Subgroups — C₂×#14271190 #16828051

Order 3712.

512 conjugacy classes of subgroups.

The subgroup lattice has 140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#90777	C₂	1	1	yes	maximal, characteristic
2	C₂³×#6597	C₂	1	1	yes	maximal, characteristic
3	#14271190	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄⋊#6597	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₉×#117	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂₉×#117	C₄	1	4	yes	—
8	C₂₉×#117	C₂²	1	4	yes	—
9	C₂×C₄⋊C₄×C₂₉	C₄	1	2	yes	—
10	C₂×C₂²⋊C₄×C₂₉	C₄	1	2	yes	—
11	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
12	C₂×#90777	—	2	4	no	—
13	C₂×#90777	C₂²	1	4	yes	—
14	C₂²×#6597	—	2	4	no	—
15	C₂²×#6597	C₂²	1	2	yes	—
16	C₂²×#6597	C₂²	1	4	yes	—
17	C₂²×#6597	C₂²	1	2	yes	—
18	C₄⋊#6597	C₂²	1	16	yes	complemented
19	C₂⁴×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₉	C₂×C₄	1	4	yes	—
21	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₂₉	D₄	1	4	yes	—
24	C₂²×C₄×C₂₉	Q₈	1	4	yes	—
25	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
26	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₂₉	C₂×C₄	1	8	yes	—
28	C₂²⋊C₄×C₂₉	C₂×C₄	1	8	yes	—
29	C₄²×C₂₉	C₂×C₄	1	4	yes	—
30	C₄²×C₂₉	C₂³	1	4	yes	—
31	#90777	—	2	8	no	—
32	C₂×#6597	—	2	4	no	—
33	C₂×#6597	—	2	8	no	—
34	C₂×#6597	—	2	4	no	—
35	C₂×#6597	C₂³	1	4	yes	—
36	C₂×#6597	C₂³	1	4	yes	—
37	C₂³×C₂₉	—	2	4	no	—
38	C₂³×C₂₉	C₄⋊C₄	1	4	yes	—
39	C₂³×C₂₉	C₂²×C₄	1	2	yes	—
40	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₂₉	—	2	8	no	—
42	C₂×C₄×C₂₉	C₄⋊C₄	1	8	yes	—
43	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
44	C₂×C₄×C₂₉	C₂²×C₄	1	8	yes	—
45	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₂₉	C₂×D₄	1	4	yes	—
49	C₂×C₄×C₂₉	C₂×Q₈	1	4	yes	—
50	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
51	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
52	#6597	—	2	4	no	—
53	#6597	—	2	4	no	—
54	C₂×#424	—	29	1	no	maximal, Sylow
55	C₂²×C₂₉	—	2	4	no	—
56	C₂²×C₂₉	—	2	8	no	—
57	C₂²×C₂₉	C₂×C₄⋊C₄	1	4	yes	—
58	C₂²×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
59	C₂²×C₂₉	#131	1	4	yes	—
60	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
61	C₄×C₂₉	—	2	8	no	—
62	C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
63	C₄×C₂₉	C₂×C₄⋊C₄	1	4	yes	—
64	C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
65	C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
66	C₂²×M₁₆	—	29	1	no	—
67	C₂³×C₈	—	29	1	no	—
68	C₂×#117	D₂₉	1	1	yes	characteristic
69	#424	—	29	8	no	—
70	C₂×C₄⋊C₈	—	29	4	no	—
71	C₂×C₂₉	—	2	4	no	—
72	C₂×C₂₉	#424	1	4	yes	complemented
73	C₂×C₂₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
74	C₂×C₂₉	C₂×#131	1	2	yes	—
75	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
76	C₂×M₁₆	—	29	4	no	—
77	C₂×M₁₆	—	58	4	no	—
78	C₂²×C₈	—	29	4	no	—
79	C₂²×C₈	—	29	2	no	—
80	C₂²×C₈	—	29	2	no	—
81	C₂²×C₈	—	58	4	no	—
82	#117	Dic₂₉	1	4	yes	—
83	#117	C₂×D₂₉	1	4	yes	—
84	C₂×C₄⋊C₄	Dic₂₉	1	2	yes	—
85	C₂×C₂²⋊C₄	Dic₂₉	1	2	yes	—
86	C₂×C₄²	C₂×D₂₉	1	2	yes	—
87	C₄⋊C₈	—	29	16	no	—
88	C₂₉	C₂×#424	1	1	yes	characteristic, complemented, Sylow
89	C₂⁴	C₂×Dic₂₉	1	1	yes	characteristic
90	C₂²×C₄	Dic₅₈	1	4	yes	—
91	C₂²×C₄	D₁₁₆	1	4	yes	—
92	C₂²×C₄	C₂×Dic₂₉	1	4	yes	—
93	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
94	C₂²×C₄	C₂×Dic₂₉	1	2	yes	—
95	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
96	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
97	M₁₆	—	58	8	no	—
98	C₂×C₈	—	29	4	no	—
99	C₂×C₈	—	29	4	no	—
100	C₂×C₈	—	58	4	no	—
101	C₂×C₈	—	58	8	no	—
102	C₂×C₈	—	58	4	no	—
103	C₄⋊C₄	C₂×Dic₂₉	1	8	yes	—
104	C₂²⋊C₄	C₂×Dic₂₉	1	8	yes	—
105	C₄²	C₂×Dic₂₉	1	4	yes	—
106	C₄²	C₂²×D₂₉	1	4	yes	—
107	C₂³	—	2	4	no	—
108	C₂³	C₄⋊Dic₂₉	1	4	yes	—
109	C₂³	C₂²×Dic₂₉	1	2	yes	—
110	C₂³	C₂²×Dic₂₉	1	1	yes	characteristic
111	C₂×C₄	—	2	8	no	—
112	C₂×C₄	C₄⋊Dic₂₉	1	8	yes	—
113	C₂×C₄	C₄⋊Dic₂₉	1	4	yes	—
114	C₂×C₄	C₂×Dic₅₈	1	4	yes	—
115	C₂×C₄	C₂×Dic₅₈	1	2	yes	—
116	C₂×C₄	C₂×D₁₁₆	1	2	yes	—
117	C₂×C₄	C₂×D₁₁₆	1	4	yes	—
118	C₂×C₄	C₂²×Dic₂₉	1	8	yes	—
119	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
120	C₂×C₄	C₂²×Dic₂₉	1	2	yes	—
121	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
122	C₈	—	58	4	no	—
123	C₈	—	58	4	no	—
124	C₂²	—	2	4	no	—
125	C₂²	—	2	8	no	—
126	C₂²	C₂×C₄⋊Dic₂₉	1	4	yes	—
127	C₂²	C₂×C₄⋊Dic₂₉	1	2	yes	—
128	C₂²	#11745310	1	4	yes	—
129	C₂²	C₂³×Dic₂₉	1	1	yes	characteristic
130	C₄	—	2	8	no	—
131	C₄	C₂×C₄⋊Dic₂₉	1	4	yes	—
132	C₄	C₂×C₄⋊Dic₂₉	1	2	yes	—
133	C₄	C₂²×Dic₅₈	1	1	yes	characteristic
134	C₄	C₂²×D₁₁₆	1	1	yes	characteristic
135	C₂	—	2	4	no	—
136	C₂	#14271190	1	4	yes	direct product factor
137	C₂	C₂²×C₄⋊Dic₂₉	1	1	yes	characteristic
138	C₂	C₂×#11745310	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₂₉
commutator	C₂²×C₂₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂×C₂₉×#117	C₂
socle	C₂³×C₂₉	C₂²×C₄
prime radical	C₂⁴×C₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₂×#117	D₂₉
hypocenter	C₂₉	C₂×#424
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
3. #14271190	C₂	direct (N × H)
4. C₂×C₄⋊#6597	C₂	semidirect
18. C₄⋊#6597	C₂²	semidirect
72. C₂×C₂₉	#424	semidirect
88. C₂₉	C₂×#424	semidirect
136. C₂	#14271190	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#90777	2
C₂³×#6597	2
#14271190	2
C₂×C₄⋊#6597	2
C₂×C₂₉×#117	2
C₂×#424	29

Subgroups — C2×#14271190 #16828051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14271190 #16828051