Subgroups — C₂×C₇×#3168 #13237886

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
2	C₇×#3168	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#488	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic
8	C₂×C₇×#465	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₇×SD₁₆	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
16	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₇×#529	—	2	8	no	—
19	C₇×#529	C₂²	1	16	yes	complemented
20	C₂×C₇×#126	—	2	2	no	—
21	C₂×C₇×#125	C₂²	1	2	yes	—
22	C₂×C₇×#124	C₂²	1	2	yes	—
23	C₂×C₇×#123	—	2	2	no	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₇×#121	C₂²	1	2	yes	—
26	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
27	C₂×C₄×C₇×D₄	—	2	2	no	—
28	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
29	C₂×C₇×#117	—	2	2	no	—
30	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
31	C₇×#499	C₂²	1	8	yes	complemented
32	C₇×#495	C₂²	1	8	yes	complemented
33	C₇×#488	C₂²	1	16	yes	complemented
34	C₇×#467	C₂²	1	8	yes	complemented
35	C₇×#466	C₂²	1	8	yes	—
36	C₇×#465	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	C₂×C₇×#107	C₂²	1	1	yes	characteristic
41	C₂×C₇×#107	C₂²	1	1	yes	characteristic
42	C₂×C₇×#106	C₂²	1	2	yes	—
43	C₂×C₇×#103	C₂²	1	2	yes	—
44	C₂×C₇×#103	C₂²	1	2	yes	—
45	C₂×C₇×#102	C₂²	1	2	yes	—
46	C₂×C₇×#102	C₂²	1	2	yes	—
47	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₇×C₈	C₂²	1	8	yes	complemented
52	C₂×#3168	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂²×C₇×Q₈	C₂³	1	2	yes	—
54	C₂²×C₇×D₄	—	2	2	no	—
55	C₂²×C₇×D₄	C₂³	1	2	yes	—
56	C₂³×C₄×C₇	—	2	2	no	—
57	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₂×C₇×Q₁₆	—	2	4	no	—
61	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
62	C₂×C₇×SD₁₆	—	2	8	no	—
63	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
64	C₂×C₇×D₈	—	2	4	no	—
65	C₂×C₇×D₈	C₂³	1	4	yes	—
66	C₂²×C₇×C₈	—	2	4	no	—
67	C₂²×C₇×C₈	—	2	4	no	—
68	C₂²×C₇×C₈	C₂³	1	4	yes	—
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂³	1	4	yes	—
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₇×#126	—	2	16	no	—
75	C₇×#125	—	2	4	no	—
76	C₇×#125	C₂³	1	8	yes	—
77	C₇×#124	—	2	4	no	—
78	C₇×#124	C₂³	1	8	yes	—
79	C₇×#123	—	2	16	no	—
80	C₇×C₂²⋊Q₈	—	2	4	no	—
81	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
82	C₇×#121	—	2	4	no	—
83	C₇×#121	C₂³	1	8	yes	—
84	C₄×C₇×Q₈	—	2	4	no	—
85	C₄×C₇×Q₈	C₂³	1	8	yes	—
86	C₄×C₇×D₄	—	2	16	no	—
87	C₄×C₇×D₄	—	2	4	no	—
88	C₄×C₇×D₄	C₂³	1	8	yes	—
89	C₇×#117	—	2	16	no	—
90	C₂×C₇×C₄⋊C₄	—	2	2	no	—
91	C₂×C₇×C₄⋊C₄	—	2	2	no	—
92	C₂×C₇×C₄⋊C₄	—	2	2	no	—
93	C₂×C₇×C₄⋊C₄	—	2	2	no	—
94	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₄²×C₇	—	2	2	no	—
102	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₇	D₄	1	4	yes	—
104	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₇	C₂³	1	4	yes	—
107	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
108	C₇×#107	C₂³	1	4	yes	—
109	C₇×#107	C₂³	1	4	yes	—
110	C₇×#106	C₂³	1	8	yes	—
111	C₇×#103	C₂³	1	8	yes	—
112	C₇×#103	C₂³	1	8	yes	—
113	C₇×#102	C₂³	1	8	yes	—
114	C₇×#102	C₂³	1	8	yes	—
115	C₄×C₇×C₈	C₂³	1	4	yes	—
116	C₄×C₇×C₈	C₂³	1	4	yes	—
117	C₄×C₇×C₈	C₂³	1	4	yes	—
118	C₄×C₇×C₈	C₂³	1	4	yes	—
119	C₂×#529	C₂×C₇	1	2	yes	complemented
120	#3168	C₂×C₇	1	16	yes	direct product factor
121	C₂×#499	C₂×C₇	1	1	yes	characteristic, complemented
122	C₂×#495	C₂×C₇	1	1	yes	characteristic, complemented
123	C₂×#488	C₂×C₇	1	2	yes	complemented
124	C₂×#467	C₂×C₇	1	1	yes	characteristic, complemented
125	C₂×#466	C₂×C₇	1	1	yes	characteristic
126	C₂×#465	C₂×C₇	1	2	yes	complemented
127	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
128	C₂×C₄×SD₁₆	C₂×C₇	1	2	yes	complemented
129	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂²×C₄×C₈	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂⁴×C₇	—	2	2	no	—
132	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₇×Q₈	—	2	2	no	—
134	C₂×C₇×Q₈	—	2	4	no	—
135	C₂×C₇×Q₈	—	2	4	no	—
136	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
137	C₂×C₇×D₄	—	2	8	no	—
138	C₂×C₇×D₄	—	2	2	no	—
139	C₂×C₇×D₄	—	2	4	no	—
140	C₂×C₇×D₄	—	2	4	no	—
141	C₂×C₇×D₄	—	4	8	no	—
142	C₂×C₇×D₄	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₇	—	2	4	no	—
144	C₂²×C₄×C₇	—	2	4	no	—
145	C₂²×C₄×C₇	—	2	2	no	—
146	C₂²×C₄×C₇	—	2	2	no	—
147	C₂²×C₄×C₇	—	2	2	no	—
148	C₂²×C₄×C₇	—	2	2	no	—
149	C₂²×C₄×C₇	—	2	2	no	—
150	C₂²×C₄×C₇	—	2	8	no	—
151	C₂²×C₄×C₇	—	4	8	no	—
152	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
162	C₇×Q₁₆	—	2	8	no	—
163	C₇×SD₁₆	—	2	16	no	—
164	C₇×D₈	—	2	8	no	—
165	C₂×C₇×C₈	—	2	2	no	—
166	C₂×C₇×C₈	—	2	2	no	—
167	C₂×C₇×C₈	—	2	8	no	—
168	C₂×C₇×C₈	—	2	8	no	—
169	C₂×C₇×C₈	#41	1	4	yes	—
170	C₂×C₇×C₈	#41	1	4	yes	—
171	C₂×C₇×C₈	C₂⁴	1	2	yes	—
172	C₂×C₇×C₈	C₂⁴	1	2	yes	—
173	C₂×C₇×C₈	C₂⁴	1	2	yes	—
174	C₂×C₇×C₈	C₂⁴	1	2	yes	—
175	C₇×C₄⋊C₄	—	2	8	no	—
176	C₇×C₄⋊C₄	—	2	8	no	—
177	C₇×C₄⋊C₄	—	2	8	no	—
178	C₇×C₄⋊C₄	—	2	8	no	—
179	C₇×C₄⋊C₄	—	2	2	no	—
180	C₇×C₄⋊C₄	—	2	2	no	—
181	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
182	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
183	C₇×C₂²⋊C₄	—	2	8	no	—
184	C₇×C₂²⋊C₄	—	2	8	no	—
185	C₇×C₂²⋊C₄	—	2	8	no	—
186	C₇×C₂²⋊C₄	—	2	8	no	—
187	C₇×C₂²⋊C₄	—	2	8	no	—
188	C₄²×C₇	—	2	8	no	—
189	C₄²×C₇	C₂×D₄	1	4	yes	—
190	C₄²×C₇	C₂×D₄	1	2	yes	—
191	C₄²×C₇	C₂×D₄	1	2	yes	—
192	C₄²×C₇	C₂×D₄	1	4	yes	—
193	C₄²×C₇	C₂⁴	1	2	yes	—
194	C₄²×C₇	C₂⁴	1	2	yes	—
195	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
196	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
197	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
198	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
199	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
200	#529	—	2	8	no	—
201	#529	C₂²×C₇	1	16	yes	complemented
202	C₂×#126	—	2	2	no	—
203	C₂×#125	C₂²×C₇	1	2	yes	—
204	C₂×#124	C₂²×C₇	1	2	yes	—
205	C₂×#123	—	2	2	no	—
206	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
207	C₂×#121	C₂²×C₇	1	2	yes	—
208	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
209	C₂×C₄×D₄	—	2	2	no	—
210	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
211	C₂×#117	—	2	2	no	—
212	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
213	#499	C₂²×C₇	1	8	yes	complemented
214	#495	C₂²×C₇	1	8	yes	complemented
215	#488	C₂²×C₇	1	16	yes	complemented
216	#467	C₂²×C₇	1	8	yes	complemented
217	#466	C₂²×C₇	1	8	yes	—
218	#465	C₂²×C₇	1	16	yes	complemented
219	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
220	C₄×SD₁₆	C₂²×C₇	1	16	yes	complemented
221	C₄×D₈	C₂²×C₇	1	8	yes	complemented
222	C₂×#107	C₂²×C₇	1	1	yes	characteristic
223	C₂×#107	C₂²×C₇	1	1	yes	characteristic
224	C₂×#106	C₂²×C₇	1	2	yes	—
225	C₂×#103	C₂²×C₇	1	2	yes	—
226	C₂×#103	C₂²×C₇	1	2	yes	—
227	C₂×#102	C₂²×C₇	1	2	yes	—
228	C₂×#102	C₂²×C₇	1	2	yes	—
229	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
232	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₇	1	8	yes	complemented
234	C₂³×C₇	—	2	2	no	—
235	C₂³×C₇	—	2	2	no	—
236	C₂³×C₇	—	2	4	no	—
237	C₂³×C₇	—	4	4	no	—
238	C₂³×C₇	—	4	4	no	—
239	C₂³×C₇	—	4	4	no	—
240	C₂³×C₇	#135	1	4	yes	—
241	C₂³×C₇	C₂²×D₄	1	2	yes	—
242	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
243	C₇×Q₈	—	2	4	no	—
244	C₇×Q₈	—	2	4	no	—
245	C₇×Q₈	—	4	4	no	—
246	C₇×D₄	—	2	4	no	—
247	C₇×D₄	—	2	4	no	—
248	C₇×D₄	—	4	16	no	—
249	C₇×D₄	—	4	4	no	—
250	C₂×C₄×C₇	—	2	2	no	—
251	C₂×C₄×C₇	—	2	8	no	—
252	C₂×C₄×C₇	—	2	2	no	—
253	C₂×C₄×C₇	—	2	2	no	—
254	C₂×C₄×C₇	—	2	2	no	—
255	C₂×C₄×C₇	—	2	4	no	—
256	C₂×C₄×C₇	—	2	8	no	—
257	C₂×C₄×C₇	—	2	2	no	—
258	C₂×C₄×C₇	—	2	2	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	—	4	4	no	—
263	C₂×C₄×C₇	—	4	4	no	—
264	C₂×C₄×C₇	—	4	4	no	—
265	C₂×C₄×C₇	—	4	16	no	—
266	C₂×C₄×C₇	#135	1	4	yes	—
267	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₇	C₂×#41	1	2	yes	—
274	C₂×C₄×C₇	C₂×#41	1	2	yes	—
275	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
276	C₇×C₈	—	2	2	no	—
277	C₇×C₈	—	2	2	no	—
278	C₇×C₈	C₂×#41	1	4	yes	—
279	C₇×C₈	C₂×#41	1	4	yes	—
280	C₂²×Q₈	C₂³×C₇	1	2	yes	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	C₂³×C₇	1	2	yes	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
285	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
287	C₂×Q₁₆	—	2	4	no	—
288	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
289	C₂×SD₁₆	—	2	8	no	—
290	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
291	C₂×D₈	—	2	4	no	—
292	C₂×D₈	C₂³×C₇	1	4	yes	—
293	C₂²×C₈	—	2	4	no	—
294	C₂²×C₈	—	2	4	no	—
295	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₇	1	4	yes	—
298	C₂²×C₈	C₂³×C₇	1	4	yes	—
299	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
301	#126	—	2	16	no	—
302	#125	—	2	4	no	—
303	#125	C₂³×C₇	1	8	yes	—
304	#124	—	2	4	no	—
305	#124	C₂³×C₇	1	8	yes	—
306	#123	—	2	16	no	—
307	C₂²⋊Q₈	—	2	4	no	—
308	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
309	#121	—	2	4	no	—
310	#121	C₂³×C₇	1	8	yes	—
311	C₄×Q₈	—	2	4	no	—
312	C₄×Q₈	C₂³×C₇	1	8	yes	—
313	C₄×D₄	—	2	16	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	C₂³×C₇	1	8	yes	—
316	#117	—	2	16	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
330	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
331	C₂×C₄²	C₇×D₄	1	4	yes	—
332	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₇	1	4	yes	—
335	#107	C₂³×C₇	1	4	yes	—
336	#107	C₂³×C₇	1	4	yes	—
337	#106	C₂³×C₇	1	8	yes	—
338	#103	C₂³×C₇	1	8	yes	—
339	#103	C₂³×C₇	1	8	yes	—
340	#102	C₂³×C₇	1	8	yes	—
341	#102	C₂³×C₇	1	8	yes	—
342	C₄×C₈	C₂³×C₇	1	4	yes	—
343	C₄×C₈	C₂³×C₇	1	4	yes	—
344	C₄×C₈	C₂³×C₇	1	4	yes	—
345	C₄×C₈	C₂³×C₇	1	4	yes	—
346	C₂²×C₇	—	2	8	no	—
347	C₂²×C₇	—	2	2	no	—
348	C₂²×C₇	—	2	2	no	—
349	C₂²×C₇	—	4	4	no	—
350	C₂²×C₇	—	4	4	no	—
351	C₂²×C₇	—	4	4	no	—
352	C₂²×C₇	—	8	8	no	—
353	C₂²×C₇	#532	1	2	yes	—
354	C₂²×C₇	C₂×#135	1	4	yes	—
355	C₂²×C₇	C₂×#135	1	2	yes	—
356	C₂²×C₇	C₂×#135	1	2	yes	—
357	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
358	C₄×C₇	—	2	2	no	—
359	C₄×C₇	—	2	2	no	—
360	C₄×C₇	—	2	2	no	—
361	C₄×C₇	—	2	2	no	—
362	C₄×C₇	—	4	4	no	—
363	C₄×C₇	—	4	4	no	—
364	C₄×C₇	—	4	4	no	—
365	C₄×C₇	#532	1	2	yes	—
366	C₄×C₇	C₂×#135	1	4	yes	—
367	C₄×C₇	C₂²×#41	1	1	yes	characteristic
368	C₄×C₇	C₂²×#41	1	1	yes	characteristic
369	C₂⁴	—	2	2	no	—
370	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	4	8	no	—
380	C₂×D₄	C₂⁴×C₇	1	4	yes	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	4	8	no	—
390	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
392	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
393	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
396	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
397	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
400	Q₁₆	—	2	8	no	—
401	SD₁₆	—	2	16	no	—
402	D₈	—	2	8	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	8	no	—
406	C₂×C₈	—	2	8	no	—
407	C₂×C₈	C₇×#41	1	4	yes	—
408	C₂×C₈	C₇×#41	1	4	yes	—
409	C₂×C₈	C₂⁴×C₇	1	2	yes	—
410	C₂×C₈	C₂⁴×C₇	1	2	yes	—
411	C₂×C₈	C₂⁴×C₇	1	2	yes	—
412	C₂×C₈	C₂⁴×C₇	1	2	yes	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
420	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₄²	—	2	8	no	—
427	C₄²	C₂×C₇×D₄	1	4	yes	—
428	C₄²	C₂×C₇×D₄	1	2	yes	—
429	C₄²	C₂×C₇×D₄	1	2	yes	—
430	C₄²	C₂×C₇×D₄	1	4	yes	—
431	C₄²	C₂⁴×C₇	1	2	yes	—
432	C₄²	C₂⁴×C₇	1	2	yes	—
433	C₂×C₇	—	2	4	no	—
434	C₂×C₇	—	8	4	no	—
435	C₂×C₇	#3168	1	4	yes	direct product factor
436	C₂×C₇	C₂×#532	1	1	yes	characteristic
437	C₂×C₇	C₂²×#135	1	1	yes	characteristic
438	C₂×C₇	C₂²×#135	1	1	yes	characteristic
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	4	no	—
445	C₂³	C₇×#135	1	4	yes	—
446	C₂³	C₂²×C₇×D₄	1	2	yes	—
447	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
448	Q₈	—	2	4	no	—
449	Q₈	—	2	4	no	—
450	Q₈	—	4	4	no	—
451	D₄	—	2	4	no	—
452	D₄	—	2	4	no	—
453	D₄	—	4	16	no	—
454	D₄	—	4	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	16	no	—
471	C₂×C₄	C₇×#135	1	4	yes	—
472	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
473	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
474	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
475	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
476	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
478	C₂×C₄	C₂×C₇×#41	1	2	yes	—
479	C₂×C₄	C₂×C₇×#41	1	2	yes	—
480	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
481	C₈	—	2	2	no	—
482	C₈	—	2	2	no	—
483	C₈	C₂×C₇×#41	1	4	yes	—
484	C₈	C₂×C₇×#41	1	4	yes	—
485	C₇	C₂×#3168	1	1	yes	characteristic, direct product factor, Sylow
486	C₂²	—	2	8	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	8	8	no	—
493	C₂²	C₇×#532	1	2	yes	—
494	C₂²	C₂×C₇×#135	1	4	yes	—
495	C₂²	C₂×C₇×#135	1	2	yes	—
496	C₂²	C₂×C₇×#135	1	2	yes	—
497	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	4	no	—
505	C₄	C₇×#532	1	2	yes	—
506	C₄	C₂×C₇×#135	1	4	yes	—
507	C₄	C₂²×C₇×#41	1	1	yes	characteristic
508	C₄	C₂²×C₇×#41	1	1	yes	characteristic
509	C₂	—	2	4	no	—
510	C₂	—	8	4	no	—
511	C₂	C₇×#3168	1	4	yes	direct product factor
512	C₂	C₂×C₇×#532	1	1	yes	characteristic
513	C₂	C₂²×C₇×#135	1	1	yes	characteristic
514	C₂	C₂²×C₇×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂³×C₇	C₂²×D₄
prime radical	C₂×C₇×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#529	C₂	semidirect
2. C₇×#3168	C₂	direct (N × H)
3. C₂×C₇×#499	C₂	semidirect
4. C₂×C₇×#495	C₂	semidirect
5. C₂×C₇×#488	C₂	semidirect
6. C₂×C₇×#467	C₂	semidirect
8. C₂×C₇×#465	C₂	semidirect
9. C₂×C₄×C₇×Q₁₆	C₂	semidirect
10. C₂×C₄×C₇×SD₁₆	C₂	semidirect
11. C₂×C₄×C₇×D₈	C₂	semidirect
12. C₂²×C₄×C₇×C₈	C₂	semidirect
19. C₇×#529	C₂²	semidirect
31. C₇×#499	C₂²	semidirect
32. C₇×#495	C₂²	semidirect
33. C₇×#488	C₂²	semidirect
34. C₇×#467	C₂²	semidirect
36. C₇×#465	C₂²	semidirect
37. C₄×C₇×Q₁₆	C₂²	semidirect
38. C₄×C₇×SD₁₆	C₂²	semidirect
39. C₄×C₇×D₈	C₂²	semidirect
51. C₂×C₄×C₇×C₈	C₂²	semidirect
52. C₂×#3168	C₇	direct (N × H)
119. C₂×#529	C₂×C₇	semidirect
120. #3168	C₂×C₇	direct (N × H)
121. C₂×#499	C₂×C₇	semidirect
122. C₂×#495	C₂×C₇	semidirect
123. C₂×#488	C₂×C₇	semidirect
124. C₂×#467	C₂×C₇	semidirect
126. C₂×#465	C₂×C₇	semidirect
127. C₂×C₄×Q₁₆	C₂×C₇	semidirect
128. C₂×C₄×SD₁₆	C₂×C₇	semidirect
129. C₂×C₄×D₈	C₂×C₇	semidirect
130. C₂²×C₄×C₈	C₂×C₇	semidirect
201. #529	C₂²×C₇	semidirect
213. #499	C₂²×C₇	semidirect
214. #495	C₂²×C₇	semidirect
215. #488	C₂²×C₇	semidirect
216. #467	C₂²×C₇	semidirect
218. #465	C₂²×C₇	semidirect
219. C₄×Q₁₆	C₂²×C₇	semidirect
220. C₄×SD₁₆	C₂²×C₇	semidirect
221. C₄×D₈	C₂²×C₇	semidirect
233. C₂×C₄×C₈	C₂²×C₇	semidirect
435. C₂×C₇	#3168	direct (N × H)
485. C₇	C₂×#3168	direct (N × H)
511. C₂	C₇×#3168	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×#529	2
C₇×#3168	2
C₂×C₇×#499	2
C₂×C₇×#495	2
C₂×C₇×#488	2
C₂×C₇×#467	2
C₂×C₇×#466	2
C₂×C₇×#465	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₄×C₇×D₈	2
C₂²×C₄×C₇×C₈	2
C₂×#3168	7

Subgroups — C2×C7×#3168 #13237886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3168 #13237886