Subgroups — #26233945

Order 12032.

778 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689160	C₂	1	1	yes	maximal, characteristic
2	#20246280	C₂	1	2	yes	maximal
3	#20244122	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243969	C₂	1	2	yes	maximal, complemented
5	#20243963	C₂	1	2	yes	maximal, complemented
6	#20243481	C₂	1	2	yes	maximal
7	#20243414	C₂	1	1	yes	maximal, characteristic
8	#107×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	C₂×#13093982	C₂²	1	2	yes	—
14	#15689160	C₄	1	8	yes	complemented
15	C₂×#13093958	C₂²	1	1	yes	characteristic
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093955	C₂²	1	2	yes	—
18	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
20	#15689022	C₂²	1	2	yes	—
21	#15689015	—	2	2	no	—
22	#15689013	—	2	2	no	—
23	#15688990	—	2	2	no	—
24	#15688980	C₂²	1	2	yes	—
25	C₄⋊C₄×Dic₄₇	—	2	2	no	—
26	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
27	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
28	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
29	#15688886	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
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	C₄₇×#389	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
41	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂×C₈×D₄₇	—	2	2	no	—
44	C₂×C₈×D₄₇	—	2	2	no	—
45	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
46	#13093982	—	2	4	no	—
47	#13093982	C₂×C₄	1	8	yes	—
48	C₂×C₄⋊Dic₄₇	—	2	2	no	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
52	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
53	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
54	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	—	2	2	no	—
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	#13093958	—	2	2	no	—
60	#13093958	C₂×C₄	1	4	yes	—
61	#13093955	C₂×C₄	1	8	yes	—
62	(C₂×D₄₇)⋊C₈	—	2	2	no	—
63	C₈×Dic₄₇	—	2	2	no	—
64	C₄₇⋊#95	—	2	2	no	—
65	C₄₇⋊#95	—	2	2	no	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₄₇⋊#95	D₄	1	1	yes	characteristic
69	C₄₇⋊#95	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	#107×C₄₇	—	2	2	no	—
77	#107×C₄₇	C₂×C₄	1	4	yes	—
78	C₄×C₈×C₄₇	—	2	2	no	—
79	#95×C₄₇	—	2	2	no	—
80	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
86	C₂²×Dic₄₇	—	2	2	no	—
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×D₄₇	—	2	1	no	—
92	C₂×C₄×D₄₇	—	2	1	no	—
93	C₂×C₄×D₄₇	—	2	1	no	—
94	C₂×C₄×D₄₇	—	2	1	no	—
95	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
96	C₂×C₄×D₄₇	#41	1	2	yes	—
97	C₂×C₈×C₄₇	—	2	1	no	—
98	C₂×C₈×C₄₇	—	2	1	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₄₇	#41	1	2	yes	—
102	C₂×C₈×C₄₇	#41	1	2	yes	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	2	no	—
105	C₄⋊C₄×C₄₇	—	2	2	no	—
106	C₄⋊C₄×C₄₇	—	4	4	no	—
107	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
108	C₄²×C₄₇	—	2	1	no	—
109	C₄²×C₄₇	—	2	1	no	—
110	(C₂×D₄₇)⋊C₄	—	2	8	no	—
111	(C₂×D₄₇)⋊C₄	—	2	2	no	—
112	(C₂×D₄₇)⋊C₄	—	2	2	no	—
113	(C₂×D₄₇)⋊C₄	—	8	2	no	—
114	C₄⋊Dic₄₇	—	2	2	no	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	—	2	2	no	—
117	C₄⋊Dic₄₇	—	4	4	no	—
118	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
119	C₄×Dic₄₇	—	2	1	no	—
120	C₄×Dic₄₇	—	2	1	no	—
121	C₄×Dic₄₇	—	2	8	no	—
122	C₄×Dic₄₇	—	8	2	no	—
123	C₄×Dic₄₇	—	8	2	no	—
124	C₂×C₄₇⋊C₈	—	2	1	no	—
125	C₂×C₄₇⋊C₈	—	2	1	no	—
126	C₂×C₄₇⋊C₈	—	2	1	no	—
127	C₂×C₄₇⋊C₈	—	2	1	no	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
130	C₈×D₄₇	—	2	8	no	—
131	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
132	C₂²×D₄₇	—	2	1	no	—
133	C₂²×D₄₇	—	2	1	no	—
134	C₂²×D₄₇	—	2	1	no	—
135	C₂²×D₄₇	—	2	1	no	—
136	C₂²×D₄₇	—	2	1	no	—
137	C₂²×D₄₇	—	2	1	no	—
138	C₂²×D₄₇	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	#135	1	2	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
156	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
157	C₂×Dic₄₇	—	2	1	no	—
158	C₂×Dic₄₇	—	2	1	no	—
159	C₂×Dic₄₇	—	2	1	no	—
160	C₂×Dic₄₇	—	2	1	no	—
161	C₂×Dic₄₇	—	2	4	no	—
162	C₂×Dic₄₇	—	2	1	no	—
163	C₂×Dic₄₇	—	2	1	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
171	C₂×Dic₄₇	#135	1	2	yes	—
172	C₄×D₄₇	—	2	2	no	—
173	C₄×D₄₇	—	2	2	no	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	2	2	no	—
176	C₈×C₄₇	—	4	1	no	—
177	C₈×C₄₇	#117	1	4	yes	—
178	C₄₇⋊C₈	—	2	2	no	—
179	C₄₇⋊C₈	—	4	1	no	—
180	#22614	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
182	C₂²×C₄₇	#547	1	1	yes	characteristic
183	C₂²×C₄₇	#547	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
186	C₂²×C₄₇	#576	1	1	yes	characteristic
187	C₂²×C₄₇	#578	1	1	yes	characteristic
188	C₂×D₄₇	—	2	2	no	—
189	C₂×D₄₇	—	2	2	no	—
190	C₂×D₄₇	—	2	2	no	—
191	C₂×D₄₇	—	4	1	no	—
192	C₂×D₄₇	—	4	1	no	—
193	C₂×D₄₇	—	4	1	no	—
194	C₂×D₄₇	—	4	1	no	—
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	—	4	1	no	—
197	C₄×C₄₇	—	4	4	no	—
198	C₄×C₄₇	—	8	2	no	—
199	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
200	C₄×C₄₇	#519	1	1	yes	characteristic
201	C₄×C₄₇	#552	1	1	yes	characteristic
202	C₄×C₄₇	#552	1	1	yes	characteristic
203	Dic₄₇	—	2	2	no	—
204	Dic₄₇	—	2	2	no	—
205	Dic₄₇	—	4	1	no	—
206	Dic₄₇	—	4	4	no	—
207	Dic₄₇	—	8	2	no	—
208	C₂×#427	—	47	1	no	—
209	#2347	—	47	2	no	—
210	#1942	—	47	1	no	—
211	#1942	D₄₇	1	1	yes	characteristic, complemented
212	#1919	—	47	2	no	—
213	#1919	—	47	2	no	—
214	#1825	—	47	2	no	—
215	#1808	—	47	1	no	—
216	C₄×#107	—	47	1	no	—
217	C₄×#107	—	47	1	no	—
218	C₈×C₂²⋊C₄	—	47	1	no	—
219	C₂×C₄₇	#2344	1	1	yes	characteristic
220	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
221	C₂×C₄₇	#2951	1	1	yes	characteristic
222	C₂×C₄₇	#3339	1	1	yes	characteristic
223	C₂×C₄₇	#3339	1	1	yes	characteristic
224	C₂×C₄₇	#3342	1	1	yes	characteristic
225	C₂×C₄₇	#3342	1	1	yes	characteristic
226	D₄₇	—	4	2	no	—
227	C₂³×C₈	—	47	1	no	—
228	C₂×#117	—	47	2	no	—
229	#427	—	47	8	no	—
230	C₂×#107	—	47	1	no	—
231	C₂×#107	—	47	1	no	—
232	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
233	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
234	C₂×#106	—	47	2	no	—
235	C₂×C₂²⋊C₈	—	47	1	no	—
236	C₂×C₄×C₈	—	47	1	no	—
237	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
238	#389	—	47	2	no	—
239	#389	C₂×D₄₇	1	2	yes	—
240	#388	—	94	2	no	—
241	#388	—	94	2	no	—
242	#383	—	94	2	no	—
243	#380	—	47	2	no	—
244	C₄×C₄⋊C₄	—	47	2	no	—
245	C₄×C₄⋊C₄	—	47	2	no	—
246	C₄×C₄⋊C₄	—	94	2	no	—
247	C₄×C₂²⋊C₄	—	47	1	no	—
248	#340	—	47	2	no	—
249	#340	—	47	2	no	—
250	#340	—	47	2	no	—
251	#340	—	47	2	no	—
252	#340	C₂×D₄₇	1	2	yes	—
253	#336	—	47	1	no	—
254	#336	—	47	1	no	—
255	C₄₇	#22614	1	1	yes	characteristic, complemented, Sylow
256	C₂³×C₄	—	47	1	no	—
257	C₂²×C₈	—	47	1	no	—
258	C₂²×C₈	—	47	4	no	—
259	C₂²×C₈	—	47	1	no	—
260	C₂²×C₈	—	94	2	no	—
261	C₂²×C₈	—	94	2	no	—
262	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
263	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
264	#117	—	47	8	no	—
265	#117	—	94	4	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	47	2	no	—
268	C₂×C₄⋊C₄	—	47	2	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
272	C₂×C₂²⋊C₄	—	47	1	no	—
273	C₂×C₂²⋊C₄	—	47	1	no	—
274	C₂×C₂²⋊C₄	—	94	2	no	—
275	C₂×C₂²⋊C₄	—	94	2	no	—
276	C₂×C₄²	—	47	1	no	—
277	C₂×C₄²	—	94	2	no	—
278	C₂×C₄²	—	94	2	no	—
279	C₂×C₄²	—	94	2	no	—
280	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
281	#107	—	2	2	no	—
282	#107	—	47	4	no	—
283	#107	—	94	2	no	—
284	#107	C₄×D₄₇	1	4	yes	—
285	#106	—	47	8	no	—
286	C₂²⋊C₈	—	94	2	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	94	2	no	—
289	#95	—	2	2	no	—
290	#95	—	47	1	no	—
291	#95	—	47	1	no	—
292	#95	—	94	2	no	—
293	#95	—	94	2	no	—
294	#95	—	94	2	no	—
295	#95	—	94	2	no	—
296	C₂⁴	—	47	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	47	1	no	—
300	C₂²×C₄	—	47	1	no	—
301	C₂²×C₄	—	47	2	no	—
302	C₂²×C₄	—	47	2	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	94	1	no	—
305	C₂²×C₄	—	94	1	no	—
306	C₂²×C₄	—	94	1	no	—
307	C₂²×C₄	—	94	1	no	—
308	C₂²×C₄	—	94	2	no	—
309	C₂²×C₄	—	94	2	no	—
310	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
312	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	47	2	no	—
317	C₂×C₈	—	94	1	no	—
318	C₂×C₈	—	94	1	no	—
319	C₂×C₈	—	94	8	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	—	94	1	no	—
322	C₂×C₈	—	94	1	no	—
323	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
324	C₂×C₈	#10625352	1	2	yes	—
325	C₂×C₈	#10625354	1	2	yes	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	47	4	no	—
331	C₄⋊C₄	—	94	2	no	—
332	C₄⋊C₄	—	94	2	no	—
333	C₄⋊C₄	—	94	2	no	—
334	C₄⋊C₄	—	188	4	no	—
335	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
336	C₂²⋊C₄	—	94	2	no	—
337	C₂²⋊C₄	—	94	8	no	—
338	C₂²⋊C₄	—	94	2	no	—
339	C₂²⋊C₄	—	376	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	94	8	no	—
343	C₄²	—	94	1	no	—
344	C₄²	—	94	1	no	—
345	C₄²	—	376	2	no	—
346	C₄²	—	376	2	no	—
347	C₂³	—	47	2	no	—
348	C₂³	—	94	1	no	—
349	C₂³	—	94	1	no	—
350	C₂³	—	94	1	no	—
351	C₂³	—	94	1	no	—
352	C₂³	—	94	1	no	—
353	C₂³	—	94	1	no	—
354	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	47	2	no	—
367	C₂×C₄	—	47	2	no	—
368	C₂×C₄	—	94	1	no	—
369	C₂×C₄	—	94	1	no	—
370	C₂×C₄	—	94	1	no	—
371	C₂×C₄	—	94	1	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	94	2	no	—
376	C₂×C₄	—	94	1	no	—
377	C₂×C₄	—	94	4	no	—
378	C₂×C₄	—	94	1	no	—
379	C₂×C₄	—	94	1	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	2	no	—
382	C₂×C₄	—	188	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	—	188	2	no	—
385	C₂×C₄	#13094043	1	2	yes	—
386	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
387	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
388	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
389	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
390	C₂×C₄	#13094071	1	1	yes	characteristic
391	C₂×C₄	#13094072	1	1	yes	characteristic
392	C₈	—	4	1	no	—
393	C₈	—	94	2	no	—
394	C₈	—	188	1	no	—
395	C₈	#13093982	1	4	yes	—
396	C₂²	—	94	2	no	—
397	C₂²	—	94	2	no	—
398	C₂²	—	94	2	no	—
399	C₂²	—	188	1	no	—
400	C₂²	—	188	1	no	—
401	C₂²	—	188	1	no	—
402	C₂²	—	188	1	no	—
403	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
404	C₂²	#15689773	1	1	yes	characteristic
405	C₂²	#15689776	1	1	yes	characteristic
406	C₂²	#135×D₄₇	1	1	yes	characteristic
407	C₂²	C₂×#13094043	1	1	yes	characteristic
408	C₂²	#15689925	1	1	yes	characteristic
409	C₂²	#15689936	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	4	no	—
413	C₄	—	8	2	no	—
414	C₄	—	94	2	no	—
415	C₄	—	94	2	no	—
416	C₄	—	376	2	no	—
417	C₄	—	188	1	no	—
418	C₄	—	188	4	no	—
419	C₄	C₂×#13093982	1	1	yes	characteristic
420	C₄	#15689599	1	1	yes	characteristic
421	C₄	#15689807	1	1	yes	characteristic
422	C₄	#15689811	1	1	yes	characteristic
423	C₂	—	188	2	no	—
424	C₂	#20246256	1	1	yes	characteristic
425	C₂	C₄×#13094043	1	1	yes	characteristic
426	C₂	#20252263	1	1	yes	characteristic
427	C₂	#20255789	1	1	yes	characteristic
428	C₂	#20255793	1	1	yes	characteristic
429	C₂	#20255815	1	1	yes	characteristic
430	C₂	#20255818	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1942	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1942	D₄₇
hypocenter	C₄₇	#22614
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1942

Complements

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

N	H ≅ G/N	type
3. #20244122	C₂	semidirect
4. #20243969	C₂	semidirect
5. #20243963	C₂	semidirect
8. #107×Dic₄₇	C₂	semidirect
9. C₄×#13093958	C₂	semidirect
11. C₄₇×#1942	C₂	semidirect
14. #15689160	C₄	semidirect
211. #1942	D₄₇	semidirect
255. C₄₇	#22614	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689160	2
#20246280	2
#20244122	2
#20243969	2
#20243963	2
#20243481	2
#20243414	2
#107×Dic₄₇	2
C₄×#13093958	2
C₈×(C₂×D₄₇)⋊C₄	2
C₄₇×#1942	2
#22614	47