Subgroups — #26226801

Order 12032.

966 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
2	#20245795	C₂	1	1	yes	maximal, characteristic
3	#20244144	C₂	1	4	yes	maximal, complemented
4	#20243576	C₂	1	4	yes	maximal
5	#20243547	C₂	1	2	yes	maximal, complemented
6	#20243515	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₇×#384	C₂	1	1	yes	maximal, characteristic
8	C₂×#13093983	—	2	1	no	—
9	#15689176	C₄	1	8	yes	complemented
10	C₂×#13093957	C₂²	1	8	yes	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
14	#15688993	C₂²	1	1	yes	characteristic
15	#15688993	C₂²	1	1	yes	characteristic
16	#15688989	—	2	1	no	—
17	#15688983	—	2	1	no	—
18	#15688983	C₂²	1	2	yes	—
19	C₄×C₄⋊Dic₄₇	—	2	1	no	—
20	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
21	#15688885	C₂²	1	8	yes	—
22	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
23	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
24	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#384	—	2	1	no	—
27	C₄₇×#384	—	2	1	no	—
28	C₄₇×#384	C₂²	1	2	yes	—
29	C₄₇×#384	C₂²	1	2	yes	—
30	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
31	#13093983	—	4	4	no	—
32	C₂×C₄⋊Dic₄₇	—	2	1	no	—
33	C₂×C₄⋊Dic₄₇	—	2	1	no	—
34	C₂×C₄⋊Dic₄₇	—	2	1	no	—
35	C₂×C₄⋊Dic₄₇	—	2	1	no	—
36	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
37	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
38	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
39	C₂×C₄×Dic₄₇	—	2	2	no	—
40	#13093957	—	4	8	no	—
41	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
42	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	—
43	C₄×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
44	C₄₇⋊#95	—	2	2	no	—
45	C₄₇⋊#95	—	2	2	no	—
46	C₂³×C₄×C₄₇	—	2	2	no	—
47	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
56	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
57	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
58	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
59	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
63	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
65	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	4	no	—
71	C₂²×C₄×C₄₇	—	4	4	no	—
72	C₂²×C₄×C₄₇	—	4	4	no	—
73	C₂²×C₄×C₄₇	—	4	4	no	—
74	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
75	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
76	C₂²×C₄×C₄₇	D₈	1	4	yes	—
77	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
78	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
86	C₂²×Dic₄₇	—	2	2	no	—
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₄⋊C₄×C₄₇	—	2	8	no	—
89	C₄⋊C₄×C₄₇	—	4	4	no	—
90	C₄⋊C₄×C₄₇	—	4	4	no	—
91	C₄⋊C₄×C₄₇	—	4	4	no	—
92	C₄⋊C₄×C₄₇	—	4	4	no	—
93	C₄⋊C₄×C₄₇	—	4	4	no	—
94	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
95	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
96	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
97	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
98	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
99	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
100	C₂²⋊Dic₄₇	—	4	4	no	—
101	C₄⋊Dic₄₇	—	2	4	no	—
102	C₄⋊Dic₄₇	—	2	4	no	—
103	C₄⋊Dic₄₇	—	4	2	no	—
104	C₄⋊Dic₄₇	—	4	2	no	—
105	C₄⋊Dic₄₇	—	4	2	no	—
106	C₄⋊Dic₄₇	—	4	2	no	—
107	C₄×Dic₄₇	—	4	4	no	—
108	C₂×C₄₇⋊C₈	—	2	4	no	—
109	C₂×C₄₇⋊C₈	—	2	4	no	—
110	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
111	C₂³×C₄₇	—	2	1	no	—
112	C₂³×C₄₇	—	2	1	no	—
113	C₂³×C₄₇	—	2	1	no	—
114	C₂³×C₄₇	—	2	1	no	—
115	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
116	C₂³×C₄₇	C₂×D₈	1	2	yes	—
117	C₂³×C₄₇	C₂×Q₁₆	1	2	yes	—
118	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
119	C₂×C₄×C₄₇	—	2	1	no	—
120	C₂×C₄×C₄₇	—	2	1	no	—
121	C₂×C₄×C₄₇	—	2	1	no	—
122	C₂×C₄×C₄₇	—	2	1	no	—
123	C₂×C₄×C₄₇	—	2	4	no	—
124	C₂×C₄×C₄₇	—	2	4	no	—
125	C₂×C₄×C₄₇	—	2	8	no	—
126	C₂×C₄×C₄₇	—	4	4	no	—
127	C₂×C₄×C₄₇	—	4	4	no	—
128	C₂×C₄×C₄₇	—	4	4	no	—
129	C₂×C₄×C₄₇	—	8	8	no	—
130	C₂×C₄×C₄₇	#107	1	16	yes	complemented
131	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
132	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
133	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
134	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
137	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
139	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
140	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
141	C₂×C₄×C₄₇	#137	1	2	yes	—
142	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
145	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
146	C₂×Dic₄₇	—	4	2	no	—
147	C₂×Dic₄₇	—	4	2	no	—
148	C₂×Dic₄₇	—	4	2	no	—
149	C₂×Dic₄₇	—	4	2	no	—
150	C₂×Dic₄₇	—	4	2	no	—
151	C₂×Dic₄₇	—	4	2	no	—
152	C₄₇⋊C₈	—	2	8	no	—
153	#21982	—	47	1	no	maximal, Sylow
154	C₂²×C₄₇	—	2	2	no	—
155	C₂²×C₄₇	—	2	2	no	—
156	C₂²×C₄₇	—	2	2	no	—
157	C₂²×C₄₇	—	2	2	no	—
158	C₂²×C₄₇	—	2	2	no	—
159	C₂²×C₄₇	—	2	2	no	—
160	C₂²×C₄₇	C₂×#107	1	4	yes	—
161	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×C₄₇	#535	1	1	yes	characteristic
163	C₂²×C₄₇	#536	1	1	yes	characteristic
164	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
165	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
166	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
168	C₄×C₄₇	—	2	2	no	—
169	C₄×C₄₇	—	2	2	no	—
170	C₄×C₄₇	—	8	4	no	—
171	C₄×C₄₇	C₂×#107	1	4	yes	—
172	C₄×C₄₇	C₂×#107	1	4	yes	—
173	C₄×C₄₇	#428	1	4	yes	—
174	C₄×C₄₇	#520	1	2	yes	—
175	C₄×C₄₇	#544	1	2	yes	—
176	Dic₄₇	—	8	2	no	—
177	Dic₄₇	—	8	2	no	—
178	C₂×#431	—	47	1	no	—
179	#2285	—	47	1	no	—
180	C₂×#384	D₄₇	1	1	yes	characteristic
181	#1947	—	47	4	no	—
182	#1852	—	47	4	no	—
183	#1845	—	47	2	no	—
184	#1834	—	47	2	no	—
185	C₂×C₄₇	—	2	4	no	—
186	C₂×C₄₇	#2317	1	1	yes	characteristic
187	C₂×C₄₇	C₂²×#107	1	1	yes	characteristic
188	C₂×C₄₇	C₂×#428	1	1	yes	characteristic
189	C₂×C₄₇	#3205	1	1	yes	characteristic
190	C₂×C₄₇	#3209	1	1	yes	characteristic
191	C₂×C₄₇	#3226	1	1	yes	characteristic
192	C₂×C₄₇	#3230	1	1	yes	characteristic
193	C₂×#117	—	94	1	no	—
194	C₂²×C₄⋊C₄	—	2	1	no	—
195	C₂²×C₄⋊C₄	—	2	1	no	—
196	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
197	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
198	#431	—	47	8	no	—
199	C₂×#107	—	47	8	no	—
200	C₂×C₄⋊C₈	—	47	2	no	—
201	C₂×C₂²⋊C₈	—	47	2	no	—
202	C₂×C₄×C₈	—	47	2	no	—
203	#384	—	2	1	no	—
204	#384	—	2	1	no	—
205	#384	—	47	1	no	—
206	#384	—	47	1	no	—
207	#384	C₂×D₄₇	1	2	yes	—
208	#384	C₂×D₄₇	1	2	yes	—
209	#382	—	94	1	no	—
210	#380	—	47	2	no	—
211	#380	—	94	1	no	—
212	C₄×C₄⋊C₄	—	47	2	no	—
213	C₄×C₄⋊C₄	—	94	1	no	—
214	#340	—	47	8	no	—
215	C₄₇	#21982	1	1	yes	characteristic, complemented, Sylow
216	C₂³×C₄	—	2	2	no	—
217	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
218	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
219	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
220	C₂²×C₈	—	47	4	no	—
221	#117	—	188	4	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	4	4	no	—
228	C₂×C₄⋊C₄	—	4	4	no	—
229	C₂×C₄⋊C₄	—	4	4	no	—
230	C₂×C₄⋊C₄	—	47	2	no	—
231	C₂×C₄⋊C₄	—	47	2	no	—
232	C₂×C₄⋊C₄	—	94	1	no	—
233	C₂×C₄⋊C₄	—	94	1	no	—
234	C₂×C₄⋊C₄	—	94	1	no	—
235	C₂×C₄⋊C₄	—	94	1	no	—
236	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
237	C₂×C₂²⋊C₄	—	94	2	no	—
238	C₂×C₄²	—	94	2	no	—
239	C₂×C₄²	Dic₉₄	1	4	yes	—
240	C₂×C₄²	C₄×D₄₇	1	4	yes	—
241	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
244	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
245	#107	—	188	8	no	—
246	C₄⋊C₈	—	47	8	no	—
247	C₂²⋊C₈	—	47	8	no	—
248	C₄×C₈	—	47	8	no	—
249	#95	—	94	2	no	—
250	#95	—	94	2	no	—
251	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	4	no	—
258	C₂²×C₄	—	4	4	no	—
259	C₂²×C₄	—	4	4	no	—
260	C₂²×C₄	—	94	2	no	—
261	C₂²×C₄	—	94	2	no	—
262	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
263	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
264	C₂²×C₄	#10625334	1	4	yes	—
265	C₂²×C₄	#10625337	1	4	yes	—
266	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
267	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
268	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
273	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
274	C₂×C₈	—	47	8	no	—
275	C₂×C₈	—	94	4	no	—
276	C₂×C₈	—	94	4	no	—
277	C₄⋊C₄	—	2	8	no	—
278	C₄⋊C₄	—	4	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₄⋊C₄	—	4	4	no	—
283	C₄⋊C₄	—	94	4	no	—
284	C₄⋊C₄	—	94	4	no	—
285	C₄⋊C₄	—	188	2	no	—
286	C₄⋊C₄	—	188	2	no	—
287	C₄⋊C₄	—	188	2	no	—
288	C₄⋊C₄	—	188	2	no	—
289	C₂²⋊C₄	—	188	4	no	—
290	C₄²	—	188	4	no	—
291	C₄²	Dic₄₇⋊C₄	1	4	yes	—
292	C₄²	Dic₄₇⋊C₄	1	4	yes	—
293	C₄²	C₂×Dic₉₄	1	2	yes	—
294	C₄²	C₂×Dic₉₄	1	2	yes	—
295	C₄²	C₂×C₄×D₄₇	1	2	yes	—
296	C₄²	C₂×C₄×D₄₇	1	2	yes	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
302	C₂³	C₂×#10625334	1	2	yes	—
303	C₂³	C₂×#10625337	1	2	yes	—
304	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	8	8	no	—
316	C₂×C₄	—	188	2	no	—
317	C₂×C₄	—	188	2	no	—
318	C₂×C₄	—	188	2	no	—
319	C₂×C₄	—	188	2	no	—
320	C₂×C₄	—	188	2	no	—
321	C₂×C₄	—	188	2	no	—
322	C₂×C₄	#13093957	1	16	yes	complemented
323	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
324	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
325	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
326	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
327	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
328	C₂×C₄	C₂×#10625334	1	2	yes	—
329	C₂×C₄	C₂×#10625334	1	2	yes	—
330	C₂×C₄	C₂×#10625337	1	2	yes	—
331	C₂×C₄	C₂×#10625337	1	2	yes	—
332	C₂×C₄	#13094050	1	2	yes	—
333	C₂×C₄	#13094055	1	2	yes	—
334	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
335	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
336	C₂×C₄	#13094069	1	2	yes	—
337	C₂×C₄	#13094072	1	2	yes	—
338	C₈	—	94	8	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	C₂×#13093957	1	4	yes	—
346	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
347	C₂²	#15689690	1	1	yes	characteristic
348	C₂²	#15689697	1	1	yes	characteristic
349	C₂²	C₂²×#10625334	1	1	yes	characteristic
350	C₂²	C₂²×#10625337	1	1	yes	characteristic
351	C₂²	C₂×#13094050	1	1	yes	characteristic
352	C₂²	C₂×#13094055	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	8	4	no	—
356	C₄	—	376	2	no	—
357	C₄	—	376	2	no	—
358	C₄	C₂×#13093957	1	4	yes	—
359	C₄	C₂×#13093957	1	4	yes	—
360	C₄	#15689163	1	4	yes	—
361	C₄	#15689604	1	2	yes	—
362	C₄	#15689754	1	2	yes	—
363	C₂	—	2	4	no	—
364	C₂	#20246012	1	1	yes	characteristic
365	C₂	C₂²×#13093957	1	1	yes	characteristic
366	C₂	C₂×#15689163	1	1	yes	characteristic
367	C₂	#20254306	1	1	yes	characteristic
368	C₂	#20254336	1	1	yes	characteristic
369	C₂	#20254509	1	1	yes	characteristic
370	C₂	#20254539	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#384	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#384	D₄₇
hypocenter	C₄₇	#21982
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
3. #20244144	C₂	semidirect
5. #20243547	C₂	semidirect
6. #20243515	C₂	semidirect
9. #15689176	C₄	semidirect
41. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
43. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
130. C₂×C₄×C₄₇	#107	semidirect
215. C₄₇	#21982	semidirect
322. C₂×C₄	#13093957	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689176	2
#20245795	2
#20244144	2
#20243576	2
#20243547	2
#20243515	2
C₂×C₄₇×#384	2
#21982	47