Subgroups — #26124891

Order 12032.

974 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093958	C₂	1	2	yes	maximal
2	C₂×#15688993	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688886	C₂	1	2	yes	maximal
4	#20241618	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₄₇	—	2	2	no	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂×#13093958	—	2	4	no	—
11	C₂×#13093958	—	2	4	no	—
12	C₂×#13093958	—	2	4	no	—
13	#15688993	—	2	4	no	—
14	C₂×C₄₇⋊#95	—	2	2	no	—
15	#15688886	—	2	4	no	—
16	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#336	C₄	1	4	yes	complemented
19	C₂³×Dic₄₇	—	2	1	no	—
20	C₂³×Dic₄₇	—	2	1	no	—
21	C₂³×Dic₄₇	—	2	2	no	—
22	C₂×C₄⋊Dic₄₇	—	2	2	no	—
23	C₂×C₄⋊Dic₄₇	—	2	2	no	—
24	C₂×C₄⋊Dic₄₇	—	2	2	no	—
25	C₂×C₄⋊Dic₄₇	—	2	2	no	—
26	C₂×C₄⋊Dic₄₇	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	8	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	1	no	—
33	C₂×C₄⋊Dic₄₇	—	2	1	no	—
34	C₂×C₄⋊Dic₄₇	—	4	4	no	—
35	C₂×C₄⋊Dic₄₇	—	4	4	no	—
36	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
37	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
38	C₂×C₄⋊Dic₄₇	Q₈	1	2	yes	—
39	#13093958	—	2	16	no	—
40	C₄₇⋊#95	—	4	4	no	—
41	C₂³×C₄×C₄₇	D₄	1	2	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₄₇	—	2	2	no	—
44	C₂²×C₈×C₄₇	—	2	2	no	—
45	C₂²×C₈×C₄₇	—	2	2	no	—
46	C₂²×C₈×C₄₇	—	2	2	no	—
47	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₄₇	D₄	1	4	yes	—
49	C₂²×C₈×C₄₇	Q₈	1	4	yes	—
50	C₂×C₄²×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	—	2	2	no	—
52	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
54	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	—	2	2	no	—
56	C₂²×C₄×C₄₇	—	2	2	no	—
57	C₂²×C₄×C₄₇	—	2	2	no	—
58	C₂²×C₄×C₄₇	—	2	2	no	—
59	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
60	C₂²×C₄×C₄₇	D₈	1	4	yes	—
61	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
62	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
67	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	#41	1	2	yes	—
70	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
72	C₂²×Dic₄₇	—	2	4	no	—
73	C₂²×Dic₄₇	—	2	2	no	—
74	C₂²×Dic₄₇	—	2	2	no	—
75	C₂²×Dic₄₇	—	4	1	no	—
76	C₂²×Dic₄₇	—	4	2	no	—
77	C₂²×Dic₄₇	—	4	1	no	—
78	C₂²×Dic₄₇	—	4	2	no	—
79	C₂²×Dic₄₇	—	4	1	no	—
80	C₂²×Dic₄₇	—	4	1	no	—
81	C₂²×Dic₄₇	—	4	2	no	—
82	C₂²×Dic₄₇	—	4	2	no	—
83	C₂²×Dic₄₇	—	4	4	no	—
84	C₂²×Dic₄₇	—	4	4	no	—
85	C₂²×Dic₄₇	—	4	2	no	—
86	C₂²×Dic₄₇	—	4	2	no	—
87	C₂×C₈×C₄₇	—	2	4	no	—
88	C₂×C₈×C₄₇	—	2	4	no	—
89	C₂×C₈×C₄₇	—	2	4	no	—
90	C₂×C₈×C₄₇	—	2	4	no	—
91	C₂×C₈×C₄₇	—	2	4	no	—
92	C₂×C₈×C₄₇	—	2	4	no	—
93	C₂×C₈×C₄₇	C₄⋊C₄	1	8	yes	complemented
94	C₄²×C₄₇	—	2	4	no	—
95	C₄²×C₄₇	—	2	4	no	—
96	C₄⋊Dic₄₇	—	2	4	no	—
97	C₄⋊Dic₄₇	—	2	4	no	—
98	C₄⋊Dic₄₇	—	2	4	no	—
99	C₄⋊Dic₄₇	—	2	4	no	—
100	C₄⋊Dic₄₇	—	4	16	no	—
101	C₄⋊Dic₄₇	—	4	2	no	—
102	C₄⋊Dic₄₇	—	4	2	no	—
103	C₄⋊Dic₄₇	—	4	2	no	—
104	C₄⋊Dic₄₇	—	4	2	no	—
105	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂³×C₄₇	#120	1	1	yes	characteristic
107	C₂³×C₄₇	#121	1	1	yes	characteristic
108	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
109	C₂³×C₄₇	#123	1	1	yes	characteristic
110	C₂³×C₄₇	#127	1	1	yes	characteristic
111	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
112	C₂³×C₄₇	C₂×D₈	1	2	yes	—
113	C₂³×C₄₇	C₂×Q₁₆	1	2	yes	—
114	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
115	C₂³×C₄₇	#137	1	2	yes	—
116	C₂×C₄×C₄₇	—	2	4	no	—
117	C₂×C₄×C₄₇	—	2	4	no	—
118	C₂×C₄×C₄₇	—	2	4	no	—
119	C₂×C₄×C₄₇	—	2	4	no	—
120	C₂×C₄×C₄₇	—	2	4	no	—
121	C₂×C₄×C₄₇	—	2	4	no	—
122	C₂×C₄×C₄₇	#107	1	8	yes	complemented
123	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
124	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
125	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
126	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
127	C₂×C₄×C₄₇	#120	1	2	yes	—
128	C₂×C₄×C₄₇	#121	1	2	yes	—
129	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
130	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
131	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
132	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
133	C₂×C₄×C₄₇	#123	1	2	yes	—
134	C₂×C₄×C₄₇	#125	1	2	yes	—
135	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
137	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
139	C₂×Dic₄₇	—	4	2	no	—
140	C₂×Dic₄₇	—	4	4	no	—
141	C₂×Dic₄₇	—	4	2	no	—
142	C₂×Dic₄₇	—	4	8	no	—
143	C₂×Dic₄₇	—	4	4	no	—
144	C₂×Dic₄₇	—	4	4	no	—
145	C₂×Dic₄₇	—	8	2	no	—
146	C₂×Dic₄₇	—	8	4	no	—
147	C₂×Dic₄₇	—	8	2	no	—
148	C₂×Dic₄₇	—	8	1	no	—
149	C₂×Dic₄₇	—	8	1	no	—
150	C₂×Dic₄₇	—	8	2	no	—
151	C₂×Dic₄₇	—	8	2	no	—
152	C₂×Dic₄₇	—	8	1	no	—
153	C₂×Dic₄₇	—	8	1	no	—
154	C₈×C₄₇	—	2	8	no	—
155	#11324	—	47	1	no	maximal, Sylow
156	C₂²×C₄₇	#384	1	1	yes	characteristic
157	C₂²×C₄₇	#385	1	1	yes	characteristic
158	C₂²×C₄₇	#389	1	1	yes	characteristic
159	C₂²×C₄₇	#392	1	1	yes	characteristic
160	C₂²×C₄₇	#395	1	1	yes	characteristic
161	C₂²×C₄₇	#398	1	1	yes	characteristic
162	C₂²×C₄₇	#399	1	1	yes	characteristic
163	C₂²×C₄₇	C₂×#107	1	2	yes	—
164	C₂²×C₄₇	#428	1	2	yes	—
165	C₂²×C₄₇	#447	1	2	yes	—
166	C₂²×C₄₇	#451	1	2	yes	—
167	C₂²×C₄₇	#459	1	2	yes	—
168	C₂²×C₄₇	#462	1	2	yes	—
169	C₂²×C₄₇	#474	1	2	yes	—
170	C₂²×C₄₇	#477	1	2	yes	—
171	C₂²×C₄₇	#480	1	2	yes	—
172	C₂²×C₄₇	#484	1	2	yes	—
173	C₂²×C₄₇	#493	1	1	yes	characteristic
174	C₂²×C₄₇	#494	1	1	yes	characteristic
175	C₂²×C₄₇	#496	1	1	yes	characteristic
176	C₂²×C₄₇	#497	1	1	yes	characteristic
177	C₂²×C₄₇	#500	1	2	yes	—
178	C₂²×C₄₇	#501	1	2	yes	—
179	C₄×C₄₇	—	2	8	no	—
180	C₄×C₄₇	#385	1	2	yes	—
181	C₄×C₄₇	#389	1	2	yes	—
182	C₄×C₄₇	#395	1	2	yes	—
183	C₄×C₄₇	#398	1	2	yes	—
184	Dic₄₇	—	8	2	no	—
185	Dic₄₇	—	8	4	no	—
186	Dic₄₇	—	8	2	no	—
187	C₂²×#107	—	47	2	no	—
188	C₂×#384	—	47	1	no	—
189	C₂×#340	—	47	2	no	—
190	C₂×#336	D₄₇	1	1	yes	characteristic
191	C₄⋊#95	—	47	1	no	—
192	C₂×C₄₇	#1444	1	1	yes	characteristic
193	C₂×C₄₇	#1845	1	1	yes	characteristic
194	C₂×C₄₇	#1847	1	1	yes	characteristic
195	C₂×C₄₇	#1852	1	2	yes	—
196	C₂×C₄₇	#1947	1	2	yes	—
197	C₂×C₄₇	#2011	1	1	yes	characteristic
198	C₂×C₄₇	#2016	1	1	yes	characteristic
199	C₂×C₄₇	#2057	1	2	yes	—
200	C₂×C₄₇	#2083	1	2	yes	—
201	C₂×C₄₇	#2093	1	1	yes	characteristic
202	C₂×C₄₇	#2095	1	1	yes	characteristic
203	C₂³×C₈	C₂×D₄₇	1	2	yes	—
204	C₂²×C₄⋊C₄	—	47	1	no	—
205	C₂²×C₄⋊C₄	—	47	2	no	—
206	C₂²×C₄⋊C₄	—	47	1	no	—
207	C₂²×C₄⋊C₄	—	94	2	no	—
208	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
209	C₂×#107	—	94	4	no	—
210	C₂×#107	—	94	4	no	—
211	C₂×#107	—	94	4	no	—
212	#384	—	94	4	no	—
213	C₂×#95	—	94	2	no	—
214	#340	—	94	4	no	—
215	#336	Dic₄₇	1	4	yes	complemented
216	C₄₇	#11324	1	1	yes	characteristic, complemented, Sylow
217	C₂³×C₄	—	94	2	no	—
218	C₂³×C₄	—	94	1	no	—
219	C₂³×C₄	—	94	1	no	—
220	C₂³×C₄	D₁₈₈	1	2	yes	—
221	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	Dic₉₄	1	4	yes	—
227	C₂²×C₈	D₁₈₈	1	4	yes	—
228	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
229	C₂×C₄⋊C₄	—	47	4	no	—
230	C₂×C₄⋊C₄	—	47	2	no	—
231	C₂×C₄⋊C₄	—	47	2	no	—
232	C₂×C₄⋊C₄	—	94	2	no	—
233	C₂×C₄⋊C₄	—	94	2	no	—
234	C₂×C₄⋊C₄	—	94	2	no	—
235	C₂×C₄⋊C₄	—	94	2	no	—
236	C₂×C₄⋊C₄	—	94	2	no	—
237	C₂×C₄⋊C₄	—	94	2	no	—
238	C₂×C₄⋊C₄	—	94	2	no	—
239	C₂×C₄⋊C₄	—	94	2	no	—
240	C₂×C₄⋊C₄	—	94	8	no	—
241	C₂×C₄⋊C₄	—	94	2	no	—
242	C₂×C₄⋊C₄	—	94	1	no	—
243	C₂×C₄⋊C₄	—	94	1	no	—
244	C₂×C₄⋊C₄	—	188	4	no	—
245	C₂×C₄⋊C₄	—	188	4	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	Dic₉₄	1	2	yes	—
249	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
250	#107	—	94	16	no	—
251	#95	—	188	4	no	—
252	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	94	4	no	—
258	C₂²×C₄	—	94	2	no	—
259	C₂²×C₄	—	94	2	no	—
260	C₂²×C₄	—	188	1	no	—
261	C₂²×C₄	—	188	2	no	—
262	C₂²×C₄	—	188	1	no	—
263	C₂²×C₄	—	188	2	no	—
264	C₂²×C₄	—	188	1	no	—
265	C₂²×C₄	—	188	1	no	—
266	C₂²×C₄	—	188	2	no	—
267	C₂²×C₄	—	188	2	no	—
268	C₂²×C₄	—	188	4	no	—
269	C₂²×C₄	—	188	4	no	—
270	C₂²×C₄	—	188	2	no	—
271	C₂²×C₄	—	188	2	no	—
272	C₂²×C₄	D₃₇₆	1	4	yes	—
273	C₂²×C₄	Dic₁₈₈	1	4	yes	—
274	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
275	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
276	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
278	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
279	C₂²×C₄	D₄×D₄₇	1	2	yes	—
280	C₂²×C₄	#10625352	1	2	yes	—
281	C₂²×C₄	#10625352	1	1	yes	characteristic
282	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
283	C₂²×C₄	#10625354	1	1	yes	characteristic
284	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	C₄⋊Dic₄₇	1	8	yes	complemented
292	C₄⋊C₄	—	94	4	no	—
293	C₄⋊C₄	—	94	4	no	—
294	C₄⋊C₄	—	94	4	no	—
295	C₄⋊C₄	—	94	4	no	—
296	C₄⋊C₄	—	188	16	no	—
297	C₄⋊C₄	—	188	2	no	—
298	C₄⋊C₄	—	188	2	no	—
299	C₄⋊C₄	—	188	2	no	—
300	C₄⋊C₄	—	188	2	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	4	no	—
303	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
304	C₂³	#13093994	1	1	yes	characteristic
305	C₂³	#13093999	1	1	yes	characteristic
306	C₂³	#13094004	1	1	yes	characteristic
307	C₂³	#13094008	1	1	yes	characteristic
308	C₂³	#13094021	1	1	yes	characteristic
309	C₂³	#13094024	1	1	yes	characteristic
310	C₂³	C₂×D₃₇₆	1	2	yes	—
311	C₂³	C₂×Dic₁₈₈	1	2	yes	—
312	C₂³	#13094052	1	2	yes	—
313	C₂³	#13094057	1	2	yes	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	376	1	no	—
321	C₂×C₄	—	376	1	no	—
322	C₂×C₄	—	376	2	no	—
323	C₂×C₄	—	376	2	no	—
324	C₂×C₄	—	376	1	no	—
325	C₂×C₄	—	376	2	no	—
326	C₂×C₄	—	376	1	no	—
327	C₂×C₄	—	376	4	no	—
328	C₂×C₄	—	376	2	no	—
329	C₂×C₄	—	188	8	no	—
330	C₂×C₄	—	188	2	no	—
331	C₂×C₄	—	188	4	no	—
332	C₂×C₄	—	188	2	no	—
333	C₂×C₄	—	188	4	no	—
334	C₂×C₄	—	188	4	no	—
335	C₂×C₄	#13093958	1	8	yes	complemented
336	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
337	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
338	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
339	C₂×C₄	Q₈×Dic₄₇	1	1	yes	characteristic
340	C₂×C₄	#13093994	1	2	yes	—
341	C₂×C₄	#13093999	1	2	yes	—
342	C₂×C₄	#13094001	1	2	yes	—
343	C₂×C₄	#13094001	1	2	yes	—
344	C₂×C₄	#13094001	1	2	yes	—
345	C₂×C₄	#13094004	1	2	yes	—
346	C₂×C₄	#13094008	1	2	yes	—
347	C₂×C₄	#13094015	1	2	yes	—
348	C₂×C₄	#13094015	1	1	yes	characteristic
349	C₂×C₄	#13094023	1	2	yes	—
350	C₂×C₄	#13094023	1	1	yes	characteristic
351	C₂×C₄	#13094024	1	2	yes	—
352	C₈	—	2	8	no	—
353	C₂²	#15688993	1	1	yes	characteristic
354	C₂²	#15688998	1	1	yes	characteristic
355	C₂²	#15689022	1	1	yes	characteristic
356	C₂²	#15689033	1	1	yes	characteristic
357	C₂²	#15689044	1	1	yes	characteristic
358	C₂²	#15689055	1	1	yes	characteristic
359	C₂²	#15689060	1	1	yes	characteristic
360	C₂²	C₂×#13093958	1	2	yes	—
361	C₂²	#15689165	1	2	yes	—
362	C₂²	#15689259	1	2	yes	—
363	C₂²	#15689281	1	2	yes	—
364	C₂²	#15689319	1	2	yes	—
365	C₂²	#15689334	1	2	yes	—
366	C₂²	#15689404	1	2	yes	—
367	C₂²	#15689419	1	2	yes	—
368	C₂²	#15689437	1	2	yes	—
369	C₂²	#15689459	1	2	yes	—
370	C₂²	#15689500	1	1	yes	characteristic
371	C₂²	#15689503	1	1	yes	characteristic
372	C₂²	#15689512	1	1	yes	characteristic
373	C₂²	#15689517	1	1	yes	characteristic
374	C₂²	#15689528	1	2	yes	—
375	C₂²	#15689532	1	2	yes	—
376	C₄	—	2	8	no	—
377	C₄	—	376	2	no	—
378	C₄	—	376	2	no	—
379	C₄	—	376	4	no	—
380	C₄	#15688998	1	2	yes	—
381	C₄	#15689022	1	2	yes	—
382	C₄	#15689044	1	2	yes	—
383	C₄	#15689055	1	2	yes	—
384	C₂	#20241653	1	1	yes	characteristic
385	C₂	#20243548	1	1	yes	characteristic
386	C₂	#20243556	1	1	yes	characteristic
387	C₂	#20243578	1	2	yes	—
388	C₂	#20244147	1	2	yes	—
389	C₂	#20244461	1	1	yes	characteristic
390	C₂	#20244490	1	1	yes	characteristic
391	C₂	#20244717	1	2	yes	—
392	C₂	#20244861	1	2	yes	—
393	C₂	#20244915	1	1	yes	characteristic
394	C₂	#20244925	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₁₈₈
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#336	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	#11324
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
18. C₄₇×#336	C₄	semidirect
93. C₂×C₈×C₄₇	C₄⋊C₄	semidirect
122. C₂×C₄×C₄₇	#107	semidirect
215. #336	Dic₄₇	semidirect
216. C₄₇	#11324	semidirect
291. C₂×C₈	C₄⋊Dic₄₇	semidirect
335. C₂×C₄	#13093958	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13093958	2
C₂×#15688993	2
C₂×#15688886	2
#20241618	2
C₂×C₄₇×#336	2
#11324	47