Subgroups — #13323403

Order 1792.

738 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#6512	C₂	1	1	yes	maximal, characteristic
3	C₂×#89460	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729393	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728690	C₂	1	2	yes	maximal, complemented
6	#11728687	C₂	1	2	yes	maximal, complemented
7	#11728598	C₂	1	2	yes	maximal, complemented
8	#11728595	C₂	1	2	yes	maximal, complemented
9	#11728510	C₂	1	1	yes	maximal, characteristic, complemented
10	#11728500	C₂	1	1	yes	maximal, characteristic, complemented
11	#11727479	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₇×#41	C₂²	1	1	yes	characteristic
13	C₂×#6512	C₄	1	1	yes	characteristic
14	C₂²×#1131	—	2	1	no	—
15	C₂×C₄×D₂₈	C₂²	1	1	yes	characteristic
16	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₇×C₈×D₄	—	2	1	no	—
19	C₇×C₈×D₄	—	2	1	no	—
20	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₇×#431	—	2	1	no	—
23	C₇×#431	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×C₈	—	2	1	no	—
25	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
26	#90004	C₄	1	1	yes	characteristic
27	C₂×(C₂×D₇)⋊C₈	—	2	1	no	—
28	#89798	C₄	1	2	yes	—
29	C₄×#1143	C₂²	1	2	yes	—
30	#89786	C₄	1	2	yes	—
31	C₄×#1141	C₂²	1	2	yes	—
32	#89773	C₄	1	1	yes	characteristic
33	#89767	C₄	1	1	yes	characteristic
34	#89697	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
36	C₄×#1136	C₂²	1	1	yes	characteristic
37	#89460	—	2	1	no	—
38	#89460	—	2	1	no	—
39	#89460	C₂²	1	2	yes	—
40	#89460	C₂²	1	2	yes	—
41	Q₈⋊(C₇⋊C₈)	C₂²	1	2	yes	complemented
42	D₄⋊(C₇⋊C₈)	C₂²	1	2	yes	complemented
43	#89278	C₂²	1	2	yes	—
44	#89278	C₂²	1	2	yes	—
45	#89275	C₂²	1	2	yes	complemented
46	#89274	C₂²	1	2	yes	complemented
47	#89250	C₂²	1	2	yes	complemented
48	#89249	C₂²	1	2	yes	complemented
49	#17871	—	7	1	no	maximal, Sylow
50	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
51	C₂²×D₂₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄×D₇	—	2	1	no	—
53	C₂²×C₇×C₈	—	2	1	no	—
54	C₂²×C₇×C₈	—	2	1	no	—
55	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
56	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
57	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
58	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
59	C₄×C₇×D₄	—	2	1	no	—
60	C₄×C₇×D₄	—	2	1	no	—
61	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
62	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
63	C₇×#117	—	2	1	no	—
64	C₇×#117	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₇	—	2	1	no	—
66	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
67	#6512	—	2	4	no	—
68	C₂×#1143	C₂×C₄	1	2	yes	—
69	C₂×#1141	C₂×C₄	1	2	yes	—
70	C₂×(C₂×D₇)⋊C₄	—	2	1	no	—
71	C₂×C₄⋊Dic₇	C₂×C₄	1	1	yes	characteristic
72	C₂×#1136	C₂×C₄	1	1	yes	characteristic
73	C₂×#1136	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₇⋊C₈	—	2	1	no	—
75	C₂×#1131	—	2	2	no	—
76	C₂×#1131	—	2	2	no	—
77	C₂×#1131	—	4	4	no	—
78	C₄×D₂₈	—	2	1	no	—
79	C₄×D₂₈	—	2	1	no	—
80	C₄×D₂₈	C₂×C₄	1	2	yes	—
81	C₄×D₂₈	C₂³	1	2	yes	—
82	C₇×C₄⋊C₈	—	2	1	no	—
83	C₇×C₄⋊C₈	—	2	1	no	—
84	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₇×C₂²⋊C₈	—	2	1	no	—
87	C₇×C₂²⋊C₈	—	2	1	no	—
88	C₇×C₂²⋊C₈	—	2	1	no	—
89	C₄×C₇×C₈	—	2	1	no	—
90	C₄×C₇×C₈	—	2	1	no	—
91	C₄×C₇×C₈	—	2	1	no	—
92	C₄×C₇×C₈	D₄	1	1	yes	characteristic
93	C₄×C₇×C₈	D₄	1	1	yes	characteristic
94	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
95	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
96	#6409	C₂×C₄	1	2	yes	—
97	#6406	C₂×C₄	1	2	yes	—
98	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
99	(C₂×D₇)⋊C₈	—	2	2	no	—
100	(C₂×D₇)⋊C₈	—	2	2	no	—
101	#6383	C₂×C₄	1	2	yes	—
102	#6383	C₂×C₄	1	2	yes	—
103	#6382	C₂×C₄	1	2	yes	—
104	#6381	C₂×C₄	1	2	yes	—
105	C₄⋊(C₇⋊C₈)	—	2	1	no	—
106	C₄⋊(C₇⋊C₈)	—	2	1	no	—
107	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
108	#6377	C₂×C₄	1	2	yes	—
109	C₄×C₇⋊C₈	C₂³	1	2	yes	—
110	C₄×C₇⋊C₈	C₂³	1	2	yes	—
111	C₈×#41	D₇	1	1	yes	characteristic, complemented
112	C₄×AGL(1,ℤ/8)	—	7	1	no	—
113	C₂×#436	—	7	1	no	—
114	#1588	—	7	2	no	—
115	#1586	—	7	2	no	—
116	#1583	—	7	2	no	—
117	#1581	—	7	2	no	—
118	#1565	—	7	1	no	—
119	#1478	—	7	1	no	—
120	#1477	—	7	1	no	—
121	#1451	—	7	1	no	—
122	C₂³×D₇	—	2	1	no	—
123	C₇×#41	—	2	2	no	—
124	C₇×#41	M₁₆	1	4	yes	complemented
125	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₇×D₄	—	2	1	no	—
127	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	—	2	1	no	—
129	C₂²×C₄×C₇	—	2	1	no	—
130	C₂²×C₄×C₇	—	2	1	no	—
131	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	#41	1	1	yes	characteristic
134	C₂²×Dic₇	—	2	1	no	—
135	C₂×D₂₈	—	2	2	no	—
136	C₂×D₂₈	—	2	2	no	—
137	C₂×D₂₈	—	2	1	no	—
138	C₂×D₂₈	C₂²×C₄	1	2	yes	—
139	C₂×C₄×D₇	—	2	2	no	—
140	C₂×C₄×D₇	—	2	2	no	—
141	C₂×C₄×D₇	—	4	2	no	—
142	C₂×C₄×D₇	—	4	2	no	—
143	C₂×C₇×C₈	—	2	2	no	—
144	C₂×C₇×C₈	—	2	1	no	—
145	C₂×C₇×C₈	—	2	1	no	—
146	C₂×C₇×C₈	—	4	1	no	—
147	C₂×C₇×C₈	—	4	2	no	—
148	C₂×C₇×C₈	—	4	2	no	—
149	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
151	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
153	C₇×C₄⋊C₄	—	2	1	no	—
154	C₇×C₄⋊C₄	—	2	1	no	—
155	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
156	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
157	C₇×C₂²⋊C₄	—	2	1	no	—
158	C₇×C₂²⋊C₄	—	2	1	no	—
159	C₇×C₂²⋊C₄	—	2	1	no	—
160	C₄²×C₇	—	2	1	no	—
161	C₄²×C₇	—	2	1	no	—
162	C₄²×C₇	—	2	1	no	—
163	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₇	#41	1	1	yes	characteristic
166	C₄²×C₇	C₂⁴	1	1	yes	characteristic
167	#1143	—	2	4	no	—
168	#1141	—	2	4	no	—
169	(C₂×D₇)⋊C₄	—	2	2	no	—
170	(C₂×D₇)⋊C₄	—	2	2	no	—
171	C₄⋊Dic₇	—	2	1	no	—
172	C₄⋊Dic₇	C₂²×C₄	1	2	yes	—
173	#1136	—	2	2	no	—
174	#1136	—	2	2	no	—
175	C₂×C₇⋊C₈	—	2	2	no	—
176	C₂×C₇⋊C₈	—	2	2	no	—
177	C₂×C₇⋊C₈	—	4	2	no	—
178	C₂×C₇⋊C₈	C₂²×C₄	1	2	yes	—
179	C₂×C₇⋊C₈	C₂²×C₄	1	2	yes	—
180	#1131	—	4	4	no	—
181	#1131	—	4	4	no	—
182	C₂×AGL(1,ℤ/8)	—	7	1	no	—
183	C₂²×M₁₆	—	14	1	no	—
184	C₄×#41	C₂×D₇	1	1	yes	characteristic
185	C₂×C₄×D₄	—	7	1	no	—
186	C₈×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
187	C₈×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
188	#442	—	7	2	no	—
189	#440	—	7	2	no	—
190	C₄×SD₁₆	—	7	2	no	—
191	C₄×D₈	—	7	2	no	—
192	#436	—	7	2	no	—
193	#436	—	7	2	no	—
194	#436	—	14	1	no	—
195	#436	—	14	1	no	—
196	C₈×D₄	—	2	1	no	—
197	C₈×D₄	—	2	1	no	—
198	C₈×D₄	C₂×D₇	1	1	yes	characteristic, complemented
199	C₈×D₄	C₂×D₇	1	1	yes	characteristic, complemented
200	#431	—	2	1	no	—
201	#431	—	7	1	no	—
202	#431	C₂×D₇	1	1	yes	characteristic
203	#428	—	7	1	no	—
204	C₂×C₄⋊C₈	—	7	1	no	—
205	#418	—	7	1	no	—
206	#417	—	7	1	no	—
207	C₂×C₂²⋊C₈	—	14	1	no	—
208	C₄×M₁₆	—	7	1	no	—
209	C₂×C₄×C₈	—	2	1	no	—
210	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
211	#335	—	7	2	no	—
212	#334	—	7	2	no	—
213	Q₈⋊C₈	—	7	2	no	—
214	D₄⋊C₈	—	7	2	no	—
215	D₄⋊C₈	—	7	2	no	—
216	D₄⋊C₈	—	7	2	no	—
217	#322	—	7	2	no	—
218	#322	—	7	2	no	—
219	C₂³×C₇	—	2	1	no	—
220	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
221	C₂²×D₇	—	2	2	no	—
222	C₂²×D₇	—	4	2	no	—
223	C₂²×D₇	—	4	2	no	—
224	C₂²×D₇	—	4	2	no	—
225	C₇×Q₈	—	2	1	no	—
226	C₇×Q₈	C₂×M₁₆	1	2	yes	complemented
227	C₇×D₄	—	2	4	no	—
228	C₇×D₄	—	2	1	no	—
229	C₇×D₄	C₂×M₁₆	1	2	yes	complemented
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	1	no	—
233	C₂×C₄×C₇	—	2	4	no	—
234	C₂×C₄×C₇	—	2	1	no	—
235	C₂×C₄×C₇	—	2	1	no	—
236	C₂×C₄×C₇	—	4	1	no	—
237	C₂×C₄×C₇	—	4	2	no	—
238	C₂×C₄×C₇	—	4	1	no	—
239	C₂×C₄×C₇	—	4	1	no	—
240	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
244	C₂×C₄×C₇	#131	1	2	yes	—
245	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
248	C₂×Dic₇	—	2	2	no	—
249	C₂×Dic₇	—	4	2	no	—
250	D₂₈	—	2	2	no	—
251	D₂₈	—	2	2	no	—
252	D₂₈	—	4	2	no	—
253	C₄×D₇	—	4	4	no	—
254	C₄×D₇	—	4	2	no	—
255	C₄×D₇	—	4	2	no	—
256	C₇×C₈	—	2	1	no	—
257	C₇×C₈	—	2	1	no	—
258	C₇×C₈	—	2	1	no	—
259	C₇×C₈	—	4	1	no	—
260	C₇×C₈	—	4	1	no	—
261	C₇×C₈	AGL(1,ℤ/8)	1	2	yes	complemented
262	C₇⋊C₈	—	2	2	no	—
263	C₇⋊C₈	—	2	2	no	—
264	C₇⋊C₈	—	4	2	no	—
265	C₇⋊C₈	—	4	2	no	—
266	C₂×#41	C₄×D₇	1	1	yes	characteristic
267	C₂²×D₄	—	7	1	no	—
268	C₂³×C₄	—	14	1	no	—
269	AGL(1,ℤ/8)	—	14	4	no	—
270	C₂×SD₁₆	—	7	2	no	—
271	C₂×D₈	—	7	2	no	—
272	C₂×M₁₆	—	7	1	no	—
273	C₂×M₁₆	—	7	1	no	—
274	C₂×M₁₆	—	14	2	no	—
275	C₂×M₁₆	—	14	2	no	—
276	C₂×M₁₆	—	28	4	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	14	1	no	—
280	C₂²×C₈	C₂²⋊D₇	1	1	yes	characteristic
281	C₂²×C₈	C₂²⋊D₇	1	1	yes	characteristic
282	C₄×Q₈	C₄×D₇	1	1	yes	characteristic
283	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	7	2	no	—
287	C₄×D₄	—	7	2	no	—
288	C₄×D₄	—	14	1	no	—
289	C₄×D₄	—	14	1	no	—
290	C₄×D₄	C₄×D₇	1	1	yes	characteristic
291	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	#117	C₄×D₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	7	1	no	—
295	C₂×C₂²⋊C₄	—	14	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
298	#107	—	7	2	no	—
299	#106	—	7	2	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	7	2	no	—
303	C₄⋊C₈	—	14	1	no	—
304	C₄⋊C₈	—	14	1	no	—
305	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
307	#103	—	7	2	no	—
308	#102	—	7	2	no	—
309	#102	—	7	2	no	—
310	#102	—	7	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	14	1	no	—
315	C₂²⋊C₈	—	14	2	no	—
316	C₂²⋊C₈	—	14	2	no	—
317	#97	—	7	2	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	7	2	no	—
322	C₄×C₈	—	7	2	no	—
323	C₄×C₈	C₂²⋊D₇	1	1	yes	characteristic
324	C₄×C₈	C₂²⋊D₇	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
327	C₂²×C₇	—	2	1	no	—
328	C₂²×C₇	—	2	1	no	—
329	C₂²×C₇	—	2	2	no	—
330	C₂²×C₇	—	4	1	no	—
331	C₂²×C₇	—	4	1	no	—
332	C₂²×C₇	#435	1	2	yes	—
333	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
334	C₂×D₇	—	4	2	no	—
335	C₂×D₇	—	4	2	no	—
336	C₂×D₇	—	4	2	no	—
337	C₂×D₇	—	8	4	no	—
338	C₄×C₇	—	2	2	no	—
339	C₄×C₇	—	2	1	no	—
340	C₄×C₇	—	2	1	no	—
341	C₄×C₇	—	2	1	no	—
342	C₄×C₇	—	4	1	no	—
343	C₄×C₇	—	4	1	no	—
344	C₄×C₇	#435	1	2	yes	—
345	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
346	C₄×C₇	C₂×#131	1	1	yes	characteristic
347	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
348	C₄×C₇	#575	1	1	yes	characteristic
349	Dic₇	—	4	2	no	—
350	C₂⁴	—	14	1	no	—
351	#41	—	2	2	no	—
352	#41	#1131	1	4	yes	complemented
353	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	7	2	no	—
356	C₂×D₄	—	14	2	no	—
357	C₂×D₄	—	14	2	no	—
358	C₂×D₄	—	14	1	no	—
359	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	14	1	no	—
364	C₂²×C₄	—	14	2	no	—
365	C₂²×C₄	—	14	2	no	—
366	C₂²×C₄	—	28	2	no	—
367	C₂²×C₄	—	28	2	no	—
368	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
369	C₂²×C₄	#1157	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
371	SD₁₆	—	14	4	no	—
372	D₈	—	14	4	no	—
373	M₁₆	—	14	2	no	—
374	M₁₆	—	14	2	no	—
375	M₁₆	—	28	4	no	—
376	M₁₆	—	28	4	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	4	1	no	—
381	C₂×C₈	—	4	2	no	—
382	C₂×C₈	—	4	2	no	—
383	C₂×C₈	—	7	2	no	—
384	C₂×C₈	—	7	2	no	—
385	C₂×C₈	—	14	2	no	—
386	C₂×C₈	—	14	2	no	—
387	C₂×C₈	—	28	2	no	—
388	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
389	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
390	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
391	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	7	2	no	—
395	C₄⋊C₄	—	14	1	no	—
396	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
397	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	14	2	no	—
402	C₂²⋊C₄	—	14	2	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
407	C₄²	#1157	1	1	yes	characteristic
408	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
409	C₄²	C₂³×D₇	1	1	yes	characteristic
410	C₂×C₇	—	2	2	no	—
411	C₂×C₇	—	4	2	no	—
412	C₂×C₇	C₂×#435	1	1	yes	characteristic
413	C₂×C₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
414	C₂×C₇	#2955	1	1	yes	characteristic
415	D₇	—	8	2	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	14	2	no	—
418	C₂³	—	28	2	no	—
419	C₂³	—	28	2	no	—
420	C₂³	—	28	2	no	—
421	C₂³	C₄×C₂²⋊D₇	1	1	yes	characteristic
422	Q₈	—	2	1	no	—
423	Q₈	C₂×#1131	1	2	yes	complemented
424	D₄	—	2	4	no	—
425	D₄	—	2	1	no	—
426	D₄	—	14	2	no	—
427	D₄	—	14	2	no	—
428	D₄	—	28	2	no	—
429	D₄	C₂×#1131	1	2	yes	complemented
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	14	2	no	—
441	C₂×C₄	—	28	4	no	—
442	C₂×C₄	—	28	2	no	—
443	C₂×C₄	—	28	2	no	—
444	C₂×C₄	—	28	2	no	—
445	C₂×C₄	C₂×#1131	1	2	yes	—
446	C₂×C₄	#6464	1	2	yes	—
447	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
448	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
449	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
451	C₂×C₄	C₂×#1157	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	4	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	14	2	no	—
459	C₈	—	14	2	no	—
460	C₈	—	28	2	no	—
461	C₈	—	28	2	no	—
462	C₈	#6512	1	2	yes	complemented
463	C₇	#17871	1	1	yes	characteristic, complemented, Sylow
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	28	2	no	—
470	C₂²	—	28	2	no	—
471	C₂²	—	28	2	no	—
472	C₂²	—	56	4	no	—
473	C₂²	#89883	1	2	yes	—
474	C₂²	C₂×C₄×C₂²⋊D₇	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	28	2	no	—
482	C₄	#89883	1	2	yes	—
483	C₄	C₂²×#1131	1	1	yes	characteristic
484	C₄	C₂×#6464	1	1	yes	characteristic
485	C₄	C₂×#6512	1	1	yes	characteristic
486	C₄	#90513	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	2	no	—
489	C₂	—	56	2	no	—
490	C₂	C₄×#6512	1	1	yes	characteristic
491	C₂	C₂×#89883	1	1	yes	characteristic
492	C₂	#11741237	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×C₈×#41	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×#6512	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	C₈×#41	D₇
hypocenter	C₇	#17871
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. C₇×C₈×#41	C₂	semidirect
3. C₂×#89460	C₂	semidirect
4. #11729393	C₂	semidirect
5. #11728690	C₂	semidirect
6. #11728687	C₂	semidirect
7. #11728598	C₂	semidirect
8. #11728595	C₂	semidirect
9. #11728510	C₂	semidirect
10. #11728500	C₂	semidirect
11. #11727479	C₂	semidirect
16. C₇×C₈×Q₈	C₂²	semidirect
17. C₇×C₈×Q₈	C₂²	semidirect
20. C₇×C₈×D₄	C₂²	semidirect
21. C₇×C₈×D₄	C₂²	semidirect
41. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
42. D₄⋊(C₇⋊C₈)	C₂²	semidirect
45. #89275	C₂²	semidirect
46. #89274	C₂²	semidirect
47. #89250	C₂²	semidirect
48. #89249	C₂²	semidirect
111. C₈×#41	D₇	semidirect
124. C₇×#41	M₁₆	semidirect
186. C₈×Q₈	C₂×D₇	semidirect
187. C₈×Q₈	C₂×D₇	semidirect
198. C₈×D₄	C₂×D₇	semidirect
199. C₈×D₄	C₂×D₇	semidirect
226. C₇×Q₈	C₂×M₁₆	semidirect
229. C₇×D₄	C₂×M₁₆	semidirect
261. C₇×C₈	AGL(1,ℤ/8)	semidirect
352. #41	#1131	semidirect
423. Q₈	C₂×#1131	semidirect
429. D₄	C₂×#1131	semidirect
462. C₈	#6512	semidirect
463. C₇	#17871	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₈×#41	2
C₄×#6512	2
C₂×#89460	2
#11729393	2
#11728690	2
#11728687	2
#11728598	2
#11728595	2
#11728510	2
#11728500	2
#11727479	2
#17871	7