Subgroups — #26234744

Order 12032.

870 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689241	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689239	C₂	1	1	yes	maximal, characteristic
3	#20252159	C₂	1	1	yes	maximal, characteristic
4	#20251955	C₂	1	2	yes	maximal, complemented
5	#20244137	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243664	C₂	1	2	yes	maximal, complemented
7	#20243662	C₂	1	2	yes	maximal, complemented
8	#20243558	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243407	C₂	1	2	yes	maximal, complemented
10	C₈×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1945	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₂×#13094032	C₂²	1	2	yes	—
14	C₂×#13094030	C₂²	1	2	yes	—
15	#15689591	C₂²	1	2	yes	—
16	#15689241	—	2	4	no	—
17	#15689239	—	2	4	no	—
18	#15689217	C₄	1	1	yes	characteristic, complemented
19	#15689217	C₄	1	1	yes	characteristic, complemented
20	#15689210	C₄	1	2	yes	complemented
21	#15689210	C₄	1	2	yes	complemented
22	#15689205	C₄	1	1	yes	characteristic, complemented
23	#15689205	C₄	1	1	yes	characteristic, complemented
24	C₂×#13093960	C₂²	1	1	yes	characteristic
25	C₂×#13093959	C₂²	1	2	yes	—
26	#15689150	C₂²	1	2	yes	—
27	#15689148	—	2	2	no	—
28	#15689148	—	2	2	no	—
29	#15689146	C₂²	1	2	yes	—
30	#15689145	—	2	2	no	—
31	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₄⋊C₈×D₄₇	—	2	2	no	—
33	C₂×#13093952	C₂²	1	2	yes	—
34	C₂×#13093950	C₂²	1	2	yes	—
35	#15689117	C₂²	1	2	yes	—
36	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
38	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
39	#15688882	C₂²	1	2	yes	—
40	#15688878	C₂²	1	1	yes	characteristic
41	#15688877	C₂²	1	1	yes	characteristic
42	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#427	C₂²	1	1	yes	characteristic
44	C₄₇×#424	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
46	C₄₇×#339	C₂²	1	2	yes	—
47	C₂×#10625350	C₂³	1	2	yes	—
48	#13094046	D₄	1	4	yes	—
49	#13094046	Q₈	1	4	yes	—
50	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
51	C₂×#10625325	C₂×C₄	1	2	yes	—
52	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
53	#13094032	—	2	4	no	—
54	#13094032	—	4	2	no	—
55	#13094030	—	2	4	no	—
56	#13094030	—	4	2	no	—
57	C₂×#10625329	C₂³	1	2	yes	—
58	C₂×#10625324	—	2	2	no	—
59	C₂×#10625324	—	2	2	no	—
60	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₄₇	—	2	2	no	—
63	C₂×C₈×D₄₇	—	2	2	no	—
64	#13093989	C₂×C₄	1	2	yes	—
65	#13093989	C₂×C₄	1	2	yes	—
66	#13093986	C₂×C₄	1	2	yes	—
67	#13093986	C₂×C₄	1	2	yes	—
68	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
69	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
70	#13093981	—	2	2	no	—
71	C₂×Dic₄₇⋊C₄	—	2	1	no	—
72	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
74	C₄²×D₄₇	—	2	2	no	—
75	#13093960	—	2	2	no	—
76	#13093959	—	4	2	no	—
77	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
78	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
79	Dic₄₇⋊C₈	—	2	2	no	—
80	Dic₄₇⋊C₈	—	2	2	no	—
81	Dic₄₇⋊C₈	D₄	1	1	yes	characteristic
82	Dic₄₇⋊C₈	D₄	1	1	yes	characteristic
83	Dic₄₇⋊C₈	D₄	1	1	yes	characteristic
84	Dic₄₇⋊C₈	D₄	1	1	yes	characteristic
85	#13093952	—	2	4	no	—
86	#13093950	—	2	4	no	—
87	#13093947	C₂×C₄	1	2	yes	—
88	#13093947	C₂×C₄	1	2	yes	—
89	#13093944	C₂×C₄	1	2	yes	—
90	#13093944	C₂×C₄	1	2	yes	—
91	C₈×Dic₄₇	—	2	2	no	—
92	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
96	C₄₇⋊#95	—	2	1	no	—
97	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
98	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	#117×C₄₇	C₂³	1	2	yes	—
101	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
102	#108×C₄₇	—	2	2	no	—
103	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
104	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
105	#106×C₄₇	C₂×C₄	1	2	yes	—
106	C₄⋊C₈×C₄₇	—	2	2	no	—
107	C₄⋊C₈×C₄₇	—	2	2	no	—
108	C₄×C₈×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂×C₂²⋊D₄₇	—	2	2	no	—
112	C₂²×Dic₄₇	—	2	1	no	—
113	C₂²×Dic₄₇	#41	1	1	yes	characteristic
114	C₂²×Dic₄₇	#41	1	1	yes	characteristic
115	#10625350	—	2	2	no	—
116	#10625350	—	2	2	no	—
117	#10625350	C₂×D₄	1	4	yes	—
118	#10625350	C₂×Q₈	1	4	yes	—
119	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
120	C₂×C₄×D₄₇	—	2	2	no	—
121	C₂×C₄×D₄₇	—	2	2	no	—
122	C₂×C₄×D₄₇	—	2	2	no	—
123	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
124	M₁₆×C₄₇	—	2	2	no	—
125	M₁₆×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
135	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
136	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂²⋊C₄×C₄₇	—	2	2	no	—
138	C₄²×C₄₇	—	2	2	no	—
139	C₄²×C₄₇	—	2	1	no	—
140	C₄²×C₄₇	—	2	1	no	—
141	(C₂×D₄₇)⋊C₄	—	2	2	no	—
142	(C₂×D₄₇)⋊C₄	—	2	2	no	—
143	Dic₄₇⋊C₄	—	2	4	no	—
144	Dic₄₇⋊C₄	—	2	2	no	—
145	Dic₄₇⋊C₄	—	2	2	no	—
146	C₄×Dic₄₇	—	2	2	no	—
147	C₄×Dic₄₇	—	2	2	no	—
148	C₄×Dic₄₇	—	2	1	no	—
149	C₄×Dic₄₇	—	2	1	no	—
150	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
154	#10625329	—	2	2	no	—
155	#10625329	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	—	2	1	no	—
158	C₂×C₄₇⋊C₈	—	2	1	no	—
159	C₂×C₄₇⋊C₈	—	2	1	no	—
160	C₂×C₄₇⋊C₈	—	2	2	no	—
161	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
165	Dic₁₈₈	C₄⋊C₄	1	4	yes	complemented
166	D₃₇₆	C₄⋊C₄	1	4	yes	complemented
167	#10625325	C₄⋊C₄	1	8	yes	complemented
168	#10625324	—	4	4	no	—
169	#10625324	—	4	4	no	—
170	C₈×D₄₇	—	4	4	no	—
171	C₈×D₄₇	—	4	4	no	—
172	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂²×D₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂²⋊D₄₇	—	2	4	no	—
186	C₂²⋊D₄₇	—	2	4	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	4	1	no	—
191	C₂×Dic₄₇	—	4	1	no	—
192	C₂×Dic₄₇	—	4	1	no	—
193	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
194	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
195	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
196	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
197	D₁₈₈	—	2	2	no	—
198	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
199	C₄×D₄₇	—	2	4	no	—
200	C₄×D₄₇	—	2	4	no	—
201	C₄×D₄₇	—	4	4	no	—
202	C₄×D₄₇	—	8	2	no	—
203	Dic₉₄	—	2	2	no	—
204	Dic₉₄	C₂×C₄⋊C₄	1	4	yes	—
205	C₈×C₄₇	—	2	1	no	—
206	C₈×C₄₇	—	2	1	no	—
207	C₈×C₄₇	—	4	2	no	—
208	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
209	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
210	C₄₇⋊C₈	—	2	1	no	—
211	C₄₇⋊C₈	—	2	1	no	—
212	C₄₇⋊C₈	—	2	1	no	—
213	C₄₇⋊C₈	—	2	1	no	—
214	C₄₇⋊C₈	—	4	2	no	—
215	#22688	—	47	1	no	maximal, Sylow
216	C₂²×C₄₇	—	2	1	no	—
217	C₂²×C₄₇	—	2	1	no	—
218	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
219	C₂²×C₄₇	#547	1	1	yes	characteristic
220	C₂²×C₄₇	#554	1	1	yes	characteristic
221	C₂×D₄₇	—	2	4	no	—
222	C₂×D₄₇	—	4	2	no	—
223	C₂×D₄₇	—	4	2	no	—
224	C₄×C₄₇	—	4	2	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	4	2	no	—
227	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
228	C₄×C₄₇	#520	1	1	yes	characteristic
229	C₄×C₄₇	D₄²	1	1	yes	characteristic
230	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
231	Dic₄₇	—	2	4	no	—
232	Dic₄₇	—	2	1	no	—
233	Dic₄₇	—	2	1	no	—
234	Dic₄₇	—	2	1	no	—
235	Dic₄₇	—	4	2	no	—
236	Dic₄₇	#443	1	2	yes	complemented
237	C₂×#443	—	47	1	no	—
238	C₂×#443	—	47	1	no	—
239	C₄×#135	—	47	1	no	—
240	#2906	—	47	2	no	—
241	#1945	—	47	1	no	—
242	#1945	D₄₇	1	1	yes	characteristic, complemented
243	#1866	—	47	2	no	—
244	#1866	—	47	2	no	—
245	#1848	—	47	1	no	—
246	#1806	—	47	2	no	—
247	C₈×C₄⋊C₄	—	47	1	no	—
248	C₂×C₄₇	—	2	1	no	—
249	C₂×C₄₇	—	2	1	no	—
250	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
251	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
252	C₂×C₄₇	#2957	1	1	yes	characteristic
253	D₄₇	—	4	4	no	—
254	C₂×#135	—	47	1	no	—
255	C₂×#131	—	47	2	no	—
256	C₂×#131	—	47	2	no	—
257	C₄×#41	—	47	2	no	—
258	#443	—	94	4	no	—
259	#443	—	94	4	no	—
260	C₄×Q₁₆	—	47	1	no	—
261	C₄×Q₁₆	—	47	1	no	—
262	C₄×SD₁₆	—	47	2	no	—
263	C₄×SD₁₆	—	47	2	no	—
264	C₄×D₈	—	47	1	no	—
265	C₄×D₈	—	47	1	no	—
266	C₂×#108	—	47	1	no	—
267	C₂×#108	—	47	2	no	—
268	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
269	#427	C₂×D₄₇	1	1	yes	characteristic
270	#424	—	47	2	no	—
271	#424	—	94	2	no	—
272	#424	—	94	2	no	—
273	#424	C₂×D₄₇	1	2	yes	—
274	#423	—	47	2	no	—
275	#423	—	94	2	no	—
276	C₂×C₄⋊C₈	—	47	1	no	—
277	C₂×C₄⋊C₈	—	94	2	no	—
278	C₂×#104	—	47	2	no	—
279	C₂×#104	—	47	2	no	—
280	#416	—	47	2	no	—
281	C₂×C₄×C₈	—	47	1	no	—
282	C₂×C₄×C₈	—	47	1	no	—
283	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
284	C₄×C₄⋊C₄	—	47	1	no	—
285	#339	—	47	2	no	—
286	#339	C₂×D₄₇	1	2	yes	—
287	#336	—	47	1	no	—
288	#336	—	47	1	no	—
289	C₄₇	#22688	1	1	yes	characteristic, complemented, Sylow
290	C₂×#41	—	47	2	no	—
291	#135	—	47	4	no	—
292	#135	—	47	4	no	—
293	C₂×Q₁₆	—	47	1	no	—
294	C₂×SD₁₆	—	47	2	no	—
295	C₂×D₈	—	47	1	no	—
296	#131	—	94	4	no	—
297	#131	—	94	4	no	—
298	#131	—	188	2	no	—
299	#131	—	188	2	no	—
300	C₂×M₁₆	—	47	2	no	—
301	C₂×M₁₆	—	94	2	no	—
302	C₂×M₁₆	—	94	2	no	—
303	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
304	C₂²×C₈	—	47	1	no	—
305	C₂²×C₈	—	47	1	no	—
306	C₂²×C₈	—	94	2	no	—
307	C₂²×C₈	—	94	2	no	—
308	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
309	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
310	C₄×Q₈	—	47	2	no	—
311	C₄×Q₈	—	47	2	no	—
312	C₄×D₄	—	47	2	no	—
313	C₄×D₄	—	47	2	no	—
314	C₄×D₄	—	94	2	no	—
315	C₄×D₄	—	94	2	no	—
316	#117	—	94	2	no	—
317	#117	C₂²×D₄₇	1	2	yes	—
318	C₂×C₄⋊C₄	—	94	1	no	—
319	C₂×C₄²	—	47	1	no	—
320	C₂×C₄²	—	47	1	no	—
321	C₂×C₄²	—	94	2	no	—
322	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
323	#108	—	2	2	no	—
324	#108	—	94	2	no	—
325	#108	—	188	2	no	—
326	#107	C₄×D₄₇	1	1	yes	characteristic
327	#107	C₄×D₄₇	1	1	yes	characteristic
328	#106	C₄×D₄₇	1	2	yes	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	47	1	no	—
332	C₄⋊C₈	—	47	1	no	—
333	C₄⋊C₈	—	47	1	no	—
334	C₄⋊C₈	—	47	1	no	—
335	C₄⋊C₈	—	94	2	no	—
336	C₄⋊C₈	—	94	2	no	—
337	C₄⋊C₈	—	94	2	no	—
338	C₄⋊C₈	—	94	2	no	—
339	#104	—	94	4	no	—
340	#104	—	94	4	no	—
341	#103	—	47	2	no	—
342	#103	—	47	2	no	—
343	#102	—	47	2	no	—
344	#102	—	47	2	no	—
345	C₄×C₈	—	2	2	no	—
346	C₄×C₈	—	47	1	no	—
347	C₄×C₈	—	47	1	no	—
348	C₄×C₈	—	47	1	no	—
349	C₄×C₈	—	47	1	no	—
350	C₄×C₈	—	94	2	no	—
351	#95	—	94	1	no	—
352	#41	—	47	4	no	—
353	#41	—	47	4	no	—
354	#41	—	94	2	no	—
355	#41	—	94	2	no	—
356	C₂×Q₈	—	47	2	no	—
357	C₂×D₄	—	47	2	no	—
358	C₂×D₄	—	94	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	47	1	no	—
361	C₂²×C₄	—	47	1	no	—
362	C₂²×C₄	—	94	2	no	—
363	C₂²×C₄	—	94	2	no	—
364	C₂²×C₄	—	94	2	no	—
365	C₂²×C₄	—	94	1	no	—
366	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
367	Q₁₆	—	47	4	no	—
368	SD₁₆	—	47	8	no	—
369	D₈	—	47	4	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	94	2	no	—
373	M₁₆	—	94	2	no	—
374	M₁₆	—	188	4	no	—
375	M₁₆	—	188	4	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	47	1	no	—
380	C₂×C₈	—	47	1	no	—
381	C₂×C₈	—	47	1	no	—
382	C₂×C₈	—	47	1	no	—
383	C₂×C₈	—	94	1	no	—
384	C₂×C₈	—	94	1	no	—
385	C₂×C₈	—	94	1	no	—
386	C₂×C₈	—	94	1	no	—
387	C₂×C₈	—	94	2	no	—
388	C₂×C₈	—	188	4	no	—
389	C₂×C₈	—	188	4	no	—
390	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
391	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
392	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
393	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
394	C₂×C₈	D₄×D₄₇	1	2	yes	—
395	C₂×C₈	Q₈×D₄₇	1	2	yes	—
396	C₄⋊C₄	—	94	2	no	—
397	C₄⋊C₄	—	94	2	no	—
398	C₄⋊C₄	—	94	4	no	—
399	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
400	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	94	2	no	—
403	C₂²⋊C₄	—	94	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	47	1	no	—
408	C₄²	—	47	1	no	—
409	C₄²	—	47	1	no	—
410	C₄²	—	47	1	no	—
411	C₄²	—	94	2	no	—
412	C₄²	—	94	2	no	—
413	C₄²	—	94	1	no	—
414	C₄²	—	94	1	no	—
415	C₂³	—	94	2	no	—
416	C₂³	#41×D₄₇	1	1	yes	characteristic
417	Q₈	—	47	4	no	—
418	Q₈	—	94	2	no	—
419	D₄	—	47	4	no	—
420	D₄	—	94	4	no	—
421	D₄	—	94	4	no	—
422	D₄	—	94	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	47	1	no	—
429	C₂×C₄	—	47	1	no	—
430	C₂×C₄	—	47	1	no	—
431	C₂×C₄	—	47	1	no	—
432	C₂×C₄	—	94	2	no	—
433	C₂×C₄	—	94	2	no	—
434	C₂×C₄	—	94	4	no	—
435	C₂×C₄	—	94	4	no	—
436	C₂×C₄	—	94	2	no	—
437	C₂×C₄	—	376	2	no	—
438	C₂×C₄	—	188	4	no	—
439	C₂×C₄	—	188	1	no	—
440	C₂×C₄	—	188	1	no	—
441	C₂×C₄	—	188	1	no	—
442	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
443	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
444	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
445	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
446	C₂×C₄	#13094070	1	1	yes	characteristic
447	C₂×C₄	#13094072	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	94	1	no	—
452	C₈	—	94	1	no	—
453	C₈	—	94	1	no	—
454	C₈	—	94	1	no	—
455	C₈	—	188	2	no	—
456	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
457	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	94	4	no	—
461	C₂²	—	188	2	no	—
462	C₂²	—	188	2	no	—
463	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
464	C₂²	#15689775	1	1	yes	characteristic
465	C₂²	#15689829	1	1	yes	characteristic
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	47	2	no	—
470	C₄	—	94	4	no	—
471	C₄	—	94	1	no	—
472	C₄	—	94	1	no	—
473	C₄	—	94	1	no	—
474	C₄	—	188	2	no	—
475	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
476	C₄	#15689605	1	1	yes	characteristic
477	C₄	#15689757	1	1	yes	characteristic
478	C₄	#15689788	1	1	yes	characteristic
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	188	4	no	—
482	C₂	#20246289	1	1	yes	characteristic
483	C₂	#443×D₄₇	1	1	yes	characteristic
484	C₂	#20252300	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1945	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094046	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1945	D₄₇
hypocenter	C₄₇	#22688
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1945

Complements

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

N	H ≅ G/N	type
4. #20251955	C₂	semidirect
5. #20244137	C₂	semidirect
6. #20243664	C₂	semidirect
7. #20243662	C₂	semidirect
8. #20243558	C₂	semidirect
9. #20243407	C₂	semidirect
10. C₈×Dic₄₇⋊C₄	C₂	semidirect
11. C₄₇×#1945	C₂	semidirect
18. #15689217	C₄	semidirect
19. #15689217	C₄	semidirect
20. #15689210	C₄	semidirect
21. #15689210	C₄	semidirect
22. #15689205	C₄	semidirect
23. #15689205	C₄	semidirect
165. Dic₁₈₈	C₄⋊C₄	semidirect
166. D₃₇₆	C₄⋊C₄	semidirect
167. #10625325	C₄⋊C₄	semidirect
236. Dic₄₇	#443	semidirect
242. #1945	D₄₇	semidirect
289. C₄₇	#22688	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689241	2
C₂×#15689239	2
#20252159	2
#20251955	2
#20244137	2
#20243664	2
#20243662	2
#20243558	2
#20243407	2
C₈×Dic₄₇⋊C₄	2
C₄₇×#1945	2
#22688	47