Subgroups — D₄×Q₈×Dic₄₇ #26376146

Order 12032.

3148 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	#20246448	C₂	1	3	yes	maximal, complemented
3	#20246397	C₂	1	6	yes	maximal, complemented
4	Q₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₄⋊Dic₄₇	C₂	1	3	yes	maximal
6	Q₈×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
7	C₄⋊Q₈×Dic₄₇	C₂	1	3	yes	maximal, complemented
8	C₂²⋊Q₈×Dic₄₇	C₂	1	6	yes	maximal, complemented
9	C₄×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×D₄×Dic₄₇	C₂	1	3	yes	maximal
11	C₂×D₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	—	2	16	no	—
13	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
14	C₂×Q₈×Dic₄₇	C₂²	1	6	yes	—
15	C₂×Q₈×Dic₄₇	C₂²	1	6	yes	—
16	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
17	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂×D₄×Dic₄₇	C₂²	1	3	yes	—
19	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊Dic₄₇	C₂²	1	6	yes	—
21	C₂²×C₄×Dic₄₇	C₂²	1	6	yes	—
22	#15689030	C₂²	1	6	yes	—
23	#15689030	C₂²	1	6	yes	—
24	#15689022	C₂²	1	6	yes	—
25	#15689022	C₂²	1	6	yes	—
26	#15689022	C₂²	1	6	yes	—
27	#15689009	C₂²	1	12	yes	—
28	#15688998	C₂²	1	12	yes	—
29	#15688993	C₂²	1	3	yes	—
30	#15688983	C₂²	1	6	yes	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	3	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	6	yes	—
33	C₄⋊C₄×Dic₄₇	C₂²	1	3	yes	—
34	C₄⋊C₄×Dic₄₇	C₂²	1	3	yes	—
35	C₄⋊C₄×Dic₄₇	C₂²	1	3	yes	—
36	C₄×C₄⋊Dic₄₇	C₂²	1	3	yes	—
37	C₄×C₄⋊Dic₄₇	C₂²	1	3	yes	—
38	C₂²⋊C₄×Dic₄₇	C₂²	1	6	yes	—
39	C₂²⋊C₄×Dic₄₇	C₂²	1	6	yes	—
40	C₄×C₂²⋊Dic₄₇	C₂²	1	6	yes	—
41	C₄²×Dic₄₇	C₂²	1	3	yes	—
42	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
43	D₄×Q₈×C₄₇	C₄	1	16	yes	complemented
44	C₂×C₄⋊Q₈×C₄₇	C₂²	1	3	yes	—
45	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	6	yes	—
46	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₄₇	C₂²	1	3	yes	—
48	C₂³×Dic₄₇	C₂³	1	6	yes	—
49	C₂³×Dic₄₇	C₂³	1	2	yes	—
50	Q₈×Dic₄₇	—	2	8	no	—
51	Q₈×Dic₄₇	—	2	4	no	—
52	Q₈×Dic₄₇	—	2	24	no	—
53	Q₈×Dic₄₇	—	2	24	no	—
54	Q₈×Dic₄₇	D₄	1	8	yes	direct product factor
55	D₄×Dic₄₇	—	2	12	no	—
56	D₄×Dic₄₇	Q₈	1	8	yes	direct product factor
57	C₂×C₄⋊Dic₄₇	—	2	24	no	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
62	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
63	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
64	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊Dic₄₇	C₂³	1	6	yes	—
66	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
67	C₂×C₄×Dic₄₇	—	2	24	no	—
68	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
69	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
70	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
71	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
72	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
73	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
74	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
75	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
76	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
77	C₄₇⋊#95	C₂³	1	6	yes	—
78	C₄₇⋊#95	C₂³	1	6	yes	—
79	C₄₇⋊#95	C₂³	1	6	yes	—
80	C₄₇⋊#95	C₂³	1	6	yes	—
81	C₄₇⋊#95	C₂³	1	12	yes	—
82	C₂²×Q₈×C₄₇	—	2	8	no	—
83	C₂²×Q₈×C₄₇	—	2	8	no	—
84	C₂²×Q₈×C₄₇	C₂×C₄	1	16	yes	complemented
85	C₂²×Q₈×C₄₇	C₂³	1	6	yes	—
86	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
89	C₄⋊Q₈×C₄₇	C₂×C₄	1	24	yes	complemented
90	C₂²⋊Q₈×C₄₇	C₂×C₄	1	48	yes	complemented
91	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
92	C₄×D₄×C₄₇	C₂×C₄	1	24	yes	—
93	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
94	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
95	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
96	C₂×C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
97	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
98	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
99	C₂×Q₈×C₄₇	—	2	64	no	—
100	C₂×Q₈×C₄₇	—	2	12	no	—
101	C₂×Q₈×C₄₇	—	2	12	no	—
102	C₂×Q₈×C₄₇	C₂²×C₄	1	24	yes	—
103	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
104	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
105	C₂×Q₈×C₄₇	#41	1	4	yes	—
106	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂×D₄×C₄₇	C₂×Q₈	1	4	yes	—
108	C₂×D₄×C₄₇	#41	1	4	yes	—
109	C₂²×C₄×C₄₇	—	2	12	no	—
110	C₂²×C₄×C₄₇	—	2	12	no	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
112	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
114	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂²×Dic₄₇	—	2	4	no	—
117	C₂²×Dic₄₇	—	2	4	no	—
118	C₂²×Dic₄₇	—	2	12	no	—
119	C₂²×Dic₄₇	—	2	12	no	—
120	C₂²×Dic₄₇	—	4	6	no	—
121	C₂²×Dic₄₇	C₂×Q₈	1	8	yes	complemented
122	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
123	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
124	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
125	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
126	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
127	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
128	C₄⋊C₄×C₄₇	C₂²×C₄	1	12	yes	—
129	C₄⋊C₄×C₄₇	C₂²×C₄	1	12	yes	—
130	C₄⋊C₄×C₄₇	C₂²×C₄	1	24	yes	—
131	C₂²⋊C₄×C₄₇	C₂²×C₄	1	24	yes	—
132	C₄²×C₄₇	C₂²×C₄	1	12	yes	—
133	C₂²⋊Dic₄₇	—	2	12	no	—
134	C₂²⋊Dic₄₇	C₂×Q₈	1	8	yes	complemented
135	C₄⋊Dic₄₇	—	2	12	no	—
136	C₄⋊Dic₄₇	—	2	6	no	—
137	C₄⋊Dic₄₇	—	2	6	no	—
138	C₄⋊Dic₄₇	—	2	24	no	—
139	C₄⋊Dic₄₇	—	4	6	no	—
140	C₄⋊Dic₄₇	C₂×D₄	1	12	yes	—
141	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	complemented
142	C₄×Dic₄₇	—	2	12	no	—
143	C₄×Dic₄₇	—	2	6	no	—
144	C₄×Dic₄₇	—	2	6	no	—
145	C₄×Dic₄₇	—	2	12	no	—
146	C₄×Dic₄₇	—	2	12	no	—
147	C₄×Dic₄₇	—	2	6	no	—
148	C₄×Dic₄₇	—	4	3	no	—
149	C₄×Dic₄₇	C₂×D₄	1	12	yes	—
150	C₄×Dic₄₇	C₂×Q₈	1	4	yes	complemented
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
156	C₂³×C₄₇	C₂²×Q₈	1	4	yes	—
157	C₂³×C₄₇	C₂×#41	1	4	yes	—
158	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
159	Q₈×C₄₇	—	2	48	no	—
160	Q₈×C₄₇	C₄×D₄	1	16	yes	complemented
161	D₄×C₄₇	C₄×Q₈	1	16	yes	complemented
162	C₂×C₄×C₄₇	—	2	6	no	—
163	C₂×C₄×C₄₇	—	2	6	no	—
164	C₂×C₄×C₄₇	—	2	3	no	—
165	C₂×C₄×C₄₇	—	2	3	no	—
166	C₂×C₄×C₄₇	—	2	48	no	—
167	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
168	C₂×C₄×C₄₇	C₂³×C₄	1	12	yes	—
169	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
170	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
172	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×#41	1	6	yes	—
174	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	3	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	3	no	—
181	C₂×Dic₄₇	—	2	16	no	—
182	C₂×Dic₄₇	—	2	6	no	—
183	C₂×Dic₄₇	—	2	3	no	—
184	C₂×Dic₄₇	—	2	3	no	—
185	C₂×Dic₄₇	—	2	6	no	—
186	C₂×Dic₄₇	—	2	3	no	—
187	C₂×Dic₄₇	—	2	6	no	—
188	C₂×Dic₄₇	—	4	24	no	—
189	C₂×Dic₄₇	C₂²×D₄	1	6	yes	—
190	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
191	C₂×Dic₄₇	C₂²×Q₈	1	2	yes	—
192	C₂×Dic₄₇	C₂²×Q₈	1	4	yes	—
193	C₂×Dic₄₇	C₂²×Q₈	1	2	yes	—
194	C₂×Dic₄₇	2₋¹⁺⁴	1	2	yes	—
195	C₄×D₄×Q₈	—	47	1	no	maximal, Sylow
196	C₂²×C₄₇	—	2	4	no	—
197	C₂²×C₄₇	—	2	4	no	—
198	C₂²×C₄₇	—	2	4	no	—
199	C₂²×C₄₇	—	2	4	no	—
200	C₂²×C₄₇	—	2	4	no	—
201	C₂²×C₄₇	—	2	4	no	—
202	C₂²×C₄₇	C₂×C₄×Q₈	1	8	yes	complemented
203	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
204	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
205	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
206	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
207	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
209	C₂²×C₄₇	#585	1	1	yes	characteristic
210	C₄×C₄₇	—	2	12	no	—
211	C₄×C₄₇	—	2	6	no	—
212	C₄×C₄₇	C₂×C₄×D₄	1	12	yes	—
213	C₄×C₄₇	C₂×C₄×Q₈	1	4	yes	complemented
214	Dic₄₇	—	2	4	no	—
215	Dic₄₇	—	2	6	no	—
216	Dic₄₇	—	2	2	no	—
217	Dic₄₇	—	4	6	no	—
218	Dic₄₇	—	4	3	no	—
219	Dic₄₇	D₄×Q₈	1	4	yes	direct product factor
220	C₂×D₄×Q₈	D₄₇	1	1	yes	characteristic
221	C₂²×C₄×Q₈	—	47	2	no	—
222	#2365	—	47	3	no	—
223	#2360	—	47	6	no	—
224	Q₈×C₄⋊C₄	—	47	1	no	—
225	D₄×C₄⋊C₄	—	47	3	no	—
226	Q₈×C₂²⋊C₄	—	47	2	no	—
227	C₄×C₄⋊Q₈	—	47	3	no	—
228	C₄×C₂²⋊Q₈	—	47	6	no	—
229	C₄²×Q₈	—	47	1	no	—
230	C₄²×D₄	—	47	3	no	—
231	C₂×C₄₇	—	2	8	no	—
232	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
233	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
234	C₂×C₄₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×C₄₇	C₂×D₄×Q₈	1	1	yes	characteristic
236	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
237	C₂×C₄₇	Q₈×#41	1	1	yes	characteristic
238	C₂×C₄₇	#3482	1	1	yes	characteristic
239	C₂³×Q₈	C₂×D₄₇	1	2	yes	—
240	D₄×Q₈	Dic₄₇	1	16	yes	direct product factor
241	C₂×C₄⋊Q₈	C₂×D₄₇	1	3	yes	—
242	C₂×C₂²⋊Q₈	C₂×D₄₇	1	6	yes	—
243	C₂×C₄×Q₈	—	47	1	no	—
244	C₂×C₄×Q₈	—	47	6	no	—
245	C₂×C₄×Q₈	—	47	1	no	—
246	C₂×C₄×Q₈	—	47	2	no	—
247	C₂×C₄×Q₈	—	47	6	no	—
248	C₂×C₄×Q₈	—	94	16	no	—
249	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
250	C₂×C₄×D₄	—	47	1	no	—
251	C₂×C₄×D₄	—	47	3	no	—
252	C₂×C₄×D₄	C₂×D₄₇	1	3	yes	—
253	C₂²×C₄⋊C₄	—	47	6	no	—
254	C₂²×C₄²	—	47	6	no	—
255	#391	—	47	6	no	—
256	#391	—	47	6	no	—
257	#389	—	47	6	no	—
258	#389	—	47	6	no	—
259	#389	—	47	6	no	—
260	#387	—	47	12	no	—
261	#385	—	47	12	no	—
262	#384	—	47	3	no	—
263	#380	—	47	6	no	—
264	C₄×C₄⋊C₄	—	47	3	no	—
265	C₄×C₄⋊C₄	—	47	6	no	—
266	C₄×C₄⋊C₄	—	47	3	no	—
267	C₄×C₄⋊C₄	—	47	3	no	—
268	C₄×C₄⋊C₄	—	47	3	no	—
269	C₄×C₄⋊C₄	—	47	3	no	—
270	C₄×C₄⋊C₄	—	47	3	no	—
271	C₄×C₂²⋊C₄	—	47	6	no	—
272	C₄×C₂²⋊C₄	—	47	6	no	—
273	C₄×C₂²⋊C₄	—	47	6	no	—
274	C₄³	—	47	3	no	—
275	C₄₇	C₄×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
276	C₂²×Q₈	—	2	8	no	—
277	C₂²×Q₈	—	2	8	no	—
278	C₂²×Q₈	C₂×Dic₄₇	1	16	yes	complemented
279	C₂²×Q₈	C₂²×D₄₇	1	6	yes	—
280	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
281	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
282	C₂³×C₄	—	47	2	no	—
283	C₂³×C₄	—	47	6	no	—
284	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
285	C₄⋊Q₈	C₂×Dic₄₇	1	24	yes	complemented
286	C₂²⋊Q₈	C₂×Dic₄₇	1	48	yes	complemented
287	C₄×Q₈	—	47	8	no	—
288	C₄×Q₈	—	94	24	no	—
289	C₄×Q₈	—	94	24	no	—
290	C₄×Q₈	—	94	8	no	—
291	C₄×Q₈	—	94	4	no	—
292	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
293	C₄×D₄	—	47	8	no	—
294	C₄×D₄	—	94	12	no	—
295	C₄×D₄	C₂×Dic₄₇	1	24	yes	—
296	C₂×C₄⋊C₄	—	47	3	no	—
297	C₂×C₄⋊C₄	—	47	1	no	—
298	C₂×C₄⋊C₄	—	47	6	no	—
299	C₂×C₄⋊C₄	—	47	12	no	—
300	C₂×C₄⋊C₄	—	47	3	no	—
301	C₂×C₄⋊C₄	—	47	3	no	—
302	C₂×C₄⋊C₄	—	47	6	no	—
303	C₂×C₄⋊C₄	—	94	24	no	—
304	C₂×C₄⋊C₄	C₂²×D₄₇	1	3	yes	—
305	C₂×C₄⋊C₄	C₂²×D₄₇	1	3	yes	—
306	C₂×C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
307	C₂×C₂²⋊C₄	—	47	2	no	—
308	C₂×C₂²⋊C₄	—	47	6	no	—
309	C₂×C₂²⋊C₄	C₂²×D₄₇	1	6	yes	—
310	C₂×C₄²	—	47	1	no	—
311	C₂×C₄²	—	47	3	no	—
312	C₂×C₄²	—	47	3	no	—
313	C₂×C₄²	—	47	6	no	—
314	C₂×C₄²	—	47	6	no	—
315	C₂×C₄²	—	47	6	no	—
316	C₂×C₄²	—	47	3	no	—
317	C₂×C₄²	—	47	3	no	—
318	C₂×C₄²	—	47	3	no	—
319	C₂×C₄²	—	94	24	no	—
320	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
321	#95	—	47	6	no	—
322	#95	—	47	6	no	—
323	#95	—	47	6	no	—
324	#95	—	47	6	no	—
325	#95	—	47	12	no	—
326	C₂⁴	C₂³×D₄₇	1	2	yes	—
327	C₂×Q₈	—	2	64	no	—
328	C₂×Q₈	—	2	12	no	—
329	C₂×Q₈	—	2	12	no	—
330	C₂×Q₈	D₄×D₄₇	1	4	yes	—
331	C₂×Q₈	#10625352	1	4	yes	—
332	C₂×Q₈	C₂²×Dic₄₇	1	24	yes	—
333	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
334	C₂×D₄	Q₈×D₄₇	1	4	yes	—
335	C₂×D₄	#10625354	1	4	yes	—
336	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
337	C₂²×C₄	—	2	12	no	—
338	C₂²×C₄	—	2	12	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	47	8	no	—
341	C₂²×C₄	—	47	1	no	—
342	C₂²×C₄	—	47	2	no	—
343	C₂²×C₄	—	47	3	no	—
344	C₂²×C₄	—	47	3	no	—
345	C₂²×C₄	—	47	6	no	—
346	C₂²×C₄	—	94	4	no	—
347	C₂²×C₄	—	94	4	no	—
348	C₂²×C₄	—	94	12	no	—
349	C₂²×C₄	—	94	12	no	—
350	C₂²×C₄	—	188	6	no	—
351	C₂²×C₄	C₂²×Dic₄₇	1	24	yes	—
352	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
353	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
354	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
355	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
356	C₄⋊C₄	—	47	12	no	—
357	C₄⋊C₄	—	47	4	no	—
358	C₄⋊C₄	—	94	24	no	—
359	C₄⋊C₄	—	94	12	no	—
360	C₄⋊C₄	—	94	6	no	—
361	C₄⋊C₄	—	94	6	no	—
362	C₄⋊C₄	—	188	6	no	—
363	C₄⋊C₄	C₂²×Dic₄₇	1	12	yes	—
364	C₄⋊C₄	C₂²×Dic₄₇	1	12	yes	—
365	C₄⋊C₄	C₂²×Dic₄₇	1	24	yes	—
366	C₂²⋊C₄	—	47	8	no	—
367	C₂²⋊C₄	—	94	12	no	—
368	C₂²⋊C₄	C₂²×Dic₄₇	1	24	yes	—
369	C₄²	—	47	12	no	—
370	C₄²	—	47	4	no	—
371	C₄²	—	94	6	no	—
372	C₄²	—	94	12	no	—
373	C₄²	—	94	12	no	—
374	C₄²	—	94	12	no	—
375	C₄²	—	94	6	no	—
376	C₄²	—	94	6	no	—
377	C₄²	—	188	3	no	—
378	C₄²	C₂²×Dic₄₇	1	12	yes	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	C₂³×Dic₄₇	1	4	yes	—
384	C₂³	C₂×Q₈×D₄₇	1	4	yes	—
385	C₂³	C₂×#10625354	1	4	yes	—
386	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
387	Q₈	—	2	48	no	—
388	Q₈	D₄×Dic₄₇	1	16	yes	direct product factor
389	D₄	Q₈×Dic₄₇	1	16	yes	direct product factor
390	C₂×C₄	—	2	6	no	—
391	C₂×C₄	—	2	6	no	—
392	C₂×C₄	—	2	3	no	—
393	C₂×C₄	—	2	3	no	—
394	C₂×C₄	—	2	48	no	—
395	C₂×C₄	—	47	2	no	—
396	C₂×C₄	—	47	2	no	—
397	C₂×C₄	—	47	2	no	—
398	C₂×C₄	—	47	6	no	—
399	C₂×C₄	—	47	2	no	—
400	C₂×C₄	—	47	4	no	—
401	C₂×C₄	—	94	16	no	—
402	C₂×C₄	—	94	2	no	—
403	C₂×C₄	—	94	1	no	—
404	C₂×C₄	—	94	3	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	94	1	no	—
407	C₂×C₄	—	94	3	no	—
408	C₂×C₄	—	94	6	no	—
409	C₂×C₄	—	94	3	no	—
410	C₂×C₄	—	94	3	no	—
411	C₂×C₄	—	94	6	no	—
412	C₂×C₄	—	94	3	no	—
413	C₂×C₄	—	94	6	no	—
414	C₂×C₄	—	188	24	no	—
415	C₂×C₄	C₂³×Dic₄₇	1	6	yes	—
416	C₂×C₄	C₂³×Dic₄₇	1	12	yes	—
417	C₂×C₄	C₂³×Dic₄₇	1	6	yes	—
418	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
419	C₂×C₄	C₂×D₄×D₄₇	1	6	yes	—
420	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
421	C₂×C₄	C₂×#10625352	1	6	yes	—
422	C₂×C₄	C₂×#10625354	1	2	yes	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	C₂×Q₈×Dic₄₇	1	8	yes	complemented
430	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
431	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
432	C₂²	C₂²×Q₈×D₄₇	1	1	yes	characteristic
433	C₂²	C₂²×#10625352	1	1	yes	characteristic
434	C₂²	C₂²×#10625354	1	1	yes	characteristic
435	C₂²	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
436	C₂²	#15689960	1	1	yes	characteristic
437	C₄	—	2	12	no	—
438	C₄	—	2	6	no	—
439	C₄	—	47	4	no	—
440	C₄	—	94	4	no	—
441	C₄	—	94	6	no	—
442	C₄	—	94	2	no	—
443	C₄	—	188	6	no	—
444	C₄	—	188	3	no	—
445	C₄	C₂×D₄×Dic₄₇	1	12	yes	—
446	C₄	C₂×Q₈×Dic₄₇	1	4	yes	complemented
447	C₂	—	2	8	no	—
448	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
449	C₂	C₂²×Q₈×Dic₄₇	1	1	yes	characteristic
450	C₂	2₋¹⁺⁴×Dic₄₇	1	1	yes	characteristic
451	C₂	D₄×Q₈×D₄₇	1	1	yes	characteristic
452	C₂	D₄×#10625354	1	1	yes	characteristic
453	C₂	Q₈×#10625352	1	1	yes	characteristic
454	C₂	#20257009	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂×D₄×Q₈×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂²×D₄×C₄₇	C₂³
hypercenter	C₂×D₄×Q₈	D₄₇
hypocenter	C₄₇	C₄×D₄×Q₈
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₈×Dic₄₇	C₂	semidirect
2. #20246448	C₂	semidirect
3. #20246397	C₂	semidirect
4. Q₈×C₄⋊Dic₄₇	C₂	semidirect
6. Q₈×C₂²⋊Dic₄₇	C₂	semidirect
7. C₄⋊Q₈×Dic₄₇	C₂	semidirect
8. C₂²⋊Q₈×Dic₄₇	C₂	semidirect
9. C₄×Q₈×Dic₄₇	C₂	semidirect
43. D₄×Q₈×C₄₇	C₄	semidirect
54. Q₈×Dic₄₇	D₄	direct (N × H)
56. D₄×Dic₄₇	Q₈	direct (N × H)
84. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
89. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
90. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
91. C₄×Q₈×C₄₇	C₂×C₄	semidirect
121. C₂²×Dic₄₇	C₂×Q₈	semidirect
134. C₂²⋊Dic₄₇	C₂×Q₈	semidirect
141. C₄⋊Dic₄₇	C₂×Q₈	semidirect
150. C₄×Dic₄₇	C₂×Q₈	semidirect
160. Q₈×C₄₇	C₄×D₄	semidirect
161. D₄×C₄₇	C₄×Q₈	semidirect
202. C₂²×C₄₇	C₂×C₄×Q₈	semidirect
213. C₄×C₄₇	C₂×C₄×Q₈	semidirect
219. Dic₄₇	D₄×Q₈	direct (N × H)
240. D₄×Q₈	Dic₄₇	direct (N × H)
275. C₄₇	C₄×D₄×Q₈	semidirect
278. C₂²×Q₈	C₂×Dic₄₇	semidirect
285. C₄⋊Q₈	C₂×Dic₄₇	semidirect
286. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
292. C₄×Q₈	C₂×Dic₄₇	semidirect
388. Q₈	D₄×Dic₄₇	direct (N × H)
389. D₄	Q₈×Dic₄₇	direct (N × H)
429. C₂²	C₂×Q₈×Dic₄₇	semidirect
446. C₄	C₂×Q₈×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Q₈×Dic₄₇	2
#20246448	2
#20246397	2
Q₈×C₄⋊Dic₄₇	2
D₄×C₄⋊Dic₄₇	2
Q₈×C₂²⋊Dic₄₇	2
C₄⋊Q₈×Dic₄₇	2
C₂²⋊Q₈×Dic₄₇	2
C₄×Q₈×Dic₄₇	2
C₄×D₄×Dic₄₇	2
C₂×D₄×Q₈×C₄₇	2
C₄×D₄×Q₈	47

Subgroups — D4×Q8×Dic47 #26376146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×Q₈×Dic₄₇ #26376146