Subgroups — C₂×C₇×#2989 #13237472

Order 1792.

2154 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic
2	C₇×#2989	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	4	yes	maximal, complemented
6	C₂×C₇×#432	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#423	C₂	1	2	yes	maximal, complemented
9	C₂²×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₇×#41	C₄	1	1	yes	characteristic
11	C₂²×C₇×M₁₆	C₂²	1	4	yes	—
12	C₂³×C₇×C₈	C₂²	1	2	yes	—
13	C₄×C₇×#41	C₄	1	8	yes	—
14	C₄×C₇×#41	C₂²	1	8	yes	—
15	C₂×C₄×C₇×Q₈	C₄	1	1	yes	characteristic
16	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×D₄	C₄	1	2	yes	—
18	C₂×C₄×C₇×D₄	C₄	1	1	yes	characteristic
19	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
20	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₇×#117	C₄	1	2	yes	—
22	C₂×C₇×#117	C₄	1	1	yes	characteristic
23	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₇	C₂²	1	2	yes	—
25	C₇×#446	C₂²	1	16	yes	complemented
26	C₇×#436	C₂²	1	16	yes	complemented
27	C₇×#435	C₂²	1	32	yes	complemented
28	C₇×#432	C₂²	1	16	yes	complemented
29	C₇×#431	C₂²	1	8	yes	complemented
30	C₇×#423	C₂²	1	16	yes	complemented
31	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
32	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	—
35	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₄⋊C₈	C₂²	1	8	yes	complemented
37	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	—
39	C₂×C₇×#97	C₂²	1	4	yes	—
40	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
41	C₂×#2989	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₇×#41	—	2	8	no	—
43	C₂×C₇×#41	C₂×C₄	1	8	yes	—
44	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
46	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇	C₂³	1	2	yes	—
53	C₂×C₇×M₁₆	—	4	8	no	—
54	C₂×C₇×M₁₆	C₂³	1	16	yes	—
55	C₂²×C₇×C₈	—	4	4	no	—
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	2	yes	—
58	C₂²×C₇×C₈	C₂³	1	4	yes	—
59	C₂²×C₇×C₈	C₂³	1	8	yes	—
60	C₄×C₇×Q₈	C₂×C₄	1	8	yes	—
61	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
62	C₄×C₇×Q₈	C₂³	1	4	yes	—
63	C₄×C₇×D₄	C₂×C₄	1	16	yes	—
64	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
65	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
66	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
67	C₄×C₇×D₄	C₂³	1	8	yes	—
68	C₄×C₇×D₄	C₂³	1	4	yes	—
69	C₇×#117	C₂×C₄	1	16	yes	—
70	C₇×#117	C₂×C₄	1	8	yes	—
71	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂×C₄	1	8	yes	—
83	C₂×C₄²×C₇	C₂×C₄	1	4	yes	—
84	C₂×C₄²×C₇	C₂³	1	4	yes	—
85	C₂×C₄²×C₇	C₂³	1	8	yes	—
86	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₇	C₂³	1	2	yes	—
89	C₇×C₄⋊C₈	C₂³	1	8	yes	—
90	C₇×C₄⋊C₈	C₂³	1	8	yes	—
91	C₇×C₄⋊C₈	C₂³	1	4	yes	—
92	C₇×C₄⋊C₈	C₂³	1	16	yes	—
93	C₇×C₄⋊C₈	C₂³	1	4	yes	—
94	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
95	C₇×C₂²⋊C₈	C₂³	1	16	yes	—
96	C₇×#97	C₂³	1	16	yes	—
97	C₄×C₇×C₈	C₂³	1	8	yes	—
98	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic
99	#2989	C₂×C₇	1	16	yes	direct product factor
100	C₂×#446	C₂×C₇	1	2	yes	complemented
101	C₂×#436	C₂×C₇	1	2	yes	complemented
102	C₂×#435	C₂×C₇	1	4	yes	complemented
103	C₂×#432	C₂×C₇	1	2	yes	complemented
104	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
105	C₂×#423	C₂×C₇	1	2	yes	complemented
106	C₂²×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
108	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₇×#41	—	2	32	no	—
110	C₂×C₇×Q₈	—	2	4	no	—
111	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
112	C₂×C₇×D₄	—	2	8	no	—
113	C₂×C₇×D₄	—	2	4	no	—
114	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
115	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₇	—	2	8	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	4	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	4	no	—
121	C₂²×C₄×C₇	—	4	2	no	—
122	C₂²×C₄×C₇	—	4	4	no	—
123	C₂²×C₄×C₇	M₁₆	1	8	yes	complemented
124	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
128	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
133	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
134	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
141	C₇×M₁₆	—	4	16	no	—
142	C₂×C₇×C₈	—	2	8	no	—
143	C₂×C₇×C₈	—	2	4	no	—
144	C₂×C₇×C₈	—	2	4	no	—
145	C₂×C₇×C₈	—	4	8	no	—
146	C₂×C₇×C₈	C₂⁴	1	4	yes	—
147	C₂×C₇×C₈	C₂⁴	1	4	yes	—
148	C₂×C₇×C₈	C₂⁴	1	8	yes	—
149	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
150	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
151	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
152	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
153	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
154	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
155	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
156	C₄²×C₇	C₂²×C₄	1	2	yes	—
157	C₄²×C₇	C₂²×C₄	1	4	yes	—
158	C₄²×C₇	C₂²×C₄	1	8	yes	—
159	C₄²×C₇	C₂²×C₄	1	8	yes	—
160	C₄²×C₇	C₂²×C₄	1	4	yes	—
161	C₄²×C₇	C₂²×C₄	1	4	yes	—
162	C₄²×C₇	C₂²×C₄	1	2	yes	—
163	C₄²×C₇	C₂⁴	1	2	yes	—
164	C₄²×C₇	C₂⁴	1	4	yes	—
165	C₄²×C₇	C₂⁴	1	2	yes	—
166	C₂²×#41	C₄×C₇	1	1	yes	characteristic
167	C₂²×M₁₆	C₂²×C₇	1	4	yes	—
168	C₂³×C₈	C₂²×C₇	1	2	yes	—
169	C₄×#41	C₄×C₇	1	8	yes	—
170	C₄×#41	C₂²×C₇	1	8	yes	—
171	C₂×C₄×Q₈	C₄×C₇	1	1	yes	characteristic
172	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
173	C₂×C₄×D₄	C₄×C₇	1	2	yes	—
174	C₂×C₄×D₄	C₄×C₇	1	1	yes	characteristic
175	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
176	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
177	C₂×#117	C₄×C₇	1	2	yes	—
178	C₂×#117	C₄×C₇	1	1	yes	characteristic
179	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
180	C₂²×C₄²	C₂²×C₇	1	2	yes	—
181	#446	C₂²×C₇	1	16	yes	complemented
182	#436	C₂²×C₇	1	16	yes	complemented
183	#435	C₂²×C₇	1	32	yes	complemented
184	#432	C₂²×C₇	1	16	yes	complemented
185	#431	C₂²×C₇	1	8	yes	complemented
186	#423	C₂²×C₇	1	16	yes	complemented
187	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	—
191	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₇	1	8	yes	complemented
193	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
194	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	—
195	C₂×#97	C₂²×C₇	1	4	yes	—
196	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
197	C₂³×C₇	—	2	2	no	—
198	C₂³×C₇	—	2	2	no	—
199	C₂³×C₇	—	2	4	no	—
200	C₂³×C₇	—	2	4	no	—
201	C₂³×C₇	—	2	4	no	—
202	C₂³×C₇	C₂×M₁₆	1	4	yes	—
203	C₂³×C₇	C₂³×C₄	1	4	yes	—
204	C₂³×C₇	C₂³×C₄	1	2	yes	—
205	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
206	C₇×Q₈	—	2	8	no	—
207	C₇×D₄	—	2	16	no	—
208	C₇×D₄	—	2	8	no	—
209	C₂×C₄×C₇	—	2	2	no	—
210	C₂×C₄×C₇	—	2	4	no	—
211	C₂×C₄×C₇	—	2	4	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	2	4	no	—
215	C₂×C₄×C₇	—	2	4	no	—
216	C₂×C₄×C₇	—	2	8	no	—
217	C₂×C₄×C₇	—	2	16	no	—
218	C₂×C₄×C₇	—	2	2	no	—
219	C₂×C₄×C₇	—	2	4	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	2	4	no	—
222	C₂×C₄×C₇	—	4	4	no	—
223	C₂×C₄×C₇	—	4	8	no	—
224	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
225	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
226	C₂×C₄×C₇	C₂×M₁₆	1	16	yes	complemented
227	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
228	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
229	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
230	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
231	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
232	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
233	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
235	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
236	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
237	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
238	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
239	C₇×C₈	—	2	8	no	—
240	C₇×C₈	—	2	4	no	—
241	C₇×C₈	—	2	4	no	—
242	C₂×#41	—	2	8	no	—
243	C₂×#41	C₂×C₄×C₇	1	8	yes	—
244	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
245	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
246	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
247	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
248	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
249	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
250	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₇	1	2	yes	—
253	C₂×M₁₆	—	4	8	no	—
254	C₂×M₁₆	C₂³×C₇	1	16	yes	—
255	C₂²×C₈	—	4	4	no	—
256	C₂²×C₈	C₂³×C₇	1	4	yes	—
257	C₂²×C₈	C₂³×C₇	1	2	yes	—
258	C₂²×C₈	C₂³×C₇	1	2	yes	—
259	C₂²×C₈	C₂³×C₇	1	8	yes	—
260	C₄×Q₈	C₂×C₄×C₇	1	8	yes	—
261	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
262	C₄×Q₈	C₂³×C₇	1	4	yes	—
263	C₄×D₄	C₂×C₄×C₇	1	16	yes	—
264	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
265	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
266	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
267	C₄×D₄	C₂³×C₇	1	8	yes	—
268	C₄×D₄	C₂³×C₇	1	4	yes	—
269	#117	C₂×C₄×C₇	1	16	yes	—
270	#117	C₂×C₄×C₇	1	8	yes	—
271	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
272	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
274	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
276	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
277	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
278	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
279	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
280	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
281	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
282	C₂×C₄²	C₂×C₄×C₇	1	8	yes	—
283	C₂×C₄²	C₂×C₄×C₇	1	4	yes	—
284	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₇	1	2	yes	—
286	C₂×C₄²	C₂³×C₇	1	4	yes	—
287	C₂×C₄²	C₂³×C₇	1	8	yes	—
288	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
289	C₄⋊C₈	C₂³×C₇	1	8	yes	—
290	C₄⋊C₈	C₂³×C₇	1	8	yes	—
291	C₄⋊C₈	C₂³×C₇	1	4	yes	—
292	C₄⋊C₈	C₂³×C₇	1	16	yes	—
293	C₄⋊C₈	C₂³×C₇	1	4	yes	—
294	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
295	C₂²⋊C₈	C₂³×C₇	1	16	yes	—
296	#97	C₂³×C₇	1	16	yes	—
297	C₄×C₈	C₂³×C₇	1	8	yes	—
298	C₂²×C₇	—	2	2	no	—
299	C₂²×C₇	—	2	8	no	—
300	C₂²×C₇	—	2	2	no	—
301	C₂²×C₇	—	2	4	no	—
302	C₂²×C₇	—	2	4	no	—
303	C₂²×C₇	—	2	4	no	—
304	C₂²×C₇	—	4	8	no	—
305	C₂²×C₇	#520	1	2	yes	—
306	C₂²×C₇	C₂²×M₁₆	1	4	yes	—
307	C₂²×C₇	C₂²×M₁₆	1	2	yes	—
308	C₂²×C₇	#568	1	2	yes	—
309	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
310	C₄×C₇	—	2	2	no	—
311	C₄×C₇	—	2	4	no	—
312	C₄×C₇	—	2	4	no	—
313	C₄×C₇	—	2	2	no	—
314	C₄×C₇	—	2	2	no	—
315	C₄×C₇	—	2	4	no	—
316	C₄×C₇	#520	1	2	yes	—
317	C₄×C₇	C₂²×M₁₆	1	4	yes	—
318	C₄×C₇	C₂²×M₁₆	1	4	yes	—
319	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
320	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
321	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
322	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
323	#41	—	2	32	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
329	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	C₇×M₁₆	1	8	yes	complemented
338	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
342	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
343	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
345	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
346	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
347	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
348	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
349	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
352	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
353	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
355	M₁₆	—	4	16	no	—
356	C₂×C₈	—	2	8	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	4	no	—
359	C₂×C₈	—	4	8	no	—
360	C₂×C₈	C₂⁴×C₇	1	4	yes	—
361	C₂×C₈	C₂⁴×C₇	1	4	yes	—
362	C₂×C₈	C₂⁴×C₇	1	8	yes	—
363	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
364	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
365	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
366	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
367	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
368	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
369	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
370	C₄²	C₂²×C₄×C₇	1	2	yes	—
371	C₄²	C₂²×C₄×C₇	1	4	yes	—
372	C₄²	C₂²×C₄×C₇	1	8	yes	—
373	C₄²	C₂²×C₄×C₇	1	8	yes	—
374	C₄²	C₂²×C₄×C₇	1	4	yes	—
375	C₄²	C₂²×C₄×C₇	1	4	yes	—
376	C₄²	C₂²×C₄×C₇	1	2	yes	—
377	C₄²	C₂⁴×C₇	1	2	yes	—
378	C₄²	C₂⁴×C₇	1	4	yes	—
379	C₄²	C₂⁴×C₇	1	2	yes	—
380	C₂×C₇	—	2	4	no	—
381	C₂×C₇	—	4	4	no	—
382	C₂×C₇	#2989	1	4	yes	direct product factor
383	C₂×C₇	C₂×#520	1	1	yes	characteristic
384	C₂×C₇	C₂³×M₁₆	1	1	yes	characteristic
385	C₂×C₇	C₂×#568	1	1	yes	characteristic
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	C₂×C₇×M₁₆	1	4	yes	—
392	C₂³	C₂³×C₄×C₇	1	4	yes	—
393	C₂³	C₂³×C₄×C₇	1	2	yes	—
394	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
395	Q₈	—	2	8	no	—
396	D₄	—	2	16	no	—
397	D₄	—	2	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	16	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
414	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
415	C₂×C₄	C₂×C₇×M₁₆	1	16	yes	complemented
416	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
417	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
418	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
419	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
420	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
421	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
422	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
423	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
424	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
425	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
426	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
427	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
428	C₈	—	2	8	no	—
429	C₈	—	2	4	no	—
430	C₈	—	2	4	no	—
431	C₇	C₂×#2989	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²	—	2	2	no	—
433	C₂²	—	2	8	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	8	no	—
439	C₂²	C₇×#520	1	2	yes	—
440	C₂²	C₂²×C₇×M₁₆	1	4	yes	—
441	C₂²	C₂²×C₇×M₁₆	1	2	yes	—
442	C₂²	C₇×#568	1	2	yes	—
443	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
444	C₄	—	2	4	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	4	no	—
450	C₄	C₇×#520	1	2	yes	—
451	C₄	C₂²×C₇×M₁₆	1	4	yes	—
452	C₄	C₂²×C₇×M₁₆	1	4	yes	—
453	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
454	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
455	C₂	—	2	4	no	—
456	C₂	—	4	4	no	—
457	C₂	C₇×#2989	1	4	yes	direct product factor
458	C₂	C₂×C₇×#520	1	1	yes	characteristic
459	C₂	C₂³×C₇×M₁₆	1	1	yes	characteristic
460	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	C₂²×C₇×#41	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×#2989	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×#432	C₂	semidirect
7. C₂×C₇×#431	C₂	semidirect
8. C₂×C₇×#423	C₂	semidirect
9. C₂²×C₇×C₄⋊C₈	C₂	semidirect
25. C₇×#446	C₂²	semidirect
26. C₇×#436	C₂²	semidirect
27. C₇×#435	C₂²	semidirect
28. C₇×#432	C₂²	semidirect
29. C₇×#431	C₂²	semidirect
30. C₇×#423	C₂²	semidirect
36. C₂×C₇×C₄⋊C₈	C₂²	semidirect
41. C₂×#2989	C₇	direct (N × H)
99. #2989	C₂×C₇	direct (N × H)
100. C₂×#446	C₂×C₇	semidirect
101. C₂×#436	C₂×C₇	semidirect
102. C₂×#435	C₂×C₇	semidirect
103. C₂×#432	C₂×C₇	semidirect
104. C₂×#431	C₂×C₇	semidirect
105. C₂×#423	C₂×C₇	semidirect
106. C₂²×C₄⋊C₈	C₂×C₇	semidirect
123. C₂²×C₄×C₇	M₁₆	semidirect
181. #446	C₂²×C₇	semidirect
182. #436	C₂²×C₇	semidirect
183. #435	C₂²×C₇	semidirect
184. #432	C₂²×C₇	semidirect
185. #431	C₂²×C₇	semidirect
186. #423	C₂²×C₇	semidirect
192. C₂×C₄⋊C₈	C₂²×C₇	semidirect
226. C₂×C₄×C₇	C₂×M₁₆	semidirect
337. C₂²×C₄	C₇×M₁₆	semidirect
382. C₂×C₇	#2989	direct (N × H)
415. C₂×C₄	C₂×C₇×M₁₆	semidirect
431. C₇	C₂×#2989	direct (N × H)
457. C₂	C₇×#2989	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×C₄×C₇×#41	2
C₇×#2989	2
C₂×C₇×#446	2
C₂×C₇×#436	2
C₂×C₇×#435	2
C₂×C₇×#432	2
C₂×C₇×#431	2
C₂×C₇×#423	2
C₂²×C₇×C₄⋊C₈	2
C₂×#2989	7

Subgroups — C2×C7×#2989 #13237472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2989 #13237472