Subgroups — C₇×#21290 #13198506

Order 1792.

862 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic
2	C₇×#2319	C₂	1	2	yes	maximal, complemented
3	C₇×#1972	C₂	1	1	yes	maximal, characteristic
4	C₇×#1970	C₂	1	1	yes	maximal, characteristic
5	C₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1936	C₂	1	2	yes	maximal, complemented
8	C₇×#1934	C₂	1	2	yes	maximal, complemented
9	C₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₇×#102	C₂	1	2	yes	maximal, complemented
11	C₇×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
14	C₇×#442	C₄	1	8	yes	complemented
15	C₂×C₇×#107	C₂²	1	1	yes	characteristic
16	C₂×C₇×#106	C₂²	1	1	yes	characteristic
17	C₂×C₇×#106	C₂²	1	1	yes	characteristic
18	C₂×C₇×#102	C₂²	1	2	yes	—
19	C₂×C₇×#102	C₂²	1	2	yes	—
20	C₂×C₇×#102	C₂²	1	2	yes	—
21	C₂×C₇×#97	C₂²	1	1	yes	characteristic
22	C₂×C₇×#97	C₂²	1	1	yes	characteristic
23	C₂×C₇×#97	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₇×#390	C₂²	1	2	yes	—
28	C₇×#390	C₂²	1	2	yes	—
29	C₇×#389	C₂²	1	2	yes	—
30	C₇×#389	C₂²	1	2	yes	—
31	C₇×#388	—	2	2	no	—
32	C₇×#388	—	2	2	no	—
33	C₇×#381	—	2	2	no	—
34	C₇×#380	—	2	2	no	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
36	C₇×#376	C₂²	1	1	yes	characteristic
37	C₇×#340	C₂²	1	2	yes	—
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	#21290	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₇×D₄	C₂³	1	2	yes	—
42	C₂³×C₄×C₇	—	2	2	no	—
43	C₂×C₇×D₈	—	2	2	no	—
44	C₂×C₇×D₈	—	2	2	no	—
45	C₂×C₇×D₈	C₂×C₄	1	4	yes	—
46	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₄×C₇×D₄	—	2	4	no	—
51	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
52	C₂×C₇×C₄⋊C₄	—	2	2	no	—
53	C₂×C₇×C₄⋊C₄	—	2	2	no	—
54	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₄²×C₇	—	2	2	no	—
63	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
66	C₇×#107	—	2	2	no	—
67	C₇×#106	—	2	2	no	—
68	C₇×#106	C₂×C₄	1	4	yes	—
69	C₇×#102	—	2	4	no	—
70	C₇×#102	—	2	4	no	—
71	C₇×#102	C₂×C₄	1	8	yes	—
72	C₇×#97	—	2	2	no	—
73	C₇×#97	—	2	2	no	—
74	C₇×#97	C₂×C₄	1	4	yes	—
75	C₄×C₇×C₈	—	2	2	no	—
76	C₄×C₇×C₈	—	2	2	no	—
77	C₄×C₇×C₈	—	2	2	no	—
78	C₇×#95	—	2	2	no	—
79	C₇×#95	—	2	2	no	—
80	C₇×#95	—	2	2	no	—
81	C₇×#95	D₄	1	2	yes	—
82	C₇×#95	D₄	1	2	yes	—
83	C₂×#442	C₂×C₇	1	1	yes	characteristic
84	#2319	C₂×C₇	1	2	yes	complemented
85	#1972	C₂×C₇	1	1	yes	characteristic
86	#1970	C₂×C₇	1	1	yes	characteristic
87	#1944	C₂×C₇	1	1	yes	characteristic, complemented
88	#1941	C₂×C₇	1	1	yes	characteristic, complemented
89	#1936	C₂×C₇	1	2	yes	complemented
90	#1934	C₂×C₇	1	2	yes	complemented
91	#1776	C₂×C₇	1	1	yes	characteristic, complemented
92	C₄×#102	C₂×C₇	1	2	yes	complemented
93	#1726	C₂×C₇	1	1	yes	characteristic, complemented
94	C₂⁴×C₇	—	2	2	no	—
95	C₂×C₇×D₄	—	2	2	no	—
96	C₂×C₇×D₄	—	2	2	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	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₇	—	2	2	no	—
102	C₂²×C₄×C₇	—	2	8	no	—
103	C₂²×C₄×C₇	—	2	2	no	—
104	C₂²×C₄×C₇	—	2	2	no	—
105	C₂²×C₄×C₇	—	8	2	no	—
106	C₂²×C₄×C₇	—	8	2	no	—
107	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
112	C₇×D₈	—	2	8	no	—
113	C₂×C₇×C₈	—	2	1	no	—
114	C₂×C₇×C₈	—	2	1	no	—
115	C₂×C₇×C₈	—	2	1	no	—
116	C₂×C₇×C₈	—	2	1	no	—
117	C₂×C₇×C₈	—	2	1	no	—
118	C₂×C₇×C₈	—	2	1	no	—
119	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
120	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₇×C₈	#41	1	2	yes	—
122	C₂×C₇×C₈	#41	1	2	yes	—
123	C₂×C₇×C₈	#41	1	2	yes	—
124	C₂×C₇×C₈	#41	1	2	yes	—
125	C₇×C₄⋊C₄	—	2	2	no	—
126	C₇×C₄⋊C₄	—	2	2	no	—
127	C₇×C₄⋊C₄	—	2	2	no	—
128	C₇×C₄⋊C₄	—	2	2	no	—
129	C₇×C₄⋊C₄	—	2	2	no	—
130	C₇×C₄⋊C₄	—	8	2	no	—
131	C₇×C₄⋊C₄	—	8	2	no	—
132	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
133	C₇×C₂²⋊C₄	—	2	8	no	—
134	C₇×C₂²⋊C₄	—	8	2	no	—
135	C₇×C₂²⋊C₄	—	8	2	no	—
136	C₇×C₂²⋊C₄	—	8	2	no	—
137	C₇×C₂²⋊C₄	—	8	2	no	—
138	C₄²×C₇	—	2	1	no	—
139	C₄²×C₇	—	2	1	no	—
140	C₄²×C₇	—	2	1	no	—
141	C₄²×C₇	—	2	1	no	—
142	C₄²×C₇	—	8	2	no	—
143	C₄²×C₇	C₂²×C₄	1	2	yes	—
144	C₄²×C₇	#41	1	2	yes	—
145	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
146	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
147	#442	C₄×C₇	1	8	yes	complemented
148	C₂×#107	C₂²×C₇	1	1	yes	characteristic
149	C₂×#106	C₂²×C₇	1	1	yes	characteristic
150	C₂×#106	C₂²×C₇	1	1	yes	characteristic
151	C₂×#102	C₂²×C₇	1	2	yes	—
152	C₂×#102	C₂²×C₇	1	2	yes	—
153	C₂×#102	C₂²×C₇	1	2	yes	—
154	C₂×#97	C₂²×C₇	1	1	yes	characteristic
155	C₂×#97	C₂²×C₇	1	1	yes	characteristic
156	C₂×#97	C₂²×C₇	1	1	yes	characteristic
157	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
158	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
159	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
160	#390	C₂²×C₇	1	2	yes	—
161	#390	C₂²×C₇	1	2	yes	—
162	#389	C₂²×C₇	1	2	yes	—
163	#389	C₂²×C₇	1	2	yes	—
164	#388	—	2	2	no	—
165	#388	—	2	2	no	—
166	#381	—	2	2	no	—
167	#380	—	2	2	no	—
168	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
169	#376	C₂²×C₇	1	1	yes	characteristic
170	#340	C₂²×C₇	1	2	yes	—
171	#340	C₂²×C₇	1	2	yes	—
172	#340	C₂²×C₇	1	2	yes	—
173	C₂³×C₇	—	2	4	no	—
174	C₂³×C₇	—	4	2	no	—
175	C₂³×C₇	—	4	2	no	—
176	C₂³×C₇	—	4	2	no	—
177	C₂³×C₇	—	4	2	no	—
178	C₂³×C₇	—	4	2	no	—
179	C₂³×C₇	—	4	2	no	—
180	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
181	C₇×D₄	—	2	4	no	—
182	C₇×D₄	—	2	4	no	—
183	C₇×D₄	—	4	2	no	—
184	C₇×D₄	—	4	2	no	—
185	C₂×C₄×C₇	—	2	2	no	—
186	C₂×C₄×C₇	—	2	2	no	—
187	C₂×C₄×C₇	—	2	4	no	—
188	C₂×C₄×C₇	—	2	1	no	—
189	C₂×C₄×C₇	—	2	1	no	—
190	C₂×C₄×C₇	—	2	2	no	—
191	C₂×C₄×C₇	—	2	2	no	—
192	C₂×C₄×C₇	—	2	2	no	—
193	C₂×C₄×C₇	—	2	2	no	—
194	C₂×C₄×C₇	—	2	2	no	—
195	C₂×C₄×C₇	—	4	2	no	—
196	C₂×C₄×C₇	—	4	2	no	—
197	C₂×C₄×C₇	—	4	2	no	—
198	C₂×C₄×C₇	—	4	2	no	—
199	C₂×C₄×C₇	—	4	2	no	—
200	C₂×C₄×C₇	—	4	2	no	—
201	C₂×C₄×C₇	—	4	2	no	—
202	C₂×C₄×C₇	—	4	2	no	—
203	C₂×C₄×C₇	—	8	8	no	—
204	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
205	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
211	C₇×C₈	—	2	2	no	—
212	C₇×C₈	—	2	2	no	—
213	C₇×C₈	—	2	2	no	—
214	C₇×C₈	#117	1	4	yes	—
215	C₂²×D₄	C₂³×C₇	1	2	yes	—
216	C₂³×C₄	—	2	2	no	—
217	C₂×D₈	—	2	2	no	—
218	C₂×D₈	—	2	2	no	—
219	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
220	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
224	C₄×D₄	—	2	4	no	—
225	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
229	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
230	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
231	C₂×C₂²⋊C₄	—	2	2	no	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
240	#107	—	2	2	no	—
241	#106	—	2	2	no	—
242	#106	C₂×C₄×C₇	1	4	yes	—
243	#102	—	2	4	no	—
244	#102	—	2	4	no	—
245	#102	C₂×C₄×C₇	1	8	yes	—
246	#97	—	2	2	no	—
247	#97	—	2	2	no	—
248	#97	C₂×C₄×C₇	1	4	yes	—
249	C₄×C₈	—	2	2	no	—
250	C₄×C₈	—	2	2	no	—
251	C₄×C₈	—	2	2	no	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	#95	—	2	2	no	—
255	#95	C₇×D₄	1	2	yes	—
256	#95	C₇×D₄	1	2	yes	—
257	C₂²×C₇	—	4	4	no	—
258	C₂²×C₇	—	4	4	no	—
259	C₂²×C₇	—	4	4	no	—
260	C₂²×C₇	—	8	2	no	—
261	C₂²×C₇	—	8	2	no	—
262	C₂²×C₇	—	8	2	no	—
263	C₂²×C₇	—	8	2	no	—
264	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
265	C₂²×C₇	#532	1	1	yes	characteristic
266	C₂²×C₇	#532	1	1	yes	characteristic
267	C₂²×C₇	#576	1	2	yes	—
268	C₂²×C₇	#577	1	2	yes	—
269	C₄×C₇	—	2	4	no	—
270	C₄×C₇	—	4	1	no	—
271	C₄×C₇	—	4	1	no	—
272	C₄×C₇	—	4	2	no	—
273	C₄×C₇	—	4	4	no	—
274	C₄×C₇	—	8	2	no	—
275	C₄×C₇	—	8	2	no	—
276	C₄×C₇	C₂×#117	1	1	yes	characteristic
277	C₄×C₇	C₄×#41	1	1	yes	characteristic
278	C₄×C₇	#529	1	1	yes	characteristic
279	C₄×C₇	#529	1	1	yes	characteristic
280	C₂⁴	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	8	2	no	—
292	C₂²×C₄	—	8	2	no	—
293	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
295	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
297	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
298	D₈	—	2	8	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
306	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
307	C₂×C₈	C₇×#41	1	2	yes	—
308	C₂×C₈	C₇×#41	1	2	yes	—
309	C₂×C₈	C₇×#41	1	2	yes	—
310	C₂×C₈	C₇×#41	1	2	yes	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	8	2	no	—
317	C₄⋊C₄	—	8	2	no	—
318	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
319	C₂²⋊C₄	—	2	8	no	—
320	C₂²⋊C₄	—	8	2	no	—
321	C₂²⋊C₄	—	8	2	no	—
322	C₂²⋊C₄	—	8	2	no	—
323	C₂²⋊C₄	—	8	2	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	8	2	no	—
329	C₄²	C₂²×C₄×C₇	1	2	yes	—
330	C₄²	C₇×#41	1	2	yes	—
331	C₂×C₇	—	8	4	no	—
332	C₂×C₇	#2293	1	1	yes	characteristic
333	C₂×C₇	#2946	1	2	yes	—
334	C₂×C₇	#3173	1	1	yes	characteristic
335	C₂×C₇	#3176	1	1	yes	characteristic
336	C₂×C₇	#3179	1	2	yes	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
345	D₄	—	2	4	no	—
346	D₄	—	2	4	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	8	no	—
368	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
369	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
370	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
371	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
372	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
373	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
374	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	C₇×#117	1	4	yes	—
379	C₇	#21290	1	1	yes	characteristic, direct product factor, Sylow
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
388	C₂²	C₇×#532	1	1	yes	characteristic
389	C₂²	C₇×#532	1	1	yes	characteristic
390	C₂²	C₇×#576	1	2	yes	—
391	C₂²	C₇×#577	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	4	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	C₂×C₇×#117	1	1	yes	characteristic
400	C₄	C₄×C₇×#41	1	1	yes	characteristic
401	C₄	C₇×#529	1	1	yes	characteristic
402	C₄	C₇×#529	1	1	yes	characteristic
403	C₂	—	8	4	no	—
404	C₂	C₇×#2293	1	1	yes	characteristic
405	C₂	C₇×#2946	1	2	yes	—
406	C₂	C₇×#3173	1	1	yes	characteristic
407	C₂	C₇×#3176	1	1	yes	characteristic
408	C₂	C₇×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2319	C₂	semidirect
5. C₇×#1944	C₂	semidirect
6. C₇×#1941	C₂	semidirect
7. C₇×#1936	C₂	semidirect
8. C₇×#1934	C₂	semidirect
9. C₇×#1776	C₂	semidirect
10. C₄×C₇×#102	C₂	semidirect
11. C₇×#1726	C₂	semidirect
14. C₇×#442	C₄	semidirect
40. #21290	C₇	direct (N × H)
84. #2319	C₂×C₇	semidirect
87. #1944	C₂×C₇	semidirect
88. #1941	C₂×C₇	semidirect
89. #1936	C₂×C₇	semidirect
90. #1934	C₂×C₇	semidirect
91. #1776	C₂×C₇	semidirect
92. C₄×#102	C₂×C₇	semidirect
93. #1726	C₂×C₇	semidirect
147. #442	C₄×C₇	semidirect
379. C₇	#21290	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×#442	2
C₇×#2319	2
C₇×#1972	2
C₇×#1970	2
C₇×#1944	2
C₇×#1941	2
C₇×#1936	2
C₇×#1934	2
C₇×#1776	2
C₄×C₇×#102	2
C₇×#1726	2
#21290	7

Subgroups — C7×#21290 #13198506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21290 #13198506