Subgroups — SD₁₆×C₂²⋊D₄₇ #20255078

Order 6016.

546 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic
4	#15689494	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689352	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689349	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689326	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689321	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689274	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689272	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689262	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689260	C₂	1	1	yes	maximal, characteristic, complemented
13	SD₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×SD₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₄₇	—	2	1	no	—
18	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
19	C₂×#10625325	C₂²	1	1	yes	characteristic, complemented
20	C₂×#10625335	C₂²	1	1	yes	characteristic
21	C₂×#10625335	C₂²	1	1	yes	characteristic, complemented
22	C₂×#10625336	C₂²	1	1	yes	characteristic, complemented
23	C₂×#10625336	C₂²	1	1	yes	characteristic, complemented
24	SD₁₆×D₄₇	—	2	4	no	—
25	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
26	#13094022	—	2	1	no	—
27	#13094022	C₂²	1	1	yes	characteristic, complemented
28	#13094020	C₂²	1	1	yes	characteristic
29	#13094003	—	2	1	no	—
30	#13094003	C₂²	1	1	yes	characteristic, complemented
31	#13094000	—	2	1	no	—
32	#13094000	C₂²	1	1	yes	characteristic, complemented
33	#13093998	C₂²	1	1	yes	characteristic
34	#13093996	—	2	1	no	—
35	#13093995	C₂²	1	1	yes	characteristic
36	#13093993	—	2	1	no	—
37	#13093992	—	2	1	no	—
38	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
39	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₄₇	—	2	1	no	—
41	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
42	#13093956	C₂²	1	1	yes	characteristic, complemented
43	Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#13093949	C₂²	1	1	yes	characteristic, complemented
45	#13093948	C₂²	1	1	yes	characteristic, complemented
46	#13093948	C₂²	1	1	yes	characteristic, complemented
47	#13093946	C₂²	1	1	yes	characteristic, complemented
48	#13093945	C₂²	1	1	yes	characteristic
49	#13093945	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
53	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×SD₁₆×C₄₇	—	2	4	no	—
56	C₂×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
58	C₂×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
59	C₂×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
60	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₄₇	—	2	1	no	—
62	C₂³×D₄₇	—	2	1	no	—
63	C₂×Q₈×C₄₇	—	2	1	no	—
64	C₂×Q₈×C₄₇	—	2	2	no	—
65	C₂×Q₈×C₄₇	—	4	1	no	—
66	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₄₇	—	2	2	no	—
69	C₂×D₄×C₄₇	—	2	1	no	—
70	C₂×D₄×C₄₇	—	4	1	no	—
71	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	—	2	1	no	—
74	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₄₇	—	2	1	no	—
76	C₂×C₂²⋊D₄₇	—	2	1	no	—
77	C₂×C₂²⋊D₄₇	—	2	1	no	—
78	C₂×C₂²⋊D₄₇	—	2	1	no	—
79	C₂×C₂²⋊D₄₇	—	2	1	no	—
80	C₂×C₂²⋊D₄₇	—	4	4	no	—
81	C₂×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
82	C₂²×Dic₄₇	—	2	1	no	—
83	Q₈×D₄₇	—	2	2	no	—
84	Q₈×D₄₇	—	4	1	no	—
85	D₄×D₄₇	—	2	2	no	—
86	D₄×D₄₇	—	4	1	no	—
87	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
88	C₂×C₄×D₄₇	—	2	1	no	—
89	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
90	C₂×Dic₉₄	—	2	1	no	—
91	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
92	SD₁₆×C₄₇	—	2	2	no	—
93	SD₁₆×C₄₇	—	2	2	no	—
94	SD₁₆×C₄₇	—	2	2	no	—
95	SD₁₆×C₄₇	D₄	1	4	yes	complemented
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²⋊Dic₄₇	—	2	1	no	—
100	C₂²⋊Dic₄₇	—	2	1	no	—
101	C₂²⋊Dic₄₇	—	2	1	no	—
102	C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
103	#10625336	—	2	2	no	—
104	#10625336	—	4	1	no	—
105	#10625335	—	2	2	no	—
106	#10625335	—	4	1	no	—
107	(C₂×D₄₇)⋊C₄	—	2	1	no	—
108	(C₂×D₄₇)⋊C₄	—	2	1	no	—
109	(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
110	C₄⋊Dic₄₇	—	2	1	no	—
111	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
113	Dic₄₇⋊C₄	—	2	1	no	—
114	Dic₄₇⋊C₄	—	2	1	no	—
115	Dic₄₇⋊C₄	—	2	1	no	—
116	Dic₄₇⋊C₄	—	2	1	no	—
117	Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
118	C₄×Dic₄₇	—	2	1	no	—
119	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
120	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
122	#10625325	—	2	2	no	—
123	C₈×D₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	—	2	1	no	—
126	C₂³×C₄₇	—	4	2	no	—
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	—	8	1	no	—
129	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×D₄₇	—	2	1	no	—
131	C₂²×D₄₇	—	4	2	no	—
132	C₂²×D₄₇	—	4	2	no	—
133	C₂²×D₄₇	—	8	1	no	—
134	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
135	Q₈×C₄₇	—	2	1	no	—
136	Q₈×C₄₇	—	2	1	no	—
137	Q₈×C₄₇	—	2	1	no	—
138	Q₈×C₄₇	—	4	2	no	—
139	Q₈×C₄₇	C₂×D₄	1	2	yes	complemented
140	D₄×C₄₇	—	2	1	no	—
141	D₄×C₄₇	—	2	1	no	—
142	D₄×C₄₇	—	2	1	no	—
143	D₄×C₄₇	—	4	2	no	—
144	D₄×C₄₇	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
152	C₂²⋊D₄₇	—	4	2	no	—
153	C₂²⋊D₄₇	—	4	2	no	—
154	C₂²⋊D₄₇	—	4	2	no	—
155	C₂²⋊D₄₇	—	4	2	no	—
156	C₂²⋊D₄₇	—	8	1	no	—
157	C₂²⋊D₄₇	SD₁₆	1	4	yes	direct product factor
158	C₂×Dic₄₇	—	2	1	no	—
159	C₂×Dic₄₇	—	2	1	no	—
160	C₂×Dic₄₇	—	2	1	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
164	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
165	D₁₈₈	—	2	1	no	—
166	D₁₈₈	—	2	1	no	—
167	C₄×D₄₇	—	2	1	no	—
168	C₄×D₄₇	—	2	1	no	—
169	C₄×D₄₇	—	4	2	no	—
170	Dic₉₄	—	2	1	no	—
171	Dic₉₄	—	2	1	no	—
172	Dic₉₄	—	4	2	no	—
173	C₈×C₄₇	—	2	1	no	—
174	C₈×C₄₇	C₂×D₄	1	2	yes	complemented
175	C₄₇⋊C₈	—	2	1	no	—
176	C₄₇⋊C₈	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	4	1	no	—
181	C₂²×C₄₇	—	4	1	no	—
182	C₂²×C₄₇	—	4	1	no	—
183	C₂²×C₄₇	—	4	1	no	—
184	C₂²×C₄₇	—	4	1	no	—
185	C₂²×C₄₇	—	8	4	no	—
186	C₂²×C₄₇	C₂×SD₁₆	1	2	yes	complemented
187	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×D₄₇	—	2	1	no	—
189	C₂×D₄₇	—	2	1	no	—
190	C₂×D₄₇	—	4	1	no	—
191	C₂×D₄₇	—	4	1	no	—
192	C₂×D₄₇	—	4	1	no	—
193	C₂×D₄₇	—	8	4	no	—
194	C₂×D₄₇	C₂×SD₁₆	1	2	yes	complemented
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	—	4	1	no	—
198	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
199	C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
200	Dic₄₇	—	2	1	no	—
201	Dic₄₇	—	2	1	no	—
202	Dic₄₇	—	4	1	no	—
203	Dic₄₇	—	4	1	no	—
204	Dic₄₇	—	4	1	no	—
205	Dic₄₇	C₂×SD₁₆	1	2	yes	complemented
206	D₄×SD₁₆	—	47	1	no	maximal, Sylow
207	C₂×C₄₇	—	2	2	no	—
208	C₂×C₄₇	—	4	2	no	—
209	C₂×C₄₇	—	8	1	no	—
210	C₂×C₄₇	D₄²	1	1	yes	characteristic
211	C₂×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
212	C₂×C₄₇	#577	1	1	yes	characteristic
213	D₄₇	—	2	2	no	—
214	D₄₇	—	8	1	no	—
215	C₂²×SD₁₆	—	47	1	no	—
216	C₂²×SD₁₆	D₄₇	1	1	yes	characteristic, complemented
217	D₄×Q₈	—	47	1	no	—
218	D₄²	—	47	1	no	—
219	#492	—	47	1	no	—
220	#465	—	47	1	no	—
221	#465	—	47	1	no	—
222	#461	—	47	1	no	—
223	#460	—	47	1	no	—
224	#450	—	47	1	no	—
225	#450	—	47	1	no	—
226	#448	—	47	1	no	—
227	#448	—	47	1	no	—
228	C₄×SD₁₆	—	47	1	no	—
229	C₈×D₄	—	47	1	no	—
230	C₄₇	D₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
231	C₂²×Q₈	—	47	1	no	—
232	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
233	C₂²×D₄	—	47	1	no	—
234	C₂²×D₄	—	94	1	no	—
235	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
236	C₂×SD₁₆	—	2	4	no	—
237	C₂×SD₁₆	—	47	1	no	—
238	C₂×SD₁₆	—	47	1	no	—
239	C₂×SD₁₆	—	47	1	no	—
240	C₂×SD₁₆	—	47	1	no	—
241	C₂×SD₁₆	—	47	1	no	—
242	C₂×SD₁₆	—	94	4	no	—
243	C₂×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
244	C₂×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
245	C₂×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
246	C₂×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
247	C₂²×C₈	—	47	1	no	—
248	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
249	C₄⋊Q₈	—	47	1	no	—
250	C₄⋊Q₈	—	94	1	no	—
251	#127	—	47	1	no	—
252	C₂²⋊Q₈	—	47	1	no	—
253	C₂²⋊Q₈	—	47	1	no	—
254	C₂²⋊Q₈	—	94	1	no	—
255	C₂²⋊Q₈	—	94	1	no	—
256	#121	—	47	1	no	—
257	#121	—	47	1	no	—
258	#121	—	94	1	no	—
259	#120	—	94	1	no	—
260	#120	—	94	1	no	—
261	C₄×Q₈	—	47	1	no	—
262	C₄×D₄	—	47	1	no	—
263	C₄×D₄	—	47	1	no	—
264	C₄×D₄	—	94	1	no	—
265	#106	—	47	1	no	—
266	C₄⋊C₈	—	47	1	no	—
267	#103	—	47	1	no	—
268	#103	—	47	1	no	—
269	#103	—	47	1	no	—
270	#102	—	47	1	no	—
271	#102	—	47	1	no	—
272	#102	—	47	1	no	—
273	C₂²⋊C₈	—	47	1	no	—
274	C₂²⋊C₈	—	47	1	no	—
275	C₄×C₈	—	47	1	no	—
276	C₂⁴	—	2	1	no	—
277	C₂⁴	—	94	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	47	1	no	—
282	C₂×Q₈	—	94	1	no	—
283	C₂×Q₈	—	94	2	no	—
284	C₂×Q₈	—	188	1	no	—
285	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
286	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	47	1	no	—
291	C₂×D₄	—	47	1	no	—
292	C₂×D₄	—	94	1	no	—
293	C₂×D₄	—	94	1	no	—
294	C₂×D₄	—	94	1	no	—
295	C₂×D₄	—	94	2	no	—
296	C₂×D₄	—	94	1	no	—
297	C₂×D₄	—	94	1	no	—
298	C₂×D₄	—	188	1	no	—
299	C₂×D₄	—	188	4	no	—
300	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
301	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	94	1	no	—
305	C₂²×C₄	—	94	1	no	—
306	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	2	2	no	—
310	SD₁₆	—	94	2	no	—
311	SD₁₆	—	94	2	no	—
312	SD₁₆	—	94	2	no	—
313	SD₁₆	—	188	1	no	—
314	SD₁₆	—	188	1	no	—
315	SD₁₆	C₂²⋊D₄₇	1	4	yes	direct product factor
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	47	1	no	—
318	C₂×C₈	—	47	1	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
321	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
322	C₄⋊C₄	—	47	1	no	—
323	C₄⋊C₄	—	47	1	no	—
324	C₄⋊C₄	—	47	1	no	—
325	C₄⋊C₄	—	94	1	no	—
326	C₄⋊C₄	—	94	1	no	—
327	C₄⋊C₄	—	94	1	no	—
328	C₄⋊C₄	—	94	1	no	—
329	C₄⋊C₄	—	94	1	no	—
330	C₂²⋊C₄	—	47	1	no	—
331	C₂²⋊C₄	—	47	1	no	—
332	C₂²⋊C₄	—	94	1	no	—
333	C₂²⋊C₄	—	94	1	no	—
334	C₂²⋊C₄	—	94	1	no	—
335	C₂²⋊C₄	—	94	1	no	—
336	C₂²⋊C₄	—	94	1	no	—
337	C₄²	—	47	1	no	—
338	C₄²	—	94	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	8	1	no	—
344	C₂³	—	47	1	no	—
345	C₂³	—	94	1	no	—
346	C₂³	—	376	1	no	—
347	C₂³	—	188	2	no	—
348	C₂³	—	188	2	no	—
349	C₂³	D₄×D₄₇	1	1	yes	characteristic
350	Q₈	—	2	1	no	—
351	Q₈	—	2	1	no	—
352	Q₈	—	2	1	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	94	1	no	—
355	Q₈	—	94	1	no	—
356	Q₈	—	188	2	no	—
357	Q₈	C₂×C₂²⋊D₄₇	1	2	yes	complemented
358	D₄	—	2	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	47	4	no	—
363	D₄	—	94	1	no	—
364	D₄	—	94	1	no	—
365	D₄	—	376	1	no	—
366	D₄	—	188	2	no	—
367	D₄	—	188	2	no	—
368	D₄	—	188	2	no	—
369	D₄	—	188	2	no	—
370	D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	47	1	no	—
377	C₂×C₄	—	47	1	no	—
378	C₂×C₄	—	47	1	no	—
379	C₂×C₄	—	94	1	no	—
380	C₂×C₄	—	94	1	no	—
381	C₂×C₄	—	94	1	no	—
382	C₂×C₄	—	94	1	no	—
383	C₂×C₄	—	94	1	no	—
384	C₂×C₄	—	188	2	no	—
385	C₂×C₄	—	188	2	no	—
386	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	94	1	no	—
390	C₈	—	94	1	no	—
391	C₈	C₂×C₂²⋊D₄₇	1	2	yes	complemented
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	8	4	no	—
401	C₂²	—	47	2	no	—
402	C₂²	—	94	1	no	—
403	C₂²	—	94	1	no	—
404	C₂²	—	376	4	no	—
405	C₂²	—	188	1	no	—
406	C₂²	—	188	1	no	—
407	C₂²	—	188	1	no	—
408	C₂²	SD₁₆×D₄₇	1	2	yes	complemented
409	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	47	2	no	—
414	C₄	—	94	1	no	—
415	C₄	—	94	1	no	—
416	C₄	—	188	1	no	—
417	C₄	—	188	1	no	—
418	C₄	—	188	1	no	—
419	C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
420	C₄	#13094069	1	1	yes	characteristic
421	C₂	—	2	2	no	—
422	C₂	—	4	2	no	—
423	C₂	—	8	1	no	—
424	C₂	—	94	2	no	—
425	C₂	—	376	1	no	—
426	C₂	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
427	C₂	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
428	C₂	#15689929	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₄₇	C₂	semidirect
2. Q₈×C₂²⋊D₄₇	C₂	semidirect
4. #15689494	C₂	semidirect
5. #15689352	C₂	semidirect
6. #15689349	C₂	semidirect
7. #15689326	C₂	semidirect
8. #15689321	C₂	semidirect
9. #15689274	C₂	semidirect
10. #15689272	C₂	semidirect
11. #15689262	C₂	semidirect
12. #15689260	C₂	semidirect
13. SD₁₆×Dic₄₇	C₂	semidirect
14. C₈×C₂²⋊D₄₇	C₂	semidirect
15. C₂²×SD₁₆×C₄₇	C₂	semidirect
16. C₂×Q₈×D₄₇	C₂²	semidirect
19. C₂×#10625325	C₂²	semidirect
21. C₂×#10625335	C₂²	semidirect
22. C₂×#10625336	C₂²	semidirect
23. C₂×#10625336	C₂²	semidirect
25. C₂×C₈×D₄₇	C₂²	semidirect
27. #13094022	C₂²	semidirect
30. #13094003	C₂²	semidirect
32. #13094000	C₂²	semidirect
38. Q₈×Dic₄₇	C₂²	semidirect
42. #13093956	C₂²	semidirect
43. Dic₄₇⋊C₈	C₂²	semidirect
44. #13093949	C₂²	semidirect
45. #13093948	C₂²	semidirect
46. #13093948	C₂²	semidirect
47. #13093946	C₂²	semidirect
49. #13093945	C₂²	semidirect
50. C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
51. (C₂×D₄₇)⋊C₈	C₂²	semidirect
52. C₈×Dic₄₇	C₂²	semidirect
53. C₂²×Q₈×C₄₇	C₂²	semidirect
58. C₂×SD₁₆×C₄₇	C₂²	semidirect
59. C₂×SD₁₆×C₄₇	C₂²	semidirect
60. C₂²×C₈×C₄₇	C₂²	semidirect
95. SD₁₆×C₄₇	D₄	semidirect
139. Q₈×C₄₇	C₂×D₄	semidirect
157. C₂²⋊D₄₇	SD₁₆	direct (N × H)
174. C₈×C₄₇	C₂×D₄	semidirect
186. C₂²×C₄₇	C₂×SD₁₆	semidirect
194. C₂×D₄₇	C₂×SD₁₆	semidirect
205. Dic₄₇	C₂×SD₁₆	semidirect
216. C₂²×SD₁₆	D₄₇	semidirect
230. C₄₇	D₄×SD₁₆	semidirect
232. C₂²×Q₈	C₂×D₄₇	semidirect
245. C₂×SD₁₆	C₂×D₄₇	semidirect
246. C₂×SD₁₆	C₂×D₄₇	semidirect
248. C₂²×C₈	C₂×D₄₇	semidirect
315. SD₁₆	C₂²⋊D₄₇	direct (N × H)
357. Q₈	C₂×C₂²⋊D₄₇	semidirect
391. C₈	C₂×C₂²⋊D₄₇	semidirect
408. C₂²	SD₁₆×D₄₇	semidirect

Subgroups — SD16×C22⋊D47 #20255078

Conjugacy classes of subgroups

Complements

Subgroups — SD₁₆×C₂²⋊D₄₇ #20255078