Subgroups — #26119051

Order 12032.

802 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689469	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244349	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244195	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244195	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#493	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625335	—	2	2	no	—
9	C₂×#13094024	C₂²	1	1	yes	characteristic
10	#15689495	—	2	2	no	—
11	#15689495	—	2	2	no	—
12	#15689469	—	2	2	no	—
13	#15689469	—	2	2	no	—
14	C₂×#13093945	—	2	2	no	—
15	C₂×#13093945	—	2	2	no	—
16	C₂×#13093945	—	2	2	no	—
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	#15688993	C₂²	1	1	yes	characteristic
20	#15688886	—	2	2	no	—
21	C₂²×D₈×C₄₇	—	2	2	no	—
22	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#493	—	2	2	no	—
25	C₄₇×#493	—	2	2	no	—
26	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×Dic₉₄	—	2	1	no	—
28	C₂×#10625335	—	2	8	no	—
29	C₂×#10625335	—	4	4	no	—
30	C₂×#10625335	—	4	4	no	—
31	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
32	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
33	#13094024	—	2	1	no	—
34	#13094024	—	2	1	no	—
35	#13094024	—	2	1	no	—
36	#13094024	D₄	1	2	yes	—
37	C₂×C₄⋊Dic₄₇	—	2	1	no	—
38	C₂×C₄⋊Dic₄₇	—	2	1	no	—
39	C₂×C₄⋊Dic₄₇	—	2	1	no	—
40	C₂×C₄⋊Dic₄₇	—	2	1	no	—
41	C₂×C₄⋊Dic₄₇	—	2	1	no	—
42	#13093945	—	2	8	no	—
43	#13093945	—	4	4	no	—
44	#13093945	—	4	4	no	—
45	C₄×C₄₇⋊C₈	—	2	1	no	—
46	C₄×C₄₇⋊C₈	—	2	1	no	—
47	C₄×C₄₇⋊C₈	—	2	1	no	—
48	C₄×C₄₇⋊C₈	—	2	1	no	—
49	C₂²×D₄×C₄₇	—	2	1	no	—
50	C₂²×D₄×C₄₇	—	2	1	no	—
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	—	2	1	no	—
53	C₂²×D₄×C₄₇	—	2	1	no	—
54	C₂²×D₄×C₄₇	—	2	1	no	—
55	C₂×D₈×C₄₇	—	2	8	no	—
56	C₂×D₈×C₄₇	—	4	4	no	—
57	C₂×D₈×C₄₇	—	4	4	no	—
58	C₂²×C₈×C₄₇	D₄	1	2	yes	—
59	#127×C₄₇	—	2	1	no	—
60	#127×C₄₇	—	2	1	no	—
61	#127×C₄₇	—	2	1	no	—
62	#127×C₄₇	—	2	1	no	—
63	#127×C₄₇	—	2	1	no	—
64	#127×C₄₇	—	2	1	no	—
65	#127×C₄₇	D₄	1	2	yes	—
66	#127×C₄₇	D₄	1	2	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₄×C₈×C₄₇	—	2	1	no	—
69	C₄×C₈×C₄₇	—	2	1	no	—
70	C₂⁴×C₄₇	—	4	1	no	—
71	C₂⁴×C₄₇	—	4	1	no	—
72	C₂×D₄×C₄₇	—	2	2	no	—
73	C₂×D₄×C₄₇	—	2	2	no	—
74	C₂×D₄×C₄₇	—	2	2	no	—
75	C₂×D₄×C₄₇	—	2	2	no	—
76	C₂×D₄×C₄₇	—	2	2	no	—
77	C₂×D₄×C₄₇	—	2	2	no	—
78	C₂×D₄×C₄₇	—	4	1	no	—
79	C₂×D₄×C₄₇	—	4	1	no	—
80	C₂×D₄×C₄₇	—	4	1	no	—
81	C₂×D₄×C₄₇	—	4	1	no	—
82	C₂×D₄×C₄₇	—	4	1	no	—
83	C₂×D₄×C₄₇	—	4	1	no	—
84	C₂×D₄×C₄₇	—	4	2	no	—
85	C₂×D₄×C₄₇	—	4	2	no	—
86	C₂×D₄×C₄₇	—	4	2	no	—
87	C₂×D₄×C₄₇	—	4	2	no	—
88	C₂×D₄×C₄₇	—	4	2	no	—
89	C₂×D₄×C₄₇	—	4	2	no	—
90	C₂×D₄×C₄₇	—	4	2	no	—
91	C₂×D₄×C₄₇	—	4	2	no	—
92	C₂×D₄×C₄₇	—	4	2	no	—
93	C₂×D₄×C₄₇	—	4	2	no	—
94	C₂×D₄×C₄₇	—	4	2	no	—
95	C₂×D₄×C₄₇	—	4	2	no	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×Dic₄₇	—	4	1	no	—
100	C₂²×Dic₄₇	—	4	1	no	—
101	C₂×Dic₉₄	—	2	2	no	—
102	C₂×Dic₉₄	—	4	2	no	—
103	C₂×Dic₉₄	—	4	2	no	—
104	C₂×Dic₉₄	—	4	1	no	—
105	D₈×C₄₇	—	4	16	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	SD₁₆	1	4	yes	complemented
109	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₄₇	#41	1	1	yes	characteristic
113	#10625335	—	4	16	no	—
114	C₄⋊Dic₄₇	—	2	2	no	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	—	4	1	no	—
117	C₄⋊Dic₄₇	—	4	1	no	—
118	C₄⋊Dic₄₇	—	4	2	no	—
119	C₄⋊Dic₄₇	—	4	2	no	—
120	C₄⋊Dic₄₇	—	4	2	no	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	D₈	1	4	yes	complemented
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	—	4	2	no	—
129	C₂³×C₄₇	—	8	1	no	—
130	C₂³×C₄₇	—	8	1	no	—
131	C₂³×C₄₇	—	8	1	no	—
132	C₂³×C₄₇	—	8	1	no	—
133	C₂³×C₄₇	—	8	1	no	—
134	C₂³×C₄₇	—	8	1	no	—
135	C₂³×C₄₇	—	8	1	no	—
136	C₂³×C₄₇	—	8	1	no	—
137	C₂³×C₄₇	—	8	1	no	—
138	C₂³×C₄₇	—	8	1	no	—
139	C₂³×C₄₇	—	8	1	no	—
140	C₂³×C₄₇	—	8	1	no	—
141	C₂³×C₄₇	#127	1	1	yes	characteristic
142	D₄×C₄₇	—	4	4	no	—
143	D₄×C₄₇	—	4	4	no	—
144	D₄×C₄₇	—	4	4	no	—
145	D₄×C₄₇	—	4	4	no	—
146	D₄×C₄₇	—	4	4	no	—
147	D₄×C₄₇	—	4	4	no	—
148	D₄×C₄₇	—	8	2	no	—
149	D₄×C₄₇	—	8	2	no	—
150	D₄×C₄₇	—	8	2	no	—
151	D₄×C₄₇	—	8	2	no	—
152	D₄×C₄₇	—	8	2	no	—
153	D₄×C₄₇	—	8	2	no	—
154	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
156	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
162	C₂×C₄×C₄₇	#135	1	2	yes	—
163	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
164	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	8	1	no	—
168	C₂×Dic₄₇	—	8	1	no	—
169	C₂×Dic₄₇	—	8	1	no	—
170	C₂×Dic₄₇	—	8	1	no	—
171	C₂×Dic₄₇	—	8	1	no	—
172	Dic₉₄	—	4	4	no	—
173	Dic₉₄	—	8	2	no	—
174	C₈×C₄₇	—	2	4	no	—
175	C₄₇⋊C₈	—	2	4	no	—
176	C₄₇⋊C₈	—	4	2	no	—
177	#10305	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	8	2	no	—
179	C₂²×C₄₇	—	8	2	no	—
180	C₂²×C₄₇	—	8	2	no	—
181	C₂²×C₄₇	—	8	2	no	—
182	C₂²×C₄₇	—	8	2	no	—
183	C₂²×C₄₇	—	8	2	no	—
184	C₂²×C₄₇	—	16	1	no	—
185	C₂²×C₄₇	—	16	1	no	—
186	C₂²×C₄₇	—	16	1	no	—
187	C₂²×C₄₇	—	16	1	no	—
188	C₂²×C₄₇	—	16	1	no	—
189	C₂²×C₄₇	—	16	1	no	—
190	C₂²×C₄₇	—	16	1	no	—
191	C₂²×C₄₇	—	16	1	no	—
192	C₂²×C₄₇	#392	1	1	yes	characteristic
193	C₂²×C₄₇	#492	1	1	yes	characteristic
194	C₂²×C₄₇	#493	1	1	yes	characteristic
195	C₂²×C₄₇	#495	1	1	yes	characteristic
196	C₂²×C₄₇	#496	1	1	yes	characteristic
197	C₂²×C₄₇	#496	1	1	yes	characteristic
198	C₂²×C₄₇	#496	1	1	yes	characteristic
199	C₄×C₄₇	#447	1	2	yes	—
200	C₄×C₄₇	#449	1	2	yes	—
201	C₄×C₄₇	#450	1	2	yes	—
202	C₄×C₄₇	#459	1	2	yes	—
203	C₄×C₄₇	#460	1	2	yes	—
204	C₄×C₄₇	#463	1	2	yes	—
205	Dic₄₇	—	8	2	no	—
206	Dic₄₇	—	16	1	no	—
207	C₂×#493	D₄₇	1	1	yes	characteristic
208	C₂×#492	—	47	1	no	—
209	C₂×#486	—	47	1	no	—
210	#1990	—	47	1	no	—
211	#1957	—	47	1	no	—
212	#1957	—	47	1	no	—
213	#1273	—	47	1	no	—
214	C₂×C₄₇	—	16	2	no	—
215	C₂×C₄₇	—	16	2	no	—
216	C₂×C₄₇	#1706	1	1	yes	characteristic
217	C₂×C₄₇	#1715	1	1	yes	characteristic
218	C₂×C₄₇	#1717	1	1	yes	characteristic
219	C₂×C₄₇	#1721	1	1	yes	characteristic
220	C₂×C₄₇	#2011	1	1	yes	characteristic
221	C₂×C₄₇	#2012	1	1	yes	characteristic
222	C₂×C₄₇	#2014	1	1	yes	characteristic
223	C₂²×SD₁₆	—	94	2	no	—
224	C₂²×D₈	—	2	2	no	—
225	C₂×C₄⋊Q₈	—	47	1	no	—
226	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
227	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
228	#493	—	2	2	no	—
229	#493	—	2	2	no	—
230	#492	—	94	2	no	—
231	#492	—	94	2	no	—
232	#486	—	94	2	no	—
233	#486	—	94	2	no	—
234	C₂×#102	—	94	2	no	—
235	C₂×#102	—	94	2	no	—
236	C₂×#102	—	94	2	no	—
237	C₂×C₄×C₈	—	47	1	no	—
238	C₂×C₄×C₈	—	47	1	no	—
239	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
240	#384	—	47	1	no	—
241	#340	—	94	2	no	—
242	C₄₇	#10305	1	1	yes	characteristic, complemented, Sylow
243	C₂²×Q₈	—	94	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂×SD₁₆	—	94	8	no	—
251	C₂×SD₁₆	—	188	4	no	—
252	C₂×SD₁₆	—	188	4	no	—
253	C₂×D₈	—	2	8	no	—
254	C₂×D₈	—	4	4	no	—
255	C₂×D₈	—	4	4	no	—
256	C₂²×C₈	—	47	2	no	—
257	C₂²×C₈	—	47	2	no	—
258	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
259	C₄⋊Q₈	—	47	2	no	—
260	C₄⋊Q₈	—	94	1	no	—
261	C₄⋊Q₈	—	94	1	no	—
262	C₄⋊Q₈	—	94	1	no	—
263	#127	—	2	1	no	—
264	#127	—	2	1	no	—
265	#127	—	2	1	no	—
266	#127	—	2	1	no	—
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#127	C₂²⋊D₄₇	1	2	yes	—
270	#127	C₂²⋊D₄₇	1	2	yes	—
271	C₂×C₄⋊C₄	—	94	1	no	—
272	C₂×C₄⋊C₄	—	94	1	no	—
273	C₂×C₄⋊C₄	—	94	1	no	—
274	C₂×C₄⋊C₄	—	94	1	no	—
275	C₂×C₄⋊C₄	—	94	1	no	—
276	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
277	#102	—	94	8	no	—
278	#102	—	188	4	no	—
279	#102	—	188	4	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	94	1	no	—
283	C₄×C₈	—	94	1	no	—
284	C₄×C₈	—	94	1	no	—
285	C₄×C₈	—	94	1	no	—
286	C₂⁴	—	4	1	no	—
287	C₂⁴	—	4	1	no	—
288	C₂×Q₈	—	94	2	no	—
289	C₂×Q₈	—	188	2	no	—
290	C₂×Q₈	—	188	2	no	—
291	C₂×Q₈	—	188	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂²×C₄	—	188	1	no	—
317	C₂²×C₄	—	188	1	no	—
318	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
321	SD₁₆	—	188	16	no	—
322	D₈	—	4	16	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	47	4	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	94	2	no	—
329	C₂×C₈	—	94	2	no	—
330	C₂×C₈	—	94	2	no	—
331	C₂×C₈	#10625335	1	4	yes	complemented
332	C₄⋊C₄	—	94	2	no	—
333	C₄⋊C₄	—	94	2	no	—
334	C₄⋊C₄	—	188	2	no	—
335	C₄⋊C₄	—	188	2	no	—
336	C₄⋊C₄	—	188	2	no	—
337	C₄⋊C₄	—	188	1	no	—
338	C₄⋊C₄	—	188	1	no	—
339	C₄²	D₄×D₄₇	1	1	yes	characteristic
340	C₄²	#10625352	1	1	yes	characteristic
341	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
342	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	1	no	—
346	C₂³	—	8	1	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	8	1	no	—
353	C₂³	—	8	1	no	—
354	C₂³	—	8	1	no	—
355	C₂³	—	8	1	no	—
356	C₂³	—	8	1	no	—
357	C₂³	#13094020	1	1	yes	characteristic
358	Q₈	—	376	2	no	—
359	Q₈	—	188	4	no	—
360	D₄	—	4	4	no	—
361	D₄	—	4	4	no	—
362	D₄	—	4	4	no	—
363	D₄	—	4	4	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	8	2	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	2	no	—
371	D₄	—	8	2	no	—
372	C₂×C₄	—	376	1	no	—
373	C₂×C₄	—	376	1	no	—
374	C₂×C₄	—	376	1	no	—
375	C₂×C₄	—	376	1	no	—
376	C₂×C₄	—	376	1	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	#13093992	1	1	yes	characteristic
379	C₂×C₄	#13093992	1	1	yes	characteristic
380	C₂×C₄	#13093993	1	1	yes	characteristic
381	C₂×C₄	#13093995	1	1	yes	characteristic
382	C₂×C₄	#13093996	1	1	yes	characteristic
383	C₂×C₄	#13093996	1	1	yes	characteristic
384	C₂×C₄	D₈×D₄₇	1	2	yes	—
385	C₂×C₄	C₂×#10625335	1	2	yes	—
386	C₂×C₄	#13094043	1	2	yes	—
387	C₂×C₄	#13094048	1	2	yes	—
388	C₂×C₄	#13094048	1	2	yes	—
389	C₂×C₄	#13094050	1	2	yes	—
390	C₈	—	2	4	no	—
391	C₈	—	94	4	no	—
392	C₈	—	188	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	16	1	no	—
400	C₂²	—	16	1	no	—
401	C₂²	—	16	1	no	—
402	C₂²	—	16	1	no	—
403	C₂²	—	16	1	no	—
404	C₂²	—	16	1	no	—
405	C₂²	—	16	1	no	—
406	C₂²	—	16	1	no	—
407	C₂²	#15689031	1	1	yes	characteristic
408	C₂²	#15689495	1	1	yes	characteristic
409	C₂²	#15689498	1	1	yes	characteristic
410	C₂²	#15689506	1	1	yes	characteristic
411	C₂²	#15689510	1	1	yes	characteristic
412	C₂²	#15689511	1	1	yes	characteristic
413	C₂²	#15689511	1	1	yes	characteristic
414	C₄	—	376	2	no	—
415	C₄	—	752	1	no	—
416	C₄	#15689255	1	2	yes	—
417	C₄	#15689265	1	2	yes	—
418	C₄	#15689274	1	2	yes	—
419	C₄	#15689316	1	2	yes	—
420	C₄	#15689320	1	2	yes	—
421	C₄	#15689336	1	2	yes	—
422	C₂	—	16	2	no	—
423	C₂	—	16	2	no	—
424	C₂	#20242977	1	1	yes	characteristic
425	C₂	#20243014	1	1	yes	characteristic
426	C₂	#20243026	1	1	yes	characteristic
427	C₂	#20243053	1	1	yes	characteristic
428	C₂	#20244457	1	1	yes	characteristic
429	C₂	#20244463	1	1	yes	characteristic
430	C₂	#20244476	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13094020
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting, prime radical	C₂×C₄₇×#493	C₂
socle	C₂³×C₄₇	#127
hypercenter	C₂×#493	D₄₇
hypocenter	C₄₇	#10305
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#493

Complements

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

N	H ≅ G/N	type
1. C₂×#15689495	C₂	semidirect
2. C₂×#15689469	C₂	semidirect
3. #20244349	C₂	semidirect
4. #20244195	C₂	semidirect
5. #20244195	C₂	semidirect
6. C₄₇⋊#1273	C₂	semidirect
108. C₂×C₈×C₄₇	SD₁₆	semidirect
126. C₂×C₄₇⋊C₈	D₈	semidirect
242. C₄₇	#10305	semidirect
331. C₂×C₈	#10625335	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689495	2
C₂×#15689469	2
#20244349	2
#20244195	2
C₄₇⋊#1273	2
C₂×C₄₇×#493	2
#10305	47