Subgroups — #26376892

Order 12032.

2706 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246463	C₂	1	4	yes	maximal, complemented
2	#20246430	C₂	1	4	yes	maximal, complemented
3	#20246361	C₂	1	2	yes	maximal, complemented
4	#20246298	C₂	1	2	yes	maximal, complemented
5	#20246229	C₂	1	2	yes	maximal, complemented
6	#20246218	C₂	1	2	yes	maximal, complemented
7	#20246083	C₂	1	4	yes	maximal, complemented
8	#20246031	C₂	1	2	yes	maximal, complemented
9	C₄⋊Q₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
10	#127×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
12	#20245749	C₂	1	2	yes	maximal, complemented
13	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
15	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	—
16	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
17	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
18	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
19	C₂×#13093983	C₂²	1	2	yes	—
20	C₂×#13093983	C₂²	1	2	yes	—
21	#15689030	C₂²	1	4	yes	—
22	#15689026	C₂²	1	4	yes	—
23	#15689026	C₂²	1	8	yes	—
24	#15689026	C₂²	1	4	yes	—
25	#15689026	C₂²	1	4	yes	—
26	#15689022	C₂²	1	4	yes	—
27	#15689022	C₂²	1	4	yes	—
28	#15689016	C₂²	1	8	yes	—
29	#15689016	C₂²	1	8	yes	—
30	#15689003	C₂²	1	8	yes	—
31	#15688998	C₂²	1	8	yes	—
32	#15688993	C₂²	1	2	yes	—
33	#15688989	C₂²	1	2	yes	—
34	#15688986	C₂²	1	4	yes	—
35	#15688983	C₂²	1	4	yes	—
36	#15688983	C₂²	1	2	yes	—
37	#15688983	C₂²	1	2	yes	—
38	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
39	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
40	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
41	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
43	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
45	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	—
46	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
47	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
48	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
50	#15688969	C₂²	1	1	yes	characteristic
51	#15688969	C₂²	1	1	yes	characteristic
52	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
53	C₄²×Dic₄₇	C₂²	1	2	yes	—
54	C₂²×#41×C₄₇	C₂²	1	2	yes	—
55	C₄₇×#532	C₄	1	16	yes	complemented
56	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
58	C₂×#124×C₄₇	C₂²	1	2	yes	—
59	C₂×#121×C₄₇	C₂²	1	2	yes	—
60	C₂×#121×C₄₇	C₂²	1	2	yes	—
61	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
62	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
63	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
64	C₂³×Dic₄₇	C₂³	1	8	yes	—
65	Q₈×Dic₄₇	—	4	8	no	—
66	D₄×Dic₄₇	—	2	16	no	—
67	D₄×Dic₄₇	—	4	8	no	—
68	D₄×Dic₄₇	—	4	8	no	—
69	#13093983	—	2	8	no	—
70	#13093983	—	4	4	no	—
71	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
72	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
73	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
74	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
75	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
76	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
77	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
78	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
79	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
80	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
81	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
82	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
83	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
84	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
85	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
86	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
87	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
88	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
89	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
90	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
91	C₄₇⋊#95	C₂³	1	1	yes	characteristic
92	C₄₇⋊#95	C₂³	1	4	yes	—
93	C₄₇⋊#95	C₂³	1	8	yes	—
94	C₄₇⋊#95	C₂³	1	1	yes	characteristic
95	C₄₇⋊#95	C₂³	1	2	yes	—
96	C₄₇⋊#95	C₂³	1	1	yes	characteristic
97	C₄₇⋊#95	C₂³	1	1	yes	characteristic
98	C₄₇⋊#95	C₂³	1	2	yes	—
99	C₄₇⋊#95	C₂³	1	4	yes	—
100	C₄₇⋊#95	C₂³	1	8	yes	—
101	C₂×#41×C₄₇	—	4	8	no	—
102	C₂×#41×C₄₇	C₂×C₄	1	16	yes	complemented
103	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
104	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
105	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
106	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
107	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
108	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
112	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
113	#127×C₄₇	C₂×C₄	1	8	yes	—
114	#124×C₄₇	C₂×C₄	1	16	yes	complemented
115	#121×C₄₇	C₂×C₄	1	16	yes	complemented
116	#121×C₄₇	C₂×C₄	1	16	yes	complemented
117	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
118	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
119	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
123	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
124	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
128	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
129	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
130	#41×C₄₇	—	4	32	no	—
131	C₂×Q₈×C₄₇	—	2	8	no	—
132	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
133	C₂×D₄×C₄₇	—	2	8	no	—
134	C₂×D₄×C₄₇	—	2	8	no	—
135	C₂×D₄×C₄₇	—	2	4	no	—
136	C₂×D₄×C₄₇	—	2	4	no	—
137	C₂×D₄×C₄₇	—	4	8	no	—
138	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
139	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
140	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
141	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
142	C₂²×C₄×C₄₇	—	2	4	no	—
143	C₂²×C₄×C₄₇	—	2	4	no	—
144	C₂²×C₄×C₄₇	—	2	2	no	—
145	C₂²×C₄×C₄₇	—	2	2	no	—
146	C₂²×C₄×C₄₇	—	4	8	no	—
147	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
149	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
150	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
151	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
158	C₂²×Dic₄₇	—	2	16	no	—
159	C₂²×Dic₄₇	—	4	8	no	—
160	C₂²×Dic₄₇	—	4	8	no	—
161	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
162	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
163	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
164	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
165	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
166	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
167	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
168	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
169	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
170	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
171	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
172	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
173	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
174	C₂²⋊Dic₄₇	—	2	4	no	—
175	C₂²⋊Dic₄₇	—	2	4	no	—
176	C₂²⋊Dic₄₇	—	2	16	no	—
177	C₂²⋊Dic₄₇	—	4	4	no	—
178	C₂²⋊Dic₄₇	—	4	8	no	—
179	C₂²⋊Dic₄₇	—	4	8	no	—
180	C₄⋊Dic₄₇	—	2	8	no	—
181	C₄⋊Dic₄₇	—	2	8	no	—
182	C₄⋊Dic₄₇	—	2	8	no	—
183	C₄⋊Dic₄₇	—	2	4	no	—
184	C₄⋊Dic₄₇	—	2	4	no	—
185	C₄⋊Dic₄₇	—	4	8	no	—
186	C₄×Dic₄₇	—	2	4	no	—
187	C₄×Dic₄₇	—	2	4	no	—
188	C₄×Dic₄₇	—	2	4	no	—
189	C₄×Dic₄₇	—	2	4	no	—
190	C₄×Dic₄₇	—	2	4	no	—
191	C₄×Dic₄₇	—	4	4	no	—
192	C₄×Dic₄₇	—	4	8	no	—
193	C₄×Dic₄₇	#41	1	8	yes	complemented
194	C₂³×C₄₇	—	2	2	no	—
195	C₂³×C₄₇	—	2	8	no	—
196	C₂³×C₄₇	—	2	1	no	—
197	C₂³×C₄₇	—	2	4	no	—
198	C₂³×C₄₇	—	2	8	no	—
199	C₂³×C₄₇	—	2	2	no	—
200	C₂³×C₄₇	—	2	1	no	—
201	C₂³×C₄₇	—	2	4	no	—
202	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
203	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
204	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
205	Q₈×C₄₇	—	2	16	no	—
206	D₄×C₄₇	—	2	16	no	—
207	D₄×C₄₇	—	2	16	no	—
208	D₄×C₄₇	—	2	16	no	—
209	D₄×C₄₇	—	4	16	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	2	1	no	—
212	C₂×C₄×C₄₇	—	2	8	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	2	1	no	—
215	C₂×C₄×C₄₇	—	2	8	no	—
216	C₂×C₄×C₄₇	—	2	8	no	—
217	C₂×C₄×C₄₇	—	2	8	no	—
218	C₂×C₄×C₄₇	—	4	16	no	—
219	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
221	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
223	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
224	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
225	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
226	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
227	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
228	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
229	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
230	C₂×Dic₄₇	—	2	2	no	—
231	C₂×Dic₄₇	—	2	2	no	—
232	C₂×Dic₄₇	—	2	2	no	—
233	C₂×Dic₄₇	—	2	2	no	—
234	C₂×Dic₄₇	—	2	2	no	—
235	C₂×Dic₄₇	—	2	2	no	—
236	C₂×Dic₄₇	—	2	8	no	—
237	C₂×Dic₄₇	—	2	2	no	—
238	C₂×Dic₄₇	—	2	2	no	—
239	C₂×Dic₄₇	—	2	2	no	—
240	C₂×Dic₄₇	—	2	8	no	—
241	C₂×Dic₄₇	—	2	8	no	—
242	C₂×Dic₄₇	—	2	2	no	—
243	C₂×Dic₄₇	—	8	16	no	—
244	C₂×Dic₄₇	C₂×#41	1	4	yes	—
245	C₂×Dic₄₇	C₂×#41	1	4	yes	—
246	#34226	—	47	1	no	maximal, Sylow
247	C₂²×C₄₇	—	2	2	no	—
248	C₂²×C₄₇	—	2	8	no	—
249	C₂²×C₄₇	—	2	2	no	—
250	C₂²×C₄₇	—	2	8	no	—
251	C₂²×C₄₇	—	2	2	no	—
252	C₂²×C₄₇	—	2	8	no	—
253	C₂²×C₄₇	—	4	8	no	—
254	C₂²×C₄₇	—	4	2	no	—
255	C₂²×C₄₇	—	4	2	no	—
256	C₂²×C₄₇	—	4	8	no	—
257	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
258	C₂²×C₄₇	C₂²×#41	1	2	yes	—
259	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
260	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
261	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
262	C₄×C₄₇	—	2	2	no	—
263	C₄×C₄₇	—	2	2	no	—
264	C₄×C₄₇	—	2	8	no	—
265	C₄×C₄₇	—	2	2	no	—
266	C₄×C₄₇	C₄×#41	1	4	yes	—
267	C₄×C₄₇	#518	1	4	yes	—
268	C₄×C₄₇	#520	1	4	yes	—
269	Dic₄₇	—	2	4	no	—
270	Dic₄₇	—	2	4	no	—
271	Dic₄₇	—	4	2	no	—
272	Dic₄₇	—	4	8	no	—
273	Dic₄₇	—	4	2	no	—
274	C₂×#532	D₄₇	1	1	yes	characteristic
275	#2367	—	47	4	no	—
276	#2363	—	47	4	no	—
277	#2357	—	47	2	no	—
278	#2349	—	47	2	no	—
279	#2341	—	47	2	no	—
280	#2339	—	47	2	no	—
281	#2324	—	47	4	no	—
282	#2319	—	47	2	no	—
283	C₄×C₄⋊Q₈	—	47	2	no	—
284	C₄×#127	—	47	2	no	—
285	#2285	—	47	1	no	—
286	#2275	—	47	2	no	—
287	C₄×#117	—	47	1	no	—
288	C₂×C₄₇	—	4	2	no	—
289	C₂×C₄₇	—	4	8	no	—
290	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
291	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
292	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
293	C₂×C₄₇	#3508	1	2	yes	—
294	C₂×C₄₇	#3511	1	2	yes	—
295	C₂²×#41	C₂×D₄₇	1	2	yes	—
296	#532	Dic₄₇	1	16	yes	complemented
297	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
298	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
299	C₂×#124	C₂×D₄₇	1	2	yes	—
300	C₂×#121	C₂×D₄₇	1	2	yes	—
301	C₂×#121	C₂×D₄₇	1	2	yes	—
302	C₂×C₄×Q₈	—	47	4	no	—
303	C₂×C₄×D₄	—	47	4	no	—
304	C₂×C₄×D₄	—	47	4	no	—
305	C₂×C₄×D₄	—	47	4	no	—
306	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
307	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
308	C₂×#117	—	47	2	no	—
309	C₂×#117	—	47	2	no	—
310	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
311	#391	—	47	4	no	—
312	#390	—	47	4	no	—
313	#390	—	47	4	no	—
314	#390	—	47	4	no	—
315	#390	—	47	8	no	—
316	#389	—	47	4	no	—
317	#389	—	47	4	no	—
318	#388	—	47	8	no	—
319	#388	—	47	8	no	—
320	#386	—	47	8	no	—
321	#385	—	47	8	no	—
322	#384	—	47	2	no	—
323	#382	—	47	2	no	—
324	#381	—	47	4	no	—
325	#380	—	47	4	no	—
326	#380	—	47	2	no	—
327	#380	—	47	2	no	—
328	C₄×C₄⋊C₄	—	47	4	no	—
329	C₄×C₄⋊C₄	—	47	4	no	—
330	C₄×C₄⋊C₄	—	47	2	no	—
331	C₄×C₄⋊C₄	—	47	1	no	—
332	C₄×C₄⋊C₄	—	47	1	no	—
333	C₄×C₄⋊C₄	—	47	2	no	—
334	C₄×C₄⋊C₄	—	47	2	no	—
335	C₄×C₂²⋊C₄	—	47	1	no	—
336	C₄×C₂²⋊C₄	—	47	1	no	—
337	C₄×C₂²⋊C₄	—	47	4	no	—
338	C₄×C₂²⋊C₄	—	47	2	no	—
339	C₄×C₂²⋊C₄	—	47	8	no	—
340	#376	—	47	1	no	—
341	#376	—	47	1	no	—
342	C₂×#95	—	47	4	no	—
343	C₄³	—	47	2	no	—
344	C₄₇	#34226	1	1	yes	characteristic, complemented, Sylow
345	C₂×#41	—	4	8	no	—
346	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
347	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
348	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
349	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
350	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
351	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
352	C₂³×C₄	—	47	8	no	—
353	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
354	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
355	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
356	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
357	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
358	#127	C₂×Dic₄₇	1	8	yes	—
359	#124	C₂×Dic₄₇	1	16	yes	complemented
360	#121	C₂×Dic₄₇	1	16	yes	complemented
361	#121	C₂×Dic₄₇	1	16	yes	complemented
362	C₄×Q₈	—	188	8	no	—
363	C₄×D₄	—	94	16	no	—
364	C₄×D₄	—	188	8	no	—
365	C₄×D₄	—	188	8	no	—
366	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
367	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
368	#117	—	94	8	no	—
369	#117	—	188	4	no	—
370	C₂×C₄⋊C₄	—	47	4	no	—
371	C₂×C₄⋊C₄	—	47	2	no	—
372	C₂×C₄⋊C₄	—	47	2	no	—
373	C₂×C₄⋊C₄	—	47	4	no	—
374	C₂×C₄⋊C₄	—	47	4	no	—
375	C₂×C₄⋊C₄	—	47	8	no	—
376	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
377	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
378	C₂×C₂²⋊C₄	—	47	2	no	—
379	C₂×C₂²⋊C₄	—	47	2	no	—
380	C₂×C₂²⋊C₄	—	47	8	no	—
381	C₂×C₂²⋊C₄	—	47	4	no	—
382	C₂×C₂²⋊C₄	—	47	8	no	—
383	C₂×C₂²⋊C₄	—	47	8	no	—
384	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
386	C₂×C₄²	—	47	2	no	—
387	C₂×C₄²	—	47	2	no	—
388	C₂×C₄²	—	47	2	no	—
389	C₂×C₄²	—	47	2	no	—
390	C₂×C₄²	—	47	2	no	—
391	C₂×C₄²	—	47	2	no	—
392	C₂×C₄²	—	47	4	no	—
393	C₂×C₄²	—	47	8	no	—
394	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
395	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
396	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
397	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
398	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
399	#95	—	47	1	no	—
400	#95	—	47	4	no	—
401	#95	—	47	8	no	—
402	#95	—	47	2	no	—
403	#95	—	47	1	no	—
404	#95	—	47	1	no	—
405	#95	—	47	1	no	—
406	#95	—	47	2	no	—
407	#95	—	47	4	no	—
408	#95	—	47	8	no	—
409	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
410	C₂⁴	C₂³×D₄₇	1	4	yes	—
411	#41	—	4	32	no	—
412	C₂×Q₈	—	2	8	no	—
413	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	4	8	no	—
419	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
420	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
421	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
422	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	4	8	no	—
428	C₂²×C₄	—	47	2	no	—
429	C₂²×C₄	—	47	2	no	—
430	C₂²×C₄	—	47	2	no	—
431	C₂²×C₄	—	47	8	no	—
432	C₂²×C₄	—	47	2	no	—
433	C₂²×C₄	—	94	16	no	—
434	C₂²×C₄	—	188	8	no	—
435	C₂²×C₄	—	188	8	no	—
436	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
437	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
438	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
439	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
440	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
441	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
442	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
443	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
444	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
445	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
446	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
447	C₄⋊C₄	—	94	4	no	—
448	C₄⋊C₄	—	94	4	no	—
449	C₄⋊C₄	—	94	8	no	—
450	C₄⋊C₄	—	94	8	no	—
451	C₄⋊C₄	—	94	8	no	—
452	C₄⋊C₄	—	188	8	no	—
453	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
454	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
455	C₂²⋊C₄	—	94	4	no	—
456	C₂²⋊C₄	—	94	4	no	—
457	C₂²⋊C₄	—	94	16	no	—
458	C₂²⋊C₄	—	188	4	no	—
459	C₂²⋊C₄	—	188	8	no	—
460	C₂²⋊C₄	—	188	8	no	—
461	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
462	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
463	C₄²	—	47	8	no	—
464	C₄²	—	94	4	no	—
465	C₄²	—	94	4	no	—
466	C₄²	—	94	4	no	—
467	C₄²	—	94	4	no	—
468	C₄²	—	94	4	no	—
469	C₄²	—	188	4	no	—
470	C₄²	—	188	8	no	—
471	C₄²	C₂²×Dic₄₇	1	4	yes	—
472	C₄²	C₂²×Dic₄₇	1	4	yes	—
473	C₄²	C₂²×Dic₄₇	1	4	yes	—
474	C₄²	C₂²×Dic₄₇	1	4	yes	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	8	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	4	no	—
483	C₂³	C₂³×Dic₄₇	1	8	yes	—
484	C₂³	C₂³×Dic₄₇	1	2	yes	—
485	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
486	Q₈	—	2	16	no	—
487	D₄	—	2	16	no	—
488	D₄	—	2	16	no	—
489	D₄	—	2	16	no	—
490	D₄	—	4	16	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	4	16	no	—
500	C₂×C₄	—	47	4	no	—
501	C₂×C₄	—	47	4	no	—
502	C₂×C₄	—	94	2	no	—
503	C₂×C₄	—	94	2	no	—
504	C₂×C₄	—	94	2	no	—
505	C₂×C₄	—	94	2	no	—
506	C₂×C₄	—	94	2	no	—
507	C₂×C₄	—	94	2	no	—
508	C₂×C₄	—	94	8	no	—
509	C₂×C₄	—	94	2	no	—
510	C₂×C₄	—	94	2	no	—
511	C₂×C₄	—	94	8	no	—
512	C₂×C₄	—	94	2	no	—
513	C₂×C₄	—	94	8	no	—
514	C₂×C₄	—	94	2	no	—
515	C₂×C₄	—	376	16	no	—
516	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
517	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
518	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
519	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
520	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
521	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
522	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
523	C₂×C₄	#41×D₄₇	1	4	yes	—
524	C₂×C₄	#13094069	1	4	yes	—
525	C₂×C₄	#13094070	1	2	yes	—
526	C₂×C₄	#13094071	1	2	yes	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	8	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	8	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	8	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	8	no	—
535	C₂²	—	4	8	no	—
536	C₂²	—	4	2	no	—
537	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
538	C₂²	C₂×#41×D₄₇	1	2	yes	—
539	C₂²	C₂×#13094069	1	2	yes	—
540	C₂²	C₂×#13094070	1	1	yes	characteristic
541	C₂²	C₂×#13094071	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	8	no	—
545	C₄	—	2	2	no	—
546	C₄	—	94	4	no	—
547	C₄	—	94	4	no	—
548	C₄	—	188	2	no	—
549	C₄	—	188	8	no	—
550	C₄	—	188	2	no	—
551	C₄	#41×Dic₄₇	1	4	yes	—
552	C₄	#15689598	1	4	yes	—
553	C₄	#15689606	1	4	yes	—
554	C₂	—	4	2	no	—
555	C₂	—	4	8	no	—
556	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
557	C₂	C₂×#15689598	1	1	yes	characteristic
558	C₂	C₂×#15689606	1	1	yes	characteristic
559	C₂	#20257257	1	2	yes	—
560	C₂	#20257289	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	#34226
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #20246463	C₂	semidirect
2. #20246430	C₂	semidirect
3. #20246361	C₂	semidirect
4. #20246298	C₂	semidirect
5. #20246229	C₂	semidirect
6. #20246218	C₂	semidirect
7. #20246083	C₂	semidirect
8. #20246031	C₂	semidirect
9. C₄⋊Q₈×Dic₄₇	C₂	semidirect
10. #127×Dic₄₇	C₂	semidirect
11. #20245795	C₂	semidirect
12. #20245749	C₂	semidirect
13. C₄×#13093983	C₂	semidirect
55. C₄₇×#532	C₄	semidirect
102. C₂×#41×C₄₇	C₂×C₄	semidirect
112. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
114. #124×C₄₇	C₂×C₄	semidirect
115. #121×C₄₇	C₂×C₄	semidirect
116. #121×C₄₇	C₂×C₄	semidirect
117. C₄×D₄×C₄₇	C₂×C₄	semidirect
118. C₄×D₄×C₄₇	C₂×C₄	semidirect
123. C₂×C₄²×C₄₇	C₂×C₄	semidirect
193. C₄×Dic₄₇	#41	semidirect
296. #532	Dic₄₇	semidirect
344. C₄₇	#34226	semidirect
346. C₂×#41	C₂×Dic₄₇	semidirect
357. C₄⋊Q₈	C₂×Dic₄₇	semidirect
359. #124	C₂×Dic₄₇	semidirect
360. #121	C₂×Dic₄₇	semidirect
361. #121	C₂×Dic₄₇	semidirect
366. C₄×D₄	C₂×Dic₄₇	semidirect
367. C₄×D₄	C₂×Dic₄₇	semidirect
394. C₂×C₄²	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246463	2
#20246430	2
#20246361	2
#20246298	2
#20246229	2
#20246218	2
#20246083	2
#20246031	2
C₄⋊Q₈×Dic₄₇	2
#127×Dic₄₇	2
#20245795	2
#20245749	2
C₄×#13093983	2
C₂×C₄₇×#532	2
#34226	47