Subgroups — #26238536

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689323	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689208	C₂	1	2	yes	maximal, complemented
3	#20246452	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244194	C₂	1	1	yes	maximal, characteristic
6	#20244151	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244072	C₂	1	2	yes	maximal, complemented
8	#20243741	C₂	1	2	yes	maximal, complemented
9	#20243650	C₂	1	2	yes	maximal, complemented
10	C₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#103×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	2	yes	—
13	C₂×#13094021	C₂²	1	1	yes	characteristic
14	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
15	C₂×C₄×D₁₈₈	—	2	1	no	—
16	C₂×#13093986	C₂²	1	2	yes	—
17	#15689323	C₄	1	8	yes	complemented
18	#15689208	—	2	8	no	—
19	C₂×#13093955	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#13093946	C₂²	1	2	yes	—
22	C₂×#13093946	C₂²	1	2	yes	—
23	C₂×#13093944	C₂²	1	2	yes	—
24	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
25	#15689025	—	2	1	no	—
26	#15689024	C₂²	1	2	yes	—
27	#15689022	—	2	2	no	—
28	#15689022	C₂²	1	2	yes	—
29	#15689001	—	2	2	no	—
30	#15688993	—	2	1	no	—
31	#15688993	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₄₇	—	2	1	no	—
33	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
34	#15688885	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	1	yes	characteristic
42	C₄₇×#340	C₂²	1	1	yes	characteristic
43	C₂²×D₁₈₈	—	2	1	no	—
44	C₂²×D₁₈₈	—	2	1	no	—
45	C₂²×D₁₈₈	C₂³	1	2	yes	—
46	C₂²×C₄×D₄₇	—	2	2	no	—
47	C₂×#10625336	—	2	4	no	—
48	C₂×#10625336	—	2	4	no	—
49	C₂×#10625336	C₂×C₄	1	8	yes	complemented
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	#13094021	—	2	2	no	—
52	#13094021	C₂×C₄	1	4	yes	—
53	Q₈×Dic₄₇	—	2	4	no	—
54	Q₈×Dic₄₇	—	4	2	no	—
55	C₄×D₁₈₈	—	4	4	no	—
56	#13093986	—	2	4	no	—
57	#13093986	—	4	2	no	—
58	C₂×C₄⋊Dic₄₇	—	2	1	no	—
59	C₂×C₄⋊Dic₄₇	—	2	2	no	—
60	C₂×C₄⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄⋊Dic₄₇	—	2	2	no	—
62	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
63	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
64	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
65	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
66	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
67	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
68	C₂×C₄×Dic₄₇	—	2	2	no	—
69	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
70	#13093955	—	2	4	no	—
71	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
72	#13093946	—	2	4	no	—
73	#13093946	—	4	2	no	—
74	#13093944	C₂×C₄	1	8	yes	complemented
75	C₈×Dic₄₇	—	2	4	no	—
76	C₄₇⋊#95	—	2	2	no	—
77	C₄₇⋊#95	D₄	1	2	yes	—
78	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₄×Q₈×C₄₇	—	2	2	no	—
82	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	#103×C₄₇	—	2	2	no	—
91	#103×C₄₇	D₄	1	4	yes	complemented
92	C₄×C₈×C₄₇	—	2	2	no	—
93	#95×C₄₇	—	2	1	no	—
94	C₂³×D₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
100	C₂×Q₈×C₄₇	#41	1	2	yes	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
108	C₂²×Dic₄₇	—	2	2	no	—
109	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
110	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	—	2	2	no	—
113	C₂×D₁₈₈	—	2	2	no	—
114	C₂×D₁₈₈	—	2	2	no	—
115	C₂×D₁₈₈	—	2	4	no	—
116	C₂×D₁₈₈	—	2	2	no	—
117	C₂×D₁₈₈	—	2	4	no	—
118	C₂×D₁₈₈	—	4	2	no	—
119	C₂×D₁₈₈	—	4	2	no	—
120	C₂×D₁₈₈	—	8	1	no	—
121	C₂×D₁₈₈	—	8	1	no	—
122	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
123	C₂×C₄×D₄₇	—	4	4	no	—
124	C₂×C₄×D₄₇	—	4	4	no	—
125	C₂×C₄×D₄₇	—	8	2	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	2	1	no	—
129	C₂×C₈×C₄₇	—	2	1	no	—
130	C₂×C₈×C₄₇	—	2	1	no	—
131	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₄₇	—	2	4	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
138	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
139	C₄²×C₄₇	—	2	4	no	—
140	C₄²×C₄₇	—	4	2	no	—
141	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
142	C₄²×C₄₇	#41	1	2	yes	—
143	#10625336	—	2	16	no	—
144	(C₂×D₄₇)⋊C₄	—	4	4	no	—
145	(C₂×D₄₇)⋊C₄	—	4	4	no	—
146	(C₂×D₄₇)⋊C₄	—	8	2	no	—
147	C₄⋊Dic₄₇	—	2	2	no	—
148	C₄⋊Dic₄₇	—	2	2	no	—
149	C₄⋊Dic₄₇	—	2	2	no	—
150	C₄⋊Dic₄₇	—	4	4	no	—
151	C₄⋊Dic₄₇	—	4	2	no	—
152	C₄⋊Dic₄₇	—	8	2	no	—
153	C₄⋊Dic₄₇	—	8	1	no	—
154	C₄⋊Dic₄₇	SD₁₆	1	4	yes	complemented
155	C₄×Dic₄₇	—	2	2	no	—
156	C₄×Dic₄₇	—	2	2	no	—
157	C₄×Dic₄₇	—	4	4	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
161	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂²×D₄₇	—	2	4	no	—
163	C₂²×D₄₇	—	4	2	no	—
164	C₂²×D₄₇	—	4	2	no	—
165	C₂²×D₄₇	—	4	2	no	—
166	C₂²×D₄₇	—	4	2	no	—
167	C₂²×D₄₇	—	4	2	no	—
168	C₂²×D₄₇	—	4	2	no	—
169	Q₈×C₄₇	—	2	2	no	—
170	Q₈×C₄₇	—	2	2	no	—
171	Q₈×C₄₇	—	2	2	no	—
172	Q₈×C₄₇	C₄×D₄	1	4	yes	complemented
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	2	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	1	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
190	C₂×C₄×C₄₇	#135	1	2	yes	—
191	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×Dic₄₇	—	2	2	no	—
198	C₂×Dic₄₇	—	2	2	no	—
199	C₂×Dic₄₇	—	2	2	no	—
200	C₂×Dic₄₇	—	2	2	no	—
201	C₂×Dic₄₇	—	2	2	no	—
202	C₂×Dic₄₇	—	4	2	no	—
203	C₂×Dic₄₇	—	4	2	no	—
204	C₂×Dic₄₇	—	4	2	no	—
205	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
206	D₁₈₈	—	2	4	no	—
207	D₁₈₈	—	2	4	no	—
208	D₁₈₈	—	4	2	no	—
209	D₁₈₈	—	4	2	no	—
210	D₁₈₈	—	4	8	no	—
211	D₁₈₈	—	8	4	no	—
212	C₄×D₄₇	—	8	8	no	—
213	C₈×C₄₇	—	2	2	no	—
214	C₈×C₄₇	—	4	1	no	—
215	C₄₇⋊C₈	—	2	4	no	—
216	#22997	—	47	1	no	maximal, Sylow
217	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₄₇	D₄²	1	1	yes	characteristic
219	C₂²×C₄₇	#548	1	1	yes	characteristic
220	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
221	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
222	C₂²×C₄₇	#576	1	1	yes	characteristic
223	C₂²×C₄₇	#577	1	1	yes	characteristic
224	C₂×D₄₇	—	4	4	no	—
225	C₂×D₄₇	—	4	4	no	—
226	C₂×D₄₇	—	4	4	no	—
227	C₂×D₄₇	—	8	2	no	—
228	C₂×D₄₇	—	8	2	no	—
229	C₂×D₄₇	—	8	2	no	—
230	C₂×D₄₇	—	8	2	no	—
231	C₄×C₄₇	—	2	4	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	4	2	no	—
234	C₄×C₄₇	—	4	2	no	—
235	C₄×C₄₇	—	8	1	no	—
236	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
237	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
238	C₄×C₄₇	#520	1	1	yes	characteristic
239	C₄×C₄₇	#547	1	1	yes	characteristic
240	C₄×C₄₇	#553	1	1	yes	characteristic
241	Dic₄₇	—	2	4	no	—
242	Dic₄₇	—	4	2	no	—
243	Dic₄₇	—	8	2	no	—
244	C₂×#460	—	47	1	no	—
245	C₂×C₄×SD₁₆	—	47	2	no	—
246	#2366	—	47	1	no	—
247	Q₈×C₄⋊C₄	—	47	1	no	—
248	#1957	—	47	1	no	—
249	#1948	—	47	1	no	—
250	#1934	—	47	2	no	—
251	#1880	—	47	2	no	—
252	#1864	—	47	2	no	—
253	C₈×C₄⋊C₄	—	47	1	no	—
254	C₄×#103	D₄₇	1	1	yes	characteristic, complemented
255	C₂×C₄₇	#2361	1	1	yes	characteristic
256	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
257	C₂×C₄₇	#2946	1	1	yes	characteristic
258	C₂×C₄₇	D₄×SD₁₆	1	1	yes	characteristic
259	C₂×C₄₇	#3287	1	1	yes	characteristic
260	C₂×C₄₇	#3362	1	1	yes	characteristic
261	C₂×C₄₇	#3365	1	1	yes	characteristic
262	D₄₇	—	8	4	no	—
263	C₂²×SD₁₆	—	47	2	no	—
264	C₂×#127	—	47	1	no	—
265	C₂×C₄×Q₈	—	47	2	no	—
266	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
267	C₂×C₄×D₄	—	47	2	no	—
268	C₂×C₄×D₄	—	94	1	no	—
269	#460	—	47	8	no	—
270	C₄×SD₁₆	—	94	8	no	—
271	C₂×#106	—	47	2	no	—
272	C₂×C₄⋊C₈	—	47	1	no	—
273	C₂×#103	C₂×D₄₇	1	1	yes	characteristic
274	C₂×#103	C₂×D₄₇	1	1	yes	characteristic
275	C₂×#102	—	47	2	no	—
276	C₂×#102	—	47	2	no	—
277	C₂×#102	—	47	2	no	—
278	C₂×C₄×C₈	—	47	2	no	—
279	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
280	#390	—	47	2	no	—
281	#390	—	94	1	no	—
282	#389	—	47	2	no	—
283	#389	—	94	2	no	—
284	#386	—	94	2	no	—
285	#384	—	47	1	no	—
286	#384	—	94	1	no	—
287	C₄×C₄⋊C₄	—	47	1	no	—
288	C₄×C₄⋊C₄	—	94	1	no	—
289	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
290	#340	—	47	2	no	—
291	#340	C₂×D₄₇	1	1	yes	characteristic
292	#340	C₂×D₄₇	1	1	yes	characteristic
293	#336	—	47	2	no	—
294	C₄₇	#22997	1	1	yes	characteristic, complemented, Sylow
295	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
296	C₂²×D₄	—	47	2	no	—
297	C₂²×D₄	—	94	1	no	—
298	C₂²×D₄	—	94	1	no	—
299	C₂³×C₄	—	94	2	no	—
300	C₂×SD₁₆	—	47	8	no	—
301	C₂×SD₁₆	—	94	4	no	—
302	C₂×SD₁₆	—	94	4	no	—
303	C₂²×C₈	—	47	2	no	—
304	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
305	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
306	#127	—	47	4	no	—
307	#127	—	94	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	94	4	no	—
310	C₄×Q₈	—	188	2	no	—
311	C₄×Q₈	C₄×D₄₇	1	4	yes	complemented
312	C₄×D₄	—	94	4	no	—
313	C₄×D₄	—	188	4	no	—
314	C₄×D₄	—	188	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	47	1	no	—
317	C₂×C₄⋊C₄	—	47	1	no	—
318	C₂×C₄⋊C₄	—	47	2	no	—
319	C₂×C₄⋊C₄	—	94	2	no	—
320	C₂×C₄⋊C₄	—	94	1	no	—
321	C₂×C₄⋊C₄	—	94	2	no	—
322	C₂×C₄⋊C₄	—	94	1	no	—
323	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	94	2	no	—
327	C₂×C₂²⋊C₄	—	94	2	no	—
328	C₂×C₂²⋊C₄	—	94	2	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	47	2	no	—
332	C₂×C₄²	—	94	2	no	—
333	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
334	#106	—	94	4	no	—
335	C₄⋊C₈	—	47	4	no	—
336	#103	—	2	2	no	—
337	#103	D₁₈₈	1	4	yes	complemented
338	#102	—	47	8	no	—
339	#102	—	94	4	no	—
340	#102	—	188	2	no	—
341	C₄×C₈	—	2	2	no	—
342	C₄×C₈	—	94	4	no	—
343	#95	—	2	1	no	—
344	#95	—	47	2	no	—
345	#95	—	94	2	no	—
346	C₂⁴	—	94	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
351	C₂×Q₈	C₂×D₁₈₈	1	2	yes	—
352	C₂×Q₈	#10625350	1	2	yes	—
353	C₂×D₄	—	47	4	no	—
354	C₂×D₄	—	94	4	no	—
355	C₂×D₄	—	94	4	no	—
356	C₂×D₄	—	94	2	no	—
357	C₂×D₄	—	94	2	no	—
358	C₂×D₄	—	94	2	no	—
359	C₂×D₄	—	94	2	no	—
360	C₂×D₄	—	94	2	no	—
361	C₂×D₄	—	376	1	no	—
362	C₂×D₄	—	376	1	no	—
363	C₂×D₄	—	188	2	no	—
364	C₂×D₄	—	188	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	47	2	no	—
370	C₂²×C₄	—	47	2	no	—
371	C₂²×C₄	—	94	2	no	—
372	C₂²×C₄	—	376	2	no	—
373	C₂²×C₄	—	188	4	no	—
374	C₂²×C₄	—	188	4	no	—
375	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
377	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
378	SD₁₆	—	94	16	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	47	4	no	—
385	C₂×C₈	—	94	2	no	—
386	C₂×C₈	—	94	2	no	—
387	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	47	4	no	—
394	C₄⋊C₄	—	94	2	no	—
395	C₄⋊C₄	—	94	2	no	—
396	C₄⋊C₄	—	94	2	no	—
397	C₄⋊C₄	—	376	1	no	—
398	C₄⋊C₄	—	376	2	no	—
399	C₄⋊C₄	—	188	4	no	—
400	C₄⋊C₄	—	188	2	no	—
401	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
402	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
403	C₂²⋊C₄	—	376	2	no	—
404	C₂²⋊C₄	—	188	4	no	—
405	C₂²⋊C₄	—	188	4	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	4	2	no	—
408	C₄²	—	94	2	no	—
409	C₄²	—	94	2	no	—
410	C₄²	—	188	4	no	—
411	C₄²	C₂×C₄×D₄₇	1	2	yes	—
412	C₄²	#10625352	1	2	yes	—
413	C₂³	—	94	4	no	—
414	C₂³	—	188	2	no	—
415	C₂³	—	188	2	no	—
416	C₂³	—	188	2	no	—
417	C₂³	—	188	2	no	—
418	C₂³	—	188	2	no	—
419	C₂³	—	188	2	no	—
420	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
421	Q₈	—	2	2	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	2	2	no	—
424	Q₈	C₄×D₁₈₈	1	4	yes	complemented
425	D₄	—	94	4	no	—
426	D₄	—	94	4	no	—
427	D₄	—	376	4	no	—
428	D₄	—	188	2	no	—
429	D₄	—	188	2	no	—
430	D₄	—	188	8	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	47	4	no	—
446	C₂×C₄	—	94	2	no	—
447	C₂×C₄	—	94	2	no	—
448	C₂×C₄	—	94	2	no	—
449	C₂×C₄	—	94	2	no	—
450	C₂×C₄	—	94	2	no	—
451	C₂×C₄	—	376	8	no	—
452	C₂×C₄	—	188	2	no	—
453	C₂×C₄	—	188	2	no	—
454	C₂×C₄	—	188	2	no	—
455	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
456	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
457	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
458	C₂×C₄	#13094047	1	2	yes	—
459	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
461	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
462	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
463	C₂×C₄	#13094070	1	1	yes	characteristic
464	C₂×C₄	#13094071	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	4	1	no	—
467	C₈	—	94	4	no	—
468	C₂²	—	376	2	no	—
469	C₂²	—	376	2	no	—
470	C₂²	—	376	2	no	—
471	C₂²	—	376	2	no	—
472	C₂²	—	188	4	no	—
473	C₂²	—	188	4	no	—
474	C₂²	—	188	4	no	—
475	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
476	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
477	C₂²	#15689782	1	1	yes	characteristic
478	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
479	C₂²	C₂×#13094047	1	1	yes	characteristic
480	C₂²	#15689925	1	1	yes	characteristic
481	C₂²	#15689930	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	1	no	—
487	C₄	—	94	4	no	—
488	C₄	—	376	2	no	—
489	C₄	—	188	2	no	—
490	C₄	#15689208	1	4	yes	complemented
491	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
492	C₄	#15689603	1	1	yes	characteristic
493	C₄	#15689777	1	1	yes	characteristic
494	C₄	#15689819	1	1	yes	characteristic
495	C₂	—	376	4	no	—
496	C₂	#20246402	1	1	yes	characteristic
497	C₂	C₂×#15689208	1	1	yes	characteristic
498	C₂	#20252223	1	1	yes	characteristic
499	C₂	SD₁₆×D₁₈₈	1	1	yes	characteristic
500	C₂	#20255147	1	1	yes	characteristic
501	C₂	#20256057	1	1	yes	characteristic
502	C₂	#20256082	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#103×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#13094021	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#103	D₄₇
hypocenter	C₄₇	#22997
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#103

Complements

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

N	H ≅ G/N	type
2. C₂×#15689208	C₂	semidirect
4. Q₈×C₄⋊Dic₄₇	C₂	semidirect
6. #20244151	C₂	semidirect
7. #20244072	C₂	semidirect
8. #20243741	C₂	semidirect
9. #20243650	C₂	semidirect
10. C₈×C₄⋊Dic₄₇	C₂	semidirect
11. C₄×#103×C₄₇	C₂	semidirect
17. #15689323	C₄	semidirect
49. C₂×#10625336	C₂×C₄	semidirect
71. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
74. #13093944	C₂×C₄	semidirect
82. C₄×Q₈×C₄₇	C₂×C₄	semidirect
91. #103×C₄₇	D₄	semidirect
154. C₄⋊Dic₄₇	SD₁₆	semidirect
172. Q₈×C₄₇	C₄×D₄	semidirect
236. C₄×C₄₇	C₄×SD₁₆	semidirect
254. C₄×#103	D₄₇	semidirect
294. C₄₇	#22997	semidirect
311. C₄×Q₈	C₄×D₄₇	semidirect
337. #103	D₁₈₈	semidirect
424. Q₈	C₄×D₁₈₈	semidirect
490. C₄	#15689208	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689323	2
C₂×#15689208	2
#20246452	2
Q₈×C₄⋊Dic₄₇	2
#20244194	2
#20244151	2
#20244072	2
#20243741	2
#20243650	2
C₈×C₄⋊Dic₄₇	2
C₄×#103×C₄₇	2
#22997	47