Subgroups — C₂×#20276843 #27538659

Order 13568.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133161	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16811040	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16810898	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276843	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16810452	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16810438	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16810436	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#472	C₂	1	1	yes	maximal, characteristic
9	C₂×#13133247	—	2	1	no	—
10	C₂²×Dic₂₁₂	C₂²	1	1	yes	characteristic
11	C₂×#13133161	—	2	1	no	—
12	C₂×#13133161	—	2	1	no	—
13	C₂×#13133161	—	2	2	no	—
14	C₂×#13133161	C₂²	1	4	yes	complemented
15	#16811040	—	2	2	no	—
16	#16811040	C₂²	1	4	yes	complemented
17	C₂×#13133157	—	2	1	no	—
18	C₂×#13133157	C₂²	1	1	yes	characteristic
19	C₂²×#11719908	—	2	1	no	—
20	C₂²×#11719908	C₂²	1	1	yes	characteristic
21	#16810898	—	2	2	no	—
22	#16810898	C₂²	1	4	yes	complemented
23	C₂×#13133153	C₂²	1	1	yes	characteristic
24	C₂×#13133135	—	2	1	no	—
25	#16810452	C₂²	1	4	yes	complemented
26	#16810438	C₂²	1	4	yes	complemented
27	#16810436	C₂²	1	4	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₅₃	—	2	1	no	—
29	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
31	C₅₃×#472	—	2	2	no	—
32	C₅₃×#472	C₂²	1	4	yes	—
33	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#100×C₅₃	—	2	1	no	—
35	C₂²×Dic₁₀₆	—	2	1	no	—
36	#13133247	—	2	4	no	—
37	#13133247	—	4	2	no	—
38	C₂×Dic₂₁₂	—	2	1	no	—
39	C₂×Dic₂₁₂	—	2	1	no	—
40	C₂×Dic₂₁₂	—	2	1	no	—
41	C₂×Dic₂₁₂	—	2	1	no	—
42	C₂×Dic₂₁₂	—	2	1	no	—
43	C₂×Dic₂₁₂	C₂³	1	2	yes	—
44	C₂×#11719925	—	4	1	no	—
45	C₂×#11719923	—	4	1	no	—
46	C₂×#11719917	—	2	1	no	—
47	#13133161	—	2	4	no	—
48	#13133161	—	2	4	no	—
49	#13133157	—	2	1	no	—
50	#13133157	—	2	4	no	—
51	#13133157	C₂³	1	2	yes	—
52	C₂×#11719908	—	2	1	no	—
53	C₂×#11719908	—	2	4	no	—
54	C₂×#11719908	D₄	1	1	yes	characteristic
55	C₂×#11719908	D₄	1	1	yes	characteristic
56	C₂×#11719908	D₄	1	2	yes	—
57	C₂×#11719908	C₂³	1	2	yes	—
58	#13133153	—	2	1	no	—
59	#13133153	C₂³	1	2	yes	—
60	#13133135	—	2	4	no	—
61	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₅₃	—	2	1	no	—
63	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
64	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
65	C₂×SD₁₆×C₅₃	—	4	1	no	—
66	C₂×D₈×C₅₃	—	2	1	no	—
67	C₂×D₈×C₅₃	—	2	1	no	—
68	C₂×D₈×C₅₃	—	2	1	no	—
69	C₂×D₈×C₅₃	—	2	1	no	—
70	C₂×D₈×C₅₃	—	2	1	no	—
71	C₂×D₈×C₅₃	—	4	1	no	—
72	C₂×D₈×C₅₃	C₂³	1	2	yes	—
73	#131×C₅₃	—	2	1	no	—
74	#131×C₅₃	—	2	1	no	—
75	#131×C₅₃	D₄	1	2	yes	—
76	#131×C₅₃	C₂³	1	2	yes	—
77	C₂×M₁₆×C₅₃	—	2	1	no	—
78	C₂×M₁₆×C₅₃	—	2	1	no	—
79	C₂×M₁₆×C₅₃	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₅₃	—	2	1	no	—
81	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
82	#108×C₅₃	—	2	1	no	—
83	#108×C₅₃	C₂³	1	2	yes	—
84	#100×C₅₃	—	2	4	no	—
85	C₂⁴×C₅₃	—	4	1	no	—
86	#41×C₅₃	—	2	1	no	—
87	#41×C₅₃	—	2	1	no	—
88	#41×C₅₃	D₈	1	2	yes	—
89	#41×C₅₃	C₂×D₄	1	2	yes	—
90	C₂×Q₈×C₅₃	D₈	1	1	yes	characteristic
91	C₂×D₄×C₅₃	—	2	1	no	—
92	C₂×D₄×C₅₃	—	2	2	no	—
93	C₂×D₄×C₅₃	—	4	1	no	—
94	C₂×D₄×C₅₃	—	4	1	no	—
95	C₂×D₄×C₅₃	—	4	1	no	—
96	C₂×D₄×C₅₃	—	4	1	no	—
97	C₂×D₄×C₅₃	—	4	1	no	—
98	C₂×D₄×C₅₃	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₅₃	—	2	1	no	—
100	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₅₃	—	4	1	no	—
102	C₂×Dic₁₀₆	—	2	2	no	—
103	C₂×Dic₁₀₆	—	4	1	no	—
104	C₂×Dic₁₀₆	—	4	1	no	—
105	C₂×Dic₁₀₆	—	4	1	no	—
106	C₂×Dic₁₀₆	—	4	1	no	—
107	C₂×Dic₁₀₆	—	4	1	no	—
108	SD₁₆×C₅₃	—	4	4	no	—
109	D₈×C₅₃	—	2	2	no	—
110	D₈×C₅₃	—	2	2	no	—
111	D₈×C₅₃	—	4	4	no	—
112	D₈×C₅₃	—	4	1	no	—
113	D₈×C₅₃	—	4	1	no	—
114	M₁₆×C₅₃	—	2	1	no	—
115	M₁₆×C₅₃	—	2	2	no	—
116	M₁₆×C₅₃	—	2	2	no	—
117	M₁₆×C₅₃	—	2	2	no	—
118	M₁₆×C₅₃	—	4	1	no	—
119	M₁₆×C₅₃	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₅₃	—	2	1	no	—
121	C₂×C₈×C₅₃	—	2	2	no	—
122	C₂×C₈×C₅₃	—	2	2	no	—
123	C₂×C₈×C₅₃	—	4	1	no	—
124	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
128	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
129	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
130	#11719925	—	4	4	no	—
131	#11719923	—	4	4	no	—
132	#11719917	—	2	2	no	—
133	#11719917	—	4	1	no	—
134	C₂×#88322	—	4	1	no	—
135	Dic₂₁₂	—	2	2	no	—
136	Dic₂₁₂	—	2	2	no	—
137	Dic₂₁₂	—	4	1	no	—
138	Dic₂₁₂	—	4	1	no	—
139	#11719908	—	2	2	no	—
140	#11719908	C₂×D₄	1	2	yes	—
141	#11719908	C₂×D₄	1	2	yes	—
142	C₂³×C₅₃	—	2	1	no	—
143	C₂³×C₅₃	—	4	2	no	—
144	C₂³×C₅₃	—	8	1	no	—
145	C₂³×C₅₃	—	8	1	no	—
146	C₂³×C₅₃	—	16	2	no	—
147	C₂³×C₅₃	#135	1	1	yes	characteristic
148	Q₈×C₅₃	—	2	1	no	—
149	Q₈×C₅₃	C₂×D₈	1	2	yes	—
150	D₄×C₅₃	—	2	2	no	—
151	D₄×C₅₃	—	2	2	no	—
152	D₄×C₅₃	—	2	1	no	—
153	D₄×C₅₃	—	4	2	no	—
154	D₄×C₅₃	—	4	2	no	—
155	D₄×C₅₃	—	8	1	no	—
156	D₄×C₅₃	—	8	1	no	—
157	D₄×C₅₃	C₂×D₈	1	2	yes	—
158	C₂×C₄×C₅₃	—	2	1	no	—
159	C₂×C₄×C₅₃	—	2	2	no	—
160	C₂×C₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×Dic₅₃	—	4	2	no	—
168	C₂×Dic₅₃	—	8	1	no	—
169	C₂×Dic₅₃	—	8	1	no	—
170	Dic₁₀₆	—	4	2	no	—
171	Dic₁₀₆	—	4	2	no	—
172	Dic₁₀₆	—	8	1	no	—
173	Dic₁₀₆	—	8	1	no	—
174	C₈×C₅₃	—	2	2	no	—
175	C₈×C₅₃	—	4	2	no	—
176	C₈×C₅₃	#121	1	1	yes	characteristic
177	C₈×C₅₃	#121	1	1	yes	characteristic
178	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
179	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
180	#88322	—	4	2	no	—
181	C₂×#2223	—	53	1	no	maximal, Sylow
182	C₂²×C₅₃	—	2	2	no	—
183	C₂²×C₅₃	—	2	2	no	—
184	C₂²×C₅₃	—	4	2	no	—
185	C₂²×C₅₃	—	8	2	no	—
186	C₂²×C₅₃	—	16	2	no	—
187	C₂²×C₅₃	—	16	2	no	—
188	C₂²×C₅₃	—	16	2	no	—
189	C₂²×C₅₃	#466	1	1	yes	characteristic
190	C₂²×C₅₃	#466	1	1	yes	characteristic
191	C₂²×C₅₃	C₂×#135	1	1	yes	characteristic
192	C₄×C₅₃	—	2	2	no	—
193	C₄×C₅₃	#466	1	1	yes	characteristic
194	C₄×C₅₃	#466	1	1	yes	characteristic
195	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
196	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
197	Dic₅₃	—	8	2	no	—
198	C₂²×SD₃₂	—	53	1	no	—
199	C₂×#504	—	53	1	no	—
200	C₂×#473	—	53	1	no	—
201	C₂×#472	D₅₃	1	1	yes	characteristic
202	#2223	—	53	8	no	—
203	C₂×#368	—	53	1	no	—
204	C₂×#362	—	53	1	no	—
205	C₂×#361	—	53	1	no	—
206	C₂×C₅₃	—	2	1	no	—
207	C₂×C₅₃	—	2	1	no	—
208	C₂×C₅₃	—	4	2	no	—
209	C₂×C₅₃	—	16	2	no	—
210	C₂×C₅₃	#2223	1	2	yes	complemented
211	C₂×C₅₃	C₂×#466	1	1	yes	characteristic
212	C₂×#137	—	106	1	no	—
213	C₂×AGL(1,ℤ/8)	—	2	1	no	—
214	C₂²×Q₁₆	—	53	1	no	—
215	C₂²×D₈	C₂×D₅₃	1	1	yes	characteristic
216	C₂×#131	C₂×D₅₃	1	1	yes	characteristic
217	C₂×SD₃₂	—	53	4	no	—
218	C₂×SD₃₂	—	106	1	no	—
219	C₂×SD₃₂	—	106	1	no	—
220	C₂×SD₃₂	—	106	2	no	—
221	#504	—	53	4	no	—
222	#504	—	106	2	no	—
223	C₂×M₃₂	—	53	1	no	—
224	C₂×M₃₂	—	106	1	no	—
225	C₂²×C₁₆	—	53	1	no	—
226	C₂²×C₁₆	—	106	1	no	—
227	#473	—	53	4	no	—
228	#473	—	106	2	no	—
229	#472	—	2	2	no	—
230	#472	C₂×D₅₃	1	4	yes	—
231	C₂×#108	—	53	1	no	—
232	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
233	C₂×#101	—	106	1	no	—
234	C₂×#100	—	2	1	no	—
235	#368	—	53	4	no	—
236	#362	—	53	4	no	—
237	#361	—	53	4	no	—
238	C₅₃	C₂×#2223	1	1	yes	characteristic, complemented, Sylow
239	C₂×#41	C₂²⋊D₅₃	1	1	yes	characteristic
240	C₂²×Q₈	—	106	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	#137	—	106	4	no	—
243	#137	—	212	2	no	—
244	AGL(1,ℤ/8)	—	2	4	no	—
245	AGL(1,ℤ/8)	—	4	2	no	—
246	C₂×Q₁₆	—	53	2	no	—
247	C₂×Q₁₆	—	106	1	no	—
248	C₂×Q₁₆	—	106	1	no	—
249	C₂×Q₁₆	—	106	1	no	—
250	C₂×Q₁₆	—	106	1	no	—
251	C₂×Q₁₆	—	106	1	no	—
252	C₂×Q₁₆	—	212	1	no	—
253	C₂×SD₁₆	—	4	1	no	—
254	C₂×SD₁₆	—	212	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	—	4	1	no	—
261	C₂×D₈	C₂²×D₅₃	1	2	yes	—
262	#131	—	2	1	no	—
263	#131	—	2	1	no	—
264	#131	C₂²⋊D₅₃	1	2	yes	—
265	#131	C₂²×D₅₃	1	2	yes	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	106	1	no	—
269	C₂×M₁₆	C₂²⋊D₅₃	1	1	yes	characteristic
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
272	SD₃₂	—	106	4	no	—
273	SD₃₂	—	106	4	no	—
274	M₃₂	—	53	2	no	—
275	M₃₂	—	106	4	no	—
276	M₃₂	—	106	1	no	—
277	C₂×C₁₆	—	53	1	no	—
278	C₂×C₁₆	—	53	1	no	—
279	C₂×C₁₆	—	53	2	no	—
280	C₂×C₁₆	—	53	2	no	—
281	C₂×C₁₆	—	106	4	no	—
282	C₂×C₁₆	—	106	1	no	—
283	#108	—	2	1	no	—
284	#108	—	53	2	no	—
285	#108	—	106	1	no	—
286	#108	C₂²×D₅₃	1	2	yes	—
287	#101	—	106	4	no	—
288	#100	—	2	4	no	—
289	C₂⁴	—	4	1	no	—
290	#41	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	#11719922	1	2	yes	—
293	#41	C₂×C₂²⋊D₅₃	1	2	yes	—
294	C₂×Q₈	—	106	2	no	—
295	C₂×Q₈	—	212	1	no	—
296	C₂×Q₈	—	212	1	no	—
297	C₂×Q₈	—	212	1	no	—
298	C₂×Q₈	—	212	1	no	—
299	C₂×Q₈	—	212	1	no	—
300	C₂×Q₈	#11719922	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	#11719922	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	212	1	no	—
311	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
312	Q₁₆	—	106	2	no	—
313	Q₁₆	—	106	2	no	—
314	Q₁₆	—	212	4	no	—
315	Q₁₆	—	212	1	no	—
316	Q₁₆	—	212	1	no	—
317	SD₁₆	—	4	4	no	—
318	SD₁₆	—	212	4	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	4	no	—
322	D₈	—	4	1	no	—
323	D₈	—	4	1	no	—
324	M₁₆	—	2	1	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	—	106	2	no	—
330	M₁₆	—	212	1	no	—
331	M₁₆	C₂×C₂²⋊D₅₃	1	2	yes	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	212	1	no	—
337	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
338	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
339	C₂×C₈	#11719947	1	1	yes	characteristic
340	C₂×C₈	#11719947	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
342	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
343	C₁₆	—	53	2	no	—
344	C₁₆	—	53	2	no	—
345	C₁₆	—	106	2	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	16	2	no	—
351	C₂³	#13133237	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	—	424	1	no	—
354	Q₈	—	424	1	no	—
355	Q₈	—	212	2	no	—
356	Q₈	—	212	2	no	—
357	Q₈	C₂×#11719922	1	2	yes	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	1	no	—
364	D₄	—	8	1	no	—
365	D₄	C₂×#11719922	1	2	yes	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	424	1	no	—
370	C₂×C₄	—	424	1	no	—
371	C₂×C₄	—	212	2	no	—
372	C₂×C₄	#13133189	1	1	yes	characteristic
373	C₂×C₄	#13133189	1	1	yes	characteristic
374	C₂×C₄	C₂×#11719922	1	1	yes	characteristic
375	C₂×C₄	C₂×#11719922	1	1	yes	characteristic
376	C₂×C₄	#13133237	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	212	2	no	—
381	C₈	#13133189	1	1	yes	characteristic
382	C₈	#13133189	1	1	yes	characteristic
383	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
384	C₈	C₂×#11719947	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	2	no	—
390	C₂²	—	16	2	no	—
391	C₂²	—	16	2	no	—
392	C₂²	#16810857	1	1	yes	characteristic
393	C₂²	#16810857	1	1	yes	characteristic
394	C₂²	C₂×#13133237	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	424	2	no	—
397	C₄	#16810857	1	1	yes	characteristic
398	C₄	#16810857	1	1	yes	characteristic
399	C₄	C₂×#13133189	1	1	yes	characteristic
400	C₄	C₂²×#11719922	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	4	2	no	—
404	C₂	—	16	2	no	—
405	C₂	#20276843	1	2	yes	direct product factor
406	C₂	C₂×#16810857	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16810857
commutator, cosocle	C₂×C₈×C₅₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₃
Fitting, prime radical	C₂×C₅₃×#472	C₂
socle	C₂²×C₅₃	#466
hypercenter	C₂×#472	D₅₃
hypocenter	C₅₃	C₂×#2223
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ C₂×#472

Complements

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

N	H ≅ G/N	type
1. C₂²×#13133161	C₂	semidirect
2. C₂×#16811040	C₂	semidirect
3. C₂×#16810898	C₂	semidirect
4. #20276843	C₂	direct (N × H)
5. C₂×#16810452	C₂	semidirect
6. C₂×#16810438	C₂	semidirect
7. C₂×#16810436	C₂	semidirect
14. C₂×#13133161	C₂²	semidirect
16. #16811040	C₂²	semidirect
22. #16810898	C₂²	semidirect
25. #16810452	C₂²	semidirect
26. #16810438	C₂²	semidirect
27. #16810436	C₂²	semidirect
210. C₂×C₅₃	#2223	semidirect
238. C₅₃	C₂×#2223	semidirect
405. C₂	#20276843	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×#13133161	2
C₂×#16811040	2
C₂×#16810898	2
#20276843	2
C₂×#16810452	2
C₂×#16810438	2
C₂×#16810436	2
C₂×C₅₃×#472	2
C₂×#2223	53

Subgroups — C2×#20276843 #27538659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20276843 #27538659