Subgroups — #26377042

Order 12032.

2750 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246478	C₂	1	2	yes	maximal, complemented
2	#20246453	C₂	1	2	yes	maximal, complemented
3	#20246408	C₂	1	4	yes	maximal, complemented
4	#20246361	C₂	1	2	yes	maximal, complemented
5	#20246298	C₂	1	2	yes	maximal, complemented
6	#20246218	C₂	1	4	yes	maximal, complemented
7	#20246203	C₂	1	4	yes	maximal, complemented
8	#20246031	C₂	1	2	yes	maximal, complemented
9	#121×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	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
14	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
15	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
16	C₂×D₄×Dic₄₇	C₂²	1	8	yes	—
17	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
18	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
19	#15689030	C₂²	1	8	yes	—
20	#15689026	C₂²	1	4	yes	—
21	#15689026	C₂²	1	4	yes	—
22	#15689022	C₂²	1	4	yes	—
23	#15689022	C₂²	1	4	yes	—
24	#15689016	C₂²	1	8	yes	—
25	#15689016	C₂²	1	8	yes	—
26	#15689003	C₂²	1	8	yes	—
27	#15689003	C₂²	1	8	yes	—
28	#15688998	C₂²	1	8	yes	—
29	#15688991	C₂²	1	2	yes	—
30	#15688989	C₂²	1	1	yes	characteristic
31	#15688989	C₂²	1	1	yes	characteristic
32	#15688986	C₂²	1	4	yes	—
33	#15688986	C₂²	1	2	yes	—
34	#15688983	C₂²	1	4	yes	—
35	#15688983	C₂²	1	2	yes	—
36	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
37	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
38	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
40	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
41	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
42	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
43	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
44	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	—
45	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
46	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
47	#15688969	C₂²	1	2	yes	—
48	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
49	C₂×C₄₇⋊#95	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	4	yes	—
61	C₂³×Dic₄₇	C₂³	1	8	yes	—
62	D₄×Dic₄₇	—	2	16	no	—
63	D₄×Dic₄₇	—	4	8	no	—
64	D₄×Dic₄₇	—	4	16	no	—
65	C₂×C₄⋊Dic₄₇	—	2	8	no	—
66	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
67	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
68	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
70	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
71	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
72	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
73	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
74	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
75	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
76	C₂×C₄×Dic₄₇	—	4	4	no	—
77	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
78	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
79	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
80	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
81	C₂×C₄×Dic₄₇	C₂³	1	2	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	4	yes	—
87	C₄₇⋊#95	C₂³	1	2	yes	—
88	C₄₇⋊#95	C₂³	1	4	yes	—
89	C₄₇⋊#95	C₂³	1	2	yes	—
90	C₄₇⋊#95	C₂³	1	2	yes	—
91	C₄₇⋊#95	C₂³	1	4	yes	—
92	C₄₇⋊#95	C₂³	1	8	yes	—
93	C₂×#41×C₄₇	—	4	8	no	—
94	C₂×#41×C₄₇	C₂×C₄	1	16	yes	complemented
95	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
96	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
97	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
98	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
99	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
100	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
104	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
105	#127×C₄₇	C₂×C₄	1	8	yes	complemented
106	#124×C₄₇	C₂×C₄	1	16	yes	complemented
107	#121×C₄₇	C₂×C₄	1	16	yes	complemented
108	#121×C₄₇	C₂×C₄	1	16	yes	complemented
109	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
110	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
115	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
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	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
120	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
121	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
122	#41×C₄₇	—	4	32	no	—
123	C₂×Q₈×C₄₇	—	4	4	no	—
124	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₄₇	—	2	16	no	—
126	C₂×D₄×C₄₇	—	2	8	no	—
127	C₂×D₄×C₄₇	—	2	4	no	—
128	C₂×D₄×C₄₇	—	2	4	no	—
129	C₂×D₄×C₄₇	—	4	4	no	—
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	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
134	C₂²×C₄×C₄₇	—	2	4	no	—
135	C₂²×C₄×C₄₇	—	2	4	no	—
136	C₂²×C₄×C₄₇	—	2	2	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	4	8	no	—
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	4	yes	—
142	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
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	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₂²×Dic₄₇	—	2	8	no	—
151	C₂²×Dic₄₇	—	2	8	no	—
152	C₂²×Dic₄₇	—	2	16	no	—
153	C₂²×Dic₄₇	—	4	4	no	—
154	C₂²×Dic₄₇	—	4	8	no	—
155	C₂²×Dic₄₇	—	4	8	no	—
156	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
157	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
158	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
159	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
160	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
161	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
162	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
163	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
164	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
165	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
166	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
167	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
168	C₂²⋊Dic₄₇	—	2	8	no	—
169	C₂²⋊Dic₄₇	—	2	16	no	—
170	C₂²⋊Dic₄₇	—	4	8	no	—
171	C₂²⋊Dic₄₇	—	4	8	no	—
172	C₄⋊Dic₄₇	—	2	4	no	—
173	C₄⋊Dic₄₇	—	2	4	no	—
174	C₄⋊Dic₄₇	—	2	4	no	—
175	C₄⋊Dic₄₇	—	2	8	no	—
176	C₄⋊Dic₄₇	—	4	8	no	—
177	C₄⋊Dic₄₇	#41	1	8	yes	complemented
178	C₄×Dic₄₇	—	2	8	no	—
179	C₄×Dic₄₇	—	2	8	no	—
180	C₄×Dic₄₇	—	4	2	no	—
181	C₄×Dic₄₇	—	4	2	no	—
182	C₄×Dic₄₇	—	4	8	no	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	2	1	no	—
185	C₂³×C₄₇	—	2	1	no	—
186	C₂³×C₄₇	—	2	8	no	—
187	C₂³×C₄₇	—	2	4	no	—
188	C₂³×C₄₇	—	2	8	no	—
189	C₂³×C₄₇	—	2	4	no	—
190	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
191	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
192	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
193	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
194	Q₈×C₄₇	—	4	8	no	—
195	D₄×C₄₇	—	2	32	no	—
196	D₄×C₄₇	—	2	16	no	—
197	D₄×C₄₇	—	2	16	no	—
198	D₄×C₄₇	—	4	8	no	—
199	C₂×C₄×C₄₇	—	2	8	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	8	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	1	no	—
206	C₂×C₄×C₄₇	—	2	8	no	—
207	C₂×C₄×C₄₇	—	2	8	no	—
208	C₂×C₄×C₄₇	—	4	16	no	—
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	2	yes	—
213	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
214	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
216	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
217	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
218	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
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	—	2	4	no	—
229	C₂×Dic₄₇	—	2	4	no	—
230	C₂×Dic₄₇	—	4	16	no	—
231	C₂×Dic₄₇	—	8	16	no	—
232	C₂×Dic₄₇	C₂×#41	1	8	yes	—
233	#34236	—	47	1	no	maximal, Sylow
234	C₂²×C₄₇	—	2	2	no	—
235	C₂²×C₄₇	—	2	2	no	—
236	C₂²×C₄₇	—	2	4	no	—
237	C₂²×C₄₇	—	2	4	no	—
238	C₂²×C₄₇	—	2	8	no	—
239	C₂²×C₄₇	—	2	8	no	—
240	C₂²×C₄₇	—	2	8	no	—
241	C₂²×C₄₇	—	4	8	no	—
242	C₂²×C₄₇	—	4	8	no	—
243	C₂²×C₄₇	#518	1	4	yes	—
244	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
245	C₂²×C₄₇	C₂²×#41	1	2	yes	—
246	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
247	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
248	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
249	C₄×C₄₇	—	2	2	no	—
250	C₄×C₄₇	—	2	2	no	—
251	C₄×C₄₇	—	2	2	no	—
252	C₄×C₄₇	—	2	8	no	—
253	C₄×C₄₇	—	2	2	no	—
254	C₄×C₄₇	C₄×#41	1	4	yes	—
255	C₄×C₄₇	#520	1	4	yes	—
256	Dic₄₇	—	2	8	no	—
257	Dic₄₇	—	4	4	no	—
258	Dic₄₇	—	4	4	no	—
259	Dic₄₇	—	4	4	no	—
260	C₂×#532	D₄₇	1	1	yes	characteristic
261	#2369	—	47	2	no	—
262	#2366	—	47	2	no	—
263	#2361	—	47	4	no	—
264	#2357	—	47	2	no	—
265	#2349	—	47	2	no	—
266	#2339	—	47	4	no	—
267	#2337	—	47	4	no	—
268	#2319	—	47	2	no	—
269	C₄×#121	—	47	4	no	—
270	#2283	—	47	1	no	—
271	#2275	—	47	2	no	—
272	C₂×C₄×C₄⋊C₄	—	47	1	no	—
273	C₂×C₄₇	—	2	4	no	—
274	C₂×C₄₇	—	4	8	no	—
275	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
276	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
277	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
278	C₂×C₄₇	#3519	1	2	yes	—
279	C₂×C₄₇	#3522	1	2	yes	—
280	C₂²×#41	C₂×D₄₇	1	2	yes	—
281	#532	Dic₄₇	1	16	yes	complemented
282	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
283	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
284	C₂×#124	C₂×D₄₇	1	2	yes	—
285	C₂×#121	C₂×D₄₇	1	2	yes	—
286	C₂×#121	C₂×D₄₇	1	2	yes	—
287	C₂×C₄×D₄	—	47	4	no	—
288	C₂×C₄×D₄	—	47	8	no	—
289	C₂×C₄×D₄	—	47	4	no	—
290	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
291	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
292	C₂²×C₄⋊C₄	—	47	2	no	—
293	C₂²×C₄²	—	47	2	no	—
294	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
295	#391	—	47	8	no	—
296	#390	—	47	4	no	—
297	#390	—	47	4	no	—
298	#389	—	47	4	no	—
299	#389	—	47	4	no	—
300	#388	—	47	8	no	—
301	#388	—	47	8	no	—
302	#386	—	47	8	no	—
303	#386	—	47	8	no	—
304	#385	—	47	8	no	—
305	#383	—	47	2	no	—
306	#382	—	47	1	no	—
307	#382	—	47	1	no	—
308	#381	—	47	4	no	—
309	#381	—	47	2	no	—
310	#380	—	47	4	no	—
311	#380	—	47	2	no	—
312	C₄×C₄⋊C₄	—	47	4	no	—
313	C₄×C₄⋊C₄	—	47	4	no	—
314	C₄×C₄⋊C₄	—	47	1	no	—
315	C₄×C₄⋊C₄	—	47	2	no	—
316	C₄×C₄⋊C₄	—	47	2	no	—
317	C₄×C₄⋊C₄	—	47	2	no	—
318	C₄×C₄⋊C₄	—	47	2	no	—
319	C₄×C₄⋊C₄	—	47	1	no	—
320	C₄×C₂²⋊C₄	—	47	4	no	—
321	C₄×C₂²⋊C₄	—	47	2	no	—
322	C₄×C₂²⋊C₄	—	47	8	no	—
323	#376	—	47	2	no	—
324	C₂×#95	—	47	2	no	—
325	C₂×#95	—	47	4	no	—
326	C₄₇	#34236	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	4	8	no	—
328	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
329	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
330	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
331	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
332	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
333	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
334	C₂³×C₄	—	47	4	no	—
335	C₂³×C₄	—	47	8	no	—
336	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
337	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
338	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
339	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
340	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
341	#127	C₂×Dic₄₇	1	8	yes	complemented
342	#124	C₂×Dic₄₇	1	16	yes	complemented
343	#121	C₂×Dic₄₇	1	16	yes	complemented
344	#121	C₂×Dic₄₇	1	16	yes	complemented
345	C₄×D₄	—	94	16	no	—
346	C₄×D₄	—	188	8	no	—
347	C₄×D₄	—	188	16	no	—
348	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
349	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
350	C₂×C₄⋊C₄	—	47	2	no	—
351	C₂×C₄⋊C₄	—	47	4	no	—
352	C₂×C₄⋊C₄	—	47	2	no	—
353	C₂×C₄⋊C₄	—	47	2	no	—
354	C₂×C₄⋊C₄	—	47	2	no	—
355	C₂×C₄⋊C₄	—	47	8	no	—
356	C₂×C₄⋊C₄	—	94	8	no	—
357	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
358	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
359	C₂×C₂²⋊C₄	—	47	4	no	—
360	C₂×C₂²⋊C₄	—	47	8	no	—
361	C₂×C₂²⋊C₄	—	47	8	no	—
362	C₂×C₂²⋊C₄	—	47	8	no	—
363	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
364	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
365	C₂×C₄²	—	47	4	no	—
366	C₂×C₄²	—	47	4	no	—
367	C₂×C₄²	—	47	8	no	—
368	C₂×C₄²	—	47	2	no	—
369	C₂×C₄²	—	47	2	no	—
370	C₂×C₄²	—	188	4	no	—
371	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
372	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
373	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
374	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
375	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
376	#95	—	47	2	no	—
377	#95	—	47	2	no	—
378	#95	—	47	8	no	—
379	#95	—	47	2	no	—
380	#95	—	47	4	no	—
381	#95	—	47	4	no	—
382	#95	—	47	2	no	—
383	#95	—	47	2	no	—
384	#95	—	47	2	no	—
385	#95	—	47	4	no	—
386	#95	—	47	8	no	—
387	C₂⁴	C₂³×D₄₇	1	4	yes	—
388	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
389	#41	—	4	32	no	—
390	C₂×Q₈	—	4	4	no	—
391	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
392	C₂×D₄	—	2	16	no	—
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
398	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
399	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
400	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	4	8	no	—
406	C₂²×C₄	—	47	4	no	—
407	C₂²×C₄	—	47	4	no	—
408	C₂²×C₄	—	47	4	no	—
409	C₂²×C₄	—	47	4	no	—
410	C₂²×C₄	—	94	16	no	—
411	C₂²×C₄	—	94	8	no	—
412	C₂²×C₄	—	94	8	no	—
413	C₂²×C₄	—	188	8	no	—
414	C₂²×C₄	—	188	8	no	—
415	C₂²×C₄	—	188	4	no	—
416	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
417	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
418	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
419	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
420	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
421	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
422	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
423	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
424	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
425	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
427	C₄⋊C₄	—	47	8	no	—
428	C₄⋊C₄	—	94	8	no	—
429	C₄⋊C₄	—	94	4	no	—
430	C₄⋊C₄	—	94	4	no	—
431	C₄⋊C₄	—	94	4	no	—
432	C₄⋊C₄	—	188	8	no	—
433	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
434	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
435	C₂²⋊C₄	—	94	16	no	—
436	C₂²⋊C₄	—	94	8	no	—
437	C₂²⋊C₄	—	188	8	no	—
438	C₂²⋊C₄	—	188	8	no	—
439	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
440	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
441	C₄²	—	94	8	no	—
442	C₄²	—	94	8	no	—
443	C₄²	—	188	2	no	—
444	C₄²	—	188	2	no	—
445	C₄²	—	188	8	no	—
446	C₄²	C₂²×Dic₄₇	1	4	yes	—
447	C₄²	C₂²×Dic₄₇	1	4	yes	—
448	C₄²	C₂²×Dic₄₇	1	4	yes	—
449	C₄²	C₂²×Dic₄₇	1	4	yes	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	8	no	—
454	C₂³	—	2	8	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	4	no	—
457	C₂³	C₂³×Dic₄₇	1	8	yes	—
458	C₂³	C₂³×Dic₄₇	1	2	yes	—
459	C₂³	#13094069	1	4	yes	—
460	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
461	Q₈	—	4	8	no	—
462	D₄	—	2	32	no	—
463	D₄	—	2	16	no	—
464	D₄	—	2	16	no	—
465	D₄	—	4	8	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	4	16	no	—
476	C₂×C₄	—	47	8	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	—	94	4	no	—
485	C₂×C₄	—	94	4	no	—
486	C₂×C₄	—	94	4	no	—
487	C₂×C₄	—	94	4	no	—
488	C₂×C₄	—	376	16	no	—
489	C₂×C₄	—	188	16	no	—
490	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
491	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
492	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
493	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
494	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
495	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
496	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
497	C₂×C₄	#41×D₄₇	1	4	yes	—
498	C₂×C₄	#13094070	1	2	yes	—
499	C₂×C₄	#13094071	1	2	yes	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	8	no	—
505	C₂²	—	2	8	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	4	8	no	—
508	C₂²	—	4	8	no	—
509	C₂²	#15689598	1	4	yes	—
510	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
511	C₂²	C₂×#41×D₄₇	1	2	yes	—
512	C₂²	C₂×#13094069	1	2	yes	—
513	C₂²	C₂×#13094070	1	1	yes	characteristic
514	C₂²	C₂×#13094071	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	8	no	—
519	C₄	—	2	2	no	—
520	C₄	—	94	8	no	—
521	C₄	—	188	4	no	—
522	C₄	—	188	4	no	—
523	C₄	—	188	4	no	—
524	C₄	#41×Dic₄₇	1	4	yes	—
525	C₄	#15689606	1	4	yes	—
526	C₂	—	2	4	no	—
527	C₂	—	4	8	no	—
528	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
529	C₂	C₂×#15689598	1	1	yes	characteristic
530	C₂	C₂×#15689606	1	1	yes	characteristic
531	C₂	#20257415	1	2	yes	—
532	C₂	#20257465	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	#34236
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. #20246478	C₂	semidirect
2. #20246453	C₂	semidirect
3. #20246408	C₂	semidirect
4. #20246361	C₂	semidirect
5. #20246298	C₂	semidirect
6. #20246218	C₂	semidirect
7. #20246203	C₂	semidirect
8. #20246031	C₂	semidirect
9. #121×Dic₄₇	C₂	semidirect
10. #20245786	C₂	semidirect
11. #20245749	C₂	semidirect
12. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
51. C₄₇×#532	C₄	semidirect
94. C₂×#41×C₄₇	C₂×C₄	semidirect
104. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
105. #127×C₄₇	C₂×C₄	semidirect
106. #124×C₄₇	C₂×C₄	semidirect
107. #121×C₄₇	C₂×C₄	semidirect
108. #121×C₄₇	C₂×C₄	semidirect
109. C₄×D₄×C₄₇	C₂×C₄	semidirect
110. C₄×D₄×C₄₇	C₂×C₄	semidirect
115. C₂×C₄²×C₄₇	C₂×C₄	semidirect
177. C₄⋊Dic₄₇	#41	semidirect
281. #532	Dic₄₇	semidirect
326. C₄₇	#34236	semidirect
328. C₂×#41	C₂×Dic₄₇	semidirect
340. C₄⋊Q₈	C₂×Dic₄₇	semidirect
341. #127	C₂×Dic₄₇	semidirect
342. #124	C₂×Dic₄₇	semidirect
343. #121	C₂×Dic₄₇	semidirect
344. #121	C₂×Dic₄₇	semidirect
348. C₄×D₄	C₂×Dic₄₇	semidirect
349. C₄×D₄	C₂×Dic₄₇	semidirect
371. 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
#20246478	2
#20246453	2
#20246408	2
#20246361	2
#20246298	2
#20246218	2
#20246203	2
#20246031	2
#121×Dic₄₇	2
#20245786	2
#20245749	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₄₇×#532	2
#34236	47