Subgroups — #26233926

Order 12032.

822 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#107×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20246261	C₂	1	2	yes	maximal
3	#20244121	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244119	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243980	C₂	1	2	yes	maximal, complemented
6	#20243978	C₂	1	2	yes	maximal, complemented
7	#20243477	C₂	1	2	yes	maximal
8	#20243414	C₂	1	1	yes	maximal, characteristic
9	#107×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄×#107×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
14	C₂×#13093958	C₂²	1	1	yes	characteristic
15	C₂×#13093958	C₂²	1	1	yes	characteristic
16	C₂×#13093957	C₂²	1	2	yes	—
17	#107×D₄₇	C₄	1	8	yes	complemented
18	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
20	#15689021	C₂²	1	2	yes	—
21	#15689019	C₂²	1	2	yes	—
22	#15689007	—	2	2	no	—
23	#15689005	—	2	2	no	—
24	#15688982	—	2	2	no	—
25	#15688980	C₂²	1	2	yes	—
26	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
27	C₄×(C₂×D₄₇)⋊C₄	—	2	2	no	—
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	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₂²×C₄×D₄₇	—	2	2	no	—
41	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂×C₈×D₄₇	—	2	2	no	—
45	C₂×C₈×D₄₇	—	2	2	no	—
46	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×Dic₄₇⋊C₄	—	2	2	no	—
50	C₂×Dic₄₇⋊C₄	—	2	2	no	—
51	C₂×Dic₄₇⋊C₄	—	2	2	no	—
52	C₄⋊C₄×D₄₇	—	2	4	no	—
53	C₄⋊C₄×D₄₇	C₂×C₄	1	8	yes	—
54	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
55	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
56	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
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	#13093957	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	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₇	—	2	2	no	—
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	—	2	8	no	—
96	C₂×C₄×D₄₇	—	8	2	no	—
97	C₂×C₄×D₄₇	—	8	2	no	—
98	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
99	C₂×C₄×D₄₇	#41	1	2	yes	—
100	C₂×C₈×C₄₇	—	2	1	no	—
101	C₂×C₈×C₄₇	—	2	1	no	—
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₄₇	#41	1	2	yes	—
105	C₂×C₈×C₄₇	#41	1	2	yes	—
106	C₄⋊C₄×C₄₇	—	2	2	no	—
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
110	C₄²×C₄₇	—	2	1	no	—
111	C₄²×C₄₇	—	2	1	no	—
112	C₄²×C₄₇	—	8	2	no	—
113	(C₂×D₄₇)⋊C₄	—	2	2	no	—
114	(C₂×D₄₇)⋊C₄	—	4	4	no	—
115	(C₂×D₄₇)⋊C₄	Q₁₆	1	4	yes	—
116	C₄⋊Dic₄₇	—	2	2	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
120	Dic₄₇⋊C₄	—	2	8	no	—
121	Dic₄₇⋊C₄	—	8	2	no	—
122	Dic₄₇⋊C₄	—	8	2	no	—
123	C₄×Dic₄₇	—	2	1	no	—
124	C₄×Dic₄₇	—	2	1	no	—
125	C₄×Dic₄₇	—	8	2	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	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
132	C₈×D₄₇	—	2	8	no	—
133	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄₇	C₂×Q₁₆	1	2	yes	—
140	C₂²×D₄₇	#135	1	2	yes	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	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	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
158	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
159	C₂×Dic₄₇	—	2	1	no	—
160	C₂×Dic₄₇	—	2	1	no	—
161	C₂×Dic₄₇	—	2	1	no	—
162	C₂×Dic₄₇	—	2	1	no	—
163	C₂×Dic₄₇	—	2	4	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
173	C₂×Dic₄₇	C₂×Q₁₆	1	2	yes	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	2	2	no	—
176	C₄×D₄₇	—	2	2	no	—
177	C₄×D₄₇	—	2	2	no	—
178	C₄×D₄₇	—	8	8	no	—
179	C₈×C₄₇	—	4	1	no	—
180	C₈×C₄₇	#117	1	4	yes	—
181	C₄₇⋊C₈	—	2	2	no	—
182	C₄₇⋊C₈	—	4	1	no	—
183	#22612	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂²×C₄₇	#547	1	1	yes	characteristic
186	C₂²×C₄₇	#547	1	1	yes	characteristic
187	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
189	C₂²×C₄₇	#576	1	1	yes	characteristic
190	C₂²×C₄₇	#576	1	1	yes	characteristic
191	C₂×D₄₇	—	2	2	no	—
192	C₂×D₄₇	—	2	2	no	—
193	C₂×D₄₇	—	2	2	no	—
194	C₂×D₄₇	—	2	2	no	—
195	C₂×D₄₇	—	2	2	no	—
196	C₂×D₄₇	—	2	2	no	—
197	C₂×D₄₇	C₄×Q₁₆	1	4	yes	—
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	4	1	no	—
200	C₄×C₄₇	—	4	4	no	—
201	C₄×C₄₇	—	8	2	no	—
202	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
203	C₄×C₄₇	#519	1	1	yes	characteristic
204	C₄×C₄₇	#552	1	1	yes	characteristic
205	C₄×C₄₇	#552	1	1	yes	characteristic
206	Dic₄₇	—	2	2	no	—
207	Dic₄₇	—	2	2	no	—
208	Dic₄₇	—	4	1	no	—
209	Dic₄₇	—	4	4	no	—
210	Dic₄₇	—	8	2	no	—
211	C₂²×#107	—	47	1	no	—
212	#2345	—	47	2	no	—
213	#1942	—	47	1	no	—
214	#1942	—	47	1	no	—
215	#1921	—	47	2	no	—
216	#1921	—	47	2	no	—
217	#1824	—	47	2	no	—
218	#1808	—	47	1	no	—
219	C₄×#107	—	47	1	no	—
220	C₄×#107	D₄₇	1	1	yes	characteristic, complemented
221	C₈×C₂²⋊C₄	—	47	1	no	—
222	C₂×C₄₇	#2344	1	1	yes	characteristic
223	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
224	C₂×C₄₇	#2948	1	1	yes	characteristic
225	C₂×C₄₇	#3338	1	1	yes	characteristic
226	C₂×C₄₇	#3338	1	1	yes	characteristic
227	C₂×C₄₇	#3339	1	1	yes	characteristic
228	C₂×C₄₇	#3339	1	1	yes	characteristic
229	D₄₇	—	2	4	no	—
230	C₂³×C₈	—	47	1	no	—
231	C₂²×C₄⋊C₄	—	47	2	no	—
232	C₂×#107	—	47	1	no	—
233	C₂×#107	—	47	2	no	—
234	C₂×#107	—	47	8	no	—
235	C₂×#107	—	47	1	no	—
236	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
237	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
238	C₂×C₂²⋊C₈	—	47	1	no	—
239	C₂×C₄×C₈	—	47	1	no	—
240	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
241	#389	—	47	2	no	—
242	#389	—	47	2	no	—
243	#387	—	94	2	no	—
244	#387	—	94	2	no	—
245	#380	—	47	2	no	—
246	#380	—	94	2	no	—
247	C₄×C₄⋊C₄	—	47	2	no	—
248	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
249	C₄×C₂²⋊C₄	—	47	1	no	—
250	C₄×C₂²⋊C₄	—	94	2	no	—
251	#340	—	47	2	no	—
252	#340	—	47	2	no	—
253	#340	—	47	2	no	—
254	#340	—	47	2	no	—
255	#340	C₂×D₄₇	1	2	yes	—
256	#336	—	47	1	no	—
257	#336	—	47	1	no	—
258	C₄₇	#22612	1	1	yes	characteristic, complemented, Sylow
259	C₂³×C₄	—	47	1	no	—
260	C₂³×C₄	—	94	2	no	—
261	C₂²×C₈	—	47	1	no	—
262	C₂²×C₈	—	47	4	no	—
263	C₂²×C₈	—	47	1	no	—
264	C₂²×C₈	—	94	2	no	—
265	C₂²×C₈	—	94	2	no	—
266	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
268	C₂×C₄⋊C₄	—	47	2	no	—
269	C₂×C₄⋊C₄	—	47	8	no	—
270	C₂×C₄⋊C₄	—	47	2	no	—
271	C₂×C₄⋊C₄	—	94	4	no	—
272	C₂×C₄⋊C₄	—	94	2	no	—
273	C₂×C₄⋊C₄	—	94	2	no	—
274	C₂×C₄⋊C₄	—	94	2	no	—
275	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
276	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
277	C₂×C₂²⋊C₄	—	47	1	no	—
278	C₂×C₂²⋊C₄	—	47	1	no	—
279	C₂×C₂²⋊C₄	—	94	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	—	47	1	no	—
282	C₂×C₄²	—	94	2	no	—
283	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
284	#107	—	2	2	no	—
285	#107	—	47	4	no	—
286	#107	—	47	8	no	—
287	#107	—	94	2	no	—
288	#107	C₄×D₄₇	1	4	yes	—
289	C₂²⋊C₈	—	94	2	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	94	2	no	—
292	#95	—	2	2	no	—
293	#95	—	47	1	no	—
294	#95	—	47	1	no	—
295	#95	—	94	2	no	—
296	#95	—	94	2	no	—
297	#95	—	94	2	no	—
298	#95	—	94	2	no	—
299	C₂⁴	—	47	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	2	no	—
305	C₂²×C₄	—	47	2	no	—
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	94	8	no	—
308	C₂²×C₄	—	94	1	no	—
309	C₂²×C₄	—	94	1	no	—
310	C₂²×C₄	—	94	1	no	—
311	C₂²×C₄	—	94	1	no	—
312	C₂²×C₄	—	94	2	no	—
313	C₂²×C₄	—	94	2	no	—
314	C₂²×C₄	—	376	2	no	—
315	C₂²×C₄	—	376	2	no	—
316	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
318	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	47	2	no	—
323	C₂×C₈	—	94	1	no	—
324	C₂×C₈	—	94	1	no	—
325	C₂×C₈	—	94	8	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	—	94	1	no	—
328	C₂×C₈	—	94	1	no	—
329	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
330	C₂×C₈	#10625350	1	2	yes	—
331	C₂×C₈	#10625350	1	2	yes	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	47	4	no	—
336	C₄⋊C₄	—	94	8	no	—
337	C₄⋊C₄	—	94	2	no	—
338	C₄⋊C₄	—	94	2	no	—
339	C₄⋊C₄	—	94	2	no	—
340	C₄⋊C₄	—	376	2	no	—
341	C₄⋊C₄	—	376	2	no	—
342	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
343	C₂²⋊C₄	—	47	4	no	—
344	C₂²⋊C₄	—	94	2	no	—
345	C₂²⋊C₄	—	188	4	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	8	2	no	—
349	C₄²	—	94	1	no	—
350	C₄²	—	94	1	no	—
351	C₄²	—	376	2	no	—
352	C₂³	—	47	2	no	—
353	C₂³	—	47	2	no	—
354	C₂³	—	47	2	no	—
355	C₂³	—	94	1	no	—
356	C₂³	—	94	1	no	—
357	C₂³	—	94	1	no	—
358	C₂³	—	94	1	no	—
359	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	47	2	no	—
372	C₂×C₄	—	47	2	no	—
373	C₂×C₄	—	94	1	no	—
374	C₂×C₄	—	94	1	no	—
375	C₂×C₄	—	94	1	no	—
376	C₂×C₄	—	94	1	no	—
377	C₂×C₄	—	94	2	no	—
378	C₂×C₄	—	94	2	no	—
379	C₂×C₄	—	94	2	no	—
380	C₂×C₄	—	94	2	no	—
381	C₂×C₄	—	94	1	no	—
382	C₂×C₄	—	94	4	no	—
383	C₂×C₄	—	94	1	no	—
384	C₂×C₄	—	94	1	no	—
385	C₂×C₄	—	376	8	no	—
386	C₂×C₄	—	188	2	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	—	188	2	no	—
391	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
392	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
395	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
396	C₂×C₄	#13094071	1	1	yes	characteristic
397	C₂×C₄	#13094072	1	1	yes	characteristic
398	C₈	—	4	1	no	—
399	C₈	—	94	2	no	—
400	C₈	—	188	1	no	—
401	C₈	#13093981	1	4	yes	—
402	C₂²	—	47	4	no	—
403	C₂²	—	94	2	no	—
404	C₂²	—	94	2	no	—
405	C₂²	—	94	2	no	—
406	C₂²	—	94	2	no	—
407	C₂²	—	94	2	no	—
408	C₂²	—	94	2	no	—
409	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
410	C₂²	#15689774	1	1	yes	characteristic
411	C₂²	#15689778	1	1	yes	characteristic
412	C₂²	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
413	C₂²	#135×D₄₇	1	1	yes	characteristic
414	C₂²	#15689924	1	1	yes	characteristic
415	C₂²	#15689925	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	4	no	—
419	C₄	—	8	2	no	—
420	C₄	—	94	2	no	—
421	C₄	—	94	2	no	—
422	C₄	—	376	2	no	—
423	C₄	—	188	1	no	—
424	C₄	—	188	4	no	—
425	C₄	C₂×#13093981	1	1	yes	characteristic
426	C₄	#15689599	1	1	yes	characteristic
427	C₄	#15689812	1	1	yes	characteristic
428	C₄	#15689814	1	1	yes	characteristic
429	C₂	—	94	4	no	—
430	C₂	#20246253	1	1	yes	characteristic
431	C₂	C₄×Q₁₆×D₄₇	1	1	yes	characteristic
432	C₂	#20252235	1	1	yes	characteristic
433	C₂	#20255778	1	1	yes	characteristic
434	C₂	#20255782	1	1	yes	characteristic
435	C₂	#20255790	1	1	yes	characteristic
436	C₂	#20255792	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	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#107	D₄₇
hypocenter	C₄₇	#22612
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
3. #20244121	C₂	semidirect
4. #20244119	C₂	semidirect
5. #20243980	C₂	semidirect
6. #20243978	C₂	semidirect
9. #107×Dic₄₇	C₂	semidirect
11. C₄×#107×C₄₇	C₂	semidirect
17. #107×D₄₇	C₄	semidirect
220. C₄×#107	D₄₇	semidirect
258. C₄₇	#22612	semidirect

Maximal subgroups

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

subgroup	index
C₂×#107×D₄₇	2
#20246261	2
#20244121	2
#20244119	2
#20243980	2
#20243978	2
#20243477	2
#20243414	2
#107×Dic₄₇	2
C₈×(C₂×D₄₇)⋊C₄	2
C₄×#107×C₄₇	2
#22612	47