Subgroups — C₂×C₇×#2993 #13237476

Order 1792.

1926 conjugacy classes of subgroups.

The subgroup lattice has 518 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×#2993	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×#436	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#435	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×#431	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#424	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
14	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
15	C₂³×C₇×C₈	C₂²	1	2	yes	—
16	C₇×#529	C₄	1	8	yes	—
17	C₇×#529	C₂²	1	8	yes	—
18	C₂×C₇×#126	C₄	1	2	yes	—
19	C₂×C₇×#125	C₄	1	1	yes	characteristic
20	C₂×C₇×#124	C₄	1	1	yes	characteristic
21	C₂×C₇×#123	C₄	1	2	yes	—
22	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
23	C₂×C₇×#121	C₄	1	1	yes	characteristic
24	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
27	C₂×C₇×#117	C₂²	1	2	yes	—
28	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
29	C₇×#446	C₂²	1	8	yes	complemented
30	C₇×C₈×Q₈	C₂²	1	8	yes	complemented
31	C₇×#436	C₂²	1	8	yes	complemented
32	C₇×#436	C₂²	1	16	yes	complemented
33	C₇×#435	C₂²	1	16	yes	complemented
34	C₇×C₈×D₄	C₂²	1	8	yes	complemented
35	C₇×#433	C₂²	1	16	yes	complemented
36	C₇×#431	C₂²	1	8	yes	complemented
37	C₇×#424	C₂²	1	16	yes	complemented
38	C₇×#423	C₂²	1	8	yes	complemented
39	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
44	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
45	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
49	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
50	C₂×C₇×#97	C₂²	1	2	yes	—
51	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
54	C₂×#2993	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	1	yes	characteristic
57	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
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	—	4	4	no	—
63	C₂×C₇×M₁₆	—	4	4	no	—
64	C₂×C₇×M₁₆	C₂³	1	8	yes	—
65	C₂×C₇×M₁₆	C₂³	1	8	yes	—
66	C₂²×C₇×C₈	—	4	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	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂³	1	2	yes	—
72	C₂²×C₇×C₈	C₂³	1	2	yes	—
73	C₂²×C₇×C₈	C₂³	1	8	yes	—
74	C₇×#126	C₂×C₄	1	16	yes	—
75	C₇×#125	C₂×C₄	1	8	yes	—
76	C₇×#124	C₂×C₄	1	8	yes	—
77	C₇×#123	C₂×C₄	1	16	yes	—
78	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
79	C₇×#121	C₂×C₄	1	8	yes	—
80	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
81	C₄×C₇×Q₈	C₂³	1	4	yes	—
82	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
83	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
84	C₄×C₇×D₄	C₂³	1	4	yes	—
85	C₄×C₇×D₄	C₂³	1	8	yes	—
86	C₇×#117	C₂×C₄	1	8	yes	—
87	C₇×#117	C₂³	1	8	yes	—
88	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
89	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
90	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊C₄	C₂×C₄	1	2	yes	—
95	C₂×C₇×C₂²⋊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×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₇	C₂×C₄	1	4	yes	—
102	C₂×C₄²×C₇	C₂³	1	4	yes	—
103	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₇	C₂³	1	2	yes	—
106	C₇×C₄⋊C₈	C₂³	1	8	yes	—
107	C₇×C₄⋊C₈	C₂³	1	4	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×C₄⋊C₈	C₂³	1	4	yes	—
113	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
114	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
115	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
116	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
117	C₇×#97	C₂³	1	8	yes	—
118	C₄×C₇×C₈	C₂³	1	4	yes	—
119	C₄×C₇×C₈	C₂³	1	4	yes	—
120	C₄×C₇×C₈	C₂³	1	8	yes	—
121	C₂×#529	C₂×C₇	1	1	yes	characteristic
122	#2993	C₂×C₇	1	16	yes	direct product factor
123	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
124	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
125	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
126	C₂×#436	C₂×C₇	1	2	yes	complemented
127	C₂×#435	C₂×C₇	1	2	yes	complemented
128	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
129	C₂×#433	C₂×C₇	1	2	yes	complemented
130	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂×#424	C₂×C₇	1	2	yes	complemented
132	C₂×#423	C₂×C₇	1	1	yes	characteristic, complemented
133	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
134	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₇×Q₈	—	2	4	no	—
136	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
137	C₂×C₇×D₄	—	2	4	no	—
138	C₂×C₇×D₄	—	4	4	no	—
139	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
140	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
141	C₂²×C₄×C₇	—	2	4	no	—
142	C₂²×C₄×C₇	—	2	4	no	—
143	C₂²×C₄×C₇	—	2	2	no	—
144	C₂²×C₄×C₇	—	2	2	no	—
145	C₂²×C₄×C₇	—	2	4	no	—
146	C₂²×C₄×C₇	—	4	2	no	—
147	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
153	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
158	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
162	C₇×M₁₆	—	4	8	no	—
163	C₇×M₁₆	—	4	8	no	—
164	C₂×C₇×C₈	—	2	2	no	—
165	C₂×C₇×C₈	—	2	4	no	—
166	C₂×C₇×C₈	—	2	2	no	—
167	C₂×C₇×C₈	—	2	4	no	—
168	C₂×C₇×C₈	—	2	2	no	—
169	C₂×C₇×C₈	—	2	2	no	—
170	C₂×C₇×C₈	—	4	8	no	—
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	C₂×C₇×C₈	C₂⁴	1	4	yes	—
176	C₂×C₇×C₈	C₂⁴	1	4	yes	—
177	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
178	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
179	C₇×C₄⋊C₄	C₂²×C₄	1	4	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×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
184	C₇×C₂²⋊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	C₄²×C₇	C₂²×C₄	1	2	yes	—
189	C₄²×C₇	C₂²×C₄	1	2	yes	—
190	C₄²×C₇	C₂²×C₄	1	4	yes	—
191	C₄²×C₇	C₂²×C₄	1	4	yes	—
192	C₄²×C₇	C₂²×C₄	1	4	yes	—
193	C₄²×C₇	C₂⁴	1	2	yes	—
194	C₄²×C₇	C₂⁴	1	4	yes	—
195	C₄²×C₇	C₂⁴	1	2	yes	—
196	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
197	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
198	C₂³×C₈	C₂²×C₇	1	2	yes	—
199	#529	C₄×C₇	1	8	yes	—
200	#529	C₂²×C₇	1	8	yes	—
201	C₂×#126	C₄×C₇	1	2	yes	—
202	C₂×#125	C₄×C₇	1	1	yes	characteristic
203	C₂×#124	C₄×C₇	1	1	yes	characteristic
204	C₂×#123	C₄×C₇	1	2	yes	—
205	C₂×C₂²⋊Q₈	C₄×C₇	1	1	yes	characteristic
206	C₂×#121	C₄×C₇	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
209	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
210	C₂×#117	C₂²×C₇	1	2	yes	—
211	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
212	#446	C₂²×C₇	1	8	yes	complemented
213	C₈×Q₈	C₂²×C₇	1	8	yes	complemented
214	#436	C₂²×C₇	1	8	yes	complemented
215	#436	C₂²×C₇	1	16	yes	complemented
216	#435	C₂²×C₇	1	16	yes	complemented
217	C₈×D₄	C₂²×C₇	1	8	yes	complemented
218	#433	C₂²×C₇	1	16	yes	complemented
219	#431	C₂²×C₇	1	8	yes	complemented
220	#424	C₂²×C₇	1	16	yes	complemented
221	#423	C₂²×C₇	1	8	yes	complemented
222	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
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	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
227	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
228	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
229	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
230	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
231	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
233	C₂×#97	C₂²×C₇	1	2	yes	—
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	2	yes	—
237	C₂³×C₇	—	2	4	no	—
238	C₂³×C₇	—	2	2	no	—
239	C₂³×C₇	—	2	2	no	—
240	C₂³×C₇	—	2	4	no	—
241	C₂³×C₇	—	2	2	no	—
242	C₂³×C₇	—	2	4	no	—
243	C₂³×C₇	C₂³×C₄	1	4	yes	—
244	C₂³×C₇	C₂³×C₄	1	2	yes	—
245	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
246	C₇×Q₈	—	2	8	no	—
247	C₇×D₄	—	2	8	no	—
248	C₇×D₄	—	4	8	no	—
249	C₂×C₄×C₇	—	2	4	no	—
250	C₂×C₄×C₇	—	2	2	no	—
251	C₂×C₄×C₇	—	2	2	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	4	no	—
256	C₂×C₄×C₇	—	2	8	no	—
257	C₂×C₄×C₇	—	2	4	no	—
258	C₂×C₄×C₇	—	2	8	no	—
259	C₂×C₄×C₇	—	2	4	no	—
260	C₂×C₄×C₇	—	2	2	no	—
261	C₂×C₄×C₇	—	2	2	no	—
262	C₂×C₄×C₇	—	2	4	no	—
263	C₂×C₄×C₇	—	4	4	no	—
264	C₂×C₄×C₇	#131	1	4	yes	—
265	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
266	C₂×C₄×C₇	C₂³×C₄	1	2	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	4	yes	—
270	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
271	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
272	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
274	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
275	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
276	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
277	C₇×C₈	—	2	2	no	—
278	C₇×C₈	—	2	4	no	—
279	C₇×C₈	—	2	2	no	—
280	C₇×C₈	—	2	4	no	—
281	C₇×C₈	—	2	2	no	—
282	C₇×C₈	—	2	2	no	—
283	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
284	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
285	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
286	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
287	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₇	1	2	yes	—
289	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
290	C₂×M₁₆	—	4	4	no	—
291	C₂×M₁₆	—	4	4	no	—
292	C₂×M₁₆	C₂³×C₇	1	8	yes	—
293	C₂×M₁₆	C₂³×C₇	1	8	yes	—
294	C₂²×C₈	—	4	4	no	—
295	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₇	1	2	yes	—
297	C₂²×C₈	C₂³×C₇	1	2	yes	—
298	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₇	1	8	yes	—
302	#126	C₂×C₄×C₇	1	16	yes	—
303	#125	C₂×C₄×C₇	1	8	yes	—
304	#124	C₂×C₄×C₇	1	8	yes	—
305	#123	C₂×C₄×C₇	1	16	yes	—
306	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
307	#121	C₂×C₄×C₇	1	8	yes	—
308	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
309	C₄×Q₈	C₂³×C₇	1	4	yes	—
310	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
311	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
312	C₄×D₄	C₂³×C₇	1	4	yes	—
313	C₄×D₄	C₂³×C₇	1	8	yes	—
314	#117	C₂×C₄×C₇	1	8	yes	—
315	#117	C₂³×C₇	1	8	yes	—
316	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
317	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
318	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
320	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
322	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
323	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
326	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
327	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
328	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
329	C₂×C₄²	C₂×C₄×C₇	1	4	yes	—
330	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₇	1	2	yes	—
332	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₇	1	4	yes	—
334	C₄⋊C₈	C₂³×C₇	1	8	yes	—
335	C₄⋊C₈	C₂³×C₇	1	4	yes	—
336	C₄⋊C₈	C₂³×C₇	1	4	yes	—
337	C₄⋊C₈	C₂³×C₇	1	4	yes	—
338	C₄⋊C₈	C₂³×C₇	1	8	yes	—
339	C₄⋊C₈	C₂³×C₇	1	8	yes	—
340	C₄⋊C₈	C₂³×C₇	1	4	yes	—
341	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
342	C₂²⋊C₈	C₂³×C₇	1	4	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	C₄×C₈	C₂³×C₇	1	4	yes	—
347	C₄×C₈	C₂³×C₇	1	4	yes	—
348	C₄×C₈	C₂³×C₇	1	8	yes	—
349	C₂²×C₇	—	2	4	no	—
350	C₂²×C₇	—	2	2	no	—
351	C₂²×C₇	—	2	2	no	—
352	C₂²×C₇	—	2	4	no	—
353	C₂²×C₇	—	2	2	no	—
354	C₂²×C₇	—	2	4	no	—
355	C₂²×C₇	—	4	4	no	—
356	C₂²×C₇	—	4	8	no	—
357	C₂²×C₇	#520	1	2	yes	—
358	C₂²×C₇	C₂×#131	1	2	yes	—
359	C₂²×C₇	#568	1	2	yes	—
360	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
361	C₄×C₇	—	2	4	no	—
362	C₄×C₇	—	2	2	no	—
363	C₄×C₇	—	2	2	no	—
364	C₄×C₇	—	2	4	no	—
365	C₄×C₇	—	2	2	no	—
366	C₄×C₇	—	2	2	no	—
367	C₄×C₇	—	2	4	no	—
368	C₄×C₇	#520	1	2	yes	—
369	C₄×C₇	C₂×#131	1	4	yes	—
370	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
371	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
372	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
373	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
379	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
388	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
392	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
393	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
394	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
395	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
396	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
397	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
401	M₁₆	—	4	8	no	—
402	M₁₆	—	4	8	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	4	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	4	8	no	—
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	C₂×C₈	C₂⁴×C₇	1	2	yes	—
414	C₂×C₈	C₂⁴×C₇	1	4	yes	—
415	C₂×C₈	C₂⁴×C₇	1	4	yes	—
416	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
417	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
418	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
419	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
420	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
421	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
422	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
423	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
424	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
425	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
426	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
427	C₄²	C₂²×C₄×C₇	1	2	yes	—
428	C₄²	C₂²×C₄×C₇	1	2	yes	—
429	C₄²	C₂²×C₄×C₇	1	4	yes	—
430	C₄²	C₂²×C₄×C₇	1	4	yes	—
431	C₄²	C₂²×C₄×C₇	1	4	yes	—
432	C₄²	C₂⁴×C₇	1	2	yes	—
433	C₄²	C₂⁴×C₇	1	4	yes	—
434	C₄²	C₂⁴×C₇	1	2	yes	—
435	C₂×C₇	—	4	2	no	—
436	C₂×C₇	—	4	4	no	—
437	C₂×C₇	#2993	1	4	yes	direct product factor
438	C₂×C₇	C₂×#520	1	1	yes	characteristic
439	C₂×C₇	C₂²×#131	1	1	yes	characteristic
440	C₂×C₇	C₂×#568	1	1	yes	characteristic
441	C₂³	—	2	4	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	4	no	—
447	C₂³	C₂³×C₄×C₇	1	4	yes	—
448	C₂³	C₂³×C₄×C₇	1	2	yes	—
449	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
450	Q₈	—	2	8	no	—
451	D₄	—	2	8	no	—
452	D₄	—	4	8	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	C₇×#131	1	4	yes	—
469	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
470	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
471	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
472	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
473	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
474	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
475	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
476	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
477	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
478	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
479	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
480	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
481	C₈	—	2	2	no	—
482	C₈	—	2	4	no	—
483	C₈	—	2	2	no	—
484	C₈	—	2	4	no	—
485	C₈	—	2	2	no	—
486	C₈	—	2	2	no	—
487	C₇	C₂×#2993	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	2	2	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	8	no	—
496	C₂²	C₇×#520	1	2	yes	—
497	C₂²	C₂×C₇×#131	1	2	yes	—
498	C₂²	C₇×#568	1	2	yes	—
499	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	4	no	—
505	C₄	—	2	4	no	—
506	C₄	—	2	2	no	—
507	C₄	C₇×#520	1	2	yes	—
508	C₄	C₂×C₇×#131	1	4	yes	—
509	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
510	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
511	C₂	—	4	2	no	—
512	C₂	—	4	4	no	—
513	C₂	C₇×#2993	1	4	yes	direct product factor
514	C₂	C₂×C₇×#520	1	1	yes	characteristic
515	C₂	C₂²×C₇×#131	1	1	yes	characteristic
516	C₂	C₂×C₇×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
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×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2993	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×#436	C₂	semidirect
7. C₂×C₇×#435	C₂	semidirect
8. C₂×C₇×C₈×D₄	C₂	semidirect
9. C₂×C₇×#433	C₂	semidirect
10. C₂×C₇×#431	C₂	semidirect
11. C₂×C₇×#424	C₂	semidirect
12. C₂×C₇×#423	C₂	semidirect
29. C₇×#446	C₂²	semidirect
30. C₇×C₈×Q₈	C₂²	semidirect
31. C₇×#436	C₂²	semidirect
32. C₇×#436	C₂²	semidirect
33. C₇×#435	C₂²	semidirect
34. C₇×C₈×D₄	C₂²	semidirect
35. C₇×#433	C₂²	semidirect
36. C₇×#431	C₂²	semidirect
37. C₇×#424	C₂²	semidirect
38. C₇×#423	C₂²	semidirect
54. C₂×#2993	C₇	direct (N × H)
122. #2993	C₂×C₇	direct (N × H)
123. C₂×#446	C₂×C₇	semidirect
124. C₂×C₈×Q₈	C₂×C₇	semidirect
125. C₂×#436	C₂×C₇	semidirect
126. C₂×#436	C₂×C₇	semidirect
127. C₂×#435	C₂×C₇	semidirect
128. C₂×C₈×D₄	C₂×C₇	semidirect
129. C₂×#433	C₂×C₇	semidirect
130. C₂×#431	C₂×C₇	semidirect
131. C₂×#424	C₂×C₇	semidirect
132. C₂×#423	C₂×C₇	semidirect
212. #446	C₂²×C₇	semidirect
213. C₈×Q₈	C₂²×C₇	semidirect
214. #436	C₂²×C₇	semidirect
215. #436	C₂²×C₇	semidirect
216. #435	C₂²×C₇	semidirect
217. C₈×D₄	C₂²×C₇	semidirect
218. #433	C₂²×C₇	semidirect
219. #431	C₂²×C₇	semidirect
220. #424	C₂²×C₇	semidirect
221. #423	C₂²×C₇	semidirect
437. C₂×C₇	#2993	direct (N × H)
487. C₇	C₂×#2993	direct (N × H)
513. C₂	C₇×#2993	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×#2993	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×#431	2
C₂×C₇×#424	2
C₂×C₇×#423	2
C₂×#2993	7

Subgroups — C2×C7×#2993 #13237476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2993 #13237476