Subgroups — C₂×#20242068 #26184618

Order 12032.

1246 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094024	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
3	#20242068	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688871	C₂	1	4	yes	maximal, complemented
5	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₉₄	C₄	1	2	yes	—
7	C₂²×#10625329	—	2	1	no	—
8	C₂×#13094024	—	2	1	no	—
9	C₂×#13094024	—	2	2	no	—
10	C₂×#13094024	—	2	1	no	—
11	C₂×#13094024	—	2	2	no	—
12	C₂×#13094024	C₄	1	4	yes	—
13	C₂×#13094024	C₄	1	2	yes	—
14	C₂×#13094024	C₂²	1	2	yes	—
15	C₂×#13094024	C₂²	1	4	yes	—
16	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
17	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
18	#15689147	—	2	2	no	—
19	#15689147	C₂²	1	4	yes	—
20	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
22	#15688871	C₂²	1	16	yes	complemented
23	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#431	—	2	2	no	—
25	C₄₇×#431	C₂²	1	4	yes	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
28	C₂×C₄×C₈×C₄₇	—	2	1	no	—
29	C₂²×Dic₉₄	—	2	4	no	—
30	C₂²×Dic₉₄	—	2	2	no	—
31	C₂²×Dic₉₄	—	4	8	no	—
32	C₂²×Dic₉₄	C₂×C₄	1	4	yes	—
33	C₂²×Dic₉₄	C₂×C₄	1	8	yes	—
34	C₂³×Dic₄₇	—	2	2	no	—
35	C₂×#10625329	—	2	4	no	—
36	C₂×#10625329	—	4	4	no	—
37	C₂²×C₄₇⋊C₈	—	2	2	no	—
38	#13094024	—	2	4	no	—
39	#13094024	—	2	4	no	—
40	#13094024	—	2	4	no	—
41	#13094024	—	2	2	no	—
42	#13094024	—	2	4	no	—
43	#13094024	—	2	2	no	—
44	#13094024	—	2	4	no	—
45	#13094024	C₂×C₄	1	4	yes	—
46	#13094024	C₂×C₄	1	8	yes	—
47	#13094024	C₂³	1	4	yes	—
48	C₂×C₄⋊Dic₄₇	—	2	2	no	—
49	C₂×C₄⋊Dic₄₇	—	2	4	no	—
50	C₂×C₄⋊Dic₄₇	—	2	4	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	—	2	4	no	—
53	C₂×C₄⋊Dic₄₇	—	2	2	no	—
54	C₂×C₄⋊Dic₄₇	—	2	4	no	—
55	C₂×C₄⋊Dic₄₇	—	2	2	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
58	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
59	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₄₇	—	2	2	no	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	D₄	1	2	yes	—
67	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	D₄	1	2	yes	—
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
71	C₄⋊C₈×C₄₇	—	2	2	no	—
72	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
73	C₂²⋊C₈×C₄₇	—	2	4	no	—
74	C₄×C₈×C₄₇	—	2	4	no	—
75	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	—	2	4	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
85	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×Dic₄₇	—	2	8	no	—
93	C₂²×Dic₄₇	—	2	4	no	—
94	C₂²×Dic₄₇	—	4	8	no	—
95	C₂×Dic₉₄	—	2	4	no	—
96	C₂×Dic₉₄	—	2	8	no	—
97	C₂×Dic₉₄	—	4	16	no	—
98	C₂×Dic₉₄	—	4	8	no	—
99	C₂×Dic₉₄	—	4	8	no	—
100	C₂×Dic₉₄	—	4	16	no	—
101	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
102	C₂×C₈×C₄₇	—	2	4	no	—
103	C₂×C₈×C₄₇	—	4	4	no	—
104	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
105	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
106	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
107	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
108	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₄₇	C₂×D₄	1	2	yes	—
110	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₄₇	C₂×D₄	1	2	yes	—
113	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
114	C₄⋊Dic₄₇	—	2	8	no	—
115	C₄⋊Dic₄₇	—	2	4	no	—
116	C₄⋊Dic₄₇	—	2	8	no	—
117	C₄⋊Dic₄₇	—	2	4	no	—
118	C₄⋊Dic₄₇	—	2	4	no	—
119	C₄⋊Dic₄₇	—	2	4	no	—
120	#10625329	—	4	8	no	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	—	4	4	no	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	#103	1	4	yes	—
126	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
127	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	#100	1	4	yes	—
135	C₂×C₄×C₄₇	#103	1	8	yes	—
136	C₂×C₄×C₄₇	#103	1	4	yes	—
137	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
145	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
146	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
147	C₂×C₄×C₄₇	#137	1	4	yes	—
148	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×Dic₄₇	—	2	8	no	—
152	C₂×Dic₄₇	—	4	16	no	—
153	C₂×Dic₄₇	—	4	8	no	—
154	Dic₉₄	—	4	8	no	—
155	Dic₉₄	—	4	16	no	—
156	Dic₉₄	—	4	8	no	—
157	C₈×C₄₇	—	4	4	no	—
158	C₄₇⋊C₈	—	4	4	no	—
159	C₂×#1548	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	—	2	8	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	2	no	—
163	C₂²×C₄₇	C₂×#100	1	2	yes	—
164	C₂²×C₄₇	C₂×#103	1	4	yes	—
165	C₂²×C₄₇	C₂×#103	1	2	yes	—
166	C₂²×C₄₇	#419	1	2	yes	—
167	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
168	C₄×C₄₇	—	2	1	no	—
169	C₄×C₄₇	—	2	1	no	—
170	C₄×C₄₇	—	2	2	no	—
171	C₄×C₄₇	C₂×#100	1	4	yes	—
172	C₄×C₄₇	C₂×#103	1	2	yes	—
173	C₄×C₄₇	C₂×#103	1	4	yes	—
174	C₄×C₄₇	#419	1	2	yes	—
175	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
176	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
177	C₄×C₄₇	C₂×#137	1	2	yes	—
178	Dic₄₇	—	4	8	no	—
179	C₂²×C₄⋊Q₈	—	47	1	no	—
180	C₂×#431	D₄₇	1	1	yes	characteristic
181	C₂×#423	—	47	1	no	—
182	#1548	—	47	8	no	—
183	C₂×#333	—	47	4	no	—
184	C₂×C₄₇	—	2	4	no	—
185	C₂×C₄₇	#1548	1	4	yes	complemented
186	C₂×C₄₇	C₂²×#100	1	1	yes	characteristic
187	C₂×C₄₇	C₂²×#103	1	1	yes	characteristic
188	C₂×C₄₇	C₂×#419	1	1	yes	characteristic
189	C₂³×Q₈	—	47	2	no	—
190	C₂²×M₁₆	—	94	1	no	—
191	C₂×C₄⋊Q₈	—	47	4	no	—
192	C₂×C₄⋊Q₈	—	47	2	no	—
193	C₂×C₄⋊Q₈	—	47	2	no	—
194	C₂×C₄⋊Q₈	—	47	4	no	—
195	C₂×C₄⋊Q₈	—	94	1	no	—
196	C₂×C₄⋊Q₈	—	94	2	no	—
197	C₂×C₄⋊Q₈	—	94	1	no	—
198	C₂×C₄⋊Q₈	—	94	2	no	—
199	C₂²×C₄⋊C₄	—	94	1	no	—
200	C₂²×C₄⋊C₄	—	94	1	no	—
201	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
202	#431	—	2	2	no	—
203	#431	C₂×D₄₇	1	4	yes	—
204	#423	—	47	4	no	—
205	#423	—	94	2	no	—
206	C₂×C₄⋊C₈	—	47	2	no	—
207	C₂×C₄⋊C₈	—	94	1	no	—
208	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
209	C₂×C₂²⋊C₈	—	2	1	no	—
210	C₂×C₄×C₈	—	2	1	no	—
211	#333	—	47	16	no	—
212	C₄₇	C₂×#1548	1	1	yes	characteristic, complemented, Sylow
213	C₂²×Q₈	—	47	8	no	—
214	C₂²×Q₈	—	47	4	no	—
215	C₂²×Q₈	—	94	4	no	—
216	C₂²×Q₈	—	94	2	no	—
217	C₂²×Q₈	—	188	8	no	—
218	C₂³×C₄	—	94	2	no	—
219	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
220	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
221	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
222	C₂×M₁₆	—	94	4	no	—
223	C₂×M₁₆	—	188	4	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	94	2	no	—
226	C₄⋊Q₈	—	47	4	no	—
227	C₄⋊Q₈	—	47	8	no	—
228	C₄⋊Q₈	—	47	4	no	—
229	C₄⋊Q₈	—	94	4	no	—
230	C₄⋊Q₈	—	94	4	no	—
231	C₄⋊Q₈	—	94	4	no	—
232	C₄⋊Q₈	—	94	2	no	—
233	C₄⋊Q₈	—	94	4	no	—
234	C₄⋊Q₈	—	94	4	no	—
235	C₄⋊Q₈	—	94	2	no	—
236	C₂×C₄⋊C₄	—	94	4	no	—
237	C₂×C₄⋊C₄	—	94	4	no	—
238	C₂×C₄⋊C₄	—	94	2	no	—
239	C₂×C₄⋊C₄	—	94	2	no	—
240	C₂×C₄⋊C₄	—	94	4	no	—
241	C₂×C₄⋊C₄	—	94	2	no	—
242	C₂×C₄⋊C₄	—	94	4	no	—
243	C₂×C₄⋊C₄	—	94	2	no	—
244	C₂×C₄²	C₄×D₄₇	1	2	yes	—
245	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
246	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
247	C₂×C₄²	D₁₈₈	1	2	yes	—
248	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
250	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
251	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	47	4	no	—
254	C₄⋊C₈	—	94	2	no	—
255	C₄⋊C₈	—	94	4	no	—
256	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
257	C₂²⋊C₈	—	2	4	no	—
258	C₄×C₈	—	2	4	no	—
259	C₂⁴	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
260	C₂×Q₈	—	47	8	no	—
261	C₂×Q₈	—	94	4	no	—
262	C₂×Q₈	—	94	8	no	—
263	C₂×Q₈	—	188	16	no	—
264	C₂×Q₈	—	188	16	no	—
265	C₂×Q₈	—	188	8	no	—
266	C₂×Q₈	—	188	8	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	94	8	no	—
270	C₂²×C₄	—	94	4	no	—
271	C₂²×C₄	—	188	8	no	—
272	C₂²×C₄	#10625325	1	4	yes	—
273	C₂²×C₄	Dic₁₈₈	1	4	yes	—
274	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
275	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
276	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
279	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
281	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
283	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
286	M₁₆	—	188	8	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	4	4	no	—
289	C₂×C₈	—	94	4	no	—
290	C₂×C₈	—	188	4	no	—
291	C₄⋊C₄	—	94	8	no	—
292	C₄⋊C₄	—	94	8	no	—
293	C₄⋊C₄	—	94	4	no	—
294	C₄⋊C₄	—	94	4	no	—
295	C₄⋊C₄	—	94	4	no	—
296	C₄⋊C₄	—	94	4	no	—
297	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
298	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
299	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
300	C₄²	C₂×C₄×D₄₇	1	2	yes	—
301	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
302	C₄²	C₂×D₁₈₈	1	2	yes	—
303	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
304	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
305	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
306	C₄²	C₂³×D₄₇	1	1	yes	characteristic
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	#13093949	1	4	yes	—
310	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
311	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
312	Q₈	—	188	8	no	—
313	Q₈	—	188	8	no	—
314	Q₈	—	188	16	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	94	8	no	—
322	C₂×C₄	—	188	16	no	—
323	C₂×C₄	—	188	8	no	—
324	C₂×C₄	#13093940	1	4	yes	—
325	C₂×C₄	#13093949	1	8	yes	—
326	C₂×C₄	#13093949	1	4	yes	—
327	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
328	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
330	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
331	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×#10625325	1	2	yes	—
334	C₂×C₄	C₂×#10625325	1	4	yes	—
335	C₂×C₄	C₂×Dic₁₈₈	1	4	yes	—
336	C₂×C₄	C₂×Dic₁₈₈	1	2	yes	—
337	C₂×C₄	#13094054	1	4	yes	—
338	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
339	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
341	C₈	—	4	4	no	—
342	C₈	—	188	4	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	C₂×#13093940	1	2	yes	—
347	C₂²	C₂×#13093949	1	4	yes	—
348	C₂²	C₂×#13093949	1	2	yes	—
349	C₂²	#15689131	1	2	yes	—
350	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	—	188	8	no	—
355	C₄	C₂×#13093940	1	4	yes	—
356	C₄	C₂×#13093949	1	2	yes	—
357	C₄	C₂×#13093949	1	4	yes	—
358	C₄	#15689131	1	2	yes	—
359	C₄	C₂²×#10625325	1	1	yes	characteristic
360	C₄	C₂²×Dic₁₈₈	1	1	yes	characteristic
361	C₄	C₂×#13094054	1	2	yes	—
362	C₂	—	2	4	no	—
363	C₂	#20242068	1	4	yes	direct product factor
364	C₂	C₂²×#13093940	1	1	yes	characteristic
365	C₂	C₂²×#13093949	1	1	yes	characteristic
366	C₂	C₂×#15689131	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#431	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×#431	D₄₇
hypocenter	C₄₇	C₂×#1548
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #20242068	C₂	direct (N × H)
4. C₂×#15688871	C₂	semidirect
22. #15688871	C₂²	semidirect
185. C₂×C₄₇	#1548	semidirect
212. C₄₇	C₂×#1548	semidirect
363. C₂	#20242068	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13094024	2
C₂×#15689147	2
#20242068	2
C₂×#15688871	2
C₂×C₄₇×#431	2
C₂×#1548	47

Subgroups — C2×#20242068 #26184618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242068 #26184618