Subgroups — #26123535

Order 12032.

882 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689161	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689097	C₂	1	2	yes	maximal
3	#20243105	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15688880	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#408	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093983	C₂²	1	2	yes	—
7	C₂×#13093983	C₂²	1	2	yes	—
8	#15689161	—	2	4	no	—
9	C₂×#13093958	—	2	1	no	—
10	C₂×#13093956	—	2	1	no	—
11	#15689097	—	2	4	no	—
12	#15689097	—	2	4	no	—
13	C₂×#13093939	—	2	4	no	—
14	#15688886	—	2	2	no	—
15	#15688880	—	2	4	no	—
16	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#408	—	2	2	no	—
20	C₄₇×#408	—	2	1	no	—
21	C₄₇×#408	—	2	1	no	—
22	C₂×C₂²⋊C₈×C₄₇	C₄	1	4	yes	complemented
23	#13093983	—	2	2	no	—
24	#13093983	—	2	2	no	—
25	#13093983	—	2	2	no	—
26	#13093983	—	2	2	no	—
27	#13093983	—	2	2	no	—
28	#13093983	—	2	2	no	—
29	#13093983	D₄	1	4	yes	—
30	#13093983	D₄	1	4	yes	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
34	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	#13093958	—	2	4	no	—
38	#13093956	—	2	4	no	—
39	#13093939	—	2	16	no	—
40	C₂×#41×C₄₇	—	2	2	no	—
41	C₂×#41×C₄₇	—	2	2	no	—
42	C₂×#41×C₄₇	—	2	1	no	—
43	C₂×#41×C₄₇	—	2	1	no	—
44	C₂×#41×C₄₇	—	2	1	no	—
45	C₂×#41×C₄₇	—	2	1	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂²×Q₈×C₄₇	Q₈	1	1	yes	characteristic
49	C₂²×D₄×C₄₇	D₄	1	2	yes	—
50	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	1	no	—
55	C₂×M₁₆×C₄₇	—	2	1	no	—
56	C₂×M₁₆×C₄₇	—	2	2	no	—
57	C₂²×C₈×C₄₇	—	2	2	no	—
58	C₂²×C₈×C₄₇	—	2	2	no	—
59	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₄₇	D₄	1	2	yes	—
62	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
64	C₂²⋊C₈×C₄₇	—	2	4	no	—
65	C₂²⋊C₈×C₄₇	—	2	4	no	—
66	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
67	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
68	#41×C₄₇	—	4	1	no	—
69	#41×C₄₇	—	4	2	no	—
70	#41×C₄₇	—	4	2	no	—
71	#41×C₄₇	—	4	2	no	—
72	#41×C₄₇	—	4	1	no	—
73	#41×C₄₇	—	4	2	no	—
74	#41×C₄₇	—	4	2	no	—
75	#41×C₄₇	—	4	1	no	—
76	#41×C₄₇	—	4	2	no	—
77	#41×C₄₇	—	4	1	no	—
78	C₂×Q₈×C₄₇	—	2	1	no	—
79	C₂×Q₈×C₄₇	—	2	1	no	—
80	C₂×Q₈×C₄₇	—	2	2	no	—
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×D₄×C₄₇	—	2	4	no	—
83	C₂×D₄×C₄₇	—	2	2	no	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	—	2	4	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	1	no	—
89	C₂×D₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×C₄×C₄₇	#41	1	2	yes	—
105	C₂²×Dic₄₇	—	4	2	no	—
106	C₂²×Dic₄₇	—	4	2	no	—
107	M₁₆×C₄₇	—	4	2	no	—
108	M₁₆×C₄₇	—	4	1	no	—
109	M₁₆×C₄₇	—	4	1	no	—
110	C₂×C₈×C₄₇	—	2	4	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	4	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	4	no	—
118	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
120	C₂²⋊Dic₄₇	—	2	4	no	—
121	C₂²⋊Dic₄₇	—	2	4	no	—
122	C₂²⋊Dic₄₇	—	4	2	no	—
123	C₂²⋊Dic₄₇	—	4	2	no	—
124	C₄⋊Dic₄₇	—	2	4	no	—
125	C₄⋊Dic₄₇	—	2	4	no	—
126	C₄⋊Dic₄₇	—	4	2	no	—
127	C₄⋊Dic₄₇	—	4	2	no	—
128	C₄×Dic₄₇	—	2	4	no	—
129	C₄×Dic₄₇	—	2	4	no	—
130	C₄×Dic₄₇	—	4	2	no	—
131	C₄×Dic₄₇	—	4	2	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	4	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	—	4	4	no	—
136	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂³×C₄₇	#120	1	2	yes	—
138	C₂³×C₄₇	#121	1	1	yes	characteristic
139	C₂³×C₄₇	#121	1	1	yes	characteristic
140	C₂³×C₄₇	#123	1	2	yes	—
141	Q₈×C₄₇	—	4	1	no	—
142	Q₈×C₄₇	—	4	2	no	—
143	Q₈×C₄₇	—	4	1	no	—
144	D₄×C₄₇	—	4	2	no	—
145	D₄×C₄₇	—	4	4	no	—
146	D₄×C₄₇	—	4	2	no	—
147	D₄×C₄₇	—	4	1	no	—
148	D₄×C₄₇	—	4	2	no	—
149	D₄×C₄₇	—	4	1	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	4	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
160	C₂×C₄×C₄₇	#121	1	2	yes	—
161	C₂×C₄×C₄₇	#121	1	2	yes	—
162	C₂×C₄×C₄₇	#121	1	2	yes	—
163	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#123	1	2	yes	—
169	C₂×C₄×C₄₇	#124	1	2	yes	—
170	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#126	1	2	yes	—
172	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
173	C₂×Dic₄₇	—	4	4	no	—
174	C₂×Dic₄₇	—	4	4	no	—
175	C₂×Dic₄₇	—	8	4	no	—
176	C₂×Dic₄₇	—	8	4	no	—
177	C₈×C₄₇	—	2	2	no	—
178	C₈×C₄₇	—	2	2	no	—
179	C₈×C₄₇	—	4	2	no	—
180	#11098	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	4	4	no	—
187	C₂²×C₄₇	—	4	2	no	—
188	C₂²×C₄₇	—	8	4	no	—
189	C₂²×C₄₇	#380	1	1	yes	characteristic
190	C₂²×C₄₇	#385	1	2	yes	—
191	C₂²×C₄₇	#392	1	1	yes	characteristic
192	C₂²×C₄₇	#394	1	2	yes	—
193	C₂²×C₄₇	#397	1	1	yes	characteristic
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	#386	1	1	yes	characteristic
196	C₄×C₄₇	#388	1	2	yes	—
197	C₄×C₄₇	#390	1	1	yes	characteristic
198	C₄×C₄₇	#393	1	1	yes	characteristic
199	C₄×C₄₇	#396	1	2	yes	—
200	C₄×C₄₇	#399	1	1	yes	characteristic
201	Dic₄₇	—	8	4	no	—
202	Dic₄₇	—	8	4	no	—
203	C₂×#427	—	47	1	no	—
204	C₂×#410	—	47	2	no	—
205	C₂×#408	D₄₇	1	1	yes	characteristic
206	#1735	—	47	1	no	—
207	C₂×H(3,ℤ/4)	—	47	2	no	—
208	C₂×C₄₇	—	2	1	no	—
209	C₂×C₄₇	—	2	2	no	—
210	C₂×C₄₇	—	2	2	no	—
211	C₂×C₄₇	—	2	1	no	—
212	C₂×C₄₇	—	8	2	no	—
213	C₂×C₄₇	#1439	1	1	yes	characteristic
214	C₂×C₄₇	#1812	1	2	yes	—
215	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
216	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
217	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
218	C₂×#117	—	47	2	no	—
219	C₂×#117	—	47	2	no	—
220	#427	—	94	4	no	—
221	C₂×#107	—	94	1	no	—
222	C₂×#106	—	94	1	no	—
223	#410	—	94	4	no	—
224	#410	—	94	4	no	—
225	C₂×#99	—	94	4	no	—
226	#408	—	2	2	no	—
227	#408	—	2	1	no	—
228	#408	—	2	1	no	—
229	C₂×C₂²⋊C₈	Dic₄₇	1	4	yes	complemented
230	#340	—	94	2	no	—
231	H(3,ℤ/4)	—	94	4	no	—
232	C₄₇	#11098	1	1	yes	characteristic, complemented, Sylow
233	C₂×#41	—	2	1	no	—
234	C₂×#41	—	2	1	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	2	no	—
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	2	1	no	—
240	C₂×#41	—	2	1	no	—
241	C₂²×Q₈	Dic₉₄	1	1	yes	characteristic
242	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
243	C₂²×D₄	D₁₈₈	1	2	yes	—
244	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
245	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
253	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
254	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
255	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
256	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
257	#117	—	47	4	no	—
258	#117	—	47	4	no	—
259	#117	—	94	2	no	—
260	#117	—	94	2	no	—
261	#117	—	94	2	no	—
262	#117	—	94	2	no	—
263	#117	—	94	2	no	—
264	#117	—	94	2	no	—
265	C₂×C₄⋊C₄	—	94	2	no	—
266	C₂×C₄⋊C₄	—	94	2	no	—
267	C₂×C₂²⋊C₄	—	94	2	no	—
268	C₂×C₂²⋊C₄	—	94	2	no	—
269	C₂×C₄²	—	94	2	no	—
270	C₂×C₄²	—	94	2	no	—
271	#107	—	94	4	no	—
272	#106	—	94	4	no	—
273	#99	—	94	16	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	C₂⁴	C₄⋊Dic₄₇	1	2	yes	—
277	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
278	#41	—	4	1	no	—
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	#41	—	4	2	no	—
282	#41	—	4	1	no	—
283	#41	—	4	2	no	—
284	#41	—	4	2	no	—
285	#41	—	4	1	no	—
286	#41	—	4	2	no	—
287	#41	—	4	1	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	188	2	no	—
305	C₂²×C₄	—	188	2	no	—
306	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
307	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
308	C₂²×C₄	#10625350	1	1	yes	characteristic
309	C₂²×C₄	#10625350	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₄₇	1	2	yes	—
311	C₂²×C₄	D₄×D₄₇	1	2	yes	—
312	C₂²×C₄	#10625352	1	2	yes	—
313	C₂²×C₄	#10625352	1	2	yes	—
314	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
317	M₁₆	—	4	2	no	—
318	M₁₆	—	4	1	no	—
319	M₁₆	—	4	1	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
329	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
330	C₄⋊C₄	—	94	4	no	—
331	C₄⋊C₄	—	94	4	no	—
332	C₄⋊C₄	—	188	2	no	—
333	C₄⋊C₄	—	188	2	no	—
334	C₂²⋊C₄	—	94	4	no	—
335	C₂²⋊C₄	—	94	4	no	—
336	C₂²⋊C₄	—	188	2	no	—
337	C₂²⋊C₄	—	188	2	no	—
338	C₄²	—	94	4	no	—
339	C₄²	—	94	4	no	—
340	C₄²	—	188	2	no	—
341	C₄²	—	188	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	4	no	—
346	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
347	C₂³	#13093994	1	2	yes	—
348	C₂³	#13093998	1	1	yes	characteristic
349	C₂³	#13093998	1	1	yes	characteristic
350	C₂³	#13094008	1	2	yes	—
351	Q₈	—	4	1	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	1	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	4	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	376	4	no	—
366	C₂×C₄	—	376	4	no	—
367	C₂×C₄	—	188	4	no	—
368	C₂×C₄	—	188	4	no	—
369	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
370	C₂×C₄	#13093983	1	1	yes	characteristic
371	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
372	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
373	C₂×C₄	#13093992	1	1	yes	characteristic
374	C₂×C₄	#13093995	1	2	yes	—
375	C₂×C₄	#13093996	1	2	yes	—
376	C₂×C₄	#13093997	1	2	yes	—
377	C₂×C₄	#13094001	1	2	yes	—
378	C₂×C₄	#13094001	1	2	yes	—
379	C₂×C₄	#13094003	1	1	yes	characteristic
380	C₂×C₄	#13094003	1	1	yes	characteristic
381	C₂×C₄	#13094005	1	1	yes	characteristic
382	C₂×C₄	#13094006	1	2	yes	—
383	C₂×C₄	#13094010	1	2	yes	—
384	C₂×C₄	#13094011	1	1	yes	characteristic
385	C₂×C₄	#13094017	1	2	yes	—
386	C₂×C₄	#13094020	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	8	4	no	—
398	C₂²	#15688983	1	1	yes	characteristic
399	C₂²	#15688998	1	2	yes	—
400	C₂²	#15689032	1	1	yes	characteristic
401	C₂²	#15689039	1	2	yes	—
402	C₂²	#15689048	1	1	yes	characteristic
403	C₄	—	4	2	no	—
404	C₄	—	376	4	no	—
405	C₄	—	376	4	no	—
406	C₄	#15689003	1	1	yes	characteristic
407	C₄	#15689016	1	2	yes	—
408	C₄	#15689026	1	1	yes	characteristic
409	C₄	#15689035	1	1	yes	characteristic
410	C₄	#15689046	1	2	yes	—
411	C₄	#15689059	1	1	yes	characteristic
412	C₂	—	2	1	no	—
413	C₂	—	2	2	no	—
414	C₂	—	2	2	no	—
415	C₂	—	2	1	no	—
416	C₂	—	8	2	no	—
417	C₂	#20241633	1	1	yes	characteristic
418	C₂	#20243434	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13093983
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#408	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#408	D₄₇
hypocenter	C₄₇	#11098
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂×#408

Complements

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

N	H ≅ G/N	type
1. C₂×#15689161	C₂	semidirect
3. #20243105	C₂	semidirect
4. C₂×#15688880	C₂	semidirect
22. C₂×C₂²⋊C₈×C₄₇	C₄	semidirect
229. C₂×C₂²⋊C₈	Dic₄₇	semidirect
232. C₄₇	#11098	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689161	2
C₂×#15689097	2
#20243105	2
C₂×#15688880	2
C₂×C₄₇×#408	2
#11098	47