Subgroups — C₂²×#16811277 #28291037

Order 13568.

12230 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11719947	C₂	1	2	yes	maximal, complemented
2	C₂×#16811277	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#13133217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13133201	C₂	1	4	yes	maximal, complemented
5	C₂²×#13133197	C₂	1	2	yes	maximal, complemented
6	C₂²×#13133191	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₄⋊Dic₅₃	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#11719947	—	2	32	no	—
11	C₂²×#11719947	C₂²	1	48	yes	complemented
12	C₂³×Dic₁₀₆	C₂²	1	2	yes	—
13	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
14	C₂³×C₂²⋊D₅₃	C₂²	1	4	yes	—
15	C₂⁴×Dic₅₃	C₂²	1	4	yes	—
16	C₂³×C₄×D₅₃	C₂²	1	2	yes	—
17	#16811277	C₂²	1	256	yes	direct product factor
18	C₂×#13133217	C₂²	1	24	yes	complemented
19	C₂×#13133201	C₂²	1	96	yes	complemented
20	C₂×#13133197	C₂²	1	48	yes	complemented
21	C₂×#13133191	C₂²	1	48	yes	complemented
22	C₂×C₄×D₂₁₂	C₂²	1	24	yes	complemented
23	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	—
25	C₂²×C₄⋊Dic₅₃	C₂²	1	4	yes	—
26	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	—
27	C₂²×C₄⋊Dic₅₃	C₂²	1	48	yes	complemented
28	C₂²×#11719921	C₂²	1	2	yes	—
29	C₂²×#11719921	C₂²	1	4	yes	—
30	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₅₃	C₂²	1	24	yes	complemented
33	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
35	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
36	C₂⁴×D₅₃	C₂³	1	2	yes	—
37	C₂×#11719947	—	2	384	no	—
38	C₂×#11719947	C₂³	1	128	yes	complemented
39	C₂²×Dic₁₀₆	—	2	16	no	—
40	C₂²×Dic₁₀₆	C₂³	1	24	yes	—
41	C₂²×D₂₁₂	—	2	8	no	—
42	C₂²×D₂₁₂	C₂³	1	12	yes	—
43	C₂²×C₂²⋊D₅₃	—	2	32	no	—
44	C₂²×C₂²⋊D₅₃	C₂³	1	48	yes	—
45	C₂³×Dic₅₃	—	2	32	no	—
46	C₂³×Dic₅₃	C₂³	1	2	yes	—
47	C₂³×Dic₅₃	C₂³	1	4	yes	—
48	C₂³×Dic₅₃	C₂³	1	48	yes	—
49	C₂²×C₄×D₅₃	—	2	16	no	—
50	C₂²×C₄×D₅₃	C₂³	1	24	yes	—
51	#13133217	C₂³	1	64	yes	complemented
52	#13133201	C₂³	1	256	yes	complemented
53	#13133197	C₂³	1	128	yes	complemented
54	#13133191	C₂³	1	128	yes	complemented
55	C₄×D₂₁₂	C₂³	1	64	yes	complemented
56	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	—
57	C₂×C₄⋊Dic₅₃	C₂³	1	24	yes	—
58	C₂×C₄⋊Dic₅₃	C₂³	1	48	yes	—
59	C₂×C₄⋊Dic₅₃	C₂³	1	24	yes	—
60	C₂×C₄⋊Dic₅₃	C₂³	1	128	yes	complemented
61	C₂×#11719921	C₂³	1	24	yes	—
62	C₂×#11719921	C₂³	1	48	yes	—
63	C₂⁵×C₅₃	C₂³	1	2	yes	—
64	C₂²×D₄×C₅₃	D₄	1	16	yes	complemented
65	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
66	C₂³×C₄×C₅₃	—	2	16	no	—
67	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₅₃	C₂³	1	24	yes	—
70	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
72	C₄×D₄×C₅₃	C₂³	1	64	yes	complemented
73	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	—
74	C₂×C₂²⋊C₄×C₅₃	C₂³	1	24	yes	—
75	C₂×C₄²×C₅₃	C₂³	1	12	yes	—
76	C₂⁴×C₅₃	—	2	8	no	—
77	C₂⁴×C₅₃	—	2	8	no	—
78	C₂⁴×C₅₃	C₂×D₄	1	16	yes	—
79	C₂⁴×C₅₃	C₂⁴	1	12	yes	—
80	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
81	C₂³×D₅₃	—	2	8	no	—
82	C₂³×D₅₃	—	2	8	no	—
83	C₂³×D₅₃	—	2	8	no	—
84	C₂³×D₅₃	C₂⁴	1	12	yes	—
85	C₂×D₄×C₅₃	C₂×D₄	1	96	yes	complemented
86	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
87	C₂²×C₄×C₅₃	—	2	8	no	—
88	C₂²×C₄×C₅₃	—	2	4	no	—
89	C₂²×C₄×C₅₃	—	2	96	no	—
90	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
91	C₂²×C₄×C₅₃	#41	1	8	yes	complemented
92	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
93	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
94	C₂²×C₄×C₅₃	C₂⁴	1	32	yes	—
95	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
96	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
97	C₂×C₂²⋊D₅₃	—	2	192	no	—
98	C₂×C₂²⋊D₅₃	C₂⁴	1	64	yes	—
99	C₂²×Dic₅₃	—	2	8	no	—
100	C₂²×Dic₅₃	—	2	16	no	—
101	C₂²×Dic₅₃	—	2	192	no	—
102	C₂²×Dic₅₃	C₂⁴	1	12	yes	—
103	C₂²×Dic₅₃	C₂⁴	1	24	yes	—
104	C₂²×Dic₅₃	C₂⁴	1	64	yes	—
105	#11719947	—	2	512	no	—
106	C₂×D₂₁₂	—	2	48	no	—
107	C₂×D₂₁₂	C₂⁴	1	16	yes	—
108	C₂×C₄×D₅₃	—	2	96	no	—
109	C₂×C₄×D₅₃	C₂⁴	1	32	yes	—
110	C₂×Dic₁₀₆	—	2	96	no	—
111	C₂×Dic₁₀₆	C₂⁴	1	32	yes	—
112	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
113	C₂²⋊C₄×C₅₃	C₂⁴	1	32	yes	—
114	C₄²×C₅₃	C₂⁴	1	16	yes	—
115	#11719921	C₂⁴	1	32	yes	—
116	#11719921	C₂⁴	1	64	yes	—
117	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
118	C₄⋊Dic₅₃	C₂⁴	1	32	yes	—
119	C₄⋊Dic₅₃	C₂⁴	1	64	yes	—
120	C₄⋊Dic₅₃	C₂⁴	1	32	yes	—
121	C₂³×C₅₃	—	2	64	no	—
122	C₂³×C₅₃	—	2	24	no	—
123	C₂³×C₅₃	—	2	24	no	—
124	C₂³×C₅₃	C₂²×D₄	1	48	yes	—
125	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
126	C₂³×C₅₃	C₂×#41	1	4	yes	—
127	C₂³×C₅₃	2₋¹⁺⁴	1	4	yes	—
128	C₂³×C₅₃	C₂⁵	1	8	yes	—
129	C₂³×C₅₃	C₂⁵	1	3	yes	—
130	C₂²×D₅₃	—	2	24	no	—
131	C₂²×D₅₃	—	2	24	no	—
132	C₂²×D₅₃	—	2	24	no	—
133	C₂²×D₅₃	—	4	32	no	—
134	C₂²×D₅₃	C₂⁵	1	8	yes	—
135	D₄×C₅₃	C₂²×D₄	1	64	yes	complemented
136	C₂×C₄×C₅₃	—	2	24	no	—
137	C₂×C₄×C₅₃	—	2	12	no	—
138	C₂×C₄×C₅₃	—	2	64	no	—
139	C₂×C₄×C₅₃	C₂²×D₄	1	24	yes	—
140	C₂×C₄×C₅₃	C₂×#41	1	24	yes	complemented
141	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
142	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
143	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
144	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
145	C₂²⋊D₅₃	—	2	128	no	—
146	C₂×Dic₅₃	—	2	48	no	—
147	C₂×Dic₅₃	—	2	24	no	—
148	C₂×Dic₅₃	—	2	128	no	—
149	C₂×Dic₅₃	C₂⁵	1	16	yes	—
150	C₂×Dic₅₃	C₂⁵	1	8	yes	—
151	D₂₁₂	—	2	32	no	—
152	C₄×D₅₃	—	2	64	no	—
153	Dic₁₀₆	—	2	64	no	—
154	C₂²×#547	—	53	1	no	maximal, Sylow
155	C₂²×C₅₃	—	2	8	no	—
156	C₂²×C₅₃	—	2	8	no	—
157	C₂²×C₅₃	—	2	96	no	—
158	C₂²×C₅₃	#547	1	16	yes	complemented
159	C₂²×C₅₃	C₂³×D₄	1	16	yes	—
160	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
161	C₂²×C₅₃	C₂²×#41	1	6	yes	—
162	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	6	yes	—
163	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
164	C₂×D₅₃	—	2	8	no	—
165	C₂×D₅₃	—	2	8	no	—
166	C₂×D₅₃	—	2	8	no	—
167	C₂×D₅₃	—	4	48	no	—
168	C₄×C₅₃	—	2	8	no	—
169	C₄×C₅₃	—	2	4	no	—
170	C₄×C₅₃	C₂³×D₄	1	8	yes	—
171	C₄×C₅₃	C₂²×#41	1	8	yes	complemented
172	Dic₅₃	—	2	16	no	—
173	Dic₅₃	—	2	8	no	—
174	C₂³×#41	—	53	2	no	—
175	C₂×#547	—	53	48	no	—
176	C₂²×C₄⋊Q₈	—	53	1	no	—
177	C₂²×#123	—	53	4	no	—
178	C₂²×C₂²⋊Q₈	—	53	2	no	—
179	C₂²×#121	—	53	2	no	—
180	C₂²×C₄×D₄	—	53	1	no	—
181	C₂²×C₄×D₄	D₅₃	1	1	yes	characteristic, complemented
182	C₂³×C₄⋊C₄	—	53	2	no	—
183	C₂×C₅₃	—	2	16	no	—
184	C₂×C₅₃	C₂×#547	1	12	yes	complemented
185	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
186	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
187	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
188	D₅₃	—	4	8	no	—
189	C₂²×#41	—	53	48	no	—
190	C₂²×#41	—	106	32	no	—
191	C₂³×Q₈	—	53	2	no	—
192	C₂³×D₄	—	53	4	no	—
193	C₂³×D₄	—	53	1	no	—
194	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
195	C₂⁴×C₄	—	53	4	no	—
196	C₂⁴×C₄	—	53	2	no	—
197	C₂⁴×C₄	C₂×D₅₃	1	2	yes	—
198	#547	—	53	256	no	—
199	C₂×C₄⋊Q₈	—	53	24	no	—
200	C₂×#123	—	53	96	no	—
201	C₂×C₂²⋊Q₈	—	53	48	no	—
202	C₂×#121	—	53	48	no	—
203	C₂×C₄×D₄	—	53	24	no	—
204	C₂×C₄×D₄	C₂×D₅₃	1	24	yes	complemented
205	C₂²×C₄⋊C₄	—	53	1	no	—
206	C₂²×C₄⋊C₄	—	53	2	no	—
207	C₂²×C₄⋊C₄	—	53	4	no	—
208	C₂²×C₄⋊C₄	—	53	2	no	—
209	C₂²×C₄⋊C₄	—	53	48	no	—
210	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
211	C₂²×C₂²⋊C₄	—	53	2	no	—
212	C₂²×C₂²⋊C₄	—	53	4	no	—
213	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	—
214	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
215	C₅₃	C₂²×#547	1	1	yes	characteristic, complemented, Sylow
216	C₂⁵	—	53	2	no	—
217	C₂⁵	C₂²×D₅₃	1	2	yes	—
218	C₂×#41	—	53	128	no	—
219	C₂×#41	—	106	384	no	—
220	C₂²×Q₈	—	53	24	no	—
221	C₂²×Q₈	—	106	16	no	—
222	C₂²×D₄	—	53	48	no	—
223	C₂²×D₄	—	53	12	no	—
224	C₂²×D₄	—	106	32	no	—
225	C₂²×D₄	—	106	8	no	—
226	C₂²×D₄	D₂₁₂	1	16	yes	complemented
227	C₂²×D₄	C₂²×D₅₃	1	12	yes	—
228	C₂³×C₄	—	2	16	no	—
229	C₂³×C₄	—	53	48	no	—
230	C₂³×C₄	—	53	2	no	—
231	C₂³×C₄	—	53	4	no	—
232	C₂³×C₄	—	53	24	no	—
233	C₂³×C₄	—	106	32	no	—
234	C₂³×C₄	—	106	16	no	—
235	C₂³×C₄	C₂²×D₅₃	1	24	yes	—
236	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
237	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
238	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
239	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
240	C₄⋊Q₈	—	53	64	no	—
241	#123	—	53	256	no	—
242	C₂²⋊Q₈	—	53	128	no	—
243	#121	—	53	128	no	—
244	C₄×D₄	—	53	64	no	—
245	C₄×D₄	C₂²×D₅₃	1	64	yes	complemented
246	C₂×C₄⋊C₄	—	53	12	no	—
247	C₂×C₄⋊C₄	—	53	24	no	—
248	C₂×C₄⋊C₄	—	53	48	no	—
249	C₂×C₄⋊C₄	—	53	128	no	—
250	C₂×C₄⋊C₄	—	53	24	no	—
251	C₂×C₄⋊C₄	C₂²×D₅₃	1	12	yes	—
252	C₂×C₂²⋊C₄	—	53	24	no	—
253	C₂×C₂²⋊C₄	—	53	48	no	—
254	C₂×C₂²⋊C₄	C₂²×D₅₃	1	24	yes	—
255	C₂×C₄²	C₂²×D₅₃	1	12	yes	—
256	C₂⁴	—	2	8	no	—
257	C₂⁴	—	2	8	no	—
258	C₂⁴	—	53	12	no	—
259	C₂⁴	—	106	8	no	—
260	C₂⁴	—	106	8	no	—
261	C₂⁴	—	106	8	no	—
262	C₂⁴	C₂×D₂₁₂	1	16	yes	—
263	C₂⁴	C₂³×D₅₃	1	12	yes	—
264	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
265	#41	—	106	512	no	—
266	C₂×Q₈	—	53	32	no	—
267	C₂×Q₈	—	106	96	no	—
268	C₂×D₄	—	53	64	no	—
269	C₂×D₄	—	53	16	no	—
270	C₂×D₄	—	106	192	no	—
271	C₂×D₄	—	106	48	no	—
272	C₂×D₄	C₂×D₂₁₂	1	96	yes	complemented
273	C₂×D₄	C₂³×D₅₃	1	16	yes	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	96	no	—
277	C₂²×C₄	—	53	12	no	—
278	C₂²×C₄	—	53	24	no	—
279	C₂²×C₄	—	53	64	no	—
280	C₂²×C₄	—	53	32	no	—
281	C₂²×C₄	—	106	8	no	—
282	C₂²×C₄	—	106	16	no	—
283	C₂²×C₄	—	106	192	no	—
284	C₂²×C₄	—	106	96	no	—
285	C₂²×C₄	C₂×D₂₁₂	1	8	yes	—
286	C₂²×C₄	#11719947	1	8	yes	complemented
287	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
288	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
289	C₂²×C₄	C₂³×D₅₃	1	32	yes	—
290	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
291	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
292	C₄⋊C₄	—	53	16	no	—
293	C₄⋊C₄	—	53	32	no	—
294	C₄⋊C₄	—	53	64	no	—
295	C₄⋊C₄	—	53	32	no	—
296	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
297	C₂²⋊C₄	—	53	32	no	—
298	C₂²⋊C₄	—	53	64	no	—
299	C₂²⋊C₄	C₂³×D₅₃	1	32	yes	—
300	C₄²	C₂³×D₅₃	1	16	yes	—
301	C₂³	—	2	64	no	—
302	C₂³	—	2	24	no	—
303	C₂³	—	2	24	no	—
304	C₂³	—	53	8	no	—
305	C₂³	—	106	24	no	—
306	C₂³	—	106	24	no	—
307	C₂³	—	106	24	no	—
308	C₂³	—	212	32	no	—
309	C₂³	C₂²×D₂₁₂	1	48	yes	—
310	C₂³	C₂²×D₂₁₂	1	4	yes	—
311	C₂³	C₂×#11719947	1	4	yes	—
312	C₂³	#13133264	1	4	yes	—
313	C₂³	C₂⁴×D₅₃	1	8	yes	—
314	C₂³	C₂⁴×D₅₃	1	3	yes	—
315	Q₈	—	106	64	no	—
316	D₄	—	106	128	no	—
317	D₄	—	106	32	no	—
318	D₄	C₂²×D₂₁₂	1	64	yes	complemented
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	64	no	—
322	C₂×C₄	—	53	8	no	—
323	C₂×C₄	—	53	16	no	—
324	C₂×C₄	—	106	24	no	—
325	C₂×C₄	—	106	48	no	—
326	C₂×C₄	—	106	128	no	—
327	C₂×C₄	—	106	64	no	—
328	C₂×C₄	C₂²×D₂₁₂	1	24	yes	—
329	C₂×C₄	C₂×#11719947	1	24	yes	complemented
330	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
331	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
332	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
333	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
334	C₂²	—	2	96	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	2	8	no	—
337	C₂²	—	106	8	no	—
338	C₂²	—	106	8	no	—
339	C₂²	—	106	8	no	—
340	C₂²	—	212	48	no	—
341	C₂²	#16811277	1	16	yes	direct product factor
342	C₂²	C₂³×D₂₁₂	1	16	yes	—
343	C₂²	C₂³×D₂₁₂	1	6	yes	—
344	C₂²	C₂²×#11719947	1	6	yes	—
345	C₂²	C₂×#13133264	1	6	yes	—
346	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
347	C₄	—	2	8	no	—
348	C₄	—	2	4	no	—
349	C₄	—	106	8	no	—
350	C₄	—	106	16	no	—
351	C₄	C₂³×D₂₁₂	1	8	yes	—
352	C₄	C₂²×#11719947	1	8	yes	complemented
353	C₂	—	2	16	no	—
354	C₂	—	212	8	no	—
355	C₂	C₂×#16811277	1	12	yes	direct product factor
356	C₂	C₂⁴×D₂₁₂	1	1	yes	characteristic
357	C₂	C₂³×#11719947	1	1	yes	characteristic
358	C₂	C₂²×#13133264	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂²×C₄×D₄×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂⁴
hypercenter	C₂²×C₄×D₄	D₅₃
hypocenter	C₅₃	C₂²×#547
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#11719947	C₂	semidirect
2. C₂×#16811277	C₂	direct (N × H)
3. C₂²×#13133217	C₂	semidirect
4. C₂²×#13133201	C₂	semidirect
5. C₂²×#13133197	C₂	semidirect
6. C₂²×#13133191	C₂	semidirect
7. C₂²×C₄×D₂₁₂	C₂	semidirect
8. C₂³×C₄⋊Dic₅₃	C₂	semidirect
9. C₂²×C₄×D₄×C₅₃	C₂	semidirect
11. C₂²×#11719947	C₂²	semidirect
17. #16811277	C₂²	direct (N × H)
18. C₂×#13133217	C₂²	semidirect
19. C₂×#13133201	C₂²	semidirect
20. C₂×#13133197	C₂²	semidirect
21. C₂×#13133191	C₂²	semidirect
22. C₂×C₄×D₂₁₂	C₂²	semidirect
27. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
32. C₂×C₄×D₄×C₅₃	C₂²	semidirect
38. C₂×#11719947	C₂³	semidirect
51. #13133217	C₂³	semidirect
52. #13133201	C₂³	semidirect
53. #13133197	C₂³	semidirect
54. #13133191	C₂³	semidirect
55. C₄×D₂₁₂	C₂³	semidirect
60. C₂×C₄⋊Dic₅₃	C₂³	semidirect
64. C₂²×D₄×C₅₃	D₄	semidirect
72. C₄×D₄×C₅₃	C₂³	semidirect
85. C₂×D₄×C₅₃	C₂×D₄	semidirect
91. C₂²×C₄×C₅₃	#41	semidirect
135. D₄×C₅₃	C₂²×D₄	semidirect
140. C₂×C₄×C₅₃	C₂×#41	semidirect
158. C₂²×C₅₃	#547	semidirect
171. C₄×C₅₃	C₂²×#41	semidirect
181. C₂²×C₄×D₄	D₅₃	semidirect
184. C₂×C₅₃	C₂×#547	semidirect
204. C₂×C₄×D₄	C₂×D₅₃	semidirect
215. C₅₃	C₂²×#547	semidirect
226. C₂²×D₄	D₂₁₂	semidirect
245. C₄×D₄	C₂²×D₅₃	semidirect
272. C₂×D₄	C₂×D₂₁₂	semidirect
286. C₂²×C₄	#11719947	semidirect
318. D₄	C₂²×D₂₁₂	semidirect
329. C₂×C₄	C₂×#11719947	semidirect
341. C₂²	#16811277	direct (N × H)
352. C₄	C₂²×#11719947	semidirect
355. C₂	C₂×#16811277	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11719947	2
C₂×#16811277	2
C₂²×#13133217	2
C₂²×#13133201	2
C₂²×#13133197	2
C₂²×#13133191	2
C₂²×C₄×D₂₁₂	2
C₂³×C₄⋊Dic₅₃	2
C₂²×C₄×D₄×C₅₃	2
C₂²×#547	53

Subgroups — C22×#16811277 #28291037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16811277 #28291037