Subgroups — #26232210

Order 12032.

1338 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252305	C₂	1	2	yes	maximal, complemented
2	#20251867	C₂	1	2	yes	maximal, complemented
3	#20244299	C₂	1	2	yes	maximal, complemented
4	#20243870	C₂	1	4	yes	maximal, complemented
5	#20243438	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243358	C₂	1	2	yes	maximal, complemented
7	#20243188	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#576	C₂	1	1	yes	maximal, characteristic
9	#15689890	C₂²	1	4	yes	complemented
10	#15689245	—	2	4	no	—
11	#15689240	—	2	4	no	—
12	C₂×#13093960	C₂²	1	2	yes	complemented
13	#15689140	C₂²	1	4	yes	complemented
14	#15689128	C₂²	1	4	yes	complemented
15	#15689107	—	2	4	no	—
16	#15689107	C₂²	1	2	yes	—
17	#15689107	C₂²	1	1	yes	characteristic
18	C₂×#13093941	—	2	4	no	—
19	C₂×#13093941	C₂²	1	4	yes	complemented
20	#15689097	C₂²	1	1	yes	characteristic
21	#15689078	C₂²	1	2	yes	complemented
22	#15688894	C₂²	1	2	yes	complemented
23	C₄₇⋊#338	C₂²	1	2	yes	complemented
24	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	2	yes	—
25	C₄₇×#576	—	2	4	no	—
26	C₄₇×#576	—	2	4	no	—
27	C₂×AGL(1,ℤ/8)×C₄₇	C₄	1	4	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
29	C₂×#135×C₄₇	C₄	1	2	yes	complemented
30	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×D₈×C₄₇	C₄	1	2	yes	complemented
32	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
34	#13094031	—	2	8	no	—
35	#13094031	—	4	4	no	—
36	C₂×#10625329	—	2	8	no	—
37	C₂×#10625329	C₂³	1	4	yes	—
38	C₂×#10625329	C₂³	1	2	yes	—
39	#13093983	C₂³	1	2	yes	—
40	#13093960	—	2	2	no	—
41	#13093960	—	2	2	no	—
42	#13093951	—	2	8	no	—
43	#13093945	—	4	4	no	—
44	#13093943	—	2	2	no	—
45	#13093943	D₄	1	2	yes	—
46	#13093941	—	2	2	no	—
47	#13093941	—	2	8	no	—
48	#13093941	D₄	1	2	yes	—
49	#13093939	—	2	2	no	—
50	#13093934	—	2	2	no	—
51	C₈×Dic₄₇	—	2	2	no	—
52	H(5,𝔽₂)×C₄₇	—	2	8	no	—
53	H(5,𝔽₂)×C₄₇	—	4	4	no	—
54	C₂×#41×C₄₇	—	2	2	no	—
55	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
56	C₂×#41×C₄₇	C₂³	1	2	yes	—
57	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₄₇	—	2	2	no	—
59	C₂²×D₄×C₄₇	—	2	4	no	—
60	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
61	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
62	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
63	AGL(1,ℤ/8)×C₄₇	—	2	16	no	—
64	#135×C₄₇	—	2	4	no	—
65	#135×C₄₇	—	2	4	no	—
66	#135×C₄₇	D₄	1	4	yes	—
67	#135×C₄₇	D₄	1	4	yes	—
68	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×SD₁₆×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×D₈×C₄₇	—	2	4	no	—
72	C₂×D₈×C₄₇	—	2	4	no	—
73	C₂×D₈×C₄₇	—	2	2	no	—
74	C₂×D₈×C₄₇	—	2	2	no	—
75	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
77	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	#131×C₄₇	—	2	2	no	—
80	#131×C₄₇	—	2	2	no	—
81	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂⁴×C₄₇	—	2	4	no	—
86	C₂⁴×C₄₇	—	2	2	no	—
87	#41×C₄₇	—	2	2	no	—
88	#41×C₄₇	—	2	2	no	—
89	#41×C₄₇	—	2	4	no	—
90	#41×C₄₇	—	2	8	no	—
91	#41×C₄₇	—	4	4	no	—
92	#41×C₄₇	—	4	8	no	—
93	#41×C₄₇	C₂×D₄	1	8	yes	—
94	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	2	8	no	—
98	C₂×D₄×C₄₇	—	2	4	no	—
99	C₂×D₄×C₄₇	—	2	4	no	—
100	C₂×D₄×C₄₇	—	2	4	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	4	no	—
103	C₂×D₄×C₄₇	—	4	4	no	—
104	C₂×D₄×C₄₇	—	4	8	no	—
105	C₂×D₄×C₄₇	—	4	16	no	—
106	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂×D₄×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₄₇	C₂²⋊C₄	1	2	yes	—
115	Q₁₆×C₄₇	C₂²⋊C₄	1	2	yes	—
116	SD₁₆×C₄₇	—	2	8	no	—
117	SD₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
118	D₈×C₄₇	—	2	8	no	—
119	D₈×C₄₇	—	2	2	no	—
120	D₈×C₄₇	—	2	2	no	—
121	D₈×C₄₇	—	2	4	no	—
122	D₈×C₄₇	C₂²⋊C₄	1	2	yes	—
123	D₈×C₄₇	C₂²⋊C₄	1	2	yes	—
124	M₁₆×C₄₇	—	2	2	no	—
125	M₁₆×C₄₇	—	2	4	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
133	C₂²⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄×Dic₄₇	—	2	2	no	—
136	#10625329	—	2	2	no	—
137	#10625329	—	2	4	no	—
138	#10625329	—	2	4	no	—
139	#10625329	—	4	8	no	—
140	#10625329	C₂×D₄	1	4	yes	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	4	no	—
143	C₂×C₄₇⋊C₈	—	4	8	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	2	4	no	—
146	C₂³×C₄₇	—	4	8	no	—
147	C₂³×C₄₇	—	4	4	no	—
148	C₂³×C₄₇	—	16	2	no	—
149	C₂³×C₄₇	—	16	4	no	—
150	C₂³×C₄₇	C₄×D₄	1	2	yes	—
151	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
152	Q₈×C₄₇	—	2	2	no	—
153	Q₈×C₄₇	—	2	2	no	—
154	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
155	D₄×C₄₇	—	2	8	no	—
156	D₄×C₄₇	—	2	4	no	—
157	D₄×C₄₇	—	2	4	no	—
158	D₄×C₄₇	—	2	2	no	—
159	D₄×C₄₇	—	2	4	no	—
160	D₄×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	4	8	no	—
162	D₄×C₄₇	—	4	8	no	—
163	D₄×C₄₇	—	4	4	no	—
164	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	8	no	—
169	C₂×C₄×C₄₇	—	4	8	no	—
170	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
174	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₈×C₄₇	—	2	2	no	—
177	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
180	C₄₇⋊C₈	—	2	4	no	—
181	C₄₇⋊C₈	—	4	4	no	—
182	#22458	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	4	1	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	4	4	no	—
188	C₂²×C₄₇	—	8	2	no	—
189	C₂²×C₄₇	—	8	4	no	—
190	C₂²×C₄₇	—	16	4	no	—
191	C₂²×C₄₇	—	16	8	no	—
192	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₄₇	#546	1	2	yes	—
194	C₄×C₄₇	—	2	4	no	—
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
197	C₄×C₄₇	#518	1	1	yes	characteristic
198	C₄×C₄₇	D₄²	1	2	yes	—
199	Dic₄₇	—	8	2	no	—
200	C₂×#576	D₄₇	1	1	yes	characteristic
201	#2957	—	47	2	no	—
202	#2888	—	47	2	no	—
203	#1978	—	47	2	no	—
204	#1903	—	47	4	no	—
205	#1813	—	47	1	no	—
206	#1795	—	47	2	no	—
207	#1757	—	47	1	no	—
208	C₂×C₄₇	—	2	2	no	—
209	C₂×C₄₇	—	2	1	no	—
210	C₂×C₄₇	—	4	2	no	—
211	C₂×C₄₇	—	4	4	no	—
212	C₂×C₄₇	—	8	4	no	—
213	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×H(5,𝔽₂)	C₂×D₄₇	1	2	yes	—
215	#576	—	2	4	no	—
216	#576	—	2	4	no	—
217	C₂×AGL(1,ℤ/8)	Dic₄₇	1	4	yes	complemented
218	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	2	yes	—
219	C₂×#135	Dic₄₇	1	2	yes	complemented
220	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
221	C₂²×D₈	Dic₄₇	1	2	yes	complemented
222	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
223	#568	—	47	4	no	—
224	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
225	#444	—	94	4	no	—
226	#443	—	94	4	no	—
227	C₂×#108	—	47	2	no	—
228	#421	—	47	4	no	—
229	#418	—	47	4	no	—
230	#413	—	47	1	no	—
231	#413	—	47	2	no	—
232	#413	—	94	4	no	—
233	C₂×#100	—	47	4	no	—
234	C₂×#100	—	94	4	no	—
235	#410	—	47	1	no	—
236	#405	—	47	2	no	—
237	#344	—	47	2	no	—
238	#338	—	47	2	no	—
239	C₄₇	#22458	1	1	yes	characteristic, complemented, Sylow
240	H(5,𝔽₂)	—	2	8	no	—
241	H(5,𝔽₂)	—	4	4	no	—
242	C₂×#41	—	2	2	no	—
243	C₂×#41	C₂×Dic₄₇	1	4	yes	—
244	C₂×#41	C₂²×D₄₇	1	2	yes	—
245	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	2	4	no	—
248	C₂²×D₄	C₂×Dic₄₇	1	4	yes	—
249	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
250	AGL(1,ℤ/8)	—	2	8	no	—
251	AGL(1,ℤ/8)	—	2	16	no	—
252	#135	—	2	4	no	—
253	#135	—	2	4	no	—
254	#135	C₂²⋊D₄₇	1	4	yes	—
255	#135	C₂²⋊D₄₇	1	4	yes	—
256	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
257	C₂×SD₁₆	C₂×Dic₄₇	1	4	yes	—
258	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
259	C₂×D₈	—	2	4	no	—
260	C₂×D₈	—	2	4	no	—
261	C₂×D₈	—	2	2	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
264	C₂×D₈	C₂×Dic₄₇	1	4	yes	—
265	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
266	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
267	#131	—	2	2	no	—
268	#131	—	2	2	no	—
269	#131	—	94	8	no	—
270	#131	—	188	4	no	—
271	C₂×M₁₆	—	47	2	no	—
272	C₂×M₁₆	—	47	4	no	—
273	C₂×M₁₆	—	94	8	no	—
274	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
275	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
276	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
277	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
278	#117	—	47	2	no	—
279	#108	—	94	2	no	—
280	#108	—	94	2	no	—
281	#104	—	94	8	no	—
282	#102	—	188	4	no	—
283	#101	—	47	2	no	—
284	#101	—	94	2	no	—
285	#100	—	47	2	no	—
286	#100	—	94	8	no	—
287	#100	—	94	2	no	—
288	#99	—	94	2	no	—
289	#97	—	94	2	no	—
290	C₄×C₈	—	94	2	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	2	no	—
293	#41	—	2	2	no	—
294	#41	—	2	4	no	—
295	#41	—	2	2	no	—
296	#41	—	2	8	no	—
297	#41	—	4	4	no	—
298	#41	—	4	8	no	—
299	#41	C₂×C₂²⋊D₄₇	1	8	yes	—
300	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
301	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	8	no	—
311	C₂×D₄	—	4	16	no	—
312	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
313	C₂×D₄	#10625352	1	2	yes	—
314	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
315	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
319	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
320	Q₁₆	C₂²⋊Dic₄₇	1	2	yes	—
321	Q₁₆	C₂²⋊Dic₄₇	1	2	yes	—
322	SD₁₆	—	2	8	no	—
323	SD₁₆	C₂²⋊Dic₄₇	1	8	yes	—
324	D₈	—	2	8	no	—
325	D₈	—	2	2	no	—
326	D₈	—	2	2	no	—
327	D₈	—	2	4	no	—
328	D₈	C₂²⋊Dic₄₇	1	2	yes	—
329	D₈	C₂²⋊Dic₄₇	1	2	yes	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	4	no	—
332	M₁₆	—	47	4	no	—
333	M₁₆	—	94	2	no	—
334	M₁₆	—	94	4	no	—
335	M₁₆	—	94	4	no	—
336	M₁₆	—	188	8	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	4	no	—
341	C₂×C₈	—	188	8	no	—
342	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
343	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
344	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
346	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
347	C₄⋊C₄	—	94	2	no	—
348	C₂²⋊C₄	—	94	2	no	—
349	C₄²	—	94	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	4	4	no	—
354	C₂³	—	16	2	no	—
355	C₂³	—	16	4	no	—
356	C₂³	D₄×Dic₄₇	1	2	yes	—
357	C₂³	C₂×#10625352	1	1	yes	characteristic
358	Q₈	—	2	2	no	—
359	Q₈	—	2	2	no	—
360	Q₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
361	D₄	—	2	8	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	2	4	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	4	no	—
367	D₄	—	4	8	no	—
368	D₄	—	4	8	no	—
369	D₄	—	4	4	no	—
370	D₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	8	no	—
376	C₂×C₄	—	188	2	no	—
377	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
378	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
381	C₂×C₄	#13094069	1	2	yes	—
382	C₈	—	2	2	no	—
383	C₈	—	94	4	no	—
384	C₈	—	188	4	no	—
385	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
386	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
387	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	4	no	—
395	C₂²	—	16	4	no	—
396	C₂²	—	16	8	no	—
397	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
398	C₂²	#15689767	1	2	yes	—
399	C₄	—	2	4	no	—
400	C₄	—	2	2	no	—
401	C₄	—	376	2	no	—
402	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
403	C₄	#15689598	1	1	yes	characteristic
404	C₄	D₄×C₂²⋊D₄₇	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	2	1	no	—
407	C₂	—	4	2	no	—
408	C₂	—	4	4	no	—
409	C₂	—	8	4	no	—
410	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#576	C₂
socle	C₂×C₄₇	D₄×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#576	D₄₇
hypocenter	C₄₇	#22458
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. #20252305	C₂	semidirect
2. #20251867	C₂	semidirect
3. #20244299	C₂	semidirect
4. #20243870	C₂	semidirect
5. #20243438	C₂	semidirect
6. #20243358	C₂	semidirect
7. #20243188	C₂	semidirect
9. #15689890	C₂²	semidirect
12. C₂×#13093960	C₂²	semidirect
13. #15689140	C₂²	semidirect
14. #15689128	C₂²	semidirect
19. C₂×#13093941	C₂²	semidirect
21. #15689078	C₂²	semidirect
22. #15688894	C₂²	semidirect
23. C₄₇⋊#338	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₄₇	C₄	semidirect
29. C₂×#135×C₄₇	C₄	semidirect
31. C₂²×D₈×C₄₇	C₄	semidirect
217. C₂×AGL(1,ℤ/8)	Dic₄₇	semidirect
219. C₂×#135	Dic₄₇	semidirect
221. C₂²×D₈	Dic₄₇	semidirect
239. C₄₇	#22458	semidirect

Maximal subgroups

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

subgroup	index
#20252305	2
#20251867	2
#20244299	2
#20243870	2
#20243438	2
#20243358	2
#20243188	2
C₂×C₄₇×#576	2
#22458	47