Subgroups — #26238821

Order 12032.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252969	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689239	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252113	C₂	1	2	yes	maximal, complemented
4	#20244274	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244134	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244035	C₂	1	2	yes	maximal, complemented
7	#20243690	C₂	1	2	yes	maximal, complemented
8	#20243660	C₂	1	2	yes	maximal, complemented
9	#20243270	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#108×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₂×#13094032	C₂²	1	2	yes	—
14	#15689634	C₂²	1	2	yes	—
15	#15689364	C₄	1	1	yes	characteristic, complemented
16	#15689364	C₄	1	1	yes	characteristic, complemented
17	#15689359	C₄	1	1	yes	characteristic, complemented
18	#15689359	C₄	1	1	yes	characteristic, complemented
19	#15689352	C₄	1	2	yes	complemented
20	#15689352	C₄	1	2	yes	complemented
21	#15689239	—	2	4	no	—
22	#15689199	—	2	2	no	—
23	#15689194	—	2	2	no	—
24	#15689192	—	2	2	no	—
25	C₈×C₂²⋊D₄₇	—	2	2	no	—
26	#15689161	C₂²	1	1	yes	characteristic
27	#15689151	C₂²	1	2	yes	—
28	C₂×#13093950	C₂²	1	2	yes	—
29	C₂×#13093950	C₂²	1	2	yes	—
30	#15689120	C₂²	1	2	yes	—
31	#15689091	C₂²	1	2	yes	—
32	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
33	#15689081	C₂²	1	2	yes	—
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
37	#15688884	C₂²	1	2	yes	—
38	#15688884	C₂²	1	2	yes	—
39	#15688877	C₂²	1	1	yes	characteristic
40	#15688877	C₂²	1	1	yes	characteristic
41	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
42	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#108×C₄₇	—	2	4	no	—
44	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#108×C₄₇	C₂²	1	2	yes	—
46	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	C₂³	1	2	yes	—
48	#13094046	—	2	2	no	—
49	#13094046	—	2	2	no	—
50	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
51	C₂×#10625325	C₂×C₄	1	2	yes	—
52	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
53	#13094032	—	2	4	no	—
54	#13094032	—	4	2	no	—
55	C₂×#10625324	—	2	2	no	—
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₄₇	—	2	2	no	—
59	#13094007	—	2	2	no	—
60	#13094003	C₂×C₄	1	2	yes	—
61	#13094003	C₂×C₄	1	2	yes	—
62	#13093998	C₂×C₄	1	2	yes	—
63	#13093998	C₂×C₄	1	2	yes	—
64	#13093993	—	2	2	no	—
65	C₄×C₂²⋊D₄₇	—	2	2	no	—
66	C₄×C₂²⋊D₄₇	—	2	2	no	—
67	#13093983	C₂³	1	2	yes	—
68	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
69	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
71	#13093958	C₂×C₄	1	1	yes	characteristic
72	#13093958	C₂×C₄	1	1	yes	characteristic
73	#13093956	C₂×C₄	1	2	yes	—
74	Dic₄₇⋊C₈	—	2	2	no	—
75	Dic₄₇⋊C₈	—	2	2	no	—
76	#13093950	—	2	4	no	—
77	#13093950	—	4	2	no	—
78	#13093949	C₂×C₄	1	2	yes	—
79	#13093949	C₂×C₄	1	2	yes	—
80	#13093946	C₂×C₄	1	2	yes	—
81	#13093946	C₂×C₄	1	2	yes	—
82	C₂²⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
83	C₂²⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
84	C₂²⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
85	C₂²⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
86	(C₂×D₄₇)⋊C₈	—	2	2	no	—
87	(C₂×D₄₇)⋊C₈	—	2	2	no	—
88	#13093934	—	2	2	no	—
89	C₈×Dic₄₇	—	2	2	no	—
90	C₈×Dic₄₇	—	2	2	no	—
91	C₈×Dic₄₇	—	2	2	no	—
92	C₄₇⋊#95	—	2	1	no	—
93	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₄₇	—	2	2	no	—
95	C₂×M₁₆×C₄₇	—	2	4	no	—
96	C₂×M₁₆×C₄₇	—	4	2	no	—
97	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
98	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
99	C₂²×C₈×C₄₇	—	2	2	no	—
100	C₂²×C₈×C₄₇	—	2	2	no	—
101	C₂²×C₈×C₄₇	—	2	2	no	—
102	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
103	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
104	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
106	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	#108×C₄₇	—	2	4	no	—
109	#108×C₄₇	—	2	2	no	—
110	#108×C₄₇	D₄	1	4	yes	complemented
111	C₂⁴×C₄₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	C₂×C₂²⋊D₄₇	—	2	2	no	—
123	C₂×C₂²⋊D₄₇	—	2	2	no	—
124	C₂×C₂²⋊D₄₇	—	2	2	no	—
125	C₂²×Dic₄₇	—	2	1	no	—
126	C₂²×Dic₄₇	—	2	1	no	—
127	#10625350	—	2	2	no	—
128	#10625350	—	2	2	no	—
129	#10625350	—	2	2	no	—
130	#10625350	—	2	2	no	—
131	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
132	C₂×C₄×D₄₇	—	2	2	no	—
133	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
134	M₁₆×C₄₇	—	2	2	no	—
135	M₁₆×C₄₇	—	2	2	no	—
136	M₁₆×C₄₇	—	2	2	no	—
137	M₁₆×C₄₇	—	4	4	no	—
138	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
139	C₂×C₈×C₄₇	—	2	1	no	—
140	C₂×C₈×C₄₇	—	2	2	no	—
141	C₂×C₈×C₄₇	—	2	1	no	—
142	C₂×C₈×C₄₇	—	2	2	no	—
143	C₂×C₈×C₄₇	—	2	2	no	—
144	C₂×C₈×C₄₇	—	2	2	no	—
145	C₂×C₈×C₄₇	—	2	2	no	—
146	C₂×C₈×C₄₇	—	2	2	no	—
147	C₂×C₈×C₄₇	—	4	4	no	—
148	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₄₇	#41	1	2	yes	—
154	C₂²⋊Dic₄₇	—	2	4	no	—
155	C₂²⋊Dic₄₇	—	2	2	no	—
156	C₂²⋊Dic₄₇	—	2	2	no	—
157	C₂²⋊Dic₄₇	—	2	2	no	—
158	(C₂×D₄₇)⋊C₄	—	2	2	no	—
159	(C₂×D₄₇)⋊C₄	—	2	2	no	—
160	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
161	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
162	Dic₄₇⋊C₄	—	2	2	no	—
163	Dic₄₇⋊C₄	—	2	2	no	—
164	C₄×Dic₄₇	—	2	2	no	—
165	C₄×Dic₄₇	—	2	1	no	—
166	C₄×Dic₄₇	—	2	1	no	—
167	C₄×Dic₄₇	—	2	1	no	—
168	C₄×Dic₄₇	—	2	1	no	—
169	C₂×C₄₇⋊C₈	—	2	1	no	—
170	C₂×C₄₇⋊C₈	—	2	1	no	—
171	C₂×C₄₇⋊C₈	—	2	1	no	—
172	C₂×C₄₇⋊C₈	—	2	1	no	—
173	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
174	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
176	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
177	Dic₁₈₈	—	2	2	no	—
178	D₃₇₆	—	2	2	no	—
179	#10625325	—	2	4	no	—
180	#10625324	—	4	4	no	—
181	C₈×D₄₇	—	4	4	no	—
182	C₂³×C₄₇	—	2	1	no	—
183	C₂³×C₄₇	—	2	1	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	4	1	no	—
186	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
187	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
188	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂²×D₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	1	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	2	1	no	—
198	C₂×C₄×C₄₇	—	2	1	no	—
199	C₂×C₄×C₄₇	—	2	1	no	—
200	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
208	C₂²⋊D₄₇	—	4	2	no	—
209	C₂²⋊D₄₇	—	4	2	no	—
210	C₂²⋊D₄₇	—	4	4	no	—
211	C₂²⋊D₄₇	—	8	2	no	—
212	C₂×Dic₄₇	—	2	2	no	—
213	C₂×Dic₄₇	—	2	2	no	—
214	C₂×Dic₄₇	—	2	2	no	—
215	C₂×Dic₄₇	—	2	2	no	—
216	C₂×Dic₄₇	—	2	2	no	—
217	C₂×Dic₄₇	—	4	1	no	—
218	C₂×Dic₄₇	—	4	1	no	—
219	C₂×Dic₄₇	—	4	1	no	—
220	C₂×Dic₄₇	—	4	1	no	—
221	D₁₈₈	—	2	2	no	—
222	D₁₈₈	—	2	2	no	—
223	C₄×D₄₇	—	4	2	no	—
224	C₄×D₄₇	—	4	2	no	—
225	Dic₉₄	—	2	2	no	—
226	Dic₉₄	—	2	2	no	—
227	C₈×C₄₇	—	2	1	no	—
228	C₈×C₄₇	—	2	1	no	—
229	C₈×C₄₇	—	2	4	no	—
230	C₈×C₄₇	—	4	2	no	—
231	C₈×C₄₇	C₄×D₄	1	2	yes	—
232	C₈×C₄₇	C₄×D₄	1	2	yes	—
233	C₄₇⋊C₈	—	2	1	no	—
234	C₄₇⋊C₈	—	2	1	no	—
235	C₄₇⋊C₈	—	2	1	no	—
236	C₄₇⋊C₈	—	2	1	no	—
237	#23018	—	47	1	no	maximal, Sylow
238	C₂²×C₄₇	—	2	1	no	—
239	C₂²×C₄₇	—	2	1	no	—
240	C₂²×C₄₇	—	2	1	no	—
241	C₂²×C₄₇	—	2	1	no	—
242	C₂²×C₄₇	—	2	1	no	—
243	C₂²×C₄₇	—	2	1	no	—
244	C₂²×C₄₇	—	2	1	no	—
245	C₂²×C₄₇	—	4	2	no	—
246	C₂²×C₄₇	—	4	2	no	—
247	C₂²×C₄₇	#443	1	2	yes	complemented
248	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
249	C₂²×C₄₇	#548	1	1	yes	characteristic
250	C₂²×C₄₇	#553	1	1	yes	characteristic
251	C₂×D₄₇	—	4	2	no	—
252	C₂×D₄₇	—	4	2	no	—
253	C₂×D₄₇	—	4	2	no	—
254	C₄×C₄₇	—	2	1	no	—
255	C₄×C₄₇	—	2	1	no	—
256	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₄₇	#520	1	1	yes	characteristic
258	C₄×C₄₇	D₄²	1	1	yes	characteristic
259	C₄×C₄₇	#547	1	1	yes	characteristic
260	Dic₄₇	—	4	2	no	—
261	Dic₄₇	—	4	2	no	—
262	Dic₄₇	—	4	2	no	—
263	Dic₄₇	—	4	2	no	—
264	Dic₄₇	—	4	2	no	—
265	#3050	—	47	1	no	—
266	C₂×#443	—	47	1	no	—
267	#2933	—	47	2	no	—
268	C₂²×#108	D₄₇	1	1	yes	characteristic, complemented
269	#1974	—	47	1	no	—
270	#1945	—	47	1	no	—
271	#1929	—	47	2	no	—
272	#1871	—	47	2	no	—
273	#1866	—	47	2	no	—
274	#1772	—	47	1	no	—
275	C₈×C₂²⋊C₄	—	47	1	no	—
276	C₂×C₄₇	—	2	1	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	2	2	no	—
279	C₂×C₄₇	—	4	1	no	—
280	C₂×C₄₇	#2361	1	1	yes	characteristic
281	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
282	C₂×C₄₇	#2957	1	1	yes	characteristic
283	D₄₇	—	8	2	no	—
284	C₂×#135	—	47	1	no	—
285	C₂×#131	—	47	2	no	—
286	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
287	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
288	#525	—	47	2	no	—
289	#467	—	47	1	no	—
290	#467	—	47	1	no	—
291	#466	—	47	1	no	—
292	#466	—	47	1	no	—
293	#465	—	47	2	no	—
294	#465	—	47	2	no	—
295	#443	—	94	4	no	—
296	#436	—	94	2	no	—
297	#435	—	94	2	no	—
298	#435	—	94	2	no	—
299	C₈×D₄	—	94	2	no	—
300	C₂×#108	—	2	4	no	—
301	C₂×#108	C₂×D₄₇	1	2	yes	—
302	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
303	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
304	#427	—	47	1	no	—
305	#424	—	47	2	no	—
306	C₂×#104	—	47	2	no	—
307	C₂×#104	—	47	2	no	—
308	#416	—	47	2	no	—
309	#408	—	47	2	no	—
310	C₂×C₂²⋊C₈	—	47	1	no	—
311	#405	—	47	2	no	—
312	C₂×C₄×C₈	—	47	1	no	—
313	C₂×C₄×C₈	—	47	1	no	—
314	C₄×C₂²⋊C₄	—	47	1	no	—
315	#339	—	47	2	no	—
316	#339	—	47	2	no	—
317	#336	—	47	1	no	—
318	#336	—	47	1	no	—
319	C₄₇	#23018	1	1	yes	characteristic, complemented, Sylow
320	C₂×#41	—	47	2	no	—
321	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
322	#135	—	94	2	no	—
323	#135	—	94	2	no	—
324	C₂×Q₁₆	—	47	1	no	—
325	C₂×SD₁₆	—	47	2	no	—
326	C₂×D₈	—	47	1	no	—
327	#131	—	94	4	no	—
328	#131	—	188	2	no	—
329	C₂×M₁₆	—	2	2	no	—
330	C₂×M₁₆	—	2	4	no	—
331	C₂×M₁₆	—	4	2	no	—
332	C₂×M₁₆	—	94	2	no	—
333	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
334	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	2	2	no	—
338	C₂²×C₈	—	47	1	no	—
339	C₂²×C₈	—	47	1	no	—
340	C₂²×C₈	—	94	2	no	—
341	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
342	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
343	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
344	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
347	#123	—	94	2	no	—
348	C₂²⋊Q₈	—	47	2	no	—
349	C₂²⋊Q₈	—	47	2	no	—
350	#121	—	47	2	no	—
351	#121	—	47	2	no	—
352	#120	—	94	2	no	—
353	C₄×D₄	—	94	2	no	—
354	C₄×D₄	—	94	2	no	—
355	#117	—	47	2	no	—
356	C₂×C₂²⋊C₄	—	94	1	no	—
357	C₂×C₄²	—	47	1	no	—
358	C₂×C₄²	—	47	1	no	—
359	#108	—	2	4	no	—
360	#108	—	2	2	no	—
361	#108	C₂²⋊D₄₇	1	4	yes	complemented
362	#107	—	47	1	no	—
363	#107	—	47	1	no	—
364	#106	—	47	2	no	—
365	C₄⋊C₈	—	94	2	no	—
366	C₄⋊C₈	—	94	2	no	—
367	#104	—	94	4	no	—
368	#104	—	188	2	no	—
369	#103	—	47	2	no	—
370	#103	—	47	2	no	—
371	#102	—	47	2	no	—
372	#102	—	47	2	no	—
373	C₂²⋊C₈	—	47	1	no	—
374	C₂²⋊C₈	—	47	1	no	—
375	C₂²⋊C₈	—	47	1	no	—
376	C₂²⋊C₈	—	47	1	no	—
377	C₂²⋊C₈	—	94	2	no	—
378	C₂²⋊C₈	—	94	2	no	—
379	#97	—	94	2	no	—
380	C₄×C₈	—	94	2	no	—
381	C₄×C₈	—	94	2	no	—
382	C₄×C₈	—	94	2	no	—
383	#95	—	94	1	no	—
384	C₂⁴	#10625354	1	1	yes	characteristic
385	#41	—	94	2	no	—
386	#41	—	94	2	no	—
387	#41	—	94	2	no	—
388	#41	—	94	2	no	—
389	C₂×Q₈	—	47	2	no	—
390	C₂×D₄	—	47	2	no	—
391	C₂×D₄	—	94	2	no	—
392	C₂×D₄	—	94	2	no	—
393	C₂×D₄	—	94	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	94	1	no	—
399	C₂²×C₄	—	94	1	no	—
400	C₂²×C₄	—	94	2	no	—
401	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
403	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
404	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
405	C₂²×C₄	#10625354	1	1	yes	characteristic
406	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
407	Q₁₆	—	94	2	no	—
408	SD₁₆	—	94	4	no	—
409	D₈	—	94	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	4	4	no	—
414	M₁₆	—	188	4	no	—
415	M₁₆	C₂×C₂²⋊D₄₇	1	4	yes	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	4	4	no	—
425	C₂×C₈	—	47	1	no	—
426	C₂×C₈	—	47	1	no	—
427	C₂×C₈	—	47	1	no	—
428	C₂×C₈	—	47	1	no	—
429	C₂×C₈	—	94	1	no	—
430	C₂×C₈	—	94	1	no	—
431	C₂×C₈	—	94	1	no	—
432	C₂×C₈	—	94	1	no	—
433	C₂×C₈	—	188	4	no	—
434	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
435	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
436	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
437	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
438	C₂×C₈	#10625350	1	2	yes	—
439	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
440	C₄⋊C₄	—	47	2	no	—
441	C₄⋊C₄	—	47	2	no	—
442	C₄⋊C₄	—	94	2	no	—
443	C₄⋊C₄	—	94	2	no	—
444	C₂²⋊C₄	—	94	4	no	—
445	C₂²⋊C₄	—	94	2	no	—
446	C₂²⋊C₄	—	94	2	no	—
447	C₂²⋊C₄	—	94	2	no	—
448	C₂²⋊C₄	—	94	2	no	—
449	C₂²⋊C₄	—	94	2	no	—
450	C₄²	—	94	2	no	—
451	C₄²	—	94	1	no	—
452	C₄²	—	94	1	no	—
453	C₄²	—	94	1	no	—
454	C₄²	—	94	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	94	2	no	—
460	C₂³	#13093986	1	1	yes	characteristic
461	C₂³	#13093986	1	1	yes	characteristic
462	C₂³	C₂×#10625354	1	1	yes	characteristic
463	Q₈	—	94	2	no	—
464	Q₈	—	94	2	no	—
465	D₄	—	94	2	no	—
466	D₄	—	94	2	no	—
467	D₄	—	376	2	no	—
468	D₄	—	188	4	no	—
469	D₄	—	188	2	no	—
470	D₄	—	188	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	94	2	no	—
482	C₂×C₄	—	94	2	no	—
483	C₂×C₄	—	94	2	no	—
484	C₂×C₄	—	94	2	no	—
485	C₂×C₄	—	94	2	no	—
486	C₂×C₄	—	188	1	no	—
487	C₂×C₄	—	188	1	no	—
488	C₂×C₄	—	188	1	no	—
489	C₂×C₄	—	188	1	no	—
490	C₂×C₄	—	188	2	no	—
491	C₂×C₄	—	188	2	no	—
492	C₂×C₄	#13093986	1	1	yes	characteristic
493	C₂×C₄	#13093986	1	1	yes	characteristic
494	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
496	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
497	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
498	C₂×C₄	#13094069	1	1	yes	characteristic
499	C₂×C₄	#13094072	1	1	yes	characteristic
500	C₈	—	2	4	no	—
501	C₈	—	2	1	no	—
502	C₈	—	2	1	no	—
503	C₈	—	4	2	no	—
504	C₈	—	94	1	no	—
505	C₈	—	94	1	no	—
506	C₈	—	94	1	no	—
507	C₈	—	94	1	no	—
508	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
509	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	188	2	no	—
520	C₂²	—	188	2	no	—
521	C₂²	—	188	2	no	—
522	C₂²	#15689239	1	2	yes	complemented
523	C₂²	C₂×#13093986	1	1	yes	characteristic
524	C₂²	#15689784	1	1	yes	characteristic
525	C₂²	#15689821	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	188	2	no	—
529	C₄	—	188	2	no	—
530	C₄	—	188	2	no	—
531	C₄	—	188	2	no	—
532	C₄	—	188	2	no	—
533	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
534	C₄	#15689604	1	1	yes	characteristic
535	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
536	C₄	#15689774	1	1	yes	characteristic
537	C₂	—	2	1	no	—
538	C₂	—	2	1	no	—
539	C₂	—	2	2	no	—
540	C₂	—	4	1	no	—
541	C₂	—	376	2	no	—
542	C₂	#20246404	1	1	yes	characteristic
543	C₂	C₂×#15689239	1	1	yes	characteristic
544	C₂	#20252304	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#108×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252969	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#108	D₄₇
hypocenter	C₄₇	#23018
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
2. C₂×#15689239	C₂	semidirect
3. #20252113	C₂	semidirect
4. #20244274	C₂	semidirect
5. #20244134	C₂	semidirect
6. #20244035	C₂	semidirect
7. #20243690	C₂	semidirect
8. #20243660	C₂	semidirect
9. #20243270	C₂	semidirect
10. C₈×C₂²⋊Dic₄₇	C₂	semidirect
11. C₂²×#108×C₄₇	C₂	semidirect
15. #15689364	C₄	semidirect
16. #15689364	C₄	semidirect
17. #15689359	C₄	semidirect
18. #15689359	C₄	semidirect
19. #15689352	C₄	semidirect
20. #15689352	C₄	semidirect
110. #108×C₄₇	D₄	semidirect
247. C₂²×C₄₇	#443	semidirect
268. C₂²×#108	D₄₇	semidirect
319. C₄₇	#23018	semidirect
361. #108	C₂²⋊D₄₇	semidirect
522. C₂²	#15689239	semidirect

Maximal subgroups

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

subgroup	index
#20252969	2
C₂×#15689239	2
#20252113	2
#20244274	2
#20244134	2
#20244035	2
#20243690	2
#20243660	2
#20243270	2
C₈×C₂²⋊Dic₄₇	2
C₂²×#108×C₄₇	2
#23018	47