Subgroups — D₁₈₁⋊#444 #37550492

Order 23168.

464 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₈₁⋊#131	C₂	1	2	yes	maximal, complemented
2	#26042326	C₂	1	2	yes	maximal, complemented
3	#26042325	C₂	1	2	yes	maximal, complemented
4	#26042324	C₂	1	4	yes	maximal, complemented
5	D₁₈₁⋊#108	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₈₁⋊#104	C₂	1	2	yes	maximal, complemented
7	C₂×#19153870	C₂	1	1	yes	maximal, characteristic, complemented
8	#135×D₁₈₁	C₂	1	1	yes	maximal, characteristic
9	#19153904	C₂²	1	4	yes	complemented
10	#19153903	—	2	4	no	—
11	#19153903	C₂²	1	4	yes	complemented
12	D₁₈₁⋊M₁₆	—	2	2	no	—
13	D₁₈₁⋊M₁₆	C₂²	1	2	yes	—
14	C₂×D₁₈₁⋊C₈	—	2	2	no	—
15	C₂×D₁₈₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×#10624382	C₂²	1	1	yes	characteristic
17	#19153887	C₂²	1	2	yes	complemented
18	#19153886	C₂²	1	2	yes	complemented
19	#19153881	C₂²	1	4	yes	complemented
20	#19153880	C₂²	1	4	yes	complemented
21	#19153870	C₂²	1	2	yes	complemented
22	#19153870	C₂²	1	2	yes	complemented
23	#41×D₁₈₁	C₂²	1	2	yes	—
24	#19153839	C₂²	1	1	yes	characteristic
25	#19153838	C₄	1	1	yes	characteristic, complemented
26	#19153837	C₂²	1	2	yes	—
27	#19153836	C₄	1	2	yes	complemented
28	#19153835	C₂²	1	1	yes	characteristic
29	Q₁₆×D₁₈₁	C₄	1	1	yes	characteristic, complemented
30	SD₁₆×D₁₈₁	C₄	1	2	yes	complemented
31	D₈×D₁₈₁	C₄	1	1	yes	characteristic, complemented
32	C₂×C₈×D₁₈₁	C₂²	1	1	yes	characteristic
33	#135×C₁₈₁	C₄	1	1	yes	characteristic, complemented
34	C₂²×#10624382	—	2	1	no	—
35	#15668459	—	2	4	no	—
36	#15668459	C₂³	1	4	yes	—
37	#15668458	—	2	4	no	—
38	#15668458	—	2	2	no	—
39	D₁₈₁⋊C₈	—	2	4	no	—
40	D₁₈₁⋊C₈	—	2	2	no	—
41	D₁₈₁⋊C₈	D₄	1	2	yes	—
42	D₁₈₁⋊C₈	C₂³	1	2	yes	—
43	C₂×#13089685	—	2	4	no	—
44	C₂×#13089685	D₄	1	2	yes	—
45	C₄×#10624382	—	2	1	no	—
46	C₄×#10624382	C₂³	1	2	yes	—
47	#15668450	C₂³	1	2	yes	—
48	#15668449	—	2	2	no	—
49	#15668449	C₂×C₄	1	2	yes	—
50	#15668448	—	2	2	no	—
51	#15668448	C₂³	1	2	yes	—
52	Q₈×D₁₈₁	C₂×C₄	1	2	yes	—
53	D₄×D₁₈₁	—	2	2	no	—
54	D₄×D₁₈₁	C₂×C₄	1	2	yes	—
55	C₂×C₄×D₁₈₁	—	2	2	no	—
56	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
57	Dic₇₂₄	C₂×C₄	1	1	yes	characteristic, complemented
58	#15668439	C₂×C₄	1	2	yes	complemented
59	#15668438	C₂×C₄	1	2	yes	complemented
60	#15668437	C₂×C₄	1	2	yes	complemented
61	#15668436	C₂×C₄	1	2	yes	complemented
62	D₁₄₄₈	C₂×C₄	1	1	yes	characteristic, complemented
63	#15668434	C₂×C₄	1	2	yes	complemented
64	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
65	C₈×D₁₈₁	C₂×C₄	1	1	yes	characteristic
66	C₈×D₁₈₁	C₂×C₄	1	1	yes	characteristic
67	C₈×D₁₈₁	C₂³	1	1	yes	characteristic
68	C₈×D₁₈₁	C₂³	1	1	yes	characteristic
69	#41×C₁₈₁	C₂×C₄	1	2	yes	—
70	Q₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic, complemented
71	SD₁₆×C₁₈₁	C₂×C₄	1	2	yes	complemented
72	D₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
74	C₂×#10624382	—	2	2	no	—
75	C₂×#10624382	—	4	2	no	—
76	#13089685	—	2	4	no	—
77	#13089685	C₂×D₄	1	4	yes	—
78	C₂²×D₁₈₁	—	2	2	no	—
79	C₂²×D₁₈₁	#41	1	1	yes	characteristic
80	Dic₃₆₂	—	2	2	no	—
81	Dic₃₆₂	C₂²×C₄	1	2	yes	—
82	D₇₂₄	—	2	2	no	—
83	D₇₂₄	C₂²×C₄	1	2	yes	—
84	C₂²⋊D₁₈₁	—	2	2	no	—
85	C₂²⋊D₁₈₁	—	2	2	no	—
86	C₂²⋊D₁₈₁	—	2	2	no	—
87	C₂×Dic₁₈₁	—	2	2	no	—
88	C₂×Dic₁₈₁	C₂×D₄	1	1	yes	characteristic
89	C₄×D₁₈₁	—	2	2	no	—
90	C₄×D₁₈₁	—	2	2	no	—
91	C₄×D₁₈₁	—	2	2	no	—
92	C₄×D₁₈₁	C₂²×C₄	1	1	yes	characteristic
93	C₄×D₁₈₁	C₂×D₄	1	1	yes	characteristic
94	C₄×D₁₈₁	#41	1	1	yes	characteristic
95	C₄×D₁₈₁	C₂⁴	1	1	yes	characteristic
96	#13089678	C₂²×C₄	1	1	yes	characteristic
97	#13089678	C₂²×C₄	1	1	yes	characteristic
98	Q₈×C₁₈₁	C₂²×C₄	1	2	yes	—
99	D₄×C₁₈₁	—	2	2	no	—
100	D₄×C₁₈₁	C₂²×C₄	1	2	yes	—
101	C₂×C₄×C₁₈₁	—	2	2	no	—
102	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
103	C₈×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
104	C₈×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₁₈₁	—	2	2	no	—
106	C₂²×C₁₈₁	C₄×D₄	1	1	yes	characteristic
107	C₂×D₁₈₁	—	2	2	no	—
108	C₂×D₁₈₁	—	2	2	no	—
109	C₂×D₁₈₁	—	4	4	no	—
110	C₂×D₁₈₁	C₄×D₄	1	1	yes	characteristic
111	C₂×D₁₈₁	C₂×#41	1	1	yes	characteristic
112	#10624382	—	4	2	no	—
113	C₄×C₁₈₁	—	2	2	no	—
114	C₄×C₁₈₁	C₄×D₄	1	1	yes	characteristic
115	C₄×C₁₈₁	C₂³×C₄	1	1	yes	characteristic
116	Dic₁₈₁	—	2	2	no	—
117	Dic₁₈₁	C₄×D₄	1	1	yes	characteristic
118	Dic₁₈₁	C₂²×D₄	1	1	yes	characteristic
119	C₂×C₁₈₁	—	2	1	no	—
120	C₂×C₁₈₁	—	4	2	no	—
121	C₂×C₁₈₁	C₂×C₄×D₄	1	1	yes	characteristic
122	D₁₈₁	—	2	1	no	—
123	D₁₈₁	—	4	2	no	—
124	D₁₈₁	#444	1	2	yes	complemented
125	C₁₈₁	C₂×#444	1	1	yes	characteristic, complemented, Sylow
126	C₂×#444	—	181	1	no	maximal, Sylow
127	C₂×#135	—	181	1	no	—
128	C₂×#131	—	181	2	no	—
129	#444	—	181	4	no	—
130	#444	—	181	2	no	—
131	#444	—	181	2	no	—
132	C₂×#108	—	181	1	no	—
133	C₂×#104	—	181	2	no	—
134	C₂×#97	—	181	1	no	—
135	C₂×#41	—	181	2	no	—
136	#135	—	181	2	no	—
137	#135	—	181	1	no	—
138	#135	—	181	2	no	—
139	#135	—	181	1	no	—
140	#135	—	181	1	no	—
141	#135	#10624382	1	1	yes	characteristic, complemented
142	C₂×Q₁₆	—	181	1	no	—
143	C₂×SD₁₆	—	181	2	no	—
144	C₂×D₈	—	181	1	no	—
145	#131	—	362	4	no	—
146	#131	—	181	4	no	—
147	#131	—	181	4	no	—
148	C₂×M₁₆	—	362	2	no	—
149	C₂×M₁₆	—	181	2	no	—
150	C₂²×C₈	—	362	2	no	—
151	C₂²×C₈	—	181	1	no	—
152	C₂²×C₈	—	181	1	no	—
153	C₂×C₄²	—	181	1	no	—
154	#108	—	181	2	no	—
155	#108	—	181	2	no	—
156	#104	—	181	4	no	—
157	#104	—	181	4	no	—
158	#97	—	181	2	no	—
159	#97	—	181	2	no	—
160	#41	—	362	2	no	—
161	#41	—	362	2	no	—
162	#41	—	181	2	no	—
163	#41	—	181	2	no	—
164	#41	—	181	2	no	—
165	#41	C₂×#10624382	1	2	yes	—
166	C₂×Q₈	—	181	2	no	—
167	C₂×D₄	—	362	2	no	—
168	C₂×D₄	—	181	2	no	—
169	C₂²×C₄	—	362	2	no	—
170	C₂²×C₄	—	362	1	no	—
171	C₂²×C₄	—	181	1	no	—
172	Q₁₆	—	181	2	no	—
173	Q₁₆	—	181	1	no	—
174	Q₁₆	C₂×#10624382	1	1	yes	characteristic, complemented
175	SD₁₆	—	181	2	no	—
176	SD₁₆	—	181	2	no	—
177	SD₁₆	—	181	2	no	—
178	SD₁₆	C₂×#10624382	1	2	yes	complemented
179	D₈	—	181	2	no	—
180	D₈	—	181	1	no	—
181	D₈	C₂×#10624382	1	1	yes	characteristic, complemented
182	M₁₆	—	362	2	no	—
183	M₁₆	—	362	4	no	—
184	M₁₆	—	362	4	no	—
185	M₁₆	—	181	4	no	—
186	C₂×C₈	—	362	2	no	—
187	C₂×C₈	—	362	4	no	—
188	C₂×C₈	—	362	4	no	—
189	C₂×C₈	—	181	2	no	—
190	C₂×C₈	—	181	2	no	—
191	C₂×C₈	—	181	2	no	—
192	C₂×C₈	—	181	1	no	—
193	C₂×C₈	—	181	1	no	—
194	C₂×C₈	—	181	1	no	—
195	C₂×C₈	—	181	1	no	—
196	C₂×C₈	—	181	1	no	—
197	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
198	C₄²	—	362	1	no	—
199	C₄²	—	181	2	no	—
200	C₂³	—	362	2	no	—
201	C₂³	—	181	1	no	—
202	Q₈	—	362	2	no	—
203	Q₈	—	181	2	no	—
204	Q₈	C₂²×#10624382	1	2	yes	—
205	D₄	—	2	2	no	—
206	D₄	—	362	2	no	—
207	D₄	—	362	2	no	—
208	D₄	—	362	2	no	—
209	D₄	—	362	2	no	—
210	D₄	—	181	2	no	—
211	D₄	C₂²×#10624382	1	2	yes	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	362	2	no	—
214	C₂×C₄	—	362	2	no	—
215	C₂×C₄	—	362	2	no	—
216	C₂×C₄	—	362	2	no	—
217	C₂×C₄	—	362	2	no	—
218	C₂×C₄	—	181	1	no	—
219	C₂×C₄	—	181	1	no	—
220	C₂×C₄	—	181	1	no	—
221	C₂×C₄	—	181	1	no	—
222	C₂×C₄	—	181	1	no	—
223	C₂×C₄	—	724	2	no	—
224	C₂×C₄	C₂²×#10624382	1	1	yes	characteristic
225	C₈	—	362	4	no	—
226	C₈	—	181	4	no	—
227	C₈	—	181	1	no	—
228	C₈	—	181	1	no	—
229	C₈	C₂²×#10624382	1	1	yes	characteristic
230	C₈	C₂²×#10624382	1	1	yes	characteristic
231	C₂²	—	2	2	no	—
232	C₂²	—	362	2	no	—
233	C₂²	—	362	2	no	—
234	C₂²	—	181	1	no	—
235	C₂²	—	181	1	no	—
236	C₂²	—	724	4	no	—
237	C₂²	D₄×#10624382	1	1	yes	characteristic
238	C₄	—	2	2	no	—
239	C₄	—	362	2	no	—
240	C₄	—	181	1	no	—
241	C₄	—	181	1	no	—
242	C₄	—	724	2	no	—
243	C₄	D₄×#10624382	1	1	yes	characteristic
244	C₄	C₂³×#10624382	1	1	yes	characteristic
245	C₂	—	2	1	no	—
246	C₂	—	4	2	no	—
247	C₂	—	362	1	no	—
248	C₂	—	181	2	no	—
249	C₂	—	724	2	no	—
250	C₂	C₂×D₄×#10624382	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×#10624382
commutator	C₄×C₁₈₁	C₂³×C₄
Frattini	C₄	C₂³×#10624382
Fitting	#135×C₁₈₁	C₄
socle	C₂×C₁₈₁	C₂×C₄×D₄
prime radical	#135×D₁₈₁	C₂
cosocle	C₄×D₁₈₁	C₂⁴
hypercenter	#135	#10624382
hypocenter	C₁₈₁	C₂×#444
LCS	G ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. D₁₈₁⋊#131	C₂	semidirect
2. #26042326	C₂	semidirect
3. #26042325	C₂	semidirect
4. #26042324	C₂	semidirect
5. D₁₈₁⋊#108	C₂	semidirect
6. D₁₈₁⋊#104	C₂	semidirect
7. C₂×#19153870	C₂	semidirect
9. #19153904	C₂²	semidirect
11. #19153903	C₂²	semidirect
17. #19153887	C₂²	semidirect
18. #19153886	C₂²	semidirect
19. #19153881	C₂²	semidirect
20. #19153880	C₂²	semidirect
21. #19153870	C₂²	semidirect
22. #19153870	C₂²	semidirect
25. #19153838	C₄	semidirect
27. #19153836	C₄	semidirect
29. Q₁₆×D₁₈₁	C₄	semidirect
30. SD₁₆×D₁₈₁	C₄	semidirect
31. D₈×D₁₈₁	C₄	semidirect
33. #135×C₁₈₁	C₄	semidirect
57. Dic₇₂₄	C₂×C₄	semidirect
58. #15668439	C₂×C₄	semidirect
59. #15668438	C₂×C₄	semidirect
60. #15668437	C₂×C₄	semidirect
61. #15668436	C₂×C₄	semidirect
62. D₁₄₄₈	C₂×C₄	semidirect
63. #15668434	C₂×C₄	semidirect
70. Q₁₆×C₁₈₁	C₂×C₄	semidirect
71. SD₁₆×C₁₈₁	C₂×C₄	semidirect
72. D₈×C₁₈₁	C₂×C₄	semidirect
124. D₁₈₁	#444	semidirect
125. C₁₈₁	C₂×#444	semidirect
141. #135	#10624382	semidirect
174. Q₁₆	C₂×#10624382	semidirect
178. SD₁₆	C₂×#10624382	semidirect
181. D₈	C₂×#10624382	semidirect

Maximal subgroups

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

subgroup	index
D₁₈₁⋊#131	2
#26042326	2
#26042325	2
#26042324	2
D₁₈₁⋊#108	2
D₁₈₁⋊#104	2
C₂×#19153870	2
#135×D₁₈₁	2
C₂×#444	181

Subgroups — D181⋊#444 #37550492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₈₁⋊#444 #37550492