Subgroups — #26236020

Order 12032.

934 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689205	C₂	1	1	yes	maximal, characteristic
2	#20246333	C₂	1	2	yes	maximal, complemented
3	#20244254	C₂	1	1	yes	maximal, characteristic
4	#20244252	C₂	1	1	yes	maximal, characteristic
5	#20244008	C₂	1	2	yes	maximal, complemented
6	#20244006	C₂	1	2	yes	maximal, complemented
7	#20243546	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243387	C₂	1	2	yes	maximal, complemented
9	#107×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#107×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
13	C₂×#13093986	C₂²	1	2	yes	—
14	C₂×#13093981	—	2	2	no	—
15	#15689205	C₄	1	8	yes	complemented
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093957	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×#13093946	C₂²	1	2	yes	—
20	C₂×#13093944	C₂²	1	2	yes	—
21	C₂×#13093944	C₂²	1	2	yes	—
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	#15689025	C₂²	1	2	yes	—
25	#15689024	C₂²	1	2	yes	—
26	#15689014	—	2	2	no	—
27	#15689012	—	2	2	no	—
28	#15688992	C₂²	1	2	yes	—
29	#15688982	—	2	2	no	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
31	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	2	yes	—
33	#15688878	C₂²	1	1	yes	characteristic
34	#15688877	C₂²	1	1	yes	characteristic
35	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₂²×D₁₈₈	C₂³	1	2	yes	—
41	C₂²×C₄×D₄₇	—	2	2	no	—
42	C₂×D₃₇₆	—	2	2	no	—
43	C₂×D₃₇₆	—	2	2	no	—
44	C₂×D₃₇₆	C₂×C₄	1	4	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	#13093986	—	2	4	no	—
48	#13093986	C₂×C₄	1	8	yes	—
49	#13093981	—	4	8	no	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×Dic₄₇⋊C₄	—	2	2	no	—
52	C₂×Dic₄₇⋊C₄	—	2	2	no	—
53	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
54	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
55	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
56	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
57	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
59	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
60	C₂×C₄×Dic₄₇	—	2	2	no	—
61	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	#13093958	—	2	2	no	—
64	#13093957	—	4	2	no	—
65	Dic₄₇⋊C₈	—	2	2	no	—
66	#13093946	—	4	2	no	—
67	#13093944	—	4	2	no	—
68	#13093944	C₂×C₄	1	8	yes	—
69	C₈×Dic₄₇	—	2	2	no	—
70	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₄₇⋊#95	D₄	1	1	yes	characteristic
73	C₄₇⋊#95	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	#107×C₄₇	—	2	2	no	—
81	#107×C₄₇	C₂×C₄	1	4	yes	—
82	C₄×C₈×C₄₇	—	2	2	no	—
83	#95×C₄₇	—	2	2	no	—
84	C₂³×D₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂²×Dic₄₇	—	2	2	no	—
91	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂×D₁₈₈	—	2	2	no	—
96	C₂×D₁₈₈	—	2	2	no	—
97	C₂×D₁₈₈	—	2	2	no	—
98	C₂×D₁₈₈	—	2	2	no	—
99	C₂×D₁₈₈	—	2	2	no	—
100	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
101	C₂×C₄×D₄₇	—	2	8	no	—
102	C₂×C₄×D₄₇	—	4	4	no	—
103	C₂×C₄×D₄₇	—	4	4	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₄₇	#41	1	2	yes	—
109	C₂×C₈×C₄₇	#41	1	2	yes	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
114	C₄²×C₄₇	—	2	1	no	—
115	C₄²×C₄₇	—	2	1	no	—
116	C₄²×C₄₇	—	4	4	no	—
117	(C₂×D₄₇)⋊C₄	—	2	8	no	—
118	(C₂×D₄₇)⋊C₄	—	4	4	no	—
119	(C₂×D₄₇)⋊C₄	—	4	4	no	—
120	(C₂×D₄₇)⋊C₄	—	8	2	no	—
121	(C₂×D₄₇)⋊C₄	—	8	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	Dic₄₇⋊C₄	—	2	2	no	—
125	Dic₄₇⋊C₄	—	4	4	no	—
126	Dic₄₇⋊C₄	—	8	2	no	—
127	Dic₄₇⋊C₄	D₈	1	4	yes	complemented
128	C₄×Dic₄₇	—	2	1	no	—
129	C₄×Dic₄₇	—	2	1	no	—
130	C₄×Dic₄₇	—	4	4	no	—
131	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
132	C₄×Dic₄₇	#41	1	2	yes	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
139	D₃₇₆	—	2	8	no	—
140	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
141	C₂²×D₄₇	—	2	4	no	—
142	C₂²×D₄₇	—	4	2	no	—
143	C₂²×D₄₇	—	4	2	no	—
144	C₂²×D₄₇	—	4	2	no	—
145	C₂²×D₄₇	—	4	2	no	—
146	C₂²×D₄₇	—	4	2	no	—
147	C₂²×D₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
160	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	2	1	no	—
168	C₂×Dic₄₇	—	2	1	no	—
169	C₂×Dic₄₇	—	2	1	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	—	2	1	no	—
172	C₂×Dic₄₇	—	2	1	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
177	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
178	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
179	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
180	C₂×Dic₄₇	#135	1	2	yes	—
181	D₁₈₈	—	2	4	no	—
182	D₁₈₈	—	2	4	no	—
183	D₁₈₈	—	4	2	no	—
184	D₁₈₈	—	4	2	no	—
185	C₄×D₄₇	—	4	16	no	—
186	C₈×C₄₇	—	4	1	no	—
187	C₈×C₄₇	#117	1	4	yes	complemented
188	C₄₇⋊C₈	—	2	2	no	—
189	C₄₇⋊C₈	—	4	1	no	—
190	#22807	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₄₇	#547	1	1	yes	characteristic
193	C₂²×C₄₇	#550	1	1	yes	characteristic
194	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
196	C₂²×C₄₇	#576	1	1	yes	characteristic
197	C₂²×C₄₇	#578	1	1	yes	characteristic
198	C₂×D₄₇	—	4	4	no	—
199	C₂×D₄₇	—	4	4	no	—
200	C₂×D₄₇	—	4	4	no	—
201	C₂×D₄₇	—	8	2	no	—
202	C₂×D₄₇	—	8	2	no	—
203	C₂×D₄₇	—	8	2	no	—
204	C₂×D₄₇	—	8	2	no	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	4	1	no	—
207	C₄×C₄₇	—	4	4	no	—
208	C₄×C₄₇	—	8	2	no	—
209	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
210	C₄×C₄₇	#520	1	1	yes	characteristic
211	C₄×C₄₇	#555	1	1	yes	characteristic
212	C₄×C₄₇	#556	1	1	yes	characteristic
213	Dic₄₇	—	2	2	no	—
214	Dic₄₇	—	2	2	no	—
215	Dic₄₇	—	4	1	no	—
216	Dic₄₇	—	8	2	no	—
217	Dic₄₇	C₄×D₈	1	4	yes	—
218	C₂×C₄×D₈	—	47	1	no	—
219	#2354	—	47	2	no	—
220	#1970	—	47	1	no	—
221	#1970	—	47	1	no	—
222	#1925	—	47	2	no	—
223	#1925	—	47	2	no	—
224	#1845	—	47	1	no	—
225	#1802	—	47	2	no	—
226	C₄×#107	—	47	1	no	—
227	C₄×#107	D₄₇	1	1	yes	characteristic, complemented
228	C₈×C₄⋊C₄	—	47	1	no	—
229	C₂×C₄₇	#2354	1	1	yes	characteristic
230	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
231	C₂×C₄₇	#2951	1	1	yes	characteristic
232	C₂×C₄₇	#3334	1	1	yes	characteristic
233	C₂×C₄₇	#3341	1	1	yes	characteristic
234	C₂×C₄₇	#3391	1	1	yes	characteristic
235	C₂×C₄₇	#3393	1	1	yes	characteristic
236	D₄₇	—	8	4	no	—
237	C₂²×D₈	—	47	1	no	—
238	C₂×C₄×D₄	—	47	2	no	—
239	C₂×#117	—	94	2	no	—
240	C₄×D₈	—	47	8	no	—
241	C₂×#107	—	47	1	no	—
242	C₂×#107	—	47	2	no	—
243	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
244	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
245	C₂×C₄⋊C₈	—	47	1	no	—
246	C₂×#102	—	47	2	no	—
247	C₂×#102	—	47	2	no	—
248	C₂×#102	—	47	2	no	—
249	C₂×C₄×C₈	—	47	1	no	—
250	C₂×C₄×C₈	—	47	1	no	—
251	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
252	#390	—	47	2	no	—
253	#390	—	47	2	no	—
254	#388	—	94	2	no	—
255	#388	—	94	2	no	—
256	#384	—	47	2	no	—
257	#380	—	94	2	no	—
258	C₄×C₄⋊C₄	—	47	1	no	—
259	C₄×C₄⋊C₄	—	47	2	no	—
260	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
261	#340	—	47	2	no	—
262	#340	C₂×D₄₇	1	2	yes	—
263	#336	—	47	1	no	—
264	#336	—	47	1	no	—
265	C₄₇	#22807	1	1	yes	characteristic, complemented, Sylow
266	C₂²×D₄	—	47	2	no	—
267	C₂³×C₄	—	94	2	no	—
268	C₂×D₈	—	47	4	no	—
269	C₂×D₈	—	94	2	no	—
270	C₂×D₈	—	94	2	no	—
271	C₂²×C₈	—	47	1	no	—
272	C₂²×C₈	—	47	1	no	—
273	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
274	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
275	C₄×D₄	—	47	8	no	—
276	C₄×D₄	—	94	4	no	—
277	#117	—	188	8	no	—
278	C₂×C₄⋊C₄	—	47	1	no	—
279	C₂×C₄⋊C₄	—	47	1	no	—
280	C₂×C₄⋊C₄	—	47	2	no	—
281	C₂×C₄⋊C₄	—	94	2	no	—
282	C₂×C₄⋊C₄	—	94	2	no	—
283	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
285	C₂×C₂²⋊C₄	—	94	2	no	—
286	C₂×C₂²⋊C₄	—	94	2	no	—
287	C₂×C₂²⋊C₄	—	94	2	no	—
288	C₂×C₂²⋊C₄	—	94	2	no	—
289	C₂×C₂²⋊C₄	—	94	2	no	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	—	47	1	no	—
292	C₂×C₄²	—	47	1	no	—
293	C₂×C₄²	—	94	2	no	—
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	#107	—	2	2	no	—
296	#107	—	94	2	no	—
297	#107	—	188	2	no	—
298	#107	C₄×D₄₇	1	4	yes	—
299	C₄⋊C₈	—	94	2	no	—
300	#102	—	47	8	no	—
301	#102	—	188	2	no	—
302	#102	—	188	2	no	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	47	4	no	—
305	C₄×C₈	—	94	2	no	—
306	#95	—	2	2	no	—
307	#95	—	47	1	no	—
308	#95	—	47	1	no	—
309	#95	—	94	2	no	—
310	C₂⁴	—	94	2	no	—
311	C₂×D₄	—	47	4	no	—
312	C₂×D₄	—	94	2	no	—
313	C₂×D₄	—	94	2	no	—
314	C₂×D₄	—	94	2	no	—
315	C₂×D₄	—	94	2	no	—
316	C₂×D₄	—	94	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	47	1	no	—
320	C₂²×C₄	—	47	1	no	—
321	C₂²×C₄	—	47	1	no	—
322	C₂²×C₄	—	47	1	no	—
323	C₂²×C₄	—	94	8	no	—
324	C₂²×C₄	—	94	2	no	—
325	C₂²×C₄	—	188	4	no	—
326	C₂²×C₄	—	188	4	no	—
327	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
328	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
329	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
330	D₈	—	94	8	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	47	2	no	—
335	C₂×C₈	—	94	1	no	—
336	C₂×C₈	—	94	1	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	94	1	no	—
340	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
341	C₂×C₈	#10625350	1	2	yes	—
342	C₂×C₈	#10625350	1	2	yes	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	47	4	no	—
347	C₄⋊C₄	—	94	2	no	—
348	C₄⋊C₄	—	94	2	no	—
349	C₄⋊C₄	—	94	2	no	—
350	C₄⋊C₄	—	376	2	no	—
351	C₄⋊C₄	—	188	4	no	—
352	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
353	C₂²⋊C₄	—	94	8	no	—
354	C₂²⋊C₄	—	376	2	no	—
355	C₂²⋊C₄	—	376	2	no	—
356	C₂²⋊C₄	—	188	4	no	—
357	C₂²⋊C₄	—	188	4	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	4	no	—
361	C₄²	—	47	2	no	—
362	C₄²	—	47	2	no	—
363	C₄²	—	94	1	no	—
364	C₄²	—	94	1	no	—
365	C₄²	—	188	4	no	—
366	C₂³	—	94	4	no	—
367	C₂³	—	188	2	no	—
368	C₂³	—	188	2	no	—
369	C₂³	—	188	2	no	—
370	C₂³	—	188	2	no	—
371	C₂³	—	188	2	no	—
372	C₂³	—	188	2	no	—
373	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
374	D₄	—	94	4	no	—
375	D₄	—	94	4	no	—
376	D₄	—	188	2	no	—
377	D₄	—	188	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	47	2	no	—
390	C₂×C₄	—	47	2	no	—
391	C₂×C₄	—	47	2	no	—
392	C₂×C₄	—	47	2	no	—
393	C₂×C₄	—	47	2	no	—
394	C₂×C₄	—	94	1	no	—
395	C₂×C₄	—	94	1	no	—
396	C₂×C₄	—	94	1	no	—
397	C₂×C₄	—	94	1	no	—
398	C₂×C₄	—	94	1	no	—
399	C₂×C₄	—	94	1	no	—
400	C₂×C₄	—	94	1	no	—
401	C₂×C₄	—	188	16	no	—
402	C₂×C₄	—	188	2	no	—
403	C₂×C₄	—	188	2	no	—
404	C₂×C₄	—	188	2	no	—
405	C₂×C₄	D₈×D₄₇	1	2	yes	—
406	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
407	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
409	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
410	C₂×C₄	#13094070	1	1	yes	characteristic
411	C₂×C₄	#13094072	1	1	yes	characteristic
412	C₈	—	4	1	no	—
413	C₈	—	94	2	no	—
414	C₈	—	188	1	no	—
415	C₈	#13093981	1	4	yes	complemented
416	C₂²	—	376	2	no	—
417	C₂²	—	376	2	no	—
418	C₂²	—	376	2	no	—
419	C₂²	—	376	2	no	—
420	C₂²	—	188	4	no	—
421	C₂²	—	188	4	no	—
422	C₂²	—	188	4	no	—
423	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
424	C₂²	#15689774	1	1	yes	characteristic
425	C₂²	#15689794	1	1	yes	characteristic
426	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
427	C₂²	#135×D₄₇	1	1	yes	characteristic
428	C₂²	#15689925	1	1	yes	characteristic
429	C₂²	#15689936	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	2	no	—
434	C₄	—	47	4	no	—
435	C₄	—	94	2	no	—
436	C₄	—	94	2	no	—
437	C₄	—	376	2	no	—
438	C₄	—	188	1	no	—
439	C₄	C₂×#13093981	1	1	yes	characteristic
440	C₄	#15689605	1	1	yes	characteristic
441	C₄	#15689836	1	1	yes	characteristic
442	C₄	#15689845	1	1	yes	characteristic
443	C₂	—	376	4	no	—
444	C₂	#20246333	1	1	yes	characteristic
445	C₂	C₄×D₈×D₄₇	1	1	yes	characteristic
446	C₂	#20252263	1	1	yes	characteristic
447	C₂	#20255733	1	1	yes	characteristic
448	C₂	#20255808	1	1	yes	characteristic
449	C₂	#20256362	1	1	yes	characteristic
450	C₂	#20256376	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#107×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₃₇₆	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#107	D₄₇
hypocenter	C₄₇	#22807
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
2. #20246333	C₂	semidirect
5. #20244008	C₂	semidirect
6. #20244006	C₂	semidirect
7. #20243546	C₂	semidirect
8. #20243387	C₂	semidirect
9. #107×Dic₄₇	C₂	semidirect
10. C₈×Dic₄₇⋊C₄	C₂	semidirect
11. C₄×#107×C₄₇	C₂	semidirect
15. #15689205	C₄	semidirect
127. Dic₄₇⋊C₄	D₈	semidirect
187. C₈×C₄₇	#117	semidirect
227. C₄×#107	D₄₇	semidirect
265. C₄₇	#22807	semidirect
415. C₈	#13093981	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689205	2
#20246333	2
#20244254	2
#20244252	2
#20244008	2
#20244006	2
#20243546	2
#20243387	2
#107×Dic₄₇	2
C₈×Dic₄₇⋊C₄	2
C₄×#107×C₄₇	2
#22807	47