Subgroups — C₂×#20243015 #26203997

Order 12032.

1030 conjugacy classes of subgroups.

The subgroup lattice has 404 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×#15689499	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689471	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15689470	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243015	C₂	1	8	yes	maximal, direct product factor
7	C₂×#15688845	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625335	—	2	2	no	—
10	C₂²×#10625334	—	2	2	no	—
11	C₂×#13094024	C₂²	1	1	yes	characteristic
12	C₂×#13094021	C₂²	1	1	yes	characteristic
13	#15689519	—	2	2	no	—
14	#15689519	C₂²	1	4	yes	complemented
15	#15689499	—	2	2	no	—
16	#15689499	C₂²	1	4	yes	—
17	#15689495	—	2	2	no	—
18	#15689495	C₂²	1	4	yes	complemented
19	#15689471	—	2	2	no	—
20	#15689471	C₂²	1	4	yes	complemented
21	#15689470	—	2	2	no	—
22	#15689470	C₂²	1	4	yes	complemented
23	C₂×#13093955	—	2	2	no	—
24	C₂×#13093946	—	2	2	no	—
25	C₂×#13093944	—	2	2	no	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	#15688845	C₂²	1	4	yes	complemented
29	C₂²×SD₁₆×C₄₇	—	2	2	no	—
30	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#492	—	2	2	no	—
33	C₄₇×#492	C₂²	1	4	yes	complemented
34	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×Dic₉₄	—	2	1	no	—
36	C₂²×D₁₈₈	—	2	1	no	—
37	C₂²×D₁₈₈	—	2	1	no	—
38	C₂²×D₁₈₈	—	2	1	no	—
39	C₂×#10625335	—	2	8	no	—
40	C₂×#10625335	—	4	8	no	—
41	C₂×#10625334	—	2	8	no	—
42	C₂×#10625334	—	4	8	no	—
43	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
44	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
45	#13094024	—	2	1	no	—
46	#13094024	—	2	1	no	—
47	#13094024	—	2	1	no	—
48	#13094024	C₂³	1	2	yes	—
49	#13094021	—	2	1	no	—
50	#13094021	—	2	1	no	—
51	#13094021	—	2	1	no	—
52	#13094021	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	—	2	1	no	—
55	#13093955	—	2	8	no	—
56	#13093946	—	2	8	no	—
57	#13093944	—	2	8	no	—
58	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
59	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
60	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
61	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
62	C₂²×Q₈×C₄₇	—	2	1	no	—
63	C₂²×D₄×C₄₇	—	2	1	no	—
64	C₂²×D₄×C₄₇	—	2	1	no	—
65	C₂²×D₄×C₄₇	—	2	1	no	—
66	C₂×SD₁₆×C₄₇	—	2	8	no	—
67	C₂×SD₁₆×C₄₇	—	4	8	no	—
68	C₂²×C₈×C₄₇	D₄	1	2	yes	—
69	C₄⋊Q₈×C₄₇	—	2	1	no	—
70	C₄⋊Q₈×C₄₇	—	2	1	no	—
71	C₄⋊Q₈×C₄₇	—	2	1	no	—
72	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
73	#127×C₄₇	—	2	1	no	—
74	#127×C₄₇	—	2	1	no	—
75	#127×C₄₇	—	2	1	no	—
76	#127×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₄₇	D₄	1	2	yes	—
81	C₄×C₈×C₄₇	C₂³	1	2	yes	—
82	C₂⁴×C₄₇	—	4	1	no	—
83	C₂³×D₄₇	—	4	1	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	—	4	1	no	—
86	C₂×Q₈×C₄₇	—	4	4	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	4	1	no	—
91	C₂×D₄×C₄₇	—	4	1	no	—
92	C₂×D₄×C₄₇	—	4	1	no	—
93	C₂×D₄×C₄₇	—	4	4	no	—
94	C₂×D₄×C₄₇	—	4	4	no	—
95	C₂×D₄×C₄₇	—	4	4	no	—
96	C₂²×C₄×C₄₇	—	4	1	no	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×Dic₄₇	—	4	1	no	—
101	C₂×D₁₈₈	—	2	2	no	—
102	C₂×D₁₈₈	—	2	2	no	—
103	C₂×D₁₈₈	—	2	2	no	—
104	C₂×D₁₈₈	—	4	4	no	—
105	C₂×D₁₈₈	—	4	4	no	—
106	C₂×D₁₈₈	—	4	4	no	—
107	C₂×D₁₈₈	—	4	1	no	—
108	C₂×D₁₈₈	—	4	1	no	—
109	C₂×D₁₈₈	—	4	1	no	—
110	C₂×Dic₉₄	—	2	2	no	—
111	C₂×Dic₉₄	—	4	4	no	—
112	C₂×Dic₉₄	—	4	1	no	—
113	SD₁₆×C₄₇	—	4	16	no	—
114	C₂×C₈×C₄₇	—	2	4	no	—
115	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	4	1	no	—
119	C₄⋊C₄×C₄₇	—	4	1	no	—
120	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
124	#10625335	—	4	16	no	—
125	#10625334	—	4	16	no	—
126	C₄⋊Dic₄₇	—	2	2	no	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	4	1	no	—
129	C₄⋊Dic₄₇	—	4	1	no	—
130	C₂×C₄₇⋊C₈	—	2	4	no	—
131	C₂×C₄₇⋊C₈	SD₁₆	1	8	yes	complemented
132	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
133	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	—	8	2	no	—
136	C₂³×C₄₇	—	8	2	no	—
137	C₂³×C₄₇	—	8	2	no	—
138	C₂³×C₄₇	#127	1	1	yes	characteristic
139	C₂²×D₄₇	—	4	2	no	—
140	C₂²×D₄₇	—	8	2	no	—
141	C₂²×D₄₇	—	8	2	no	—
142	C₂²×D₄₇	—	8	2	no	—
143	Q₈×C₄₇	—	4	4	no	—
144	Q₈×C₄₇	—	8	2	no	—
145	D₄×C₄₇	—	4	4	no	—
146	D₄×C₄₇	—	4	4	no	—
147	D₄×C₄₇	—	4	4	no	—
148	D₄×C₄₇	—	8	2	no	—
149	D₄×C₄₇	—	8	2	no	—
150	D₄×C₄₇	—	8	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	8	2	no	—
153	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
157	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
158	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	8	2	no	—
164	D₁₈₈	—	4	4	no	—
165	D₁₈₈	—	4	4	no	—
166	D₁₈₈	—	4	4	no	—
167	D₁₈₈	—	8	2	no	—
168	D₁₈₈	—	8	2	no	—
169	D₁₈₈	—	8	2	no	—
170	Dic₉₄	—	4	4	no	—
171	Dic₉₄	—	8	2	no	—
172	C₈×C₄₇	—	2	4	no	—
173	C₄₇⋊C₈	—	2	4	no	—
174	C₄₇⋊C₈	C₂×SD₁₆	1	8	yes	complemented
175	C₂×#1715	—	47	1	no	maximal, Sylow
176	C₂²×C₄₇	—	8	2	no	—
177	C₂²×C₄₇	—	8	2	no	—
178	C₂²×C₄₇	—	8	2	no	—
179	C₂²×C₄₇	—	16	4	no	—
180	C₂²×C₄₇	#492	1	2	yes	—
181	C₂²×C₄₇	#496	1	2	yes	—
182	C₂²×C₄₇	#496	1	2	yes	—
183	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
184	C₂×D₄₇	—	8	2	no	—
185	C₂×D₄₇	—	8	2	no	—
186	C₂×D₄₇	—	8	2	no	—
187	C₂×D₄₇	—	16	4	no	—
188	C₄×C₄₇	—	8	2	no	—
189	C₄×C₄₇	#492	1	2	yes	—
190	C₄×C₄₇	#496	1	2	yes	—
191	C₄×C₄₇	#496	1	2	yes	—
192	C₄×C₄₇	C₂²×SD₁₆	1	2	yes	—
193	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
194	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
195	Dic₄₇	—	8	2	no	—
196	C₂×#498	—	47	1	no	—
197	C₂×#493	—	47	1	no	—
198	C₂×#492	—	47	1	no	—
199	C₂×#492	D₄₇	1	1	yes	characteristic, complemented
200	C₂×#486	—	47	1	no	—
201	C₂×#486	—	47	1	no	—
202	#1715	—	47	8	no	—
203	C₂×#322	—	47	1	no	—
204	C₂×C₄₇	—	16	2	no	—
205	C₂×C₄₇	#1715	1	4	yes	complemented
206	C₂×C₄₇	C₂×#492	1	1	yes	characteristic
207	C₂×C₄₇	C₂×#496	1	1	yes	characteristic
208	C₂×C₄₇	C₂×#496	1	1	yes	characteristic
209	D₄₇	—	16	2	no	—
210	C₂²×SD₁₆	—	2	2	no	—
211	C₂²×SD₁₆	—	94	2	no	—
212	C₂²×D₈	—	94	2	no	—
213	C₂×C₄⋊Q₈	—	47	1	no	—
214	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
215	C₂×#127	—	47	1	no	—
216	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
217	#498	—	47	4	no	—
218	#498	—	94	2	no	—
219	#493	—	47	4	no	—
220	#493	—	94	2	no	—
221	#492	—	2	2	no	—
222	#492	—	47	4	no	—
223	#492	—	94	2	no	—
224	#492	C₂×D₄₇	1	4	yes	complemented
225	#486	—	47	4	no	—
226	#486	—	47	4	no	—
227	#486	—	94	2	no	—
228	#486	—	94	2	no	—
229	C₂×#106	—	94	2	no	—
230	C₂×#102	—	94	2	no	—
231	C₂×#102	—	94	2	no	—
232	C₂×C₄×C₈	—	47	1	no	—
233	C₂×C₄×C₈	—	47	1	no	—
234	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
235	#322	—	47	4	no	—
236	C₄₇	C₂×#1715	1	1	yes	characteristic, complemented, Sylow
237	C₂²×Q₈	—	2	1	no	—
238	C₂²×Q₈	—	94	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	94	1	no	—
243	C₂²×D₄	—	94	1	no	—
244	C₂²×D₄	—	94	1	no	—
245	C₂×SD₁₆	—	2	8	no	—
246	C₂×SD₁₆	—	4	8	no	—
247	C₂×SD₁₆	—	94	8	no	—
248	C₂×SD₁₆	—	188	8	no	—
249	C₂×D₈	—	94	8	no	—
250	C₂×D₈	—	188	8	no	—
251	C₂²×C₈	—	47	2	no	—
252	C₂²×C₈	—	47	2	no	—
253	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	47	2	no	—
258	C₄⋊Q₈	—	94	1	no	—
259	C₄⋊Q₈	—	94	1	no	—
260	C₄⋊Q₈	—	94	1	no	—
261	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#127	—	2	1	no	—
265	#127	—	47	2	no	—
266	#127	—	94	1	no	—
267	#127	—	94	1	no	—
268	#127	—	94	1	no	—
269	#127	C₂²×D₄₇	1	2	yes	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	94	1	no	—
273	C₂×C₄⋊C₄	—	94	1	no	—
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	#106	—	94	8	no	—
276	#102	—	94	8	no	—
277	#102	—	94	8	no	—
278	C₄×C₈	—	47	2	no	—
279	C₄×C₈	—	47	2	no	—
280	C₄×C₈	—	47	2	no	—
281	C₄×C₈	—	47	2	no	—
282	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
283	C₄×C₈	C₂²×D₄₇	1	2	yes	—
284	C₂⁴	—	4	1	no	—
285	C₂⁴	—	188	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	94	2	no	—
290	C₂×Q₈	—	188	4	no	—
291	C₂×Q₈	—	188	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	4	no	—
299	C₂×D₄	—	4	4	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	94	2	no	—
302	C₂×D₄	—	94	2	no	—
303	C₂×D₄	—	94	2	no	—
304	C₂×D₄	—	188	1	no	—
305	C₂×D₄	—	188	1	no	—
306	C₂×D₄	—	188	1	no	—
307	C₂×D₄	—	188	4	no	—
308	C₂×D₄	—	188	4	no	—
309	C₂×D₄	—	188	4	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	188	1	no	—
312	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
313	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
315	SD₁₆	—	4	16	no	—
316	SD₁₆	—	188	16	no	—
317	D₈	—	188	16	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	47	8	no	—
320	C₂×C₈	—	47	4	no	—
321	C₂×C₈	—	47	4	no	—
322	C₂×C₈	—	94	4	no	—
323	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	94	2	no	—
329	C₄⋊C₄	—	94	2	no	—
330	C₄⋊C₄	—	188	1	no	—
331	C₄⋊C₄	—	188	1	no	—
332	C₄²	D₄×D₄₇	1	1	yes	characteristic
333	C₄²	D₄×D₄₇	1	1	yes	characteristic
334	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
335	C₄²	C₂³×D₄₇	1	1	yes	characteristic
336	C₂³	—	4	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	—	376	2	no	—
341	C₂³	—	376	2	no	—
342	C₂³	—	376	2	no	—
343	C₂³	—	188	2	no	—
344	C₂³	#13094020	1	1	yes	characteristic
345	Q₈	—	4	4	no	—
346	Q₈	—	8	2	no	—
347	Q₈	—	376	2	no	—
348	Q₈	—	188	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	376	2	no	—
356	D₄	—	376	2	no	—
357	D₄	—	376	2	no	—
358	D₄	—	188	4	no	—
359	D₄	—	188	4	no	—
360	D₄	—	188	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	376	2	no	—
364	C₂×C₄	—	188	2	no	—
365	C₂×C₄	#13094020	1	1	yes	characteristic
366	C₂×C₄	#13094020	1	1	yes	characteristic
367	C₂×C₄	#13094020	1	1	yes	characteristic
368	C₂×C₄	SD₁₆×D₄₇	1	4	yes	—
369	C₂×C₄	#13094050	1	4	yes	—
370	C₂×C₄	#13094051	1	4	yes	—
371	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
374	C₈	—	2	4	no	—
375	C₈	—	47	8	no	—
376	C₈	—	94	4	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	16	4	no	—
381	C₂²	—	376	2	no	—
382	C₂²	—	376	2	no	—
383	C₂²	—	376	2	no	—
384	C₂²	—	752	4	no	—
385	C₂²	#15689494	1	2	yes	—
386	C₂²	#15689509	1	2	yes	—
387	C₂²	#15689510	1	2	yes	—
388	C₂²	C₂×#13094020	1	1	yes	characteristic
389	C₄	—	8	2	no	—
390	C₄	—	376	2	no	—
391	C₄	#15689494	1	2	yes	—
392	C₄	#15689509	1	2	yes	—
393	C₄	#15689510	1	2	yes	—
394	C₄	C₂×SD₁₆×D₄₇	1	2	yes	—
395	C₄	C₂×#13094050	1	2	yes	—
396	C₄	C₂×#13094051	1	2	yes	—
397	C₂	—	16	2	no	—
398	C₂	—	752	2	no	—
399	C₂	#20243015	1	4	yes	direct product factor
400	C₂	C₂×#15689494	1	1	yes	characteristic
401	C₂	C₂×#15689509	1	1	yes	characteristic
402	C₂	C₂×#15689510	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#492	C₂
socle	C₂³×C₄₇	#127
prime radical	C₂×#15689499	C₂
hypercenter	C₂×#492	D₄₇
hypocenter	C₄₇	C₂×#1715
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#492

Complements

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

N	H ≅ G/N	type
1. C₂×#15689519	C₂	semidirect
3. C₂×#15689495	C₂	semidirect
4. C₂×#15689471	C₂	semidirect
5. C₂×#15689470	C₂	semidirect
6. #20243015	C₂	direct (N × H)
7. C₂×#15688845	C₂	semidirect
8. C₂×C₄₇×#492	C₂	semidirect
14. #15689519	C₂²	semidirect
18. #15689495	C₂²	semidirect
20. #15689471	C₂²	semidirect
22. #15689470	C₂²	semidirect
28. #15688845	C₂²	semidirect
33. C₄₇×#492	C₂²	semidirect
131. C₂×C₄₇⋊C₈	SD₁₆	semidirect
174. C₄₇⋊C₈	C₂×SD₁₆	semidirect
199. C₂×#492	D₄₇	semidirect
205. C₂×C₄₇	#1715	semidirect
224. #492	C₂×D₄₇	semidirect
236. C₄₇	C₂×#1715	semidirect
399. C₂	#20243015	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×#15689499	2
C₂×#15689495	2
C₂×#15689471	2
C₂×#15689470	2
#20243015	2
C₂×#15688845	2
C₂×C₄₇×#492	2
C₂×#1715	47

Subgroups — C2×#20243015 #26203997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243015 #26203997