Subgroups — C₇×#19101 #13196317

Order 1792.

802 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3100	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1669	C₂	1	2	yes	maximal, complemented
5	C₇×#1667	C₂	1	2	yes	maximal, complemented
6	C₇×#1665	C₂	1	4	yes	maximal, complemented
7	C₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1540	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#135	—	2	1	no	—
10	C₂×C₇×#135	—	2	1	no	—
11	C₂³×C₇×C₈	—	2	1	no	—
12	C₇×#532	C₂²	1	2	yes	—
13	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
14	C₇×#495	—	2	1	no	—
15	C₇×#495	—	2	1	no	—
16	C₇×#494	C₂²	1	1	yes	characteristic, complemented
17	C₇×#493	C₂²	1	1	yes	characteristic, complemented
18	C₇×#492	C₂²	1	2	yes	complemented
19	C₇×#480	—	2	2	no	—
20	C₇×#474	C₂²	1	4	yes	—
21	C₇×#459	C₂²	1	4	yes	—
22	C₇×#447	—	2	2	no	—
23	C₄×C₇×D₈	—	2	4	no	—
24	C₇×C₈×D₄	—	2	1	no	—
25	C₇×C₈×D₄	—	2	1	no	—
26	C₇×C₈×D₄	C₂²	1	2	yes	—
27	C₇×C₈×D₄	C₂²	1	2	yes	—
28	C₇×#431	C₂²	1	2	yes	—
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₇×#335	C₂²	1	2	yes	complemented
33	C₇×#334	C₂²	1	2	yes	complemented
34	C₇×#332	C₂²	1	4	yes	complemented
35	C₇×#331	C₂²	1	4	yes	complemented
36	#19101	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₇×#41	—	2	2	no	—
38	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₇	—	2	1	no	—
40	C₇×#135	—	4	4	no	—
41	C₇×#135	—	4	4	no	—
42	C₂×C₇×Q₁₆	—	2	1	no	—
43	C₂×C₇×Q₁₆	—	2	1	no	—
44	C₂×C₇×SD₁₆	—	2	2	no	—
45	C₂×C₇×SD₁₆	—	2	2	no	—
46	C₂×C₇×D₈	—	2	4	no	—
47	C₂×C₇×D₈	—	2	1	no	—
48	C₂×C₇×D₈	—	2	1	no	—
49	C₂²×C₇×C₈	—	2	1	no	—
50	C₂²×C₇×C₈	—	2	2	no	—
51	C₂²×C₇×C₈	—	2	2	no	—
52	C₂²×C₇×C₈	—	4	4	no	—
53	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
54	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
55	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₇×#127	C₂³	1	2	yes	—
57	C₇×#124	—	2	2	no	—
58	C₇×#121	—	2	2	no	—
59	C₇×#121	—	2	2	no	—
60	C₄×C₇×D₄	—	2	1	no	—
61	C₄×C₇×D₄	—	2	2	no	—
62	C₄×C₇×D₄	—	2	1	no	—
63	C₄×C₇×D₄	—	2	2	no	—
64	C₄×C₇×D₄	D₄	1	2	yes	—
65	C₄×C₇×D₄	C₂³	1	2	yes	—
66	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
69	C₇×#107	—	2	4	no	—
70	C₇×C₄⋊C₈	—	2	1	no	—
71	C₇×C₄⋊C₈	C₂³	1	4	yes	—
72	C₇×C₄⋊C₈	C₂³	1	2	yes	—
73	C₇×#102	—	2	4	no	—
74	C₇×#102	—	2	4	no	—
75	C₇×C₂²⋊C₈	—	2	2	no	—
76	C₇×C₂²⋊C₈	—	2	2	no	—
77	C₇×C₂²⋊C₈	—	2	2	no	—
78	C₄×C₇×C₈	—	2	2	no	—
79	C₄×C₇×C₈	D₄	1	1	yes	characteristic
80	C₄×C₇×C₈	D₄	1	1	yes	characteristic
81	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
83	#3147	C₂×C₇	1	1	yes	characteristic, complemented
84	#3100	C₂×C₇	1	2	yes	complemented
85	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
86	#1669	C₂×C₇	1	2	yes	complemented
87	#1667	C₂×C₇	1	2	yes	complemented
88	#1665	C₂×C₇	1	4	yes	complemented
89	#1564	C₂×C₇	1	1	yes	characteristic, complemented
90	#1540	C₂×C₇	1	2	yes	complemented
91	C₂⁴×C₇	—	2	1	no	—
92	C₇×#41	—	4	4	no	—
93	C₇×#41	—	4	4	no	—
94	C₂×C₇×Q₈	—	2	2	no	—
95	C₂×C₇×D₄	—	2	4	no	—
96	C₂×C₇×D₄	—	2	1	no	—
97	C₂×C₇×D₄	—	2	2	no	—
98	C₂×C₇×D₄	—	2	2	no	—
99	C₂×C₇×D₄	—	2	2	no	—
100	C₂×C₇×D₄	—	4	2	no	—
101	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₇	—	2	1	no	—
103	C₂²×C₄×C₇	—	2	2	no	—
104	C₂²×C₄×C₇	—	2	2	no	—
105	C₂²×C₄×C₇	—	4	2	no	—
106	C₂²×C₄×C₇	—	4	2	no	—
107	C₂²×C₄×C₇	—	4	2	no	—
108	C₂²×C₄×C₇	C₂×D₄	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	—	4	2	no	—
112	C₇×Q₁₆	—	4	2	no	—
113	C₇×SD₁₆	—	4	4	no	—
114	C₇×SD₁₆	—	4	4	no	—
115	C₇×D₈	—	4	2	no	—
116	C₇×D₈	—	4	8	no	—
117	C₇×D₈	—	4	2	no	—
118	C₂×C₇×C₈	—	2	2	no	—
119	C₂×C₇×C₈	—	2	4	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	4	2	no	—
122	C₂×C₇×C₈	—	4	4	no	—
123	C₂×C₇×C₈	—	4	4	no	—
124	C₂×C₇×C₈	D₈	1	4	yes	complemented
125	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
126	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
127	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
129	C₇×C₄⋊C₄	—	2	1	no	—
130	C₇×C₄⋊C₄	—	2	2	no	—
131	C₇×C₄⋊C₄	—	2	2	no	—
132	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
133	C₇×C₂²⋊C₄	—	2	2	no	—
134	C₇×C₂²⋊C₄	—	2	2	no	—
135	C₇×C₂²⋊C₄	—	4	2	no	—
136	C₇×C₂²⋊C₄	—	4	2	no	—
137	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₇	#41	1	1	yes	characteristic
140	C₄²×C₇	C₂⁴	1	1	yes	characteristic
141	C₂×#135	—	2	1	no	—
142	C₂×#135	—	2	1	no	—
143	C₂³×C₈	—	2	1	no	—
144	#532	C₂²×C₇	1	2	yes	—
145	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
146	#495	—	2	1	no	—
147	#495	—	2	1	no	—
148	#494	C₂²×C₇	1	1	yes	characteristic, complemented
149	#493	C₂²×C₇	1	1	yes	characteristic, complemented
150	#492	C₂²×C₇	1	2	yes	complemented
151	#480	—	2	2	no	—
152	#474	C₂²×C₇	1	4	yes	—
153	#459	C₂²×C₇	1	4	yes	—
154	#447	—	2	2	no	—
155	C₄×D₈	—	2	4	no	—
156	C₈×D₄	—	2	1	no	—
157	C₈×D₄	—	2	1	no	—
158	C₈×D₄	C₂²×C₇	1	2	yes	—
159	C₈×D₄	C₂²×C₇	1	2	yes	—
160	#431	C₂²×C₇	1	2	yes	—
161	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
162	C₂×C₂²⋊C₈	—	2	1	no	—
163	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
164	#335	C₂²×C₇	1	2	yes	complemented
165	#334	C₂²×C₇	1	2	yes	complemented
166	#332	C₂²×C₇	1	4	yes	complemented
167	#331	C₂²×C₇	1	4	yes	complemented
168	C₂³×C₇	—	2	4	no	—
169	C₂³×C₇	—	2	2	no	—
170	C₂³×C₇	—	4	2	no	—
171	C₂³×C₇	—	4	2	no	—
172	C₂³×C₇	—	4	2	no	—
173	C₂³×C₇	#121	1	1	yes	characteristic
174	C₇×Q₈	—	4	2	no	—
175	C₇×Q₈	—	4	2	no	—
176	C₇×D₄	—	2	4	no	—
177	C₇×D₄	—	2	2	no	—
178	C₇×D₄	—	4	2	no	—
179	C₇×D₄	—	4	4	no	—
180	C₇×D₄	—	4	2	no	—
181	C₇×D₄	—	8	2	no	—
182	C₇×D₄	—	8	4	no	—
183	C₇×D₄	#135	1	4	yes	complemented
184	C₂×C₄×C₇	—	2	2	no	—
185	C₂×C₄×C₇	—	2	2	no	—
186	C₂×C₄×C₇	—	4	1	no	—
187	C₂×C₄×C₇	—	4	2	no	—
188	C₂×C₄×C₇	—	4	2	no	—
189	C₂×C₄×C₇	—	4	2	no	—
190	C₂×C₄×C₇	—	4	4	no	—
191	C₂×C₄×C₇	—	4	2	no	—
192	C₂×C₄×C₇	—	8	4	no	—
193	C₂×C₄×C₇	#121	1	1	yes	characteristic
194	C₂×C₄×C₇	#121	1	1	yes	characteristic
195	C₂×C₄×C₇	#121	1	1	yes	characteristic
196	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
197	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
198	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
201	C₇×C₈	—	2	1	no	—
202	C₇×C₈	—	2	1	no	—
203	C₇×C₈	—	4	2	no	—
204	C₇×C₈	—	4	4	no	—
205	C₇×C₈	C₂×D₈	1	2	yes	—
206	C₇×C₈	C₂×D₈	1	2	yes	—
207	C₂×#41	—	2	2	no	—
208	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
209	C₂³×C₄	—	2	1	no	—
210	#135	—	4	4	no	—
211	#135	—	4	4	no	—
212	C₂×Q₁₆	—	2	1	no	—
213	C₂×Q₁₆	—	2	1	no	—
214	C₂×SD₁₆	—	2	2	no	—
215	C₂×SD₁₆	—	2	2	no	—
216	C₂×D₈	—	2	4	no	—
217	C₂×D₈	—	2	1	no	—
218	C₂×D₈	—	2	1	no	—
219	C₂²×C₈	—	2	1	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	4	4	no	—
223	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
224	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
225	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
226	#127	C₂³×C₇	1	2	yes	—
227	#124	—	2	2	no	—
228	#121	—	2	2	no	—
229	#121	—	2	2	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	C₇×D₄	1	2	yes	—
235	C₄×D₄	C₂³×C₇	1	2	yes	—
236	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
239	#107	—	2	4	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	C₂³×C₇	1	2	yes	—
242	C₄⋊C₈	C₂³×C₇	1	4	yes	—
243	#102	—	2	4	no	—
244	#102	—	2	4	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	C₇×D₄	1	1	yes	characteristic
250	C₄×C₈	C₇×D₄	1	1	yes	characteristic
251	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
252	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
253	C₂²×C₇	—	2	1	no	—
254	C₂²×C₇	—	2	1	no	—
255	C₂²×C₇	—	2	4	no	—
256	C₂²×C₇	—	4	8	no	—
257	C₂²×C₇	—	4	2	no	—
258	C₂²×C₇	—	4	2	no	—
259	C₂²×C₇	—	8	2	no	—
260	C₂²×C₇	—	8	2	no	—
261	C₂²×C₇	—	8	2	no	—
262	C₂²×C₇	#459	1	2	yes	—
263	C₂²×C₇	C₂×#121	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	—	4	2	no	—
268	C₄×C₇	—	8	2	no	—
269	C₄×C₇	#459	1	2	yes	—
270	C₄×C₇	C₂²×D₈	1	1	yes	characteristic
271	C₄×C₇	C₂×#135	1	2	yes	—
272	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₂⁴	—	2	1	no	—
274	#41	—	4	4	no	—
275	#41	—	4	4	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
292	C₂²×C₄	C₇×#41	1	1	yes	characteristic
293	Q₁₆	—	4	2	no	—
294	Q₁₆	—	4	2	no	—
295	SD₁₆	—	4	4	no	—
296	SD₁₆	—	4	4	no	—
297	D₈	—	4	2	no	—
298	D₈	—	4	8	no	—
299	D₈	—	4	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	—	4	4	no	—
306	C₂×C₈	C₇×D₈	1	4	yes	complemented
307	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
308	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
309	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
310	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
320	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
321	C₄²	C₇×#41	1	1	yes	characteristic
322	C₄²	C₂⁴×C₇	1	1	yes	characteristic
323	C₂×C₇	—	2	2	no	—
324	C₂×C₇	—	4	4	no	—
325	C₂×C₇	—	16	2	no	—
326	C₂×C₇	C₂×#459	1	1	yes	characteristic
327	C₂×C₇	#3050	1	1	yes	characteristic
328	C₂×C₇	#3067	1	1	yes	characteristic
329	C₂³	—	2	4	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	C₇×#121	1	1	yes	characteristic
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	D₄	—	2	4	no	—
338	D₄	—	2	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	2	no	—
342	D₄	—	8	2	no	—
343	D₄	—	8	4	no	—
344	D₄	C₇×#135	1	4	yes	complemented
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	8	4	no	—
354	C₂×C₄	C₇×#121	1	1	yes	characteristic
355	C₂×C₄	C₇×#121	1	1	yes	characteristic
356	C₂×C₄	C₇×#121	1	1	yes	characteristic
357	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
358	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
359	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
361	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	4	2	no	—
365	C₈	—	4	4	no	—
366	C₈	C₂×C₇×D₈	1	2	yes	—
367	C₈	C₂×C₇×D₈	1	2	yes	—
368	C₇	#19101	1	1	yes	characteristic, direct product factor, Sylow
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	C₇×#459	1	2	yes	—
379	C₂²	C₂×C₇×#121	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	2	no	—
385	C₄	C₇×#459	1	2	yes	—
386	C₄	C₂²×C₇×D₈	1	1	yes	characteristic
387	C₄	C₂×C₇×#135	1	2	yes	—
388	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	4	4	no	—
391	C₂	—	16	2	no	—
392	C₂	C₂×C₇×#459	1	1	yes	characteristic
393	C₂	C₇×#3050	1	1	yes	characteristic
394	C₂	C₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3147	C₂	semidirect
2. C₇×#3100	C₂	semidirect
3. C₂×C₇×C₈×D₄	C₂	semidirect
4. C₇×#1669	C₂	semidirect
5. C₇×#1667	C₂	semidirect
6. C₇×#1665	C₂	semidirect
7. C₇×#1564	C₂	semidirect
8. C₇×#1540	C₂	semidirect
16. C₇×#494	C₂²	semidirect
17. C₇×#493	C₂²	semidirect
18. C₇×#492	C₂²	semidirect
32. C₇×#335	C₂²	semidirect
33. C₇×#334	C₂²	semidirect
34. C₇×#332	C₂²	semidirect
35. C₇×#331	C₂²	semidirect
36. #19101	C₇	direct (N × H)
83. #3147	C₂×C₇	semidirect
84. #3100	C₂×C₇	semidirect
85. C₂×C₈×D₄	C₂×C₇	semidirect
86. #1669	C₂×C₇	semidirect
87. #1667	C₂×C₇	semidirect
88. #1665	C₂×C₇	semidirect
89. #1564	C₂×C₇	semidirect
90. #1540	C₂×C₇	semidirect
124. C₂×C₇×C₈	D₈	semidirect
148. #494	C₂²×C₇	semidirect
149. #493	C₂²×C₇	semidirect
150. #492	C₂²×C₇	semidirect
164. #335	C₂²×C₇	semidirect
165. #334	C₂²×C₇	semidirect
166. #332	C₂²×C₇	semidirect
167. #331	C₂²×C₇	semidirect
183. C₇×D₄	#135	semidirect
306. C₂×C₈	C₇×D₈	semidirect
344. D₄	C₇×#135	semidirect
368. C₇	#19101	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×#3147	2
C₇×#3100	2
C₂×C₇×C₈×D₄	2
C₇×#1669	2
C₇×#1667	2
C₇×#1665	2
C₇×#1564	2
C₇×#1540	2
#19101	7

Subgroups — C7×#19101 #13196317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19101 #13196317