂²×C₇	1	2	yes	—
161	#433	—	2	2	no	—
162	#431	C₂²×C₇	1	1	yes	characteristic
163	#431	C₂²×C₇	1	1	yes	characteristic
164	#424	—	2	2	no	—
165	#423	C₂²×C₇	1	2	yes	—
166	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
167	#334	C₂²×C₇	1	2	yes	—
168	#334	C₂²×C₇	1	1	yes	characteristic
169	#334	C₂²×C₇	1	1	yes	characteristic
170	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
171	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
172	D₄⋊C₈	C₂²×C₇	1	2	yes	—
173	D₄⋊C₈	C₂²×C₇	1	2	yes	—
174	#322	C₂²×C₇	1	1	yes	characteristic
175	#322	C₂²×C₇	1	1	yes	characteristic
176	C₈²	C₂²×C₇	1	1	yes	characteristic
177	C₈²	C₂²×C₇	1	1	yes	characteristic
178	C₂³×C₇	—	2	2	no	—
179	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
180	C₇×Q₈	—	2	2	no	—
181	C₇×Q₈	—	2	2	no	—
182	C₇×D₄	—	2	2	no	—
183	C₇×D₄	—	2	2	no	—
184	C₇×D₄	—	8	2	no	—
185	C₂×C₄×C₇	—	2	1	no	—
186	C₂×C₄×C₇	—	2	1	no	—
187	C₂×C₄×C₇	—	2	2	no	—
188	C₂×C₄×C₇	—	2	2	no	—
189	C₂×C₄×C₇	—	2	2	no	—
190	C₂×C₄×C₇	—	2	2	no	—
191	C₂×C₄×C₇	—	4	1	no	—
192	C₂×C₄×C₇	—	4	2	no	—
193	C₂×C₄×C₇	—	4	2	no	—
194	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
200	C₇×C₈	—	2	1	no	—
201	C₇×C₈	—	2	1	no	—
202	C₇×C₈	—	2	2	no	—
203	C₇×C₈	—	2	2	no	—
204	C₇×C₈	—	4	1	no	—
205	C₇×C₈	—	4	1	no	—
206	C₇×C₈	—	4	2	no	—
207	C₇×C₈	—	4	2	no	—
208	C₇×C₈	#131	1	2	yes	—
209	C₇×C₈	#131	1	2	yes	—
210	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
211	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
212	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	—	2	2	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
217	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
218	#126	—	2	2	no	—
219	#125	C₂×C₄×C₇	1	2	yes	—
220	#124	C₂×C₄×C₇	1	2	yes	—
221	#123	—	2	2	no	—
222	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
223	#121	C₂×C₄×C₇	1	2	yes	—
224	C₄×Q₈	C₂³×C₇	1	2	yes	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	C₂³×C₇	1	2	yes	—
227	#117	—	2	2	no	—
228	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
229	#107	C₂×C₄×C₇	1	1	yes	characteristic
230	#107	C₂×C₄×C₇	1	1	yes	characteristic
231	#106	C₂×C₄×C₇	1	2	yes	—
232	C₄⋊C₈	—	2	2	no	—
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	2	1	no	—
236	C₄⋊C₈	C₇×D₄	1	2	yes	—
237	C₄⋊C₈	C₂³×C₇	1	2	yes	—
238	C₄⋊C₈	C₂³×C₇	1	2	yes	—
239	#103	C₂×C₄×C₇	1	2	yes	—
240	#103	C₂×C₄×C₇	1	2	yes	—
241	#102	C₂×C₄×C₇	1	2	yes	—
242	#102	C₂×C₄×C₇	1	2	yes	—
243	C₂²⋊C₈	—	2	1	no	—
244	C₂²⋊C₈	—	2	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	C₇×D₄	1	2	yes	—
247	#97	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
250	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
251	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
252	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
253	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
254	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
255	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
256	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
257	C₂²×C₇	—	2	1	no	—
258	C₂²×C₇	—	2	1	no	—
259	C₂²×C₇	—	2	1	no	—
260	C₂²×C₇	—	4	2	no	—
261	C₂²×C₇	—	4	2	no	—
262	C₂²×C₇	—	4	2	no	—
263	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
264	C₄×C₇	—	2	1	no	—
265	C₄×C₇	—	2	1	no	—
266	C₄×C₇	—	2	1	no	—
267	C₄×C₇	—	2	1	no	—
268	C₄×C₇	—	4	2	no	—
269	C₄×C₇	—	4	2	no	—
270	C₄×C₇	—	4	2	no	—
271	C₄×C₇	C₂×#131	1	1	yes	characteristic
272	C₄×C₇	C₂×#131	1	1	yes	characteristic
273	C₄×C₇	#577	1	2	yes	—
274	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
280	C₂²×C₄	C₇×#41	1	1	yes	characteristic
281	Q₁₆	—	2	2	no	—
282	SD₁₆	—	2	4	no	—
283	D₈	—	2	2	no	—
284	M₁₆	—	8	2	no	—
285	M₁₆	—	8	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	8	2	no	—
293	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
294	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
295	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
296	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
297	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
298	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
304	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
312	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
313	C₄²	C₇×#41	1	1	yes	characteristic
314	C₄²	C₂⁴×C₇	1	1	yes	characteristic
315	C₂×C₇	—	4	1	no	—
316	C₂×C₇	—	8	2	no	—
317	C₂×C₇	#2931	1	1	yes	characteristic
318	C₂×C₇	#2952	1	1	yes	characteristic
319	C₂×C₇	#2957	1	1	yes	characteristic
320	C₂³	—	2	2	no	—
321	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
322	Q₈	—	2	2	no	—
323	Q₈	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	8	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
337	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
338	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
339	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
340	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
341	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	2	2	no	—
345	C₈	—	2	2	no	—
346	C₈	—	4	1	no	—
347	C₈	—	4	1	no	—
348	C₈	—	4	2	no	—
349	C₈	—	4	2	no	—
350	C₈	C₇×#131	1	2	yes	—
351	C₈	C₇×#131	1	2	yes	—
352	C₇	#17974	1	1	yes	characteristic, direct product factor, Sylow
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	C₂×C₇×#131	1	1	yes	characteristic
368	C₄	C₂×C₇×#131	1	1	yes	characteristic
369	C₄	C₇×#577	1	2	yes	—
370	C₂	—	4	1	no	—
371	C₂	—	8	2	no	—
372	C₂	C₇×#2931	1	1	yes	characteristic
373	C₂	C₇×#2952	1	1	yes	characteristic
374	C₂	C₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₇×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2993	C₂	semidirect
3. C₇×#1594	C₂	semidirect
4. C₇×#1593	C₂	semidirect
5. C₇×#1590	C₂	semidirect
6. C₇×#1580	C₂	semidirect
7. C₇×#1579	C₂	semidirect
8. C₇×C₈×SD₁₆	C₂	semidirect
9. C₇×#1566	C₂	semidirect
10. C₇×#1495	C₂	semidirect
11. C₇×#1450	C₂	semidirect
45. #17974	C₇	direct (N × H)
94. #2993	C₂×C₇	semidirect
95. #1594	C₂×C₇	semidirect
96. #1593	C₂×C₇	semidirect
97. #1590	C₂×C₇	semidirect
98. #1580	C₂×C₇	semidirect
99. #1579	C₂×C₇	semidirect
100. C₈×SD₁₆	C₂×C₇	semidirect
101. #1566	C₂×C₇	semidirect
102. #1495	C₂×C₇	semidirect
103. #1450	C₂×C₇	semidirect
352. C₇	#17974	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×#3168	2
C₇×#2993	2
C₇×#1594	2
C₇×#1593	2
C₇×#1590	2
C₇×#1580	2
C₇×#1579	2
C₇×C₈×SD₁₆	2
C₇×#1566	2
C₇×#1495	2
C₇×#1450	2
#17974	7

Subgroups — C7×#17974 #13195190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17974 #13195190