Subgroups — C₂×#20274063 #27366412

Order 13568.

786 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810996	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810908	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16810823	C₂	1	1	yes	maximal, characteristic
4	#20274063	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16810374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16810370	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16810366	C₂	1	1	yes	maximal, characteristic
8	C₂×C₈×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#11719913	—	2	1	no	—
10	C₂²×#11719913	—	2	1	no	—
11	C₂²×#11719924	—	2	1	no	—
12	C₂×#13133217	C₂²	1	1	yes	characteristic
13	C₂×#13133214	C₂²	1	1	yes	characteristic
14	#16810996	—	2	2	no	—
15	#16810996	C₂²	1	4	yes	—
16	#16810908	—	2	2	no	—
17	#16810908	C₂²	1	4	yes	complemented
18	#16810823	—	2	2	no	—
19	#16810823	C₂²	1	4	yes	—
20	C₂×#13133148	—	2	1	no	—
21	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
23	C₂×#13133141	—	2	1	no	—
24	C₂×#13133137	—	2	1	no	—
25	#16810374	C₂²	1	4	yes	complemented
26	#16810370	C₂²	1	4	yes	complemented
27	#16810366	C₂²	1	4	yes	—
28	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₈×Q₈×C₅₃	—	2	2	no	—
30	C₈×Q₈×C₅₃	C₂²	1	4	yes	complemented
31	C₂×C₄⋊C₈×C₅₃	—	2	1	no	—
32	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₅₃	—	2	1	no	—
34	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₂²×Dic₁₀₆	—	2	1	no	—
36	C₂²×D₂₁₂	—	2	1	no	—
37	C₂²×D₂₁₂	—	2	1	no	—
38	C₂²×D₂₁₂	—	2	1	no	—
39	C₂×#11719913	—	2	4	no	—
40	C₂×#11719913	—	2	4	no	—
41	C₂×#11719913	—	4	4	no	—
42	C₂×#11719913	—	4	4	no	—
43	C₂×#11719924	—	2	4	no	—
44	C₂×#11719924	—	4	4	no	—
45	C₂²×#88322	—	2	1	no	—
46	C₂²×#88322	—	2	1	no	—
47	#13133217	—	2	1	no	—
48	#13133217	—	2	1	no	—
49	#13133217	—	2	1	no	—
50	#13133217	C₂³	1	2	yes	—
51	#13133214	—	2	1	no	—
52	#13133214	—	2	1	no	—
53	#13133214	—	2	1	no	—
54	#13133214	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₅₃	—	2	1	no	—
56	C₂×C₄⋊Dic₅₃	—	2	1	no	—
57	#13133148	—	2	4	no	—
58	C₄⋊#88322	—	2	1	no	—
59	C₄⋊#88322	—	2	1	no	—
60	C₄⋊#88322	C₂³	1	2	yes	—
61	C₄⋊#88322	C₂³	1	2	yes	—
62	#13133141	—	2	4	no	—
63	#13133137	—	2	4	no	—
64	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₅₃	—	2	1	no	—
66	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
67	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
68	C₄×Q₈×C₅₃	—	2	1	no	—
69	C₄×Q₈×C₅₃	—	2	1	no	—
70	C₄×Q₈×C₅₃	D₄	1	2	yes	—
71	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₅₃	—	2	1	no	—
75	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₅₃	—	2	4	no	—
77	C₄⋊C₈×C₅₃	—	2	1	no	—
78	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
79	C₄×C₈×C₅₃	—	2	4	no	—
80	C₄×C₈×C₅₃	D₄	1	2	yes	—
81	C₄×C₈×C₅₃	C₂³	1	2	yes	—
82	C₂³×D₅₃	—	4	1	no	—
83	C₂×Q₈×C₅₃	—	2	1	no	—
84	C₂×Q₈×C₅₃	—	2	2	no	—
85	C₂×Q₈×C₅₃	SD₁₆	1	4	yes	complemented
86	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₅₃	—	2	1	no	—
88	C₂²×C₄×C₅₃	—	2	1	no	—
89	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
92	C₂²×Dic₅₃	—	4	1	no	—
93	C₂×D₂₁₂	—	2	2	no	—
94	C₂×D₂₁₂	—	2	2	no	—
95	C₂×D₂₁₂	—	2	2	no	—
96	C₂×D₂₁₂	—	4	2	no	—
97	C₂×D₂₁₂	—	4	2	no	—
98	C₂×D₂₁₂	—	4	2	no	—
99	C₂×D₂₁₂	—	4	2	no	—
100	C₂×D₂₁₂	—	4	1	no	—
101	C₂×D₂₁₂	—	4	1	no	—
102	C₂×D₂₁₂	—	4	1	no	—
103	C₂×D₂₁₂	—	8	2	no	—
104	C₂×Dic₁₀₆	—	2	2	no	—
105	C₂×Dic₁₀₆	—	4	2	no	—
106	C₂×Dic₁₀₆	—	4	2	no	—
107	C₂×Dic₁₀₆	—	4	1	no	—
108	C₂×C₈×C₅₃	—	2	2	no	—
109	C₂×C₈×C₅₃	—	2	2	no	—
110	C₂×C₈×C₅₃	—	4	2	no	—
111	C₂×C₈×C₅₃	SD₁₆	1	4	yes	complemented
112	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
114	C₄⋊C₄×C₅₃	—	2	2	no	—
115	C₄⋊C₄×C₅₃	—	2	1	no	—
116	C₄⋊C₄×C₅₃	—	2	2	no	—
117	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
118	C₄²×C₅₃	—	2	2	no	—
119	C₄²×C₅₃	—	2	2	no	—
120	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₅₃	#41	1	1	yes	characteristic
123	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
124	#11719924	—	4	8	no	—
125	C₄⋊Dic₅₃	—	2	2	no	—
126	C₄⋊Dic₅₃	—	2	2	no	—
127	C₄⋊Dic₅₃	—	4	1	no	—
128	C₄⋊Dic₅₃	—	4	1	no	—
129	C₂×#88322	—	2	2	no	—
130	C₂×#88322	—	2	2	no	—
131	C₂×#88322	—	4	2	no	—
132	C₂×#88322	—	4	2	no	—
133	#11719913	—	4	8	no	—
134	#11719913	—	4	8	no	—
135	C₂³×C₅₃	#121	1	1	yes	characteristic
136	C₂²×D₅₃	—	4	2	no	—
137	C₂²×D₅₃	—	8	2	no	—
138	C₂²×D₅₃	—	8	2	no	—
139	C₂²×D₅₃	—	8	2	no	—
140	Q₈×C₅₃	—	2	2	no	—
141	Q₈×C₅₃	—	2	4	no	—
142	Q₈×C₅₃	C₂×SD₁₆	1	4	yes	complemented
143	C₂×C₄×C₅₃	—	2	2	no	—
144	C₂×C₄×C₅₃	—	2	4	no	—
145	C₂×C₄×C₅₃	—	2	2	no	—
146	C₂×C₄×C₅₃	—	2	2	no	—
147	C₂×C₄×C₅₃	—	4	2	no	—
148	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
149	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
150	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
153	C₂×C₄×C₅₃	#135	1	2	yes	—
154	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₅₃	C₂²×D₄	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	C₂×Dic₅₃	—	4	2	no	—
159	C₂×Dic₅₃	—	8	2	no	—
160	D₂₁₂	—	4	2	no	—
161	D₂₁₂	—	4	2	no	—
162	D₂₁₂	—	4	2	no	—
163	D₂₁₂	—	4	2	no	—
164	D₂₁₂	—	8	2	no	—
165	D₂₁₂	—	8	2	no	—
166	D₂₁₂	—	8	2	no	—
167	D₂₁₂	—	8	2	no	—
168	Dic₁₀₆	—	4	2	no	—
169	Dic₁₀₆	—	4	2	no	—
170	Dic₁₀₆	—	8	2	no	—
171	C₈×C₅₃	—	2	2	no	—
172	C₈×C₅₃	—	4	2	no	—
173	C₈×C₅₃	C₂×SD₁₆	1	4	yes	complemented
174	#88322	—	4	2	no	—
175	#88322	—	4	2	no	—
176	C₂×#1666	—	53	1	no	maximal, Sylow
177	C₂²×C₅₃	#460	1	2	yes	—
178	C₂²×C₅₃	#465	1	2	yes	—
179	C₂²×C₅₃	#471	1	2	yes	—
180	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
181	C₂×D₅₃	—	8	2	no	—
182	C₂×D₅₃	—	8	2	no	—
183	C₂×D₅₃	—	8	2	no	—
184	C₂×D₅₃	—	16	4	no	—
185	C₄×C₅₃	—	2	4	no	—
186	C₄×C₅₃	—	2	1	no	—
187	C₄×C₅₃	—	2	1	no	—
188	C₄×C₅₃	—	4	2	no	—
189	C₄×C₅₃	#460	1	2	yes	—
190	C₄×C₅₃	#465	1	2	yes	—
191	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
192	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
193	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
194	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	Dic₅₃	—	8	2	no	—
196	C₂×#492	—	53	1	no	—
197	C₂×#475	—	53	1	no	—
198	C₂×#460	—	53	1	no	—
199	C₂×C₈×Q₈	D₅₃	1	1	yes	characteristic, complemented
200	#1666	—	53	8	no	—
201	C₂×#334	—	53	1	no	—
202	C₂×#332	—	53	1	no	—
203	C₂×#331	—	53	1	no	—
204	C₂×C₅₃	#1666	1	4	yes	complemented
205	C₂×C₅₃	C₂×#460	1	1	yes	characteristic
206	C₂×C₅₃	C₂×#465	1	1	yes	characteristic
207	C₂×C₅₃	C₂×#471	1	1	yes	characteristic
208	D₅₃	—	16	2	no	—
209	C₂²×SD₁₆	—	106	1	no	—
210	C₂²×SD₁₆	—	106	1	no	—
211	C₂²×SD₁₆	—	106	1	no	—
212	C₂×C₄⋊Q₈	—	53	1	no	—
213	C₂×#127	—	53	1	no	—
214	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
215	#492	—	53	4	no	—
216	#492	—	106	2	no	—
217	#475	—	53	4	no	—
218	#475	—	106	2	no	—
219	#460	—	53	4	no	—
220	#460	—	106	2	no	—
221	C₈×Q₈	—	2	2	no	—
222	C₈×Q₈	C₂×D₅₃	1	4	yes	complemented
223	C₂×#106	—	106	1	no	—
224	C₂×C₄⋊C₈	—	2	1	no	—
225	C₂×C₄⋊C₈	—	53	1	no	—
226	C₂×C₄⋊C₈	—	53	1	no	—
227	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
228	C₂×#103	—	106	1	no	—
229	C₂×#102	—	106	1	no	—
230	C₂×C₄×C₈	—	2	1	no	—
231	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
232	#334	—	53	4	no	—
233	#332	—	53	4	no	—
234	#331	—	53	4	no	—
235	C₅₃	C₂×#1666	1	1	yes	characteristic, complemented, Sylow
236	C₂²×Q₈	—	106	1	no	—
237	C₂²×Q₈	D₂₁₂	1	1	yes	characteristic
238	C₂²×D₄	—	106	1	no	—
239	C₂²×D₄	—	106	1	no	—
240	C₂²×D₄	—	106	1	no	—
241	C₂×SD₁₆	—	106	4	no	—
242	C₂×SD₁₆	—	106	4	no	—
243	C₂×SD₁₆	—	106	4	no	—
244	C₂×SD₁₆	—	212	4	no	—
245	C₂×SD₁₆	—	212	4	no	—
246	C₂×SD₁₆	—	212	4	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	106	1	no	—
249	C₂²×C₈	—	106	1	no	—
250	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
251	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
252	C₄⋊Q₈	—	53	2	no	—
253	C₄⋊Q₈	—	106	1	no	—
254	C₄⋊Q₈	—	106	1	no	—
255	C₄⋊Q₈	—	106	1	no	—
256	#127	—	53	2	no	—
257	#127	—	106	1	no	—
258	#127	—	106	1	no	—
259	#127	—	106	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	D₂₁₂	1	2	yes	—
263	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	106	1	no	—
266	C₂×C₄⋊C₄	—	106	1	no	—
267	C₂×C₄⋊C₄	D₂₁₂	1	1	yes	characteristic
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
270	#106	—	106	4	no	—
271	C₄⋊C₈	—	2	4	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	53	2	no	—
274	C₄⋊C₈	—	53	2	no	—
275	C₄⋊C₈	—	106	1	no	—
276	C₄⋊C₈	—	106	1	no	—
277	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
278	#103	—	106	4	no	—
279	#102	—	106	4	no	—
280	C₄×C₈	—	2	4	no	—
281	C₄×C₈	C₂²⋊D₅₃	1	2	yes	—
282	C₄×C₈	C₂²×D₅₃	1	2	yes	—
283	C₂⁴	—	212	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	106	2	no	—
287	C₂×Q₈	—	212	2	no	—
288	C₂×Q₈	—	212	2	no	—
289	C₂×Q₈	—	212	1	no	—
290	C₂×Q₈	#11719913	1	4	yes	complemented
291	C₂×Q₈	C₂×D₂₁₂	1	2	yes	—
292	C₂×D₄	—	106	2	no	—
293	C₂×D₄	—	106	2	no	—
294	C₂×D₄	—	106	2	no	—
295	C₂×D₄	—	424	2	no	—
296	C₂×D₄	—	212	1	no	—
297	C₂×D₄	—	212	1	no	—
298	C₂×D₄	—	212	1	no	—
299	C₂×D₄	—	212	2	no	—
300	C₂×D₄	—	212	2	no	—
301	C₂×D₄	—	212	2	no	—
302	C₂×D₄	—	212	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	212	1	no	—
306	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
307	C₂²×C₄	#11719945	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
309	SD₁₆	—	212	8	no	—
310	SD₁₆	—	212	8	no	—
311	SD₁₆	—	212	8	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	106	2	no	—
316	C₂×C₈	—	106	2	no	—
317	C₂×C₈	—	212	2	no	—
318	C₂×C₈	—	212	2	no	—
319	C₂×C₈	#11719924	1	4	yes	complemented
320	C₂×C₈	C₂×C₂²⋊D₅₃	1	2	yes	—
321	C₂×C₈	C₂×C₂²⋊D₅₃	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	106	2	no	—
326	C₄⋊C₄	—	106	2	no	—
327	C₄⋊C₄	—	212	1	no	—
328	C₄⋊C₄	—	212	1	no	—
329	C₄⋊C₄	C₂×D₂₁₂	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
333	C₄²	#11719945	1	1	yes	characteristic
334	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
335	C₄²	C₂³×D₅₃	1	1	yes	characteristic
336	C₂³	—	424	2	no	—
337	C₂³	—	424	2	no	—
338	C₂³	—	424	2	no	—
339	C₂³	—	212	2	no	—
340	C₂³	#13133191	1	1	yes	characteristic
341	Q₈	—	2	4	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	424	2	no	—
344	Q₈	—	212	2	no	—
345	Q₈	—	212	2	no	—
346	Q₈	C₂×#11719913	1	4	yes	complemented
347	D₄	—	424	2	no	—
348	D₄	—	424	2	no	—
349	D₄	—	424	2	no	—
350	D₄	—	424	2	no	—
351	D₄	—	212	2	no	—
352	D₄	—	212	2	no	—
353	D₄	—	212	2	no	—
354	D₄	—	212	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	424	2	no	—
361	C₂×C₄	—	212	2	no	—
362	C₂×C₄	#13133191	1	1	yes	characteristic
363	C₂×C₄	#13133191	1	1	yes	characteristic
364	C₂×C₄	#13133191	1	1	yes	characteristic
365	C₂×C₄	C₂×#11719924	1	2	yes	—
366	C₂×C₄	C₂×#11719913	1	2	yes	—
367	C₂×C₄	#13133239	1	2	yes	—
368	C₂×C₄	#13133242	1	2	yes	—
369	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
371	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
372	C₈	—	2	2	no	—
373	C₈	—	4	2	no	—
374	C₈	—	212	2	no	—
375	C₈	—	212	2	no	—
376	C₈	C₂×#11719924	1	4	yes	complemented
377	C₂²	—	848	4	no	—
378	C₂²	—	424	2	no	—
379	C₂²	—	424	2	no	—
380	C₂²	—	424	2	no	—
381	C₂²	#16810823	1	2	yes	—
382	C₂²	#16810852	1	2	yes	—
383	C₂²	#16810886	1	2	yes	—
384	C₂²	C₂×#13133191	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	424	2	no	—
390	C₄	#16810823	1	2	yes	—
391	C₄	#16810852	1	2	yes	—
392	C₄	C₂²×#11719924	1	1	yes	characteristic
393	C₄	C₂²×#11719913	1	1	yes	characteristic
394	C₄	C₂×#13133239	1	1	yes	characteristic
395	C₄	C₂×#13133242	1	1	yes	characteristic
396	C₂	—	848	2	no	—
397	C₂	#20274063	1	4	yes	direct product factor
398	C₂	C₂×#16810823	1	1	yes	characteristic
399	C₂	C₂×#16810852	1	1	yes	characteristic
400	C₂	C₂×#16810886	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13133191
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₂×C₈×Q₈×C₅₃	C₂
socle	C₂³×C₅₃	#121
prime radical	C₂×#13133214	C₂²
hypercenter	C₂×C₈×Q₈	D₅₃
hypocenter	C₅₃	C₂×#1666
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×#16810908	C₂	semidirect
4. #20274063	C₂	direct (N × H)
5. C₂×#16810374	C₂	semidirect
6. C₂×#16810370	C₂	semidirect
8. C₂×C₈×Q₈×C₅₃	C₂	semidirect
17. #16810908	C₂²	semidirect
25. #16810374	C₂²	semidirect
26. #16810370	C₂²	semidirect
30. C₈×Q₈×C₅₃	C₂²	semidirect
85. C₂×Q₈×C₅₃	SD₁₆	semidirect
111. C₂×C₈×C₅₃	SD₁₆	semidirect
142. Q₈×C₅₃	C₂×SD₁₆	semidirect
173. C₈×C₅₃	C₂×SD₁₆	semidirect
199. C₂×C₈×Q₈	D₅₃	semidirect
204. C₂×C₅₃	#1666	semidirect
222. C₈×Q₈	C₂×D₅₃	semidirect
235. C₅₃	C₂×#1666	semidirect
290. C₂×Q₈	#11719913	semidirect
319. C₂×C₈	#11719924	semidirect
346. Q₈	C₂×#11719913	semidirect
376. C₈	C₂×#11719924	semidirect
397. C₂	#20274063	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×#16810996	2
C₂×#16810908	2
C₂×#16810823	2
#20274063	2
C₂×#16810374	2
C₂×#16810370	2
C₂×#16810366	2
C₂×C₈×Q₈×C₅₃	2
C₂×#1666	53

Subgroups — C2×#20274063 #27366412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20274063 #27366412