Subgroups — #26185907

Order 12032.

700 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094050	C₂	1	1	yes	maximal, characteristic
3	#20242252	C₂	1	2	yes	maximal, complemented
4	#20242245	C₂	1	2	yes	maximal, complemented
5	#20242224	C₂	1	2	yes	maximal, complemented
6	#20242217	C₂	1	2	yes	maximal, complemented
7	#20242141	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241768	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241678	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094050	C₄	1	1	yes	characteristic
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689253	C₂²	1	2	yes	complemented
15	#15689233	C₄	1	2	yes	—
16	#15689223	C₄	1	2	yes	—
17	C₄×#10625335	C₂²	1	2	yes	—
18	C₄×#10625334	C₂²	1	2	yes	—
19	#15689202	C₂²	1	2	yes	complemented
20	#15689191	—	2	2	no	—
21	#15689179	—	2	1	no	—
22	#15689163	C₄	1	1	yes	characteristic
23	#15689145	—	2	1	no	—
24	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
25	#15689128	C₄	1	1	yes	characteristic
26	#15689122	C₄	1	1	yes	characteristic
27	C₄×#10625329	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	#15688875	C₂²	1	2	yes	complemented
30	#15688873	C₂²	1	2	yes	complemented
31	#15688853	C₂²	1	1	yes	characteristic, complemented
32	#15688853	C₂²	1	1	yes	characteristic, complemented
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
34	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
35	#15688850	C₂²	1	1	yes	characteristic, complemented
36	#15688850	C₂²	1	1	yes	characteristic, complemented
37	#15688845	C₂²	1	2	yes	complemented
38	#15688844	C₂²	1	2	yes	complemented
39	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₄₇	—	2	1	no	—
41	C₈×D₄×C₄₇	—	2	1	no	—
42	C₈×D₄×C₄₇	C₂²	1	2	yes	—
43	C₈×D₄×C₄₇	C₂²	1	2	yes	—
44	C₄₇×#431	C₂²	1	1	yes	characteristic
45	C₄₇×#431	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
47	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
48	#13094050	—	2	4	no	—
49	C₂×#10625335	C₂×C₄	1	2	yes	—
50	C₂×#10625334	C₂×C₄	1	2	yes	—
51	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
52	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
53	C₂×#10625324	—	2	2	no	—
54	C₂²×C₄₇⋊C₈	—	2	1	no	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
57	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
58	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
59	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
60	C₄×C₂²⋊D₄₇	—	2	1	no	—
61	C₄×C₂²⋊D₄₇	—	2	1	no	—
62	#13093983	C₂×C₄	1	1	yes	characteristic
63	#13093981	—	2	1	no	—
64	C₄²×D₄₇	—	2	1	no	—
65	#13093957	C₂×C₄	1	2	yes	—
66	#13093955	C₂×C₄	1	2	yes	—
67	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
69	Dic₄₇⋊C₈	—	2	2	no	—
70	#13093947	C₂×C₄	1	2	yes	—
71	#13093945	C₂×C₄	1	2	yes	—
72	#13093945	C₂×C₄	1	2	yes	—
73	#13093944	C₂×C₄	1	2	yes	—
74	(C₂×D₄₇)⋊C₈	—	2	2	no	—
75	#13093935	C₂×C₄	1	2	yes	—
76	#13093934	—	2	2	no	—
77	C₄×C₄₇⋊C₈	—	2	1	no	—
78	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
81	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₄₇	—	2	1	no	—
83	C₂²×C₈×C₄₇	—	2	2	no	—
84	C₂²×C₈×C₄₇	—	2	2	no	—
85	C₄×D₄×C₄₇	—	2	1	no	—
86	C₄×D₄×C₄₇	—	2	1	no	—
87	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
88	C₄×D₄×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
94	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₂²⋊C₈×C₄₇	—	2	1	no	—
97	C₂²⋊C₈×C₄₇	—	2	2	no	—
98	C₂²⋊C₈×C₄₇	—	2	2	no	—
99	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
100	C₄×C₈×C₄₇	—	2	1	no	—
101	C₄×C₈×C₄₇	C₂³	1	2	yes	—
102	C₂⁴×C₄₇	—	2	1	no	—
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	—	2	2	no	—
105	C₂×D₄×C₄₇	M₁₆	1	4	yes	complemented
106	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	8	1	no	—
111	C₂²×C₄×C₄₇	—	8	1	no	—
112	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
115	C₂×C₂²⋊D₄₇	—	2	1	no	—
116	#10625350	—	2	2	no	—
117	#10625350	—	2	2	no	—
118	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₄₇	—	2	1	no	—
120	C₂×C₄×D₄₇	—	2	1	no	—
121	C₂×C₄×D₄₇	—	2	1	no	—
122	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	8	2	no	—
126	C₂×C₈×C₄₇	—	8	2	no	—
127	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂²⋊C₄×C₄₇	—	2	2	no	—
132	C₂²⋊C₄×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	#41	1	1	yes	characteristic
136	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
137	C₂²⋊Dic₄₇	—	2	1	no	—
138	#10625335	—	2	4	no	—
139	#10625334	—	2	4	no	—
140	(C₂×D₄₇)⋊C₄	—	2	1	no	—
141	(C₂×D₄₇)⋊C₄	—	2	1	no	—
142	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
144	Dic₄₇⋊C₄	—	2	1	no	—
145	Dic₄₇⋊C₄	—	2	1	no	—
146	C₄×Dic₄₇	—	2	1	no	—
147	C₄×Dic₄₇	—	2	1	no	—
148	C₄×Dic₄₇	—	2	1	no	—
149	#10625329	—	2	2	no	—
150	#10625329	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	4	2	no	—
155	C₂×C₄₇⋊C₈	—	8	1	no	—
156	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
157	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
158	#10625324	—	8	2	no	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	2	4	no	—
161	C₂³×C₄₇	—	8	1	no	—
162	C₂³×C₄₇	—	8	1	no	—
163	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
164	C₂²×D₄₇	—	2	1	no	—
165	D₄×C₄₇	—	2	2	no	—
166	D₄×C₄₇	—	2	4	no	—
167	D₄×C₄₇	C₂×M₁₆	1	4	yes	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	8	2	no	—
175	C₂×C₄×C₄₇	—	8	1	no	—
176	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
180	C₂×C₄×C₄₇	#131	1	2	yes	—
181	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂²⋊D₄₇	—	4	2	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	—	2	1	no	—
188	D₁₈₈	—	2	1	no	—
189	D₁₈₈	—	2	1	no	—
190	C₄×D₄₇	—	4	1	no	—
191	C₄×D₄₇	—	4	1	no	—
192	C₄×D₄₇	—	4	2	no	—
193	C₄×D₄₇	—	8	1	no	—
194	Dic₉₄	—	2	1	no	—
195	Dic₉₄	—	2	1	no	—
196	C₈×C₄₇	—	2	2	no	—
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	4	1	no	—
199	C₈×C₄₇	—	4	1	no	—
200	C₄₇⋊C₈	—	2	2	no	—
201	C₄₇⋊C₈	—	2	2	no	—
202	C₄₇⋊C₈	—	2	2	no	—
203	C₄₇⋊C₈	—	4	1	no	—
204	C₄₇⋊C₈	—	4	2	no	—
205	#17873	—	47	1	no	maximal, Sylow
206	C₂²×C₄₇	—	2	1	no	—
207	C₂²×C₄₇	—	2	1	no	—
208	C₂²×C₄₇	—	2	4	no	—
209	C₂²×C₄₇	—	4	2	no	—
210	C₂²×C₄₇	—	4	2	no	—
211	C₂²×C₄₇	—	8	4	no	—
212	C₂²×C₄₇	#435	1	2	yes	—
213	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂×D₄₇	—	4	1	no	—
215	C₂×D₄₇	—	4	1	no	—
216	C₂×D₄₇	—	4	1	no	—
217	C₄×C₄₇	—	2	1	no	—
218	C₄×C₄₇	—	2	1	no	—
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	#435	1	2	yes	—
222	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
223	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
224	C₄×C₄₇	#576	1	1	yes	characteristic
225	C₄×C₄₇	#577	1	1	yes	characteristic
226	Dic₄₇	—	4	1	no	—
227	Dic₄₇	—	4	1	no	—
228	Dic₄₇	—	4	1	no	—
229	#2989	—	47	1	no	—
230	#2972	D₄₇	1	1	yes	characteristic, complemented
231	C₄×AGL(1,ℤ/8)	—	47	1	no	—
232	#1586	—	47	2	no	—
233	#1585	—	47	2	no	—
234	#1582	—	47	2	no	—
235	#1581	—	47	2	no	—
236	#1565	—	47	1	no	—
237	#1476	—	47	1	no	—
238	C₂×D₄⋊C₈	—	47	1	no	—
239	#1451	—	47	1	no	—
240	C₂×C₄₇	—	2	2	no	—
241	C₂×C₄₇	—	4	4	no	—
242	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
243	C₂×C₄₇	#2946	1	1	yes	characteristic
244	C₂×C₄₇	#2956	1	1	yes	characteristic
245	D₄₇	—	8	1	no	—
246	C₂×AGL(1,ℤ/8)	—	47	1	no	—
247	C₄×#41	—	47	1	no	—
248	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
249	#446	—	47	2	no	—
250	#442	—	47	2	no	—
251	#440	—	47	2	no	—
252	C₄×SD₁₆	—	47	2	no	—
253	C₄×D₈	—	47	2	no	—
254	#436	—	47	2	no	—
255	#435	—	94	2	no	—
256	C₈×D₄	—	2	1	no	—
257	C₈×D₄	—	2	1	no	—
258	C₈×D₄	C₂×D₄₇	1	2	yes	—
259	C₈×D₄	C₂×D₄₇	1	2	yes	—
260	#432	—	94	1	no	—
261	#431	C₂×D₄₇	1	1	yes	characteristic
262	#431	C₂×D₄₇	1	1	yes	characteristic
263	#428	—	47	1	no	—
264	#423	—	94	1	no	—
265	C₂×C₄⋊C₈	—	47	1	no	—
266	#418	—	47	1	no	—
267	#417	—	47	1	no	—
268	C₂×C₂²⋊C₈	—	2	2	no	—
269	C₄×M₁₆	—	47	1	no	—
270	C₂×C₄×C₈	—	47	1	no	—
271	#335	—	47	2	no	—
272	#334	—	47	2	no	—
273	Q₈⋊C₈	—	47	1	no	—
274	Q₈⋊C₈	—	47	1	no	—
275	D₄⋊C₈	—	47	2	no	—
276	D₄⋊C₈	—	47	2	no	—
277	D₄⋊C₈	—	47	1	no	—
278	D₄⋊C₈	—	47	1	no	—
279	#322	—	47	2	no	—
280	#322	—	47	2	no	—
281	C₄₇	#17873	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	—	47	1	no	—
283	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	AGL(1,ℤ/8)	—	94	4	no	—
286	C₂×SD₁₆	—	47	2	no	—
287	C₂×D₈	—	47	2	no	—
288	C₂×M₁₆	—	47	1	no	—
289	C₂×M₁₆	—	47	1	no	—
290	C₂×M₁₆	—	94	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	94	1	no	—
294	C₂²×C₈	—	94	1	no	—
295	C₄×Q₈	—	47	1	no	—
296	C₄×Q₈	—	47	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	47	1	no	—
300	C₄×D₄	—	47	1	no	—
301	C₄×D₄	—	94	1	no	—
302	C₄×D₄	—	94	1	no	—
303	C₄×D₄	C₄×D₄₇	1	2	yes	—
304	C₄×D₄	C₂²×D₄₇	1	2	yes	—
305	#117	—	47	1	no	—
306	#117	—	94	1	no	—
307	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₄²	—	94	1	no	—
310	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
311	#107	—	47	2	no	—
312	#106	—	47	2	no	—
313	C₄⋊C₈	—	47	2	no	—
314	C₄⋊C₈	—	94	2	no	—
315	C₄⋊C₈	—	94	1	no	—
316	C₄⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
317	C₄⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
318	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
319	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
320	#103	—	47	2	no	—
321	#102	—	47	2	no	—
322	#102	—	47	2	no	—
323	#102	—	47	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	94	2	no	—
328	C₂²⋊C₈	C₂²⋊D₄₇	1	2	yes	—
329	#97	—	47	2	no	—
330	#97	—	94	2	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	47	2	no	—
333	C₄×C₈	—	47	1	no	—
334	C₄×C₈	—	47	1	no	—
335	C₄×C₈	—	94	1	no	—
336	C₄×C₈	C₂²×D₄₇	1	2	yes	—
337	C₂⁴	—	2	1	no	—
338	#41	—	94	2	no	—
339	#41	—	94	2	no	—
340	C₂×Q₈	—	47	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	47	1	no	—
344	C₂×D₄	—	94	1	no	—
345	C₂×D₄	#10625324	1	4	yes	complemented
346	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	8	1	no	—
351	C₂²×C₄	—	8	1	no	—
352	C₂²×C₄	—	94	1	no	—
353	C₂²×C₄	—	94	1	no	—
354	C₂²×C₄	—	94	1	no	—
355	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
356	C₂²×C₄	#10625350	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
358	SD₁₆	—	94	4	no	—
359	D₈	—	94	4	no	—
360	M₁₆	—	94	2	no	—
361	M₁₆	—	94	2	no	—
362	M₁₆	—	376	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	8	2	no	—
366	C₂×C₈	—	8	2	no	—
367	C₂×C₈	—	47	2	no	—
368	C₂×C₈	—	47	2	no	—
369	C₂×C₈	—	94	1	no	—
370	C₂×C₈	—	94	2	no	—
371	C₂×C₈	—	94	1	no	—
372	C₂×C₈	—	376	1	no	—
373	C₂×C₈	—	188	2	no	—
374	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
375	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	47	1	no	—
378	C₄⋊C₄	—	47	1	no	—
379	C₄⋊C₄	—	94	1	no	—
380	C₄⋊C₄	—	94	1	no	—
381	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	94	1	no	—
385	C₂²⋊C₄	—	94	1	no	—
386	C₂²⋊C₄	—	94	1	no	—
387	C₄²	—	94	1	no	—
388	C₄²	—	94	1	no	—
389	C₄²	—	94	1	no	—
390	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
391	C₄²	#10625350	1	1	yes	characteristic
392	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
393	C₄²	C₂³×D₄₇	1	1	yes	characteristic
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	8	1	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	94	1	no	—
399	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
400	Q₈	—	94	1	no	—
401	Q₈	—	94	1	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	4	no	—
404	D₄	—	94	1	no	—
405	D₄	—	94	1	no	—
406	D₄	—	188	2	no	—
407	D₄	C₂×#10625324	1	4	yes	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	8	1	no	—
416	C₂×C₄	—	94	1	no	—
417	C₂×C₄	—	94	1	no	—
418	C₂×C₄	—	94	1	no	—
419	C₂×C₄	—	376	1	no	—
420	C₂×C₄	—	188	1	no	—
421	C₂×C₄	—	188	1	no	—
422	C₂×C₄	—	188	2	no	—
423	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
424	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
425	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂×#10625324	1	2	yes	—
427	C₂×C₄	#13094030	1	2	yes	—
428	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	94	2	no	—
436	C₈	—	94	2	no	—
437	C₈	—	94	2	no	—
438	C₈	—	188	1	no	—
439	C₈	—	188	2	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	4	no	—
446	C₂²	—	188	1	no	—
447	C₂²	—	188	1	no	—
448	C₂²	—	188	1	no	—
449	C₂²	#15689194	1	2	yes	—
450	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	188	1	no	—
456	C₄	—	188	1	no	—
457	C₄	—	188	1	no	—
458	C₄	#15689194	1	2	yes	—
459	C₄	C₂²×#10625324	1	1	yes	characteristic
460	C₄	C₂×#13094030	1	1	yes	characteristic
461	C₄	#15689926	1	1	yes	characteristic
462	C₄	#15689934	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	4	no	—
465	C₂	—	376	1	no	—
466	C₂	C₂×#15689194	1	1	yes	characteristic
467	C₂	#20252220	1	1	yes	characteristic
468	C₂	#20252295	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#2972	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094050	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#2972	D₄₇
hypocenter	C₄₇	#17873
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2972

Complements

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

N	H ≅ G/N	type
1. #20252501	C₂	semidirect
3. #20242252	C₂	semidirect
4. #20242245	C₂	semidirect
5. #20242224	C₂	semidirect
6. #20242217	C₂	semidirect
7. #20242141	C₂	semidirect
8. #20241768	C₂	semidirect
9. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
10. #20241678	C₂	semidirect
11. C₄₇×#2972	C₂	semidirect
14. #15689253	C₂²	semidirect
19. #15689202	C₂²	semidirect
29. #15688875	C₂²	semidirect
30. #15688873	C₂²	semidirect
31. #15688853	C₂²	semidirect
32. #15688853	C₂²	semidirect
35. #15688850	C₂²	semidirect
36. #15688850	C₂²	semidirect
37. #15688845	C₂²	semidirect
38. #15688844	C₂²	semidirect
105. C₂×D₄×C₄₇	M₁₆	semidirect
230. #2972	D₄₇	semidirect
281. C₄₇	#17873	semidirect
345. C₂×D₄	#10625324	semidirect

Maximal subgroups

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

subgroup	index
#20252501	2
C₄×#13094050	2
#20242252	2
#20242245	2
#20242224	2
#20242217	2
#20242141	2
#20241768	2
C₂×D₄⋊(C₄₇⋊C₈)	2
#20241678	2
C₄₇×#2972	2
#17873	47