Subgroups — #26258804

Order 12032.

910 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689393	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253009	C₂	1	2	yes	maximal, complemented
3	C₂×#15689359	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13093960	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244747	C₂	1	2	yes	maximal, complemented
6	#20244679	C₂	1	2	yes	maximal, complemented
7	#20244298	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244173	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243849	C₂	1	2	yes	maximal, complemented
10	#20243452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094049	C₂²	1	2	yes	—
13	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
14	C₂²×#10625329	C₂²	1	2	yes	—
15	C₂×#13093998	C₂²	1	2	yes	—
16	#15689393	—	2	4	no	—
17	#15689374	—	2	2	no	—
18	#15689371	—	2	2	no	—
19	#15689359	—	2	1	no	—
20	#15689359	—	2	1	no	—
21	#15689359	—	2	1	no	—
22	#15689359	—	2	1	no	—
23	#15689357	—	2	2	no	—
24	#15689354	—	2	2	no	—
25	C₂×#13093960	—	2	4	no	—
26	C₂×#13093960	C₂²	1	2	yes	—
27	C₂×#13093960	C₂²	1	1	yes	characteristic
28	C₂×#13093960	C₂²	1	1	yes	characteristic
29	#15689166	C₂²	1	2	yes	—
30	C₂×#13093958	C₂²	1	1	yes	characteristic
31	#15689127	C₂²	1	2	yes	—
32	#15689124	C₂²	1	2	yes	—
33	C₂×#13093946	C₂²	1	2	yes	—
34	C₂×#13093940	C₂²	1	2	yes	—
35	C₂×#13093940	C₂²	1	2	yes	—
36	#15688891	C₂²	1	2	yes	—
37	#15688891	C₂²	1	2	yes	—
38	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
39	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#525	C₂²	1	1	yes	characteristic
41	C₄₇×#435	—	2	1	no	—
42	C₄₇×#435	—	2	1	no	—
43	C₈×D₄×C₄₇	—	2	1	no	—
44	C₈×D₄×C₄₇	—	2	1	no	—
45	C₄₇×#424	C₂²	1	1	yes	characteristic
46	C₄₇×#408	C₂²	1	1	yes	characteristic
47	C₄₇×#407	C₂²	1	1	yes	characteristic
48	C₄₇×#405	C₂²	1	1	yes	characteristic
49	C₂²×D₁₈₈	C₂³	1	2	yes	—
50	C₂²×C₂²⋊D₄₇	—	2	2	no	—
51	#13094049	—	2	4	no	—
52	#13094049	—	4	2	no	—
53	C₂×#10625336	—	2	2	no	—
54	C₂×D₃₇₆	—	2	1	no	—
55	C₂×D₃₇₆	—	2	1	no	—
56	C₂×D₃₇₆	—	2	2	no	—
57	C₂×D₃₇₆	—	2	2	no	—
58	C₂×#10625334	—	2	2	no	—
59	C₂×#10625329	—	2	2	no	—
60	C₂×#10625329	—	2	4	no	—
61	C₂×#10625329	—	4	2	no	—
62	C₂×#10625329	C₂³	1	2	yes	—
63	C₂×#10625329	C₂³	1	2	yes	—
64	C₂²×C₄₇⋊C₈	—	2	2	no	—
65	#13093998	—	2	2	no	—
66	#13093998	—	2	2	no	—
67	#13093998	—	2	2	no	—
68	#13093998	—	2	2	no	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
70	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
71	#13093960	—	2	2	no	—
72	#13093960	—	2	4	no	—
73	#13093960	D₄	1	4	yes	complemented
74	#13093958	—	2	1	no	—
75	#13093958	—	2	1	no	—
76	#13093957	—	2	2	no	—
77	#13093955	—	2	2	no	—
78	#13093948	—	2	2	no	—
79	#13093946	—	2	2	no	—
80	#13093946	—	2	2	no	—
81	#13093945	—	2	2	no	—
82	#13093944	—	2	2	no	—
83	#13093944	—	2	2	no	—
84	#13093940	—	2	4	no	—
85	#13093940	—	4	2	no	—
86	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	#131×C₄₇	—	2	2	no	—
89	#131×C₄₇	—	2	2	no	—
90	C₂×M₁₆×C₄₇	—	2	1	no	—
91	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₄₇	—	2	2	no	—
94	C₂²×C₈×C₄₇	—	2	2	no	—
95	C₂²×C₈×C₄₇	—	2	1	no	—
96	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	#123×C₄₇	—	2	1	no	—
103	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
104	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
105	#121×C₄₇	D₄	1	1	yes	characteristic
106	#121×C₄₇	D₄	1	1	yes	characteristic
107	#120×C₄₇	—	2	1	no	—
108	C₄×D₄×C₄₇	—	2	1	no	—
109	C₄×D₄×C₄₇	—	2	1	no	—
110	#117×C₄₇	C₂³	1	1	yes	characteristic
111	C₄⋊C₈×C₄₇	—	2	1	no	—
112	C₄⋊C₈×C₄₇	—	2	1	no	—
113	C₂²⋊C₈×C₄₇	—	2	1	no	—
114	C₂²⋊C₈×C₄₇	—	2	1	no	—
115	C₂²⋊C₈×C₄₇	—	2	1	no	—
116	C₂²⋊C₈×C₄₇	—	2	1	no	—
117	#97×C₄₇	—	2	1	no	—
118	C₄×C₈×C₄₇	—	2	1	no	—
119	C₂⁴×C₄₇	#41	1	1	yes	characteristic
120	C₂³×D₄₇	—	2	2	no	—
121	#41×C₄₇	—	2	1	no	—
122	#41×C₄₇	—	2	1	no	—
123	#41×C₄₇	—	2	1	no	—
124	#41×C₄₇	—	2	1	no	—
125	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×D₄×C₄₇	—	2	1	no	—
127	C₂×D₄×C₄₇	—	2	1	no	—
128	C₂×D₄×C₄₇	—	2	1	no	—
129	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	1	no	—
133	C₂²×C₄×C₄₇	—	2	1	no	—
134	C₂²×C₄×C₄₇	—	2	1	no	—
135	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
141	C₂×C₂²⋊D₄₇	—	4	2	no	—
142	C₂×C₂²⋊D₄₇	—	4	2	no	—
143	C₂×C₂²⋊D₄₇	—	8	4	no	—
144	C₂²×Dic₄₇	—	2	2	no	—
145	C₂×D₁₈₈	—	2	2	no	—
146	C₂×D₁₈₈	—	2	2	no	—
147	C₂×D₁₈₈	—	2	2	no	—
148	C₂×D₁₈₈	—	2	2	no	—
149	C₂×D₁₈₈	—	2	2	no	—
150	C₂×D₁₈₈	—	2	2	no	—
151	M₁₆×C₄₇	—	2	1	no	—
152	M₁₆×C₄₇	—	2	1	no	—
153	M₁₆×C₄₇	—	2	1	no	—
154	M₁₆×C₄₇	—	2	1	no	—
155	M₁₆×C₄₇	—	4	2	no	—
156	C₂×C₈×C₄₇	—	2	1	no	—
157	C₂×C₈×C₄₇	—	2	1	no	—
158	C₂×C₈×C₄₇	—	2	2	no	—
159	C₂×C₈×C₄₇	—	2	2	no	—
160	C₂×C₈×C₄₇	—	2	2	no	—
161	C₂×C₈×C₄₇	—	2	2	no	—
162	C₂×C₈×C₄₇	—	2	1	no	—
163	C₂×C₈×C₄₇	—	2	1	no	—
164	C₂×C₈×C₄₇	—	4	2	no	—
165	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
168	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₄₇	#41	1	2	yes	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	—	2	1	no	—
173	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
174	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
175	C₂²⋊C₄×C₄₇	—	2	1	no	—
176	C₂²⋊C₄×C₄₇	—	2	1	no	—
177	C₂²⋊C₄×C₄₇	—	2	1	no	—
178	C₂²⋊C₄×C₄₇	—	2	1	no	—
179	C₂²⋊C₄×C₄₇	—	2	1	no	—
180	C₄²×C₄₇	—	2	1	no	—
181	#10625336	—	4	4	no	—
182	#10625334	—	4	4	no	—
183	(C₂×D₄₇)⋊C₄	—	4	2	no	—
184	(C₂×D₄₇)⋊C₄	—	4	2	no	—
185	C₄⋊Dic₄₇	—	2	2	no	—
186	C₄⋊Dic₄₇	—	2	2	no	—
187	#10625329	—	2	2	no	—
188	#10625329	—	2	2	no	—
189	#10625329	—	2	2	no	—
190	#10625329	—	4	4	no	—
191	#10625329	C₂×D₄	1	4	yes	—
192	C₂×C₄₇⋊C₈	—	2	2	no	—
193	C₂×C₄₇⋊C₈	—	2	2	no	—
194	C₂×C₄₇⋊C₈	—	4	4	no	—
195	D₃₇₆	—	4	2	no	—
196	D₃₇₆	—	4	2	no	—
197	C₂³×C₄₇	—	2	1	no	—
198	C₂³×C₄₇	—	2	1	no	—
199	C₂³×C₄₇	—	2	2	no	—
200	C₂³×C₄₇	—	2	1	no	—
201	C₂³×C₄₇	—	4	1	no	—
202	C₂³×C₄₇	#121	1	1	yes	characteristic
203	C₂³×C₄₇	#121	1	1	yes	characteristic
204	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
205	C₂²×D₄₇	—	4	2	no	—
206	C₂²×D₄₇	—	4	2	no	—
207	C₂²×D₄₇	—	4	2	no	—
208	C₂²×D₄₇	—	8	2	no	—
209	C₂²×D₄₇	—	8	2	no	—
210	Q₈×C₄₇	—	2	1	no	—
211	Q₈×C₄₇	—	2	1	no	—
212	D₄×C₄₇	—	2	1	no	—
213	D₄×C₄₇	—	2	1	no	—
214	D₄×C₄₇	—	4	2	no	—
215	D₄×C₄₇	—	4	1	no	—
216	D₄×C₄₇	—	4	1	no	—
217	D₄×C₄₇	—	4	2	no	—
218	C₂×C₄×C₄₇	—	2	1	no	—
219	C₂×C₄×C₄₇	—	2	1	no	—
220	C₂×C₄×C₄₇	—	2	1	no	—
221	C₂×C₄×C₄₇	—	2	1	no	—
222	C₂×C₄×C₄₇	—	2	1	no	—
223	C₂×C₄×C₄₇	—	2	1	no	—
224	C₂×C₄×C₄₇	—	2	1	no	—
225	C₂×C₄×C₄₇	—	2	1	no	—
226	C₂×C₄×C₄₇	—	2	1	no	—
227	C₂×C₄×C₄₇	—	2	1	no	—
228	C₂×C₄×C₄₇	—	2	1	no	—
229	C₂×C₄×C₄₇	—	2	1	no	—
230	C₂×C₄×C₄₇	—	2	1	no	—
231	C₂×C₄×C₄₇	—	4	1	no	—
232	C₂×C₄×C₄₇	—	4	1	no	—
233	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
241	C₂²⋊D₄₇	—	8	4	no	—
242	C₂²⋊D₄₇	—	8	4	no	—
243	C₂×Dic₄₇	—	4	2	no	—
244	C₂×Dic₄₇	—	8	2	no	—
245	D₁₈₈	—	4	2	no	—
246	D₁₈₈	—	4	2	no	—
247	D₁₈₈	—	4	2	no	—
248	D₁₈₈	—	4	2	no	—
249	C₈×C₄₇	—	2	1	no	—
250	C₈×C₄₇	—	2	1	no	—
251	C₈×C₄₇	—	4	1	no	—
252	C₈×C₄₇	—	4	1	no	—
253	C₈×C₄₇	#121	1	2	yes	—
254	C₈×C₄₇	#121	1	2	yes	—
255	C₄₇⋊C₈	—	2	4	no	—
256	C₄₇⋊C₈	—	4	2	no	—
257	#24803	—	47	1	no	maximal, Sylow
258	C₂²×C₄₇	—	2	1	no	—
259	C₂²×C₄₇	—	2	1	no	—
260	C₂²×C₄₇	—	2	1	no	—
261	C₂²×C₄₇	—	2	1	no	—
262	C₂²×C₄₇	—	2	1	no	—
263	C₂²×C₄₇	—	2	1	no	—
264	C₂²×C₄₇	—	2	1	no	—
265	C₂²×C₄₇	—	4	2	no	—
266	C₂²×C₄₇	—	4	2	no	—
267	C₂²×C₄₇	—	4	1	no	—
268	C₂²×C₄₇	—	4	1	no	—
269	C₂²×C₄₇	—	4	1	no	—
270	C₂²×C₄₇	#472	1	2	yes	complemented
271	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
272	C₂²×C₄₇	#548	1	1	yes	characteristic
273	C₂²×C₄₇	#553	1	1	yes	characteristic
274	C₂×D₄₇	—	8	2	no	—
275	C₂×D₄₇	—	8	2	no	—
276	C₂×D₄₇	—	8	2	no	—
277	C₂×D₄₇	—	16	2	no	—
278	C₂×D₄₇	—	16	2	no	—
279	C₄×C₄₇	—	2	1	no	—
280	C₄×C₄₇	—	2	1	no	—
281	C₄×C₄₇	—	4	1	no	—
282	C₄×C₄₇	—	4	1	no	—
283	C₄×C₄₇	—	4	1	no	—
284	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
285	C₄×C₄₇	#537	1	1	yes	characteristic
286	C₄×C₄₇	D₄²	1	1	yes	characteristic
287	C₄×C₄₇	#547	1	1	yes	characteristic
288	Dic₄₇	—	8	2	no	—
289	C₂×#472	—	47	1	no	—
290	#3055	—	47	2	no	—
291	C₂×#466	—	47	1	no	—
292	#2929	D₄₇	1	1	yes	characteristic, complemented
293	C₂²×#108	—	47	1	no	—
294	#2063	—	47	2	no	—
295	#2051	—	47	2	no	—
296	#1978	—	47	1	no	—
297	#1952	—	47	1	no	—
298	#1900	—	47	2	no	—
299	#1816	—	47	1	no	—
300	C₂×C₄₇	—	2	1	no	—
301	C₂×C₄₇	—	2	1	no	—
302	C₂×C₄₇	—	2	2	no	—
303	C₂×C₄₇	—	4	1	no	—
304	C₂×C₄₇	—	8	1	no	—
305	C₂×C₄₇	#2416	1	1	yes	characteristic
306	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
307	C₂×C₄₇	#3067	1	1	yes	characteristic
308	D₄₇	—	16	2	no	—
309	C₂×AGL(1,ℤ/8)	—	47	2	no	—
310	C₂²×D₈	—	47	1	no	—
311	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
312	C₂²×M₁₆	—	47	2	no	—
313	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
314	#525	C₂×D₄₇	1	1	yes	characteristic
315	C₂×#121	—	47	2	no	—
316	#472	—	94	4	no	—
317	#469	—	94	2	no	—
318	#468	—	94	2	no	—
319	#466	—	94	1	no	—
320	#466	—	94	1	no	—
321	#466	—	94	1	no	—
322	#466	—	94	1	no	—
323	#466	—	94	2	no	—
324	#465	—	94	2	no	—
325	#435	—	2	1	no	—
326	#435	—	2	1	no	—
327	C₈×D₄	—	2	1	no	—
328	C₈×D₄	—	2	1	no	—
329	C₂×#108	—	47	1	no	—
330	C₂×#108	—	47	2	no	—
331	C₂×#108	—	47	1	no	—
332	C₂×#108	—	94	4	no	—
333	#428	—	47	2	no	—
334	C₂×#107	—	47	1	no	—
335	#424	C₂×D₄₇	1	1	yes	characteristic
336	#418	—	47	2	no	—
337	#417	—	47	2	no	—
338	C₂×#102	—	47	2	no	—
339	C₂×#100	—	47	2	no	—
340	C₂×#100	—	47	2	no	—
341	#408	C₂×D₄₇	1	1	yes	characteristic
342	#407	C₂×D₄₇	1	1	yes	characteristic
343	#405	C₂×D₄₇	1	1	yes	characteristic
344	#343	—	47	2	no	—
345	#343	—	47	2	no	—
346	C₄₇	#24803	1	1	yes	characteristic, complemented, Sylow
347	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
348	C₂²×D₄	—	47	2	no	—
349	C₂²×D₄	—	94	2	no	—
350	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
351	AGL(1,ℤ/8)	—	94	4	no	—
352	AGL(1,ℤ/8)	—	188	2	no	—
353	C₂×SD₁₆	—	94	2	no	—
354	C₂×D₈	—	94	2	no	—
355	C₂×D₈	—	94	2	no	—
356	C₂×D₈	—	94	2	no	—
357	C₂×D₈	—	94	1	no	—
358	C₂×D₈	—	94	1	no	—
359	#131	—	2	2	no	—
360	#131	—	2	2	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	47	2	no	—
363	C₂×M₁₆	—	47	2	no	—
364	C₂×M₁₆	—	94	2	no	—
365	C₂×M₁₆	—	94	4	no	—
366	C₂×M₁₆	—	188	2	no	—
367	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
368	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
369	C₂²×C₈	—	2	2	no	—
370	C₂²×C₈	—	2	2	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	94	2	no	—
373	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
374	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
375	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
376	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
377	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
378	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
379	#123	—	2	1	no	—
380	C₂²⋊Q₈	D₁₈₈	1	1	yes	characteristic
381	C₂²⋊Q₈	D₁₈₈	1	1	yes	characteristic
382	#121	—	94	2	no	—
383	#121	—	94	2	no	—
384	#121	—	94	2	no	—
385	#121	—	94	2	no	—
386	#121	D₁₈₈	1	1	yes	characteristic
387	#121	D₁₈₈	1	1	yes	characteristic
388	#120	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	#117	C₂²×D₄₇	1	1	yes	characteristic
392	C₂×C₄⋊C₄	—	47	2	no	—
393	C₂×C₂²⋊C₄	—	94	2	no	—
394	#108	—	47	4	no	—
395	#108	—	94	4	no	—
396	#108	—	94	2	no	—
397	#107	—	94	1	no	—
398	#107	—	94	1	no	—
399	#107	—	94	2	no	—
400	#106	—	94	2	no	—
401	C₄⋊C₈	—	2	1	no	—
402	C₄⋊C₈	—	2	1	no	—
403	#103	—	94	2	no	—
404	#102	—	94	2	no	—
405	#102	—	94	2	no	—
406	#102	—	94	2	no	—
407	#102	—	94	2	no	—
408	#102	—	94	2	no	—
409	#100	—	94	4	no	—
410	#100	—	188	2	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	#97	—	2	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₂⁴	—	94	2	no	—
418	C₂⁴	#10625350	1	1	yes	characteristic
419	#41	—	2	1	no	—
420	#41	—	2	1	no	—
421	#41	—	2	1	no	—
422	#41	—	2	1	no	—
423	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	94	2	no	—
428	C₂×D₄	—	94	2	no	—
429	C₂×D₄	—	94	2	no	—
430	C₂×D₄	—	94	2	no	—
431	C₂×D₄	—	94	2	no	—
432	C₂×D₄	—	94	2	no	—
433	C₂×D₄	—	376	4	no	—
434	C₂×D₄	—	188	2	no	—
435	C₂×D₄	—	188	2	no	—
436	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	94	2	no	—
443	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
445	C₂²×C₄	#10625350	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
448	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
449	SD₁₆	—	188	4	no	—
450	D₈	—	188	4	no	—
451	D₈	—	188	2	no	—
452	D₈	—	188	2	no	—
453	M₁₆	—	2	1	no	—
454	M₁₆	—	2	1	no	—
455	M₁₆	—	2	1	no	—
456	M₁₆	—	2	1	no	—
457	M₁₆	—	4	2	no	—
458	M₁₆	—	47	4	no	—
459	M₁₆	—	94	2	no	—
460	M₁₆	—	94	2	no	—
461	M₁₆	—	94	2	no	—
462	M₁₆	—	188	4	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	4	2	no	—
472	C₂×C₈	—	94	2	no	—
473	C₂×C₈	—	94	2	no	—
474	C₂×C₈	—	188	4	no	—
475	C₂×C₈	D₄×D₄₇	1	2	yes	—
476	C₂×C₈	#10625352	1	2	yes	—
477	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
478	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
479	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
480	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	94	2	no	—
484	C₄⋊C₄	—	94	2	no	—
485	C₄⋊C₄	C₂×D₁₈₈	1	1	yes	characteristic
486	C₄⋊C₄	C₂×D₁₈₈	1	1	yes	characteristic
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	188	2	no	—
493	C₂²⋊C₄	—	188	2	no	—
494	C₄²	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	376	2	no	—
501	C₂³	—	376	2	no	—
502	C₂³	—	188	2	no	—
503	C₂³	—	188	2	no	—
504	C₂³	—	188	2	no	—
505	C₂³	#13093998	1	1	yes	characteristic
506	C₂³	#13093998	1	1	yes	characteristic
507	C₂³	C₂×#10625350	1	1	yes	characteristic
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	2	no	—
516	D₄	—	376	4	no	—
517	D₄	—	376	4	no	—
518	D₄	—	188	2	no	—
519	D₄	—	188	2	no	—
520	D₄	—	188	2	no	—
521	D₄	—	188	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	376	2	no	—
538	C₂×C₄	—	188	2	no	—
539	C₂×C₄	#13093998	1	1	yes	characteristic
540	C₂×C₄	#13093998	1	1	yes	characteristic
541	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
542	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
544	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
545	C₂×C₄	#13094070	1	1	yes	characteristic
546	C₂×C₄	#13094071	1	1	yes	characteristic
547	C₈	—	2	1	no	—
548	C₈	—	2	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	94	4	no	—
552	C₈	—	188	2	no	—
553	C₈	#13093996	1	2	yes	—
554	C₈	#13093996	1	2	yes	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	376	2	no	—
568	C₂²	—	376	2	no	—
569	C₂²	—	376	2	no	—
570	C₂²	—	752	2	no	—
571	C₂²	—	752	2	no	—
572	C₂²	#15689393	1	2	yes	complemented
573	C₂²	C₂×#13093998	1	1	yes	characteristic
574	C₂²	#15689782	1	1	yes	characteristic
575	C₂²	#15689819	1	1	yes	characteristic
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	376	2	no	—
582	C₄	C₂×#13093996	1	1	yes	characteristic
583	C₄	#15689701	1	1	yes	characteristic
584	C₄	D₄×D₁₈₈	1	1	yes	characteristic
585	C₄	#15689777	1	1	yes	characteristic
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	2	no	—
589	C₂	—	4	1	no	—
590	C₂	—	8	1	no	—
591	C₂	—	752	2	no	—
592	C₂	#20246828	1	1	yes	characteristic
593	C₂	C₂×#15689393	1	1	yes	characteristic
594	C₂	#20253108	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093998
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2929	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	#2929	D₄₇
hypocenter	C₄₇	#24803
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2929

Complements

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

N	H ≅ G/N	type
1. C₂×#15689393	C₂	semidirect
2. #20253009	C₂	semidirect
3. C₂×#15689359	C₂	semidirect
4. C₂²×#13093960	C₂	semidirect
5. #20244747	C₂	semidirect
6. #20244679	C₂	semidirect
7. #20244298	C₂	semidirect
8. #20244173	C₂	semidirect
9. #20243849	C₂	semidirect
10. #20243452	C₂	semidirect
11. C₄₇×#2929	C₂	semidirect
73. #13093960	D₄	semidirect
270. C₂²×C₄₇	#472	semidirect
292. #2929	D₄₇	semidirect
346. C₄₇	#24803	semidirect
572. C₂²	#15689393	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689393	2
#20253009	2
C₂×#15689359	2
C₂²×#13093960	2
#20244747	2
#20244679	2
#20244298	2
#20244173	2
#20243849	2
#20243452	2
C₄₇×#2929	2
#24803	47