Subgroups — #26226823

Order 12032.

806 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689175	C₂	1	1	yes	maximal, characteristic
2	#20245793	C₂	1	1	yes	maximal, characteristic
3	#20245784	C₂	1	1	yes	maximal, characteristic
4	#20244152	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244146	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244144	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243588	C₂	1	2	yes	maximal
8	#20243586	C₂	1	2	yes	maximal
9	#20243549	C₂	1	2	yes	maximal, complemented
10	#20243517	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13093982	C₂²	1	2	yes	—
13	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
14	#15689175	C₄	1	8	yes	complemented
15	C₂×#13093957	C₂²	1	2	yes	—
16	C₂×#13093957	C₂²	1	2	yes	—
17	C₂×#13093956	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
20	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
21	#15688993	C₂²	1	1	yes	characteristic
22	#15688990	—	2	1	no	—
23	#15688988	C₂²	1	1	yes	characteristic
24	#15688988	C₂²	1	1	yes	characteristic
25	#15688988	C₂²	1	2	yes	—
26	#15688985	—	2	1	no	—
27	#15688980	—	2	1	no	—
28	#15688980	—	2	1	no	—
29	#15688980	C₂²	1	1	yes	characteristic
30	#15688980	C₂²	1	1	yes	characteristic
31	C₄⋊C₄×Dic₄₇	—	2	1	no	—
32	C₄⋊C₄×Dic₄₇	—	2	1	no	—
33	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
34	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
35	#15688969	—	2	1	no	—
36	#15688886	C₂²	1	2	yes	—
37	#15688885	C₂²	1	2	yes	—
38	#15688885	C₂²	1	2	yes	—
39	C₂×#106×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#384	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#340	C₂²	1	2	yes	—
44	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	#13093982	—	4	2	no	—
49	#13093982	—	4	2	no	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	C₂×C₄⋊Dic₄₇	—	2	1	no	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
56	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
57	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
58	C₂×C₄×Dic₄₇	—	2	1	no	—
59	C₂×C₄×Dic₄₇	—	2	2	no	—
60	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	C₄²×D₄₇	C₂×C₄	1	4	yes	—
64	C₄²×D₄₇	Q₈	1	4	yes	—
65	#13093957	—	4	2	no	—
66	#13093957	—	4	2	no	—
67	#13093956	—	4	2	no	—
68	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
69	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	—
70	C₈×Dic₄₇	C₂×C₄	1	8	yes	—
71	C₄₇⋊#95	—	2	1	no	—
72	C₄₇⋊#95	—	2	1	no	—
73	C₄₇⋊#95	—	2	1	no	—
74	C₄₇⋊#95	—	2	1	no	—
75	C₄₇⋊#95	—	2	1	no	—
76	C₄₇⋊#95	—	2	1	no	—
77	C₄₇⋊#95	—	2	1	no	—
78	C₄₇⋊#95	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	#106×C₄₇	—	4	2	no	—
89	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
90	#95×C₄₇	—	2	1	no	—
91	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	—	2	1	no	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	2	1	no	—
99	C₂²×Dic₄₇	—	2	1	no	—
100	C₂²×Dic₄₇	—	2	2	no	—
101	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	—	2	2	no	—
106	C₂×C₄×D₄₇	—	2	1	no	—
107	C₂×C₄×D₄₇	—	2	1	no	—
108	C₂×C₄×D₄₇	—	2	1	no	—
109	C₂×C₄×D₄₇	—	2	1	no	—
110	C₂×C₄×D₄₇	—	4	1	no	—
111	C₂×C₄×D₄₇	—	4	1	no	—
112	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
113	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
114	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
115	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	—	2	1	no	—
125	C₄⋊C₄×C₄₇	—	4	2	no	—
126	C₄⋊C₄×C₄₇	—	4	2	no	—
127	C₄²×C₄₇	—	4	2	no	—
128	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
129	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
130	(C₂×D₄₇)⋊C₄	—	4	2	no	—
131	(C₂×D₄₇)⋊C₄	—	4	2	no	—
132	(C₂×D₄₇)⋊C₄	—	4	4	no	—
133	C₄⋊Dic₄₇	—	2	1	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	1	no	—
138	C₄⋊Dic₄₇	—	2	1	no	—
139	C₄⋊Dic₄₇	—	4	2	no	—
140	C₄⋊Dic₄₇	—	4	2	no	—
141	C₄×Dic₄₇	—	4	4	no	—
142	C₄×Dic₄₇	—	4	2	no	—
143	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
144	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
145	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
146	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
150	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	C₂²×D₄₇	—	2	1	no	—
152	C₂²×D₄₇	—	2	1	no	—
153	C₂²×D₄₇	—	2	1	no	—
154	C₂²×D₄₇	—	2	1	no	—
155	C₂²×D₄₇	—	2	1	no	—
156	C₂²×D₄₇	—	2	1	no	—
157	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₄₇	#135	1	2	yes	—
172	C₂×C₄×C₄₇	#135	1	2	yes	—
173	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
178	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	1	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	C₂×Dic₄₇	—	2	1	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	—	4	1	no	—
187	C₂×Dic₄₇	—	4	1	no	—
188	C₂×Dic₄₇	—	4	1	no	—
189	C₂×Dic₄₇	—	4	1	no	—
190	C₂×Dic₄₇	—	4	2	no	—
191	C₂×Dic₄₇	—	4	2	no	—
192	C₂×Dic₄₇	—	4	1	no	—
193	C₂×Dic₄₇	—	4	1	no	—
194	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
195	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
196	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
197	C₄×D₄₇	—	2	2	no	—
198	C₄×D₄₇	—	2	2	no	—
199	C₄×D₄₇	—	2	2	no	—
200	C₄×D₄₇	—	2	2	no	—
201	C₄×D₄₇	—	2	8	no	—
202	C₄×D₄₇	—	4	4	no	—
203	C₈×C₄₇	—	2	4	no	—
204	C₄₇⋊C₈	—	2	4	no	—
205	#21985	—	47	1	no	maximal, Sylow
206	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
207	C₂²×C₄₇	#535	1	1	yes	characteristic
208	C₂²×C₄₇	#536	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
211	C₂²×C₄₇	#575	1	1	yes	characteristic
212	C₂²×C₄₇	#575	1	1	yes	characteristic
213	C₂×D₄₇	—	2	2	no	—
214	C₂×D₄₇	—	2	2	no	—
215	C₂×D₄₇	—	2	2	no	—
216	C₂×D₄₇	—	4	1	no	—
217	C₂×D₄₇	—	4	1	no	—
218	C₂×D₄₇	—	4	1	no	—
219	C₂×D₄₇	—	4	1	no	—
220	C₄×C₄₇	—	2	2	no	—
221	C₄×C₄₇	—	8	1	no	—
222	C₄×C₄₇	—	8	2	no	—
223	C₄×C₄₇	—	8	1	no	—
224	C₄×C₄₇	#427	1	4	yes	—
225	C₄×C₄₇	#520	1	1	yes	characteristic
226	C₄×C₄₇	#520	1	1	yes	characteristic
227	C₄×C₄₇	#544	1	1	yes	characteristic
228	C₄×C₄₇	#544	1	1	yes	characteristic
229	Dic₄₇	—	2	2	no	—
230	Dic₄₇	—	2	2	no	—
231	Dic₄₇	—	2	2	no	—
232	Dic₄₇	—	8	2	no	—
233	Dic₄₇	—	8	1	no	—
234	Dic₄₇	—	8	1	no	—
235	C₂×#431	—	47	1	no	—
236	#2285	—	47	1	no	—
237	#2283	—	47	1	no	—
238	#1948	—	47	1	no	—
239	#1948	D₄₇	1	1	yes	characteristic, complemented
240	#1947	—	47	1	no	—
241	#1947	—	47	1	no	—
242	#1854	—	47	2	no	—
243	#1854	—	47	2	no	—
244	#1846	—	47	2	no	—
245	#1835	—	47	2	no	—
246	C₂×C₄₇	#2317	1	1	yes	characteristic
247	C₂×C₄₇	C₂×#427	1	1	yes	characteristic
248	C₂×C₄₇	#2911	1	1	yes	characteristic
249	C₂×C₄₇	#3212	1	1	yes	characteristic
250	C₂×C₄₇	#3212	1	1	yes	characteristic
251	C₂×C₄₇	#3233	1	1	yes	characteristic
252	C₂×C₄₇	#3233	1	1	yes	characteristic
253	D₄₇	—	4	2	no	—
254	C₂×#117	—	47	2	no	—
255	C₂²×C₄²	—	47	1	no	—
256	#431	—	47	8	no	—
257	C₂×#107	—	47	2	no	—
258	C₂×#107	—	47	2	no	—
259	C₂×#106	—	47	2	no	—
260	C₂×#106	C₂×D₄₇	1	2	yes	—
261	C₂×C₄⋊C₈	—	47	1	no	—
262	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
263	C₂×C₂²⋊C₈	—	47	2	no	—
264	C₂×C₄×C₈	—	47	2	no	—
265	#384	—	47	1	no	—
266	#384	C₂×D₄₇	1	1	yes	characteristic
267	#383	—	94	1	no	—
268	#382	—	47	1	no	—
269	#382	—	47	2	no	—
270	#382	—	47	1	no	—
271	#381	—	94	1	no	—
272	#380	—	47	1	no	—
273	#380	—	47	1	no	—
274	#380	—	94	1	no	—
275	#380	—	94	1	no	—
276	C₄×C₄⋊C₄	—	47	1	no	—
277	C₄×C₄⋊C₄	—	94	1	no	—
278	C₄×C₄⋊C₄	—	94	1	no	—
279	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
280	C₄×C₂²⋊C₄	—	94	1	no	—
281	#376	—	94	1	no	—
282	#340	—	47	2	no	—
283	#340	—	47	2	no	—
284	#340	—	47	2	no	—
285	#340	C₂×D₄₇	1	2	yes	—
286	C₄₇	#21985	1	1	yes	characteristic, complemented, Sylow
287	C₂³×C₄	—	47	1	no	—
288	C₂³×C₄	—	47	1	no	—
289	C₂³×C₄	—	47	1	no	—
290	C₂²×C₈	—	47	2	no	—
291	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
292	#117	—	188	2	no	—
293	#117	—	188	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	47	2	no	—
297	C₂×C₄⋊C₄	—	47	1	no	—
298	C₂×C₄⋊C₄	—	47	1	no	—
299	C₂×C₄⋊C₄	—	94	1	no	—
300	C₂×C₄⋊C₄	—	94	1	no	—
301	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
302	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	94	2	no	—
305	C₂×C₂²⋊C₄	—	94	1	no	—
306	C₂×C₂²⋊C₄	—	94	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	47	1	no	—
309	C₂×C₄²	—	47	1	no	—
310	C₂×C₄²	—	47	1	no	—
311	C₂×C₄²	—	47	4	no	—
312	C₂×C₄²	—	47	4	no	—
313	C₂×C₄²	—	94	2	no	—
314	C₂×C₄²	—	94	1	no	—
315	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
316	#107	—	188	2	no	—
317	#107	—	188	2	no	—
318	#106	—	4	2	no	—
319	#106	—	188	2	no	—
320	C₄⋊C₈	—	47	4	no	—
321	C₄⋊C₈	C₄×D₄₇	1	4	yes	—
322	C₂²⋊C₈	—	47	8	no	—
323	C₄×C₈	—	47	8	no	—
324	#95	—	2	1	no	—
325	#95	—	94	1	no	—
326	#95	—	94	1	no	—
327	#95	—	94	1	no	—
328	#95	—	94	1	no	—
329	#95	—	94	1	no	—
330	#95	—	94	1	no	—
331	#95	—	94	2	no	—
332	#95	—	94	2	no	—
333	#95	—	94	1	no	—
334	C₂⁴	—	47	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	47	1	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	47	1	no	—
341	C₂²×C₄	—	47	4	no	—
342	C₂²×C₄	—	47	2	no	—
343	C₂²×C₄	—	47	2	no	—
344	C₂²×C₄	—	47	4	no	—
345	C₂²×C₄	—	94	2	no	—
346	C₂²×C₄	—	94	2	no	—
347	C₂²×C₄	—	94	1	no	—
348	C₂²×C₄	—	94	1	no	—
349	C₂²×C₄	—	94	1	no	—
350	C₂²×C₄	—	94	1	no	—
351	C₂²×C₄	—	94	1	no	—
352	C₂²×C₄	—	94	1	no	—
353	C₂²×C₄	—	94	2	no	—
354	C₂²×C₄	—	188	1	no	—
355	C₂²×C₄	—	188	1	no	—
356	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
357	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
358	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	47	4	no	—
362	C₂×C₈	—	94	2	no	—
363	C₂×C₈	—	94	2	no	—
364	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	94	1	no	—
374	C₄⋊C₄	—	94	2	no	—
375	C₄⋊C₄	—	94	1	no	—
376	C₄⋊C₄	—	94	2	no	—
377	C₄⋊C₄	—	94	1	no	—
378	C₄⋊C₄	—	94	1	no	—
379	C₄⋊C₄	—	188	2	no	—
380	C₄⋊C₄	—	188	2	no	—
381	C₂²⋊C₄	—	188	2	no	—
382	C₂²⋊C₄	—	188	2	no	—
383	C₂²⋊C₄	—	188	4	no	—
384	C₄²	—	4	2	no	—
385	C₄²	—	47	4	no	—
386	C₄²	—	47	4	no	—
387	C₄²	—	47	2	no	—
388	C₄²	—	47	2	no	—
389	C₄²	—	188	4	no	—
390	C₄²	—	188	2	no	—
391	C₄²	C₂×C₄×D₄₇	1	2	yes	—
392	C₄²	Q₈×D₄₇	1	2	yes	—
393	C₂³	—	47	2	no	—
394	C₂³	—	94	1	no	—
395	C₂³	—	94	1	no	—
396	C₂³	—	94	1	no	—
397	C₂³	—	94	1	no	—
398	C₂³	—	94	1	no	—
399	C₂³	—	94	1	no	—
400	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	47	2	no	—
413	C₂×C₄	—	47	2	no	—
414	C₂×C₄	—	47	2	no	—
415	C₂×C₄	—	94	1	no	—
416	C₂×C₄	—	94	1	no	—
417	C₂×C₄	—	94	1	no	—
418	C₂×C₄	—	94	1	no	—
419	C₂×C₄	—	94	1	no	—
420	C₂×C₄	—	94	1	no	—
421	C₂×C₄	—	94	2	no	—
422	C₂×C₄	—	94	2	no	—
423	C₂×C₄	—	94	2	no	—
424	C₂×C₄	—	94	2	no	—
425	C₂×C₄	—	94	8	no	—
426	C₂×C₄	—	188	4	no	—
427	C₂×C₄	—	188	1	no	—
428	C₂×C₄	—	188	1	no	—
429	C₂×C₄	—	188	2	no	—
430	C₂×C₄	—	188	1	no	—
431	C₂×C₄	—	188	1	no	—
432	C₂×C₄	—	188	2	no	—
433	C₂×C₄	—	188	2	no	—
434	C₂×C₄	—	188	1	no	—
435	C₂×C₄	—	188	1	no	—
436	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
437	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
438	C₂×C₄	#13094045	1	2	yes	—
439	C₂×C₄	#13094045	1	2	yes	—
440	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
441	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
442	C₂×C₄	#13094069	1	1	yes	characteristic
443	C₂×C₄	#13094070	1	1	yes	characteristic
444	C₂×C₄	#13094071	1	1	yes	characteristic
445	C₂×C₄	#13094072	1	1	yes	characteristic
446	C₈	—	2	4	no	—
447	C₈	—	94	4	no	—
448	C₂²	—	94	2	no	—
449	C₂²	—	94	2	no	—
450	C₂²	—	94	2	no	—
451	C₂²	—	188	1	no	—
452	C₂²	—	188	1	no	—
453	C₂²	—	188	1	no	—
454	C₂²	—	188	1	no	—
455	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
456	C₂²	#15689689	1	1	yes	characteristic
457	C₂²	#15689696	1	1	yes	characteristic
458	C₂²	C₂×#13094045	1	1	yes	characteristic
459	C₂²	C₂×#13094045	1	1	yes	characteristic
460	C₂²	#15689919	1	1	yes	characteristic
461	C₂²	#15689922	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	8	1	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	2	no	—
466	C₄	—	94	2	no	—
467	C₄	—	94	2	no	—
468	C₄	—	94	2	no	—
469	C₄	—	376	1	no	—
470	C₄	—	376	2	no	—
471	C₄	—	376	1	no	—
472	C₄	#15689158	1	4	yes	—
473	C₄	#15689602	1	1	yes	characteristic
474	C₄	#15689605	1	1	yes	characteristic
475	C₄	#15689750	1	1	yes	characteristic
476	C₄	#15689753	1	1	yes	characteristic
477	C₂	—	188	2	no	—
478	C₂	#20246010	1	1	yes	characteristic
479	C₂	C₂×#15689158	1	1	yes	characteristic
480	C₂	#20251975	1	1	yes	characteristic
481	C₂	#20254363	1	1	yes	characteristic
482	C₂	#20254368	1	1	yes	characteristic
483	C₂	#20254566	1	1	yes	characteristic
484	C₂	#20254571	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×#1948	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1948	D₄₇
hypocenter	C₄₇	#21985
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1948

Complements

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

N	H ≅ G/N	type
4. #20244152	C₂	semidirect
5. #20244146	C₂	semidirect
6. #20244144	C₂	semidirect
9. #20243549	C₂	semidirect
10. #20243517	C₂	semidirect
11. C₄₇×#1948	C₂	semidirect
14. #15689175	C₄	semidirect
239. #1948	D₄₇	semidirect
286. C₄₇	#21985	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689175	2
#20245793	2
#20245784	2
#20244152	2
#20244146	2
#20244144	2
#20243588	2
#20243586	2
#20243549	2
#20243517	2
C₄₇×#1948	2
#21985	47