Subgroups — C₂²×#16811690 #28330804

Order 13568.

14590 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	C₂×#16811690	C₂	1	48	yes	maximal, direct product factor
2	C₂²×D₄×#6157	C₂	1	8	yes	maximal, complemented
3	C₂²×#13133296	C₂	1	2	yes	maximal, complemented
4	C₂³×C₂²⋊#6157	C₂	1	4	yes	maximal, complemented
5	C₂³×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂⁴×#6157	C₂²	1	8	yes	complemented
7	#16811690	C₂²	1	256	yes	direct product factor
8	C₂×D₄×#6157	C₂²	1	192	yes	complemented
9	C₂×#13133296	C₂²	1	48	yes	complemented
10	C₂²×C₄⋊#6157	C₂²	1	4	yes	complemented
11	C₂²×C₂²⋊#6157	C₂²	1	4	yes	—
12	C₂²×C₂²⋊#6157	C₂²	1	96	yes	complemented
13	C₂²×C₂²⋊#6157	C₂²	1	8	yes	complemented
14	C₂²×C₄×#6157	C₂²	1	4	yes	complemented
15	C₂⁵×D₅₃	C₂²	1	2	yes	—
16	C₂³×D₂₁₂	C₄	1	1	yes	characteristic, complemented
17	C₂³×C₂²⋊D₅₃	C₄	1	2	yes	complemented
18	C₂²×D₄×D₅₃	C₄	1	4	yes	complemented
19	C₂²×D₄×D₅₃	C₄	1	24	yes	complemented
20	C₂²×D₄×D₅₃	C₂²	1	4	yes	—
21	C₂²×D₄×D₅₃	C₂²	1	24	yes	—
22	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
23	C₂³×D₄×C₅₃	C₄	1	1	yes	characteristic, complemented
24	C₂³×#6157	—	4	32	no	—
25	C₂³×#6157	C₂³	1	8	yes	—
26	C₂³×#6157	C₂³	1	96	yes	complemented
27	D₄×#6157	C₂³	1	512	yes	complemented
28	#13133296	C₂³	1	128	yes	complemented
29	C₂×C₄⋊#6157	C₂³	1	48	yes	complemented
30	C₂×C₂²⋊#6157	C₂³	1	48	yes	—
31	C₂×C₂²⋊#6157	C₂³	1	256	yes	complemented
32	C₂×C₂²⋊#6157	C₂³	1	96	yes	complemented
33	C₂×C₄×#6157	C₂³	1	48	yes	complemented
34	C₂⁴×D₅₃	—	4	16	no	—
35	C₂⁴×D₅₃	C₂×C₄	1	24	yes	complemented
36	C₂⁴×D₅₃	C₂×C₄	1	4	yes	complemented
37	C₂⁴×D₅₃	C₂×C₄	1	2	yes	complemented
38	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
39	C₂⁴×D₅₃	C₂³	1	4	yes	—
40	C₂⁴×D₅₃	C₂³	1	24	yes	—
41	C₂²×D₂₁₂	C₂×C₄	1	4	yes	complemented
42	C₂²×D₂₁₂	C₂×C₄	1	24	yes	complemented
43	C₂²×C₂²⋊D₅₃	C₂×C₄	1	8	yes	complemented
44	C₂²×C₂²⋊D₅₃	C₂×C₄	1	48	yes	complemented
45	C₂×D₄×D₅₃	C₂×C₄	1	48	yes	complemented
46	C₂×D₄×D₅₃	C₂×C₄	1	192	yes	complemented
47	C₂×D₄×D₅₃	C₂×C₄	1	96	yes	complemented
48	C₂×D₄×D₅₃	C₂³	1	48	yes	—
49	C₂×D₄×D₅₃	C₂³	1	64	yes	—
50	C₂³×Dic₅₃	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂²×C₄×D₅₃	C₂×C₄	1	12	yes	complemented
52	C₂²×C₄×D₅₃	C₂×C₄	1	2	yes	complemented
53	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
54	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
55	C₂⁵×C₅₃	C₂×C₄	1	2	yes	complemented
56	C₂²×D₄×C₅₃	C₂×C₄	1	4	yes	complemented
57	C₂²×D₄×C₅₃	C₂×C₄	1	24	yes	complemented
58	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂⁴×C₅₃	—	4	8	no	—
60	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
61	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
62	C₂⁴×C₅₃	C₂²×C₄	1	24	yes	complemented
63	C₂³×D₅₃	—	2	8	no	—
64	C₂³×D₅₃	—	2	32	no	—
65	C₂³×D₅₃	—	4	96	no	—
66	C₂³×D₅₃	—	4	96	no	—
67	C₂³×D₅₃	—	4	16	no	—
68	C₂³×D₅₃	—	4	8	no	—
69	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
70	C₂³×D₅₃	C₂²×C₄	1	6	yes	—
71	C₂³×D₅₃	C₂²×C₄	1	24	yes	—
72	C₂³×D₅₃	C₂²×C₄	1	4	yes	—
73	C₂³×D₅₃	C₂²×C₄	1	96	yes	complemented
74	C₂³×D₅₃	C₂²×C₄	1	48	yes	complemented
75	C₂³×D₅₃	C₂²×C₄	1	24	yes	complemented
76	C₂³×D₅₃	C₂⁴	1	6	yes	—
77	C₂³×D₅₃	C₂⁴	1	24	yes	—
78	C₂³×D₅₃	C₂⁴	1	32	yes	—
79	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
80	C₂²×#6157	—	2	32	no	—
81	C₂²×#6157	—	4	192	no	—
82	C₂²×#6157	C₂⁴	1	48	yes	—
83	C₂²×#6157	C₂⁴	1	128	yes	complemented
84	C₂×D₄×C₅₃	C₂²×C₄	1	48	yes	complemented
85	C₂×D₄×C₅₃	C₂²×C₄	1	64	yes	complemented
86	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₅₃	C₂²×C₄	1	12	yes	complemented
88	C₂×C₂²⋊D₅₃	C₂²×C₄	1	96	yes	complemented
89	C₂×C₂²⋊D₅₃	C₂²×C₄	1	128	yes	complemented
90	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
91	C₂²×Dic₅₃	C₂²×C₄	1	12	yes	complemented
92	D₄×D₅₃	C₂²×C₄	1	192	yes	complemented
93	D₄×D₅₃	C₂²×C₄	1	256	yes	complemented
94	D₄×D₅₃	C₂⁴	1	64	yes	—
95	C₂×D₂₁₂	C₂²×C₄	1	48	yes	complemented
96	C₂×D₂₁₂	C₂²×C₄	1	64	yes	complemented
97	C₂×C₄×D₅₃	C₂²×C₄	1	12	yes	—
98	C₂×C₄×D₅₃	C₂²×C₄	1	48	yes	complemented
99	C₂×C₄×D₅₃	C₂²×C₄	1	24	yes	complemented
100	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
101	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
102	C₂²⋊#6157	C₂⁴	1	64	yes	—
103	C₂²⋊#6157	C₂⁴	1	128	yes	complemented
104	C₄⋊#6157	C₂⁴	1	64	yes	complemented
105	C₄×#6157	C₂⁴	1	64	yes	complemented
106	C₂³×C₅₃	—	2	4	no	—
107	C₂³×C₅₃	—	2	16	no	—
108	C₂³×C₅₃	—	4	48	no	—
109	C₂³×C₅₃	C₂³×C₄	1	6	yes	—
110	C₂³×C₅₃	C₂³×C₄	1	24	yes	—
111	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
112	C₂³×C₅₃	C₂³×C₄	1	32	yes	complemented
113	C₂²×D₅₃	—	2	4	no	—
114	C₂²×D₅₃	—	2	16	no	—
115	C₂²×D₅₃	—	2	24	no	—
116	C₂²×D₅₃	—	2	96	no	—
117	C₂²×D₅₃	—	2	96	no	—
118	C₂²×D₅₃	—	2	24	no	—
119	C₂²×D₅₃	—	4	192	no	—
120	C₂²×D₅₃	—	4	64	no	—
121	C₂²×D₅₃	—	4	96	no	—
122	C₂²×D₅₃	—	4	48	no	—
123	C₂²×D₅₃	C₂³×C₄	1	6	yes	—
124	C₂²×D₅₃	C₂³×C₄	1	12	yes	—
125	C₂²×D₅₃	C₂³×C₄	1	24	yes	—
126	C₂²×D₅₃	C₂³×C₄	1	48	yes	—
127	C₂²×D₅₃	C₂³×C₄	1	3	yes	—
128	C₂²×D₅₃	C₂³×C₄	1	32	yes	complemented
129	C₂²×D₅₃	C₂³×C₄	1	64	yes	complemented
130	C₂²×D₅₃	H(5,𝔽₂)	1	8	yes	—
131	C₂²×D₅₃	C₂⁵	1	4	yes	—
132	C₂²×D₅₃	C₂⁵	1	16	yes	—
133	C₂²×D₅₃	C₂⁵	1	3	yes	—
134	C₂×#6157	—	2	96	no	—
135	C₂×#6157	—	4	128	no	—
136	C₂×#6157	C₂⁵	1	32	yes	—
137	D₄×C₅₃	C₂³×C₄	1	64	yes	complemented
138	C₂×C₄×C₅₃	C₂³×C₄	1	12	yes	—
139	C₂×C₄×C₅₃	C₂³×C₄	1	16	yes	complemented
140	C₂²⋊D₅₃	C₂³×C₄	1	128	yes	complemented
141	C₂×Dic₅₃	C₂³×C₄	1	12	yes	—
142	C₂×Dic₅₃	C₂³×C₄	1	16	yes	complemented
143	D₂₁₂	C₂³×C₄	1	64	yes	complemented
144	C₄×D₅₃	C₂³×C₄	1	24	yes	—
145	C₄×D₅₃	C₂³×C₄	1	32	yes	complemented
146	C₄×D₅₃	C₂⁵	1	8	yes	—
147	C₂²×#518	—	53	1	no	maximal, Sylow
148	C₂²×C₅₃	—	2	12	no	—
149	C₂²×C₅₃	—	2	48	no	—
150	C₂²×C₅₃	—	4	32	no	—
151	C₂²×C₅₃	#518	1	4	yes	complemented
152	C₂²×C₅₃	C₂⁴×C₄	1	4	yes	—
153	C₂²×C₅₃	C₂⁴×C₄	1	16	yes	—
154	C₂²×C₅₃	C₂⁴×C₄	1	3	yes	—
155	C₂×D₅₃	—	2	12	no	—
156	C₂×D₅₃	—	2	48	no	—
157	C₂×D₅₃	—	2	32	no	—
158	C₂×D₅₃	—	2	8	no	—
159	C₂×D₅₃	—	2	24	no	—
160	C₂×D₅₃	—	2	96	no	—
161	C₂×D₅₃	—	4	64	no	—
162	C₂×D₅₃	—	4	32	no	—
163	C₂×D₅₃	#518	1	12	yes	complemented
164	C₂×D₅₃	C₂⁴×C₄	1	4	yes	—
165	C₂×D₅₃	C₂⁴×C₄	1	16	yes	—
166	C₂×D₅₃	C₂⁴×C₄	1	3	yes	—
167	C₂×D₅₃	C₂×H(5,𝔽₂)	1	12	yes	—
168	C₂×D₅₃	C₂⁶	1	1	yes	characteristic
169	#6157	—	2	32	no	—
170	C₄×C₅₃	C₂⁴×C₄	1	8	yes	—
171	Dic₅₃	C₂⁴×C₄	1	8	yes	—
172	C₂⁴×D₄	—	53	1	no	—
173	C₂×#518	—	53	48	no	—
174	C₂²×C₄×D₄	—	53	8	no	—
175	C₂²×#117	—	53	2	no	—
176	C₂³×C₂²⋊C₄	—	53	4	no	—
177	C₂×C₅₃	—	2	4	no	—
178	C₂×C₅₃	—	2	16	no	—
179	C₂×C₅₃	C₂×#518	1	6	yes	complemented
180	C₂×C₅₃	C₂⁵×C₄	1	1	yes	characteristic
181	D₅₃	—	2	4	no	—
182	D₅₃	—	2	16	no	—
183	D₅₃	C₂×#518	1	6	yes	complemented
184	D₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
185	C₂⁶	—	53	2	no	—
186	C₂³×D₄	—	53	2	no	—
187	C₂³×D₄	—	53	4	no	—
188	C₂³×D₄	—	53	24	no	—
189	C₂³×D₄	—	53	4	no	—
190	C₂³×D₄	—	53	24	no	—
191	C₂³×D₄	—	53	1	no	—
192	C₂³×D₄	#6157	1	1	yes	characteristic, complemented
193	C₂⁴×C₄	—	53	1	no	—
194	C₂⁴×C₄	—	53	8	no	—
195	#518	—	53	256	no	—
196	C₂×C₄×D₄	—	53	192	no	—
197	C₂×#117	—	53	48	no	—
198	C₂²×C₄⋊C₄	—	53	4	no	—
199	C₂²×C₂²⋊C₄	—	53	4	no	—
200	C₂²×C₂²⋊C₄	—	53	8	no	—
201	C₂²×C₂²⋊C₄	—	53	96	no	—
202	C₂²×C₄²	—	53	4	no	—
203	C₅₃	C₂²×#518	1	1	yes	characteristic, complemented, Sylow
204	C₂⁵	—	53	1	no	—
205	C₂⁵	—	53	4	no	—
206	C₂⁵	—	53	4	no	—
207	C₂⁵	—	53	2	no	—
208	C₂⁵	—	53	24	no	—
209	C₂⁵	—	53	24	no	—
210	C₂⁵	—	212	16	no	—
211	C₂⁵	C₂×#6157	1	2	yes	complemented
212	C₂²×D₄	—	53	8	no	—
213	C₂²×D₄	—	53	48	no	—
214	C₂²×D₄	—	53	48	no	—
215	C₂²×D₄	—	53	64	no	—
216	C₂²×D₄	—	53	48	no	—
217	C₂²×D₄	—	53	96	no	—
218	C₂²×D₄	—	53	192	no	—
219	C₂²×D₄	—	53	4	no	—
220	C₂²×D₄	—	53	24	no	—
221	C₂²×D₄	C₂×#6157	1	4	yes	complemented
222	C₂²×D₄	C₂×#6157	1	24	yes	complemented
223	C₂³×C₄	—	53	1	no	—
224	C₂³×C₄	—	53	2	no	—
225	C₂³×C₄	—	53	2	no	—
226	C₂³×C₄	—	53	12	no	—
227	C₂³×C₄	—	53	12	no	—
228	C₂³×C₄	—	53	8	no	—
229	C₂³×C₄	—	53	96	no	—
230	C₂³×C₄	—	212	32	no	—
231	C₂³×C₄	C₂×#6157	1	1	yes	characteristic, complemented
232	C₄×D₄	—	53	512	no	—
233	#117	—	53	128	no	—
234	C₂×C₄⋊C₄	—	53	48	no	—
235	C₂×C₂²⋊C₄	—	53	48	no	—
236	C₂×C₂²⋊C₄	—	53	96	no	—
237	C₂×C₂²⋊C₄	—	53	256	no	—
238	C₂×C₄²	—	53	48	no	—
239	C₂⁴	—	4	8	no	—
240	C₂⁴	—	53	1	no	—
241	C₂⁴	—	53	6	no	—
242	C₂⁴	—	53	24	no	—
243	C₂⁴	—	53	6	no	—
244	C₂⁴	—	53	24	no	—
245	C₂⁴	—	53	1	no	—
246	C₂⁴	—	53	4	no	—
247	C₂⁴	—	53	48	no	—
248	C₂⁴	—	53	24	no	—
249	C₂⁴	—	53	96	no	—
250	C₂⁴	—	53	32	no	—
251	C₂⁴	—	106	32	no	—
252	C₂⁴	—	106	8	no	—
253	C₂⁴	—	212	8	no	—
254	C₂⁴	—	212	16	no	—
255	C₂⁴	—	212	96	no	—
256	C₂⁴	—	212	96	no	—
257	C₂⁴	C₂²×#6157	1	1	yes	characteristic
258	C₂⁴	C₂²×#6157	1	4	yes	—
259	C₂⁴	C₂²×#6157	1	24	yes	complemented
260	C₂×D₄	—	53	96	no	—
261	C₂×D₄	—	53	128	no	—
262	C₂×D₄	—	53	192	no	—
263	C₂×D₄	—	53	256	no	—
264	C₂×D₄	—	53	64	no	—
265	C₂×D₄	—	53	48	no	—
266	C₂×D₄	—	53	64	no	—
267	C₂×D₄	C₂²×#6157	1	48	yes	complemented
268	C₂×D₄	C₂²×#6157	1	64	yes	complemented
269	C₂²×C₄	—	53	12	no	—
270	C₂²×C₄	—	53	2	no	—
271	C₂²×C₄	—	53	12	no	—
272	C₂²×C₄	—	53	24	no	—
273	C₂²×C₄	—	53	12	no	—
274	C₂²×C₄	—	53	48	no	—
275	C₂²×C₄	—	53	16	no	—
276	C₂²×C₄	—	53	48	no	—
277	C₂²×C₄	—	53	128	no	—
278	C₂²×C₄	—	106	32	no	—
279	C₂²×C₄	—	212	192	no	—
280	C₂²×C₄	C₂²×#6157	1	2	yes	—
281	C₂²×C₄	C₂²×#6157	1	12	yes	complemented
282	C₄⋊C₄	—	53	64	no	—
283	C₂²⋊C₄	—	53	64	no	—
284	C₂²⋊C₄	—	53	128	no	—
285	C₄²	—	53	64	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	16	no	—
288	C₂³	—	4	48	no	—
289	C₂³	—	53	8	no	—
290	C₂³	—	53	3	no	—
291	C₂³	—	53	3	no	—
292	C₂³	—	53	12	no	—
293	C₂³	—	53	6	no	—
294	C₂³	—	53	48	no	—
295	C₂³	—	53	24	no	—
296	C₂³	—	53	4	no	—
297	C₂³	—	53	16	no	—
298	C₂³	—	53	64	no	—
299	C₂³	—	53	32	no	—
300	C₂³	—	106	96	no	—
301	C₂³	—	106	96	no	—
302	C₂³	—	106	24	no	—
303	C₂³	—	106	24	no	—
304	C₂³	—	106	16	no	—
305	C₂³	—	106	4	no	—
306	C₂³	—	212	48	no	—
307	C₂³	—	212	96	no	—
308	C₂³	—	212	64	no	—
309	C₂³	—	212	192	no	—
310	C₂³	C₂³×#6157	1	6	yes	—
311	C₂³	C₂³×#6157	1	24	yes	—
312	C₂³	C₂³×#6157	1	1	yes	characteristic
313	C₂³	C₂³×#6157	1	32	yes	complemented
314	D₄	—	53	128	no	—
315	D₄	—	53	64	no	—
316	D₄	C₂³×#6157	1	64	yes	complemented
317	C₂×C₄	—	53	12	no	—
318	C₂×C₄	—	53	16	no	—
319	C₂×C₄	—	53	24	no	—
320	C₂×C₄	—	53	32	no	—
321	C₂×C₄	—	53	8	no	—
322	C₂×C₄	—	53	32	no	—
323	C₂×C₄	—	106	96	no	—
324	C₂×C₄	—	212	128	no	—
325	C₂×C₄	C₂³×#6157	1	12	yes	—
326	C₂×C₄	C₂³×#6157	1	16	yes	complemented
327	C₂²	—	2	12	no	—
328	C₂²	—	2	48	no	—
329	C₂²	—	4	32	no	—
330	C₂²	—	53	12	no	—
331	C₂²	—	53	12	no	—
332	C₂²	—	53	1	no	—
333	C₂²	—	53	3	no	—
334	C₂²	—	53	4	no	—
335	C₂²	—	53	16	no	—
336	C₂²	—	106	32	no	—
337	C₂²	—	106	8	no	—
338	C₂²	—	106	24	no	—
339	C₂²	—	106	96	no	—
340	C₂²	—	106	12	no	—
341	C₂²	—	106	48	no	—
342	C₂²	—	212	32	no	—
343	C₂²	—	212	64	no	—
344	C₂²	#16811690	1	4	yes	direct product factor
345	C₂²	C₂⁴×#6157	1	4	yes	—
346	C₂²	C₂⁴×#6157	1	16	yes	—
347	C₂²	C₂⁴×#6157	1	3	yes	—
348	C₄	—	53	8	no	—
349	C₄	—	106	32	no	—
350	C₄	C₂⁴×#6157	1	8	yes	—
351	C₂	—	2	4	no	—
352	C₂	—	2	16	no	—
353	C₂	—	53	2	no	—
354	C₂	—	53	6	no	—
355	C₂	—	106	4	no	—
356	C₂	—	106	16	no	—
357	C₂	C₂×#16811690	1	6	yes	direct product factor
358	C₂	C₂⁵×#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×#6157
commutator	C₂×C₅₃	C₂⁵×C₄
Frattini	C₂	C₂⁵×#6157
Fitting	C₂³×D₄×C₅₃	C₄
socle	C₂³×C₅₃	C₂³×C₄
prime radical	C₂³×D₄×D₅₃	C₂
cosocle	C₂×D₅₃	C₂⁶
hypercenter	C₂³×D₄	#6157
hypocenter	C₅₃	C₂²×#518
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#16811690	C₂	direct (N × H)
2. C₂²×D₄×#6157	C₂	semidirect
3. C₂²×#13133296	C₂	semidirect
4. C₂³×C₂²⋊#6157	C₂	semidirect
6. C₂⁴×#6157	C₂²	semidirect
7. #16811690	C₂²	direct (N × H)
8. C₂×D₄×#6157	C₂²	semidirect
9. C₂×#13133296	C₂²	semidirect
10. C₂²×C₄⋊#6157	C₂²	semidirect
12. C₂²×C₂²⋊#6157	C₂²	semidirect
13. C₂²×C₂²⋊#6157	C₂²	semidirect
14. C₂²×C₄×#6157	C₂²	semidirect
16. C₂³×D₂₁₂	C₄	semidirect
17. C₂³×C₂²⋊D₅₃	C₄	semidirect
18. C₂²×D₄×D₅₃	C₄	semidirect
19. C₂²×D₄×D₅₃	C₄	semidirect
23. C₂³×D₄×C₅₃	C₄	semidirect
26. C₂³×#6157	C₂³	semidirect
27. D₄×#6157	C₂³	semidirect
28. #13133296	C₂³	semidirect
29. C₂×C₄⋊#6157	C₂³	semidirect
31. C₂×C₂²⋊#6157	C₂³	semidirect
32. C₂×C₂²⋊#6157	C₂³	semidirect
33. C₂×C₄×#6157	C₂³	semidirect
35. C₂⁴×D₅₃	C₂×C₄	semidirect
36. C₂⁴×D₅₃	C₂×C₄	semidirect
37. C₂⁴×D₅₃	C₂×C₄	semidirect
41. C₂²×D₂₁₂	C₂×C₄	semidirect
42. C₂²×D₂₁₂	C₂×C₄	semidirect
43. C₂²×C₂²⋊D₅₃	C₂×C₄	semidirect
44. C₂²×C₂²⋊D₅₃	C₂×C₄	semidirect
45. C₂×D₄×D₅₃	C₂×C₄	semidirect
46. C₂×D₄×D₅₃	C₂×C₄	semidirect
47. C₂×D₄×D₅₃	C₂×C₄	semidirect
50. C₂³×Dic₅₃	C₂×C₄	semidirect
51. C₂²×C₄×D₅₃	C₂×C₄	semidirect
52. C₂²×C₄×D₅₃	C₂×C₄	semidirect
55. C₂⁵×C₅₃	C₂×C₄	semidirect
56. C₂²×D₄×C₅₃	C₂×C₄	semidirect
57. C₂²×D₄×C₅₃	C₂×C₄	semidirect
58. C₂³×C₄×C₅₃	C₂×C₄	semidirect
62. C₂⁴×C₅₃	C₂²×C₄	semidirect
73. C₂³×D₅₃	C₂²×C₄	semidirect
74. C₂³×D₅₃	C₂²×C₄	semidirect
75. C₂³×D₅₃	C₂²×C₄	semidirect
83. C₂²×#6157	C₂⁴	semidirect
84. C₂×D₄×C₅₃	C₂²×C₄	semidirect
85. C₂×D₄×C₅₃	C₂²×C₄	semidirect
87. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
88. C₂×C₂²⋊D₅₃	C₂²×C₄	semidirect
89. C₂×C₂²⋊D₅₃	C₂²×C₄	semidirect
91. C₂²×Dic₅₃	C₂²×C₄	semidirect
92. D₄×D₅₃	C₂²×C₄	semidirect
93. D₄×D₅₃	C₂²×C₄	semidirect
95. C₂×D₂₁₂	C₂²×C₄	semidirect
96. C₂×D₂₁₂	C₂²×C₄	semidirect
98. C₂×C₄×D₅₃	C₂²×C₄	semidirect
99. C₂×C₄×D₅₃	C₂²×C₄	semidirect
103. C₂²⋊#6157	C₂⁴	semidirect
104. C₄⋊#6157	C₂⁴	semidirect
105. C₄×#6157	C₂⁴	semidirect
112. C₂³×C₅₃	C₂³×C₄	semidirect
128. C₂²×D₅₃	C₂³×C₄	semidirect
129. C₂²×D₅₃	C₂³×C₄	semidirect
137. D₄×C₅₃	C₂³×C₄	semidirect
139. C₂×C₄×C₅₃	C₂³×C₄	semidirect
140. C₂²⋊D₅₃	C₂³×C₄	semidirect
142. C₂×Dic₅₃	C₂³×C₄	semidirect
143. D₂₁₂	C₂³×C₄	semidirect
145. C₄×D₅₃	C₂³×C₄	semidirect
151. C₂²×C₅₃	#518	semidirect
163. C₂×D₅₃	#518	semidirect
179. C₂×C₅₃	C₂×#518	semidirect
183. D₅₃	C₂×#518	semidirect
192. C₂³×D₄	#6157	semidirect
203. C₅₃	C₂²×#518	semidirect
211. C₂⁵	C₂×#6157	semidirect
221. C₂²×D₄	C₂×#6157	semidirect
222. C₂²×D₄	C₂×#6157	semidirect
231. C₂³×C₄	C₂×#6157	semidirect
259. C₂⁴	C₂²×#6157	semidirect
267. C₂×D₄	C₂²×#6157	semidirect
268. C₂×D₄	C₂²×#6157	semidirect
281. C₂²×C₄	C₂²×#6157	semidirect
313. C₂³	C₂³×#6157	semidirect
316. D₄	C₂³×#6157	semidirect
326. C₂×C₄	C₂³×#6157	semidirect
344. C₂²	#16811690	direct (N × H)
357. C₂	C₂×#16811690	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×#16811690	2
C₂²×D₄×#6157	2
C₂²×#13133296	2
C₂³×C₂²⋊#6157	2
C₂³×D₄×D₅₃	2
C₂²×#518	53

Subgroups — C22×#16811690 #28330804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16811690 #28330804