Subgroups — C₂²×C₄×C₄⋊#6157 #28328618

Order 13568.

5758 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊#6157	C₂	1	2	yes	maximal
2	C₂³×C₄×#6157	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊#6157	C₂	1	24	yes	maximal, direct product factor
4	C₂²×(C₂×#6157)⋊C₄	C₂	1	2	yes	maximal
5	C₂²×C₄²×D₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂⁴×#6157	C₂²	1	4	yes	—
7	C₂²×C₄⋊#6157	C₄	1	32	yes	direct product factor
8	C₂²×C₄⋊#6157	C₂²	1	24	yes	—
9	C₂²×C₄×#6157	—	2	16	no	—
10	C₂²×C₄×#6157	C₂²	1	24	yes	—
11	C₄×C₄⋊#6157	C₂²	1	64	yes	direct product factor
12	C₂×(C₂×#6157)⋊C₄	C₂²	1	24	yes	—
13	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
14	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄×Dic₅₃	C₄	1	1	yes	characteristic, complemented
17	C₂²×C₄×Dic₅₃	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₄×Dic₅₃	C₄	1	1	yes	characteristic, complemented
19	C₂×C₄²×D₅₃	C₄	1	12	yes	complemented
20	C₂×C₄²×D₅₃	C₂²	1	12	yes	—
21	C₂²×C₄²×C₅₃	C₄	1	1	yes	characteristic, complemented
22	C₂³×#6157	—	2	16	no	—
23	C₂³×#6157	—	2	16	no	—
24	C₂³×#6157	C₂×C₄	1	32	yes	—
25	C₂³×#6157	C₂³	1	24	yes	—
26	C₂×C₄⋊#6157	C₂×C₄	1	192	yes	direct product factor
27	C₂×C₄⋊#6157	C₂³	1	32	yes	—
28	C₂×C₄×#6157	—	2	96	no	—
29	C₂×C₄×#6157	C₂³	1	32	yes	—
30	(C₂×#6157)⋊C₄	C₂³	1	32	yes	—
31	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
32	C₂³×Dic₅₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×Dic₅₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×Dic₅₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₅₃	—	2	8	no	—
36	C₂²×C₄×D₅₃	C₂×C₄	1	6	yes	—
37	C₂²×C₄×D₅₃	C₂×C₄	1	6	yes	—
38	C₂²×C₄×D₅₃	C₂×C₄	1	16	yes	—
39	C₂²×C₄×D₅₃	C₂×C₄	1	6	yes	—
40	C₂²×C₄×D₅₃	D₄	1	8	yes	—
41	C₂²×C₄×D₅₃	Q₈	1	8	yes	—
42	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
43	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
44	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
45	C₂×C₄×Dic₅₃	C₂×C₄	1	12	yes	complemented
46	C₂×C₄×Dic₅₃	C₂×C₄	1	12	yes	complemented
47	C₂×C₄×Dic₅₃	C₂×C₄	1	12	yes	complemented
48	C₄²×D₅₃	C₂×C₄	1	48	yes	complemented
49	C₄²×D₅₃	C₂³	1	16	yes	—
50	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅₃	C₂×C₄	1	12	yes	complemented
54	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
55	C₂³×D₅₃	C₂²×C₄	1	3	yes	—
56	C₂³×D₅₃	C₂²×C₄	1	8	yes	—
57	C₂³×D₅₃	C₂×D₄	1	4	yes	—
58	C₂³×D₅₃	C₂×Q₈	1	4	yes	—
59	C₂³×D₅₃	#41	1	8	yes	—
60	C₂³×D₅₃	C₂⁴	1	3	yes	—
61	C₂²×#6157	—	2	128	no	—
62	C₂²×#6157	—	2	48	no	—
63	C₂²×#6157	—	2	48	no	—
64	C₂²×#6157	C₂²×C₄	1	96	yes	—
65	C₂²×#6157	C₂⁴	1	16	yes	—
66	C₂²×C₄×C₅₃	—	2	4	no	—
67	C₂²×C₄×C₅₃	C₄²	1	8	yes	complemented
68	C₂²×C₄×C₅₃	C₄⋊C₄	1	8	yes	complemented
69	C₂²×C₄×C₅₃	C₂²×C₄	1	6	yes	—
70	C₂²×C₄×C₅₃	C₂²×C₄	1	6	yes	—
71	C₂²×C₄×C₅₃	C₂²×C₄	1	6	yes	—
72	C₂²×Dic₅₃	—	2	4	no	—
73	C₂²×Dic₅₃	C₄²	1	8	yes	complemented
74	C₂²×Dic₅₃	C₄⋊C₄	1	8	yes	complemented
75	C₂²×Dic₅₃	C₂²×C₄	1	6	yes	—
76	C₂²×Dic₅₃	C₂²×C₄	1	6	yes	—
77	C₂²×Dic₅₃	C₂²×C₄	1	6	yes	—
78	C₂×C₄×D₅₃	—	2	24	no	—
79	C₂×C₄×D₅₃	—	2	24	no	—
80	C₂×C₄×D₅₃	C₄²	1	48	yes	complemented
81	C₂×C₄×D₅₃	C₄⋊C₄	1	48	yes	complemented
82	C₂×C₄×D₅₃	C₂²×C₄	1	12	yes	—
83	C₂×C₄×D₅₃	C₂²×C₄	1	12	yes	—
84	C₂×C₄×D₅₃	C₂²×C₄	1	48	yes	—
85	C₂×C₄×D₅₃	C₂²×C₄	1	12	yes	—
86	C₂×C₄×D₅₃	C₂×D₄	1	24	yes	—
87	C₂×C₄×D₅₃	C₂×Q₈	1	24	yes	—
88	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
89	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
90	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
91	C₄⋊#6157	C₂²×C₄	1	128	yes	direct product factor
92	C₄×#6157	—	2	64	no	—
93	C₄²×C₅₃	C₂²×C₄	1	16	yes	complemented
94	C₄×Dic₅₃	C₂²×C₄	1	16	yes	complemented
95	C₄×Dic₅₃	C₂²×C₄	1	16	yes	complemented
96	C₄×Dic₅₃	C₂²×C₄	1	16	yes	complemented
97	C₂³×C₅₃	C₂×C₄²	1	4	yes	—
98	C₂³×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
99	C₂³×C₅₃	#117	1	4	yes	—
100	C₂³×C₅₃	C₂³×C₄	1	3	yes	—
101	C₂²×D₅₃	C₂×C₄²	1	12	yes	—
102	C₂²×D₅₃	C₂×C₄⋊C₄	1	12	yes	—
103	C₂²×D₅₃	#117	1	12	yes	—
104	C₂²×D₅₃	C₄×D₄	1	32	yes	—
105	C₂²×D₅₃	C₄×Q₈	1	32	yes	—
106	C₂²×D₅₃	C₂³×C₄	1	3	yes	—
107	C₂²×D₅₃	C₂³×C₄	1	12	yes	—
108	C₂²×D₅₃	C₂²×D₄	1	6	yes	—
109	C₂²×D₅₃	C₂²×Q₈	1	6	yes	—
110	C₂²×D₅₃	C₂×#41	1	12	yes	—
111	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
112	C₂×#6157	—	2	192	no	—
113	C₂×#6157	—	2	16	no	—
114	C₂×#6157	—	2	16	no	—
115	C₂×#6157	C₂³×C₄	1	32	yes	—
116	C₂×C₄×C₅₃	—	2	12	no	—
117	C₂×C₄×C₅₃	C₂×C₄²	1	24	yes	complemented
118	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	24	yes	complemented
119	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
120	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
121	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
122	C₂×Dic₅₃	—	2	12	no	—
123	C₂×Dic₅₃	C₂×C₄²	1	24	yes	complemented
124	C₂×Dic₅₃	C₂×C₄⋊C₄	1	24	yes	complemented
125	C₂×Dic₅₃	C₂³×C₄	1	4	yes	—
126	C₂×Dic₅₃	C₂³×C₄	1	4	yes	—
127	C₂×Dic₅₃	C₂³×C₄	1	4	yes	—
128	C₄×D₅₃	—	2	24	no	—
129	C₄×D₅₃	—	2	8	no	—
130	C₄×D₅₃	C₂×C₄²	1	48	yes	complemented
131	C₄×D₅₃	C₂×C₄⋊C₄	1	48	yes	complemented
132	C₄×D₅₃	C₂³×C₄	1	16	yes	—
133	C₄×D₅₃	C₂²×D₄	1	8	yes	—
134	C₄×D₅₃	C₂²×Q₈	1	8	yes	—
135	C₂²×C₄×C₄⋊C₄	—	53	1	no	maximal, Sylow
136	C₂²×C₅₃	C₄×C₄⋊C₄	1	16	yes	complemented
137	C₂²×C₅₃	C₂²×C₄²	1	6	yes	—
138	C₂²×C₅₃	C₂²×C₄⋊C₄	1	6	yes	—
139	C₂²×C₅₃	C₂×#117	1	6	yes	—
140	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
141	C₂×D₅₃	C₄×C₄⋊C₄	1	48	yes	complemented
142	C₂×D₅₃	C₂²×C₄²	1	6	yes	—
143	C₂×D₅₃	C₂²×C₄⋊C₄	1	6	yes	—
144	C₂×D₅₃	C₂×#117	1	6	yes	—
145	C₂×D₅₃	C₂×C₄×D₄	1	24	yes	—
146	C₂×D₅₃	C₂×C₄×Q₈	1	24	yes	—
147	C₂×D₅₃	C₂⁴×C₄	1	2	yes	—
148	C₂×D₅₃	C₂³×D₄	1	1	yes	characteristic
149	C₂×D₅₃	C₂³×Q₈	1	1	yes	characteristic
150	C₂×D₅₃	C₂²×#41	1	2	yes	—
151	#6157	—	2	32	no	—
152	C₄×C₅₃	—	2	4	no	—
153	C₄×C₅₃	C₂²×C₄²	1	8	yes	complemented
154	C₄×C₅₃	C₂²×C₄⋊C₄	1	8	yes	complemented
155	Dic₅₃	—	2	4	no	—
156	Dic₅₃	C₂²×C₄²	1	8	yes	complemented
157	Dic₅₃	C₂²×C₄⋊C₄	1	8	yes	complemented
158	C₂³×C₄⋊C₄	—	53	2	no	—
159	C₂³×C₄²	—	53	1	no	—
160	C₂³×C₄²	—	53	2	no	—
161	C₂×C₄×C₄⋊C₄	—	53	24	no	—
162	C₂²×#95	—	53	2	no	—
163	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	12	yes	complemented
164	C₂×C₅₃	C₂³×C₄²	1	1	yes	characteristic
165	C₂×C₅₃	C₂³×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₅₃	C₂²×#117	1	1	yes	characteristic
167	D₅₃	C₂×C₄×C₄⋊C₄	1	12	yes	complemented
168	D₅₃	C₂²×C₄×D₄	1	2	yes	—
169	D₅₃	C₂²×C₄×Q₈	1	2	yes	—
170	C₂⁴×C₄	—	53	1	no	—
171	C₂⁴×C₄	—	53	1	no	—
172	C₂⁴×C₄	—	53	4	no	—
173	C₂⁴×C₄	—	53	1	no	—
174	C₂²×C₄⋊C₄	—	53	32	no	—
175	C₂²×C₄⋊C₄	—	53	24	no	—
176	C₂²×C₄²	—	53	1	no	—
177	C₂²×C₄²	—	53	1	no	—
178	C₂²×C₄²	—	53	1	no	—
179	C₂²×C₄²	—	53	12	no	—
180	C₂²×C₄²	—	53	12	no	—
181	C₂²×C₄²	—	53	24	no	—
182	C₂²×C₄²	—	106	16	no	—
183	C₂²×C₄²	#6157	1	1	yes	characteristic, complemented
184	C₄×C₄⋊C₄	—	53	64	no	—
185	C₂×#95	—	53	24	no	—
186	C₅₃	C₂²×C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
187	C₂⁵	—	53	1	no	—
188	C₂³×C₄	—	53	1	no	—
189	C₂³×C₄	—	53	1	no	—
190	C₂³×C₄	—	53	16	no	—
191	C₂³×C₄	—	53	8	no	—
192	C₂³×C₄	—	53	8	no	—
193	C₂³×C₄	—	53	6	no	—
194	C₂³×C₄	—	53	6	no	—
195	C₂³×C₄	—	53	6	no	—
196	C₂³×C₄	—	53	6	no	—
197	C₂³×C₄	—	53	24	no	—
198	C₂³×C₄	—	53	32	no	—
199	C₂³×C₄	—	53	1	no	—
200	C₂³×C₄	—	53	6	no	—
201	C₂³×C₄	—	53	6	no	—
202	C₂³×C₄	—	106	8	no	—
203	C₂³×C₄	—	106	16	no	—
204	C₂³×C₄	—	106	16	no	—
205	C₂³×C₄	C₂×#6157	1	1	yes	characteristic
206	C₂³×C₄	C₂×#6157	1	1	yes	characteristic
207	C₂³×C₄	C₂×#6157	1	1	yes	characteristic
208	C₂×C₄⋊C₄	—	53	32	no	—
209	C₂×C₄⋊C₄	—	53	192	no	—
210	C₂×C₄²	—	53	12	no	—
211	C₂×C₄²	—	53	12	no	—
212	C₂×C₄²	—	53	12	no	—
213	C₂×C₄²	—	53	48	no	—
214	C₂×C₄²	—	53	16	no	—
215	C₂×C₄²	—	53	32	no	—
216	C₂×C₄²	—	106	96	no	—
217	C₂×C₄²	C₂×#6157	1	12	yes	complemented
218	#95	—	53	32	no	—
219	C₂⁴	—	53	8	no	—
220	C₂⁴	—	53	4	no	—
221	C₂⁴	—	53	4	no	—
222	C₂⁴	—	53	8	no	—
223	C₂⁴	—	53	3	no	—
224	C₂⁴	—	53	3	no	—
225	C₂⁴	C₂²×#6157	1	1	yes	characteristic
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	53	8	no	—
228	C₂²×C₄	—	53	8	no	—
229	C₂²×C₄	—	53	6	no	—
230	C₂²×C₄	—	53	6	no	—
231	C₂²×C₄	—	53	48	no	—
232	C₂²×C₄	—	53	48	no	—
233	C₂²×C₄	—	53	48	no	—
234	C₂²×C₄	—	53	24	no	—
235	C₂²×C₄	—	53	24	no	—
236	C₂²×C₄	—	53	12	no	—
237	C₂²×C₄	—	53	12	no	—
238	C₂²×C₄	—	53	4	no	—
239	C₂²×C₄	—	53	4	no	—
240	C₂²×C₄	—	53	96	no	—
241	C₂²×C₄	—	53	16	no	—
242	C₂²×C₄	—	53	6	no	—
243	C₂²×C₄	—	53	12	no	—
244	C₂²×C₄	—	53	4	no	—
245	C₂²×C₄	—	106	24	no	—
246	C₂²×C₄	—	106	24	no	—
247	C₂²×C₄	—	106	48	no	—
248	C₂²×C₄	—	106	128	no	—
249	C₂²×C₄	—	106	48	no	—
250	C₂²×C₄	—	106	4	no	—
251	C₂²×C₄	C₄×#6157	1	8	yes	complemented
252	C₂²×C₄	C₄⋊#6157	1	8	yes	direct product factor
253	C₂²×C₄	C₂²×#6157	1	6	yes	—
254	C₂²×C₄	C₂²×#6157	1	6	yes	—
255	C₂²×C₄	C₂²×#6157	1	6	yes	—
256	C₄⋊C₄	—	53	128	no	—
257	C₄²	—	53	16	no	—
258	C₄²	—	53	16	no	—
259	C₄²	—	53	16	no	—
260	C₄²	—	106	64	no	—
261	C₄²	C₂²×#6157	1	16	yes	complemented
262	C₂³	—	53	32	no	—
263	C₂³	—	53	32	no	—
264	C₂³	—	53	12	no	—
265	C₂³	—	53	12	no	—
266	C₂³	—	53	12	no	—
267	C₂³	—	53	6	no	—
268	C₂³	—	53	6	no	—
269	C₂³	—	53	12	no	—
270	C₂³	—	53	12	no	—
271	C₂³	—	53	3	no	—
272	C₂³	—	53	1	no	—
273	C₂³	C₂×C₄×#6157	1	4	yes	—
274	C₂³	C₂×C₄⋊#6157	1	4	yes	—
275	C₂³	#13133296	1	4	yes	—
276	C₂³	C₂³×#6157	1	3	yes	—
277	C₂×C₄	—	2	12	no	—
278	C₂×C₄	—	53	24	no	—
279	C₂×C₄	—	53	24	no	—
280	C₂×C₄	—	53	4	no	—
281	C₂×C₄	—	53	4	no	—
282	C₂×C₄	—	53	48	no	—
283	C₂×C₄	—	53	16	no	—
284	C₂×C₄	—	53	48	no	—
285	C₂×C₄	—	53	8	no	—
286	C₂×C₄	—	53	8	no	—
287	C₂×C₄	—	53	32	no	—
288	C₂×C₄	—	53	4	no	—
289	C₂×C₄	—	106	8	no	—
290	C₂×C₄	—	106	24	no	—
291	C₂×C₄	—	106	16	no	—
292	C₂×C₄	—	106	192	no	—
293	C₂×C₄	—	106	16	no	—
294	C₂×C₄	—	106	12	no	—
295	C₂×C₄	C₂×C₄×#6157	1	24	yes	complemented
296	C₂×C₄	C₂×C₄⋊#6157	1	24	yes	direct product factor
297	C₂×C₄	C₂³×#6157	1	4	yes	—
298	C₂×C₄	C₂³×#6157	1	4	yes	—
299	C₂×C₄	C₂³×#6157	1	4	yes	—
300	C₂²	—	53	24	no	—
301	C₂²	—	53	24	no	—
302	C₂²	—	53	48	no	—
303	C₂²	—	53	2	no	—
304	C₂²	—	53	6	no	—
305	C₂²	—	53	1	no	—
306	C₂²	—	53	6	no	—
307	C₂²	—	53	1	no	—
308	C₂²	—	53	2	no	—
309	C₂²	—	53	6	no	—
310	C₂²	C₄×C₄⋊#6157	1	16	yes	direct product factor
311	C₂²	C₂²×C₄×#6157	1	6	yes	—
312	C₂²	C₂²×C₄⋊#6157	1	6	yes	—
313	C₂²	C₂×#13133296	1	6	yes	—
314	C₂²	C₂⁴×#6157	1	1	yes	characteristic
315	C₄	—	2	4	no	—
316	C₄	—	53	8	no	—
317	C₄	—	53	8	no	—
318	C₄	—	106	32	no	—
319	C₄	—	106	4	no	—
320	C₄	C₂²×C₄×#6157	1	8	yes	complemented
321	C₄	C₂²×C₄⋊#6157	1	8	yes	direct product factor
322	C₂	—	53	2	no	—
323	C₂	—	53	2	no	—
324	C₂	—	53	12	no	—
325	C₂	C₂×C₄×C₄⋊#6157	1	12	yes	direct product factor
326	C₂	C₂³×C₄×#6157	1	1	yes	characteristic
327	C₂	C₂³×C₄⋊#6157	1	1	yes	characteristic
328	C₂	C₂²×#13133296	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×#6157
commutator	C₂×C₅₃	C₂³×C₄²
Frattini	C₂²	C₂⁴×#6157
Fitting	C₂²×C₄²×C₅₃	C₄
socle	C₂⁴×C₅₃	C₂²×C₄
prime radical	C₂⁴×D₅₃	C₂³
cosocle	C₂²×D₅₃	C₂⁵
hypercenter	C₂²×C₄²	#6157
hypocenter	C₅₃	C₂²×C₄×C₄⋊C₄
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₄⋊#6157	C₂	direct (N × H)
7. C₂²×C₄⋊#6157	C₄	direct (N × H)
11. C₄×C₄⋊#6157	C₂²	direct (N × H)
16. C₂²×C₄×Dic₅₃	C₄	semidirect
17. C₂²×C₄×Dic₅₃	C₄	semidirect
18. C₂²×C₄×Dic₅₃	C₄	semidirect
19. C₂×C₄²×D₅₃	C₄	semidirect
21. C₂²×C₄²×C₅₃	C₄	semidirect
26. C₂×C₄⋊#6157	C₂×C₄	direct (N × H)
45. C₂×C₄×Dic₅₃	C₂×C₄	semidirect
46. C₂×C₄×Dic₅₃	C₂×C₄	semidirect
47. C₂×C₄×Dic₅₃	C₂×C₄	semidirect
48. C₄²×D₅₃	C₂×C₄	semidirect
53. C₂×C₄²×C₅₃	C₂×C₄	semidirect
67. C₂²×C₄×C₅₃	C₄²	semidirect
68. C₂²×C₄×C₅₃	C₄⋊C₄	semidirect
73. C₂²×Dic₅₃	C₄²	semidirect
74. C₂²×Dic₅₃	C₄⋊C₄	semidirect
80. C₂×C₄×D₅₃	C₄²	semidirect
81. C₂×C₄×D₅₃	C₄⋊C₄	semidirect
91. C₄⋊#6157	C₂²×C₄	direct (N × H)
93. C₄²×C₅₃	C₂²×C₄	semidirect
94. C₄×Dic₅₃	C₂²×C₄	semidirect
95. C₄×Dic₅₃	C₂²×C₄	semidirect
96. C₄×Dic₅₃	C₂²×C₄	semidirect
117. C₂×C₄×C₅₃	C₂×C₄²	semidirect
118. C₂×C₄×C₅₃	C₂×C₄⋊C₄	semidirect
123. C₂×Dic₅₃	C₂×C₄²	semidirect
124. C₂×Dic₅₃	C₂×C₄⋊C₄	semidirect
130. C₄×D₅₃	C₂×C₄²	semidirect
131. C₄×D₅₃	C₂×C₄⋊C₄	semidirect
136. C₂²×C₅₃	C₄×C₄⋊C₄	semidirect
141. C₂×D₅₃	C₄×C₄⋊C₄	semidirect
153. C₄×C₅₃	C₂²×C₄²	semidirect
154. C₄×C₅₃	C₂²×C₄⋊C₄	semidirect
156. Dic₅₃	C₂²×C₄²	semidirect
157. Dic₅₃	C₂²×C₄⋊C₄	semidirect
163. C₂×C₅₃	C₂×C₄×C₄⋊C₄	semidirect
167. D₅₃	C₂×C₄×C₄⋊C₄	semidirect
183. C₂²×C₄²	#6157	semidirect
186. C₅₃	C₂²×C₄×C₄⋊C₄	semidirect
217. C₂×C₄²	C₂×#6157	semidirect
251. C₂²×C₄	C₄×#6157	semidirect
252. C₂²×C₄	C₄⋊#6157	direct (N × H)
261. C₄²	C₂²×#6157	semidirect
295. C₂×C₄	C₂×C₄×#6157	semidirect
296. C₂×C₄	C₂×C₄⋊#6157	direct (N × H)
310. C₂²	C₄×C₄⋊#6157	direct (N × H)
320. C₄	C₂²×C₄×#6157	semidirect
321. C₄	C₂²×C₄⋊#6157	direct (N × H)
325. C₂	C₂×C₄×C₄⋊#6157	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×C₄⋊#6157	2
C₂³×C₄×#6157	2
C₂×C₄×C₄⋊#6157	2
C₂²×(C₂×#6157)⋊C₄	2
C₂²×C₄²×D₅₃	2
C₂²×C₄×C₄⋊C₄	53

Subgroups — C22×C4×C4⋊#6157 #28328618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₄⋊#6157 #28328618