Subgroups — C₂×C₇×#2561 #13212057

Order 1792.

4166 conjugacy classes of subgroups.

The subgroup lattice has 444 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	1	yes	maximal, characteristic, complemented
2	C₂³×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#2561	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#397	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#393	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#388	C₂	1	4	yes	maximal, complemented
7	C₂×C₇×#381	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#379	C₂	1	2	yes	maximal
9	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁶×C₇	C₂²	1	1	yes	characteristic
11	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
12	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₂²⋊Q₈	—	2	8	no	—
15	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
16	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
18	C₂²×C₇×C₂²⋊C₄	—	2	8	no	—
19	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
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	4	yes	—
26	C₂²×C₄²×C₇	C₂²	1	2	yes	complemented
27	C₇×#397	C₂²	1	16	yes	complemented
28	C₇×#393	C₂²	1	16	yes	complemented
29	C₇×#388	C₂²	1	32	yes	complemented
30	C₇×#381	C₂²	1	16	yes	complemented
31	C₇×#379	C₂²	1	16	yes	—
32	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	complemented
33	C₂×C₇×#95	C₂²	1	2	yes	complemented
34	C₂×C₇×#95	C₂²	1	4	yes	complemented
35	C₂×C₇×#95	C₂²	1	4	yes	complemented
36	C₂×#2561	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂⁵×C₇	—	2	4	no	—
38	C₂⁵×C₇	—	2	8	no	—
39	C₂⁵×C₇	—	2	8	no	—
40	C₂⁵×C₇	—	4	4	no	—
41	C₂⁵×C₇	C₂³	1	2	yes	—
42	C₂⁵×C₇	C₂³	1	4	yes	—
43	C₂⁵×C₇	C₂³	1	1	yes	characteristic
44	C₂²×C₇×Q₈	—	2	4	no	—
45	C₂²×C₇×Q₈	—	4	4	no	—
46	C₂²×C₇×Q₈	C₂³	1	4	yes	complemented
47	C₂³×C₄×C₇	—	2	4	no	—
48	C₂³×C₄×C₇	—	2	8	no	—
49	C₂³×C₄×C₇	—	4	4	no	—
50	C₂³×C₄×C₇	D₄	1	8	yes	—
51	C₂³×C₄×C₇	C₂³	1	4	yes	—
52	C₂³×C₄×C₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₇	C₂³	1	4	yes	—
54	C₂³×C₄×C₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₇	C₂³	1	4	yes	—
59	C₇×C₂²⋊Q₈	—	2	32	no	—
60	C₂×C₇×C₄⋊C₄	—	2	4	no	—
61	C₂×C₇×C₄⋊C₄	—	2	8	no	—
62	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
63	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
64	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
65	C₂×C₇×C₂²⋊C₄	—	2	16	no	—
66	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
67	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
68	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
69	C₂×C₇×C₂²⋊C₄	—	2	32	no	—
70	C₂×C₇×C₂²⋊C₄	—	4	8	no	—
71	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
72	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
73	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
74	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
76	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
77	C₂×C₄²×C₇	—	4	4	no	—
78	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
79	C₇×#95	C₂³	1	8	yes	complemented
80	C₇×#95	C₂³	1	16	yes	complemented
81	C₇×#95	C₂³	1	16	yes	complemented
82	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
83	C₂³×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
84	#2561	C₂×C₇	1	16	yes	direct product factor
85	C₂×#397	C₂×C₇	1	2	yes	complemented
86	C₂×#393	C₂×C₇	1	2	yes	complemented
87	C₂×#388	C₂×C₇	1	4	yes	complemented
88	C₂×#381	C₂×C₇	1	2	yes	complemented
89	C₂×#379	C₂×C₇	1	2	yes	—
90	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
91	C₂⁴×C₇	—	2	4	no	—
92	C₂⁴×C₇	—	2	4	no	—
93	C₂⁴×C₇	—	2	32	no	—
94	C₂⁴×C₇	—	2	8	no	—
95	C₂⁴×C₇	—	2	4	no	—
96	C₂⁴×C₇	—	2	16	no	—
97	C₂⁴×C₇	—	2	4	no	—
98	C₂⁴×C₇	—	2	8	no	—
99	C₂⁴×C₇	—	2	8	no	—
100	C₂⁴×C₇	—	2	16	no	—
101	C₂⁴×C₇	—	4	8	no	—
102	C₂⁴×C₇	—	4	64	no	—
103	C₂⁴×C₇	—	4	16	no	—
104	C₂⁴×C₇	—	4	16	no	—
105	C₂⁴×C₇	C₂×D₄	1	4	yes	—
106	C₂⁴×C₇	#41	1	8	yes	—
107	C₂⁴×C₇	#41	1	8	yes	—
108	C₂⁴×C₇	C₂⁴	1	4	yes	—
109	C₂⁴×C₇	C₂⁴	1	2	yes	—
110	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
111	C₂×C₇×Q₈	—	2	8	no	—
112	C₂×C₇×Q₈	—	4	8	no	—
113	C₂×C₇×Q₈	—	4	16	no	—
114	C₂²×C₄×C₇	—	2	4	no	—
115	C₂²×C₄×C₇	—	2	4	no	—
116	C₂²×C₄×C₇	—	2	8	no	—
117	C₂²×C₄×C₇	—	2	4	no	—
118	C₂²×C₄×C₇	—	2	4	no	—
119	C₂²×C₄×C₇	—	2	4	no	—
120	C₂²×C₄×C₇	—	2	8	no	—
121	C₂²×C₄×C₇	—	2	8	no	—
122	C₂²×C₄×C₇	—	2	8	no	—
123	C₂²×C₄×C₇	—	2	16	no	—
124	C₂²×C₄×C₇	—	2	8	no	—
125	C₂²×C₄×C₇	—	2	8	no	—
126	C₂²×C₄×C₇	—	2	8	no	—
127	C₂²×C₄×C₇	—	4	16	no	—
128	C₂²×C₄×C₇	—	4	8	no	—
129	C₂²×C₄×C₇	—	4	16	no	—
130	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₇	C₂×D₄	1	16	yes	—
133	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
135	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
139	C₇×C₄⋊C₄	—	2	8	no	—
140	C₇×C₄⋊C₄	—	2	16	no	—
141	C₇×C₂²⋊C₄	—	2	16	no	—
142	C₇×C₂²⋊C₄	—	2	32	no	—
143	C₇×C₂²⋊C₄	—	2	16	no	—
144	C₇×C₂²⋊C₄	—	2	16	no	—
145	C₇×C₂²⋊C₄	—	2	16	no	—
146	C₇×C₂²⋊C₄	—	4	16	no	—
147	C₄²×C₇	—	4	8	no	—
148	C₂⁶	C₂²×C₇	1	1	yes	characteristic
149	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
150	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
151	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
152	C₂×C₂²⋊Q₈	—	2	8	no	—
153	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	complemented
154	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
155	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
156	C₂²×C₂²⋊C₄	—	2	8	no	—
157	C₂²×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
158	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
159	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
160	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
161	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
162	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
163	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
164	C₂²×C₄²	C₂²×C₇	1	2	yes	complemented
165	#397	C₂²×C₇	1	16	yes	complemented
166	#393	C₂²×C₇	1	16	yes	complemented
167	#388	C₂²×C₇	1	32	yes	complemented
168	#381	C₂²×C₇	1	16	yes	complemented
169	#379	C₂²×C₇	1	16	yes	—
170	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	complemented
171	C₂×#95	C₂²×C₇	1	2	yes	complemented
172	C₂×#95	C₂²×C₇	1	4	yes	complemented
173	C₂×#95	C₂²×C₇	1	4	yes	complemented
174	C₂³×C₇	—	2	8	no	—
175	C₂³×C₇	—	2	8	no	—
176	C₂³×C₇	—	2	32	no	—
177	C₂³×C₇	—	2	4	no	—
178	C₂³×C₇	—	2	4	no	—
179	C₂³×C₇	—	2	32	no	—
180	C₂³×C₇	—	2	16	no	—
181	C₂³×C₇	—	2	32	no	—
182	C₂³×C₇	—	2	4	no	—
183	C₂³×C₇	—	2	4	no	—
184	C₂³×C₇	—	2	8	no	—
185	C₂³×C₇	—	2	8	no	—
186	C₂³×C₇	—	4	64	no	—
187	C₂³×C₇	—	4	128	no	—
188	C₂³×C₇	—	4	16	no	—
189	C₂³×C₇	—	4	16	no	—
190	C₂³×C₇	—	4	8	no	—
191	C₂³×C₇	—	4	8	no	—
192	C₂³×C₇	—	4	16	no	—
193	C₂³×C₇	#124	1	16	yes	—
194	C₂³×C₇	C₂²×D₄	1	4	yes	—
195	C₂³×C₇	C₂²×D₄	1	2	yes	—
196	C₂³×C₇	C₂×#41	1	8	yes	—
197	C₂³×C₇	C₂×#41	1	8	yes	—
198	C₂³×C₇	C₂×#41	1	4	yes	—
199	C₂³×C₇	C₂×#41	1	4	yes	—
200	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
201	C₂³×C₇	C₂⁵	1	1	yes	characteristic
202	C₇×Q₈	—	4	16	no	—
203	C₂×C₄×C₇	—	2	8	no	—
204	C₂×C₄×C₇	—	2	8	no	—
205	C₂×C₄×C₇	—	2	4	no	—
206	C₂×C₄×C₇	—	2	4	no	—
207	C₂×C₄×C₇	—	2	4	no	—
208	C₂×C₄×C₇	—	2	4	no	—
209	C₂×C₄×C₇	—	2	4	no	—
210	C₂×C₄×C₇	—	2	8	no	—
211	C₂×C₄×C₇	—	2	8	no	—
212	C₂×C₄×C₇	—	2	8	no	—
213	C₂×C₄×C₇	—	2	8	no	—
214	C₂×C₄×C₇	—	2	8	no	—
215	C₂×C₄×C₇	—	2	8	no	—
216	C₂×C₄×C₇	—	4	16	no	—
217	C₂×C₄×C₇	—	4	8	no	—
218	C₂×C₄×C₇	—	4	16	no	—
219	C₂×C₄×C₇	—	4	8	no	—
220	C₂×C₄×C₇	—	4	8	no	—
221	C₂×C₄×C₇	—	4	16	no	—
222	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
224	C₂⁵	—	2	4	no	—
225	C₂⁵	—	2	8	no	—
226	C₂⁵	—	2	8	no	—
227	C₂⁵	—	4	4	no	—
228	C₂⁵	C₂³×C₇	1	2	yes	—
229	C₂⁵	C₂³×C₇	1	4	yes	—
230	C₂⁵	C₂³×C₇	1	1	yes	characteristic
231	C₂²×Q₈	—	2	4	no	—
232	C₂²×Q₈	—	4	4	no	—
233	C₂²×Q₈	C₂³×C₇	1	4	yes	complemented
234	C₂³×C₄	—	2	4	no	—
235	C₂³×C₄	—	2	8	no	—
236	C₂³×C₄	—	4	4	no	—
237	C₂³×C₄	C₇×D₄	1	8	yes	—
238	C₂³×C₄	C₂³×C₇	1	2	yes	—
239	C₂³×C₄	C₂³×C₇	1	2	yes	—
240	C₂³×C₄	C₂³×C₇	1	4	yes	—
241	C₂³×C₄	C₂³×C₇	1	2	yes	—
242	C₂³×C₄	C₂³×C₇	1	4	yes	—
243	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
244	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₇	1	4	yes	—
246	C₂²⋊Q₈	—	2	32	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	8	no	—
249	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
250	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
251	C₂×C₂²⋊C₄	—	2	8	no	—
252	C₂×C₂²⋊C₄	—	2	16	no	—
253	C₂×C₂²⋊C₄	—	2	8	no	—
254	C₂×C₂²⋊C₄	—	2	8	no	—
255	C₂×C₂²⋊C₄	—	2	8	no	—
256	C₂×C₂²⋊C₄	—	2	32	no	—
257	C₂×C₂²⋊C₄	—	4	8	no	—
258	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
260	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
261	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
262	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
263	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
264	C₂×C₄²	—	4	4	no	—
265	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
266	#95	C₂³×C₇	1	8	yes	complemented
267	#95	C₂³×C₇	1	16	yes	complemented
268	#95	C₂³×C₇	1	16	yes	complemented
269	C₂²×C₇	—	2	32	no	—
270	C₂²×C₇	—	2	4	no	—
271	C₂²×C₇	—	2	4	no	—
272	C₂²×C₇	—	2	16	no	—
273	C₂²×C₇	—	2	8	no	—
274	C₂²×C₇	—	2	16	no	—
275	C₂²×C₇	—	4	64	no	—
276	C₂²×C₇	—	4	32	no	—
277	C₂²×C₇	—	4	4	no	—
278	C₂²×C₇	—	4	4	no	—
279	C₂²×C₇	—	4	8	no	—
280	C₂²×C₇	#525	1	4	yes	—
281	C₂²×C₇	C₂×#124	1	8	yes	—
282	C₂²×C₇	C₂×#124	1	4	yes	—
283	C₂²×C₇	#534	1	4	yes	—
284	C₂²×C₇	#551	1	16	yes	—
285	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
286	C₂²×C₇	C₂²×#41	1	2	yes	—
287	C₂²×C₇	C₂²×#41	1	2	yes	—
288	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
289	C₄×C₇	—	2	4	no	—
290	C₄×C₇	—	2	4	no	—
291	C₄×C₇	—	4	4	no	—
292	C₄×C₇	—	4	4	no	—
293	C₄×C₇	—	4	4	no	—
294	C₄×C₇	—	4	8	no	—
295	C₂⁴	—	2	4	no	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	—	2	32	no	—
298	C₂⁴	—	2	8	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	16	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	2	8	no	—
303	C₂⁴	—	2	8	no	—
304	C₂⁴	—	2	16	no	—
305	C₂⁴	—	4	8	no	—
306	C₂⁴	—	4	64	no	—
307	C₂⁴	—	4	16	no	—
308	C₂⁴	—	4	16	no	—
309	C₂⁴	C₂×C₇×D₄	1	4	yes	—
310	C₂⁴	C₇×#41	1	8	yes	—
311	C₂⁴	C₇×#41	1	8	yes	—
312	C₂⁴	C₂⁴×C₇	1	4	yes	—
313	C₂⁴	C₂⁴×C₇	1	2	yes	—
314	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
315	C₂×Q₈	—	2	8	no	—
316	C₂×Q₈	—	4	8	no	—
317	C₂×Q₈	—	4	16	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	16	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	4	16	no	—
332	C₂²×C₄	—	4	8	no	—
333	C₂²×C₄	—	4	16	no	—
334	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
335	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
336	C₂²×C₄	C₂×C₇×D₄	1	16	yes	—
337	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
338	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
339	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	2	16	no	—
345	C₂²⋊C₄	—	2	16	no	—
346	C₂²⋊C₄	—	2	32	no	—
347	C₂²⋊C₄	—	2	16	no	—
348	C₂²⋊C₄	—	2	16	no	—
349	C₂²⋊C₄	—	2	16	no	—
350	C₂²⋊C₄	—	4	16	no	—
351	C₄²	—	4	8	no	—
352	C₂×C₇	—	2	8	no	—
353	C₂×C₇	—	4	8	no	—
354	C₂×C₇	#2561	1	8	yes	direct product factor
355	C₂×C₇	C₂×#525	1	1	yes	characteristic
356	C₂×C₇	C₂²×#124	1	1	yes	characteristic
357	C₂×C₇	C₂×#534	1	1	yes	characteristic
358	C₂×C₇	C₂×#551	1	4	yes	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	32	no	—
364	C₂³	—	2	32	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	8	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	2	16	no	—
370	C₂³	—	2	32	no	—
371	C₂³	—	4	64	no	—
372	C₂³	—	4	16	no	—
373	C₂³	—	4	128	no	—
374	C₂³	—	4	16	no	—
375	C₂³	—	4	8	no	—
376	C₂³	—	4	8	no	—
377	C₂³	—	4	16	no	—
378	C₂³	C₇×#124	1	16	yes	—
379	C₂³	C₂²×C₇×D₄	1	4	yes	—
380	C₂³	C₂²×C₇×D₄	1	2	yes	—
381	C₂³	C₂×C₇×#41	1	8	yes	—
382	C₂³	C₂×C₇×#41	1	8	yes	—
383	C₂³	C₂×C₇×#41	1	4	yes	—
384	C₂³	C₂×C₇×#41	1	4	yes	—
385	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
386	C₂³	C₂⁵×C₇	1	1	yes	characteristic
387	Q₈	—	4	16	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	4	16	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	16	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	—	4	16	no	—
407	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
408	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
409	C₇	C₂×#2561	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	4	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	16	no	—
413	C₂²	—	2	32	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	2	16	no	—
416	C₂²	—	4	64	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	8	no	—
420	C₂²	—	4	32	no	—
421	C₂²	C₇×#525	1	4	yes	—
422	C₂²	C₂×C₇×#124	1	8	yes	—
423	C₂²	C₂×C₇×#124	1	4	yes	—
424	C₂²	C₇×#534	1	4	yes	—
425	C₂²	C₇×#551	1	16	yes	—
426	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
427	C₂²	C₂²×C₇×#41	1	2	yes	—
428	C₂²	C₂²×C₇×#41	1	2	yes	—
429	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	8	no	—
436	C₂	—	2	8	no	—
437	C₂	—	4	8	no	—
438	C₂	C₇×#2561	1	8	yes	direct product factor
439	C₂	C₂×C₇×#525	1	1	yes	characteristic
440	C₂	C₂²×C₇×#124	1	1	yes	characteristic
441	C₂	C₂×C₇×#534	1	1	yes	characteristic
442	C₂	C₂×C₇×#551	1	4	yes	—

	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×#2561	C₂	direct (N × H)
4. C₂×C₇×#397	C₂	semidirect
5. C₂×C₇×#393	C₂	semidirect
6. C₂×C₇×#388	C₂	semidirect
7. C₂×C₇×#381	C₂	semidirect
9. C₂×C₄×C₇×C₂²⋊C₄	C₂	semidirect
11. C₂³×C₇×Q₈	C₂²	semidirect
15. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
16. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
17. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
26. C₂²×C₄²×C₇	C₂²	semidirect
27. C₇×#397	C₂²	semidirect
28. C₇×#393	C₂²	semidirect
29. C₇×#388	C₂²	semidirect
30. C₇×#381	C₂²	semidirect
32. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
33. C₂×C₇×#95	C₂²	semidirect
34. C₂×C₇×#95	C₂²	semidirect
35. C₂×C₇×#95	C₂²	semidirect
36. C₂×#2561	C₇	direct (N × H)
46. C₂²×C₇×Q₈	C₂³	semidirect
62. C₂×C₇×C₄⋊C₄	C₂³	semidirect
63. C₂×C₇×C₄⋊C₄	C₂³	semidirect
78. C₂×C₄²×C₇	C₂³	semidirect
79. C₇×#95	C₂³	semidirect
80. C₇×#95	C₂³	semidirect
81. C₇×#95	C₂³	semidirect
82. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
84. #2561	C₂×C₇	direct (N × H)
85. C₂×#397	C₂×C₇	semidirect
86. C₂×#393	C₂×C₇	semidirect
87. C₂×#388	C₂×C₇	semidirect
88. C₂×#381	C₂×C₇	semidirect
90. C₂×C₄×C₂²⋊C₄	C₂×C₇	semidirect
149. C₂³×Q₈	C₂²×C₇	semidirect
153. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
154. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
155. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
164. C₂²×C₄²	C₂²×C₇	semidirect
165. #397	C₂²×C₇	semidirect
166. #393	C₂²×C₇	semidirect
167. #388	C₂²×C₇	semidirect
168. #381	C₂²×C₇	semidirect
170. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
171. C₂×#95	C₂²×C₇	semidirect
172. C₂×#95	C₂²×C₇	semidirect
173. C₂×#95	C₂²×C₇	semidirect
233. C₂²×Q₈	C₂³×C₇	semidirect
249. C₂×C₄⋊C₄	C₂³×C₇	semidirect
250. C₂×C₄⋊C₄	C₂³×C₇	semidirect
265. C₂×C₄²	C₂³×C₇	semidirect
266. #95	C₂³×C₇	semidirect
267. #95	C₂³×C₇	semidirect
268. #95	C₂³×C₇	semidirect
354. C₂×C₇	#2561	direct (N × H)
409. C₇	C₂×#2561	direct (N × H)
438. C₂	C₇×#2561	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×#2561	2
C₂×C₇×#397	2
C₂×C₇×#393	2
C₂×C₇×#388	2
C₂×C₇×#381	2
C₂×C₇×#379	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂×#2561	7

Subgroups — C2×C7×#2561 #13212057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2561 #13212057