Subgroups — C₂×C₇×#1666 #13196327

Order 1792.

786 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1666	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#331	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₇×SD₁₆	—	2	1	no	—
10	C₂²×C₇×SD₁₆	—	2	1	no	—
11	C₂²×C₇×SD₁₆	—	2	1	no	—
12	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₇×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
15	C₇×#492	—	2	2	no	—
16	C₇×#492	C₂²	1	4	yes	—
17	C₇×#475	—	2	2	no	—
18	C₇×#475	C₂²	1	4	yes	complemented
19	C₇×#460	—	2	2	no	—
20	C₇×#460	C₂²	1	4	yes	—
21	C₇×C₈×Q₈	—	2	2	no	—
22	C₇×C₈×Q₈	C₂²	1	4	yes	complemented
23	C₂×C₇×#106	—	2	1	no	—
24	C₂×C₇×C₄⋊C₈	—	2	1	no	—
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×#103	—	2	1	no	—
29	C₂×C₇×#102	—	2	1	no	—
30	C₂×C₄×C₇×C₈	—	2	1	no	—
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₇×#334	C₂²	1	4	yes	complemented
33	C₇×#332	C₂²	1	4	yes	complemented
34	C₇×#331	C₂²	1	4	yes	—
35	C₂×#1666	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₇×Q₈	—	2	1	no	—
37	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
38	C₂²×C₇×D₄	—	2	1	no	—
39	C₂²×C₇×D₄	—	2	1	no	—
40	C₂²×C₇×D₄	—	2	1	no	—
41	C₂×C₇×SD₁₆	—	2	4	no	—
42	C₂×C₇×SD₁₆	—	2	4	no	—
43	C₂×C₇×SD₁₆	—	2	4	no	—
44	C₂×C₇×SD₁₆	—	4	4	no	—
45	C₂×C₇×SD₁₆	—	4	4	no	—
46	C₂×C₇×SD₁₆	—	4	4	no	—
47	C₂²×C₇×C₈	—	2	1	no	—
48	C₂²×C₇×C₈	—	2	1	no	—
49	C₂²×C₇×C₈	—	2	1	no	—
50	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
51	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
52	C₇×C₄⋊Q₈	—	2	1	no	—
53	C₇×C₄⋊Q₈	—	2	1	no	—
54	C₇×C₄⋊Q₈	—	2	1	no	—
55	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₇×#127	—	2	1	no	—
57	C₇×#127	—	2	1	no	—
58	C₇×#127	—	2	1	no	—
59	C₇×#127	C₂³	1	2	yes	—
60	C₄×C₇×Q₈	—	2	1	no	—
61	C₄×C₇×Q₈	—	2	1	no	—
62	C₄×C₇×Q₈	D₄	1	2	yes	—
63	C₄×C₇×Q₈	C₂³	1	2	yes	—
64	C₂×C₇×C₄⋊C₄	—	2	1	no	—
65	C₂×C₇×C₄⋊C₄	—	2	1	no	—
66	C₂×C₇×C₄⋊C₄	—	2	1	no	—
67	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₇	—	2	1	no	—
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₇×#106	—	2	4	no	—
71	C₇×C₄⋊C₈	—	2	4	no	—
72	C₇×C₄⋊C₈	—	2	1	no	—
73	C₇×C₄⋊C₈	—	2	1	no	—
74	C₇×C₄⋊C₈	—	2	1	no	—
75	C₇×C₄⋊C₈	C₂³	1	2	yes	—
76	C₇×C₄⋊C₈	C₂³	1	2	yes	—
77	C₇×C₄⋊C₈	C₂³	1	2	yes	—
78	C₇×#103	—	2	4	no	—
79	C₇×#102	—	2	4	no	—
80	C₄×C₇×C₈	—	2	4	no	—
81	C₄×C₇×C₈	D₄	1	2	yes	—
82	C₄×C₇×C₈	C₂³	1	2	yes	—
83	C₂×#492	C₂×C₇	1	1	yes	characteristic
84	C₂×#475	C₂×C₇	1	1	yes	characteristic, complemented
85	C₂×#460	C₂×C₇	1	1	yes	characteristic
86	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
87	#1666	C₂×C₇	1	8	yes	direct product factor
88	C₂×#334	C₂×C₇	1	1	yes	characteristic, complemented
89	C₂×#332	C₂×C₇	1	1	yes	characteristic, complemented
90	C₂×#331	C₂×C₇	1	1	yes	characteristic
91	C₂⁴×C₇	—	4	1	no	—
92	C₂×C₇×Q₈	—	2	1	no	—
93	C₂×C₇×Q₈	—	2	2	no	—
94	C₂×C₇×Q₈	—	2	2	no	—
95	C₂×C₇×Q₈	—	4	1	no	—
96	C₂×C₇×Q₈	—	4	2	no	—
97	C₂×C₇×Q₈	—	4	2	no	—
98	C₂×C₇×Q₈	SD₁₆	1	4	yes	complemented
99	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
100	C₂×C₇×D₄	—	2	2	no	—
101	C₂×C₇×D₄	—	2	2	no	—
102	C₂×C₇×D₄	—	2	2	no	—
103	C₂×C₇×D₄	—	4	1	no	—
104	C₂×C₇×D₄	—	4	1	no	—
105	C₂×C₇×D₄	—	4	1	no	—
106	C₂×C₇×D₄	—	4	2	no	—
107	C₂×C₇×D₄	—	4	2	no	—
108	C₂×C₇×D₄	—	4	2	no	—
109	C₂×C₇×D₄	—	4	2	no	—
110	C₂×C₇×D₄	—	8	2	no	—
111	C₂²×C₄×C₇	—	2	1	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	4	1	no	—
114	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇	#41	1	1	yes	characteristic
117	C₇×SD₁₆	—	4	8	no	—
118	C₇×SD₁₆	—	4	8	no	—
119	C₇×SD₁₆	—	4	8	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	2	2	no	—
123	C₂×C₇×C₈	—	2	2	no	—
124	C₂×C₇×C₈	—	4	2	no	—
125	C₂×C₇×C₈	—	4	2	no	—
126	C₂×C₇×C₈	—	4	2	no	—
127	C₂×C₇×C₈	SD₁₆	1	4	yes	complemented
128	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
129	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
130	C₇×C₄⋊C₄	—	2	2	no	—
131	C₇×C₄⋊C₄	—	2	1	no	—
132	C₇×C₄⋊C₄	—	2	2	no	—
133	C₇×C₄⋊C₄	—	2	2	no	—
134	C₇×C₄⋊C₄	—	2	2	no	—
135	C₇×C₄⋊C₄	—	4	1	no	—
136	C₇×C₄⋊C₄	—	4	1	no	—
137	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
138	C₄²×C₇	—	2	2	no	—
139	C₄²×C₇	—	2	2	no	—
140	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₇	#41	1	1	yes	characteristic
143	C₄²×C₇	C₂⁴	1	1	yes	characteristic
144	C₂²×SD₁₆	—	2	1	no	—
145	C₂²×SD₁₆	—	2	1	no	—
146	C₂²×SD₁₆	—	2	1	no	—
147	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
148	C₂×#127	C₂²×C₇	1	1	yes	characteristic
149	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
150	#492	—	2	2	no	—
151	#492	C₂²×C₇	1	4	yes	—
152	#475	—	2	2	no	—
153	#475	C₂²×C₇	1	4	yes	complemented
154	#460	—	2	2	no	—
155	#460	C₂²×C₇	1	4	yes	—
156	C₈×Q₈	—	2	2	no	—
157	C₈×Q₈	C₂²×C₇	1	4	yes	complemented
158	C₂×#106	—	2	1	no	—
159	C₂×C₄⋊C₈	—	2	1	no	—
160	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
161	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
162	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
163	C₂×#103	—	2	1	no	—
164	C₂×#102	—	2	1	no	—
165	C₂×C₄×C₈	—	2	1	no	—
166	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
167	#334	C₂²×C₇	1	4	yes	complemented
168	#332	C₂²×C₇	1	4	yes	complemented
169	#331	C₂²×C₇	1	4	yes	—
170	C₂³×C₇	—	4	2	no	—
171	C₂³×C₇	—	8	2	no	—
172	C₂³×C₇	—	8	2	no	—
173	C₂³×C₇	—	8	2	no	—
174	C₂³×C₇	#121	1	1	yes	characteristic
175	C₇×Q₈	—	2	2	no	—
176	C₇×Q₈	—	2	4	no	—
177	C₇×Q₈	—	4	2	no	—
178	C₇×Q₈	—	4	2	no	—
179	C₇×Q₈	—	8	2	no	—
180	C₇×Q₈	C₂×SD₁₆	1	4	yes	complemented
181	C₇×D₄	—	4	2	no	—
182	C₇×D₄	—	4	2	no	—
183	C₇×D₄	—	4	2	no	—
184	C₇×D₄	—	4	2	no	—
185	C₇×D₄	—	8	2	no	—
186	C₇×D₄	—	8	2	no	—
187	C₇×D₄	—	8	2	no	—
188	C₇×D₄	—	8	2	no	—
189	C₂×C₄×C₇	—	2	2	no	—
190	C₂×C₄×C₇	—	2	4	no	—
191	C₂×C₄×C₇	—	2	2	no	—
192	C₂×C₄×C₇	—	2	2	no	—
193	C₂×C₄×C₇	—	4	2	no	—
194	C₂×C₄×C₇	—	4	2	no	—
195	C₂×C₄×C₇	—	8	2	no	—
196	C₂×C₄×C₇	#121	1	1	yes	characteristic
197	C₂×C₄×C₇	#121	1	1	yes	characteristic
198	C₂×C₄×C₇	#121	1	1	yes	characteristic
199	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
200	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
201	C₂×C₄×C₇	#135	1	2	yes	—
202	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
203	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
206	C₇×C₈	—	2	2	no	—
207	C₇×C₈	—	4	2	no	—
208	C₇×C₈	—	4	2	no	—
209	C₇×C₈	—	4	2	no	—
210	C₇×C₈	C₂×SD₁₆	1	4	yes	complemented
211	C₂²×Q₈	—	2	1	no	—
212	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
213	C₂²×D₄	—	2	1	no	—
214	C₂²×D₄	—	2	1	no	—
215	C₂²×D₄	—	2	1	no	—
216	C₂×SD₁₆	—	2	4	no	—
217	C₂×SD₁₆	—	2	4	no	—
218	C₂×SD₁₆	—	2	4	no	—
219	C₂×SD₁₆	—	4	4	no	—
220	C₂×SD₁₆	—	4	4	no	—
221	C₂×SD₁₆	—	4	4	no	—
222	C₂²×C₈	—	2	1	no	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
226	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
231	#127	—	2	1	no	—
232	#127	—	2	1	no	—
233	#127	—	2	1	no	—
234	#127	C₂³×C₇	1	2	yes	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	C₇×D₄	1	2	yes	—
238	C₄×Q₈	C₂³×C₇	1	2	yes	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
245	#106	—	2	4	no	—
246	C₄⋊C₈	—	2	4	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	C₂³×C₇	1	2	yes	—
251	C₄⋊C₈	C₂³×C₇	1	2	yes	—
252	C₄⋊C₈	C₂³×C₇	1	2	yes	—
253	#103	—	2	4	no	—
254	#102	—	2	4	no	—
255	C₄×C₈	—	2	4	no	—
256	C₄×C₈	C₇×D₄	1	2	yes	—
257	C₄×C₈	C₂³×C₇	1	2	yes	—
258	C₂²×C₇	—	8	2	no	—
259	C₂²×C₇	—	8	2	no	—
260	C₂²×C₇	—	8	2	no	—
261	C₂²×C₇	—	16	4	no	—
262	C₂²×C₇	#460	1	2	yes	—
263	C₂²×C₇	#465	1	2	yes	—
264	C₂²×C₇	#471	1	2	yes	—
265	C₂²×C₇	C₂×#121	1	1	yes	characteristic
266	C₄×C₇	—	2	4	no	—
267	C₄×C₇	—	2	1	no	—
268	C₄×C₇	—	2	1	no	—
269	C₄×C₇	—	4	2	no	—
270	C₄×C₇	—	8	2	no	—
271	C₄×C₇	#460	1	2	yes	—
272	C₄×C₇	#465	1	2	yes	—
273	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
274	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
275	C₄×C₇	C₂×#135	1	1	yes	characteristic
276	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₂⁴	—	4	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	C₇×SD₁₆	1	4	yes	complemented
285	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
302	C₂²×C₄	C₇×#41	1	1	yes	characteristic
303	SD₁₆	—	4	8	no	—
304	SD₁₆	—	4	8	no	—
305	SD₁₆	—	4	8	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	4	2	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	4	2	no	—
313	C₂×C₈	C₇×SD₁₆	1	4	yes	complemented
314	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
315	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
327	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
328	C₄²	C₇×#41	1	1	yes	characteristic
329	C₄²	C₂⁴×C₇	1	1	yes	characteristic
330	C₂×C₇	—	16	2	no	—
331	C₂×C₇	#1666	1	4	yes	direct product factor
332	C₂×C₇	C₂×#460	1	1	yes	characteristic
333	C₂×C₇	C₂×#465	1	1	yes	characteristic
334	C₂×C₇	C₂×#471	1	1	yes	characteristic
335	C₂³	—	4	2	no	—
336	C₂³	—	8	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	C₇×#121	1	1	yes	characteristic
340	Q₈	—	2	2	no	—
341	Q₈	—	2	4	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	8	2	no	—
345	Q₈	C₂×C₇×SD₁₆	1	4	yes	complemented
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	8	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	C₇×#121	1	1	yes	characteristic
362	C₂×C₄	C₇×#121	1	1	yes	characteristic
363	C₂×C₄	C₇×#121	1	1	yes	characteristic
364	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
365	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
366	C₂×C₄	C₇×#135	1	2	yes	—
367	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
368	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
369	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
370	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
371	C₈	—	2	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₈	C₂×C₇×SD₁₆	1	4	yes	complemented
376	C₇	C₂×#1666	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	16	4	no	—
381	C₂²	C₇×#460	1	2	yes	—
382	C₂²	C₇×#465	1	2	yes	—
383	C₂²	C₇×#471	1	2	yes	—
384	C₂²	C₂×C₇×#121	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	8	2	no	—
390	C₄	C₇×#460	1	2	yes	—
391	C₄	C₇×#465	1	2	yes	—
392	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
393	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
394	C₄	C₂×C₇×#135	1	1	yes	characteristic
395	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂	—	16	2	no	—
397	C₂	C₇×#1666	1	4	yes	direct product factor
398	C₂	C₂×C₇×#460	1	1	yes	characteristic
399	C₂	C₂×C₇×#465	1	1	yes	characteristic
400	C₂	C₂×C₇×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₂×C₇×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#475	C₂	semidirect
4. C₂×C₇×C₈×Q₈	C₂	semidirect
5. C₇×#1666	C₂	direct (N × H)
6. C₂×C₇×#334	C₂	semidirect
7. C₂×C₇×#332	C₂	semidirect
18. C₇×#475	C₂²	semidirect
22. C₇×C₈×Q₈	C₂²	semidirect
32. C₇×#334	C₂²	semidirect
33. C₇×#332	C₂²	semidirect
35. C₂×#1666	C₇	direct (N × H)
84. C₂×#475	C₂×C₇	semidirect
86. C₂×C₈×Q₈	C₂×C₇	semidirect
87. #1666	C₂×C₇	direct (N × H)
88. C₂×#334	C₂×C₇	semidirect
89. C₂×#332	C₂×C₇	semidirect
98. C₂×C₇×Q₈	SD₁₆	semidirect
127. C₂×C₇×C₈	SD₁₆	semidirect
153. #475	C₂²×C₇	semidirect
157. C₈×Q₈	C₂²×C₇	semidirect
167. #334	C₂²×C₇	semidirect
168. #332	C₂²×C₇	semidirect
180. C₇×Q₈	C₂×SD₁₆	semidirect
210. C₇×C₈	C₂×SD₁₆	semidirect
284. C₂×Q₈	C₇×SD₁₆	semidirect
313. C₂×C₈	C₇×SD₁₆	semidirect
331. C₂×C₇	#1666	direct (N × H)
345. Q₈	C₂×C₇×SD₁₆	semidirect
375. C₈	C₂×C₇×SD₁₆	semidirect
376. C₇	C₂×#1666	direct (N × H)
397. C₂	C₇×#1666	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×#492	2
C₂×C₇×#475	2
C₂×C₇×#460	2
C₂×C₇×C₈×Q₈	2
C₇×#1666	2
C₂×C₇×#334	2
C₂×C₇×#332	2
C₂×C₇×#331	2
C₂×#1666	7

Subgroups — C2×C7×#1666 #13196327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#1666 #13196327