Subgroups — C₂×C₇×#2497 #13211985

Order 1792.

2270 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2497	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₇×#400	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×#396	C₂	1	2	yes	maximal
4	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#388	C₂	1	2	yes	maximal
7	C₂×C₇×#387	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#384	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic
10	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
14	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₇	C₂²	1	2	yes	—
29	C₇×#400	C₂²	1	16	yes	complemented
30	C₇×#396	C₂²	1	16	yes	—
31	C₇×#389	C₂²	1	8	yes	complemented
32	C₇×#389	C₂²	1	8	yes	complemented
33	C₇×#388	C₂²	1	16	yes	—
34	C₇×#387	C₂²	1	16	yes	complemented
35	C₇×#384	C₂²	1	8	yes	complemented
36	C₇×#380	C₂²	1	8	yes	—
37	C₇×#380	C₂²	1	8	yes	—
38	C₄×C₇×C₄⋊C₄	C₂²	1	8	yes	complemented
39	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
40	C₂×C₇×#95	C₂²	1	2	yes	—
41	C₂×C₇×#95	C₂²	1	1	yes	characteristic
42	C₂×C₇×#95	C₂²	1	2	yes	—
43	C₂×C₇×#95	C₂²	1	2	yes	—
44	C₂×C₇×#95	C₂²	1	2	yes	—
45	C₂×C₇×#95	C₂²	1	1	yes	characteristic
46	C₂×C₇×#95	C₂²	1	2	yes	—
47	C₂×#2497	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁵×C₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₇	—	2	4	no	—
50	C₂³×C₄×C₇	—	2	4	no	—
51	C₂³×C₄×C₇	—	2	4	no	—
52	C₂³×C₄×C₇	C₂³	1	4	yes	—
53	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₇	C₂³	1	2	yes	—
58	C₂³×C₄×C₇	C₂³	1	2	yes	—
59	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂×C₇×C₄⋊C₄	—	2	8	no	—
64	C₂×C₇×C₄⋊C₄	—	2	4	no	—
65	C₂×C₇×C₄⋊C₄	—	2	4	no	—
66	C₂×C₇×C₄⋊C₄	—	2	4	no	—
67	C₂×C₇×C₄⋊C₄	—	2	4	no	—
68	C₂×C₇×C₄⋊C₄	—	4	4	no	—
69	C₂×C₇×C₄⋊C₄	—	4	4	no	—
70	C₂×C₇×C₄⋊C₄	—	4	4	no	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
76	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
77	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
78	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
80	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
81	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
82	C₂×C₇×C₂²⋊C₄	Q₈	1	8	yes	—
83	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₄²×C₇	—	2	4	no	—
88	C₂×C₄²×C₇	—	2	4	no	—
89	C₂×C₄²×C₇	—	4	4	no	—
90	C₂×C₄²×C₇	C₂³	1	4	yes	—
91	C₂×C₄²×C₇	C₂³	1	4	yes	—
92	C₂×C₄²×C₇	C₂³	1	8	yes	—
93	C₇×#95	C₂³	1	4	yes	—
94	C₇×#95	C₂³	1	4	yes	—
95	C₇×#95	C₂³	1	8	yes	—
96	C₇×#95	C₂³	1	8	yes	—
97	C₇×#95	C₂³	1	8	yes	—
98	C₇×#95	C₂³	1	8	yes	—
99	C₇×#95	C₂³	1	8	yes	—
100	#2497	C₂×C₇	1	16	yes	direct product factor
101	C₂×#400	C₂×C₇	1	2	yes	complemented
102	C₂×#396	C₂×C₇	1	2	yes	—
103	C₂×#389	C₂×C₇	1	1	yes	characteristic, complemented
104	C₂×#389	C₂×C₇	1	1	yes	characteristic, complemented
105	C₂×#388	C₂×C₇	1	2	yes	—
106	C₂×#387	C₂×C₇	1	2	yes	complemented
107	C₂×#384	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂×#380	C₂×C₇	1	1	yes	characteristic
109	C₂×#380	C₂×C₇	1	1	yes	characteristic
110	C₂×C₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
111	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
112	C₂⁴×C₇	—	2	2	no	—
113	C₂⁴×C₇	—	2	2	no	—
114	C₂⁴×C₇	—	2	2	no	—
115	C₂⁴×C₇	—	2	2	no	—
116	C₂⁴×C₇	—	2	2	no	—
117	C₂⁴×C₇	—	2	2	no	—
118	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
119	C₂⁴×C₇	C₂⁴	1	2	yes	—
120	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
121	C₂²×C₄×C₇	—	2	2	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	2	2	no	—
127	C₂²×C₄×C₇	—	2	2	no	—
128	C₂²×C₄×C₇	—	2	2	no	—
129	C₂²×C₄×C₇	—	2	4	no	—
130	C₂²×C₄×C₇	—	2	4	no	—
131	C₂²×C₄×C₇	—	2	4	no	—
132	C₂²×C₄×C₇	—	2	4	no	—
133	C₂²×C₄×C₇	—	2	4	no	—
134	C₂²×C₄×C₇	—	2	4	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	2	2	no	—
137	C₂²×C₄×C₇	—	2	2	no	—
138	C₂²×C₄×C₇	—	2	4	no	—
139	C₂²×C₄×C₇	—	2	4	no	—
140	C₂²×C₄×C₇	—	2	4	no	—
141	C₂²×C₄×C₇	—	2	4	no	—
142	C₂²×C₄×C₇	—	2	4	no	—
143	C₂²×C₄×C₇	—	2	4	no	—
144	C₂²×C₄×C₇	—	2	2	no	—
145	C₂²×C₄×C₇	—	2	8	no	—
146	C₂²×C₄×C₇	—	2	8	no	—
147	C₂²×C₄×C₇	—	2	8	no	—
148	C₂²×C₄×C₇	—	4	16	no	—
149	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
150	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
151	C₂²×C₄×C₇	#41	1	4	yes	—
152	C₂²×C₄×C₇	#41	1	4	yes	—
153	C₂²×C₄×C₇	#41	1	4	yes	—
154	C₂²×C₄×C₇	#41	1	4	yes	—
155	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
165	C₇×C₄⋊C₄	—	2	16	no	—
166	C₇×C₄⋊C₄	—	2	8	no	—
167	C₇×C₄⋊C₄	—	2	8	no	—
168	C₇×C₄⋊C₄	—	2	8	no	—
169	C₇×C₄⋊C₄	—	2	8	no	—
170	C₇×C₄⋊C₄	—	4	8	no	—
171	C₇×C₄⋊C₄	—	4	8	no	—
172	C₇×C₄⋊C₄	—	4	8	no	—
173	C₇×C₂²⋊C₄	—	2	8	no	—
174	C₇×C₂²⋊C₄	—	4	8	no	—
175	C₇×C₂²⋊C₄	—	4	8	no	—
176	C₇×C₂²⋊C₄	C₂×Q₈	1	16	yes	—
177	C₄²×C₇	—	2	8	no	—
178	C₄²×C₇	—	2	8	no	—
179	C₄²×C₇	—	4	8	no	—
180	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
181	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
183	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
186	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
187	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
188	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
189	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
190	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
191	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
192	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
193	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
194	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
195	C₂²×C₄²	C₂²×C₇	1	2	yes	—
196	#400	C₂²×C₇	1	16	yes	complemented
197	#396	C₂²×C₇	1	16	yes	—
198	#389	C₂²×C₇	1	8	yes	complemented
199	#389	C₂²×C₇	1	8	yes	complemented
200	#388	C₂²×C₇	1	16	yes	—
201	#387	C₂²×C₇	1	16	yes	complemented
202	#384	C₂²×C₇	1	8	yes	complemented
203	#380	C₂²×C₇	1	8	yes	—
204	#380	C₂²×C₇	1	8	yes	—
205	C₄×C₄⋊C₄	C₂²×C₇	1	8	yes	complemented
206	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
207	C₂×#95	C₂²×C₇	1	2	yes	—
208	C₂×#95	C₂²×C₇	1	1	yes	characteristic
209	C₂×#95	C₂²×C₇	1	2	yes	—
210	C₂×#95	C₂²×C₇	1	2	yes	—
211	C₂×#95	C₂²×C₇	1	2	yes	—
212	C₂×#95	C₂²×C₇	1	1	yes	characteristic
213	C₂×#95	C₂²×C₇	1	2	yes	—
214	C₂³×C₇	—	2	8	no	—
215	C₂³×C₇	—	2	8	no	—
216	C₂³×C₇	—	2	8	no	—
217	C₂³×C₇	—	2	2	no	—
218	C₂³×C₇	—	2	2	no	—
219	C₂³×C₇	—	2	2	no	—
220	C₂³×C₇	—	2	2	no	—
221	C₂³×C₇	—	2	2	no	—
222	C₂³×C₇	—	2	2	no	—
223	C₂³×C₇	—	4	4	no	—
224	C₂³×C₇	—	4	4	no	—
225	C₂³×C₇	—	4	4	no	—
226	C₂³×C₇	—	4	4	no	—
227	C₂³×C₇	C₂²×Q₈	1	4	yes	—
228	C₂³×C₇	C₂²×Q₈	1	2	yes	—
229	C₂³×C₇	C₂×#41	1	2	yes	—
230	C₂³×C₇	C₂×#41	1	2	yes	—
231	C₂³×C₇	C₂×#41	1	2	yes	—
232	C₂³×C₇	C₂×#41	1	2	yes	—
233	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
234	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
235	C₂³×C₇	C₂⁵	1	1	yes	characteristic
236	C₂×C₄×C₇	—	2	8	no	—
237	C₂×C₄×C₇	—	2	8	no	—
238	C₂×C₄×C₇	—	2	8	no	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	2	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	2	no	—
244	C₂×C₄×C₇	—	2	2	no	—
245	C₂×C₄×C₇	—	2	2	no	—
246	C₂×C₄×C₇	—	2	2	no	—
247	C₂×C₄×C₇	—	2	4	no	—
248	C₂×C₄×C₇	—	2	4	no	—
249	C₂×C₄×C₇	—	2	4	no	—
250	C₂×C₄×C₇	—	2	4	no	—
251	C₂×C₄×C₇	—	2	4	no	—
252	C₂×C₄×C₇	—	2	4	no	—
253	C₂×C₄×C₇	—	2	2	no	—
254	C₂×C₄×C₇	—	2	2	no	—
255	C₂×C₄×C₇	—	2	2	no	—
256	C₂×C₄×C₇	—	2	4	no	—
257	C₂×C₄×C₇	—	2	4	no	—
258	C₂×C₄×C₇	—	2	4	no	—
259	C₂×C₄×C₇	—	2	4	no	—
260	C₂×C₄×C₇	—	2	4	no	—
261	C₂×C₄×C₇	—	2	4	no	—
262	C₂×C₄×C₇	—	2	2	no	—
263	C₂×C₄×C₇	—	4	4	no	—
264	C₂×C₄×C₇	—	4	8	no	—
265	C₂×C₄×C₇	—	4	8	no	—
266	C₂×C₄×C₇	—	4	8	no	—
267	C₂×C₄×C₇	—	4	4	no	—
268	C₂×C₄×C₇	—	4	8	no	—
269	C₂×C₄×C₇	—	4	16	no	—
270	C₂×C₄×C₇	#126	1	16	yes	—
271	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
272	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
273	C₂×C₄×C₇	C₂×#41	1	4	yes	—
274	C₂×C₄×C₇	C₂×#41	1	4	yes	—
275	C₂×C₄×C₇	C₂×#41	1	4	yes	—
276	C₂×C₄×C₇	C₂×#41	1	4	yes	—
277	C₂⁵	C₂³×C₇	1	1	yes	characteristic
278	C₂³×C₄	—	2	4	no	—
279	C₂³×C₄	—	2	4	no	—
280	C₂³×C₄	—	2	4	no	—
281	C₂³×C₄	C₂³×C₇	1	2	yes	—
282	C₂³×C₄	C₂³×C₇	1	2	yes	—
283	C₂³×C₄	C₂³×C₇	1	2	yes	—
284	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₇	1	2	yes	—
286	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₇	1	4	yes	—
288	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	—	2	8	no	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	4	4	no	—
298	C₂×C₄⋊C₄	—	4	4	no	—
299	C₂×C₄⋊C₄	—	4	4	no	—
300	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
301	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
302	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
303	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
304	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
305	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
306	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
307	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
308	C₂×C₂²⋊C₄	—	2	4	no	—
309	C₂×C₂²⋊C₄	—	4	4	no	—
310	C₂×C₂²⋊C₄	—	4	4	no	—
311	C₂×C₂²⋊C₄	C₇×Q₈	1	8	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
316	C₂×C₄²	—	2	4	no	—
317	C₂×C₄²	—	2	4	no	—
318	C₂×C₄²	—	4	4	no	—
319	C₂×C₄²	C₂³×C₇	1	4	yes	—
320	C₂×C₄²	C₂³×C₇	1	4	yes	—
321	C₂×C₄²	C₂³×C₇	1	8	yes	—
322	#95	C₂³×C₇	1	4	yes	—
323	#95	C₂³×C₇	1	4	yes	—
324	#95	C₂³×C₇	1	8	yes	—
325	#95	C₂³×C₇	1	8	yes	—
326	#95	C₂³×C₇	1	8	yes	—
327	#95	C₂³×C₇	1	8	yes	—
328	#95	C₂³×C₇	1	8	yes	—
329	C₂²×C₇	—	2	4	no	—
330	C₂²×C₇	—	2	4	no	—
331	C₂²×C₇	—	2	4	no	—
332	C₂²×C₇	—	4	2	no	—
333	C₂²×C₇	—	4	2	no	—
334	C₂²×C₇	—	4	2	no	—
335	C₂²×C₇	—	4	2	no	—
336	C₂²×C₇	—	4	16	no	—
337	C₂²×C₇	C₂×#126	1	4	yes	—
338	C₂²×C₇	#533	1	4	yes	—
339	C₂²×C₇	#540	1	4	yes	—
340	C₂²×C₇	#553	1	4	yes	—
341	C₂²×C₇	#554	1	4	yes	—
342	C₂²×C₇	#554	1	4	yes	—
343	C₂²×C₇	#555	1	4	yes	—
344	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
345	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
346	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
347	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
348	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
349	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
351	C₄×C₇	—	2	4	no	—
352	C₄×C₇	—	2	4	no	—
353	C₄×C₇	—	2	4	no	—
354	C₄×C₇	—	4	2	no	—
355	C₄×C₇	—	4	4	no	—
356	C₄×C₇	—	4	4	no	—
357	C₄×C₇	—	4	4	no	—
358	C₄×C₇	—	4	2	no	—
359	C₄×C₇	—	4	4	no	—
360	C₄×C₇	C₂×#126	1	8	yes	—
361	C₂⁴	—	2	2	no	—
362	C₂⁴	—	2	2	no	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	—	2	2	no	—
365	C₂⁴	—	2	2	no	—
366	C₂⁴	—	2	2	no	—
367	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
368	C₂⁴	C₂⁴×C₇	1	2	yes	—
369	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	2	8	no	—
397	C₂²×C₄	—	4	16	no	—
398	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
399	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
400	C₂²×C₄	C₇×#41	1	4	yes	—
401	C₂²×C₄	C₇×#41	1	4	yes	—
402	C₂²×C₄	C₇×#41	1	4	yes	—
403	C₂²×C₄	C₇×#41	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
406	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
412	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
414	C₄⋊C₄	—	2	16	no	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	4	8	no	—
420	C₄⋊C₄	—	4	8	no	—
421	C₄⋊C₄	—	4	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	4	8	no	—
424	C₂²⋊C₄	—	4	8	no	—
425	C₂²⋊C₄	C₂×C₇×Q₈	1	16	yes	—
426	C₄²	—	2	8	no	—
427	C₄²	—	2	8	no	—
428	C₄²	—	4	8	no	—
429	C₂×C₇	—	4	4	no	—
430	C₂×C₇	#2497	1	8	yes	direct product factor
431	C₂×C₇	C₂²×#126	1	1	yes	characteristic
432	C₂×C₇	C₂×#533	1	1	yes	characteristic
433	C₂×C₇	C₂×#540	1	1	yes	characteristic
434	C₂×C₇	C₂×#553	1	1	yes	characteristic
435	C₂×C₇	C₂×#554	1	1	yes	characteristic
436	C₂×C₇	C₂×#554	1	1	yes	characteristic
437	C₂×C₇	C₂×#555	1	1	yes	characteristic
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	8	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	8	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	4	no	—
451	C₂³	C₂²×C₇×Q₈	1	4	yes	—
452	C₂³	C₂²×C₇×Q₈	1	2	yes	—
453	C₂³	C₂×C₇×#41	1	2	yes	—
454	C₂³	C₂×C₇×#41	1	2	yes	—
455	C₂³	C₂×C₇×#41	1	2	yes	—
456	C₂³	C₂×C₇×#41	1	2	yes	—
457	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
458	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
459	C₂³	C₂⁵×C₇	1	1	yes	characteristic
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	8	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	8	no	—
493	C₂×C₄	—	4	16	no	—
494	C₂×C₄	C₇×#126	1	16	yes	—
495	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
496	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
497	C₂×C₄	C₂×C₇×#41	1	4	yes	—
498	C₂×C₄	C₂×C₇×#41	1	4	yes	—
499	C₂×C₄	C₂×C₇×#41	1	4	yes	—
500	C₂×C₄	C₂×C₇×#41	1	4	yes	—
501	C₇	C₂×#2497	1	1	yes	characteristic, direct product factor, Sylow
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	4	16	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	C₂×C₇×#126	1	4	yes	—
511	C₂²	C₇×#533	1	4	yes	—
512	C₂²	C₇×#540	1	4	yes	—
513	C₂²	C₇×#553	1	4	yes	—
514	C₂²	C₇×#554	1	4	yes	—
515	C₂²	C₇×#554	1	4	yes	—
516	C₂²	C₇×#555	1	4	yes	—
517	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
518	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
519	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
520	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
521	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
522	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
524	C₄	—	2	4	no	—
525	C₄	—	2	4	no	—
526	C₄	—	2	4	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	4	no	—
529	C₄	—	4	4	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	4	no	—
533	C₄	C₂×C₇×#126	1	8	yes	—
534	C₂	—	4	4	no	—
535	C₂	C₇×#2497	1	8	yes	direct product factor
536	C₂	C₂²×C₇×#126	1	1	yes	characteristic
537	C₂	C₂×C₇×#533	1	1	yes	characteristic
538	C₂	C₂×C₇×#540	1	1	yes	characteristic
539	C₂	C₂×C₇×#553	1	1	yes	characteristic
540	C₂	C₂×C₇×#554	1	1	yes	characteristic
541	C₂	C₂×C₇×#554	1	1	yes	characteristic
542	C₂	C₂×C₇×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁵×C₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2497	C₂	direct (N × H)
2. C₂×C₇×#400	C₂	semidirect
4. C₂×C₇×#389	C₂	semidirect
5. C₂×C₇×#389	C₂	semidirect
7. C₂×C₇×#387	C₂	semidirect
8. C₂×C₇×#384	C₂	semidirect
11. C₂×C₄×C₇×C₄⋊C₄	C₂	semidirect
29. C₇×#400	C₂²	semidirect
31. C₇×#389	C₂²	semidirect
32. C₇×#389	C₂²	semidirect
34. C₇×#387	C₂²	semidirect
35. C₇×#384	C₂²	semidirect
38. C₄×C₇×C₄⋊C₄	C₂²	semidirect
47. C₂×#2497	C₇	direct (N × H)
100. #2497	C₂×C₇	direct (N × H)
101. C₂×#400	C₂×C₇	semidirect
103. C₂×#389	C₂×C₇	semidirect
104. C₂×#389	C₂×C₇	semidirect
106. C₂×#387	C₂×C₇	semidirect
107. C₂×#384	C₂×C₇	semidirect
110. C₂×C₄×C₄⋊C₄	C₂×C₇	semidirect
196. #400	C₂²×C₇	semidirect
198. #389	C₂²×C₇	semidirect
199. #389	C₂²×C₇	semidirect
201. #387	C₂²×C₇	semidirect
202. #384	C₂²×C₇	semidirect
205. C₄×C₄⋊C₄	C₂²×C₇	semidirect
430. C₂×C₇	#2497	direct (N × H)
501. C₇	C₂×#2497	direct (N × H)
535. C₂	C₇×#2497	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2497	2
C₂×C₇×#400	2
C₂×C₇×#396	2
C₂×C₇×#389	2
C₂×C₇×#388	2
C₂×C₇×#387	2
C₂×C₇×#384	2
C₂×C₇×#380	2
C₂×C₄×C₇×C₄⋊C₄	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂×#2497	7

Subgroups — C2×C7×#2497 #13211985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2497 #13211985