Subgroups — C₂×C₇×#2440 #13211890

Order 1792.

3550 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal
3	C₂³×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#2440	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₇×#398	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#395	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#385	C₂	1	2	yes	maximal
10	C₂×C₇×#384	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂³×C₇×Q₈	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊Q₈	—	2	8	no	—
17	C₂×C₇×C₄⋊Q₈	C₂²	1	8	yes	complemented
18	C₂×C₇×C₂²⋊Q₈	—	2	16	no	—
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	16	yes	—
20	C₂²×C₇×C₄⋊C₄	—	2	8	no	—
21	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₇×C₄⋊C₄	C₂²	1	8	yes	—
27	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
37	C₇×#398	C₂²	1	16	yes	complemented
38	C₇×#395	C₂²	1	16	yes	complemented
39	C₇×#389	C₂²	1	8	yes	complemented
40	C₇×#389	C₂²	1	8	yes	complemented
41	C₇×#385	C₂²	1	16	yes	—
42	C₇×#384	C₂²	1	8	yes	complemented
43	C₇×#380	C₂²	1	8	yes	—
44	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
45	C₂×C₇×#95	C₂²	1	1	yes	characteristic
46	C₂×C₇×#95	C₂²	1	2	yes	—
47	C₂×C₇×#95	C₂²	1	2	yes	—
48	C₂×C₇×#95	C₂²	1	1	yes	characteristic
49	C₂×C₇×#95	C₂²	1	2	yes	—
50	C₂×#2440	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂⁵×C₇	C₂³	1	1	yes	characteristic
52	C₂²×C₇×Q₈	—	2	8	no	—
53	C₂²×C₇×Q₈	—	2	8	no	—
54	C₂²×C₇×Q₈	—	4	4	no	—
55	C₂²×C₇×Q₈	C₂³	1	8	yes	—
56	C₂³×C₄×C₇	—	2	4	no	—
57	C₂³×C₄×C₇	—	2	4	no	—
58	C₂³×C₄×C₇	—	2	8	no	—
59	C₂³×C₄×C₇	—	2	8	no	—
60	C₂³×C₄×C₇	—	4	4	no	—
61	C₂³×C₄×C₇	Q₈	1	8	yes	complemented
62	C₂³×C₄×C₇	C₂³	1	2	yes	—
63	C₂³×C₄×C₇	C₂³	1	2	yes	—
64	C₂³×C₄×C₇	C₂³	1	2	yes	—
65	C₂³×C₄×C₇	C₂³	1	8	yes	—
66	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	C₂³	1	2	yes	—
68	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	C₂³	1	4	yes	—
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₇×C₄⋊Q₈	—	2	32	no	—
75	C₇×C₂²⋊Q₈	—	2	64	no	—
76	C₂×C₇×C₄⋊C₄	—	2	8	no	—
77	C₂×C₇×C₄⋊C₄	—	2	4	no	—
78	C₂×C₇×C₄⋊C₄	—	2	8	no	—
79	C₂×C₇×C₄⋊C₄	—	2	8	no	—
80	C₂×C₇×C₄⋊C₄	—	2	8	no	—
81	C₂×C₇×C₄⋊C₄	—	2	8	no	—
82	C₂×C₇×C₄⋊C₄	—	2	4	no	—
83	C₂×C₇×C₄⋊C₄	—	2	4	no	—
84	C₂×C₇×C₄⋊C₄	—	2	32	no	—
85	C₂×C₇×C₄⋊C₄	—	4	4	no	—
86	C₂×C₇×C₄⋊C₄	D₄	1	8	yes	—
87	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
89	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
92	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
93	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
94	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
95	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
96	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
98	C₂×C₇×C₂²⋊C₄	D₄	1	8	yes	—
99	C₂×C₇×C₂²⋊C₄	Q₈	1	8	yes	complemented
100	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₂×C₄²×C₇	—	2	4	no	—
104	C₂×C₄²×C₇	—	2	4	no	—
105	C₂×C₄²×C₇	C₂³	1	4	yes	—
106	C₂×C₄²×C₇	C₂³	1	4	yes	—
107	C₇×#95	C₂³	1	4	yes	—
108	C₇×#95	C₂³	1	4	yes	—
109	C₇×#95	C₂³	1	8	yes	—
110	C₇×#95	C₂³	1	8	yes	—
111	C₇×#95	C₂³	1	8	yes	—
112	C₂²×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
113	C₂²×C₂²⋊Q₈	C₂×C₇	1	2	yes	—
114	C₂³×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
115	#2440	C₂×C₇	1	16	yes	direct product factor
116	C₂×#398	C₂×C₇	1	2	yes	complemented
117	C₂×#395	C₂×C₇	1	2	yes	complemented
118	C₂×#389	C₂×C₇	1	1	yes	characteristic, complemented
119	C₂×#389	C₂×C₇	1	1	yes	characteristic, complemented
120	C₂×#385	C₂×C₇	1	2	yes	—
121	C₂×#384	C₂×C₇	1	1	yes	characteristic, complemented
122	C₂×#380	C₂×C₇	1	1	yes	characteristic
123	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
124	C₂⁴×C₇	—	2	2	no	—
125	C₂⁴×C₇	—	2	2	no	—
126	C₂⁴×C₇	—	2	2	no	—
127	C₂⁴×C₇	—	2	2	no	—
128	C₂⁴×C₇	C₂×D₄	1	4	yes	—
129	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
130	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
131	C₂⁴×C₇	C₂⁴	1	2	yes	—
132	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
133	C₂×C₇×Q₈	—	2	16	no	—
134	C₂×C₇×Q₈	—	2	16	no	—
135	C₂×C₇×Q₈	—	4	8	no	—
136	C₂×C₇×Q₈	—	4	32	no	—
137	C₂²×C₄×C₇	—	2	2	no	—
138	C₂²×C₄×C₇	—	2	2	no	—
139	C₂²×C₄×C₇	—	2	2	no	—
140	C₂²×C₄×C₇	—	2	4	no	—
141	C₂²×C₄×C₇	—	2	2	no	—
142	C₂²×C₄×C₇	—	2	2	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	—	2	2	no	—
147	C₂²×C₄×C₇	—	2	2	no	—
148	C₂²×C₄×C₇	—	2	2	no	—
149	C₂²×C₄×C₇	—	2	32	no	—
150	C₂²×C₄×C₇	—	2	8	no	—
151	C₂²×C₄×C₇	—	2	8	no	—
152	C₂²×C₄×C₇	—	2	4	no	—
153	C₂²×C₄×C₇	—	2	4	no	—
154	C₂²×C₄×C₇	—	2	4	no	—
155	C₂²×C₄×C₇	—	2	4	no	—
156	C₂²×C₄×C₇	—	2	4	no	—
157	C₂²×C₄×C₇	—	2	16	no	—
158	C₂²×C₄×C₇	—	2	4	no	—
159	C₂²×C₄×C₇	—	2	4	no	—
160	C₂²×C₄×C₇	—	2	4	no	—
161	C₂²×C₄×C₇	—	2	4	no	—
162	C₂²×C₄×C₇	—	2	16	no	—
163	C₂²×C₄×C₇	—	4	8	no	—
164	C₂²×C₄×C₇	—	4	32	no	—
165	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
168	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
170	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
171	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
172	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
173	C₂²×C₄×C₇	C₂×Q₈	1	16	yes	complemented
174	C₂²×C₄×C₇	#41	1	4	yes	—
175	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
185	C₇×C₄⋊C₄	—	2	16	no	—
186	C₇×C₄⋊C₄	—	2	8	no	—
187	C₇×C₄⋊C₄	—	2	16	no	—
188	C₇×C₄⋊C₄	—	2	16	no	—
189	C₇×C₄⋊C₄	—	2	16	no	—
190	C₇×C₄⋊C₄	—	2	16	no	—
191	C₇×C₄⋊C₄	—	2	8	no	—
192	C₇×C₄⋊C₄	—	2	8	no	—
193	C₇×C₄⋊C₄	—	4	8	no	—
194	C₇×C₄⋊C₄	C₂×D₄	1	16	yes	—
195	C₇×C₂²⋊C₄	—	2	16	no	—
196	C₇×C₂²⋊C₄	C₂×D₄	1	16	yes	—
197	C₇×C₂²⋊C₄	C₂×Q₈	1	16	yes	complemented
198	C₄²×C₇	—	2	8	no	—
199	C₄²×C₇	—	2	8	no	—
200	C₂³×Q₈	C₂²×C₇	1	2	yes	—
201	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
202	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	—	2	8	no	—
204	C₂×C₄⋊Q₈	C₂²×C₇	1	8	yes	complemented
205	C₂×C₂²⋊Q₈	—	2	16	no	—
206	C₂×C₂²⋊Q₈	C₂²×C₇	1	16	yes	—
207	C₂²×C₄⋊C₄	—	2	8	no	—
208	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
210	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
211	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
212	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
213	C₂²×C₄⋊C₄	C₂²×C₇	1	8	yes	—
214	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
215	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
216	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
219	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
220	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
221	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
222	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
223	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
224	#398	C₂²×C₇	1	16	yes	complemented
225	#395	C₂²×C₇	1	16	yes	complemented
226	#389	C₂²×C₇	1	8	yes	complemented
227	#389	C₂²×C₇	1	8	yes	complemented
228	#385	C₂²×C₇	1	16	yes	—
229	#384	C₂²×C₇	1	8	yes	complemented
230	#380	C₂²×C₇	1	8	yes	—
231	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
232	C₂×#95	C₂²×C₇	1	1	yes	characteristic
233	C₂×#95	C₂²×C₇	1	2	yes	—
234	C₂×#95	C₂²×C₇	1	2	yes	—
235	C₂×#95	C₂²×C₇	1	1	yes	characteristic
236	C₂×#95	C₂²×C₇	1	2	yes	—
237	C₂³×C₇	—	2	8	no	—
238	C₂³×C₇	—	2	8	no	—
239	C₂³×C₇	—	2	8	no	—
240	C₂³×C₇	—	2	8	no	—
241	C₂³×C₇	—	2	8	no	—
242	C₂³×C₇	—	2	8	no	—
243	C₂³×C₇	—	2	2	no	—
244	C₂³×C₇	—	2	2	no	—
245	C₂³×C₇	—	2	2	no	—
246	C₂³×C₇	—	2	2	no	—
247	C₂³×C₇	C₄⋊Q₈	1	16	yes	complemented
248	C₂³×C₇	C₂²×D₄	1	4	yes	—
249	C₂³×C₇	C₂²×D₄	1	2	yes	—
250	C₂³×C₇	C₂²×D₄	1	2	yes	—
251	C₂³×C₇	C₂²×Q₈	1	4	yes	—
252	C₂³×C₇	C₂²×Q₈	1	4	yes	—
253	C₂³×C₇	C₂²×Q₈	1	2	yes	—
254	C₂³×C₇	C₂²×Q₈	1	2	yes	—
255	C₂³×C₇	C₂×#41	1	2	yes	—
256	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
257	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
258	C₂³×C₇	C₂⁵	1	1	yes	characteristic
259	C₇×Q₈	—	4	32	no	—
260	C₂×C₄×C₇	—	2	8	no	—
261	C₂×C₄×C₇	—	2	16	no	—
262	C₂×C₄×C₇	—	2	8	no	—
263	C₂×C₄×C₇	—	2	8	no	—
264	C₂×C₄×C₇	—	2	8	no	—
265	C₂×C₄×C₇	—	2	8	no	—
266	C₂×C₄×C₇	—	2	2	no	—
267	C₂×C₄×C₇	—	2	2	no	—
268	C₂×C₄×C₇	—	2	2	no	—
269	C₂×C₄×C₇	—	2	4	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	4	no	—
275	C₂×C₄×C₇	—	2	2	no	—
276	C₂×C₄×C₇	—	2	2	no	—
277	C₂×C₄×C₇	—	2	2	no	—
278	C₂×C₄×C₇	—	2	32	no	—
279	C₂×C₄×C₇	—	2	4	no	—
280	C₂×C₄×C₇	—	2	4	no	—
281	C₂×C₄×C₇	—	2	4	no	—
282	C₂×C₄×C₇	—	2	4	no	—
283	C₂×C₄×C₇	—	2	4	no	—
284	C₂×C₄×C₇	—	2	4	no	—
285	C₂×C₄×C₇	—	2	4	no	—
286	C₂×C₄×C₇	—	2	4	no	—
287	C₂×C₄×C₇	—	2	4	no	—
288	C₂×C₄×C₇	—	4	32	no	—
289	C₂×C₄×C₇	—	4	8	no	—
290	C₂×C₄×C₇	—	4	8	no	—
291	C₂×C₄×C₇	—	4	8	no	—
292	C₂×C₄×C₇	C₂²⋊Q₈	1	16	yes	complemented
293	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
294	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
295	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
296	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
298	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
299	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
300	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
301	C₂×C₄×C₇	C₂×#41	1	4	yes	—
302	C₂⁵	C₂³×C₇	1	1	yes	characteristic
303	C₂²×Q₈	—	2	8	no	—
304	C₂²×Q₈	—	2	8	no	—
305	C₂²×Q₈	—	4	4	no	—
306	C₂²×Q₈	C₂³×C₇	1	8	yes	—
307	C₂³×C₄	—	2	4	no	—
308	C₂³×C₄	—	2	4	no	—
309	C₂³×C₄	—	2	8	no	—
310	C₂³×C₄	—	2	8	no	—
311	C₂³×C₄	—	4	4	no	—
312	C₂³×C₄	C₇×Q₈	1	8	yes	complemented
313	C₂³×C₄	C₂³×C₇	1	2	yes	—
314	C₂³×C₄	C₂³×C₇	1	2	yes	—
315	C₂³×C₄	C₂³×C₇	1	2	yes	—
316	C₂³×C₄	C₂³×C₇	1	8	yes	—
317	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₇	1	2	yes	—
320	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₇	1	4	yes	—
324	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
325	C₄⋊Q₈	—	2	32	no	—
326	C₂²⋊Q₈	—	2	64	no	—
327	C₂×C₄⋊C₄	—	2	8	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	—	2	8	no	—
330	C₂×C₄⋊C₄	—	2	8	no	—
331	C₂×C₄⋊C₄	—	2	8	no	—
332	C₂×C₄⋊C₄	—	2	8	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	—	2	4	no	—
335	C₂×C₄⋊C₄	—	2	32	no	—
336	C₂×C₄⋊C₄	—	4	4	no	—
337	C₂×C₄⋊C₄	C₇×D₄	1	8	yes	—
338	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
340	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
341	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
342	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
343	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
345	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
347	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
348	C₂×C₂²⋊C₄	—	2	8	no	—
349	C₂×C₂²⋊C₄	C₇×D₄	1	8	yes	—
350	C₂×C₂²⋊C₄	C₇×Q₈	1	8	yes	complemented
351	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	—	2	4	no	—
356	C₂×C₄²	C₂³×C₇	1	4	yes	—
357	C₂×C₄²	C₂³×C₇	1	4	yes	—
358	#95	C₂³×C₇	1	4	yes	—
359	#95	C₂³×C₇	1	4	yes	—
360	#95	C₂³×C₇	1	8	yes	—
361	#95	C₂³×C₇	1	8	yes	—
362	#95	C₂³×C₇	1	8	yes	—
363	C₂²×C₇	—	2	4	no	—
364	C₂²×C₇	—	2	4	no	—
365	C₂²×C₇	—	2	4	no	—
366	C₂²×C₇	—	2	32	no	—
367	C₂²×C₇	—	2	4	no	—
368	C₂²×C₇	—	2	4	no	—
369	C₂²×C₇	—	2	4	no	—
370	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
371	C₂²×C₇	C₂×C₄⋊Q₈	1	4	yes	—
372	C₂²×C₇	C₂×C₄⋊Q₈	1	8	yes	complemented
373	C₂²×C₇	#544	1	4	yes	—
374	C₂²×C₇	D₄²	1	4	yes	—
375	C₂²×C₇	#547	1	4	yes	—
376	C₂²×C₇	D₄×Q₈	1	4	yes	—
377	C₂²×C₇	#554	1	4	yes	—
378	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
379	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
380	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
381	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
382	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
383	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
385	C₄×C₇	—	2	4	no	—
386	C₄×C₇	—	2	8	no	—
387	C₄×C₇	—	2	4	no	—
388	C₄×C₇	—	2	4	no	—
389	C₄×C₇	—	2	4	no	—
390	C₄×C₇	—	2	4	no	—
391	C₄×C₇	—	4	4	no	—
392	C₄×C₇	—	4	4	no	—
393	C₄×C₇	—	4	4	no	—
394	C₄×C₇	C₂×C₂²⋊Q₈	1	8	yes	complemented
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	2	2	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	C₂×C₇×D₄	1	4	yes	—
400	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
401	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
402	C₂⁴	C₂⁴×C₇	1	2	yes	—
403	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
404	C₂×Q₈	—	2	16	no	—
405	C₂×Q₈	—	2	16	no	—
406	C₂×Q₈	—	4	8	no	—
407	C₂×Q₈	—	4	32	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	32	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	8	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	16	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	16	no	—
434	C₂²×C₄	—	4	8	no	—
435	C₂²×C₄	—	4	32	no	—
436	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
437	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
438	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
439	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
440	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
441	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
442	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
443	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
444	C₂²×C₄	C₂×C₇×Q₈	1	16	yes	complemented
445	C₂²×C₄	C₇×#41	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
456	C₄⋊C₄	—	2	16	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	16	no	—
459	C₄⋊C₄	—	2	16	no	—
460	C₄⋊C₄	—	2	16	no	—
461	C₄⋊C₄	—	2	16	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	4	8	no	—
465	C₄⋊C₄	C₂×C₇×D₄	1	16	yes	—
466	C₂²⋊C₄	—	2	16	no	—
467	C₂²⋊C₄	C₂×C₇×D₄	1	16	yes	—
468	C₂²⋊C₄	C₂×C₇×Q₈	1	16	yes	complemented
469	C₄²	—	2	8	no	—
470	C₄²	—	2	8	no	—
471	C₂×C₇	—	2	8	no	—
472	C₂×C₇	#2440	1	8	yes	direct product factor
473	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
474	C₂×C₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
475	C₂×C₇	C₂×#544	1	1	yes	characteristic
476	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
477	C₂×C₇	C₂×#547	1	1	yes	characteristic
478	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
479	C₂×C₇	C₂×#554	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	8	no	—
485	C₂³	—	2	8	no	—
486	C₂³	—	2	8	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	8	no	—
489	C₂³	—	2	8	no	—
490	C₂³	C₇×C₄⋊Q₈	1	16	yes	complemented
491	C₂³	C₂²×C₇×D₄	1	4	yes	—
492	C₂³	C₂²×C₇×D₄	1	2	yes	—
493	C₂³	C₂²×C₇×D₄	1	2	yes	—
494	C₂³	C₂²×C₇×Q₈	1	4	yes	—
495	C₂³	C₂²×C₇×Q₈	1	4	yes	—
496	C₂³	C₂²×C₇×Q₈	1	2	yes	—
497	C₂³	C₂²×C₇×Q₈	1	2	yes	—
498	C₂³	C₂×C₇×#41	1	2	yes	—
499	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
500	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
501	C₂³	C₂⁵×C₇	1	1	yes	characteristic
502	Q₈	—	4	32	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	8	no	—
516	C₂×C₄	—	2	16	no	—
517	C₂×C₄	—	2	8	no	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	2	8	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	32	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	4	32	no	—
532	C₂×C₄	—	4	8	no	—
533	C₂×C₄	—	4	8	no	—
534	C₂×C₄	—	4	8	no	—
535	C₂×C₄	C₇×C₂²⋊Q₈	1	16	yes	complemented
536	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
537	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
538	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
539	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
540	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
541	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
542	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
543	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
544	C₂×C₄	C₂×C₇×#41	1	4	yes	—
545	C₇	C₂×#2440	1	1	yes	characteristic, direct product factor, Sylow
546	C₂²	—	2	32	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	4	no	—
553	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
554	C₂²	C₂×C₇×C₄⋊Q₈	1	4	yes	—
555	C₂²	C₂×C₇×C₄⋊Q₈	1	8	yes	complemented
556	C₂²	C₇×#544	1	4	yes	—
557	C₂²	C₇×D₄²	1	4	yes	—
558	C₂²	C₇×#547	1	4	yes	—
559	C₂²	C₇×D₄×Q₈	1	4	yes	—
560	C₂²	C₇×#554	1	4	yes	—
561	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
562	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
563	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
564	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
565	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
566	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
568	C₄	—	2	4	no	—
569	C₄	—	2	8	no	—
570	C₄	—	2	4	no	—
571	C₄	—	2	4	no	—
572	C₄	—	2	4	no	—
573	C₄	—	2	4	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	4	no	—
576	C₄	—	4	4	no	—
577	C₄	C₂×C₇×C₂²⋊Q₈	1	8	yes	complemented
578	C₂	—	2	8	no	—
579	C₂	C₇×#2440	1	8	yes	direct product factor
580	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
581	C₂	C₂²×C₇×C₄⋊Q₈	1	1	yes	characteristic
582	C₂	C₂×C₇×#544	1	1	yes	characteristic
583	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
584	C₂	C₂×C₇×#547	1	1	yes	characteristic
585	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
586	C₂	C₂×C₇×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁵×C₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×C₄⋊Q₈	C₂	semidirect
4. C₇×#2440	C₂	direct (N × H)
5. C₂×C₇×#398	C₂	semidirect
6. C₂×C₇×#395	C₂	semidirect
7. C₂×C₇×#389	C₂	semidirect
8. C₂×C₇×#389	C₂	semidirect
10. C₂×C₇×#384	C₂	semidirect
17. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
37. C₇×#398	C₂²	semidirect
38. C₇×#395	C₂²	semidirect
39. C₇×#389	C₂²	semidirect
40. C₇×#389	C₂²	semidirect
42. C₇×#384	C₂²	semidirect
50. C₂×#2440	C₇	direct (N × H)
61. C₂³×C₄×C₇	Q₈	semidirect
99. C₂×C₇×C₂²⋊C₄	Q₈	semidirect
112. C₂²×C₄⋊Q₈	C₂×C₇	semidirect
115. #2440	C₂×C₇	direct (N × H)
116. C₂×#398	C₂×C₇	semidirect
117. C₂×#395	C₂×C₇	semidirect
118. C₂×#389	C₂×C₇	semidirect
119. C₂×#389	C₂×C₇	semidirect
121. C₂×#384	C₂×C₇	semidirect
173. C₂²×C₄×C₇	C₂×Q₈	semidirect
197. C₇×C₂²⋊C₄	C₂×Q₈	semidirect
204. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
224. #398	C₂²×C₇	semidirect
225. #395	C₂²×C₇	semidirect
226. #389	C₂²×C₇	semidirect
227. #389	C₂²×C₇	semidirect
229. #384	C₂²×C₇	semidirect
247. C₂³×C₇	C₄⋊Q₈	semidirect
292. C₂×C₄×C₇	C₂²⋊Q₈	semidirect
312. C₂³×C₄	C₇×Q₈	semidirect
350. C₂×C₂²⋊C₄	C₇×Q₈	semidirect
372. C₂²×C₇	C₂×C₄⋊Q₈	semidirect
394. C₄×C₇	C₂×C₂²⋊Q₈	semidirect
444. C₂²×C₄	C₂×C₇×Q₈	semidirect
468. C₂²⋊C₄	C₂×C₇×Q₈	semidirect
472. C₂×C₇	#2440	direct (N × H)
490. C₂³	C₇×C₄⋊Q₈	semidirect
535. C₂×C₄	C₇×C₂²⋊Q₈	semidirect
545. C₇	C₂×#2440	direct (N × H)
555. C₂²	C₂×C₇×C₄⋊Q₈	semidirect
577. C₄	C₂×C₇×C₂²⋊Q₈	semidirect
579. C₂	C₇×#2440	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇×C₄⋊Q₈	2
C₂²×C₇×C₂²⋊Q₈	2
C₂³×C₇×C₄⋊C₄	2
C₇×#2440	2
C₂×C₇×#398	2
C₂×C₇×#395	2
C₂×C₇×#389	2
C₂×C₇×#385	2
C₂×C₇×#384	2
C₂×C₇×#380	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂×#2440	7

Subgroups — C2×C7×#2440 #13211890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2440 #13211890