Subgroups — C₄×#11745269 #16827916

Order 3712.

572 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745269	C₂	1	2	yes	maximal
2	C₄×#90805	C₂	1	1	yes	maximal, characteristic
3	#14271121	C₂	1	2	yes	maximal, complemented
4	#14271120	C₂	1	4	yes	maximal, complemented
5	C₄×#90772	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×#6597	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₈×D₂₉	C₂	1	2	yes	maximal, complemented
8	C₄×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#90805	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
11	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
12	C₄×C₂²⋊D₂₉	C₄	1	4	yes	—
13	#11745288	C₂²	1	1	yes	characteristic
14	C₂²×#6597	C₂²	1	2	yes	—
15	#11745269	C₄	1	16	yes	direct product factor
16	C₂×#90772	C₂²	1	4	yes	—
17	C₂×C₈×D₂₉	C₂²	1	4	yes	—
18	C₄×D₁₁₆	C₄	1	2	yes	—
19	#11745234	C₂²	1	2	yes	—
20	C₄²×D₂₉	C₂²	1	2	yes	—
21	C₄×Dic₅₈	C₄	1	2	yes	—
22	C₂₉×#97	C₂²	1	2	yes	—
23	C₄×C₈×C₂₉	C₂²	1	2	yes	—
24	#11745163	C₂²	1	4	yes	—
25	C₈×Dic₂₉	C₂²	1	4	yes	—
26	C₄×#6597	C₂²	1	1	yes	characteristic
27	C₄×#6597	C₂²	1	1	yes	characteristic
28	C₄×#6597	C₂²	1	2	yes	—
29	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
31	C₂×C₂²⋊D₂₉	C₂×C₄	1	2	yes	—
32	#90805	C₂×C₄	1	8	yes	—
33	C₂×D₁₁₆	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×D₂₉	C₂×C₄	1	4	yes	—
35	C₂×C₄×D₂₉	C₂³	1	2	yes	—
36	C₂×Dic₅₈	C₂×C₄	1	1	yes	characteristic
37	M₁₆×C₂₉	C₂×C₄	1	8	yes	complemented
38	C₂×C₈×C₂₉	C₂³	1	4	yes	—
39	C₄²×C₂₉	C₂×C₄	1	2	yes	—
40	C₄²×C₂₉	C₂³	1	1	yes	characteristic
41	C₄²×C₂₉	C₂³	1	1	yes	characteristic
42	C₂²⋊Dic₂₉	C₂×C₄	1	2	yes	—
43	#90781	C₂×C₄	1	4	yes	—
44	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
45	#90779	C₂×C₄	1	4	yes	—
46	C₄×Dic₂₉	C₂×C₄	1	4	yes	—
47	C₄×Dic₂₉	C₂³	1	2	yes	—
48	C₂×#6597	C₂×C₄	1	8	yes	complemented
49	C₂×#6597	C₂³	1	2	yes	—
50	C₂×#6597	C₂³	1	2	yes	—
51	#90772	C₂×C₄	1	16	yes	complemented
52	C₈×D₂₉	C₂×C₄	1	16	yes	complemented
53	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×D₂₉	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₂₉	—	2	4	no	—
56	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
60	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
61	C₂²⋊D₂₉	C₄²	1	8	yes	—
62	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
63	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
64	D₁₁₆	C₄²	1	4	yes	—
65	C₄×D₂₉	—	2	8	no	—
66	C₄×D₂₉	C₂²×C₄	1	8	yes	—
67	Dic₅₈	C₄²	1	4	yes	—
68	C₈×C₂₉	C₂²×C₄	1	8	yes	—
69	#6597	C₂²×C₄	1	4	yes	—
70	#6597	C₂²×C₄	1	4	yes	—
71	C₄×#131	—	29	1	no	maximal, Sylow
72	C₂²×C₂₉	—	2	2	no	—
73	C₂²×C₂₉	C₂×C₄²	1	2	yes	—
74	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
75	C₂×D₂₉	—	2	4	no	—
76	C₂×D₂₉	C₂×C₄²	1	4	yes	—
77	C₄×C₂₉	—	2	2	no	—
78	C₄×C₂₉	C₂×C₄²	1	2	yes	—
79	C₄×C₂₉	#131	1	4	yes	complemented
80	C₄×C₂₉	C₂³×C₄	1	2	yes	—
81	Dic₂₉	—	2	4	no	—
82	Dic₂₉	C₂×C₄²	1	4	yes	—
83	C₂×#131	—	29	2	no	—
84	C₄×#41	—	29	1	no	—
85	#405	—	29	2	no	—
86	#405	—	29	4	no	—
87	C₄×M₁₆	—	29	2	no	—
88	C₄×M₁₆	D₂₉	1	1	yes	characteristic, complemented
89	C₂×C₄×C₈	—	29	1	no	—
90	C₂×C₄×C₈	—	29	2	no	—
91	C₂×C₂₉	—	2	2	no	—
92	C₂×C₂₉	C₂²×C₄²	1	1	yes	characteristic
93	C₂×C₂₉	C₂×#131	1	2	yes	—
94	D₂₉	—	2	4	no	—
95	C₂×#41	—	29	1	no	—
96	#131	—	29	16	no	—
97	C₂×M₁₆	—	29	4	no	—
98	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
99	C₂²×C₈	—	29	2	no	—
100	C₂²×C₈	—	29	4	no	—
101	C₄×Q₈	—	29	2	no	—
102	C₄×D₄	—	29	4	no	—
103	C₄×D₄	—	29	2	no	—
104	#117	—	29	1	no	—
105	#117	—	29	2	no	—
106	C₂×C₄²	—	29	2	no	—
107	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
108	#97	—	29	4	no	—
109	#97	C₂×D₂₉	1	2	yes	—
110	C₄×C₈	—	29	4	no	—
111	C₄×C₈	—	29	2	no	—
112	C₄×C₈	—	29	1	no	—
113	C₄×C₈	—	29	1	no	—
114	C₄×C₈	C₂×D₂₉	1	2	yes	—
115	C₂₉	C₄×#131	1	1	yes	characteristic, complemented, Sylow
116	#41	—	29	8	no	—
117	C₂×Q₈	—	29	1	no	—
118	C₂×D₄	—	29	2	no	—
119	C₂×D₄	—	29	1	no	—
120	C₂²×C₄	—	29	2	no	—
121	C₂²×C₄	—	29	4	no	—
122	C₂²×C₄	C₄×D₂₉	1	2	yes	—
123	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
124	M₁₆	—	29	16	no	—
125	M₁₆	C₄×D₂₉	1	8	yes	complemented
126	C₂×C₈	—	29	8	no	—
127	C₂×C₈	—	29	2	no	—
128	C₂×C₈	—	29	2	no	—
129	C₂×C₈	—	29	16	no	—
130	C₂×C₈	C₂²×D₂₉	1	4	yes	—
131	C₄⋊C₄	—	29	4	no	—
132	C₄⋊C₄	—	29	2	no	—
133	C₂²⋊C₄	—	29	2	no	—
134	C₂²⋊C₄	—	29	4	no	—
135	C₄²	—	29	4	no	—
136	C₄²	—	29	2	no	—
137	C₄²	C₄×D₂₉	1	2	yes	—
138	C₄²	C₂²×D₂₉	1	1	yes	characteristic
139	C₄²	C₂²×D₂₉	1	1	yes	characteristic
140	C₂³	—	29	2	no	—
141	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
142	Q₈	—	29	4	no	—
143	D₄	—	29	8	no	—
144	D₄	—	29	4	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	29	2	no	—
147	C₂×C₄	—	29	8	no	—
148	C₂×C₄	—	29	4	no	—
149	C₂×C₄	—	58	8	no	—
150	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
151	C₂×C₄	C₂×C₄×D₂₉	1	4	yes	—
152	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
153	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
154	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
155	C₈	—	29	4	no	—
156	C₈	—	29	4	no	—
157	C₈	C₂×C₄×D₂₉	1	8	yes	—
158	C₂²	—	2	2	no	—
159	C₂²	—	29	4	no	—
160	C₂²	—	58	4	no	—
161	C₂²	C₄²×D₂₉	1	2	yes	—
162	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
163	C₄	—	2	2	no	—
164	C₄	—	29	4	no	—
165	C₄	—	58	4	no	—
166	C₄	C₄²×D₂₉	1	2	yes	—
167	C₄	#11745269	1	4	yes	direct product factor
168	C₄	C₂²×C₄×D₂₉	1	2	yes	—
169	C₂	—	2	2	no	—
170	C₂	—	58	4	no	—
171	C₂	C₂×C₄²×D₂₉	1	1	yes	characteristic
172	C₂	C₂×#11745269	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²×D₂₉
commutator	C₂×C₂₉	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₄×M₁₆×C₂₉	C₂
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂×#90805	C₂²
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₄×M₁₆	D₂₉
hypocenter	C₂₉	C₄×#131
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #14271121	C₂	semidirect
4. #14271120	C₂	semidirect
5. C₄×#90772	C₂	semidirect
6. C₂×C₄×#6597	C₂	semidirect
7. C₄×C₈×D₂₉	C₂	semidirect
8. C₄×M₁₆×C₂₉	C₂	semidirect
15. #11745269	C₄	direct (N × H)
37. M₁₆×C₂₉	C₂×C₄	semidirect
48. C₂×#6597	C₂×C₄	semidirect
51. #90772	C₂×C₄	semidirect
52. C₈×D₂₉	C₂×C₄	semidirect
79. C₄×C₂₉	#131	semidirect
88. C₄×M₁₆	D₂₉	semidirect
115. C₂₉	C₄×#131	semidirect
125. M₁₆	C₄×D₂₉	semidirect
167. C₄	#11745269	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11745269	2
C₄×#90805	2
#14271121	2
#14271120	2
C₄×#90772	2
C₂×C₄×#6597	2
C₄×C₈×D₂₉	2
C₄×M₁₆×C₂₉	2
C₄×#131	29

Subgroups — C4×#11745269 #16827916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11745269 #16827916