Subgroups — SD₁₆×C₄⋊Dic₄₇ #26234681

Order 12032.

1030 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×Dic₄₇	C₂	1	2	yes	maximal
2	Q₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20244117	C₂	1	2	yes	maximal, complemented
5	#20243658	C₂	1	2	yes	maximal, complemented
6	#20243651	C₂	1	2	yes	maximal
7	#20243545	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243393	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243388	C₂	1	1	yes	maximal, characteristic
10	C₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×SD₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
15	SD₁₆×Dic₄₇	—	2	8	no	—
16	C₂×#13093956	C₂²	1	2	yes	—
17	C₂×#13093956	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#13093948	C₂²	1	2	yes	—
20	C₂×#13093945	C₂²	1	2	yes	—
21	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
22	#15689022	—	2	2	no	—
23	#15689022	C₂²	1	2	yes	—
24	#15689022	C₂²	1	2	yes	—
25	#15688998	—	2	2	no	—
26	#15688993	—	2	1	no	—
27	#15688993	C₂²	1	1	yes	characteristic
28	#15688993	C₂²	1	1	yes	characteristic
29	#15688983	—	2	1	no	—
30	C₄×C₄⋊Dic₄₇	—	2	1	no	—
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×SD₁₆×C₄₇	C₄	1	8	yes	complemented
39	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂³×Dic₄₇	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	Q₈×Dic₄₇	—	2	4	no	—
46	Q₈×Dic₄₇	—	4	2	no	—
47	D₄×Dic₄₇	—	2	4	no	—
48	D₄×Dic₄₇	—	4	2	no	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	—	2	1	no	—
55	C₂×C₄⋊Dic₄₇	—	2	2	no	—
56	C₂×C₄⋊Dic₄₇	—	4	4	no	—
57	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
61	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
62	C₂×C₄×Dic₄₇	—	2	2	no	—
63	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
64	#13093956	—	2	4	no	—
65	#13093956	—	4	2	no	—
66	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
67	#13093948	—	2	4	no	—
68	#13093945	—	2	4	no	—
69	C₈×Dic₄₇	—	2	4	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₄₇⋊#95	D₄	1	2	yes	—
73	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₄₇	—	2	1	no	—
76	C₂×SD₁₆×C₄₇	C₂×C₄	1	4	yes	—
77	C₂×SD₁₆×C₄₇	D₄	1	4	yes	—
78	C₂×SD₁₆×C₄₇	Q₈	1	4	yes	—
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₄×Q₈×C₄₇	—	2	2	no	—
82	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
83	C₄×D₄×C₄₇	—	2	2	no	—
84	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
85	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	#106×C₄₇	C₂×C₄	1	4	yes	complemented
92	#103×C₄₇	C₂×C₄	1	4	yes	complemented
93	#102×C₄₇	C₂×C₄	1	4	yes	—
94	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
95	C₂⁴×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	—	2	1	no	—
99	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
101	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
102	C₂×D₄×C₄₇	—	2	1	no	—
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	—	2	1	no	—
105	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₄₇	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	4	2	no	—
113	C₂²×C₄×C₄₇	—	4	2	no	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂²×Dic₄₇	—	2	2	no	—
118	C₂²×Dic₄₇	—	2	2	no	—
119	C₂²×Dic₄₇	—	4	4	no	—
120	C₂²×Dic₄₇	—	4	4	no	—
121	C₂²×Dic₄₇	—	8	2	no	—
122	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
123	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
124	SD₁₆×C₄₇	C₄⋊C₄	1	16	yes	complemented
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
131	C₄⋊C₄×C₄₇	—	2	4	no	—
132	C₄⋊C₄×C₄₇	—	2	1	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
135	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
136	C₂²⋊C₄×C₄₇	—	2	4	no	—
137	C₄²×C₄₇	—	2	4	no	—
138	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₇	#41	1	2	yes	—
140	C₂²⋊Dic₄₇	—	4	4	no	—
141	C₄⋊Dic₄₇	—	2	2	no	—
142	C₄⋊Dic₄₇	—	2	2	no	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	—	2	2	no	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	—	4	4	no	—
147	C₄⋊Dic₄₇	—	4	2	no	—
148	C₄⋊Dic₄₇	—	4	2	no	—
149	C₄⋊Dic₄₇	—	4	4	no	—
150	C₄⋊Dic₄₇	—	8	2	no	—
151	C₄⋊Dic₄₇	—	8	1	no	—
152	C₄⋊Dic₄₇	—	8	1	no	—
153	C₄⋊Dic₄₇	SD₁₆	1	4	yes	direct product factor
154	C₄×Dic₄₇	—	2	2	no	—
155	C₄×Dic₄₇	—	2	2	no	—
156	C₄×Dic₄₇	—	4	4	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	2	2	no	—
162	C₂³×C₄₇	—	2	2	no	—
163	C₂³×C₄₇	—	4	1	no	—
164	C₂³×C₄₇	—	4	1	no	—
165	C₂³×C₄₇	—	4	1	no	—
166	C₂³×C₄₇	—	4	1	no	—
167	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₄₇	—	2	2	no	—
169	Q₈×C₄₇	—	2	2	no	—
170	Q₈×C₄₇	—	2	2	no	—
171	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	complemented
172	D₄×C₄₇	—	2	2	no	—
173	D₄×C₄₇	—	2	2	no	—
174	D₄×C₄₇	—	2	2	no	—
175	D₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	8	no	—
188	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
191	C₂×C₄×C₄₇	#135	1	2	yes	—
192	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
198	C₂×Dic₄₇	—	2	2	no	—
199	C₂×Dic₄₇	—	2	2	no	—
200	C₂×Dic₄₇	—	2	2	no	—
201	C₂×Dic₄₇	—	2	2	no	—
202	C₂×Dic₄₇	—	2	2	no	—
203	C₂×Dic₄₇	—	4	2	no	—
204	C₂×Dic₄₇	—	4	2	no	—
205	C₂×Dic₄₇	—	4	2	no	—
206	C₂×Dic₄₇	—	4	2	no	—
207	C₂×Dic₄₇	—	4	2	no	—
208	C₂×Dic₄₇	—	4	2	no	—
209	C₂×Dic₄₇	—	8	8	no	—
210	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
211	C₈×C₄₇	—	2	2	no	—
212	C₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	complemented
213	C₄₇⋊C₈	—	4	2	no	—
214	C₄⋊C₄×SD₁₆	—	47	1	no	maximal, Sylow
215	C₂²×C₄₇	—	2	4	no	—
216	C₂²×C₄₇	—	4	2	no	—
217	C₂²×C₄₇	—	4	2	no	—
218	C₂²×C₄₇	—	4	2	no	—
219	C₂²×C₄₇	—	4	2	no	—
220	C₂²×C₄₇	—	4	2	no	—
221	C₂²×C₄₇	—	4	2	no	—
222	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂²×C₄₇	D₄²	1	1	yes	characteristic
224	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
225	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
226	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
227	C₂²×C₄₇	#577	1	1	yes	characteristic
228	C₂²×C₄₇	#577	1	1	yes	characteristic
229	C₄×C₄₇	—	2	4	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	4	2	no	—
232	C₄×C₄₇	—	4	2	no	—
233	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
234	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
235	C₄×C₄₇	#520	1	1	yes	characteristic
236	C₄×C₄₇	#547	1	1	yes	characteristic
237	C₄×C₄₇	#554	1	1	yes	characteristic
238	Dic₄₇	—	2	4	no	—
239	Dic₄₇	—	4	2	no	—
240	Dic₄₇	—	8	2	no	—
241	Dic₄₇	—	8	2	no	—
242	C₂×C₄×SD₁₆	—	47	2	no	—
243	C₂×C₄×SD₁₆	D₄₇	1	1	yes	characteristic
244	Q₈×C₄⋊C₄	—	47	1	no	—
245	D₄×C₄⋊C₄	—	47	1	no	—
246	#1941	—	47	2	no	—
247	#1865	—	47	2	no	—
248	#1864	—	47	2	no	—
249	#1844	—	47	1	no	—
250	#1803	—	47	1	no	—
251	#1802	—	47	1	no	—
252	C₈×C₄⋊C₄	—	47	1	no	—
253	C₂×C₄₇	—	4	4	no	—
254	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
255	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
256	C₂×C₄₇	#2952	1	1	yes	characteristic
257	C₂×C₄₇	D₄×SD₁₆	1	1	yes	characteristic
258	C₂×C₄₇	#3284	1	1	yes	characteristic
259	C₂×C₄₇	Q₈×SD₁₆	1	1	yes	characteristic
260	C₂×C₄₇	#3381	1	1	yes	characteristic
261	C₂²×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
262	C₂×C₄×Q₈	—	47	2	no	—
263	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
264	C₂×C₄×D₄	—	47	2	no	—
265	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	—	94	1	no	—
267	C₄×SD₁₆	—	94	8	no	—
268	C₄×SD₁₆	Dic₄₇	1	8	yes	complemented
269	C₂×#106	—	47	2	no	—
270	C₂×#106	—	47	2	no	—
271	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
272	C₂×C₄⋊C₈	—	47	1	no	—
273	C₂×#103	—	47	2	no	—
274	C₂×#103	C₂×D₄₇	1	1	yes	characteristic
275	C₂×#102	—	47	2	no	—
276	C₂×#102	C₂×D₄₇	1	1	yes	characteristic
277	C₂×C₄×C₈	—	47	2	no	—
278	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
279	#389	—	47	2	no	—
280	#389	—	47	2	no	—
281	#389	—	94	2	no	—
282	#385	—	94	2	no	—
283	#384	—	47	1	no	—
284	#384	—	47	1	no	—
285	#384	—	94	1	no	—
286	#380	—	94	1	no	—
287	C₄×C₄⋊C₄	—	47	1	no	—
288	C₄×C₄⋊C₄	—	94	1	no	—
289	#340	—	47	2	no	—
290	#340	—	47	2	no	—
291	#336	—	47	2	no	—
292	C₄₇	C₄⋊C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
293	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
294	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	—	94	2	no	—
297	C₂×SD₁₆	Dic₉₄	1	4	yes	—
298	C₂×SD₁₆	D₁₈₈	1	4	yes	—
299	C₂×SD₁₆	C₂×Dic₄₇	1	4	yes	—
300	C₂²×C₈	—	47	2	no	—
301	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
302	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	94	4	no	—
305	C₄×Q₈	—	188	2	no	—
306	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	94	4	no	—
309	C₄×D₄	—	188	2	no	—
310	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	47	1	no	—
313	C₂×C₄⋊C₄	—	47	1	no	—
314	C₂×C₄⋊C₄	—	47	2	no	—
315	C₂×C₄⋊C₄	—	47	2	no	—
316	C₂×C₄⋊C₄	—	94	2	no	—
317	C₂×C₄⋊C₄	—	94	1	no	—
318	C₂×C₄⋊C₄	—	94	1	no	—
319	C₂×C₄⋊C₄	—	94	2	no	—
320	C₂×C₄⋊C₄	—	94	2	no	—
321	C₂×C₄⋊C₄	—	94	1	no	—
322	C₂×C₄⋊C₄	—	94	1	no	—
323	C₂×C₄⋊C₄	—	188	4	no	—
324	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	94	2	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	47	2	no	—
330	C₂×C₄²	—	94	2	no	—
331	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
332	#106	—	94	4	no	—
333	#106	—	188	2	no	—
334	#106	C₂×Dic₄₇	1	4	yes	complemented
335	C₄⋊C₈	—	94	2	no	—
336	#103	—	94	4	no	—
337	#103	C₂×Dic₄₇	1	4	yes	complemented
338	#102	—	94	4	no	—
339	#102	C₂×Dic₄₇	1	4	yes	—
340	C₄×C₈	—	94	4	no	—
341	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
342	#95	—	47	2	no	—
343	#95	—	94	2	no	—
344	#95	—	94	2	no	—
345	C₂⁴	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	C₂×Dic₉₄	1	2	yes	—
350	C₂×Q₈	C₂×D₁₈₈	1	2	yes	—
351	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	C₂×Dic₉₄	1	2	yes	—
356	C₂×D₄	C₂×D₁₈₈	1	2	yes	—
357	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	47	2	no	—
365	C₂²×C₄	—	47	2	no	—
366	C₂²×C₄	—	94	2	no	—
367	C₂²×C₄	—	94	2	no	—
368	C₂²×C₄	—	376	2	no	—
369	C₂²×C₄	—	188	4	no	—
370	C₂²×C₄	—	188	4	no	—
371	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
372	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
373	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
374	SD₁₆	C₄⋊Dic₄₇	1	16	yes	direct product factor
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	94	2	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	C₂×Dic₉₄	1	2	yes	—
381	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
382	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
383	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	47	4	no	—
388	C₄⋊C₄	—	94	2	no	—
389	C₄⋊C₄	—	94	2	no	—
390	C₄⋊C₄	—	94	2	no	—
391	C₄⋊C₄	—	94	2	no	—
392	C₄⋊C₄	—	94	2	no	—
393	C₄⋊C₄	—	376	1	no	—
394	C₄⋊C₄	—	376	1	no	—
395	C₄⋊C₄	—	376	2	no	—
396	C₄⋊C₄	—	188	4	no	—
397	C₄⋊C₄	—	188	4	no	—
398	C₄⋊C₄	—	188	2	no	—
399	C₄⋊C₄	—	188	2	no	—
400	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
401	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	188	4	no	—
404	C₄²	—	2	4	no	—
405	C₄²	—	94	2	no	—
406	C₄²	—	94	2	no	—
407	C₄²	—	188	4	no	—
408	C₄²	#10625352	1	2	yes	—
409	C₄²	C₂²×Dic₄₇	1	2	yes	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	2	2	no	—
421	Q₈	C₂×C₄⋊Dic₄₇	1	4	yes	complemented
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	2	no	—
425	D₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	—	47	4	no	—
439	C₂×C₄	—	94	2	no	—
440	C₂×C₄	—	94	2	no	—
441	C₂×C₄	—	94	2	no	—
442	C₂×C₄	—	94	2	no	—
443	C₂×C₄	—	94	2	no	—
444	C₂×C₄	—	376	8	no	—
445	C₂×C₄	—	188	2	no	—
446	C₂×C₄	—	188	2	no	—
447	C₂×C₄	—	188	2	no	—
448	C₂×C₄	—	188	2	no	—
449	C₂×C₄	—	188	2	no	—
450	C₂×C₄	—	188	2	no	—
451	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
452	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
453	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
454	C₂×C₄	#13094045	1	2	yes	—
455	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
457	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
458	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
459	C₂×C₄	#13094070	1	1	yes	characteristic
460	C₂×C₄	#13094071	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	188	2	no	—
463	C₈	C₂×C₄⋊Dic₄₇	1	4	yes	complemented
464	C₂²	—	2	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
472	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
473	C₂²	D₄×Dic₉₄	1	1	yes	characteristic
474	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
475	C₂²	C₂×#13094045	1	1	yes	characteristic
476	C₂²	#15689930	1	1	yes	characteristic
477	C₂²	#15689930	1	1	yes	characteristic
478	C₄	—	2	4	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	94	4	no	—
483	C₄	—	376	2	no	—
484	C₄	—	376	2	no	—
485	C₄	—	188	2	no	—
486	C₄	SD₁₆×Dic₄₇	1	4	yes	complemented
487	C₄	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
488	C₄	#15689606	1	1	yes	characteristic
489	C₄	#15689777	1	1	yes	characteristic
490	C₄	#15689830	1	1	yes	characteristic
491	C₂	—	4	4	no	—
492	C₂	D₄×C₄⋊Dic₄₇	1	1	yes	characteristic
493	C₂	C₂×SD₁₆×Dic₄₇	1	1	yes	characteristic
494	C₂	#20252272	1	1	yes	characteristic
495	C₂	SD₁₆×D₁₈₈	1	1	yes	characteristic
496	C₂	#20255119	1	1	yes	characteristic
497	C₂	SD₁₆×Dic₉₄	1	1	yes	characteristic
498	C₂	#20256261	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×SD₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₄×C₄₇	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₄₇
hypocenter	C₄₇	C₄⋊C₄×SD₁₆
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×C₄⋊Dic₄₇	C₂	semidirect
4. #20244117	C₂	semidirect
5. #20243658	C₂	semidirect
7. #20243545	C₂	semidirect
8. #20243393	C₂	semidirect
10. C₈×C₄⋊Dic₄₇	C₂	semidirect
38. C₄×SD₁₆×C₄₇	C₄	semidirect
82. C₄×Q₈×C₄₇	C₂×C₄	semidirect
91. #106×C₄₇	C₂×C₄	semidirect
92. #103×C₄₇	C₂×C₄	semidirect
94. C₄×C₈×C₄₇	C₂×C₄	semidirect
124. SD₁₆×C₄₇	C₄⋊C₄	semidirect
153. C₄⋊Dic₄₇	SD₁₆	direct (N × H)
171. Q₈×C₄₇	C₂×C₄⋊C₄	semidirect
212. C₈×C₄₇	C₂×C₄⋊C₄	semidirect
233. C₄×C₄₇	C₄×SD₁₆	semidirect
268. C₄×SD₁₆	Dic₄₇	semidirect
292. C₄₇	C₄⋊C₄×SD₁₆	semidirect
306. C₄×Q₈	C₂×Dic₄₇	semidirect
334. #106	C₂×Dic₄₇	semidirect
337. #103	C₂×Dic₄₇	semidirect
341. C₄×C₈	C₂×Dic₄₇	semidirect
374. SD₁₆	C₄⋊Dic₄₇	direct (N × H)
421. Q₈	C₂×C₄⋊Dic₄₇	semidirect
463. C₈	C₂×C₄⋊Dic₄₇	semidirect
486. C₄	SD₁₆×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×Dic₄₇	2
Q₈×C₄⋊Dic₄₇	2
D₄×C₄⋊Dic₄₇	2
#20244117	2
#20243658	2
#20243651	2
#20243545	2
#20243393	2
#20243388	2
C₈×C₄⋊Dic₄₇	2
C₂×C₄×SD₁₆×C₄₇	2
C₄⋊C₄×SD₁₆	47

Subgroups — SD16×C4⋊Dic47 #26234681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×C₄⋊Dic₄₇ #26234681