Subgroups — #26221096

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689179	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093982	C₂	1	1	yes	maximal, characteristic
4	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244104	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243572	C₂	1	2	yes	maximal
8	#20243569	C₂	1	2	yes	maximal
9	#20243243	C₂	1	2	yes	maximal, complemented
10	#20243240	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×#10625324	C₂²	1	1	yes	characteristic
14	C₂×#13093982	C₄	1	1	yes	characteristic
15	C₂×#13093982	C₄	1	1	yes	characteristic
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	#15689179	—	2	4	no	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
22	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
23	C₄×#10625324	—	2	4	no	—
24	C₂×#13093934	C₂²	1	1	yes	characteristic
25	C₂×#13093934	C₂²	1	2	yes	—
26	C₂×#13093934	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
29	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
30	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
32	#15688970	C₄	1	2	yes	—
33	#15688968	C₄	1	2	yes	—
34	C₄²×Dic₄₇	C₂²	1	2	yes	—
35	#15688878	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
46	C₂×#10625324	—	2	2	no	—
47	C₂×#10625324	—	2	2	no	—
48	C₂×#10625324	—	2	2	no	—
49	C₂×#10625324	—	2	2	no	—
50	C₂×#10625324	—	2	2	no	—
51	C₂×#10625324	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	#13093982	—	2	4	no	—
56	#13093982	—	2	4	no	—
57	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	C₄²×D₄₇	D₄	1	4	yes	—
70	C₄²×D₄₇	Q₈	1	4	yes	—
71	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
72	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
73	Dic₄₇⋊C₈	—	2	4	no	—
74	Dic₄₇⋊C₈	—	2	4	no	—
75	(C₂×D₄₇)⋊C₈	—	2	4	no	—
76	#13093934	—	2	2	no	—
77	#13093934	—	2	2	no	—
78	#13093934	—	2	4	no	—
79	C₄×C₄₇⋊C₈	—	2	2	no	—
80	C₄₇⋊#95	C₂×C₄	1	2	yes	—
81	C₄₇⋊#95	C₂×C₄	1	2	yes	—
82	C₄₇⋊#95	C₂×C₄	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₇	—	2	4	no	—
91	C₄⋊C₈×C₄₇	—	2	2	no	—
92	C₄×C₈×C₄₇	—	2	2	no	—
93	#95×C₄₇	C₂×C₄	1	2	yes	—
94	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
105	C₂×C₄×D₄₇	—	2	2	no	—
106	C₂×C₄×D₄₇	—	2	2	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	—	2	1	no	—
111	C₂×C₄×D₄₇	—	4	1	no	—
112	C₂×C₄×D₄₇	—	4	1	no	—
113	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
114	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
115	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
116	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
117	C₂×C₈×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	#41	1	2	yes	—
125	C₂×C₈×C₄₇	#41	1	2	yes	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	M₁₆	1	4	yes	complemented
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	C₂×D₄	1	2	yes	—
131	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
132	(C₂×D₄₇)⋊C₄	—	2	4	no	—
133	(C₂×D₄₇)⋊C₄	—	2	4	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	M₁₆	1	4	yes	complemented
136	C₄×Dic₄₇	—	2	4	no	—
137	C₄×Dic₄₇	—	2	2	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	4	no	—
140	C₄×Dic₄₇	—	4	2	no	—
141	C₄×Dic₄₇	—	4	2	no	—
142	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
143	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
144	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
145	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	#41	1	2	yes	—
154	C₂×C₄₇⋊C₈	#41	1	2	yes	—
155	#10625324	—	2	8	no	—
156	#10625324	—	2	8	no	—
157	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
158	C₂²×D₄₇	—	2	1	no	—
159	C₂²×D₄₇	—	2	1	no	—
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	—	2	1	no	—
162	C₂²×D₄₇	—	2	1	no	—
163	C₂²×D₄₇	—	2	1	no	—
164	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	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	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
176	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	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×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	—	2	1	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	2	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	2	2	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	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
198	C₄×D₄₇	—	2	2	no	—
199	C₄×D₄₇	—	2	2	no	—
200	C₄×D₄₇	—	2	2	no	—
201	C₄×D₄₇	—	2	2	no	—
202	C₄×D₄₇	—	2	8	no	—
203	C₄×D₄₇	—	4	4	no	—
204	C₈×C₄₇	—	2	2	no	—
205	C₈×C₄₇	—	2	2	no	—
206	C₈×C₄₇	—	4	2	no	—
207	C₄₇⋊C₈	—	2	2	no	—
208	C₄₇⋊C₈	—	2	2	no	—
209	C₄₇⋊C₈	—	4	2	no	—
210	#21356	—	47	1	no	maximal, Sylow
211	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
212	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
213	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
214	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
215	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
216	C₂²×C₄₇	#568	1	1	yes	characteristic
217	C₂²×C₄₇	#568	1	1	yes	characteristic
218	C₂×D₄₇	—	2	2	no	—
219	C₂×D₄₇	—	2	2	no	—
220	C₂×D₄₇	—	2	2	no	—
221	C₂×D₄₇	—	4	1	no	—
222	C₂×D₄₇	—	4	1	no	—
223	C₂×D₄₇	—	4	1	no	—
224	C₂×D₄₇	—	4	1	no	—
225	C₄×C₄₇	—	2	2	no	—
226	C₄×C₄₇	—	2	4	no	—
227	C₄×C₄₇	—	4	2	no	—
228	C₄×C₄₇	#423	1	4	yes	—
229	C₄×C₄₇	#525	1	1	yes	characteristic
230	C₄×C₄₇	#525	1	1	yes	characteristic
231	C₄×C₄₇	#533	1	1	yes	characteristic
232	C₄×C₄₇	#533	1	1	yes	characteristic
233	Dic₄₇	—	2	2	no	—
234	Dic₄₇	—	2	2	no	—
235	Dic₄₇	—	2	4	no	—
236	Dic₄₇	—	2	2	no	—
237	Dic₄₇	—	4	2	no	—
238	C₂×#432	—	47	1	no	—
239	C₂×C₄×M₁₆	—	47	1	no	—
240	C₄×#117	—	47	1	no	—
241	#1939	—	47	1	no	—
242	#1939	—	47	1	no	—
243	#1939	—	47	1	no	—
244	#1939	D₄₇	1	1	yes	characteristic, complemented
245	#1851	—	47	2	no	—
246	#1851	—	47	2	no	—
247	#1767	—	47	2	no	—
248	#1767	—	47	2	no	—
249	C₂×C₄₇	#2296	1	1	yes	characteristic
250	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
251	C₂×C₄₇	#2905	1	1	yes	characteristic
252	C₂×C₄₇	#2970	1	1	yes	characteristic
253	C₂×C₄₇	#2970	1	1	yes	characteristic
254	C₂×C₄₇	#2971	1	1	yes	characteristic
255	C₂×C₄₇	#2971	1	1	yes	characteristic
256	D₄₇	—	4	2	no	—
257	C₂²×M₁₆	—	47	1	no	—
258	C₂²×M₁₆	—	47	1	no	—
259	C₂×#117	—	47	1	no	—
260	C₂×#117	—	47	1	no	—
261	C₂²×C₄²	—	47	1	no	—
262	#432	—	94	4	no	—
263	C₂×C₄⋊C₈	—	47	2	no	—
264	C₂×C₄⋊C₈	—	47	2	no	—
265	C₂×C₄⋊C₈	—	47	2	no	—
266	C₂×C₄⋊C₈	—	47	1	no	—
267	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
268	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	—	47	2	no	—
270	C₄×M₁₆	—	94	4	no	—
271	C₂×#97	—	47	1	no	—
272	C₂×#97	—	47	1	no	—
273	C₂×#97	—	47	2	no	—
274	C₂×C₄×C₈	—	47	1	no	—
275	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
276	C₄×C₄⋊C₄	—	47	1	no	—
277	C₄×C₄⋊C₄	—	47	1	no	—
278	C₄×C₄⋊C₄	—	47	1	no	—
279	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
280	C₄×C₂²⋊C₄	—	47	2	no	—
281	C₄×C₂²⋊C₄	—	47	2	no	—
282	#376	—	47	2	no	—
283	C₄³	—	47	2	no	—
284	#336	—	47	2	no	—
285	#336	—	47	2	no	—
286	#336	—	47	2	no	—
287	#336	C₂×D₄₇	1	2	yes	—
288	C₄₇	#21356	1	1	yes	characteristic, complemented, Sylow
289	C₂³×C₄	—	47	1	no	—
290	C₂³×C₄	—	47	1	no	—
291	C₂³×C₄	—	47	1	no	—
292	C₂×M₁₆	—	94	2	no	—
293	C₂×M₁₆	—	94	2	no	—
294	C₂×M₁₆	—	94	2	no	—
295	C₂×M₁₆	—	94	2	no	—
296	C₂×M₁₆	—	94	2	no	—
297	C₂×M₁₆	—	94	2	no	—
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	—	47	1	no	—
300	C₂²×C₈	—	47	2	no	—
301	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
302	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
303	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
304	#117	—	94	4	no	—
305	#117	—	94	4	no	—
306	C₂×C₄⋊C₄	—	47	1	no	—
307	C₂×C₄⋊C₄	—	47	1	no	—
308	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	47	2	no	—
311	C₂×C₂²⋊C₄	—	47	2	no	—
312	C₂×C₄²	—	47	1	no	—
313	C₂×C₄²	—	47	1	no	—
314	C₂×C₄²	—	47	1	no	—
315	C₂×C₄²	—	47	4	no	—
316	C₂×C₄²	—	47	4	no	—
317	C₂×C₄²	—	47	2	no	—
318	C₂×C₄²	—	47	2	no	—
319	C₂×C₄²	—	47	2	no	—
320	C₂×C₄²	—	47	2	no	—
321	C₂×C₄²	—	47	2	no	—
322	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
323	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
324	C₄⋊C₈	—	2	4	no	—
325	C₄⋊C₈	—	2	2	no	—
326	C₄⋊C₈	—	94	4	no	—
327	C₄⋊C₈	—	94	4	no	—
328	C₄⋊C₈	—	94	4	no	—
329	C₄⋊C₈	—	94	2	no	—
330	C₂²⋊C₈	—	94	4	no	—
331	#97	—	94	2	no	—
332	#97	—	94	2	no	—
333	#97	—	94	4	no	—
334	C₄×C₈	—	2	2	no	—
335	C₄×C₈	—	94	2	no	—
336	#95	—	47	2	no	—
337	#95	—	47	2	no	—
338	#95	—	47	2	no	—
339	#95	C₄×D₄₇	1	2	yes	—
340	C₂⁴	—	47	1	no	—
341	C₂²×C₄	—	47	1	no	—
342	C₂²×C₄	—	47	2	no	—
343	C₂²×C₄	—	47	1	no	—
344	C₂²×C₄	—	47	1	no	—
345	C₂²×C₄	—	47	4	no	—
346	C₂²×C₄	—	47	2	no	—
347	C₂²×C₄	—	47	2	no	—
348	C₂²×C₄	—	47	4	no	—
349	C₂²×C₄	—	47	2	no	—
350	C₂²×C₄	—	94	2	no	—
351	C₂²×C₄	—	94	2	no	—
352	C₂²×C₄	—	94	1	no	—
353	C₂²×C₄	—	94	1	no	—
354	C₂²×C₄	—	94	1	no	—
355	C₂²×C₄	—	94	1	no	—
356	C₂²×C₄	—	188	1	no	—
357	C₂²×C₄	—	188	1	no	—
358	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
359	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
361	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
362	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
363	M₁₆	—	94	8	no	—
364	M₁₆	—	94	8	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	47	2	no	—
373	C₂×C₈	—	47	2	no	—
374	C₂×C₈	—	94	1	no	—
375	C₂×C₈	—	94	1	no	—
376	C₂×C₈	—	94	1	no	—
377	C₂×C₈	—	94	1	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	94	2	no	—
381	C₂×C₈	#10625352	1	2	yes	—
382	C₂×C₈	#10625354	1	2	yes	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	47	4	no	—
385	C₄⋊C₄	—	94	2	no	—
386	C₄⋊C₄	#10625324	1	4	yes	complemented
387	C₂²⋊C₄	—	94	4	no	—
388	C₂²⋊C₄	—	94	4	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	47	4	no	—
392	C₄²	—	47	4	no	—
393	C₄²	—	47	2	no	—
394	C₄²	—	47	2	no	—
395	C₄²	—	94	4	no	—
396	C₄²	—	94	4	no	—
397	C₄²	—	94	2	no	—
398	C₄²	—	94	2	no	—
399	C₄²	—	188	2	no	—
400	C₄²	—	188	2	no	—
401	C₄²	D₄×D₄₇	1	2	yes	—
402	C₄²	Q₈×D₄₇	1	2	yes	—
403	C₂³	—	47	2	no	—
404	C₂³	—	94	1	no	—
405	C₂³	—	94	1	no	—
406	C₂³	—	94	1	no	—
407	C₂³	—	94	1	no	—
408	C₂³	—	94	1	no	—
409	C₂³	—	94	1	no	—
410	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	47	2	no	—
419	C₂×C₄	—	47	2	no	—
420	C₂×C₄	—	47	2	no	—
421	C₂×C₄	—	47	4	no	—
422	C₂×C₄	—	94	1	no	—
423	C₂×C₄	—	94	2	no	—
424	C₂×C₄	—	94	1	no	—
425	C₂×C₄	—	94	1	no	—
426	C₂×C₄	—	94	1	no	—
427	C₂×C₄	—	94	1	no	—
428	C₂×C₄	—	94	1	no	—
429	C₂×C₄	—	94	2	no	—
430	C₂×C₄	—	94	2	no	—
431	C₂×C₄	—	94	2	no	—
432	C₂×C₄	—	94	8	no	—
433	C₂×C₄	—	94	2	no	—
434	C₂×C₄	—	94	2	no	—
435	C₂×C₄	—	94	2	no	—
436	C₂×C₄	—	94	2	no	—
437	C₂×C₄	—	94	2	no	—
438	C₂×C₄	—	188	4	no	—
439	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
440	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
441	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
442	C₂×C₄	C₂×#10625324	1	4	yes	—
443	C₂×C₄	C₂×#10625324	1	2	yes	—
444	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
445	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
446	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
447	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
448	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
449	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	4	2	no	—
453	C₈	—	94	2	no	—
454	C₈	—	94	2	no	—
455	C₈	—	188	2	no	—
456	C₂²	—	94	2	no	—
457	C₂²	—	94	2	no	—
458	C₂²	—	94	2	no	—
459	C₂²	—	188	1	no	—
460	C₂²	—	188	1	no	—
461	C₂²	—	188	1	no	—
462	C₂²	—	188	1	no	—
463	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
464	C₂²	C₄×#10625352	1	1	yes	characteristic
465	C₂²	C₄×#10625354	1	1	yes	characteristic
466	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
467	C₂²	C₂²×#10625324	1	1	yes	characteristic
468	C₂²	#15689888	1	1	yes	characteristic
469	C₂²	#15689888	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	2	4	no	—
472	C₄	—	4	2	no	—
473	C₄	—	94	2	no	—
474	C₄	—	94	2	no	—
475	C₄	—	94	2	no	—
476	C₄	—	94	4	no	—
477	C₄	—	188	2	no	—
478	C₄	#15689145	1	4	yes	—
479	C₄	#15689633	1	1	yes	characteristic
480	C₄	#15689636	1	1	yes	characteristic
481	C₄	#15689678	1	1	yes	characteristic
482	C₄	#15689679	1	1	yes	characteristic
483	C₂	—	188	2	no	—
484	C₂	#20245869	1	1	yes	characteristic
485	C₂	C₂×#15689145	1	1	yes	characteristic
486	C₂	#20251949	1	1	yes	characteristic
487	C₂	#20252396	1	1	yes	characteristic
488	C₂	#20252401	1	1	yes	characteristic
489	C₂	#20252404	1	1	yes	characteristic
490	C₂	#20252407	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1939	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1939	D₄₇
hypocenter	C₄₇	#21356
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
4. #20244107	C₂	semidirect
5. #20244106	C₂	semidirect
6. #20244104	C₂	semidirect
9. #20243243	C₂	semidirect
10. #20243240	C₂	semidirect
11. C₄₇×#1939	C₂	semidirect
127. C₄⋊C₄×C₄₇	M₁₆	semidirect
135. C₄⋊Dic₄₇	M₁₆	semidirect
244. #1939	D₄₇	semidirect
288. C₄₇	#21356	semidirect
386. C₄⋊C₄	#10625324	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689179	2
C₂×C₄×#10625324	2
C₄×#13093982	2
#20244107	2
#20244106	2
#20244104	2
#20243572	2
#20243569	2
#20243243	2
#20243240	2
C₄₇×#1939	2
#21356	47