Subgroups — #26223089

Order 12032.

906 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	C₂×#15689245	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252092	C₂	1	2	yes	maximal, complemented
3	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244282	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244142	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244094	C₂	1	2	yes	maximal, complemented
7	#20243837	C₂	1	2	yes	maximal, complemented
8	#20243426	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243274	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243228	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3050	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	2	yes	—
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	C₂×#13093983	C₂²	1	1	yes	characteristic
15	#15689245	—	2	4	no	—
16	#15689201	—	2	4	no	—
17	#15689195	—	2	4	no	—
18	C₂×#13093960	C₂²	1	1	yes	characteristic
19	C₂×#13093960	C₂²	1	1	yes	characteristic
20	#15689150	C₂²	1	2	yes	—
21	C₂×#13093951	C₂²	1	2	yes	—
22	C₂×#13093951	C₂²	1	2	yes	—
23	#15689090	C₂²	1	2	yes	—
24	#15689087	C₂²	1	2	yes	—
25	#15689079	C₂²	1	2	yes	—
26	#15689078	—	2	4	no	—
27	C₂×#13093934	C₂²	1	1	yes	characteristic
28	C₂×#13093934	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688888	C₂²	1	2	yes	—
32	#15688882	C₂²	1	2	yes	—
33	#15688882	C₂²	1	2	yes	—
34	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#525	C₂²	1	2	yes	—
37	C₄₇×#467	C₄	1	2	yes	complemented
38	C₄₇×#466	C₄	1	2	yes	complemented
39	C₄₇×#465	C₄	1	4	yes	complemented
40	C₄₇×#427	C₂²	1	1	yes	characteristic
41	C₄₇×#416	C₂²	1	2	yes	—
42	#13094031	—	2	4	no	—
43	#13094031	—	2	4	no	—
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625329	—	2	2	no	—
47	C₂×#10625329	D₄	1	4	yes	—
48	C₂×#10625329	C₂³	1	2	yes	—
49	C₂×#10625329	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	—	2	2	no	—
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	#13093983	—	2	2	no	—
54	#13093983	—	2	2	no	—
55	C₂×C₄⋊Dic₄₇	—	2	1	no	—
56	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
57	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	#13093960	—	2	2	no	—
60	#13093960	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
62	#13093951	—	2	4	no	—
63	#13093951	—	2	4	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
66	#13093935	—	2	2	no	—
67	#13093934	—	2	2	no	—
68	#13093934	D₄	1	4	yes	complemented
69	C₄×C₄₇⋊C₈	—	2	2	no	—
70	C₈×Dic₄₇	—	2	2	no	—
71	C₈×Dic₄₇	—	2	2	no	—
72	C₂×#41×C₄₇	C₂³	1	2	yes	—
73	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
74	#135×C₄₇	—	2	2	no	—
75	#135×C₄₇	—	2	2	no	—
76	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	—	2	2	no	—
80	C₂²×C₈×C₄₇	—	2	2	no	—
81	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
82	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	#123×C₄₇	—	2	2	no	—
86	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
87	#121×C₄₇	C₂×C₄	1	4	yes	—
88	#120×C₄₇	—	2	2	no	—
89	C₄×D₄×C₄₇	—	2	4	no	—
90	#117×C₄₇	C₂³	1	2	yes	—
91	#107×C₄₇	C₂×C₄	1	2	yes	—
92	#106×C₄₇	C₂×C₄	1	2	yes	—
93	#103×C₄₇	C₂×C₄	1	4	yes	—
94	#102×C₄₇	C₂×C₄	1	4	yes	—
95	C₂⁴×C₄₇	#41	1	1	yes	characteristic
96	#41×C₄₇	—	2	2	no	—
97	#41×C₄₇	—	2	2	no	—
98	#41×C₄₇	—	2	2	no	—
99	#41×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	4	no	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₇	—	2	1	no	—
114	C₂²×Dic₄₇	—	2	1	no	—
115	Q₁₆×C₄₇	—	2	2	no	—
116	SD₁₆×C₄₇	—	2	4	no	—
117	D₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	—	2	4	no	—
121	C₂×C₈×C₄₇	—	2	4	no	—
122	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₇	#41	1	2	yes	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
129	C₂²⋊C₄×C₄₇	—	2	4	no	—
130	C₂²⋊C₄×C₄₇	—	2	2	no	—
131	C₂²⋊C₄×C₄₇	—	2	4	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₂²⋊Dic₄₇	—	2	4	no	—
134	C₄⋊Dic₄₇	—	2	4	no	—
135	C₄×Dic₄₇	—	2	1	no	—
136	C₄×Dic₄₇	—	2	1	no	—
137	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
138	C₄×Dic₄₇	#41	1	2	yes	—
139	#10625329	—	2	8	no	—
140	#10625329	—	2	2	no	—
141	#10625329	—	2	2	no	—
142	#10625329	—	2	2	no	—
143	#10625329	—	2	2	no	—
144	#10625329	—	4	4	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	4	4	no	—
150	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
153	C₂×C₄₇⋊C₈	#41	1	2	yes	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	4	2	no	—
158	C₂³×C₄₇	C₄×D₄	1	2	yes	—
159	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
160	Q₈×C₄₇	—	2	2	no	—
161	Q₈×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	2	no	—
163	D₄×C₄₇	—	2	2	no	—
164	D₄×C₄₇	—	4	2	no	—
165	D₄×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	8	4	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	4	2	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	C₄×D₄	1	2	yes	—
190	C₈×C₄₇	C₄×D₄	1	2	yes	—
191	C₄₇⋊C₈	—	2	2	no	—
192	C₄₇⋊C₈	—	4	2	no	—
193	C₄₇⋊C₈	—	4	2	no	—
194	C₄₇⋊C₈	#121	1	4	yes	—
195	#21547	—	47	1	no	maximal, Sylow
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	2	2	no	—
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	—	4	2	no	—
202	C₂²×C₄₇	—	4	4	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₄₇	#525	1	1	yes	characteristic
206	C₂²×C₄₇	#529	1	1	yes	characteristic
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	—	4	4	no	—
209	C₄×C₄₇	—	4	2	no	—
210	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
211	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
212	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
213	C₄×C₄₇	#532	1	1	yes	characteristic
214	Dic₄₇	—	4	2	no	—
215	Dic₄₇	—	4	2	no	—
216	#3050	D₄₇	1	1	yes	characteristic
217	C₂×#444	—	47	1	no	—
218	#2930	—	47	2	no	—
219	C₂×#405	—	47	1	no	—
220	#1975	—	47	1	no	—
221	#1946	—	47	1	no	—
222	#1937	—	47	2	no	—
223	#1897	—	47	2	no	—
224	#1810	—	47	1	no	—
225	#1773	—	47	1	no	—
226	#1764	—	47	2	no	—
227	C₂×C₄₇	—	2	1	no	—
228	C₂×C₄₇	—	2	1	no	—
229	C₂×C₄₇	—	4	2	no	—
230	C₂×C₄₇	—	8	2	no	—
231	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
232	C₂×C₄₇	#2957	1	2	yes	—
233	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
234	C₂×#131	—	47	2	no	—
235	C₂²×M₁₆	—	47	1	no	—
236	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
237	#525	C₂×D₄₇	1	2	yes	—
238	C₂×#117	—	47	1	no	—
239	#467	Dic₄₇	1	2	yes	complemented
240	#466	Dic₄₇	1	2	yes	complemented
241	#465	Dic₄₇	1	4	yes	complemented
242	#444	—	94	4	no	—
243	#436	—	94	4	no	—
244	#435	—	94	4	no	—
245	C₂×#108	—	47	1	no	—
246	C₂×#108	—	47	1	no	—
247	#427	C₂×D₄₇	1	1	yes	characteristic
248	#424	—	47	2	no	—
249	C₂×#104	—	47	2	no	—
250	C₂×#104	—	47	2	no	—
251	#416	C₂×D₄₇	1	2	yes	—
252	#408	—	47	2	no	—
253	#407	—	47	2	no	—
254	#405	—	47	2	no	—
255	#405	—	94	4	no	—
256	C₂×#97	—	47	1	no	—
257	C₂×#97	—	47	1	no	—
258	C₂×C₄×C₈	—	47	1	no	—
259	C₂×C₄×C₈	—	47	1	no	—
260	#341	—	47	2	no	—
261	#339	—	47	2	no	—
262	#339	—	47	2	no	—
263	C₄₇	#21547	1	1	yes	characteristic, complemented, Sylow
264	C₂×#41	C₂²×D₄₇	1	2	yes	—
265	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
266	#135	—	2	2	no	—
267	#135	—	2	2	no	—
268	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
269	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
270	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
271	#131	—	94	4	no	—
272	#131	—	94	4	no	—
273	C₂×M₁₆	—	47	4	no	—
274	C₂×M₁₆	—	47	2	no	—
275	C₂×M₁₆	—	47	2	no	—
276	C₂×M₁₆	—	94	2	no	—
277	C₂×M₁₆	—	94	2	no	—
278	C₂×M₁₆	—	94	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	—	47	1	no	—
283	C₂²×C₈	—	94	2	no	—
284	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
285	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
286	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
288	#123	—	2	2	no	—
289	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
290	#121	C₂×Dic₄₇	1	4	yes	—
291	#120	—	2	2	no	—
292	C₄×D₄	—	2	4	no	—
293	#117	—	94	2	no	—
294	#117	—	94	2	no	—
295	#117	C₂²×D₄₇	1	2	yes	—
296	C₂×C₄⋊C₄	—	94	1	no	—
297	C₂×C₂²⋊C₄	—	94	1	no	—
298	C₂×C₄²	—	47	1	no	—
299	C₂×C₄²	—	47	1	no	—
300	#108	—	94	2	no	—
301	#108	—	94	2	no	—
302	#107	C₂×Dic₄₇	1	2	yes	—
303	#106	C₂×Dic₄₇	1	2	yes	—
304	C₄⋊C₈	—	94	4	no	—
305	#104	—	94	4	no	—
306	#104	—	94	4	no	—
307	#103	C₂×Dic₄₇	1	4	yes	—
308	#102	C₂×Dic₄₇	1	4	yes	—
309	C₂²⋊C₈	—	94	4	no	—
310	C₂²⋊C₈	—	94	4	no	—
311	#97	—	47	4	no	—
312	#97	—	94	2	no	—
313	#97	—	94	2	no	—
314	C₄×C₈	—	94	2	no	—
315	C₄×C₈	—	94	2	no	—
316	C₄×C₈	—	94	2	no	—
317	C₂⁴	#10625352	1	1	yes	characteristic
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	94	1	no	—
332	C₂²×C₄	—	94	1	no	—
333	C₂²×C₄	D₄×D₄₇	1	2	yes	—
334	C₂²×C₄	#10625352	1	1	yes	characteristic
335	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
336	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
337	Q₁₆	—	2	2	no	—
338	SD₁₆	—	2	4	no	—
339	D₈	—	2	2	no	—
340	M₁₆	—	94	8	no	—
341	M₁₆	—	94	2	no	—
342	M₁₆	—	94	2	no	—
343	M₁₆	—	94	2	no	—
344	M₁₆	—	94	2	no	—
345	M₁₆	—	188	4	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	47	2	no	—
351	C₂×C₈	—	47	2	no	—
352	C₂×C₈	—	47	2	no	—
353	C₂×C₈	—	47	2	no	—
354	C₂×C₈	—	94	1	no	—
355	C₂×C₈	—	94	1	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	—	188	4	no	—
359	C₂×C₈	D₄×D₄₇	1	2	yes	—
360	C₂×C₈	#10625352	1	2	yes	—
361	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
362	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
363	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	94	4	no	—
366	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	94	4	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	47	2	no	—
373	C₄²	—	47	2	no	—
374	C₄²	—	94	1	no	—
375	C₄²	—	94	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	D₄×Dic₄₇	1	2	yes	—
381	C₂³	C₂×#10625352	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	8	4	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	94	2	no	—
400	C₂×C₄	—	94	2	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	—	188	2	no	—
403	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
404	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
407	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
408	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	47	4	no	—
412	C₈	—	94	2	no	—
413	C₈	—	188	2	no	—
414	C₈	—	188	2	no	—
415	C₈	D₄×Dic₄₇	1	2	yes	—
416	C₈	D₄×Dic₄₇	1	2	yes	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	4	no	—
425	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
426	C₂²	#15689633	1	1	yes	characteristic
427	C₂²	#15689654	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	4	no	—
431	C₄	—	188	2	no	—
432	C₄	—	188	2	no	—
433	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
434	C₄	#41×Dic₄₇	1	1	yes	characteristic
435	C₄	#121×D₄₇	1	1	yes	characteristic
436	C₄	#15689668	1	1	yes	characteristic
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	—	4	2	no	—
440	C₂	—	8	2	no	—
441	C₂	#121×Dic₄₇	1	1	yes	characteristic
442	C₂	#20252305	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3050	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3050	D₄₇
hypocenter	C₄₇	#21547
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3050

Complements

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

N	H ≅ G/N	type
1. C₂×#15689245	C₂	semidirect
2. #20252092	C₂	semidirect
3. C₂×#15689078	C₂	semidirect
4. #20244282	C₂	semidirect
5. #20244142	C₂	semidirect
6. #20244094	C₂	semidirect
7. #20243837	C₂	semidirect
8. #20243426	C₂	semidirect
9. #20243274	C₂	semidirect
10. #20243228	C₂	semidirect
37. C₄₇×#467	C₄	semidirect
38. C₄₇×#466	C₄	semidirect
39. C₄₇×#465	C₄	semidirect
68. #13093934	D₄	semidirect
239. #467	Dic₄₇	semidirect
240. #466	Dic₄₇	semidirect
241. #465	Dic₄₇	semidirect
263. C₄₇	#21547	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689245	2
#20252092	2
C₂×#15689078	2
#20244282	2
#20244142	2
#20244094	2
#20243837	2
#20243426	2
#20243274	2
#20243228	2
C₄₇×#3050	2
#21547	47