Subgroups — #20252036

Order 6016.

384 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689591	C₂	1	1	yes	maximal, characteristic
2	#15689185	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689184	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689182	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689179	C₂	1	2	yes	maximal, complemented
6	#15689177	C₂	1	2	yes	maximal, complemented
7	#15689148	C₂	1	2	yes	maximal, complemented
8	#15689088	C₂	1	2	yes	maximal
9	C₄×#10625324	C₂	1	1	yes	maximal, characteristic, complemented
10	#97×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10625350	C₂²	1	1	yes	characteristic
13	C₂×#10625324	C₂²	1	2	yes	—
14	C₂×C₈×D₄₇	C₂²	1	2	yes	—
15	#13093989	C₄	1	2	yes	—
16	#13093986	C₄	1	2	yes	—
17	(C₂²⋊D₄₇)⋊C₄	C₄	1	2	yes	—
18	(C₂²⋊D₄₇)⋊C₄	C₄	1	2	yes	—
19	#13093981	C₂²	1	1	yes	characteristic
20	#13093981	C₂²	1	1	yes	characteristic
21	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₄²×D₄₇	C₂²	1	1	yes	characteristic
23	C₄²×D₄₇	C₂²	1	1	yes	characteristic
24	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
25	Dic₄₇⋊C₈	C₂²	1	2	yes	—
26	Dic₄₇⋊C₈	C₂²	1	2	yes	—
27	C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
28	(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
29	(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
30	#13093935	C₂²	1	1	yes	characteristic
31	#13093934	C₂²	1	2	yes	—
32	#13093934	C₂²	1	2	yes	—
33	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	#117×C₄₇	C₂²	1	1	yes	characteristic
35	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
36	C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
37	#97×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
43	#10625350	—	2	4	no	—
44	C₂×D₁₈₈	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₄₇	C₂×C₄	1	2	yes	—
46	C₂×C₄×D₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
48	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
49	C₂×Dic₉₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×C₄₇	C₂³	1	2	yes	—
51	C₂×C₈×C₄₇	C₂³	1	2	yes	—
52	C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
53	C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₄²×C₄₇	C₂³	1	1	yes	characteristic
55	C₄²×C₄₇	C₂³	1	1	yes	characteristic
56	(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
57	(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
58	Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
59	Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
60	C₄×Dic₄₇	C₂×C₄	1	2	yes	—
61	C₄×Dic₄₇	C₂×C₄	1	2	yes	—
62	C₄×Dic₄₇	C₂×C₄	1	2	yes	—
63	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
64	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
66	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
67	#10625324	—	2	4	no	—
68	C₈×D₄₇	—	2	4	no	—
69	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
70	C₂²×D₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×D₄₇	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₄×C₄₇	—	2	2	no	—
73	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
75	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
76	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
77	C₂²⋊D₄₇	—	2	2	no	—
78	C₂²⋊D₄₇	—	2	2	no	—
79	C₂×Dic₄₇	—	4	2	no	—
80	C₂×Dic₄₇	C₂²×C₄	1	2	yes	—
81	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂×Dic₄₇	C₂²×C₄	1	2	yes	—
83	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
84	D₁₈₈	—	2	2	no	—
85	C₄×D₄₇	—	2	2	no	—
86	C₄×D₄₇	—	4	2	no	—
87	C₄×D₄₇	—	4	2	no	—
88	C₄×D₄₇	#41	1	4	yes	—
89	Dic₉₄	—	2	2	no	—
90	C₈×C₄₇	—	2	2	no	—
91	C₈×C₄₇	—	2	2	no	—
92	C₄₇⋊C₈	—	2	2	no	—
93	C₄₇⋊C₈	—	2	2	no	—
94	C₂²×C₄₇	—	2	1	no	—
95	C₂²×C₄₇	—	2	2	no	—
96	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
97	C₂×D₄₇	—	2	2	no	—
98	C₂×D₄₇	—	2	1	no	—
99	C₂×D₄₇	—	2	2	no	—
100	C₂×D₄₇	#117	1	2	yes	—
101	C₄×C₄₇	—	2	1	no	—
102	C₄×C₄₇	—	2	2	no	—
103	C₄×C₄₇	—	2	2	no	—
104	C₄×C₄₇	C₂×#41	1	2	yes	—
105	Dic₄₇	—	2	1	no	—
106	Dic₄₇	—	2	2	no	—
107	Dic₄₇	—	2	2	no	—
108	Dic₄₇	#117	1	2	yes	—
109	#2923	—	47	1	no	maximal, Sylow
110	C₂×C₄₇	—	4	1	no	—
111	C₂×C₄₇	C₂×#117	1	1	yes	characteristic
112	C₂×C₄₇	#568	1	2	yes	—
113	D₄₇	—	2	2	no	—
114	D₄₇	—	4	1	no	—
115	C₄×#41	—	47	1	no	—
116	#433	—	47	1	no	—
117	#433	—	47	1	no	—
118	#433	—	47	1	no	—
119	#433	D₄₇	1	1	yes	characteristic, complemented
120	#432	—	47	2	no	—
121	#432	—	47	2	no	—
122	#424	—	47	2	no	—
123	#408	—	47	2	no	—
124	C₄×M₁₆	—	47	1	no	—
125	C₂×#97	—	47	1	no	—
126	C₄₇	#2923	1	1	yes	characteristic, complemented, Sylow
127	C₂×#41	—	47	1	no	—
128	C₂×M₁₆	—	47	2	no	—
129	C₂²×C₈	—	47	2	no	—
130	C₄×Q₈	—	47	2	no	—
131	C₄×D₄	—	47	2	no	—
132	C₄×D₄	—	47	2	no	—
133	C₄×D₄	—	47	2	no	—
134	#117	—	47	1	no	—
135	#117	—	47	1	no	—
136	#117	C₂×D₄₇	1	1	yes	characteristic
137	C₂×C₄²	—	47	1	no	—
138	C₂×C₄²	—	47	1	no	—
139	C₂×C₄²	—	47	1	no	—
140	C₄⋊C₈	—	47	2	no	—
141	C₄⋊C₈	—	47	2	no	—
142	C₄⋊C₈	—	47	2	no	—
143	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
144	C₂²⋊C₈	—	47	2	no	—
145	C₂²⋊C₈	—	47	2	no	—
146	C₂²⋊C₈	—	47	2	no	—
147	C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
148	#97	—	47	2	no	—
149	#97	—	47	2	no	—
150	#97	—	47	1	no	—
151	#97	C₂×D₄₇	1	1	yes	characteristic
152	C₄×C₈	—	47	1	no	—
153	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
154	#41	—	94	4	no	—
155	C₂×Q₈	—	47	1	no	—
156	C₂×D₄	—	47	1	no	—
157	C₂×D₄	—	47	1	no	—
158	C₂×D₄	—	47	1	no	—
159	C₂²×C₄	—	47	1	no	—
160	C₂²×C₄	—	47	2	no	—
161	C₂²×C₄	—	47	1	no	—
162	C₂²×C₄	—	47	2	no	—
163	C₂²×C₄	—	47	2	no	—
164	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
165	M₁₆	—	94	4	no	—
166	C₂×C₈	—	47	2	no	—
167	C₂×C₈	—	47	2	no	—
168	C₂×C₈	—	94	4	no	—
169	C₂×C₈	C₂²×D₄₇	1	2	yes	—
170	C₂×C₈	C₂²×D₄₇	1	2	yes	—
171	C₄⋊C₄	—	47	2	no	—
172	C₄⋊C₄	—	47	2	no	—
173	C₄⋊C₄	C₄×D₄₇	1	2	yes	—
174	C₂²⋊C₄	—	47	2	no	—
175	C₂²⋊C₄	—	47	2	no	—
176	C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
177	C₄²	—	47	2	no	—
178	C₄²	—	47	2	no	—
179	C₄²	—	47	2	no	—
180	C₄²	—	47	1	no	—
181	C₄²	—	47	1	no	—
182	C₄²	C₂²×D₄₇	1	1	yes	characteristic
183	C₄²	C₂²×D₄₇	1	1	yes	characteristic
184	C₂³	—	47	1	no	—
185	C₂³	—	47	1	no	—
186	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
187	Q₈	—	94	2	no	—
188	D₄	—	94	2	no	—
189	D₄	—	94	2	no	—
190	D₄	—	94	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	47	1	no	—
193	C₂×C₄	—	47	4	no	—
194	C₂×C₄	—	47	2	no	—
195	C₂×C₄	—	47	2	no	—
196	C₂×C₄	—	47	1	no	—
197	C₂×C₄	—	94	2	no	—
198	C₂×C₄	—	188	2	no	—
199	C₂×C₄	—	188	2	no	—
200	C₂×C₄	—	188	2	no	—
201	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
202	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
203	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
204	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
205	C₈	—	2	2	no	—
206	C₈	—	2	2	no	—
207	C₈	—	94	2	no	—
208	C₈	—	94	2	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	2	no	—
211	C₂²	—	47	2	no	—
212	C₂²	—	94	2	no	—
213	C₂²	—	94	1	no	—
214	C₂²	—	94	2	no	—
215	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	47	2	no	—
220	C₄	—	94	1	no	—
221	C₄	—	94	2	no	—
222	C₄	—	94	2	no	—
223	C₄	#41×D₄₇	1	2	yes	—
224	C₂	—	4	1	no	—
225	C₂	—	94	2	no	—
226	C₂	—	188	1	no	—
227	C₂	#117×D₄₇	1	1	yes	characteristic
228	C₂	#15689888	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₄
Fitting	C₄₇×#433	C₂
hypercenter	#433	D₄₇
hypocenter	C₄₇	#2923
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
2. #15689185	C₂	semidirect
3. #15689184	C₂	semidirect
4. #15689182	C₂	semidirect
5. #15689179	C₂	semidirect
6. #15689177	C₂	semidirect
7. #15689148	C₂	semidirect
9. C₄×#10625324	C₂	semidirect
10. #97×D₄₇	C₂	semidirect
11. C₄₇×#433	C₂	semidirect
119. #433	D₄₇	semidirect
126. C₄₇	#2923	semidirect