Subgroups — #26234366

Order 12032.

964 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689193	C₂	1	2	yes	maximal
2	C₂×#15689148	C₂	1	2	yes	maximal, complemented
3	#20245852	C₂	1	1	yes	maximal, characteristic
4	#20244109	C₂	1	2	yes	maximal, complemented
5	#20243569	C₂	1	2	yes	maximal, complemented
6	#20243564	C₂	1	2	yes	maximal, complemented
7	#20243369	C₂	1	2	yes	maximal, complemented
8	#20243241	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#10625324	C₂²	1	2	yes	—
11	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
12	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
13	C₂×#13093981	C₂²	1	2	yes	—
14	#15689193	—	2	8	no	—
15	#15689148	—	2	8	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
22	C₂×#13093935	C₂²	1	2	yes	—
23	#15689025	C₄	1	1	yes	characteristic
24	#15689025	C₄	1	1	yes	characteristic
25	#15689021	C₄	1	1	yes	characteristic
26	#15689021	C₄	1	1	yes	characteristic
27	#15689014	C₄	1	2	yes	—
28	#15689014	C₄	1	2	yes	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
31	#15688878	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
35	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄³×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
41	C₂×#10625324	—	2	4	no	—
42	C₂×#10625324	—	2	4	no	—
43	C₂×#10625324	—	4	2	no	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₂×C₈×D₄₇	—	2	4	no	—
47	C₂×C₈×D₄₇	—	2	4	no	—
48	C₂×C₈×D₄₇	—	4	2	no	—
49	C₄×D₁₈₈	D₄	1	4	yes	—
50	C₄×D₁₈₈	Q₈	1	4	yes	—
51	#13093981	—	2	4	no	—
52	#13093981	—	2	4	no	—
53	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
64	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	complemented
66	Dic₄₇⋊C₈	—	2	4	no	—
67	Dic₄₇⋊C₈	—	2	4	no	—
68	(C₂×D₄₇)⋊C₈	—	2	4	no	—
69	(C₂×D₄₇)⋊C₈	—	2	4	no	—
70	#13093935	—	2	4	no	—
71	C₄₇⋊#95	C₂×C₄	1	2	yes	—
72	C₄₇⋊#95	C₂×C₄	1	2	yes	—
73	C₄₇⋊#95	C₂×C₄	1	2	yes	—
74	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₇	—	2	4	no	—
84	C₄⋊C₈×C₄₇	—	2	4	no	—
85	C₄⋊C₈×C₄₇	—	4	1	no	—
86	C₄⋊C₈×C₄₇	—	4	1	no	—
87	C₂³×D₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
98	C₂×D₁₈₈	—	4	1	no	—
99	C₂×D₁₈₈	—	4	1	no	—
100	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
101	C₂×C₄×D₄₇	—	2	2	no	—
102	C₂×C₄×D₄₇	—	2	2	no	—
103	C₂×C₄×D₄₇	—	2	2	no	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	C₂×D₄	1	4	yes	—
106	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	—	2	2	no	—
114	C₄²×C₄₇	—	2	1	no	—
115	C₄²×C₄₇	—	2	1	no	—
116	C₄²×C₄₇	—	4	1	no	—
117	C₄²×C₄₇	—	4	1	no	—
118	C₄²×C₄₇	—	4	1	no	—
119	C₄²×C₄₇	C₂×D₄	1	2	yes	—
120	C₄²×C₄₇	C₂×D₄	1	2	yes	—
121	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
122	C₄²×C₄₇	#41	1	2	yes	—
123	(C₂×D₄₇)⋊C₄	—	2	4	no	—
124	(C₂×D₄₇)⋊C₄	—	2	4	no	—
125	(C₂×D₄₇)⋊C₄	—	2	4	no	—
126	(C₂×D₄₇)⋊C₄	—	4	2	no	—
127	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	8	yes	—
128	C₄⋊Dic₄₇	—	4	1	no	—
129	C₄⋊Dic₄₇	—	4	1	no	—
130	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
131	Dic₄₇⋊C₄	—	2	4	no	—
132	Dic₄₇⋊C₄	—	2	4	no	—
133	C₄×Dic₄₇	—	2	2	no	—
134	C₄×Dic₄₇	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
141	#10625324	—	4	8	no	—
142	C₈×D₄₇	—	4	8	no	—
143	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
144	C₂²×D₄₇	—	2	2	no	—
145	C₂²×D₄₇	—	2	2	no	—
146	C₂²×D₄₇	—	2	2	no	—
147	C₂²×D₄₇	—	2	2	no	—
148	C₂²×D₄₇	—	2	2	no	—
149	C₂²×D₄₇	—	2	2	no	—
150	C₂²×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₄₇	#131	1	2	yes	—
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
184	D₁₈₈	—	4	4	no	—
185	C₄×D₄₇	—	2	4	no	—
186	C₄×D₄₇	—	2	4	no	—
187	C₄×D₄₇	—	2	4	no	—
188	C₄×D₄₇	—	2	4	no	—
189	C₈×C₄₇	—	4	2	no	—
190	C₈×C₄₇	—	4	2	no	—
191	C₄₇⋊C₈	—	2	4	no	—
192	C₄₇⋊C₈	—	4	2	no	—
193	#22652	—	47	1	no	maximal, Sylow
194	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₄₇	#520	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
198	C₂²×C₄₇	#568	1	1	yes	characteristic
199	C₂²×C₄₇	#568	1	1	yes	characteristic
200	C₂²×C₄₇	#568	1	1	yes	characteristic
201	C₂×D₄₇	—	2	4	no	—
202	C₂×D₄₇	—	2	4	no	—
203	C₂×D₄₇	—	2	4	no	—
204	C₂×D₄₇	—	4	2	no	—
205	C₂×D₄₇	—	4	2	no	—
206	C₂×D₄₇	—	4	2	no	—
207	C₂×D₄₇	—	4	2	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	2	2	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	4	1	no	—
214	C₄×C₄₇	D₄²	1	1	yes	characteristic
215	C₄×C₄₇	#547	1	1	yes	characteristic
216	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
217	C₄×C₄₇	#554	1	1	yes	characteristic
218	Dic₄₇	—	2	4	no	—
219	Dic₄₇	—	4	2	no	—
220	Dic₄₇	—	4	2	no	—
221	C₂×#435	—	47	2	no	—
222	C₂×#424	—	47	2	no	—
223	#2293	—	47	1	no	—
224	#1940	—	47	2	no	—
225	#1851	—	47	2	no	—
226	#1850	—	47	2	no	—
227	#1842	D₄₇	1	1	yes	characteristic, complemented
228	#1798	—	47	2	no	—
229	#1767	—	47	1	no	—
230	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄₇	#2905	1	1	yes	characteristic
232	C₂×C₄₇	#2906	1	1	yes	characteristic
233	C₂×C₄₇	#2932	1	1	yes	characteristic
234	C₂×C₄₇	#2935	1	1	yes	characteristic
235	C₂×C₄₇	#2992	1	1	yes	characteristic
236	C₂×C₄₇	#2995	1	1	yes	characteristic
237	D₄₇	—	4	4	no	—
238	C₂²×M₁₆	—	47	2	no	—
239	C₂³×C₈	—	47	2	no	—
240	C₂×C₄×D₄	—	47	1	no	—
241	C₂×#117	—	47	2	no	—
242	#435	—	94	8	no	—
243	#424	—	94	8	no	—
244	C₂×C₄⋊C₈	—	47	1	no	—
245	C₂×C₄⋊C₈	—	47	2	no	—
246	C₂×C₄⋊C₈	—	47	2	no	—
247	C₂×C₄⋊C₈	—	47	1	no	—
248	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
249	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
250	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
252	C₂×C₂²⋊C₈	—	47	2	no	—
253	C₂×C₂²⋊C₈	—	47	2	no	—
254	C₂×#97	—	47	2	no	—
255	#390	—	47	1	no	—
256	#390	—	47	1	no	—
257	#389	—	47	1	no	—
258	#389	—	47	1	no	—
259	#388	—	47	2	no	—
260	#388	—	47	2	no	—
261	C₄×C₄⋊C₄	—	47	1	no	—
262	C₄×C₂²⋊C₄	—	47	2	no	—
263	C₄³	C₂×D₄₇	1	1	yes	characteristic
264	#336	—	47	2	no	—
265	#336	—	47	2	no	—
266	#336	—	47	2	no	—
267	C₄₇	#22652	1	1	yes	characteristic, complemented, Sylow
268	C₂²×D₄	—	47	1	no	—
269	C₂³×C₄	—	47	2	no	—
270	C₂×M₁₆	—	94	4	no	—
271	C₂×M₁₆	—	94	4	no	—
272	C₂×M₁₆	—	188	2	no	—
273	C₂²×C₈	—	47	2	no	—
274	C₂²×C₈	—	47	2	no	—
275	C₂²×C₈	—	94	4	no	—
276	C₂²×C₈	—	94	4	no	—
277	C₂²×C₈	—	188	2	no	—
278	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
279	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
280	C₄×D₄	—	47	4	no	—
281	C₄×D₄	—	47	4	no	—
282	#117	—	94	4	no	—
283	#117	—	94	4	no	—
284	C₂×C₄⋊C₄	—	47	1	no	—
285	C₂×C₄⋊C₄	—	47	2	no	—
286	C₂×C₄⋊C₄	—	47	2	no	—
287	C₂×C₄⋊C₄	—	47	1	no	—
288	C₂×C₄⋊C₄	—	47	1	no	—
289	C₂×C₂²⋊C₄	—	47	2	no	—
290	C₂×C₂²⋊C₄	—	47	2	no	—
291	C₂×C₂²⋊C₄	—	47	2	no	—
292	C₂×C₂²⋊C₄	—	47	2	no	—
293	C₂×C₂²⋊C₄	—	47	2	no	—
294	C₂×C₄²	—	47	2	no	—
295	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
296	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
297	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
298	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
299	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
300	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
301	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
302	C₄⋊C₈	—	2	4	no	—
303	C₄⋊C₈	—	2	4	no	—
304	C₄⋊C₈	—	4	1	no	—
305	C₄⋊C₈	—	4	1	no	—
306	C₄⋊C₈	—	47	4	no	—
307	C₄⋊C₈	—	94	4	no	—
308	C₄⋊C₈	—	94	4	no	—
309	C₄⋊C₈	—	94	2	no	—
310	C₂²⋊C₈	—	94	4	no	—
311	C₂²⋊C₈	—	94	4	no	—
312	#97	—	94	4	no	—
313	#95	—	47	2	no	—
314	#95	—	47	2	no	—
315	#95	—	47	2	no	—
316	C₂⁴	—	47	2	no	—
317	C₂×D₄	—	47	4	no	—
318	C₂×D₄	—	188	1	no	—
319	C₂×D₄	—	188	1	no	—
320	C₂²×C₄	—	47	2	no	—
321	C₂²×C₄	—	47	4	no	—
322	C₂²×C₄	—	47	4	no	—
323	C₂²×C₄	—	47	2	no	—
324	C₂²×C₄	—	47	2	no	—
325	C₂²×C₄	—	94	2	no	—
326	C₂²×C₄	—	94	2	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	94	2	no	—
329	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
335	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
336	M₁₆	—	188	8	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	47	4	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	94	2	no	—
346	C₂×C₈	—	94	2	no	—
347	C₂×C₈	—	94	2	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	188	8	no	—
350	C₄⋊C₄	—	47	4	no	—
351	C₄⋊C₄	—	94	4	no	—
352	C₄⋊C₄	—	94	4	no	—
353	C₄⋊C₄	—	188	1	no	—
354	C₄⋊C₄	—	188	1	no	—
355	C₂²⋊C₄	—	47	8	no	—
356	C₂²⋊C₄	—	94	4	no	—
357	C₂²⋊C₄	—	94	4	no	—
358	C₂²⋊C₄	—	94	4	no	—
359	C₂²⋊C₄	—	188	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	4	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	94	2	no	—
367	C₄²	—	94	2	no	—
368	C₄²	D₄×D₄₇	1	2	yes	—
369	C₄²	D₄×D₄₇	1	2	yes	—
370	C₄²	Q₈×D₄₇	1	2	yes	—
371	C₄²	#10625354	1	2	yes	—
372	C₂³	—	47	4	no	—
373	C₂³	—	94	2	no	—
374	C₂³	—	94	2	no	—
375	C₂³	—	94	2	no	—
376	C₂³	—	94	2	no	—
377	C₂³	—	94	2	no	—
378	C₂³	—	94	2	no	—
379	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
380	D₄	—	188	4	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	47	4	no	—
395	C₂×C₄	—	94	2	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	94	4	no	—
398	C₂×C₄	—	94	4	no	—
399	C₂×C₄	—	94	4	no	—
400	C₂×C₄	—	94	4	no	—
401	C₂×C₄	—	94	2	no	—
402	C₂×C₄	—	94	2	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	2	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	94	2	no	—
407	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
408	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
409	C₂×C₄	#13093986	1	2	yes	—
410	C₂×C₄	#13093986	1	2	yes	—
411	C₂×C₄	#13094030	1	2	yes	—
412	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
416	C₂×C₄	#13094069	1	1	yes	characteristic
417	C₂×C₄	#13094072	1	1	yes	characteristic
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	94	4	no	—
421	C₈	—	188	2	no	—
422	C₂²	—	94	4	no	—
423	C₂²	—	94	4	no	—
424	C₂²	—	94	4	no	—
425	C₂²	—	188	2	no	—
426	C₂²	—	188	2	no	—
427	C₂²	—	188	2	no	—
428	C₂²	—	188	2	no	—
429	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
430	C₂²	C₂×#13093986	1	1	yes	characteristic
431	C₂²	#15689604	1	1	yes	characteristic
432	C₂²	C₂×#13094030	1	1	yes	characteristic
433	C₂²	#15689889	1	1	yes	characteristic
434	C₂²	#15689889	1	1	yes	characteristic
435	C₂²	#15689889	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	4	1	no	—
442	C₄	—	94	4	no	—
443	C₄	—	188	2	no	—
444	C₄	—	188	2	no	—
445	C₄	#15689758	1	1	yes	characteristic
446	C₄	#15689776	1	1	yes	characteristic
447	C₄	#15689788	1	1	yes	characteristic
448	C₄	#15689834	1	1	yes	characteristic
449	C₂	—	188	4	no	—
450	C₂	#20246288	1	1	yes	characteristic
451	C₂	#20251950	1	1	yes	characteristic
452	C₂	#20251953	1	1	yes	characteristic
453	C₂	#20252105	1	1	yes	characteristic
454	C₂	#20252131	1	1	yes	characteristic
455	C₂	#20252524	1	1	yes	characteristic
456	C₂	#20252555	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1842	C₂
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1842	D₄₇
hypocenter	C₄₇	#22652
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1842

Complements

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

N	H ≅ G/N	type
2. C₂×#15689148	C₂	semidirect
4. #20244109	C₂	semidirect
5. #20243569	C₂	semidirect
6. #20243564	C₂	semidirect
7. #20243369	C₂	semidirect
8. #20243241	C₂	semidirect
9. C₄₇×#1842	C₂	semidirect
65. C₄⋊(C₄₇⋊C₈)	D₄	semidirect
227. #1842	D₄₇	semidirect
267. C₄₇	#22652	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689193	2
C₂×#15689148	2
#20245852	2
#20244109	2
#20243569	2
#20243564	2
#20243369	2
#20243241	2
C₄₇×#1842	2
#22652	47