Subgroups — C₂²×#16811178 #28290796

Order 13568.

8238 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811178	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#13133217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13133208	C₂	1	2	yes	maximal, complemented
4	C₂²×#13133197	C₂	1	2	yes	maximal
5	C₂²×#13133193	C₂	1	2	yes	maximal
6	C₂²×Q₈×Dic₅₃	C₂	1	2	yes	maximal, complemented
7	C₂²×#13133182	C₂	1	2	yes	maximal, complemented
8	C₂²×#13133175	C₂	1	2	yes	maximal
9	C₂²×C₄²×D₅₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Dic₁₀₆	C₂²	1	2	yes	—
12	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
13	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
14	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
15	#16811178	C₂²	1	256	yes	direct product factor
16	C₂×#13133217	C₂²	1	24	yes	complemented
17	C₂×#13133208	C₂²	1	48	yes	complemented
18	C₂×#13133197	C₂²	1	48	yes	—
19	C₂×#13133193	C₂²	1	48	yes	—
20	C₂×Q₈×Dic₅₃	C₂²	1	48	yes	complemented
21	C₂×#13133182	C₂²	1	48	yes	complemented
22	C₂×#13133175	C₂²	1	48	yes	—
23	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	—
24	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	—
25	C₂²×C₄⋊Dic₅₃	C₂²	1	4	yes	—
26	C₂²×#11719919	C₂²	1	4	yes	—
27	C₂²×#11719921	C₂²	1	4	yes	—
28	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄×Dic₅₃	C₂²	1	4	yes	—
32	C₂×C₄²×D₅₃	C₂²	1	24	yes	—
33	C₂³×Q₈×C₅₃	C₂²	1	2	yes	—
34	C₂×C₄⋊Q₈×C₅₃	C₂²	1	24	yes	complemented
35	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
37	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
38	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
39	C₂²×Dic₁₀₆	—	2	16	no	—
40	C₂²×Dic₁₀₆	C₂³	1	24	yes	—
41	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
42	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
43	C₂³×Dic₅₃	C₂³	1	4	yes	—
44	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
45	C₂²×C₄×D₅₃	—	2	8	no	—
46	C₂²×C₄×D₅₃	—	2	8	no	—
47	C₂²×C₄×D₅₃	Q₈	1	16	yes	complemented
48	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
49	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
50	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
51	#13133217	C₂³	1	64	yes	complemented
52	#13133208	C₂³	1	128	yes	complemented
53	#13133197	C₂³	1	128	yes	—
54	#13133193	C₂³	1	128	yes	—
55	Q₈×Dic₅₃	C₂³	1	128	yes	complemented
56	#13133182	C₂³	1	128	yes	complemented
57	#13133175	C₂³	1	128	yes	—
58	C₂×C₄⋊Dic₅₃	C₂³	1	24	yes	—
59	C₂×C₄⋊Dic₅₃	C₂³	1	24	yes	—
60	C₂×C₄⋊Dic₅₃	C₂³	1	48	yes	—
61	C₂×#11719919	C₂³	1	48	yes	—
62	C₂×#11719921	C₂³	1	48	yes	—
63	C₂×C₄×Dic₅₃	C₂³	1	12	yes	—
64	C₂×C₄×Dic₅₃	C₂³	1	12	yes	—
65	C₂×C₄×Dic₅₃	C₂³	1	12	yes	—
66	C₂×C₄×Dic₅₃	C₂³	1	48	yes	—
67	C₄²×D₅₃	C₂³	1	64	yes	—
68	C₂²×Q₈×C₅₃	—	2	16	no	—
69	C₂²×Q₈×C₅₃	C₂³	1	24	yes	—
70	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
74	C₄⋊Q₈×C₅₃	C₂³	1	64	yes	complemented
75	C₂×C₄⋊C₄×C₅₃	C₂³	1	24	yes	—
76	C₂×C₄⋊C₄×C₅₃	C₂³	1	24	yes	—
77	C₂×C₄²×C₅₃	C₂³	1	12	yes	—
78	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
79	C₂³×D₅₃	—	2	4	no	—
80	C₂³×D₅₃	—	2	4	no	—
81	C₂³×D₅₃	C₂×Q₈	1	8	yes	—
82	C₂³×D₅₃	C₂⁴	1	6	yes	—
83	C₂×Q₈×C₅₃	—	2	96	no	—
84	C₂×Q₈×C₅₃	C₂⁴	1	32	yes	—
85	C₂²×C₄×C₅₃	—	2	16	no	—
86	C₂²×C₄×C₅₃	C₂×Q₈	1	8	yes	—
87	C₂²×C₄×C₅₃	#41	1	8	yes	—
88	C₂²×C₄×C₅₃	#41	1	8	yes	—
89	C₂²×C₄×C₅₃	C₂⁴	1	24	yes	—
90	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
91	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
92	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
93	C₂²×Dic₅₃	—	2	4	no	—
94	C₂²×Dic₅₃	—	2	4	no	—
95	C₂²×Dic₅₃	—	2	16	no	—
96	C₂²×Dic₅₃	C₂×Q₈	1	8	yes	—
97	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
98	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
99	C₂²×Dic₅₃	C₂⁴	1	24	yes	—
100	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
101	C₂×C₄×D₅₃	—	2	48	no	—
102	C₂×C₄×D₅₃	—	2	48	no	—
103	C₂×C₄×D₅₃	C₂×Q₈	1	96	yes	complemented
104	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
105	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
106	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
107	C₂×Dic₁₀₆	—	2	96	no	—
108	C₂×Dic₁₀₆	C₂⁴	1	32	yes	—
109	C₄⋊C₄×C₅₃	C₂⁴	1	32	yes	—
110	C₄⋊C₄×C₅₃	C₂⁴	1	32	yes	—
111	C₄²×C₅₃	C₂⁴	1	16	yes	—
112	#11719921	C₂⁴	1	64	yes	—
113	C₄⋊Dic₅₃	C₂⁴	1	32	yes	—
114	C₄⋊Dic₅₃	C₂⁴	1	32	yes	—
115	C₄⋊Dic₅₃	C₂⁴	1	64	yes	—
116	#11719919	C₂⁴	1	64	yes	—
117	C₄×Dic₅₃	C₂⁴	1	16	yes	—
118	C₄×Dic₅₃	C₂⁴	1	16	yes	—
119	C₄×Dic₅₃	C₂⁴	1	16	yes	—
120	C₄×Dic₅₃	C₂⁴	1	64	yes	—
121	C₂³×C₅₃	C₂²×Q₈	1	4	yes	—
122	C₂³×C₅₃	C₂×#41	1	4	yes	—
123	C₂³×C₅₃	C₂×#41	1	4	yes	—
124	C₂³×C₅₃	C₂⁵	1	3	yes	—
125	C₂²×D₅₃	—	2	32	no	—
126	C₂²×D₅₃	—	2	12	no	—
127	C₂²×D₅₃	—	2	12	no	—
128	C₂²×D₅₃	C₂²×Q₈	1	24	yes	—
129	C₂²×D₅₃	C₂⁵	1	4	yes	—
130	Q₈×C₅₃	—	2	64	no	—
131	C₂×C₄×C₅₃	—	2	48	no	—
132	C₂×C₄×C₅₃	C₂²×Q₈	1	24	yes	—
133	C₂×C₄×C₅₃	C₂×#41	1	24	yes	—
134	C₂×C₄×C₅₃	C₂×#41	1	24	yes	—
135	C₂×C₄×C₅₃	C₂⁵	1	16	yes	—
136	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
137	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
138	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
139	C₂×Dic₅₃	—	2	48	no	—
140	C₂×Dic₅₃	—	2	12	no	—
141	C₂×Dic₅₃	—	2	12	no	—
142	C₂×Dic₅₃	C₂²×Q₈	1	24	yes	—
143	C₂×Dic₅₃	C₂⁵	1	16	yes	—
144	C₂×Dic₅₃	C₂⁵	1	4	yes	—
145	C₂×Dic₅₃	C₂⁵	1	4	yes	—
146	C₂×Dic₅₃	C₂⁵	1	4	yes	—
147	C₄×D₅₃	—	2	32	no	—
148	C₄×D₅₃	—	2	32	no	—
149	C₄×D₅₃	C₂²×Q₈	1	64	yes	complemented
150	Dic₁₀₆	—	2	64	no	—
151	C₂²×#533	—	53	1	no	maximal, Sylow
152	C₂²×C₅₃	#533	1	16	yes	complemented
153	C₂²×C₅₃	C₂³×Q₈	1	6	yes	—
154	C₂²×C₅₃	C₂²×#41	1	6	yes	—
155	C₂²×C₅₃	C₂²×#41	1	6	yes	—
156	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
157	C₂×D₅₃	—	2	4	no	—
158	C₂×D₅₃	—	2	4	no	—
159	C₂×D₅₃	—	2	48	no	—
160	C₂×D₅₃	C₂³×Q₈	1	8	yes	—
161	C₄×C₅₃	—	2	16	no	—
162	C₄×C₅₃	C₂³×Q₈	1	8	yes	—
163	C₄×C₅₃	C₂²×#41	1	8	yes	—
164	C₄×C₅₃	C₂²×#41	1	8	yes	—
165	Dic₅₃	—	2	16	no	—
166	Dic₅₃	—	2	4	no	—
167	Dic₅₃	—	2	4	no	—
168	Dic₅₃	C₂³×Q₈	1	8	yes	—
169	C₂×#533	—	53	48	no	—
170	C₂²×C₄⋊Q₈	—	53	1	no	—
171	C₂²×C₄⋊Q₈	D₅₃	1	1	yes	characteristic, complemented
172	C₂²×#125	—	53	2	no	—
173	C₂²×C₂²⋊Q₈	—	53	2	no	—
174	C₂²×C₂²⋊Q₈	—	53	2	no	—
175	C₂²×C₄×Q₈	—	53	2	no	—
176	C₂²×C₄×Q₈	—	53	2	no	—
177	C₂²×#117	—	53	2	no	—
178	C₂³×C₄²	—	53	1	no	—
179	C₂×C₅₃	C₂×#533	1	12	yes	complemented
180	C₂×C₅₃	C₂⁴×Q₈	1	1	yes	characteristic
181	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
182	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
183	D₅₃	—	2	8	no	—
184	C₂³×Q₈	—	53	2	no	—
185	C₂³×Q₈	C₂×D₅₃	1	2	yes	—
186	C₂⁴×C₄	—	53	1	no	—
187	C₂⁴×C₄	—	53	1	no	—
188	C₂⁴×C₄	—	53	1	no	—
189	#533	—	53	256	no	—
190	C₂×C₄⋊Q₈	—	53	24	no	—
191	C₂×C₄⋊Q₈	C₂×D₅₃	1	24	yes	complemented
192	C₂×#125	—	53	48	no	—
193	C₂×C₂²⋊Q₈	—	53	48	no	—
194	C₂×C₂²⋊Q₈	—	53	48	no	—
195	C₂×C₄×Q₈	—	53	48	no	—
196	C₂×C₄×Q₈	—	53	48	no	—
197	C₂×#117	—	53	48	no	—
198	C₂²×C₄⋊C₄	—	53	4	no	—
199	C₂²×C₄⋊C₄	—	53	2	no	—
200	C₂²×C₄⋊C₄	—	53	4	no	—
201	C₂²×C₄⋊C₄	—	53	2	no	—
202	C₂²×C₄⋊C₄	C₂×D₅₃	1	2	yes	—
203	C₂²×C₄⋊C₄	C₂×D₅₃	1	2	yes	—
204	C₂²×C₂²⋊C₄	—	53	4	no	—
205	C₂²×C₄²	—	53	1	no	—
206	C₂²×C₄²	—	53	1	no	—
207	C₂²×C₄²	—	53	1	no	—
208	C₂²×C₄²	—	53	4	no	—
209	C₂²×C₄²	—	53	24	no	—
210	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
211	C₅₃	C₂²×#533	1	1	yes	characteristic, complemented, Sylow
212	C₂⁵	—	53	1	no	—
213	C₂²×Q₈	—	2	16	no	—
214	C₂²×Q₈	—	53	24	no	—
215	C₂²×Q₈	—	106	16	no	—
216	C₂²×Q₈	C₂²×D₅₃	1	24	yes	—
217	C₂³×C₄	—	53	1	no	—
218	C₂³×C₄	—	53	16	no	—
219	C₂³×C₄	—	53	12	no	—
220	C₂³×C₄	—	53	4	no	—
221	C₂³×C₄	—	53	1	no	—
222	C₂³×C₄	—	53	1	no	—
223	C₂³×C₄	—	53	12	no	—
224	C₂³×C₄	—	53	12	no	—
225	C₂³×C₄	—	106	8	no	—
226	C₂³×C₄	—	106	8	no	—
227	C₂³×C₄	C₂²×D₅₃	1	4	yes	—
228	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
229	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
230	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
231	C₄⋊Q₈	—	53	64	no	—
232	C₄⋊Q₈	C₂²×D₅₃	1	64	yes	complemented
233	#125	—	53	128	no	—
234	C₂²⋊Q₈	—	53	128	no	—
235	C₂²⋊Q₈	—	53	128	no	—
236	C₄×Q₈	—	53	128	no	—
237	C₄×Q₈	—	53	128	no	—
238	#117	—	53	128	no	—
239	C₂×C₄⋊C₄	—	53	24	no	—
240	C₂×C₄⋊C₄	—	53	48	no	—
241	C₂×C₄⋊C₄	—	53	48	no	—
242	C₂×C₄⋊C₄	—	53	24	no	—
243	C₂×C₄⋊C₄	C₂²×D₅₃	1	24	yes	—
244	C₂×C₄⋊C₄	C₂²×D₅₃	1	24	yes	—
245	C₂×C₂²⋊C₄	—	53	48	no	—
246	C₂×C₄²	—	53	48	no	—
247	C₂×C₄²	—	53	12	no	—
248	C₂×C₄²	—	53	12	no	—
249	C₂×C₄²	—	53	12	no	—
250	C₂×C₄²	—	53	64	no	—
251	C₂×C₄²	C₂²×D₅₃	1	12	yes	—
252	C₂⁴	—	53	8	no	—
253	C₂⁴	—	53	6	no	—
254	C₂⁴	—	106	4	no	—
255	C₂⁴	—	106	4	no	—
256	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
257	C₂×Q₈	—	2	96	no	—
258	C₂×Q₈	—	53	32	no	—
259	C₂×Q₈	—	106	96	no	—
260	C₂×Q₈	C₂³×D₅₃	1	32	yes	—
261	C₂²×C₄	—	2	16	no	—
262	C₂²×C₄	—	53	8	no	—
263	C₂²×C₄	—	53	6	no	—
264	C₂²×C₄	—	53	96	no	—
265	C₂²×C₄	—	53	16	no	—
266	C₂²×C₄	—	53	6	no	—
267	C₂²×C₄	—	53	6	no	—
268	C₂²×C₄	—	53	24	no	—
269	C₂²×C₄	—	53	16	no	—
270	C₂²×C₄	—	53	16	no	—
271	C₂²×C₄	—	106	4	no	—
272	C₂²×C₄	—	106	4	no	—
273	C₂²×C₄	—	106	16	no	—
274	C₂²×C₄	—	106	48	no	—
275	C₂²×C₄	—	106	48	no	—
276	C₂²×C₄	#11719947	1	8	yes	—
277	C₂²×C₄	Q₈×D₅₃	1	8	yes	—
278	C₂²×C₄	#11719949	1	8	yes	—
279	C₂²×C₄	C₂³×D₅₃	1	24	yes	—
280	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
281	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
282	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
283	C₄⋊C₄	—	53	32	no	—
284	C₄⋊C₄	—	53	64	no	—
285	C₄⋊C₄	—	53	64	no	—
286	C₄⋊C₄	—	53	32	no	—
287	C₄⋊C₄	C₂³×D₅₃	1	32	yes	—
288	C₄⋊C₄	C₂³×D₅₃	1	32	yes	—
289	C₂²⋊C₄	—	53	64	no	—
290	C₄²	—	53	16	no	—
291	C₄²	—	53	16	no	—
292	C₄²	—	53	16	no	—
293	C₄²	—	53	64	no	—
294	C₄²	C₂³×D₅₃	1	16	yes	—
295	C₂³	—	53	24	no	—
296	C₂³	—	53	4	no	—
297	C₂³	—	106	32	no	—
298	C₂³	—	106	12	no	—
299	C₂³	—	106	12	no	—
300	C₂³	C₂×Q₈×D₅₃	1	4	yes	—
301	C₂³	C₂×#11719947	1	4	yes	—
302	C₂³	C₂×#11719949	1	4	yes	—
303	C₂³	C₂⁴×D₅₃	1	3	yes	—
304	Q₈	—	2	64	no	—
305	Q₈	—	106	64	no	—
306	C₂×C₄	—	2	48	no	—
307	C₂×C₄	—	53	24	no	—
308	C₂×C₄	—	53	4	no	—
309	C₂×C₄	—	53	64	no	—
310	C₂×C₄	—	53	4	no	—
311	C₂×C₄	—	53	4	no	—
312	C₂×C₄	—	53	16	no	—
313	C₂×C₄	—	106	12	no	—
314	C₂×C₄	—	106	12	no	—
315	C₂×C₄	—	106	48	no	—
316	C₂×C₄	—	106	32	no	—
317	C₂×C₄	—	106	32	no	—
318	C₂×C₄	C₂×Q₈×D₅₃	1	24	yes	—
319	C₂×C₄	C₂×#11719947	1	24	yes	—
320	C₂×C₄	C₂×#11719949	1	24	yes	—
321	C₂×C₄	C₂⁴×D₅₃	1	16	yes	—
322	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
323	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
324	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
325	C₂²	—	53	8	no	—
326	C₂²	—	106	48	no	—
327	C₂²	—	106	4	no	—
328	C₂²	—	106	4	no	—
329	C₂²	#16811178	1	16	yes	direct product factor
330	C₂²	C₂²×Q₈×D₅₃	1	6	yes	—
331	C₂²	C₂²×#11719947	1	6	yes	—
332	C₂²	C₂²×#11719949	1	6	yes	—
333	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
334	C₄	—	2	16	no	—
335	C₄	—	53	8	no	—
336	C₄	—	106	4	no	—
337	C₄	—	106	4	no	—
338	C₄	—	106	16	no	—
339	C₄	C₂²×Q₈×D₅₃	1	8	yes	—
340	C₄	C₂²×#11719947	1	8	yes	—
341	C₄	C₂²×#11719949	1	8	yes	—
342	C₂	—	106	8	no	—
343	C₂	C₂×#16811178	1	12	yes	direct product factor
344	C₂	C₂³×Q₈×D₅₃	1	1	yes	characteristic
345	C₂	C₂³×#11719947	1	1	yes	characteristic
346	C₂	C₂³×#11719949	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂²×C₄⋊Q₈×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂⁴
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	C₂²×C₄⋊Q₈	D₅₃
hypocenter	C₅₃	C₂²×#533
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#16811178	C₂	direct (N × H)
2. C₂²×#13133217	C₂	semidirect
3. C₂²×#13133208	C₂	semidirect
6. C₂²×Q₈×Dic₅₃	C₂	semidirect
7. C₂²×#13133182	C₂	semidirect
10. C₂²×C₄⋊Q₈×C₅₃	C₂	semidirect
15. #16811178	C₂²	direct (N × H)
16. C₂×#13133217	C₂²	semidirect
17. C₂×#13133208	C₂²	semidirect
20. C₂×Q₈×Dic₅₃	C₂²	semidirect
21. C₂×#13133182	C₂²	semidirect
34. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
47. C₂²×C₄×D₅₃	Q₈	semidirect
51. #13133217	C₂³	semidirect
52. #13133208	C₂³	semidirect
55. Q₈×Dic₅₃	C₂³	semidirect
56. #13133182	C₂³	semidirect
74. C₄⋊Q₈×C₅₃	C₂³	semidirect
103. C₂×C₄×D₅₃	C₂×Q₈	semidirect
149. C₄×D₅₃	C₂²×Q₈	semidirect
152. C₂²×C₅₃	#533	semidirect
171. C₂²×C₄⋊Q₈	D₅₃	semidirect
179. C₂×C₅₃	C₂×#533	semidirect
191. C₂×C₄⋊Q₈	C₂×D₅₃	semidirect
211. C₅₃	C₂²×#533	semidirect
232. C₄⋊Q₈	C₂²×D₅₃	semidirect
329. C₂²	#16811178	direct (N × H)
343. C₂	C₂×#16811178	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×#16811178	2
C₂²×#13133217	2
C₂²×#13133208	2
C₂²×#13133197	2
C₂²×#13133193	2
C₂²×Q₈×Dic₅₃	2
C₂²×#13133182	2
C₂²×#13133175	2
C₂²×C₄²×D₅₃	2
C₂²×C₄⋊Q₈×C₅₃	2
C₂²×#533	53

Subgroups — C22×#16811178 #28290796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16811178 #28290796