Subgroups — C₈×#13133236 #27353465

Order 13568.

750 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11719947	C₂	1	2	yes	maximal, complemented
2	C₄×#13133236	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#20273521	C₂	1	1	yes	maximal, characteristic, complemented
5	#20273518	C₂	1	2	yes	maximal, complemented
6	C₈×#11719923	C₂	1	2	yes	maximal, complemented
7	D₈×#88322	C₂	1	1	yes	maximal, characteristic, complemented
8	#20273462	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273094	C₂	1	2	yes	maximal, complemented
10	C₈²×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133236	C₄	1	1	yes	characteristic
13	C₄×#11719947	C₂²	1	2	yes	—
14	C₈×Dic₁₀₆	C₂²	1	2	yes	—
15	#16810747	C₂²	1	2	yes	—
16	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
17	#16810717	C₄	1	1	yes	characteristic
18	#16810714	C₄	1	2	yes	—
19	C₄×#11719923	C₂²	1	2	yes	—
20	D₈×Dic₅₃	C₄	1	1	yes	characteristic
21	D₄×#88322	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₅₃	—	2	2	no	—
23	#16810686	—	2	2	no	—
24	#16810675	C₂²	1	2	yes	—
25	#16810673	—	2	2	no	—
26	#16810660	C₄	1	1	yes	characteristic
27	#16810616	C₄	1	2	yes	—
28	C₂×C₈×Dic₅₃	—	2	2	no	—
29	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	#16810376	C₂²	1	1	yes	characteristic
33	#16810373	C₂²	1	2	yes	—
34	#16810355	C₂²	1	2	yes	—
35	#16810353	C₂²	1	2	yes	—
36	D₄⋊#88322	C₂²	1	2	yes	—
37	C₈×#88322	C₂²	1	1	yes	characteristic
38	C₈×#88322	C₂²	1	1	yes	characteristic
39	C₈×#88322	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₅₃	C₂²	1	2	yes	—
42	C₅₃×#335	C₂²	1	1	yes	characteristic
43	C₅₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×#11719947	C₂×C₄	1	2	yes	—
46	#13133236	C₈	1	8	yes	direct product factor
47	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic
48	C₂×#11719923	C₂×C₄	1	2	yes	—
49	C₂²×#88322	—	2	2	no	—
50	C₂×C₈×D₅₃	—	2	1	no	—
51	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
54	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
55	C₄×Dic₁₀₆	C₂³	1	2	yes	—
56	#13133182	C₂×C₄	1	2	yes	—
57	D₄×Dic₅₃	C₂×C₄	1	2	yes	—
58	C₄×C₂²⋊D₅₃	—	2	2	no	—
59	#13133177	—	2	2	no	—
60	#13133175	C₂×C₄	1	2	yes	—
61	#13133173	—	2	2	no	—
62	C₂×C₄×Dic₅₃	—	2	2	no	—
63	C₄²×D₅₃	C₂³	1	1	yes	characteristic
64	#13133151	C₂×C₄	1	1	yes	characteristic
65	#13133148	C₂×C₄	1	2	yes	—
66	C₄⋊#88322	C₂³	1	2	yes	—
67	#13133146	—	2	2	no	—
68	#13133146	—	2	2	no	—
69	#13133142	C₂×C₄	1	2	yes	—
70	#13133140	C₂×C₄	1	2	yes	—
71	#13133138	C₂×C₄	1	2	yes	—
72	C₂²⋊#88322	—	2	2	no	—
73	#13133129	—	2	2	no	—
74	C₄×#88322	C₂³	1	1	yes	characteristic
75	C₄×#88322	C₂³	1	1	yes	characteristic
76	C₄×#88322	C₂³	1	1	yes	characteristic
77	C₈×Dic₅₃	—	2	2	no	—
78	C₈×Dic₅₃	—	2	2	no	—
79	C₈×Dic₅₃	—	2	1	no	—
80	C₈×Dic₅₃	—	2	2	no	—
81	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅₃	D₄	1	1	yes	characteristic
84	C₈×Dic₅₃	D₄	1	1	yes	characteristic
85	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₅₃	—	2	2	no	—
87	C₄×D₄×C₅₃	C₂³	1	2	yes	—
88	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
90	#102×C₅₃	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₅₃	—	2	2	no	—
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅₃	—	2	2	no	—
97	C₂×C₂²⋊D₅₃	—	2	2	no	—
98	C₂²×Dic₅₃	—	2	2	no	—
99	C₂²×Dic₅₃	—	2	2	no	—
100	#11719947	—	2	4	no	—
101	#11719947	C₂×C₈	1	8	yes	complemented
102	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
105	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
106	D₈×C₅₃	C₂×C₈	1	4	yes	complemented
107	C₂×C₈×C₅₃	—	2	1	no	—
108	C₂×C₈×C₅₃	—	2	2	no	—
109	C₂×C₈×C₅₃	—	4	4	no	—
110	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
114	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
115	C₂²⋊C₄×C₅₃	—	2	2	no	—
116	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
117	C₂²⋊Dic₅₃	—	2	2	no	—
118	#11719923	C₂×C₈	1	8	yes	complemented
119	#11719921	—	2	2	no	—
120	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
121	#11719919	—	2	2	no	—
122	#11719919	—	2	2	no	—
123	C₄×Dic₅₃	—	2	2	no	—
124	C₄×Dic₅₃	—	2	2	no	—
125	C₄×Dic₅₃	—	2	2	no	—
126	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₅₃	#41	1	1	yes	characteristic
129	C₂×#88322	—	2	1	no	—
130	C₂×#88322	—	2	2	no	—
131	C₂×#88322	—	4	4	no	—
132	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
133	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
134	C₂×#88322	C₂×D₄	1	1	yes	characteristic
135	C₂×#88322	C₂×D₄	1	1	yes	characteristic
136	Dic₂₁₂	C₂×C₈	1	4	yes	complemented
137	C₈×D₅₃	—	2	4	no	—
138	C₈×D₅₃	—	2	2	no	—
139	C₈×D₅₃	—	2	2	no	—
140	C₈×D₅₃	—	2	2	no	—
141	C₈×D₅₃	C₂×C₈	1	4	yes	complemented
142	C₂³×C₅₃	—	2	2	no	—
143	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
144	D₄×C₅₃	—	2	2	no	—
145	D₄×C₅₃	C₂²×C₈	1	4	yes	—
146	C₂×C₄×C₅₃	—	2	2	no	—
147	C₂×C₄×C₅₃	—	4	2	no	—
148	C₂×C₄×C₅₃	—	4	2	no	—
149	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
152	C₂²⋊D₅₃	—	2	8	no	—
153	C₂×Dic₅₃	—	2	2	no	—
154	C₂×Dic₅₃	—	2	8	no	—
155	C₂×Dic₅₃	—	2	2	no	—
156	C₂×Dic₅₃	—	4	4	no	—
157	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
158	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
159	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
160	C₄×D₅₃	—	2	1	no	—
161	C₄×D₅₃	—	2	1	no	—
162	C₄×D₅₃	—	2	2	no	—
163	C₄×D₅₃	C₂²×C₈	1	2	yes	—
164	C₄×D₅₃	#131	1	2	yes	—
165	Dic₁₀₆	—	2	2	no	—
166	Dic₁₀₆	C₂²×C₈	1	4	yes	—
167	C₈×C₅₃	—	2	2	no	—
168	C₈×C₅₃	—	2	1	no	—
169	C₈×C₅₃	—	2	1	no	—
170	C₈×C₅₃	—	4	2	no	—
171	C₈×C₅₃	C₂²×C₈	1	2	yes	—
172	C₈×C₅₃	#135	1	2	yes	complemented
173	#88322	—	2	2	no	—
174	#88322	—	2	1	no	—
175	#88322	—	2	1	no	—
176	#88322	—	4	2	no	—
177	#88322	C₂²×C₈	1	2	yes	—
178	#88322	#135	1	2	yes	complemented
179	C₈×#135	—	53	1	no	maximal, Sylow
180	C₂²×C₅₃	—	2	4	no	—
181	C₂²×C₅₃	—	4	2	no	—
182	C₂²×C₅₃	—	4	2	no	—
183	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂×D₅₃	—	2	1	no	—
185	C₂×D₅₃	—	2	1	no	—
186	C₂×D₅₃	C₈×D₄	1	2	yes	—
187	C₄×C₅₃	—	2	1	no	—
188	C₄×C₅₃	—	4	2	no	—
189	C₄×C₅₃	C₂³×C₈	1	1	yes	characteristic
190	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
191	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
192	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
193	Dic₅₃	—	2	4	no	—
194	Dic₅₃	—	2	1	no	—
195	Dic₅₃	—	4	2	no	—
196	Dic₅₃	C₈×D₄	1	2	yes	—
197	Dic₅₃	#443	1	2	yes	—
198	C₈×#41	—	53	2	no	—
199	C₄×#135	—	53	1	no	—
200	C₈×Q₁₆	—	53	1	no	—
201	C₈×Q₁₆	—	53	1	no	—
202	C₈×SD₁₆	—	53	2	no	—
203	C₈×SD₁₆	—	53	2	no	—
204	C₈×D₈	—	53	1	no	—
205	C₈×D₈	D₅₃	1	1	yes	characteristic, complemented
206	#1564	—	53	1	no	—
207	#1476	—	53	2	no	—
208	C₂×C₈²	—	53	1	no	—
209	C₂×C₅₃	—	4	4	no	—
210	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
211	C₂×C₅₃	C₄×#135	1	1	yes	characteristic
212	C₂×C₅₃	C₂×#443	1	1	yes	characteristic
213	D₅₃	—	2	2	no	—
214	C₂×#135	—	53	1	no	—
215	C₄×#41	—	53	2	no	—
216	C₈×Q₈	—	53	2	no	—
217	C₈×Q₈	—	53	2	no	—
218	C₄×Q₁₆	—	53	1	no	—
219	C₄×Q₁₆	—	53	1	no	—
220	C₄×SD₁₆	—	53	2	no	—
221	C₄×SD₁₆	—	53	2	no	—
222	C₄×D₈	—	53	1	no	—
223	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
224	C₈×D₄	—	53	2	no	—
225	C₈×D₄	—	106	2	no	—
226	C₈×D₄	—	106	2	no	—
227	C₈×D₄	C₂×D₅₃	1	2	yes	—
228	#431	—	53	2	no	—
229	#431	—	106	2	no	—
230	#427	—	53	1	no	—
231	#416	—	53	2	no	—
232	C₂×C₄×C₈	—	53	1	no	—
233	C₂×C₄×C₈	—	53	1	no	—
234	C₂×C₄×C₈	—	53	1	no	—
235	C₂×C₄×C₈	—	106	2	no	—
236	#335	—	53	1	no	—
237	#335	C₂×D₅₃	1	1	yes	characteristic
238	#334	—	53	2	no	—
239	Q₈⋊C₈	—	53	2	no	—
240	Q₈⋊C₈	—	53	2	no	—
241	D₄⋊C₈	—	53	2	no	—
242	D₄⋊C₈	C₂×D₅₃	1	2	yes	—
243	C₈²	—	53	1	no	—
244	C₈²	—	53	1	no	—
245	C₈²	—	53	1	no	—
246	C₈²	C₂×D₅₃	1	1	yes	characteristic
247	C₅₃	C₈×#135	1	1	yes	characteristic, complemented, Sylow
248	C₂×#41	—	53	2	no	—
249	#135	—	53	8	no	—
250	C₂×Q₁₆	—	53	1	no	—
251	C₂×SD₁₆	—	53	2	no	—
252	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	53	1	no	—
255	C₂²×C₈	—	53	1	no	—
256	C₂²×C₈	—	53	1	no	—
257	C₂²×C₈	—	53	1	no	—
258	C₂²×C₈	—	106	1	no	—
259	C₂²×C₈	—	106	2	no	—
260	C₄×Q₈	—	53	2	no	—
261	C₄×Q₈	—	53	2	no	—
262	C₄×D₄	—	53	2	no	—
263	C₄×D₄	—	106	2	no	—
264	C₄×D₄	—	106	2	no	—
265	C₄×D₄	C₂²×D₅₃	1	2	yes	—
266	#117	—	53	2	no	—
267	#117	—	106	2	no	—
268	C₂×C₄²	—	53	1	no	—
269	C₂×C₄²	—	106	2	no	—
270	#107	—	53	1	no	—
271	#107	C₄×D₅₃	1	1	yes	characteristic
272	#106	—	53	2	no	—
273	C₄⋊C₈	—	53	2	no	—
274	C₄⋊C₈	—	106	2	no	—
275	C₄⋊C₈	—	106	2	no	—
276	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
277	#103	—	53	2	no	—
278	#103	—	53	2	no	—
279	#102	—	53	2	no	—
280	#102	C₄×D₅₃	1	2	yes	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	—	106	2	no	—
283	C₂²⋊C₈	—	106	2	no	—
284	C₄×C₈	—	53	1	no	—
285	C₄×C₈	—	53	1	no	—
286	C₄×C₈	—	53	1	no	—
287	C₄×C₈	—	53	1	no	—
288	C₄×C₈	—	53	1	no	—
289	C₄×C₈	—	53	1	no	—
290	C₄×C₈	—	53	1	no	—
291	C₄×C₈	—	106	1	no	—
292	C₄×C₈	—	106	2	no	—
293	C₄×C₈	—	106	2	no	—
294	C₄×C₈	—	106	2	no	—
295	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
296	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
298	#41	—	53	8	no	—
299	#41	—	106	4	no	—
300	C₂×Q₈	—	53	2	no	—
301	C₂×D₄	—	106	2	no	—
302	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	53	1	no	—
307	C₂²×C₄	—	106	2	no	—
308	C₂²×C₄	—	106	2	no	—
309	Q₁₆	—	53	4	no	—
310	SD₁₆	—	53	8	no	—
311	D₈	C₈×D₅₃	1	4	yes	complemented
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	4	4	no	—
315	C₂×C₈	—	53	1	no	—
316	C₂×C₈	—	53	1	no	—
317	C₂×C₈	—	53	4	no	—
318	C₂×C₈	—	53	1	no	—
319	C₂×C₈	—	53	1	no	—
320	C₂×C₈	—	106	2	no	—
321	C₂×C₈	—	106	2	no	—
322	C₂×C₈	—	106	4	no	—
323	C₂×C₈	—	106	1	no	—
324	C₂×C₈	—	106	2	no	—
325	C₂×C₈	—	106	2	no	—
326	C₂×C₈	—	212	4	no	—
327	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
328	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
329	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
330	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
331	C₄⋊C₄	—	53	2	no	—
332	C₄⋊C₄	—	106	2	no	—
333	C₄⋊C₄	—	106	2	no	—
334	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	106	2	no	—
337	C₂²⋊C₄	—	106	2	no	—
338	C₄²	—	53	1	no	—
339	C₄²	—	53	1	no	—
340	C₄²	—	53	1	no	—
341	C₄²	—	106	2	no	—
342	C₄²	—	106	2	no	—
343	C₄²	—	106	2	no	—
344	C₄²	C₂³×D₅₃	1	1	yes	characteristic
345	C₂³	—	2	2	no	—
346	C₂³	—	53	1	no	—
347	Q₈	—	53	4	no	—
348	Q₈	—	106	2	no	—
349	D₄	—	2	2	no	—
350	D₄	—	106	8	no	—
351	D₄	C₂×C₈×D₅₃	1	4	yes	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	53	1	no	—
356	C₂×C₄	—	53	1	no	—
357	C₂×C₄	—	53	2	no	—
358	C₂×C₄	—	53	2	no	—
359	C₂×C₄	—	53	1	no	—
360	C₂×C₄	—	106	2	no	—
361	C₂×C₄	—	106	8	no	—
362	C₂×C₄	—	106	2	no	—
363	C₂×C₄	—	106	1	no	—
364	C₂×C₄	—	106	1	no	—
365	C₂×C₄	—	106	2	no	—
366	C₂×C₄	—	212	4	no	—
367	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
369	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	4	2	no	—
374	C₈	—	53	2	no	—
375	C₈	—	53	2	no	—
376	C₈	—	106	2	no	—
377	C₈	—	106	1	no	—
378	C₈	—	106	1	no	—
379	C₈	—	212	2	no	—
380	C₈	C₂×C₈×D₅₃	1	2	yes	—
381	C₈	#13133236	1	2	yes	direct product factor
382	C₂²	—	2	4	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	53	2	no	—
386	C₂²	—	106	1	no	—
387	C₂²	—	106	1	no	—
388	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	53	2	no	—
392	C₄	—	53	2	no	—
393	C₄	—	106	1	no	—
394	C₄	—	106	4	no	—
395	C₄	—	212	2	no	—
396	C₄	C₂²×C₈×D₅₃	1	1	yes	characteristic
397	C₄	#131×D₅₃	1	1	yes	characteristic
398	C₄	#135×D₅₃	1	1	yes	characteristic
399	C₄	C₂×#13133236	1	1	yes	characteristic
400	C₂	—	4	4	no	—
401	C₂	—	106	2	no	—
402	C₂	C₈×D₄×D₅₃	1	1	yes	characteristic
403	C₂	C₄×#13133236	1	1	yes	characteristic
404	C₂	#443×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₅₃
commutator	C₄×C₅₃	C₂³×C₈
Frattini	C₄²	C₂³×D₅₃
Fitting	C₈×D₈×C₅₃	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×#13133236	C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	C₈×D₈	D₅₃
hypocenter	C₅₃	C₈×#135
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
1. C₈×#11719947	C₂	semidirect
3. C₈×Dic₂₁₂	C₂	semidirect
4. #20273521	C₂	semidirect
5. #20273518	C₂	semidirect
6. C₈×#11719923	C₂	semidirect
7. D₈×#88322	C₂	semidirect
8. #20273462	C₂	semidirect
9. #20273094	C₂	semidirect
10. C₈²×D₅₃	C₂	semidirect
11. C₈×D₈×C₅₃	C₂	semidirect
46. #13133236	C₈	direct (N × H)
101. #11719947	C₂×C₈	semidirect
106. D₈×C₅₃	C₂×C₈	semidirect
118. #11719923	C₂×C₈	semidirect
136. Dic₂₁₂	C₂×C₈	semidirect
141. C₈×D₅₃	C₂×C₈	semidirect
172. C₈×C₅₃	#135	semidirect
178. #88322	#135	semidirect
205. C₈×D₈	D₅₃	semidirect
247. C₅₃	C₈×#135	semidirect
311. D₈	C₈×D₅₃	semidirect
381. C₈	#13133236	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#11719947	2
C₄×#13133236	2
C₈×Dic₂₁₂	2
#20273521	2
#20273518	2
C₈×#11719923	2
D₈×#88322	2
#20273462	2
#20273094	2
C₈²×D₅₃	2
C₈×D₈×C₅₃	2
C₈×#135	53

Subgroups — C8×#13133236 #27353465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13133236 #27353465