Subgroups — #26222252

Order 12032.

1282 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258100	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252291	C₂	1	2	yes	maximal, complemented
3	#20252106	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243772	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243752	C₂	1	2	yes	maximal, complemented
6	#20243630	C₂	1	2	yes	maximal, complemented
7	#20243610	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243352	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243233	C₂	1	2	yes	maximal, complemented
10	#20243191	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3018	C₂	1	1	yes	maximal, characteristic
12	#15689890	—	2	4	no	—
13	#15689890	—	2	2	no	—
14	#15689890	C₂²	1	2	yes	—
15	#15689890	C₂²	1	1	yes	characteristic
16	C₂×#13094031	—	2	4	no	—
17	C₂×#13094031	—	2	2	no	—
18	C₂×#13094031	C₂²	1	2	yes	—
19	C₂×#13094031	C₂²	1	1	yes	characteristic
20	C₂×#13094031	C₂²	1	1	yes	characteristic, complemented
21	#15689245	—	2	4	no	—
22	#15689240	—	2	4	no	—
23	#15689195	—	2	2	no	—
24	#15689195	—	2	2	no	—
25	#15689172	C₂²	1	2	yes	complemented
26	#15689147	C₂²	1	1	yes	characteristic, complemented
27	#15689140	C₂²	1	2	yes	—
28	#15689140	C₂²	1	2	yes	complemented
29	#15689119	C₂²	1	2	yes	—
30	#15689097	C₂²	1	1	yes	characteristic
31	#15689090	C₂²	1	1	yes	characteristic
32	#15689090	C₂²	1	1	yes	characteristic, complemented
33	#15689081	C₂²	1	2	yes	complemented
34	C₂×#13093935	C₂²	1	1	yes	characteristic, complemented
35	#15688895	C₂²	1	2	yes	complemented
36	#15688887	C₂²	1	2	yes	complemented
37	#15688883	C₂²	1	2	yes	complemented
38	C₄₇×#585	C₂²	1	1	yes	characteristic
39	C₄₇×#575	C₂²	1	2	yes	—
40	C₄₇×#532	C₂²	1	1	yes	characteristic
41	C₄₇×#456	C₄	1	2	yes	complemented
42	C₄₇×#455	C₄	1	2	yes	complemented
43	C₄₇×#454	C₄	1	2	yes	complemented
44	C₄₇×#453	C₄	1	2	yes	complemented
45	C₂×#104×C₄₇	C₂²	1	2	yes	—
46	C₄₇×#413	C₂²	1	1	yes	characteristic
47	#13094031	—	2	4	no	—
48	#13094031	—	2	8	no	—
49	#13094031	—	2	4	no	—
50	#13094031	—	2	4	no	—
51	#13094031	—	2	4	no	—
52	#13094031	—	2	2	no	—
53	#13094031	—	2	2	no	—
54	#13094031	—	2	4	no	—
55	#13094031	—	2	2	no	—
56	#13094031	—	2	2	no	—
57	#13094031	—	2	2	no	—
58	#13094031	—	2	2	no	—
59	#13094031	D₄	1	4	yes	complemented
60	#13094031	D₄	1	4	yes	complemented
61	C₂×#10625329	—	2	8	no	—
62	C₂×#10625329	—	2	4	no	—
63	C₂×#10625329	—	2	2	no	—
64	C₂×#10625329	—	2	4	no	—
65	C₂×#10625329	—	2	2	no	—
66	C₂×#10625329	—	2	1	no	—
67	C₂×#10625329	D₄	1	2	yes	—
68	C₂×#10625329	C₂³	1	1	yes	characteristic
69	C₂×#10625329	C₂³	1	2	yes	—
70	C₂×#10625329	C₂³	1	1	yes	characteristic
71	C₂²×C₄₇⋊C₈	—	2	4	no	—
72	C₂²×C₄₇⋊C₈	—	2	2	no	—
73	C₂²×C₄₇⋊C₈	—	2	1	no	—
74	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
75	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
77	#13093983	C₂³	1	2	yes	—
78	#13093960	—	2	4	no	—
79	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
80	#13093951	—	2	4	no	—
81	#13093951	—	2	4	no	—
82	#13093948	—	2	2	no	—
83	#13093945	—	2	2	no	—
84	#13093939	—	2	2	no	—
85	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
86	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
87	#13093935	—	2	1	no	—
88	#13093935	—	2	1	no	—
89	#13093934	—	2	2	no	—
90	C₈×Dic₄₇	—	2	2	no	—
91	2₋¹⁺⁴×C₄₇	—	2	2	no	—
92	2₋¹⁺⁴×C₄₇	C₂×C₄	1	2	yes	—
93	H(5,𝔽₂)×C₄₇	—	2	2	no	—
94	H(5,𝔽₂)×C₄₇	—	2	2	no	—
95	H(5,𝔽₂)×C₄₇	C₂×C₄	1	2	yes	—
96	C₂×#41×C₄₇	—	2	4	no	—
97	C₂×#41×C₄₇	—	2	2	no	—
98	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
99	C₂×#41×C₄₇	C₂³	1	2	yes	—
100	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
101	#137×C₄₇	—	2	2	no	—
102	#137×C₄₇	C₂×C₄	1	4	yes	—
103	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
104	AGL(1,ℤ/8)×C₄₇	C₂×C₄	1	4	yes	—
105	#135×C₄₇	—	2	4	no	—
106	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
108	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
109	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
110	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
111	#121×C₄₇	—	2	2	no	—
112	C₄×D₄×C₄₇	—	2	2	no	—
113	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
114	#104×C₄₇	C₂×C₄	1	4	yes	—
115	#104×C₄₇	C₂×C₄	1	4	yes	—
116	#101×C₄₇	C₂×C₄	1	2	yes	—
117	#100×C₄₇	C₂×C₄	1	2	yes	—
118	#41×C₄₇	—	2	4	no	—
119	#41×C₄₇	—	2	8	no	—
120	#41×C₄₇	—	2	4	no	—
121	#41×C₄₇	—	2	4	no	—
122	#41×C₄₇	—	2	4	no	—
123	#41×C₄₇	—	2	4	no	—
124	#41×C₄₇	—	2	2	no	—
125	#41×C₄₇	—	2	2	no	—
126	#41×C₄₇	—	2	2	no	—
127	#41×C₄₇	—	2	2	no	—
128	#41×C₄₇	—	2	2	no	—
129	#41×C₄₇	—	2	2	no	—
130	#41×C₄₇	C₂²×C₄	1	4	yes	—
131	#41×C₄₇	C₂×D₄	1	4	yes	—
132	C₂×Q₈×C₄₇	—	2	2	no	—
133	C₂×Q₈×C₄₇	—	2	4	no	—
134	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×Q₈×C₄₇	#41	1	2	yes	—
137	C₂×D₄×C₄₇	—	2	8	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	2	4	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	2	4	no	—
142	C₂×D₄×C₄₇	—	2	1	no	—
143	C₂×D₄×C₄₇	—	2	2	no	—
144	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₄×C₄₇	#41	1	2	yes	—
147	C₂×D₄×C₄₇	#41	1	2	yes	—
148	C₂²×C₄×C₄₇	—	2	4	no	—
149	C₂²×C₄×C₄₇	—	2	2	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	2	1	no	—
152	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₄₇	—	2	4	no	—
155	SD₁₆×C₄₇	—	2	4	no	—
156	SD₁₆×C₄₇	—	2	4	no	—
157	D₈×C₄₇	—	2	4	no	—
158	M₁₆×C₄₇	—	2	2	no	—
159	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
160	C₂×C₈×C₄₇	—	2	2	no	—
161	C₄⋊C₄×C₄₇	—	2	2	no	—
162	C₂²⋊C₄×C₄₇	—	2	2	no	—
163	C₂²⋊C₄×C₄₇	—	2	2	no	—
164	C₄²×C₄₇	—	2	1	no	—
165	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²⋊Dic₄₇	—	2	2	no	—
168	C₄⋊Dic₄₇	—	2	2	no	—
169	C₄×Dic₄₇	—	2	2	no	—
170	#10625329	—	2	4	no	—
171	#10625329	—	2	8	no	—
172	#10625329	—	2	2	no	—
173	#10625329	—	2	2	no	—
174	#10625329	—	2	4	no	—
175	#10625329	—	2	4	no	—
176	#10625329	—	2	4	no	—
177	#10625329	—	2	2	no	—
178	#10625329	—	4	1	no	—
179	#10625329	—	4	1	no	—
180	#10625329	C₂×D₄	1	4	yes	—
181	C₂×C₄₇⋊C₈	—	2	4	no	—
182	C₂×C₄₇⋊C₈	—	2	8	no	—
183	C₂×C₄₇⋊C₈	—	2	2	no	—
184	C₂×C₄₇⋊C₈	—	2	4	no	—
185	C₂×C₄₇⋊C₈	—	2	2	no	—
186	C₂×C₄₇⋊C₈	—	2	4	no	—
187	C₂×C₄₇⋊C₈	—	2	2	no	—
188	C₂×C₄₇⋊C₈	—	2	1	no	—
189	C₂×C₄₇⋊C₈	—	2	1	no	—
190	C₂×C₄₇⋊C₈	—	2	2	no	—
191	C₂×C₄₇⋊C₈	—	4	2	no	—
192	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
193	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
194	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
195	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
197	C₂³×C₄₇	—	2	4	no	—
198	C₂³×C₄₇	—	2	2	no	—
199	C₂³×C₄₇	—	2	1	no	—
200	C₂³×C₄₇	C₄×D₄	1	2	yes	—
201	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
202	Q₈×C₄₇	—	2	4	no	—
203	Q₈×C₄₇	—	2	2	no	—
204	Q₈×C₄₇	—	2	2	no	—
205	Q₈×C₄₇	—	2	2	no	—
206	Q₈×C₄₇	C₄×D₄	1	4	yes	—
207	D₄×C₄₇	—	2	8	no	—
208	D₄×C₄₇	—	2	4	no	—
209	D₄×C₄₇	—	2	4	no	—
210	D₄×C₄₇	—	2	4	no	—
211	D₄×C₄₇	—	2	4	no	—
212	D₄×C₄₇	—	2	2	no	—
213	D₄×C₄₇	—	2	2	no	—
214	D₄×C₄₇	—	2	2	no	—
215	D₄×C₄₇	—	4	2	no	—
216	D₄×C₄₇	—	8	2	no	—
217	D₄×C₄₇	C₄×D₄	1	4	yes	—
218	C₂×C₄×C₄₇	—	2	4	no	—
219	C₂×C₄×C₄₇	—	2	8	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	4	no	—
222	C₂×C₄×C₄₇	—	2	4	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	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	—	4	1	no	—
229	C₂×C₄×C₄₇	—	4	1	no	—
230	C₂×C₄×C₄₇	—	8	1	no	—
231	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
232	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
236	C₂×Dic₄₇	—	4	2	no	—
237	C₈×C₄₇	—	2	4	no	—
238	C₄₇⋊C₈	—	2	4	no	—
239	C₄₇⋊C₈	—	2	2	no	—
240	C₄₇⋊C₈	—	4	1	no	—
241	C₄₇⋊C₈	—	4	1	no	—
242	C₄₇⋊C₈	#120	1	1	yes	characteristic
243	C₄₇⋊C₈	#120	1	2	yes	—
244	C₄₇⋊C₈	#120	1	1	yes	characteristic
245	#21478	—	47	1	no	maximal, Sylow
246	C₂²×C₄₇	—	2	2	no	—
247	C₂²×C₄₇	—	2	4	no	—
248	C₂²×C₄₇	—	4	1	no	—
249	C₂²×C₄₇	—	4	2	no	—
250	C₂²×C₄₇	—	4	2	no	—
251	C₂²×C₄₇	—	4	1	no	—
252	C₂²×C₄₇	—	8	2	no	—
253	C₂²×C₄₇	—	8	4	no	—
254	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂²×C₄₇	#525	1	2	yes	—
256	C₄×C₄₇	—	2	4	no	—
257	C₄×C₄₇	—	2	2	no	—
258	C₄×C₄₇	—	4	1	no	—
259	C₄×C₄₇	—	4	1	no	—
260	C₄×C₄₇	—	4	1	no	—
261	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
262	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
263	C₄×C₄₇	#525	1	1	yes	characteristic
264	Dic₄₇	—	8	2	no	—
265	#3573	—	47	1	no	—
266	#3018	D₄₇	1	1	yes	characteristic
267	#2955	—	47	2	no	—
268	#2932	—	47	1	no	—
269	#1884	—	47	1	no	—
270	#1881	—	47	2	no	—
271	#1861	—	47	2	no	—
272	#1858	—	47	1	no	—
273	#1794	—	47	1	no	—
274	#1765	—	47	2	no	—
275	#1757	—	47	1	no	—
276	C₂×C₄₇	—	2	2	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	4	2	no	—
279	C₂×C₄₇	—	4	4	no	—
280	C₂×C₄₇	—	8	1	no	—
281	C₂×C₄₇	C₄×#120	1	1	yes	characteristic
282	#585	C₂×D₄₇	1	1	yes	characteristic
283	#575	C₂×D₄₇	1	2	yes	—
284	#568	—	47	1	no	—
285	#568	—	47	2	no	—
286	#568	—	94	2	no	—
287	#568	—	94	4	no	—
288	C₂×#131	—	47	1	no	—
289	C₂×#131	—	47	2	no	—
290	C₂×#131	—	47	1	no	—
291	C₂×#131	—	94	2	no	—
292	C₂×#131	—	94	4	no	—
293	#532	C₂×D₄₇	1	1	yes	characteristic
294	#456	Dic₄₇	1	2	yes	complemented
295	#455	Dic₄₇	1	2	yes	complemented
296	#454	Dic₄₇	1	2	yes	complemented
297	#453	Dic₄₇	1	2	yes	complemented
298	#444	—	94	4	no	—
299	#443	—	94	4	no	—
300	#435	—	94	2	no	—
301	#435	—	94	2	no	—
302	#430	—	47	2	no	—
303	#423	—	47	1	no	—
304	#421	—	47	2	no	—
305	#421	—	47	2	no	—
306	C₂×#104	C₂×D₄₇	1	2	yes	—
307	#416	—	47	2	no	—
308	#413	C₂×D₄₇	1	1	yes	characteristic
309	#410	—	47	1	no	—
310	#408	—	47	1	no	—
311	#408	—	47	1	no	—
312	#405	—	47	2	no	—
313	C₂×#97	—	47	1	no	—
314	#344	—	47	2	no	—
315	#341	—	47	2	no	—
316	#339	—	47	2	no	—
317	C₄₇	#21478	1	1	yes	characteristic, complemented, Sylow
318	2₋¹⁺⁴	—	2	2	no	—
319	2₋¹⁺⁴	C₂×Dic₄₇	1	2	yes	—
320	H(5,𝔽₂)	—	2	2	no	—
321	H(5,𝔽₂)	—	2	2	no	—
322	H(5,𝔽₂)	C₂×Dic₄₇	1	2	yes	—
323	C₂×#41	—	2	4	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	C₂²×D₄₇	1	2	yes	—
326	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
327	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
328	#137	—	2	2	no	—
329	#137	C₂×Dic₄₇	1	4	yes	—
330	AGL(1,ℤ/8)	—	2	2	no	—
331	AGL(1,ℤ/8)	C₂×Dic₄₇	1	4	yes	—
332	#135	—	2	4	no	—
333	#131	—	47	4	no	—
334	#131	—	47	4	no	—
335	#131	—	94	2	no	—
336	#131	—	94	2	no	—
337	#131	—	94	2	no	—
338	#131	—	94	2	no	—
339	#131	—	94	4	no	—
340	#131	—	94	2	no	—
341	#131	—	94	2	no	—
342	#131	—	94	4	no	—
343	#131	—	94	4	no	—
344	#131	—	94	4	no	—
345	#131	—	94	8	no	—
346	#131	—	94	4	no	—
347	C₂×M₁₆	—	47	2	no	—
348	C₂×M₁₆	—	47	1	no	—
349	C₂×M₁₆	—	47	2	no	—
350	C₂×M₁₆	—	47	1	no	—
351	C₂×M₁₆	—	94	2	no	—
352	C₂×M₁₆	—	94	1	no	—
353	C₂×M₁₆	—	94	4	no	—
354	C₂×M₁₆	—	94	4	no	—
355	C₂×M₁₆	—	94	8	no	—
356	C₂×M₁₆	—	94	2	no	—
357	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
358	C₂²×C₈	—	47	1	no	—
359	C₂²×C₈	—	47	2	no	—
360	C₂²×C₈	—	47	1	no	—
361	C₂²×C₈	—	94	2	no	—
362	C₂²×C₈	—	94	1	no	—
363	C₂²×C₈	—	94	4	no	—
364	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
365	#127	C₂×Dic₄₇	1	1	yes	characteristic
366	#124	C₂×Dic₄₇	1	1	yes	characteristic
367	#124	C₂×Dic₄₇	1	1	yes	characteristic
368	#121	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	#117	—	47	2	no	—
371	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
372	#108	—	94	4	no	—
373	C₄⋊C₈	—	94	2	no	—
374	#104	—	94	4	no	—
375	#104	—	94	4	no	—
376	#104	C₂×Dic₄₇	1	4	yes	—
377	#104	C₂×Dic₄₇	1	4	yes	—
378	#103	—	94	2	no	—
379	#102	—	94	2	no	—
380	#101	C₂×Dic₄₇	1	2	yes	—
381	#100	C₂×Dic₄₇	1	2	yes	—
382	#99	—	94	2	no	—
383	C₂²⋊C₈	—	94	2	no	—
384	C₂²⋊C₈	—	94	2	no	—
385	#97	—	94	1	no	—
386	#97	—	94	1	no	—
387	#97	—	94	2	no	—
388	C₄×C₈	—	94	2	no	—
389	#41	—	2	4	no	—
390	#41	—	2	8	no	—
391	#41	—	2	4	no	—
392	#41	—	2	4	no	—
393	#41	—	2	4	no	—
394	#41	—	2	4	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	D₄×D₄₇	1	4	yes	—
402	#41	C₂²×Dic₄₇	1	4	yes	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	#10625352	1	2	yes	—
406	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
407	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	#10625352	1	2	yes	—
416	C₂×D₄	#10625352	1	2	yes	—
417	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
418	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	D₄×D₄₇	1	2	yes	—
424	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
425	Q₁₆	—	2	4	no	—
426	SD₁₆	—	2	4	no	—
427	SD₁₆	—	2	4	no	—
428	D₈	—	2	4	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	47	4	no	—
431	M₁₆	—	94	4	no	—
432	M₁₆	—	94	4	no	—
433	M₁₆	—	94	4	no	—
434	M₁₆	—	94	8	no	—
435	M₁₆	—	94	4	no	—
436	M₁₆	—	94	2	no	—
437	M₁₆	—	94	2	no	—
438	M₁₆	—	94	2	no	—
439	M₁₆	—	188	1	no	—
440	M₁₆	—	188	1	no	—
441	M₁₆	C₂²×Dic₄₇	1	4	yes	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	47	2	no	—
444	C₂×C₈	—	47	1	no	—
445	C₂×C₈	—	47	1	no	—
446	C₂×C₈	—	47	2	no	—
447	C₂×C₈	—	47	2	no	—
448	C₂×C₈	—	94	2	no	—
449	C₂×C₈	—	94	2	no	—
450	C₂×C₈	—	94	4	no	—
451	C₂×C₈	—	94	4	no	—
452	C₂×C₈	—	94	8	no	—
453	C₂×C₈	—	94	4	no	—
454	C₂×C₈	—	94	2	no	—
455	C₂×C₈	—	94	1	no	—
456	C₂×C₈	—	94	1	no	—
457	C₂×C₈	—	94	2	no	—
458	C₂×C₈	—	188	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	94	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	94	2	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	94	2	no	—
466	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
467	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
468	C₂³	—	2	4	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	1	no	—
471	C₂³	D₄×Dic₄₇	1	2	yes	—
472	C₂³	C₂×#10625352	1	1	yes	characteristic
473	Q₈	—	2	4	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	2	2	no	—
477	Q₈	D₄×Dic₄₇	1	4	yes	—
478	D₄	—	2	8	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	4	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	8	2	no	—
488	D₄	D₄×Dic₄₇	1	4	yes	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	8	1	no	—
502	C₂×C₄	—	188	2	no	—
503	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
504	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
505	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
506	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
507	C₂×C₄	C₂×#10625352	1	2	yes	—
508	C₈	—	2	4	no	—
509	C₈	—	47	1	no	—
510	C₈	—	47	2	no	—
511	C₈	—	47	1	no	—
512	C₈	—	94	2	no	—
513	C₈	—	94	4	no	—
514	C₈	—	188	1	no	—
515	C₈	—	188	1	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	4	no	—
524	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
525	C₂²	#15689629	1	2	yes	—
526	C₄	—	2	4	no	—
527	C₄	—	2	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	376	2	no	—
532	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
533	C₄	#120×D₄₇	1	1	yes	characteristic
534	C₄	#15689629	1	1	yes	characteristic
535	C₂	—	2	1	no	—
536	C₂	—	2	2	no	—
537	C₂	—	4	2	no	—
538	C₂	—	4	4	no	—
539	C₂	—	8	1	no	—
540	C₂	#120×Dic₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#120×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3018	C₂
socle	C₂×C₄₇	C₄×#120
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3018	D₄₇
hypocenter	C₄₇	#21478
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3018

Complements

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

N	H ≅ G/N	type
1. #20258100	C₂	semidirect
2. #20252291	C₂	semidirect
3. #20252106	C₂	semidirect
4. #20243772	C₂	semidirect
5. #20243752	C₂	semidirect
6. #20243630	C₂	semidirect
7. #20243610	C₂	semidirect
8. #20243352	C₂	semidirect
9. #20243233	C₂	semidirect
10. #20243191	C₂	semidirect
20. C₂×#13094031	C₂²	semidirect
25. #15689172	C₂²	semidirect
26. #15689147	C₂²	semidirect
28. #15689140	C₂²	semidirect
32. #15689090	C₂²	semidirect
33. #15689081	C₂²	semidirect
34. C₂×#13093935	C₂²	semidirect
35. #15688895	C₂²	semidirect
36. #15688887	C₂²	semidirect
37. #15688883	C₂²	semidirect
41. C₄₇×#456	C₄	semidirect
42. C₄₇×#455	C₄	semidirect
43. C₄₇×#454	C₄	semidirect
44. C₄₇×#453	C₄	semidirect
59. #13094031	D₄	semidirect
60. #13094031	D₄	semidirect
294. #456	Dic₄₇	semidirect
295. #455	Dic₄₇	semidirect
296. #454	Dic₄₇	semidirect
297. #453	Dic₄₇	semidirect
317. C₄₇	#21478	semidirect

Maximal subgroups

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

subgroup	index
#20258100	2
#20252291	2
#20252106	2
#20243772	2
#20243752	2
#20243630	2
#20243610	2
#20243352	2
#20243233	2
#20243191	2
C₄₇×#3018	2
#21478	47