Subgroups — #26219739

Order 12032.

1026 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×#15689159	C₂	1	2	yes	maximal
2	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
4	#20244154	C₂	1	4	yes	maximal, complemented
5	#20244149	C₂	1	2	yes	maximal, complemented
6	#20244144	C₂	1	2	yes	maximal, complemented
7	#20243104	C₂	1	2	yes	maximal
8	C₄₇×#2285	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
10	C₂×#13093983	C₂²	1	1	yes	characteristic
11	C₂×#13093983	C₂²	1	1	yes	characteristic
12	#15689159	—	2	8	no	—
13	C₂×#13093957	C₂²	1	4	yes	—
14	C₂×#13093955	C₂²	1	4	yes	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	8	yes	complemented
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
21	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
22	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
23	#15688969	—	2	1	no	—
24	C₄²×Dic₄₇	—	2	1	no	—
25	#15688885	C₂²	1	4	yes	—
26	#15688885	C₂²	1	4	yes	—
27	C₂×#117×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#384	C₂²	1	2	yes	—
30	C₄₇×#382	C₂²	1	2	yes	—
31	C₄₇×#380	—	2	1	no	—
32	C₄₇×#380	—	2	1	no	—
33	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
34	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
35	C₂²×C₄₇⋊C₈	—	2	4	no	—
36	C₂²×C₄₇⋊C₈	—	2	4	no	—
37	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
38	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
39	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
40	#13093983	—	2	2	no	—
41	#13093983	—	2	2	no	—
42	#13093983	D₄	1	4	yes	—
43	#13093983	Q₈	1	4	yes	—
44	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
46	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
47	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
48	C₂×C₄×Dic₄₇	—	2	1	no	—
49	C₂×C₄×Dic₄₇	—	2	1	no	—
50	C₂×C₄×Dic₄₇	—	2	2	no	—
51	C₂×C₄×Dic₄₇	—	2	2	no	—
52	#13093957	—	2	8	no	—
53	#13093955	—	2	8	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
55	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	—
57	C₄₇⋊#95	—	2	2	no	—
58	C₄₇⋊#95	—	2	2	no	—
59	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	#117×C₄₇	—	2	4	no	—
63	#117×C₄₇	—	2	4	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	#95×C₄₇	—	2	2	no	—
76	#95×C₄₇	—	2	2	no	—
77	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	4	2	no	—
81	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
82	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	#41	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₄⋊C₄×C₄₇	—	2	4	no	—
98	C₄⋊C₄×C₄₇	—	2	4	no	—
99	C₄⋊C₄×C₄₇	—	4	4	no	—
100	C₄⋊C₄×C₄₇	—	4	4	no	—
101	C₂²⋊C₄×C₄₇	—	4	4	no	—
102	C₄²×C₄₇	—	4	4	no	—
103	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
104	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
105	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
106	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
107	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
108	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
109	C₂²⋊Dic₄₇	—	2	4	no	—
110	C₂²⋊Dic₄₇	—	2	4	no	—
111	C₄⋊Dic₄₇	—	2	2	no	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
114	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	—
115	C₄×Dic₄₇	—	2	4	no	—
116	C₄×Dic₄₇	—	2	4	no	—
117	C₄×Dic₄₇	—	4	4	no	—
118	C₄×Dic₄₇	—	4	4	no	—
119	C₂×C₄₇⋊C₈	—	2	16	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	C₂²×C₄	1	4	yes	—
125	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
129	C₂³×C₄₇	#121	1	2	yes	—
130	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
131	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	8	no	—
136	C₂×C₄×C₄₇	—	4	4	no	—
137	C₂×C₄×C₄₇	—	4	4	no	—
138	C₂×C₄×C₄₇	—	4	4	no	—
139	C₂×C₄×C₄₇	—	4	4	no	—
140	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
146	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
147	C₂×C₄×C₄₇	#121	1	2	yes	—
148	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₄₇	#125	1	4	yes	—
150	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
151	C₂×C₄×C₄₇	#135	1	4	yes	—
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×Dic₄₇	—	2	4	no	—
159	C₂×Dic₄₇	—	2	4	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₄₇⋊C₈	—	2	4	no	—
165	C₄₇⋊C₈	—	2	4	no	—
166	#21169	—	47	1	no	maximal, Sylow
167	C₂²×C₄₇	—	2	4	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	2	4	no	—
171	C₂²×C₄₇	#389	1	4	yes	—
172	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×#135	1	2	yes	—
176	C₂²×C₄₇	#575	1	2	yes	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	8	4	no	—
181	C₄×C₄₇	#389	1	4	yes	—
182	C₄×C₄₇	#427	1	4	yes	complemented
183	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
184	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
185	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
186	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
187	Dic₄₇	—	4	4	no	—
188	Dic₄₇	—	4	4	no	—
189	C₂×#427	—	47	2	no	—
190	C₂²×C₄⋊C₈	—	47	1	no	—
191	#2285	D₄₇	1	1	yes	characteristic
192	C₄×#117	—	47	1	no	—
193	#1949	—	47	4	no	—
194	#1948	—	47	2	no	—
195	#1947	—	47	2	no	—
196	#1735	—	47	2	no	—
197	C₂×C₄₇	—	2	4	no	—
198	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#427	1	1	yes	characteristic
200	C₂×C₄₇	#2911	1	1	yes	characteristic
201	C₂×C₄₇	#3035	1	2	yes	—
202	C₂×C₄₇	#3076	1	2	yes	—
203	C₂³×C₈	—	47	2	no	—
204	C₂×#117	—	47	1	no	—
205	C₂×#117	—	47	1	no	—
206	C₂×#117	C₂×D₄₇	1	2	yes	—
207	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
208	#427	—	94	8	no	—
209	C₂×#107	—	47	4	no	—
210	C₂×#106	—	47	4	no	—
211	C₂×C₄⋊C₈	—	47	8	no	—
212	C₂×C₄⋊C₈	—	47	1	no	—
213	C₂×C₄⋊C₈	—	47	1	no	—
214	C₂×C₄⋊C₈	—	47	2	no	—
215	#384	C₂×D₄₇	1	2	yes	—
216	#382	C₂×D₄₇	1	2	yes	—
217	#380	—	2	1	no	—
218	#380	—	2	1	no	—
219	C₄×C₄⋊C₄	—	2	1	no	—
220	C₄×C₄⋊C₄	—	2	1	no	—
221	C₄×C₄⋊C₄	—	47	2	no	—
222	C₄×C₄⋊C₄	—	47	2	no	—
223	C₄×C₂²⋊C₄	—	94	1	no	—
224	C₄×C₂²⋊C₄	—	94	1	no	—
225	#376	—	94	1	no	—
226	C₄³	—	94	1	no	—
227	#340	—	47	4	no	—
228	#340	—	47	4	no	—
229	C₄₇	#21169	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
231	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
232	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
233	C₂²×C₈	—	47	8	no	—
234	C₂²×C₈	—	47	2	no	—
235	C₂²×C₈	—	47	2	no	—
236	C₂²×C₈	—	94	4	no	—
237	C₂²×C₈	—	94	4	no	—
238	#117	—	2	4	no	—
239	#117	—	2	4	no	—
240	#117	—	47	4	no	—
241	#117	—	47	4	no	—
242	#117	—	94	2	no	—
243	#117	—	94	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	47	2	no	—
247	C₂×C₄⋊C₄	—	47	2	no	—
248	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	94	1	no	—
251	C₂×C₂²⋊C₄	—	94	1	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	94	1	no	—
254	C₂×C₄²	—	94	1	no	—
255	C₂×C₄²	—	94	2	no	—
256	C₂×C₄²	—	94	2	no	—
257	C₂×C₄²	Dic₉₄	1	4	yes	—
258	C₂×C₄²	C₄×D₄₇	1	4	yes	—
259	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
260	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
261	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
263	#107	—	94	8	no	—
264	#106	—	94	8	no	—
265	C₄⋊C₈	—	47	4	no	—
266	C₄⋊C₈	—	47	4	no	—
267	C₄⋊C₈	—	47	8	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	94	2	no	—
271	#95	—	94	2	no	—
272	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	94	2	no	—
277	C₂²×C₄	—	94	2	no	—
278	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
279	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
280	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
281	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
282	C₂²×C₄	D₄×D₄₇	1	2	yes	—
283	C₂²×C₄	#10625352	1	2	yes	—
284	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
285	C₂²×C₄	#10625354	1	2	yes	—
286	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
292	C₂×C₈	—	47	4	no	—
293	C₂×C₈	—	47	4	no	—
294	C₂×C₈	—	94	16	no	—
295	C₂×C₈	—	94	2	no	—
296	C₂×C₈	—	94	2	no	—
297	C₂×C₈	—	94	2	no	—
298	C₂×C₈	—	94	2	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	4	4	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₄⋊C₄	—	47	4	no	—
304	C₄⋊C₄	—	47	4	no	—
305	C₄⋊C₄	—	94	2	no	—
306	C₄⋊C₄	—	94	2	no	—
307	C₂²⋊C₄	—	4	4	no	—
308	C₂²⋊C₄	—	94	4	no	—
309	C₂²⋊C₄	—	94	4	no	—
310	C₄²	—	4	4	no	—
311	C₄²	—	94	4	no	—
312	C₄²	—	94	4	no	—
313	C₄²	—	188	4	no	—
314	C₄²	—	188	4	no	—
315	C₄²	Dic₄₇⋊C₄	1	4	yes	—
316	C₄²	Dic₄₇⋊C₄	1	4	yes	—
317	C₄²	C₂×Dic₉₄	1	2	yes	—
318	C₄²	C₂×Dic₉₄	1	2	yes	—
319	C₄²	C₂×C₄×D₄₇	1	2	yes	—
320	C₄²	C₂×C₄×D₄₇	1	2	yes	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
324	C₂³	#13093995	1	2	yes	—
325	C₂³	#13094000	1	2	yes	—
326	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	94	4	no	—
336	C₂×C₄	—	94	4	no	—
337	C₂×C₄	—	188	2	no	—
338	C₂×C₄	—	188	2	no	—
339	C₂×C₄	—	188	2	no	—
340	C₂×C₄	—	188	2	no	—
341	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
342	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
343	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
344	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
345	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
346	C₂×C₄	#13093986	1	4	yes	—
347	C₂×C₄	#13093989	1	4	yes	—
348	C₂×C₄	#13093995	1	2	yes	—
349	C₂×C₄	#13094000	1	2	yes	—
350	C₂×C₄	#13094015	1	4	yes	—
351	C₂×C₄	#13094023	1	4	yes	—
352	C₂×C₄	#13094044	1	4	yes	—
353	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
357	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
358	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
359	C₈	—	94	4	no	—
360	C₈	—	94	4	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	#15689019	1	4	yes	—
366	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
367	C₂²	C₂×#13093995	1	1	yes	characteristic
368	C₂²	C₂×#13094000	1	1	yes	characteristic
369	C₂²	C₂×#13094044	1	2	yes	—
370	C₂²	#15689921	1	2	yes	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	8	4	no	—
375	C₄	—	188	4	no	—
376	C₄	—	188	4	no	—
377	C₄	#15689019	1	4	yes	—
378	C₄	#15689159	1	4	yes	complemented
379	C₄	C₂×#13093986	1	1	yes	characteristic
380	C₄	C₂×#13093989	1	1	yes	characteristic
381	C₄	C₂×#13094015	1	1	yes	characteristic
382	C₄	C₂×#13094023	1	1	yes	characteristic
383	C₂	—	2	4	no	—
384	C₂	C₂×#15689019	1	1	yes	characteristic
385	C₂	C₂×#15689159	1	1	yes	characteristic
386	C₂	#20251977	1	1	yes	characteristic
387	C₂	#20252837	1	2	yes	—
388	C₂	#20253170	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2285	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2285	D₄₇
hypocenter	C₄₇	#21169
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ #2285

Complements

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

N	H ≅ G/N	type
4. #20244154	C₂	semidirect
5. #20244149	C₂	semidirect
6. #20244144	C₂	semidirect
15. C₂×C₄⋊(C₄₇⋊C₈)	C₄	semidirect
182. C₄×C₄₇	#427	semidirect
229. C₄₇	#21169	semidirect
378. C₄	#15689159	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689159	2
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₄×#13093983	2
#20244154	2
#20244149	2
#20244144	2
#20243104	2
C₄₇×#2285	2
#21169	47