Subgroups — C₂₉×#2948 #16816662

Order 3712.

528 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#518	C₂	1	2	yes	maximal, complemented
3	C₂₉×#442	C₂	1	4	yes	maximal, complemented
4	C₄×D₈×C₂₉	C₂	1	4	yes	maximal, complemented
5	C₂₉×#427	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#418	C₂	1	2	yes	maximal, complemented
7	C₂₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₄×C₂₉	C₂²	1	2	yes	—
9	C₂×D₈×C₂₉	C₄	1	8	yes	complemented
10	C₂×D₈×C₂₉	C₂²	1	2	yes	—
11	C₂×D₈×C₂₉	C₂²	1	2	yes	—
12	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
14	C₄×D₄×C₂₉	—	2	4	no	—
15	C₄×D₄×C₂₉	C₂²	1	8	yes	complemented
16	C₂₉×#117	C₂²	1	2	yes	—
17	C₂₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
19	C₂₉×#107	C₂²	1	2	yes	complemented
20	C₂₉×#106	C₂²	1	2	yes	complemented
21	C₂₉×#102	C₂²	1	8	yes	complemented
22	C₂₉×#97	C₂²	1	2	yes	complemented
23	C₄×C₈×C₂₉	C₂²	1	2	yes	complemented
24	C₂⁴×C₂₉	—	2	2	no	—
25	C₂×D₄×C₂₉	—	2	2	no	—
26	C₂×D₄×C₂₉	—	2	4	no	—
27	C₂×D₄×C₂₉	C₂×C₄	1	8	yes	complemented
28	C₂×D₄×C₂₉	C₂³	1	4	yes	—
29	C₂²×C₄×C₂₉	—	2	8	no	—
30	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
31	D₈×C₂₉	C₂×C₄	1	8	yes	complemented
32	D₈×C₂₉	C₂×C₄	1	8	yes	complemented
33	M₁₆×C₂₉	—	2	2	no	—
34	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	complemented
35	C₂×C₈×C₂₉	C₂³	1	2	yes	—
36	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
37	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
38	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
39	C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
40	C₂²⋊C₄×C₂₉	—	2	2	no	—
41	C₂²⋊C₄×C₂₉	—	2	8	no	—
42	C₂²⋊C₄×C₂₉	D₄	1	2	yes	—
43	C₄²×C₂₉	—	2	2	no	—
44	C₄²×C₂₉	C₂³	1	2	yes	—
45	C₂³×C₂₉	—	2	4	no	—
46	C₂³×C₂₉	—	2	8	no	—
47	C₂³×C₂₉	—	8	4	no	—
48	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
49	D₄×C₂₉	—	2	8	no	—
50	D₄×C₂₉	—	2	4	no	—
51	D₄×C₂₉	C₂²×C₄	1	8	yes	—
52	C₂×C₄×C₂₉	—	2	4	no	—
53	C₂×C₄×C₂₉	—	8	8	no	—
54	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₂₉	C₂×D₄	1	4	yes	—
56	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₂₉	#41	1	2	yes	—
58	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
59	C₈×C₂₉	—	2	2	no	—
60	C₈×C₂₉	C₂²×C₄	1	2	yes	—
61	C₈×C₂₉	C₂²×C₄	1	2	yes	—
62	#2948	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₂₉	—	2	2	no	—
64	C₂²×C₂₉	—	2	8	no	—
65	C₂²×C₂₉	—	4	8	no	—
66	C₂²×C₂₉	—	8	8	no	—
67	C₂²×C₂₉	C₄×D₄	1	2	yes	—
68	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
69	C₄×C₂₉	—	2	4	no	—
70	C₄×C₂₉	—	4	4	no	—
71	C₄×C₂₉	C₄×D₄	1	2	yes	—
72	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
73	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
74	C₂²×D₈	C₂×C₂₉	1	1	yes	characteristic
75	#518	C₂×C₂₉	1	2	yes	complemented
76	#442	C₂×C₂₉	1	4	yes	complemented
77	C₄×D₈	C₂×C₂₉	1	4	yes	complemented
78	#427	C₂×C₂₉	1	1	yes	characteristic, complemented
79	#418	C₂×C₂₉	1	2	yes	complemented
80	#405	C₂×C₂₉	1	1	yes	characteristic, complemented
81	C₂×C₂₉	—	2	2	no	—
82	C₂×C₂₉	—	4	8	no	—
83	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
84	C₂×C₂₉	#576	1	2	yes	—
85	C₂²×D₄	C₂²×C₂₉	1	2	yes	—
86	C₂×D₈	C₄×C₂₉	1	8	yes	complemented
87	C₂×D₈	C₂²×C₂₉	1	2	yes	—
88	C₂×D₈	C₂²×C₂₉	1	2	yes	—
89	C₂×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
90	C₂²×C₈	C₂²×C₂₉	1	1	yes	characteristic
91	C₄×D₄	—	2	4	no	—
92	C₄×D₄	C₂²×C₂₉	1	8	yes	complemented
93	#117	C₂²×C₂₉	1	2	yes	—
94	#117	C₂²×C₂₉	1	1	yes	characteristic
95	C₂×C₂²⋊C₄	—	2	4	no	—
96	#107	C₂²×C₂₉	1	2	yes	complemented
97	#106	C₂²×C₂₉	1	2	yes	complemented
98	#102	C₂²×C₂₉	1	8	yes	complemented
99	#97	C₂²×C₂₉	1	2	yes	complemented
100	C₄×C₈	C₂²×C₂₉	1	2	yes	complemented
101	C₂₉	#2948	1	1	yes	characteristic, direct product factor, Sylow
102	C₂⁴	—	2	2	no	—
103	C₂×D₄	—	2	2	no	—
104	C₂×D₄	—	2	4	no	—
105	C₂×D₄	C₂×C₄×C₂₉	1	8	yes	complemented
106	C₂×D₄	C₂³×C₂₉	1	4	yes	—
107	C₂²×C₄	—	2	8	no	—
108	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
109	D₈	C₂×C₄×C₂₉	1	8	yes	complemented
110	D₈	C₂×C₄×C₂₉	1	8	yes	complemented
111	M₁₆	—	2	2	no	—
112	C₂×C₈	C₂×C₄×C₂₉	1	4	yes	complemented
113	C₂×C₈	C₂³×C₂₉	1	2	yes	—
114	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
115	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
116	C₄⋊C₄	D₄×C₂₉	1	2	yes	—
117	C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
118	C₂²⋊C₄	—	2	2	no	—
119	C₂²⋊C₄	—	2	8	no	—
120	C₂²⋊C₄	D₄×C₂₉	1	2	yes	—
121	C₄²	—	2	2	no	—
122	C₄²	C₂³×C₂₉	1	2	yes	—
123	C₂³	—	2	4	no	—
124	C₂³	—	2	8	no	—
125	C₂³	—	8	4	no	—
126	C₂³	C₂×D₄×C₂₉	1	1	yes	characteristic
127	D₄	—	2	8	no	—
128	D₄	—	2	4	no	—
129	D₄	C₂²×C₄×C₂₉	1	8	yes	—
130	C₂×C₄	—	2	4	no	—
131	C₂×C₄	—	8	8	no	—
132	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
133	C₂×C₄	C₂×D₄×C₂₉	1	4	yes	—
134	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
135	C₂×C₄	#41×C₂₉	1	2	yes	—
136	C₂×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
137	C₈	—	2	2	no	—
138	C₈	C₂²×C₄×C₂₉	1	2	yes	—
139	C₈	C₂²×C₄×C₂₉	1	2	yes	—
140	C₂²	—	2	2	no	—
141	C₂²	—	2	8	no	—
142	C₂²	—	4	8	no	—
143	C₂²	—	8	8	no	—
144	C₂²	C₄×D₄×C₂₉	1	2	yes	—
145	C₂²	C₂²×D₄×C₂₉	1	1	yes	characteristic
146	C₄	—	2	4	no	—
147	C₄	—	4	4	no	—
148	C₄	C₄×D₄×C₂₉	1	2	yes	—
149	C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
150	C₄	C₂×#41×C₂₉	1	1	yes	characteristic
151	C₂	—	2	2	no	—
152	C₂	—	4	8	no	—
153	C₂	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
154	C₂	C₂₉×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂²×D₈×C₂₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#518	C₂	semidirect
3. C₂₉×#442	C₂	semidirect
4. C₄×D₈×C₂₉	C₂	semidirect
5. C₂₉×#427	C₂	semidirect
6. C₂₉×#418	C₂	semidirect
7. C₂₉×#405	C₂	semidirect
9. C₂×D₈×C₂₉	C₄	semidirect
15. C₄×D₄×C₂₉	C₂²	semidirect
19. C₂₉×#107	C₂²	semidirect
20. C₂₉×#106	C₂²	semidirect
21. C₂₉×#102	C₂²	semidirect
22. C₂₉×#97	C₂²	semidirect
23. C₄×C₈×C₂₉	C₂²	semidirect
27. C₂×D₄×C₂₉	C₂×C₄	semidirect
31. D₈×C₂₉	C₂×C₄	semidirect
32. D₈×C₂₉	C₂×C₄	semidirect
34. C₂×C₈×C₂₉	C₂×C₄	semidirect
62. #2948	C₂₉	direct (N × H)
75. #518	C₂×C₂₉	semidirect
76. #442	C₂×C₂₉	semidirect
77. C₄×D₈	C₂×C₂₉	semidirect
78. #427	C₂×C₂₉	semidirect
79. #418	C₂×C₂₉	semidirect
80. #405	C₂×C₂₉	semidirect
86. C₂×D₈	C₄×C₂₉	semidirect
92. C₄×D₄	C₂²×C₂₉	semidirect
96. #107	C₂²×C₂₉	semidirect
97. #106	C₂²×C₂₉	semidirect
98. #102	C₂²×C₂₉	semidirect
99. #97	C₂²×C₂₉	semidirect
100. C₄×C₈	C₂²×C₂₉	semidirect
101. C₂₉	#2948	direct (N × H)
105. C₂×D₄	C₂×C₄×C₂₉	semidirect
109. D₈	C₂×C₄×C₂₉	semidirect
110. D₈	C₂×C₄×C₂₉	semidirect
112. C₂×C₈	C₂×C₄×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₈×C₂₉	2
C₂₉×#518	2
C₂₉×#442	2
C₄×D₈×C₂₉	2
C₂₉×#427	2
C₂₉×#418	2
C₂₉×#405	2
#2948	29

Subgroups — C29×#2948 #16816662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#2948 #16816662