Subgroups — C₂²×#16811296 #28291067

Order 13568.

9526 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811296	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#13133212	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13133212	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13133203	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13133201	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13133199	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13133197	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13133194	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#13133185	C₂	1	1	yes	maximal, characteristic
10	C₂²×D₄×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#13133177	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#13133176	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#13133175	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×#11719921	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic
18	C₂³×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
20	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
21	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic
22	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
24	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
25	#16811296	C₂²	1	256	yes	direct product factor
26	C₂×#13133212	C₂²	1	24	yes	complemented
27	C₂×#13133212	C₂²	1	24	yes	complemented
28	C₂×#13133203	C₂²	1	24	yes	complemented
29	C₂×#13133201	C₂²	1	24	yes	complemented
30	C₂×#13133199	C₂²	1	24	yes	complemented
31	C₂×#13133197	C₂²	1	24	yes	complemented
32	C₂×#13133194	C₂²	1	24	yes	complemented
33	C₂×#13133185	C₂²	1	24	yes	—
34	C₂×D₄×Dic₅₃	C₂²	1	24	yes	complemented
35	C₂×#13133177	C₂²	1	24	yes	complemented
36	C₂×#13133176	C₂²	1	24	yes	complemented
37	C₂×#13133175	C₂²	1	24	yes	complemented
38	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₂²×#11719921	C₂²	1	1	yes	characteristic
48	C₂²×#11719921	C₂²	1	1	yes	characteristic
49	C₂²×#11719921	C₂²	1	1	yes	characteristic
50	C₂²×#11719921	C₂²	1	1	yes	characteristic
51	C₂²×#11719921	C₂²	1	1	yes	characteristic
52	C₂²×#11719921	C₂²	1	1	yes	characteristic
53	C₂²×#11719921	C₂²	1	1	yes	characteristic
54	C₂²×#11719921	C₂²	1	1	yes	characteristic
55	C₂²×#11719921	C₂²	1	24	yes	complemented
56	C₂×C₂²⋊C₄×D₅₃	C₂²	1	24	yes	complemented
57	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×#123×C₅₃	C₂²	1	24	yes	complemented
63	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
66	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₂⁴×D₅₃	—	2	8	no	—
69	C₂⁴×D₅₃	—	2	8	no	—
70	C₂⁴×D₅₃	—	4	4	no	—
71	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
72	C₂⁴×D₅₃	C₂³	1	12	yes	—
73	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
74	C₂²×Dic₁₀₆	—	4	4	no	—
75	C₂²×Dic₁₀₆	C₂³	1	12	yes	complemented
76	C₂²×C₂²⋊D₅₃	—	2	8	no	—
77	C₂²×C₂²⋊D₅₃	—	4	4	no	—
78	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
79	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
80	C₂³×Dic₅₃	—	4	4	no	—
81	C₂³×Dic₅₃	—	4	4	no	—
82	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
83	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
84	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
85	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
86	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
87	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
88	C₂³×Dic₅₃	C₂³	1	12	yes	—
89	C₂³×Dic₅₃	C₂³	1	12	yes	complemented
90	C₂²×C₄×D₅₃	—	2	8	no	—
91	C₂²×C₄×D₅₃	—	4	4	no	—
92	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
93	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
94	#13133212	C₂³	1	64	yes	complemented
95	#13133212	C₂³	1	64	yes	complemented
96	#13133203	C₂³	1	64	yes	complemented
97	#13133201	C₂³	1	64	yes	complemented
98	#13133199	C₂³	1	64	yes	complemented
99	#13133197	C₂³	1	64	yes	complemented
100	#13133194	C₂³	1	64	yes	complemented
101	#13133185	C₂³	1	64	yes	—
102	D₄×Dic₅₃	C₂³	1	64	yes	complemented
103	#13133177	C₂³	1	64	yes	complemented
104	#13133176	C₂³	1	64	yes	complemented
105	#13133175	C₂³	1	64	yes	complemented
106	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
107	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
108	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
109	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
110	C₂×#11719919	C₂³	1	12	yes	complemented
111	C₂×#11719919	C₂³	1	12	yes	complemented
112	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
113	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
114	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
115	C₂×#11719921	C₂³	1	12	yes	—
116	C₂×#11719921	C₂³	1	12	yes	—
117	C₂×#11719921	C₂³	1	12	yes	—
118	C₂×#11719921	C₂³	1	12	yes	—
119	C₂×#11719921	C₂³	1	12	yes	—
120	C₂×#11719921	C₂³	1	12	yes	—
121	C₂×#11719921	C₂³	1	12	yes	—
122	C₂×#11719921	C₂³	1	12	yes	—
123	C₂×#11719921	C₂³	1	64	yes	complemented
124	C₂²⋊C₄×D₅₃	C₂³	1	64	yes	complemented
125	C₂×C₄×Dic₅₃	C₂³	1	12	yes	complemented
126	C₂×C₄×Dic₅₃	C₂³	1	12	yes	complemented
127	C₂×C₄×Dic₅₃	C₂³	1	12	yes	complemented
128	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
129	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₅₃	—	2	8	no	—
131	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
132	C₂³×C₄×C₅₃	—	2	8	no	—
133	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₃	C₂³	1	12	yes	—
139	#123×C₅₃	C₂³	1	64	yes	complemented
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	complemented
141	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	complemented
142	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
143	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	complemented
144	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	complemented
145	C₂⁴×C₅₃	—	2	4	no	—
146	C₂⁴×C₅₃	—	2	4	no	—
147	C₂⁴×C₅₃	—	2	4	no	—
148	C₂⁴×C₅₃	—	2	4	no	—
149	C₂⁴×C₅₃	—	2	4	no	—
150	C₂⁴×C₅₃	#41	1	8	yes	—
151	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
152	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
153	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
154	C₂³×D₅₃	—	2	4	no	—
155	C₂³×D₅₃	—	2	4	no	—
156	C₂³×D₅₃	—	2	48	no	—
157	C₂³×D₅₃	—	2	4	no	—
158	C₂³×D₅₃	—	2	4	no	—
159	C₂³×D₅₃	—	2	4	no	—
160	C₂³×D₅₃	—	2	48	no	—
161	C₂³×D₅₃	—	4	24	no	—
162	C₂³×D₅₃	—	4	64	no	—
163	C₂³×D₅₃	#41	1	8	yes	—
164	C₂³×D₅₃	C₂⁴	1	6	yes	—
165	C₂³×D₅₃	C₂⁴	1	16	yes	—
166	C₂³×D₅₃	C₂⁴	1	6	yes	—
167	C₂×D₄×C₅₃	—	2	48	no	—
168	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
169	C₂²×C₄×C₅₃	—	2	48	no	—
170	C₂²×C₄×C₅₃	—	2	4	no	—
171	C₂²×C₄×C₅₃	—	2	4	no	—
172	C₂²×C₄×C₅₃	—	2	4	no	—
173	C₂²×C₄×C₅₃	—	2	4	no	—
174	C₂²×C₄×C₅₃	—	2	4	no	—
175	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
176	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
177	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
178	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
179	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
180	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
181	C₂×C₂²⋊D₅₃	—	2	48	no	—
182	C₂×C₂²⋊D₅₃	—	4	24	no	—
183	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
184	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
185	C₂²×Dic₅₃	—	2	4	no	—
186	C₂²×Dic₅₃	—	2	4	no	—
187	C₂²×Dic₅₃	—	2	4	no	—
188	C₂²×Dic₅₃	—	2	4	no	—
189	C₂²×Dic₅₃	—	2	4	no	—
190	C₂²×Dic₅₃	—	2	4	no	—
191	C₂²×Dic₅₃	—	4	24	no	—
192	C₂²×Dic₅₃	—	4	24	no	—
193	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
194	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
195	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
196	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
197	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
198	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
199	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
200	C₂²×Dic₅₃	C₂⁴	1	16	yes	complemented
201	C₂×C₄×D₅₃	—	2	48	no	—
202	C₂×C₄×D₅₃	—	4	24	no	—
203	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
204	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
205	C₂×Dic₁₀₆	—	4	24	no	—
206	C₂×Dic₁₀₆	C₂⁴	1	16	yes	complemented
207	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
208	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
209	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
210	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
211	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
212	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
213	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
214	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
215	#11719921	C₂⁴	1	16	yes	—
216	#11719921	C₂⁴	1	16	yes	—
217	#11719921	C₂⁴	1	16	yes	—
218	#11719921	C₂⁴	1	16	yes	—
219	#11719921	C₂⁴	1	16	yes	—
220	#11719921	C₂⁴	1	16	yes	—
221	#11719921	C₂⁴	1	16	yes	—
222	#11719921	C₂⁴	1	16	yes	—
223	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
224	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
225	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
226	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
227	#11719919	C₂⁴	1	16	yes	complemented
228	#11719919	C₂⁴	1	16	yes	complemented
229	C₄×Dic₅₃	C₂⁴	1	16	yes	complemented
230	C₄×Dic₅₃	C₂⁴	1	16	yes	complemented
231	C₄×Dic₅₃	C₂⁴	1	16	yes	complemented
232	C₂³×C₅₃	—	2	32	no	—
233	C₂³×C₅₃	—	2	12	no	—
234	C₂³×C₅₃	—	2	12	no	—
235	C₂³×C₅₃	—	2	12	no	—
236	C₂³×C₅₃	—	2	12	no	—
237	C₂³×C₅₃	—	2	12	no	—
238	C₂³×C₅₃	—	4	16	no	—
239	C₂³×C₅₃	C₂×#41	1	4	yes	—
240	C₂³×C₅₃	C₂×#41	1	24	yes	—
241	C₂³×C₅₃	C₂×#41	1	4	yes	—
242	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
243	C₂³×C₅₃	C₂⁵	1	4	yes	—
244	C₂³×C₅₃	C₂⁵	1	4	yes	—
245	C₂³×C₅₃	C₂⁵	1	3	yes	—
246	C₂²×D₅₃	—	2	32	no	—
247	C₂²×D₅₃	—	2	12	no	—
248	C₂²×D₅₃	—	2	12	no	—
249	C₂²×D₅₃	—	2	12	no	—
250	C₂²×D₅₃	—	2	32	no	—
251	C₂²×D₅₃	—	2	12	no	—
252	C₂²×D₅₃	—	2	12	no	—
253	C₂²×D₅₃	—	2	32	no	—
254	C₂²×D₅₃	—	4	16	no	—
255	C₂²×D₅₃	—	4	192	no	—
256	C₂²×D₅₃	—	4	16	no	—
257	C₂²×D₅₃	C₂×#41	1	24	yes	—
258	C₂²×D₅₃	C₂⁵	1	4	yes	—
259	C₂²×D₅₃	C₂⁵	1	4	yes	—
260	D₄×C₅₃	—	2	32	no	—
261	C₂×C₄×C₅₃	—	2	12	no	—
262	C₂×C₄×C₅₃	—	2	32	no	—
263	C₂×C₄×C₅₃	—	2	12	no	—
264	C₂×C₄×C₅₃	—	2	12	no	—
265	C₂×C₄×C₅₃	—	2	12	no	—
266	C₂×C₄×C₅₃	—	2	12	no	—
267	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
268	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
269	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
270	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
271	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
272	C₂²⋊D₅₃	—	2	32	no	—
273	C₂²⋊D₅₃	—	4	16	no	—
274	C₂×Dic₅₃	—	2	12	no	—
275	C₂×Dic₅₃	—	2	12	no	—
276	C₂×Dic₅₃	—	2	12	no	—
277	C₂×Dic₅₃	—	2	12	no	—
278	C₂×Dic₅₃	—	2	12	no	—
279	C₂×Dic₅₃	—	2	12	no	—
280	C₂×Dic₅₃	—	4	16	no	—
281	C₂×Dic₅₃	—	4	16	no	—
282	C₂×Dic₅₃	C₂⁵	1	4	yes	—
283	C₂×Dic₅₃	C₂⁵	1	4	yes	—
284	C₂×Dic₅₃	C₂⁵	1	4	yes	—
285	C₂×Dic₅₃	C₂⁵	1	4	yes	—
286	C₂×Dic₅₃	C₂⁵	1	4	yes	—
287	C₂×Dic₅₃	C₂⁵	1	4	yes	—
288	C₄×D₅₃	—	2	32	no	—
289	C₄×D₅₃	—	4	16	no	—
290	Dic₁₀₆	—	4	16	no	—
291	C₂²×#551	—	53	1	no	maximal, Sylow
292	C₂²×C₅₃	—	2	4	no	—
293	C₂²×C₅₃	—	2	4	no	—
294	C₂²×C₅₃	—	2	48	no	—
295	C₂²×C₅₃	—	2	4	no	—
296	C₂²×C₅₃	—	2	4	no	—
297	C₂²×C₅₃	—	2	4	no	—
298	C₂²×C₅₃	—	4	24	no	—
299	C₂²×C₅₃	#551	1	16	yes	complemented
300	C₂²×C₅₃	C₂²×#41	1	6	yes	—
301	C₂²×C₅₃	C₂²×#41	1	8	yes	—
302	C₂²×C₅₃	C₂²×#41	1	6	yes	—
303	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
304	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
305	C₂×D₅₃	—	2	4	no	—
306	C₂×D₅₃	—	2	4	no	—
307	C₂×D₅₃	—	2	48	no	—
308	C₂×D₅₃	—	2	4	no	—
309	C₂×D₅₃	—	2	4	no	—
310	C₂×D₅₃	—	2	4	no	—
311	C₂×D₅₃	—	4	64	no	—
312	C₂×D₅₃	—	4	24	no	—
313	C₂×D₅₃	C₂²×#41	1	8	yes	—
314	C₄×C₅₃	—	2	4	no	—
315	C₄×C₅₃	—	2	4	no	—
316	C₄×C₅₃	—	2	4	no	—
317	C₄×C₅₃	—	2	4	no	—
318	C₄×C₅₃	—	2	4	no	—
319	Dic₅₃	—	2	4	no	—
320	Dic₅₃	—	2	4	no	—
321	Dic₅₃	—	2	4	no	—
322	Dic₅₃	—	2	4	no	—
323	Dic₅₃	—	2	4	no	—
324	Dic₅₃	—	2	4	no	—
325	C₂×#551	—	53	48	no	—
326	C₂²×#126	—	53	1	no	—
327	C₂²×#126	—	53	1	no	—
328	C₂²×#124	—	53	1	no	—
329	C₂²×#123	—	53	1	no	—
330	C₂²×#123	—	53	1	no	—
331	C₂²×#123	D₅₃	1	1	yes	characteristic, complemented
332	C₂²×C₂²⋊Q₈	—	53	1	no	—
333	C₂²×C₂²⋊Q₈	—	53	1	no	—
334	C₂²×#120	—	53	1	no	—
335	C₂²×C₄×D₄	—	53	1	no	—
336	C₂²×C₄×D₄	—	53	1	no	—
337	C₂²×#117	—	53	1	no	—
338	C₂²×#117	—	53	1	no	—
339	C₂³×C₂²⋊C₄	—	53	1	no	—
340	C₂³×C₂²⋊C₄	—	53	1	no	—
341	C₂×C₅₃	—	2	8	no	—
342	C₂×C₅₃	—	4	4	no	—
343	C₂×C₅₃	C₂×#551	1	12	yes	complemented
344	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
345	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
346	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
347	D₅₃	—	2	8	no	—
348	D₅₃	—	4	4	no	—
349	C₂⁶	—	53	1	no	—
350	C₂³×Q₈	—	53	1	no	—
351	C₂³×D₄	—	53	1	no	—
352	C₂³×D₄	—	53	1	no	—
353	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
354	C₂⁴×C₄	—	53	1	no	—
355	C₂⁴×C₄	—	53	1	no	—
356	C₂⁴×C₄	—	53	1	no	—
357	C₂⁴×C₄	—	53	1	no	—
358	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic
359	#551	—	53	256	no	—
360	C₂×#126	—	53	24	no	—
361	C₂×#126	—	53	24	no	—
362	C₂×#124	—	53	24	no	—
363	C₂×#123	—	53	24	no	—
364	C₂×#123	—	53	24	no	—
365	C₂×#123	C₂×D₅₃	1	24	yes	complemented
366	C₂×C₂²⋊Q₈	—	53	24	no	—
367	C₂×C₂²⋊Q₈	—	53	24	no	—
368	C₂×#120	—	53	24	no	—
369	C₂×C₄×D₄	—	53	24	no	—
370	C₂×C₄×D₄	—	53	24	no	—
371	C₂×#117	—	53	24	no	—
372	C₂×#117	—	53	24	no	—
373	C₂²×C₄⋊C₄	—	53	1	no	—
374	C₂²×C₄⋊C₄	—	53	1	no	—
375	C₂²×C₄⋊C₄	—	53	1	no	—
376	C₂²×C₄⋊C₄	—	53	1	no	—
377	C₂²×C₄⋊C₄	—	53	1	no	—
378	C₂²×C₄⋊C₄	—	53	1	no	—
379	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
380	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
381	C₂²×C₂²⋊C₄	—	53	1	no	—
382	C₂²×C₂²⋊C₄	—	53	1	no	—
383	C₂²×C₂²⋊C₄	—	53	1	no	—
384	C₂²×C₂²⋊C₄	—	53	1	no	—
385	C₂²×C₂²⋊C₄	—	53	1	no	—
386	C₂²×C₂²⋊C₄	—	53	1	no	—
387	C₂²×C₂²⋊C₄	—	53	1	no	—
388	C₂²×C₂²⋊C₄	—	53	1	no	—
389	C₂²×C₂²⋊C₄	—	53	1	no	—
390	C₂²×C₂²⋊C₄	—	53	1	no	—
391	C₂²×C₂²⋊C₄	—	53	1	no	—
392	C₂²×C₂²⋊C₄	—	53	24	no	—
393	C₂²×C₂²⋊C₄	—	53	24	no	—
394	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
396	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
397	C₂²×C₄²	—	53	1	no	—
398	C₂²×C₄²	—	53	1	no	—
399	C₂²×C₄²	—	53	1	no	—
400	C₅₃	C₂²×#551	1	1	yes	characteristic, complemented, Sylow
401	C₂⁵	—	53	1	no	—
402	C₂⁵	—	53	1	no	—
403	C₂⁵	—	53	12	no	—
404	C₂⁵	—	106	8	no	—
405	C₂⁵	—	106	8	no	—
406	C₂⁵	—	212	4	no	—
407	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
408	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
409	C₂²×Q₈	—	53	12	no	—
410	C₂²×Q₈	—	212	4	no	—
411	C₂²×D₄	—	2	8	no	—
412	C₂²×D₄	—	53	12	no	—
413	C₂²×D₄	—	53	12	no	—
414	C₂²×D₄	—	106	8	no	—
415	C₂²×D₄	—	212	4	no	—
416	C₂²×D₄	C₂²×D₅₃	1	12	yes	—
417	C₂³×C₄	—	2	8	no	—
418	C₂³×C₄	—	53	1	no	—
419	C₂³×C₄	—	53	1	no	—
420	C₂³×C₄	—	53	1	no	—
421	C₂³×C₄	—	53	1	no	—
422	C₂³×C₄	—	53	1	no	—
423	C₂³×C₄	—	53	1	no	—
424	C₂³×C₄	—	53	12	no	—
425	C₂³×C₄	—	53	12	no	—
426	C₂³×C₄	—	53	12	no	—
427	C₂³×C₄	—	53	12	no	—
428	C₂³×C₄	—	106	8	no	—
429	C₂³×C₄	—	212	4	no	—
430	C₂³×C₄	—	212	4	no	—
431	C₂³×C₄	—	212	4	no	—
432	C₂³×C₄	C₂²×D₅₃	1	12	yes	—
433	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
434	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
435	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
436	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
437	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
438	#126	—	53	64	no	—
439	#126	—	53	64	no	—
440	#124	—	53	64	no	—
441	#123	—	53	64	no	—
442	#123	—	53	64	no	—
443	#123	C₂²×D₅₃	1	64	yes	complemented
444	C₂²⋊Q₈	—	53	64	no	—
445	C₂²⋊Q₈	—	53	64	no	—
446	#120	—	53	64	no	—
447	C₄×D₄	—	53	64	no	—
448	C₄×D₄	—	53	64	no	—
449	#117	—	53	64	no	—
450	#117	—	53	64	no	—
451	C₂×C₄⋊C₄	—	53	12	no	—
452	C₂×C₄⋊C₄	—	53	12	no	—
453	C₂×C₄⋊C₄	—	53	12	no	—
454	C₂×C₄⋊C₄	—	53	12	no	—
455	C₂×C₄⋊C₄	—	53	12	no	—
456	C₂×C₄⋊C₄	—	53	12	no	—
457	C₂×C₄⋊C₄	C₂²×D₅₃	1	12	yes	complemented
458	C₂×C₄⋊C₄	C₂²×D₅₃	1	12	yes	complemented
459	C₂×C₂²⋊C₄	—	53	12	no	—
460	C₂×C₂²⋊C₄	—	53	12	no	—
461	C₂×C₂²⋊C₄	—	53	12	no	—
462	C₂×C₂²⋊C₄	—	53	12	no	—
463	C₂×C₂²⋊C₄	—	53	12	no	—
464	C₂×C₂²⋊C₄	—	53	12	no	—
465	C₂×C₂²⋊C₄	—	53	12	no	—
466	C₂×C₂²⋊C₄	—	53	12	no	—
467	C₂×C₂²⋊C₄	—	53	12	no	—
468	C₂×C₂²⋊C₄	—	53	64	no	—
469	C₂×C₂²⋊C₄	—	53	12	no	—
470	C₂×C₂²⋊C₄	—	53	12	no	—
471	C₂×C₂²⋊C₄	—	53	64	no	—
472	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	—
473	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	complemented
474	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	complemented
475	C₂×C₄²	—	53	12	no	—
476	C₂×C₄²	—	53	12	no	—
477	C₂×C₄²	—	53	12	no	—
478	C₂⁴	—	2	4	no	—
479	C₂⁴	—	2	4	no	—
480	C₂⁴	—	2	4	no	—
481	C₂⁴	—	2	4	no	—
482	C₂⁴	—	2	4	no	—
483	C₂⁴	—	53	8	no	—
484	C₂⁴	—	53	6	no	—
485	C₂⁴	—	53	6	no	—
486	C₂⁴	—	53	16	no	—
487	C₂⁴	—	106	48	no	—
488	C₂⁴	—	106	4	no	—
489	C₂⁴	—	106	4	no	—
490	C₂⁴	—	106	4	no	—
491	C₂⁴	—	106	48	no	—
492	C₂⁴	—	106	4	no	—
493	C₂⁴	—	106	4	no	—
494	C₂⁴	—	212	24	no	—
495	C₂⁴	—	212	64	no	—
496	C₂⁴	#11719947	1	8	yes	—
497	C₂⁴	C₂³×D₅₃	1	6	yes	—
498	C₂⁴	C₂³×D₅₃	1	6	yes	—
499	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
500	C₂×Q₈	—	53	16	no	—
501	C₂×Q₈	—	212	24	no	—
502	C₂×D₄	—	2	48	no	—
503	C₂×D₄	—	53	16	no	—
504	C₂×D₄	—	53	16	no	—
505	C₂×D₄	—	106	48	no	—
506	C₂×D₄	—	212	24	no	—
507	C₂×D₄	C₂³×D₅₃	1	16	yes	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	48	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	53	6	no	—
515	C₂²×C₄	—	53	6	no	—
516	C₂²×C₄	—	53	6	no	—
517	C₂²×C₄	—	53	6	no	—
518	C₂²×C₄	—	53	6	no	—
519	C₂²×C₄	—	53	6	no	—
520	C₂²×C₄	—	53	16	no	—
521	C₂²×C₄	—	53	16	no	—
522	C₂²×C₄	—	53	16	no	—
523	C₂²×C₄	—	53	16	no	—
524	C₂²×C₄	—	106	48	no	—
525	C₂²×C₄	—	106	4	no	—
526	C₂²×C₄	—	106	4	no	—
527	C₂²×C₄	—	106	4	no	—
528	C₂²×C₄	—	106	4	no	—
529	C₂²×C₄	—	106	4	no	—
530	C₂²×C₄	—	106	4	no	—
531	C₂²×C₄	—	212	24	no	—
532	C₂²×C₄	—	212	24	no	—
533	C₂²×C₄	—	212	24	no	—
534	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
535	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
536	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
537	C₂²×C₄	C₂³×D₅₃	1	16	yes	—
538	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
539	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
540	C₄⋊C₄	—	53	16	no	—
541	C₄⋊C₄	—	53	16	no	—
542	C₄⋊C₄	—	53	16	no	—
543	C₄⋊C₄	—	53	16	no	—
544	C₄⋊C₄	—	53	16	no	—
545	C₄⋊C₄	—	53	16	no	—
546	C₄⋊C₄	C₂³×D₅₃	1	16	yes	complemented
547	C₄⋊C₄	C₂³×D₅₃	1	16	yes	complemented
548	C₂²⋊C₄	—	53	16	no	—
549	C₂²⋊C₄	—	53	16	no	—
550	C₂²⋊C₄	—	53	16	no	—
551	C₂²⋊C₄	—	53	16	no	—
552	C₂²⋊C₄	—	53	16	no	—
553	C₂²⋊C₄	—	53	16	no	—
554	C₂²⋊C₄	—	53	16	no	—
555	C₂²⋊C₄	—	53	16	no	—
556	C₂²⋊C₄	—	53	16	no	—
557	C₂²⋊C₄	—	53	16	no	—
558	C₂²⋊C₄	—	53	16	no	—
559	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
560	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
561	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
562	C₄²	—	53	16	no	—
563	C₄²	—	53	16	no	—
564	C₄²	—	53	16	no	—
565	C₂³	—	2	32	no	—
566	C₂³	—	2	12	no	—
567	C₂³	—	2	12	no	—
568	C₂³	—	2	12	no	—
569	C₂³	—	2	12	no	—
570	C₂³	—	2	12	no	—
571	C₂³	—	4	16	no	—
572	C₂³	—	53	24	no	—
573	C₂³	—	53	4	no	—
574	C₂³	—	53	4	no	—
575	C₂³	—	106	32	no	—
576	C₂³	—	106	32	no	—
577	C₂³	—	106	12	no	—
578	C₂³	—	106	12	no	—
579	C₂³	—	106	12	no	—
580	C₂³	—	106	32	no	—
581	C₂³	—	106	12	no	—
582	C₂³	—	106	12	no	—
583	C₂³	—	212	16	no	—
584	C₂³	—	212	192	no	—
585	C₂³	—	212	16	no	—
586	C₂³	#41×D₅₃	1	4	yes	—
587	C₂³	C₂×#11719947	1	24	yes	—
588	C₂³	C₂×#11719947	1	4	yes	—
589	C₂³	#13133263	1	4	yes	—
590	C₂³	C₂⁴×D₅₃	1	4	yes	—
591	C₂³	C₂⁴×D₅₃	1	4	yes	—
592	C₂³	C₂⁴×D₅₃	1	3	yes	—
593	Q₈	—	212	16	no	—
594	D₄	—	2	32	no	—
595	D₄	—	106	32	no	—
596	D₄	—	212	16	no	—
597	C₂×C₄	—	2	12	no	—
598	C₂×C₄	—	2	32	no	—
599	C₂×C₄	—	2	12	no	—
600	C₂×C₄	—	2	12	no	—
601	C₂×C₄	—	2	12	no	—
602	C₂×C₄	—	2	12	no	—
603	C₂×C₄	—	53	4	no	—
604	C₂×C₄	—	53	4	no	—
605	C₂×C₄	—	53	4	no	—
606	C₂×C₄	—	53	4	no	—
607	C₂×C₄	—	53	4	no	—
608	C₂×C₄	—	53	4	no	—
609	C₂×C₄	—	106	32	no	—
610	C₂×C₄	—	106	12	no	—
611	C₂×C₄	—	106	12	no	—
612	C₂×C₄	—	106	12	no	—
613	C₂×C₄	—	106	12	no	—
614	C₂×C₄	—	106	12	no	—
615	C₂×C₄	—	106	12	no	—
616	C₂×C₄	—	212	16	no	—
617	C₂×C₄	—	212	16	no	—
618	C₂×C₄	—	212	16	no	—
619	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
620	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
621	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
622	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
623	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
624	C₂²	—	2	48	no	—
625	C₂²	—	2	4	no	—
626	C₂²	—	2	4	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	4	24	no	—
631	C₂²	—	53	8	no	—
632	C₂²	—	106	48	no	—
633	C₂²	—	106	4	no	—
634	C₂²	—	106	4	no	—
635	C₂²	—	106	4	no	—
636	C₂²	—	106	4	no	—
637	C₂²	—	106	4	no	—
638	C₂²	—	212	64	no	—
639	C₂²	—	212	24	no	—
640	C₂²	#16811296	1	16	yes	direct product factor
641	C₂²	C₂×#41×D₅₃	1	6	yes	—
642	C₂²	C₂²×#11719947	1	8	yes	—
643	C₂²	C₂²×#11719947	1	6	yes	—
644	C₂²	C₂×#13133263	1	6	yes	—
645	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
646	C₄	—	2	4	no	—
647	C₄	—	2	4	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	4	no	—
650	C₄	—	2	4	no	—
651	C₄	—	106	4	no	—
652	C₄	—	106	4	no	—
653	C₄	—	106	4	no	—
654	C₄	—	106	4	no	—
655	C₄	—	106	4	no	—
656	C₄	—	106	4	no	—
657	C₂	—	2	8	no	—
658	C₂	—	4	4	no	—
659	C₂	—	106	8	no	—
660	C₂	—	212	4	no	—
661	C₂	C₂×#16811296	1	12	yes	direct product factor
662	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
663	C₂	C₂³×#11719947	1	1	yes	characteristic
664	C₂	C₂²×#13133263	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂²×#123×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂⁴
prime radical	C₂²×#13133185	C₂
hypercenter	C₂²×#123	D₅₃
hypocenter	C₅₃	C₂²×#551
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#123

Complements

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

N	H ≅ G/N	type
1. C₂×#16811296	C₂	direct (N × H)
2. C₂²×#13133212	C₂	semidirect
3. C₂²×#13133212	C₂	semidirect
4. C₂²×#13133203	C₂	semidirect
5. C₂²×#13133201	C₂	semidirect
6. C₂²×#13133199	C₂	semidirect
7. C₂²×#13133197	C₂	semidirect
8. C₂²×#13133194	C₂	semidirect
10. C₂²×D₄×Dic₅₃	C₂	semidirect
11. C₂²×#13133177	C₂	semidirect
12. C₂²×#13133176	C₂	semidirect
13. C₂²×#13133175	C₂	semidirect
14. C₂³×#11719921	C₂	semidirect
15. C₂²×C₂²⋊C₄×D₅₃	C₂	semidirect
16. C₂²×#123×C₅₃	C₂	semidirect
18. C₂³×Dic₁₀₆	C₂²	semidirect
22. C₂⁴×Dic₅₃	C₂²	semidirect
25. #16811296	C₂²	direct (N × H)
26. C₂×#13133212	C₂²	semidirect
27. C₂×#13133212	C₂²	semidirect
28. C₂×#13133203	C₂²	semidirect
29. C₂×#13133201	C₂²	semidirect
30. C₂×#13133199	C₂²	semidirect
31. C₂×#13133197	C₂²	semidirect
32. C₂×#13133194	C₂²	semidirect
34. C₂×D₄×Dic₅₃	C₂²	semidirect
35. C₂×#13133177	C₂²	semidirect
36. C₂×#13133176	C₂²	semidirect
37. C₂×#13133175	C₂²	semidirect
38. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
39. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
40. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
41. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
42. C₂²×#11719919	C₂²	semidirect
43. C₂²×#11719919	C₂²	semidirect
46. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
55. C₂²×#11719921	C₂²	semidirect
56. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
57. C₂²×C₄×Dic₅₃	C₂²	semidirect
58. C₂²×C₄×Dic₅₃	C₂²	semidirect
59. C₂²×C₄×Dic₅₃	C₂²	semidirect
62. C₂×#123×C₅₃	C₂²	semidirect
63. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
64. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
66. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
67. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
75. C₂²×Dic₁₀₆	C₂³	semidirect
89. C₂³×Dic₅₃	C₂³	semidirect
94. #13133212	C₂³	semidirect
95. #13133212	C₂³	semidirect
96. #13133203	C₂³	semidirect
97. #13133201	C₂³	semidirect
98. #13133199	C₂³	semidirect
99. #13133197	C₂³	semidirect
100. #13133194	C₂³	semidirect
102. D₄×Dic₅₃	C₂³	semidirect
103. #13133177	C₂³	semidirect
104. #13133176	C₂³	semidirect
105. #13133175	C₂³	semidirect
106. C₂×C₄⋊Dic₅₃	C₂³	semidirect
107. C₂×C₄⋊Dic₅₃	C₂³	semidirect
108. C₂×C₄⋊Dic₅₃	C₂³	semidirect
109. C₂×C₄⋊Dic₅₃	C₂³	semidirect
110. C₂×#11719919	C₂³	semidirect
111. C₂×#11719919	C₂³	semidirect
114. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
123. C₂×#11719921	C₂³	semidirect
124. C₂²⋊C₄×D₅₃	C₂³	semidirect
125. C₂×C₄×Dic₅₃	C₂³	semidirect
126. C₂×C₄×Dic₅₃	C₂³	semidirect
127. C₂×C₄×Dic₅₃	C₂³	semidirect
139. #123×C₅₃	C₂³	semidirect
140. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
141. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
143. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
144. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
200. C₂²×Dic₅₃	C₂⁴	semidirect
206. C₂×Dic₁₀₆	C₂⁴	semidirect
207. C₄⋊C₄×C₅₃	C₂⁴	semidirect
208. C₄⋊C₄×C₅₃	C₂⁴	semidirect
210. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
211. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
214. C₂²⋊Dic₅₃	C₂⁴	semidirect
223. C₄⋊Dic₅₃	C₂⁴	semidirect
224. C₄⋊Dic₅₃	C₂⁴	semidirect
225. C₄⋊Dic₅₃	C₂⁴	semidirect
226. C₄⋊Dic₅₃	C₂⁴	semidirect
227. #11719919	C₂⁴	semidirect
228. #11719919	C₂⁴	semidirect
229. C₄×Dic₅₃	C₂⁴	semidirect
230. C₄×Dic₅₃	C₂⁴	semidirect
231. C₄×Dic₅₃	C₂⁴	semidirect
299. C₂²×C₅₃	#551	semidirect
331. C₂²×#123	D₅₃	semidirect
343. C₂×C₅₃	C₂×#551	semidirect
365. C₂×#123	C₂×D₅₃	semidirect
379. C₂²×C₄⋊C₄	C₂×D₅₃	semidirect
380. C₂²×C₄⋊C₄	C₂×D₅₃	semidirect
395. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
396. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
400. C₅₃	C₂²×#551	semidirect
443. #123	C₂²×D₅₃	semidirect
457. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
458. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
473. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
474. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
546. C₄⋊C₄	C₂³×D₅₃	semidirect
547. C₄⋊C₄	C₂³×D₅₃	semidirect
560. C₂²⋊C₄	C₂³×D₅₃	semidirect
561. C₂²⋊C₄	C₂³×D₅₃	semidirect
640. C₂²	#16811296	direct (N × H)
661. C₂	C₂×#16811296	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×#16811296	2
C₂²×#13133212	2
C₂²×#13133203	2
C₂²×#13133201	2
C₂²×#13133199	2
C₂²×#13133197	2
C₂²×#13133194	2
C₂²×#13133185	2
C₂²×D₄×Dic₅₃	2
C₂²×#13133177	2
C₂²×#13133176	2
C₂²×#13133175	2
C₂³×#11719921	2
C₂²×C₂²⋊C₄×D₅₃	2
C₂²×#123×C₅₃	2
C₂²×#551	53

Subgroups — C22×#16811296 #28291067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16811296 #28291067