Subgroups — C₇×#8043 #13185259

Order 1792.

790 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#384	C₂	1	1	yes	maximal, characteristic
4	C₇×#1296	C₂	1	4	yes	maximal, complemented
5	C₂²×C₇×M₁₆	—	2	1	no	—
6	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
7	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
8	C₂²×C₇×C₄⋊C₄	C₄	1	2	yes	—
9	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
10	C₇×#431	—	2	2	no	—
11	C₇×#431	C₄	1	4	yes	complemented
12	C₇×#423	—	2	2	no	—
13	C₇×#423	C₄	1	4	yes	complemented
14	C₂×C₇×C₄⋊C₈	—	2	1	no	—
15	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₇×C₂²⋊C₈	—	2	1	no	—
18	C₂×C₄×C₇×C₈	—	2	1	no	—
19	C₇×#384	—	2	1	no	—
20	C₇×#384	—	2	1	no	—
21	C₇×#384	C₄	1	2	yes	—
22	C₇×#384	C₂²	1	2	yes	—
23	#8043	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂³×C₄×C₇	—	2	2	no	—
25	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
28	C₂×C₇×M₁₆	—	2	4	no	—
29	C₂×C₇×M₁₆	—	4	2	no	—
30	C₂×C₇×M₁₆	—	4	2	no	—
31	C₂²×C₇×C₈	—	2	2	no	—
32	C₂²×C₇×C₈	—	2	2	no	—
33	C₂×C₇×C₄⋊C₄	—	2	2	no	—
34	C₂×C₇×C₄⋊C₄	—	2	2	no	—
35	C₂×C₇×C₄⋊C₄	—	2	2	no	—
36	C₂×C₇×C₄⋊C₄	—	2	2	no	—
37	C₂×C₇×C₄⋊C₄	—	2	2	no	—
38	C₂×C₇×C₄⋊C₄	—	4	4	no	—
39	C₂×C₇×C₄⋊C₄	—	4	2	no	—
40	C₂×C₇×C₄⋊C₄	—	4	2	no	—
41	C₂×C₇×C₄⋊C₄	—	4	4	no	—
42	C₂×C₇×C₄⋊C₄	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₇	D₄	1	2	yes	—
49	C₂×C₄²×C₇	Q₈	1	2	yes	—
50	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
51	C₇×C₄⋊C₈	—	2	4	no	—
52	C₇×C₄⋊C₈	—	2	2	no	—
53	C₇×C₄⋊C₈	—	2	2	no	—
54	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
55	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
56	C₇×C₂²⋊C₈	—	2	4	no	—
57	C₄×C₇×C₈	—	2	4	no	—
58	C₂×#431	C₂×C₇	1	1	yes	characteristic
59	C₂×#423	C₂×C₇	1	1	yes	characteristic
60	C₂×#384	C₂×C₇	1	1	yes	characteristic
61	#1296	C₂×C₇	1	4	yes	complemented
62	C₂⁴×C₇	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₇	—	2	2	no	—
64	C₂²×C₄×C₇	—	2	2	no	—
65	C₂²×C₄×C₇	—	2	2	no	—
66	C₂²×C₄×C₇	—	2	2	no	—
67	C₂²×C₄×C₇	—	2	4	no	—
68	C₂²×C₄×C₇	—	4	4	no	—
69	C₂²×C₄×C₇	—	4	4	no	—
70	C₂²×C₄×C₇	—	4	4	no	—
71	C₂²×C₄×C₇	C₄²	1	2	yes	—
72	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
77	C₂²×C₄×C₇	C₄⋊C₄	1	2	yes	—
78	C₂²×C₄×C₇	C₄⋊C₄	1	2	yes	—
79	C₂²×C₄×C₇	C₄⋊C₄	1	2	yes	—
80	C₂²×C₄×C₇	D₈	1	2	yes	—
81	C₂²×C₄×C₇	SD₁₆	1	2	yes	—
82	C₂²×C₄×C₇	SD₁₆	1	2	yes	—
83	C₂²×C₄×C₇	Q₁₆	1	2	yes	—
84	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
87	C₇×M₁₆	—	4	8	no	—
88	C₂×C₇×C₈	—	2	4	no	—
89	C₂×C₇×C₈	—	2	4	no	—
90	C₂×C₇×C₈	—	4	2	no	—
91	C₂×C₇×C₈	—	4	2	no	—
92	C₂×C₇×C₈	—	4	2	no	—
93	C₂×C₇×C₈	—	4	2	no	—
94	C₇×C₄⋊C₄	—	4	4	no	—
95	C₇×C₄⋊C₄	—	4	4	no	—
96	C₇×C₄⋊C₄	—	4	4	no	—
97	C₇×C₄⋊C₄	—	4	4	no	—
98	C₇×C₄⋊C₄	—	4	2	no	—
99	C₇×C₄⋊C₄	—	4	2	no	—
100	C₇×C₄⋊C₄	—	4	4	no	—
101	C₄²×C₇	C₄²	1	2	yes	—
102	C₄²×C₇	C₂²⋊C₄	1	2	yes	—
103	C₄²×C₇	C₂²⋊C₄	1	2	yes	—
104	C₄²×C₇	C₄⋊C₄	1	2	yes	—
105	C₄²×C₇	C₄⋊C₄	1	2	yes	—
106	C₄²×C₇	C₄⋊C₄	1	2	yes	—
107	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
111	C₂²×M₁₆	—	2	1	no	—
112	C₂²×C₄⋊C₄	—	2	1	no	—
113	C₂²×C₄⋊C₄	—	2	1	no	—
114	C₂²×C₄⋊C₄	C₄×C₇	1	2	yes	—
115	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
116	#431	—	2	2	no	—
117	#431	C₄×C₇	1	4	yes	complemented
118	#423	—	2	2	no	—
119	#423	C₄×C₇	1	4	yes	complemented
120	C₂×C₄⋊C₈	—	2	1	no	—
121	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
122	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
123	C₂×C₂²⋊C₈	—	2	1	no	—
124	C₂×C₄×C₈	—	2	1	no	—
125	#384	—	2	1	no	—
126	#384	—	2	1	no	—
127	#384	C₄×C₇	1	2	yes	—
128	#384	C₂²×C₇	1	2	yes	—
129	C₂³×C₇	—	2	1	no	—
130	C₂³×C₇	—	2	1	no	—
131	C₂³×C₇	—	2	1	no	—
132	C₂³×C₇	—	2	1	no	—
133	C₂³×C₇	#95	1	2	yes	—
134	C₂³×C₇	#102	1	2	yes	—
135	C₂³×C₇	#103	1	2	yes	—
136	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₇	—	2	1	no	—
138	C₂×C₄×C₇	—	2	1	no	—
139	C₂×C₄×C₇	—	2	1	no	—
140	C₂×C₄×C₇	—	2	1	no	—
141	C₂×C₄×C₇	—	2	4	no	—
142	C₂×C₄×C₇	—	2	4	no	—
143	C₂×C₄×C₇	—	2	4	no	—
144	C₂×C₄×C₇	—	2	4	no	—
145	C₂×C₄×C₇	—	4	4	no	—
146	C₂×C₄×C₇	—	4	4	no	—
147	C₂×C₄×C₇	—	4	4	no	—
148	C₂×C₄×C₇	—	8	8	no	—
149	C₂×C₄×C₇	#95	1	2	yes	—
150	C₂×C₄×C₇	#95	1	2	yes	—
151	C₂×C₄×C₇	#95	1	2	yes	—
152	C₂×C₄×C₇	#100	1	2	yes	—
153	C₂×C₄×C₇	#101	1	2	yes	—
154	C₂×C₄×C₇	#102	1	2	yes	—
155	C₂×C₄×C₇	#102	1	4	yes	—
156	C₂×C₄×C₇	#103	1	2	yes	—
157	C₂×C₄×C₇	#103	1	4	yes	—
158	C₂×C₄×C₇	#106	1	4	yes	—
159	C₂×C₄×C₇	#107	1	4	yes	—
160	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₇	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₇	C₂×SD₁₆	1	1	yes	characteristic
168	C₂×C₄×C₇	C₂×SD₁₆	1	1	yes	characteristic
169	C₂×C₄×C₇	C₂×Q₁₆	1	1	yes	characteristic
170	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₇	#137	1	2	yes	—
172	C₇×C₈	—	4	4	no	—
173	C₇×C₈	—	4	4	no	—
174	C₂³×C₄	—	2	2	no	—
175	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
176	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
177	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
178	C₂×M₁₆	—	2	4	no	—
179	C₂×M₁₆	—	4	2	no	—
180	C₂×M₁₆	—	4	2	no	—
181	C₂²×C₈	—	2	2	no	—
182	C₂²×C₈	—	2	2	no	—
183	C₂×C₄⋊C₄	—	2	2	no	—
184	C₂×C₄⋊C₄	—	2	2	no	—
185	C₂×C₄⋊C₄	—	2	2	no	—
186	C₂×C₄⋊C₄	—	2	2	no	—
187	C₂×C₄⋊C₄	—	2	2	no	—
188	C₂×C₄⋊C₄	—	4	4	no	—
189	C₂×C₄⋊C₄	—	4	2	no	—
190	C₂×C₄⋊C₄	—	4	2	no	—
191	C₂×C₄⋊C₄	—	4	4	no	—
192	C₂×C₄⋊C₄	C₂×C₄×C₇	1	4	yes	—
193	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
194	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
195	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
196	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
197	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
198	C₂×C₄²	C₇×D₄	1	2	yes	—
199	C₂×C₄²	C₇×Q₈	1	2	yes	—
200	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
201	C₄⋊C₈	—	2	4	no	—
202	C₄⋊C₈	—	2	2	no	—
203	C₄⋊C₈	—	2	2	no	—
204	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
205	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
206	C₂²⋊C₈	—	2	4	no	—
207	C₄×C₈	—	2	4	no	—
208	C₂²×C₇	—	2	2	no	—
209	C₂²×C₇	—	2	2	no	—
210	C₂²×C₇	—	2	2	no	—
211	C₂²×C₇	—	2	2	no	—
212	C₂²×C₇	—	2	2	no	—
213	C₂²×C₇	—	2	2	no	—
214	C₂²×C₇	#340	1	4	yes	—
215	C₂²×C₇	C₂×#95	1	1	yes	characteristic
216	C₂²×C₇	C₂×#100	1	1	yes	characteristic
217	C₂²×C₇	C₂×#101	1	1	yes	characteristic
218	C₂²×C₇	C₂×#102	1	1	yes	characteristic
219	C₂²×C₇	C₂×#103	1	1	yes	characteristic
220	C₂²×C₇	#418	1	1	yes	characteristic
221	C₂²×C₇	#419	1	1	yes	characteristic
222	C₄×C₇	—	2	2	no	—
223	C₄×C₇	—	2	1	no	—
224	C₄×C₇	—	2	1	no	—
225	C₄×C₇	—	8	4	no	—
226	C₄×C₇	#340	1	4	yes	—
227	C₄×C₇	#343	1	4	yes	—
228	C₄×C₇	C₂×#102	1	1	yes	characteristic
229	C₄×C₇	C₂×#103	1	1	yes	characteristic
230	C₄×C₇	#417	1	2	yes	—
231	C₄×C₇	C₂×#106	1	1	yes	characteristic
232	C₄×C₇	C₂×#107	1	1	yes	characteristic
233	C₄×C₇	#428	1	2	yes	—
234	C₂⁴	C₇×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	4	4	no	—
241	C₂²×C₄	—	4	4	no	—
242	C₂²×C₄	—	4	4	no	—
243	C₂²×C₄	C₄²×C₇	1	2	yes	—
244	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₄	C₇×C₂²⋊C₄	1	2	yes	—
246	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₄	C₇×C₂²⋊C₄	1	2	yes	—
249	C₂²×C₄	C₇×C₄⋊C₄	1	2	yes	—
250	C₂²×C₄	C₇×C₄⋊C₄	1	2	yes	—
251	C₂²×C₄	C₇×C₄⋊C₄	1	2	yes	—
252	C₂²×C₄	C₇×D₈	1	2	yes	—
253	C₂²×C₄	C₇×SD₁₆	1	2	yes	—
254	C₂²×C₄	C₇×SD₁₆	1	2	yes	—
255	C₂²×C₄	C₇×Q₁₆	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
259	M₁₆	—	4	8	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	4	2	no	—
263	C₂×C₈	—	4	2	no	—
264	C₂×C₈	—	4	2	no	—
265	C₂×C₈	—	4	2	no	—
266	C₄⋊C₄	—	4	4	no	—
267	C₄⋊C₄	—	4	4	no	—
268	C₄⋊C₄	—	4	4	no	—
269	C₄⋊C₄	—	4	4	no	—
270	C₄⋊C₄	—	4	2	no	—
271	C₄⋊C₄	—	4	2	no	—
272	C₄⋊C₄	—	4	4	no	—
273	C₄²	C₄²×C₇	1	2	yes	—
274	C₄²	C₇×C₂²⋊C₄	1	2	yes	—
275	C₄²	C₇×C₂²⋊C₄	1	2	yes	—
276	C₄²	C₇×C₄⋊C₄	1	2	yes	—
277	C₄²	C₇×C₄⋊C₄	1	2	yes	—
278	C₄²	C₇×C₄⋊C₄	1	2	yes	—
279	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
280	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
281	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
282	C₄²	C₂×C₇×Q₈	1	1	yes	characteristic
283	C₂×C₇	—	2	4	no	—
284	C₂×C₇	#1545	1	1	yes	characteristic
285	C₂×C₇	#1546	1	1	yes	characteristic
286	C₂×C₇	#1548	1	1	yes	characteristic
287	C₂×C₇	#1549	1	1	yes	characteristic
288	C₂×C₇	C₂×#340	1	1	yes	characteristic
289	C₂×C₇	#1736	1	1	yes	characteristic
290	C₂×C₇	C₂×#343	1	1	yes	characteristic
291	C₂³	—	2	1	no	—
292	C₂³	—	2	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	C₇×#95	1	2	yes	—
296	C₂³	C₇×#102	1	2	yes	—
297	C₂³	C₇×#103	1	2	yes	—
298	C₂³	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	8	8	no	—
311	C₂×C₄	C₇×#95	1	2	yes	—
312	C₂×C₄	C₇×#95	1	2	yes	—
313	C₂×C₄	C₇×#95	1	2	yes	—
314	C₂×C₄	C₇×#100	1	2	yes	—
315	C₂×C₄	C₇×#101	1	2	yes	—
316	C₂×C₄	C₇×#102	1	2	yes	—
317	C₂×C₄	C₇×#102	1	4	yes	—
318	C₂×C₄	C₇×#103	1	2	yes	—
319	C₂×C₄	C₇×#103	1	4	yes	—
320	C₂×C₄	C₇×#106	1	4	yes	—
321	C₂×C₄	C₇×#107	1	4	yes	—
322	C₂×C₄	C₂×C₄²×C₇	1	1	yes	characteristic
323	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
324	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
326	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
327	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
328	C₂×C₄	C₂×C₇×D₈	1	1	yes	characteristic
329	C₂×C₄	C₂×C₇×SD₁₆	1	1	yes	characteristic
330	C₂×C₄	C₂×C₇×SD₁₆	1	1	yes	characteristic
331	C₂×C₄	C₂×C₇×Q₁₆	1	1	yes	characteristic
332	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
333	C₂×C₄	C₇×#137	1	2	yes	—
334	C₈	—	4	4	no	—
335	C₈	—	4	4	no	—
336	C₇	#8043	1	1	yes	characteristic, direct product factor, Sylow
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	C₇×#340	1	4	yes	—
344	C₂²	C₂×C₇×#95	1	1	yes	characteristic
345	C₂²	C₂×C₇×#100	1	1	yes	characteristic
346	C₂²	C₂×C₇×#101	1	1	yes	characteristic
347	C₂²	C₂×C₇×#102	1	1	yes	characteristic
348	C₂²	C₂×C₇×#103	1	1	yes	characteristic
349	C₂²	C₇×#418	1	1	yes	characteristic
350	C₂²	C₇×#419	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	8	4	no	—
355	C₄	C₇×#340	1	4	yes	—
356	C₄	C₇×#343	1	4	yes	—
357	C₄	C₂×C₇×#102	1	1	yes	characteristic
358	C₄	C₂×C₇×#103	1	1	yes	characteristic
359	C₄	C₇×#417	1	2	yes	—
360	C₄	C₂×C₇×#106	1	1	yes	characteristic
361	C₄	C₂×C₇×#107	1	1	yes	characteristic
362	C₄	C₇×#428	1	2	yes	—
363	C₂	—	2	4	no	—
364	C₂	C₇×#1545	1	1	yes	characteristic
365	C₂	C₇×#1546	1	1	yes	characteristic
366	C₂	C₇×#1548	1	1	yes	characteristic
367	C₂	C₇×#1549	1	1	yes	characteristic
368	C₂	C₂×C₇×#340	1	1	yes	characteristic
369	C₂	C₇×#1736	1	1	yes	characteristic
370	C₂	C₂×C₇×#343	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₇×#1296	C₂	semidirect
11. C₇×#431	C₄	semidirect
13. C₇×#423	C₄	semidirect
23. #8043	C₇	direct (N × H)
54. C₇×C₄⋊C₈	C₂×C₄	semidirect
55. C₇×C₄⋊C₈	C₂×C₄	semidirect
61. #1296	C₂×C₇	semidirect
117. #431	C₄×C₇	semidirect
119. #423	C₄×C₇	semidirect
204. C₄⋊C₈	C₂×C₄×C₇	semidirect
205. C₄⋊C₈	C₂×C₄×C₇	semidirect
336. C₇	#8043	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×#431	2
C₂×C₇×#423	2
C₂×C₇×#384	2
C₇×#1296	2
#8043	7

Subgroups — C7×#8043 #13185259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#8043 #13185259