Subgroups — C₂×C₇×#2995 #13237478

Order 1792.

1882 conjugacy classes of subgroups.

The subgroup lattice has 490 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×#2995	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#446	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#436	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#435	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#435	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#433	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#424	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
14	C₂³×C₇×C₈	C₂²	1	2	yes	—
15	C₇×#529	C₄	1	8	yes	—
16	C₇×#529	C₂²	1	8	yes	—
17	C₂×C₇×#126	C₄	1	2	yes	—
18	C₂×C₇×#125	C₄	1	1	yes	characteristic
19	C₂×C₇×#124	C₄	1	1	yes	characteristic
20	C₂×C₇×#123	C₄	1	2	yes	—
21	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
22	C₂×C₇×#121	C₄	1	1	yes	characteristic
23	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
26	C₂×C₇×#117	C₂²	1	2	yes	—
27	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
28	C₇×#446	C₂²	1	16	yes	complemented
29	C₇×#436	C₂²	1	16	yes	complemented
30	C₇×#435	C₂²	1	16	yes	complemented
31	C₇×#435	C₂²	1	16	yes	complemented
32	C₇×#433	C₂²	1	16	yes	complemented
33	C₇×#432	C₂²	1	8	yes	complemented
34	C₇×#424	C₂²	1	16	yes	complemented
35	C₇×#423	C₂²	1	8	yes	complemented
36	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
37	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
38	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
41	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
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	C₂×C₇×#97	C₂²	1	2	yes	—
46	C₂×C₇×#97	C₂²	1	2	yes	—
47	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
48	C₂×#2995	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
51	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₇	C₂³	1	2	yes	—
56	C₂×C₇×M₁₆	—	4	2	no	—
57	C₂×C₇×M₁₆	—	4	4	no	—
58	C₂×C₇×M₁₆	—	4	2	no	—
59	C₂×C₇×M₁₆	C₂³	1	4	yes	—
60	C₂×C₇×M₁₆	C₂³	1	4	yes	—
61	C₂×C₇×M₁₆	C₂³	1	8	yes	—
62	C₂²×C₇×C₈	—	4	4	no	—
63	C₂²×C₇×C₈	C₂³	1	2	yes	—
64	C₂²×C₇×C₈	C₂³	1	2	yes	—
65	C₂²×C₇×C₈	C₂³	1	2	yes	—
66	C₂²×C₇×C₈	C₂³	1	2	yes	—
67	C₂²×C₇×C₈	C₂³	1	8	yes	—
68	C₇×#126	C₂×C₄	1	16	yes	—
69	C₇×#125	C₂×C₄	1	8	yes	—
70	C₇×#124	C₂×C₄	1	8	yes	—
71	C₇×#123	C₂×C₄	1	16	yes	—
72	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
73	C₇×#121	C₂×C₄	1	8	yes	—
74	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
75	C₄×C₇×Q₈	C₂³	1	4	yes	—
76	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
77	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
78	C₄×C₇×D₄	C₂³	1	4	yes	—
79	C₄×C₇×D₄	C₂³	1	8	yes	—
80	C₇×#117	C₂×C₄	1	8	yes	—
81	C₇×#117	C₂³	1	8	yes	—
82	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
83	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
84	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
86	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
88	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
89	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
90	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
91	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
92	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
93	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₇	C₂×C₄	1	4	yes	—
96	C₂×C₄²×C₇	C₂³	1	4	yes	—
97	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₇	C₂³	1	2	yes	—
100	C₇×C₄⋊C₈	C₂³	1	8	yes	—
101	C₇×C₄⋊C₈	C₂³	1	8	yes	—
102	C₇×C₄⋊C₈	C₂³	1	4	yes	—
103	C₇×C₄⋊C₈	C₂³	1	8	yes	—
104	C₇×C₄⋊C₈	C₂³	1	8	yes	—
105	C₇×C₄⋊C₈	C₂³	1	4	yes	—
106	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
107	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
109	C₇×#97	C₂³	1	8	yes	—
110	C₇×#97	C₂³	1	8	yes	—
111	C₄×C₇×C₈	C₂³	1	8	yes	—
112	C₂×#529	C₂×C₇	1	1	yes	characteristic
113	#2995	C₂×C₇	1	16	yes	direct product factor
114	C₂×#446	C₂×C₇	1	2	yes	complemented
115	C₂×#436	C₂×C₇	1	2	yes	complemented
116	C₂×#435	C₂×C₇	1	2	yes	complemented
117	C₂×#435	C₂×C₇	1	2	yes	complemented
118	C₂×#433	C₂×C₇	1	2	yes	complemented
119	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
120	C₂×#424	C₂×C₇	1	2	yes	complemented
121	C₂×#423	C₂×C₇	1	1	yes	characteristic, complemented
122	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
123	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₇×Q₈	—	4	2	no	—
125	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
126	C₂×C₇×D₄	—	4	2	no	—
127	C₂×C₇×D₄	—	4	4	no	—
128	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
129	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₇	—	2	4	no	—
131	C₂²×C₄×C₇	—	2	2	no	—
132	C₂²×C₄×C₇	—	2	2	no	—
133	C₂²×C₄×C₇	—	2	4	no	—
134	C₂²×C₄×C₇	—	4	2	no	—
135	C₂²×C₄×C₇	—	4	2	no	—
136	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
146	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
151	C₇×M₁₆	—	4	4	no	—
152	C₇×M₁₆	—	4	8	no	—
153	C₇×M₁₆	—	4	4	no	—
154	C₂×C₇×C₈	—	2	4	no	—
155	C₂×C₇×C₈	—	2	4	no	—
156	C₂×C₇×C₈	—	2	4	no	—
157	C₂×C₇×C₈	—	2	4	no	—
158	C₂×C₇×C₈	—	4	8	no	—
159	C₂×C₇×C₈	C₂⁴	1	4	yes	—
160	C₂×C₇×C₈	C₂⁴	1	4	yes	—
161	C₂×C₇×C₈	C₂⁴	1	4	yes	—
162	C₂×C₇×C₈	C₂⁴	1	4	yes	—
163	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
164	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
165	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
166	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
167	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
168	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
169	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
170	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
171	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
172	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
173	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
174	C₄²×C₇	C₂²×C₄	1	2	yes	—
175	C₄²×C₇	C₂²×C₄	1	2	yes	—
176	C₄²×C₇	C₂²×C₄	1	4	yes	—
177	C₄²×C₇	C₂²×C₄	1	4	yes	—
178	C₄²×C₇	C₂²×C₄	1	4	yes	—
179	C₄²×C₇	C₂⁴	1	4	yes	—
180	C₄²×C₇	C₂⁴	1	2	yes	—
181	C₄²×C₇	C₂⁴	1	2	yes	—
182	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
183	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
184	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
185	C₂³×C₈	C₂²×C₇	1	2	yes	—
186	#529	C₄×C₇	1	8	yes	—
187	#529	C₂²×C₇	1	8	yes	—
188	C₂×#126	C₄×C₇	1	2	yes	—
189	C₂×#125	C₄×C₇	1	1	yes	characteristic
190	C₂×#124	C₄×C₇	1	1	yes	characteristic
191	C₂×#123	C₄×C₇	1	2	yes	—
192	C₂×C₂²⋊Q₈	C₄×C₇	1	1	yes	characteristic
193	C₂×#121	C₄×C₇	1	1	yes	characteristic
194	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
196	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
197	C₂×#117	C₂²×C₇	1	2	yes	—
198	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
199	#446	C₂²×C₇	1	16	yes	complemented
200	#436	C₂²×C₇	1	16	yes	complemented
201	#435	C₂²×C₇	1	16	yes	complemented
202	#435	C₂²×C₇	1	16	yes	complemented
203	#433	C₂²×C₇	1	16	yes	complemented
204	#432	C₂²×C₇	1	8	yes	complemented
205	#424	C₂²×C₇	1	16	yes	complemented
206	#423	C₂²×C₇	1	8	yes	complemented
207	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
208	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
209	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
211	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
212	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
213	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
215	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
216	C₂×#97	C₂²×C₇	1	2	yes	—
217	C₂×#97	C₂²×C₇	1	2	yes	—
218	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
219	C₂³×C₇	—	2	4	no	—
220	C₂³×C₇	—	2	2	no	—
221	C₂³×C₇	—	2	2	no	—
222	C₂³×C₇	—	2	2	no	—
223	C₂³×C₇	—	2	4	no	—
224	C₂³×C₇	—	2	4	no	—
225	C₂³×C₇	C₂³×C₄	1	4	yes	—
226	C₂³×C₇	C₂³×C₄	1	2	yes	—
227	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
228	C₇×Q₈	—	4	4	no	—
229	C₇×D₄	—	4	4	no	—
230	C₇×D₄	—	4	8	no	—
231	C₂×C₄×C₇	—	2	4	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	2	no	—
234	C₂×C₄×C₇	—	2	2	no	—
235	C₂×C₄×C₇	—	2	2	no	—
236	C₂×C₄×C₇	—	2	2	no	—
237	C₂×C₄×C₇	—	2	4	no	—
238	C₂×C₄×C₇	—	2	4	no	—
239	C₂×C₄×C₇	—	2	8	no	—
240	C₂×C₄×C₇	—	2	4	no	—
241	C₂×C₄×C₇	—	2	4	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	2	no	—
244	C₂×C₄×C₇	—	2	4	no	—
245	C₂×C₄×C₇	—	4	4	no	—
246	C₂×C₄×C₇	—	4	4	no	—
247	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
248	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
249	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
250	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
251	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
252	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
253	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
254	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
255	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
257	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
258	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
259	C₇×C₈	—	2	4	no	—
260	C₇×C₈	—	2	4	no	—
261	C₇×C₈	—	2	4	no	—
262	C₇×C₈	—	2	4	no	—
263	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
264	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
265	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
266	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
267	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
268	C₂³×C₄	C₂³×C₇	1	2	yes	—
269	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
270	C₂×M₁₆	—	4	2	no	—
271	C₂×M₁₆	—	4	4	no	—
272	C₂×M₁₆	—	4	2	no	—
273	C₂×M₁₆	C₂³×C₇	1	4	yes	—
274	C₂×M₁₆	C₂³×C₇	1	4	yes	—
275	C₂×M₁₆	C₂³×C₇	1	8	yes	—
276	C₂²×C₈	—	4	4	no	—
277	C₂²×C₈	C₂³×C₇	1	2	yes	—
278	C₂²×C₈	C₂³×C₇	1	2	yes	—
279	C₂²×C₈	C₂³×C₇	1	2	yes	—
280	C₂²×C₈	C₂³×C₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₇	1	8	yes	—
282	#126	C₂×C₄×C₇	1	16	yes	—
283	#125	C₂×C₄×C₇	1	8	yes	—
284	#124	C₂×C₄×C₇	1	8	yes	—
285	#123	C₂×C₄×C₇	1	16	yes	—
286	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
287	#121	C₂×C₄×C₇	1	8	yes	—
288	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
289	C₄×Q₈	C₂³×C₇	1	4	yes	—
290	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
291	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
292	C₄×D₄	C₂³×C₇	1	4	yes	—
293	C₄×D₄	C₂³×C₇	1	8	yes	—
294	#117	C₂×C₄×C₇	1	8	yes	—
295	#117	C₂³×C₇	1	8	yes	—
296	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
297	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
298	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
303	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
305	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
307	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
308	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
309	C₂×C₄²	C₂×C₄×C₇	1	4	yes	—
310	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₇	1	2	yes	—
312	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₇	1	4	yes	—
314	C₄⋊C₈	C₂³×C₇	1	8	yes	—
315	C₄⋊C₈	C₂³×C₇	1	8	yes	—
316	C₄⋊C₈	C₂³×C₇	1	4	yes	—
317	C₄⋊C₈	C₂³×C₇	1	8	yes	—
318	C₄⋊C₈	C₂³×C₇	1	8	yes	—
319	C₄⋊C₈	C₂³×C₇	1	4	yes	—
320	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
321	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
322	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
323	#97	C₂³×C₇	1	8	yes	—
324	#97	C₂³×C₇	1	8	yes	—
325	C₄×C₈	C₂³×C₇	1	8	yes	—
326	C₂²×C₇	—	2	4	no	—
327	C₂²×C₇	—	2	2	no	—
328	C₂²×C₇	—	2	2	no	—
329	C₂²×C₇	—	2	2	no	—
330	C₂²×C₇	—	2	4	no	—
331	C₂²×C₇	—	2	4	no	—
332	C₂²×C₇	—	4	4	no	—
333	C₂²×C₇	—	4	8	no	—
334	C₂²×C₇	#520	1	2	yes	—
335	C₂²×C₇	#568	1	2	yes	—
336	C₂²×C₇	#568	1	2	yes	—
337	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
338	C₄×C₇	—	2	4	no	—
339	C₄×C₇	—	2	2	no	—
340	C₄×C₇	—	2	2	no	—
341	C₄×C₇	—	2	2	no	—
342	C₄×C₇	—	2	2	no	—
343	C₄×C₇	—	2	2	no	—
344	C₄×C₇	—	2	4	no	—
345	C₄×C₇	—	2	4	no	—
346	C₄×C₇	#520	1	2	yes	—
347	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
349	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
350	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
356	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
365	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
367	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
370	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
371	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
372	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
373	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
374	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
377	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
378	M₁₆	—	4	4	no	—
379	M₁₆	—	4	8	no	—
380	M₁₆	—	4	4	no	—
381	C₂×C₈	—	2	4	no	—
382	C₂×C₈	—	2	4	no	—
383	C₂×C₈	—	2	4	no	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	—	4	8	no	—
386	C₂×C₈	C₂⁴×C₇	1	4	yes	—
387	C₂×C₈	C₂⁴×C₇	1	4	yes	—
388	C₂×C₈	C₂⁴×C₇	1	4	yes	—
389	C₂×C₈	C₂⁴×C₇	1	4	yes	—
390	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
391	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
392	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
393	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
394	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
395	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
396	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
397	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
398	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
399	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
400	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
401	C₄²	C₂²×C₄×C₇	1	2	yes	—
402	C₄²	C₂²×C₄×C₇	1	2	yes	—
403	C₄²	C₂²×C₄×C₇	1	4	yes	—
404	C₄²	C₂²×C₄×C₇	1	4	yes	—
405	C₄²	C₂²×C₄×C₇	1	4	yes	—
406	C₄²	C₂⁴×C₇	1	4	yes	—
407	C₄²	C₂⁴×C₇	1	2	yes	—
408	C₄²	C₂⁴×C₇	1	2	yes	—
409	C₂×C₇	—	4	2	no	—
410	C₂×C₇	—	4	4	no	—
411	C₂×C₇	#2995	1	4	yes	direct product factor
412	C₂×C₇	C₂×#520	1	1	yes	characteristic
413	C₂×C₇	C₂×#568	1	1	yes	characteristic
414	C₂×C₇	C₂×#568	1	1	yes	characteristic
415	C₂³	—	2	4	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	4	no	—
421	C₂³	C₂³×C₄×C₇	1	4	yes	—
422	C₂³	C₂³×C₄×C₇	1	2	yes	—
423	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
424	Q₈	—	4	4	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	8	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
444	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
445	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
446	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
447	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
448	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
449	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
450	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
451	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
452	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
453	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
454	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	2	4	no	—
457	C₈	—	2	4	no	—
458	C₈	—	2	4	no	—
459	C₇	C₂×#2995	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	8	no	—
468	C₂²	C₇×#520	1	2	yes	—
469	C₂²	C₇×#568	1	2	yes	—
470	C₂²	C₇×#568	1	2	yes	—
471	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	4	no	—
477	C₄	—	2	4	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	2	no	—
480	C₄	C₇×#520	1	2	yes	—
481	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
482	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
483	C₂	—	4	2	no	—
484	C₂	—	4	4	no	—
485	C₂	C₇×#2995	1	4	yes	direct product factor
486	C₂	C₂×C₇×#520	1	1	yes	characteristic
487	C₂	C₂×C₇×#568	1	1	yes	characteristic
488	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×#2995	C₂	direct (N × H)
3. C₂×C₇×#446	C₂	semidirect
4. C₂×C₇×#436	C₂	semidirect
5. C₂×C₇×#435	C₂	semidirect
6. C₂×C₇×#435	C₂	semidirect
7. C₂×C₇×#433	C₂	semidirect
8. C₂×C₇×#432	C₂	semidirect
9. C₂×C₇×#424	C₂	semidirect
10. C₂×C₇×#423	C₂	semidirect
28. C₇×#446	C₂²	semidirect
29. C₇×#436	C₂²	semidirect
30. C₇×#435	C₂²	semidirect
31. C₇×#435	C₂²	semidirect
32. C₇×#433	C₂²	semidirect
33. C₇×#432	C₂²	semidirect
34. C₇×#424	C₂²	semidirect
35. C₇×#423	C₂²	semidirect
48. C₂×#2995	C₇	direct (N × H)
113. #2995	C₂×C₇	direct (N × H)
114. C₂×#446	C₂×C₇	semidirect
115. C₂×#436	C₂×C₇	semidirect
116. C₂×#435	C₂×C₇	semidirect
117. C₂×#435	C₂×C₇	semidirect
118. C₂×#433	C₂×C₇	semidirect
119. C₂×#432	C₂×C₇	semidirect
120. C₂×#424	C₂×C₇	semidirect
121. C₂×#423	C₂×C₇	semidirect
199. #446	C₂²×C₇	semidirect
200. #436	C₂²×C₇	semidirect
201. #435	C₂²×C₇	semidirect
202. #435	C₂²×C₇	semidirect
203. #433	C₂²×C₇	semidirect
204. #432	C₂²×C₇	semidirect
205. #424	C₂²×C₇	semidirect
206. #423	C₂²×C₇	semidirect
411. C₂×C₇	#2995	direct (N × H)
459. C₇	C₂×#2995	direct (N × H)
485. C₂	C₇×#2995	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×#2995	2
C₂×C₇×#446	2
C₂×C₇×#436	2
C₂×C₇×#435	2
C₂×C₇×#433	2
C₂×C₇×#432	2
C₂×C₇×#424	2
C₂×C₇×#423	2
C₂×#2995	7

Subgroups — C2×C7×#2995 #13237478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2995 #13237478