Subgroups — C₂×#20245966 #26374828

Order 12032.

8142 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
2	#20245966	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689003	C₂	1	8	yes	maximal, complemented
4	C₂×#15688986	C₂	1	2	yes	maximal, complemented
5	C₂×#15688979	C₂	1	2	yes	maximal, complemented
6	C₂⁴×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂⁴×Dic₄₇	C₂²	1	4	yes	complemented
8	C₂²×C₂²⋊Dic₄₇	—	2	16	no	—
9	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
10	C₂²×C₂²⋊Dic₄₇	C₂²	1	16	yes	complemented
11	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
12	C₂²×C₂²⋊Dic₄₇	C₂²	1	8	yes	complemented
13	#15689003	C₂²	1	64	yes	complemented
14	#15688986	C₂²	1	16	yes	complemented
15	#15688979	C₂²	1	16	yes	complemented
16	C₂×C₄₇⋊#95	C₂²	1	8	yes	complemented
17	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
18	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₄₇	—	2	16	no	—
20	C₂³×D₄×C₄₇	C₄	1	16	yes	complemented
21	C₂³×D₄×C₄₇	C₂²	1	4	yes	—
22	C₂³×D₄×C₄₇	C₂²	1	8	yes	—
23	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂³×Dic₄₇	—	2	16	no	—
25	C₂³×Dic₄₇	—	4	16	no	—
26	C₂³×Dic₄₇	C₂³	1	8	yes	—
27	C₂³×Dic₄₇	C₂³	1	16	yes	complemented
28	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
29	C₂×C₂²⋊Dic₄₇	—	2	64	no	—
30	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
31	C₂×C₂²⋊Dic₄₇	—	4	16	no	—
32	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
33	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	complemented
34	C₂×C₂²⋊Dic₄₇	C₂³	1	32	yes	complemented
35	C₄₇⋊#95	C₂³	1	32	yes	complemented
36	C₂⁵×C₄₇	—	2	8	no	—
37	C₂⁵×C₄₇	—	4	8	no	—
38	C₂⁵×C₄₇	—	4	8	no	—
39	C₂⁵×C₄₇	C₂×C₄	1	8	yes	—
40	C₂⁵×C₄₇	C₂×C₄	1	8	yes	complemented
41	C₂⁵×C₄₇	D₄	1	16	yes	—
42	C₂⁵×C₄₇	C₂³	1	2	yes	—
43	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
44	C₂⁵×C₄₇	C₂³	1	2	yes	—
45	C₂⁵×C₄₇	C₂³	1	4	yes	—
46	C₂⁵×C₄₇	C₂³	1	4	yes	—
47	C₂²×D₄×C₄₇	—	2	128	no	—
48	C₂²×D₄×C₄₇	—	2	16	no	—
49	C₂²×D₄×C₄₇	—	2	16	no	—
50	C₂²×D₄×C₄₇	—	2	64	no	—
51	C₂²×D₄×C₄₇	C₂×C₄	1	32	yes	complemented
52	C₂²×D₄×C₄₇	C₂×C₄	1	64	yes	complemented
53	C₂²×D₄×C₄₇	C₂³	1	16	yes	—
54	C₂³×C₄×C₄₇	—	2	8	no	—
55	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
56	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
58	C₂⁴×C₄₇	—	2	8	no	—
59	C₂⁴×C₄₇	—	2	16	no	—
60	C₂⁴×C₄₇	—	2	32	no	—
61	C₂⁴×C₄₇	—	2	8	no	—
62	C₂⁴×C₄₇	—	2	16	no	—
63	C₂⁴×C₄₇	—	2	16	no	—
64	C₂⁴×C₄₇	—	4	32	no	—
65	C₂⁴×C₄₇	—	4	32	no	—
66	C₂⁴×C₄₇	—	4	64	no	—
67	C₂⁴×C₄₇	—	4	16	no	—
68	C₂⁴×C₄₇	—	4	16	no	—
69	C₂⁴×C₄₇	—	4	64	no	—
70	C₂⁴×C₄₇	C₂²⋊C₄	1	64	yes	complemented
71	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
72	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
73	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
74	C₂⁴×C₄₇	C₂²×C₄	1	16	yes	—
75	C₂⁴×C₄₇	C₂²×C₄	1	16	yes	complemented
76	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
77	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
78	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
79	C₂⁴×C₄₇	C₂×D₄	1	32	yes	—
80	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
81	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
82	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
83	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
84	C₂×D₄×C₄₇	—	2	128	no	—
85	C₂×D₄×C₄₇	—	2	256	no	—
86	C₂×D₄×C₄₇	—	2	32	no	—
87	C₂×D₄×C₄₇	—	2	32	no	—
88	C₂×D₄×C₄₇	C₂²×C₄	1	64	yes	complemented
89	C₂²×C₄×C₄₇	—	2	32	no	—
90	C₂²×C₄×C₄₇	—	2	8	no	—
91	C₂²×C₄×C₄₇	—	2	16	no	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
94	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
95	C₂²×Dic₄₇	—	2	16	no	—
96	C₂²×Dic₄₇	—	2	32	no	—
97	C₂²×Dic₄₇	—	2	32	no	—
98	C₂²×Dic₄₇	—	4	32	no	—
99	C₂²×Dic₄₇	—	4	64	no	—
100	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
101	C₂²⋊Dic₄₇	—	2	32	no	—
102	C₂²⋊Dic₄₇	—	2	32	no	—
103	C₂²⋊Dic₄₇	—	4	32	no	—
104	C₂³×C₄₇	—	2	16	no	—
105	C₂³×C₄₇	—	2	32	no	—
106	C₂³×C₄₇	—	2	32	no	—
107	C₂³×C₄₇	—	2	32	no	—
108	C₂³×C₄₇	—	2	32	no	—
109	C₂³×C₄₇	—	2	16	no	—
110	C₂³×C₄₇	—	2	8	no	—
111	C₂³×C₄₇	—	2	16	no	—
112	C₂³×C₄₇	—	2	32	no	—
113	C₂³×C₄₇	—	2	32	no	—
114	C₂³×C₄₇	—	2	8	no	—
115	C₂³×C₄₇	—	2	16	no	—
116	C₂³×C₄₇	—	4	128	no	—
117	C₂³×C₄₇	—	4	32	no	—
118	C₂³×C₄₇	—	4	32	no	—
119	C₂³×C₄₇	—	4	64	no	—
120	C₂³×C₄₇	—	4	128	no	—
121	C₂³×C₄₇	—	4	64	no	—
122	C₂³×C₄₇	—	4	32	no	—
123	C₂³×C₄₇	C₂×C₂²⋊C₄	1	16	yes	—
124	C₂³×C₄₇	C₂×C₂²⋊C₄	1	32	yes	—
125	C₂³×C₄₇	C₂×C₂²⋊C₄	1	64	yes	complemented
126	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
127	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
128	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
129	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
130	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
131	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
132	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
133	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
134	C₂³×C₄₇	H(5,𝔽₂)	1	8	yes	—
135	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
136	D₄×C₄₇	—	2	128	no	—
137	C₂×C₄×C₄₇	—	2	16	no	—
138	C₂×C₄×C₄₇	—	2	32	no	—
139	C₂×C₄×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
141	C₂×Dic₄₇	—	2	16	no	—
142	C₂×Dic₄₇	—	2	32	no	—
143	C₂×Dic₄₇	—	4	64	no	—
144	C₂×Dic₄₇	—	4	32	no	—
145	C₂×#2308	—	47	1	no	maximal, Sylow
146	C₂²×C₄₇	—	2	32	no	—
147	C₂²×C₄₇	—	2	64	no	—
148	C₂²×C₄₇	—	2	8	no	—
149	C₂²×C₄₇	—	2	16	no	—
150	C₂²×C₄₇	—	2	16	no	—
151	C₂²×C₄₇	—	2	16	no	—
152	C₂²×C₄₇	—	2	16	no	—
153	C₂²×C₄₇	—	2	8	no	—
154	C₂²×C₄₇	—	2	16	no	—
155	C₂²×C₄₇	—	4	64	no	—
156	C₂²×C₄₇	—	4	64	no	—
157	C₂²×C₄₇	—	4	32	no	—
158	C₂²×C₄₇	—	4	16	no	—
159	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	8	yes	—
160	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	16	yes	—
161	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	4	yes	—
162	C₂²×C₄₇	#518	1	8	yes	—
163	C₂²×C₄₇	#534	1	16	yes	—
164	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
165	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
166	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
167	C₄×C₄₇	—	2	8	no	—
168	Dic₄₇	—	4	16	no	—
169	C₂⁴×D₄	D₄₇	1	1	yes	characteristic
170	C₂³×C₂²⋊C₄	—	47	2	no	—
171	#2308	—	47	16	no	—
172	C₂×#386	—	47	8	no	—
173	C₂×#381	—	47	2	no	—
174	C₂×#379	—	47	2	no	—
175	C₂×C₄₇	—	2	8	no	—
176	C₂×C₄₇	—	2	16	no	—
177	C₂×C₄₇	—	4	8	no	—
178	C₂×C₄₇	#2308	1	8	yes	complemented
179	C₂×C₄₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄₇	C₂×#518	1	2	yes	—
181	C₂×C₄₇	C₂×#534	1	4	yes	—
182	C₂⁶	C₂×D₄₇	1	1	yes	characteristic
183	C₂⁶	C₂×D₄₇	1	1	yes	characteristic
184	C₂³×D₄	—	2	16	no	—
185	C₂³×D₄	Dic₄₇	1	16	yes	complemented
186	C₂³×D₄	C₂×D₄₇	1	8	yes	—
187	C₂³×D₄	C₂×D₄₇	1	4	yes	—
188	C₂⁴×C₄	—	47	4	no	—
189	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
190	C₂²×C₂²⋊C₄	—	47	16	no	—
191	C₂²×C₂²⋊C₄	—	47	4	no	—
192	C₂²×C₂²⋊C₄	—	47	4	no	—
193	C₂²×C₂²⋊C₄	—	47	8	no	—
194	C₂²×C₂²⋊C₄	—	94	16	no	—
195	#386	—	47	64	no	—
196	#381	—	47	16	no	—
197	#379	—	47	16	no	—
198	C₂×#95	—	47	8	no	—
199	C₄₇	C₂×#2308	1	1	yes	characteristic, complemented, Sylow
200	C₂⁵	—	2	8	no	—
201	C₂⁵	—	4	8	no	—
202	C₂⁵	—	4	8	no	—
203	C₂⁵	C₂×Dic₄₇	1	8	yes	—
204	C₂⁵	C₂×Dic₄₇	1	8	yes	complemented
205	C₂⁵	C₂²⋊D₄₇	1	16	yes	—
206	C₂⁵	C₂²×D₄₇	1	2	yes	—
207	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
208	C₂⁵	C₂²×D₄₇	1	2	yes	—
209	C₂⁵	C₂²×D₄₇	1	4	yes	—
210	C₂⁵	C₂²×D₄₇	1	4	yes	—
211	C₂²×D₄	—	2	128	no	—
212	C₂²×D₄	—	2	16	no	—
213	C₂²×D₄	—	2	16	no	—
214	C₂²×D₄	—	2	64	no	—
215	C₂²×D₄	C₂×Dic₄₇	1	32	yes	complemented
216	C₂²×D₄	C₂×Dic₄₇	1	64	yes	complemented
217	C₂²×D₄	C₂²×D₄₇	1	16	yes	—
218	C₂³×C₄	—	2	8	no	—
219	C₂³×C₄	—	47	8	no	—
220	C₂³×C₄	—	47	16	no	—
221	C₂³×C₄	—	94	16	no	—
222	C₂³×C₄	—	188	16	no	—
223	C₂³×C₄	C₂×Dic₄₇	1	8	yes	complemented
224	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
225	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
226	C₂×C₂²⋊C₄	—	47	16	no	—
227	C₂×C₂²⋊C₄	—	47	16	no	—
228	C₂×C₂²⋊C₄	—	47	32	no	—
229	C₂×C₂²⋊C₄	—	94	16	no	—
230	C₂×C₂²⋊C₄	—	94	16	no	—
231	C₂×C₂²⋊C₄	—	94	64	no	—
232	C₂×C₂²⋊C₄	—	188	16	no	—
233	#95	—	47	32	no	—
234	C₂⁴	—	2	16	no	—
235	C₂⁴	—	2	8	no	—
236	C₂⁴	—	2	32	no	—
237	C₂⁴	—	2	8	no	—
238	C₂⁴	—	2	16	no	—
239	C₂⁴	—	2	16	no	—
240	C₂⁴	—	4	32	no	—
241	C₂⁴	—	4	32	no	—
242	C₂⁴	—	4	64	no	—
243	C₂⁴	—	4	16	no	—
244	C₂⁴	—	4	16	no	—
245	C₂⁴	—	4	64	no	—
246	C₂⁴	C₂²⋊Dic₄₇	1	64	yes	complemented
247	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
248	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
249	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
250	C₂⁴	C₂²×Dic₄₇	1	16	yes	—
251	C₂⁴	C₂²×Dic₄₇	1	16	yes	complemented
252	C₂⁴	C₂×C₂²⋊D₄₇	1	8	yes	—
253	C₂⁴	C₂×C₂²⋊D₄₇	1	8	yes	—
254	C₂⁴	C₂×C₂²⋊D₄₇	1	8	yes	—
255	C₂⁴	C₂×C₂²⋊D₄₇	1	32	yes	—
256	C₂⁴	C₂³×D₄₇	1	4	yes	—
257	C₂⁴	C₂³×D₄₇	1	2	yes	—
258	C₂⁴	C₂³×D₄₇	1	4	yes	—
259	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
260	C₂×D₄	—	2	128	no	—
261	C₂×D₄	—	2	256	no	—
262	C₂×D₄	—	2	32	no	—
263	C₂×D₄	—	2	32	no	—
264	C₂×D₄	C₂²×Dic₄₇	1	64	yes	complemented
265	C₂²×C₄	—	2	32	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	16	no	—
268	C₂²×C₄	—	47	16	no	—
269	C₂²×C₄	—	94	32	no	—
270	C₂²×C₄	—	94	16	no	—
271	C₂²×C₄	—	94	32	no	—
272	C₂²×C₄	—	188	32	no	—
273	C₂²×C₄	—	188	64	no	—
274	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
275	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	complemented
276	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
277	C₂²⋊C₄	—	94	32	no	—
278	C₂²⋊C₄	—	94	32	no	—
279	C₂²⋊C₄	—	188	32	no	—
280	C₂³	—	2	16	no	—
281	C₂³	—	2	32	no	—
282	C₂³	—	2	32	no	—
283	C₂³	—	2	32	no	—
284	C₂³	—	2	32	no	—
285	C₂³	—	2	16	no	—
286	C₂³	—	2	8	no	—
287	C₂³	—	2	16	no	—
288	C₂³	—	2	32	no	—
289	C₂³	—	2	32	no	—
290	C₂³	—	2	8	no	—
291	C₂³	—	2	16	no	—
292	C₂³	—	4	128	no	—
293	C₂³	—	4	32	no	—
294	C₂³	—	4	32	no	—
295	C₂³	—	4	64	no	—
296	C₂³	—	4	64	no	—
297	C₂³	—	4	128	no	—
298	C₂³	—	4	32	no	—
299	C₂³	C₂×C₂²⋊Dic₄₇	1	16	yes	—
300	C₂³	C₂×C₂²⋊Dic₄₇	1	32	yes	—
301	C₂³	C₂×C₂²⋊Dic₄₇	1	64	yes	complemented
302	C₂³	C₂³×Dic₄₇	1	8	yes	—
303	C₂³	C₂³×Dic₄₇	1	4	yes	—
304	C₂³	C₂³×Dic₄₇	1	8	yes	—
305	C₂³	C₂³×Dic₄₇	1	2	yes	—
306	C₂³	C₂²×C₂²⋊D₄₇	1	8	yes	—
307	C₂³	C₂²×C₂²⋊D₄₇	1	8	yes	—
308	C₂³	C₂²×C₂²⋊D₄₇	1	8	yes	—
309	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
310	C₂³	#13094069	1	8	yes	—
311	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
312	D₄	—	2	128	no	—
313	C₂×C₄	—	2	16	no	—
314	C₂×C₄	—	2	32	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	94	16	no	—
317	C₂×C₄	—	94	32	no	—
318	C₂×C₄	—	188	64	no	—
319	C₂×C₄	—	188	32	no	—
320	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	16	no	—
323	C₂²	—	2	16	no	—
324	C₂²	—	2	16	no	—
325	C₂²	—	2	16	no	—
326	C₂²	—	2	32	no	—
327	C₂²	—	2	64	no	—
328	C₂²	—	2	8	no	—
329	C₂²	—	2	16	no	—
330	C₂²	—	4	64	no	—
331	C₂²	—	4	64	no	—
332	C₂²	—	4	16	no	—
333	C₂²	—	4	32	no	—
334	C₂²	C₂²×C₂²⋊Dic₄₇	1	8	yes	—
335	C₂²	C₂²×C₂²⋊Dic₄₇	1	16	yes	—
336	C₂²	C₂²×C₂²⋊Dic₄₇	1	4	yes	—
337	C₂²	#15689598	1	8	yes	—
338	C₂²	#15689682	1	16	yes	—
339	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
340	C₂²	C₂³×C₂²⋊D₄₇	1	2	yes	—
341	C₂²	C₂×#13094069	1	4	yes	—
342	C₄	—	2	8	no	—
343	C₄	—	188	16	no	—
344	C₂	—	2	8	no	—
345	C₂	—	2	16	no	—
346	C₂	—	4	8	no	—
347	C₂	#20245966	1	8	yes	direct product factor
348	C₂	C₂³×C₂²⋊Dic₄₇	1	1	yes	characteristic
349	C₂	C₂×#15689598	1	2	yes	—
350	C₂	C₂×#15689682	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting, prime radical	C₂⁴×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂⁴×D₄	D₄₇
hypocenter	C₄₇	C₂×#2308
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂²⋊Dic₄₇	C₂	semidirect
2. #20245966	C₂	direct (N × H)
3. C₂×#15689003	C₂	semidirect
4. C₂×#15688986	C₂	semidirect
5. C₂×#15688979	C₂	semidirect
7. C₂⁴×Dic₄₇	C₂²	semidirect
10. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
11. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
12. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
13. #15689003	C₂²	semidirect
14. #15688986	C₂²	semidirect
15. #15688979	C₂²	semidirect
16. C₂×C₄₇⋊#95	C₂²	semidirect
20. C₂³×D₄×C₄₇	C₄	semidirect
27. C₂³×Dic₄₇	C₂³	semidirect
33. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
34. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
35. C₄₇⋊#95	C₂³	semidirect
40. C₂⁵×C₄₇	C₂×C₄	semidirect
51. C₂²×D₄×C₄₇	C₂×C₄	semidirect
52. C₂²×D₄×C₄₇	C₂×C₄	semidirect
55. C₂³×C₄×C₄₇	C₂×C₄	semidirect
70. C₂⁴×C₄₇	C₂²⋊C₄	semidirect
75. C₂⁴×C₄₇	C₂²×C₄	semidirect
88. C₂×D₄×C₄₇	C₂²×C₄	semidirect
93. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
125. C₂³×C₄₇	C₂×C₂²⋊C₄	semidirect
178. C₂×C₄₇	#2308	semidirect
185. C₂³×D₄	Dic₄₇	semidirect
199. C₄₇	C₂×#2308	semidirect
204. C₂⁵	C₂×Dic₄₇	semidirect
215. C₂²×D₄	C₂×Dic₄₇	semidirect
216. C₂²×D₄	C₂×Dic₄₇	semidirect
223. C₂³×C₄	C₂×Dic₄₇	semidirect
246. C₂⁴	C₂²⋊Dic₄₇	semidirect
251. C₂⁴	C₂²×Dic₄₇	semidirect
264. C₂×D₄	C₂²×Dic₄₇	semidirect
275. C₂²×C₄	C₂²×Dic₄₇	semidirect
301. C₂³	C₂×C₂²⋊Dic₄₇	semidirect
347. C₂	#20245966	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×C₂²⋊Dic₄₇	2
#20245966	2
C₂×#15689003	2
C₂×#15688986	2
C₂×#15688979	2
C₂⁴×D₄×C₄₇	2
C₂×#2308	47

Subgroups — C2×#20245966 #26374828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245966 #26374828