Subgroups — #26234740

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×#15689240	C₂	1	1	yes	maximal, characteristic
2	#135×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20251954	C₂	1	2	yes	maximal, complemented
4	#20244136	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244134	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243663	C₂	1	2	yes	maximal, complemented
7	#20243661	C₂	1	2	yes	maximal, complemented
8	#20243558	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243406	C₂	1	2	yes	maximal, complemented
10	C₈×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#443	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	2	yes	—
13	#41×Dic₄₇	C₂²	1	2	yes	—
14	#15689240	—	2	4	no	—
15	Q₁₆×Dic₄₇	C₄	1	1	yes	characteristic, complemented
16	Q₁₆×Dic₄₇	C₄	1	1	yes	characteristic, complemented
17	SD₁₆×Dic₄₇	C₄	1	2	yes	complemented
18	SD₁₆×Dic₄₇	C₄	1	2	yes	complemented
19	D₈×Dic₄₇	C₄	1	1	yes	characteristic, complemented
20	D₈×Dic₄₇	C₄	1	1	yes	characteristic, complemented
21	C₂×#13093960	C₂²	1	1	yes	characteristic
22	C₂×#13093959	C₂²	1	2	yes	—
23	#15689161	C₂²	1	1	yes	characteristic
24	#15689151	—	2	2	no	—
25	#15689151	C₂²	1	2	yes	—
26	#15689149	—	2	2	no	—
27	#15689149	C₂²	1	2	yes	—
28	#15689146	—	2	2	no	—
29	#15689146	C₂²	1	2	yes	—
30	C₂×Dic₄₇⋊C₈	—	2	2	no	—
31	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×#13093951	C₂²	1	2	yes	—
33	#15689119	C₂²	1	2	yes	—
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
37	#15688884	C₂²	1	2	yes	—
38	#15688883	C₂²	1	2	yes	—
39	#15688878	C₂²	1	1	yes	characteristic
40	#15688877	C₂²	1	1	yes	characteristic
41	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#131×C₄₇	C₂²	1	2	yes	—
43	C₄₇×#443	—	2	4	no	—
44	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#104×C₄₇	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	#13094031	—	2	4	no	—
48	#13094031	—	4	2	no	—
49	C₂×#10625329	—	2	2	no	—
50	C₂×#10625329	C₂³	1	2	yes	—
51	C₂²×C₄₇⋊C₈	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
54	Q₈×Dic₄₇	C₂×C₄	1	2	yes	—
55	Q₈×Dic₄₇	C₂×C₄	1	2	yes	—
56	D₄×Dic₄₇	—	2	2	no	—
57	D₄×Dic₄₇	—	2	2	no	—
58	D₄×Dic₄₇	C₂×C₄	1	2	yes	—
59	D₄×Dic₄₇	C₂×C₄	1	2	yes	—
60	#13093983	—	2	2	no	—
61	#13093983	C₂³	1	2	yes	—
62	C₂×Dic₄₇⋊C₄	—	2	1	no	—
63	C₂×C₄×Dic₄₇	—	2	2	no	—
64	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	#13093960	—	2	2	no	—
67	#13093959	—	4	2	no	—
68	#13093958	C₂×C₄	1	1	yes	characteristic
69	#13093958	C₂×C₄	1	1	yes	characteristic
70	#13093956	C₂×C₄	1	2	yes	—
71	Dic₄₇⋊C₈	—	2	2	no	—
72	Dic₄₇⋊C₈	—	2	2	no	—
73	Dic₄₇⋊C₈	—	2	2	no	—
74	Dic₄₇⋊C₈	—	2	2	no	—
75	Dic₄₇⋊C₈	—	2	2	no	—
76	Dic₄₇⋊C₈	—	2	2	no	—
77	Dic₄₇⋊C₈	D₄	1	1	yes	characteristic
78	Dic₄₇⋊C₈	D₄	1	1	yes	characteristic
79	Dic₄₇⋊C₈	D₄	1	1	yes	characteristic
80	Dic₄₇⋊C₈	D₄	1	1	yes	characteristic
81	#13093951	—	2	4	no	—
82	#13093948	C₂×C₄	1	2	yes	—
83	#13093948	C₂×C₄	1	2	yes	—
84	#13093945	C₂×C₄	1	2	yes	—
85	#13093945	C₂×C₄	1	2	yes	—
86	C₈×Dic₄₇	—	2	2	no	—
87	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
90	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
91	C₄₇⋊#95	—	2	1	no	—
92	C₂×#41×C₄₇	C₂³	1	2	yes	—
93	#135×C₄₇	D₄	1	4	yes	—
94	#135×C₄₇	Q₈	1	4	yes	—
95	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
97	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
98	#131×C₄₇	—	2	4	no	—
99	#131×C₄₇	—	4	2	no	—
100	C₂×M₁₆×C₄₇	—	2	2	no	—
101	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
102	C₂²×C₈×C₄₇	—	2	2	no	—
103	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
106	#108×C₄₇	—	2	2	no	—
107	#104×C₄₇	—	2	4	no	—
108	C₄×C₈×C₄₇	—	2	2	no	—
109	#41×C₄₇	—	2	2	no	—
110	#41×C₄₇	—	2	2	no	—
111	#41×C₄₇	C₂×D₄	1	4	yes	—
112	#41×C₄₇	C₂×Q₈	1	4	yes	—
113	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
114	C₂×D₄×C₄₇	—	2	2	no	—
115	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
119	C₂²×Dic₄₇	—	2	1	no	—
120	C₂²×Dic₄₇	—	2	2	no	—
121	C₂²×Dic₄₇	—	2	2	no	—
122	C₂²×Dic₄₇	#41	1	1	yes	characteristic
123	C₂²×Dic₄₇	#41	1	1	yes	characteristic
124	Q₁₆×C₄₇	C₄⋊C₄	1	4	yes	complemented
125	SD₁₆×C₄₇	C₄⋊C₄	1	8	yes	complemented
126	D₈×C₄₇	C₄⋊C₄	1	4	yes	complemented
127	M₁₆×C₄₇	—	2	2	no	—
128	M₁₆×C₄₇	—	2	2	no	—
129	M₁₆×C₄₇	—	4	4	no	—
130	C₂×C₈×C₄₇	—	2	1	no	—
131	C₂×C₈×C₄₇	—	2	1	no	—
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₂×C₈×C₄₇	—	4	4	no	—
134	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
140	C₄²×C₄₇	—	2	1	no	—
141	C₄²×C₄₇	—	2	1	no	—
142	C₂²⋊Dic₄₇	—	2	2	no	—
143	C₂²⋊Dic₄₇	—	2	2	no	—
144	C₂²⋊Dic₄₇	—	2	2	no	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	—	2	2	no	—
147	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
148	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
149	Dic₄₇⋊C₄	—	2	4	no	—
150	C₄×Dic₄₇	—	2	2	no	—
151	C₄×Dic₄₇	—	2	2	no	—
152	C₄×Dic₄₇	—	2	2	no	—
153	C₄×Dic₄₇	—	2	1	no	—
154	C₄×Dic₄₇	—	2	1	no	—
155	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
158	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
159	#10625329	—	2	2	no	—
160	#10625329	—	2	2	no	—
161	#10625329	—	4	4	no	—
162	C₂×C₄₇⋊C₈	—	2	1	no	—
163	C₂×C₄₇⋊C₈	—	2	1	no	—
164	C₂×C₄₇⋊C₈	—	2	1	no	—
165	C₂×C₄₇⋊C₈	—	2	1	no	—
166	C₂×C₄₇⋊C₈	—	2	2	no	—
167	C₂×C₄₇⋊C₈	—	4	4	no	—
168	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
174	Q₈×C₄₇	—	2	2	no	—
175	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
176	D₄×C₄₇	—	2	4	no	—
177	D₄×C₄₇	—	2	4	no	—
178	D₄×C₄₇	—	2	2	no	—
179	D₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	2	4	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	2	2	no	—
195	C₂×Dic₄₇	—	2	2	no	—
196	C₂×Dic₄₇	—	4	1	no	—
197	C₂×Dic₄₇	—	4	1	no	—
198	C₂×Dic₄₇	—	4	1	no	—
199	C₂×Dic₄₇	—	4	4	no	—
200	C₂×Dic₄₇	—	8	2	no	—
201	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
202	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
203	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
204	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
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	—	2	4	no	—
219	C₂²×C₄₇	—	4	2	no	—
220	C₂²×C₄₇	—	4	2	no	—
221	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂²×C₄₇	#547	1	1	yes	characteristic
223	C₂²×C₄₇	#554	1	1	yes	characteristic
224	C₄×C₄₇	—	2	4	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
227	C₄×C₄₇	#520	1	1	yes	characteristic
228	C₄×C₄₇	D₄²	1	1	yes	characteristic
229	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
230	Dic₄₇	—	2	1	no	—
231	Dic₄₇	—	2	1	no	—
232	Dic₄₇	—	2	1	no	—
233	Dic₄₇	—	4	2	no	—
234	Dic₄₇	—	4	2	no	—
235	Dic₄₇	—	4	2	no	—
236	Dic₄₇	#443	1	2	yes	complemented
237	C₂×#443	—	47	1	no	—
238	C₂×#443	D₄₇	1	1	yes	characteristic
239	C₄×#135	—	47	1	no	—
240	#2906	—	47	2	no	—
241	#1945	—	47	1	no	—
242	#1945	—	47	1	no	—
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	—	4	4	no	—
251	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
252	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
253	C₂×C₄₇	#2957	1	1	yes	characteristic
254	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
255	C₂×#131	—	47	2	no	—
256	C₂×#131	C₂×D₄₇	1	2	yes	—
257	C₄×#41	—	47	2	no	—
258	#443	—	2	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	—	47	1	no	—
270	#424	—	47	2	no	—
271	#424	—	47	2	no	—
272	#424	—	94	2	no	—
273	#424	—	94	2	no	—
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	C₂×D₄₇	1	2	yes	—
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	—	47	2	no	—
287	#336	—	47	1	no	—
288	#336	—	47	1	no	—
289	C₄₇	#22688	1	1	yes	characteristic, complemented, Sylow
290	C₂×#41	C₂²×D₄₇	1	2	yes	—
291	#135	Dic₉₄	1	4	yes	—
292	#135	C₂²⋊D₄₇	1	4	yes	—
293	C₂×Q₁₆	C₄×D₄₇	1	1	yes	characteristic
294	C₂×SD₁₆	C₄×D₄₇	1	2	yes	—
295	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic
296	#131	—	2	4	no	—
297	#131	—	4	2	no	—
298	#131	—	94	4	no	—
299	#131	—	188	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	47	2	no	—
302	C₂×M₁₆	—	94	2	no	—
303	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	—	47	1	no	—
306	C₂²×C₈	—	47	1	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	—	47	2	no	—
317	#117	—	94	2	no	—
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	—	47	1	no	—
327	#107	—	47	1	no	—
328	#106	—	47	2	no	—
329	C₄⋊C₈	—	47	1	no	—
330	C₄⋊C₈	—	47	1	no	—
331	C₄⋊C₈	—	47	1	no	—
332	C₄⋊C₈	—	47	1	no	—
333	C₄⋊C₈	—	94	2	no	—
334	C₄⋊C₈	—	94	2	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	—	2	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	—	2	2	no	—
353	#41	—	2	2	no	—
354	#41	C₂×Dic₉₄	1	4	yes	—
355	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
356	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	47	1	no	—
362	C₂²×C₄	—	47	1	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	Dic₄₇⋊C₄	1	4	yes	complemented
368	SD₁₆	Dic₄₇⋊C₄	1	8	yes	complemented
369	D₈	Dic₄₇⋊C₄	1	4	yes	complemented
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	4	4	no	—
373	M₁₆	—	94	2	no	—
374	M₁₆	—	94	2	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	—	4	4	no	—
380	C₂×C₈	—	47	1	no	—
381	C₂×C₈	—	47	1	no	—
382	C₂×C₈	—	47	1	no	—
383	C₂×C₈	—	47	1	no	—
384	C₂×C₈	—	94	1	no	—
385	C₂×C₈	—	94	1	no	—
386	C₂×C₈	—	94	1	no	—
387	C₂×C₈	—	94	1	no	—
388	C₂×C₈	—	94	2	no	—
389	C₂×C₈	—	188	4	no	—
390	C₂×C₈	C₂×Dic₉₄	1	2	yes	—
391	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
392	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
394	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
395	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
396	C₄⋊C₄	—	47	2	no	—
397	C₄⋊C₄	—	47	2	no	—
398	C₄⋊C₄	—	94	2	no	—
399	C₄⋊C₄	—	94	2	no	—
400	C₄⋊C₄	—	94	4	no	—
401	C₂²⋊C₄	—	94	2	no	—
402	C₂²⋊C₄	—	94	2	no	—
403	C₂²⋊C₄	—	94	2	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	47	1	no	—
407	C₄²	—	47	1	no	—
408	C₄²	—	47	1	no	—
409	C₄²	—	47	1	no	—
410	C₄²	—	94	2	no	—
411	C₄²	—	94	2	no	—
412	C₄²	—	94	2	no	—
413	C₄²	—	94	1	no	—
414	C₄²	—	94	1	no	—
415	C₂³	—	2	2	no	—
416	C₂³	#41×D₄₇	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	C₂×Dic₄₇⋊C₄	1	4	yes	—
419	D₄	—	2	4	no	—
420	D₄	—	2	4	no	—
421	D₄	—	2	2	no	—
422	D₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	47	1	no	—
430	C₂×C₄	—	47	1	no	—
431	C₂×C₄	—	47	1	no	—
432	C₂×C₄	—	47	1	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	—	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	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
445	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
446	C₂×C₄	#13094069	1	1	yes	characteristic
447	C₂×C₄	#13094071	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	C₂×Dic₄₇⋊C₄	1	2	yes	—
457	C₈	C₂×Dic₄₇⋊C₄	1	2	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
464	C₂²	#15689772	1	1	yes	characteristic
465	C₂²	#15689832	1	1	yes	characteristic
466	C₄	—	2	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	47	2	no	—
469	C₄	—	94	1	no	—
470	C₄	—	94	1	no	—
471	C₄	—	94	1	no	—
472	C₄	—	188	2	no	—
473	C₄	—	188	2	no	—
474	C₄	—	188	2	no	—
475	C₄	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
476	C₄	#15689602	1	1	yes	characteristic
477	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
478	C₄	D₄×Dic₉₄	1	1	yes	characteristic
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	4	4	no	—
482	C₂	D₄×Dic₄₇⋊C₄	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	C₂×C₄₇×#443	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#135×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#443	D₄₇
hypocenter	C₄₇	#22688
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
3. #20251954	C₂	semidirect
4. #20244136	C₂	semidirect
5. #20244134	C₂	semidirect
6. #20243663	C₂	semidirect
7. #20243661	C₂	semidirect
8. #20243558	C₂	semidirect
9. #20243406	C₂	semidirect
10. C₈×Dic₄₇⋊C₄	C₂	semidirect
15. Q₁₆×Dic₄₇	C₄	semidirect
16. Q₁₆×Dic₄₇	C₄	semidirect
17. SD₁₆×Dic₄₇	C₄	semidirect
18. SD₁₆×Dic₄₇	C₄	semidirect
19. D₈×Dic₄₇	C₄	semidirect
20. D₈×Dic₄₇	C₄	semidirect
124. Q₁₆×C₄₇	C₄⋊C₄	semidirect
125. SD₁₆×C₄₇	C₄⋊C₄	semidirect
126. D₈×C₄₇	C₄⋊C₄	semidirect
236. Dic₄₇	#443	semidirect
289. C₄₇	#22688	semidirect
367. Q₁₆	Dic₄₇⋊C₄	semidirect
368. SD₁₆	Dic₄₇⋊C₄	semidirect
369. D₈	Dic₄₇⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689240	2
#135×Dic₄₇	2
#20251954	2
#20244136	2
#20244134	2
#20243663	2
#20243661	2
#20243558	2
#20243406	2
C₈×Dic₄₇⋊C₄	2
C₂×C₄₇×#443	2
#22688	47