Subgroups — C₄×#19098391 #34203672

Order 20224.

366 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098391	C₂	1	2	yes	maximal
2	C₄×#14579095	C₂	1	2	yes	maximal
3	#23761492	C₂	1	2	yes	maximal
4	C₂×C₄×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#14579095	C₂²	1	4	yes	—
6	C₄×C₄⋊Dic₇₉	—	2	2	no	—
7	#19098391	C₄	1	8	yes	direct product factor
8	#19098326	—	2	2	no	—
9	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
10	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
12	C₄×C₁₆×C₇₉	C₄	1	4	yes	complemented
13	C₂×C₄⋊Dic₇₉	—	2	4	no	—
14	C₂×C₄×Dic₇₉	—	4	2	no	—
15	#14579095	—	2	4	no	—
16	#14579095	C₂×C₄	1	8	yes	—
17	C₇₉⋊#95	—	4	2	no	—
18	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
20	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
21	C₂×C₁₆×C₇₉	—	2	2	no	—
22	C₂×C₁₆×C₇₉	C₂×C₄	1	4	yes	—
23	C₂×C₁₆×C₇₉	C₂×C₄	1	2	yes	—
24	C₂×C₁₆×C₇₉	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₇₉	Q₈	1	2	yes	—
27	C₂²×Dic₇₉	—	4	4	no	—
28	C₄⋊Dic₇₉	—	2	8	no	—
29	C₄⋊Dic₇₉	—	4	4	no	—
30	C₄×Dic₇₉	—	8	4	no	—
31	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
32	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
33	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₈×C₇₉	—	2	2	no	—
35	C₂×C₈×C₇₉	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
38	C₂×C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₈×C₇₉	#41	1	2	yes	—
40	C₄²×C₇₉	C₄⋊C₄	1	2	yes	—
41	C₄²×C₇₉	Q₁₆	1	2	yes	—
42	C₁₆×C₇₉	—	2	2	no	—
43	C₁₆×C₇₉	C₄²	1	4	yes	complemented
44	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
45	C₂×C₄×C₇₉	—	2	2	no	—
46	C₂×C₄×C₇₉	#107	1	2	yes	—
47	C₂×C₄×C₇₉	#107	1	2	yes	—
48	C₂×C₄×C₇₉	SD₃₂	1	4	yes	—
49	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
51	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
52	C₂×C₄×C₇₉	#135	1	2	yes	—
53	C₂×Dic₇₉	—	4	8	no	—
54	C₂×Dic₇₉	—	8	4	no	—
55	C₂×Dic₇₉	—	8	4	no	—
56	C₈×C₇₉	—	2	2	no	—
57	C₈×C₇₉	C₂×C₄²	1	1	yes	characteristic
58	C₈×C₇₉	#117	1	1	yes	characteristic
59	C₈×C₇₉	C₄×Q₈	1	2	yes	—
60	C₂²×C₇₉	C₂×#107	1	1	yes	characteristic
61	C₂²×C₇₉	C₄×D₈	1	2	yes	—
62	C₂²×C₇₉	C₂×SD₃₂	1	2	yes	—
63	C₂²×C₇₉	#508	1	2	yes	—
64	C₄×C₇₉	—	2	2	no	—
65	C₄×C₇₉	#367	1	4	yes	complemented
66	C₄×C₇₉	C₄×C₄⋊C₄	1	1	yes	characteristic
67	C₄×C₇₉	#427	1	1	yes	characteristic
68	C₄×C₇₉	C₄×Q₁₆	1	2	yes	—
69	Dic₇₉	—	8	8	no	—
70	C₄×#367	—	79	1	no	maximal, Sylow
71	C₂×C₇₉	C₄×#107	1	1	yes	characteristic
72	C₂×C₇₉	C₂×#367	1	1	yes	characteristic
73	C₂×C₇₉	#2158	1	1	yes	characteristic
74	C₂×C₇₉	C₄×SD₃₂	1	4	yes	—
75	C₂×#367	—	79	2	no	—
76	C₂×C₄×C₁₆	D₇₉	1	1	yes	characteristic
77	C₄×#107	—	79	2	no	—
78	#1380	—	79	2	no	—
79	C₇₉	C₄×#367	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₁₆	C₂×D₇₉	1	1	yes	characteristic
81	C₂²×C₁₆	C₂×D₇₉	1	1	yes	characteristic
82	C₂×#107	—	79	4	no	—
83	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
84	C₄×C₄⋊C₄	—	158	2	no	—
85	#367	—	79	8	no	—
86	C₄×C₁₆	Dic₇₉	1	4	yes	complemented
87	#340	—	158	2	no	—
88	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
89	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
90	C₂×C₄⋊C₄	—	158	4	no	—
91	C₂×C₄²	—	316	2	no	—
92	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
93	C₂×C₁₆	—	2	2	no	—
94	C₂×C₁₆	C₄×D₇₉	1	4	yes	—
95	C₂×C₁₆	C₂×Dic₇₉	1	2	yes	—
96	C₂×C₁₆	C₂×Dic₇₉	1	2	yes	—
97	#107	—	79	8	no	—
98	#107	—	158	4	no	—
99	C₄×C₈	Dic₁₅₈	1	2	yes	—
100	C₄×C₈	C₂×Dic₇₉	1	2	yes	—
101	#95	—	316	2	no	—
102	C₂²×C₄	—	316	4	no	—
103	C₂²×C₄	D₆₃₂	1	1	yes	characteristic
104	C₂²×C₄	D₆₃₂	1	1	yes	characteristic
105	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	C₄⋊Dic₇₉	1	2	yes	—
108	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
109	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
110	C₂×C₈	C₂×Dic₁₅₈	1	1	yes	characteristic
111	C₂×C₈	#11929624	1	2	yes	—
112	C₄⋊C₄	—	316	4	no	—
113	C₄⋊C₄	—	158	8	no	—
114	C₄²	—	632	4	no	—
115	C₄²	C₄⋊Dic₇₉	1	2	yes	—
116	C₄²	Dic₃₁₆	1	2	yes	—
117	C₁₆	—	2	2	no	—
118	C₁₆	C₄×Dic₇₉	1	4	yes	complemented
119	C₂³	C₂×D₆₃₂	1	1	yes	characteristic
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	316	8	no	—
122	C₂×C₄	—	632	4	no	—
123	C₂×C₄	—	632	4	no	—
124	C₂×C₄	#14579095	1	2	yes	—
125	C₂×C₄	#14579095	1	2	yes	—
126	C₂×C₄	#14579106	1	4	yes	—
127	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
128	C₂×C₄	C₄×D₃₁₆	1	2	yes	—
129	C₂×C₄	C₂×Dic₃₁₆	1	1	yes	characteristic
130	C₂×C₄	#14579183	1	2	yes	—
131	C₈	—	2	2	no	—
132	C₈	C₂×C₄×Dic₇₉	1	1	yes	characteristic
133	C₈	#14579120	1	1	yes	characteristic
134	C₈	C₄×Dic₁₅₈	1	2	yes	—
135	C₂²	C₂×#14579095	1	1	yes	characteristic
136	C₂²	C₄×D₆₃₂	1	2	yes	—
137	C₂²	C₂×#14579106	1	2	yes	—
138	C₂²	#19098995	1	2	yes	—
139	C₄	—	2	2	no	—
140	C₄	—	632	8	no	—
141	C₄	#19098391	1	4	yes	direct product factor
142	C₄	C₄×C₄⋊Dic₇₉	1	1	yes	characteristic
143	C₄	#19098601	1	1	yes	characteristic
144	C₄	C₄×Dic₃₁₆	1	2	yes	—
145	C₂	C₄×#14579095	1	1	yes	characteristic
146	C₂	C₂×#19098391	1	1	yes	characteristic
147	C₂	#23765184	1	1	yes	characteristic
148	C₂	C₄×#14579106	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	D₆₃₂
commutator	C₈×C₇₉	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₂×C₄×C₁₆×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₈
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	C₂×C₄×C₁₆	D₇₉
hypocenter	C₇₉	C₄×#367
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
7. #19098391	C₄	direct (N × H)
12. C₄×C₁₆×C₇₉	C₄	semidirect
43. C₁₆×C₇₉	C₄²	semidirect
65. C₄×C₇₉	#367	semidirect
79. C₇₉	C₄×#367	semidirect
86. C₄×C₁₆	Dic₇₉	semidirect
118. C₁₆	C₄×Dic₇₉	semidirect
141. C₄	#19098391	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×#19098391	2
C₄×#14579095	2
#23761492	2
C₂×C₄×C₁₆×C₇₉	2
C₄×#367	79

Subgroups — C4×#19098391 #34203672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19098391 #34203672