Subgroups — C₄₇×#33857 #26073555

Order 12032.

646 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3416	C₂	1	2	yes	maximal, complemented
2	C₄₇×#3290	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2223	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2212	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2195	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2192	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2178	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2170	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#578	C₂²	1	2	yes	—
11	C₄₇×#577	—	2	2	no	—
12	C₄₇×#576	C₂²	1	2	yes	complemented
13	C₄₇×#510	—	2	2	no	—
14	C₄₇×#510	C₂²	1	2	yes	complemented
15	C₄₇×#509	—	2	2	no	—
16	C₄₇×#509	C₂²	1	2	yes	—
17	C₄₇×#508	—	2	2	no	—
18	C₄₇×#508	C₂²	1	1	yes	characteristic
19	C₂×Q₃₂×C₄₇	C₂²	1	1	yes	characteristic, complemented
20	C₂×SD₃₂×C₄₇	—	2	2	no	—
21	C₂×SD₃₂×C₄₇	C₂²	1	2	yes	complemented
22	C₂×D₁₆×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#504	C₂²	1	2	yes	complemented
24	C₄₇×#495	C₂²	1	2	yes	complemented
25	C₄₇×#473	C₂²	1	2	yes	complemented
26	C₄₇×#472	C₂²	1	2	yes	—
27	C₄₇×#471	—	2	2	no	—
28	C₄₇×#455	—	2	2	no	—
29	C₄₇×#454	—	2	2	no	—
30	C₄₇×#443	C₂²	1	1	yes	characteristic
31	C₄₇×#443	C₂²	1	2	yes	complemented
32	C₄₇×#368	C₂²	1	1	yes	characteristic, complemented
33	C₄₇×#364	C₂²	1	1	yes	characteristic, complemented
34	C₄₇×#362	C₂²	1	2	yes	complemented
35	C₄₇×#361	C₂²	1	2	yes	complemented
36	C₄₇×#359	C₂²	1	2	yes	complemented
37	C₄₇×#350	C₂²	1	2	yes	complemented
38	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
39	2₋¹⁺⁴×C₄₇	—	2	2	no	—
40	H(5,𝔽₂)×C₄₇	—	2	2	no	—
41	#137×C₄₇	—	2	2	no	—
42	#137×C₄₇	—	2	2	no	—
43	#137×C₄₇	—	4	2	no	—
44	#137×C₄₇	—	4	2	no	—
45	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
46	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
47	AGL(1,ℤ/8)×C₄₇	—	4	2	no	—
48	AGL(1,ℤ/8)×C₄₇	—	4	2	no	—
49	#135×C₄₇	—	2	2	no	—
50	#135×C₄₇	—	2	2	no	—
51	#135×C₄₇	—	4	2	no	—
52	#135×C₄₇	D₄	1	1	yes	characteristic
53	#135×C₄₇	C₂³	1	2	yes	—
54	C₂×Q₁₆×C₄₇	—	2	2	no	—
55	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
56	C₂×SD₁₆×C₄₇	—	2	2	no	—
57	C₂×SD₁₆×C₄₇	—	4	2	no	—
58	C₂×D₈×C₄₇	—	2	2	no	—
59	C₂×D₈×C₄₇	C₂³	1	2	yes	—
60	#131×C₄₇	—	2	2	no	—
61	#131×C₄₇	C₂³	1	2	yes	—
62	#124×C₄₇	—	2	2	no	—
63	Q₃₂×C₄₇	—	2	2	no	—
64	Q₃₂×C₄₇	—	4	1	no	—
65	Q₃₂×C₄₇	D₄	1	1	yes	characteristic
66	SD₃₂×C₄₇	—	2	2	no	—
67	SD₃₂×C₄₇	—	2	2	no	—
68	SD₃₂×C₄₇	—	2	2	no	—
69	SD₃₂×C₄₇	—	2	2	no	—
70	SD₃₂×C₄₇	D₄	1	2	yes	—
71	D₁₆×C₄₇	—	2	2	no	—
72	D₁₆×C₄₇	—	4	1	no	—
73	D₁₆×C₄₇	D₄	1	1	yes	characteristic
74	M₃₂×C₄₇	—	2	2	no	—
75	M₃₂×C₄₇	C₂³	1	2	yes	—
76	C₂×C₁₆×C₄₇	—	2	2	no	—
77	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
79	#108×C₄₇	D₄	1	1	yes	characteristic
80	#108×C₄₇	C₂³	1	2	yes	—
81	#104×C₄₇	—	2	2	no	—
82	#104×C₄₇	D₄	1	2	yes	—
83	#101×C₄₇	—	2	2	no	—
84	#100×C₄₇	—	2	2	no	—
85	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	#41×C₄₇	—	2	2	no	—
87	#41×C₄₇	—	4	2	no	—
88	#41×C₄₇	—	4	2	no	—
89	#41×C₄₇	—	4	2	no	—
90	#41×C₄₇	—	4	2	no	—
91	#41×C₄₇	—	8	2	no	—
92	#41×C₄₇	C₂×D₄	1	2	yes	—
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	—	4	2	no	—
95	C₂×Q₈×C₄₇	—	4	2	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	4	2	no	—
98	C₂×D₄×C₄₇	—	4	2	no	—
99	C₂×D₄×C₄₇	—	8	2	no	—
100	Q₁₆×C₄₇	—	2	2	no	—
101	Q₁₆×C₄₇	—	2	2	no	—
102	Q₁₆×C₄₇	—	4	2	no	—
103	Q₁₆×C₄₇	—	4	2	no	—
104	Q₁₆×C₄₇	D₈	1	1	yes	characteristic
105	Q₁₆×C₄₇	C₂×D₄	1	2	yes	—
106	SD₁₆×C₄₇	—	2	2	no	—
107	SD₁₆×C₄₇	—	4	2	no	—
108	SD₁₆×C₄₇	—	4	2	no	—
109	SD₁₆×C₄₇	—	4	2	no	—
110	SD₁₆×C₄₇	—	4	2	no	—
111	SD₁₆×C₄₇	—	4	2	no	—
112	SD₁₆×C₄₇	—	4	2	no	—
113	SD₁₆×C₄₇	D₈	1	2	yes	—
114	D₈×C₄₇	—	2	2	no	—
115	D₈×C₄₇	—	2	2	no	—
116	D₈×C₄₇	—	4	2	no	—
117	D₈×C₄₇	—	4	2	no	—
118	D₈×C₄₇	D₈	1	1	yes	characteristic
119	D₈×C₄₇	C₂×D₄	1	2	yes	—
120	M₁₆×C₄₇	—	2	2	no	—
121	M₁₆×C₄₇	—	2	2	no	—
122	M₁₆×C₄₇	—	4	2	no	—
123	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	4	2	no	—
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂²⋊C₄×C₄₇	—	8	2	no	—
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₁₆×C₄₇	—	2	2	no	—
131	C₁₆×C₄₇	—	2	1	no	—
132	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	—	8	2	no	—
136	Q₈×C₄₇	—	2	2	no	—
137	Q₈×C₄₇	—	4	2	no	—
138	Q₈×C₄₇	—	4	2	no	—
139	Q₈×C₄₇	—	8	2	no	—
140	Q₈×C₄₇	C₂×D₈	1	2	yes	—
141	D₄×C₄₇	—	2	2	no	—
142	D₄×C₄₇	—	2	2	no	—
143	D₄×C₄₇	—	4	2	no	—
144	D₄×C₄₇	—	4	2	no	—
145	D₄×C₄₇	—	4	2	no	—
146	D₄×C₄₇	—	8	2	no	—
147	D₄×C₄₇	—	8	2	no	—
148	D₄×C₄₇	—	8	2	no	—
149	D₄×C₄₇	C₂×D₈	1	2	yes	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	8	2	no	—
155	C₂×C₄×C₄₇	—	8	2	no	—
156	C₂×C₄×C₄₇	—	8	2	no	—
157	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₄₇	—	2	2	no	—
159	C₈×C₄₇	—	4	2	no	—
160	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
161	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
162	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
164	#33857	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	4	2	no	—
167	C₂²×C₄₇	—	8	2	no	—
168	C₂²×C₄₇	—	16	2	no	—
169	C₂²×C₄₇	—	32	2	no	—
170	C₂²×C₄₇	#576	1	1	yes	characteristic
171	C₄×C₄₇	—	2	2	no	—
172	C₄×C₄₇	—	4	1	no	—
173	C₄×C₄₇	—	4	2	no	—
174	C₄×C₄₇	—	8	2	no	—
175	C₄×C₄₇	D₄²	1	1	yes	characteristic
176	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
177	#3416	C₂×C₄₇	1	2	yes	complemented
178	#3290	C₂×C₄₇	1	2	yes	complemented
179	#2249	C₂×C₄₇	1	1	yes	characteristic, complemented
180	#2223	C₂×C₄₇	1	2	yes	complemented
181	#2212	C₂×C₄₇	1	2	yes	complemented
182	#2195	C₂×C₄₇	1	2	yes	complemented
183	#2192	C₂×C₄₇	1	2	yes	complemented
184	#2178	C₂×C₄₇	1	1	yes	characteristic, complemented
185	#2170	C₂×C₄₇	1	1	yes	characteristic, complemented
186	C₂×C₄₇	—	2	1	no	—
187	C₂×C₄₇	—	4	2	no	—
188	C₂×C₄₇	—	8	2	no	—
189	C₂×C₄₇	—	16	2	no	—
190	C₂×C₄₇	D₄×D₈	1	1	yes	characteristic
191	#578	C₂²×C₄₇	1	2	yes	—
192	#577	—	2	2	no	—
193	#576	C₂²×C₄₇	1	2	yes	complemented
194	#510	—	2	2	no	—
195	#510	C₂²×C₄₇	1	2	yes	complemented
196	#509	—	2	2	no	—
197	#509	C₂²×C₄₇	1	2	yes	—
198	#508	—	2	2	no	—
199	#508	C₂²×C₄₇	1	1	yes	characteristic
200	C₂×Q₃₂	C₂²×C₄₇	1	1	yes	characteristic, complemented
201	C₂×SD₃₂	—	2	2	no	—
202	C₂×SD₃₂	C₂²×C₄₇	1	2	yes	complemented
203	C₂×D₁₆	C₂²×C₄₇	1	1	yes	characteristic
204	#504	C₂²×C₄₇	1	2	yes	complemented
205	#495	C₂²×C₄₇	1	2	yes	complemented
206	#473	C₂²×C₄₇	1	2	yes	complemented
207	#472	C₂²×C₄₇	1	2	yes	—
208	#471	—	2	2	no	—
209	#455	—	2	2	no	—
210	#454	—	2	2	no	—
211	#443	C₂²×C₄₇	1	1	yes	characteristic
212	#443	C₂²×C₄₇	1	2	yes	complemented
213	#368	C₂²×C₄₇	1	1	yes	characteristic, complemented
214	#364	C₂²×C₄₇	1	1	yes	characteristic, complemented
215	#362	C₂²×C₄₇	1	2	yes	complemented
216	#361	C₂²×C₄₇	1	2	yes	complemented
217	#359	C₂²×C₄₇	1	2	yes	complemented
218	#350	C₂²×C₄₇	1	2	yes	complemented
219	C₄×C₁₆	C₂²×C₄₇	1	1	yes	characteristic, complemented
220	C₄₇	#33857	1	1	yes	characteristic, direct product factor, Sylow
221	2₋¹⁺⁴	—	2	2	no	—
222	H(5,𝔽₂)	—	2	2	no	—
223	#137	—	2	2	no	—
224	#137	—	2	2	no	—
225	#137	—	4	2	no	—
226	#137	—	4	2	no	—
227	AGL(1,ℤ/8)	—	2	2	no	—
228	AGL(1,ℤ/8)	—	2	2	no	—
229	AGL(1,ℤ/8)	—	4	2	no	—
230	AGL(1,ℤ/8)	—	4	2	no	—
231	#135	—	2	2	no	—
232	#135	—	2	2	no	—
233	#135	—	4	2	no	—
234	#135	D₄×C₄₇	1	1	yes	characteristic
235	#135	C₂³×C₄₇	1	2	yes	—
236	C₂×Q₁₆	—	2	2	no	—
237	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
238	C₂×SD₁₆	—	2	2	no	—
239	C₂×SD₁₆	—	4	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×D₈	C₂³×C₄₇	1	2	yes	—
242	#131	—	2	2	no	—
243	#131	C₂³×C₄₇	1	2	yes	—
244	#124	—	2	2	no	—
245	Q₃₂	—	2	2	no	—
246	Q₃₂	—	4	1	no	—
247	Q₃₂	D₄×C₄₇	1	1	yes	characteristic
248	SD₃₂	—	2	2	no	—
249	SD₃₂	—	2	2	no	—
250	SD₃₂	—	2	2	no	—
251	SD₃₂	—	2	2	no	—
252	SD₃₂	D₄×C₄₇	1	2	yes	—
253	D₁₆	—	2	2	no	—
254	D₁₆	—	4	1	no	—
255	D₁₆	D₄×C₄₇	1	1	yes	characteristic
256	M₃₂	—	2	2	no	—
257	M₃₂	C₂³×C₄₇	1	2	yes	—
258	C₂×C₁₆	—	2	2	no	—
259	C₂×C₁₆	C₂³×C₄₇	1	1	yes	characteristic
260	C₂×C₁₆	C₂³×C₄₇	1	1	yes	characteristic
261	#108	D₄×C₄₇	1	1	yes	characteristic
262	#108	C₂³×C₄₇	1	2	yes	—
263	#104	—	2	2	no	—
264	#104	D₄×C₄₇	1	2	yes	—
265	#101	—	2	2	no	—
266	#100	—	2	2	no	—
267	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
268	#41	—	2	2	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	#41	—	4	2	no	—
273	#41	—	8	2	no	—
274	#41	C₂×D₄×C₄₇	1	2	yes	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	8	2	no	—
282	Q₁₆	—	2	2	no	—
283	Q₁₆	—	2	2	no	—
284	Q₁₆	—	4	2	no	—
285	Q₁₆	—	4	2	no	—
286	Q₁₆	D₈×C₄₇	1	1	yes	characteristic
287	Q₁₆	C₂×D₄×C₄₇	1	2	yes	—
288	SD₁₆	—	2	2	no	—
289	SD₁₆	—	4	2	no	—
290	SD₁₆	—	4	2	no	—
291	SD₁₆	—	4	2	no	—
292	SD₁₆	—	4	2	no	—
293	SD₁₆	—	4	2	no	—
294	SD₁₆	—	4	2	no	—
295	SD₁₆	D₈×C₄₇	1	2	yes	—
296	D₈	—	2	2	no	—
297	D₈	—	2	2	no	—
298	D₈	—	4	2	no	—
299	D₈	—	4	2	no	—
300	D₈	D₈×C₄₇	1	1	yes	characteristic
301	D₈	C₂×D₄×C₄₇	1	2	yes	—
302	M₁₆	—	2	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	4	2	no	—
305	M₁₆	C₂×D₄×C₄₇	1	2	yes	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
309	C₂×C₈	C₂⁴×C₄₇	1	1	yes	characteristic
310	C₂²⋊C₄	—	8	2	no	—
311	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
312	C₁₆	—	2	2	no	—
313	C₁₆	—	2	1	no	—
314	C₁₆	C₂×D₄×C₄₇	1	1	yes	characteristic
315	C₁₆	C₂×D₄×C₄₇	1	1	yes	characteristic
316	C₂³	—	4	2	no	—
317	C₂³	—	8	2	no	—
318	Q₈	—	2	2	no	—
319	Q₈	—	4	2	no	—
320	Q₈	—	4	2	no	—
321	Q₈	—	8	2	no	—
322	Q₈	C₂×D₈×C₄₇	1	2	yes	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	D₄	—	8	2	no	—
331	D₄	C₂×D₈×C₄₇	1	2	yes	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
340	C₈	—	2	2	no	—
341	C₈	—	4	2	no	—
342	C₈	C₂×D₈×C₄₇	1	1	yes	characteristic
343	C₈	C₂×D₈×C₄₇	1	1	yes	characteristic
344	C₈	C₂²×D₄×C₄₇	1	1	yes	characteristic
345	C₈	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
346	C₂²	—	2	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	16	2	no	—
350	C₂²	—	32	2	no	—
351	C₂²	C₄₇×#576	1	1	yes	characteristic
352	C₄	—	2	2	no	—
353	C₄	—	4	1	no	—
354	C₄	—	4	2	no	—
355	C₄	—	8	2	no	—
356	C₄	D₄²×C₄₇	1	1	yes	characteristic
357	C₄	C₂²×D₈×C₄₇	1	1	yes	characteristic
358	C₂	—	2	1	no	—
359	C₂	—	4	2	no	—
360	C₂	—	8	2	no	—
361	C₂	—	16	2	no	—
362	C₂	D₄×D₈×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₇	D₄×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₇ ◁ C₂×C₄×C₄₇ ◁ C₄₇×#443 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3416	C₂	semidirect
2. C₄₇×#3290	C₂	semidirect
3. C₄₇×#2249	C₂	semidirect
4. C₄₇×#2223	C₂	semidirect
5. C₄₇×#2212	C₂	semidirect
6. C₄₇×#2195	C₂	semidirect
7. C₄₇×#2192	C₂	semidirect
8. C₄₇×#2178	C₂	semidirect
9. C₄₇×#2170	C₂	semidirect
12. C₄₇×#576	C₂²	semidirect
14. C₄₇×#510	C₂²	semidirect
19. C₂×Q₃₂×C₄₇	C₂²	semidirect
21. C₂×SD₃₂×C₄₇	C₂²	semidirect
23. C₄₇×#504	C₂²	semidirect
24. C₄₇×#495	C₂²	semidirect
25. C₄₇×#473	C₂²	semidirect
31. C₄₇×#443	C₂²	semidirect
32. C₄₇×#368	C₂²	semidirect
33. C₄₇×#364	C₂²	semidirect
34. C₄₇×#362	C₂²	semidirect
35. C₄₇×#361	C₂²	semidirect
36. C₄₇×#359	C₂²	semidirect
37. C₄₇×#350	C₂²	semidirect
38. C₄×C₁₆×C₄₇	C₂²	semidirect
164. #33857	C₄₇	direct (N × H)
177. #3416	C₂×C₄₇	semidirect
178. #3290	C₂×C₄₇	semidirect
179. #2249	C₂×C₄₇	semidirect
180. #2223	C₂×C₄₇	semidirect
181. #2212	C₂×C₄₇	semidirect
182. #2195	C₂×C₄₇	semidirect
183. #2192	C₂×C₄₇	semidirect
184. #2178	C₂×C₄₇	semidirect
185. #2170	C₂×C₄₇	semidirect
193. #576	C₂²×C₄₇	semidirect
195. #510	C₂²×C₄₇	semidirect
200. C₂×Q₃₂	C₂²×C₄₇	semidirect
202. C₂×SD₃₂	C₂²×C₄₇	semidirect
204. #504	C₂²×C₄₇	semidirect
205. #495	C₂²×C₄₇	semidirect
206. #473	C₂²×C₄₇	semidirect
212. #443	C₂²×C₄₇	semidirect
213. #368	C₂²×C₄₇	semidirect
214. #364	C₂²×C₄₇	semidirect
215. #362	C₂²×C₄₇	semidirect
216. #361	C₂²×C₄₇	semidirect
217. #359	C₂²×C₄₇	semidirect
218. #350	C₂²×C₄₇	semidirect
219. C₄×C₁₆	C₂²×C₄₇	semidirect
220. C₄₇	#33857	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₇×#3416	2
C₄₇×#3290	2
C₄₇×#2249	2
C₄₇×#2223	2
C₄₇×#2212	2
C₄₇×#2195	2
C₄₇×#2192	2
C₄₇×#2178	2
C₄₇×#2170	2
#33857	47

Subgroups — C47×#33857 #26073555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#33857 #26073555