Subgroups — #26232286

Order 12032.

1312 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689245	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252272	C₂	1	1	yes	maximal, characteristic, complemented
3	#20251921	C₂	1	2	yes	maximal, complemented
4	#20244304	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244260	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243905	C₂	1	2	yes	maximal, complemented
7	#20243759	C₂	1	2	yes	maximal, complemented
8	#20243447	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243347	C₂	1	2	yes	maximal, complemented
10	#20243230	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#578	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	2	yes	—
13	#15689606	C₂²	1	2	yes	—
14	#15689245	—	2	4	no	—
15	#15689235	—	2	1	no	—
16	#15689230	—	2	1	no	—
17	SD₁₆×Dic₄₇	—	2	2	no	—
18	C₂×#13093960	C₂²	1	1	yes	characteristic
19	C₂×#13093956	C₂²	1	1	yes	characteristic
20	C₂×#13093951	C₂²	1	1	yes	characteristic
21	C₂×#13093951	C₂²	1	2	yes	—
22	#15689132	—	2	2	no	—
23	#15689132	C₂²	1	2	yes	—
24	#15689124	—	2	2	no	—
25	#15689124	C₂²	1	2	yes	—
26	#15689124	C₂²	1	2	yes	—
27	#15689119	—	2	2	no	—
28	#15689119	C₂²	1	1	yes	characteristic
29	C₂×#13093948	—	2	2	no	—
30	C₂×#13093948	C₂²	1	2	yes	—
31	C₂×#13093943	C₂²	1	2	yes	—
32	#15689078	C₂²	1	1	yes	characteristic
33	C₂×#13093934	C₂²	1	1	yes	characteristic
34	#15689030	C₂²	1	2	yes	—
35	#15688891	C₂²	1	2	yes	—
36	#15688887	C₂²	1	1	yes	characteristic
37	#15688884	C₂²	1	1	yes	characteristic
38	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#578	—	2	4	no	—
40	C₄₇×#578	C₄	1	8	yes	complemented
41	C₂×#137×C₄₇	—	2	2	no	—
42	C₂×#137×C₄₇	C₂²	1	2	yes	—
43	C₂×#135×C₄₇	—	2	1	no	—
44	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×Q₁₆×C₄₇	—	2	1	no	—
46	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
48	#13094031	—	2	4	no	—
49	#13094031	—	4	2	no	—
50	C₂×#10625329	—	2	2	no	—
51	C₂×#10625329	C₂³	1	1	yes	characteristic
52	C₂×#10625329	C₂³	1	2	yes	—
53	C₂²×C₄₇⋊C₈	—	2	2	no	—
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	Q₈×Dic₄₇	—	2	2	no	—
56	D₄×Dic₄₇	—	2	2	no	—
57	D₄×Dic₄₇	—	4	2	no	—
58	#13093983	—	2	2	no	—
59	#13093983	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊Dic₄₇	—	2	2	no	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	#13093960	—	2	2	no	—
64	#13093956	—	2	1	no	—
65	#13093956	—	2	1	no	—
66	#13093951	—	2	4	no	—
67	#13093951	—	2	2	no	—
68	#13093948	—	2	2	no	—
69	#13093948	—	2	2	no	—
70	#13093948	—	2	2	no	—
71	#13093948	—	2	2	no	—
72	#13093948	—	2	2	no	—
73	#13093948	—	2	2	no	—
74	#13093948	D₄	1	2	yes	—
75	#13093945	—	2	2	no	—
76	#13093945	—	2	2	no	—
77	#13093945	D₄	1	2	yes	—
78	#13093943	—	4	2	no	—
79	#13093934	—	2	1	no	—
80	#13093934	—	2	2	no	—
81	C₈×Dic₄₇	—	2	1	no	—
82	C₄₇⋊#95	—	4	2	no	—
83	2₋¹⁺⁴×C₄₇	—	2	4	no	—
84	2₋¹⁺⁴×C₄₇	—	2	4	no	—
85	2₋¹⁺⁴×C₄₇	—	4	2	no	—
86	2₋¹⁺⁴×C₄₇	C₂×C₄	1	8	yes	complemented
87	C₂×#41×C₄₇	—	2	2	no	—
88	C₂×#41×C₄₇	—	2	2	no	—
89	C₂×#41×C₄₇	—	4	2	no	—
90	C₂×#41×C₄₇	C₂³	1	2	yes	—
91	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
92	C₂²×Q₈×C₄₇	—	2	2	no	—
93	C₂²×Q₈×C₄₇	—	2	2	no	—
94	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
95	#137×C₄₇	—	2	4	no	—
96	#137×C₄₇	—	2	16	no	—
97	#137×C₄₇	C₂×C₄	1	8	yes	complemented
98	#135×C₄₇	—	2	8	no	—
99	#135×C₄₇	C₂×C₄	1	4	yes	—
100	#135×C₄₇	D₄	1	4	yes	—
101	C₂×Q₁₆×C₄₇	—	2	2	no	—
102	C₂×Q₁₆×C₄₇	—	2	8	no	—
103	C₂×Q₁₆×C₄₇	—	2	1	no	—
104	C₂×Q₁₆×C₄₇	—	2	1	no	—
105	C₂×Q₁₆×C₄₇	—	2	2	no	—
106	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
107	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic
108	C₂×SD₁₆×C₄₇	—	2	2	no	—
109	C₂×SD₁₆×C₄₇	D₄	1	2	yes	—
110	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic
111	#131×C₄₇	—	2	2	no	—
112	#131×C₄₇	C₂×C₄	1	4	yes	complemented
113	C₂×M₁₆×C₄₇	—	2	1	no	—
114	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	—	2	1	no	—
116	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
117	#41×C₄₇	—	2	1	no	—
118	#41×C₄₇	—	2	2	no	—
119	#41×C₄₇	—	2	1	no	—
120	#41×C₄₇	—	2	2	no	—
121	#41×C₄₇	—	2	8	no	—
122	#41×C₄₇	—	2	8	no	—
123	#41×C₄₇	—	4	8	no	—
124	#41×C₄₇	—	4	4	no	—
125	#41×C₄₇	—	4	4	no	—
126	#41×C₄₇	—	4	8	no	—
127	#41×C₄₇	C₂²×C₄	1	4	yes	—
128	#41×C₄₇	C₂²×C₄	1	2	yes	—
129	#41×C₄₇	C₂×D₄	1	4	yes	—
130	#41×C₄₇	#41	1	2	yes	—
131	C₂×Q₈×C₄₇	—	2	2	no	—
132	C₂×Q₈×C₄₇	—	2	8	no	—
133	C₂×Q₈×C₄₇	—	2	8	no	—
134	C₂×Q₈×C₄₇	—	2	2	no	—
135	C₂×Q₈×C₄₇	—	2	2	no	—
136	C₂×Q₈×C₄₇	—	2	2	no	—
137	C₂×Q₈×C₄₇	—	2	2	no	—
138	C₂×Q₈×C₄₇	—	4	2	no	—
139	C₂×Q₈×C₄₇	—	4	4	no	—
140	C₂×Q₈×C₄₇	—	4	4	no	—
141	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
142	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
143	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₄₇	—	2	1	no	—
145	C₂×D₄×C₄₇	—	2	2	no	—
146	C₂×D₄×C₄₇	—	4	2	no	—
147	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
148	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	2	no	—
151	C₂²×C₄×C₄₇	—	2	2	no	—
152	C₂²×C₄×C₄₇	—	4	2	no	—
153	C₂²×C₄×C₄₇	—	4	2	no	—
154	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
155	C₂²×Dic₄₇	—	2	1	no	—
156	C₂²×Dic₄₇	—	2	2	no	—
157	C₂²×Dic₄₇	—	4	2	no	—
158	Q₁₆×C₄₇	—	2	8	no	—
159	Q₁₆×C₄₇	—	2	4	no	—
160	Q₁₆×C₄₇	—	2	4	no	—
161	Q₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
162	SD₁₆×C₄₇	—	2	8	no	—
163	SD₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
164	D₈×C₄₇	C₂²⋊C₄	1	4	yes	—
165	M₁₆×C₄₇	—	2	1	no	—
166	M₁₆×C₄₇	—	2	4	no	—
167	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₄₇	—	2	1	no	—
169	C₂×C₈×C₄₇	—	2	4	no	—
170	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
171	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
174	C₂²⋊Dic₄₇	—	2	1	no	—
175	C₂²⋊Dic₄₇	—	4	2	no	—
176	C₄⋊Dic₄₇	—	2	2	no	—
177	C₄⋊Dic₄₇	—	2	2	no	—
178	C₄⋊Dic₄₇	—	4	2	no	—
179	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
180	C₄×Dic₄₇	—	2	1	no	—
181	C₄×Dic₄₇	—	2	1	no	—
182	C₄×Dic₄₇	—	2	1	no	—
183	C₄×Dic₄₇	—	4	2	no	—
184	#10625329	—	2	2	no	—
185	#10625329	—	2	1	no	—
186	#10625329	—	2	1	no	—
187	#10625329	—	2	2	no	—
188	#10625329	—	4	4	no	—
189	C₂×C₄₇⋊C₈	—	2	1	no	—
190	C₂×C₄₇⋊C₈	—	2	1	no	—
191	C₂×C₄₇⋊C₈	—	2	1	no	—
192	C₂×C₄₇⋊C₈	—	2	2	no	—
193	C₂×C₄₇⋊C₈	—	4	4	no	—
194	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
195	C₂³×C₄₇	—	2	2	no	—
196	C₂³×C₄₇	—	2	1	no	—
197	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
198	Q₈×C₄₇	—	2	1	no	—
199	Q₈×C₄₇	—	2	2	no	—
200	Q₈×C₄₇	—	2	4	no	—
201	Q₈×C₄₇	—	2	4	no	—
202	Q₈×C₄₇	—	4	8	no	—
203	Q₈×C₄₇	—	4	2	no	—
204	Q₈×C₄₇	—	4	2	no	—
205	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
206	Q₈×C₄₇	C₄×D₄	1	2	yes	—
207	D₄×C₄₇	—	2	2	no	—
208	D₄×C₄₇	—	2	4	no	—
209	D₄×C₄₇	—	2	2	no	—
210	D₄×C₄₇	—	2	4	no	—
211	D₄×C₄₇	—	2	1	no	—
212	D₄×C₄₇	—	2	2	no	—
213	D₄×C₄₇	—	4	8	no	—
214	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
215	D₄×C₄₇	C₄×D₄	1	2	yes	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	1	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	4	no	—
220	C₂×C₄×C₄₇	—	2	4	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	4	no	—
223	C₂×C₄×C₄₇	—	4	8	no	—
224	C₂×C₄×C₄₇	—	4	8	no	—
225	C₂×C₄×C₄₇	—	4	2	no	—
226	C₂×C₄×C₄₇	—	4	2	no	—
227	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×Dic₄₇	—	2	2	no	—
234	C₂×Dic₄₇	—	4	2	no	—
235	C₂×Dic₄₇	—	4	2	no	—
236	C₂×Dic₄₇	—	4	1	no	—
237	C₂×Dic₄₇	—	8	2	no	—
238	C₂×Dic₄₇	—	16	2	no	—
239	C₈×C₄₇	—	2	2	no	—
240	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
241	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
242	C₄₇⋊C₈	—	2	2	no	—
243	C₄₇⋊C₈	—	4	2	no	—
244	C₄₇⋊C₈	—	4	1	no	—
245	#22465	—	47	1	no	maximal, Sylow
246	C₂²×C₄₇	—	2	2	no	—
247	C₂²×C₄₇	—	2	2	no	—
248	C₂²×C₄₇	—	2	4	no	—
249	C₂²×C₄₇	—	4	2	no	—
250	C₂²×C₄₇	—	4	2	no	—
251	C₂²×C₄₇	—	4	2	no	—
252	C₂²×C₄₇	#518	1	1	yes	characteristic
253	C₂²×C₄₇	D₄²	1	1	yes	characteristic
254	C₂²×C₄₇	#546	1	1	yes	characteristic
255	C₄×C₄₇	—	2	2	no	—
256	C₄×C₄₇	—	2	4	no	—
257	C₄×C₄₇	—	4	4	no	—
258	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
259	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
260	C₄×C₄₇	D₄²	1	1	yes	characteristic
261	C₄×C₄₇	#546	1	1	yes	characteristic
262	Dic₄₇	—	4	2	no	—
263	Dic₄₇	—	8	1	no	—
264	Dic₄₇	—	8	2	no	—
265	C₂×#578	D₄₇	1	1	yes	characteristic
266	C₂×#444	—	47	1	no	—
267	#2952	—	47	1	no	—
268	#2898	—	47	2	no	—
269	#1979	—	47	1	no	—
270	#1971	—	47	1	no	—
271	#1908	—	47	2	no	—
272	#1882	—	47	2	no	—
273	#1815	—	47	1	no	—
274	#1793	—	47	2	no	—
275	#1765	—	47	1	no	—
276	C₂×C₄₇	—	2	1	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	4	2	no	—
279	C₂×C₄₇	—	4	4	no	—
280	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₄₇	#3289	1	2	yes	—
282	C₂×2₋¹⁺⁴	C₂×D₄₇	1	2	yes	—
283	#578	—	2	4	no	—
284	#578	Dic₄₇	1	8	yes	complemented
285	C₂×#137	—	2	2	no	—
286	C₂×#137	C₂×D₄₇	1	2	yes	—
287	C₂×#135	—	2	1	no	—
288	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
289	C₂²×Q₁₆	—	2	1	no	—
290	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
291	C₂×#131	—	47	2	no	—
292	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
293	#520	—	47	2	no	—
294	#444	—	94	4	no	—
295	#442	—	94	1	no	—
296	#441	—	94	1	no	—
297	C₄×SD₁₆	—	94	2	no	—
298	C₂×#108	—	47	1	no	—
299	C₂×#106	—	47	1	no	—
300	C₂×#104	—	47	1	no	—
301	C₂×#104	—	47	2	no	—
302	#419	—	47	2	no	—
303	#419	—	94	2	no	—
304	#417	—	47	2	no	—
305	#417	—	47	2	no	—
306	#417	—	94	2	no	—
307	#416	—	47	1	no	—
308	#416	—	94	2	no	—
309	C₂×#103	—	47	2	no	—
310	C₂×#103	—	94	2	no	—
311	C₂×#101	—	47	2	no	—
312	#405	—	47	1	no	—
313	C₂×#97	—	47	1	no	—
314	#391	—	47	2	no	—
315	#343	—	47	2	no	—
316	#341	—	47	1	no	—
317	#339	—	47	1	no	—
318	C₄₇	#22465	1	1	yes	characteristic, complemented, Sylow
319	2₋¹⁺⁴	—	2	4	no	—
320	2₋¹⁺⁴	—	2	4	no	—
321	2₋¹⁺⁴	—	4	2	no	—
322	2₋¹⁺⁴	C₂×Dic₄₇	1	8	yes	complemented
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	4	2	no	—
326	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
327	C₂×#41	C₂²×D₄₇	1	2	yes	—
328	C₂²×Q₈	—	2	2	no	—
329	C₂²×Q₈	—	2	2	no	—
330	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
331	#137	—	2	4	no	—
332	#137	—	2	16	no	—
333	#137	C₂×Dic₄₇	1	8	yes	complemented
334	#135	—	2	8	no	—
335	#135	C₂×Dic₄₇	1	4	yes	—
336	#135	C₂²⋊D₄₇	1	4	yes	—
337	C₂×Q₁₆	—	2	2	no	—
338	C₂×Q₁₆	—	2	8	no	—
339	C₂×Q₁₆	—	2	1	no	—
340	C₂×Q₁₆	—	2	1	no	—
341	C₂×Q₁₆	—	2	2	no	—
342	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	complemented
343	C₂×Q₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
344	C₂×SD₁₆	—	2	2	no	—
345	C₂×SD₁₆	C₂²⋊D₄₇	1	2	yes	—
346	C₂×D₈	C₂²⋊D₄₇	1	1	yes	characteristic
347	#131	—	2	2	no	—
348	#131	—	94	4	no	—
349	#131	—	188	2	no	—
350	#131	C₂×Dic₄₇	1	4	yes	complemented
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	47	2	no	—
353	C₂×M₁₆	—	47	1	no	—
354	C₂×M₁₆	—	94	2	no	—
355	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	—	47	1	no	—
358	C₂²×C₈	—	94	2	no	—
359	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
360	C₄×Q₈	—	94	2	no	—
361	C₄×D₄	—	94	2	no	—
362	C₄×D₄	—	188	2	no	—
363	#117	—	47	1	no	—
364	#117	—	94	2	no	—
365	C₂×C₄⋊C₄	—	47	2	no	—
366	C₂×C₄⋊C₄	—	94	2	no	—
367	C₂×C₄²	—	47	1	no	—
368	#108	—	94	2	no	—
369	#106	—	94	1	no	—
370	#106	—	94	1	no	—
371	#104	—	94	2	no	—
372	#104	—	94	4	no	—
373	#103	—	47	2	no	—
374	#103	—	94	2	no	—
375	#103	—	94	2	no	—
376	#103	—	94	2	no	—
377	#103	—	94	2	no	—
378	#103	—	94	2	no	—
379	#103	—	94	2	no	—
380	#102	—	47	2	no	—
381	#102	—	94	2	no	—
382	#102	—	94	2	no	—
383	#101	—	188	2	no	—
384	#97	—	94	2	no	—
385	#97	—	94	1	no	—
386	C₄×C₈	—	94	1	no	—
387	#95	—	188	2	no	—
388	#41	—	2	1	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	1	no	—
392	#41	—	2	8	no	—
393	#41	—	2	8	no	—
394	#41	—	4	8	no	—
395	#41	—	4	4	no	—
396	#41	—	4	4	no	—
397	#41	—	4	8	no	—
398	#41	#10625352	1	2	yes	—
399	#41	C₂²×Dic₄₇	1	4	yes	—
400	#41	C₂²×Dic₄₇	1	2	yes	—
401	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	8	no	—
404	C₂×Q₈	—	2	8	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	4	2	no	—
410	C₂×Q₈	—	4	4	no	—
411	C₂×Q₈	—	4	4	no	—
412	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
413	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
414	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
419	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	94	2	no	—
426	C₂²×C₄	—	94	1	no	—
427	C₂²×C₄	—	188	2	no	—
428	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
429	Q₁₆	—	2	8	no	—
430	Q₁₆	—	2	4	no	—
431	Q₁₆	—	2	4	no	—
432	Q₁₆	C₂²⋊Dic₄₇	1	4	yes	—
433	SD₁₆	—	2	8	no	—
434	SD₁₆	C₂²⋊Dic₄₇	1	8	yes	—
435	D₈	C₂²⋊Dic₄₇	1	4	yes	—
436	M₁₆	—	2	1	no	—
437	M₁₆	—	2	4	no	—
438	M₁₆	—	94	2	no	—
439	M₁₆	—	94	1	no	—
440	M₁₆	—	94	1	no	—
441	M₁₆	—	94	2	no	—
442	M₁₆	—	188	4	no	—
443	M₁₆	C₂²×Dic₄₇	1	2	yes	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	4	no	—
446	C₂×C₈	—	47	2	no	—
447	C₂×C₈	—	94	1	no	—
448	C₂×C₈	—	94	1	no	—
449	C₂×C₈	—	94	2	no	—
450	C₂×C₈	—	94	1	no	—
451	C₂×C₈	—	188	4	no	—
452	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
453	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
454	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
455	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
456	C₄⋊C₄	—	47	2	no	—
457	C₄⋊C₄	—	94	2	no	—
458	C₄⋊C₄	—	94	2	no	—
459	C₄⋊C₄	—	188	2	no	—
460	C₂²⋊C₄	—	94	1	no	—
461	C₂²⋊C₄	—	188	2	no	—
462	C₄²	—	94	1	no	—
463	C₄²	—	94	1	no	—
464	C₄²	—	94	1	no	—
465	C₄²	—	188	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	1	no	—
468	C₂³	#13094069	1	1	yes	characteristic
469	Q₈	—	2	1	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	4	no	—
472	Q₈	—	2	4	no	—
473	Q₈	—	4	8	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	2	no	—
476	Q₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
477	Q₈	D₄×Dic₄₇	1	2	yes	—
478	D₄	—	2	2	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	2	no	—
484	D₄	—	4	8	no	—
485	D₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
486	D₄	D₄×Dic₄₇	1	2	yes	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	94	2	no	—
499	C₂×C₄	—	376	2	no	—
500	C₂×C₄	—	188	2	no	—
501	C₂×C₄	—	188	2	no	—
502	C₂×C₄	—	188	1	no	—
503	C₂×C₄	—	752	2	no	—
504	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
505	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
506	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
507	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
508	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
509	C₂×C₄	#13094069	1	1	yes	characteristic
510	C₈	—	2	2	no	—
511	C₈	—	94	2	no	—
512	C₈	—	188	2	no	—
513	C₈	—	188	1	no	—
514	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
515	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	#15689598	1	1	yes	characteristic
523	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
524	C₂²	#15689767	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	2	4	no	—
527	C₄	—	4	4	no	—
528	C₄	—	376	1	no	—
529	C₄	—	376	2	no	—
530	C₄	—	188	2	no	—
531	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
532	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
533	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
534	C₄	#15689767	1	1	yes	characteristic
535	C₂	—	2	1	no	—
536	C₂	—	2	1	no	—
537	C₂	—	4	2	no	—
538	C₂	—	4	4	no	—
539	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
540	C₂	#20255159	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#578	C₂
socle	C₂²×C₄₇	D₄²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#578	D₄₇
hypocenter	C₄₇	#22465
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#578

Complements

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

N	H ≅ G/N	type
1. C₂×#15689245	C₂	semidirect
2. #20252272	C₂	semidirect
3. #20251921	C₂	semidirect
4. #20244304	C₂	semidirect
5. #20244260	C₂	semidirect
6. #20243905	C₂	semidirect
7. #20243759	C₂	semidirect
8. #20243447	C₂	semidirect
9. #20243347	C₂	semidirect
10. #20243230	C₂	semidirect
40. C₄₇×#578	C₄	semidirect
86. 2₋¹⁺⁴×C₄₇	C₂×C₄	semidirect
97. #137×C₄₇	C₂×C₄	semidirect
106. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
112. #131×C₄₇	C₂×C₄	semidirect
284. #578	Dic₄₇	semidirect
318. C₄₇	#22465	semidirect
322. 2₋¹⁺⁴	C₂×Dic₄₇	semidirect
333. #137	C₂×Dic₄₇	semidirect
342. C₂×Q₁₆	C₂×Dic₄₇	semidirect
350. #131	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689245	2
#20252272	2
#20251921	2
#20244304	2
#20244260	2
#20243905	2
#20243759	2
#20243447	2
#20243347	2
#20243230	2
C₂×C₄₇×#578	2
#22465	47