Subgroups — C₂×D₄×C₂²⋊Dic₄₇ #26375452

Order 12032.

8774 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	C₂³×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
3	D₄×C₂²⋊Dic₄₇	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689026	C₂	1	2	yes	maximal, complemented
5	C₂×#15689003	C₂	1	4	yes	maximal, complemented
6	C₂×#15688983	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688979	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂⁴×Dic₄₇	C₂²	1	4	yes	complemented
11	C₂×D₄×Dic₄₇	—	2	16	no	—
12	C₂×D₄×Dic₄₇	C₂²	1	16	yes	complemented
13	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
14	C₂²×C₂²⋊Dic₄₇	—	2	16	no	—
15	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊Dic₄₇	C₂²	1	16	yes	complemented
19	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
20	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
21	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
22	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	complemented
23	#15689026	C₂²	1	16	yes	complemented
24	#15689003	C₂²	1	32	yes	complemented
25	#15688983	C₂²	1	8	yes	complemented
26	#15688979	C₂²	1	16	yes	complemented
27	C₄×C₂²⋊Dic₄₇	C₂²	1	8	yes	complemented
28	C₂×C₄₇⋊#95	C₂²	1	2	yes	complemented
29	C₂×C₄₇⋊#95	C₂²	1	2	yes	complemented
30	C₂⁶×C₄₇	C₂²	1	2	yes	—
31	C₂³×D₄×C₄₇	—	2	16	no	—
32	C₂³×D₄×C₄₇	C₄	1	16	yes	complemented
33	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
34	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₂³×D₄×C₄₇	C₂²	1	8	yes	—
36	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₂³×Dic₄₇	—	2	16	no	—
39	C₂³×Dic₄₇	—	2	16	no	—
40	C₂³×Dic₄₇	—	4	8	no	—
41	C₂³×Dic₄₇	C₂³	1	2	yes	—
42	C₂³×Dic₄₇	C₂³	1	4	yes	—
43	C₂³×Dic₄₇	C₂³	1	2	yes	—
44	C₂³×Dic₄₇	C₂³	1	16	yes	complemented
45	D₄×Dic₄₇	—	2	64	no	—
46	C₂×C₄⋊Dic₄₇	—	2	8	no	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	complemented
48	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
49	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
50	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
51	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
52	C₂×C₂²⋊Dic₄₇	—	2	64	no	—
53	C₂×C₂²⋊Dic₄₇	—	4	8	no	—
54	C₂×C₂²⋊Dic₄₇	D₄	1	8	yes	direct product factor
55	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
56	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
57	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
58	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	complemented
59	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	complemented
60	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	complemented
61	C₂×C₄×Dic₄₇	—	2	8	no	—
62	C₂×C₄×Dic₄₇	C₂³	1	8	yes	complemented
63	C₄₇⋊#95	C₂³	1	8	yes	complemented
64	C₄₇⋊#95	C₂³	1	8	yes	complemented
65	C₂⁵×C₄₇	—	2	8	no	—
66	C₂⁵×C₄₇	—	2	16	no	—
67	C₂⁵×C₄₇	—	2	8	no	—
68	C₂⁵×C₄₇	—	4	8	no	—
69	C₂⁵×C₄₇	C₂×C₄	1	16	yes	complemented
70	C₂⁵×C₄₇	C₂³	1	2	yes	—
71	C₂⁵×C₄₇	C₂³	1	8	yes	—
72	C₂⁵×C₄₇	C₂³	1	2	yes	—
73	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₄₇	—	2	16	no	—
75	C₂²×D₄×C₄₇	—	2	128	no	—
76	C₂²×D₄×C₄₇	—	2	64	no	—
77	C₂²×D₄×C₄₇	—	2	8	no	—
78	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
79	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
80	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
81	C₂²×D₄×C₄₇	C₂×C₄	1	64	yes	complemented
82	C₂²×D₄×C₄₇	D₄	1	16	yes	—
83	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
84	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
85	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
86	C₂³×C₄×C₄₇	—	2	8	no	—
87	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
88	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂⁴×C₄₇	—	2	4	no	—
92	C₂⁴×C₄₇	—	2	4	no	—
93	C₂⁴×C₄₇	—	2	4	no	—
94	C₂⁴×C₄₇	—	2	4	no	—
95	C₂⁴×C₄₇	—	2	8	no	—
96	C₂⁴×C₄₇	—	2	64	no	—
97	C₂⁴×C₄₇	—	2	64	no	—
98	C₂⁴×C₄₇	—	2	32	no	—
99	C₂⁴×C₄₇	—	2	8	no	—
100	C₂⁴×C₄₇	—	2	16	no	—
101	C₂⁴×C₄₇	—	2	4	no	—
102	C₂⁴×C₄₇	—	2	16	no	—
103	C₂⁴×C₄₇	—	2	4	no	—
104	C₂⁴×C₄₇	—	2	8	no	—
105	C₂⁴×C₄₇	—	4	32	no	—
106	C₂⁴×C₄₇	—	4	16	no	—
107	C₂⁴×C₄₇	—	4	64	no	—
108	C₂⁴×C₄₇	—	4	64	no	—
109	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
110	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
111	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
112	C₂⁴×C₄₇	C₂²×C₄	1	32	yes	complemented
113	C₂⁴×C₄₇	C₂×D₄	1	16	yes	—
114	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
115	C₂⁴×C₄₇	#41	1	4	yes	—
116	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
117	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
118	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
119	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂×D₄×C₄₇	—	2	64	no	—
121	C₂×D₄×C₄₇	—	2	32	no	—
122	C₂×D₄×C₄₇	—	2	256	no	—
123	C₂×D₄×C₄₇	—	2	32	no	—
124	C₂×D₄×C₄₇	—	2	16	no	—
125	C₂×D₄×C₄₇	C₂²⋊C₄	1	64	yes	complemented
126	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
127	C₂×D₄×C₄₇	C₂²×C₄	1	32	yes	complemented
128	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	complemented
129	C₂×D₄×C₄₇	C₂×D₄	1	32	yes	—
130	C₂²×C₄×C₄₇	—	2	4	no	—
131	C₂²×C₄×C₄₇	—	2	32	no	—
132	C₂²×C₄×C₄₇	—	2	16	no	—
133	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
136	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
137	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
139	C₂²×Dic₄₇	—	2	4	no	—
140	C₂²×Dic₄₇	—	2	4	no	—
141	C₂²×Dic₄₇	—	2	4	no	—
142	C₂²×Dic₄₇	—	2	8	no	—
143	C₂²×Dic₄₇	—	2	8	no	—
144	C₂²×Dic₄₇	—	2	32	no	—
145	C₂²×Dic₄₇	—	2	4	no	—
146	C₂²×Dic₄₇	—	2	4	no	—
147	C₂²×Dic₄₇	—	2	8	no	—
148	C₂²×Dic₄₇	—	2	32	no	—
149	C₂²×Dic₄₇	—	4	16	no	—
150	C₂²×Dic₄₇	—	4	64	no	—
151	C₂²×Dic₄₇	C₂×D₄	1	8	yes	complemented
152	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
153	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
154	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
155	C₂²⋊Dic₄₇	—	2	16	no	—
156	C₂²⋊Dic₄₇	—	2	32	no	—
157	C₂²⋊Dic₄₇	—	2	8	no	—
158	C₂²⋊Dic₄₇	—	2	32	no	—
159	C₂²⋊Dic₄₇	—	4	16	no	—
160	C₂²⋊Dic₄₇	C₂×D₄	1	16	yes	direct product factor
161	C₄⋊Dic₄₇	—	2	16	no	—
162	C₄×Dic₄₇	—	2	16	no	—
163	C₂³×C₄₇	—	2	8	no	—
164	C₂³×C₄₇	—	2	16	no	—
165	C₂³×C₄₇	—	2	8	no	—
166	C₂³×C₄₇	—	2	16	no	—
167	C₂³×C₄₇	—	2	32	no	—
168	C₂³×C₄₇	—	2	16	no	—
169	C₂³×C₄₇	—	2	16	no	—
170	C₂³×C₄₇	—	2	32	no	—
171	C₂³×C₄₇	—	2	4	no	—
172	C₂³×C₄₇	—	2	4	no	—
173	C₂³×C₄₇	—	2	4	no	—
174	C₂³×C₄₇	—	2	8	no	—
175	C₂³×C₄₇	—	2	4	no	—
176	C₂³×C₄₇	—	2	16	no	—
177	C₂³×C₄₇	—	2	64	no	—
178	C₂³×C₄₇	—	2	16	no	—
179	C₂³×C₄₇	—	2	64	no	—
180	C₂³×C₄₇	—	2	16	no	—
181	C₂³×C₄₇	—	2	4	no	—
182	C₂³×C₄₇	—	2	8	no	—
183	C₂³×C₄₇	—	2	4	no	—
184	C₂³×C₄₇	—	2	8	no	—
185	C₂³×C₄₇	—	4	32	no	—
186	C₂³×C₄₇	—	4	256	no	—
187	C₂³×C₄₇	—	4	64	no	—
188	C₂³×C₄₇	—	4	64	no	—
189	C₂³×C₄₇	—	4	16	no	—
190	C₂³×C₄₇	—	4	16	no	—
191	C₂³×C₄₇	C₂×C₂²⋊C₄	1	32	yes	complemented
192	C₂³×C₄₇	C₄×D₄	1	16	yes	complemented
193	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
194	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
195	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
196	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
197	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
198	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
199	C₂³×C₄₇	C₂²×D₄	1	16	yes	—
200	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
201	C₂³×C₄₇	C₂×#41	1	4	yes	—
202	C₂³×C₄₇	C₂×#41	1	2	yes	—
203	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
204	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
205	D₄×C₄₇	—	2	64	no	—
206	D₄×C₄₇	—	2	32	no	—
207	D₄×C₄₇	C₂×C₂²⋊C₄	1	64	yes	complemented
208	C₂×C₄×C₄₇	—	2	8	no	—
209	C₂×C₄×C₄₇	—	2	4	no	—
210	C₂×C₄×C₄₇	—	2	32	no	—
211	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	16	yes	complemented
212	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
213	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
214	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
215	C₂×Dic₄₇	—	2	16	no	—
216	C₂×Dic₄₇	—	2	4	no	—
217	C₂×Dic₄₇	—	2	4	no	—
218	C₂×Dic₄₇	—	2	4	no	—
219	C₂×Dic₄₇	—	2	8	no	—
220	C₂×Dic₄₇	—	2	8	no	—
221	C₂×Dic₄₇	—	2	4	no	—
222	C₂×Dic₄₇	—	2	4	no	—
223	C₂×Dic₄₇	—	2	8	no	—
224	C₂×Dic₄₇	—	4	64	no	—
225	C₂×Dic₄₇	—	4	16	no	—
226	C₂×Dic₄₇	—	4	8	no	—
227	C₂×Dic₄₇	C₂²×D₄	1	8	yes	complemented
228	C₂×D₄×C₂²⋊C₄	—	47	1	no	maximal, Sylow
229	C₂²×C₄₇	—	2	32	no	—
230	C₂²×C₄₇	—	2	64	no	—
231	C₂²×C₄₇	—	2	4	no	—
232	C₂²×C₄₇	—	2	8	no	—
233	C₂²×C₄₇	—	2	4	no	—
234	C₂²×C₄₇	—	2	8	no	—
235	C₂²×C₄₇	—	2	16	no	—
236	C₂²×C₄₇	—	2	8	no	—
237	C₂²×C₄₇	—	2	8	no	—
238	C₂²×C₄₇	—	2	16	no	—
239	C₂²×C₄₇	—	2	8	no	—
240	C₂²×C₄₇	—	2	8	no	—
241	C₂²×C₄₇	—	2	8	no	—
242	C₂²×C₄₇	—	4	128	no	—
243	C₂²×C₄₇	—	4	32	no	—
244	C₂²×C₄₇	—	4	8	no	—
245	C₂²×C₄₇	—	4	8	no	—
246	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	4	yes	—
247	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	16	yes	complemented
248	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
249	C₂²×C₄₇	C₂×C₄×D₄	1	8	yes	complemented
250	C₂²×C₄₇	#518	1	4	yes	—
251	C₂²×C₄₇	D₄²	1	8	yes	—
252	C₂²×C₄₇	#546	1	8	yes	—
253	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
254	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
255	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
256	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
257	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
258	C₄×C₄₇	—	2	4	no	—
259	C₄×C₄₇	C₂²×C₂²⋊C₄	1	8	yes	complemented
260	Dic₄₇	—	2	8	no	—
261	Dic₄₇	—	4	8	no	—
262	Dic₄₇	—	4	4	no	—
263	C₂⁴×D₄	D₄₇	1	1	yes	characteristic
264	C₂²×C₄×D₄	—	47	2	no	—
265	C₂³×C₂²⋊C₄	—	47	2	no	—
266	D₄×C₂²⋊C₄	—	47	16	no	—
267	C₂×#390	—	47	2	no	—
268	C₂×#386	—	47	4	no	—
269	C₂×#380	—	47	1	no	—
270	C₂×#379	—	47	2	no	—
271	C₂×C₄×C₂²⋊C₄	—	47	1	no	—
272	C₂×C₄₇	—	2	8	no	—
273	C₂×C₄₇	—	2	16	no	—
274	C₂×C₄₇	—	4	8	no	—
275	C₂×C₄₇	D₄×C₂²⋊C₄	1	8	yes	complemented
276	C₂×C₄₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
278	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
279	C₂×C₄₇	C₂×D₄²	1	2	yes	—
280	C₂×C₄₇	C₂×#546	1	2	yes	—
281	C₂⁶	C₂×D₄₇	1	2	yes	—
282	C₂³×D₄	—	2	16	no	—
283	C₂³×D₄	Dic₄₇	1	16	yes	complemented
284	C₂³×D₄	C₂×D₄₇	1	8	yes	—
285	C₂³×D₄	C₂×D₄₇	1	2	yes	—
286	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
287	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
288	C₂⁴×C₄	—	47	4	no	—
289	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
290	C₂×C₄×D₄	—	47	16	no	—
291	C₂×C₄×D₄	—	94	16	no	—
292	C₂²×C₄⋊C₄	—	47	2	no	—
293	C₂²×C₂²⋊C₄	—	47	1	no	—
294	C₂²×C₂²⋊C₄	—	47	16	no	—
295	C₂²×C₂²⋊C₄	—	47	2	no	—
296	C₂²×C₂²⋊C₄	—	47	4	no	—
297	C₂²×C₂²⋊C₄	—	47	4	no	—
298	C₂²×C₂²⋊C₄	—	47	1	no	—
299	C₂²×C₂²⋊C₄	—	47	4	no	—
300	C₂²×C₂²⋊C₄	—	94	16	no	—
301	C₂²×C₄²	—	47	2	no	—
302	#390	—	47	16	no	—
303	#386	—	47	32	no	—
304	#380	—	47	8	no	—
305	#379	—	47	16	no	—
306	C₄×C₂²⋊C₄	—	47	8	no	—
307	C₂×#95	—	47	2	no	—
308	C₂×#95	—	47	2	no	—
309	C₄₇	C₂×D₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
310	C₂⁵	—	2	8	no	—
311	C₂⁵	—	2	8	no	—
312	C₂⁵	—	2	16	no	—
313	C₂⁵	—	4	8	no	—
314	C₂⁵	C₂×Dic₄₇	1	16	yes	complemented
315	C₂⁵	C₂²×D₄₇	1	2	yes	—
316	C₂⁵	C₂²×D₄₇	1	8	yes	—
317	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
318	C₂⁵	C₂²×D₄₇	1	2	yes	—
319	C₂²×D₄	—	2	16	no	—
320	C₂²×D₄	—	2	128	no	—
321	C₂²×D₄	—	2	64	no	—
322	C₂²×D₄	—	2	8	no	—
323	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
324	C₂²×D₄	C₂×Dic₄₇	1	16	yes	complemented
325	C₂²×D₄	C₂×Dic₄₇	1	8	yes	complemented
326	C₂²×D₄	C₂×Dic₄₇	1	64	yes	complemented
327	C₂²×D₄	C₂²⋊D₄₇	1	16	yes	—
328	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
329	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
330	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
331	C₂³×C₄	—	2	8	no	—
332	C₂³×C₄	—	47	2	no	—
333	C₂³×C₄	—	47	2	no	—
334	C₂³×C₄	—	47	4	no	—
335	C₂³×C₄	—	47	16	no	—
336	C₂³×C₄	—	94	16	no	—
337	C₂³×C₄	—	94	16	no	—
338	C₂³×C₄	—	188	8	no	—
339	C₂³×C₄	C₂×Dic₄₇	1	8	yes	complemented
340	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
341	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
342	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
343	C₄×D₄	—	94	64	no	—
344	C₂×C₄⋊C₄	—	47	8	no	—
345	C₂×C₄⋊C₄	—	94	8	no	—
346	C₂×C₂²⋊C₄	—	47	8	no	—
347	C₂×C₂²⋊C₄	—	47	4	no	—
348	C₂×C₂²⋊C₄	—	47	8	no	—
349	C₂×C₂²⋊C₄	—	47	16	no	—
350	C₂×C₂²⋊C₄	—	47	16	no	—
351	C₂×C₂²⋊C₄	—	47	4	no	—
352	C₂×C₂²⋊C₄	—	47	16	no	—
353	C₂×C₂²⋊C₄	—	94	64	no	—
354	C₂×C₂²⋊C₄	—	94	16	no	—
355	C₂×C₂²⋊C₄	—	94	8	no	—
356	C₂×C₂²⋊C₄	—	94	4	no	—
357	C₂×C₂²⋊C₄	—	94	16	no	—
358	C₂×C₂²⋊C₄	—	188	8	no	—
359	C₂×C₄²	—	47	8	no	—
360	C₂×C₄²	—	94	8	no	—
361	#95	—	47	8	no	—
362	#95	—	47	8	no	—
363	C₂⁴	—	2	4	no	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	—	2	8	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	64	no	—
369	C₂⁴	—	2	64	no	—
370	C₂⁴	—	2	16	no	—
371	C₂⁴	—	2	4	no	—
372	C₂⁴	—	2	32	no	—
373	C₂⁴	—	2	8	no	—
374	C₂⁴	—	2	16	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	2	8	no	—
377	C₂⁴	—	4	32	no	—
378	C₂⁴	—	4	16	no	—
379	C₂⁴	—	4	64	no	—
380	C₂⁴	—	4	64	no	—
381	C₂⁴	D₄×D₄₇	1	4	yes	—
382	C₂⁴	#10625352	1	4	yes	—
383	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
384	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
385	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
386	C₂⁴	C₂²×Dic₄₇	1	32	yes	complemented
387	C₂⁴	C₂×C₂²⋊D₄₇	1	16	yes	—
388	C₂⁴	C₂³×D₄₇	1	4	yes	—
389	C₂⁴	C₂³×D₄₇	1	2	yes	—
390	C₂⁴	C₂³×D₄₇	1	4	yes	—
391	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
392	C₂×D₄	—	2	64	no	—
393	C₂×D₄	—	2	32	no	—
394	C₂×D₄	—	2	256	no	—
395	C₂×D₄	—	2	32	no	—
396	C₂×D₄	—	2	16	no	—
397	C₂×D₄	C₂²⋊Dic₄₇	1	64	yes	direct product factor
398	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
399	C₂×D₄	C₂²×Dic₄₇	1	32	yes	complemented
400	C₂×D₄	C₂²×Dic₄₇	1	16	yes	complemented
401	C₂×D₄	C₂×C₂²⋊D₄₇	1	32	yes	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	32	no	—
404	C₂²×C₄	—	2	16	no	—
405	C₂²×C₄	—	47	8	no	—
406	C₂²×C₄	—	47	4	no	—
407	C₂²×C₄	—	47	4	no	—
408	C₂²×C₄	—	47	8	no	—
409	C₂²×C₄	—	94	32	no	—
410	C₂²×C₄	—	94	4	no	—
411	C₂²×C₄	—	94	4	no	—
412	C₂²×C₄	—	94	8	no	—
413	C₂²×C₄	—	94	4	no	—
414	C₂²×C₄	—	94	8	no	—
415	C₂²×C₄	—	94	32	no	—
416	C₂²×C₄	—	94	4	no	—
417	C₂²×C₄	—	94	4	no	—
418	C₂²×C₄	—	94	8	no	—
419	C₂²×C₄	—	188	16	no	—
420	C₂²×C₄	—	188	64	no	—
421	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
422	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
423	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	complemented
424	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
425	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
426	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
427	C₄⋊C₄	—	94	16	no	—
428	C₂²⋊C₄	—	47	16	no	—
429	C₂²⋊C₄	—	94	32	no	—
430	C₂²⋊C₄	—	94	16	no	—
431	C₂²⋊C₄	—	94	32	no	—
432	C₂²⋊C₄	—	94	8	no	—
433	C₂²⋊C₄	—	188	16	no	—
434	C₄²	—	94	16	no	—
435	C₂³	—	2	32	no	—
436	C₂³	—	2	16	no	—
437	C₂³	—	2	16	no	—
438	C₂³	—	2	32	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	16	no	—
441	C₂³	—	2	8	no	—
442	C₂³	—	2	16	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	8	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	16	no	—
449	C₂³	—	2	64	no	—
450	C₂³	—	2	16	no	—
451	C₂³	—	2	64	no	—
452	C₂³	—	2	16	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	2	8	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	8	no	—
457	C₂³	—	4	32	no	—
458	C₂³	—	4	64	no	—
459	C₂³	—	4	64	no	—
460	C₂³	—	4	256	no	—
461	C₂³	—	4	16	no	—
462	C₂³	—	4	16	no	—
463	C₂³	C₂×C₂²⋊Dic₄₇	1	32	yes	complemented
464	C₂³	D₄×Dic₄₇	1	16	yes	complemented
465	C₂³	C₂³×Dic₄₇	1	8	yes	—
466	C₂³	C₂³×Dic₄₇	1	8	yes	—
467	C₂³	C₂³×Dic₄₇	1	4	yes	—
468	C₂³	C₂³×Dic₄₇	1	2	yes	—
469	C₂³	C₂×D₄×D₄₇	1	4	yes	—
470	C₂³	C₂×D₄×D₄₇	1	2	yes	—
471	C₂³	C₂²×C₂²⋊D₄₇	1	16	yes	—
472	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
473	C₂³	C₂×#10625352	1	4	yes	—
474	C₂³	C₂×#10625352	1	2	yes	—
475	C₂³	#13094069	1	4	yes	—
476	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
477	D₄	—	2	64	no	—
478	D₄	—	2	32	no	—
479	D₄	C₂×C₂²⋊Dic₄₇	1	64	yes	direct product factor
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	32	no	—
483	C₂×C₄	—	47	8	no	—
484	C₂×C₄	—	94	16	no	—
485	C₂×C₄	—	94	4	no	—
486	C₂×C₄	—	94	4	no	—
487	C₂×C₄	—	94	8	no	—
488	C₂×C₄	—	94	4	no	—
489	C₂×C₄	—	94	8	no	—
490	C₂×C₄	—	94	4	no	—
491	C₂×C₄	—	94	4	no	—
492	C₂×C₄	—	94	8	no	—
493	C₂×C₄	—	188	64	no	—
494	C₂×C₄	—	188	16	no	—
495	C₂×C₄	—	188	8	no	—
496	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	16	yes	complemented
497	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
498	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
499	C₂×C₄	C₂²×C₂²⋊D₄₇	1	8	yes	—
500	C₂²	—	2	4	no	—
501	C₂²	—	2	8	no	—
502	C₂²	—	2	16	no	—
503	C₂²	—	2	8	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	8	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	2	16	no	—
508	C₂²	—	2	32	no	—
509	C₂²	—	2	64	no	—
510	C₂²	—	2	8	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	2	8	no	—
513	C₂²	—	4	128	no	—
514	C₂²	—	4	8	no	—
515	C₂²	—	4	8	no	—
516	C₂²	—	4	32	no	—
517	C₂²	C₂²×C₂²⋊Dic₄₇	1	4	yes	—
518	C₂²	C₂²×C₂²⋊Dic₄₇	1	16	yes	complemented
519	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
520	C₂²	C₂×D₄×Dic₄₇	1	8	yes	complemented
521	C₂²	#15689598	1	4	yes	—
522	C₂²	D₄×C₂²⋊D₄₇	1	8	yes	—
523	C₂²	#15689767	1	8	yes	—
524	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
525	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
526	C₂²	C₂³×C₂²⋊D₄₇	1	2	yes	—
527	C₂²	C₂²×#10625352	1	1	yes	characteristic
528	C₂²	C₂×#13094069	1	2	yes	—
529	C₄	—	2	4	no	—
530	C₄	—	94	8	no	—
531	C₄	—	188	8	no	—
532	C₄	—	188	4	no	—
533	C₄	C₂²×C₂²⋊Dic₄₇	1	8	yes	complemented
534	C₂	—	2	8	no	—
535	C₂	—	2	16	no	—
536	C₂	—	4	8	no	—
537	C₂	D₄×C₂²⋊Dic₄₇	1	8	yes	direct product factor
538	C₂	C₂³×C₂²⋊Dic₄₇	1	1	yes	characteristic
539	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
540	C₂	C₂×#15689598	1	1	yes	characteristic
541	C₂	C₂×D₄×C₂²⋊D₄₇	1	2	yes	—
542	C₂	C₂×#15689767	1	2	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×D₄×C₂²⋊C₄
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. C₂²×D₄×Dic₄₇	C₂	semidirect
2. C₂³×C₂²⋊Dic₄₇	C₂	semidirect
3. D₄×C₂²⋊Dic₄₇	C₂	direct (N × H)
4. C₂×#15689026	C₂	semidirect
5. C₂×#15689003	C₂	semidirect
6. C₂×#15688983	C₂	semidirect
7. C₂×#15688979	C₂	semidirect
8. C₂×C₄×C₂²⋊Dic₄₇	C₂	semidirect
10. C₂⁴×Dic₄₇	C₂²	semidirect
12. C₂×D₄×Dic₄₇	C₂²	semidirect
13. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
18. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
19. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
20. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
21. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
22. C₂²×C₄×Dic₄₇	C₂²	semidirect
23. #15689026	C₂²	semidirect
24. #15689003	C₂²	semidirect
25. #15688983	C₂²	semidirect
26. #15688979	C₂²	semidirect
27. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
28. C₂×C₄₇⋊#95	C₂²	semidirect
29. C₂×C₄₇⋊#95	C₂²	semidirect
32. C₂³×D₄×C₄₇	C₄	semidirect
44. C₂³×Dic₄₇	C₂³	semidirect
47. C₂×C₄⋊Dic₄₇	C₂³	semidirect
54. C₂×C₂²⋊Dic₄₇	D₄	direct (N × H)
58. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
59. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
60. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
62. C₂×C₄×Dic₄₇	C₂³	semidirect
63. C₄₇⋊#95	C₂³	semidirect
64. C₄₇⋊#95	C₂³	semidirect
69. C₂⁵×C₄₇	C₂×C₄	semidirect
79. C₂²×D₄×C₄₇	C₂×C₄	semidirect
80. C₂²×D₄×C₄₇	C₂×C₄	semidirect
81. C₂²×D₄×C₄₇	C₂×C₄	semidirect
87. C₂³×C₄×C₄₇	C₂×C₄	semidirect
112. C₂⁴×C₄₇	C₂²×C₄	semidirect
125. C₂×D₄×C₄₇	C₂²⋊C₄	semidirect
127. C₂×D₄×C₄₇	C₂²×C₄	semidirect
128. C₂×D₄×C₄₇	C₂²×C₄	semidirect
135. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
151. C₂²×Dic₄₇	C₂×D₄	semidirect
160. C₂²⋊Dic₄₇	C₂×D₄	direct (N × H)
191. C₂³×C₄₇	C₂×C₂²⋊C₄	semidirect
192. C₂³×C₄₇	C₄×D₄	semidirect
207. D₄×C₄₇	C₂×C₂²⋊C₄	semidirect
211. C₂×C₄×C₄₇	C₂×C₂²⋊C₄	semidirect
227. C₂×Dic₄₇	C₂²×D₄	semidirect
247. C₂²×C₄₇	C₂²×C₂²⋊C₄	semidirect
249. C₂²×C₄₇	C₂×C₄×D₄	semidirect
259. C₄×C₄₇	C₂²×C₂²⋊C₄	semidirect
275. C₂×C₄₇	D₄×C₂²⋊C₄	semidirect
283. C₂³×D₄	Dic₄₇	semidirect
309. C₄₇	C₂×D₄×C₂²⋊C₄	semidirect
314. C₂⁵	C₂×Dic₄₇	semidirect
324. C₂²×D₄	C₂×Dic₄₇	semidirect
325. C₂²×D₄	C₂×Dic₄₇	semidirect
326. C₂²×D₄	C₂×Dic₄₇	semidirect
339. C₂³×C₄	C₂×Dic₄₇	semidirect
386. C₂⁴	C₂²×Dic₄₇	semidirect
397. C₂×D₄	C₂²⋊Dic₄₇	direct (N × H)
399. C₂×D₄	C₂²×Dic₄₇	semidirect
400. C₂×D₄	C₂²×Dic₄₇	semidirect
423. C₂²×C₄	C₂²×Dic₄₇	semidirect
463. C₂³	C₂×C₂²⋊Dic₄₇	semidirect
464. C₂³	D₄×Dic₄₇	semidirect
479. D₄	C₂×C₂²⋊Dic₄₇	direct (N × H)
496. C₂×C₄	C₂×C₂²⋊Dic₄₇	semidirect
518. C₂²	C₂²×C₂²⋊Dic₄₇	semidirect
520. C₂²	C₂×D₄×Dic₄₇	semidirect
533. C₄	C₂²×C₂²⋊Dic₄₇	semidirect
537. C₂	D₄×C₂²⋊Dic₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₄×Dic₄₇	2
C₂³×C₂²⋊Dic₄₇	2
D₄×C₂²⋊Dic₄₇	2
C₂×#15689026	2
C₂×#15689003	2
C₂×#15688983	2
C₂×#15688979	2
C₂×C₄×C₂²⋊Dic₄₇	2
C₂⁴×D₄×C₄₇	2
C₂×D₄×C₂²⋊C₄	47

Subgroups — C2×D4×C22⋊Dic47 #26375452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₂²⋊Dic₄₇ #26375452