Subgroups — #26220755

Order 12032.

1162 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689150	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689079	C₂	1	1	yes	maximal, characteristic
3	#20244329	C₂	1	4	yes	maximal, complemented
4	#20244325	C₂	1	4	yes	maximal, complemented
5	#20243085	C₂	1	1	yes	maximal, characteristic
6	#20243085	C₂	1	1	yes	maximal, characteristic
7	#20243082	C₂	1	1	yes	maximal, characteristic
8	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	#15689150	—	2	4	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
16	#15689079	—	2	4	no	—
17	C₂×#13093935	C₂²	1	2	yes	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
19	#15688878	C₂²	1	2	yes	—
20	#15688878	C₂²	1	2	yes	—
21	#15688878	C₂²	1	4	yes	—
22	#15688878	C₂²	1	4	yes	—
23	#15688878	C₂²	1	2	yes	—
24	#15688878	C₂²	1	2	yes	—
25	C₄₇×#533	—	2	4	no	—
26	C₄₇×#533	—	2	4	no	—
27	C₂×C₄⋊Q₈×C₄₇	C₄	1	2	yes	—
28	C₂×#125×C₄₇	C₄	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₄₇	C₄	1	4	yes	—
30	C₂×C₄×Q₈×C₄₇	C₂²	1	4	yes	—
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	Q₈	1	4	yes	complemented
40	C₂²×C₄₇⋊C₈	—	2	2	no	—
41	C₂²×C₄₇⋊C₈	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	complemented
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
52	#13093935	—	2	4	no	—
53	C₄×C₄₇⋊C₈	—	2	4	no	—
54	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
55	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₄₇	—	2	8	no	—
58	#125×C₄₇	—	2	8	no	—
59	C₂²⋊Q₈×C₄₇	—	2	16	no	—
60	C₄×Q₈×C₄₇	—	2	8	no	—
61	C₄×Q₈×C₄₇	—	2	8	no	—
62	#117×C₄₇	—	2	2	no	—
63	#117×C₄₇	—	2	2	no	—
64	#117×C₄₇	D₄	1	4	yes	—
65	#117×C₄₇	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
68	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₄₇	—	2	2	no	—
73	C₂×C₄²×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
79	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂×Q₈×C₄₇	—	2	8	no	—
81	C₂×Q₈×C₄₇	—	2	8	no	—
82	C₂×Q₈×C₄₇	—	4	4	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₄₇	#41	1	2	yes	—
96	C₂²×C₄×C₄₇	#41	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₄⋊C₄×C₄₇	—	2	4	no	—
99	C₄⋊C₄×C₄₇	—	2	16	no	—
100	C₄⋊C₄×C₄₇	—	2	8	no	—
101	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
102	C₂²⋊C₄×C₄₇	—	2	4	no	—
103	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
104	C₄²×C₄₇	—	2	2	no	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	—	2	2	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	C₂×D₄	1	4	yes	—
111	C₄²×C₄₇	C₂×D₄	1	4	yes	—
112	#10625329	—	2	8	no	—
113	#10625329	—	4	4	no	—
114	C₂×C₄₇⋊C₈	—	2	8	no	—
115	C₂×C₄₇⋊C₈	—	2	1	no	—
116	C₂×C₄₇⋊C₈	—	2	2	no	—
117	C₂×C₄₇⋊C₈	—	2	1	no	—
118	C₂×C₄₇⋊C₈	—	2	1	no	—
119	C₂×C₄₇⋊C₈	—	2	1	no	—
120	C₂×C₄₇⋊C₈	—	2	2	no	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	4	4	no	—
128	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
129	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
130	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
135	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
136	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
137	Q₈×C₄₇	—	4	16	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	4	8	no	—
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
152	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
154	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₄₇	#124	1	4	yes	—
156	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
157	C₂×C₄×C₄₇	#131	1	4	yes	—
158	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₄₇⋊C₈	—	2	2	no	—
165	C₄₇⋊C₈	—	2	2	no	—
166	C₄₇⋊C₈	—	2	4	no	—
167	C₄₇⋊C₈	—	4	2	no	—
168	C₄₇⋊C₈	—	4	2	no	—
169	#21304	—	47	1	no	maximal, Sylow
170	C₂²×C₄₇	—	2	4	no	—
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	2	4	no	—
174	C₂²×C₄₇	#391	1	4	yes	—
175	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
177	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#131	1	2	yes	—
179	C₂²×C₄₇	#568	1	2	yes	—
180	C₄×C₄₇	—	2	4	no	—
181	C₄×C₄₇	—	2	8	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	4	4	no	—
184	C₄×C₄₇	#391	1	4	yes	—
185	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
186	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
187	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
188	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
189	C₂×#533	D₄₇	1	1	yes	characteristic
190	C₂×#424	—	47	1	no	—
191	C₂×#405	—	47	1	no	—
192	#1985	—	47	4	no	—
193	#1984	—	47	4	no	—
194	#1729	—	47	1	no	—
195	#1729	—	47	1	no	—
196	#1728	—	47	1	no	—
197	C₂×#336	—	47	1	no	—
198	C₂×C₄₇	—	2	4	no	—
199	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
200	C₂×C₄₇	#2880	1	2	yes	—
201	C₂×C₄₇	#2960	1	1	yes	characteristic
202	C₂×C₄₇	#2961	1	1	yes	characteristic
203	C₂×C₄₇	#2962	1	2	yes	—
204	C₂²×M₁₆	—	47	1	no	—
205	C₂²×M₁₆	—	47	1	no	—
206	C₂³×C₈	—	47	1	no	—
207	C₂³×C₈	—	47	1	no	—
208	#533	—	2	4	no	—
209	#533	—	2	4	no	—
210	C₂×C₄⋊Q₈	Dic₄₇	1	2	yes	—
211	C₂×#125	Dic₄₇	1	2	yes	—
212	C₂×C₂²⋊Q₈	Dic₄₇	1	4	yes	—
213	C₂×C₄×Q₈	C₂×D₄₇	1	4	yes	—
214	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
215	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
216	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
217	#424	—	94	4	no	—
218	C₂×C₄⋊C₈	—	47	4	no	—
219	#405	—	94	4	no	—
220	C₂×#97	—	47	2	no	—
221	C₂×C₄×C₈	—	47	2	no	—
222	#336	—	47	2	no	—
223	#336	—	47	2	no	—
224	#336	—	47	4	no	—
225	#336	—	47	2	no	—
226	#336	—	47	4	no	—
227	#336	—	47	2	no	—
228	C₄₇	#21304	1	1	yes	characteristic, complemented, Sylow
229	C₂²×Q₈	C₂×Dic₄₇	1	4	yes	—
230	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
231	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
232	C₂×M₁₆	—	47	4	no	—
233	C₂×M₁₆	—	94	2	no	—
234	C₂×M₁₆	—	94	2	no	—
235	C₂×M₁₆	—	94	2	no	—
236	C₂×M₁₆	—	94	2	no	—
237	C₂×M₁₆	—	94	2	no	—
238	C₂²×C₈	—	47	4	no	—
239	C₂²×C₈	—	47	1	no	—
240	C₂²×C₈	—	47	1	no	—
241	C₂²×C₈	—	47	2	no	—
242	C₂²×C₈	—	47	2	no	—
243	C₂²×C₈	—	47	2	no	—
244	C₂²×C₈	—	94	2	no	—
245	C₂²×C₈	—	94	2	no	—
246	C₂²×C₈	—	94	2	no	—
247	C₂²×C₈	—	94	2	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₄⋊Q₈	—	2	8	no	—
250	#125	—	2	8	no	—
251	C₂²⋊Q₈	—	2	16	no	—
252	C₄×Q₈	—	2	8	no	—
253	C₄×Q₈	—	2	8	no	—
254	#117	—	2	2	no	—
255	#117	—	2	2	no	—
256	#117	C₂²⋊D₄₇	1	4	yes	—
257	#117	C₂²⋊D₄₇	1	4	yes	—
258	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
260	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
261	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
267	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
269	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
270	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
271	C₄⋊C₈	—	94	8	no	—
272	#97	—	94	4	no	—
273	C₄×C₈	—	94	4	no	—
274	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
275	C₂×Q₈	—	2	8	no	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
282	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
283	C₂²×C₄	#10625354	1	2	yes	—
284	C₂²×C₄	#10625354	1	2	yes	—
285	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
286	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
287	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
288	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
289	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
291	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
292	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
293	M₁₆	—	94	8	no	—
294	M₁₆	—	188	4	no	—
295	C₂×C₈	—	47	2	no	—
296	C₂×C₈	—	47	2	no	—
297	C₂×C₈	—	47	4	no	—
298	C₂×C₈	—	94	8	no	—
299	C₂×C₈	—	94	1	no	—
300	C₂×C₈	—	94	2	no	—
301	C₂×C₈	—	94	1	no	—
302	C₂×C₈	—	94	1	no	—
303	C₂×C₈	—	94	1	no	—
304	C₂×C₈	—	94	2	no	—
305	C₂×C₈	—	94	2	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	94	2	no	—
308	C₂×C₈	—	94	2	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	—	94	2	no	—
311	C₂×C₈	—	188	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	16	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	C₂²⋊Dic₄₇	1	8	yes	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	C₂²⋊Dic₄₇	1	8	yes	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
325	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
329	C₂³	Q₈×Dic₄₇	1	2	yes	—
330	C₂³	Q₈×Dic₄₇	1	2	yes	—
331	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
332	Q₈	—	4	16	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	8	yes	—
345	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
346	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
347	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
348	C₂×C₄	#13094000	1	4	yes	—
349	C₂×C₄	#13094000	1	4	yes	—
350	C₂×C₄	#13094013	1	4	yes	—
351	C₂×C₄	#13094022	1	4	yes	—
352	C₂×C₄	#13094031	1	4	yes	—
353	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
358	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
359	C₈	—	94	2	no	—
360	C₈	—	94	2	no	—
361	C₈	—	94	4	no	—
362	C₈	—	188	2	no	—
363	C₈	—	188	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	4	no	—
368	C₂²	#15689030	1	4	yes	—
369	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
370	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
371	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
372	C₂²	C₂×#13094031	1	2	yes	—
373	C₂²	#15689890	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	2	8	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	4	no	—
378	C₄	#15689030	1	4	yes	—
379	C₄	C₂×#13094000	1	1	yes	characteristic
380	C₄	C₂×#13094000	1	1	yes	characteristic
381	C₄	C₂×#13094013	1	1	yes	characteristic
382	C₄	C₂×#13094022	1	1	yes	characteristic
383	C₂	—	2	4	no	—
384	C₂	C₂×#15689030	1	1	yes	characteristic
385	C₂	#20251837	1	2	yes	—
386	C₂	#20252323	1	1	yes	characteristic
387	C₂	#20252329	1	1	yes	characteristic
388	C₂	#20252337	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₂×C₄₇×#533	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	#21304
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #20244329	C₂	semidirect
4. #20244325	C₂	semidirect
39. C₂×#10625329	Q₈	semidirect
45. C₂²×C₄₇⋊C₈	Q₈	semidirect
228. C₄₇	#21304	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689150	2
C₂×#15689079	2
#20244329	2
#20244325	2
#20243085	2
#20243082	2
C₂×#15688878	2
C₂×C₄₇×#533	2
#21304	47