Subgroups — #26235499

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246361	C₂	1	1	yes	maximal, characteristic, complemented
2	#20246298	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244087	C₂	1	2	yes	maximal, complemented
4	#20243961	C₂	1	2	yes	maximal, complemented
5	#20243738	C₂	1	2	yes	maximal
6	#20243519	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243398	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243398	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243255	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243215	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#13093945	C₂²	1	2	yes	—
15	C₂×#13093945	C₂²	1	2	yes	—
16	C₂×#13093934	C₂²	1	2	yes	—
17	#15689026	C₂²	1	2	yes	—
18	#15689022	C₂²	1	2	yes	—
19	#15689016	—	2	2	no	—
20	#15688998	—	2	2	no	—
21	#15688989	C₂²	1	1	yes	characteristic
22	#15688989	C₂²	1	1	yes	characteristic
23	#15688986	—	2	1	no	—
24	#15688983	—	2	1	no	—
25	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
28	C₂×C₄₇⋊#95	—	2	1	no	—
29	#15688886	C₂²	1	2	yes	—
30	#15688886	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₄×D₈×C₄₇	C₄	1	8	yes	complemented
38	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂³×Dic₄₇	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	D₄×Dic₄₇	—	2	4	no	—
45	D₄×Dic₄₇	—	4	2	no	—
46	C₂×C₄⋊Dic₄₇	—	2	2	no	—
47	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
51	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
52	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	2	2	no	—
54	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
55	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
56	#13093945	—	2	4	no	—
57	#13093945	—	4	2	no	—
58	#13093934	—	4	2	no	—
59	C₄₇⋊#95	—	2	1	no	—
60	C₄₇⋊#95	—	2	1	no	—
61	C₄₇⋊#95	—	2	1	no	—
62	C₄₇⋊#95	—	2	1	no	—
63	C₄₇⋊#95	—	2	2	no	—
64	C₄₇⋊#95	—	2	2	no	—
65	C₄₇⋊#95	D₄	1	1	yes	characteristic
66	C₄₇⋊#95	D₄	1	1	yes	characteristic
67	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₄₇	—	2	1	no	—
70	C₂³×C₄×C₄₇	—	2	1	no	—
71	C₂×D₈×C₄₇	—	2	2	no	—
72	C₂×D₈×C₄₇	—	2	2	no	—
73	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₄₇	—	2	2	no	—
77	C₄×D₄×C₄₇	—	2	2	no	—
78	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
79	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	#107×C₄₇	C₂×C₄	1	4	yes	complemented
86	#102×C₄₇	C₂×C₄	1	4	yes	—
87	#102×C₄₇	C₂×C₄	1	4	yes	complemented
88	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
89	C₂⁴×C₄₇	—	2	1	no	—
90	C₂⁴×C₄₇	—	2	1	no	—
91	C₂×D₄×C₄₇	—	2	1	no	—
92	C₂×D₄×C₄₇	—	2	1	no	—
93	C₂×D₄×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	—	2	1	no	—
95	C₂×D₄×C₄₇	—	2	1	no	—
96	C₂×D₄×C₄₇	—	2	1	no	—
97	C₂×D₄×C₄₇	—	2	1	no	—
98	C₂×D₄×C₄₇	—	2	1	no	—
99	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₄₇	#41	1	2	yes	—
102	C₂×D₄×C₄₇	#41	1	2	yes	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	—	8	2	no	—
108	C₂²×C₄×C₄₇	—	8	2	no	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
112	C₂²×Dic₄₇	—	2	2	no	—
113	C₂²×Dic₄₇	—	2	2	no	—
114	C₂²×Dic₄₇	—	4	4	no	—
115	C₂²×Dic₄₇	—	4	4	no	—
116	C₂²×Dic₄₇	—	8	2	no	—
117	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
118	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
119	D₈×C₄₇	—	2	8	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
129	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂²⋊C₄×C₄₇	—	2	4	no	—
131	C₂²⋊C₄×C₄₇	—	2	4	no	—
132	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
133	C₄²×C₄₇	#41	1	2	yes	—
134	C₂²⋊Dic₄₇	—	4	4	no	—
135	C₂²⋊Dic₄₇	—	4	4	no	—
136	C₂²⋊Dic₄₇	—	8	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	—	2	2	no	—
140	C₄⋊Dic₄₇	—	2	2	no	—
141	C₄⋊Dic₄₇	—	4	2	no	—
142	C₄⋊Dic₄₇	—	8	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	8	2	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	4	2	no	—
154	C₂³×C₄₇	—	4	2	no	—
155	C₂³×C₄₇	—	4	1	no	—
156	C₂³×C₄₇	—	4	1	no	—
157	C₂³×C₄₇	—	4	2	no	—
158	C₂³×C₄₇	—	4	2	no	—
159	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	2	no	—
163	D₄×C₄₇	—	2	2	no	—
164	D₄×C₄₇	—	2	2	no	—
165	D₄×C₄₇	—	4	1	no	—
166	D₄×C₄₇	—	4	1	no	—
167	D₄×C₄₇	#117	1	4	yes	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	8	4	no	—
175	C₂×C₄×C₄₇	—	8	4	no	—
176	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	2	2	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	4	2	no	—
191	C₂×Dic₄₇	—	4	2	no	—
192	C₂×Dic₄₇	—	4	2	no	—
193	C₂×Dic₄₇	—	4	2	no	—
194	C₂×Dic₄₇	—	4	2	no	—
195	C₂×Dic₄₇	—	4	2	no	—
196	C₂×Dic₄₇	—	8	8	no	—
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	2	2	no	—
199	C₄₇⋊C₈	—	4	2	no	—
200	#22764	—	47	1	no	maximal, Sylow
201	C₂²×C₄₇	—	2	4	no	—
202	C₂²×C₄₇	—	4	4	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	4	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	—	4	2	no	—
209	C₂²×C₄₇	—	8	2	no	—
210	C₂²×C₄₇	—	8	2	no	—
211	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂²×C₄₇	#546	1	1	yes	characteristic
213	C₂²×C₄₇	#548	1	1	yes	characteristic
214	C₂²×C₄₇	#575	1	2	yes	—
215	C₂²×C₄₇	#576	1	2	yes	—
216	C₄×C₄₇	—	2	2	no	—
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	4	2	no	—
219	C₄×C₄₇	—	4	2	no	—
220	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
221	C₄×C₄₇	#520	1	1	yes	characteristic
222	C₄×C₄₇	#552	1	1	yes	characteristic
223	C₄×C₄₇	#553	1	1	yes	characteristic
224	Dic₄₇	—	4	2	no	—
225	Dic₄₇	—	4	2	no	—
226	Dic₄₇	—	8	2	no	—
227	Dic₄₇	—	8	2	no	—
228	C₂×C₄×D₈	D₄₇	1	1	yes	characteristic
229	#2357	—	47	1	no	—
230	#2349	—	47	1	no	—
231	#1936	—	47	2	no	—
232	#1918	—	47	2	no	—
233	#1879	—	47	2	no	—
234	#1835	—	47	1	no	—
235	#1804	—	47	1	no	—
236	#1804	—	47	1	no	—
237	#1770	—	47	1	no	—
238	#1762	—	47	2	no	—
239	C₂×C₄₇	—	4	4	no	—
240	C₂×C₄₇	—	8	2	no	—
241	C₂×C₄₇	#2352	1	1	yes	characteristic
242	C₂×C₄₇	#2943	1	1	yes	characteristic
243	C₂×C₄₇	#2948	1	1	yes	characteristic
244	C₂×C₄₇	#3322	1	2	yes	—
245	C₂×C₄₇	#3370	1	2	yes	—
246	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
247	C₂×C₄×D₄	—	47	2	no	—
248	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
250	C₄×D₈	Dic₄₇	1	8	yes	complemented
251	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
252	C₂×C₄⋊C₈	—	47	1	no	—
253	C₂×#102	—	47	2	no	—
254	C₂×#102	—	47	2	no	—
255	C₂×#102	C₂×D₄₇	1	1	yes	characteristic
256	C₂×#102	C₂×D₄₇	1	1	yes	characteristic
257	C₂×#97	—	47	2	no	—
258	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
259	#390	—	47	2	no	—
260	#389	—	47	2	no	—
261	#388	—	94	2	no	—
262	#385	—	94	2	no	—
263	#382	—	47	1	no	—
264	#382	—	47	1	no	—
265	#381	—	94	1	no	—
266	#380	—	94	1	no	—
267	C₄×C₄⋊C₄	—	47	1	no	—
268	C₄×C₄⋊C₄	—	47	2	no	—
269	C₄×C₂²⋊C₄	—	94	1	no	—
270	C₂×#95	—	94	1	no	—
271	#340	—	47	2	no	—
272	#340	—	47	2	no	—
273	#340	—	47	2	no	—
274	#340	—	47	2	no	—
275	#336	—	47	2	no	—
276	C₄₇	#22764	1	1	yes	characteristic, complemented, Sylow
277	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
278	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	—	2	1	no	—
281	C₂³×C₄	—	94	2	no	—
282	C₂×D₈	—	2	2	no	—
283	C₂×D₈	—	2	2	no	—
284	C₂×D₈	C₂×Dic₄₇	1	4	yes	—
285	C₂²×C₈	—	47	2	no	—
286	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	94	4	no	—
291	C₄×D₄	—	188	2	no	—
292	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
293	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
294	C₂×C₄⋊C₄	—	47	2	no	—
295	C₂×C₄⋊C₄	—	47	2	no	—
296	C₂×C₄⋊C₄	—	47	2	no	—
297	C₂×C₄⋊C₄	—	94	2	no	—
298	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	94	2	no	—
303	C₂×C₂²⋊C₄	—	94	2	no	—
304	C₂×C₂²⋊C₄	—	94	2	no	—
305	C₂×C₄²	—	47	2	no	—
306	C₂×C₄²	—	94	2	no	—
307	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
308	#107	C₂×Dic₄₇	1	4	yes	complemented
309	C₄⋊C₈	—	94	2	no	—
310	#102	—	94	4	no	—
311	#102	—	188	2	no	—
312	#102	C₂×Dic₄₇	1	4	yes	—
313	#102	C₂×Dic₄₇	1	4	yes	complemented
314	#97	—	188	2	no	—
315	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
316	#95	—	47	1	no	—
317	#95	—	47	1	no	—
318	#95	—	94	2	no	—
319	#95	—	94	2	no	—
320	#95	—	94	1	no	—
321	#95	—	94	1	no	—
322	#95	—	94	1	no	—
323	#95	—	94	1	no	—
324	C₂⁴	—	2	1	no	—
325	C₂⁴	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	#10625350	1	2	yes	—
335	C₂×D₄	#10625350	1	2	yes	—
336	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
337	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	8	2	no	—
343	C₂²×C₄	—	8	2	no	—
344	C₂²×C₄	—	47	2	no	—
345	C₂²×C₄	—	47	2	no	—
346	C₂²×C₄	—	94	2	no	—
347	C₂²×C₄	—	94	2	no	—
348	C₂²×C₄	—	376	2	no	—
349	C₂²×C₄	—	188	4	no	—
350	C₂²×C₄	—	188	4	no	—
351	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
354	D₈	—	2	8	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	94	2	no	—
360	C₂×C₈	—	94	2	no	—
361	C₂×C₈	—	94	2	no	—
362	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
363	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	94	2	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	—	94	2	no	—
369	C₄⋊C₄	—	94	2	no	—
370	C₄⋊C₄	—	376	2	no	—
371	C₄⋊C₄	—	188	2	no	—
372	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
373	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	376	2	no	—
377	C₂²⋊C₄	—	188	4	no	—
378	C₂²⋊C₄	—	188	4	no	—
379	C₄²	—	94	2	no	—
380	C₄²	—	94	2	no	—
381	C₄²	—	376	2	no	—
382	C₄²	#10625352	1	2	yes	—
383	C₄²	C₂²×Dic₄₇	1	2	yes	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	4	1	no	—
401	D₄	—	4	1	no	—
402	D₄	#13093983	1	4	yes	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	4	no	—
410	C₂×C₄	—	8	4	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	94	2	no	—
414	C₂×C₄	—	94	2	no	—
415	C₂×C₄	—	94	2	no	—
416	C₂×C₄	—	94	2	no	—
417	C₂×C₄	—	376	8	no	—
418	C₂×C₄	—	188	2	no	—
419	C₂×C₄	—	188	2	no	—
420	C₂×C₄	—	188	2	no	—
421	C₂×C₄	—	188	2	no	—
422	C₂×C₄	—	188	2	no	—
423	C₂×C₄	—	188	2	no	—
424	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
425	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
426	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
427	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
428	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
429	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
430	C₂×C₄	#13094070	1	1	yes	characteristic
431	C₂×C₄	#13094071	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	188	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
446	C₂²	#15689769	1	1	yes	characteristic
447	C₂²	#15689782	1	1	yes	characteristic
448	C₂²	#15689920	1	2	yes	—
449	C₂²	#15689924	1	2	yes	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	376	2	no	—
455	C₄	—	376	2	no	—
456	C₄	—	188	2	no	—
457	C₄	—	188	2	no	—
458	C₄	C₂×#13093983	1	1	yes	characteristic
459	C₄	#15689606	1	1	yes	characteristic
460	C₄	#15689813	1	1	yes	characteristic
461	C₄	#15689819	1	1	yes	characteristic
462	C₂	—	4	4	no	—
463	C₂	—	8	2	no	—
464	C₂	#20246317	1	1	yes	characteristic
465	C₂	#20252189	1	1	yes	characteristic
466	C₂	#20252240	1	1	yes	characteristic
467	C₂	#20255594	1	2	yes	—
468	C₂	#20256137	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×D₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₈×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×D₈	D₄₇
hypocenter	C₄₇	#22764
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #20246361	C₂	semidirect
2. #20246298	C₂	semidirect
3. #20244087	C₂	semidirect
4. #20243961	C₂	semidirect
6. #20243519	C₂	semidirect
7. #20243398	C₂	semidirect
8. #20243398	C₂	semidirect
9. #20243255	C₂	semidirect
10. #20243215	C₂	semidirect
37. C₄×D₈×C₄₇	C₄	semidirect
79. C₄×D₄×C₄₇	C₂×C₄	semidirect
85. #107×C₄₇	C₂×C₄	semidirect
87. #102×C₄₇	C₂×C₄	semidirect
88. C₄×C₈×C₄₇	C₂×C₄	semidirect
250. C₄×D₈	Dic₄₇	semidirect
276. C₄₇	#22764	semidirect
293. C₄×D₄	C₂×Dic₄₇	semidirect
308. #107	C₂×Dic₄₇	semidirect
313. #102	C₂×Dic₄₇	semidirect
315. C₄×C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246361	2
#20246298	2
#20244087	2
#20243961	2
#20243738	2
#20243519	2
#20243398	2
#20243255	2
#20243215	2
C₂×C₄×D₈×C₄₇	2
#22764	47