Subgroups — #26232297

Order 12032.

1384 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689240	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252264	C₂	1	1	yes	maximal, characteristic, complemented
3	#20251914	C₂	1	2	yes	maximal, complemented
4	#20244299	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244255	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243898	C₂	1	2	yes	maximal, complemented
7	#20243766	C₂	1	2	yes	maximal, complemented
8	#20243452	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243342	C₂	1	2	yes	maximal, complemented
10	#20243223	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#576	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	2	yes	complemented
13	#15689606	C₂²	1	2	yes	complemented
14	#15689240	—	2	4	no	—
15	#15689224	—	2	2	no	—
16	Q₁₆×Dic₄₇	—	2	1	no	—
17	D₈×Dic₄₇	—	2	1	no	—
18	C₂×#13093960	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13093958	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13093951	C₂²	1	1	yes	characteristic
21	C₂×#13093951	C₂²	1	2	yes	complemented
22	#15689128	—	2	2	no	—
23	#15689128	C₂²	1	2	yes	complemented
24	#15689124	—	2	2	no	—
25	#15689124	C₂²	1	2	yes	—
26	#15689124	C₂²	1	2	yes	complemented
27	#15689119	—	2	2	no	—
28	#15689119	C₂²	1	1	yes	characteristic
29	C₂×#13093945	—	2	2	no	—
30	C₂×#13093945	C₂²	1	2	yes	complemented
31	C₂×#13093941	C₂²	1	2	yes	complemented
32	#15689078	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
34	#15689026	C₂²	1	2	yes	complemented
35	#15688891	C₂²	1	2	yes	complemented
36	#15688887	C₂²	1	1	yes	characteristic, complemented
37	#15688884	C₂²	1	1	yes	characteristic, complemented
38	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#576	—	2	4	no	—
40	C₄₇×#576	C₄	1	8	yes	complemented
41	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
42	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
43	C₂×#135×C₄₇	—	2	1	no	—
44	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×D₈×C₄₇	—	2	1	no	—
46	C₂²×D₈×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×C₂²⋊Dic₄₇	—	4	2	no	—
63	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
64	#13093960	—	2	2	no	—
65	#13093958	—	2	1	no	—
66	#13093958	—	2	1	no	—
67	#13093951	—	2	4	no	—
68	#13093951	—	2	2	no	—
69	#13093948	—	2	2	no	—
70	#13093948	—	2	2	no	—
71	#13093948	D₄	1	1	yes	characteristic
72	#13093948	D₄	1	1	yes	characteristic
73	#13093945	—	2	2	no	—
74	#13093945	—	2	2	no	—
75	#13093945	—	2	2	no	—
76	#13093945	—	2	2	no	—
77	#13093945	—	2	2	no	—
78	#13093945	—	2	2	no	—
79	#13093945	D₄	1	1	yes	characteristic
80	#13093945	D₄	1	1	yes	characteristic
81	#13093941	—	4	2	no	—
82	#13093934	—	2	1	no	—
83	C₈×Dic₄₇	—	2	1	no	—
84	C₈×Dic₄₇	—	2	2	no	—
85	H(5,𝔽₂)×C₄₇	—	2	4	no	—
86	H(5,𝔽₂)×C₄₇	—	2	4	no	—
87	H(5,𝔽₂)×C₄₇	—	4	2	no	—
88	H(5,𝔽₂)×C₄₇	C₂×C₄	1	8	yes	complemented
89	C₂×#41×C₄₇	—	2	2	no	—
90	C₂×#41×C₄₇	—	2	2	no	—
91	C₂×#41×C₄₇	C₂³	1	2	yes	—
92	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₄₇	—	2	2	no	—
94	C₂²×D₄×C₄₇	—	2	2	no	—
95	C₂²×D₄×C₄₇	—	4	2	no	—
96	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
97	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
98	AGL(1,ℤ/8)×C₄₇	—	2	16	no	—
99	AGL(1,ℤ/8)×C₄₇	C₂×C₄	1	8	yes	complemented
100	#135×C₄₇	—	2	8	no	—
101	#135×C₄₇	C₂×C₄	1	4	yes	—
102	#135×C₄₇	D₄	1	4	yes	—
103	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic
104	C₂×SD₁₆×C₄₇	—	2	2	no	—
105	C₂×SD₁₆×C₄₇	D₄	1	2	yes	—
106	C₂×D₈×C₄₇	—	2	2	no	—
107	C₂×D₈×C₄₇	—	2	8	no	—
108	C₂×D₈×C₄₇	—	2	1	no	—
109	C₂×D₈×C₄₇	—	2	1	no	—
110	C₂×D₈×C₄₇	—	2	2	no	—
111	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
112	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic
113	#131×C₄₇	—	2	2	no	—
114	#131×C₄₇	C₂×C₄	1	4	yes	complemented
115	C₂×M₁₆×C₄₇	—	2	1	no	—
116	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₄₇	—	2	1	no	—
118	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
119	C₂⁴×C₄₇	—	2	2	no	—
120	C₂⁴×C₄₇	—	4	2	no	—
121	#41×C₄₇	—	2	1	no	—
122	#41×C₄₇	—	2	2	no	—
123	#41×C₄₇	—	2	1	no	—
124	#41×C₄₇	—	2	2	no	—
125	#41×C₄₇	—	2	8	no	—
126	#41×C₄₇	—	2	8	no	—
127	#41×C₄₇	—	4	4	no	—
128	#41×C₄₇	—	4	4	no	—
129	#41×C₄₇	C₂²×C₄	1	4	yes	—
130	#41×C₄₇	C₂²×C₄	1	2	yes	—
131	#41×C₄₇	C₂×D₄	1	4	yes	—
132	#41×C₄₇	#41	1	2	yes	—
133	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₄₇	—	2	1	no	—
136	C₂×D₄×C₄₇	—	2	2	no	—
137	C₂×D₄×C₄₇	—	2	8	no	—
138	C₂×D₄×C₄₇	—	2	8	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	2	2	no	—
142	C₂×D₄×C₄₇	—	2	2	no	—
143	C₂×D₄×C₄₇	—	2	2	no	—
144	C₂×D₄×C₄₇	—	4	4	no	—
145	C₂×D₄×C₄₇	—	4	4	no	—
146	C₂×D₄×C₄₇	—	4	2	no	—
147	C₂×D₄×C₄₇	—	4	2	no	—
148	C₂×D₄×C₄₇	—	4	8	no	—
149	C₂×D₄×C₄₇	—	4	8	no	—
150	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
151	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	—	2	1	no	—
154	C₂²×C₄×C₄₇	—	2	2	no	—
155	C₂²×C₄×C₄₇	—	4	2	no	—
156	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
157	C₂²×Dic₄₇	—	2	1	no	—
158	C₂²×Dic₄₇	—	2	2	no	—
159	C₂²×Dic₄₇	—	4	2	no	—
160	Q₁₆×C₄₇	C₂²⋊C₄	1	4	yes	complemented
161	SD₁₆×C₄₇	—	2	8	no	—
162	SD₁₆×C₄₇	C₂²⋊C₄	1	8	yes	complemented
163	D₈×C₄₇	—	2	8	no	—
164	D₈×C₄₇	—	2	4	no	—
165	D₈×C₄₇	—	2	4	no	—
166	D₈×C₄₇	C₂²⋊C₄	1	4	yes	complemented
167	M₁₆×C₄₇	—	2	1	no	—
168	M₁₆×C₄₇	—	2	4	no	—
169	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₄₇	—	2	1	no	—
171	C₂×C₈×C₄₇	—	2	4	no	—
172	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
173	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
176	C₂²⋊Dic₄₇	—	2	1	no	—
177	C₂²⋊Dic₄₇	—	4	2	no	—
178	C₂²⋊Dic₄₇	—	8	4	no	—
179	C₄⋊Dic₄₇	—	2	2	no	—
180	C₄⋊Dic₄₇	—	2	2	no	—
181	C₄⋊Dic₄₇	—	4	2	no	—
182	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
183	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
184	C₄×Dic₄₇	—	2	1	no	—
185	C₄×Dic₄₇	—	2	1	no	—
186	C₄×Dic₄₇	—	2	1	no	—
187	C₄×Dic₄₇	—	4	2	no	—
188	#10625329	—	2	2	no	—
189	#10625329	—	2	1	no	—
190	#10625329	—	2	1	no	—
191	#10625329	—	2	2	no	—
192	#10625329	—	4	4	no	—
193	C₂×C₄₇⋊C₈	—	2	1	no	—
194	C₂×C₄₇⋊C₈	—	2	1	no	—
195	C₂×C₄₇⋊C₈	—	2	1	no	—
196	C₂×C₄₇⋊C₈	—	2	2	no	—
197	C₂×C₄₇⋊C₈	—	4	4	no	—
198	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
199	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
200	C₂³×C₄₇	—	2	2	no	—
201	C₂³×C₄₇	—	2	1	no	—
202	C₂³×C₄₇	—	2	4	no	—
203	C₂³×C₄₇	—	4	8	no	—
204	C₂³×C₄₇	—	4	2	no	—
205	C₂³×C₄₇	—	4	2	no	—
206	C₂³×C₄₇	—	8	2	no	—
207	C₂³×C₄₇	—	8	2	no	—
208	C₂³×C₄₇	—	16	2	no	—
209	C₂³×C₄₇	—	16	2	no	—
210	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
211	Q₈×C₄₇	—	2	1	no	—
212	Q₈×C₄₇	—	2	2	no	—
213	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
214	Q₈×C₄₇	C₄×D₄	1	2	yes	—
215	D₄×C₄₇	—	2	2	no	—
216	D₄×C₄₇	—	2	4	no	—
217	D₄×C₄₇	—	2	2	no	—
218	D₄×C₄₇	—	2	4	no	—
219	D₄×C₄₇	—	2	4	no	—
220	D₄×C₄₇	—	2	4	no	—
221	D₄×C₄₇	—	2	1	no	—
222	D₄×C₄₇	—	2	2	no	—
223	D₄×C₄₇	—	4	8	no	—
224	D₄×C₄₇	—	4	8	no	—
225	D₄×C₄₇	—	4	2	no	—
226	D₄×C₄₇	—	4	2	no	—
227	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
228	D₄×C₄₇	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	2	1	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	2	4	no	—
233	C₂×C₄×C₄₇	—	2	4	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	4	8	no	—
236	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×Dic₄₇	—	2	2	no	—
243	C₂×Dic₄₇	—	2	1	no	—
244	C₂×Dic₄₇	—	2	1	no	—
245	C₂×Dic₄₇	—	4	1	no	—
246	C₂×Dic₄₇	—	4	1	no	—
247	C₂×Dic₄₇	—	4	2	no	—
248	C₂×Dic₄₇	—	8	2	no	—
249	C₂×Dic₄₇	—	16	2	no	—
250	C₈×C₄₇	—	2	2	no	—
251	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
252	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
253	C₄₇⋊C₈	—	2	1	no	—
254	C₄₇⋊C₈	—	2	1	no	—
255	C₄₇⋊C₈	—	4	2	no	—
256	C₄₇⋊C₈	—	4	1	no	—
257	#22466	—	47	1	no	maximal, Sylow
258	C₂²×C₄₇	—	2	1	no	—
259	C₂²×C₄₇	—	2	1	no	—
260	C₂²×C₄₇	—	2	2	no	—
261	C₂²×C₄₇	—	2	4	no	—
262	C₂²×C₄₇	—	4	2	no	—
263	C₂²×C₄₇	—	4	1	no	—
264	C₂²×C₄₇	—	4	2	no	—
265	C₂²×C₄₇	—	4	1	no	—
266	C₂²×C₄₇	—	4	4	no	—
267	C₂²×C₄₇	—	8	4	no	—
268	C₂²×C₄₇	—	8	2	no	—
269	C₂²×C₄₇	—	8	2	no	—
270	C₂²×C₄₇	—	16	2	no	—
271	C₂²×C₄₇	—	16	8	no	—
272	C₂²×C₄₇	#518	1	1	yes	characteristic
273	C₂²×C₄₇	D₄²	1	1	yes	characteristic
274	C₂²×C₄₇	#546	1	1	yes	characteristic
275	C₄×C₄₇	—	2	2	no	—
276	C₄×C₄₇	—	2	4	no	—
277	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
278	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
279	C₄×C₄₇	D₄²	1	1	yes	characteristic
280	C₄×C₄₇	#546	1	1	yes	characteristic
281	Dic₄₇	—	4	2	no	—
282	Dic₄₇	—	4	1	no	—
283	Dic₄₇	—	4	1	no	—
284	Dic₄₇	—	8	2	no	—
285	C₂×#576	D₄₇	1	1	yes	characteristic
286	C₂×#443	—	47	1	no	—
287	#2951	—	47	1	no	—
288	#2897	—	47	2	no	—
289	#1978	—	47	1	no	—
290	#1970	—	47	1	no	—
291	#1907	—	47	2	no	—
292	#1883	—	47	2	no	—
293	#1816	—	47	1	no	—
294	#1792	—	47	2	no	—
295	#1764	—	47	1	no	—
296	C₂×C₄₇	—	2	1	no	—
297	C₂×C₄₇	—	2	1	no	—
298	C₂×C₄₇	—	4	4	no	—
299	C₂×C₄₇	—	4	2	no	—
300	C₂×C₄₇	—	8	4	no	—
301	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₄₇	#3290	1	1	yes	characteristic
303	C₂×C₄₇	#3292	1	1	yes	characteristic
304	C₂×H(5,𝔽₂)	C₂×D₄₇	1	2	yes	—
305	#576	—	2	4	no	—
306	#576	Dic₄₇	1	8	yes	complemented
307	C₂×AGL(1,ℤ/8)	—	2	2	no	—
308	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	2	yes	—
309	C₂×#135	—	2	1	no	—
310	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
311	C₂²×D₈	—	2	1	no	—
312	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
313	C₂×#131	—	47	2	no	—
314	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
315	#520	—	47	2	no	—
316	#443	—	94	4	no	—
317	#440	—	94	2	no	—
318	C₄×Q₁₆	—	94	1	no	—
319	C₄×D₈	—	94	1	no	—
320	C₂×#108	—	47	1	no	—
321	C₂×#107	—	47	1	no	—
322	C₂×#104	—	47	1	no	—
323	C₂×#104	—	47	2	no	—
324	#418	—	47	2	no	—
325	#418	—	94	2	no	—
326	#417	—	47	2	no	—
327	#417	—	47	2	no	—
328	#417	—	94	2	no	—
329	#416	—	47	1	no	—
330	#416	—	94	2	no	—
331	C₂×#102	—	47	2	no	—
332	C₂×#102	—	94	2	no	—
333	C₂×#100	—	47	2	no	—
334	#405	—	47	1	no	—
335	C₂×C₄×C₈	—	47	1	no	—
336	#390	—	47	2	no	—
337	#343	—	47	2	no	—
338	#341	—	47	1	no	—
339	#339	—	47	1	no	—
340	C₄₇	#22466	1	1	yes	characteristic, complemented, Sylow
341	H(5,𝔽₂)	—	2	4	no	—
342	H(5,𝔽₂)	—	2	4	no	—
343	H(5,𝔽₂)	—	4	2	no	—
344	H(5,𝔽₂)	C₂×Dic₄₇	1	8	yes	complemented
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
348	C₂×#41	C₂²×D₄₇	1	2	yes	—
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	—	4	2	no	—
352	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
353	AGL(1,ℤ/8)	—	2	4	no	—
354	AGL(1,ℤ/8)	—	2	16	no	—
355	AGL(1,ℤ/8)	C₂×Dic₄₇	1	8	yes	complemented
356	#135	—	2	8	no	—
357	#135	C₂×Dic₄₇	1	4	yes	—
358	#135	C₂²⋊D₄₇	1	4	yes	—
359	C₂×Q₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂×SD₁₆	—	2	2	no	—
361	C₂×SD₁₆	C₂²⋊D₄₇	1	2	yes	—
362	C₂×D₈	—	2	2	no	—
363	C₂×D₈	—	2	8	no	—
364	C₂×D₈	—	2	1	no	—
365	C₂×D₈	—	2	1	no	—
366	C₂×D₈	—	2	2	no	—
367	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
368	C₂×D₈	C₂²⋊D₄₇	1	1	yes	characteristic
369	#131	—	2	2	no	—
370	#131	—	94	4	no	—
371	#131	—	188	2	no	—
372	#131	C₂×Dic₄₇	1	4	yes	complemented
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	47	2	no	—
375	C₂×M₁₆	—	47	1	no	—
376	C₂×M₁₆	—	94	2	no	—
377	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	47	1	no	—
380	C₂²×C₈	—	94	2	no	—
381	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
382	C₄×Q₈	—	94	2	no	—
383	C₄×D₄	—	94	2	no	—
384	C₄×D₄	—	188	2	no	—
385	#117	—	47	1	no	—
386	#117	—	94	2	no	—
387	C₂×C₄⋊C₄	—	47	2	no	—
388	C₂×C₄⋊C₄	—	94	2	no	—
389	C₂×C₂²⋊C₄	—	188	2	no	—
390	C₂×C₄²	—	47	1	no	—
391	#108	—	94	2	no	—
392	#107	—	94	1	no	—
393	#107	—	94	1	no	—
394	#104	—	94	2	no	—
395	#104	—	94	4	no	—
396	#103	—	47	1	no	—
397	#103	—	47	1	no	—
398	#103	—	94	2	no	—
399	#103	—	94	2	no	—
400	#102	—	47	1	no	—
401	#102	—	47	1	no	—
402	#102	—	94	2	no	—
403	#102	—	94	2	no	—
404	#102	—	94	2	no	—
405	#102	—	94	2	no	—
406	#102	—	94	2	no	—
407	#102	—	94	2	no	—
408	#100	—	188	2	no	—
409	#97	—	94	1	no	—
410	C₄×C₈	—	94	2	no	—
411	C₄×C₈	—	94	1	no	—
412	C₂⁴	—	2	2	no	—
413	C₂⁴	—	4	2	no	—
414	#41	—	2	1	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	1	no	—
418	#41	—	2	8	no	—
419	#41	—	2	8	no	—
420	#41	—	4	4	no	—
421	#41	—	4	4	no	—
422	#41	#10625352	1	2	yes	—
423	#41	C₂²×Dic₄₇	1	4	yes	—
424	#41	C₂²×Dic₄₇	1	2	yes	—
425	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
426	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
427	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	8	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	—	4	2	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	8	no	—
442	C₂×D₄	—	4	8	no	—
443	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
444	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
445	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	94	1	no	—
450	C₂²×C₄	—	94	2	no	—
451	C₂²×C₄	—	188	2	no	—
452	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
453	Q₁₆	C₂²⋊Dic₄₇	1	4	yes	complemented
454	SD₁₆	—	2	8	no	—
455	SD₁₆	C₂²⋊Dic₄₇	1	8	yes	complemented
456	D₈	—	2	8	no	—
457	D₈	—	2	4	no	—
458	D₈	—	2	4	no	—
459	D₈	C₂²⋊Dic₄₇	1	4	yes	complemented
460	M₁₆	—	2	1	no	—
461	M₁₆	—	2	4	no	—
462	M₁₆	—	94	2	no	—
463	M₁₆	—	94	1	no	—
464	M₁₆	—	94	1	no	—
465	M₁₆	—	94	2	no	—
466	M₁₆	—	188	4	no	—
467	M₁₆	C₂²×Dic₄₇	1	2	yes	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	4	no	—
470	C₂×C₈	—	47	1	no	—
471	C₂×C₈	—	47	1	no	—
472	C₂×C₈	—	94	1	no	—
473	C₂×C₈	—	94	1	no	—
474	C₂×C₈	—	94	2	no	—
475	C₂×C₈	—	94	1	no	—
476	C₂×C₈	—	188	4	no	—
477	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
478	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
479	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
480	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
481	C₄⋊C₄	—	47	1	no	—
482	C₄⋊C₄	—	47	1	no	—
483	C₄⋊C₄	—	94	2	no	—
484	C₄⋊C₄	—	94	2	no	—
485	C₄⋊C₄	—	188	2	no	—
486	C₂²⋊C₄	—	94	1	no	—
487	C₂²⋊C₄	—	376	4	no	—
488	C₂²⋊C₄	—	188	2	no	—
489	C₄²	—	94	1	no	—
490	C₄²	—	94	1	no	—
491	C₄²	—	94	1	no	—
492	C₄²	—	188	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	4	8	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	8	2	no	—
500	C₂³	—	8	2	no	—
501	C₂³	—	16	2	no	—
502	C₂³	—	16	2	no	—
503	C₂³	#13094069	1	1	yes	characteristic
504	Q₈	—	2	1	no	—
505	Q₈	—	2	2	no	—
506	Q₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
507	Q₈	D₄×Dic₄₇	1	2	yes	—
508	D₄	—	2	2	no	—
509	D₄	—	2	4	no	—
510	D₄	—	2	2	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	1	no	—
513	D₄	—	2	2	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	4	no	—
516	D₄	—	4	8	no	—
517	D₄	—	4	8	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
521	D₄	D₄×Dic₄₇	1	2	yes	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	4	8	no	—
529	C₂×C₄	—	94	2	no	—
530	C₂×C₄	—	94	1	no	—
531	C₂×C₄	—	94	1	no	—
532	C₂×C₄	—	376	2	no	—
533	C₂×C₄	—	188	2	no	—
534	C₂×C₄	—	188	1	no	—
535	C₂×C₄	—	188	1	no	—
536	C₂×C₄	—	752	2	no	—
537	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
538	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
539	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
540	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
541	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
542	C₂×C₄	#13094069	1	1	yes	characteristic
543	C₈	—	2	2	no	—
544	C₈	—	94	1	no	—
545	C₈	—	94	1	no	—
546	C₈	—	188	2	no	—
547	C₈	—	188	1	no	—
548	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
549	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	8	4	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	8	2	no	—
562	C₂²	—	16	2	no	—
563	C₂²	—	16	8	no	—
564	C₂²	#15689598	1	1	yes	characteristic
565	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
566	C₂²	#15689767	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	4	no	—
569	C₄	—	376	2	no	—
570	C₄	—	188	2	no	—
571	C₄	—	188	1	no	—
572	C₄	—	188	1	no	—
573	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
574	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
575	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
576	C₄	#15689767	1	1	yes	characteristic
577	C₂	—	2	1	no	—
578	C₂	—	2	1	no	—
579	C₂	—	4	2	no	—
580	C₂	—	4	4	no	—
581	C₂	—	8	4	no	—
582	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
583	C₂	#20255170	1	1	yes	characteristic
584	C₂	#20255185	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#576	C₂
socle	C₂²×C₄₇	D₄²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#576	D₄₇
hypocenter	C₄₇	#22466
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. C₂×#15689240	C₂	semidirect
2. #20252264	C₂	semidirect
3. #20251914	C₂	semidirect
4. #20244299	C₂	semidirect
5. #20244255	C₂	semidirect
6. #20243898	C₂	semidirect
7. #20243766	C₂	semidirect
8. #20243452	C₂	semidirect
9. #20243342	C₂	semidirect
10. #20243223	C₂	semidirect
12. C₂×#13094031	C₂²	semidirect
13. #15689606	C₂²	semidirect
18. C₂×#13093960	C₂²	semidirect
19. C₂×#13093958	C₂²	semidirect
21. C₂×#13093951	C₂²	semidirect
23. #15689128	C₂²	semidirect
26. #15689124	C₂²	semidirect
30. C₂×#13093945	C₂²	semidirect
31. C₂×#13093941	C₂²	semidirect
32. #15689078	C₂²	semidirect
33. C₂×C₈×Dic₄₇	C₂²	semidirect
34. #15689026	C₂²	semidirect
35. #15688891	C₂²	semidirect
36. #15688887	C₂²	semidirect
37. #15688884	C₂²	semidirect
40. C₄₇×#576	C₄	semidirect
88. H(5,𝔽₂)×C₄₇	C₂×C₄	semidirect
99. AGL(1,ℤ/8)×C₄₇	C₂×C₄	semidirect
111. C₂×D₈×C₄₇	C₂×C₄	semidirect
114. #131×C₄₇	C₂×C₄	semidirect
160. Q₁₆×C₄₇	C₂²⋊C₄	semidirect
162. SD₁₆×C₄₇	C₂²⋊C₄	semidirect
166. D₈×C₄₇	C₂²⋊C₄	semidirect
306. #576	Dic₄₇	semidirect
340. C₄₇	#22466	semidirect
344. H(5,𝔽₂)	C₂×Dic₄₇	semidirect
355. AGL(1,ℤ/8)	C₂×Dic₄₇	semidirect
367. C₂×D₈	C₂×Dic₄₇	semidirect
372. #131	C₂×Dic₄₇	semidirect
453. Q₁₆	C₂²⋊Dic₄₇	semidirect
455. SD₁₆	C₂²⋊Dic₄₇	semidirect
459. D₈	C₂²⋊Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689240	2
#20252264	2
#20251914	2
#20244299	2
#20244255	2
#20243898	2
#20243766	2
#20243452	2
#20243342	2
#20243223	2
C₂×C₄₇×#576	2
#22466	47