Subgroups — #26185929

Order 12032.

698 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	#20252499	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252429	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242267	C₂	1	2	yes	maximal, complemented
4	#20242253	C₂	1	2	yes	maximal, complemented
5	#20242232	C₂	1	2	yes	maximal, complemented
6	#20242218	C₂	1	2	yes	maximal, complemented
7	#20242140	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×AGL(1,ℤ/8)×C₄₇	C₂	1	1	yes	maximal, characteristic
12	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
13	#15689201	—	2	1	no	—
14	#15689201	—	2	1	no	—
15	#15689201	C₂²	1	2	yes	—
16	#15689201	C₂²	1	2	yes	—
17	D₄×C₄₇⋊C₈	—	2	2	no	—
18	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
19	#15689176	—	2	1	no	—
20	#15689176	C₂²	1	1	yes	characteristic
21	#15689176	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	#15689087	—	2	2	no	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	#15688876	C₂²	1	2	yes	complemented
27	#15688874	C₂²	1	2	yes	complemented
28	Q₈⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
29	Q₈⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
30	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
31	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
32	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
34	#15688845	C₂²	1	2	yes	complemented
35	#15688845	C₂²	1	2	yes	complemented
36	C₂×AGL(1,ℤ/8)×C₄₇	C₄	1	1	yes	characteristic
37	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#442	C₄	1	2	yes	—
40	C₄₇×#440	C₄	1	2	yes	—
41	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	—
42	C₄×D₈×C₄₇	C₂²	1	2	yes	—
43	C₄₇×#428	C₄	1	1	yes	characteristic
44	C₄₇×#418	C₄	1	1	yes	characteristic
45	C₄₇×#417	C₄	1	1	yes	characteristic
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625329	—	2	2	no	—
48	C₂×#10625329	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	—	2	1	no	—
50	C₂²×C₄₇⋊C₈	—	2	1	no	—
51	C₂²×C₄₇⋊C₈	—	2	2	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
54	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
55	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
58	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
59	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
60	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
64	C₄×C₄₇⋊C₈	—	2	1	no	—
65	C₄×C₄₇⋊C₈	—	2	1	no	—
66	C₄×C₄₇⋊C₈	—	2	2	no	—
67	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
70	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₄₇	—	2	1	no	—
73	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
74	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₄₇	—	2	1	no	—
81	C₄×D₄×C₄₇	—	2	1	no	—
82	C₄×D₄×C₄₇	—	2	1	no	—
83	C₄×D₄×C₄₇	—	2	1	no	—
84	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
85	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₄×D₄×C₄₇	C₂³	1	2	yes	—
87	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
88	#117×C₄₇	—	2	1	no	—
89	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	—	2	1	no	—
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	#107×C₄₇	C₂×C₄	1	2	yes	—
95	#106×C₄₇	C₂×C₄	1	2	yes	—
96	#103×C₄₇	C₂×C₄	1	2	yes	—
97	#102×C₄₇	C₂×C₄	1	2	yes	—
98	#102×C₄₇	C₂×C₄	1	2	yes	—
99	#102×C₄₇	C₂×C₄	1	2	yes	—
100	#97×C₄₇	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₄₇	C₂³	1	2	yes	—
102	C₂⁴×C₄₇	—	2	1	no	—
103	#41×C₄₇	—	2	2	no	—
104	#41×C₄₇	M₁₆	1	4	yes	complemented
105	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×D₄×C₄₇	—	2	1	no	—
107	C₂×D₄×C₄₇	—	2	1	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	2	2	no	—
110	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	8	1	no	—
119	C₂²×C₄×C₄₇	—	8	1	no	—
120	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	SD₁₆×C₄₇	—	2	4	no	—
124	D₈×C₄₇	—	2	4	no	—
125	M₁₆×C₄₇	—	2	2	no	—
126	M₁₆×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²⋊C₄×C₄₇	—	2	1	no	—
136	C₂²⋊C₄×C₄₇	—	2	2	no	—
137	C₂²⋊C₄×C₄₇	—	2	1	no	—
138	C₂²⋊C₄×C₄₇	—	2	2	no	—
139	C₂²⋊C₄×C₄₇	—	2	1	no	—
140	C₄²×C₄₇	—	2	1	no	—
141	C₄²×C₄₇	—	2	1	no	—
142	C₄²×C₄₇	—	2	1	no	—
143	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₇	#41	1	1	yes	characteristic
146	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
147	#10625329	—	8	2	no	—
148	#10625329	—	8	2	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	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	2	no	—
156	C₂×C₄₇⋊C₈	—	8	1	no	—
157	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
158	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
159	C₂³×C₄₇	—	2	1	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	—	8	1	no	—
163	C₂³×C₄₇	—	8	1	no	—
164	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
165	Q₈×C₄₇	—	2	1	no	—
166	Q₈×C₄₇	C₂×M₁₆	1	2	yes	—
167	D₄×C₄₇	—	2	4	no	—
168	D₄×C₄₇	—	2	2	no	—
169	D₄×C₄₇	—	2	1	no	—
170	D₄×C₄₇	—	2	2	no	—
171	D₄×C₄₇	—	4	2	no	—
172	D₄×C₄₇	C₂×M₁₆	1	2	yes	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	8	1	no	—
186	C₂×C₄×C₄₇	—	8	2	no	—
187	C₂×C₄×C₄₇	—	8	1	no	—
188	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₄₇	#131	1	2	yes	—
193	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
196	C₈×C₄₇	—	2	2	no	—
197	C₈×C₄₇	—	2	2	no	—
198	C₄₇⋊C₈	—	2	2	no	—
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	—	2	2	no	—
201	C₄₇⋊C₈	—	4	1	no	—
202	C₄₇⋊C₈	—	4	2	no	—
203	C₄₇⋊C₈	—	4	1	no	—
204	C₄₇⋊C₈	—	4	1	no	—
205	#17875	—	47	1	no	maximal, Sylow
206	C₂²×C₄₇	—	2	1	no	—
207	C₂²×C₄₇	—	2	1	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	4	1	no	—
210	C₂²×C₄₇	—	4	1	no	—
211	C₂²×C₄₇	—	4	2	no	—
212	C₂²×C₄₇	—	4	2	no	—
213	C₂²×C₄₇	—	4	2	no	—
214	C₂²×C₄₇	—	8	4	no	—
215	C₂²×C₄₇	#435	1	2	yes	—
216	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	2	1	no	—
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	2	1	no	—
221	C₄×C₄₇	—	4	1	no	—
222	C₄×C₄₇	—	4	2	no	—
223	C₄×C₄₇	—	4	1	no	—
224	C₄×C₄₇	#435	1	2	yes	—
225	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
226	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
227	C₄×C₄₇	#576	1	1	yes	characteristic
228	C₄×C₄₇	#577	1	1	yes	characteristic
229	#2988	—	47	1	no	—
230	#2975	—	47	1	no	—
231	C₄×AGL(1,ℤ/8)	D₄₇	1	1	yes	characteristic
232	#1588	—	47	2	no	—
233	#1586	—	47	2	no	—
234	#1583	—	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	2	no	—
242	C₂×C₄₇	—	8	2	no	—
243	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
244	C₂×C₄₇	#2946	1	1	yes	characteristic
245	C₂×C₄₇	#2956	1	1	yes	characteristic
246	C₂×AGL(1,ℤ/8)	Dic₄₇	1	1	yes	characteristic
247	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
249	C₈×Q₈	—	47	2	no	—
250	#442	Dic₄₇	1	2	yes	—
251	#440	Dic₄₇	1	2	yes	—
252	C₄×SD₁₆	C₂×D₄₇	1	2	yes	—
253	C₄×D₈	C₂×D₄₇	1	2	yes	—
254	#436	—	47	2	no	—
255	#436	—	47	2	no	—
256	#436	—	94	1	no	—
257	#436	—	94	1	no	—
258	C₈×D₄	—	47	2	no	—
259	C₈×D₄	—	94	2	no	—
260	#431	—	47	1	no	—
261	#431	—	47	1	no	—
262	#431	—	94	1	no	—
263	#428	Dic₄₇	1	1	yes	characteristic
264	C₂×C₄⋊C₈	—	47	1	no	—
265	C₂×C₄⋊C₈	—	94	1	no	—
266	#418	Dic₄₇	1	1	yes	characteristic
267	#417	Dic₄₇	1	1	yes	characteristic
268	#407	—	94	2	no	—
269	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
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	1	no	—
276	D₄⋊C₈	—	47	2	no	—
277	D₄⋊C₈	—	47	1	no	—
278	D₄⋊C₈	—	47	2	no	—
279	#322	—	47	2	no	—
280	#322	—	47	2	no	—
281	C₄₇	#17875	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
283	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	AGL(1,ℤ/8)	—	2	4	no	—
286	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
287	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
288	C₂×M₁₆	—	94	2	no	—
289	C₂×M₁₆	—	94	2	no	—
290	C₂×M₁₆	C₂×Dic₄₇	1	1	yes	characteristic
291	C₂×M₁₆	C₂×Dic₄₇	1	1	yes	characteristic
292	C₂²×C₈	—	94	2	no	—
293	C₂²×C₈	—	94	1	no	—
294	C₂²×C₈	—	94	1	no	—
295	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
296	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
302	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
303	C₄×D₄	C₂²×D₄₇	1	2	yes	—
304	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
305	#117	—	2	1	no	—
306	#117	C₂×Dic₄₇	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
311	#107	C₂×Dic₄₇	1	2	yes	—
312	#106	C₂×Dic₄₇	1	2	yes	—
313	C₄⋊C₈	—	47	1	no	—
314	C₄⋊C₈	—	47	1	no	—
315	C₄⋊C₈	—	47	2	no	—
316	C₄⋊C₈	—	47	1	no	—
317	C₄⋊C₈	—	47	1	no	—
318	C₄⋊C₈	—	94	2	no	—
319	C₄⋊C₈	—	94	1	no	—
320	#103	C₂×Dic₄₇	1	2	yes	—
321	#102	C₂×Dic₄₇	1	2	yes	—
322	#102	C₂×Dic₄₇	1	2	yes	—
323	#102	C₂×Dic₄₇	1	2	yes	—
324	C₂²⋊C₈	—	47	2	no	—
325	C₂²⋊C₈	—	94	2	no	—
326	C₂²⋊C₈	—	94	2	no	—
327	C₂²⋊C₈	—	94	2	no	—
328	C₂²⋊C₈	—	94	1	no	—
329	#97	C₂×Dic₄₇	1	2	yes	—
330	C₄×C₈	—	47	2	no	—
331	C₄×C₈	—	47	1	no	—
332	C₄×C₈	—	47	1	no	—
333	C₄×C₈	—	94	2	no	—
334	C₄×C₈	—	94	1	no	—
335	C₄×C₈	—	94	1	no	—
336	C₄×C₈	C₂²×D₄₇	1	2	yes	—
337	C₂⁴	—	2	1	no	—
338	#41	—	2	2	no	—
339	#41	#10625329	1	4	yes	complemented
340	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
346	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	8	1	no	—
354	C₂²×C₄	—	8	1	no	—
355	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
356	C₂²×C₄	#10625352	1	1	yes	characteristic
357	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
358	SD₁₆	—	2	4	no	—
359	D₈	—	2	4	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	376	2	no	—
363	M₁₆	—	376	2	no	—
364	C₂×C₈	—	47	2	no	—
365	C₂×C₈	—	47	2	no	—
366	C₂×C₈	—	94	1	no	—
367	C₂×C₈	—	94	1	no	—
368	C₂×C₈	—	94	1	no	—
369	C₂×C₈	—	94	2	no	—
370	C₂×C₈	—	94	1	no	—
371	C₂×C₈	—	376	2	no	—
372	C₂×C₈	—	376	1	no	—
373	C₂×C₈	—	188	2	no	—
374	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
375	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
381	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	D₄×D₄₇	1	1	yes	characteristic
391	C₄²	#10625352	1	1	yes	characteristic
392	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
393	C₄²	C₂³×D₄₇	1	1	yes	characteristic
394	C₂³	—	2	1	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	8	1	no	—
399	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	C₂×#10625329	1	2	yes	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	1	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	2	no	—
407	D₄	C₂×#10625329	1	2	yes	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	8	1	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
424	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
425	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂×#10625329	1	2	yes	—
427	C₂×C₄	#13094031	1	2	yes	—
428	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	94	2	no	—
434	C₈	—	94	2	no	—
435	C₈	—	94	2	no	—
436	C₈	—	188	1	no	—
437	C₈	—	188	2	no	—
438	C₈	—	188	1	no	—
439	C₈	—	188	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	4	no	—
449	C₂²	#15689195	1	2	yes	—
450	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	#15689195	1	2	yes	—
459	C₄	C₂²×#10625329	1	1	yes	characteristic
460	C₄	C₂×#13094031	1	1	yes	characteristic
461	C₄	#15689927	1	1	yes	characteristic
462	C₄	#15689933	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	2	no	—
465	C₂	—	8	2	no	—
466	C₂	C₂×#15689195	1	1	yes	characteristic
467	C₂	#20252221	1	1	yes	characteristic
468	C₂	#20252298	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄×AGL(1,ℤ/8)×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×AGL(1,ℤ/8)×C₄₇	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₄×AGL(1,ℤ/8)	D₄₇
hypocenter	C₄₇	#17875
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #20252499	C₂	semidirect
2. #20252429	C₂	semidirect
3. #20242267	C₂	semidirect
4. #20242253	C₂	semidirect
5. #20242232	C₂	semidirect
6. #20242218	C₂	semidirect
7. #20242140	C₂	semidirect
8. #20241770	C₂	semidirect
9. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
10. #20241675	C₂	semidirect
12. Q₈×C₄₇⋊C₈	C₂²	semidirect
18. D₄×C₄₇⋊C₈	C₂²	semidirect
26. #15688876	C₂²	semidirect
27. #15688874	C₂²	semidirect
28. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
29. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
32. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
33. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
34. #15688845	C₂²	semidirect
35. #15688845	C₂²	semidirect
104. #41×C₄₇	M₁₆	semidirect
281. C₄₇	#17875	semidirect
339. #41	#10625329	semidirect

Maximal subgroups

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

subgroup	index
#20252499	2
#20252429	2
#20242267	2
#20242253	2
#20242232	2
#20242218	2
#20242140	2
#20241770	2
C₂×D₄⋊(C₄₇⋊C₈)	2
#20241675	2
C₄×AGL(1,ℤ/8)×C₄₇	2
#17875	47