Subgroups — C₂×#20273618 #27353849

Order 13568.

730 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810754	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16810701	C₂	1	1	yes	maximal, characteristic
3	#20273618	C₂	1	8	yes	maximal, direct product factor
4	C₂×#16810376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈⋊#88322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊#88322	C₂	1	1	yes	maximal, characteristic
7	C₂×#16810344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11719917	—	2	1	no	—
10	#16810754	—	2	2	no	—
11	#16810754	C₂²	1	4	yes	complemented
12	#16810701	—	2	2	no	—
13	#16810701	C₂²	1	4	yes	—
14	C₂×C₄⋊#88322	—	2	1	no	—
15	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊#88322	—	2	1	no	—
18	C₂×#13133128	—	2	1	no	—
19	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
20	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
21	#16810376	C₂²	1	4	yes	complemented
22	Q₈⋊#88322	C₂²	1	4	yes	complemented
23	D₄⋊#88322	C₂²	1	4	yes	—
24	#16810344	C₂²	1	4	yes	complemented
25	C₂²×SD₁₆×C₅₃	C₄	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
28	C₄×SD₁₆×C₅₃	C₄	1	4	yes	—
29	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
30	C₂×#106×C₅₃	C₄	1	1	yes	characteristic
31	C₂×#103×C₅₃	C₄	1	1	yes	characteristic
32	C₂×#102×C₅₃	C₄	1	1	yes	characteristic
33	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#11719917	—	2	4	no	—
35	C₂×#11719917	—	4	4	no	—
36	C₂²×#88322	—	2	1	no	—
37	C₂²×#88322	—	2	1	no	—
38	C₂²×#88322	—	2	1	no	—
39	C₂²×#88322	D₄	1	1	yes	characteristic
40	C₂²×#88322	D₄	1	1	yes	characteristic
41	C₄⋊#88322	—	2	1	no	—
42	C₄⋊#88322	—	2	1	no	—
43	C₄⋊#88322	—	2	4	no	—
44	C₄⋊#88322	C₂³	1	2	yes	—
45	C₄⋊#88322	C₂³	1	2	yes	—
46	C₂²⋊#88322	—	2	4	no	—
47	#13133128	—	2	4	no	—
48	C₄×#88322	—	2	1	no	—
49	C₄×#88322	D₄	1	2	yes	—
50	C₄×#88322	C₂³	1	2	yes	—
51	C₄×#88322	C₂³	1	2	yes	—
52	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₅₃	—	2	1	no	—
55	C₂×SD₁₆×C₅₃	—	2	4	no	—
56	C₂×SD₁₆×C₅₃	C₂×C₄	1	4	yes	—
57	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₅₃	—	2	1	no	—
60	C₄×Q₈×C₅₃	—	2	1	no	—
61	C₄×Q₈×C₅₃	C₂×C₄	1	2	yes	—
62	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
63	C₄×D₄×C₅₃	—	2	1	no	—
64	C₄×D₄×C₅₃	—	2	1	no	—
65	C₄×D₄×C₅₃	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₅₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
71	C₂×C₄²×C₅₃	—	2	1	no	—
72	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
73	#106×C₅₃	C₂×C₄	1	4	yes	—
74	#103×C₅₃	C₂×C₄	1	4	yes	—
75	#102×C₅₃	C₂×C₄	1	4	yes	—
76	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₅₃	C₂³	1	2	yes	—
78	C₂⁴×C₅₃	—	2	1	no	—
79	C₂×Q₈×C₅₃	—	2	1	no	—
80	C₂×Q₈×C₅₃	—	2	2	no	—
81	C₂×Q₈×C₅₃	—	2	2	no	—
82	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
83	C₂×D₄×C₅₃	—	2	1	no	—
84	C₂×D₄×C₅₃	—	2	2	no	—
85	C₂×D₄×C₅₃	—	2	2	no	—
86	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₅₃	—	2	1	no	—
88	C₂²×C₄×C₅₃	—	2	1	no	—
89	C₂²×C₄×C₅₃	—	2	1	no	—
90	C₂²×C₄×C₅₃	—	2	2	no	—
91	C₂²×C₄×C₅₃	—	2	2	no	—
92	C₂²×C₄×C₅₃	—	4	2	no	—
93	C₂²×C₄×C₅₃	—	4	2	no	—
94	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
97	SD₁₆×C₅₃	—	2	8	no	—
98	C₂×C₈×C₅₃	—	2	2	no	—
99	C₂×C₈×C₅₃	M₁₆	1	4	yes	complemented
100	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
102	C₄⋊C₄×C₅₃	—	2	2	no	—
103	C₄⋊C₄×C₅₃	—	2	1	no	—
104	C₄⋊C₄×C₅₃	—	2	1	no	—
105	C₄⋊C₄×C₅₃	—	2	2	no	—
106	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
107	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
108	C₂²⋊C₄×C₅₃	—	2	2	no	—
109	C₂²⋊C₄×C₅₃	—	2	2	no	—
110	C₄²×C₅₃	—	2	2	no	—
111	C₄²×C₅₃	—	2	2	no	—
112	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₅₃	#41	1	1	yes	characteristic
115	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
116	#11719917	—	4	8	no	—
117	C₂×#88322	—	2	2	no	—
118	C₂×#88322	—	2	2	no	—
119	C₂×#88322	—	2	2	no	—
120	C₂×#88322	—	2	2	no	—
121	C₂×#88322	—	2	2	no	—
122	C₂×#88322	—	4	2	no	—
123	C₂×#88322	—	4	2	no	—
124	C₂×#88322	—	4	2	no	—
125	C₂×#88322	C₂×D₄	1	2	yes	—
126	C₂×#88322	C₂×D₄	1	2	yes	—
127	C₂³×C₅₃	—	2	2	no	—
128	C₂³×C₅₃	—	4	2	no	—
129	C₂³×C₅₃	—	4	2	no	—
130	C₂³×C₅₃	—	4	2	no	—
131	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
132	Q₈×C₅₃	—	2	2	no	—
133	Q₈×C₅₃	—	2	2	no	—
134	Q₈×C₅₃	—	4	2	no	—
135	D₄×C₅₃	—	2	2	no	—
136	D₄×C₅₃	—	2	2	no	—
137	D₄×C₅₃	—	4	2	no	—
138	C₂×C₄×C₅₃	—	2	2	no	—
139	C₂×C₄×C₅₃	—	2	2	no	—
140	C₂×C₄×C₅₃	—	2	2	no	—
141	C₂×C₄×C₅₃	—	2	2	no	—
142	C₂×C₄×C₅₃	—	4	2	no	—
143	C₂×C₄×C₅₃	—	4	2	no	—
144	C₂×C₄×C₅₃	—	4	2	no	—
145	C₂×C₄×C₅₃	—	4	2	no	—
146	C₂×C₄×C₅₃	—	4	2	no	—
147	C₂×C₄×C₅₃	—	4	4	no	—
148	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
152	C₂×C₄×C₅₃	#131	1	2	yes	—
153	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₅₃	#137	1	2	yes	—
155	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
158	C₈×C₅₃	—	2	2	no	—
159	C₈×C₅₃	C₂×M₁₆	1	4	yes	complemented
160	#88322	—	2	2	no	—
161	#88322	—	2	2	no	—
162	#88322	—	4	2	no	—
163	#88322	—	4	2	no	—
164	#88322	—	4	2	no	—
165	C₂×#1592	—	53	1	no	maximal, Sylow
166	C₂²×C₅₃	—	4	2	no	—
167	C₂²×C₅₃	—	4	2	no	—
168	C₂²×C₅₃	—	4	2	no	—
169	C₂²×C₅₃	—	8	4	no	—
170	C₂²×C₅₃	#436	1	2	yes	—
171	C₂²×C₅₃	#440	1	2	yes	—
172	C₂²×C₅₃	#444	1	2	yes	—
173	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
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	—	4	2	no	—
179	C₄×C₅₃	#436	1	2	yes	—
180	C₄×C₅₃	#440	1	2	yes	—
181	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
182	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
183	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
185	C₂×#446	—	53	1	no	—
186	C₂×C₄×SD₁₆	D₅₃	1	1	yes	characteristic
187	C₂×#436	—	53	1	no	—
188	#1592	—	53	8	no	—
189	C₂×#335	—	53	1	no	—
190	C₂×Q₈⋊C₈	—	53	1	no	—
191	C₂×D₄⋊C₈	—	53	1	no	—
192	C₂×#322	—	53	1	no	—
193	C₂×C₅₃	—	8	2	no	—
194	C₂×C₅₃	#1592	1	4	yes	complemented
195	C₂×C₅₃	C₂×#436	1	1	yes	characteristic
196	C₂×C₅₃	C₂×#440	1	1	yes	characteristic
197	C₂×C₅₃	C₂×#444	1	1	yes	characteristic
198	C₂²×SD₁₆	Dic₅₃	1	1	yes	characteristic
199	C₂²×M₁₆	—	106	1	no	—
200	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
202	#446	—	53	4	no	—
203	#446	—	106	2	no	—
204	C₄×SD₁₆	Dic₅₃	1	4	yes	—
205	C₄×SD₁₆	C₂×D₅₃	1	4	yes	—
206	#436	—	53	4	no	—
207	#436	—	106	2	no	—
208	C₂×#106	Dic₅₃	1	1	yes	characteristic
209	C₂×C₄⋊C₈	—	53	1	no	—
210	C₂×C₄⋊C₈	—	53	1	no	—
211	C₂×C₄⋊C₈	—	106	1	no	—
212	C₂×#103	Dic₅₃	1	1	yes	characteristic
213	C₂×#102	Dic₅₃	1	1	yes	characteristic
214	C₂×C₂²⋊C₈	—	106	1	no	—
215	C₂×#97	—	106	1	no	—
216	C₂×C₄×C₈	—	53	1	no	—
217	C₂×C₄×C₈	—	53	1	no	—
218	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
219	#335	—	53	4	no	—
220	Q₈⋊C₈	—	53	4	no	—
221	D₄⋊C₈	—	53	4	no	—
222	#322	—	53	4	no	—
223	C₅₃	C₂×#1592	1	1	yes	characteristic, complemented, Sylow
224	C₂²×Q₈	C₂×Dic₅₃	1	1	yes	characteristic
225	C₂²×D₄	C₂×Dic₅₃	1	1	yes	characteristic
226	C₂³×C₄	—	2	1	no	—
227	C₂×SD₁₆	—	2	4	no	—
228	C₂×SD₁₆	C₂×Dic₅₃	1	4	yes	—
229	C₂×M₁₆	—	106	4	no	—
230	C₂×M₁₆	—	212	4	no	—
231	C₂²×C₈	—	53	1	no	—
232	C₂²×C₈	—	53	1	no	—
233	C₂²×C₈	—	106	1	no	—
234	C₂²×C₈	—	106	1	no	—
235	C₂²×C₈	—	106	1	no	—
236	C₂²×C₈	C₂×Dic₅₃	1	1	yes	characteristic
237	C₂²×C₈	C₂×Dic₅₃	1	1	yes	characteristic
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₂×Dic₅₃	1	2	yes	—
241	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	C₂×Dic₅₃	1	2	yes	—
245	C₄×D₄	C₂²×D₅₃	1	2	yes	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
252	#106	C₂×Dic₅₃	1	4	yes	—
253	C₄⋊C₈	—	53	2	no	—
254	C₄⋊C₈	—	53	2	no	—
255	C₄⋊C₈	—	106	4	no	—
256	C₄⋊C₈	—	106	1	no	—
257	C₄⋊C₈	—	106	1	no	—
258	#103	C₂×Dic₅₃	1	4	yes	—
259	#102	C₂×Dic₅₃	1	4	yes	—
260	C₂²⋊C₈	—	106	4	no	—
261	#97	—	106	4	no	—
262	C₄×C₈	—	53	2	no	—
263	C₄×C₈	—	53	2	no	—
264	C₄×C₈	—	53	2	no	—
265	C₄×C₈	—	106	1	no	—
266	C₄×C₈	C₂×Dic₅₃	1	2	yes	—
267	C₄×C₈	C₂²×D₅₃	1	2	yes	—
268	C₂⁴	—	2	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	C₂²×Dic₅₃	1	2	yes	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	C₂²×Dic₅₃	1	2	yes	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
285	C₂²×C₄	#11719947	1	1	yes	characteristic
286	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
287	SD₁₆	—	2	8	no	—
288	M₁₆	—	212	8	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	53	2	no	—
291	C₂×C₈	—	53	2	no	—
292	C₂×C₈	—	106	2	no	—
293	C₂×C₈	—	106	2	no	—
294	C₂×C₈	—	106	2	no	—
295	C₂×C₈	—	106	2	no	—
296	C₂×C₈	—	106	2	no	—
297	C₂×C₈	—	212	2	no	—
298	C₂×C₈	—	212	2	no	—
299	C₂×C₈	—	212	2	no	—
300	C₂×C₈	#11719917	1	4	yes	complemented
301	C₂×C₈	C₂²×Dic₅₃	1	2	yes	—
302	C₂×C₈	C₂²×Dic₅₃	1	2	yes	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
308	C₄⋊C₄	C₂²×Dic₅₃	1	2	yes	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	D₄×D₅₃	1	1	yes	characteristic
314	C₄²	#11719947	1	1	yes	characteristic
315	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
316	C₄²	C₂³×D₅₃	1	1	yes	characteristic
317	C₂³	—	2	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	D₄×Dic₅₃	1	1	yes	characteristic
322	Q₈	—	2	2	no	—
323	Q₈	—	2	2	no	—
324	Q₈	—	4	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
339	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
340	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
341	C₂×C₄	C₂×#11719917	1	2	yes	—
342	C₂×C₄	#13133224	1	2	yes	—
343	C₂×C₄	#13133244	1	2	yes	—
344	C₂×C₄	#13133246	1	2	yes	—
345	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
346	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
347	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	—	106	2	no	—
350	C₈	—	106	2	no	—
351	C₈	—	212	2	no	—
352	C₈	—	212	2	no	—
353	C₈	—	212	2	no	—
354	C₈	C₂×#11719917	1	4	yes	complemented
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	4	no	—
359	C₂²	#16810701	1	2	yes	—
360	C₂²	#16810724	1	2	yes	—
361	C₂²	#16810745	1	2	yes	—
362	C₂²	C₂×D₄×Dic₅₃	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	#16810701	1	2	yes	—
369	C₄	#16810724	1	2	yes	—
370	C₄	C₂²×#11719917	1	1	yes	characteristic
371	C₄	C₂×#13133224	1	1	yes	characteristic
372	C₄	C₂×#13133244	1	1	yes	characteristic
373	C₄	C₂×#13133246	1	1	yes	characteristic
374	C₂	—	8	2	no	—
375	C₂	#20273618	1	4	yes	direct product factor
376	C₂	C₂×#16810701	1	1	yes	characteristic
377	C₂	C₂×#16810724	1	1	yes	characteristic
378	C₂	C₂×#16810745	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₂×C₄×SD₁₆×C₅₃	C₂
socle	C₂³×C₅₃	C₄×D₄
prime radical	C₂²×D₄×C₅₃	C₂×C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₅₃
hypocenter	C₅₃	C₂×#1592
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#16810754	C₂	semidirect
3. #20273618	C₂	direct (N × H)
4. C₂×#16810376	C₂	semidirect
5. C₂×Q₈⋊#88322	C₂	semidirect
7. C₂×#16810344	C₂	semidirect
11. #16810754	C₂²	semidirect
21. #16810376	C₂²	semidirect
22. Q₈⋊#88322	C₂²	semidirect
24. #16810344	C₂²	semidirect
99. C₂×C₈×C₅₃	M₁₆	semidirect
159. C₈×C₅₃	C₂×M₁₆	semidirect
194. C₂×C₅₃	#1592	semidirect
223. C₅₃	C₂×#1592	semidirect
300. C₂×C₈	#11719917	semidirect
354. C₈	C₂×#11719917	semidirect
375. C₂	#20273618	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16810754	2
C₂×#16810701	2
#20273618	2
C₂×#16810376	2
C₂×Q₈⋊#88322	2
C₂×D₄⋊#88322	2
C₂×#16810344	2
C₂×C₄×SD₁₆×C₅₃	2
C₂×#1592	53

Subgroups — C2×#20273618 #27353849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20273618 #27353849