Subgroups — D₈×#11719917 #27355515

Order 13568.

794 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#11719917	C₂	1	2	yes	maximal, complemented
2	#20273600	C₂	1	2	yes	maximal, complemented
3	#20273545	C₂	1	4	yes	maximal, complemented
4	D₈×#88322	C₂	1	2	yes	maximal, complemented
5	#20273474	C₂	1	1	yes	maximal, characteristic, complemented
6	#20273140	C₂	1	2	yes	maximal, complemented
7	C₈×#11719917	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11719917	—	2	2	no	—
10	#16810701	C₂²	1	4	yes	complemented
11	#16810695	—	2	4	no	—
12	D₄×#88322	C₂²	1	4	yes	complemented
13	#16810676	C₂²	1	1	yes	characteristic
14	#16810647	C₂²	1	2	yes	—
15	#16810587	—	2	2	no	—
16	C₄×#11719917	C₂²	1	1	yes	characteristic
17	#16810376	C₂²	1	2	yes	complemented
18	#16810376	C₂²	1	2	yes	complemented
19	D₄⋊#88322	C₂²	1	4	yes	complemented
20	D₄⋊#88322	C₂²	1	4	yes	complemented
21	#16810345	C₂²	1	2	yes	complemented
22	C₈×#88322	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₅₃	C₄	1	1	yes	characteristic
24	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
25	C₄×D₈×C₅₃	C₄	1	2	yes	—
26	C₄×D₈×C₅₃	C₄	1	1	yes	characteristic
27	C₄×D₈×C₅₃	C₄	1	1	yes	characteristic
28	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₅₃	C₂²	1	2	yes	—
30	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#107×C₅₃	C₄	1	1	yes	characteristic
32	C₂×#102×C₅₃	C₄	1	2	yes	—
33	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#11719917	—	2	4	no	—
35	C₂×#11719917	—	2	2	no	—
36	C₂×#11719917	—	4	8	no	—
37	C₂×#11719917	D₄	1	1	yes	characteristic
38	C₂×#11719917	D₄	1	1	yes	characteristic
39	C₂²×#88322	—	2	4	no	—
40	C₄⋊#88322	—	2	2	no	—
41	C₄⋊#88322	—	2	1	no	—
42	C₄⋊#88322	C₂³	1	4	yes	—
43	C₂²⋊#88322	—	2	4	no	—
44	C₂²⋊#88322	—	2	4	no	—
45	C₂²⋊#88322	—	2	1	no	—
46	#13133128	D₄	1	2	yes	—
47	C₄×#88322	C₂³	1	2	yes	—
48	C₄×#88322	C₂³	1	2	yes	—
49	C₂²×D₄×C₅₃	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₅₃	—	2	2	no	—
51	C₂×D₈×C₅₃	—	2	4	no	—
52	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×D₈×C₅₃	C₂×C₄	1	2	yes	—
54	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
57	C₄×D₄×C₅₃	—	2	2	no	—
58	C₄×D₄×C₅₃	—	2	2	no	—
59	C₄×D₄×C₅₃	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₅₃	C₂×C₄	1	2	yes	—
61	C₄×D₄×C₅₃	C₂³	1	2	yes	—
62	C₄×D₄×C₅₃	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
65	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
66	#107×C₅₃	C₂×C₄	1	2	yes	—
67	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
68	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
69	#102×C₅₃	C₂×C₄	1	2	yes	—
70	#102×C₅₃	C₂×C₄	1	2	yes	—
71	#102×C₅₃	C₂×C₄	1	2	yes	—
72	#102×C₅₃	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
77	C₂⁴×C₅₃	—	2	2	no	—
78	C₂×D₄×C₅₃	—	2	4	no	—
79	C₂×D₄×C₅₃	—	2	2	no	—
80	C₂×D₄×C₅₃	—	4	2	no	—
81	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
82	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₅₃	—	2	2	no	—
84	C₂²×C₄×C₅₃	—	2	2	no	—
85	C₂²×C₄×C₅₃	—	2	2	no	—
86	C₂²×C₄×C₅₃	—	2	2	no	—
87	C₂²×C₄×C₅₃	—	2	2	no	—
88	C₂²×C₄×C₅₃	—	4	4	no	—
89	C₂²×C₄×C₅₃	—	4	4	no	—
90	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
93	D₈×C₅₃	—	2	4	no	—
94	D₈×C₅₃	—	2	2	no	—
95	D₈×C₅₃	M₁₆	1	4	yes	complemented
96	C₂×C₈×C₅₃	—	2	2	no	—
97	C₂×C₈×C₅₃	—	4	1	no	—
98	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
102	C₄⋊C₄×C₅₃	—	2	2	no	—
103	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
104	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
105	C₂²⋊C₄×C₅₃	—	2	2	no	—
106	C₂²⋊C₄×C₅₃	—	2	2	no	—
107	C₂²⋊C₄×C₅₃	—	2	2	no	—
108	C₂²⋊C₄×C₅₃	—	2	2	no	—
109	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₅₃	#41	1	1	yes	characteristic
112	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
113	#11719917	—	2	2	no	—
114	#11719917	—	4	4	no	—
115	#11719917	—	4	8	no	—
116	#11719917	D₈	1	4	yes	direct product factor
117	C₂×#88322	—	2	4	no	—
118	C₂×#88322	—	2	2	no	—
119	C₂×#88322	—	4	8	no	—
120	C₂×#88322	C₂×D₄	1	2	yes	—
121	C₂×#88322	C₂×D₄	1	2	yes	—
122	C₂³×C₅₃	—	2	2	no	—
123	C₂³×C₅₃	—	2	2	no	—
124	C₂³×C₅₃	—	4	4	no	—
125	C₂³×C₅₃	—	4	4	no	—
126	C₂³×C₅₃	—	8	2	no	—
127	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
128	D₄×C₅₃	—	2	2	no	—
129	D₄×C₅₃	—	2	2	no	—
130	D₄×C₅₃	—	2	2	no	—
131	D₄×C₅₃	—	4	4	no	—
132	D₄×C₅₃	C₂×M₁₆	1	4	yes	complemented
133	C₂×C₄×C₅₃	—	2	1	no	—
134	C₂×C₄×C₅₃	—	2	1	no	—
135	C₂×C₄×C₅₃	—	2	2	no	—
136	C₂×C₄×C₅₃	—	2	2	no	—
137	C₂×C₄×C₅₃	—	4	1	no	—
138	C₂×C₄×C₅₃	—	4	4	no	—
139	C₂×C₄×C₅₃	—	4	2	no	—
140	C₂×C₄×C₅₃	—	4	2	no	—
141	C₂×C₄×C₅₃	—	4	2	no	—
142	C₂×C₄×C₅₃	—	4	2	no	—
143	C₂×C₄×C₅₃	—	4	4	no	—
144	C₂×C₄×C₅₃	—	4	4	no	—
145	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂×D₈	1	2	yes	—
149	C₂×C₄×C₅₃	#135	1	2	yes	—
150	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
153	C₈×C₅₃	—	2	1	no	—
154	C₈×C₅₃	—	2	1	no	—
155	C₈×C₅₃	—	2	1	no	—
156	C₈×C₅₃	C₂×M₁₆	1	2	yes	complemented
157	#88322	—	2	2	no	—
158	#88322	—	4	2	no	—
159	#88322	—	4	4	no	—
160	#88322	C₂×D₈	1	4	yes	complemented
161	M₁₆×D₈	—	53	1	no	maximal, Sylow
162	C₂²×C₅₃	—	2	1	no	—
163	C₂²×C₅₃	—	2	1	no	—
164	C₂²×C₅₃	—	2	4	no	—
165	C₂²×C₅₃	—	4	2	no	—
166	C₂²×C₅₃	—	4	2	no	—
167	C₂²×C₅₃	—	4	2	no	—
168	C₂²×C₅₃	—	4	2	no	—
169	C₂²×C₅₃	—	4	2	no	—
170	C₂²×C₅₃	—	8	8	no	—
171	C₂²×C₅₃	C₄×D₈	1	2	yes	—
172	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
173	C₄×C₅₃	—	2	1	no	—
174	C₄×C₅₃	—	2	1	no	—
175	C₄×C₅₃	—	2	1	no	—
176	C₄×C₅₃	—	4	2	no	—
177	C₄×C₅₃	—	4	2	no	—
178	C₄×C₅₃	C₄×D₈	1	2	yes	—
179	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
180	C₄×C₅₃	#568	1	1	yes	characteristic
181	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
182	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
183	C₂×C₄×D₈	D₅₃	1	1	yes	characteristic
184	D₄×M₁₆	—	53	2	no	—
185	#1589	—	53	2	no	—
186	#1581	—	53	4	no	—
187	C₈×D₈	—	53	2	no	—
188	#1567	—	53	1	no	—
189	#1486	—	53	2	no	—
190	C₈×M₁₆	—	53	1	no	—
191	C₂×C₅₃	—	2	2	no	—
192	C₂×C₅₃	—	4	4	no	—
193	C₂×C₅₃	—	8	2	no	—
194	C₂×C₅₃	D₄×M₁₆	1	1	yes	characteristic
195	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
196	C₂×C₅₃	#2957	1	1	yes	characteristic
197	C₂²×D₈	Dic₅₃	1	1	yes	characteristic
198	C₂²×M₁₆	—	106	2	no	—
199	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	—
200	C₄×D₈	Dic₅₃	1	2	yes	—
201	C₄×D₈	Dic₅₃	1	1	yes	characteristic
202	C₄×D₈	Dic₅₃	1	1	yes	characteristic
203	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
204	C₄×D₈	C₂×D₅₃	1	2	yes	—
205	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
206	#436	—	53	4	no	—
207	#435	—	106	4	no	—
208	C₈×D₄	—	53	4	no	—
209	#431	—	53	1	no	—
210	C₂×#107	Dic₅₃	1	1	yes	characteristic
211	#423	—	53	2	no	—
212	C₂×#102	Dic₅₃	1	2	yes	—
213	#407	—	106	2	no	—
214	C₄×M₁₆	—	53	1	no	—
215	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
216	#335	—	53	2	no	—
217	#335	—	53	2	no	—
218	D₄⋊C₈	—	53	4	no	—
219	D₄⋊C₈	—	53	4	no	—
220	#322	—	53	2	no	—
221	C₈²	—	53	2	no	—
222	C₅₃	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
223	C₂²×D₄	C₂×Dic₅₃	1	2	yes	—
224	C₂³×C₄	—	2	2	no	—
225	C₂×D₈	—	2	4	no	—
226	C₂×D₈	C₂×Dic₅₃	1	2	yes	—
227	C₂×D₈	C₂×Dic₅₃	1	1	yes	characteristic
228	C₂×D₈	C₂×Dic₅₃	1	1	yes	characteristic
229	C₂×M₁₆	—	53	1	no	—
230	C₂×M₁₆	—	53	1	no	—
231	C₂×M₁₆	—	106	4	no	—
232	C₂×M₁₆	—	106	2	no	—
233	C₂×M₁₆	—	212	8	no	—
234	C₂²×C₈	—	106	4	no	—
235	C₂²×C₈	C₂×Dic₅₃	1	1	yes	characteristic
236	C₂²×C₈	C₂×Dic₅₃	1	1	yes	characteristic
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	C₂×Dic₅₃	1	2	yes	—
240	C₄×D₄	C₂×Dic₅₃	1	2	yes	—
241	C₄×D₄	C₂²×D₅₃	1	2	yes	—
242	C₄×D₄	C₂²×D₅₃	1	2	yes	—
243	C₂×C₄⋊C₄	C₂×Dic₅₃	1	2	yes	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
246	#107	C₂×Dic₅₃	1	2	yes	—
247	#107	C₂×Dic₅₃	1	1	yes	characteristic
248	#107	C₂×Dic₅₃	1	1	yes	characteristic
249	C₄⋊C₈	—	53	4	no	—
250	C₄⋊C₈	—	106	2	no	—
251	C₄⋊C₈	—	106	1	no	—
252	#102	C₂×Dic₅₃	1	2	yes	—
253	#102	C₂×Dic₅₃	1	2	yes	—
254	#102	C₂×Dic₅₃	1	2	yes	—
255	#102	C₂×Dic₅₃	1	2	yes	—
256	C₂²⋊C₈	—	106	4	no	—
257	C₂²⋊C₈	—	106	4	no	—
258	C₂²⋊C₈	—	106	1	no	—
259	#97	—	53	2	no	—
260	C₄×C₈	—	53	2	no	—
261	C₄×C₈	—	53	2	no	—
262	C₄×C₈	C₂×Dic₅₃	1	1	yes	characteristic
263	C₄×C₈	C₂×Dic₅₃	1	1	yes	characteristic
264	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
265	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
266	C₂⁴	—	2	2	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	C₂²×Dic₅₃	1	2	yes	—
271	C₂×D₄	C₂²×Dic₅₃	1	2	yes	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
280	C₂²×C₄	#11719947	1	1	yes	characteristic
281	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
282	D₈	—	2	4	no	—
283	D₈	—	2	2	no	—
284	D₈	#11719917	1	4	yes	direct product factor
285	M₁₆	—	53	4	no	—
286	M₁₆	—	106	2	no	—
287	M₁₆	—	212	8	no	—
288	M₁₆	—	212	4	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	53	2	no	—
292	C₂×C₈	—	53	2	no	—
293	C₂×C₈	—	106	4	no	—
294	C₂×C₈	—	106	2	no	—
295	C₂×C₈	—	212	8	no	—
296	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
297	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
298	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
299	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
302	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₄²	D₄×D₅₃	1	1	yes	characteristic
308	C₄²	#11719947	1	1	yes	characteristic
309	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
310	C₄²	C₂³×D₅₃	1	1	yes	characteristic
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	8	2	no	—
316	C₂³	D₄×Dic₅₃	1	1	yes	characteristic
317	D₄	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	4	4	no	—
321	D₄	C₂×#11719917	1	4	yes	complemented
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
335	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
336	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
337	C₂×C₄	D₈×D₅₃	1	2	yes	—
338	C₂×C₄	#13133236	1	2	yes	—
339	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
340	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
341	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	53	4	no	—
346	C₈	—	106	2	no	—
347	C₈	—	212	2	no	—
348	C₈	—	212	4	no	—
349	C₈	C₂×#11719917	1	2	yes	complemented
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	8	no	—
359	C₂²	D₈×Dic₅₃	1	2	yes	—
360	C₂²	C₂×D₄×Dic₅₃	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	D₈×Dic₅₃	1	2	yes	—
367	C₄	C₂²×#11719917	1	1	yes	characteristic
368	C₄	#16811390	1	1	yes	characteristic
369	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
370	C₄	C₂×#13133236	1	1	yes	characteristic
371	C₂	—	2	2	no	—
372	C₂	—	4	4	no	—
373	C₂	—	8	2	no	—
374	C₂	D₄×#11719917	1	1	yes	characteristic
375	C₂	C₂×D₈×Dic₅₃	1	1	yes	characteristic
376	C₂	#20283632	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₂×C₄×D₈×C₅₃	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂²×D₈×C₅₃	C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	C₂×C₄×D₈	D₅₃
hypocenter	C₅₃	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#11719917	C₂	semidirect
2. #20273600	C₂	semidirect
3. #20273545	C₂	semidirect
4. D₈×#88322	C₂	semidirect
5. #20273474	C₂	semidirect
6. #20273140	C₂	semidirect
7. C₈×#11719917	C₂	semidirect
10. #16810701	C₂²	semidirect
12. D₄×#88322	C₂²	semidirect
17. #16810376	C₂²	semidirect
18. #16810376	C₂²	semidirect
19. D₄⋊#88322	C₂²	semidirect
20. D₄⋊#88322	C₂²	semidirect
21. #16810345	C₂²	semidirect
22. C₈×#88322	C₂²	semidirect
95. D₈×C₅₃	M₁₆	semidirect
116. #11719917	D₈	direct (N × H)
132. D₄×C₅₃	C₂×M₁₆	semidirect
156. C₈×C₅₃	C₂×M₁₆	semidirect
160. #88322	C₂×D₈	semidirect
222. C₅₃	M₁₆×D₈	semidirect
284. D₈	#11719917	direct (N × H)
321. D₄	C₂×#11719917	semidirect
349. C₈	C₂×#11719917	semidirect

Maximal subgroups

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

subgroup	index
D₄×#11719917	2
#20273600	2
#20273545	2
D₈×#88322	2
#20273474	2
#20273140	2
C₈×#11719917	2
C₂×C₄×D₈×C₅₃	2
M₁₆×D₈	53

Subgroups — D8×#11719917 #27355515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×#11719917 #27355515