Subgroups — #26235479

Order 12032.

902 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×C₄×#10625335	C₂	1	1	yes	maximal, characteristic
2	#20246347	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20244079	C₂	1	2	yes	maximal, complemented
5	#20243976	C₂	1	2	yes	maximal, complemented
6	#20243720	C₂	1	2	yes	maximal
7	#20243515	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243394	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243215	C₂	1	2	yes	maximal
11	C₄₇×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625335	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
16	C₄×#10625335	C₄	1	8	yes	complemented
17	C₂×#13093955	C₂²	1	1	yes	characteristic
18	C₂×#13093949	C₂²	1	2	yes	—
19	C₂×#13093947	C₂²	1	1	yes	characteristic
20	C₂×#13093945	C₂²	1	1	yes	characteristic
21	C₂×#13093934	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	#15689028	C₂²	1	2	yes	—
24	#15689022	C₂²	1	2	yes	—
25	#15689004	—	2	2	no	—
26	#15688998	—	2	2	no	—
27	#15688993	C₂²	1	1	yes	characteristic
28	#15688988	—	2	1	no	—
29	#15688983	—	2	1	no	—
30	C₄⋊C₄×Dic₄₇	—	2	1	no	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
32	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
33	#15688886	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#102×C₄₇	C₂²	1	2	yes	—
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
43	C₂³×Dic₄₇	—	2	2	no	—
44	C₂×#10625335	—	2	2	no	—
45	C₂×#10625335	—	2	2	no	—
46	C₂×#10625335	C₂×C₄	1	4	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₄×Dic₉₄	—	2	2	no	—
50	C₄×Dic₉₄	C₂×C₄	1	4	yes	complemented
51	D₄×Dic₄₇	—	2	4	no	—
52	D₄×Dic₄₇	—	4	2	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	—	2	2	no	—
55	C₂×C₄⋊Dic₄₇	—	2	1	no	—
56	C₂×C₄⋊Dic₄₇	—	4	4	no	—
57	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂×Dic₄₇⋊C₄	—	2	1	no	—
62	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
63	C₂×C₄×Dic₄₇	—	2	1	no	—
64	C₂×C₄×Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
66	#13093955	C₂×C₄	1	4	yes	complemented
67	#13093949	—	4	2	no	—
68	#13093947	C₂×C₄	1	4	yes	complemented
69	#13093945	C₂×C₄	1	4	yes	—
70	#13093934	—	4	2	no	—
71	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	D₄	1	2	yes	—
77	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₄₇	—	2	1	no	—
79	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
80	C₄×D₄×C₄₇	—	2	2	no	—
81	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
82	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	—	2	2	no	—
89	#102×C₄₇	—	2	4	no	—
90	C₂⁴×C₄₇	—	2	1	no	—
91	C₂×D₄×C₄₇	—	2	1	no	—
92	C₂×D₄×C₄₇	—	2	1	no	—
93	C₂×D₄×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₄₇	#41	1	2	yes	—
96	C₂×D₄×C₄₇	#41	1	2	yes	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	4	2	no	—
101	C₂²×C₄×C₄₇	—	4	2	no	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	—	2	1	no	—
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	—	2	2	no	—
108	C₂²×Dic₄₇	—	4	4	no	—
109	C₂²×Dic₄₇	—	4	4	no	—
110	C₂²×Dic₄₇	—	8	2	no	—
111	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
112	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
113	C₂×Dic₉₄	—	2	1	no	—
114	C₂×Dic₉₄	—	2	1	no	—
115	C₂×Dic₉₄	—	2	1	no	—
116	C₂×Dic₉₄	—	2	1	no	—
117	C₂×Dic₉₄	—	2	1	no	—
118	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	4	2	no	—
126	C₄⋊C₄×C₄₇	—	8	1	no	—
127	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₄₇	—	2	4	no	—
129	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
130	C₄²×C₄₇	#41	1	2	yes	—
131	C₂²⋊Dic₄₇	—	4	4	no	—
132	#10625335	—	2	8	no	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	4	4	no	—
139	C₄⋊Dic₄₇	—	4	2	no	—
140	C₄⋊Dic₄₇	—	8	1	no	—
141	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
142	Dic₄₇⋊C₄	—	2	4	no	—
143	C₄×Dic₄₇	—	2	4	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	2	2	no	—
146	C₄×Dic₄₇	—	8	2	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	1	no	—
151	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	—	2	2	no	—
156	C₂³×C₄₇	—	4	1	no	—
157	C₂³×C₄₇	—	4	1	no	—
158	C₂³×C₄₇	—	4	1	no	—
159	C₂³×C₄₇	—	4	1	no	—
160	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	D₄×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	2	no	—
163	D₄×C₄₇	—	2	2	no	—
164	D₄×C₄₇	#117	1	4	yes	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	8	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₄₇	#137	1	2	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	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	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	2	2	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	2	2	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	4	1	no	—
193	C₂×Dic₄₇	—	4	1	no	—
194	C₂×Dic₄₇	—	4	1	no	—
195	C₂×Dic₄₇	—	4	1	no	—
196	C₂×Dic₄₇	—	4	2	no	—
197	C₂×Dic₄₇	—	4	2	no	—
198	C₂×Dic₄₇	—	4	2	no	—
199	C₂×Dic₄₇	—	8	8	no	—
200	Dic₉₄	—	2	2	no	—
201	Dic₉₄	—	2	2	no	—
202	Dic₉₄	—	4	1	no	—
203	Dic₉₄	—	4	1	no	—
204	C₈×C₄₇	—	4	2	no	—
205	C₄₇⋊C₈	—	2	2	no	—
206	C₄₇⋊C₈	—	2	2	no	—
207	#22762	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	—	2	4	no	—
209	C₂²×C₄₇	—	4	2	no	—
210	C₂²×C₄₇	—	4	2	no	—
211	C₂²×C₄₇	—	4	2	no	—
212	C₂²×C₄₇	—	4	2	no	—
213	C₂²×C₄₇	—	4	2	no	—
214	C₂²×C₄₇	—	4	2	no	—
215	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₂²×C₄₇	#546	1	1	yes	characteristic
217	C₂²×C₄₇	#548	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
220	C₂²×C₄₇	#577	1	1	yes	characteristic
221	C₂²×C₄₇	#577	1	1	yes	characteristic
222	C₄×C₄₇	—	2	2	no	—
223	C₄×C₄₇	—	4	2	no	—
224	C₄×C₄₇	—	8	2	no	—
225	C₄×C₄₇	#440	1	4	yes	—
226	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
227	C₄×C₄₇	#520	1	1	yes	characteristic
228	C₄×C₄₇	#552	1	1	yes	characteristic
229	C₄×C₄₇	#553	1	1	yes	characteristic
230	Dic₄₇	—	4	2	no	—
231	Dic₄₇	—	4	2	no	—
232	Dic₄₇	—	4	2	no	—
233	Dic₄₇	—	4	2	no	—
234	Dic₄₇	—	8	2	no	—
235	C₂×C₄×SD₁₆	—	47	1	no	—
236	#2355	—	47	1	no	—
237	D₄×C₄⋊C₄	—	47	1	no	—
238	#1935	—	47	2	no	—
239	#1920	—	47	2	no	—
240	#1877	—	47	2	no	—
241	#1834	—	47	1	no	—
242	#1803	—	47	1	no	—
243	#1802	D₄₇	1	1	yes	characteristic
244	#1770	—	47	1	no	—
245	#1762	—	47	2	no	—
246	C₂×C₄₇	—	4	4	no	—
247	C₂×C₄₇	#2352	1	1	yes	characteristic
248	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
249	C₂×C₄₇	#2952	1	1	yes	characteristic
250	C₂×C₄₇	#3324	1	1	yes	characteristic
251	C₂×C₄₇	#3331	1	1	yes	characteristic
252	C₂×C₄₇	#3372	1	1	yes	characteristic
253	C₂×C₄₇	#3373	1	1	yes	characteristic
254	C₂²×SD₁₆	—	47	1	no	—
255	C₂×C₄×Q₈	—	47	1	no	—
256	C₂×C₄×D₄	—	47	2	no	—
257	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	—	94	1	no	—
259	C₄×SD₁₆	—	47	8	no	—
260	C₂×#106	—	47	1	no	—
261	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
262	C₂×#103	—	47	1	no	—
263	C₂×#103	—	47	2	no	—
264	C₂×#102	—	47	1	no	—
265	C₂×#102	C₂×D₄₇	1	2	yes	—
266	C₂×#97	—	47	2	no	—
267	C₂×C₄×C₈	—	47	1	no	—
268	#391	—	47	2	no	—
269	#389	—	47	2	no	—
270	#387	—	94	2	no	—
271	#385	—	94	2	no	—
272	#384	—	47	1	no	—
273	#384	C₂×D₄₇	1	1	yes	characteristic
274	#382	—	94	1	no	—
275	#380	—	94	1	no	—
276	C₄×C₄⋊C₄	—	47	1	no	—
277	C₄×C₄⋊C₄	—	47	2	no	—
278	C₄×C₄⋊C₄	—	94	1	no	—
279	#340	—	47	2	no	—
280	#340	—	47	2	no	—
281	#340	—	47	2	no	—
282	#340	C₂×D₄₇	1	2	yes	—
283	#336	—	47	2	no	—
284	C₄₇	#22762	1	1	yes	characteristic, complemented, Sylow
285	C₂²×Q₈	—	47	1	no	—
286	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
287	C₂³×C₄	—	2	1	no	—
288	C₂³×C₄	—	94	2	no	—
289	C₂×SD₁₆	—	47	4	no	—
290	C₂×SD₁₆	—	94	2	no	—
291	C₂×SD₁₆	—	94	2	no	—
292	C₂²×C₈	—	47	1	no	—
293	C₂²×C₈	—	47	1	no	—
294	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
295	C₄×Q₈	—	47	4	no	—
296	C₄×Q₈	—	94	2	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	94	4	no	—
299	C₄×D₄	—	188	2	no	—
300	C₄×D₄	C₄×D₄₇	1	4	yes	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	47	1	no	—
304	C₂×C₄⋊C₄	—	47	1	no	—
305	C₂×C₄⋊C₄	—	47	1	no	—
306	C₂×C₄⋊C₄	—	47	2	no	—
307	C₂×C₄⋊C₄	—	94	1	no	—
308	C₂×C₄⋊C₄	—	94	1	no	—
309	C₂×C₄⋊C₄	—	94	2	no	—
310	C₂×C₄⋊C₄	—	94	1	no	—
311	C₂×C₄⋊C₄	—	188	4	no	—
312	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
313	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	94	2	no	—
316	C₂×C₄²	—	47	2	no	—
317	C₂×C₄²	—	94	1	no	—
318	C₂×C₄²	—	94	2	no	—
319	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
320	#106	—	47	4	no	—
321	C₄⋊C₈	—	2	2	no	—
322	#103	—	47	4	no	—
323	#103	—	188	2	no	—
324	#102	—	2	4	no	—
325	#102	—	47	4	no	—
326	#97	—	188	2	no	—
327	C₄×C₈	—	47	4	no	—
328	#95	—	47	2	no	—
329	#95	—	94	2	no	—
330	#95	—	94	2	no	—
331	#95	—	94	2	no	—
332	#95	—	94	2	no	—
333	C₂⁴	—	2	1	no	—
334	C₂×Q₈	—	47	2	no	—
335	C₂×Q₈	—	94	1	no	—
336	C₂×Q₈	—	94	1	no	—
337	C₂×Q₈	—	94	1	no	—
338	C₂×Q₈	—	94	1	no	—
339	C₂×Q₈	—	94	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
344	C₂×D₄	#10625352	1	2	yes	—
345	C₂×D₄	#10625354	1	2	yes	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	47	2	no	—
352	C₂²×C₄	—	47	2	no	—
353	C₂²×C₄	—	94	1	no	—
354	C₂²×C₄	—	94	1	no	—
355	C₂²×C₄	—	94	2	no	—
356	C₂²×C₄	—	376	2	no	—
357	C₂²×C₄	—	188	4	no	—
358	C₂²×C₄	—	188	4	no	—
359	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
360	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
361	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
362	SD₁₆	—	94	8	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	47	2	no	—
367	C₂×C₈	—	47	2	no	—
368	C₂×C₈	—	94	1	no	—
369	C₂×C₈	—	94	1	no	—
370	C₂×C₈	—	94	1	no	—
371	C₂×C₈	—	94	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	8	1	no	—
377	C₄⋊C₄	—	47	2	no	—
378	C₄⋊C₄	—	94	4	no	—
379	C₄⋊C₄	—	94	2	no	—
380	C₄⋊C₄	—	94	2	no	—
381	C₄⋊C₄	—	94	1	no	—
382	C₄⋊C₄	—	94	2	no	—
383	C₄⋊C₄	—	94	2	no	—
384	C₄⋊C₄	—	376	1	no	—
385	C₄⋊C₄	—	188	4	no	—
386	C₄⋊C₄	—	188	2	no	—
387	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	188	4	no	—
390	C₄²	—	94	4	no	—
391	C₄²	—	94	2	no	—
392	C₄²	—	94	2	no	—
393	C₄²	—	376	2	no	—
394	C₄²	C₂×C₄×D₄₇	1	2	yes	—
395	C₄²	#10625352	1	2	yes	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
404	Q₈	—	94	2	no	—
405	Q₈	—	94	2	no	—
406	Q₈	—	188	1	no	—
407	Q₈	—	188	1	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	#13093982	1	4	yes	—
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	8	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	94	2	no	—
422	C₂×C₄	—	94	2	no	—
423	C₂×C₄	—	94	2	no	—
424	C₂×C₄	—	94	2	no	—
425	C₂×C₄	—	94	2	no	—
426	C₂×C₄	—	94	2	no	—
427	C₂×C₄	—	94	2	no	—
428	C₂×C₄	—	94	2	no	—
429	C₂×C₄	—	376	8	no	—
430	C₂×C₄	—	188	2	no	—
431	C₂×C₄	—	188	2	no	—
432	C₂×C₄	—	188	2	no	—
433	C₂×C₄	—	188	1	no	—
434	C₂×C₄	—	188	1	no	—
435	C₂×C₄	—	188	1	no	—
436	C₂×C₄	—	188	1	no	—
437	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
438	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
439	C₂×C₄	#13094048	1	2	yes	—
440	C₂×C₄	#13094053	1	2	yes	—
441	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
442	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
443	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
444	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
445	C₂×C₄	#13094070	1	1	yes	characteristic
446	C₂×C₄	#13094071	1	1	yes	characteristic
447	C₈	—	4	2	no	—
448	C₈	—	94	2	no	—
449	C₈	—	94	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
458	C₂²	#15689764	1	1	yes	characteristic
459	C₂²	#15689779	1	1	yes	characteristic
460	C₂²	C₂×#13094048	1	1	yes	characteristic
461	C₂²	C₂×#13094053	1	1	yes	characteristic
462	C₂²	#15689932	1	1	yes	characteristic
463	C₂²	#15689933	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	2	no	—
467	C₄	—	376	2	no	—
468	C₄	—	188	2	no	—
469	C₄	—	188	2	no	—
470	C₄	—	188	2	no	—
471	C₄	—	188	2	no	—
472	C₄	#15689220	1	4	yes	—
473	C₄	C₂×#13093982	1	1	yes	characteristic
474	C₄	#15689603	1	1	yes	characteristic
475	C₄	#15689815	1	1	yes	characteristic
476	C₄	#15689825	1	1	yes	characteristic
477	C₂	—	4	4	no	—
478	C₂	#20246319	1	1	yes	characteristic
479	C₂	C₂×#15689220	1	1	yes	characteristic
480	C₂	#20252267	1	1	yes	characteristic
481	C₂	#20255616	1	1	yes	characteristic
482	C₂	#20255701	1	1	yes	characteristic
483	C₂	#20256173	1	1	yes	characteristic
484	C₂	#20256184	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1802	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₄×C₄₇	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1802	D₄₇
hypocenter	C₄₇	#22762
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1802

Complements

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

N	H ≅ G/N	type
2. #20246347	C₂	semidirect
4. #20244079	C₂	semidirect
5. #20243976	C₂	semidirect
7. #20243515	C₂	semidirect
8. #20243394	C₂	semidirect
9. #20243258	C₂	semidirect
16. C₄×#10625335	C₄	semidirect
50. C₄×Dic₉₄	C₂×C₄	semidirect
66. #13093955	C₂×C₄	semidirect
68. #13093947	C₂×C₄	semidirect
71. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
284. C₄₇	#22762	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625335	2
#20246347	2
D₄×C₄⋊Dic₄₇	2
#20244079	2
#20243976	2
#20243720	2
#20243515	2
#20243394	2
#20243258	2
#20243215	2
C₄₇×#1802	2
#22762	47