Subgroups — #26237147

Order 12032.

996 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252736	C₂	1	1	yes	maximal, characteristic
2	#20252295	C₂	1	2	yes	maximal, complemented
3	#20251934	C₂	1	2	yes	maximal, complemented
4	#20244221	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244060	C₂	1	2	yes	maximal, complemented
6	#20243886	C₂	1	2	yes	maximal, complemented
7	#20243629	C₂	1	2	yes	maximal, complemented
8	#20243197	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1884	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689959	C₂²	1	1	yes	characteristic
11	#15689921	C₂²	1	2	yes	—
12	#15689889	C₂²	1	2	yes	—
13	#15689591	C₂²	1	2	yes	—
14	#15689305	C₄	1	2	yes	complemented
15	#15689300	C₄	1	2	yes	complemented
16	#15689295	C₄	1	2	yes	complemented
17	#15689290	C₄	1	2	yes	complemented
18	#15689243	—	2	4	no	—
19	#15689238	—	2	4	no	—
20	#15689171	C₂²	1	2	yes	complemented
21	#15689147	C₂²	1	1	yes	characteristic, complemented
22	#15689141	C₂²	1	2	yes	—
23	#15689138	—	2	4	no	—
24	C₂×#13093952	C₂²	1	2	yes	—
25	C₂×#13093951	C₂²	1	2	yes	—
26	C₂×#13093951	C₂²	1	2	yes	complemented
27	C₂×#13093950	C₂²	1	2	yes	—
28	#104×D₄₇	—	2	4	no	—
29	#15689107	C₂²	1	1	yes	characteristic
30	M₁₆×Dic₄₇	C₂²	1	2	yes	complemented
31	#15688969	C₂²	1	1	yes	characteristic, complemented
32	#15688893	C₂²	1	2	yes	complemented
33	#15688882	C₂²	1	2	yes	complemented
34	C₄₇×#568	C₂²	1	1	yes	characteristic, complemented
35	C₄₇×#532	C₂²	1	1	yes	characteristic
36	C₄₇×#421	C₂²	1	2	yes	—
37	C₄₇×#410	C₂²	1	1	yes	characteristic, complemented
38	C₄₇×#339	C₂²	1	2	yes	complemented
39	#13094072	C₂×C₄	1	2	yes	—
40	#13094071	—	2	2	no	—
41	#13094070	—	2	2	no	—
42	#13094069	—	4	1	no	—
43	#13094069	C₂×C₄	1	2	yes	—
44	C₂×#10625350	—	4	1	no	—
45	C₂×#10625350	C₂³	1	2	yes	—
46	#41×D₄₇	—	2	4	no	—
47	#13094055	C₂×C₄	1	4	yes	complemented
48	#13094054	—	2	2	no	—
49	#13094050	C₂×C₄	1	4	yes	complemented
50	#13094049	—	2	2	no	—
51	#13094044	—	2	4	no	—
52	#13094032	—	4	2	no	—
53	#13094030	—	2	4	no	—
54	C₂×#10625329	C₂³	1	2	yes	—
55	C₂×#10625329	C₂³	1	2	yes	—
56	M₁₆×D₄₇	—	2	4	no	—
57	#13093989	—	2	2	no	—
58	#13093986	—	2	2	no	—
59	(C₂²⋊D₄₇)⋊C₄	—	4	2	no	—
60	#13093981	—	2	2	no	—
61	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
62	C₄²×D₄₇	—	2	2	no	—
63	#13093959	—	2	4	no	—
64	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
65	#13093952	—	2	4	no	—
66	#13093952	C₂×C₄	1	4	yes	complemented
67	#13093952	C₂×C₄	1	4	yes	complemented
68	#13093951	—	2	2	no	—
69	#13093951	—	2	2	no	—
70	#13093951	—	2	2	no	—
71	#13093951	—	2	2	no	—
72	#13093950	D₄	1	4	yes	complemented
73	#13093950	D₄	1	4	yes	complemented
74	#13093943	C₂×C₄	1	2	yes	complemented
75	#13093941	C₂×C₄	1	2	yes	complemented
76	#13093934	—	2	2	no	—
77	C₈×Dic₄₇	—	2	2	no	—
78	C₄₇⋊#95	—	4	1	no	—
79	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
81	#131×C₄₇	—	2	4	no	—
82	C₂×M₁₆×C₄₇	—	4	1	no	—
83	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
84	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
85	#127×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
86	#124×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
87	#124×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
88	#121×C₄₇	—	4	1	no	—
89	C₄×D₄×C₄₇	—	4	1	no	—
90	#117×C₄₇	C₂³	1	2	yes	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	#104×C₄₇	—	2	4	no	—
93	#99×C₄₇	—	4	1	no	—
94	#41×C₄₇	—	2	2	no	—
95	#41×C₄₇	—	2	2	no	—
96	#41×C₄₇	—	2	2	no	—
97	#41×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂×D₄×C₄₇	—	2	1	no	—
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	—	4	1	no	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂×C₂²⋊D₄₇	—	2	2	no	—
110	C₂×C₂²⋊D₄₇	—	4	2	no	—
111	C₂²×Dic₄₇	—	2	2	no	—
112	#10625354	—	2	4	no	—
113	Q₈×D₄₇	—	2	4	no	—
114	#10625352	—	2	4	no	—
115	#10625352	—	4	4	no	—
116	D₄×D₄₇	—	2	4	no	—
117	D₄×D₄₇	—	4	4	no	—
118	#10625350	—	2	2	no	—
119	#10625350	—	2	2	no	—
120	#10625350	—	4	2	no	—
121	#10625350	—	4	2	no	—
122	#10625350	—	4	2	no	—
123	#10625350	C₂²×C₄	1	4	yes	—
124	#10625350	C₂×D₄	1	4	yes	—
125	C₂×D₁₈₈	—	4	1	no	—
126	C₂×D₁₈₈	#41	1	2	yes	—
127	C₂×C₄×D₄₇	—	2	2	no	—
128	C₂×C₄×D₄₇	—	4	2	no	—
129	C₂×C₄×D₄₇	—	4	2	no	—
130	C₂×Dic₉₄	—	4	1	no	—
131	C₂×Dic₉₄	#41	1	2	yes	—
132	M₁₆×C₄₇	—	2	2	no	—
133	M₁₆×C₄₇	—	4	2	no	—
134	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	4	2	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	4	1	no	—
139	C₂²⋊C₄×C₄₇	—	2	2	no	—
140	C₂²⋊C₄×C₄₇	—	4	1	no	—
141	C₂²⋊C₄×C₄₇	—	4	1	no	—
142	C₄²×C₄₇	—	2	1	no	—
143	C₄²×C₄₇	—	2	2	no	—
144	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	#10625337	—	2	4	no	—
147	#10625336	—	2	4	no	—
148	#10625335	—	2	4	no	—
149	#10625334	—	2	4	no	—
150	(C₂×D₄₇)⋊C₄	—	4	2	no	—
151	Dic₄₇⋊C₄	—	4	2	no	—
152	C₄×Dic₄₇	—	2	2	no	—
153	C₄×Dic₄₇	—	4	2	no	—
154	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
155	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
156	#10625329	—	2	2	no	—
157	#10625329	—	2	2	no	—
158	#10625329	—	2	2	no	—
159	#10625329	C₂²×C₄	1	4	yes	—
160	C₂×C₄₇⋊C₈	—	2	2	no	—
161	C₂×C₄₇⋊C₈	—	2	2	no	—
162	#10625324	—	4	4	no	—
163	C₈×D₄₇	—	4	4	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	—	2	1	no	—
166	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²×D₄₇	—	2	2	no	—
168	C₂²×D₄₇	—	4	2	no	—
169	Q₈×C₄₇	—	2	2	no	—
170	Q₈×C₄₇	—	2	2	no	—
171	D₄×C₄₇	—	2	2	no	—
172	D₄×C₄₇	—	2	2	no	—
173	D₄×C₄₇	—	4	2	no	—
174	D₄×C₄₇	—	4	2	no	—
175	D₄×C₄₇	—	8	2	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	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	2	no	—
185	C₂×C₄×C₄₇	—	8	1	no	—
186	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
189	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂²⋊D₄₇	—	2	4	no	—
191	C₂²⋊D₄₇	—	2	4	no	—
192	C₂²⋊D₄₇	—	4	4	no	—
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	2	2	no	—
195	C₂×Dic₄₇	—	2	2	no	—
196	C₂×Dic₄₇	—	4	2	no	—
197	C₂×Dic₄₇	—	8	2	no	—
198	D₁₈₈	—	2	2	no	—
199	D₁₈₈	—	4	2	no	—
200	D₁₈₈	C₄×D₄	1	4	yes	—
201	C₄×D₄₇	—	2	4	no	—
202	C₄×D₄₇	—	2	4	no	—
203	C₄×D₄₇	—	4	4	no	—
204	C₄×D₄₇	—	8	4	no	—
205	Dic₉₄	—	2	2	no	—
206	Dic₉₄	—	4	2	no	—
207	Dic₉₄	C₄×D₄	1	4	yes	—
208	C₈×C₄₇	—	2	4	no	—
209	C₄₇⋊C₈	—	2	4	no	—
210	C₄₇⋊C₈	—	4	2	no	—
211	#22898	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	—	4	1	no	—
213	C₂²×C₄₇	—	4	1	no	—
214	C₂²×C₄₇	—	4	1	no	—
215	C₂²×C₄₇	—	8	1	no	—
216	C₂²×C₄₇	—	8	1	no	—
217	C₂²×C₄₇	#518	1	1	yes	characteristic
218	C₂²×C₄₇	#546	1	2	yes	—
219	C₂×D₄₇	—	2	4	no	—
220	C₂×D₄₇	—	8	2	no	—
221	C₂×D₄₇	—	16	2	no	—
222	C₄×C₄₇	—	4	1	no	—
223	C₄×C₄₇	—	4	1	no	—
224	C₄×C₄₇	—	4	1	no	—
225	C₄×C₄₇	—	4	1	no	—
226	C₄×C₄₇	—	8	2	no	—
227	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
228	C₄×C₄₇	D₄²	1	1	yes	characteristic
229	C₄×C₄₇	#551	1	1	yes	characteristic
230	Dic₄₇	—	2	4	no	—
231	Dic₄₇	—	4	2	no	—
232	Dic₄₇	—	4	2	no	—
233	#3018	—	47	1	no	—
234	#2956	—	47	2	no	—
235	#2901	—	47	2	no	—
236	#1963	—	47	1	no	—
237	#1932	—	47	2	no	—
238	#1906	—	47	2	no	—
239	#1884	D₄₇	1	1	yes	characteristic, complemented
240	#1861	—	47	2	no	—
241	#1759	—	47	2	no	—
242	C₂×C₄₇	—	2	2	no	—
243	C₂×C₄₇	—	2	1	no	—
244	C₂×C₄₇	—	8	1	no	—
245	C₂×C₄₇	—	8	1	no	—
246	C₂×C₄₇	#2358	1	1	yes	characteristic
247	D₄₇	—	4	4	no	—
248	#585	—	47	1	no	—
249	#575	—	47	2	no	—
250	#568	—	47	2	no	—
251	#568	C₂×D₄₇	1	1	yes	characteristic, complemented
252	#532	C₂×D₄₇	1	1	yes	characteristic
253	C₄×#41	—	47	2	no	—
254	#456	—	47	2	no	—
255	#455	—	47	2	no	—
256	#454	—	47	2	no	—
257	#453	—	47	2	no	—
258	#444	—	94	4	no	—
259	#443	—	94	4	no	—
260	#430	—	47	2	no	—
261	#423	—	47	1	no	—
262	#421	—	47	2	no	—
263	#421	—	94	4	no	—
264	#421	C₂×D₄₇	1	2	yes	—
265	C₂×#104	—	47	2	no	—
266	C₂×#104	—	47	2	no	—
267	C₂×#104	—	47	2	no	—
268	C₂×#104	—	47	2	no	—
269	C₂×#104	—	94	4	no	—
270	#413	—	47	1	no	—
271	#410	C₂×D₄₇	1	1	yes	characteristic, complemented
272	C₄×M₁₆	—	47	2	no	—
273	#376	—	47	1	no	—
274	#344	—	47	2	no	—
275	#339	—	47	2	no	—
276	#339	C₂×D₄₇	1	2	yes	complemented
277	C₄₇	#22898	1	1	yes	characteristic, complemented, Sylow
278	2₋¹⁺⁴	—	47	2	no	—
279	2₋¹⁺⁴	—	94	2	no	—
280	H(5,𝔽₂)	—	47	2	no	—
281	H(5,𝔽₂)	—	94	2	no	—
282	H(5,𝔽₂)	—	188	1	no	—
283	C₂×#41	—	47	2	no	—
284	C₂×#41	—	94	4	no	—
285	C₂×#41	—	188	1	no	—
286	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
287	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
288	#137	—	47	4	no	—
289	#137	—	94	2	no	—
290	AGL(1,ℤ/8)	—	47	4	no	—
291	AGL(1,ℤ/8)	—	94	2	no	—
292	#135	—	94	4	no	—
293	#131	—	2	4	no	—
294	#131	—	94	4	no	—
295	#131	—	188	2	no	—
296	C₂×M₁₆	—	4	1	no	—
297	C₂×M₁₆	—	47	2	no	—
298	C₂×M₁₆	—	47	2	no	—
299	C₂×M₁₆	—	94	4	no	—
300	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
301	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic, complemented
302	#127	C₄×D₄₇	1	1	yes	characteristic, complemented
303	#124	C₄×D₄₇	1	1	yes	characteristic, complemented
304	#124	C₄×D₄₇	1	1	yes	characteristic, complemented
305	#121	—	4	1	no	—
306	C₄×Q₈	—	94	2	no	—
307	C₄×D₄	—	4	1	no	—
308	C₄×D₄	—	94	2	no	—
309	C₄×D₄	—	188	2	no	—
310	#117	—	94	2	no	—
311	#117	C₂²×D₄₇	1	2	yes	—
312	C₂×C₄²	—	47	2	no	—
313	C₂×C₄²	—	94	2	no	—
314	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
315	#108	—	94	4	no	—
316	C₄⋊C₈	—	188	1	no	—
317	#104	—	2	4	no	—
318	#104	—	47	4	no	—
319	#104	—	47	4	no	—
320	#104	—	47	4	no	—
321	#104	—	47	4	no	—
322	#104	—	94	4	no	—
323	#104	—	94	2	no	—
324	#104	—	94	2	no	—
325	#104	—	94	2	no	—
326	#104	—	94	2	no	—
327	#101	—	47	2	no	—
328	#100	—	47	2	no	—
329	#99	—	4	1	no	—
330	#97	—	94	2	no	—
331	C₄×C₈	—	94	2	no	—
332	#95	—	188	1	no	—
333	#41	—	2	2	no	—
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	#41	—	2	2	no	—
337	#41	—	47	4	no	—
338	#41	—	47	4	no	—
339	#41	—	94	2	no	—
340	#41	—	94	2	no	—
341	#41	—	94	4	no	—
342	#41	—	94	4	no	—
343	#41	—	188	2	no	—
344	#41	—	188	2	no	—
345	#41	—	188	2	no	—
346	#41	—	188	4	no	—
347	C₂×Q₈	—	47	2	no	—
348	C₂×Q₈	—	94	4	no	—
349	C₂×Q₈	—	188	1	no	—
350	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
351	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	47	2	no	—
356	C₂×D₄	—	94	4	no	—
357	C₂×D₄	—	94	2	no	—
358	C₂×D₄	—	188	1	no	—
359	C₂×D₄	—	188	4	no	—
360	C₂×D₄	—	188	2	no	—
361	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
362	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	94	2	no	—
367	C₂²×C₄	—	94	2	no	—
368	C₂²×C₄	—	188	2	no	—
369	C₂²×C₄	—	188	2	no	—
370	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
371	Q₁₆	—	94	4	no	—
372	SD₁₆	—	94	4	no	—
373	SD₁₆	—	94	4	no	—
374	D₈	—	94	4	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	4	2	no	—
377	M₁₆	—	47	4	no	—
378	M₁₆	—	94	2	no	—
379	M₁₆	—	94	2	no	—
380	M₁₆	—	94	2	no	—
381	M₁₆	—	188	4	no	—
382	M₁₆	D₄×D₄₇	1	4	yes	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	—	94	2	no	—
386	C₂×C₈	—	94	2	no	—
387	C₂×C₈	—	188	4	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	188	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	188	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	47	2	no	—
398	C₄²	—	47	2	no	—
399	C₄²	—	94	2	no	—
400	C₄²	—	188	2	no	—
401	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
402	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	94	2	no	—
406	C₂³	—	188	2	no	—
407	C₂³	#13094069	1	1	yes	characteristic
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	47	4	no	—
411	Q₈	—	94	2	no	—
412	Q₈	—	188	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	2	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	8	2	no	—
418	D₄	—	47	4	no	—
419	D₄	—	94	4	no	—
420	D₄	—	94	4	no	—
421	D₄	—	94	2	no	—
422	D₄	—	188	2	no	—
423	D₄	—	188	4	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	8	1	no	—
434	C₂×C₄	—	94	2	no	—
435	C₂×C₄	—	94	4	no	—
436	C₂×C₄	—	94	4	no	—
437	C₂×C₄	—	94	2	no	—
438	C₂×C₄	—	94	2	no	—
439	C₂×C₄	—	376	4	no	—
440	C₂×C₄	—	376	2	no	—
441	C₂×C₄	—	188	4	no	—
442	C₂×C₄	—	188	2	no	—
443	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
444	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
445	C₂×C₄	#41×D₄₇	1	2	yes	—
446	C₂×C₄	#13094069	1	1	yes	characteristic
447	C₈	—	2	4	no	—
448	C₈	—	94	4	no	—
449	C₈	—	188	2	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	94	4	no	—
456	C₂²	—	376	2	no	—
457	C₂²	—	752	2	no	—
458	C₂²	#15689596	1	1	yes	characteristic
459	C₂²	#15689770	1	2	yes	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	8	2	no	—
465	C₄	—	94	4	no	—
466	C₄	—	188	2	no	—
467	C₄	—	188	2	no	—
468	C₄	C₄×D₄×D₄₇	1	2	yes	—
469	C₄	#15689755	1	1	yes	characteristic
470	C₄	#15689801	1	1	yes	characteristic
471	C₂	—	2	1	no	—
472	C₂	—	2	2	no	—
473	C₂	—	8	1	no	—
474	C₂	—	8	1	no	—
475	C₂	—	188	4	no	—
476	C₂	#20246371	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15689755
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1884	C₂
socle	C₂×C₄₇	#2358
prime radical	#20252736	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1884	D₄₇
hypocenter	C₄₇	#22898
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1884

Complements

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

N	H ≅ G/N	type
2. #20252295	C₂	semidirect
3. #20251934	C₂	semidirect
4. #20244221	C₂	semidirect
5. #20244060	C₂	semidirect
6. #20243886	C₂	semidirect
7. #20243629	C₂	semidirect
8. #20243197	C₂	semidirect
9. C₄₇×#1884	C₂	semidirect
14. #15689305	C₄	semidirect
15. #15689300	C₄	semidirect
16. #15689295	C₄	semidirect
17. #15689290	C₄	semidirect
20. #15689171	C₂²	semidirect
21. #15689147	C₂²	semidirect
26. C₂×#13093951	C₂²	semidirect
30. M₁₆×Dic₄₇	C₂²	semidirect
31. #15688969	C₂²	semidirect
32. #15688893	C₂²	semidirect
33. #15688882	C₂²	semidirect
34. C₄₇×#568	C₂²	semidirect
37. C₄₇×#410	C₂²	semidirect
38. C₄₇×#339	C₂²	semidirect
47. #13094055	C₂×C₄	semidirect
49. #13094050	C₂×C₄	semidirect
66. #13093952	C₂×C₄	semidirect
67. #13093952	C₂×C₄	semidirect
72. #13093950	D₄	semidirect
73. #13093950	D₄	semidirect
74. #13093943	C₂×C₄	semidirect
75. #13093941	C₂×C₄	semidirect
84. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
85. #127×C₄₇	C₂×C₄	semidirect
86. #124×C₄₇	C₂×C₄	semidirect
87. #124×C₄₇	C₂×C₄	semidirect
239. #1884	D₄₇	semidirect
251. #568	C₂×D₄₇	semidirect
271. #410	C₂×D₄₇	semidirect
276. #339	C₂×D₄₇	semidirect
277. C₄₇	#22898	semidirect
301. C₄⋊Q₈	C₄×D₄₇	semidirect
302. #127	C₄×D₄₇	semidirect
303. #124	C₄×D₄₇	semidirect
304. #124	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252736	2
#20252295	2
#20251934	2
#20244221	2
#20244060	2
#20243886	2
#20243629	2
#20243197	2
C₄₇×#1884	2
#22898	47