Subgroups — #26188312

Order 12032.

644 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253963	C₂	1	1	yes	maximal, characteristic
2	#20252455	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252454	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242299	C₂	1	2	yes	maximal, complemented
5	#20242220	C₂	1	2	yes	maximal, complemented
6	#20242214	C₂	1	2	yes	maximal, complemented
7	#20242209	C₂	1	2	yes	maximal, complemented
8	#20242134	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241806	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689673	C₂²	1	1	yes	characteristic
13	#15689526	C₄	1	1	yes	characteristic
14	#15689499	C₄	1	1	yes	characteristic
15	#15689471	C₄	1	1	yes	characteristic
16	#15689469	C₄	1	1	yes	characteristic
17	#15689357	C₄	1	2	yes	—
18	#15689357	C₄	1	2	yes	—
19	C₄×#10625334	C₂²	1	2	yes	—
20	C₄×#10625334	C₂²	1	2	yes	—
21	#15689202	—	2	1	no	—
22	#15689201	—	2	1	no	—
23	#15689201	C₂²	1	2	yes	—
24	#15689200	C₂²	1	2	yes	—
25	C₈×D₁₈₈	—	2	1	no	—
26	D₄×C₄₇⋊C₈	—	2	1	no	—
27	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
28	#15689188	C₂²	1	2	yes	—
29	#15689176	C₂²	1	1	yes	characteristic
30	#15689176	C₂²	1	1	yes	characteristic
31	#15689090	—	2	2	no	—
32	#15689088	—	2	2	no	—
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	#15688875	C₂²	1	1	yes	characteristic
35	#15688875	C₂²	1	1	yes	characteristic
36	#15688873	C₂²	1	1	yes	characteristic
37	#15688873	C₂²	1	1	yes	characteristic
38	#15688852	C₂²	1	2	yes	—
39	#15688852	C₂²	1	2	yes	—
40	#15688845	C₂²	1	2	yes	—
41	#15688845	C₂²	1	2	yes	—
42	C₄₇×#532	C₂²	1	1	yes	characteristic
43	C₄₇×#431	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
46	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
47	C₂×#10625350	—	2	1	no	—
48	C₂×#10625334	C₂×C₄	1	2	yes	—
49	C₂×#10625334	C₂×C₄	1	2	yes	—
50	C₂×#10625329	—	2	2	no	—
51	C₂×#10625324	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	—	2	2	no	—
53	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₄₇	—	2	2	no	—
56	#13094024	C₂×C₄	1	1	yes	characteristic
57	#13094021	C₂×C₄	1	1	yes	characteristic
58	#13094012	—	2	1	no	—
59	#13093998	—	2	1	no	—
60	#13093998	C₂×C₄	1	2	yes	—
61	C₄×D₁₈₈	—	2	1	no	—
62	C₄×D₁₈₈	C₂³	1	2	yes	—
63	#13093957	C₂×C₄	1	2	yes	—
64	#13093957	C₂×C₄	1	2	yes	—
65	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
66	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	#13093945	C₂×C₄	1	2	yes	—
70	#13093945	C₂×C₄	1	2	yes	—
71	#13093944	C₂×C₄	1	2	yes	—
72	#13093944	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
75	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
76	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
77	(C₂×D₄₇)⋊C₈	—	2	2	no	—
78	(C₂×D₄₇)⋊C₈	—	2	2	no	—
79	C₄×C₄₇⋊C₈	—	2	1	no	—
80	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
83	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
84	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
85	C₂×#41×C₄₇	—	2	1	no	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
88	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
89	#124×C₄₇	—	2	1	no	—
90	#121×C₄₇	—	2	1	no	—
91	#121×C₄₇	C₂×C₄	1	2	yes	—
92	C₄×D₄×C₄₇	—	2	1	no	—
93	C₄×D₄×C₄₇	C₂³	1	2	yes	—
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₂²⋊C₈×C₄₇	—	2	1	no	—
98	#97×C₄₇	—	2	1	no	—
99	C₄×C₈×C₄₇	—	2	1	no	—
100	C₄×C₈×C₄₇	C₂³	1	2	yes	—
101	#41×C₄₇	—	8	1	no	—
102	#41×C₄₇	—	8	1	no	—
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	—	2	2	no	—
105	C₂×D₄×C₄₇	—	2	1	no	—
106	C₂×D₄×C₄₇	—	2	1	no	—
107	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₇	—	2	2	no	—
113	#10625350	—	8	1	no	—
114	#10625350	—	8	1	no	—
115	C₂×D₁₈₈	—	2	1	no	—
116	C₂×D₁₈₈	—	2	1	no	—
117	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₄₇	—	2	2	no	—
119	C₂×Dic₉₄	—	2	1	no	—
120	M₁₆×C₄₇	—	4	2	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	1	no	—
125	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂²⋊C₄×C₄₇	—	2	2	no	—
127	C₂²⋊C₄×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₇	#41	1	1	yes	characteristic
131	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
132	#10625334	—	2	4	no	—
133	#10625334	—	4	2	no	—
134	(C₂×D₄₇)⋊C₄	—	2	2	no	—
135	(C₂×D₄₇)⋊C₄	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	1	no	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
138	#10625329	—	8	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	4	1	no	—
143	C₂×C₄₇⋊C₈	—	8	2	no	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
149	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
150	#10625324	—	8	2	no	—
151	C₈×D₄₇	—	8	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
154	C₂²×D₄₇	—	2	2	no	—
155	Q₈×C₄₇	—	8	1	no	—
156	D₄×C₄₇	—	2	2	no	—
157	D₄×C₄₇	—	2	2	no	—
158	D₄×C₄₇	—	4	2	no	—
159	D₄×C₄₇	—	8	1	no	—
160	D₄×C₄₇	—	8	2	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂²⋊D₄₇	—	8	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	D₁₈₈	—	2	2	no	—
178	D₁₈₈	—	2	2	no	—
179	D₁₈₈	—	4	2	no	—
180	D₁₈₈	—	8	1	no	—
181	C₄×D₄₇	—	4	2	no	—
182	C₄×D₄₇	—	4	2	no	—
183	Dic₉₄	—	8	1	no	—
184	C₈×C₄₇	—	4	2	no	—
185	C₈×C₄₇	—	4	1	no	—
186	C₈×C₄₇	—	4	1	no	—
187	C₄₇⋊C₈	—	2	1	no	—
188	C₄₇⋊C₈	—	2	1	no	—
189	C₄₇⋊C₈	—	2	1	no	—
190	C₄₇⋊C₈	—	2	2	no	—
191	C₄₇⋊C₈	—	2	2	no	—
192	C₄₇⋊C₈	—	4	1	no	—
193	C₄₇⋊C₈	—	4	1	no	—
194	C₄₇⋊C₈	#131	1	2	yes	—
195	#18091	—	47	1	no	maximal, Sylow
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	—	4	2	no	—
202	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂×D₄₇	—	4	2	no	—
204	C₂×D₄₇	—	4	2	no	—
205	C₂×D₄₇	—	4	2	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	4	2	no	—
210	C₄×C₄₇	#444	1	2	yes	—
211	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
212	C₄×C₄₇	#568	1	1	yes	characteristic
213	C₄×C₄₇	#576	1	1	yes	characteristic
214	C₄×C₄₇	#576	1	1	yes	characteristic
215	Dic₄₇	—	4	2	no	—
216	#3169	—	47	1	no	—
217	#2979	—	47	1	no	—
218	#2979	—	47	1	no	—
219	#1594	—	47	2	no	—
220	#1581	—	47	2	no	—
221	#1581	—	47	2	no	—
222	#1580	—	47	2	no	—
223	#1564	—	47	1	no	—
224	#1484	—	47	1	no	—
225	#1484	D₄₇	1	1	yes	characteristic, complemented
226	#1451	—	47	1	no	—
227	C₂×C₄₇	—	4	1	no	—
228	C₂×C₄₇	—	8	2	no	—
229	C₂×C₄₇	#2935	1	1	yes	characteristic
230	C₂×C₄₇	#2948	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
232	D₄₇	—	8	2	no	—
233	#532	—	47	1	no	—
234	#532	C₂×D₄₇	1	1	yes	characteristic
235	#500	—	47	1	no	—
236	#493	—	47	1	no	—
237	#486	—	47	1	no	—
238	#486	—	47	1	no	—
239	#466	—	47	2	no	—
240	#466	—	47	2	no	—
241	C₄×D₈	—	47	2	no	—
242	C₄×D₈	—	47	2	no	—
243	#436	—	47	2	no	—
244	#436	—	47	2	no	—
245	#436	—	94	1	no	—
246	#436	—	94	1	no	—
247	C₈×D₄	—	47	2	no	—
248	C₈×D₄	—	47	2	no	—
249	C₈×D₄	—	94	1	no	—
250	C₈×D₄	—	94	1	no	—
251	#431	—	47	1	no	—
252	#431	—	47	1	no	—
253	#431	C₂×D₄₇	1	1	yes	characteristic
254	#408	—	94	2	no	—
255	#408	—	94	2	no	—
256	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
257	C₂×C₄×C₈	—	47	1	no	—
258	#335	—	47	1	no	—
259	#335	—	47	1	no	—
260	#334	—	47	1	no	—
261	#334	—	47	1	no	—
262	D₄⋊C₈	—	47	2	no	—
263	D₄⋊C₈	—	47	2	no	—
264	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
265	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
266	#322	—	47	2	no	—
267	#322	—	47	2	no	—
268	C₄₇	#18091	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	94	1	no	—
271	C₂×D₈	—	47	2	no	—
272	C₂×D₈	—	47	2	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	94	2	no	—
275	C₂×M₁₆	—	94	2	no	—
276	C₂²×C₈	—	47	1	no	—
277	C₂²×C₈	—	47	1	no	—
278	C₂²×C₈	—	94	2	no	—
279	C₂²×C₈	—	94	2	no	—
280	C₄⋊Q₈	—	47	1	no	—
281	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
282	#127	—	47	1	no	—
283	#127	C₄×D₄₇	1	1	yes	characteristic
284	#124	—	2	1	no	—
285	#124	—	94	1	no	—
286	#121	—	2	1	no	—
287	#121	—	47	2	no	—
288	#121	—	94	1	no	—
289	#121	C₄×D₄₇	1	2	yes	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	47	2	no	—
292	C₄×D₄	—	94	1	no	—
293	C₄×D₄	C₂²×D₄₇	1	2	yes	—
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	#107	—	47	2	no	—
296	#107	—	47	2	no	—
297	C₄⋊C₈	—	47	1	no	—
298	C₄⋊C₈	—	47	1	no	—
299	C₄⋊C₈	—	47	1	no	—
300	C₄⋊C₈	—	47	1	no	—
301	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
302	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
303	#102	—	47	2	no	—
304	#102	—	47	2	no	—
305	#102	—	47	2	no	—
306	#102	—	47	2	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	47	2	no	—
309	C₂²⋊C₈	—	94	2	no	—
310	C₂²⋊C₈	—	94	2	no	—
311	C₂²⋊C₈	—	94	2	no	—
312	C₂²⋊C₈	—	94	2	no	—
313	C₂²⋊C₈	—	94	1	no	—
314	#97	—	2	1	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	47	1	no	—
317	C₄×C₈	—	47	1	no	—
318	C₄×C₈	—	47	1	no	—
319	C₄×C₈	—	47	1	no	—
320	C₄×C₈	—	47	2	no	—
321	C₄×C₈	—	94	1	no	—
322	C₄×C₈	C₂²×D₄₇	1	2	yes	—
323	#41	—	8	1	no	—
324	#41	—	8	1	no	—
325	#41	—	376	1	no	—
326	#41	—	376	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	94	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	47	2	no	—
333	C₂×D₄	—	94	2	no	—
334	C₂×D₄	—	94	1	no	—
335	C₂×D₄	—	94	1	no	—
336	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	94	2	no	—
339	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
341	C₂²×C₄	#10625352	1	1	yes	characteristic
342	D₈	—	94	4	no	—
343	D₈	—	188	2	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	376	2	no	—
346	M₁₆	—	376	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	47	1	no	—
351	C₂×C₈	—	47	1	no	—
352	C₂×C₈	—	47	1	no	—
353	C₂×C₈	—	47	1	no	—
354	C₂×C₈	—	47	2	no	—
355	C₂×C₈	—	47	2	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	94	1	no	—
358	C₂×C₈	—	94	1	no	—
359	C₂×C₈	—	376	2	no	—
360	C₂×C₈	—	376	2	no	—
361	C₂×C₈	—	188	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	47	2	no	—
364	C₄⋊C₄	—	94	1	no	—
365	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	94	2	no	—
369	C₂²⋊C₄	—	94	2	no	—
370	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
371	C₄²	D₄×D₄₇	1	1	yes	characteristic
372	C₄²	#10625352	1	1	yes	characteristic
373	C₄²	C₂³×D₄₇	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	—	94	2	no	—
376	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
377	Q₈	—	8	1	no	—
378	Q₈	—	376	1	no	—
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	8	1	no	—
383	D₄	—	8	2	no	—
384	D₄	—	94	2	no	—
385	D₄	—	94	2	no	—
386	D₄	—	376	1	no	—
387	D₄	—	376	2	no	—
388	D₄	—	188	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	94	2	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
401	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
402	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
406	C₈	—	4	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₈	—	47	2	no	—
410	C₈	—	94	1	no	—
411	C₈	—	94	1	no	—
412	C₈	—	94	1	no	—
413	C₈	—	94	2	no	—
414	C₈	—	94	2	no	—
415	C₈	—	188	1	no	—
416	C₈	—	188	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	188	2	no	—
424	C₂²	—	188	2	no	—
425	C₂²	—	188	2	no	—
426	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	2	no	—
431	C₄	—	188	2	no	—
432	C₄	#15689242	1	2	yes	—
433	C₄	#131×D₄₇	1	1	yes	characteristic
434	C₄	#15689888	1	1	yes	characteristic
435	C₄	#15689927	1	1	yes	characteristic
436	C₄	#15689927	1	1	yes	characteristic
437	C₂	—	4	1	no	—
438	C₂	—	8	2	no	—
439	C₂	—	376	2	no	—
440	C₂	#20252128	1	1	yes	characteristic
441	C₂	#20252236	1	1	yes	characteristic
442	C₂	C₂×#15689242	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1484	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253963	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1484	D₄₇
hypocenter	C₄₇	#18091
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1484

Complements

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

N	H ≅ G/N	type
2. #20252455	C₂	semidirect
3. #20252454	C₂	semidirect
4. #20242299	C₂	semidirect
5. #20242220	C₂	semidirect
6. #20242214	C₂	semidirect
7. #20242209	C₂	semidirect
8. #20242134	C₂	semidirect
9. #20241806	C₂	semidirect
10. #20241675	C₂	semidirect
11. C₄₇×#1484	C₂	semidirect
225. #1484	D₄₇	semidirect
268. C₄₇	#18091	semidirect

Maximal subgroups

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

subgroup	index
#20253963	2
#20252455	2
#20252454	2
#20242299	2
#20242220	2
#20242214	2
#20242209	2
#20242134	2
#20241806	2
#20241675	2
C₄₇×#1484	2
#18091	47