Subgroups — C₂×C₇×#2367 #13211356

Order 1792.

3678 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×#124	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#2367	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#390	C₂	1	1	yes	maximal, characteristic
7	C₂×C₇×#388	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#388	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#385	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
13	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
14	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
16	C₂×C₇×#124	C₄	1	16	yes	complemented
17	C₂×C₇×#124	C₂²	1	8	yes	—
18	C₂×C₄×C₇×Q₈	—	2	8	no	—
19	C₂×C₄×C₇×Q₈	C₂²	1	8	yes	complemented
20	C₂×C₄×C₇×D₄	—	2	8	no	—
21	C₂×C₄×C₇×D₄	C₂²	1	8	yes	—
22	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₇	C₂²	1	2	yes	—
34	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₇	C₂²	1	2	yes	—
36	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
37	C₇×#391	C₂²	1	8	yes	complemented
38	C₇×#390	C₂²	1	8	yes	—
39	C₇×#388	C₂²	1	16	yes	complemented
40	C₇×#388	C₂²	1	16	yes	complemented
41	C₇×#385	C₂²	1	16	yes	complemented
42	C₄×C₇×C₄⋊C₄	C₂²	1	8	yes	complemented
43	C₄×C₇×C₄⋊C₄	C₂²	1	8	yes	complemented
44	C₄×C₇×C₂²⋊C₄	C₂²	1	16	yes	complemented
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×#2367	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂⁵×C₇	C₂³	1	2	yes	—
52	C₂²×C₇×Q₈	—	2	4	no	—
53	C₂²×C₇×Q₈	—	2	4	no	—
54	C₂²×C₇×Q₈	C₂×C₄	1	8	yes	complemented
55	C₂²×C₇×Q₈	C₂³	1	4	yes	—
56	C₂²×C₇×D₄	—	2	4	no	—
57	C₂²×C₇×D₄	—	2	4	no	—
58	C₂²×C₇×D₄	C₂×C₄	1	8	yes	—
59	C₂²×C₇×D₄	C₂³	1	4	yes	—
60	C₂³×C₄×C₇	—	2	8	no	—
61	C₂³×C₄×C₇	—	2	8	no	—
62	C₂³×C₄×C₇	—	4	4	no	—
63	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇	C₂³	1	2	yes	—
65	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₇	C₂³	1	8	yes	—
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	2	yes	—
71	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₇×#124	C₂×C₄	1	64	yes	complemented
75	C₄×C₇×Q₈	—	2	32	no	—
76	C₄×C₇×D₄	—	2	32	no	—
77	C₂×C₇×C₄⋊C₄	—	2	8	no	—
78	C₂×C₇×C₄⋊C₄	—	2	4	no	—
79	C₂×C₇×C₄⋊C₄	—	2	4	no	—
80	C₂×C₇×C₄⋊C₄	—	2	4	no	—
81	C₂×C₇×C₄⋊C₄	D₄	1	8	yes	—
82	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
83	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
86	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
89	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
90	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
91	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
92	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
94	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₂×C₄²×C₇	—	2	4	no	—
98	C₂×C₄²×C₇	—	2	8	no	—
99	C₂×C₄²×C₇	—	2	4	no	—
100	C₂×C₄²×C₇	—	4	4	no	—
101	C₂×C₄²×C₇	C₂×C₄	1	8	yes	complemented
102	C₂×C₄²×C₇	C₂³	1	8	yes	—
103	C₂×C₄²×C₇	C₂³	1	4	yes	—
104	C₂×C₄²×C₇	C₂³	1	4	yes	—
105	C₂×C₄²×C₇	C₂³	1	8	yes	—
106	C₂×C₄²×C₇	C₂³	1	4	yes	—
107	C₇×#95	C₂³	1	4	yes	—
108	C₇×#95	C₂³	1	8	yes	—
109	C₇×#95	C₂³	1	8	yes	—
110	C₇×#95	C₂³	1	4	yes	—
111	C₇×#95	C₂³	1	8	yes	—
112	C₂²×#124	C₂×C₇	1	1	yes	characteristic
113	C₂²×C₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
114	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic
115	#2367	C₂×C₇	1	16	yes	direct product factor
116	C₂×#391	C₂×C₇	1	1	yes	characteristic, complemented
117	C₂×#390	C₂×C₇	1	1	yes	characteristic
118	C₂×#388	C₂×C₇	1	2	yes	complemented
119	C₂×#388	C₂×C₇	1	2	yes	complemented
120	C₂×#385	C₂×C₇	1	2	yes	complemented
121	C₂×C₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
122	C₂×C₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
123	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	2	yes	complemented
124	C₂⁴×C₇	—	2	4	no	—
125	C₂⁴×C₇	—	2	4	no	—
126	C₂⁴×C₇	—	2	4	no	—
127	C₂⁴×C₇	—	2	4	no	—
128	C₂⁴×C₇	—	2	4	no	—
129	C₂⁴×C₇	—	2	4	no	—
130	C₂⁴×C₇	C₂²×C₄	1	8	yes	—
131	C₂⁴×C₇	C₂⁴	1	4	yes	—
132	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
133	C₂×C₇×Q₈	—	2	32	no	—
134	C₂×C₇×Q₈	—	2	8	no	—
135	C₂×C₇×Q₈	—	2	8	no	—
136	C₂×C₇×Q₈	C₂²×C₄	1	16	yes	complemented
137	C₂×C₇×D₄	—	2	32	no	—
138	C₂×C₇×D₄	—	2	8	no	—
139	C₂×C₇×D₄	—	2	8	no	—
140	C₂×C₇×D₄	C₂²×C₄	1	16	yes	—
141	C₂²×C₄×C₇	—	2	2	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	2	no	—
146	C₂²×C₄×C₇	—	2	4	no	—
147	C₂²×C₄×C₇	—	2	4	no	—
148	C₂²×C₄×C₇	—	2	2	no	—
149	C₂²×C₄×C₇	—	2	4	no	—
150	C₂²×C₄×C₇	—	2	2	no	—
151	C₂²×C₄×C₇	—	2	2	no	—
152	C₂²×C₄×C₇	—	2	2	no	—
153	C₂²×C₄×C₇	—	2	2	no	—
154	C₂²×C₄×C₇	—	2	2	no	—
155	C₂²×C₄×C₇	—	2	4	no	—
156	C₂²×C₄×C₇	—	2	2	no	—
157	C₂²×C₄×C₇	—	2	2	no	—
158	C₂²×C₄×C₇	—	2	4	no	—
159	C₂²×C₄×C₇	—	2	4	no	—
160	C₂²×C₄×C₇	—	2	2	no	—
161	C₂²×C₄×C₇	—	2	2	no	—
162	C₂²×C₄×C₇	—	2	16	no	—
163	C₂²×C₄×C₇	—	2	16	no	—
164	C₂²×C₄×C₇	—	4	8	no	—
165	C₂²×C₄×C₇	—	4	32	no	—
166	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
167	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
168	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
169	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
170	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
171	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₇	#41	1	4	yes	—
173	C₂²×C₄×C₇	#41	1	4	yes	—
174	C₂²×C₄×C₇	#41	1	4	yes	—
175	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₇	C₂⁴	1	2	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	4	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	8	no	—
188	C₇×C₄⋊C₄	—	2	8	no	—
189	C₇×C₄⋊C₄	C₂×D₄	1	16	yes	—
190	C₇×C₂²⋊C₄	—	2	16	no	—
191	C₇×C₂²⋊C₄	—	2	16	no	—
192	C₇×C₂²⋊C₄	—	4	8	no	—
193	C₇×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
194	C₇×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
195	C₄²×C₇	—	2	8	no	—
196	C₄²×C₇	—	2	16	no	—
197	C₄²×C₇	—	2	8	no	—
198	C₄²×C₇	—	4	8	no	—
199	C₄²×C₇	C₂²×C₄	1	16	yes	complemented
200	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
201	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
202	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
203	C₂×#124	C₄×C₇	1	16	yes	complemented
204	C₂×#124	C₂²×C₇	1	8	yes	—
205	C₂×C₄×Q₈	—	2	8	no	—
206	C₂×C₄×Q₈	C₂²×C₇	1	8	yes	complemented
207	C₂×C₄×D₄	—	2	8	no	—
208	C₂×C₄×D₄	C₂²×C₇	1	8	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
210	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
211	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
212	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
213	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
214	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
215	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
216	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
217	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
218	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
219	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
220	C₂²×C₄²	C₂²×C₇	1	2	yes	—
221	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
222	C₂²×C₄²	C₂²×C₇	1	2	yes	—
223	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
224	#391	C₂²×C₇	1	8	yes	complemented
225	#390	C₂²×C₇	1	8	yes	—
226	#388	C₂²×C₇	1	16	yes	complemented
227	#388	C₂²×C₇	1	16	yes	complemented
228	#385	C₂²×C₇	1	16	yes	complemented
229	C₄×C₄⋊C₄	C₂²×C₇	1	8	yes	complemented
230	C₄×C₄⋊C₄	C₂²×C₇	1	8	yes	complemented
231	C₄×C₂²⋊C₄	C₂²×C₇	1	16	yes	complemented
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	16	no	—
238	C₂³×C₇	—	2	16	no	—
239	C₂³×C₇	—	2	16	no	—
240	C₂³×C₇	—	2	4	no	—
241	C₂³×C₇	—	2	4	no	—
242	C₂³×C₇	—	2	4	no	—
243	C₂³×C₇	—	2	4	no	—
244	C₂³×C₇	—	2	4	no	—
245	C₂³×C₇	—	2	4	no	—
246	C₂³×C₇	—	4	8	no	—
247	C₂³×C₇	—	4	8	no	—
248	C₂³×C₇	—	4	8	no	—
249	C₂³×C₇	—	4	8	no	—
250	C₂³×C₇	C₂³×C₄	1	8	yes	—
251	C₂³×C₇	C₂³×C₄	1	2	yes	—
252	C₂³×C₇	C₂²×D₄	1	2	yes	—
253	C₂³×C₇	C₂×#41	1	2	yes	—
254	C₂³×C₇	C₂×#41	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	—	2	32	no	—
260	C₇×D₄	—	2	32	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	16	no	—
266	C₂×C₄×C₇	—	2	8	no	—
267	C₂×C₄×C₇	—	2	2	no	—
268	C₂×C₄×C₇	—	2	4	no	—
269	C₂×C₄×C₇	—	2	2	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	4	no	—
273	C₂×C₄×C₇	—	2	4	no	—
274	C₂×C₄×C₇	—	2	2	no	—
275	C₂×C₄×C₇	—	2	4	no	—
276	C₂×C₄×C₇	—	2	2	no	—
277	C₂×C₄×C₇	—	2	2	no	—
278	C₂×C₄×C₇	—	2	2	no	—
279	C₂×C₄×C₇	—	2	2	no	—
280	C₂×C₄×C₇	—	2	2	no	—
281	C₂×C₄×C₇	—	2	4	no	—
282	C₂×C₄×C₇	—	2	2	no	—
283	C₂×C₄×C₇	—	2	2	no	—
284	C₂×C₄×C₇	—	2	4	no	—
285	C₂×C₄×C₇	—	2	4	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	4	32	no	—
289	C₂×C₄×C₇	—	4	4	no	—
290	C₂×C₄×C₇	—	4	4	no	—
291	C₂×C₄×C₇	—	4	8	no	—
292	C₂×C₄×C₇	C₄×D₄	1	16	yes	—
293	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₇	C₂³×C₄	1	8	yes	—
296	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
297	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
298	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
299	C₂×C₄×C₇	C₂×#41	1	4	yes	—
300	C₂×C₄×C₇	C₂×#41	1	4	yes	—
301	C₂×C₄×C₇	C₂×#41	1	4	yes	—
302	C₂⁵	C₂³×C₇	1	2	yes	—
303	C₂²×Q₈	—	2	4	no	—
304	C₂²×Q₈	—	2	4	no	—
305	C₂²×Q₈	C₂×C₄×C₇	1	8	yes	complemented
306	C₂²×Q₈	C₂³×C₇	1	4	yes	—
307	C₂²×D₄	—	2	4	no	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	C₂×C₄×C₇	1	8	yes	—
310	C₂²×D₄	C₂³×C₇	1	4	yes	—
311	C₂³×C₄	—	2	8	no	—
312	C₂³×C₄	—	2	8	no	—
313	C₂³×C₄	—	4	4	no	—
314	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₇	1	2	yes	—
317	C₂³×C₄	C₂³×C₇	1	8	yes	—
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	2	yes	—
322	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
325	#124	C₂×C₄×C₇	1	64	yes	complemented
326	C₄×Q₈	—	2	32	no	—
327	C₄×D₄	—	2	32	no	—
328	C₂×C₄⋊C₄	—	2	8	no	—
329	C₂×C₄⋊C₄	—	2	4	no	—
330	C₂×C₄⋊C₄	—	2	4	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	C₇×D₄	1	8	yes	—
333	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
334	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
338	C₂×C₂²⋊C₄	—	2	8	no	—
339	C₂×C₂²⋊C₄	—	2	8	no	—
340	C₂×C₂²⋊C₄	—	4	4	no	—
341	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	16	yes	complemented
342	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	16	yes	complemented
343	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
348	C₂×C₄²	—	2	4	no	—
349	C₂×C₄²	—	2	8	no	—
350	C₂×C₄²	—	2	4	no	—
351	C₂×C₄²	—	4	4	no	—
352	C₂×C₄²	C₂×C₄×C₇	1	8	yes	complemented
353	C₂×C₄²	C₂³×C₇	1	4	yes	—
354	C₂×C₄²	C₂³×C₇	1	8	yes	—
355	C₂×C₄²	C₂³×C₇	1	4	yes	—
356	C₂×C₄²	C₂³×C₇	1	8	yes	—
357	C₂×C₄²	C₂³×C₇	1	4	yes	—
358	#95	C₂³×C₇	1	4	yes	—
359	#95	C₂³×C₇	1	8	yes	—
360	#95	C₂³×C₇	1	8	yes	—
361	#95	C₂³×C₇	1	4	yes	—
362	#95	C₂³×C₇	1	8	yes	—
363	C₂²×C₇	—	2	8	no	—
364	C₂²×C₇	—	2	8	no	—
365	C₂²×C₇	—	2	8	no	—
366	C₂²×C₇	—	4	32	no	—
367	C₂²×C₇	—	4	4	no	—
368	C₂²×C₇	—	4	4	no	—
369	C₂²×C₇	—	4	4	no	—
370	C₂²×C₇	—	4	4	no	—
371	C₂²×C₇	C₂×C₄×D₄	1	4	yes	—
372	C₂²×C₇	C₄×#41	1	4	yes	—
373	C₂²×C₇	#520	1	4	yes	—
374	C₂²×C₇	#546	1	4	yes	—
375	C₂²×C₇	#548	1	4	yes	—
376	C₂²×C₇	#556	1	4	yes	—
377	C₂²×C₇	#559	1	4	yes	—
378	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
379	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
380	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
381	C₂²×C₇	C₂²×#41	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	8	no	—
386	C₄×C₇	—	2	4	no	—
387	C₄×C₇	—	2	4	no	—
388	C₄×C₇	—	2	4	no	—
389	C₄×C₇	—	2	8	no	—
390	C₄×C₇	—	2	4	no	—
391	C₄×C₇	—	4	2	no	—
392	C₄×C₇	—	4	2	no	—
393	C₄×C₇	—	4	4	no	—
394	C₄×C₇	C₂×C₄×D₄	1	8	yes	—
395	C₂⁴	—	2	4	no	—
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	2	4	no	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	C₂²×C₄×C₇	1	8	yes	—
402	C₂⁴	C₂⁴×C₇	1	4	yes	—
403	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
404	C₂×Q₈	—	2	32	no	—
405	C₂×Q₈	—	2	8	no	—
406	C₂×Q₈	—	2	8	no	—
407	C₂×Q₈	C₂²×C₄×C₇	1	16	yes	complemented
408	C₂×D₄	—	2	32	no	—
409	C₂×D₄	—	2	8	no	—
410	C₂×D₄	—	2	8	no	—
411	C₂×D₄	C₂²×C₄×C₇	1	16	yes	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	16	no	—
434	C₂²×C₄	—	2	16	no	—
435	C₂²×C₄	—	4	8	no	—
436	C₂²×C₄	—	4	32	no	—
437	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
438	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
439	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
440	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
441	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
442	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
443	C₂²×C₄	C₇×#41	1	4	yes	—
444	C₂²×C₄	C₇×#41	1	4	yes	—
445	C₂²×C₄	C₇×#41	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₇	1	2	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	4	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	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	C₂×C₇×D₄	1	16	yes	—
461	C₂²⋊C₄	—	2	16	no	—
462	C₂²⋊C₄	—	2	16	no	—
463	C₂²⋊C₄	—	4	8	no	—
464	C₂²⋊C₄	C₂²×C₄×C₇	1	32	yes	complemented
465	C₂²⋊C₄	C₂²×C₄×C₇	1	32	yes	complemented
466	C₄²	—	2	8	no	—
467	C₄²	—	2	16	no	—
468	C₄²	—	2	8	no	—
469	C₄²	—	4	8	no	—
470	C₄²	C₂²×C₄×C₇	1	16	yes	complemented
471	C₂×C₇	—	4	8	no	—
472	C₂×C₇	#2367	1	8	yes	direct product factor
473	C₂×C₇	C₂²×C₄×D₄	1	1	yes	characteristic
474	C₂×C₇	C₂×C₄×#41	1	1	yes	characteristic
475	C₂×C₇	C₂×#520	1	1	yes	characteristic
476	C₂×C₇	C₂×#546	1	1	yes	characteristic
477	C₂×C₇	C₂×#548	1	1	yes	characteristic
478	C₂×C₇	C₂×#556	1	1	yes	characteristic
479	C₂×C₇	C₂×#559	1	1	yes	characteristic
480	C₂³	—	2	4	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	16	no	—
487	C₂³	—	2	16	no	—
488	C₂³	—	2	16	no	—
489	C₂³	—	4	8	no	—
490	C₂³	—	4	8	no	—
491	C₂³	—	4	8	no	—
492	C₂³	—	4	8	no	—
493	C₂³	C₂³×C₄×C₇	1	8	yes	—
494	C₂³	C₂³×C₄×C₇	1	2	yes	—
495	C₂³	C₂²×C₇×D₄	1	2	yes	—
496	C₂³	C₂×C₇×#41	1	2	yes	—
497	C₂³	C₂×C₇×#41	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	—	2	32	no	—
503	D₄	—	2	32	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	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	16	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	4	32	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	8	no	—
535	C₂×C₄	C₄×C₇×D₄	1	16	yes	—
536	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
537	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
538	C₂×C₄	C₂³×C₄×C₇	1	8	yes	—
539	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
540	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
541	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
542	C₂×C₄	C₂×C₇×#41	1	4	yes	—
543	C₂×C₄	C₂×C₇×#41	1	4	yes	—
544	C₂×C₄	C₂×C₇×#41	1	4	yes	—
545	C₇	C₂×#2367	1	1	yes	characteristic, direct product factor, Sylow
546	C₂²	—	2	8	no	—
547	C₂²	—	2	8	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	32	no	—
554	C₂²	C₂×C₄×C₇×D₄	1	4	yes	—
555	C₂²	C₄×C₇×#41	1	4	yes	—
556	C₂²	C₇×#520	1	4	yes	—
557	C₂²	C₇×#546	1	4	yes	—
558	C₂²	C₇×#548	1	4	yes	—
559	C₂²	C₇×#556	1	4	yes	—
560	C₂²	C₇×#559	1	4	yes	—
561	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
562	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
563	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
564	C₂²	C₂²×C₇×#41	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	8	no	—
569	C₄	—	2	4	no	—
570	C₄	—	2	4	no	—
571	C₄	—	2	4	no	—
572	C₄	—	2	8	no	—
573	C₄	—	2	4	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	4	no	—
577	C₄	C₂×C₄×C₇×D₄	1	8	yes	—
578	C₂	—	4	8	no	—
579	C₂	C₇×#2367	1	8	yes	direct product factor
580	C₂	C₂²×C₄×C₇×D₄	1	1	yes	characteristic
581	C₂	C₂×C₄×C₇×#41	1	1	yes	characteristic
582	C₂	C₂×C₇×#520	1	1	yes	characteristic
583	C₂	C₂×C₇×#546	1	1	yes	characteristic
584	C₂	C₂×C₇×#548	1	1	yes	characteristic
585	C₂	C₂×C₇×#556	1	1	yes	characteristic
586	C₂	C₂×C₇×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂³×C₇×D₄	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₇×Q₈	C₂	semidirect
4. C₇×#2367	C₂	direct (N × H)
5. C₂×C₇×#391	C₂	semidirect
7. C₂×C₇×#388	C₂	semidirect
8. C₂×C₇×#388	C₂	semidirect
9. C₂×C₇×#385	C₂	semidirect
10. C₂×C₄×C₇×C₄⋊C₄	C₂	semidirect
11. C₂×C₄×C₇×C₄⋊C₄	C₂	semidirect
12. C₂×C₄×C₇×C₂²⋊C₄	C₂	semidirect
16. C₂×C₇×#124	C₄	semidirect
19. C₂×C₄×C₇×Q₈	C₂²	semidirect
37. C₇×#391	C₂²	semidirect
39. C₇×#388	C₂²	semidirect
40. C₇×#388	C₂²	semidirect
41. C₇×#385	C₂²	semidirect
42. C₄×C₇×C₄⋊C₄	C₂²	semidirect
43. C₄×C₇×C₄⋊C₄	C₂²	semidirect
44. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
50. C₂×#2367	C₇	direct (N × H)
54. C₂²×C₇×Q₈	C₂×C₄	semidirect
74. C₇×#124	C₂×C₄	semidirect
90. C₂×C₇×C₂²⋊C₄	C₂×C₄	semidirect
91. C₂×C₇×C₂²⋊C₄	C₂×C₄	semidirect
101. C₂×C₄²×C₇	C₂×C₄	semidirect
113. C₂²×C₄×Q₈	C₂×C₇	semidirect
115. #2367	C₂×C₇	direct (N × H)
116. C₂×#391	C₂×C₇	semidirect
118. C₂×#388	C₂×C₇	semidirect
119. C₂×#388	C₂×C₇	semidirect
120. C₂×#385	C₂×C₇	semidirect
121. C₂×C₄×C₄⋊C₄	C₂×C₇	semidirect
122. C₂×C₄×C₄⋊C₄	C₂×C₇	semidirect
123. C₂×C₄×C₂²⋊C₄	C₂×C₇	semidirect
136. C₂×C₇×Q₈	C₂²×C₄	semidirect
193. C₇×C₂²⋊C₄	C₂²×C₄	semidirect
194. C₇×C₂²⋊C₄	C₂²×C₄	semidirect
199. C₄²×C₇	C₂²×C₄	semidirect
203. C₂×#124	C₄×C₇	semidirect
206. C₂×C₄×Q₈	C₂²×C₇	semidirect
224. #391	C₂²×C₇	semidirect
226. #388	C₂²×C₇	semidirect
227. #388	C₂²×C₇	semidirect
228. #385	C₂²×C₇	semidirect
229. C₄×C₄⋊C₄	C₂²×C₇	semidirect
230. C₄×C₄⋊C₄	C₂²×C₇	semidirect
231. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
305. C₂²×Q₈	C₂×C₄×C₇	semidirect
325. #124	C₂×C₄×C₇	semidirect
341. C₂×C₂²⋊C₄	C₂×C₄×C₇	semidirect
342. C₂×C₂²⋊C₄	C₂×C₄×C₇	semidirect
352. C₂×C₄²	C₂×C₄×C₇	semidirect
407. C₂×Q₈	C₂²×C₄×C₇	semidirect
464. C₂²⋊C₄	C₂²×C₄×C₇	semidirect
465. C₂²⋊C₄	C₂²×C₄×C₇	semidirect
470. C₄²	C₂²×C₄×C₇	semidirect
472. C₂×C₇	#2367	direct (N × H)
545. C₇	C₂×#2367	direct (N × H)
579. C₂	C₇×#2367	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×#124	2
C₂²×C₄×C₇×Q₈	2
C₂²×C₄×C₇×D₄	2
C₇×#2367	2
C₂×C₇×#391	2
C₂×C₇×#390	2
C₂×C₇×#388	2
C₂×C₇×#385	2
C₂×C₄×C₇×C₄⋊C₄	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂×#2367	7

Subgroups — C2×C7×#2367 #13211356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2367 #13211356