Subgroups — #26275246

Order 12032.

714 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246335	C₂	1	1	yes	maximal, characteristic
2	#20244912	C₂	1	2	yes	maximal
3	#20244773	C₂	1	2	yes	maximal
4	#20244154	C₂	1	2	yes	maximal, complemented
5	#20244151	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243977	C₂	1	2	yes	maximal, complemented
8	#20243547	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243385	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093944	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#2571	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
13	C₂×#13093982	—	2	1	no	—
14	C₂×#13093957	C₂²	1	2	yes	—
15	C₂×#13093957	C₂²	1	2	yes	—
16	C₂×#13093955	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#13093944	C₂²	1	1	yes	characteristic
20	C₂×#13093944	C₂²	1	1	yes	characteristic
21	C₂×#13093944	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	#15689025	C₂²	1	2	yes	—
24	#15689015	—	2	2	no	—
25	#15688993	C₂²	1	1	yes	characteristic
26	#15688980	—	2	1	no	—
27	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
28	#15688885	C₂²	1	1	yes	characteristic
29	#15688885	C₂²	1	1	yes	characteristic
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688878	C₂²	1	2	yes	—
33	C₄₇×#400	—	2	2	no	—
34	C₄₇×#389	—	2	1	no	—
35	C₄₇×#389	C₂²	1	2	yes	—
36	C₄₇×#384	C₂²	1	1	yes	characteristic
37	C₄₇×#382	—	2	1	no	—
38	C₄₇×#382	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₄×D₁₈₈	—	2	2	no	—
47	C₄×D₁₈₈	Q₈	1	4	yes	—
48	#13093982	—	4	4	no	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
54	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
55	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	#13093957	—	2	4	no	—
58	#13093957	—	4	2	no	—
59	#13093955	—	4	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
62	#13093944	—	2	2	no	—
63	#13093944	—	2	2	no	—
64	#13093944	—	4	2	no	—
65	C₄×C₄₇⋊C₈	—	2	2	no	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₄₇	—	2	1	no	—
76	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	#95×C₄₇	—	2	1	no	—
79	#95×C₄₇	—	2	2	no	—
80	#95×C₄₇	—	2	2	no	—
81	#95×C₄₇	—	2	2	no	—
82	#95×C₄₇	D₄	1	2	yes	—
83	C₂³×D₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	1	no	—
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₄₇	—	2	1	no	—
93	C₂²×Dic₄₇	—	2	2	no	—
94	C₂×D₁₈₈	—	2	1	no	—
95	C₂×D₁₈₈	—	2	1	no	—
96	C₂×D₁₈₈	—	2	1	no	—
97	C₂×D₁₈₈	—	2	1	no	—
98	C₂×D₁₈₈	—	2	1	no	—
99	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
100	C₂×C₄×D₄₇	—	2	4	no	—
101	C₂×C₄×D₄₇	—	4	2	no	—
102	C₂×C₄×D₄₇	—	4	2	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	2	no	—
105	C₄⋊C₄×C₄₇	—	2	1	no	—
106	C₄⋊C₄×C₄₇	—	2	1	no	—
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	1	no	—
110	C₄⋊C₄×C₄₇	—	2	1	no	—
111	C₄⋊C₄×C₄₇	—	4	2	no	—
112	C₄⋊C₄×C₄₇	—	8	1	no	—
113	C₄⋊C₄×C₄₇	—	8	2	no	—
114	C₄²×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	4	2	no	—
117	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
118	C₄²×C₄₇	#41	1	2	yes	—
119	(C₂×D₄₇)⋊C₄	—	2	4	no	—
120	(C₂×D₄₇)⋊C₄	—	4	4	no	—
121	(C₂×D₄₇)⋊C₄	—	8	2	no	—
122	C₄⋊Dic₄₇	—	2	1	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	—	2	2	no	—
125	C₄⋊Dic₄₇	—	4	2	no	—
126	C₄⋊Dic₄₇	—	8	1	no	—
127	C₄⋊Dic₄₇	C₂×Q₈	1	2	yes	—
128	C₄×Dic₄₇	—	4	4	no	—
129	C₂×C₄₇⋊C₈	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	#41	1	2	yes	—
137	C₂×C₄₇⋊C₈	#41	1	2	yes	—
138	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	C₂²×D₄₇	—	2	2	no	—
140	C₂²×D₄₇	—	4	1	no	—
141	C₂²×D₄₇	—	4	1	no	—
142	C₂²×D₄₇	—	4	1	no	—
143	C₂²×D₄₇	—	4	1	no	—
144	C₂²×D₄₇	—	4	1	no	—
145	C₂²×D₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	4	1	no	—
155	C₂×C₄×C₄₇	—	4	1	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	1	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₄₇	#135	1	2	yes	—
166	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	4	1	no	—
175	C₂×Dic₄₇	—	4	1	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	D₁₈₈	—	2	2	no	—
180	D₁₈₈	—	2	2	no	—
181	D₁₈₈	—	4	1	no	—
182	D₁₈₈	—	4	1	no	—
183	C₄×D₄₇	—	4	8	no	—
184	C₄₇⋊C₈	—	2	2	no	—
185	C₄₇⋊C₈	—	2	2	no	—
186	C₄₇⋊C₈	—	4	2	no	—
187	#26087	—	47	1	no	maximal, Sylow
188	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
189	C₂²×C₄₇	#547	1	1	yes	characteristic
190	C₂²×C₄₇	#550	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂²×C₄₇	#576	1	1	yes	characteristic
194	C₂²×C₄₇	#578	1	1	yes	characteristic
195	C₂×D₄₇	—	4	2	no	—
196	C₂×D₄₇	—	4	2	no	—
197	C₂×D₄₇	—	4	2	no	—
198	C₂×D₄₇	—	8	1	no	—
199	C₂×D₄₇	—	8	1	no	—
200	C₂×D₄₇	—	8	1	no	—
201	C₂×D₄₇	—	8	1	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	4	2	no	—
204	C₄×C₄₇	—	4	2	no	—
205	C₄×C₄₇	—	8	1	no	—
206	C₄×C₄₇	—	8	1	no	—
207	C₄×C₄₇	—	8	2	no	—
208	C₄×C₄₇	#478	1	4	yes	—
209	C₄×C₄₇	#533	1	1	yes	characteristic
210	C₄×C₄₇	#544	1	1	yes	characteristic
211	C₄×C₄₇	#552	1	1	yes	characteristic
212	C₄×C₄₇	#553	1	1	yes	characteristic
213	Dic₄₇	—	4	2	no	—
214	Dic₄₇	—	8	2	no	—
215	#2571	D₄₇	1	1	yes	characteristic, complemented
216	#2354	—	47	1	no	—
217	#2092	—	47	2	no	—
218	#2067	—	47	2	no	—
219	#1949	—	47	2	no	—
220	#1948	—	47	1	no	—
221	#1939	—	47	1	no	—
222	#1921	—	47	2	no	—
223	#1845	—	47	1	no	—
224	#1802	—	47	1	no	—
225	C₄×#102	—	47	1	no	—
226	C₂×C₄₇	#2441	1	1	yes	characteristic
227	C₂×C₄₇	C₂×#478	1	1	yes	characteristic
228	C₂×C₄₇	#3083	1	1	yes	characteristic
229	C₂×C₄₇	#3341	1	1	yes	characteristic
230	C₂×C₄₇	#3353	1	1	yes	characteristic
231	C₂×C₄₇	#3393	1	1	yes	characteristic
232	C₂×C₄₇	#3399	1	1	yes	characteristic
233	D₄₇	—	8	2	no	—
234	C₂×C₄×D₄	—	47	1	no	—
235	C₂×#117	—	94	1	no	—
236	C₂×#107	—	47	2	no	—
237	C₂×#107	—	47	2	no	—
238	C₂×#106	—	47	2	no	—
239	C₂×C₄⋊C₈	—	47	1	no	—
240	C₂×C₄⋊C₈	—	47	2	no	—
241	C₂×#102	—	47	1	no	—
242	C₂×#102	—	47	1	no	—
243	C₂×#102	—	47	2	no	—
244	C₂×C₄×C₈	—	47	1	no	—
245	#400	—	2	2	no	—
246	#390	—	47	2	no	—
247	#389	—	2	1	no	—
248	#389	C₂×D₄₇	1	2	yes	—
249	#388	—	94	2	no	—
250	#384	—	47	1	no	—
251	#384	C₂×D₄₇	1	1	yes	characteristic
252	#382	—	2	1	no	—
253	#382	C₂×D₄₇	1	2	yes	—
254	#380	—	94	1	no	—
255	C₄×C₄⋊C₄	—	47	2	no	—
256	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
257	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
258	#340	—	47	2	no	—
259	#340	—	47	2	no	—
260	#340	—	47	1	no	—
261	#340	—	47	1	no	—
262	#336	—	47	2	no	—
263	C₄₇	#26087	1	1	yes	characteristic, complemented, Sylow
264	C₂²×D₄	—	47	1	no	—
265	C₂³×C₄	—	94	1	no	—
266	C₂²×C₈	—	47	1	no	—
267	C₂²×C₈	—	47	1	no	—
268	C₂²×C₈	—	47	2	no	—
269	C₄×D₄	—	47	4	no	—
270	C₄×D₄	—	94	2	no	—
271	#117	—	188	4	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	47	1	no	—
276	C₂×C₄⋊C₄	—	47	2	no	—
277	C₂×C₄⋊C₄	—	94	1	no	—
278	C₂×C₄⋊C₄	—	94	1	no	—
279	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
284	C₂×C₂²⋊C₄	—	94	1	no	—
285	C₂×C₂²⋊C₄	—	94	2	no	—
286	C₂×C₂²⋊C₄	—	94	2	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	94	2	no	—
289	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
290	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
291	#107	—	94	4	no	—
292	#107	—	188	2	no	—
293	#106	—	188	2	no	—
294	C₄⋊C₈	—	94	4	no	—
295	C₄⋊C₈	—	94	2	no	—
296	#102	—	94	2	no	—
297	#102	—	94	2	no	—
298	#102	—	188	2	no	—
299	C₄×C₈	—	94	2	no	—
300	#95	—	2	1	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	94	2	no	—
305	#95	C₂²⋊D₄₇	1	2	yes	—
306	C₂⁴	—	94	1	no	—
307	C₂×D₄	—	47	2	no	—
308	C₂×D₄	—	94	1	no	—
309	C₂×D₄	—	94	1	no	—
310	C₂×D₄	—	94	1	no	—
311	C₂×D₄	—	94	1	no	—
312	C₂×D₄	—	94	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	94	1	no	—
317	C₂²×C₄	—	94	4	no	—
318	C₂²×C₄	—	94	2	no	—
319	C₂²×C₄	—	188	2	no	—
320	C₂²×C₄	—	188	2	no	—
321	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
323	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
326	C₂×C₈	—	47	2	no	—
327	C₂×C₈	—	47	2	no	—
328	C₂×C₈	—	94	1	no	—
329	C₂×C₈	—	94	1	no	—
330	C₂×C₈	—	94	1	no	—
331	C₂×C₈	—	94	1	no	—
332	C₂×C₈	—	94	2	no	—
333	C₂×C₈	—	94	2	no	—
334	C₂×C₈	—	94	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	8	1	no	—
345	C₄⋊C₄	—	8	2	no	—
346	C₄⋊C₄	—	47	2	no	—
347	C₄⋊C₄	—	94	1	no	—
348	C₄⋊C₄	—	94	2	no	—
349	C₄⋊C₄	—	94	2	no	—
350	C₄⋊C₄	—	376	1	no	—
351	C₄⋊C₄	—	188	2	no	—
352	C₂²⋊C₄	—	94	4	no	—
353	C₂²⋊C₄	—	376	2	no	—
354	C₂²⋊C₄	—	188	4	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	4	2	no	—
358	C₄²	—	188	4	no	—
359	C₄²	Q₈×D₄₇	1	2	yes	—
360	C₄²	#10625354	1	2	yes	—
361	C₂³	—	94	2	no	—
362	C₂³	—	188	1	no	—
363	C₂³	—	188	1	no	—
364	C₂³	—	188	1	no	—
365	C₂³	—	188	1	no	—
366	C₂³	—	188	1	no	—
367	C₂³	—	188	1	no	—
368	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
369	D₄	—	94	2	no	—
370	D₄	—	94	2	no	—
371	D₄	—	188	1	no	—
372	D₄	—	188	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	188	2	no	—
392	C₂×C₄	—	188	2	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	—	188	1	no	—
395	C₂×C₄	—	188	1	no	—
396	C₂×C₄	—	188	8	no	—
397	C₂×C₄	#13094000	1	2	yes	—
398	C₂×C₄	#13094000	1	2	yes	—
399	C₂×C₄	#13094044	1	2	yes	—
400	C₂×C₄	#13094049	1	2	yes	—
401	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
402	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
403	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
405	C₂×C₄	#13094070	1	1	yes	characteristic
406	C₂×C₄	#13094071	1	1	yes	characteristic
407	C₈	—	94	2	no	—
408	C₈	—	94	2	no	—
409	C₈	—	188	2	no	—
410	C₂²	—	376	1	no	—
411	C₂²	—	376	1	no	—
412	C₂²	—	376	1	no	—
413	C₂²	—	376	1	no	—
414	C₂²	—	188	2	no	—
415	C₂²	—	188	2	no	—
416	C₂²	—	188	2	no	—
417	C₂²	C₂×#13094000	1	1	yes	characteristic
418	C₂²	#15689772	1	1	yes	characteristic
419	C₂²	#15689792	1	1	yes	characteristic
420	C₂²	C₂×#13094044	1	1	yes	characteristic
421	C₂²	C₂×#13094049	1	1	yes	characteristic
422	C₂²	#15689926	1	1	yes	characteristic
423	C₂²	#15689938	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	376	2	no	—
431	C₄	—	188	2	no	—
432	C₄	#15689420	1	4	yes	—
433	C₄	#15689679	1	1	yes	characteristic
434	C₄	#15689753	1	1	yes	characteristic
435	C₄	#15689811	1	1	yes	characteristic
436	C₄	#15689826	1	1	yes	characteristic
437	C₂	—	376	2	no	—
438	C₂	#20247097	1	1	yes	characteristic
439	C₂	C₂×#15689420	1	1	yes	characteristic
440	C₂	#20253235	1	1	yes	characteristic
441	C₂	#20255806	1	1	yes	characteristic
442	C₂	#20255966	1	1	yes	characteristic
443	C₂	#20256372	1	1	yes	characteristic
444	C₂	#20256426	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2571	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
hypercenter	#2571	D₄₇
hypocenter	C₄₇	#26087
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2571

Complements

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

N	H ≅ G/N	type
4. #20244154	C₂	semidirect
5. #20244151	C₂	semidirect
6. #20244107	C₂	semidirect
7. #20243977	C₂	semidirect
8. #20243547	C₂	semidirect
11. C₄₇×#2571	C₂	semidirect
215. #2571	D₄₇	semidirect
263. C₄₇	#26087	semidirect

Maximal subgroups

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

subgroup	index
#20246335	2
#20244912	2
#20244773	2
#20244154	2
#20244151	2
#20244107	2
#20243977	2
#20243547	2
#20243385	2
C₄×#13093944	2
C₄₇×#2571	2
#26087	47