Subgroups — #26378851

Order 12032.

2124 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246488	C₂	1	6	yes	maximal
2	#20246448	C₂	1	3	yes	maximal
3	Q₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₄⋊Dic₄₇	C₂	1	2	yes	maximal
5	Q₈×C₄⋊Dic₄₇	C₂	1	3	yes	maximal
6	#20246130	C₂	1	6	yes	maximal
7	C₄⋊Q₈×Dic₄₇	C₂	1	3	yes	maximal
8	#20245866	C₂	1	3	yes	maximal
9	#20245753	C₂	1	2	yes	maximal
10	C₄×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄₇×#557	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
14	C₂×Q₈×Dic₄₇	C₂²	1	6	yes	—
15	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	#15689030	C₂²	1	3	yes	—
17	#15689030	C₂²	1	3	yes	—
18	#15689022	C₂²	1	3	yes	—
19	#15689022	C₂²	1	6	yes	—
20	#15689022	C₂²	1	6	yes	—
21	#15689022	C₂²	1	12	yes	—
22	#15689022	C₂²	1	6	yes	—
23	#15689022	C₂²	1	1	yes	characteristic
24	#15689022	C₂²	1	6	yes	—
25	#15689009	C₂²	1	6	yes	—
26	#15689009	C₂²	1	6	yes	—
27	#15689009	C₂²	1	12	yes	—
28	#15688993	C₂²	1	6	yes	—
29	#15688993	C₂²	1	3	yes	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	3	yes	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	6	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	6	yes	—
33	C₄⋊C₄×Dic₄₇	C₂²	1	6	yes	—
34	C₄⋊C₄×Dic₄₇	C₂²	1	3	yes	—
35	C₄×C₄⋊Dic₄₇	C₂²	1	3	yes	—
36	C₄×C₄⋊Dic₄₇	C₂²	1	6	yes	—
37	C₄×C₄⋊Dic₄₇	C₂²	1	3	yes	—
38	C₄×C₄⋊Dic₄₇	C₂²	1	6	yes	—
39	#15688969	C₂²	1	6	yes	—
40	C₄²×Dic₄₇	C₂²	1	3	yes	—
41	C₄₇×#557	C₄	1	16	yes	complemented
42	C₂×C₄⋊Q₈×C₄₇	C₂²	1	3	yes	—
43	C₂×#125×C₄₇	C₂²	1	6	yes	—
44	C₂×C₄×Q₈×C₄₇	C₂²	1	3	yes	—
45	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
47	Q₈×Dic₄₇	—	2	4	no	—
48	Q₈×Dic₄₇	—	2	8	no	—
49	Q₈×Dic₄₇	—	4	12	no	—
50	Q₈×Dic₄₇	Q₈	1	8	yes	complemented
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
62	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
63	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
64	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
65	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
66	C₂×C₄×Dic₄₇	C₂³	1	12	yes	—
67	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
68	C₄₇⋊#95	C₂³	1	2	yes	—
69	C₄₇⋊#95	C₂³	1	6	yes	—
70	C₄₇⋊#95	C₂³	1	6	yes	—
71	C₄₇⋊#95	C₂³	1	6	yes	—
72	C₄₇⋊#95	C₂³	1	6	yes	—
73	C₄₇⋊#95	C₂³	1	6	yes	—
74	C₄₇⋊#95	C₂³	1	6	yes	—
75	C₄₇⋊#95	C₂³	1	6	yes	—
76	C₂²×Q₈×C₄₇	C₂³	1	3	yes	—
77	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₄₇	C₂×C₄	1	24	yes	—
79	#125×C₄₇	C₂×C₄	1	48	yes	—
80	C₄×Q₈×C₄₇	C₂×C₄	1	16	yes	—
81	C₄×Q₈×C₄₇	C₂×C₄	1	24	yes	—
82	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
87	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	6	yes	—
90	C₂×Q₈×C₄₇	—	2	6	no	—
91	C₂×Q₈×C₄₇	—	2	6	no	—
92	C₂×Q₈×C₄₇	C₂²×C₄	1	12	yes	—
93	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
94	C₂×Q₈×C₄₇	C₂×Q₈	1	4	yes	—
95	C₂×Q₈×C₄₇	#41	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
98	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
99	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
100	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
102	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
103	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
104	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
106	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
107	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
108	C₄⋊C₄×C₄₇	C₂²×C₄	1	24	yes	—
109	C₄⋊C₄×C₄₇	C₂²×C₄	1	12	yes	—
110	C₄⋊C₄×C₄₇	C₂²×C₄	1	24	yes	—
111	C₄⋊C₄×C₄₇	C₂²×C₄	1	24	yes	—
112	C₄²×C₄₇	C₂²×C₄	1	24	yes	—
113	C₄²×C₄₇	C₂²×C₄	1	12	yes	—
114	C₄⋊Dic₄₇	—	2	6	no	—
115	C₄⋊Dic₄₇	—	2	12	no	—
116	C₄⋊Dic₄₇	—	2	6	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	—	2	4	no	—
119	C₄⋊Dic₄₇	—	4	6	no	—
120	C₄⋊Dic₄₇	—	4	6	no	—
121	C₄⋊Dic₄₇	—	4	12	no	—
122	C₄⋊Dic₄₇	C₂×Q₈	1	12	yes	—
123	C₄×Dic₄₇	—	2	6	no	—
124	C₄×Dic₄₇	—	2	12	no	—
125	C₄×Dic₄₇	—	2	6	no	—
126	C₄×Dic₄₇	—	2	2	no	—
127	C₄×Dic₄₇	—	2	6	no	—
128	C₄×Dic₄₇	—	4	3	no	—
129	C₄×Dic₄₇	—	4	12	no	—
130	C₄×Dic₄₇	C₂×Q₈	1	12	yes	—
131	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
132	Q₈×C₄₇	—	2	24	no	—
133	Q₈×C₄₇	C₄×Q₈	1	16	yes	complemented
134	C₂×C₄×C₄₇	—	2	6	no	—
135	C₂×C₄×C₄₇	—	2	3	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	6	no	—
138	C₂×C₄×C₄₇	—	2	3	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
141	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
142	C₂×C₄×C₄₇	C₂³×C₄	1	12	yes	—
143	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
144	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₂²×Q₈	1	6	yes	—
146	C₂×C₄×C₄₇	C₂×#41	1	6	yes	—
147	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
148	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
149	C₂×Dic₄₇	—	2	1	no	—
150	C₂×Dic₄₇	—	2	3	no	—
151	C₂×Dic₄₇	—	2	3	no	—
152	C₂×Dic₄₇	—	2	1	no	—
153	C₂×Dic₄₇	—	2	1	no	—
154	C₂×Dic₄₇	—	2	1	no	—
155	C₂×Dic₄₇	—	2	2	no	—
156	C₂×Dic₄₇	—	2	3	no	—
157	C₂×Dic₄₇	—	2	6	no	—
158	C₂×Dic₄₇	—	2	3	no	—
159	C₂×Dic₄₇	—	2	6	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	3	no	—
163	C₂×Dic₄₇	—	2	6	no	—
164	C₂×Dic₄₇	C₂²×Q₈	1	2	yes	—
165	C₂×Dic₄₇	C₂²×Q₈	1	6	yes	—
166	C₂×Dic₄₇	2₋¹⁺⁴	1	2	yes	—
167	#34337	—	47	1	no	maximal, Sylow
168	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
169	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
170	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
171	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
174	C₂²×C₄₇	#585	1	1	yes	characteristic
175	C₄×C₄₇	—	2	12	no	—
176	C₄×C₄₇	—	2	6	no	—
177	C₄×C₄₇	—	2	4	no	—
178	C₄×C₄₇	C₂×C₄×Q₈	1	12	yes	—
179	C₄×C₄₇	#520	1	4	yes	—
180	Dic₄₇	—	2	2	no	—
181	Dic₄₇	—	2	6	no	—
182	Dic₄₇	—	2	2	no	—
183	Dic₄₇	—	4	3	no	—
184	Dic₄₇	—	4	6	no	—
185	Dic₄₇	—	4	2	no	—
186	C₂×#557	D₄₇	1	1	yes	characteristic
187	#2370	—	47	6	no	—
188	#2365	—	47	3	no	—
189	Q₈×C₄⋊C₄	—	47	2	no	—
190	Q₈×C₄⋊C₄	—	47	1	no	—
191	Q₈×C₄⋊C₄	—	47	3	no	—
192	#2330	—	47	6	no	—
193	C₄×C₄⋊Q₈	—	47	3	no	—
194	#2295	—	47	3	no	—
195	#2276	—	47	2	no	—
196	C₄²×Q₈	—	47	1	no	—
197	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
198	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
199	C₂×C₄₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
200	C₂×C₄₇	#3502	1	1	yes	characteristic
201	C₂×C₄₇	#3503	1	1	yes	characteristic
202	C₂×C₄₇	#3517	1	1	yes	characteristic
203	C₂×C₄₇	#3523	1	1	yes	characteristic
204	#557	Dic₄₇	1	16	yes	complemented
205	C₂×C₄⋊Q₈	C₂×D₄₇	1	3	yes	—
206	C₂×#125	C₂×D₄₇	1	6	yes	—
207	C₂×C₄×Q₈	—	47	1	no	—
208	C₂×C₄×Q₈	—	47	1	no	—
209	C₂×C₄×Q₈	—	47	2	no	—
210	C₂×C₄×Q₈	—	47	6	no	—
211	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
213	C₂×C₄×Q₈	C₂×D₄₇	1	3	yes	—
214	#391	—	47	3	no	—
215	#391	—	47	3	no	—
216	#389	—	47	6	no	—
217	#389	—	47	6	no	—
218	#389	—	47	6	no	—
219	#389	—	47	12	no	—
220	#389	—	47	6	no	—
221	#389	—	47	3	no	—
222	#389	—	47	1	no	—
223	#387	—	47	6	no	—
224	#387	—	47	12	no	—
225	#387	—	47	6	no	—
226	#384	—	47	3	no	—
227	#384	—	47	6	no	—
228	C₄×C₄⋊C₄	—	47	6	no	—
229	C₄×C₄⋊C₄	—	47	6	no	—
230	C₄×C₄⋊C₄	—	47	3	no	—
231	C₄×C₄⋊C₄	—	47	6	no	—
232	C₄×C₄⋊C₄	—	47	3	no	—
233	C₄×C₄⋊C₄	—	47	3	no	—
234	C₄×C₄⋊C₄	—	47	3	no	—
235	C₄×C₄⋊C₄	—	47	6	no	—
236	C₄×C₄⋊C₄	—	47	6	no	—
237	#376	—	47	6	no	—
238	C₄³	—	47	3	no	—
239	C₄₇	#34337	1	1	yes	characteristic, complemented, Sylow
240	C₂²×Q₈	C₂²×D₄₇	1	3	yes	—
241	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
242	C₄⋊Q₈	C₂×Dic₄₇	1	24	yes	—
243	#125	C₂×Dic₄₇	1	48	yes	—
244	C₄×Q₈	—	47	8	no	—
245	C₄×Q₈	—	94	4	no	—
246	C₄×Q₈	—	94	8	no	—
247	C₄×Q₈	—	188	12	no	—
248	C₄×Q₈	C₂×Dic₄₇	1	16	yes	—
249	C₄×Q₈	C₂×Dic₄₇	1	24	yes	—
250	C₄×Q₈	C₂×Dic₄₇	1	8	yes	—
251	C₂×C₄⋊C₄	—	47	3	no	—
252	C₂×C₄⋊C₄	—	47	3	no	—
253	C₂×C₄⋊C₄	—	47	3	no	—
254	C₂×C₄⋊C₄	—	47	6	no	—
255	C₂×C₄⋊C₄	—	47	2	no	—
256	C₂×C₄⋊C₄	—	47	1	no	—
257	C₂×C₄⋊C₄	—	47	12	no	—
258	C₂×C₄⋊C₄	—	47	6	no	—
259	C₂×C₄⋊C₄	—	47	6	no	—
260	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂²×D₄₇	1	3	yes	—
262	C₂×C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
263	C₂×C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
264	C₂×C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
265	C₂×C₄²	—	47	3	no	—
266	C₂×C₄²	—	47	3	no	—
267	C₂×C₄²	—	47	3	no	—
268	C₂×C₄²	—	47	6	no	—
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	3	no	—
271	C₂×C₄²	—	47	12	no	—
272	C₂×C₄²	—	47	3	no	—
273	C₂×C₄²	C₂²×D₄₇	1	6	yes	—
274	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
275	#95	—	47	2	no	—
276	#95	—	47	6	no	—
277	#95	—	47	6	no	—
278	#95	—	47	6	no	—
279	#95	—	47	6	no	—
280	#95	—	47	6	no	—
281	#95	—	47	6	no	—
282	#95	—	47	6	no	—
283	C₂×Q₈	—	2	6	no	—
284	C₂×Q₈	—	2	6	no	—
285	C₂×Q₈	Q₈×D₄₇	1	4	yes	—
286	C₂×Q₈	#10625354	1	4	yes	—
287	C₂×Q₈	C₂²×Dic₄₇	1	12	yes	—
288	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
289	C₂²×C₄	—	47	1	no	—
290	C₂²×C₄	—	47	3	no	—
291	C₂²×C₄	—	47	1	no	—
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	—	47	3	no	—
294	C₂²×C₄	—	47	6	no	—
295	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
296	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
297	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
298	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
299	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
300	C₄⋊C₄	—	47	12	no	—
301	C₄⋊C₄	—	94	4	no	—
302	C₄⋊C₄	—	94	6	no	—
303	C₄⋊C₄	—	94	12	no	—
304	C₄⋊C₄	—	94	6	no	—
305	C₄⋊C₄	—	94	2	no	—
306	C₄⋊C₄	—	188	6	no	—
307	C₄⋊C₄	—	188	6	no	—
308	C₄⋊C₄	—	188	12	no	—
309	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
310	C₄⋊C₄	C₂²×Dic₄₇	1	24	yes	—
311	C₄⋊C₄	C₂²×Dic₄₇	1	12	yes	—
312	C₄⋊C₄	C₂²×Dic₄₇	1	24	yes	—
313	C₄⋊C₄	C₂²×Dic₄₇	1	24	yes	—
314	C₄²	—	47	12	no	—
315	C₄²	—	94	6	no	—
316	C₄²	—	94	6	no	—
317	C₄²	—	94	12	no	—
318	C₄²	—	94	6	no	—
319	C₄²	—	94	2	no	—
320	C₄²	—	188	3	no	—
321	C₄²	—	188	12	no	—
322	C₄²	C₂²×Dic₄₇	1	24	yes	—
323	C₄²	C₂²×Dic₄₇	1	12	yes	—
324	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
325	Q₈	—	2	24	no	—
326	Q₈	Q₈×Dic₄₇	1	16	yes	complemented
327	C₂×C₄	—	2	6	no	—
328	C₂×C₄	—	2	3	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	6	no	—
331	C₂×C₄	—	2	3	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	47	2	no	—
334	C₂×C₄	—	47	6	no	—
335	C₂×C₄	—	47	2	no	—
336	C₂×C₄	—	94	1	no	—
337	C₂×C₄	—	94	3	no	—
338	C₂×C₄	—	94	3	no	—
339	C₂×C₄	—	94	1	no	—
340	C₂×C₄	—	94	1	no	—
341	C₂×C₄	—	94	1	no	—
342	C₂×C₄	—	94	2	no	—
343	C₂×C₄	—	94	3	no	—
344	C₂×C₄	—	94	6	no	—
345	C₂×C₄	—	94	3	no	—
346	C₂×C₄	—	94	6	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	94	2	no	—
349	C₂×C₄	—	94	3	no	—
350	C₂×C₄	—	94	6	no	—
351	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
352	C₂×C₄	C₂³×Dic₄₇	1	6	yes	—
353	C₂×C₄	C₂³×Dic₄₇	1	12	yes	—
354	C₂×C₄	C₂³×Dic₄₇	1	6	yes	—
355	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
356	C₂×C₄	C₂×Q₈×D₄₇	1	6	yes	—
357	C₂×C₄	C₂×#10625354	1	6	yes	—
358	C₂×C₄	#13094070	1	2	yes	—
359	C₂×C₄	#13094071	1	2	yes	—
360	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
361	C₂²	C₂²×Q₈×D₄₇	1	1	yes	characteristic
362	C₂²	C₂²×#10625354	1	1	yes	characteristic
363	C₂²	C₂×#13094070	1	1	yes	characteristic
364	C₂²	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
365	C₂²	C₂×#13094071	1	1	yes	characteristic
366	C₂²	#15689960	1	1	yes	characteristic
367	C₄	—	2	12	no	—
368	C₄	—	2	6	no	—
369	C₄	—	2	4	no	—
370	C₄	—	94	2	no	—
371	C₄	—	94	6	no	—
372	C₄	—	94	2	no	—
373	C₄	—	188	3	no	—
374	C₄	—	188	6	no	—
375	C₄	—	188	2	no	—
376	C₄	C₂×Q₈×Dic₄₇	1	12	yes	—
377	C₄	#15689606	1	4	yes	—
378	C₂	C₂²×Q₈×Dic₄₇	1	1	yes	characteristic
379	C₂	C₂×#15689606	1	1	yes	characteristic
380	C₂	2₋¹⁺⁴×Dic₄₇	1	1	yes	characteristic
381	C₂	#20257192	1	1	yes	characteristic
382	C₂	#20257205	1	1	yes	characteristic
383	C₂	#20257395	1	1	yes	characteristic
384	C₂	#20257485	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂×C₄₇×#557	C₂
socle, prime radical, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#557	D₄₇
hypocenter	C₄₇	#34337
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#557

Complements

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

N	H ≅ G/N	type
41. C₄₇×#557	C₄	semidirect
50. Q₈×Dic₄₇	Q₈	semidirect
133. Q₈×C₄₇	C₄×Q₈	semidirect
204. #557	Dic₄₇	semidirect
239. C₄₇	#34337	semidirect
326. Q₈	Q₈×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246488	2
#20246448	2
Q₈×C₄⋊Dic₄₇	2
#20246130	2
C₄⋊Q₈×Dic₄₇	2
#20245866	2
#20245753	2
C₄×Q₈×Dic₄₇	2
C₂×C₄₇×#557	2
#34337	47