Subgroups — C₂×C₇×#1590 #13195100

Order 1792.

746 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic
4	C₇×#1590	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂×C₇×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×SD₁₆	C₄	1	1	yes	characteristic
10	C₂²×C₇×M₁₆	—	2	1	no	—
11	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
13	C₇×#446	—	2	2	no	—
14	C₇×#446	C₂²	1	4	yes	complemented
15	C₄×C₇×SD₁₆	C₄	1	4	yes	—
16	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
17	C₇×#436	—	2	2	no	—
18	C₇×#436	C₂²	1	4	yes	—
19	C₂×C₇×#106	C₄	1	1	yes	characteristic
20	C₂×C₇×C₄⋊C₈	—	2	1	no	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×#103	C₄	1	1	yes	characteristic
24	C₂×C₇×#102	C₄	1	1	yes	characteristic
25	C₂×C₇×C₂²⋊C₈	—	2	1	no	—
26	C₂×C₇×#97	—	2	1	no	—
27	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₇×#334	C₂²	1	4	yes	complemented
31	C₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
32	C₇×D₄⋊C₈	C₂²	1	4	yes	—
33	C₇×C₈²	C₂²	1	4	yes	complemented
34	C₂×#1590	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₇	—	2	1	no	—
38	C₂×C₇×SD₁₆	—	2	4	no	—
39	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
40	C₂×C₇×M₁₆	—	2	4	no	—
41	C₂×C₇×M₁₆	—	4	4	no	—
42	C₂²×C₇×C₈	—	2	1	no	—
43	C₂²×C₇×C₈	—	2	1	no	—
44	C₂²×C₇×C₈	—	2	1	no	—
45	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
48	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
49	C₄×C₇×Q₈	—	2	1	no	—
50	C₄×C₇×Q₈	—	2	1	no	—
51	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
52	C₄×C₇×Q₈	C₂³	1	2	yes	—
53	C₄×C₇×D₄	—	2	1	no	—
54	C₄×C₇×D₄	—	2	1	no	—
55	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
56	C₄×C₇×D₄	C₂³	1	2	yes	—
57	C₂×C₇×C₄⋊C₄	—	2	1	no	—
58	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
61	C₂×C₄²×C₇	—	2	1	no	—
62	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
63	C₇×#106	C₂×C₄	1	4	yes	—
64	C₇×C₄⋊C₈	—	2	4	no	—
65	C₇×C₄⋊C₈	—	2	1	no	—
66	C₇×C₄⋊C₈	—	2	1	no	—
67	C₇×C₄⋊C₈	C₂³	1	2	yes	—
68	C₇×C₄⋊C₈	C₂³	1	2	yes	—
69	C₇×#103	C₂×C₄	1	4	yes	—
70	C₇×#102	C₂×C₄	1	4	yes	—
71	C₇×C₂²⋊C₈	—	2	4	no	—
72	C₇×#97	—	2	4	no	—
73	C₄×C₇×C₈	—	2	1	no	—
74	C₄×C₇×C₈	C₂×C₄	1	2	yes	—
75	C₄×C₇×C₈	D₄	1	2	yes	—
76	C₄×C₇×C₈	C₂³	1	2	yes	—
77	C₄×C₇×C₈	C₂³	1	2	yes	—
78	C₄×C₇×C₈	C₂³	1	2	yes	—
79	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
80	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
81	C₂×#436	C₂×C₇	1	1	yes	characteristic
82	#1590	C₂×C₇	1	8	yes	direct product factor
83	C₂×#334	C₂×C₇	1	1	yes	characteristic, complemented
84	C₂×Q₈⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
85	C₂×D₄⋊C₈	C₂×C₇	1	1	yes	characteristic
86	C₂×C₈²	C₂×C₇	1	1	yes	characteristic, complemented
87	C₂⁴×C₇	—	2	1	no	—
88	C₂×C₇×Q₈	—	2	1	no	—
89	C₂×C₇×Q₈	—	2	2	no	—
90	C₂×C₇×Q₈	—	2	2	no	—
91	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
92	C₂×C₇×D₄	—	2	1	no	—
93	C₂×C₇×D₄	—	2	2	no	—
94	C₂×C₇×D₄	—	2	2	no	—
95	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₇	—	2	1	no	—
97	C₂²×C₄×C₇	—	2	1	no	—
98	C₂²×C₄×C₇	—	2	1	no	—
99	C₂²×C₄×C₇	—	2	2	no	—
100	C₂²×C₄×C₇	—	2	2	no	—
101	C₂²×C₄×C₇	—	4	2	no	—
102	C₂²×C₄×C₇	—	4	2	no	—
103	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₇	#41	1	1	yes	characteristic
106	C₇×SD₁₆	—	2	8	no	—
107	C₇×M₁₆	—	4	8	no	—
108	C₂×C₇×C₈	—	2	4	no	—
109	C₂×C₇×C₈	—	2	2	no	—
110	C₂×C₇×C₈	—	2	2	no	—
111	C₂×C₇×C₈	—	2	2	no	—
112	C₂×C₇×C₈	—	2	2	no	—
113	C₂×C₇×C₈	—	2	2	no	—
114	C₂×C₇×C₈	—	4	2	no	—
115	C₂×C₇×C₈	—	4	2	no	—
116	C₂×C₇×C₈	M₁₆	1	4	yes	complemented
117	C₂×C₇×C₈	SD₁₆	1	4	yes	complemented
118	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
119	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
120	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
121	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
122	C₇×C₄⋊C₄	—	2	2	no	—
123	C₇×C₄⋊C₄	—	2	1	no	—
124	C₇×C₄⋊C₄	—	2	1	no	—
125	C₇×C₄⋊C₄	—	2	2	no	—
126	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
127	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
128	C₇×C₂²⋊C₄	—	2	2	no	—
129	C₇×C₂²⋊C₄	—	2	2	no	—
130	C₄²×C₇	—	2	2	no	—
131	C₄²×C₇	—	2	2	no	—
132	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₇	#41	1	1	yes	characteristic
135	C₄²×C₇	C₂⁴	1	1	yes	characteristic
136	C₂²×SD₁₆	C₄×C₇	1	1	yes	characteristic
137	C₂²×M₁₆	—	2	1	no	—
138	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
139	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
140	#446	—	2	2	no	—
141	#446	C₂²×C₇	1	4	yes	complemented
142	C₄×SD₁₆	C₄×C₇	1	4	yes	—
143	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
144	#436	—	2	2	no	—
145	#436	C₂²×C₇	1	4	yes	—
146	C₂×#106	C₄×C₇	1	1	yes	characteristic
147	C₂×C₄⋊C₈	—	2	1	no	—
148	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
149	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
150	C₂×#103	C₄×C₇	1	1	yes	characteristic
151	C₂×#102	C₄×C₇	1	1	yes	characteristic
152	C₂×C₂²⋊C₈	—	2	1	no	—
153	C₂×#97	—	2	1	no	—
154	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
155	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
156	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
157	#334	C₂²×C₇	1	4	yes	complemented
158	Q₈⋊C₈	C₂²×C₇	1	4	yes	complemented
159	D₄⋊C₈	C₂²×C₇	1	4	yes	—
160	C₈²	C₂²×C₇	1	4	yes	complemented
161	C₂³×C₇	—	2	2	no	—
162	C₂³×C₇	—	4	2	no	—
163	C₂³×C₇	—	4	2	no	—
164	C₂³×C₇	—	4	2	no	—
165	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
166	C₇×Q₈	—	2	2	no	—
167	C₇×Q₈	—	2	2	no	—
168	C₇×Q₈	—	4	2	no	—
169	C₇×D₄	—	2	2	no	—
170	C₇×D₄	—	2	2	no	—
171	C₇×D₄	—	4	2	no	—
172	C₂×C₄×C₇	—	2	2	no	—
173	C₂×C₄×C₇	—	2	2	no	—
174	C₂×C₄×C₇	—	2	2	no	—
175	C₂×C₄×C₇	—	2	2	no	—
176	C₂×C₄×C₇	—	4	2	no	—
177	C₂×C₄×C₇	—	4	2	no	—
178	C₂×C₄×C₇	—	4	2	no	—
179	C₂×C₄×C₇	—	4	2	no	—
180	C₂×C₄×C₇	—	4	2	no	—
181	C₂×C₄×C₇	—	4	4	no	—
182	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
186	C₂×C₄×C₇	#131	1	2	yes	—
187	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
188	C₂×C₄×C₇	#135	1	2	yes	—
189	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
192	C₇×C₈	—	2	4	no	—
193	C₇×C₈	—	2	2	no	—
194	C₇×C₈	—	2	2	no	—
195	C₇×C₈	—	4	2	no	—
196	C₇×C₈	—	4	2	no	—
197	C₇×C₈	C₂×M₁₆	1	4	yes	complemented
198	C₇×C₈	C₂×SD₁₆	1	4	yes	complemented
199	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
200	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
201	C₂³×C₄	—	2	1	no	—
202	C₂×SD₁₆	—	2	4	no	—
203	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
204	C₂×M₁₆	—	2	4	no	—
205	C₂×M₁₆	—	4	4	no	—
206	C₂²×C₈	—	2	1	no	—
207	C₂²×C₈	—	2	1	no	—
208	C₂²×C₈	—	2	1	no	—
209	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
210	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
211	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
212	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
213	C₄×Q₈	—	2	1	no	—
214	C₄×Q₈	—	2	1	no	—
215	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
216	C₄×Q₈	C₂³×C₇	1	2	yes	—
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
220	C₄×D₄	C₂³×C₇	1	2	yes	—
221	C₂×C₄⋊C₄	—	2	1	no	—
222	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
224	C₂×C₂²⋊C₄	—	2	1	no	—
225	C₂×C₄²	—	2	1	no	—
226	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
227	#106	C₂×C₄×C₇	1	4	yes	—
228	C₄⋊C₈	—	2	4	no	—
229	C₄⋊C₈	—	2	1	no	—
230	C₄⋊C₈	—	2	1	no	—
231	C₄⋊C₈	C₂³×C₇	1	2	yes	—
232	C₄⋊C₈	C₂³×C₇	1	2	yes	—
233	#103	C₂×C₄×C₇	1	4	yes	—
234	#102	C₂×C₄×C₇	1	4	yes	—
235	C₂²⋊C₈	—	2	4	no	—
236	#97	—	2	4	no	—
237	C₄×C₈	—	2	1	no	—
238	C₄×C₈	C₂×C₄×C₇	1	2	yes	—
239	C₄×C₈	C₇×D₄	1	2	yes	—
240	C₄×C₈	C₂³×C₇	1	2	yes	—
241	C₄×C₈	C₂³×C₇	1	2	yes	—
242	C₄×C₈	C₂³×C₇	1	2	yes	—
243	C₂²×C₇	—	4	2	no	—
244	C₂²×C₇	—	4	2	no	—
245	C₂²×C₇	—	4	2	no	—
246	C₂²×C₇	—	8	4	no	—
247	C₂²×C₇	#436	1	2	yes	—
248	C₂²×C₇	C₄×SD₁₆	1	2	yes	—
249	C₂²×C₇	#443	1	2	yes	—
250	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
251	C₄×C₇	—	2	1	no	—
252	C₄×C₇	—	2	1	no	—
253	C₄×C₇	—	4	2	no	—
254	C₄×C₇	—	4	2	no	—
255	C₄×C₇	—	4	2	no	—
256	C₄×C₇	#436	1	2	yes	—
257	C₄×C₇	C₄×SD₁₆	1	2	yes	—
258	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
259	C₄×C₇	C₂×#131	1	1	yes	characteristic
260	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
261	C₄×C₇	C₂×#135	1	1	yes	characteristic
262	C₂⁴	—	2	1	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	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	SD₁₆	—	2	8	no	—
282	M₁₆	—	4	8	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	C₇×M₁₆	1	4	yes	complemented
292	C₂×C₈	C₇×SD₁₆	1	4	yes	complemented
293	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
294	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
295	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
296	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
302	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
308	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
309	C₄²	C₇×#41	1	1	yes	characteristic
310	C₄²	C₂⁴×C₇	1	1	yes	characteristic
311	C₂×C₇	—	8	2	no	—
312	C₂×C₇	#1590	1	4	yes	direct product factor
313	C₂×C₇	C₂×#436	1	1	yes	characteristic
314	C₂×C₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
315	C₂×C₇	C₂×#443	1	1	yes	characteristic
316	C₂³	—	2	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
321	Q₈	—	2	2	no	—
322	Q₈	—	2	2	no	—
323	Q₈	—	4	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	4	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
338	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
339	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
340	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
341	C₂×C₄	C₇×#131	1	2	yes	—
342	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
343	C₂×C₄	C₇×#135	1	2	yes	—
344	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
346	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
347	C₈	—	2	4	no	—
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₈	—	4	2	no	—
351	C₈	—	4	2	no	—
352	C₈	C₂×C₇×M₁₆	1	4	yes	complemented
353	C₈	C₂×C₇×SD₁₆	1	4	yes	complemented
354	C₇	C₂×#1590	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	4	no	—
359	C₂²	C₇×#436	1	2	yes	—
360	C₂²	C₄×C₇×SD₁₆	1	2	yes	—
361	C₂²	C₇×#443	1	2	yes	—
362	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	C₇×#436	1	2	yes	—
369	C₄	C₄×C₇×SD₁₆	1	2	yes	—
370	C₄	C₂²×C₇×M₁₆	1	1	yes	characteristic
371	C₄	C₂×C₇×#131	1	1	yes	characteristic
372	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
373	C₄	C₂×C₇×#135	1	1	yes	characteristic
374	C₂	—	8	2	no	—
375	C₂	C₇×#1590	1	4	yes	direct product factor
376	C₂	C₂×C₇×#436	1	1	yes	characteristic
377	C₂	C₂×C₄×C₇×SD₁₆	1	1	yes	characteristic
378	C₂	C₂×C₇×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂³×C₇	C₄×D₄
prime radical	C₂²×C₇×D₄	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂×C₄×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#446	C₂	semidirect
4. C₇×#1590	C₂	direct (N × H)
5. C₂×C₇×#334	C₂	semidirect
6. C₂×C₇×Q₈⋊C₈	C₂	semidirect
8. C₂×C₇×C₈²	C₂	semidirect
14. C₇×#446	C₂²	semidirect
30. C₇×#334	C₂²	semidirect
31. C₇×Q₈⋊C₈	C₂²	semidirect
33. C₇×C₈²	C₂²	semidirect
34. C₂×#1590	C₇	direct (N × H)
79. C₂×#446	C₂×C₇	semidirect
82. #1590	C₂×C₇	direct (N × H)
83. C₂×#334	C₂×C₇	semidirect
84. C₂×Q₈⋊C₈	C₂×C₇	semidirect
86. C₂×C₈²	C₂×C₇	semidirect
116. C₂×C₇×C₈	M₁₆	semidirect
117. C₂×C₇×C₈	SD₁₆	semidirect
141. #446	C₂²×C₇	semidirect
157. #334	C₂²×C₇	semidirect
158. Q₈⋊C₈	C₂²×C₇	semidirect
160. C₈²	C₂²×C₇	semidirect
197. C₇×C₈	C₂×M₁₆	semidirect
198. C₇×C₈	C₂×SD₁₆	semidirect
291. C₂×C₈	C₇×M₁₆	semidirect
292. C₂×C₈	C₇×SD₁₆	semidirect
312. C₂×C₇	#1590	direct (N × H)
352. C₈	C₂×C₇×M₁₆	semidirect
353. C₈	C₂×C₇×SD₁₆	semidirect
354. C₇	C₂×#1590	direct (N × H)
375. C₂	C₇×#1590	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×#446	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₇×#436	2
C₇×#1590	2
C₂×C₇×#334	2
C₂×C₇×Q₈⋊C₈	2
C₂×C₇×D₄⋊C₈	2
C₂×C₇×C₈²	2
C₂×#1590	7

Subgroups — C2×C7×#1590 #13195100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#1590 #13195100