Subgroups — #26376984

Order 12032.

2606 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246453	C₂	1	2	yes	maximal, complemented
2	#20246448	C₂	1	2	yes	maximal, complemented
3	#20246430	C₂	1	4	yes	maximal, complemented
4	#20246328	C₂	1	4	yes	maximal, complemented
5	#20246229	C₂	1	2	yes	maximal, complemented
6	#20246218	C₂	1	2	yes	maximal, complemented
7	#20246155	C₂	1	4	yes	maximal, complemented
8	#20246031	C₂	1	2	yes	maximal, complemented
9	#124×Dic₄₇	C₂	1	4	yes	maximal, complemented
10	#20245786	C₂	1	1	yes	maximal, characteristic, complemented
11	#20245749	C₂	1	2	yes	maximal, complemented
12	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
14	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	—
15	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
16	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
17	C₂×#13093983	C₂²	1	2	yes	—
18	#15689030	C₂²	1	4	yes	—
19	#15689026	C₂²	1	4	yes	—
20	#15689026	C₂²	1	8	yes	—
21	#15689026	C₂²	1	4	yes	—
22	#15689022	C₂²	1	4	yes	—
23	#15689016	C₂²	1	8	yes	—
24	#15689016	C₂²	1	8	yes	—
25	#15689009	C₂²	1	8	yes	—
26	#15689003	C₂²	1	8	yes	—
27	#15689003	C₂²	1	8	yes	—
28	#15688991	C₂²	1	2	yes	—
29	#15688989	C₂²	1	2	yes	—
30	#15688986	C₂²	1	4	yes	—
31	#15688986	C₂²	1	2	yes	—
32	#15688983	C₂²	1	4	yes	—
33	#15688983	C₂²	1	1	yes	characteristic
34	#15688983	C₂²	1	1	yes	characteristic
35	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
36	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
38	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
39	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
40	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	—
41	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	—
42	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
43	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
44	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
45	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
46	#15688969	C₂²	1	2	yes	—
47	#15688969	C₂²	1	2	yes	—
48	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
49	C₄²×Dic₄₇	C₂²	1	2	yes	—
50	C₂²×#41×C₄₇	C₂²	1	2	yes	—
51	C₄₇×#532	C₄	1	16	yes	complemented
52	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×#124×C₄₇	C₂²	1	2	yes	—
55	C₂×#121×C₄₇	C₂²	1	2	yes	—
56	C₂×#121×C₄₇	C₂²	1	2	yes	—
57	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
58	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
59	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
60	C₂³×Dic₄₇	C₂³	1	8	yes	—
61	Q₈×Dic₄₇	—	4	8	no	—
62	D₄×Dic₄₇	—	2	16	no	—
63	D₄×Dic₄₇	—	4	8	no	—
64	#13093983	—	2	8	no	—
65	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
66	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
68	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
70	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
71	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
72	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
73	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
74	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
75	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
76	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
77	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
78	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
79	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
80	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
81	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
82	C₄₇⋊#95	C₂³	1	2	yes	—
83	C₄₇⋊#95	C₂³	1	2	yes	—
84	C₄₇⋊#95	C₂³	1	8	yes	—
85	C₄₇⋊#95	C₂³	1	2	yes	—
86	C₄₇⋊#95	C₂³	1	2	yes	—
87	C₄₇⋊#95	C₂³	1	4	yes	—
88	C₄₇⋊#95	C₂³	1	4	yes	—
89	C₄₇⋊#95	C₂³	1	4	yes	—
90	C₄₇⋊#95	C₂³	1	8	yes	—
91	C₄₇⋊#95	C₂³	1	4	yes	—
92	C₂×#41×C₄₇	—	4	8	no	—
93	C₂×#41×C₄₇	C₂×C₄	1	16	yes	complemented
94	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
95	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
96	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
97	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
98	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
99	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
102	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
104	#127×C₄₇	C₂×C₄	1	8	yes	—
105	#124×C₄₇	C₂×C₄	1	16	yes	complemented
106	#121×C₄₇	C₂×C₄	1	16	yes	complemented
107	#121×C₄₇	C₂×C₄	1	16	yes	complemented
108	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
109	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
114	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
115	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
119	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
120	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
121	#41×C₄₇	—	4	32	no	—
122	C₂×Q₈×C₄₇	—	2	8	no	—
123	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
124	C₂×D₄×C₄₇	—	2	8	no	—
125	C₂×D₄×C₄₇	—	2	8	no	—
126	C₂×D₄×C₄₇	—	4	2	no	—
127	C₂×D₄×C₄₇	—	4	2	no	—
128	C₂×D₄×C₄₇	—	4	8	no	—
129	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
130	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
131	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
132	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
133	C₂²×C₄×C₄₇	—	2	4	no	—
134	C₂²×C₄×C₄₇	—	2	4	no	—
135	C₂²×C₄×C₄₇	—	4	1	no	—
136	C₂²×C₄×C₄₇	—	4	1	no	—
137	C₂²×C₄×C₄₇	—	4	8	no	—
138	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
142	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
149	C₂²×Dic₄₇	—	2	16	no	—
150	C₂²×Dic₄₇	—	4	8	no	—
151	C₂²×Dic₄₇	—	4	8	no	—
152	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
153	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
154	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
155	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
156	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
157	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
158	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
159	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
160	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
161	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
162	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
163	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
164	C₂²⋊Dic₄₇	—	2	8	no	—
165	C₂²⋊Dic₄₇	—	2	16	no	—
166	C₂²⋊Dic₄₇	—	4	8	no	—
167	C₂²⋊Dic₄₇	—	4	2	no	—
168	C₂²⋊Dic₄₇	—	4	2	no	—
169	C₂²⋊Dic₄₇	—	4	8	no	—
170	C₄⋊Dic₄₇	—	2	4	no	—
171	C₄⋊Dic₄₇	—	2	4	no	—
172	C₄⋊Dic₄₇	—	2	4	no	—
173	C₄⋊Dic₄₇	—	4	8	no	—
174	C₄⋊Dic₄₇	#41	1	8	yes	complemented
175	C₄×Dic₄₇	—	2	8	no	—
176	C₄×Dic₄₇	—	2	8	no	—
177	C₄×Dic₄₇	—	2	8	no	—
178	C₄×Dic₄₇	—	4	2	no	—
179	C₄×Dic₄₇	—	4	2	no	—
180	C₄×Dic₄₇	—	4	8	no	—
181	C₂³×C₄₇	—	2	2	no	—
182	C₂³×C₄₇	—	2	8	no	—
183	C₂³×C₄₇	—	2	8	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	2	1	no	—
186	C₂³×C₄₇	—	2	1	no	—
187	C₂³×C₄₇	—	2	4	no	—
188	C₂³×C₄₇	—	2	4	no	—
189	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
190	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
191	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
192	Q₈×C₄₇	—	2	16	no	—
193	D₄×C₄₇	—	2	16	no	—
194	D₄×C₄₇	—	2	16	no	—
195	D₄×C₄₇	—	4	8	no	—
196	D₄×C₄₇	—	4	16	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	8	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	1	no	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	1	no	—
203	C₂×C₄×C₄₇	—	2	1	no	—
204	C₂×C₄×C₄₇	—	2	8	no	—
205	C₂×C₄×C₄₇	—	2	8	no	—
206	C₂×C₄×C₄₇	—	4	4	no	—
207	C₂×C₄×C₄₇	—	4	16	no	—
208	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
209	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
210	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
211	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
212	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
213	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
214	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
216	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
217	C₂×Dic₄₇	—	2	4	no	—
218	C₂×Dic₄₇	—	2	4	no	—
219	C₂×Dic₄₇	—	2	4	no	—
220	C₂×Dic₄₇	—	2	4	no	—
221	C₂×Dic₄₇	—	2	4	no	—
222	C₂×Dic₄₇	—	2	4	no	—
223	C₂×Dic₄₇	—	2	4	no	—
224	C₂×Dic₄₇	—	2	4	no	—
225	C₂×Dic₄₇	—	2	4	no	—
226	C₂×Dic₄₇	—	2	4	no	—
227	C₂×Dic₄₇	—	2	4	no	—
228	C₂×Dic₄₇	—	8	16	no	—
229	C₂×Dic₄₇	C₂×#41	1	8	yes	—
230	#34232	—	47	1	no	maximal, Sylow
231	C₂²×C₄₇	—	2	2	no	—
232	C₂²×C₄₇	—	2	8	no	—
233	C₂²×C₄₇	—	2	2	no	—
234	C₂²×C₄₇	—	2	8	no	—
235	C₂²×C₄₇	—	2	2	no	—
236	C₂²×C₄₇	—	2	8	no	—
237	C₂²×C₄₇	—	4	8	no	—
238	C₂²×C₄₇	—	4	2	no	—
239	C₂²×C₄₇	—	4	2	no	—
240	C₂²×C₄₇	—	4	8	no	—
241	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
242	C₂²×C₄₇	C₂²×#41	1	2	yes	—
243	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
244	C₂²×C₄₇	#585	1	1	yes	characteristic
245	C₂²×C₄₇	#585	1	1	yes	characteristic
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	2	no	—
248	C₄×C₄₇	—	2	8	no	—
249	C₄×C₄₇	—	2	2	no	—
250	C₄×C₄₇	—	2	2	no	—
251	C₄×C₄₇	C₄×#41	1	4	yes	—
252	C₄×C₄₇	#518	1	4	yes	—
253	Dic₄₇	—	2	8	no	—
254	Dic₄₇	—	4	4	no	—
255	Dic₄₇	—	4	4	no	—
256	Dic₄₇	—	4	4	no	—
257	C₂×#532	D₄₇	1	1	yes	characteristic
258	#2366	—	47	2	no	—
259	#2365	—	47	2	no	—
260	#2363	—	47	4	no	—
261	#2353	—	47	4	no	—
262	#2341	—	47	2	no	—
263	#2339	—	47	2	no	—
264	#2333	—	47	4	no	—
265	#2319	—	47	2	no	—
266	C₄×#124	—	47	4	no	—
267	#2283	—	47	1	no	—
268	#2275	—	47	2	no	—
269	C₄×#117	—	47	1	no	—
270	C₂×C₄₇	—	4	2	no	—
271	C₂×C₄₇	—	4	8	no	—
272	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
273	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
274	C₂×C₄₇	#3428	1	1	yes	characteristic
275	C₂×C₄₇	#3514	1	2	yes	—
276	C₂×C₄₇	#3517	1	2	yes	—
277	C₂²×#41	C₂×D₄₇	1	2	yes	—
278	#532	Dic₄₇	1	16	yes	complemented
279	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
280	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
281	C₂×#124	C₂×D₄₇	1	2	yes	—
282	C₂×#121	C₂×D₄₇	1	2	yes	—
283	C₂×#121	C₂×D₄₇	1	2	yes	—
284	C₂×C₄×Q₈	—	47	4	no	—
285	C₂×C₄×D₄	—	47	4	no	—
286	C₂×C₄×D₄	—	47	4	no	—
287	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
288	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
289	C₂×#117	—	47	2	no	—
290	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
291	#391	—	47	4	no	—
292	#390	—	47	4	no	—
293	#390	—	47	8	no	—
294	#390	—	47	4	no	—
295	#389	—	47	4	no	—
296	#388	—	47	8	no	—
297	#388	—	47	8	no	—
298	#387	—	47	8	no	—
299	#386	—	47	8	no	—
300	#386	—	47	8	no	—
301	#383	—	47	2	no	—
302	#382	—	47	2	no	—
303	#381	—	47	4	no	—
304	#381	—	47	2	no	—
305	#380	—	47	4	no	—
306	#380	—	47	1	no	—
307	#380	—	47	1	no	—
308	C₄×C₄⋊C₄	—	47	4	no	—
309	C₄×C₄⋊C₄	—	47	1	no	—
310	C₄×C₄⋊C₄	—	47	2	no	—
311	C₄×C₄⋊C₄	—	47	2	no	—
312	C₄×C₄⋊C₄	—	47	1	no	—
313	C₄×C₂²⋊C₄	—	47	2	no	—
314	C₄×C₂²⋊C₄	—	47	2	no	—
315	C₄×C₂²⋊C₄	—	47	4	no	—
316	C₄×C₂²⋊C₄	—	47	2	no	—
317	C₄×C₂²⋊C₄	—	47	8	no	—
318	C₄×C₂²⋊C₄	—	47	8	no	—
319	#376	—	47	2	no	—
320	#376	—	47	2	no	—
321	C₂×#95	—	47	4	no	—
322	C₄³	—	47	2	no	—
323	C₄₇	#34232	1	1	yes	characteristic, complemented, Sylow
324	C₂×#41	—	4	8	no	—
325	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
326	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
327	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
328	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
329	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
330	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
331	C₂³×C₄	—	47	8	no	—
332	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
333	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
334	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
335	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
336	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
337	#127	C₂×Dic₄₇	1	8	yes	—
338	#124	C₂×Dic₄₇	1	16	yes	complemented
339	#121	C₂×Dic₄₇	1	16	yes	complemented
340	#121	C₂×Dic₄₇	1	16	yes	complemented
341	C₄×Q₈	—	188	8	no	—
342	C₄×D₄	—	94	16	no	—
343	C₄×D₄	—	188	8	no	—
344	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
345	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
346	#117	—	94	8	no	—
347	C₂×C₄⋊C₄	—	47	2	no	—
348	C₂×C₄⋊C₄	—	47	2	no	—
349	C₂×C₄⋊C₄	—	47	2	no	—
350	C₂×C₄⋊C₄	—	47	2	no	—
351	C₂×C₄⋊C₄	—	47	8	no	—
352	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
353	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
354	C₂×C₂²⋊C₄	—	47	4	no	—
355	C₂×C₂²⋊C₄	—	47	8	no	—
356	C₂×C₂²⋊C₄	—	47	8	no	—
357	C₂×C₂²⋊C₄	—	47	2	no	—
358	C₂×C₂²⋊C₄	—	47	2	no	—
359	C₂×C₂²⋊C₄	—	47	8	no	—
360	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
361	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
362	C₂×C₄²	—	47	4	no	—
363	C₂×C₄²	—	47	4	no	—
364	C₂×C₄²	—	47	4	no	—
365	C₂×C₄²	—	47	8	no	—
366	C₂×C₄²	—	47	2	no	—
367	C₂×C₄²	—	47	2	no	—
368	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
369	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
370	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
371	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
372	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
373	#95	—	47	2	no	—
374	#95	—	47	2	no	—
375	#95	—	47	8	no	—
376	#95	—	47	2	no	—
377	#95	—	47	4	no	—
378	#95	—	47	2	no	—
379	#95	—	47	4	no	—
380	#95	—	47	4	no	—
381	#95	—	47	8	no	—
382	#95	—	47	4	no	—
383	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
384	C₂⁴	C₂³×D₄₇	1	4	yes	—
385	#41	—	4	32	no	—
386	C₂×Q₈	—	2	8	no	—
387	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	8	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	8	no	—
393	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
394	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
395	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
396	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	8	no	—
402	C₂²×C₄	—	47	4	no	—
403	C₂²×C₄	—	47	4	no	—
404	C₂²×C₄	—	47	4	no	—
405	C₂²×C₄	—	47	4	no	—
406	C₂²×C₄	—	94	16	no	—
407	C₂²×C₄	—	188	8	no	—
408	C₂²×C₄	—	188	8	no	—
409	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
410	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
411	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
412	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
413	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
414	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
415	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
416	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
417	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
418	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
419	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
420	C₄⋊C₄	—	47	8	no	—
421	C₄⋊C₄	—	94	4	no	—
422	C₄⋊C₄	—	94	4	no	—
423	C₄⋊C₄	—	94	4	no	—
424	C₄⋊C₄	—	188	8	no	—
425	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
426	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
427	C₂²⋊C₄	—	94	8	no	—
428	C₂²⋊C₄	—	94	16	no	—
429	C₂²⋊C₄	—	188	8	no	—
430	C₂²⋊C₄	—	188	2	no	—
431	C₂²⋊C₄	—	188	2	no	—
432	C₂²⋊C₄	—	188	8	no	—
433	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
434	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
435	C₄²	—	94	8	no	—
436	C₄²	—	94	8	no	—
437	C₄²	—	94	8	no	—
438	C₄²	—	188	2	no	—
439	C₄²	—	188	2	no	—
440	C₄²	—	188	8	no	—
441	C₄²	C₂²×Dic₄₇	1	4	yes	—
442	C₄²	C₂²×Dic₄₇	1	4	yes	—
443	C₄²	C₂²×Dic₄₇	1	4	yes	—
444	C₄²	C₂²×Dic₄₇	1	4	yes	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	8	no	—
447	C₂³	—	2	8	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	C₂³×Dic₄₇	1	8	yes	—
454	C₂³	C₂³×Dic₄₇	1	2	yes	—
455	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
456	Q₈	—	2	16	no	—
457	D₄	—	2	16	no	—
458	D₄	—	2	16	no	—
459	D₄	—	4	8	no	—
460	D₄	—	4	16	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	16	no	—
472	C₂×C₄	—	47	8	no	—
473	C₂×C₄	—	94	4	no	—
474	C₂×C₄	—	94	4	no	—
475	C₂×C₄	—	94	4	no	—
476	C₂×C₄	—	94	4	no	—
477	C₂×C₄	—	94	4	no	—
478	C₂×C₄	—	94	4	no	—
479	C₂×C₄	—	94	4	no	—
480	C₂×C₄	—	94	4	no	—
481	C₂×C₄	—	94	4	no	—
482	C₂×C₄	—	94	4	no	—
483	C₂×C₄	—	94	4	no	—
484	C₂×C₄	—	376	16	no	—
485	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
486	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
487	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
488	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
489	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
490	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
491	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
492	C₂×C₄	#41×D₄₇	1	4	yes	—
493	C₂×C₄	#13094069	1	4	yes	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	8	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	8	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	8	no	—
500	C₂²	—	4	8	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	8	no	—
504	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
505	C₂²	C₂×#41×D₄₇	1	2	yes	—
506	C₂²	C₂×#13094069	1	2	yes	—
507	C₂²	#15689959	1	1	yes	characteristic
508	C₂²	#15689959	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	8	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	94	8	no	—
515	C₄	—	188	4	no	—
516	C₄	—	188	4	no	—
517	C₄	—	188	4	no	—
518	C₄	#41×Dic₄₇	1	4	yes	—
519	C₄	#15689598	1	4	yes	—
520	C₂	—	4	2	no	—
521	C₂	—	4	8	no	—
522	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
523	C₂	C₂×#15689598	1	1	yes	characteristic
524	C₂	#20256591	1	1	yes	characteristic
525	C₂	#20257344	1	2	yes	—
526	C₂	#20257386	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	#34232
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. #20246453	C₂	semidirect
2. #20246448	C₂	semidirect
3. #20246430	C₂	semidirect
4. #20246328	C₂	semidirect
5. #20246229	C₂	semidirect
6. #20246218	C₂	semidirect
7. #20246155	C₂	semidirect
8. #20246031	C₂	semidirect
9. #124×Dic₄₇	C₂	semidirect
10. #20245786	C₂	semidirect
11. #20245749	C₂	semidirect
12. C₄×#13093983	C₂	semidirect
51. C₄₇×#532	C₄	semidirect
93. C₂×#41×C₄₇	C₂×C₄	semidirect
103. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
105. #124×C₄₇	C₂×C₄	semidirect
106. #121×C₄₇	C₂×C₄	semidirect
107. #121×C₄₇	C₂×C₄	semidirect
108. C₄×D₄×C₄₇	C₂×C₄	semidirect
109. C₄×D₄×C₄₇	C₂×C₄	semidirect
114. C₂×C₄²×C₄₇	C₂×C₄	semidirect
174. C₄⋊Dic₄₇	#41	semidirect
278. #532	Dic₄₇	semidirect
323. C₄₇	#34232	semidirect
325. C₂×#41	C₂×Dic₄₇	semidirect
336. C₄⋊Q₈	C₂×Dic₄₇	semidirect
338. #124	C₂×Dic₄₇	semidirect
339. #121	C₂×Dic₄₇	semidirect
340. #121	C₂×Dic₄₇	semidirect
344. C₄×D₄	C₂×Dic₄₇	semidirect
345. C₄×D₄	C₂×Dic₄₇	semidirect
368. 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
#20246453	2
#20246448	2
#20246430	2
#20246328	2
#20246229	2
#20246218	2
#20246155	2
#20246031	2
#124×Dic₄₇	2
#20245786	2
#20245749	2
C₄×#13093983	2
C₂×C₄₇×#532	2
#34232	47