Subgroups — #26232183

Order 12032.

1378 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	#20252240	C₂	1	2	yes	maximal, complemented
2	#20251849	C₂	1	2	yes	maximal, complemented
3	#20244287	C₂	1	2	yes	maximal, complemented
4	#20243877	C₂	1	4	yes	maximal, complemented
5	#20243434	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	#15689598	C₂²	1	4	yes	complemented
10	#15689235	—	2	4	no	—
11	D₈×Dic₄₇	—	2	4	no	—
12	#15689161	C₂²	1	2	yes	complemented
13	#15689140	C₂²	1	4	yes	complemented
14	#15689128	C₂²	1	4	yes	complemented
15	#15689107	C₂²	1	1	yes	characteristic
16	#15689097	C₂²	1	2	yes	—
17	#15689097	C₂²	1	1	yes	characteristic
18	#15689097	C₂²	1	4	yes	complemented
19	C₂×#13093939	—	2	8	no	—
20	#15689078	C₂²	1	2	yes	complemented
21	#15688894	C₂²	1	2	yes	complemented
22	#15688880	C₂²	1	2	yes	complemented
23	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	2	yes	—
24	C₄₇×#576	—	2	4	no	—
25	C₄₇×#576	—	2	4	no	—
26	C₂×AGL(1,ℤ/8)×C₄₇	C₄	1	4	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
28	C₂×#135×C₄₇	C₄	1	2	yes	complemented
29	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×D₈×C₄₇	C₄	1	2	yes	complemented
31	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#10625329	C₂³	1	2	yes	—
34	D₄×Dic₄₇	—	2	8	no	—
35	D₄×Dic₄₇	—	4	4	no	—
36	#13093983	C₂³	1	4	yes	—
37	#13093983	C₂³	1	2	yes	—
38	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
39	#13093958	—	2	2	no	—
40	#13093956	—	2	2	no	—
41	#13093951	—	4	4	no	—
42	#13093945	—	2	8	no	—
43	#13093943	—	2	1	no	—
44	#13093941	—	2	1	no	—
45	#13093939	—	2	4	no	—
46	#13093939	—	2	8	no	—
47	#13093939	D₄	1	4	yes	—
48	#13093934	—	2	2	no	—
49	C₈×Dic₄₇	—	2	2	no	—
50	H(5,𝔽₂)×C₄₇	—	2	8	no	—
51	H(5,𝔽₂)×C₄₇	—	4	4	no	—
52	C₂×#41×C₄₇	—	2	2	no	—
53	C₂×#41×C₄₇	C₂×C₄	1	4	yes	complemented
54	C₂×#41×C₄₇	C₂³	1	2	yes	—
55	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₄₇	—	2	4	no	—
57	C₂²×D₄×C₄₇	—	2	2	no	—
58	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
59	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
60	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
61	AGL(1,ℤ/8)×C₄₇	—	2	16	no	—
62	#135×C₄₇	—	2	4	no	—
63	#135×C₄₇	—	2	4	no	—
64	#135×C₄₇	—	2	2	no	—
65	#135×C₄₇	—	2	2	no	—
66	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×SD₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
68	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
69	C₂×D₈×C₄₇	—	2	4	no	—
70	C₂×D₈×C₄₇	—	2	4	no	—
71	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
75	C₂×D₈×C₄₇	D₄	1	4	yes	—
76	C₂×D₈×C₄₇	D₄	1	4	yes	—
77	#131×C₄₇	—	2	2	no	—
78	#131×C₄₇	—	2	2	no	—
79	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
80	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	complemented
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂⁴×C₄₇	—	2	2	no	—
84	C₂⁴×C₄₇	—	2	4	no	—
85	#41×C₄₇	—	2	2	no	—
86	#41×C₄₇	—	2	2	no	—
87	#41×C₄₇	—	2	8	no	—
88	#41×C₄₇	—	2	4	no	—
89	#41×C₄₇	—	2	4	no	—
90	#41×C₄₇	—	4	4	no	—
91	#41×C₄₇	—	4	8	no	—
92	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂×Q₈×C₄₇	#41	1	1	yes	characteristic
94	C₂×D₄×C₄₇	—	2	8	no	—
95	C₂×D₄×C₄₇	—	2	4	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	2	4	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	4	no	—
100	C₂×D₄×C₄₇	—	4	4	no	—
101	C₂×D₄×C₄₇	—	4	8	no	—
102	C₂×D₄×C₄₇	—	4	16	no	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
105	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₄₇	C₂×D₄	1	8	yes	—
107	C₂×D₄×C₄₇	#41	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
112	C₂²×Dic₄₇	—	4	8	no	—
113	Q₁₆×C₄₇	—	2	1	no	—
114	Q₁₆×C₄₇	—	2	1	no	—
115	SD₁₆×C₄₇	—	2	8	no	—
116	SD₁₆×C₄₇	—	2	4	no	—
117	D₈×C₄₇	—	2	8	no	—
118	D₈×C₄₇	—	2	1	no	—
119	D₈×C₄₇	—	2	1	no	—
120	D₈×C₄₇	C₂²⋊C₄	1	4	yes	—
121	D₈×C₄₇	C₂²⋊C₄	1	4	yes	—
122	D₈×C₄₇	C₂²⋊C₄	1	8	yes	—
123	M₁₆×C₄₇	—	2	2	no	—
124	M₁₆×C₄₇	—	2	4	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₂²⋊Dic₄₇	—	2	4	no	—
133	C₂²⋊Dic₄₇	—	4	8	no	—
134	C₂²⋊Dic₄₇	C₂×D₄	1	4	yes	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	4	no	—
137	C₄×Dic₄₇	—	2	2	no	—
138	C₄×Dic₄₇	—	2	4	no	—
139	#10625329	—	2	2	no	—
140	#10625329	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂³×C₄₇	—	2	4	no	—
143	C₂³×C₄₇	—	2	8	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	4	8	no	—
146	C₂³×C₄₇	—	16	2	no	—
147	C₂³×C₄₇	—	16	4	no	—
148	C₂³×C₄₇	C₄×D₄	1	2	yes	—
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₄₇	—	2	2	no	—
151	Q₈×C₄₇	—	2	2	no	—
152	Q₈×C₄₇	—	2	2	no	—
153	D₄×C₄₇	—	2	4	no	—
154	D₄×C₄₇	—	2	2	no	—
155	D₄×C₄₇	—	2	4	no	—
156	D₄×C₄₇	—	2	2	no	—
157	D₄×C₄₇	—	2	8	no	—
158	D₄×C₄₇	—	2	2	no	—
159	D₄×C₄₇	—	4	8	no	—
160	D₄×C₄₇	—	4	8	no	—
161	D₄×C₄₇	—	4	4	no	—
162	D₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	4	8	no	—
167	C₂×C₄×C₄₇	—	4	4	no	—
168	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
173	C₂×Dic₄₇	—	2	4	no	—
174	C₂×Dic₄₇	—	4	4	no	—
175	C₂×Dic₄₇	—	16	8	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	—	4	2	no	—
181	#22455	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	8	no	—
184	C₂²×C₄₇	—	4	1	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	8	8	no	—
188	C₂²×C₄₇	—	8	4	no	—
189	C₂²×C₄₇	—	8	2	no	—
190	C₂²×C₄₇	—	16	8	no	—
191	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₄₇	D₄²	1	2	yes	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
196	C₄×C₄₇	#518	1	1	yes	characteristic
197	C₄×C₄₇	#546	1	2	yes	—
198	Dic₄₇	—	4	4	no	—
199	Dic₄₇	—	8	4	no	—
200	C₂×#576	D₄₇	1	1	yes	characteristic
201	#2948	—	47	2	no	—
202	#2883	—	47	2	no	—
203	#1976	—	47	2	no	—
204	#1904	—	47	4	no	—
205	#1812	—	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	8	no	—
212	C₂×C₄₇	—	8	2	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	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
224	#518	—	47	4	no	—
225	#442	—	94	4	no	—
226	C₄×D₈	—	94	4	no	—
227	#427	—	47	2	no	—
228	#421	—	47	4	no	—
229	#418	—	47	4	no	—
230	#413	—	47	1	no	—
231	#410	—	47	1	no	—
232	#410	—	47	2	no	—
233	#410	—	47	4	no	—
234	C₂×#99	—	94	8	no	—
235	#405	—	47	2	no	—
236	#344	—	47	2	no	—
237	H(3,ℤ/4)	—	47	2	no	—
238	C₄₇	#22455	1	1	yes	characteristic, complemented, Sylow
239	H(5,𝔽₂)	—	2	8	no	—
240	H(5,𝔽₂)	—	4	4	no	—
241	C₂×#41	—	2	2	no	—
242	C₂×#41	C₂×Dic₄₇	1	4	yes	complemented
243	C₂×#41	C₂²×D₄₇	1	2	yes	—
244	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
245	C₂²×D₄	—	2	4	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂×Dic₄₇	1	4	yes	complemented
248	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
249	AGL(1,ℤ/8)	—	2	8	no	—
250	AGL(1,ℤ/8)	—	2	16	no	—
251	#135	—	2	4	no	—
252	#135	—	2	4	no	—
253	#135	—	2	2	no	—
254	#135	—	2	2	no	—
255	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic, complemented
256	C₂×SD₁₆	C₂×Dic₄₇	1	4	yes	complemented
257	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	complemented
258	C₂×D₈	—	2	4	no	—
259	C₂×D₈	—	2	4	no	—
260	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
261	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
262	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
263	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
264	C₂×D₈	C₂²⋊D₄₇	1	4	yes	—
265	C₂×D₈	C₂²⋊D₄₇	1	4	yes	—
266	#131	—	2	2	no	—
267	#131	—	2	2	no	—
268	C₂×M₁₆	—	47	2	no	—
269	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	complemented
270	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
271	C₂²×C₈	C₂×Dic₄₇	1	2	yes	complemented
272	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
273	C₄×D₄	—	94	8	no	—
274	C₄×D₄	—	188	4	no	—
275	#117	—	47	2	no	—
276	#117	—	47	4	no	—
277	C₂×C₂²⋊C₄	—	94	8	no	—
278	#107	—	94	2	no	—
279	#106	—	94	2	no	—
280	#104	—	188	4	no	—
281	#102	—	94	8	no	—
282	#101	—	94	1	no	—
283	#100	—	94	1	no	—
284	#99	—	47	4	no	—
285	#99	—	94	8	no	—
286	#99	—	94	4	no	—
287	#97	—	94	2	no	—
288	C₄×C₈	—	94	2	no	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	—	2	4	no	—
291	#41	—	2	2	no	—
292	#41	—	2	2	no	—
293	#41	—	2	8	no	—
294	#41	—	2	4	no	—
295	#41	—	2	4	no	—
296	#41	—	4	4	no	—
297	#41	—	4	8	no	—
298	C₂×Q₈	#10625352	1	1	yes	characteristic
299	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	4	4	no	—
307	C₂×D₄	—	4	8	no	—
308	C₂×D₄	—	4	16	no	—
309	C₂×D₄	D₄×D₄₇	1	2	yes	—
310	C₂×D₄	#10625352	1	1	yes	characteristic
311	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
312	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
313	C₂×D₄	C₂×C₂²⋊D₄₇	1	8	yes	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	188	8	no	—
317	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
318	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
319	Q₁₆	—	2	1	no	—
320	Q₁₆	—	2	1	no	—
321	SD₁₆	—	2	8	no	—
322	SD₁₆	—	2	4	no	—
323	D₈	—	2	8	no	—
324	D₈	—	2	1	no	—
325	D₈	—	2	1	no	—
326	D₈	C₂²⋊Dic₄₇	1	4	yes	—
327	D₈	C₂²⋊Dic₄₇	1	4	yes	—
328	D₈	C₂²⋊Dic₄₇	1	8	yes	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	4	no	—
331	M₁₆	—	94	2	no	—
332	M₁₆	—	94	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	94	2	no	—
336	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
337	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
338	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
339	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
340	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
341	C₄⋊C₄	—	94	2	no	—
342	C₄⋊C₄	—	94	4	no	—
343	C₂²⋊C₄	—	47	4	no	—
344	C₂²⋊C₄	—	94	4	no	—
345	C₂²⋊C₄	—	188	8	no	—
346	C₄²	—	94	2	no	—
347	C₄²	—	94	4	no	—
348	C₂³	—	2	8	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	16	2	no	—
353	C₂³	—	16	4	no	—
354	C₂³	D₄×Dic₄₇	1	2	yes	—
355	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
356	Q₈	—	2	2	no	—
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	D₄	—	2	4	no	—
360	D₄	—	2	8	no	—
361	D₄	—	2	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	2	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	8	no	—
367	D₄	—	4	4	no	—
368	D₄	C₂×C₂²⋊Dic₄₇	1	8	yes	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	94	4	no	—
375	C₂×C₄	—	188	4	no	—
376	C₂×C₄	—	752	8	no	—
377	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
378	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
380	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
381	C₂×C₄	#13094069	1	2	yes	—
382	C₈	—	2	2	no	—
383	C₈	—	188	2	no	—
384	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
385	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
386	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	8	no	—
393	C₂²	—	8	4	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	16	8	no	—
396	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
397	C₂²	D₄×C₂²⋊D₄₇	1	2	yes	—
398	C₄	—	2	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	376	4	no	—
401	C₄	—	188	4	no	—
402	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
403	C₄	#15689598	1	1	yes	characteristic
404	C₄	#15689767	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	2	1	no	—
407	C₂	—	4	2	no	—
408	C₂	—	4	8	no	—
409	C₂	—	8	2	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	#22455
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. #20252240	C₂	semidirect
2. #20251849	C₂	semidirect
3. #20244287	C₂	semidirect
4. #20243877	C₂	semidirect
5. #20243434	C₂	semidirect
6. #20243358	C₂	semidirect
7. #20243188	C₂	semidirect
9. #15689598	C₂²	semidirect
12. #15689161	C₂²	semidirect
13. #15689140	C₂²	semidirect
14. #15689128	C₂²	semidirect
18. #15689097	C₂²	semidirect
20. #15689078	C₂²	semidirect
21. #15688894	C₂²	semidirect
22. #15688880	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₄₇	C₄	semidirect
28. C₂×#135×C₄₇	C₄	semidirect
30. C₂²×D₈×C₄₇	C₄	semidirect
53. C₂×#41×C₄₇	C₂×C₄	semidirect
58. C₂²×D₄×C₄₇	C₂×C₄	semidirect
66. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
67. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
68. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
73. C₂×D₈×C₄₇	C₂×C₄	semidirect
74. C₂×D₈×C₄₇	C₂×C₄	semidirect
79. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
81. C₂²×C₈×C₄₇	C₂×C₄	semidirect
217. C₂×AGL(1,ℤ/8)	Dic₄₇	semidirect
219. C₂×#135	Dic₄₇	semidirect
221. C₂²×D₈	Dic₄₇	semidirect
238. C₄₇	#22455	semidirect
242. C₂×#41	C₂×Dic₄₇	semidirect
247. C₂²×D₄	C₂×Dic₄₇	semidirect
255. C₂×Q₁₆	C₂×Dic₄₇	semidirect
256. C₂×SD₁₆	C₂×Dic₄₇	semidirect
257. C₂×SD₁₆	C₂×Dic₄₇	semidirect
262. C₂×D₈	C₂×Dic₄₇	semidirect
263. C₂×D₈	C₂×Dic₄₇	semidirect
269. C₂×M₁₆	C₂×Dic₄₇	semidirect
271. C₂²×C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252240	2
#20251849	2
#20244287	2
#20243877	2
#20243434	2
#20243358	2
#20243188	2
C₂×C₄₇×#576	2
#22455	47