Subgroups — #26219416

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246031	C₂	1	1	yes	maximal, characteristic, complemented
2	#20245749	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244010	C₂	1	2	yes	maximal, complemented
4	#20243982	C₂	1	2	yes	maximal, complemented
5	#20243738	C₂	1	2	yes	maximal
6	#20243637	C₂	1	2	yes	maximal, complemented
7	C₄×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243213	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243213	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
13	C₂×#13093958	C₂²	1	2	yes	—
14	C₂×#13093945	C₂²	1	2	yes	—
15	C₂×#13093945	C₂²	1	2	yes	—
16	C₂×#13093935	C₂²	1	1	yes	characteristic
17	#15689026	C₂²	1	2	yes	—
18	#15689022	C₂²	1	2	yes	—
19	#15689016	—	2	2	no	—
20	#15688986	—	2	1	no	—
21	#15688983	—	2	1	no	—
22	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
23	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
26	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
27	#15688969	C₂²	1	1	yes	characteristic
28	C₂×C₄₇⋊#95	—	2	1	no	—
29	#15688886	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688877	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	—	2	4	no	—
46	C₂×C₄⋊Dic₄₇	—	2	2	no	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
50	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
51	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄×Dic₄₇	—	2	1	no	—
53	C₂×C₄×Dic₄₇	—	2	1	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
56	#13093958	—	2	4	no	—
57	#13093945	—	2	4	no	—
58	#13093945	—	2	4	no	—
59	#13093935	—	2	2	no	—
60	C₄₇⋊#95	—	2	1	no	—
61	C₄₇⋊#95	—	2	1	no	—
62	C₄₇⋊#95	—	2	2	no	—
63	C₄₇⋊#95	—	2	2	no	—
64	C₄₇⋊#95	D₄	1	1	yes	characteristic
65	C₄₇⋊#95	D₄	1	1	yes	characteristic
66	C₄₇⋊#95	D₄	1	2	yes	—
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	4	no	—
72	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×D₄×C₄₇	—	2	2	no	—
76	C₄×D₄×C₄₇	—	2	2	no	—
77	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
78	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	#107×C₄₇	C₂×C₄	1	4	yes	complemented
85	#102×C₄₇	C₂×C₄	1	4	yes	—
86	#102×C₄₇	C₂×C₄	1	4	yes	complemented
87	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
88	C₂⁴×C₄₇	—	2	1	no	—
89	C₂⁴×C₄₇	—	2	1	no	—
90	C₂×D₄×C₄₇	—	2	1	no	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	1	no	—
95	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₄₇	#41	1	4	yes	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	8	2	no	—
103	C₂²×C₄×C₄₇	—	8	2	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂²×Dic₄₇	—	2	2	no	—
108	C₂²×Dic₄₇	—	2	8	no	—
109	C₂²×Dic₄₇	—	2	2	no	—
110	C₂²×Dic₄₇	—	8	2	no	—
111	C₂²×Dic₄₇	—	8	2	no	—
112	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
113	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
114	D₈×C₄₇	—	2	8	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
122	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂²⋊C₄×C₄₇	—	2	4	no	—
124	C₂²⋊C₄×C₄₇	—	2	4	no	—
125	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₇	#41	1	2	yes	—
127	C₂²⋊Dic₄₇	—	2	8	no	—
128	C₂²⋊Dic₄₇	—	8	2	no	—
129	C₂²⋊Dic₄₇	—	8	2	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	8	2	no	—
134	C₄⋊Dic₄₇	#41	1	4	yes	—
135	C₄×Dic₄₇	—	2	2	no	—
136	C₄×Dic₄₇	—	2	2	no	—
137	C₄×Dic₄₇	—	8	2	no	—
138	C₄×Dic₄₇	—	8	1	no	—
139	C₄×Dic₄₇	—	8	1	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	2	4	no	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	—	4	1	no	—
147	C₂³×C₄₇	—	4	2	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	—	4	2	no	—
150	C₂³×C₄₇	—	4	1	no	—
151	C₂³×C₄₇	—	4	2	no	—
152	C₂³×C₄₇	—	4	1	no	—
153	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	D₄×C₄₇	—	2	2	no	—
155	D₄×C₄₇	—	2	2	no	—
156	D₄×C₄₇	—	2	2	no	—
157	D₄×C₄₇	—	2	4	no	—
158	D₄×C₄₇	—	4	2	no	—
159	D₄×C₄₇	#117	1	4	yes	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	8	4	no	—
168	C₂×C₄×C₄₇	—	8	4	no	—
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	4	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	4	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	8	8	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	—	2	2	no	—
190	C₄₇⋊C₈	—	4	2	no	—
191	#21129	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	4	no	—
193	C₂²×C₄₇	—	4	4	no	—
194	C₂²×C₄₇	—	4	4	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	—	4	2	no	—
198	C₂²×C₄₇	—	4	2	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	—	8	2	no	—
201	C₂²×C₄₇	—	8	2	no	—
202	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂²×C₄₇	#525	1	2	yes	—
204	C₂²×C₄₇	#576	1	2	yes	—
205	C₂²×C₄₇	#576	1	1	yes	characteristic
206	C₂²×C₄₇	#578	1	1	yes	characteristic
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	4	2	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
212	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
213	C₄×C₄₇	#529	1	2	yes	—
214	Dic₄₇	—	4	2	no	—
215	Dic₄₇	—	4	4	no	—
216	Dic₄₇	—	4	2	no	—
217	Dic₄₇	—	8	2	no	—
218	C₂×C₄×D₈	D₄₇	1	1	yes	characteristic
219	#2319	—	47	1	no	—
220	#2275	—	47	1	no	—
221	#1925	—	47	2	no	—
222	#1921	—	47	2	no	—
223	#1879	—	47	2	no	—
224	#1862	—	47	2	no	—
225	C₄×#107	—	47	1	no	—
226	#1762	—	47	1	no	—
227	#1762	—	47	1	no	—
228	#1746	—	47	1	no	—
229	C₂×C₄₇	—	4	4	no	—
230	C₂×C₄₇	—	8	2	no	—
231	C₂×C₄₇	#2290	1	1	yes	characteristic
232	C₂×C₄₇	#2948	1	1	yes	characteristic
233	C₂×C₄₇	#2951	1	1	yes	characteristic
234	C₂×C₄₇	#3122	1	2	yes	—
235	C₂×C₄₇	#3124	1	2	yes	—
236	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
237	C₂×C₄×D₄	—	47	2	no	—
238	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
240	C₄×D₈	Dic₄₇	1	8	yes	complemented
241	C₂×#107	—	47	2	no	—
242	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
243	C₂×#102	—	47	2	no	—
244	C₂×#102	—	47	2	no	—
245	C₂×#102	C₂×D₄₇	1	1	yes	characteristic
246	C₂×#102	C₂×D₄₇	1	1	yes	characteristic
247	C₂×#97	—	47	1	no	—
248	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
249	#390	—	47	2	no	—
250	#389	—	47	2	no	—
251	#388	—	94	2	no	—
252	#381	—	94	1	no	—
253	#380	—	94	1	no	—
254	C₄×C₄⋊C₄	—	47	2	no	—
255	C₄×C₄⋊C₄	—	47	1	no	—
256	C₄×C₄⋊C₄	—	47	1	no	—
257	C₄×C₂²⋊C₄	—	94	2	no	—
258	C₄×C₂²⋊C₄	—	94	1	no	—
259	#376	—	47	1	no	—
260	C₂×#95	—	94	1	no	—
261	#340	—	47	2	no	—
262	#340	—	47	2	no	—
263	#340	—	47	2	no	—
264	#336	—	47	2	no	—
265	#336	—	47	2	no	—
266	C₄₇	#21129	1	1	yes	characteristic, complemented, Sylow
267	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
268	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	94	2	no	—
272	C₂×D₈	—	2	4	no	—
273	C₂×D₈	C₂×Dic₄₇	1	4	yes	—
274	C₂²×C₈	—	47	2	no	—
275	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
276	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
277	C₄×D₄	—	2	2	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	94	4	no	—
280	C₄×D₄	—	94	4	no	—
281	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
282	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
283	C₂×C₄⋊C₄	—	47	2	no	—
284	C₂×C₄⋊C₄	—	47	2	no	—
285	C₂×C₄⋊C₄	—	94	2	no	—
286	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	94	2	no	—
291	C₂×C₂²⋊C₄	—	94	2	no	—
292	C₂×C₂²⋊C₄	—	94	2	no	—
293	C₂×C₄²	—	47	2	no	—
294	C₂×C₄²	—	94	2	no	—
295	C₂×C₄²	—	94	1	no	—
296	C₂×C₄²	—	94	1	no	—
297	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
298	#107	—	94	4	no	—
299	#107	C₂×Dic₄₇	1	4	yes	complemented
300	#102	—	94	4	no	—
301	#102	—	94	4	no	—
302	#102	C₂×Dic₄₇	1	4	yes	—
303	#102	C₂×Dic₄₇	1	4	yes	complemented
304	#97	—	94	2	no	—
305	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
306	#95	—	47	1	no	—
307	#95	—	47	1	no	—
308	#95	—	47	2	no	—
309	#95	—	94	2	no	—
310	#95	—	94	2	no	—
311	#95	—	94	1	no	—
312	#95	—	94	1	no	—
313	C₂⁴	—	2	1	no	—
314	C₂⁴	—	2	1	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	#10625350	1	4	yes	—
321	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
322	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	8	2	no	—
328	C₂²×C₄	—	8	2	no	—
329	C₂²×C₄	—	47	2	no	—
330	C₂²×C₄	—	47	2	no	—
331	C₂²×C₄	—	94	8	no	—
332	C₂²×C₄	—	94	2	no	—
333	C₂²×C₄	—	94	2	no	—
334	C₂²×C₄	—	376	2	no	—
335	C₂²×C₄	—	376	2	no	—
336	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
337	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
338	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
339	D₈	—	2	8	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	94	2	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
346	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	47	4	no	—
350	C₄⋊C₄	—	94	2	no	—
351	C₄⋊C₄	—	94	2	no	—
352	C₄⋊C₄	—	94	2	no	—
353	C₄⋊C₄	—	376	2	no	—
354	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
355	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	94	8	no	—
359	C₂²⋊C₄	—	376	2	no	—
360	C₂²⋊C₄	—	376	2	no	—
361	C₄²	—	94	2	no	—
362	C₄²	—	94	2	no	—
363	C₄²	—	376	1	no	—
364	C₄²	—	376	1	no	—
365	C₄²	—	376	2	no	—
366	C₄²	#10625352	1	2	yes	—
367	C₄²	C₂²×Dic₄₇	1	2	yes	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	4	no	—
383	D₄	—	4	2	no	—
384	D₄	#13093983	1	4	yes	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	8	4	no	—
393	C₂×C₄	—	8	4	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	94	2	no	—
396	C₂×C₄	—	94	4	no	—
397	C₂×C₄	—	94	2	no	—
398	C₂×C₄	—	94	2	no	—
399	C₂×C₄	—	94	2	no	—
400	C₂×C₄	—	94	2	no	—
401	C₂×C₄	—	376	8	no	—
402	C₂×C₄	—	188	2	no	—
403	C₂×C₄	—	188	2	no	—
404	C₂×C₄	—	188	2	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
408	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
409	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
410	C₂×C₄	#41×D₄₇	1	2	yes	—
411	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
412	C₂×C₄	C₂×#10625350	1	2	yes	—
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	188	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
427	C₂²	#15689632	1	2	yes	—
428	C₂²	#15689924	1	2	yes	—
429	C₂²	#15689925	1	1	yes	characteristic
430	C₂²	#15689937	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	376	2	no	—
436	C₄	—	188	2	no	—
437	C₄	—	188	4	no	—
438	C₄	—	188	2	no	—
439	C₄	C₂×#13093983	1	1	yes	characteristic
440	C₄	#41×Dic₄₇	1	1	yes	characteristic
441	C₄	#15689653	1	2	yes	—
442	C₂	—	4	4	no	—
443	C₂	—	8	2	no	—
444	C₂	#20245833	1	1	yes	characteristic
445	C₂	#20252240	1	1	yes	characteristic
446	C₂	#20252264	1	1	yes	characteristic
447	C₂	#20253628	1	2	yes	—
448	C₂	#20253646	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	#21129
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. #20246031	C₂	semidirect
2. #20245749	C₂	semidirect
3. #20244010	C₂	semidirect
4. #20243982	C₂	semidirect
6. #20243637	C₂	semidirect
7. C₄×#13093958	C₂	semidirect
8. #20243213	C₂	semidirect
9. #20243213	C₂	semidirect
10. #20243139	C₂	semidirect
37. C₄×D₈×C₄₇	C₄	semidirect
78. C₄×D₄×C₄₇	C₂×C₄	semidirect
84. #107×C₄₇	C₂×C₄	semidirect
86. #102×C₄₇	C₂×C₄	semidirect
87. C₄×C₈×C₄₇	C₂×C₄	semidirect
240. C₄×D₈	Dic₄₇	semidirect
266. C₄₇	#21129	semidirect
282. C₄×D₄	C₂×Dic₄₇	semidirect
299. #107	C₂×Dic₄₇	semidirect
303. #102	C₂×Dic₄₇	semidirect
305. 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
#20246031	2
#20245749	2
#20244010	2
#20243982	2
#20243738	2
#20243637	2
C₄×#13093958	2
#20243213	2
#20243139	2
C₂×C₄×D₈×C₄₇	2
#21129	47