Subgroups — #26215871

Order 12032.

1438 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×#15689161	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13093956	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245980	C₂	1	2	yes	maximal
4	#20243421	C₂	1	4	yes	maximal, complemented
5	#20243413	C₂	1	4	yes	maximal, complemented
6	#20243108	C₂	1	2	yes	maximal, complemented
7	C₂²×#131×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#13093983	C₂²	1	2	yes	—
9	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	#15689161	—	2	4	no	—
11	C₂×#13093958	C₂²	1	2	yes	—
12	C₂×#13093956	—	2	4	no	—
13	C₂×#13093956	C₂²	1	2	yes	—
14	C₂×#13093956	C₂²	1	2	yes	—
15	C₂×#13093956	C₂²	1	2	yes	—
16	#15689030	—	2	2	no	—
17	#15689026	—	2	2	no	—
18	#15689003	—	2	4	no	—
19	#15688983	C₂²	1	8	yes	—
20	#15688886	C₂²	1	8	yes	—
21	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#131×C₄₇	—	2	4	no	—
23	C₂×#131×C₄₇	—	2	4	no	—
24	C₂×#131×C₄₇	C₄	1	8	yes	complemented
25	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
27	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
28	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂³×Dic₄₇	—	2	2	no	—
30	#13093983	—	2	4	no	—
31	#13093983	—	2	4	no	—
32	C₂×C₄⋊Dic₄₇	—	2	4	no	—
33	C₂×C₄⋊Dic₄₇	—	2	4	no	—
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
36	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
37	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
38	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
39	C₂×C₄×Dic₄₇	—	2	2	no	—
40	#13093958	—	2	4	no	—
41	#13093956	—	2	4	no	—
42	#13093956	—	2	4	no	—
43	#13093956	—	2	4	no	—
44	C₄₇⋊#95	—	2	8	no	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	—	2	2	no	—
49	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
50	C₂×#41×C₄₇	Q₈	1	4	yes	—
51	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₄₇	D₄	1	2	yes	—
53	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	#131×C₄₇	—	2	32	no	—
57	C₂×M₁₆×C₄₇	—	2	2	no	—
58	C₂×M₁₆×C₄₇	—	2	2	no	—
59	C₂×M₁₆×C₄₇	—	2	4	no	—
60	C₂×M₁₆×C₄₇	—	2	4	no	—
61	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
62	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
63	C₂²×C₈×C₄₇	—	2	4	no	—
64	C₂²×C₈×C₄₇	—	2	4	no	—
65	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
66	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
67	C₂²×C₈×C₄₇	D₄	1	4	yes	—
68	C₂²×C₈×C₄₇	D₄	1	4	yes	—
69	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
70	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
72	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
73	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
74	#41×C₄₇	—	2	8	no	—
75	#41×C₄₇	—	2	8	no	—
76	#41×C₄₇	—	2	8	no	—
77	#41×C₄₇	—	2	8	no	—
78	C₂×Q₈×C₄₇	—	2	2	no	—
79	C₂×Q₈×C₄₇	—	2	2	no	—
80	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
81	C₂×D₄×C₄₇	—	2	4	no	—
82	C₂×D₄×C₄₇	—	2	4	no	—
83	C₂×D₄×C₄₇	—	2	2	no	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	C₄⋊C₄	1	8	yes	—
86	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₄₇	#41	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₇	—	2	4	no	—
103	C₂²×Dic₄₇	—	2	4	no	—
104	C₂²×Dic₄₇	—	4	4	no	—
105	C₂²×Dic₄₇	—	8	4	no	—
106	M₁₆×C₄₇	—	2	8	no	—
107	M₁₆×C₄₇	—	2	16	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	16	no	—
111	C₂×C₈×C₄₇	C₂²⋊C₄	1	16	yes	complemented
112	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
119	C₂²⋊Dic₄₇	—	4	4	no	—
120	C₂²⋊Dic₄₇	—	8	8	no	—
121	C₄⋊Dic₄₇	—	2	4	no	—
122	C₄⋊Dic₄₇	—	2	4	no	—
123	C₄⋊Dic₄₇	—	2	4	no	—
124	C₄⋊Dic₄₇	—	2	4	no	—
125	C₄⋊Dic₄₇	—	4	4	no	—
126	C₄×Dic₄₇	—	4	4	no	—
127	C₂³×C₄₇	—	2	4	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	8	no	—
131	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
132	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
133	C₂³×C₄₇	#121	1	2	yes	—
134	C₂³×C₄₇	#121	1	2	yes	—
135	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₄₇	—	2	8	no	—
137	D₄×C₄₇	—	2	16	no	—
138	D₄×C₄₇	—	2	8	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
146	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	#117	1	4	yes	—
149	C₂×C₄×C₄₇	#121	1	2	yes	—
150	C₂×C₄×C₄₇	#121	1	2	yes	—
151	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
152	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	—	4	4	no	—
161	C₂×Dic₄₇	—	4	4	no	—
162	C₂×Dic₄₇	—	4	8	no	—
163	C₂×Dic₄₇	—	4	4	no	—
164	C₂×Dic₄₇	—	8	8	no	—
165	C₈×C₄₇	—	2	4	no	—
166	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
167	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
168	#20662	—	47	1	no	maximal, Sylow
169	C₂²×C₄₇	—	2	4	no	—
170	C₂²×C₄₇	—	2	4	no	—
171	C₂²×C₄₇	—	2	4	no	—
172	C₂²×C₄₇	—	2	8	no	—
173	C₂²×C₄₇	—	2	4	no	—
174	C₂²×C₄₇	—	4	4	no	—
175	C₂²×C₄₇	—	4	4	no	—
176	C₂²×C₄₇	#380	1	4	yes	—
177	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
180	C₂²×C₄₇	#577	1	4	yes	—
181	C₄×C₄₇	—	2	4	no	—
182	C₄×C₄₇	#380	1	4	yes	—
183	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
184	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
185	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
186	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
187	Dic₄₇	—	8	4	no	—
188	Dic₄₇	—	8	4	no	—
189	C₂²×#131	D₄₇	1	1	yes	characteristic
190	C₂×#427	—	47	1	no	—
191	C₂²×#106	—	47	1	no	—
192	#2311	—	47	2	no	—
193	#1809	—	47	4	no	—
194	#1807	—	47	4	no	—
195	#1736	—	47	2	no	—
196	C₂×C₄₇	—	2	4	no	—
197	C₂×C₄₇	—	4	4	no	—
198	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
199	C₂×C₄₇	#2912	1	2	yes	—
200	C₂×C₄₇	#3057	1	2	yes	—
201	C₂×C₄₇	#3060	1	2	yes	—
202	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
203	C₂×#131	—	2	4	no	—
204	C₂×#131	—	2	4	no	—
205	C₂×#131	Dic₄₇	1	8	yes	complemented
206	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
207	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
208	C₂³×C₈	C₂×D₄₇	1	2	yes	—
209	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
210	C₂×#117	—	47	2	no	—
211	C₂²×C₄⋊C₄	—	47	2	no	—
212	#427	—	94	4	no	—
213	C₂×#107	—	47	2	no	—
214	C₂×#106	—	47	2	no	—
215	C₂×#106	—	47	2	no	—
216	C₂×#106	—	47	2	no	—
217	C₂×#106	—	94	4	no	—
218	#391	—	94	2	no	—
219	#390	—	94	2	no	—
220	#386	—	94	4	no	—
221	#380	—	47	8	no	—
222	#340	—	47	8	no	—
223	C₄₇	#20662	1	1	yes	characteristic, complemented, Sylow
224	C₂×#41	—	2	2	no	—
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	2	2	no	—
228	C₂×#41	Dic₉₄	1	4	yes	—
229	C₂×#41	C₂×Dic₄₇	1	4	yes	—
230	C₂²×Q₈	D₁₈₈	1	1	yes	characteristic
231	C₂²×D₄	D₁₈₈	1	2	yes	—
232	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
233	C₂³×C₄	—	94	2	no	—
234	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
235	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
236	#131	—	2	32	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	—	2	4	no	—
241	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
242	C₂×M₁₆	C₂×Dic₄₇	1	8	yes	complemented
243	C₂²×C₈	—	2	4	no	—
244	C₂²×C₈	—	2	4	no	—
245	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
246	C₂²×C₈	C₂×Dic₄₇	1	8	yes	complemented
247	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
248	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
249	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
250	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
251	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
252	#117	—	94	4	no	—
253	#117	—	94	4	no	—
254	C₂×C₄⋊C₄	—	47	4	no	—
255	C₂×C₄⋊C₄	—	47	4	no	—
256	C₂×C₄⋊C₄	—	94	4	no	—
257	C₂×C₄⋊C₄	—	94	4	no	—
258	C₂×C₄⋊C₄	—	94	2	no	—
259	C₂×C₂²⋊C₄	—	94	8	no	—
260	C₂×C₂²⋊C₄	—	94	2	no	—
261	C₂×C₄²	—	94	2	no	—
262	#107	—	94	4	no	—
263	#106	—	94	4	no	—
264	#106	—	94	4	no	—
265	#106	—	94	4	no	—
266	#95	—	94	8	no	—
267	C₂⁴	C₂×D₁₈₈	1	2	yes	—
268	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
269	#41	—	2	8	no	—
270	#41	—	2	8	no	—
271	#41	—	2	8	no	—
272	#41	—	2	8	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	C₄⋊Dic₄₇	1	4	yes	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	C₄⋊Dic₄₇	1	8	yes	—
281	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	94	4	no	—
287	C₂²×C₄	—	94	4	no	—
288	C₂²×C₄	—	376	4	no	—
289	C₂²×C₄	—	188	4	no	—
290	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
291	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
292	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
293	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
294	C₂²×C₄	#10625350	1	2	yes	—
295	C₂²×C₄	#10625350	1	2	yes	—
296	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
297	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
298	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
300	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
301	M₁₆	—	2	8	no	—
302	M₁₆	—	2	16	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	16	no	—
306	C₂×C₈	C₂²⋊Dic₄₇	1	16	yes	complemented
307	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
308	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
309	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
310	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
311	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
312	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
313	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
314	C₄⋊C₄	—	94	4	no	—
315	C₄⋊C₄	—	94	4	no	—
316	C₄⋊C₄	—	94	4	no	—
317	C₄⋊C₄	—	94	4	no	—
318	C₄⋊C₄	—	188	4	no	—
319	C₂²⋊C₄	—	376	8	no	—
320	C₂²⋊C₄	—	188	4	no	—
321	C₄²	—	188	4	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	8	no	—
326	C₂³	C₂×C₄⋊Dic₄₇	1	4	yes	—
327	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
328	C₂³	#13093998	1	2	yes	—
329	C₂³	#13093998	1	2	yes	—
330	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
331	Q₈	—	2	8	no	—
332	D₄	—	2	16	no	—
333	D₄	—	2	8	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	376	8	no	—
341	C₂×C₄	—	188	4	no	—
342	C₂×C₄	—	188	4	no	—
343	C₂×C₄	—	188	4	no	—
344	C₂×C₄	—	188	8	no	—
345	C₂×C₄	—	188	4	no	—
346	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
347	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
348	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
349	C₂×C₄	#13093983	1	4	yes	—
350	C₂×C₄	#13093998	1	2	yes	—
351	C₂×C₄	#13093998	1	2	yes	—
352	C₂×C₄	#13094003	1	4	yes	—
353	C₂×C₄	#13094003	1	4	yes	—
354	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
358	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
359	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
360	C₈	—	2	4	no	—
361	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
362	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	8	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	#15688983	1	4	yes	—
371	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
372	C₂²	C₂×#13093998	1	1	yes	characteristic
373	C₂²	C₂×#13093998	1	1	yes	characteristic
374	C₂²	#15689935	1	4	yes	—
375	C₄	—	2	4	no	—
376	C₄	—	376	4	no	—
377	C₄	—	376	4	no	—
378	C₄	#15688983	1	4	yes	—
379	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
380	C₄	C₂×#13093983	1	1	yes	characteristic
381	C₄	C₂×#13094003	1	1	yes	characteristic
382	C₄	C₂×#13094003	1	1	yes	characteristic
383	C₂	—	2	4	no	—
384	C₂	—	4	4	no	—
385	C₂	C₂×#15688983	1	1	yes	characteristic
386	C₂	#20251983	1	2	yes	—
387	C₂	#20253027	1	2	yes	—
388	C₂	#20253050	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#131×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#131	D₄₇
hypocenter	C₄₇	#20662
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#41 ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
1. C₂×#15689161	C₂	semidirect
2. C₂²×#13093956	C₂	semidirect
4. #20243421	C₂	semidirect
5. #20243413	C₂	semidirect
6. #20243108	C₂	semidirect
24. C₂×#131×C₄₇	C₄	semidirect
62. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
66. C₂²×C₈×C₄₇	C₂×C₄	semidirect
111. C₂×C₈×C₄₇	C₂²⋊C₄	semidirect
205. C₂×#131	Dic₄₇	semidirect
223. C₄₇	#20662	semidirect
242. C₂×M₁₆	C₂×Dic₄₇	semidirect
246. C₂²×C₈	C₂×Dic₄₇	semidirect
306. C₂×C₈	C₂²⋊Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689161	2
C₂²×#13093956	2
#20245980	2
#20243421	2
#20243413	2
#20243108	2
C₂²×#131×C₄₇	2
#20662	47