Subgroups — C₂²×C₄₇×#416 #26099777

Order 12032.

5326 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#416	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#103×C₄₇	C₂	1	2	yes	maximal, complemented
6	C₂²×#102×C₄₇	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₇	—	2	8	no	—
8	C₂²×#41×C₄₇	—	2	6	no	—
9	C₂²×#41×C₄₇	C₄	1	16	yes	complemented
10	C₂²×#41×C₄₇	C₂²	1	12	yes	—
11	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₄₇	—	2	1	no	—
13	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₄₇	—	2	1	no	—
15	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₄₇	—	2	8	no	—
17	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
18	C₂³×C₈×C₄₇	C₂²	1	12	yes	complemented
19	C₂×#117×C₄₇	—	2	6	no	—
20	C₂×#117×C₄₇	C₂²	1	12	yes	complemented
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
23	C₂²×C₄²×C₄₇	—	2	1	no	—
24	C₄₇×#416	C₂²	1	64	yes	direct product factor
25	C₂×#103×C₄₇	C₂²	1	24	yes	complemented
26	C₂×#102×C₄₇	C₂²	1	24	yes	complemented
27	C₂⁵×C₄₇	—	2	1	no	—
28	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
29	C₂×#41×C₄₇	—	2	96	no	—
30	C₂×#41×C₄₇	—	2	48	no	—
31	C₂×#41×C₄₇	—	2	24	no	—
32	C₂×#41×C₄₇	C₂×C₄	1	96	yes	complemented
33	C₂×#41×C₄₇	C₂³	1	16	yes	—
34	C₂²×Q₈×C₄₇	—	2	4	no	—
35	C₂²×Q₈×C₄₇	—	2	3	no	—
36	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	—
37	C₂²×Q₈×C₄₇	C₂³	1	6	yes	—
38	C₂²×D₄×C₄₇	—	2	16	no	—
39	C₂²×D₄×C₄₇	—	2	12	no	—
40	C₂²×D₄×C₄₇	—	2	3	no	—
41	C₂²×D₄×C₄₇	—	2	4	no	—
42	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
43	C₂²×D₄×C₄₇	C₂³	1	6	yes	—
44	C₂³×C₄×C₄₇	—	2	1	no	—
45	C₂³×C₄×C₄₇	—	2	16	no	—
46	C₂³×C₄×C₄₇	—	2	12	no	—
47	C₂³×C₄×C₄₇	—	2	2	no	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
49	C₂³×C₄×C₄₇	D₄	1	6	yes	—
50	C₂³×C₄×C₄₇	D₄	1	8	yes	—
51	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
54	C₂²×C₈×C₄₇	—	2	8	no	—
55	C₂²×C₈×C₄₇	—	2	48	no	—
56	C₂²×C₈×C₄₇	C₂³	1	12	yes	—
57	C₂²×C₈×C₄₇	C₂³	1	16	yes	complemented
58	#117×C₄₇	—	2	24	no	—
59	#117×C₄₇	C₂³	1	16	yes	complemented
60	C₂×C₄⋊C₄×C₄₇	—	2	6	no	—
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
62	C₂×C₂²⋊C₄×C₄₇	—	2	12	no	—
63	C₂×C₄²×C₄₇	—	2	12	no	—
64	#103×C₄₇	C₂³	1	32	yes	complemented
65	#102×C₄₇	C₂³	1	32	yes	complemented
66	C₂⁴×C₄₇	—	2	8	no	—
67	C₂⁴×C₄₇	—	2	8	no	—
68	C₂⁴×C₄₇	—	2	6	no	—
69	C₂⁴×C₄₇	—	4	8	no	—
70	C₂⁴×C₄₇	C₂²⋊C₄	1	8	yes	—
71	C₂⁴×C₄₇	C₂×D₄	1	6	yes	—
72	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
73	#41×C₄₇	—	2	192	no	—
74	#41×C₄₇	—	2	32	no	—
75	#41×C₄₇	C₂²×C₄	1	64	yes	complemented
76	C₂×Q₈×C₄₇	—	2	24	no	—
77	C₂×Q₈×C₄₇	—	2	12	no	—
78	C₂×Q₈×C₄₇	—	2	6	no	—
79	C₂×Q₈×C₄₇	C₂²×C₄	1	24	yes	—
80	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
81	C₂×D₄×C₄₇	—	2	96	no	—
82	C₂×D₄×C₄₇	—	2	16	no	—
83	C₂×D₄×C₄₇	—	2	24	no	—
84	C₂×D₄×C₄₇	—	2	6	no	—
85	C₂×D₄×C₄₇	—	2	12	no	—
86	C₂×D₄×C₄₇	C₂²×C₄	1	24	yes	—
87	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
88	C₂²×C₄×C₄₇	—	2	8	no	—
89	C₂²×C₄×C₄₇	—	2	6	no	—
90	C₂²×C₄×C₄₇	—	2	96	no	—
91	C₂²×C₄×C₄₇	—	2	16	no	—
92	C₂²×C₄×C₄₇	—	2	12	no	—
93	C₂²×C₄×C₄₇	—	4	8	no	—
94	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	48	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	6	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	12	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	24	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
105	C₂×C₈×C₄₇	—	2	24	no	—
106	C₂×C₈×C₄₇	—	2	32	no	—
107	C₂×C₈×C₄₇	C₂⁴	1	8	yes	—
108	C₄⋊C₄×C₄₇	—	2	12	no	—
109	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
110	C₂²⋊C₄×C₄₇	—	2	16	no	—
111	C₄²×C₄₇	—	2	16	no	—
112	C₂³×C₄₇	—	2	24	no	—
113	C₂³×C₄₇	—	2	32	no	—
114	C₂³×C₄₇	—	2	24	no	—
115	C₂³×C₄₇	—	2	4	no	—
116	C₂³×C₄₇	—	4	24	no	—
117	C₂³×C₄₇	—	4	32	no	—
118	C₂³×C₄₇	C₂×C₂²⋊C₄	1	24	yes	—
119	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
120	C₂³×C₄₇	#135	1	8	yes	—
121	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
122	C₂³×C₄₇	C₂²×D₄	1	3	yes	—
123	Q₈×C₄₇	—	2	24	no	—
124	Q₈×C₄₇	—	2	4	no	—
125	Q₈×C₄₇	C₂³×C₄	1	8	yes	—
126	D₄×C₄₇	—	2	64	no	—
127	D₄×C₄₇	—	2	24	no	—
128	D₄×C₄₇	—	2	4	no	—
129	D₄×C₄₇	C₂³×C₄	1	8	yes	—
130	C₂×C₄×C₄₇	—	2	24	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	64	no	—
133	C₂×C₄×C₄₇	—	2	8	no	—
134	C₂×C₄×C₄₇	—	4	24	no	—
135	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	24	yes	—
136	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	12	yes	—
137	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	48	yes	—
138	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
139	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
140	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
141	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
142	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
143	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
144	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
145	C₈×C₄₇	—	2	8	no	—
146	C₂²×#416	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂²×C₄₇	—	2	48	no	—
148	C₂²×C₄₇	—	2	8	no	—
149	C₂²×C₄₇	—	2	8	no	—
150	C₂²×C₄₇	—	4	48	no	—
151	C₂²×C₄₇	—	4	8	no	—
152	C₂²×C₄₇	#416	1	16	yes	direct product factor
153	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	8	yes	—
154	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	6	yes	—
155	C₂²×C₄₇	C₂×#135	1	12	yes	—
156	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
157	C₄×C₄₇	—	2	8	no	—
158	C₄×C₄₇	—	4	8	no	—
159	C₄×C₄₇	C₂²×C₂²⋊C₄	1	8	yes	—
160	C₄×C₄₇	C₂²×C₂²⋊C₄	1	6	yes	—
161	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
162	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
163	C₂³×#41	C₂×C₄₇	1	1	yes	characteristic
164	C₂⁴×C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
165	C₂²×#117	C₂×C₄₇	1	1	yes	characteristic, complemented
166	C₂×#416	C₂×C₄₇	1	24	yes	direct product factor
167	C₂²×#103	C₂×C₄₇	1	2	yes	complemented
168	C₂²×#102	C₂×C₄₇	1	2	yes	complemented
169	C₂×C₄₇	—	2	8	no	—
170	C₂×C₄₇	—	4	8	no	—
171	C₂×C₄₇	C₂×#416	1	12	yes	direct product factor
172	C₂×C₄₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄₇	C₂²×#135	1	2	yes	—
174	C₂²×#41	—	2	8	no	—
175	C₂²×#41	—	2	6	no	—
176	C₂²×#41	C₄×C₄₇	1	16	yes	complemented
177	C₂²×#41	C₂²×C₄₇	1	12	yes	—
178	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
179	C₂³×D₄	—	2	1	no	—
180	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
181	C₂⁴×C₄	—	2	1	no	—
182	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
183	C₂³×C₈	—	2	8	no	—
184	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
185	C₂³×C₈	C₂²×C₄₇	1	12	yes	complemented
186	C₂×#117	—	2	6	no	—
187	C₂×#117	C₂²×C₄₇	1	12	yes	complemented
188	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
189	C₂²×C₂²⋊C₄	—	2	1	no	—
190	C₂²×C₄²	—	2	1	no	—
191	#416	C₂²×C₄₇	1	64	yes	direct product factor
192	C₂×#103	C₂²×C₄₇	1	24	yes	complemented
193	C₂×#102	C₂²×C₄₇	1	24	yes	complemented
194	C₄₇	C₂²×#416	1	1	yes	characteristic, direct product factor, Sylow
195	C₂⁵	—	2	1	no	—
196	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
197	C₂×#41	—	2	96	no	—
198	C₂×#41	—	2	48	no	—
199	C₂×#41	—	2	24	no	—
200	C₂×#41	C₂×C₄×C₄₇	1	96	yes	complemented
201	C₂×#41	C₂³×C₄₇	1	16	yes	—
202	C₂²×Q₈	—	2	4	no	—
203	C₂²×Q₈	—	2	3	no	—
204	C₂²×Q₈	C₂×C₄×C₄₇	1	8	yes	—
205	C₂²×Q₈	C₂³×C₄₇	1	6	yes	—
206	C₂²×D₄	—	2	16	no	—
207	C₂²×D₄	—	2	12	no	—
208	C₂²×D₄	—	2	3	no	—
209	C₂²×D₄	—	2	4	no	—
210	C₂²×D₄	C₂×C₄×C₄₇	1	8	yes	—
211	C₂²×D₄	C₂³×C₄₇	1	6	yes	—
212	C₂³×C₄	—	2	1	no	—
213	C₂³×C₄	—	2	16	no	—
214	C₂³×C₄	—	2	12	no	—
215	C₂³×C₄	—	2	2	no	—
216	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	—
217	C₂³×C₄	D₄×C₄₇	1	6	yes	—
218	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
219	C₂³×C₄	D₄×C₄₇	1	8	yes	—
220	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
221	C₂³×C₄	C₂³×C₄₇	1	6	yes	—
222	C₂²×C₈	—	2	8	no	—
223	C₂²×C₈	—	2	48	no	—
224	C₂²×C₈	C₂³×C₄₇	1	12	yes	—
225	C₂²×C₈	C₂³×C₄₇	1	16	yes	complemented
226	#117	—	2	24	no	—
227	#117	C₂³×C₄₇	1	16	yes	complemented
228	C₂×C₄⋊C₄	—	2	6	no	—
229	C₂×C₄⋊C₄	C₂³×C₄₇	1	12	yes	—
230	C₂×C₂²⋊C₄	—	2	12	no	—
231	C₂×C₄²	—	2	12	no	—
232	#103	C₂³×C₄₇	1	32	yes	complemented
233	#102	C₂³×C₄₇	1	32	yes	complemented
234	C₂⁴	—	2	8	no	—
235	C₂⁴	—	2	8	no	—
236	C₂⁴	—	2	6	no	—
237	C₂⁴	—	4	8	no	—
238	C₂⁴	C₂²⋊C₄×C₄₇	1	8	yes	—
239	C₂⁴	C₂×D₄×C₄₇	1	6	yes	—
240	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
241	#41	—	2	192	no	—
242	#41	—	2	32	no	—
243	#41	C₂²×C₄×C₄₇	1	64	yes	complemented
244	C₂×Q₈	—	2	24	no	—
245	C₂×Q₈	—	2	12	no	—
246	C₂×Q₈	—	2	6	no	—
247	C₂×Q₈	C₂²×C₄×C₄₇	1	24	yes	—
248	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
249	C₂×D₄	—	2	96	no	—
250	C₂×D₄	—	2	16	no	—
251	C₂×D₄	—	2	24	no	—
252	C₂×D₄	—	2	6	no	—
253	C₂×D₄	—	2	12	no	—
254	C₂×D₄	C₂²×C₄×C₄₇	1	24	yes	—
255	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	6	no	—
258	C₂²×C₄	—	2	96	no	—
259	C₂²×C₄	—	2	16	no	—
260	C₂²×C₄	—	2	12	no	—
261	C₂²×C₄	—	4	8	no	—
262	C₂²×C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
263	C₂²×C₄	C₂²⋊C₄×C₄₇	1	48	yes	—
264	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
265	C₂²×C₄	C₂²×C₄×C₄₇	1	24	yes	—
266	C₂²×C₄	C₂×D₄×C₄₇	1	6	yes	—
267	C₂²×C₄	C₂×D₄×C₄₇	1	3	yes	—
268	C₂²×C₄	C₂×D₄×C₄₇	1	12	yes	—
269	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
270	C₂²×C₄	C₂×D₄×C₄₇	1	24	yes	—
271	C₂²×C₄	C₂⁴×C₄₇	1	3	yes	—
272	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
273	C₂×C₈	—	2	24	no	—
274	C₂×C₈	—	2	32	no	—
275	C₂×C₈	C₂⁴×C₄₇	1	8	yes	—
276	C₄⋊C₄	—	2	12	no	—
277	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
278	C₂²⋊C₄	—	2	16	no	—
279	C₄²	—	2	16	no	—
280	C₂³	—	2	24	no	—
281	C₂³	—	2	32	no	—
282	C₂³	—	2	24	no	—
283	C₂³	—	2	4	no	—
284	C₂³	—	4	24	no	—
285	C₂³	—	4	32	no	—
286	C₂³	C₂×C₂²⋊C₄×C₄₇	1	24	yes	—
287	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
288	C₂³	#135×C₄₇	1	8	yes	—
289	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
290	C₂³	C₂²×D₄×C₄₇	1	3	yes	—
291	Q₈	—	2	24	no	—
292	Q₈	—	2	4	no	—
293	Q₈	C₂³×C₄×C₄₇	1	8	yes	—
294	D₄	—	2	64	no	—
295	D₄	—	2	24	no	—
296	D₄	—	2	4	no	—
297	D₄	C₂³×C₄×C₄₇	1	8	yes	—
298	C₂×C₄	—	2	24	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	64	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	4	24	no	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	24	yes	—
304	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	12	yes	—
305	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	48	yes	—
306	C₂×C₄	C₂³×C₄×C₄₇	1	6	yes	—
307	C₂×C₄	C₂³×C₄×C₄₇	1	8	yes	—
308	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₄₇	1	3	yes	—
310	C₂×C₄	C₂²×D₄×C₄₇	1	6	yes	—
311	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
312	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
313	C₈	—	2	8	no	—
314	C₂²	—	2	8	no	—
315	C₂²	—	2	48	no	—
316	C₂²	—	2	8	no	—
317	C₂²	—	4	8	no	—
318	C₂²	—	4	48	no	—
319	C₂²	C₄₇×#416	1	16	yes	direct product factor
320	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	8	yes	—
321	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	6	yes	—
322	C₂²	C₂×#135×C₄₇	1	12	yes	—
323	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
324	C₄	—	2	8	no	—
325	C₄	—	4	8	no	—
326	C₄	C₂²×C₂²⋊C₄×C₄₇	1	8	yes	—
327	C₄	C₂²×C₂²⋊C₄×C₄₇	1	6	yes	—
328	C₄	C₂⁴×C₄×C₄₇	1	1	yes	characteristic
329	C₄	C₂³×D₄×C₄₇	1	1	yes	characteristic
330	C₂	—	2	8	no	—
331	C₂	—	4	8	no	—
332	C₂	C₂×C₄₇×#416	1	12	yes	direct product factor
333	C₂	C₂³×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
334	C₂	C₂²×#135×C₄₇	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₇	D₄
commutator	C₄	C₂⁴×C₄×C₄₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
socle	C₂⁴×C₄₇	C₂×D₄
prime radical	C₂³×#41×C₄₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₇ ◁ C₂⁴×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₈×C₄₇	C₂	semidirect
3. C₂²×#117×C₄₇	C₂	semidirect
4. C₂×C₄₇×#416	C₂	direct (N × H)
5. C₂²×#103×C₄₇	C₂	semidirect
6. C₂²×#102×C₄₇	C₂	semidirect
9. C₂²×#41×C₄₇	C₄	semidirect
18. C₂³×C₈×C₄₇	C₂²	semidirect
20. C₂×#117×C₄₇	C₂²	semidirect
24. C₄₇×#416	C₂²	direct (N × H)
25. C₂×#103×C₄₇	C₂²	semidirect
26. C₂×#102×C₄₇	C₂²	semidirect
32. C₂×#41×C₄₇	C₂×C₄	semidirect
57. C₂²×C₈×C₄₇	C₂³	semidirect
59. #117×C₄₇	C₂³	semidirect
64. #103×C₄₇	C₂³	semidirect
65. #102×C₄₇	C₂³	semidirect
75. #41×C₄₇	C₂²×C₄	semidirect
146. C₂²×#416	C₄₇	direct (N × H)
152. C₂²×C₄₇	#416	direct (N × H)
164. C₂⁴×C₈	C₂×C₄₇	semidirect
165. C₂²×#117	C₂×C₄₇	semidirect
166. C₂×#416	C₂×C₄₇	direct (N × H)
167. C₂²×#103	C₂×C₄₇	semidirect
168. C₂²×#102	C₂×C₄₇	semidirect
171. C₂×C₄₇	C₂×#416	direct (N × H)
176. C₂²×#41	C₄×C₄₇	semidirect
185. C₂³×C₈	C₂²×C₄₇	semidirect
187. C₂×#117	C₂²×C₄₇	semidirect
191. #416	C₂²×C₄₇	direct (N × H)
192. C₂×#103	C₂²×C₄₇	semidirect
193. C₂×#102	C₂²×C₄₇	semidirect
194. C₄₇	C₂²×#416	direct (N × H)
200. C₂×#41	C₂×C₄×C₄₇	semidirect
225. C₂²×C₈	C₂³×C₄₇	semidirect
227. #117	C₂³×C₄₇	semidirect
232. #103	C₂³×C₄₇	semidirect
233. #102	C₂³×C₄₇	semidirect
243. #41	C₂²×C₄×C₄₇	semidirect
319. C₂²	C₄₇×#416	direct (N × H)
332. C₂	C₂×C₄₇×#416	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₄₇	2
C₂⁴×C₈×C₄₇	2
C₂²×#117×C₄₇	2
C₂×C₄₇×#416	2
C₂²×#103×C₄₇	2
C₂²×#102×C₄₇	2
C₂²×#416	47

Subgroups — C22×C47×#416 #26099777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄₇×#416 #26099777