Subgroups — C₂×#20245287 #26369720

Order 12032.

710 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689245	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689235	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245287	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688936	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688933	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688900	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#509	C₂	1	1	yes	maximal, characteristic
9	C₂×#13094031	—	2	1	no	—
10	C₂×D₄×Dic₄₇	—	2	1	no	—
11	C₂×#13093964	C₂²	1	1	yes	characteristic
12	#15689245	—	2	2	no	—
13	#15689245	C₂²	1	4	yes	complemented
14	#15689235	—	2	2	no	—
15	#15689235	C₂²	1	4	yes	complemented
16	C₂×#13093960	C₂²	1	1	yes	characteristic
17	C₂×#13093956	C₂²	1	1	yes	characteristic
18	C₂×#13093951	—	2	1	no	—
19	C₂×#13093945	—	2	1	no	—
20	C₂×#13093934	C₂²	1	1	yes	characteristic
21	#15688946	C₂²	1	4	yes	complemented
22	#15688936	C₂²	1	4	yes	complemented
23	#15688933	C₂²	1	4	yes	complemented
24	#15688900	C₂²	1	4	yes	complemented
25	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#509	C₄	1	4	yes	complemented
28	C₄₇×#509	C₂²	1	4	yes	—
29	C₂×SD₃₂×C₄₇	C₄	1	2	yes	complemented
30	C₂×D₁₆×C₄₇	C₄	1	2	yes	complemented
31	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
32	C₂³×Dic₄₇	—	4	1	no	—
33	#13094031	—	2	4	no	—
34	#13094031	—	4	2	no	—
35	C₂×#10625329	—	2	1	no	—
36	C₂×#10625329	—	4	1	no	—
37	C₂²×C₄₇⋊C₈	—	4	1	no	—
38	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
39	D₄×Dic₄₇	—	2	4	no	—
40	D₄×Dic₄₇	—	4	2	no	—
41	C₂×C₄⋊Dic₄₇	—	2	1	no	—
42	C₂×C₂²⋊Dic₄₇	—	4	1	no	—
43	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
44	#13093964	—	2	1	no	—
45	#13093964	C₂³	1	2	yes	—
46	C₂×C₄₇⋊C₁₆	—	2	1	no	—
47	#13093960	—	2	1	no	—
48	#13093960	C₂³	1	2	yes	—
49	#13093956	—	2	1	no	—
50	#13093956	C₂³	1	2	yes	—
51	#13093951	—	2	4	no	—
52	#13093945	—	2	4	no	—
53	#13093934	D₄	1	2	yes	—
54	#13093934	C₂³	1	2	yes	—
55	C₂×#41×C₄₇	—	2	1	no	—
56	C₂²×D₄×C₄₇	—	2	1	no	—
57	#135×C₄₇	—	2	1	no	—
58	#135×C₄₇	—	2	1	no	—
59	#135×C₄₇	C₂×C₄	1	2	yes	complemented
60	#135×C₄₇	C₂³	1	2	yes	—
61	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂×SD₁₆×C₄₇	—	2	1	no	—
63	C₂×D₈×C₄₇	—	2	1	no	—
64	C₂×D₈×C₄₇	—	2	1	no	—
65	C₂×D₈×C₄₇	—	2	1	no	—
66	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂×D₈×C₄₇	C₂³	1	2	yes	—
70	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
71	SD₃₂×C₄₇	C₂×C₄	1	8	yes	complemented
72	D₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
73	M₃₂×C₄₇	C₂×C₄	1	2	yes	complemented
74	M₃₂×C₄₇	C₂³	1	2	yes	—
75	C₂×C₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
76	C₂⁴×C₄₇	—	4	1	no	—
77	#41×C₄₇	—	2	2	no	—
78	#41×C₄₇	—	2	2	no	—
79	#41×C₄₇	—	4	1	no	—
80	#41×C₄₇	—	4	1	no	—
81	C₂×Q₈×C₄₇	—	2	1	no	—
82	C₂×D₄×C₄₇	—	2	2	no	—
83	C₂×D₄×C₄₇	—	2	2	no	—
84	C₂×D₄×C₄₇	—	2	1	no	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	4	1	no	—
87	C₂×D₄×C₄₇	—	4	1	no	—
88	C₂×D₄×C₄₇	—	4	1	no	—
89	C₂×D₄×C₄₇	—	4	1	no	—
90	C₂²×C₄×C₄₇	—	4	1	no	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×Dic₄₇	—	2	1	no	—
93	C₂²×Dic₄₇	—	4	4	no	—
94	C₂²×Dic₄₇	—	4	1	no	—
95	C₂²×Dic₄₇	—	8	4	no	—
96	Q₁₆×C₄₇	—	2	1	no	—
97	Q₁₆×C₄₇	C₂²×C₄	1	2	yes	complemented
98	SD₁₆×C₄₇	—	2	2	no	—
99	SD₁₆×C₄₇	—	2	2	no	—
100	D₈×C₄₇	—	2	2	no	—
101	D₈×C₄₇	—	2	2	no	—
102	D₈×C₄₇	—	2	1	no	—
103	D₈×C₄₇	—	2	2	no	—
104	D₈×C₄₇	C₂²×C₄	1	4	yes	—
105	D₈×C₄₇	C₂²×C₄	1	2	yes	complemented
106	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
110	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
111	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
112	C₂²⋊Dic₄₇	—	4	4	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	—	4	1	no	—
115	C₄×Dic₄₇	—	2	1	no	—
116	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
117	#10625329	—	2	2	no	—
118	#10625329	—	4	4	no	—
119	#10625329	—	4	1	no	—
120	C₂×C₄₇⋊C₈	—	2	1	no	—
121	C₂×C₄₇⋊C₈	—	2	1	no	—
122	C₂×C₄₇⋊C₈	—	4	4	no	—
123	C₂×C₄₇⋊C₈	—	4	1	no	—
124	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
125	C₁₆×C₄₇	C₂²×C₄	1	4	yes	complemented
126	C₄₇⋊C₁₆	—	2	2	no	—
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	—	4	1	no	—
129	C₂³×C₄₇	—	4	2	no	—
130	C₂³×C₄₇	—	4	2	no	—
131	C₂³×C₄₇	—	8	2	no	—
132	C₂³×C₄₇	—	8	2	no	—
133	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
134	Q₈×C₄₇	—	2	2	no	—
135	Q₈×C₄₇	—	4	1	no	—
136	D₄×C₄₇	—	2	4	no	—
137	D₄×C₄₇	—	2	2	no	—
138	D₄×C₄₇	—	4	2	no	—
139	D₄×C₄₇	—	4	2	no	—
140	D₄×C₄₇	—	4	2	no	—
141	D₄×C₄₇	—	4	2	no	—
142	D₄×C₄₇	—	4	2	no	—
143	D₄×C₄₇	—	4	1	no	—
144	C₂×C₄×C₄₇	—	4	1	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	4	2	no	—
155	C₂×Dic₄₇	—	4	2	no	—
156	C₂×Dic₄₇	—	8	8	no	—
157	C₂×Dic₄₇	—	8	2	no	—
158	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
159	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
161	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₄₇⋊C₈	—	2	2	no	—
163	C₄₇⋊C₈	—	4	2	no	—
164	C₂×AGL(1,ℤ/16)	—	47	1	no	maximal, Sylow
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	4	2	no	—
167	C₂²×C₄₇	—	4	4	no	—
168	C₂²×C₄₇	—	8	2	no	—
169	C₂²×C₄₇	—	8	2	no	—
170	C₂²×C₄₇	—	8	4	no	—
171	C₂²×C₄₇	—	8	2	no	—
172	C₂²×C₄₇	—	8	4	no	—
173	C₂²×C₄₇	#442	1	1	yes	characteristic
174	C₂²×C₄₇	#442	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₄×C₄₇	—	4	2	no	—
177	C₄×C₄₇	#442	1	1	yes	characteristic
178	C₄×C₄₇	#442	1	1	yes	characteristic
179	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
180	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
181	Dic₄₇	—	4	2	no	—
182	Dic₄₇	—	8	2	no	—
183	C₂×#509	D₄₇	1	1	yes	characteristic
184	C₂×#444	—	47	1	no	—
185	C₂×#442	—	47	1	no	—
186	AGL(1,ℤ/16)	—	47	8	no	—
187	C₂×#365	—	47	1	no	—
188	C₂×#361	—	47	1	no	—
189	C₂×#360	—	47	1	no	—
190	C₂×#347	—	47	1	no	—
191	C₂×C₄₇	—	2	1	no	—
192	C₂×C₄₇	—	2	1	no	—
193	C₂×C₄₇	—	8	2	no	—
194	C₂×C₄₇	—	8	4	no	—
195	C₂×C₄₇	AGL(1,ℤ/16)	1	2	yes	complemented
196	C₂×C₄₇	C₂×#442	1	1	yes	characteristic
197	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
198	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
199	C₂×#131	—	94	1	no	—
200	C₂×C₄×D₄	—	94	1	no	—
201	#509	Dic₄₇	1	4	yes	complemented
202	#509	C₂×D₄₇	1	4	yes	—
203	C₂×SD₃₂	Dic₄₇	1	2	yes	complemented
204	C₂×D₁₆	Dic₄₇	1	2	yes	complemented
205	C₂×M₃₂	—	47	1	no	—
206	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
207	#444	—	47	4	no	—
208	#444	—	94	2	no	—
209	#442	—	47	4	no	—
210	#442	—	94	2	no	—
211	C₂×#108	—	47	1	no	—
212	C₂×#106	—	47	1	no	—
213	C₂×#104	—	94	1	no	—
214	C₂×#102	—	94	1	no	—
215	C₂×#97	—	47	1	no	—
216	#365	—	47	4	no	—
217	#361	—	47	4	no	—
218	#360	—	47	4	no	—
219	#347	—	47	4	no	—
220	C₄₇	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic, complemented, Sylow
221	C₂×#41	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂³×C₄	—	188	1	no	—
224	#135	—	2	1	no	—
225	#135	—	2	1	no	—
226	#135	C₂×Dic₄₇	1	2	yes	complemented
227	#135	C₂²×D₄₇	1	2	yes	—
228	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic, complemented
229	C₂×SD₁₆	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	—	2	1	no	—
233	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
234	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
235	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
236	C₂×D₈	C₂²×D₄₇	1	2	yes	—
237	#131	—	94	4	no	—
238	#131	—	188	2	no	—
239	C₂×M₁₆	—	94	1	no	—
240	C₂×M₁₆	—	188	1	no	—
241	C₂²×C₈	—	47	1	no	—
242	C₂²×C₈	—	188	1	no	—
243	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
244	C₄×D₄	—	94	4	no	—
245	C₄×D₄	—	188	2	no	—
246	C₂×C₄⋊C₄	—	94	1	no	—
247	C₂×C₂²⋊C₄	—	188	1	no	—
248	C₂×C₄²	—	47	1	no	—
249	SD₃₂	C₂×Dic₄₇	1	8	yes	complemented
250	D₁₆	C₂×Dic₄₇	1	8	yes	complemented
251	M₃₂	—	47	2	no	—
252	M₃₂	—	94	1	no	—
253	M₃₂	C₂×Dic₄₇	1	2	yes	complemented
254	M₃₂	C₂²×D₄₇	1	2	yes	—
255	C₂×C₁₆	—	94	1	no	—
256	C₂×C₁₆	C₂×Dic₄₇	1	2	yes	complemented
257	#108	—	47	2	no	—
258	#108	—	94	1	no	—
259	#106	—	47	2	no	—
260	#106	—	94	1	no	—
261	#104	—	94	4	no	—
262	#102	—	94	4	no	—
263	#97	—	47	2	no	—
264	#97	—	47	2	no	—
265	C₂⁴	—	4	1	no	—
266	#41	—	2	2	no	—
267	#41	—	2	2	no	—
268	#41	—	4	1	no	—
269	#41	—	4	1	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	94	1	no	—
281	C₂²×C₄	—	376	4	no	—
282	C₂²×C₄	—	188	4	no	—
283	C₂²×C₄	—	188	1	no	—
284	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
285	Q₁₆	—	2	1	no	—
286	Q₁₆	C₂²×Dic₄₇	1	2	yes	complemented
287	SD₁₆	—	2	2	no	—
288	SD₁₆	—	2	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	2	no	—
291	D₈	—	2	1	no	—
292	D₈	—	2	2	no	—
293	D₈	C₂²×Dic₄₇	1	4	yes	—
294	D₈	C₂²×Dic₄₇	1	2	yes	complemented
295	M₁₆	—	94	2	no	—
296	M₁₆	—	188	4	no	—
297	M₁₆	—	188	1	no	—
298	C₂×C₈	—	47	2	no	—
299	C₂×C₈	—	94	1	no	—
300	C₂×C₈	—	94	1	no	—
301	C₂×C₈	—	188	4	no	—
302	C₂×C₈	—	188	1	no	—
303	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
304	C₂×C₈	#10625352	1	1	yes	characteristic
305	C₂×C₈	#10625352	1	1	yes	characteristic
306	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
307	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
308	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
309	C₄⋊C₄	—	94	2	no	—
310	C₄⋊C₄	—	188	1	no	—
311	C₂²⋊C₄	—	188	4	no	—
312	C₄²	—	47	2	no	—
313	C₄²	—	94	1	no	—
314	C₁₆	—	94	2	no	—
315	C₁₆	C₂²×Dic₄₇	1	4	yes	complemented
316	C₂³	—	4	2	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	8	2	no	—
321	C₂³	—	8	2	no	—
322	C₂³	#13094048	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	4	1	no	—
325	D₄	—	2	4	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	1	no	—
332	D₄	—	4	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	94	2	no	—
337	C₂×C₄	—	376	2	no	—
338	C₂×C₄	—	376	8	no	—
339	C₂×C₄	—	188	2	no	—
340	C₂×C₄	—	188	2	no	—
341	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
342	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
343	C₂×C₄	#13094048	1	1	yes	characteristic
344	C₂×C₄	#13094048	1	1	yes	characteristic
345	C₂×C₄	#13094048	1	1	yes	characteristic
346	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
347	C₈	—	94	2	no	—
348	C₈	—	188	2	no	—
349	C₈	D₄×Dic₄₇	1	1	yes	characteristic
350	C₈	D₄×Dic₄₇	1	1	yes	characteristic
351	C₈	C₂³×Dic₄₇	1	1	yes	characteristic
352	C₈	C₂×#10625352	1	1	yes	characteristic
353	C₂²	—	2	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	4	no	—
359	C₂²	—	8	4	no	—
360	C₂²	—	8	2	no	—
361	C₂²	#15689235	1	1	yes	characteristic
362	C₂²	#15689235	1	1	yes	characteristic
363	C₂²	C₂×#13094048	1	1	yes	characteristic
364	C₄	—	4	2	no	—
365	C₄	—	376	2	no	—
366	C₄	—	188	2	no	—
367	C₄	#15689235	1	1	yes	characteristic
368	C₄	#15689235	1	1	yes	characteristic
369	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
370	C₄	C₂×#13094048	1	1	yes	characteristic
371	C₂	—	2	1	no	—
372	C₂	—	2	1	no	—
373	C₂	—	8	4	no	—
374	C₂	—	8	2	no	—
375	C₂	#20245287	1	2	yes	direct product factor
376	C₂	C₂×#15689235	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689235
commutator	C₈×C₄₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#509	C₂
socle	C₂²×C₄₇	#442
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	C₂×#509	D₄₇
hypocenter	C₄₇	C₂×AGL(1,ℤ/16)
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#509

Complements

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

N	H ≅ G/N	type
1. C₂×#15689245	C₂	semidirect
2. C₂×#15689235	C₂	semidirect
3. #20245287	C₂	direct (N × H)
4. C₂×#15688946	C₂	semidirect
5. C₂×#15688936	C₂	semidirect
6. C₂×#15688933	C₂	semidirect
7. C₂×#15688900	C₂	semidirect
13. #15689245	C₂²	semidirect
15. #15689235	C₂²	semidirect
21. #15688946	C₂²	semidirect
22. #15688936	C₂²	semidirect
23. #15688933	C₂²	semidirect
24. #15688900	C₂²	semidirect
27. C₄₇×#509	C₄	semidirect
29. C₂×SD₃₂×C₄₇	C₄	semidirect
30. C₂×D₁₆×C₄₇	C₄	semidirect
59. #135×C₄₇	C₂×C₄	semidirect
61. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
68. C₂×D₈×C₄₇	C₂×C₄	semidirect
71. SD₃₂×C₄₇	C₂×C₄	semidirect
72. D₁₆×C₄₇	C₂×C₄	semidirect
73. M₃₂×C₄₇	C₂×C₄	semidirect
75. C₂×C₁₆×C₄₇	C₂×C₄	semidirect
97. Q₁₆×C₄₇	C₂²×C₄	semidirect
105. D₈×C₄₇	C₂²×C₄	semidirect
125. C₁₆×C₄₇	C₂²×C₄	semidirect
195. C₂×C₄₇	AGL(1,ℤ/16)	semidirect
201. #509	Dic₄₇	semidirect
203. C₂×SD₃₂	Dic₄₇	semidirect
204. C₂×D₁₆	Dic₄₇	semidirect
220. C₄₇	C₂×AGL(1,ℤ/16)	semidirect
226. #135	C₂×Dic₄₇	semidirect
228. C₂×Q₁₆	C₂×Dic₄₇	semidirect
235. C₂×D₈	C₂×Dic₄₇	semidirect
249. SD₃₂	C₂×Dic₄₇	semidirect
250. D₁₆	C₂×Dic₄₇	semidirect
253. M₃₂	C₂×Dic₄₇	semidirect
256. C₂×C₁₆	C₂×Dic₄₇	semidirect
286. Q₁₆	C₂²×Dic₄₇	semidirect
294. D₈	C₂²×Dic₄₇	semidirect
315. C₁₆	C₂²×Dic₄₇	semidirect
375. C₂	#20245287	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×#15689245	2
C₂×#15689235	2
#20245287	2
C₂×#15688946	2
C₂×#15688936	2
C₂×#15688933	2
C₂×#15688900	2
C₂×C₄₇×#509	2
C₂×AGL(1,ℤ/16)	47

Subgroups — C2×#20245287 #26369720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245287 #26369720