Subgroups — C₂×C₄×#13133285 #28318361

Order 13568.

1358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133285	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊#6157	C₂	1	2	yes	maximal
3	C₄×#13133285	C₂	1	8	yes	maximal, direct product factor
4	C₂×#16811497	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊#6157	C₂²	1	4	yes	—
7	C₂²×C₄×#6157	—	2	2	no	—
8	C₂×#13133285	C₄	1	16	yes	direct product factor
9	C₂×#13133285	C₂²	1	8	yes	—
10	C₄×C₄⋊#6157	—	2	4	no	—
11	C₄×C₄⋊#6157	C₂²	1	8	yes	—
12	C₂×(C₂×#6157)⋊C₄	—	2	2	no	—
13	#16811497	C₂²	1	8	yes	—
14	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
15	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
16	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×#88322	C₄	1	1	yes	characteristic, complemented
18	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic, complemented
19	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic, complemented
20	C₄×C₈×D₅₃	C₄	1	4	yes	complemented
21	C₄×C₈×D₅₃	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₅₃	C₄	1	1	yes	characteristic, complemented
23	C₂³×#6157	—	2	4	no	—
24	C₂×C₄⋊#6157	—	2	4	no	—
25	C₂×C₄⋊#6157	—	2	8	no	—
26	C₂×C₄⋊#6157	C₂×C₄	1	16	yes	—
27	C₂×C₄⋊#6157	C₂³	1	8	yes	—
28	C₂×C₄×#6157	—	2	8	no	—
29	C₂×C₄×#6157	—	4	8	no	—
30	#13133285	C₂×C₄	1	32	yes	direct product factor
31	(C₂×#6157)⋊C₄	—	2	8	no	—
32	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
33	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
35	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
36	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
37	C₂×C₈×D₅₃	—	2	4	no	—
38	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₅₃	C₂×C₄	1	8	yes	—
41	C₂×C₈×D₅₃	C₂³	1	2	yes	—
42	C₂×C₈×D₅₃	C₂³	1	2	yes	—
43	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
45	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
46	C₄²×D₅₃	C₂×C₄	1	2	yes	—
47	C₄²×D₅₃	D₄	1	2	yes	—
48	C₄²×D₅₃	Q₈	1	2	yes	—
49	C₄²×D₅₃	C₂³	1	2	yes	—
50	C₄×#88322	C₂×C₄	1	4	yes	complemented
51	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
52	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
53	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
56	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
57	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×#6157	—	2	16	no	—
59	C₂²×#6157	—	2	8	no	—
60	C₂²×#6157	—	4	8	no	—
61	C₂²×#6157	—	4	8	no	—
62	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
65	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
68	C₂×C₄×D₅₃	—	2	4	no	—
69	C₂×C₄×D₅₃	C₄⋊C₄	1	2	yes	—
70	C₂×C₄×D₅₃	C₄⋊C₄	1	2	yes	—
71	C₂×C₄×D₅₃	SD₁₆	1	8	yes	—
72	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
74	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
75	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
77	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
78	C₂×C₄×D₅₃	#41	1	4	yes	—
79	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
80	C₄⋊#6157	—	2	16	no	—
81	C₄⋊#6157	—	2	8	no	—
82	C₄⋊#6157	C₂²×C₄	1	16	yes	—
83	C₄×#6157	—	4	16	no	—
84	C₂×C₈×C₅₃	—	2	2	no	—
85	C₂×C₈×C₅₃	C₄²	1	4	yes	complemented
86	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
87	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
88	C₄²×C₅₃	C₄⋊C₄	1	2	yes	—
89	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
90	C₄×Dic₅₃	C₄⋊C₄	1	2	yes	—
91	C₄×Dic₅₃	C₄⋊C₄	1	2	yes	—
92	C₄×Dic₅₃	C₄⋊C₄	1	2	yes	—
93	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
94	C₄×Dic₅₃	C₂×Q₈	1	2	yes	—
95	C₄×Dic₅₃	C₂×Q₈	1	2	yes	—
96	C₂×#88322	—	2	2	no	—
97	C₂×#88322	C₄²	1	4	yes	complemented
98	C₂×#88322	C₂²×C₄	1	2	yes	—
99	C₂×#88322	C₂²×C₄	1	2	yes	—
100	C₈×D₅₃	—	2	4	no	—
101	C₈×D₅₃	—	2	4	no	—
102	C₈×D₅₃	C₄²	1	8	yes	complemented
103	C₈×D₅₃	C₂²×C₄	1	8	yes	—
104	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂²×D₅₃	C₄×D₄	1	4	yes	—
107	C₂²×D₅₃	C₂×SD₁₆	1	4	yes	—
108	C₂²×D₅₃	#135	1	4	yes	—
109	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
110	C₂×#6157	—	2	16	no	—
111	C₂×#6157	—	4	8	no	—
112	C₂×#6157	—	4	8	no	—
113	C₂×#6157	—	4	32	no	—
114	C₂×C₄×C₅₃	—	2	2	no	—
115	C₂×C₄×C₅₃	#106	1	4	yes	complemented
116	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
117	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
118	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
120	C₂×C₄×C₅₃	#117	1	2	yes	—
121	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
122	C₂×Dic₅₃	—	2	2	no	—
123	C₂×Dic₅₃	#106	1	4	yes	complemented
124	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
125	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×Dic₅₃	C₄×Q₈	1	4	yes	—
128	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
129	C₄×D₅₃	—	2	4	no	—
130	C₄×D₅₃	—	2	4	no	—
131	C₄×D₅₃	#106	1	8	yes	complemented
132	C₄×D₅₃	C₂×C₄²	1	2	yes	—
133	C₄×D₅₃	#117	1	2	yes	—
134	C₄×D₅₃	C₄×D₄	1	4	yes	—
135	C₄×D₅₃	C₄×Q₈	1	4	yes	—
136	C₄×D₅₃	C₂×SD₁₆	1	8	yes	—
137	C₄×D₅₃	C₂³×C₄	1	2	yes	—
138	C₄×D₅₃	C₂×#41	1	2	yes	—
139	C₈×C₅₃	—	2	2	no	—
140	C₈×C₅₃	C₂×C₄²	1	4	yes	complemented
141	#88322	—	2	2	no	—
142	#88322	C₂×C₄²	1	4	yes	complemented
143	C₂×C₄×#106	—	53	1	no	maximal, Sylow
144	C₂²×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
145	C₂²×C₅₃	C₂×#106	1	2	yes	—
146	C₂²×C₅₃	#427	1	2	yes	—
147	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
148	C₂×D₅₃	C₄×C₄⋊C₄	1	2	yes	—
149	C₂×D₅₃	C₂×#106	1	2	yes	—
150	C₂×D₅₃	#427	1	2	yes	—
151	C₂×D₅₃	C₄×SD₁₆	1	16	yes	—
152	C₂×D₅₃	C₂×C₄×D₄	1	2	yes	—
153	C₂×D₅₃	C₂²×SD₁₆	1	2	yes	—
154	C₂×D₅₃	C₂×#135	1	2	yes	—
155	#6157	—	4	16	no	—
156	C₄×C₅₃	—	2	2	no	—
157	C₄×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
158	C₄×C₅₃	C₂×#106	1	4	yes	complemented
159	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
160	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
161	Dic₅₃	—	2	2	no	—
162	Dic₅₃	C₄×C₄⋊C₄	1	2	yes	—
163	Dic₅₃	C₂×#106	1	4	yes	complemented
164	Dic₅₃	C₂×C₄×Q₈	1	2	yes	—
165	C₂²×#106	—	53	2	no	—
166	C₂²×C₄×C₈	—	53	1	no	—
167	C₂×C₄×C₄⋊C₄	—	53	2	no	—
168	C₄×#106	—	53	8	no	—
169	C₂×#340	—	53	2	no	—
170	C₂×C₅₃	C₄×#106	1	4	yes	complemented
171	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₅₃	C₂²×#106	1	1	yes	characteristic
173	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
174	D₅₃	C₄×#106	1	4	yes	complemented
175	D₅₃	C₂×C₄×SD₁₆	1	4	yes	—
176	C₂³×C₈	—	53	1	no	—
177	C₂³×C₈	—	53	1	no	—
178	C₂²×C₄⋊C₄	—	53	4	no	—
179	C₂²×C₄²	—	53	1	no	—
180	C₂²×C₄²	—	106	2	no	—
181	C₂×#106	—	53	16	no	—
182	C₂×#106	—	53	8	no	—
183	C₂×C₄×C₈	—	53	1	no	—
184	C₂×C₄×C₈	—	53	1	no	—
185	C₂×C₄×C₈	—	53	1	no	—
186	C₂×C₄×C₈	—	53	4	no	—
187	C₂×C₄×C₈	—	53	4	no	—
188	C₂×C₄×C₈	#6157	1	1	yes	characteristic, complemented
189	C₄×C₄⋊C₄	—	53	8	no	—
190	C₄×C₄⋊C₄	—	106	4	no	—
191	C₂×#95	—	106	2	no	—
192	#340	—	53	8	no	—
193	C₅₃	C₂×C₄×#106	1	1	yes	characteristic, complemented, Sylow
194	C₂³×C₄	—	53	1	no	—
195	C₂³×C₄	—	53	1	no	—
196	C₂³×C₄	—	53	1	no	—
197	C₂³×C₄	—	106	4	no	—
198	C₂²×C₈	—	53	1	no	—
199	C₂²×C₈	—	53	8	no	—
200	C₂²×C₈	—	53	2	no	—
201	C₂²×C₈	—	53	2	no	—
202	C₂²×C₈	—	53	1	no	—
203	C₂²×C₈	—	53	2	no	—
204	C₂²×C₈	—	53	2	no	—
205	C₂²×C₈	—	106	4	no	—
206	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
207	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
208	C₂×C₄⋊C₄	—	53	8	no	—
209	C₂×C₄⋊C₄	—	53	16	no	—
210	C₂×C₄⋊C₄	—	106	4	no	—
211	C₂×C₄⋊C₄	—	106	8	no	—
212	C₂×C₄²	—	53	1	no	—
213	C₂×C₄²	—	53	1	no	—
214	C₂×C₄²	—	53	1	no	—
215	C₂×C₄²	—	53	2	no	—
216	C₂×C₄²	—	53	2	no	—
217	C₂×C₄²	—	53	2	no	—
218	C₂×C₄²	—	53	2	no	—
219	C₂×C₄²	—	106	8	no	—
220	C₂×C₄²	—	212	8	no	—
221	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
222	#106	—	53	32	no	—
223	C₄×C₈	—	53	4	no	—
224	C₄×C₈	—	53	4	no	—
225	C₄×C₈	—	53	4	no	—
226	C₄×C₈	C₂×#6157	1	4	yes	complemented
227	#95	—	106	8	no	—
228	C₂⁴	—	53	1	no	—
229	C₂²×C₄	—	53	1	no	—
230	C₂²×C₄	—	53	1	no	—
231	C₂²×C₄	—	53	8	no	—
232	C₂²×C₄	—	53	4	no	—
233	C₂²×C₄	—	53	2	no	—
234	C₂²×C₄	—	53	2	no	—
235	C₂²×C₄	—	53	1	no	—
236	C₂²×C₄	—	53	1	no	—
237	C₂²×C₄	—	53	4	no	—
238	C₂²×C₄	—	53	1	no	—
239	C₂²×C₄	—	53	1	no	—
240	C₂²×C₄	—	53	1	no	—
241	C₂²×C₄	—	53	2	no	—
242	C₂²×C₄	—	53	2	no	—
243	C₂²×C₄	—	106	4	no	—
244	C₂²×C₄	—	106	8	no	—
245	C₂²×C₄	—	106	16	no	—
246	C₂²×C₄	—	212	8	no	—
247	C₂²×C₄	—	212	8	no	—
248	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
249	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
250	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	53	4	no	—
253	C₂×C₈	—	53	2	no	—
254	C₂×C₈	—	53	8	no	—
255	C₂×C₈	—	53	8	no	—
256	C₂×C₈	—	53	2	no	—
257	C₂×C₈	—	106	4	no	—
258	C₂×C₈	—	106	4	no	—
259	C₂×C₈	—	106	2	no	—
260	C₂×C₈	C₄×#6157	1	4	yes	complemented
261	C₂×C₈	C₂²×#6157	1	2	yes	—
262	C₂×C₈	C₂²×#6157	1	2	yes	—
263	C₄⋊C₄	—	53	16	no	—
264	C₄⋊C₄	—	106	16	no	—
265	C₄⋊C₄	—	106	8	no	—
266	C₄²	—	53	2	no	—
267	C₄²	—	53	2	no	—
268	C₄²	—	53	2	no	—
269	C₄²	—	53	2	no	—
270	C₄²	—	53	2	no	—
271	C₄²	—	53	2	no	—
272	C₄²	—	212	16	no	—
273	C₄²	C₄⋊#6157	1	2	yes	—
274	C₄²	C₂²×#6157	1	2	yes	—
275	C₂³	—	53	4	no	—
276	C₂³	—	53	4	no	—
277	C₂³	—	53	4	no	—
278	C₂³	—	53	1	no	—
279	C₂³	—	53	1	no	—
280	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	53	4	no	—
283	C₂×C₄	—	53	4	no	—
284	C₂×C₄	—	53	2	no	—
285	C₂×C₄	—	53	1	no	—
286	C₂×C₄	—	53	1	no	—
287	C₂×C₄	—	53	4	no	—
288	C₂×C₄	—	53	4	no	—
289	C₂×C₄	—	53	8	no	—
290	C₂×C₄	—	53	8	no	—
291	C₂×C₄	—	53	2	no	—
292	C₂×C₄	—	53	2	no	—
293	C₂×C₄	—	53	2	no	—
294	C₂×C₄	—	53	2	no	—
295	C₂×C₄	—	53	2	no	—
296	C₂×C₄	—	106	4	no	—
297	C₂×C₄	—	106	4	no	—
298	C₂×C₄	—	106	2	no	—
299	C₂×C₄	—	106	16	no	—
300	C₂×C₄	—	212	8	no	—
301	C₂×C₄	—	212	8	no	—
302	C₂×C₄	—	212	32	no	—
303	C₂×C₄	#13133285	1	4	yes	direct product factor
304	C₂×C₄	C₂×C₄×#6157	1	2	yes	—
305	C₂×C₄	C₂×C₄⋊#6157	1	2	yes	—
306	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
307	C₂×C₄	C₂×C₄⋊#6157	1	2	yes	—
308	C₂×C₄	#13133296	1	2	yes	—
309	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
310	C₈	—	2	2	no	—
311	C₈	—	53	4	no	—
312	C₈	—	106	2	no	—
313	C₈	C₂×C₄×#6157	1	4	yes	complemented
314	C₂²	—	53	2	no	—
315	C₂²	—	53	2	no	—
316	C₂²	—	53	2	no	—
317	C₂²	—	53	2	no	—
318	C₂²	—	53	2	no	—
319	C₂²	—	53	2	no	—
320	C₂²	—	53	16	no	—
321	C₂²	C₄×C₄⋊#6157	1	2	yes	—
322	C₂²	C₂×#13133285	1	2	yes	—
323	C₂²	#16811633	1	2	yes	—
324	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
325	C₄	—	2	2	no	—
326	C₄	—	53	4	no	—
327	C₄	—	53	2	no	—
328	C₄	—	53	2	no	—
329	C₄	—	106	2	no	—
330	C₄	—	212	16	no	—
331	C₄	C₄×C₄⋊#6157	1	2	yes	—
332	C₄	C₂×#13133285	1	4	yes	direct product factor
333	C₄	C₂²×C₄×#6157	1	1	yes	characteristic
334	C₄	C₂×#13133296	1	1	yes	characteristic
335	C₂	—	53	4	no	—
336	C₂	—	53	4	no	—
337	C₂	C₄×#13133285	1	4	yes	direct product factor
338	C₂	C₂×C₄×C₄⋊#6157	1	1	yes	characteristic
339	C₂	C₂²×#13133285	1	1	yes	characteristic
340	C₂	C₂×#16811633	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₄⋊#6157
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×C₄×C₈×C₅₃	C₄
socle	C₂³×C₅₃	C₂×C₄⋊C₄
prime radical	C₂³×D₅₃	C₂×D₄
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	C₂×C₄×C₈	#6157
hypocenter	C₅₃	C₂×C₄×#106
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₄×#13133285	C₂	direct (N × H)
8. C₂×#13133285	C₄	direct (N × H)
17. C₂×C₄×#88322	C₄	semidirect
18. C₂×C₈×Dic₅₃	C₄	semidirect
19. C₂×C₈×Dic₅₃	C₄	semidirect
20. C₄×C₈×D₅₃	C₄	semidirect
22. C₂×C₄×C₈×C₅₃	C₄	semidirect
30. #13133285	C₂×C₄	direct (N × H)
50. C₄×#88322	C₂×C₄	semidirect
51. C₈×Dic₅₃	C₂×C₄	semidirect
52. C₈×Dic₅₃	C₂×C₄	semidirect
56. C₄×C₈×C₅₃	C₂×C₄	semidirect
85. C₂×C₈×C₅₃	C₄²	semidirect
97. C₂×#88322	C₄²	semidirect
102. C₈×D₅₃	C₄²	semidirect
115. C₂×C₄×C₅₃	#106	semidirect
123. C₂×Dic₅₃	#106	semidirect
131. C₄×D₅₃	#106	semidirect
140. C₈×C₅₃	C₂×C₄²	semidirect
142. #88322	C₂×C₄²	semidirect
158. C₄×C₅₃	C₂×#106	semidirect
163. Dic₅₃	C₂×#106	semidirect
170. C₂×C₅₃	C₄×#106	semidirect
174. D₅₃	C₄×#106	semidirect
188. C₂×C₄×C₈	#6157	semidirect
193. C₅₃	C₂×C₄×#106	semidirect
226. C₄×C₈	C₂×#6157	semidirect
260. C₂×C₈	C₄×#6157	semidirect
303. C₂×C₄	#13133285	direct (N × H)
313. C₈	C₂×C₄×#6157	semidirect
332. C₄	C₂×#13133285	direct (N × H)
337. C₂	C₄×#13133285	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×#13133285	2
C₂×C₄×C₄⋊#6157	2
C₄×#13133285	2
C₂×#16811497	2
C₂×C₄×C₈×D₅₃	2
C₂×C₄×#106	53

Subgroups — C2×C4×#13133285 #28318361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#13133285 #28318361