Subgroups — #26238531

Order 12032.

1030 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×Dic₄₇	C₂	1	2	yes	maximal
2	#20246448	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20244191	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244152	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244066	C₂	1	2	yes	maximal, complemented
7	#20243724	C₂	1	2	yes	maximal
8	#20243658	C₂	1	2	yes	maximal, complemented
9	#20243253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093945	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄₇×#461	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
15	SD₁₆×Dic₄₇	—	2	8	no	—
16	C₂×#13093956	C₂²	1	2	yes	—
17	C₂×#13093948	C₂²	1	2	yes	—
18	C₂×#13093948	C₂²	1	2	yes	—
19	C₂×#13093945	C₂²	1	1	yes	characteristic
20	C₂×#13093945	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
23	#15689030	C₂²	1	2	yes	—
24	#15689022	—	2	1	no	—
25	#15689022	C₂²	1	2	yes	—
26	#15689009	—	2	2	no	—
27	#15688998	—	2	2	no	—
28	#15688993	C₂²	1	1	yes	characteristic
29	#15688983	—	2	1	no	—
30	C₄⋊C₄×Dic₄₇	—	2	1	no	—
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
33	#15688886	C₂²	1	2	yes	—
34	#15688885	C₂²	1	1	yes	characteristic
35	#15688885	C₂²	1	1	yes	characteristic
36	#15688877	C₂²	1	2	yes	—
37	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#461	C₄	1	8	yes	complemented
41	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#103×C₄₇	C₂²	1	2	yes	—
43	C₂³×Dic₄₇	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	Q₈×Dic₄₇	—	2	4	no	—
47	Q₈×Dic₄₇	—	4	2	no	—
48	D₄×Dic₄₇	—	2	4	no	—
49	D₄×Dic₄₇	—	4	2	no	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	—	4	4	no	—
55	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	C₂×C₄×Dic₄₇	—	2	2	no	—
63	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
64	#13093956	—	2	4	no	—
65	#13093948	—	2	4	no	—
66	#13093948	—	4	2	no	—
67	#13093945	—	2	2	no	—
68	#13093945	D₄	1	4	yes	—
69	C₄×C₄₇⋊C₈	—	2	2	no	—
70	C₈×Dic₄₇	—	2	4	no	—
71	C₄₇⋊#95	—	2	1	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	D₄	1	2	yes	—
76	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
77	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₄₇	—	2	1	no	—
79	C₂×SD₁₆×C₄₇	—	2	4	no	—
80	C₂×SD₁₆×C₄₇	—	2	4	no	—
81	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	—
82	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
83	C₄⋊Q₈×C₄₇	—	2	2	no	—
84	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
85	C₄×D₄×C₄₇	—	2	2	no	—
86	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
87	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₇	C₂³	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	C₂×C₄	1	4	yes	complemented
93	#103×C₄₇	C₂×C₄	1	8	yes	complemented
94	C₂⁴×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	—	2	1	no	—
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₄₇	#41	1	2	yes	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	4	2	no	—
111	C₂²×C₄×C₄₇	—	4	2	no	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
115	C₂²×Dic₄₇	—	2	1	no	—
116	C₂²×Dic₄₇	—	2	1	no	—
117	C₂²×Dic₄₇	—	2	2	no	—
118	C₂²×Dic₄₇	—	4	4	no	—
119	C₂²×Dic₄₇	—	4	4	no	—
120	C₂²×Dic₄₇	—	8	2	no	—
121	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
122	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
123	SD₁₆×C₄₇	—	2	16	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	4	no	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂²⋊C₄×C₄₇	—	2	4	no	—
132	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
133	C₄²×C₄₇	#41	1	2	yes	—
134	C₂²⋊Dic₄₇	—	4	4	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	1	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	1	no	—
139	C₄⋊Dic₄₇	—	2	2	no	—
140	C₄⋊Dic₄₇	—	2	1	no	—
141	C₄⋊Dic₄₇	—	4	4	no	—
142	C₄⋊Dic₄₇	—	4	2	no	—
143	C₄⋊Dic₄₇	—	4	4	no	—
144	C₄⋊Dic₄₇	—	8	1	no	—
145	C₄⋊Dic₄₇	SD₁₆	1	4	yes	complemented
146	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
147	C₄×Dic₄₇	—	2	2	no	—
148	C₄×Dic₄₇	—	2	2	no	—
149	C₄×Dic₄₇	—	4	4	no	—
150	C₄×Dic₄₇	—	4	2	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	4	1	no	—
161	C₂³×C₄₇	—	4	1	no	—
162	C₂³×C₄₇	—	4	1	no	—
163	C₂³×C₄₇	—	4	1	no	—
164	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₄₇	—	2	4	no	—
166	Q₈×C₄₇	—	2	4	no	—
167	Q₈×C₄₇	—	4	2	no	—
168	Q₈×C₄₇	—	4	2	no	—
169	D₄×C₄₇	—	2	2	no	—
170	D₄×C₄₇	—	2	2	no	—
171	D₄×C₄₇	—	2	2	no	—
172	D₄×C₄₇	C₄×D₄	1	4	yes	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	4	8	no	—
182	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₄₇	#135	1	2	yes	—
186	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×#41	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	—	2	2	no	—
197	C₂×Dic₄₇	—	2	2	no	—
198	C₂×Dic₄₇	—	4	1	no	—
199	C₂×Dic₄₇	—	4	1	no	—
200	C₂×Dic₄₇	—	4	2	no	—
201	C₂×Dic₄₇	—	4	1	no	—
202	C₂×Dic₄₇	—	4	2	no	—
203	C₂×Dic₄₇	—	4	1	no	—
204	C₂×Dic₄₇	—	4	2	no	—
205	C₂×Dic₄₇	—	4	1	no	—
206	C₂×Dic₄₇	—	8	8	no	—
207	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
208	C₈×C₄₇	—	2	4	no	—
209	C₄₇⋊C₈	—	2	2	no	—
210	C₄₇⋊C₈	—	4	1	no	—
211	#22996	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	—	2	4	no	—
213	C₂²×C₄₇	—	4	2	no	—
214	C₂²×C₄₇	—	4	2	no	—
215	C₂²×C₄₇	—	4	2	no	—
216	C₂²×C₄₇	—	4	2	no	—
217	C₂²×C₄₇	—	4	2	no	—
218	C₂²×C₄₇	—	4	2	no	—
219	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₄₇	D₄²	1	1	yes	characteristic
221	C₂²×C₄₇	#548	1	1	yes	characteristic
222	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
223	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
224	C₂²×C₄₇	#577	1	1	yes	characteristic
225	C₂²×C₄₇	#578	1	1	yes	characteristic
226	C₄×C₄₇	—	2	2	no	—
227	C₄×C₄₇	—	4	4	no	—
228	C₄×C₄₇	—	4	2	no	—
229	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
230	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
231	C₄×C₄₇	#520	1	1	yes	characteristic
232	C₄×C₄₇	#547	1	1	yes	characteristic
233	C₄×C₄₇	#553	1	1	yes	characteristic
234	Dic₄₇	—	2	4	no	—
235	Dic₄₇	—	4	2	no	—
236	Dic₄₇	—	4	2	no	—
237	Dic₄₇	—	8	1	no	—
238	Dic₄₇	—	8	2	no	—
239	C₂×#461	D₄₇	1	1	yes	characteristic
240	C₂×C₄×SD₁₆	—	47	2	no	—
241	#2365	—	47	1	no	—
242	D₄×C₄⋊C₄	—	47	1	no	—
243	#1956	—	47	1	no	—
244	#1948	—	47	1	no	—
245	#1933	—	47	2	no	—
246	#1877	—	47	2	no	—
247	#1865	—	47	2	no	—
248	C₈×C₄⋊C₄	—	47	1	no	—
249	C₄×#102	—	47	1	no	—
250	C₂×C₄₇	—	4	4	no	—
251	C₂×C₄₇	#2361	1	1	yes	characteristic
252	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
253	C₂×C₄₇	#2947	1	1	yes	characteristic
254	C₂×C₄₇	D₄×SD₁₆	1	1	yes	characteristic
255	C₂×C₄₇	#3283	1	1	yes	characteristic
256	C₂×C₄₇	#3359	1	1	yes	characteristic
257	C₂×C₄₇	#3360	1	1	yes	characteristic
258	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
259	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
260	C₂×C₄×Q₈	—	47	2	no	—
261	C₂×C₄×D₄	—	47	2	no	—
262	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	—	94	1	no	—
264	#461	Dic₄₇	1	8	yes	complemented
265	C₄×SD₁₆	—	94	8	no	—
266	C₂×#106	—	47	2	no	—
267	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
268	C₂×#103	—	47	2	no	—
269	C₂×#103	—	47	2	no	—
270	C₂×#103	C₂×D₄₇	1	2	yes	—
271	C₂×#102	—	47	1	no	—
272	C₂×#102	—	47	1	no	—
273	C₂×C₄×C₈	—	47	2	no	—
274	C₂×C₄×C₈	—	47	1	no	—
275	#391	—	47	2	no	—
276	#389	—	47	2	no	—
277	#389	—	94	1	no	—
278	#387	—	94	2	no	—
279	#385	—	94	2	no	—
280	#384	—	47	1	no	—
281	#380	—	94	1	no	—
282	C₄×C₄⋊C₄	—	47	1	no	—
283	C₄×C₄⋊C₄	—	47	1	no	—
284	C₄×C₄⋊C₄	—	94	1	no	—
285	#340	—	47	2	no	—
286	#340	—	47	1	no	—
287	#340	—	47	1	no	—
288	#336	—	47	2	no	—
289	C₄₇	#22996	1	1	yes	characteristic, complemented, Sylow
290	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
291	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
292	C₂³×C₄	—	2	1	no	—
293	C₂³×C₄	—	94	2	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×SD₁₆	C₂×Dic₄₇	1	8	yes	—
297	C₂²×C₈	—	47	1	no	—
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
302	C₄×Q₈	—	94	4	no	—
303	C₄×Q₈	—	188	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	94	4	no	—
306	C₄×D₄	—	188	2	no	—
307	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	47	1	no	—
311	C₂×C₄⋊C₄	—	47	1	no	—
312	C₂×C₄⋊C₄	—	47	1	no	—
313	C₂×C₄⋊C₄	—	47	2	no	—
314	C₂×C₄⋊C₄	—	47	1	no	—
315	C₂×C₄⋊C₄	—	94	1	no	—
316	C₂×C₄⋊C₄	—	94	2	no	—
317	C₂×C₄⋊C₄	—	94	2	no	—
318	C₂×C₄⋊C₄	—	94	1	no	—
319	C₂×C₄⋊C₄	—	188	4	no	—
320	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	94	2	no	—
323	C₂×C₄²	—	47	2	no	—
324	C₂×C₄²	—	94	2	no	—
325	C₂×C₄²	—	94	1	no	—
326	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
327	#106	—	94	4	no	—
328	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
329	#103	—	94	4	no	—
330	#103	—	188	2	no	—
331	#103	C₂×Dic₄₇	1	8	yes	complemented
332	#102	—	47	4	no	—
333	#102	—	94	2	no	—
334	C₄×C₈	—	94	4	no	—
335	C₄×C₈	—	94	2	no	—
336	#95	—	47	2	no	—
337	#95	—	94	2	no	—
338	#95	—	94	2	no	—
339	#95	—	94	2	no	—
340	#95	—	94	1	no	—
341	C₂⁴	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	D₄×D₄₇	1	2	yes	—
352	C₂×D₄	#10625352	1	2	yes	—
353	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	47	2	no	—
360	C₂²×C₄	—	47	2	no	—
361	C₂²×C₄	—	94	1	no	—
362	C₂²×C₄	—	94	1	no	—
363	C₂²×C₄	—	94	2	no	—
364	C₂²×C₄	—	376	2	no	—
365	C₂²×C₄	—	188	4	no	—
366	C₂²×C₄	—	188	4	no	—
367	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
368	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
370	SD₁₆	—	2	16	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	47	2	no	—
374	C₂×C₈	—	94	1	no	—
375	C₂×C₈	—	94	1	no	—
376	C₂×C₈	—	94	1	no	—
377	C₂×C₈	—	94	1	no	—
378	C₂×C₈	—	94	1	no	—
379	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	47	4	no	—
384	C₄⋊C₄	—	47	2	no	—
385	C₄⋊C₄	—	94	2	no	—
386	C₄⋊C₄	—	94	1	no	—
387	C₄⋊C₄	—	94	2	no	—
388	C₄⋊C₄	—	94	1	no	—
389	C₄⋊C₄	—	94	2	no	—
390	C₄⋊C₄	—	94	1	no	—
391	C₄⋊C₄	—	376	1	no	—
392	C₄⋊C₄	—	188	4	no	—
393	C₄⋊C₄	—	188	4	no	—
394	C₄⋊C₄	—	188	2	no	—
395	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	188	4	no	—
398	C₄²	—	94	2	no	—
399	C₄²	—	94	2	no	—
400	C₄²	—	188	4	no	—
401	C₄²	—	188	2	no	—
402	C₄²	#10625352	1	2	yes	—
403	C₄²	C₂²×Dic₄₇	1	2	yes	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
412	Q₈	—	2	4	no	—
413	Q₈	—	2	4	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	D₄×Dic₄₇	1	4	yes	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	8	no	—
429	C₂×C₄	—	47	4	no	—
430	C₂×C₄	—	94	2	no	—
431	C₂×C₄	—	94	2	no	—
432	C₂×C₄	—	94	2	no	—
433	C₂×C₄	—	94	2	no	—
434	C₂×C₄	—	94	2	no	—
435	C₂×C₄	—	94	2	no	—
436	C₂×C₄	—	376	8	no	—
437	C₂×C₄	—	188	2	no	—
438	C₂×C₄	—	188	1	no	—
439	C₂×C₄	—	188	2	no	—
440	C₂×C₄	—	188	1	no	—
441	C₂×C₄	—	188	2	no	—
442	C₂×C₄	—	188	1	no	—
443	C₂×C₄	—	188	1	no	—
444	C₂×C₄	—	188	1	no	—
445	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
446	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
447	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
448	C₂×C₄	#13094045	1	2	yes	—
449	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
451	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
452	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
453	C₂×C₄	#13094070	1	1	yes	characteristic
454	C₂×C₄	#13094071	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	94	2	no	—
457	C₈	—	188	1	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
466	C₂²	#15689757	1	1	yes	characteristic
467	C₂²	#15689779	1	1	yes	characteristic
468	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
469	C₂²	C₂×#13094045	1	1	yes	characteristic
470	C₂²	#15689932	1	1	yes	characteristic
471	C₂²	#15689939	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	2	no	—
475	C₄	—	94	4	no	—
476	C₄	—	376	1	no	—
477	C₄	—	376	2	no	—
478	C₄	—	188	2	no	—
479	C₄	—	188	2	no	—
480	C₄	SD₁₆×Dic₄₇	1	4	yes	complemented
481	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
482	C₄	#15689606	1	1	yes	characteristic
483	C₄	#15689773	1	1	yes	characteristic
484	C₄	#15689825	1	1	yes	characteristic
485	C₂	—	4	4	no	—
486	C₂	#20246408	1	1	yes	characteristic
487	C₂	C₂×SD₁₆×Dic₄₇	1	1	yes	characteristic
488	C₂	#20252232	1	1	yes	characteristic
489	C₂	#20255087	1	1	yes	characteristic
490	C₂	#20255105	1	1	yes	characteristic
491	C₂	#20256025	1	1	yes	characteristic
492	C₂	#20256041	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#461	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₄×C₄₇	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#461	D₄₇
hypocenter	C₄₇	#22996
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#461

Complements

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

N	H ≅ G/N	type
2. #20246448	C₂	semidirect
4. #20244191	C₂	semidirect
5. #20244152	C₂	semidirect
6. #20244066	C₂	semidirect
8. #20243658	C₂	semidirect
9. #20243253	C₂	semidirect
40. C₄₇×#461	C₄	semidirect
84. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
92. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
93. #103×C₄₇	C₂×C₄	semidirect
145. C₄⋊Dic₄₇	SD₁₆	semidirect
229. C₄×C₄₇	C₄×SD₁₆	semidirect
264. #461	Dic₄₇	semidirect
289. C₄₇	#22996	semidirect
301. C₄⋊Q₈	C₂×Dic₄₇	semidirect
328. C₄⋊C₈	C₂×Dic₄₇	semidirect
331. #103	C₂×Dic₄₇	semidirect
480. C₄	SD₁₆×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×Dic₄₇	2
#20246448	2
D₄×C₄⋊Dic₄₇	2
#20244191	2
#20244152	2
#20244066	2
#20243724	2
#20243658	2
#20243253	2
C₄×#13093945	2
C₂×C₄₇×#461	2
#22996	47