Subgroups — C₂×C₇×#2966 #13237414

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 522 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	1	yes	maximal, characteristic
2	C₇×#2966	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#435	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×C₈×D₄	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#433	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#405	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
14	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₂³×C₇×C₈	C₂²	1	2	yes	—
17	C₇×#529	C₄	1	8	yes	—
18	C₇×#529	C₂²	1	8	yes	—
19	C₂×C₇×#126	C₄	1	2	yes	—
20	C₂×C₇×#125	C₄	1	1	yes	characteristic
21	C₂×C₇×#124	C₄	1	1	yes	characteristic
22	C₂×C₇×#123	C₄	1	2	yes	—
23	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
24	C₂×C₇×#121	C₄	1	1	yes	characteristic
25	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
27	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₇×#117	C₂²	1	2	yes	—
29	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
30	C₇×#446	C₂²	1	8	yes	complemented
31	C₇×C₈×Q₈	C₂²	1	8	yes	complemented
32	C₇×#436	C₂²	1	8	yes	complemented
33	C₇×#435	C₂²	1	16	yes	complemented
34	C₇×C₈×D₄	C₂²	1	8	yes	complemented
35	C₇×C₈×D₄	C₂²	1	16	yes	complemented
36	C₇×#433	C₂²	1	16	yes	complemented
37	C₇×#432	C₂²	1	8	yes	complemented
38	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
41	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
42	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
44	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₇×#405	C₂²	1	16	yes	complemented
46	C₂×C₇×#97	C₂²	1	2	yes	—
47	C₂×C₇×#97	C₂²	1	2	yes	—
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	2	yes	—
52	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₇×C₈	C₂²	1	8	yes	complemented
54	C₂×#2966	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
57	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₇	C₂³	1	2	yes	—
62	C₂×C₇×M₁₆	—	2	8	no	—
63	C₂×C₇×M₁₆	C₂³	1	8	yes	—
64	C₂²×C₇×C₈	—	2	4	no	—
65	C₂²×C₇×C₈	—	2	8	no	—
66	C₂²×C₇×C₈	—	2	4	no	—
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	2	yes	—
70	C₂²×C₇×C₈	C₂³	1	4	yes	—
71	C₂²×C₇×C₈	C₂³	1	4	yes	—
72	C₂²×C₇×C₈	C₂³	1	2	yes	—
73	C₂²×C₇×C₈	C₂³	1	8	yes	—
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₇×#126	C₂×C₄	1	16	yes	—
77	C₇×#125	C₂×C₄	1	8	yes	—
78	C₇×#124	C₂×C₄	1	8	yes	—
79	C₇×#123	C₂×C₄	1	16	yes	—
80	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
81	C₇×#121	C₂×C₄	1	8	yes	—
82	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
83	C₄×C₇×Q₈	C₂³	1	4	yes	—
84	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
85	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
86	C₄×C₇×D₄	C₂³	1	8	yes	—
87	C₄×C₇×D₄	C₂³	1	4	yes	—
88	C₇×#117	C₂×C₄	1	8	yes	—
89	C₇×#117	C₂³	1	8	yes	—
90	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
91	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
92	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
94	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
96	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
97	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
98	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
99	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
100	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
101	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₇	C₂×C₄	1	4	yes	—
104	C₂×C₄²×C₇	C₂³	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	2	yes	—
108	C₇×C₄⋊C₈	C₂³	1	4	yes	—
109	C₇×C₄⋊C₈	C₂³	1	4	yes	—
110	C₇×C₄⋊C₈	C₂³	1	8	yes	—
111	C₇×C₄⋊C₈	C₂³	1	8	yes	—
112	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
113	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
114	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
115	C₇×#97	C₂³	1	8	yes	—
116	C₇×#97	C₂³	1	8	yes	—
117	C₄×C₇×C₈	C₂³	1	4	yes	—
118	C₄×C₇×C₈	C₂³	1	4	yes	—
119	C₄×C₇×C₈	C₂³	1	4	yes	—
120	C₄×C₇×C₈	C₂³	1	4	yes	—
121	C₄×C₇×C₈	C₂³	1	8	yes	—
122	C₂×#529	C₂×C₇	1	1	yes	characteristic
123	#2966	C₂×C₇	1	16	yes	direct product factor
124	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
125	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
126	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
127	C₂×#435	C₂×C₇	1	2	yes	complemented
128	C₂×C₈×D₄	C₂×C₇	1	2	yes	complemented
129	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂×#433	C₂×C₇	1	2	yes	complemented
131	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#405	C₂×C₇	1	2	yes	complemented
133	C₂²×C₄×C₈	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
135	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₇×Q₈	—	2	4	no	—
137	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
138	C₂×C₇×D₄	—	2	8	no	—
139	C₂×C₇×D₄	—	2	4	no	—
140	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
141	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
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	2	no	—
146	C₂²×C₄×C₇	—	2	4	no	—
147	C₂²×C₄×C₇	—	2	4	no	—
148	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
155	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
159	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
163	C₇×M₁₆	—	2	16	no	—
164	C₂×C₇×C₈	—	2	2	no	—
165	C₂×C₇×C₈	—	2	2	no	—
166	C₂×C₇×C₈	—	2	4	no	—
167	C₂×C₇×C₈	—	2	4	no	—
168	C₂×C₇×C₈	—	2	8	no	—
169	C₂×C₇×C₈	—	2	16	no	—
170	C₂×C₇×C₈	—	2	8	no	—
171	C₂×C₇×C₈	#41	1	4	yes	—
172	C₂×C₇×C₈	#41	1	4	yes	—
173	C₂×C₇×C₈	C₂⁴	1	2	yes	—
174	C₂×C₇×C₈	C₂⁴	1	2	yes	—
175	C₂×C₇×C₈	C₂⁴	1	4	yes	—
176	C₂×C₇×C₈	C₂⁴	1	4	yes	—
177	C₂×C₇×C₈	C₂⁴	1	2	yes	—
178	C₂×C₇×C₈	C₂⁴	1	2	yes	—
179	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
180	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
181	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
182	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
183	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
184	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
185	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
186	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
187	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
188	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
189	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
190	C₄²×C₇	C₂²×C₄	1	2	yes	—
191	C₄²×C₇	C₂²×C₄	1	2	yes	—
192	C₄²×C₇	C₂²×C₄	1	4	yes	—
193	C₄²×C₇	C₂²×C₄	1	4	yes	—
194	C₄²×C₇	C₂²×C₄	1	4	yes	—
195	C₄²×C₇	C₂⁴	1	2	yes	—
196	C₄²×C₇	C₂⁴	1	2	yes	—
197	C₄²×C₇	C₂⁴	1	4	yes	—
198	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
199	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
200	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
201	C₂³×C₈	C₂²×C₇	1	2	yes	—
202	#529	C₄×C₇	1	8	yes	—
203	#529	C₂²×C₇	1	8	yes	—
204	C₂×#126	C₄×C₇	1	2	yes	—
205	C₂×#125	C₄×C₇	1	1	yes	characteristic
206	C₂×#124	C₄×C₇	1	1	yes	characteristic
207	C₂×#123	C₄×C₇	1	2	yes	—
208	C₂×C₂²⋊Q₈	C₄×C₇	1	1	yes	characteristic
209	C₂×#121	C₄×C₇	1	1	yes	characteristic
210	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
212	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
213	C₂×#117	C₂²×C₇	1	2	yes	—
214	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
215	#446	C₂²×C₇	1	8	yes	complemented
216	C₈×Q₈	C₂²×C₇	1	8	yes	complemented
217	#436	C₂²×C₇	1	8	yes	complemented
218	#435	C₂²×C₇	1	16	yes	complemented
219	C₈×D₄	C₂²×C₇	1	8	yes	complemented
220	C₈×D₄	C₂²×C₇	1	16	yes	complemented
221	#433	C₂²×C₇	1	16	yes	complemented
222	#432	C₂²×C₇	1	8	yes	complemented
223	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
226	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
229	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
230	#405	C₂²×C₇	1	16	yes	complemented
231	C₂×#97	C₂²×C₇	1	2	yes	—
232	C₂×#97	C₂²×C₇	1	2	yes	—
233	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
238	C₂×C₄×C₈	C₂²×C₇	1	8	yes	complemented
239	C₂³×C₇	—	2	2	no	—
240	C₂³×C₇	—	2	2	no	—
241	C₂³×C₇	—	2	4	no	—
242	C₂³×C₇	—	2	4	no	—
243	C₂³×C₇	—	2	4	no	—
244	C₂³×C₇	#131	1	4	yes	—
245	C₂³×C₇	C₂³×C₄	1	4	yes	—
246	C₂³×C₇	C₂³×C₄	1	2	yes	—
247	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
248	C₇×Q₈	—	2	8	no	—
249	C₇×D₄	—	2	16	no	—
250	C₇×D₄	—	2	8	no	—
251	C₂×C₄×C₇	—	2	2	no	—
252	C₂×C₄×C₇	—	2	4	no	—
253	C₂×C₄×C₇	—	2	8	no	—
254	C₂×C₄×C₇	—	2	2	no	—
255	C₂×C₄×C₇	—	2	2	no	—
256	C₂×C₄×C₇	—	2	2	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	8	no	—
261	C₂×C₄×C₇	—	2	8	no	—
262	C₂×C₄×C₇	—	2	2	no	—
263	C₂×C₄×C₇	—	2	2	no	—
264	C₂×C₄×C₇	—	2	4	no	—
265	C₂×C₄×C₇	—	2	4	no	—
266	C₂×C₄×C₇	#131	1	4	yes	—
267	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
268	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
271	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
272	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
273	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
274	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
275	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
276	C₂×C₄×C₇	C₂×#41	1	2	yes	—
277	C₂×C₄×C₇	C₂×#41	1	2	yes	—
278	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
279	C₇×C₈	—	2	2	no	—
280	C₇×C₈	—	2	2	no	—
281	C₇×C₈	—	2	4	no	—
282	C₇×C₈	—	2	4	no	—
283	C₇×C₈	C₂×#41	1	4	yes	—
284	C₇×C₈	C₂×#41	1	4	yes	—
285	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
286	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
287	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
288	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
289	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₇	1	2	yes	—
291	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
292	C₂×M₁₆	—	2	8	no	—
293	C₂×M₁₆	C₂³×C₇	1	8	yes	—
294	C₂²×C₈	—	2	4	no	—
295	C₂²×C₈	—	2	8	no	—
296	C₂²×C₈	—	2	4	no	—
297	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₇	1	4	yes	—
300	C₂²×C₈	C₂³×C₇	1	4	yes	—
301	C₂²×C₈	C₂³×C₇	1	2	yes	—
302	C₂²×C₈	C₂³×C₇	1	8	yes	—
303	C₂²×C₈	C₂³×C₇	1	2	yes	—
304	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
306	#126	C₂×C₄×C₇	1	16	yes	—
307	#125	C₂×C₄×C₇	1	8	yes	—
308	#124	C₂×C₄×C₇	1	8	yes	—
309	#123	C₂×C₄×C₇	1	16	yes	—
310	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
311	#121	C₂×C₄×C₇	1	8	yes	—
312	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
313	C₄×Q₈	C₂³×C₇	1	4	yes	—
314	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
315	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
316	C₄×D₄	C₂³×C₇	1	8	yes	—
317	C₄×D₄	C₂³×C₇	1	4	yes	—
318	#117	C₂×C₄×C₇	1	8	yes	—
319	#117	C₂³×C₇	1	8	yes	—
320	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
321	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
322	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
324	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
326	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
330	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
331	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
332	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
333	C₂×C₄²	C₂×C₄×C₇	1	4	yes	—
334	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₇	1	2	yes	—
336	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₇	1	4	yes	—
338	C₄⋊C₈	C₂³×C₇	1	4	yes	—
339	C₄⋊C₈	C₂³×C₇	1	4	yes	—
340	C₄⋊C₈	C₂³×C₇	1	8	yes	—
341	C₄⋊C₈	C₂³×C₇	1	8	yes	—
342	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
343	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
344	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
345	#97	C₂³×C₇	1	8	yes	—
346	#97	C₂³×C₇	1	8	yes	—
347	C₄×C₈	C₂³×C₇	1	4	yes	—
348	C₄×C₈	C₂³×C₇	1	4	yes	—
349	C₄×C₈	C₂³×C₇	1	4	yes	—
350	C₄×C₈	C₂³×C₇	1	4	yes	—
351	C₄×C₈	C₂³×C₇	1	8	yes	—
352	C₂²×C₇	—	2	2	no	—
353	C₂²×C₇	—	2	8	no	—
354	C₂²×C₇	—	2	2	no	—
355	C₂²×C₇	—	2	4	no	—
356	C₂²×C₇	—	2	4	no	—
357	C₂²×C₇	—	2	4	no	—
358	C₂²×C₇	—	4	8	no	—
359	C₂²×C₇	C₄×#41	1	2	yes	—
360	C₂²×C₇	C₂×#131	1	4	yes	—
361	C₂²×C₇	C₂×#131	1	2	yes	—
362	C₂²×C₇	C₂×#131	1	2	yes	—
363	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
364	C₄×C₇	—	2	2	no	—
365	C₄×C₇	—	2	4	no	—
366	C₄×C₇	—	2	2	no	—
367	C₄×C₇	—	2	2	no	—
368	C₄×C₇	—	2	2	no	—
369	C₄×C₇	—	2	4	no	—
370	C₄×C₇	—	2	4	no	—
371	C₄×C₇	C₄×#41	1	2	yes	—
372	C₄×C₇	C₂×#131	1	4	yes	—
373	C₄×C₇	C₂²×#41	1	1	yes	characteristic
374	C₄×C₇	C₂²×#41	1	1	yes	characteristic
375	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
376	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
377	C₂×Q₈	—	2	4	no	—
378	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
382	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	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	C₂²×C₄×C₇	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
391	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
395	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
396	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
397	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
398	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
399	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
400	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
404	M₁₆	—	2	16	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	4	no	—
408	C₂×C₈	—	2	4	no	—
409	C₂×C₈	—	2	8	no	—
410	C₂×C₈	—	2	16	no	—
411	C₂×C₈	—	2	8	no	—
412	C₂×C₈	C₇×#41	1	4	yes	—
413	C₂×C₈	C₇×#41	1	4	yes	—
414	C₂×C₈	C₂⁴×C₇	1	2	yes	—
415	C₂×C₈	C₂⁴×C₇	1	2	yes	—
416	C₂×C₈	C₂⁴×C₇	1	4	yes	—
417	C₂×C₈	C₂⁴×C₇	1	4	yes	—
418	C₂×C₈	C₂⁴×C₇	1	2	yes	—
419	C₂×C₈	C₂⁴×C₇	1	2	yes	—
420	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
421	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
422	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
423	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
424	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
425	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
426	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
427	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
428	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
429	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
430	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
431	C₄²	C₂²×C₄×C₇	1	2	yes	—
432	C₄²	C₂²×C₄×C₇	1	2	yes	—
433	C₄²	C₂²×C₄×C₇	1	4	yes	—
434	C₄²	C₂²×C₄×C₇	1	4	yes	—
435	C₄²	C₂²×C₄×C₇	1	4	yes	—
436	C₄²	C₂⁴×C₇	1	2	yes	—
437	C₄²	C₂⁴×C₇	1	2	yes	—
438	C₄²	C₂⁴×C₇	1	4	yes	—
439	C₂×C₇	—	2	4	no	—
440	C₂×C₇	—	4	4	no	—
441	C₂×C₇	#2966	1	4	yes	direct product factor
442	C₂×C₇	C₂×C₄×#41	1	1	yes	characteristic
443	C₂×C₇	C₂²×#131	1	1	yes	characteristic
444	C₂×C₇	C₂²×#131	1	1	yes	characteristic
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	4	no	—
450	C₂³	C₇×#131	1	4	yes	—
451	C₂³	C₂³×C₄×C₇	1	4	yes	—
452	C₂³	C₂³×C₄×C₇	1	2	yes	—
453	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
454	Q₈	—	2	8	no	—
455	D₄	—	2	16	no	—
456	D₄	—	2	8	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	C₇×#131	1	4	yes	—
473	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
474	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
475	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
476	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
477	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
478	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
479	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
480	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
481	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
482	C₂×C₄	C₂×C₇×#41	1	2	yes	—
483	C₂×C₄	C₂×C₇×#41	1	2	yes	—
484	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
485	C₈	—	2	2	no	—
486	C₈	—	2	2	no	—
487	C₈	—	2	4	no	—
488	C₈	—	2	4	no	—
489	C₈	C₂×C₇×#41	1	4	yes	—
490	C₈	C₂×C₇×#41	1	4	yes	—
491	C₇	C₂×#2966	1	1	yes	characteristic, direct product factor, Sylow
492	C₂²	—	2	2	no	—
493	C₂²	—	2	8	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	4	8	no	—
499	C₂²	C₄×C₇×#41	1	2	yes	—
500	C₂²	C₂×C₇×#131	1	4	yes	—
501	C₂²	C₂×C₇×#131	1	2	yes	—
502	C₂²	C₂×C₇×#131	1	2	yes	—
503	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	4	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	4	no	—
511	C₄	C₄×C₇×#41	1	2	yes	—
512	C₄	C₂×C₇×#131	1	4	yes	—
513	C₄	C₂²×C₇×#41	1	1	yes	characteristic
514	C₄	C₂²×C₇×#41	1	1	yes	characteristic
515	C₂	—	2	4	no	—
516	C₂	—	4	4	no	—
517	C₂	C₇×#2966	1	4	yes	direct product factor
518	C₂	C₂×C₄×C₇×#41	1	1	yes	characteristic
519	C₂	C₂²×C₇×#131	1	1	yes	characteristic
520	C₂	C₂²×C₇×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₇×C₈	C₂³
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂×C₇×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2966	C₂	direct (N × H)
3. C₂×C₇×#446	C₂	semidirect
4. C₂×C₇×C₈×Q₈	C₂	semidirect
5. C₂×C₇×#436	C₂	semidirect
6. C₂×C₇×#435	C₂	semidirect
7. C₂×C₇×C₈×D₄	C₂	semidirect
8. C₂×C₇×C₈×D₄	C₂	semidirect
9. C₂×C₇×#433	C₂	semidirect
10. C₂×C₇×#432	C₂	semidirect
11. C₂×C₇×#405	C₂	semidirect
12. C₂²×C₄×C₇×C₈	C₂	semidirect
30. C₇×#446	C₂²	semidirect
31. C₇×C₈×Q₈	C₂²	semidirect
32. C₇×#436	C₂²	semidirect
33. C₇×#435	C₂²	semidirect
34. C₇×C₈×D₄	C₂²	semidirect
35. C₇×C₈×D₄	C₂²	semidirect
36. C₇×#433	C₂²	semidirect
37. C₇×#432	C₂²	semidirect
45. C₇×#405	C₂²	semidirect
53. C₂×C₄×C₇×C₈	C₂²	semidirect
54. C₂×#2966	C₇	direct (N × H)
123. #2966	C₂×C₇	direct (N × H)
124. C₂×#446	C₂×C₇	semidirect
125. C₂×C₈×Q₈	C₂×C₇	semidirect
126. C₂×#436	C₂×C₇	semidirect
127. C₂×#435	C₂×C₇	semidirect
128. C₂×C₈×D₄	C₂×C₇	semidirect
129. C₂×C₈×D₄	C₂×C₇	semidirect
130. C₂×#433	C₂×C₇	semidirect
131. C₂×#432	C₂×C₇	semidirect
132. C₂×#405	C₂×C₇	semidirect
133. C₂²×C₄×C₈	C₂×C₇	semidirect
215. #446	C₂²×C₇	semidirect
216. C₈×Q₈	C₂²×C₇	semidirect
217. #436	C₂²×C₇	semidirect
218. #435	C₂²×C₇	semidirect
219. C₈×D₄	C₂²×C₇	semidirect
220. C₈×D₄	C₂²×C₇	semidirect
221. #433	C₂²×C₇	semidirect
222. #432	C₂²×C₇	semidirect
230. #405	C₂²×C₇	semidirect
238. C₂×C₄×C₈	C₂²×C₇	semidirect
441. C₂×C₇	#2966	direct (N × H)
491. C₇	C₂×#2966	direct (N × H)
517. C₂	C₇×#2966	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×#2966	2
C₂×C₇×#446	2
C₂×C₇×C₈×Q₈	2
C₂×C₇×#436	2
C₂×C₇×#435	2
C₂×C₇×C₈×D₄	2
C₂×C₇×#433	2
C₂×C₇×#432	2
C₂×C₇×#405	2
C₂²×C₄×C₇×C₈	2
C₂×#2966	7

Subgroups — C2×C7×#2966 #13237414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2966 #13237414