Subgroups — C₂×#20242766 #26198530

Order 12032.

758 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689410	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689329	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689188	C₂	1	1	yes	maximal, characteristic
5	#20242766	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688868	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#333	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625325	—	2	1	no	—
10	C₂²×C₈×D₄₇	—	2	1	no	—
11	C₂×#13094024	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
13	#15689519	—	2	2	no	—
14	#15689519	C₂²	1	4	yes	complemented
15	#15689410	—	2	2	no	—
16	#15689410	C₂²	1	4	yes	—
17	#15689329	—	2	2	no	—
18	#15689329	C₂²	1	4	yes	—
19	#15689188	—	2	2	no	—
20	#15689188	C₂²	1	4	yes	—
21	C₂×#13093955	—	2	1	no	—
22	C₂×#13093955	—	2	1	no	—
23	C₂×#13093955	—	2	1	no	—
24	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×#13093949	—	2	1	no	—
26	C₂×#13093944	—	2	1	no	—
27	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	#15688873	C₂²	1	4	yes	complemented
30	#15688868	C₂²	1	4	yes	complemented
31	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#333	C₂²	1	4	yes	complemented
35	C₂²×Dic₉₄	—	2	1	no	—
36	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
37	C₂²×C₄×D₄₇	—	2	1	no	—
38	C₂×#10625325	—	2	4	no	—
39	C₂×#10625325	—	4	4	no	—
40	C₂²×C₄₇⋊C₈	—	2	1	no	—
41	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
43	C₂×C₈×D₄₇	—	2	4	no	—
44	C₂×C₈×D₄₇	—	4	4	no	—
45	#13094024	—	2	1	no	—
46	#13094024	—	2	1	no	—
47	#13094024	—	2	1	no	—
48	#13094024	C₂³	1	2	yes	—
49	C₄×D₁₈₈	—	2	1	no	—
50	C₄×D₁₈₈	—	2	1	no	—
51	C₄×D₁₈₈	D₄	1	2	yes	—
52	C₄×D₁₈₈	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	—	2	1	no	—
55	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
56	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
57	#13093955	—	2	4	no	—
58	#13093955	—	2	4	no	—
59	#13093955	—	2	4	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
62	#13093949	—	2	4	no	—
63	#13093944	—	2	4	no	—
64	(C₂×D₄₇)⋊C₈	—	2	4	no	—
65	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
66	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
67	C₂²×Q₈×C₄₇	—	2	1	no	—
68	C₂²×C₈×C₄₇	—	2	1	no	—
69	C₂²×C₈×C₄₇	—	2	1	no	—
70	C₄⋊Q₈×C₄₇	—	2	1	no	—
71	C₄⋊Q₈×C₄₇	—	2	1	no	—
72	C₄⋊Q₈×C₄₇	—	2	1	no	—
73	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₄₇	—	2	1	no	—
78	C₄⋊C₈×C₄₇	—	2	1	no	—
79	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
80	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
81	C₂³×D₄₇	—	2	1	no	—
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	—	4	1	no	—
84	C₂×Q₈×C₄₇	—	8	2	no	—
85	C₂²×C₄×C₄₇	—	4	1	no	—
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
89	C₂²×Dic₄₇	—	2	1	no	—
90	C₂²×Dic₄₇	—	4	1	no	—
91	C₂×D₁₈₈	—	2	1	no	—
92	C₂×D₁₈₈	—	2	2	no	—
93	C₂×D₁₈₈	SD₁₆	1	4	yes	—
94	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
95	C₂×C₄×D₄₇	—	2	2	no	—
96	C₂×C₄×D₄₇	—	2	2	no	—
97	C₂×C₄×D₄₇	—	4	2	no	—
98	C₂×C₄×D₄₇	—	4	2	no	—
99	C₂×Dic₉₄	—	2	2	no	—
100	C₂×Dic₉₄	—	4	2	no	—
101	C₂×Dic₉₄	—	4	2	no	—
102	C₂×Dic₉₄	—	4	1	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	4	2	no	—
106	C₂×C₈×C₄₇	—	4	2	no	—
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	4	1	no	—
110	C₄⋊C₄×C₄₇	—	4	1	no	—
111	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₄₇	#41	1	1	yes	characteristic
114	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
115	(C₂×D₄₇)⋊C₄	—	2	2	no	—
116	(C₂×D₄₇)⋊C₄	—	2	2	no	—
117	C₄⋊Dic₄₇	—	2	1	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	4	1	no	—
121	C₄⋊Dic₄₇	—	4	1	no	—
122	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	4	2	no	—
126	C₂×C₄₇⋊C₈	SD₁₆	1	4	yes	complemented
127	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
128	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
129	#10625325	—	4	8	no	—
130	C₈×D₄₇	—	4	8	no	—
131	C₂³×C₄₇	#121	1	1	yes	characteristic
132	C₂²×D₄₇	—	2	2	no	—
133	C₂²×D₄₇	—	2	4	no	—
134	C₂²×D₄₇	—	4	2	no	—
135	C₂²×D₄₇	—	4	2	no	—
136	Q₈×C₄₇	—	8	2	no	—
137	Q₈×C₄₇	—	8	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	8	2	no	—
141	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
143	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
145	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
146	C₂×C₄×C₄₇	#135	1	2	yes	—
147	C₂×C₄×C₄₇	#137	1	2	yes	—
148	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	4	2	no	—
153	C₂×Dic₄₇	—	4	2	no	—
154	C₂×Dic₄₇	—	8	2	no	—
155	D₁₈₈	—	2	2	no	—
156	D₁₈₈	—	2	4	no	—
157	D₁₈₈	C₂×SD₁₆	1	4	yes	—
158	C₄×D₄₇	—	4	2	no	—
159	C₄×D₄₇	—	4	2	no	—
160	C₄×D₄₇	—	4	4	no	—
161	Dic₉₄	—	4	2	no	—
162	Dic₉₄	—	4	2	no	—
163	Dic₉₄	—	8	2	no	—
164	C₈×C₄₇	—	4	2	no	—
165	C₈×C₄₇	—	4	2	no	—
166	C₄₇⋊C₈	—	2	2	no	—
167	C₄₇⋊C₈	—	4	2	no	—
168	C₄₇⋊C₈	C₂×SD₁₆	1	4	yes	complemented
169	C₂×#1671	—	47	1	no	maximal, Sylow
170	C₂²×C₄₇	#461	1	2	yes	—
171	C₂²×C₄₇	#465	1	2	yes	—
172	C₂²×C₄₇	#471	1	2	yes	—
173	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
174	C₂×D₄₇	—	2	4	no	—
175	C₂×D₄₇	—	4	8	no	—
176	C₂×D₄₇	—	4	2	no	—
177	C₂×D₄₇	—	4	2	no	—
178	C₄×C₄₇	—	2	1	no	—
179	C₄×C₄₇	—	2	1	no	—
180	C₄×C₄₇	—	8	2	no	—
181	C₄×C₄₇	#461	1	2	yes	—
182	C₄×C₄₇	#465	1	2	yes	—
183	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
184	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
185	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
186	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
187	Dic₄₇	—	4	2	no	—
188	Dic₄₇	—	8	2	no	—
189	C₂×#498	—	47	1	no	—
190	C₂×#476	—	47	1	no	—
191	C₂×#461	—	47	1	no	—
192	C₂×C₈×D₄	—	47	1	no	—
193	#1671	—	47	8	no	—
194	C₂×#334	—	47	1	no	—
195	C₂×#333	D₄₇	1	1	yes	characteristic, complemented
196	C₂×#332	—	47	1	no	—
197	C₂×C₄₇	#1671	1	4	yes	complemented
198	C₂×C₄₇	C₂×#461	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
200	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
201	D₄₇	—	4	4	no	—
202	C₂²×SD₁₆	—	94	1	no	—
203	C₂³×C₈	—	94	1	no	—
204	C₂×C₄⋊Q₈	—	47	1	no	—
205	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
206	C₂×C₄×D₄	—	47	1	no	—
207	#498	—	47	4	no	—
208	#498	—	94	2	no	—
209	#476	—	47	4	no	—
210	#476	—	94	2	no	—
211	#461	—	47	4	no	—
212	#461	—	94	2	no	—
213	C₈×D₄	—	47	4	no	—
214	C₈×D₄	—	94	2	no	—
215	C₂×#106	—	94	1	no	—
216	C₂×#106	—	94	1	no	—
217	C₂×#106	—	94	1	no	—
218	C₂×C₄⋊C₈	—	47	1	no	—
219	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
221	C₂×#103	—	94	1	no	—
222	C₂×#102	—	94	1	no	—
223	C₂×C₂²⋊C₈	—	94	1	no	—
224	C₂×C₄×C₈	—	47	1	no	—
225	#334	—	47	4	no	—
226	#333	C₂×D₄₇	1	4	yes	complemented
227	#332	—	47	4	no	—
228	C₄₇	C₂×#1671	1	1	yes	characteristic, complemented, Sylow
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	—	94	1	no	—
231	C₂²×D₄	—	47	1	no	—
232	C₂³×C₄	—	94	1	no	—
233	C₂×SD₁₆	—	94	4	no	—
234	C₂×SD₁₆	—	188	4	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	47	1	no	—
238	C₂²×C₈	—	47	1	no	—
239	C₂²×C₈	—	94	4	no	—
240	C₂²×C₈	—	94	1	no	—
241	C₂²×C₈	—	188	4	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	47	2	no	—
246	C₄⋊Q₈	—	94	1	no	—
247	C₄⋊Q₈	—	94	1	no	—
248	C₄⋊Q₈	—	94	1	no	—
249	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
250	C₄×D₄	—	47	2	no	—
251	C₄×D₄	—	47	2	no	—
252	C₄×D₄	—	94	1	no	—
253	C₄×D₄	—	94	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	47	1	no	—
257	C₂×C₄⋊C₄	—	94	1	no	—
258	C₂×C₄⋊C₄	—	94	1	no	—
259	C₂×C₂²⋊C₄	—	94	1	no	—
260	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
261	#106	—	94	4	no	—
262	#106	—	94	4	no	—
263	#106	—	94	4	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	47	2	no	—
267	C₄⋊C₈	—	94	1	no	—
268	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
269	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
270	#103	—	94	4	no	—
271	#102	—	94	4	no	—
272	C₂²⋊C₈	—	94	4	no	—
273	C₄×C₈	—	47	2	no	—
274	C₄×C₈	—	47	2	no	—
275	C₂⁴	—	94	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	—	8	2	no	—
279	C₂×Q₈	—	94	2	no	—
280	C₂×Q₈	—	188	2	no	—
281	C₂×Q₈	—	188	2	no	—
282	C₂×Q₈	—	188	1	no	—
283	C₂×D₄	—	47	4	no	—
284	C₂×D₄	—	47	2	no	—
285	C₂×D₄	—	94	1	no	—
286	C₂×D₄	—	94	2	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	94	1	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	—	94	2	no	—
291	C₂²×C₄	—	188	1	no	—
292	C₂²×C₄	—	188	2	no	—
293	C₂²×C₄	—	188	2	no	—
294	C₂²×C₄	#10625350	1	1	yes	characteristic
295	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
296	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
297	SD₁₆	—	188	8	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	47	4	no	—
303	C₂×C₈	—	47	2	no	—
304	C₂×C₈	—	47	2	no	—
305	C₂×C₈	—	94	2	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	188	8	no	—
308	C₂×C₈	—	188	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	47	2	no	—
314	C₄⋊C₄	—	94	1	no	—
315	C₄⋊C₄	—	94	2	no	—
316	C₄⋊C₄	—	94	2	no	—
317	C₄⋊C₄	—	188	1	no	—
318	C₄⋊C₄	—	188	1	no	—
319	C₂²⋊C₄	—	94	2	no	—
320	C₂²⋊C₄	—	94	2	no	—
321	C₄²	#10625350	1	1	yes	characteristic
322	C₄²	D₄×D₄₇	1	1	yes	characteristic
323	C₄²	D₄×D₄₇	1	1	yes	characteristic
324	C₄²	C₂³×D₄₇	1	1	yes	characteristic
325	C₂³	—	94	4	no	—
326	C₂³	—	94	2	no	—
327	C₂³	—	188	2	no	—
328	C₂³	—	188	2	no	—
329	C₂³	#13093997	1	1	yes	characteristic
330	Q₈	—	8	2	no	—
331	Q₈	—	8	2	no	—
332	Q₈	—	376	2	no	—
333	Q₈	—	188	2	no	—
334	Q₈	—	188	2	no	—
335	D₄	—	47	4	no	—
336	D₄	—	94	4	no	—
337	D₄	—	94	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	—	94	2	no	—
342	C₂×C₄	—	376	2	no	—
343	C₂×C₄	—	188	2	no	—
344	C₂×C₄	—	188	2	no	—
345	C₂×C₄	—	188	4	no	—
346	C₂×C₄	—	188	2	no	—
347	C₂×C₄	—	188	2	no	—
348	C₂×C₄	#13093997	1	1	yes	characteristic
349	C₂×C₄	#13093997	1	1	yes	characteristic
350	C₂×C₄	#13093997	1	1	yes	characteristic
351	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
352	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
353	C₂×C₄	#13094047	1	2	yes	—
354	C₂×C₄	#13094056	1	2	yes	—
355	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
358	C₈	—	4	2	no	—
359	C₈	—	4	2	no	—
360	C₈	—	47	4	no	—
361	C₈	—	94	2	no	—
362	C₈	—	188	2	no	—
363	C₂²	—	94	4	no	—
364	C₂²	—	188	8	no	—
365	C₂²	—	188	2	no	—
366	C₂²	—	188	2	no	—
367	C₂²	#15689327	1	2	yes	—
368	C₂²	#15689355	1	2	yes	—
369	C₂²	#15689385	1	2	yes	—
370	C₂²	C₂×#13093997	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	8	2	no	—
374	C₄	—	376	2	no	—
375	C₄	—	188	2	no	—
376	C₄	#15689327	1	2	yes	—
377	C₄	#15689355	1	2	yes	—
378	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
379	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
380	C₄	C₂×#13094047	1	1	yes	characteristic
381	C₄	C₂×#13094056	1	1	yes	characteristic
382	C₂	—	188	4	no	—
383	C₂	#20242766	1	4	yes	direct product factor
384	C₂	C₂×#15689327	1	1	yes	characteristic
385	C₂	C₂×#15689355	1	1	yes	characteristic
386	C₂	C₂×#15689385	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093997
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#333	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×D₁₈₈	D₄
hypercenter	C₂×#333	D₄₇
hypocenter	C₄₇	C₂×#1671
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

Complements

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

N	H ≅ G/N	type
1. C₂×#15689519	C₂	semidirect
5. #20242766	C₂	direct (N × H)
6. C₂×#15688873	C₂	semidirect
7. C₂×#15688868	C₂	semidirect
8. C₂×C₄₇×#333	C₂	semidirect
14. #15689519	C₂²	semidirect
29. #15688873	C₂²	semidirect
30. #15688868	C₂²	semidirect
34. C₄₇×#333	C₂²	semidirect
126. C₂×C₄₇⋊C₈	SD₁₆	semidirect
168. C₄₇⋊C₈	C₂×SD₁₆	semidirect
195. C₂×#333	D₄₇	semidirect
197. C₂×C₄₇	#1671	semidirect
226. #333	C₂×D₄₇	semidirect
228. C₄₇	C₂×#1671	semidirect
383. C₂	#20242766	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×#15689519	2
C₂×#15689410	2
C₂×#15689329	2
C₂×#15689188	2
#20242766	2
C₂×#15688873	2
C₂×#15688868	2
C₂×C₄₇×#333	2
C₂×#1671	47

Subgroups — C2×#20242766 #26198530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242766 #26198530