Subgroups — #131×#1181 #16836059

Order 3712.

572 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉⋊#131	C₂	1	1	yes	maximal, characteristic
2	#41×#1181	C₂	1	1	yes	maximal, characteristic
3	#14272129	C₂	1	3	yes	maximal, complemented
4	#14272126	C₂	1	3	yes	maximal, complemented
5	M₁₆×#1181	C₂	1	3	yes	maximal, complemented
6	C₂×C₈×#1181	C₂	1	3	yes	maximal, complemented
7	#131×D₂₉	C₂	1	1	yes	maximal, characteristic
8	#41×D₂₉	C₂²	1	1	yes	characteristic
9	Q₈×#1181	C₄	1	2	yes	—
10	#11745348	C₄	1	2	yes	complemented
11	D₄×#1181	C₄	1	6	yes	—
12	#11745346	C₄	1	6	yes	complemented
13	#11745345	C₂²	1	3	yes	—
14	C₂×C₄×#1181	C₂²	1	3	yes	—
15	D₂₉⋊M₁₆	C₂²	1	3	yes	—
16	C₂×D₂₉⋊C₈	C₂²	1	3	yes	—
17	C₂₉×#131	C₄	1	1	yes	characteristic, complemented
18	#11745310	C₄	1	1	yes	characteristic, complemented
19	#11745269	C₄	1	3	yes	complemented
20	M₁₆×D₂₉	C₂²	1	3	yes	—
21	#11745263	C₄	1	3	yes	complemented
22	C₂×C₈×D₂₉	C₂²	1	3	yes	—
23	#11745208	C₂²	1	6	yes	—
24	C₈×#1181	C₂²	1	1	yes	characteristic
25	C₈×#1181	C₂²	1	3	yes	—
26	C₈×#1181	C₂²	1	3	yes	—
27	C₈×#1181	C₂²	1	3	yes	—
28	C₂²×#1181	C₂×C₄	1	6	yes	—
29	#41×C₂₉	C₂×C₄	1	1	yes	characteristic
30	#90809	C₂×C₄	1	1	yes	characteristic
31	Q₈×D₂₉	C₂×C₄	1	1	yes	characteristic
32	#90807	C₂×C₄	1	3	yes	—
33	D₄×D₂₉	C₂×C₄	1	3	yes	—
34	#90805	C₂×C₄	1	3	yes	—
35	C₂×C₄×D₂₉	C₂³	1	3	yes	—
36	C₂²⋊#1181	C₂×C₄	1	6	yes	—
37	#90800	C₂×C₄	1	6	yes	complemented
38	C₂×#6599	C₂×C₄	1	6	yes	complemented
39	C₄⋊#1181	C₂×C₄	1	6	yes	—
40	C₄×#1181	C₂×C₄	1	6	yes	—
41	C₄×#1181	C₂³	1	1	yes	characteristic
42	C₄×#1181	C₂³	1	3	yes	—
43	#90796	C₂×C₄	1	6	yes	complemented
44	D₂₉⋊C₈	C₂×C₄	1	6	yes	complemented
45	D₂₉⋊C₈	C₂³	1	1	yes	characteristic
46	D₂₉⋊C₈	C₂³	1	3	yes	—
47	M₁₆×C₂₉	C₂×C₄	1	3	yes	complemented
48	C₂×C₈×C₂₉	C₂×C₄	1	3	yes	complemented
49	#90777	C₂×C₄	1	3	yes	complemented
50	C₂×#6597	C₂×C₄	1	3	yes	complemented
51	#90772	C₂×C₄	1	6	yes	complemented
52	C₈×D₂₉	C₂×C₄	1	3	yes	complemented
53	C₈×D₂₉	C₂×C₄	1	3	yes	complemented
54	C₈×D₂₉	C₂³	1	1	yes	characteristic
55	C₈×D₂₉	C₂³	1	3	yes	—
56	C₂²×D₂₉	C₂²×C₄	1	3	yes	—
57	C₂×#1181	—	2	12	no	—
58	C₂×#1181	C₂²×C₄	1	6	yes	—
59	C₂×#1181	C₂²×C₄	1	2	yes	—
60	Q₈×C₂₉	C₄²	1	1	yes	characteristic
61	D₄×C₂₉	C₄²	1	3	yes	—
62	C₂×C₄×C₂₉	C₂²×C₄	1	3	yes	—
63	C₂²⋊D₂₉	C₄²	1	6	yes	—
64	C₂×Dic₂₉	C₂²×C₄	1	3	yes	—
65	D₁₁₆	C₄²	1	3	yes	—
66	C₄×D₂₉	C₂²×C₄	1	3	yes	—
67	C₄×D₂₉	C₂²×C₄	1	3	yes	—
68	C₄×D₂₉	C₂²×C₄	1	3	yes	—
69	C₄×D₂₉	C₂⁴	1	1	yes	characteristic
70	Dic₅₈	C₄²	1	3	yes	—
71	#6599	C₂²×C₄	1	2	yes	—
72	#6599	C₂²×C₄	1	6	yes	—
73	C₈×C₂₉	C₂²×C₄	1	3	yes	—
74	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
75	#6597	C₂²×C₄	1	1	yes	characteristic
76	#6597	C₂²×C₄	1	3	yes	—
77	C₄×#131	—	29	1	no	maximal, Sylow
78	C₂²×C₂₉	C₂×C₄²	1	3	yes	—
79	C₂×D₂₉	—	2	6	no	—
80	C₂×D₂₉	C₂×C₄²	1	3	yes	—
81	C₂×D₂₉	C₂³×C₄	1	1	yes	characteristic
82	#1181	—	2	6	no	—
83	#1181	#131	1	4	yes	direct product factor
84	C₄×C₂₉	C₂×C₄²	1	3	yes	—
85	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
86	Dic₂₉	C₂×C₄²	1	3	yes	—
87	Dic₂₉	C₂³×C₄	1	1	yes	characteristic
88	C₂×#131	—	29	1	no	—
89	C₂×#131	—	29	1	no	—
90	C₄×#41	—	29	1	no	—
91	#405	—	29	3	no	—
92	#405	—	29	3	no	—
93	C₄×M₁₆	—	29	3	no	—
94	C₂×C₄×C₈	—	29	3	no	—
95	C₂×C₂₉	—	2	3	no	—
96	C₂×C₂₉	C₂²×C₄²	1	1	yes	characteristic
97	D₂₉	—	2	3	no	—
98	D₂₉	C₂×#131	1	2	yes	—
99	C₂×#41	—	29	1	no	—
100	#131	—	29	6	no	—
101	#131	—	29	2	no	—
102	#131	—	29	1	no	—
103	#131	—	29	3	no	—
104	#131	—	29	3	no	—
105	#131	#1181	1	1	yes	characteristic, direct product factor
106	C₂×M₁₆	—	29	3	no	—
107	C₂×M₁₆	—	29	3	no	—
108	C₂²×C₈	—	29	3	no	—
109	C₂²×C₈	—	29	3	no	—
110	C₄×Q₈	—	29	2	no	—
111	C₄×D₄	—	29	6	no	—
112	#117	—	29	3	no	—
113	C₂×C₄²	—	29	3	no	—
114	#97	—	29	6	no	—
115	C₄×C₈	—	29	1	no	—
116	C₄×C₈	—	29	3	no	—
117	C₄×C₈	—	29	3	no	—
118	C₄×C₈	—	29	3	no	—
119	C₂₉	C₄×#131	1	1	yes	characteristic, complemented, Sylow
120	#41	—	29	1	no	—
121	#41	—	29	3	no	—
122	#41	—	29	3	no	—
123	#41	C₂×#1181	1	1	yes	characteristic
124	C₂×Q₈	—	29	1	no	—
125	C₂×D₄	—	29	3	no	—
126	C₂²×C₄	—	29	3	no	—
127	C₂²×C₄	—	29	6	no	—
128	M₁₆	—	29	6	no	—
129	M₁₆	—	29	6	no	—
130	M₁₆	—	29	3	no	—
131	M₁₆	—	29	6	no	—
132	M₁₆	C₂×#1181	1	3	yes	complemented
133	C₂×C₈	—	29	1	no	—
134	C₂×C₈	—	29	3	no	—
135	C₂×C₈	—	29	6	no	—
136	C₂×C₈	—	29	6	no	—
137	C₂×C₈	—	29	3	no	—
138	C₂×C₈	—	29	3	no	—
139	C₂×C₈	—	29	3	no	—
140	C₂×C₈	—	29	1	no	—
141	C₂×C₈	—	29	3	no	—
142	C₂×C₈	C₂×#1181	1	3	yes	complemented
143	C₄⋊C₄	—	29	6	no	—
144	C₂²⋊C₄	—	29	6	no	—
145	C₄²	—	29	1	no	—
146	C₄²	—	29	3	no	—
147	C₄²	—	29	6	no	—
148	C₂³	—	29	3	no	—
149	Q₈	—	29	3	no	—
150	Q₈	C₄×#1181	1	1	yes	characteristic
151	D₄	—	29	6	no	—
152	D₄	—	29	3	no	—
153	D₄	C₄×#1181	1	3	yes	—
154	C₂×C₄	—	29	2	no	—
155	C₂×C₄	—	29	3	no	—
156	C₂×C₄	—	29	3	no	—
157	C₂×C₄	—	29	3	no	—
158	C₂×C₄	—	29	1	no	—
159	C₂×C₄	—	29	3	no	—
160	C₂×C₄	—	29	6	no	—
161	C₂×C₄	—	58	12	no	—
162	C₂×C₄	C₂²×#1181	1	3	yes	—
163	C₈	—	29	2	no	—
164	C₈	—	29	6	no	—
165	C₈	—	29	1	no	—
166	C₈	—	29	3	no	—
167	C₈	C₂²×#1181	1	3	yes	—
168	C₈	C₂²×#1181	1	1	yes	characteristic
169	C₂²	—	29	1	no	—
170	C₂²	—	29	3	no	—
171	C₂²	—	58	6	no	—
172	C₂²	C₂×C₄×#1181	1	3	yes	—
173	C₄	—	29	4	no	—
174	C₄	—	29	1	no	—
175	C₄	—	29	3	no	—
176	C₄	—	58	6	no	—
177	C₄	C₂×C₄×#1181	1	3	yes	—
178	C₄	C₂³×#1181	1	1	yes	characteristic
179	C₂	—	2	3	no	—
180	C₂	—	29	2	no	—
181	C₂	—	58	3	no	—
182	C₂	C₂²×C₄×#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²×#1181
commutator, socle	C₂×C₂₉	C₂²×C₄²
Frattini	C₄	C₂³×#1181
Fitting	C₂₉×#131	C₄
prime radical	#41×D₂₉	C₂²
cosocle	C₄×D₂₉	C₂⁴
hypercenter	#131	#1181
hypocenter	C₂₉	C₄×#131
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
3. #14272129	C₂	semidirect
4. #14272126	C₂	semidirect
5. M₁₆×#1181	C₂	semidirect
6. C₂×C₈×#1181	C₂	semidirect
10. #11745348	C₄	semidirect
12. #11745346	C₄	semidirect
17. C₂₉×#131	C₄	semidirect
18. #11745310	C₄	semidirect
19. #11745269	C₄	semidirect
21. #11745263	C₄	semidirect
37. #90800	C₂×C₄	semidirect
38. C₂×#6599	C₂×C₄	semidirect
43. #90796	C₂×C₄	semidirect
44. D₂₉⋊C₈	C₂×C₄	semidirect
47. M₁₆×C₂₉	C₂×C₄	semidirect
48. C₂×C₈×C₂₉	C₂×C₄	semidirect
49. #90777	C₂×C₄	semidirect
50. C₂×#6597	C₂×C₄	semidirect
51. #90772	C₂×C₄	semidirect
52. C₈×D₂₉	C₂×C₄	semidirect
53. C₈×D₂₉	C₂×C₄	semidirect
83. #1181	#131	direct (N × H)
105. #131	#1181	direct (N × H)
119. C₂₉	C₄×#131	semidirect
132. M₁₆	C₂×#1181	semidirect
142. C₂×C₈	C₂×#1181	semidirect

Maximal subgroups

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

subgroup	index
D₂₉⋊#131	2
#41×#1181	2
#14272129	2
#14272126	2
M₁₆×#1181	2
C₂×C₈×#1181	2
#131×D₂₉	2
C₄×#131	29