Subgroups — #26110866

Order 12032.

584 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625325	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689202	C₂	1	1	yes	maximal, characteristic
3	#20244324	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15688855	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688852	C₂	1	1	yes	maximal, characteristic
6	#20241223	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625325	C₄	1	1	yes	characteristic
9	C₂²×#10625324	—	2	1	no	—
10	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
12	C₄×#10625325	—	2	2	no	—
13	C₄×#10625325	—	2	2	no	—
14	#15689202	—	2	2	no	—
15	#15689202	—	2	2	no	—
16	C₂×#13093956	C₄	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#13093949	C₄	1	1	yes	characteristic
20	C₂×#13093946	C₄	1	1	yes	characteristic
21	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
22	#15688877	—	2	1	no	—
23	#15688877	—	2	1	no	—
24	#15688855	—	2	2	no	—
25	#15688852	—	2	2	no	—
26	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	—	2	1	no	—
32	C₂×#10625325	—	2	2	no	—
33	C₂×#10625325	—	2	2	no	—
34	C₂×#10625325	—	2	2	no	—
35	C₂×#10625324	—	2	4	no	—
36	C₂×#10625324	—	4	2	no	—
37	C₂×#10625324	—	4	2	no	—
38	C₂²×C₄₇⋊C₈	—	2	1	no	—
39	C₂²×C₄₇⋊C₈	—	2	1	no	—
40	C₄×Dic₉₄	—	2	1	no	—
41	C₄×Dic₉₄	—	2	1	no	—
42	C₄×Dic₉₄	—	2	1	no	—
43	C₄×Dic₉₄	—	2	1	no	—
44	C₄×D₁₈₈	—	2	1	no	—
45	C₄×D₁₈₈	—	2	1	no	—
46	C₄×D₁₈₈	D₄	1	2	yes	—
47	C₄×D₁₈₈	D₄	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₄₇⋊C₄	—	2	1	no	—
51	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
52	C₂×C₄×Dic₄₇	—	2	1	no	—
53	#13093956	—	2	2	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
57	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
58	#13093949	—	2	2	no	—
59	#13093946	—	2	2	no	—
60	(C₂×D₄₇)⋊C₈	—	2	4	no	—
61	C₂²×C₈×C₄₇	—	2	1	no	—
62	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₄₇	—	2	1	no	—
68	C₄×C₈×C₄₇	—	2	1	no	—
69	C₄×C₈×C₄₇	—	2	1	no	—
70	C₄×C₈×C₄₇	—	2	1	no	—
71	C₄×C₈×C₄₇	—	2	1	no	—
72	C₄×C₈×C₄₇	—	2	1	no	—
73	C₂³×D₄₇	—	2	1	no	—
74	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
77	C₂²×Dic₄₇	—	2	1	no	—
78	C₂²×Dic₄₇	—	2	1	no	—
79	C₂²×Dic₄₇	—	2	1	no	—
80	C₂×D₁₈₈	—	2	1	no	—
81	C₂×D₁₈₈	—	2	1	no	—
82	C₂×D₁₈₈	—	2	1	no	—
83	C₂×D₁₈₈	—	2	1	no	—
84	C₂×D₁₈₈	—	2	1	no	—
85	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
86	C₂×C₄×D₄₇	—	2	2	no	—
87	C₂×C₄×D₄₇	—	2	2	no	—
88	C₂×C₄×D₄₇	—	4	1	no	—
89	C₂×C₄×D₄₇	—	4	1	no	—
90	C₂×C₄×D₄₇	—	4	1	no	—
91	C₂×C₄×D₄₇	—	4	1	no	—
92	C₂×Dic₉₄	—	2	1	no	—
93	C₂×Dic₉₄	—	2	1	no	—
94	C₂×Dic₉₄	—	2	1	no	—
95	C₂×Dic₉₄	—	2	1	no	—
96	C₂×Dic₉₄	—	2	1	no	—
97	C₂×Dic₉₄	M₁₆	1	2	yes	complemented
98	C₂×C₈×C₄₇	—	2	1	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	—	2	1	no	—
101	C₂×C₈×C₄₇	—	2	1	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	—	2	1	no	—
109	C₂×C₈×C₄₇	—	4	1	no	—
110	C₂×C₈×C₄₇	—	4	1	no	—
111	C₂×C₈×C₄₇	M₁₆	1	2	yes	complemented
112	C₂×C₈×C₄₇	SD₁₆	1	2	yes	complemented
113	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₄₇	#41	1	1	yes	characteristic
117	(C₂×D₄₇)⋊C₄	—	2	2	no	—
118	(C₂×D₄₇)⋊C₄	—	2	2	no	—
119	C₄⋊Dic₄₇	—	2	1	no	—
120	C₄⋊Dic₄₇	—	2	1	no	—
121	C₄⋊Dic₄₇	—	2	1	no	—
122	C₄⋊Dic₄₇	C₂²⋊C₄	1	2	yes	—
123	Dic₄₇⋊C₄	—	4	1	no	—
124	Dic₄₇⋊C₄	—	4	1	no	—
125	C₄×Dic₄₇	—	4	1	no	—
126	C₄×Dic₄₇	—	4	1	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	4	1	no	—
129	C₂×C₄₇⋊C₈	—	4	1	no	—
130	C₂×C₄₇⋊C₈	—	4	1	no	—
131	C₂×C₄₇⋊C₈	—	4	1	no	—
132	C₂×C₄₇⋊C₈	—	4	1	no	—
133	#10625325	—	2	8	no	—
134	#10625324	—	4	8	no	—
135	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
136	C₂²×D₄₇	—	2	2	no	—
137	C₂²×D₄₇	—	4	1	no	—
138	C₂²×D₄₇	—	4	1	no	—
139	C₂²×D₄₇	—	4	1	no	—
140	C₂²×D₄₇	—	4	1	no	—
141	C₂²×D₄₇	—	4	1	no	—
142	C₂²×D₄₇	—	4	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
157	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	4	1	no	—
162	C₂×Dic₄₇	—	4	1	no	—
163	C₂×Dic₄₇	—	4	1	no	—
164	C₂×Dic₄₇	—	4	1	no	—
165	C₂×Dic₄₇	—	4	1	no	—
166	C₂×Dic₄₇	—	4	1	no	—
167	C₂×Dic₄₇	—	4	1	no	—
168	D₁₈₈	—	2	2	no	—
169	D₁₈₈	—	2	2	no	—
170	D₁₈₈	—	4	1	no	—
171	D₁₈₈	—	4	1	no	—
172	C₄×D₄₇	—	4	2	no	—
173	C₄×D₄₇	—	4	2	no	—
174	C₄×D₄₇	—	4	2	no	—
175	C₄×D₄₇	—	4	2	no	—
176	Dic₉₄	—	2	2	no	—
177	Dic₉₄	—	2	2	no	—
178	Dic₉₄	—	4	1	no	—
179	Dic₉₄	—	4	1	no	—
180	C₈×C₄₇	—	2	2	no	—
181	C₈×C₄₇	—	2	2	no	—
182	C₈×C₄₇	—	4	2	no	—
183	C₈×C₄₇	—	4	1	no	—
184	C₈×C₄₇	—	4	1	no	—
185	C₄₇⋊C₈	—	4	2	no	—
186	C₄₇⋊C₈	—	8	1	no	—
187	#8949	—	47	1	no	maximal, Sylow
188	C₂²×C₄₇	#386	1	1	yes	characteristic
189	C₂²×C₄₇	#435	1	1	yes	characteristic
190	C₂²×C₄₇	#436	1	1	yes	characteristic
191	C₂²×C₄₇	C₄×SD₁₆	1	1	yes	characteristic
192	C₂²×C₄₇	#440	1	1	yes	characteristic
193	C₂²×C₄₇	#443	1	1	yes	characteristic
194	C₂²×C₄₇	#444	1	1	yes	characteristic
195	C₂×D₄₇	—	4	2	no	—
196	C₂×D₄₇	—	4	2	no	—
197	C₂×D₄₇	—	4	2	no	—
198	C₂×D₄₇	—	8	1	no	—
199	C₂×D₄₇	—	8	1	no	—
200	C₂×D₄₇	—	8	1	no	—
201	C₂×D₄₇	—	8	1	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	—	2	1	no	—
204	C₄×C₄₇	#407	1	1	yes	characteristic
205	C₄×C₄₇	#408	1	1	yes	characteristic
206	C₄×C₄₇	#435	1	1	yes	characteristic
207	C₄×C₄₇	#436	1	1	yes	characteristic
208	C₄×C₄₇	#450	1	1	yes	characteristic
209	C₄×C₄₇	#452	1	1	yes	characteristic
210	C₄×C₄₇	#461	1	1	yes	characteristic
211	C₄×C₄₇	#463	1	1	yes	characteristic
212	Dic₄₇	—	4	2	no	—
213	Dic₄₇	—	4	2	no	—
214	Dic₄₇	—	8	1	no	—
215	C₂×C₄×SD₁₆	—	47	1	no	—
216	C₂×#436	—	47	1	no	—
217	#1984	—	47	1	no	—
218	C₂×Q₈⋊C₈	—	47	1	no	—
219	C₂×D₄⋊C₈	—	47	1	no	—
220	#1277	—	47	1	no	—
221	#1273	D₄₇	1	1	yes	characteristic, complemented
222	C₂×C₄₇	#1583	1	1	yes	characteristic
223	C₂×C₄₇	#1588	1	1	yes	characteristic
224	C₂×C₄₇	#1590	1	1	yes	characteristic
225	C₂×C₄₇	#1592	1	1	yes	characteristic
226	C₂×C₄₇	#1870	1	1	yes	characteristic
227	C₂×C₄₇	#1876	1	1	yes	characteristic
228	C₂×C₄₇	#1877	1	1	yes	characteristic
229	D₄₇	—	8	2	no	—
230	C₂²×SD₁₆	—	47	1	no	—
231	C₂²×M₁₆	—	94	1	no	—
232	C₂×C₄×Q₈	—	47	1	no	—
233	C₂×C₄×D₄	—	47	1	no	—
234	C₄×SD₁₆	—	94	2	no	—
235	C₄×SD₁₆	—	94	2	no	—
236	#436	—	94	2	no	—
237	#436	—	94	2	no	—
238	C₂×#106	—	47	1	no	—
239	C₂×C₄⋊C₈	—	47	1	no	—
240	C₂×C₄⋊C₈	—	47	1	no	—
241	C₂×#103	—	47	1	no	—
242	C₂×#102	—	47	1	no	—
243	C₂×C₂²⋊C₈	—	94	1	no	—
244	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
247	#336	—	94	1	no	—
248	#336	—	94	1	no	—
249	Q₈⋊C₈	—	94	2	no	—
250	D₄⋊C₈	—	94	2	no	—
251	C₄₇	#8949	1	1	yes	characteristic, complemented, Sylow
252	C₂²×Q₈	—	47	1	no	—
253	C₂²×D₄	—	47	1	no	—
254	C₂³×C₄	—	94	1	no	—
255	C₂×SD₁₆	—	94	2	no	—
256	C₂×SD₁₆	—	94	2	no	—
257	C₂×SD₁₆	—	94	2	no	—
258	C₂×M₁₆	—	94	4	no	—
259	C₂×M₁₆	—	188	2	no	—
260	C₂×M₁₆	—	188	2	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	94	1	no	—
263	C₂²×C₈	—	94	1	no	—
264	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
265	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
266	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
267	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
268	C₄×Q₈	—	94	1	no	—
269	C₄×Q₈	—	94	1	no	—
270	C₄×Q₈	—	94	1	no	—
271	C₄×Q₈	—	94	1	no	—
272	C₄×D₄	—	47	2	no	—
273	C₄×D₄	—	47	2	no	—
274	C₄×D₄	—	94	1	no	—
275	C₄×D₄	—	94	1	no	—
276	C₂×C₄⋊C₄	—	47	1	no	—
277	C₂×C₄⋊C₄	—	47	1	no	—
278	C₂×C₄⋊C₄	—	94	1	no	—
279	C₂×C₂²⋊C₄	—	94	1	no	—
280	C₂×C₄²	—	94	1	no	—
281	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
282	#106	—	94	2	no	—
283	C₄⋊C₈	—	47	2	no	—
284	C₄⋊C₈	—	94	1	no	—
285	C₄⋊C₈	—	94	1	no	—
286	C₄⋊C₈	—	94	1	no	—
287	#103	—	94	2	no	—
288	#102	—	94	2	no	—
289	C₂²⋊C₈	—	94	4	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₂⁴	—	94	1	no	—
297	C₂×Q₈	—	47	2	no	—
298	C₂×Q₈	—	94	1	no	—
299	C₂×Q₈	—	94	1	no	—
300	C₂×Q₈	—	94	1	no	—
301	C₂×Q₈	—	94	1	no	—
302	C₂×Q₈	—	94	1	no	—
303	C₂×D₄	—	47	2	no	—
304	C₂×D₄	—	94	1	no	—
305	C₂×D₄	—	94	1	no	—
306	C₂×D₄	—	94	1	no	—
307	C₂×D₄	—	94	1	no	—
308	C₂×D₄	—	94	1	no	—
309	C₂²×C₄	—	94	1	no	—
310	C₂²×C₄	—	94	1	no	—
311	C₂²×C₄	—	94	2	no	—
312	C₂²×C₄	—	94	2	no	—
313	C₂²×C₄	—	94	1	no	—
314	C₂²×C₄	—	188	1	no	—
315	C₂²×C₄	—	188	1	no	—
316	C₂²×C₄	—	188	1	no	—
317	C₂²×C₄	—	188	1	no	—
318	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
320	C₂²×C₄	#10625350	1	1	yes	characteristic
321	SD₁₆	—	94	8	no	—
322	M₁₆	—	188	8	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	94	2	no	—
337	C₂×C₈	—	188	1	no	—
338	C₂×C₈	—	188	1	no	—
339	C₂×C₈	—	188	1	no	—
340	C₂×C₈	—	188	1	no	—
341	C₂×C₈	—	188	1	no	—
342	C₂×C₈	#10625324	1	2	yes	complemented
343	C₂×C₈	#10625325	1	2	yes	complemented
344	C₄⋊C₄	—	47	2	no	—
345	C₄⋊C₄	—	94	1	no	—
346	C₄⋊C₄	—	94	1	no	—
347	C₄⋊C₄	—	94	1	no	—
348	C₄⋊C₄	—	188	1	no	—
349	C₄⋊C₄	—	188	1	no	—
350	C₂²⋊C₄	—	94	2	no	—
351	C₂²⋊C₄	—	94	2	no	—
352	C₄²	—	188	1	no	—
353	C₄²	—	188	1	no	—
354	C₄²	D₄×D₄₇	1	1	yes	characteristic
355	C₄²	D₄×D₄₇	1	1	yes	characteristic
356	C₄²	D₄×D₄₇	1	1	yes	characteristic
357	C₄²	#10625354	1	1	yes	characteristic
358	C₂³	—	94	2	no	—
359	C₂³	—	188	1	no	—
360	C₂³	—	188	1	no	—
361	C₂³	—	188	1	no	—
362	C₂³	—	188	1	no	—
363	C₂³	—	188	1	no	—
364	C₂³	—	188	1	no	—
365	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
366	Q₈	—	94	2	no	—
367	Q₈	—	94	2	no	—
368	Q₈	—	188	1	no	—
369	Q₈	—	188	1	no	—
370	D₄	—	94	2	no	—
371	D₄	—	94	2	no	—
372	D₄	—	188	1	no	—
373	D₄	—	188	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	94	2	no	—
377	C₂×C₄	—	94	2	no	—
378	C₂×C₄	—	188	1	no	—
379	C₂×C₄	—	188	1	no	—
380	C₂×C₄	—	188	1	no	—
381	C₂×C₄	—	188	1	no	—
382	C₂×C₄	—	188	1	no	—
383	C₂×C₄	—	188	1	no	—
384	C₂×C₄	—	188	1	no	—
385	C₂×C₄	—	188	2	no	—
386	C₂×C₄	—	188	2	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
390	C₂×C₄	#13093986	1	1	yes	characteristic
391	C₂×C₄	#13093994	1	1	yes	characteristic
392	C₂×C₄	#13093997	1	1	yes	characteristic
393	C₂×C₄	#13093999	1	1	yes	characteristic
394	C₂×C₄	#13094009	1	1	yes	characteristic
395	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
397	C₂×C₄	#13094030	1	1	yes	characteristic
398	C₂×C₄	#13094032	1	1	yes	characteristic
399	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
400	C₂×C₄	#13094046	1	1	yes	characteristic
401	C₂×C₄	#13094052	1	1	yes	characteristic
402	C₂×C₄	#13094057	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	2	2	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	1	no	—
408	C₈	—	376	1	no	—
409	C₈	—	188	2	no	—
410	C₂²	—	376	1	no	—
411	C₂²	—	376	1	no	—
412	C₂²	—	376	1	no	—
413	C₂²	—	376	1	no	—
414	C₂²	—	188	2	no	—
415	C₂²	—	188	2	no	—
416	C₂²	—	188	2	no	—
417	C₂²	#15689001	1	1	yes	characteristic
418	C₂²	#15689196	1	1	yes	characteristic
419	C₂²	#15689202	1	1	yes	characteristic
420	C₂²	C₄×#10625325	1	1	yes	characteristic
421	C₂²	#15689225	1	1	yes	characteristic
422	C₂²	#15689241	1	1	yes	characteristic
423	C₂²	#15689246	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	376	1	no	—
427	C₄	—	188	2	no	—
428	C₄	—	188	2	no	—
429	C₄	#15689085	1	1	yes	characteristic
430	C₄	#15689088	1	1	yes	characteristic
431	C₄	#15689193	1	1	yes	characteristic
432	C₄	#15689200	1	1	yes	characteristic
433	C₄	#15689276	1	1	yes	characteristic
434	C₄	#15689287	1	1	yes	characteristic
435	C₄	#15689329	1	1	yes	characteristic
436	C₄	#15689339	1	1	yes	characteristic
437	C₂	—	376	2	no	—
438	C₂	#20242233	1	1	yes	characteristic
439	C₂	#20242268	1	1	yes	characteristic
440	C₂	#20242280	1	1	yes	characteristic
441	C₂	#20242292	1	1	yes	characteristic
442	C₂	#20243684	1	1	yes	characteristic
443	C₂	#20243714	1	1	yes	characteristic
444	C₂	#20243721	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1273	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1273	D₄₇
hypocenter	C₄₇	#8949
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1273

Complements

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

N	H ≅ G/N	type
3. #20244324	C₂	semidirect
4. C₂×#15688855	C₂	semidirect
6. #20241223	C₂	semidirect
7. C₄₇×#1273	C₂	semidirect
97. C₂×Dic₉₄	M₁₆	semidirect
111. C₂×C₈×C₄₇	M₁₆	semidirect
112. C₂×C₈×C₄₇	SD₁₆	semidirect
221. #1273	D₄₇	semidirect
251. C₄₇	#8949	semidirect
342. C₂×C₈	#10625324	semidirect
343. C₂×C₈	#10625325	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625325	2
C₂×#15689202	2
#20244324	2
C₂×#15688855	2
C₂×#15688852	2
#20241223	2
C₄₇×#1273	2
#8949	47