Subgroups — C₂×C₇×#3365 #13238518

Order 1792.

1894 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3365	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#488	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic
10	C₂×C₇×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₇×SD₁₆	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
15	C₇×#559	—	2	4	no	—
16	C₇×#559	C₂²	1	8	yes	—
17	C₇×#557	—	2	4	no	—
18	C₇×#557	C₂²	1	8	yes	complemented
19	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#127	C₂²	1	1	yes	characteristic
22	C₂×C₇×#125	—	2	2	no	—
23	C₂×C₇×#125	C₂²	1	2	yes	—
24	C₂×C₇×#124	—	2	1	no	—
25	C₂×C₇×#124	C₂²	1	2	yes	—
26	C₂×C₇×#123	—	2	2	no	—
27	C₂×C₄×C₇×Q₈	—	2	1	no	—
28	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	—	2	1	no	—
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
34	C₇×#488	C₂²	1	16	yes	complemented
35	C₇×#486	C₂²	1	8	yes	—
36	C₇×#478	C₂²	1	16	yes	complemented
37	C₇×#475	C₂²	1	8	yes	complemented
38	C₇×#464	C₂²	1	16	yes	complemented
39	C₇×#460	C₂²	1	8	yes	—
40	C₇×C₈×Q₈	C₂²	1	8	yes	complemented
41	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
42	C₄×C₇×SD₁₆	C₂²	1	16	yes	complemented
43	C₂×C₇×#107	C₂²	1	1	yes	characteristic
44	C₂×C₇×#106	C₂²	1	2	yes	—
45	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
47	C₂×C₇×#103	C₂²	1	1	yes	characteristic
48	C₂×C₇×#103	C₂²	1	1	yes	characteristic
49	C₂×C₇×#103	C₂²	1	2	yes	—
50	C₂×C₇×#102	C₂²	1	2	yes	—
51	C₂×C₇×#102	C₂²	1	2	yes	—
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3365	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂²×C₇×Q₈	—	2	1	no	—
57	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
58	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
60	C₂²×C₇×D₄	—	2	1	no	—
61	C₂²×C₇×D₄	—	2	1	no	—
62	C₂²×C₇×D₄	C₂³	1	2	yes	—
63	C₂³×C₄×C₇	—	2	2	no	—
64	C₂×C₇×Q₁₆	—	2	4	no	—
65	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
66	C₂×C₇×SD₁₆	—	2	8	no	—
67	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	2	yes	—
71	C₇×C₄⋊Q₈	—	2	8	no	—
72	C₇×C₄⋊Q₈	—	2	2	no	—
73	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
74	C₇×#127	—	2	2	no	—
75	C₇×#127	C₂³	1	4	yes	—
76	C₇×#125	—	2	16	no	—
77	C₇×#125	—	2	4	no	—
78	C₇×#125	C₂³	1	8	yes	—
79	C₇×#124	—	2	8	no	—
80	C₇×#124	—	2	4	no	—
81	C₇×#124	C₂³	1	8	yes	—
82	C₇×#123	—	2	16	no	—
83	C₄×C₇×Q₈	—	2	8	no	—
84	C₄×C₇×Q₈	—	2	4	no	—
85	C₄×C₇×Q₈	—	2	2	no	—
86	C₄×C₇×Q₈	—	2	2	no	—
87	C₄×C₇×Q₈	D₄	1	4	yes	—
88	C₄×C₇×Q₈	C₂³	1	4	yes	—
89	C₄×C₇×Q₈	C₂³	1	8	yes	—
90	C₄×C₇×Q₈	C₂³	1	4	yes	—
91	C₄×C₇×Q₈	C₂³	1	4	yes	—
92	C₄×C₇×D₄	—	2	8	no	—
93	C₄×C₇×D₄	—	2	4	no	—
94	C₄×C₇×D₄	C₂³	1	8	yes	—
95	C₂×C₇×C₄⋊C₄	—	2	2	no	—
96	C₂×C₇×C₄⋊C₄	—	2	1	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	2	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	2	no	—
101	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₄²×C₇	—	2	1	no	—
110	C₂×C₄²×C₇	—	2	2	no	—
111	C₂×C₄²×C₇	—	2	1	no	—
112	C₂×C₄²×C₇	C₂³	1	2	yes	—
113	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
114	C₇×#107	C₂³	1	4	yes	—
115	C₇×#106	C₂³	1	8	yes	—
116	C₇×C₄⋊C₈	C₂³	1	4	yes	—
117	C₇×C₄⋊C₈	C₂³	1	8	yes	—
118	C₇×#103	C₂³	1	8	yes	—
119	C₇×#103	C₂³	1	4	yes	—
120	C₇×#103	C₂³	1	4	yes	—
121	C₇×#102	C₂³	1	8	yes	—
122	C₇×#102	C₂³	1	8	yes	—
123	C₇×#102	C₂³	1	8	yes	—
124	C₄×C₇×C₈	C₂³	1	4	yes	—
125	C₄×C₇×C₈	C₂³	1	8	yes	—
126	C₂×#559	C₂×C₇	1	1	yes	characteristic
127	C₂×#557	C₂×C₇	1	1	yes	characteristic, complemented
128	#3365	C₂×C₇	1	16	yes	direct product factor
129	C₂×#488	C₂×C₇	1	2	yes	complemented
130	C₂×#486	C₂×C₇	1	1	yes	characteristic
131	C₂×#475	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#478	C₂×C₇	1	2	yes	complemented
133	C₂×#464	C₂×C₇	1	2	yes	complemented
134	C₂×#460	C₂×C₇	1	1	yes	characteristic
135	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×C₄×SD₁₆	C₂×C₇	1	2	yes	complemented
138	C₂⁴×C₇	—	2	2	no	—
139	C₂×C₇×Q₈	—	2	4	no	—
140	C₂×C₇×Q₈	—	2	1	no	—
141	C₂×C₇×Q₈	—	2	1	no	—
142	C₂×C₇×Q₈	—	2	4	no	—
143	C₂×C₇×Q₈	—	2	2	no	—
144	C₂×C₇×Q₈	—	2	2	no	—
145	C₂×C₇×Q₈	—	2	2	no	—
146	C₂×C₇×Q₈	—	4	4	no	—
147	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
148	C₂×C₇×Q₈	#41	1	4	yes	—
149	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
150	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
151	C₂×C₇×D₄	—	2	2	no	—
152	C₂×C₇×D₄	—	2	4	no	—
153	C₂×C₇×D₄	—	2	4	no	—
154	C₂×C₇×D₄	—	2	4	no	—
155	C₂×C₇×D₄	—	2	4	no	—
156	C₂×C₇×D₄	—	4	4	no	—
157	C₂×C₇×D₄	—	8	2	no	—
158	C₂×C₇×D₄	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₇	—	2	1	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	2	2	no	—
164	C₂²×C₄×C₇	—	2	8	no	—
165	C₂²×C₄×C₇	—	8	4	no	—
166	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
171	C₇×Q₁₆	—	2	8	no	—
172	C₇×SD₁₆	—	2	16	no	—
173	C₂×C₇×C₈	—	2	4	no	—
174	C₂×C₇×C₈	—	2	2	no	—
175	C₂×C₇×C₈	—	2	2	no	—
176	C₂×C₇×C₈	C₂⁴	1	2	yes	—
177	C₂×C₇×C₈	C₂⁴	1	2	yes	—
178	C₂×C₇×C₈	C₂⁴	1	4	yes	—
179	C₇×C₄⋊C₄	—	2	8	no	—
180	C₇×C₄⋊C₄	—	2	4	no	—
181	C₇×C₄⋊C₄	—	2	4	no	—
182	C₇×C₄⋊C₄	—	2	8	no	—
183	C₇×C₄⋊C₄	—	2	4	no	—
184	C₇×C₄⋊C₄	—	2	8	no	—
185	C₇×C₄⋊C₄	—	2	1	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	2	no	—
188	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
189	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
190	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
191	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
192	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
193	C₇×C₂²⋊C₄	—	2	8	no	—
194	C₇×C₂²⋊C₄	—	2	8	no	—
195	C₇×C₂²⋊C₄	—	2	8	no	—
196	C₄²×C₇	—	2	4	no	—
197	C₄²×C₇	—	2	8	no	—
198	C₄²×C₇	—	2	4	no	—
199	C₄²×C₇	C₂×D₄	1	4	yes	—
200	C₄²×C₇	C₂×D₄	1	2	yes	—
201	C₄²×C₇	C₂⁴	1	4	yes	—
202	C₄²×C₇	C₂⁴	1	2	yes	—
203	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
204	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
205	#559	—	2	4	no	—
206	#559	C₂²×C₇	1	8	yes	—
207	#557	—	2	4	no	—
208	#557	C₂²×C₇	1	8	yes	complemented
209	C₂×C₄⋊Q₈	—	2	1	no	—
210	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
211	C₂×#127	C₂²×C₇	1	1	yes	characteristic
212	C₂×#125	—	2	2	no	—
213	C₂×#125	C₂²×C₇	1	2	yes	—
214	C₂×#124	—	2	1	no	—
215	C₂×#124	C₂²×C₇	1	2	yes	—
216	C₂×#123	—	2	2	no	—
217	C₂×C₄×Q₈	—	2	1	no	—
218	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
220	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
222	C₂×C₄×D₄	—	2	1	no	—
223	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
224	#488	C₂²×C₇	1	16	yes	complemented
225	#486	C₂²×C₇	1	8	yes	—
226	#478	C₂²×C₇	1	16	yes	complemented
227	#475	C₂²×C₇	1	8	yes	complemented
228	#464	C₂²×C₇	1	16	yes	complemented
229	#460	C₂²×C₇	1	8	yes	—
230	C₈×Q₈	C₂²×C₇	1	8	yes	complemented
231	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
232	C₄×SD₁₆	C₂²×C₇	1	16	yes	complemented
233	C₂×#107	C₂²×C₇	1	1	yes	characteristic
234	C₂×#106	C₂²×C₇	1	2	yes	—
235	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
236	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
237	C₂×#103	C₂²×C₇	1	2	yes	—
238	C₂×#103	C₂²×C₇	1	1	yes	characteristic
239	C₂×#103	C₂²×C₇	1	1	yes	characteristic
240	C₂×#102	C₂²×C₇	1	2	yes	—
241	C₂×#102	C₂²×C₇	1	2	yes	—
242	C₂×#102	C₂²×C₇	1	2	yes	—
243	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
245	C₂³×C₇	—	2	4	no	—
246	C₂³×C₇	—	4	4	no	—
247	C₂³×C₇	—	4	4	no	—
248	C₂³×C₇	—	4	4	no	—
249	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
250	C₇×Q₈	—	2	4	no	—
251	C₇×Q₈	—	2	8	no	—
252	C₇×Q₈	—	2	2	no	—
253	C₇×Q₈	—	2	2	no	—
254	C₇×Q₈	—	2	2	no	—
255	C₇×Q₈	—	4	2	no	—
256	C₇×Q₈	—	4	8	no	—
257	C₇×Q₈	C₂×#41	1	4	yes	—
258	C₇×D₄	—	2	4	no	—
259	C₇×D₄	—	2	4	no	—
260	C₇×D₄	—	4	4	no	—
261	C₇×D₄	—	4	8	no	—
262	C₇×D₄	—	8	4	no	—
263	C₂×C₄×C₇	—	2	4	no	—
264	C₂×C₄×C₇	—	2	4	no	—
265	C₂×C₄×C₇	—	2	4	no	—
266	C₂×C₄×C₇	—	2	2	no	—
267	C₂×C₄×C₇	—	2	2	no	—
268	C₂×C₄×C₇	—	2	2	no	—
269	C₂×C₄×C₇	—	2	2	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	2	4	no	—
272	C₂×C₄×C₇	—	4	2	no	—
273	C₂×C₄×C₇	—	4	4	no	—
274	C₂×C₄×C₇	—	4	2	no	—
275	C₂×C₄×C₇	—	4	2	no	—
276	C₂×C₄×C₇	—	8	8	no	—
277	C₂×C₄×C₇	#135	1	4	yes	—
278	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
280	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₇	C₂×#41	1	2	yes	—
284	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
285	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
286	C₇×C₈	—	2	4	no	—
287	C₇×C₈	—	2	2	no	—
288	C₇×C₈	—	2	2	no	—
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	C₂³×C₇	1	2	yes	—
296	C₂³×C₄	—	2	2	no	—
297	C₂×Q₁₆	—	2	4	no	—
298	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
299	C₂×SD₁₆	—	2	8	no	—
300	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
301	C₂²×C₈	C₂³×C₇	1	2	yes	—
302	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
304	C₄⋊Q₈	—	2	8	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
307	#127	—	2	2	no	—
308	#127	C₂³×C₇	1	4	yes	—
309	#125	—	2	16	no	—
310	#125	—	2	4	no	—
311	#125	C₂³×C₇	1	8	yes	—
312	#124	—	2	8	no	—
313	#124	—	2	4	no	—
314	#124	C₂³×C₇	1	8	yes	—
315	#123	—	2	16	no	—
316	C₄×Q₈	—	2	8	no	—
317	C₄×Q₈	—	2	4	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	C₇×D₄	1	4	yes	—
321	C₄×Q₈	C₂³×C₇	1	8	yes	—
322	C₄×Q₈	C₂³×C₇	1	4	yes	—
323	C₄×Q₈	C₂³×C₇	1	4	yes	—
324	C₄×Q₈	C₂³×C₇	1	4	yes	—
325	C₄×D₄	—	2	8	no	—
326	C₄×D₄	—	2	4	no	—
327	C₄×D₄	C₂³×C₇	1	8	yes	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	C₂³×C₇	1	2	yes	—
346	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
347	#107	C₂³×C₇	1	4	yes	—
348	#106	C₂³×C₇	1	8	yes	—
349	C₄⋊C₈	C₂³×C₇	1	4	yes	—
350	C₄⋊C₈	C₂³×C₇	1	8	yes	—
351	#103	C₂³×C₇	1	4	yes	—
352	#103	C₂³×C₇	1	4	yes	—
353	#103	C₂³×C₇	1	8	yes	—
354	#102	C₂³×C₇	1	8	yes	—
355	#102	C₂³×C₇	1	8	yes	—
356	#102	C₂³×C₇	1	8	yes	—
357	C₄×C₈	C₂³×C₇	1	8	yes	—
358	C₄×C₈	C₂³×C₇	1	4	yes	—
359	C₂²×C₇	—	4	4	no	—
360	C₂²×C₇	—	4	4	no	—
361	C₂²×C₇	—	4	4	no	—
362	C₂²×C₇	—	8	8	no	—
363	C₂²×C₇	#548	1	2	yes	—
364	C₂²×C₇	C₂×#135	1	2	yes	—
365	C₂²×C₇	#577	1	2	yes	—
366	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
367	C₄×C₇	—	2	4	no	—
368	C₄×C₇	—	2	4	no	—
369	C₄×C₇	—	2	4	no	—
370	C₄×C₇	—	2	2	no	—
371	C₄×C₇	—	4	2	no	—
372	C₄×C₇	—	4	4	no	—
373	C₄×C₇	—	4	2	no	—
374	C₄×C₇	—	4	2	no	—
375	C₄×C₇	#548	1	2	yes	—
376	C₄×C₇	C₂×#135	1	4	yes	—
377	C₄×C₇	C₂²×#41	1	1	yes	characteristic
378	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
379	C₂⁴	—	2	2	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	4	4	no	—
388	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
389	C₂×Q₈	C₇×#41	1	4	yes	—
390	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
391	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	8	2	no	—
399	C₂×D₄	C₂⁴×C₇	1	4	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	8	no	—
406	C₂²×C₄	—	8	4	no	—
407	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
408	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
409	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
410	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
412	Q₁₆	—	2	8	no	—
413	SD₁₆	—	2	16	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	C₂⁴×C₇	1	2	yes	—
418	C₂×C₈	C₂⁴×C₇	1	2	yes	—
419	C₂×C₈	C₂⁴×C₇	1	4	yes	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	8	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	8	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
430	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
431	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
432	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
433	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₄²	—	2	4	no	—
438	C₄²	—	2	8	no	—
439	C₄²	—	2	4	no	—
440	C₄²	C₂×C₇×D₄	1	4	yes	—
441	C₄²	C₂×C₇×D₄	1	2	yes	—
442	C₄²	C₂⁴×C₇	1	4	yes	—
443	C₄²	C₂⁴×C₇	1	2	yes	—
444	C₂×C₇	—	8	4	no	—
445	C₂×C₇	#3365	1	4	yes	direct product factor
446	C₂×C₇	C₂×#548	1	1	yes	characteristic
447	C₂×C₇	C₂²×#135	1	1	yes	characteristic
448	C₂×C₇	C₂×#577	1	1	yes	characteristic
449	C₂³	—	2	4	no	—
450	C₂³	—	4	4	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	4	no	—
453	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	Q₈	—	2	4	no	—
456	Q₈	—	2	8	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	8	no	—
461	Q₈	C₂×C₇×#41	1	4	yes	—
462	D₄	—	2	4	no	—
463	D₄	—	2	4	no	—
464	D₄	—	4	4	no	—
465	D₄	—	4	8	no	—
466	D₄	—	8	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	8	8	no	—
481	C₂×C₄	C₇×#135	1	4	yes	—
482	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
483	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
484	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
485	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
487	C₂×C₄	C₂×C₇×#41	1	2	yes	—
488	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
489	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
490	C₈	—	2	4	no	—
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₇	C₂×#3365	1	1	yes	characteristic, direct product factor, Sylow
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	8	8	no	—
498	C₂²	C₇×#548	1	2	yes	—
499	C₂²	C₂×C₇×#135	1	2	yes	—
500	C₂²	C₇×#577	1	2	yes	—
501	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
502	C₄	—	2	4	no	—
503	C₄	—	2	4	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	4	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	C₇×#548	1	2	yes	—
511	C₄	C₂×C₇×#135	1	4	yes	—
512	C₄	C₂²×C₇×#41	1	1	yes	characteristic
513	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
514	C₂	—	8	4	no	—
515	C₂	C₇×#3365	1	4	yes	direct product factor
516	C₂	C₂×C₇×#548	1	1	yes	characteristic
517	C₂	C₂²×C₇×#135	1	1	yes	characteristic
518	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#557	C₂	semidirect
3. C₇×#3365	C₂	direct (N × H)
4. C₂×C₇×#488	C₂	semidirect
6. C₂×C₇×#475	C₂	semidirect
7. C₂×C₇×#478	C₂	semidirect
8. C₂×C₇×#464	C₂	semidirect
10. C₂×C₇×C₈×Q₈	C₂	semidirect
11. C₂×C₄×C₇×Q₁₆	C₂	semidirect
12. C₂×C₄×C₇×SD₁₆	C₂	semidirect
18. C₇×#557	C₂²	semidirect
34. C₇×#488	C₂²	semidirect
36. C₇×#478	C₂²	semidirect
37. C₇×#475	C₂²	semidirect
38. C₇×#464	C₂²	semidirect
40. C₇×C₈×Q₈	C₂²	semidirect
41. C₄×C₇×Q₁₆	C₂²	semidirect
42. C₄×C₇×SD₁₆	C₂²	semidirect
55. C₂×#3365	C₇	direct (N × H)
127. C₂×#557	C₂×C₇	semidirect
128. #3365	C₂×C₇	direct (N × H)
129. C₂×#488	C₂×C₇	semidirect
131. C₂×#475	C₂×C₇	semidirect
132. C₂×#478	C₂×C₇	semidirect
133. C₂×#464	C₂×C₇	semidirect
135. C₂×C₈×Q₈	C₂×C₇	semidirect
136. C₂×C₄×Q₁₆	C₂×C₇	semidirect
137. C₂×C₄×SD₁₆	C₂×C₇	semidirect
208. #557	C₂²×C₇	semidirect
224. #488	C₂²×C₇	semidirect
226. #478	C₂²×C₇	semidirect
227. #475	C₂²×C₇	semidirect
228. #464	C₂²×C₇	semidirect
230. C₈×Q₈	C₂²×C₇	semidirect
231. C₄×Q₁₆	C₂²×C₇	semidirect
232. C₄×SD₁₆	C₂²×C₇	semidirect
445. C₂×C₇	#3365	direct (N × H)
493. C₇	C₂×#3365	direct (N × H)
515. C₂	C₇×#3365	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×#559	2
C₂×C₇×#557	2
C₇×#3365	2
C₂×C₇×#488	2
C₂×C₇×#486	2
C₂×C₇×#475	2
C₂×C₇×#478	2
C₂×C₇×#464	2
C₂×C₇×#460	2
C₂×C₇×C₈×Q₈	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₄×C₇×SD₁₆	2
C₂×#3365	7

Subgroups — C2×C7×#3365 #13238518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3365 #13238518