Subgroups — #550×Dic₄₇ #26376135

Order 12032.

3420 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	#20246453	C₂	1	3	yes	maximal, complemented
3	#20246430	C₂	1	6	yes	maximal, complemented
4	#20246337	C₂	1	3	yes	maximal, complemented
5	Q₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#20246229	C₂	1	2	yes	maximal, complemented
7	#127×Dic₄₇	C₂	1	3	yes	maximal, complemented
8	#121×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, complemented
11	C₂×C₄₇×#550	C₂	1	1	yes	maximal, characteristic
12	#41×Dic₄₇	—	2	16	no	—
13	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
14	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×D₄×Dic₄₇	C₂²	1	6	yes	—
17	C₂×D₄×Dic₄₇	C₂²	1	6	yes	—
18	C₂×D₄×Dic₄₇	C₂²	1	3	yes	—
19	C₂×D₄×Dic₄₇	C₂²	1	3	yes	—
20	C₂×D₄×Dic₄₇	C₂²	1	6	yes	—
21	C₂×#13093983	C₂²	1	6	yes	—
22	C₂²×C₄×Dic₄₇	C₂²	1	6	yes	—
23	#15689026	C₂²	1	6	yes	—
24	#15689026	C₂²	1	6	yes	—
25	#15689026	C₂²	1	6	yes	—
26	#15689026	C₂²	1	6	yes	—
27	#15689022	C₂²	1	6	yes	—
28	#15689016	C₂²	1	12	yes	—
29	#15689003	C₂²	1	12	yes	—
30	#15688993	C₂²	1	3	yes	—
31	#15688983	C₂²	1	6	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	3	yes	—
33	C₄⋊C₄×Dic₄₇	C₂²	1	3	yes	—
34	C₄⋊C₄×Dic₄₇	C₂²	1	3	yes	—
35	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
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	C₂²×#41×C₄₇	C₂²	1	2	yes	—
43	C₄₇×#550	C₄	1	16	yes	complemented
44	C₂×#127×C₄₇	C₂²	1	3	yes	—
45	C₂×#121×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	6	yes	—
50	Q₈×Dic₄₇	—	2	8	no	—
51	Q₈×Dic₄₇	—	2	4	no	—
52	Q₈×Dic₄₇	D₄	1	8	yes	complemented
53	D₄×Dic₄₇	—	2	24	no	—
54	D₄×Dic₄₇	—	2	12	no	—
55	D₄×Dic₄₇	—	2	24	no	—
56	D₄×Dic₄₇	—	2	12	no	—
57	D₄×Dic₄₇	—	4	12	no	—
58	#13093983	—	2	24	no	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	6	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	6	yes	—
67	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	—
68	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	—
69	C₂×C₄×Dic₄₇	—	2	24	no	—
70	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
71	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
72	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
73	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
74	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
75	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
76	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
77	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
78	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
79	C₄₇⋊#95	C₂³	1	2	yes	—
80	C₄₇⋊#95	C₂³	1	6	yes	—
81	C₄₇⋊#95	C₂³	1	6	yes	—
82	C₄₇⋊#95	C₂³	1	6	yes	—
83	C₂×#41×C₄₇	—	2	8	no	—
84	C₂×#41×C₄₇	—	2	8	no	—
85	C₂×#41×C₄₇	C₂×C₄	1	16	yes	complemented
86	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₄₇	C₂³	1	3	yes	—
88	C₂²×D₄×C₄₇	C₂³	1	6	yes	—
89	C₂²×D₄×C₄₇	C₂³	1	6	yes	—
90	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
91	#127×C₄₇	C₂×C₄	1	24	yes	complemented
92	#121×C₄₇	C₂×C₄	1	48	yes	complemented
93	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
94	C₄×D₄×C₄₇	C₂×C₄	1	24	yes	complemented
95	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
97	C₂×C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
98	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
99	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
100	#41×C₄₇	—	2	64	no	—
101	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
102	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
103	C₂×Q₈×C₄₇	#41	1	4	yes	—
104	C₂×D₄×C₄₇	—	2	12	no	—
105	C₂×D₄×C₄₇	—	2	12	no	—
106	C₂×D₄×C₄₇	—	2	6	no	—
107	C₂×D₄×C₄₇	—	2	6	no	—
108	C₂×D₄×C₄₇	—	4	6	no	—
109	C₂×D₄×C₄₇	—	4	6	no	—
110	C₂×D₄×C₄₇	C₂²×C₄	1	12	yes	—
111	C₂×D₄×C₄₇	C₂²×C₄	1	24	yes	—
112	C₂×D₄×C₄₇	C₂²×C₄	1	24	yes	—
113	C₂²×C₄×C₄₇	—	2	12	no	—
114	C₂²×C₄×C₄₇	—	2	12	no	—
115	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
116	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
117	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
119	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂²×Dic₄₇	—	2	12	no	—
121	C₂²×Dic₄₇	—	2	12	no	—
122	C₂²×Dic₄₇	—	2	12	no	—
123	C₂²×Dic₄₇	—	2	12	no	—
124	C₂²×Dic₄₇	—	2	12	no	—
125	C₂²×Dic₄₇	—	4	6	no	—
126	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
127	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
128	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
129	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
130	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
131	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
132	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₄₇	C₂²×C₄	1	12	yes	—
134	C₂²⋊C₄×C₄₇	C₂²×C₄	1	24	yes	—
135	C₄²×C₄₇	C₂²×C₄	1	12	yes	—
136	C₂²⋊Dic₄₇	—	2	24	no	—
137	C₂²⋊Dic₄₇	—	2	12	no	—
138	C₂²⋊Dic₄₇	—	2	12	no	—
139	C₂²⋊Dic₄₇	—	4	12	no	—
140	C₄⋊Dic₄₇	—	2	12	no	—
141	C₄⋊Dic₄₇	—	2	6	no	—
142	C₄⋊Dic₄₇	—	2	6	no	—
143	C₄⋊Dic₄₇	—	4	6	no	—
144	C₄⋊Dic₄₇	C₂×D₄	1	12	yes	—
145	C₄⋊Dic₄₇	#41	1	4	yes	complemented
146	C₄×Dic₄₇	—	2	12	no	—
147	C₄×Dic₄₇	—	2	6	no	—
148	C₄×Dic₄₇	—	2	6	no	—
149	C₄×Dic₄₇	—	2	4	no	—
150	C₄×Dic₄₇	—	2	12	no	—
151	C₄×Dic₄₇	—	2	6	no	—
152	C₄×Dic₄₇	—	4	3	no	—
153	C₄×Dic₄₇	C₂×D₄	1	12	yes	—
154	C₄×Dic₄₇	#41	1	4	yes	complemented
155	C₂³×C₄₇	—	2	6	no	—
156	C₂³×C₄₇	—	2	6	no	—
157	C₂³×C₄₇	—	2	6	no	—
158	C₂³×C₄₇	—	2	6	no	—
159	C₂³×C₄₇	—	2	6	no	—
160	C₂³×C₄₇	—	2	6	no	—
161	C₂³×C₄₇	C₂³×C₄	1	12	yes	—
162	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
163	Q₈×C₄₇	C₄×D₄	1	16	yes	complemented
164	D₄×C₄₇	—	2	48	no	—
165	D₄×C₄₇	—	2	24	no	—
166	D₄×C₄₇	—	4	24	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	3	no	—
170	C₂×C₄×C₄₇	—	2	3	no	—
171	C₂×C₄×C₄₇	—	2	48	no	—
172	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
173	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
174	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
175	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
177	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
178	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
179	C₂×C₄×C₄₇	C₂×#41	1	6	yes	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	3	no	—
183	C₂×Dic₄₇	—	2	1	no	—
184	C₂×Dic₄₇	—	2	3	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	2	6	no	—
187	C₂×Dic₄₇	—	2	3	no	—
188	C₂×Dic₄₇	—	2	3	no	—
189	C₂×Dic₄₇	—	2	6	no	—
190	C₂×Dic₄₇	—	2	3	no	—
191	C₂×Dic₄₇	—	2	6	no	—
192	C₂×Dic₄₇	—	4	24	no	—
193	C₂×Dic₄₇	—	4	24	no	—
194	C₂×Dic₄₇	C₂²×D₄	1	6	yes	—
195	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
196	C₂×Dic₄₇	C₂×#41	1	2	yes	—
197	C₂×Dic₄₇	C₂×#41	1	4	yes	—
198	C₂×Dic₄₇	C₂×#41	1	2	yes	—
199	C₂×Dic₄₇	H(5,𝔽₂)	1	2	yes	—
200	C₄×#550	—	47	1	no	maximal, Sylow
201	C₂²×C₄₇	—	2	12	no	—
202	C₂²×C₄₇	—	2	12	no	—
203	C₂²×C₄₇	—	2	12	no	—
204	C₂²×C₄₇	—	4	6	no	—
205	C₂²×C₄₇	—	4	6	no	—
206	C₂²×C₄₇	—	4	6	no	—
207	C₂²×C₄₇	—	4	6	no	—
208	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
209	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
210	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
211	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
212	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
214	C₂²×C₄₇	#585	1	1	yes	characteristic
215	C₄×C₄₇	—	2	4	no	—
216	C₄×C₄₇	—	2	6	no	—
217	C₄×C₄₇	C₂×C₄×D₄	1	12	yes	—
218	C₄×C₄₇	C₄×#41	1	4	yes	complemented
219	Dic₄₇	—	2	4	no	—
220	Dic₄₇	—	2	6	no	—
221	Dic₄₇	—	2	2	no	—
222	Dic₄₇	—	4	6	no	—
223	Dic₄₇	—	4	3	no	—
224	Dic₄₇	#550	1	4	yes	direct product factor
225	C₂×#550	D₄₇	1	1	yes	characteristic
226	C₂×C₄×#41	—	47	2	no	—
227	#2366	—	47	3	no	—
228	#2363	—	47	6	no	—
229	#2354	—	47	3	no	—
230	Q₈×C₄⋊C₄	—	47	1	no	—
231	#2341	—	47	2	no	—
232	C₄×#127	—	47	3	no	—
233	C₄×#121	—	47	6	no	—
234	C₄²×Q₈	—	47	1	no	—
235	C₄²×D₄	—	47	3	no	—
236	C₂×C₄₇	—	4	12	no	—
237	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
238	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
239	C₂×C₄₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄₇	C₂×#550	1	1	yes	characteristic
241	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
242	C₂×C₄₇	#3480	1	1	yes	characteristic
243	C₂×C₄₇	#3483	1	1	yes	characteristic
244	C₂²×#41	C₂×D₄₇	1	2	yes	—
245	#550	Dic₄₇	1	16	yes	direct product factor
246	C₂×#127	C₂×D₄₇	1	3	yes	—
247	C₂×#121	C₂×D₄₇	1	6	yes	—
248	C₄×#41	—	94	16	no	—
249	C₂×C₄×Q₈	—	47	1	no	—
250	C₂×C₄×Q₈	—	47	1	no	—
251	C₂×C₄×Q₈	—	47	2	no	—
252	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
253	C₂×C₄×D₄	—	47	3	no	—
254	C₂×C₄×D₄	—	47	6	no	—
255	C₂×C₄×D₄	—	47	6	no	—
256	C₂×C₄×D₄	—	47	3	no	—
257	C₂×C₄×D₄	—	47	6	no	—
258	C₂×C₄×D₄	C₂×D₄₇	1	3	yes	—
259	C₂×#117	—	47	6	no	—
260	C₂²×C₄²	—	47	6	no	—
261	#390	—	47	6	no	—
262	#390	—	47	6	no	—
263	#390	—	47	6	no	—
264	#390	—	47	6	no	—
265	#389	—	47	6	no	—
266	#388	—	47	12	no	—
267	#386	—	47	12	no	—
268	#384	—	47	3	no	—
269	#380	—	47	6	no	—
270	C₄×C₄⋊C₄	—	47	3	no	—
271	C₄×C₄⋊C₄	—	47	3	no	—
272	C₄×C₄⋊C₄	—	47	1	no	—
273	C₄×C₄⋊C₄	—	47	3	no	—
274	C₄×C₄⋊C₄	—	47	3	no	—
275	C₄×C₄⋊C₄	—	47	3	no	—
276	C₄×C₂²⋊C₄	—	47	6	no	—
277	C₄×C₂²⋊C₄	—	47	6	no	—
278	C₄×C₂²⋊C₄	—	47	6	no	—
279	C₄³	—	47	3	no	—
280	C₄₇	C₄×#550	1	1	yes	characteristic, complemented, Sylow
281	C₂×#41	—	2	8	no	—
282	C₂×#41	—	2	8	no	—
283	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
284	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
285	C₂²×D₄	C₂²×D₄₇	1	3	yes	—
286	C₂²×D₄	C₂²×D₄₇	1	6	yes	—
287	C₂²×D₄	C₂²×D₄₇	1	6	yes	—
288	C₂³×C₄	—	47	6	no	—
289	C₂³×C₄	—	47	6	no	—
290	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
291	#127	C₂×Dic₄₇	1	24	yes	complemented
292	#121	C₂×Dic₄₇	1	48	yes	complemented
293	C₄×Q₈	—	47	8	no	—
294	C₄×Q₈	—	94	8	no	—
295	C₄×Q₈	—	94	4	no	—
296	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
297	C₄×D₄	—	94	24	no	—
298	C₄×D₄	—	94	12	no	—
299	C₄×D₄	—	94	24	no	—
300	C₄×D₄	—	94	12	no	—
301	C₄×D₄	—	188	12	no	—
302	C₄×D₄	C₂×Dic₄₇	1	24	yes	complemented
303	#117	—	94	24	no	—
304	C₂×C₄⋊C₄	—	47	3	no	—
305	C₂×C₄⋊C₄	—	47	1	no	—
306	C₂×C₄⋊C₄	—	47	6	no	—
307	C₂×C₄⋊C₄	—	47	3	no	—
308	C₂×C₄⋊C₄	—	47	3	no	—
309	C₂×C₄⋊C₄	—	47	6	no	—
310	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂²×D₄₇	1	3	yes	—
312	C₂×C₂²⋊C₄	—	47	12	no	—
313	C₂×C₂²⋊C₄	—	47	6	no	—
314	C₂×C₂²⋊C₄	—	47	6	no	—
315	C₂×C₂²⋊C₄	—	47	12	no	—
316	C₂×C₂²⋊C₄	C₂²×D₄₇	1	6	yes	—
317	C₂×C₄²	—	47	1	no	—
318	C₂×C₄²	—	47	3	no	—
319	C₂×C₄²	—	47	6	no	—
320	C₂×C₄²	—	47	3	no	—
321	C₂×C₄²	—	47	6	no	—
322	C₂×C₄²	—	47	3	no	—
323	C₂×C₄²	—	47	3	no	—
324	C₂×C₄²	—	47	2	no	—
325	C₂×C₄²	—	47	3	no	—
326	C₂×C₄²	—	94	24	no	—
327	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
328	#95	—	47	2	no	—
329	#95	—	47	6	no	—
330	#95	—	47	6	no	—
331	#95	—	47	6	no	—
332	C₂⁴	C₂³×D₄₇	1	6	yes	—
333	#41	—	2	64	no	—
334	C₂×Q₈	D₄×D₄₇	1	4	yes	—
335	C₂×Q₈	#10625352	1	4	yes	—
336	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
337	C₂×D₄	—	2	12	no	—
338	C₂×D₄	—	2	6	no	—
339	C₂×D₄	—	2	6	no	—
340	C₂×D₄	—	2	12	no	—
341	C₂×D₄	—	4	6	no	—
342	C₂×D₄	—	4	6	no	—
343	C₂×D₄	C₂²×Dic₄₇	1	12	yes	—
344	C₂×D₄	C₂²×Dic₄₇	1	24	yes	—
345	C₂×D₄	C₂²×Dic₄₇	1	24	yes	—
346	C₂²×C₄	—	2	12	no	—
347	C₂²×C₄	—	2	12	no	—
348	C₂²×C₄	—	47	1	no	—
349	C₂²×C₄	—	47	2	no	—
350	C₂²×C₄	—	47	1	no	—
351	C₂²×C₄	—	47	3	no	—
352	C₂²×C₄	—	47	3	no	—
353	C₂²×C₄	—	47	6	no	—
354	C₂²×C₄	—	94	12	no	—
355	C₂²×C₄	—	94	12	no	—
356	C₂²×C₄	—	94	12	no	—
357	C₂²×C₄	—	94	12	no	—
358	C₂²×C₄	—	94	12	no	—
359	C₂²×C₄	—	188	6	no	—
360	C₂²×C₄	C₂²×Dic₄₇	1	24	yes	—
361	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
362	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
363	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
364	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
365	C₄⋊C₄	—	47	12	no	—
366	C₄⋊C₄	—	47	4	no	—
367	C₄⋊C₄	—	94	12	no	—
368	C₄⋊C₄	—	94	6	no	—
369	C₄⋊C₄	—	94	6	no	—
370	C₄⋊C₄	—	188	6	no	—
371	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
372	C₄⋊C₄	C₂²×Dic₄₇	1	12	yes	—
373	C₂²⋊C₄	—	94	24	no	—
374	C₂²⋊C₄	—	94	12	no	—
375	C₂²⋊C₄	—	94	12	no	—
376	C₂²⋊C₄	—	188	12	no	—
377	C₂²⋊C₄	C₂²×Dic₄₇	1	24	yes	—
378	C₄²	—	47	12	no	—
379	C₄²	—	47	4	no	—
380	C₄²	—	94	4	no	—
381	C₄²	—	94	12	no	—
382	C₄²	—	94	6	no	—
383	C₄²	—	94	12	no	—
384	C₄²	—	94	6	no	—
385	C₄²	—	94	6	no	—
386	C₄²	—	188	3	no	—
387	C₄²	C₂²×Dic₄₇	1	12	yes	—
388	C₂³	—	2	6	no	—
389	C₂³	—	2	6	no	—
390	C₂³	—	2	6	no	—
391	C₂³	—	2	6	no	—
392	C₂³	—	2	6	no	—
393	C₂³	—	2	6	no	—
394	C₂³	C₂³×Dic₄₇	1	12	yes	—
395	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
396	Q₈	D₄×Dic₄₇	1	16	yes	complemented
397	D₄	—	2	48	no	—
398	D₄	—	2	24	no	—
399	D₄	—	4	24	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	3	no	—
403	C₂×C₄	—	2	3	no	—
404	C₂×C₄	—	2	48	no	—
405	C₂×C₄	—	47	2	no	—
406	C₂×C₄	—	47	2	no	—
407	C₂×C₄	—	47	2	no	—
408	C₂×C₄	—	47	6	no	—
409	C₂×C₄	—	47	2	no	—
410	C₂×C₄	—	47	4	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	3	no	—
413	C₂×C₄	—	94	1	no	—
414	C₂×C₄	—	94	1	no	—
415	C₂×C₄	—	94	3	no	—
416	C₂×C₄	—	94	2	no	—
417	C₂×C₄	—	94	6	no	—
418	C₂×C₄	—	94	3	no	—
419	C₂×C₄	—	94	6	no	—
420	C₂×C₄	—	94	3	no	—
421	C₂×C₄	—	94	3	no	—
422	C₂×C₄	—	94	6	no	—
423	C₂×C₄	—	188	24	no	—
424	C₂×C₄	—	188	24	no	—
425	C₂×C₄	C₂³×Dic₄₇	1	6	yes	—
426	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
427	C₂×C₄	C₂³×Dic₄₇	1	6	yes	—
428	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
429	C₂×C₄	C₂×D₄×D₄₇	1	6	yes	—
430	C₂×C₄	#41×D₄₇	1	2	yes	—
431	C₂×C₄	#41×D₄₇	1	2	yes	—
432	C₂×C₄	C₂×#10625352	1	6	yes	—
433	C₂²	—	2	12	no	—
434	C₂²	—	2	12	no	—
435	C₂²	—	2	12	no	—
436	C₂²	—	4	6	no	—
437	C₂²	—	4	6	no	—
438	C₂²	—	4	6	no	—
439	C₂²	—	4	6	no	—
440	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
441	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
442	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
443	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
444	C₂²	C₂²×#10625352	1	1	yes	characteristic
445	C₂²	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
446	C₂²	#15689958	1	1	yes	characteristic
447	C₄	—	2	4	no	—
448	C₄	—	2	6	no	—
449	C₄	—	47	4	no	—
450	C₄	—	94	4	no	—
451	C₄	—	94	6	no	—
452	C₄	—	94	2	no	—
453	C₄	—	188	6	no	—
454	C₄	—	188	3	no	—
455	C₄	C₂×D₄×Dic₄₇	1	12	yes	—
456	C₄	#41×Dic₄₇	1	4	yes	complemented
457	C₂	—	4	12	no	—
458	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
459	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
460	C₂	H(5,𝔽₂)×Dic₄₇	1	1	yes	characteristic
461	C₂	#550×D₄₇	1	1	yes	characteristic
462	C₂	#20256878	1	1	yes	characteristic
463	C₂	#20256987	1	1	yes	characteristic
464	C₂	#20257011	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	C₂×C₄₇×#550	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#550	D₄₇
hypocenter	C₄₇	C₄×#550
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#550

Complements

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

N	H ≅ G/N	type
1. C₂×#41×Dic₄₇	C₂	semidirect
2. #20246453	C₂	semidirect
3. #20246430	C₂	semidirect
4. #20246337	C₂	semidirect
5. Q₈×C₄⋊Dic₄₇	C₂	semidirect
6. #20246229	C₂	semidirect
7. #127×Dic₄₇	C₂	semidirect
8. #121×Dic₄₇	C₂	semidirect
9. C₄×Q₈×Dic₄₇	C₂	semidirect
10. C₄×D₄×Dic₄₇	C₂	semidirect
43. C₄₇×#550	C₄	semidirect
52. Q₈×Dic₄₇	D₄	semidirect
85. C₂×#41×C₄₇	C₂×C₄	semidirect
91. #127×C₄₇	C₂×C₄	semidirect
92. #121×C₄₇	C₂×C₄	semidirect
93. C₄×Q₈×C₄₇	C₂×C₄	semidirect
94. C₄×D₄×C₄₇	C₂×C₄	semidirect
145. C₄⋊Dic₄₇	#41	semidirect
154. C₄×Dic₄₇	#41	semidirect
163. Q₈×C₄₇	C₄×D₄	semidirect
218. C₄×C₄₇	C₄×#41	semidirect
224. Dic₄₇	#550	direct (N × H)
245. #550	Dic₄₇	direct (N × H)
280. C₄₇	C₄×#550	semidirect
283. C₂×#41	C₂×Dic₄₇	semidirect
291. #127	C₂×Dic₄₇	semidirect
292. #121	C₂×Dic₄₇	semidirect
296. C₄×Q₈	C₂×Dic₄₇	semidirect
302. C₄×D₄	C₂×Dic₄₇	semidirect
396. Q₈	D₄×Dic₄₇	semidirect
456. C₄	#41×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×Dic₄₇	2
#20246453	2
#20246430	2
#20246337	2
Q₈×C₄⋊Dic₄₇	2
#20246229	2
#127×Dic₄₇	2
#121×Dic₄₇	2
C₄×Q₈×Dic₄₇	2
C₄×D₄×Dic₄₇	2
C₂×C₄₇×#550	2
C₄×#550	47

Subgroups — #550×Dic47 #26376135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #550×Dic₄₇ #26376135