Subgroups — C₇×#60167 #13237383

Order 1792.

2706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#135	C₂	1	1	yes	maximal, characteristic
2	C₇×#3428	C₂	1	2	yes	maximal, complemented
3	C₇×#2952	C₂	1	4	yes	maximal, complemented
4	C₇×#2951	C₂	1	4	yes	maximal, complemented
5	C₇×#2950	C₂	1	2	yes	maximal, complemented
6	C₇×#2949	C₂	1	4	yes	maximal, complemented
7	C₇×#2948	C₂	1	2	yes	maximal, complemented
8	C₇×#2943	C₂	1	4	yes	maximal, complemented
9	C₄×C₇×#135	C₂	1	4	yes	maximal, complemented
10	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2896	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	2	yes	—
14	C₂×C₇×#135	C₄	1	16	yes	complemented
15	C₂×C₇×#135	C₂²	1	2	yes	—
16	C₂×C₇×#135	C₂²	1	2	yes	—
17	C₂×C₇×#135	C₂²	1	2	yes	—
18	C₂×C₇×#135	C₂²	1	2	yes	—
19	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
21	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₇×#520	—	2	4	no	—
25	C₇×#520	C₂²	1	8	yes	complemented
26	C₇×#519	C₂²	1	4	yes	—
27	C₇×#518	—	2	4	no	—
28	C₇×#518	C₂²	1	4	yes	—
29	C₄×C₇×#41	—	2	4	no	—
30	C₄×C₇×#41	C₂²	1	8	yes	complemented
31	C₂×C₇×#117	—	2	4	no	—
32	C₂×C₇×#117	C₂²	1	2	yes	—
33	C₂×C₇×#117	C₂²	1	1	yes	characteristic
34	C₇×#442	C₂²	1	8	yes	complemented
35	C₇×#441	C₂²	1	8	yes	complemented
36	C₇×#440	C₂²	1	16	yes	complemented
37	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
38	C₄×C₇×SD₁₆	C₂²	1	16	yes	complemented
39	C₄×C₇×D₈	C₂²	1	8	yes	complemented
40	C₇×#427	C₂²	1	2	yes	—
41	C₇×#427	C₂²	1	2	yes	—
42	C₇×#427	C₂²	1	2	yes	complemented
43	C₇×#427	C₂²	1	2	yes	complemented
44	C₂×C₇×#107	C₂²	1	2	yes	complemented
45	C₂×C₇×#106	C₂²	1	2	yes	complemented
46	C₇×#419	C₂²	1	4	yes	—
47	C₇×#418	C₂²	1	4	yes	—
48	C₇×#417	C₂²	1	8	yes	complemented
49	C₇×#416	C₂²	1	8	yes	complemented
50	C₇×#405	C₂²	1	2	yes	—
51	C₇×#405	C₂²	1	2	yes	—
52	C₇×#405	C₂²	1	2	yes	complemented
53	C₇×#405	C₂²	1	2	yes	complemented
54	C₂×C₇×#97	C₂²	1	2	yes	complemented
55	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
56	#60167	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂×C₇×#41	—	2	2	no	—
58	C₂×C₇×#41	—	2	2	no	—
59	C₂×C₇×#41	—	2	8	no	—
60	C₂×C₇×#41	C₂×C₄	1	16	yes	complemented
61	C₂×C₇×#41	C₂³	1	4	yes	—
62	C₂×C₇×#41	C₂³	1	4	yes	—
63	C₂²×C₇×Q₈	C₂³	1	2	yes	—
64	C₂²×C₇×D₄	—	2	2	no	—
65	C₂²×C₇×D₄	C₂³	1	2	yes	—
66	C₂³×C₄×C₇	—	2	2	no	—
67	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₇×#135	C₂×C₄	1	16	yes	complemented
69	C₇×#135	C₂×C₄	1	16	yes	complemented
70	C₇×#135	C₂×C₄	1	16	yes	complemented
71	C₇×#135	C₂×C₄	1	16	yes	complemented
72	C₂×C₇×Q₁₆	C₂×C₄	1	8	yes	complemented
73	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
74	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
75	C₂×C₇×SD₁₆	C₂×C₄	1	16	yes	complemented
76	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
77	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
78	C₂×C₇×D₈	C₂×C₄	1	8	yes	complemented
79	C₂×C₇×D₈	C₂³	1	2	yes	—
80	C₂×C₇×D₈	C₂³	1	2	yes	—
81	C₂×C₇×M₁₆	—	2	4	no	—
82	C₂×C₇×M₁₆	C₂³	1	2	yes	—
83	C₂×C₇×M₁₆	C₂³	1	2	yes	—
84	C₂²×C₇×C₈	C₂×C₄	1	8	yes	complemented
85	C₂²×C₇×C₈	C₂³	1	2	yes	—
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
91	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₇×Q₈	—	2	8	no	—
93	C₄×C₇×Q₈	C₂³	1	16	yes	—
94	C₄×C₇×D₄	—	2	16	no	—
95	C₄×C₇×D₄	—	2	8	no	—
96	C₄×C₇×D₄	—	2	16	no	—
97	C₄×C₇×D₄	C₂³	1	16	yes	—
98	C₇×#117	—	2	2	no	—
99	C₇×#117	—	2	2	no	—
100	C₇×#117	—	2	8	no	—
101	C₇×#117	—	2	8	no	—
102	C₇×#117	—	2	8	no	—
103	C₇×#117	D₄	1	2	yes	—
104	C₇×#117	D₄	1	2	yes	—
105	C₇×#117	C₂³	1	4	yes	—
106	C₇×#117	C₂³	1	4	yes	—
107	C₇×#117	C₂³	1	2	yes	—
108	C₇×#117	C₂³	1	2	yes	—
109	C₂×C₇×C₄⋊C₄	—	2	8	no	—
110	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
111	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
114	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
115	C₂×C₄²×C₇	—	2	2	no	—
116	C₂×C₄²×C₇	—	2	8	no	—
117	C₂×C₄²×C₇	C₂³	1	2	yes	—
118	C₇×#107	C₂³	1	4	yes	—
119	C₇×#107	C₂³	1	4	yes	—
120	C₇×#106	C₂³	1	4	yes	—
121	C₇×#106	C₂³	1	4	yes	—
122	C₇×#103	C₂³	1	16	yes	—
123	C₇×#102	C₂³	1	16	yes	—
124	C₇×#97	C₂³	1	4	yes	—
125	C₇×#97	C₂³	1	4	yes	—
126	C₄×C₇×C₈	C₂³	1	4	yes	—
127	C₄×C₇×C₈	C₂³	1	4	yes	—
128	C₂²×#135	C₂×C₇	1	1	yes	characteristic
129	#3428	C₂×C₇	1	2	yes	complemented
130	#2952	C₂×C₇	1	4	yes	complemented
131	#2951	C₂×C₇	1	4	yes	complemented
132	#2950	C₂×C₇	1	2	yes	complemented
133	#2949	C₂×C₇	1	4	yes	complemented
134	#2948	C₂×C₇	1	2	yes	complemented
135	#2943	C₂×C₇	1	4	yes	complemented
136	C₄×#135	C₂×C₇	1	4	yes	complemented
137	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
138	#2896	C₂×C₇	1	2	yes	complemented
139	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂⁴×C₇	—	2	2	no	—
141	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
142	C₇×#41	—	2	16	no	—
143	C₇×#41	—	2	16	no	—
144	C₇×#41	—	2	8	no	—
145	C₇×#41	—	2	8	no	—
146	C₇×#41	C₂²×C₄	1	16	yes	—
147	C₇×#41	C₂²×C₄	1	16	yes	—
148	C₂×C₇×Q₈	—	2	2	no	—
149	C₂×C₇×Q₈	—	2	4	no	—
150	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
151	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
152	C₂×C₇×D₄	—	2	16	no	—
153	C₂×C₇×D₄	—	2	4	no	—
154	C₂×C₇×D₄	—	2	4	no	—
155	C₂×C₇×D₄	—	2	2	no	—
156	C₂×C₇×D₄	—	2	4	no	—
157	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
158	C₂×C₇×D₄	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₇	—	2	2	no	—
160	C₂²×C₄×C₇	—	2	16	no	—
161	C₂²×C₄×C₇	—	2	4	no	—
162	C₂²×C₄×C₇	—	2	4	no	—
163	C₂²×C₄×C₇	—	2	4	no	—
164	C₂²×C₄×C₇	—	2	16	no	—
165	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
166	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	#41	1	4	yes	—
171	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
174	C₇×Q₁₆	C₂²×C₄	1	8	yes	—
175	C₇×Q₁₆	C₂²×C₄	1	8	yes	—
176	C₇×SD₁₆	C₂²×C₄	1	16	yes	—
177	C₇×SD₁₆	C₂²×C₄	1	16	yes	—
178	C₇×D₈	C₂²×C₄	1	8	yes	—
179	C₇×D₈	C₂²×C₄	1	8	yes	—
180	C₇×M₁₆	—	2	4	no	—
181	C₇×M₁₆	—	2	4	no	—
182	C₂×C₇×C₈	—	2	4	no	—
183	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
184	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
185	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
186	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
187	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
188	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
189	C₂×C₇×C₈	C₂⁴	1	4	yes	—
190	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
191	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
192	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
193	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
194	C₇×C₄⋊C₄	—	2	4	no	—
195	C₇×C₄⋊C₄	—	2	16	no	—
196	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
197	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
198	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
199	C₇×C₂²⋊C₄	—	2	4	no	—
200	C₇×C₂²⋊C₄	—	2	4	no	—
201	C₇×C₂²⋊C₄	—	2	16	no	—
202	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
203	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
204	C₄²×C₇	—	2	16	no	—
205	C₄²×C₇	—	2	4	no	—
206	C₄²×C₇	—	2	4	no	—
207	C₄²×C₇	C₂×D₄	1	4	yes	—
208	C₄²×C₇	C₂⁴	1	4	yes	—
209	C₂²×#41	C₂²×C₇	1	2	yes	—
210	C₂×#135	C₄×C₇	1	16	yes	complemented
211	C₂×#135	C₂²×C₇	1	2	yes	—
212	C₂×#135	C₂²×C₇	1	2	yes	—
213	C₂×#135	C₂²×C₇	1	2	yes	—
214	C₂×#135	C₂²×C₇	1	2	yes	—
215	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
216	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
217	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
218	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
219	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
220	#520	—	2	4	no	—
221	#520	C₂²×C₇	1	8	yes	complemented
222	#519	C₂²×C₇	1	4	yes	—
223	#518	—	2	4	no	—
224	#518	C₂²×C₇	1	4	yes	—
225	C₄×#41	—	2	4	no	—
226	C₄×#41	C₂²×C₇	1	8	yes	complemented
227	C₂×#117	—	2	4	no	—
228	C₂×#117	C₂²×C₇	1	2	yes	—
229	C₂×#117	C₂²×C₇	1	1	yes	characteristic
230	#442	C₂²×C₇	1	8	yes	complemented
231	#441	C₂²×C₇	1	8	yes	complemented
232	#440	C₂²×C₇	1	16	yes	complemented
233	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
234	C₄×SD₁₆	C₂²×C₇	1	16	yes	complemented
235	C₄×D₈	C₂²×C₇	1	8	yes	complemented
236	#427	C₂²×C₇	1	2	yes	—
237	#427	C₂²×C₇	1	2	yes	—
238	#427	C₂²×C₇	1	2	yes	complemented
239	#427	C₂²×C₇	1	2	yes	complemented
240	C₂×#107	C₂²×C₇	1	2	yes	complemented
241	C₂×#106	C₂²×C₇	1	2	yes	complemented
242	#419	C₂²×C₇	1	4	yes	—
243	#418	C₂²×C₇	1	4	yes	—
244	#417	C₂²×C₇	1	8	yes	complemented
245	#416	C₂²×C₇	1	8	yes	complemented
246	#405	C₂²×C₇	1	2	yes	—
247	#405	C₂²×C₇	1	2	yes	—
248	#405	C₂²×C₇	1	2	yes	complemented
249	#405	C₂²×C₇	1	2	yes	complemented
250	C₂×#97	C₂²×C₇	1	2	yes	complemented
251	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
252	C₂³×C₇	—	2	4	no	—
253	C₂³×C₇	—	2	8	no	—
254	C₂³×C₇	—	4	2	no	—
255	C₂³×C₇	—	8	4	no	—
256	C₂³×C₇	C₄×D₄	1	4	yes	—
257	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
258	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
259	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
260	C₇×Q₈	—	2	8	no	—
261	C₇×Q₈	—	2	4	no	—
262	C₇×Q₈	C₂³×C₄	1	8	yes	—
263	C₇×D₄	—	2	16	no	—
264	C₇×D₄	—	2	16	no	—
265	C₇×D₄	—	2	8	no	—
266	C₇×D₄	—	2	4	no	—
267	C₇×D₄	C₂³×C₄	1	8	yes	—
268	C₂×C₄×C₇	—	2	8	no	—
269	C₂×C₄×C₇	—	2	4	no	—
270	C₂×C₄×C₇	—	2	16	no	—
271	C₂×C₄×C₇	—	2	16	no	—
272	C₂×C₄×C₇	—	2	8	no	—
273	C₂×C₄×C₇	—	4	4	no	—
274	C₂×C₄×C₇	—	8	16	no	—
275	C₂×C₄×C₇	—	8	4	no	—
276	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
277	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
278	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
279	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
280	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
281	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
282	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
283	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₇	C₂×#41	1	2	yes	—
287	C₂×C₄×C₇	C₂×#41	1	2	yes	—
288	C₂×C₄×C₇	C₂×#41	1	2	yes	—
289	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
290	C₇×C₈	—	2	4	no	—
291	C₇×C₈	C₂³×C₄	1	2	yes	—
292	C₇×C₈	C₂³×C₄	1	2	yes	—
293	C₇×C₈	C₂³×C₄	1	2	yes	—
294	C₇×C₈	C₂³×C₄	1	2	yes	—
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	2	no	—
297	C₂×#41	—	2	8	no	—
298	C₂×#41	C₂×C₄×C₇	1	16	yes	complemented
299	C₂×#41	C₂³×C₇	1	4	yes	—
300	C₂×#41	C₂³×C₇	1	4	yes	—
301	C₂²×Q₈	C₂³×C₇	1	2	yes	—
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	C₂³×C₇	1	2	yes	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
306	#135	C₂×C₄×C₇	1	16	yes	complemented
307	#135	C₂×C₄×C₇	1	16	yes	complemented
308	#135	C₂×C₄×C₇	1	16	yes	complemented
309	#135	C₂×C₄×C₇	1	16	yes	complemented
310	C₂×Q₁₆	C₂×C₄×C₇	1	8	yes	complemented
311	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
312	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
313	C₂×SD₁₆	C₂×C₄×C₇	1	16	yes	complemented
314	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
315	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
316	C₂×D₈	C₂×C₄×C₇	1	8	yes	complemented
317	C₂×D₈	C₂³×C₇	1	2	yes	—
318	C₂×D₈	C₂³×C₇	1	2	yes	—
319	C₂×M₁₆	—	2	4	no	—
320	C₂×M₁₆	C₂³×C₇	1	2	yes	—
321	C₂×M₁₆	C₂³×C₇	1	2	yes	—
322	C₂²×C₈	C₂×C₄×C₇	1	8	yes	complemented
323	C₂²×C₈	C₂³×C₇	1	2	yes	—
324	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
330	C₄×Q₈	—	2	8	no	—
331	C₄×Q₈	C₂³×C₇	1	16	yes	—
332	C₄×D₄	—	2	16	no	—
333	C₄×D₄	—	2	8	no	—
334	C₄×D₄	—	2	16	no	—
335	C₄×D₄	C₂³×C₇	1	16	yes	—
336	#117	—	2	2	no	—
337	#117	—	2	2	no	—
338	#117	—	2	8	no	—
339	#117	—	2	8	no	—
340	#117	—	2	8	no	—
341	#117	C₇×D₄	1	2	yes	—
342	#117	C₇×D₄	1	2	yes	—
343	#117	C₂³×C₇	1	4	yes	—
344	#117	C₂³×C₇	1	4	yes	—
345	#117	C₂³×C₇	1	2	yes	—
346	#117	C₂³×C₇	1	2	yes	—
347	C₂×C₄⋊C₄	—	2	8	no	—
348	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	8	no	—
352	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	—	2	8	no	—
355	C₂×C₄²	C₂³×C₇	1	2	yes	—
356	#107	C₂³×C₇	1	4	yes	—
357	#107	C₂³×C₇	1	4	yes	—
358	#106	C₂³×C₇	1	4	yes	—
359	#106	C₂³×C₇	1	4	yes	—
360	#103	C₂³×C₇	1	16	yes	—
361	#102	C₂³×C₇	1	16	yes	—
362	#97	C₂³×C₇	1	4	yes	—
363	#97	C₂³×C₇	1	4	yes	—
364	C₄×C₈	C₂³×C₇	1	4	yes	—
365	C₄×C₈	C₂³×C₇	1	4	yes	—
366	C₂²×C₇	—	2	2	no	—
367	C₂²×C₇	—	2	2	no	—
368	C₂²×C₇	—	2	2	no	—
369	C₂²×C₇	—	2	8	no	—
370	C₂²×C₇	—	4	4	no	—
371	C₂²×C₇	—	4	8	no	—
372	C₂²×C₇	—	8	8	no	—
373	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
374	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
375	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
376	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
377	C₄×C₇	—	2	8	no	—
378	C₄×C₇	—	2	8	no	—
379	C₄×C₇	—	4	8	no	—
380	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
381	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
382	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
383	C₄×C₇	C₂⁴×C₄	1	1	yes	characteristic
384	C₄×C₇	C₂²×#41	1	1	yes	characteristic
385	C₂⁴	—	2	2	no	—
386	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
387	#41	—	2	16	no	—
388	#41	—	2	16	no	—
389	#41	—	2	8	no	—
390	#41	—	2	8	no	—
391	#41	C₂²×C₄×C₇	1	16	yes	—
392	#41	C₂²×C₄×C₇	1	16	yes	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	—
396	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
397	C₂×D₄	—	2	16	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
403	C₂×D₄	C₂⁴×C₇	1	4	yes	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	16	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	16	no	—
410	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
411	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
412	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
413	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
414	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
415	C₂²×C₄	C₇×#41	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
419	Q₁₆	C₂²×C₄×C₇	1	8	yes	—
420	Q₁₆	C₂²×C₄×C₇	1	8	yes	—
421	SD₁₆	C₂²×C₄×C₇	1	16	yes	—
422	SD₁₆	C₂²×C₄×C₇	1	16	yes	—
423	D₈	C₂²×C₄×C₇	1	8	yes	—
424	D₈	C₂²×C₄×C₇	1	8	yes	—
425	M₁₆	—	2	4	no	—
426	M₁₆	—	2	4	no	—
427	C₂×C₈	—	2	4	no	—
428	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
429	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
430	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
431	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
432	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
433	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
434	C₂×C₈	C₂⁴×C₇	1	4	yes	—
435	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
436	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
437	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
438	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	16	no	—
441	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
442	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
443	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	16	no	—
447	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
448	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	16	no	—
451	C₄²	—	2	4	no	—
452	C₄²	C₂×C₇×D₄	1	4	yes	—
453	C₄²	C₂⁴×C₇	1	4	yes	—
454	C₂×C₇	—	2	2	no	—
455	C₂×C₇	—	2	2	no	—
456	C₂×C₇	—	2	2	no	—
457	C₂×C₇	—	4	8	no	—
458	C₂×C₇	C₂²×C₄×D₄	1	1	yes	characteristic
459	C₂×C₇	#3584	1	2	yes	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	8	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	8	4	no	—
464	C₂³	C₄×C₇×D₄	1	4	yes	—
465	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
466	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
467	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
468	Q₈	—	2	4	no	—
469	Q₈	—	2	8	no	—
470	Q₈	C₂³×C₄×C₇	1	8	yes	—
471	D₄	—	2	16	no	—
472	D₄	—	2	16	no	—
473	D₄	—	2	4	no	—
474	D₄	—	2	8	no	—
475	D₄	C₂³×C₄×C₇	1	8	yes	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	16	no	—
479	C₂×C₄	—	2	16	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	8	16	no	—
483	C₂×C₄	—	8	4	no	—
484	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
485	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
486	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
487	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
488	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
489	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
490	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
491	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
492	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
493	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
494	C₂×C₄	C₂×C₇×#41	1	2	yes	—
495	C₂×C₄	C₂×C₇×#41	1	2	yes	—
496	C₂×C₄	C₂×C₇×#41	1	2	yes	—
497	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
498	C₈	—	2	4	no	—
499	C₈	C₂³×C₄×C₇	1	2	yes	—
500	C₈	C₂³×C₄×C₇	1	2	yes	—
501	C₈	C₂³×C₄×C₇	1	2	yes	—
502	C₈	C₂³×C₄×C₇	1	2	yes	—
503	C₇	#60167	1	1	yes	characteristic, direct product factor, Sylow
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	8	no	—
510	C₂²	—	8	8	no	—
511	C₂²	C₂×C₄×C₇×D₄	1	2	yes	—
512	C₂²	C₂×C₄×C₇×D₄	1	2	yes	—
513	C₂²	C₂×C₄×C₇×D₄	1	2	yes	—
514	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
515	C₄	—	2	8	no	—
516	C₄	—	2	8	no	—
517	C₄	—	4	8	no	—
518	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
519	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
520	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
521	C₄	C₂⁴×C₄×C₇	1	1	yes	characteristic
522	C₄	C₂²×C₇×#41	1	1	yes	characteristic
523	C₂	—	2	2	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	2	no	—
526	C₂	—	4	8	no	—
527	C₂	C₂²×C₄×C₇×D₄	1	1	yes	characteristic
528	C₂	C₇×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
prime radical	C₂²×C₇×#135	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3428	C₂	semidirect
3. C₇×#2952	C₂	semidirect
4. C₇×#2951	C₂	semidirect
5. C₇×#2950	C₂	semidirect
6. C₇×#2949	C₂	semidirect
7. C₇×#2948	C₂	semidirect
8. C₇×#2943	C₂	semidirect
9. C₄×C₇×#135	C₂	semidirect
10. C₂×C₇×#427	C₂	semidirect
11. C₇×#2896	C₂	semidirect
12. C₂×C₇×#405	C₂	semidirect
14. C₂×C₇×#135	C₄	semidirect
25. C₇×#520	C₂²	semidirect
30. C₄×C₇×#41	C₂²	semidirect
34. C₇×#442	C₂²	semidirect
35. C₇×#441	C₂²	semidirect
36. C₇×#440	C₂²	semidirect
37. C₄×C₇×Q₁₆	C₂²	semidirect
38. C₄×C₇×SD₁₆	C₂²	semidirect
39. C₄×C₇×D₈	C₂²	semidirect
42. C₇×#427	C₂²	semidirect
43. C₇×#427	C₂²	semidirect
44. C₂×C₇×#107	C₂²	semidirect
45. C₂×C₇×#106	C₂²	semidirect
48. C₇×#417	C₂²	semidirect
49. C₇×#416	C₂²	semidirect
52. C₇×#405	C₂²	semidirect
53. C₇×#405	C₂²	semidirect
54. C₂×C₇×#97	C₂²	semidirect
55. C₂×C₄×C₇×C₈	C₂²	semidirect
56. #60167	C₇	direct (N × H)
60. C₂×C₇×#41	C₂×C₄	semidirect
68. C₇×#135	C₂×C₄	semidirect
69. C₇×#135	C₂×C₄	semidirect
70. C₇×#135	C₂×C₄	semidirect
71. C₇×#135	C₂×C₄	semidirect
72. C₂×C₇×Q₁₆	C₂×C₄	semidirect
75. C₂×C₇×SD₁₆	C₂×C₄	semidirect
78. C₂×C₇×D₈	C₂×C₄	semidirect
84. C₂²×C₇×C₈	C₂×C₄	semidirect
129. #3428	C₂×C₇	semidirect
130. #2952	C₂×C₇	semidirect
131. #2951	C₂×C₇	semidirect
132. #2950	C₂×C₇	semidirect
133. #2949	C₂×C₇	semidirect
134. #2948	C₂×C₇	semidirect
135. #2943	C₂×C₇	semidirect
136. C₄×#135	C₂×C₇	semidirect
137. C₂×#427	C₂×C₇	semidirect
138. #2896	C₂×C₇	semidirect
139. C₂×#405	C₂×C₇	semidirect
210. C₂×#135	C₄×C₇	semidirect
221. #520	C₂²×C₇	semidirect
226. C₄×#41	C₂²×C₇	semidirect
230. #442	C₂²×C₇	semidirect
231. #441	C₂²×C₇	semidirect
232. #440	C₂²×C₇	semidirect
233. C₄×Q₁₆	C₂²×C₇	semidirect
234. C₄×SD₁₆	C₂²×C₇	semidirect
235. C₄×D₈	C₂²×C₇	semidirect
238. #427	C₂²×C₇	semidirect
239. #427	C₂²×C₇	semidirect
240. C₂×#107	C₂²×C₇	semidirect
241. C₂×#106	C₂²×C₇	semidirect
244. #417	C₂²×C₇	semidirect
245. #416	C₂²×C₇	semidirect
248. #405	C₂²×C₇	semidirect
249. #405	C₂²×C₇	semidirect
250. C₂×#97	C₂²×C₇	semidirect
251. C₂×C₄×C₈	C₂²×C₇	semidirect
298. C₂×#41	C₂×C₄×C₇	semidirect
306. #135	C₂×C₄×C₇	semidirect
307. #135	C₂×C₄×C₇	semidirect
308. #135	C₂×C₄×C₇	semidirect
309. #135	C₂×C₄×C₇	semidirect
310. C₂×Q₁₆	C₂×C₄×C₇	semidirect
313. C₂×SD₁₆	C₂×C₄×C₇	semidirect
316. C₂×D₈	C₂×C₄×C₇	semidirect
322. C₂²×C₈	C₂×C₄×C₇	semidirect
503. C₇	#60167	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇×#135	2
C₇×#3428	2
C₇×#2952	2
C₇×#2951	2
C₇×#2950	2
C₇×#2949	2
C₇×#2948	2
C₇×#2943	2
C₄×C₇×#135	2
C₂×C₇×#427	2
C₇×#2896	2
C₂×C₇×#405	2
#60167	7

Subgroups — C7×#60167 #13237383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60167 #13237383