Subgroups — C₂×C₇×#2437 #13211863

Order 1792.

4926 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
2	C₂³×C₇×C₂²⋊C₄	C₂	1	2	yes	maximal
3	C₇×#2437	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#396	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#385	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#385	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#380	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#379	C₂	1	1	yes	maximal, characteristic
11	C₂⁶×C₇	C₂²	1	1	yes	characteristic
12	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
15	C₂×C₇×C₂²⋊Q₈	—	2	16	no	—
16	C₂×C₇×C₂²⋊Q₈	C₂²	1	16	yes	complemented
17	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
18	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
19	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
20	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
21	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₇×C₂²⋊C₄	—	2	16	no	—
23	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₇×C₂²⋊C₄	C₂²	1	16	yes	—
26	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₇×#399	C₂²	1	8	yes	complemented
33	C₇×#396	C₂²	1	16	yes	complemented
34	C₇×#393	C₂²	1	8	yes	complemented
35	C₇×#385	C₂²	1	16	yes	complemented
36	C₇×#385	C₂²	1	16	yes	complemented
37	C₇×#380	C₂²	1	16	yes	complemented
38	C₇×#379	C₂²	1	8	yes	—
39	C₂×C₇×#95	C₂²	1	2	yes	complemented
40	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×#95	C₂²	1	2	yes	complemented
43	C₂×#2437	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂⁵×C₇	—	2	8	no	—
45	C₂⁵×C₇	—	2	8	no	—
46	C₂⁵×C₇	—	4	2	no	—
47	C₂⁵×C₇	—	4	2	no	—
48	C₂⁵×C₇	Q₈	1	8	yes	complemented
49	C₂⁵×C₇	C₂³	1	1	yes	characteristic
50	C₂⁵×C₇	C₂³	1	4	yes	—
51	C₂⁵×C₇	C₂³	1	2	yes	—
52	C₂²×C₇×Q₈	—	2	8	no	—
53	C₂²×C₇×Q₈	—	4	2	no	—
54	C₂²×C₇×Q₈	C₂³	1	4	yes	complemented
55	C₂³×C₄×C₇	—	2	8	no	—
56	C₂³×C₄×C₇	—	2	8	no	—
57	C₂³×C₄×C₇	—	2	8	no	—
58	C₂³×C₄×C₇	—	2	8	no	—
59	C₂³×C₄×C₇	—	4	4	no	—
60	C₂³×C₄×C₇	—	4	4	no	—
61	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₇	C₂³	1	2	yes	—
64	C₂³×C₄×C₇	C₂³	1	2	yes	—
65	C₂³×C₄×C₇	C₂³	1	2	yes	—
66	C₂³×C₄×C₇	C₂³	1	8	yes	—
67	C₂³×C₄×C₇	C₂³	1	8	yes	—
68	C₂³×C₄×C₇	C₂³	1	2	yes	—
69	C₂³×C₄×C₇	C₂³	1	2	yes	—
70	C₇×C₂²⋊Q₈	—	2	64	no	—
71	C₂×C₇×C₄⋊C₄	—	2	8	no	—
72	C₂×C₇×C₄⋊C₄	—	2	8	no	—
73	C₂×C₇×C₄⋊C₄	—	2	8	no	—
74	C₂×C₇×C₄⋊C₄	—	4	4	no	—
75	C₂×C₇×C₄⋊C₄	—	4	2	no	—
76	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
77	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
78	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
79	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
80	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
81	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
82	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
83	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
84	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
85	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
86	C₂×C₇×C₂²⋊C₄	—	2	64	no	—
87	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
88	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
89	C₂×C₇×C₂²⋊C₄	D₄	1	16	yes	—
90	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
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	4	yes	—
96	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₇×#95	C₂³	1	4	yes	complemented
99	C₇×#95	C₂³	1	8	yes	complemented
100	C₇×#95	C₂³	1	8	yes	complemented
101	C₇×#95	C₂³	1	4	yes	complemented
102	C₂²×C₂²⋊Q₈	C₂×C₇	1	2	yes	complemented
103	C₂³×C₂²⋊C₄	C₂×C₇	1	2	yes	—
104	#2437	C₂×C₇	1	16	yes	direct product factor
105	C₂×#399	C₂×C₇	1	1	yes	characteristic, complemented
106	C₂×#396	C₂×C₇	1	2	yes	complemented
107	C₂×#393	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂×#385	C₂×C₇	1	2	yes	complemented
109	C₂×#385	C₂×C₇	1	2	yes	complemented
110	C₂×#380	C₂×C₇	1	2	yes	complemented
111	C₂×#379	C₂×C₇	1	1	yes	characteristic
112	C₂⁴×C₇	—	2	4	no	—
113	C₂⁴×C₇	—	2	4	no	—
114	C₂⁴×C₇	—	2	4	no	—
115	C₂⁴×C₇	—	2	4	no	—
116	C₂⁴×C₇	—	2	64	no	—
117	C₂⁴×C₇	—	2	16	no	—
118	C₂⁴×C₇	—	2	4	no	—
119	C₂⁴×C₇	—	2	16	no	—
120	C₂⁴×C₇	—	2	4	no	—
121	C₂⁴×C₇	—	2	2	no	—
122	C₂⁴×C₇	—	2	2	no	—
123	C₂⁴×C₇	—	4	16	no	—
124	C₂⁴×C₇	—	4	4	no	—
125	C₂⁴×C₇	—	4	4	no	—
126	C₂⁴×C₇	—	4	16	no	—
127	C₂⁴×C₇	—	4	32	no	—
128	C₂⁴×C₇	—	4	16	no	—
129	C₂⁴×C₇	C₂×D₄	1	8	yes	—
130	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
131	C₂⁴×C₇	C₂×Q₈	1	8	yes	—
132	C₂⁴×C₇	C₂×Q₈	1	16	yes	complemented
133	C₂⁴×C₇	#41	1	8	yes	—
134	C₂⁴×C₇	C₂⁴	1	2	yes	—
135	C₂⁴×C₇	C₂⁴	1	4	yes	—
136	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
137	C₂×C₇×Q₈	—	2	16	no	—
138	C₂×C₇×Q₈	—	4	4	no	—
139	C₂×C₇×Q₈	—	4	16	no	—
140	C₂²×C₄×C₇	—	2	4	no	—
141	C₂²×C₄×C₇	—	2	4	no	—
142	C₂²×C₄×C₇	—	2	4	no	—
143	C₂²×C₄×C₇	—	2	4	no	—
144	C₂²×C₄×C₇	—	2	4	no	—
145	C₂²×C₄×C₇	—	2	4	no	—
146	C₂²×C₄×C₇	—	2	4	no	—
147	C₂²×C₄×C₇	—	2	4	no	—
148	C₂²×C₄×C₇	—	2	4	no	—
149	C₂²×C₄×C₇	—	2	16	no	—
150	C₂²×C₄×C₇	—	2	4	no	—
151	C₂²×C₄×C₇	—	2	4	no	—
152	C₂²×C₄×C₇	—	2	16	no	—
153	C₂²×C₄×C₇	—	2	4	no	—
154	C₂²×C₄×C₇	—	2	4	no	—
155	C₂²×C₄×C₇	—	2	2	no	—
156	C₂²×C₄×C₇	—	2	2	no	—
157	C₂²×C₄×C₇	—	2	4	no	—
158	C₂²×C₄×C₇	—	2	4	no	—
159	C₂²×C₄×C₇	—	2	16	no	—
160	C₂²×C₄×C₇	—	2	16	no	—
161	C₂²×C₄×C₇	—	4	8	no	—
162	C₂²×C₄×C₇	—	4	8	no	—
163	C₂²×C₄×C₇	—	4	32	no	—
164	C₂²×C₄×C₇	—	4	32	no	—
165	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
166	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
167	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
174	C₇×C₄⋊C₄	—	2	16	no	—
175	C₇×C₄⋊C₄	—	2	16	no	—
176	C₇×C₄⋊C₄	—	2	16	no	—
177	C₇×C₄⋊C₄	—	4	8	no	—
178	C₇×C₄⋊C₄	—	4	4	no	—
179	C₇×C₂²⋊C₄	—	2	16	no	—
180	C₇×C₂²⋊C₄	—	2	16	no	—
181	C₇×C₂²⋊C₄	—	2	16	no	—
182	C₇×C₂²⋊C₄	—	2	16	no	—
183	C₇×C₂²⋊C₄	—	2	16	no	—
184	C₇×C₂²⋊C₄	—	4	4	no	—
185	C₇×C₂²⋊C₄	—	4	4	no	—
186	C₇×C₂²⋊C₄	C₂×D₄	1	32	yes	—
187	C₂⁶	C₂²×C₇	1	1	yes	characteristic
188	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
189	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
190	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
191	C₂×C₂²⋊Q₈	—	2	16	no	—
192	C₂×C₂²⋊Q₈	C₂²×C₇	1	16	yes	complemented
193	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
194	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
195	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
196	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
197	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
198	C₂²×C₂²⋊C₄	—	2	16	no	—
199	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
200	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
201	C₂²×C₂²⋊C₄	C₂²×C₇	1	16	yes	—
202	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
203	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
204	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
205	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
206	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
207	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
208	#399	C₂²×C₇	1	8	yes	complemented
209	#396	C₂²×C₇	1	16	yes	complemented
210	#393	C₂²×C₇	1	8	yes	complemented
211	#385	C₂²×C₇	1	16	yes	complemented
212	#385	C₂²×C₇	1	16	yes	complemented
213	#380	C₂²×C₇	1	16	yes	complemented
214	#379	C₂²×C₇	1	8	yes	—
215	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
216	C₂×#95	C₂²×C₇	1	2	yes	complemented
217	C₂×#95	C₂²×C₇	1	2	yes	complemented
218	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
219	C₂³×C₇	—	2	16	no	—
220	C₂³×C₇	—	2	16	no	—
221	C₂³×C₇	—	2	16	no	—
222	C₂³×C₇	—	2	16	no	—
223	C₂³×C₇	—	2	16	no	—
224	C₂³×C₇	—	2	16	no	—
225	C₂³×C₇	—	2	4	no	—
226	C₂³×C₇	—	2	4	no	—
227	C₂³×C₇	—	2	4	no	—
228	C₂³×C₇	—	2	4	no	—
229	C₂³×C₇	—	2	16	no	—
230	C₂³×C₇	—	2	64	no	—
231	C₂³×C₇	—	2	8	no	—
232	C₂³×C₇	—	2	4	no	—
233	C₂³×C₇	—	2	4	no	—
234	C₂³×C₇	—	2	2	no	—
235	C₂³×C₇	—	2	2	no	—
236	C₂³×C₇	—	4	16	no	—
237	C₂³×C₇	—	4	128	no	—
238	C₂³×C₇	—	4	16	no	—
239	C₂³×C₇	—	4	32	no	—
240	C₂³×C₇	—	4	16	no	—
241	C₂³×C₇	—	4	4	no	—
242	C₂³×C₇	—	4	8	no	—
243	C₂³×C₇	—	4	4	no	—
244	C₂³×C₇	C₂²⋊Q₈	1	32	yes	complemented
245	C₂³×C₇	C₂²×D₄	1	8	yes	—
246	C₂³×C₇	C₂²×D₄	1	4	yes	—
247	C₂³×C₇	C₂²×Q₈	1	4	yes	—
248	C₂³×C₇	C₂²×Q₈	1	8	yes	—
249	C₂³×C₇	C₂²×Q₈	1	2	yes	—
250	C₂³×C₇	C₂×#41	1	8	yes	—
251	C₂³×C₇	C₂×#41	1	4	yes	—
252	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
253	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
254	C₂³×C₇	C₂⁵	1	1	yes	characteristic
255	C₇×Q₈	—	4	16	no	—
256	C₂×C₄×C₇	—	2	16	no	—
257	C₂×C₄×C₇	—	2	16	no	—
258	C₂×C₄×C₇	—	2	4	no	—
259	C₂×C₄×C₇	—	2	4	no	—
260	C₂×C₄×C₇	—	2	4	no	—
261	C₂×C₄×C₇	—	2	4	no	—
262	C₂×C₄×C₇	—	2	4	no	—
263	C₂×C₄×C₇	—	2	4	no	—
264	C₂×C₄×C₇	—	2	4	no	—
265	C₂×C₄×C₇	—	2	4	no	—
266	C₂×C₄×C₇	—	2	4	no	—
267	C₂×C₄×C₇	—	2	4	no	—
268	C₂×C₄×C₇	—	2	4	no	—
269	C₂×C₄×C₇	—	2	4	no	—
270	C₂×C₄×C₇	—	2	4	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	2	4	no	—
274	C₂×C₄×C₇	—	2	4	no	—
275	C₂×C₄×C₇	—	4	32	no	—
276	C₂×C₄×C₇	—	4	32	no	—
277	C₂×C₄×C₇	—	4	8	no	—
278	C₂×C₄×C₇	—	4	4	no	—
279	C₂×C₄×C₇	—	4	8	no	—
280	C₂×C₄×C₇	—	4	8	no	—
281	C₂×C₄×C₇	—	4	4	no	—
282	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
283	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
284	C₂⁵	—	2	8	no	—
285	C₂⁵	—	2	8	no	—
286	C₂⁵	—	4	2	no	—
287	C₂⁵	—	4	2	no	—
288	C₂⁵	C₇×Q₈	1	8	yes	complemented
289	C₂⁵	C₂³×C₇	1	1	yes	characteristic
290	C₂⁵	C₂³×C₇	1	4	yes	—
291	C₂⁵	C₂³×C₇	1	2	yes	—
292	C₂²×Q₈	—	2	8	no	—
293	C₂²×Q₈	—	4	2	no	—
294	C₂²×Q₈	C₂³×C₇	1	4	yes	complemented
295	C₂³×C₄	—	2	8	no	—
296	C₂³×C₄	—	2	8	no	—
297	C₂³×C₄	—	2	8	no	—
298	C₂³×C₄	—	2	8	no	—
299	C₂³×C₄	—	4	4	no	—
300	C₂³×C₄	—	4	4	no	—
301	C₂³×C₄	C₂³×C₇	1	2	yes	—
302	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₇	1	2	yes	—
305	C₂³×C₄	C₂³×C₇	1	2	yes	—
306	C₂³×C₄	C₂³×C₇	1	8	yes	—
307	C₂³×C₄	C₂³×C₇	1	8	yes	—
308	C₂³×C₄	C₂³×C₇	1	2	yes	—
309	C₂³×C₄	C₂³×C₇	1	2	yes	—
310	C₂²⋊Q₈	—	2	64	no	—
311	C₂×C₄⋊C₄	—	2	8	no	—
312	C₂×C₄⋊C₄	—	2	8	no	—
313	C₂×C₄⋊C₄	—	2	8	no	—
314	C₂×C₄⋊C₄	—	4	4	no	—
315	C₂×C₄⋊C₄	—	4	2	no	—
316	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
317	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
318	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
319	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
320	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
321	C₂×C₂²⋊C₄	—	2	8	no	—
322	C₂×C₂²⋊C₄	—	2	8	no	—
323	C₂×C₂²⋊C₄	—	2	8	no	—
324	C₂×C₂²⋊C₄	—	2	8	no	—
325	C₂×C₂²⋊C₄	—	2	8	no	—
326	C₂×C₂²⋊C₄	—	2	64	no	—
327	C₂×C₂²⋊C₄	—	4	2	no	—
328	C₂×C₂²⋊C₄	—	4	2	no	—
329	C₂×C₂²⋊C₄	C₇×D₄	1	16	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
338	#95	C₂³×C₇	1	4	yes	complemented
339	#95	C₂³×C₇	1	8	yes	complemented
340	#95	C₂³×C₇	1	8	yes	complemented
341	#95	C₂³×C₇	1	4	yes	complemented
342	C₂²×C₇	—	2	8	no	—
343	C₂²×C₇	—	2	8	no	—
344	C₂²×C₇	—	2	64	no	—
345	C₂²×C₇	—	2	8	no	—
346	C₂²×C₇	—	2	8	no	—
347	C₂²×C₇	—	2	8	no	—
348	C₂²×C₇	—	2	8	no	—
349	C₂²×C₇	—	2	8	no	—
350	C₂²×C₇	—	2	4	no	—
351	C₂²×C₇	—	4	64	no	—
352	C₂²×C₇	—	4	16	no	—
353	C₂²×C₇	—	4	2	no	—
354	C₂²×C₇	—	4	4	no	—
355	C₂²×C₇	—	4	2	no	—
356	C₂²×C₇	C₂×C₂²⋊Q₈	1	8	yes	—
357	C₂²×C₇	C₂×C₂²⋊Q₈	1	16	yes	complemented
358	C₂²×C₇	#543	1	4	yes	—
359	C₂²×C₇	D₄²	1	4	yes	—
360	C₂²×C₇	#546	1	8	yes	—
361	C₂²×C₇	#551	1	4	yes	—
362	C₂²×C₇	C₂³×D₄	1	2	yes	—
363	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
364	C₂²×C₇	C₂²×#41	1	2	yes	—
365	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
367	C₄×C₇	—	2	8	no	—
368	C₄×C₇	—	2	8	no	—
369	C₄×C₇	—	4	4	no	—
370	C₄×C₇	—	4	2	no	—
371	C₄×C₇	—	4	4	no	—
372	C₄×C₇	—	4	4	no	—
373	C₄×C₇	—	4	2	no	—
374	C₂⁴	—	2	4	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	—	2	4	no	—
378	C₂⁴	—	2	64	no	—
379	C₂⁴	—	2	16	no	—
380	C₂⁴	—	2	4	no	—
381	C₂⁴	—	2	16	no	—
382	C₂⁴	—	2	4	no	—
383	C₂⁴	—	2	2	no	—
384	C₂⁴	—	2	2	no	—
385	C₂⁴	—	4	16	no	—
386	C₂⁴	—	4	4	no	—
387	C₂⁴	—	4	4	no	—
388	C₂⁴	—	4	16	no	—
389	C₂⁴	—	4	32	no	—
390	C₂⁴	—	4	16	no	—
391	C₂⁴	C₂×C₇×D₄	1	8	yes	—
392	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
393	C₂⁴	C₂×C₇×Q₈	1	8	yes	—
394	C₂⁴	C₂×C₇×Q₈	1	16	yes	complemented
395	C₂⁴	C₇×#41	1	8	yes	—
396	C₂⁴	C₂⁴×C₇	1	2	yes	—
397	C₂⁴	C₂⁴×C₇	1	4	yes	—
398	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
399	C₂×Q₈	—	2	16	no	—
400	C₂×Q₈	—	4	4	no	—
401	C₂×Q₈	—	4	16	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	16	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	16	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	16	no	—
422	C₂²×C₄	—	2	16	no	—
423	C₂²×C₄	—	4	8	no	—
424	C₂²×C₄	—	4	8	no	—
425	C₂²×C₄	—	4	32	no	—
426	C₂²×C₄	—	4	32	no	—
427	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
428	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
429	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
434	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
436	C₄⋊C₄	—	2	16	no	—
437	C₄⋊C₄	—	2	16	no	—
438	C₄⋊C₄	—	2	16	no	—
439	C₄⋊C₄	—	4	8	no	—
440	C₄⋊C₄	—	4	4	no	—
441	C₂²⋊C₄	—	2	16	no	—
442	C₂²⋊C₄	—	2	16	no	—
443	C₂²⋊C₄	—	2	16	no	—
444	C₂²⋊C₄	—	2	16	no	—
445	C₂²⋊C₄	—	2	16	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₂²⋊C₄	—	4	4	no	—
448	C₂²⋊C₄	C₂×C₇×D₄	1	32	yes	—
449	C₂×C₇	—	2	16	no	—
450	C₂×C₇	—	4	4	no	—
451	C₂×C₇	#2437	1	8	yes	direct product factor
452	C₂×C₇	C₂²×C₂²⋊Q₈	1	2	yes	—
453	C₂×C₇	C₂×#543	1	1	yes	characteristic
454	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
455	C₂×C₇	C₂×#546	1	2	yes	—
456	C₂×C₇	C₂×#551	1	1	yes	characteristic
457	C₂³	—	2	4	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	16	no	—
462	C₂³	—	2	16	no	—
463	C₂³	—	2	16	no	—
464	C₂³	—	2	16	no	—
465	C₂³	—	2	16	no	—
466	C₂³	—	2	16	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	16	no	—
472	C₂³	—	2	64	no	—
473	C₂³	—	2	8	no	—
474	C₂³	—	4	16	no	—
475	C₂³	—	4	128	no	—
476	C₂³	—	4	16	no	—
477	C₂³	—	4	32	no	—
478	C₂³	—	4	16	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	4	no	—
482	C₂³	C₇×C₂²⋊Q₈	1	32	yes	complemented
483	C₂³	C₂²×C₇×D₄	1	8	yes	—
484	C₂³	C₂²×C₇×D₄	1	4	yes	—
485	C₂³	C₂²×C₇×Q₈	1	4	yes	—
486	C₂³	C₂²×C₇×Q₈	1	8	yes	—
487	C₂³	C₂²×C₇×Q₈	1	2	yes	—
488	C₂³	C₂×C₇×#41	1	8	yes	—
489	C₂³	C₂×C₇×#41	1	4	yes	—
490	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
491	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
492	C₂³	C₂⁵×C₇	1	1	yes	characteristic
493	Q₈	—	4	16	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	16	no	—
499	C₂×C₄	—	2	16	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	4	32	no	—
514	C₂×C₄	—	4	32	no	—
515	C₂×C₄	—	4	8	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	4	8	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
521	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
522	C₇	C₂×#2437	1	1	yes	characteristic, direct product factor, Sylow
523	C₂²	—	2	64	no	—
524	C₂²	—	2	8	no	—
525	C₂²	—	2	8	no	—
526	C₂²	—	2	8	no	—
527	C₂²	—	2	8	no	—
528	C₂²	—	2	8	no	—
529	C₂²	—	2	8	no	—
530	C₂²	—	2	8	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	4	64	no	—
533	C₂²	—	4	16	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	2	no	—
537	C₂²	C₂×C₇×C₂²⋊Q₈	1	8	yes	—
538	C₂²	C₂×C₇×C₂²⋊Q₈	1	16	yes	complemented
539	C₂²	C₇×#543	1	4	yes	—
540	C₂²	C₇×D₄²	1	4	yes	—
541	C₂²	C₇×#546	1	8	yes	—
542	C₂²	C₇×#551	1	4	yes	—
543	C₂²	C₂³×C₇×D₄	1	2	yes	—
544	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
545	C₂²	C₂²×C₇×#41	1	2	yes	—
546	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
548	C₄	—	2	8	no	—
549	C₄	—	2	8	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	4	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	2	no	—
555	C₂	—	2	16	no	—
556	C₂	—	4	4	no	—
557	C₂	C₇×#2437	1	8	yes	direct product factor
558	C₂	C₂²×C₇×C₂²⋊Q₈	1	2	yes	—
559	C₂	C₂×C₇×#543	1	1	yes	characteristic
560	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
561	C₂	C₂×C₇×#546	1	2	yes	—
562	C₂	C₂×C₇×#551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁶×C₇	C₂²
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×C₂²⋊Q₈	C₂	semidirect
3. C₇×#2437	C₂	direct (N × H)
4. C₂×C₇×#399	C₂	semidirect
5. C₂×C₇×#396	C₂	semidirect
6. C₂×C₇×#393	C₂	semidirect
7. C₂×C₇×#385	C₂	semidirect
8. C₂×C₇×#385	C₂	semidirect
9. C₂×C₇×#380	C₂	semidirect
12. C₂³×C₇×Q₈	C₂²	semidirect
16. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
17. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
18. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
19. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
20. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
21. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
32. C₇×#399	C₂²	semidirect
33. C₇×#396	C₂²	semidirect
34. C₇×#393	C₂²	semidirect
35. C₇×#385	C₂²	semidirect
36. C₇×#385	C₂²	semidirect
37. C₇×#380	C₂²	semidirect
39. C₂×C₇×#95	C₂²	semidirect
40. C₂×C₇×#95	C₂²	semidirect
41. C₂×C₇×#95	C₂²	semidirect
42. C₂×C₇×#95	C₂²	semidirect
43. C₂×#2437	C₇	direct (N × H)
48. C₂⁵×C₇	Q₈	semidirect
54. C₂²×C₇×Q₈	C₂³	semidirect
76. C₂×C₇×C₄⋊C₄	C₂³	semidirect
77. C₂×C₇×C₄⋊C₄	C₂³	semidirect
78. C₂×C₇×C₄⋊C₄	C₂³	semidirect
79. C₂×C₇×C₄⋊C₄	C₂³	semidirect
80. C₂×C₇×C₄⋊C₄	C₂³	semidirect
98. C₇×#95	C₂³	semidirect
99. C₇×#95	C₂³	semidirect
100. C₇×#95	C₂³	semidirect
101. C₇×#95	C₂³	semidirect
102. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
104. #2437	C₂×C₇	direct (N × H)
105. C₂×#399	C₂×C₇	semidirect
106. C₂×#396	C₂×C₇	semidirect
107. C₂×#393	C₂×C₇	semidirect
108. C₂×#385	C₂×C₇	semidirect
109. C₂×#385	C₂×C₇	semidirect
110. C₂×#380	C₂×C₇	semidirect
132. C₂⁴×C₇	C₂×Q₈	semidirect
188. C₂³×Q₈	C₂²×C₇	semidirect
192. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
193. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
194. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
195. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
196. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
197. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
208. #399	C₂²×C₇	semidirect
209. #396	C₂²×C₇	semidirect
210. #393	C₂²×C₇	semidirect
211. #385	C₂²×C₇	semidirect
212. #385	C₂²×C₇	semidirect
213. #380	C₂²×C₇	semidirect
215. C₂×#95	C₂²×C₇	semidirect
216. C₂×#95	C₂²×C₇	semidirect
217. C₂×#95	C₂²×C₇	semidirect
218. C₂×#95	C₂²×C₇	semidirect
244. C₂³×C₇	C₂²⋊Q₈	semidirect
288. C₂⁵	C₇×Q₈	semidirect
294. C₂²×Q₈	C₂³×C₇	semidirect
316. C₂×C₄⋊C₄	C₂³×C₇	semidirect
317. C₂×C₄⋊C₄	C₂³×C₇	semidirect
318. C₂×C₄⋊C₄	C₂³×C₇	semidirect
319. C₂×C₄⋊C₄	C₂³×C₇	semidirect
320. C₂×C₄⋊C₄	C₂³×C₇	semidirect
338. #95	C₂³×C₇	semidirect
339. #95	C₂³×C₇	semidirect
340. #95	C₂³×C₇	semidirect
341. #95	C₂³×C₇	semidirect
357. C₂²×C₇	C₂×C₂²⋊Q₈	semidirect
394. C₂⁴	C₂×C₇×Q₈	semidirect
451. C₂×C₇	#2437	direct (N × H)
482. C₂³	C₇×C₂²⋊Q₈	semidirect
522. C₇	C₂×#2437	direct (N × H)
538. C₂²	C₂×C₇×C₂²⋊Q₈	semidirect
557. C₂	C₇×#2437	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×C₂²⋊Q₈	2
C₂³×C₇×C₂²⋊C₄	2
C₇×#2437	2
C₂×C₇×#399	2
C₂×C₇×#396	2
C₂×C₇×#393	2
C₂×C₇×#385	2
C₂×C₇×#380	2
C₂×C₇×#379	2
C₂×#2437	7

Subgroups — C2×C7×#2437 #13211863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2437 #13211863