Subgroups — C₂×#20272556 #27273617

Order 13568.

974 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊#88322	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×#88322	C₂	1	1	yes	maximal, characteristic
3	#20272556	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×#88322	—	2	1	no	—
6	C₂³×#88322	—	2	1	no	—
7	C₂×C₄⋊#88322	—	2	2	no	—
8	C₂×C₄⋊#88322	—	2	1	no	—
9	C₂×C₄⋊#88322	C₄	1	4	yes	complemented
10	C₂×C₄⋊#88322	C₂²	1	2	yes	—
11	C₂×C₄×#88322	—	2	2	no	—
12	C₂×C₄×#88322	—	2	1	no	—
13	C₂×C₄×#88322	C₄	1	4	yes	complemented
14	C₂×C₄×#88322	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₅₃	C₄	1	2	yes	—
16	C₂²×C₄²×C₅₃	—	2	1	no	—
17	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₅₃	—	2	1	no	—
19	C₄×C₄⋊C₄×C₅₃	—	2	1	no	—
20	C₄×C₄⋊C₄×C₅₃	C₄	1	2	yes	—
21	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
22	C₂×#95×C₅₃	—	2	1	no	—
23	C₂²×#88322	—	2	8	no	—
24	C₂²×#88322	—	2	4	no	—
25	C₂²×#88322	—	2	4	no	—
26	C₂²×#88322	—	2	2	no	—
27	C₂²×#88322	—	2	2	no	—
28	C₂²×#88322	—	4	2	no	—
29	C₂²×#88322	—	4	2	no	—
30	C₄⋊#88322	—	2	4	no	—
31	C₄⋊#88322	—	2	2	no	—
32	C₄⋊#88322	C₂×C₄	1	4	yes	complemented
33	C₄×#88322	—	2	4	no	—
34	C₄×#88322	—	2	2	no	—
35	C₄×#88322	C₂×C₄	1	4	yes	complemented
36	C₂³×C₄×C₅₃	—	2	2	no	—
37	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₅₃	C₈	1	8	yes	complemented
43	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₅₃	—	2	2	no	—
45	C₂×C₄²×C₅₃	—	2	2	no	—
46	C₂×C₄²×C₅₃	—	4	2	no	—
47	C₂×C₄²×C₅₃	—	4	2	no	—
48	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅₃	D₄	1	2	yes	—
52	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₅₃	Q₈	1	2	yes	—
55	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
56	#95×C₅₃	—	2	2	no	—
57	#95×C₅₃	—	2	2	no	—
58	C₂⁴×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₅₃	—	2	4	no	—
60	C₂²×C₄×C₅₃	—	2	8	no	—
61	C₂²×C₄×C₅₃	—	2	4	no	—
62	C₂²×C₄×C₅₃	—	4	4	no	—
63	C₂²×C₄×C₅₃	—	4	4	no	—
64	C₂²×C₄×C₅₃	C₄²	1	2	yes	—
65	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₅₃	C₂×C₈	1	4	yes	—
74	C₂²×C₄×C₅₃	M₁₆	1	4	yes	—
75	C₂²×C₄×C₅₃	D₈	1	2	yes	—
76	C₂²×C₄×C₅₃	SD₁₆	1	2	yes	—
77	C₂²×C₄×C₅₃	SD₁₆	1	2	yes	—
78	C₂²×C₄×C₅₃	Q₁₆	1	2	yes	—
79	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
82	C₄⋊C₄×C₅₃	—	2	8	no	—
83	C₄⋊C₄×C₅₃	—	2	4	no	—
84	C₄⋊C₄×C₅₃	C₂×C₈	1	8	yes	complemented
85	C₄²×C₅₃	—	4	4	no	—
86	C₄²×C₅₃	—	4	2	no	—
87	C₄²×C₅₃	—	4	2	no	—
88	C₄²×C₅₃	C₄²	1	2	yes	—
89	C₄²×C₅₃	C₂²⋊C₄	1	2	yes	—
90	C₄²×C₅₃	C₂²⋊C₄	1	2	yes	—
91	C₄²×C₅₃	C₄⋊C₄	1	2	yes	—
92	C₄²×C₅₃	C₄⋊C₄	1	2	yes	—
93	C₄²×C₅₃	C₄⋊C₄	1	2	yes	—
94	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
95	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
96	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
97	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
98	C₂×#88322	—	2	16	no	—
99	C₂×#88322	—	2	8	no	—
100	C₂×#88322	—	2	4	no	—
101	C₂×#88322	—	2	4	no	—
102	C₂×#88322	—	4	8	no	—
103	C₂×#88322	—	4	2	no	—
104	C₂×#88322	—	4	2	no	—
105	C₂³×C₅₃	#95	1	2	yes	—
106	C₂³×C₅₃	C₂²⋊C₈	1	4	yes	—
107	C₂³×C₅₃	#102	1	2	yes	—
108	C₂³×C₅₃	#103	1	2	yes	—
109	C₂³×C₅₃	#104	1	4	yes	—
110	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₅₃	—	2	4	no	—
112	C₂×C₄×C₅₃	—	2	4	no	—
113	C₂×C₄×C₅₃	—	2	2	no	—
114	C₂×C₄×C₅₃	—	2	2	no	—
115	C₂×C₄×C₅₃	—	2	8	no	—
116	C₂×C₄×C₅₃	—	4	16	no	—
117	C₂×C₄×C₅₃	—	4	4	no	—
118	C₂×C₄×C₅₃	—	4	4	no	—
119	C₂×C₄×C₅₃	#95	1	2	yes	—
120	C₂×C₄×C₅₃	#95	1	2	yes	—
121	C₂×C₄×C₅₃	#95	1	2	yes	—
122	C₂×C₄×C₅₃	C₄×C₈	1	4	yes	—
123	C₂×C₄×C₅₃	#97	1	4	yes	—
124	C₂×C₄×C₅₃	C₂²⋊C₈	1	4	yes	—
125	C₂×C₄×C₅₃	#102	1	4	yes	—
126	C₂×C₄×C₅₃	#102	1	2	yes	—
127	C₂×C₄×C₅₃	#103	1	4	yes	—
128	C₂×C₄×C₅₃	#103	1	2	yes	—
129	C₂×C₄×C₅₃	C₄⋊C₈	1	8	yes	—
130	C₂×C₄×C₅₃	#106	1	4	yes	—
131	C₂×C₄×C₅₃	#107	1	4	yes	—
132	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
139	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
140	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
141	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
142	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
143	C₂×C₄×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
144	#88322	—	2	8	no	—
145	#88322	—	4	4	no	—
146	C₂×#1279	—	53	1	no	maximal, Sylow
147	C₂²×C₅₃	D₄⋊C₈	1	8	yes	—
148	C₂²×C₅₃	Q₈⋊C₈	1	8	yes	—
149	C₂²×C₅₃	#336	1	4	yes	—
150	C₂²×C₅₃	#339	1	4	yes	—
151	C₂²×C₅₃	#340	1	4	yes	—
152	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
153	C₂²×C₅₃	C₂×C₂²⋊C₈	1	2	yes	—
154	C₂²×C₅₃	C₂×#102	1	1	yes	characteristic
155	C₂²×C₅₃	C₂×#103	1	1	yes	characteristic
156	C₂²×C₅₃	C₂×#104	1	2	yes	—
157	C₄×C₅₃	—	2	1	no	—
158	C₄×C₅₃	—	2	2	no	—
159	C₄×C₅₃	—	2	1	no	—
160	C₄×C₅₃	—	4	8	no	—
161	C₄×C₅₃	#336	1	4	yes	—
162	C₄×C₅₃	#340	1	4	yes	—
163	C₄×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
164	C₄×C₅₃	C₂×#97	1	1	yes	characteristic
165	C₄×C₅₃	C₂×#102	1	1	yes	characteristic
166	C₄×C₅₃	C₂×#103	1	1	yes	characteristic
167	C₄×C₅₃	C₂×C₄⋊C₈	1	2	yes	—
168	C₄×C₅₃	C₂×#106	1	1	yes	characteristic
169	C₄×C₅₃	C₂×#107	1	1	yes	characteristic
170	C₂²×C₄⋊C₈	—	53	1	no	—
171	C₂²×C₄×C₈	—	53	1	no	—
172	C₂×C₄×C₄⋊C₄	D₅₃	1	1	yes	characteristic
173	#1279	—	53	4	no	—
174	C₂×C₅₃	#1279	1	8	yes	complemented
175	C₂×C₅₃	C₂×D₄⋊C₈	1	2	yes	—
176	C₂×C₅₃	C₂×Q₈⋊C₈	1	2	yes	—
177	C₂×C₅₃	C₂×#336	1	1	yes	characteristic
178	C₂×C₅₃	C₂×#339	1	1	yes	characteristic
179	C₂×C₅₃	C₂×#340	1	1	yes	characteristic
180	C₂³×C₈	—	106	1	no	—
181	C₂³×C₈	—	106	1	no	—
182	C₂²×C₄⋊C₄	Dic₅₃	1	2	yes	—
183	C₂²×C₄²	—	2	1	no	—
184	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
185	C₂×C₄⋊C₈	—	53	4	no	—
186	C₂×C₄⋊C₈	—	53	2	no	—
187	C₂×C₄⋊C₈	—	106	2	no	—
188	C₂×C₄⋊C₈	—	106	1	no	—
189	C₂×C₄×C₈	—	53	4	no	—
190	C₂×C₄×C₈	—	53	2	no	—
191	C₂×C₄×C₈	—	106	2	no	—
192	C₂×C₄×C₈	—	106	1	no	—
193	C₄×C₄⋊C₄	—	2	1	no	—
194	C₄×C₄⋊C₄	—	2	1	no	—
195	C₄×C₄⋊C₄	Dic₅₃	1	2	yes	—
196	C₄×C₄⋊C₄	C₂×D₅₃	1	2	yes	—
197	C₂×#95	—	2	1	no	—
198	C₅₃	C₂×#1279	1	1	yes	characteristic, complemented, Sylow
199	C₂³×C₄	—	2	2	no	—
200	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
201	C₂³×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
202	C₂³×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
203	C₂²×C₈	—	106	8	no	—
204	C₂²×C₈	—	106	2	no	—
205	C₂²×C₈	—	106	4	no	—
206	C₂²×C₈	—	106	2	no	—
207	C₂²×C₈	—	106	4	no	—
208	C₂²×C₈	—	212	2	no	—
209	C₂²×C₈	—	212	2	no	—
210	C₂×C₄⋊C₄	—	2	4	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	#88322	1	8	yes	complemented
213	C₂×C₄⋊C₄	C₂×Dic₅₃	1	4	yes	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	—	2	2	no	—
216	C₂×C₄²	—	4	2	no	—
217	C₂×C₄²	—	4	2	no	—
218	C₂×C₄²	Dic₁₀₆	1	2	yes	—
219	C₂×C₄²	C₄×D₅₃	1	2	yes	—
220	C₂×C₄²	C₄×D₅₃	1	2	yes	—
221	C₂×C₄²	D₂₁₂	1	2	yes	—
222	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
223	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
224	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
225	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
226	C₄⋊C₈	—	53	4	no	—
227	C₄⋊C₈	—	106	2	no	—
228	C₄⋊C₈	—	106	4	no	—
229	C₄×C₈	—	53	4	no	—
230	C₄×C₈	—	106	2	no	—
231	C₄×C₈	—	106	4	no	—
232	#95	—	2	2	no	—
233	#95	—	2	2	no	—
234	C₂⁴	C₂²⋊Dic₅₃	1	1	yes	characteristic
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	8	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	4	4	no	—
239	C₂²×C₄	—	4	4	no	—
240	C₂²×C₄	C₂×#88322	1	4	yes	—
241	C₂²×C₄	#11719917	1	4	yes	—
242	C₂²×C₄	C₄×Dic₅₃	1	2	yes	—
243	C₂²×C₄	#11719919	1	2	yes	—
244	C₂²×C₄	#11719919	1	2	yes	—
245	C₂²×C₄	C₄⋊Dic₅₃	1	2	yes	—
246	C₂²×C₄	#11719921	1	2	yes	—
247	C₂²×C₄	#11719921	1	2	yes	—
248	C₂²×C₄	#11719922	1	2	yes	—
249	C₂²×C₄	#11719923	1	2	yes	—
250	C₂²×C₄	#11719924	1	2	yes	—
251	C₂²×C₄	#11719925	1	2	yes	—
252	C₂²×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
253	C₂²×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
254	C₂²×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
255	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
258	C₂×C₈	—	106	8	no	—
259	C₂×C₈	—	106	16	no	—
260	C₂×C₈	—	106	4	no	—
261	C₂×C₈	—	106	4	no	—
262	C₂×C₈	—	212	8	no	—
263	C₂×C₈	—	212	2	no	—
264	C₂×C₈	—	212	2	no	—
265	C₄⋊C₄	—	2	8	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	C₂×#88322	1	8	yes	complemented
268	C₄²	—	4	4	no	—
269	C₄²	—	4	2	no	—
270	C₄²	—	4	2	no	—
271	C₄²	C₄×Dic₅₃	1	2	yes	—
272	C₄²	#11719919	1	2	yes	—
273	C₄²	#11719919	1	2	yes	—
274	C₄²	C₄⋊Dic₅₃	1	2	yes	—
275	C₄²	#11719921	1	2	yes	—
276	C₄²	#11719921	1	2	yes	—
277	C₄²	C₂×Dic₁₀₆	1	1	yes	characteristic
278	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
279	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
280	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
281	C₂³	#13133124	1	2	yes	—
282	C₂³	C₂²⋊#88322	1	4	yes	—
283	C₂³	#13133138	1	2	yes	—
284	C₂³	#13133141	1	2	yes	—
285	C₂³	#13133144	1	4	yes	—
286	C₂³	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	4	16	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	#13133124	1	2	yes	—
296	C₂×C₄	#13133124	1	2	yes	—
297	C₂×C₄	#13133124	1	2	yes	—
298	C₂×C₄	C₄×#88322	1	4	yes	—
299	C₂×C₄	#13133128	1	4	yes	—
300	C₂×C₄	C₂²⋊#88322	1	4	yes	—
301	C₂×C₄	#13133137	1	4	yes	—
302	C₂×C₄	#13133138	1	2	yes	—
303	C₂×C₄	#13133140	1	4	yes	—
304	C₂×C₄	#13133141	1	2	yes	—
305	C₂×C₄	C₄⋊#88322	1	8	yes	—
306	C₂×C₄	#13133148	1	4	yes	—
307	C₂×C₄	#13133150	1	4	yes	—
308	C₂×C₄	C₂×C₄×Dic₅₃	1	1	yes	characteristic
309	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
310	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
311	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
312	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
313	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
314	C₂×C₄	C₂²×#88322	1	2	yes	—
315	C₂×C₄	C₂×#11719917	1	2	yes	—
316	C₂×C₄	C₂×#11719922	1	1	yes	characteristic
317	C₂×C₄	C₂×#11719924	1	1	yes	characteristic
318	C₂×C₄	C₂×#11719923	1	1	yes	characteristic
319	C₂×C₄	C₂×#11719925	1	1	yes	characteristic
320	C₈	—	106	8	no	—
321	C₈	—	212	4	no	—
322	C₂²	D₄⋊#88322	1	8	yes	—
323	C₂²	Q₈⋊#88322	1	8	yes	—
324	C₂²	#16810378	1	4	yes	—
325	C₂²	#16810382	1	4	yes	—
326	C₂²	#16810385	1	4	yes	—
327	C₂²	C₂×#13133124	1	1	yes	characteristic
328	C₂²	C₂×C₂²⋊#88322	1	2	yes	—
329	C₂²	C₂×#13133138	1	1	yes	characteristic
330	C₂²	C₂×#13133141	1	1	yes	characteristic
331	C₂²	C₂×#13133144	1	2	yes	—
332	C₄	—	2	1	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	1	no	—
335	C₄	—	4	8	no	—
336	C₄	#16810378	1	4	yes	—
337	C₄	#16810385	1	4	yes	—
338	C₄	C₂×C₄×#88322	1	1	yes	characteristic
339	C₄	C₂×#13133128	1	1	yes	characteristic
340	C₄	C₂×#13133137	1	1	yes	characteristic
341	C₄	C₂×#13133140	1	1	yes	characteristic
342	C₄	C₂×C₄⋊#88322	1	2	yes	—
343	C₄	C₂×#13133148	1	1	yes	characteristic
344	C₄	C₂×#13133150	1	1	yes	characteristic
345	C₂	#20272556	1	8	yes	direct product factor
346	C₂	C₂×D₄⋊#88322	1	2	yes	—
347	C₂	C₂×Q₈⋊#88322	1	2	yes	—
348	C₂	C₂×#16810378	1	1	yes	characteristic
349	C₂	C₂×#16810382	1	1	yes	characteristic
350	C₂	C₂×#16810385	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²⋊D₅₃
commutator	C₄×C₅₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₂×C₄×C₄⋊C₄×C₅₃	C₂
socle, prime radical	C₂⁴×C₅₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₅₃
hypocenter	C₅₃	C₂×#1279
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #20272556	C₂	direct (N × H)
9. C₂×C₄⋊#88322	C₄	semidirect
13. C₂×C₄×#88322	C₄	semidirect
32. C₄⋊#88322	C₂×C₄	semidirect
35. C₄×#88322	C₂×C₄	semidirect
42. C₂×C₄⋊C₄×C₅₃	C₈	semidirect
84. C₄⋊C₄×C₅₃	C₂×C₈	semidirect
174. C₂×C₅₃	#1279	semidirect
198. C₅₃	C₂×#1279	semidirect
212. C₂×C₄⋊C₄	#88322	semidirect
267. C₄⋊C₄	C₂×#88322	semidirect
345. C₂	#20272556	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊#88322	2
C₂²×C₄×#88322	2
#20272556	2
C₂×C₄×C₄⋊C₄×C₅₃	2
C₂×#1279	53

Subgroups — C2×#20272556 #27273617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20272556 #27273617