Subgroups — #26123262

Order 12032.

958 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689132	C₂	1	2	yes	maximal
2	#20246006	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688892	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688883	C₂	1	2	yes	maximal
5	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂×#13093983	C₂²	1	2	yes	—
8	#15689132	—	2	4	no	—
9	#15689132	—	2	4	no	—
10	C₂×#13093948	—	2	4	no	—
11	#15689022	—	2	4	no	—
12	#15688983	—	2	2	no	—
13	#15688892	—	2	2	no	—
14	#15688883	—	2	4	no	—
15	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#391	—	2	2	no	—
19	C₄₇×#391	C₄	1	4	yes	complemented
20	C₂×#95×C₄₇	—	2	2	no	—
21	C₂×#10625329	—	2	2	no	—
22	C₂×#10625329	—	2	2	no	—
23	C₂×#10625329	—	2	2	no	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	D₄	1	4	yes	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	#13093983	—	2	2	no	—
29	#13093983	—	2	2	no	—
30	#13093983	—	2	2	no	—
31	#13093983	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	4	no	—
33	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
34	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	#13093948	—	2	16	no	—
37	C₄₇⋊#95	—	2	4	no	—
38	C₂²×Q₈×C₄₇	—	2	1	no	—
39	C₂²×Q₈×C₄₇	—	2	1	no	—
40	C₂²×Q₈×C₄₇	—	2	1	no	—
41	C₂²×Q₈×C₄₇	—	2	2	no	—
42	C₂²×Q₈×C₄₇	—	2	2	no	—
43	C₂²×Q₈×C₄₇	—	2	2	no	—
44	C₂²×Q₈×C₄₇	—	2	2	no	—
45	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
46	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
47	C₂²×Q₈×C₄₇	Q₈	1	2	yes	—
48	C₂³×C₄×C₄₇	—	2	1	no	—
49	C₂³×C₄×C₄₇	—	2	1	no	—
50	C₂³×C₄×C₄₇	D₄	1	2	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
56	C₂×C₄²×C₄₇	—	2	2	no	—
57	C₂×C₄²×C₄₇	—	2	2	no	—
58	C₂×C₄²×C₄₇	—	2	1	no	—
59	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
60	#95×C₄₇	—	2	8	no	—
61	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
62	C₂×Q₈×C₄₇	—	2	2	no	—
63	C₂×Q₈×C₄₇	—	2	2	no	—
64	C₂×Q₈×C₄₇	—	2	2	no	—
65	C₂×Q₈×C₄₇	—	2	4	no	—
66	C₂×Q₈×C₄₇	—	2	4	no	—
67	C₂×Q₈×C₄₇	—	2	4	no	—
68	C₂×Q₈×C₄₇	—	2	4	no	—
69	C₂×Q₈×C₄₇	—	2	4	no	—
70	C₂×Q₈×C₄₇	—	2	4	no	—
71	C₂×Q₈×C₄₇	—	4	2	no	—
72	C₂×Q₈×C₄₇	—	4	2	no	—
73	C₂×Q₈×C₄₇	—	4	2	no	—
74	C₂×Q₈×C₄₇	—	4	2	no	—
75	C₂×Q₈×C₄₇	—	4	2	no	—
76	C₂×Q₈×C₄₇	—	4	2	no	—
77	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	complemented
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
86	C₂²×C₄×C₄₇	—	4	1	no	—
87	C₂²×C₄×C₄₇	—	4	1	no	—
88	C₂²×C₄×C₄₇	—	4	1	no	—
89	C₂²×C₄×C₄₇	—	4	1	no	—
90	C₂²×C₄×C₄₇	—	4	1	no	—
91	C₂²×C₄×C₄₇	—	4	1	no	—
92	C₂²×C₄×C₄₇	—	4	4	no	—
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	#41	1	2	yes	—
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×Dic₄₇	—	2	4	no	—
105	C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₄⋊C₄×C₄₇	—	2	4	no	—
107	C₄²×C₄₇	—	2	4	no	—
108	C₄²×C₄₇	—	4	2	no	—
109	C₂²⋊Dic₄₇	—	4	2	no	—
110	C₂²⋊Dic₄₇	—	4	2	no	—
111	C₄⋊Dic₄₇	—	2	4	no	—
112	C₄⋊Dic₄₇	—	2	4	no	—
113	C₄⋊Dic₄₇	—	8	4	no	—
114	C₄×Dic₄₇	—	4	2	no	—
115	C₄×Dic₄₇	—	4	2	no	—
116	#10625329	—	2	4	no	—
117	#10625329	—	2	4	no	—
118	#10625329	—	4	2	no	—
119	#10625329	—	4	2	no	—
120	C₂×C₄₇⋊C₈	—	2	4	no	—
121	C₂×C₄₇⋊C₈	—	4	2	no	—
122	C₂×C₄₇⋊C₈	—	4	2	no	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂³×C₄₇	#120	1	1	yes	characteristic
127	C₂³×C₄₇	#121	1	1	yes	characteristic
128	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
129	C₂³×C₄₇	#123	1	1	yes	characteristic
130	C₂³×C₄₇	#124	1	1	yes	characteristic
131	C₂³×C₄₇	#127	1	1	yes	characteristic
132	Q₈×C₄₇	—	2	8	no	—
133	Q₈×C₄₇	—	4	4	no	—
134	Q₈×C₄₇	—	4	4	no	—
135	Q₈×C₄₇	—	4	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	4	4	no	—
141	C₂×C₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	8	2	no	—
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₇	#120	1	2	yes	—
157	C₂×C₄×C₄₇	#121	1	2	yes	—
158	C₂×C₄×C₄₇	#121	1	2	yes	—
159	C₂×C₄×C₄₇	#121	1	2	yes	—
160	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
162	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
163	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#123	1	2	yes	—
165	C₂×C₄×C₄₇	#123	1	2	yes	—
166	C₂×C₄×C₄₇	#124	1	2	yes	—
167	C₂×C₄×C₄₇	#126	1	2	yes	—
168	C₂×Dic₄₇	—	4	4	no	—
169	C₂×Dic₄₇	—	4	4	no	—
170	C₂×Dic₄₇	—	4	4	no	—
171	C₄₇⋊C₈	—	4	4	no	—
172	#11055	—	47	1	no	maximal, Sylow
173	C₂²×C₄₇	—	2	1	no	—
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	#380	1	1	yes	characteristic
182	C₂²×C₄₇	#386	1	1	yes	characteristic
183	C₂²×C₄₇	#390	1	1	yes	characteristic
184	C₂²×C₄₇	#392	1	1	yes	characteristic
185	C₂²×C₄₇	#393	1	1	yes	characteristic
186	C₂²×C₄₇	#397	1	1	yes	characteristic
187	C₂²×C₄₇	#399	1	1	yes	characteristic
188	C₂²×C₄₇	#455	1	2	yes	—
189	C₂²×C₄₇	#456	1	2	yes	—
190	C₄×C₄₇	—	4	4	no	—
191	C₄×C₄₇	—	4	4	no	—
192	C₄×C₄₇	—	4	4	no	—
193	C₄×C₄₇	#385	1	2	yes	—
194	C₄×C₄₇	#388	1	2	yes	—
195	C₄×C₄₇	#394	1	2	yes	—
196	C₄×C₄₇	#396	1	2	yes	—
197	Dic₄₇	—	8	4	no	—
198	C₂×#419	—	47	2	no	—
199	#2316	—	47	1	no	—
200	C₂×#391	D₄₇	1	1	yes	characteristic
201	C₂×#343	—	47	1	no	—
202	C₂×#339	—	47	2	no	—
203	C₂×C₄₇	—	2	1	no	—
204	C₂×C₄₇	—	2	1	no	—
205	C₂×C₄₇	—	2	1	no	—
206	C₂×C₄₇	—	2	1	no	—
207	C₂×C₄₇	#1439	1	1	yes	characteristic
208	C₂×C₄₇	#1885	1	1	yes	characteristic
209	C₂×C₄₇	#1886	1	1	yes	characteristic
210	C₂×C₄₇	#2007	1	2	yes	—
211	C₂×C₄₇	#2028	1	2	yes	—
212	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
213	C₂²×M₁₆	—	47	2	no	—
214	C₂×#117	—	47	2	no	—
215	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
216	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
217	#419	—	94	4	no	—
218	#419	—	94	4	no	—
219	C₂×#103	—	94	4	no	—
220	#391	—	2	2	no	—
221	#391	Dic₄₇	1	4	yes	complemented
222	#389	—	94	4	no	—
223	#380	—	94	2	no	—
224	C₂×#95	—	2	2	no	—
225	#343	—	94	2	no	—
226	#339	—	94	4	no	—
227	C₄₇	#11055	1	1	yes	characteristic, complemented, Sylow
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	—	2	2	no	—
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	2	no	—
235	C₂²×Q₈	Dic₉₄	1	2	yes	—
236	C₂²×Q₈	D₁₈₈	1	2	yes	—
237	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
241	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
242	C₂×M₁₆	—	47	4	no	—
243	C₂×M₁₆	—	94	2	no	—
244	C₂×M₁₆	—	94	2	no	—
245	C₂×M₁₆	—	94	2	no	—
246	C₂×M₁₆	—	94	2	no	—
247	C₂×M₁₆	—	94	2	no	—
248	C₂²×C₈	—	94	2	no	—
249	#117	—	94	2	no	—
250	#117	—	94	2	no	—
251	#117	—	94	2	no	—
252	#117	—	94	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	47	4	no	—
256	C₂×C₄⋊C₄	—	94	4	no	—
257	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
259	C₂×C₂²⋊C₄	—	94	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	—	94	2	no	—
264	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
265	#103	—	94	16	no	—
266	#95	—	2	8	no	—
267	#95	—	94	4	no	—
268	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	C₄⋊Dic₄₇	1	4	yes	complemented
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	—	94	4	no	—
301	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
302	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
304	C₂²×C₄	#10625350	1	1	yes	characteristic
305	C₂²×C₄	#10625350	1	1	yes	characteristic
306	C₂²×C₄	D₄×D₄₇	1	2	yes	—
307	C₂²×C₄	D₄×D₄₇	1	2	yes	—
308	C₂²×C₄	#10625352	1	2	yes	—
309	C₂²×C₄	#10625352	1	2	yes	—
310	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
312	M₁₆	—	94	4	no	—
313	M₁₆	—	94	4	no	—
314	M₁₆	—	188	2	no	—
315	M₁₆	—	188	2	no	—
316	C₂×C₈	—	94	4	no	—
317	C₂×C₈	—	188	2	no	—
318	C₂×C₈	—	188	2	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	94	4	no	—
322	C₄⋊C₄	—	94	4	no	—
323	C₄⋊C₄	—	376	4	no	—
324	C₂²⋊C₄	—	188	2	no	—
325	C₂²⋊C₄	—	188	2	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	4	2	no	—
328	C₄²	—	188	2	no	—
329	C₄²	—	188	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
333	C₂³	#13093992	1	1	yes	characteristic
334	C₂³	#13093998	1	1	yes	characteristic
335	C₂³	#13094003	1	1	yes	characteristic
336	C₂³	#13094005	1	1	yes	characteristic
337	C₂³	#13094011	1	1	yes	characteristic
338	C₂³	#13094020	1	1	yes	characteristic
339	Q₈	—	2	8	no	—
340	Q₈	—	4	4	no	—
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	188	4	no	—
360	C₂×C₄	—	188	4	no	—
361	C₂×C₄	—	188	4	no	—
362	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
363	C₂×C₄	#13093983	1	1	yes	characteristic
364	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
365	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
366	C₂×C₄	#13093994	1	2	yes	—
367	C₂×C₄	#13093995	1	2	yes	—
368	C₂×C₄	#13093996	1	2	yes	—
369	C₂×C₄	#13093997	1	2	yes	—
370	C₂×C₄	#13093998	1	1	yes	characteristic
371	C₂×C₄	#13094001	1	2	yes	—
372	C₂×C₄	#13094001	1	2	yes	—
373	C₂×C₄	#13094003	1	1	yes	characteristic
374	C₂×C₄	#13094006	1	2	yes	—
375	C₂×C₄	#13094008	1	2	yes	—
376	C₂×C₄	#13094010	1	2	yes	—
377	C₂×C₄	#13094017	1	2	yes	—
378	C₈	—	188	4	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	#15688983	1	1	yes	characteristic
388	C₂²	#15689003	1	1	yes	characteristic
389	C₂²	#15689026	1	1	yes	characteristic
390	C₂²	#15689032	1	1	yes	characteristic
391	C₂²	#15689035	1	1	yes	characteristic
392	C₂²	#15689048	1	1	yes	characteristic
393	C₂²	#15689059	1	1	yes	characteristic
394	C₂²	#15689300	1	2	yes	—
395	C₂²	#15689305	1	2	yes	—
396	C₄	—	4	4	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	4	no	—
399	C₄	—	376	4	no	—
400	C₄	#15688998	1	2	yes	—
401	C₄	#15689016	1	2	yes	—
402	C₄	#15689039	1	2	yes	—
403	C₄	#15689046	1	2	yes	—
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	#20241633	1	1	yes	characteristic
409	C₂	#20243777	1	1	yes	characteristic
410	C₂	#20243782	1	1	yes	characteristic
411	C₂	#20244434	1	2	yes	—
412	C₂	#20244549	1	2	yes	—

	subgroup	G/H
center	C₂³	#13093992
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#391	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#391	D₄₇
hypocenter	C₄₇	#11055
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#391

Complements

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

N	H ≅ G/N	type
19. C₄₇×#391	C₄	semidirect
77. C₂×Q₈×C₄₇	C₄⋊C₄	semidirect
221. #391	Dic₄₇	semidirect
227. C₄₇	#11055	semidirect
284. C₂×Q₈	C₄⋊Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689132	2
#20246006	2
C₂×#15688892	2
C₂×#15688883	2
C₂×C₄₇×#391	2
#11055	47