Subgroups — C₄×#17989474 #34012078

Order 18688.

510 conjugacy classes of subgroups.

The subgroup lattice has 170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989474	C₂	1	4	yes	maximal
2	C₄×#14556664	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×#64408	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556664	C₂²	1	2	yes	—
6	C₄×#11924036	C₄	1	1	yes	characteristic
7	C₂×C₈×#64408	C₄	1	2	yes	—
8	C₂×C₈×#64408	C₂²	1	2	yes	—
9	C₄²×#64408	C₄	1	1	yes	characteristic
10	#17989474	C₄	1	16	yes	direct product factor
11	#17989473	C₄	1	2	yes	complemented
12	C₄×#11924031	C₄	1	2	yes	complemented
13	C₂×C₁₆×D₇₃	C₂²	1	2	yes	—
14	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
15	C₄×#11924003	C₄	1	1	yes	characteristic, complemented
16	C₁₆×Dic₇₃	C₄	1	2	yes	complemented
17	C₄×C₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
18	C₂×#11924036	C₂×C₄	1	2	yes	—
19	C₂×C₄×#64408	C₈	1	4	yes	—
20	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
21	#14556664	C₂×C₄	1	8	yes	—
22	C₂×#11924031	C₂×C₄	1	4	yes	—
23	C₄×#10596833	C₈	1	4	yes	—
24	C₈×#64408	C₈	1	8	yes	—
25	C₈×#64408	C₂×C₄	1	8	yes	—
26	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
28	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×#11924003	C₂×C₄	1	2	yes	—
30	C₁₆×D₇₃	C₂×C₄	1	8	yes	—
31	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
32	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
33	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×#64408	C₂×C₈	1	4	yes	—
37	#11924036	C₄²	1	4	yes	—
38	#11924036	C₂×C₈	1	4	yes	—
39	C₂×#10596833	C₂×C₈	1	4	yes	—
40	C₄×#64408	—	2	8	no	—
41	C₄×#64408	C₄²	1	4	yes	—
42	C₄×#64408	C₂×C₈	1	4	yes	—
43	#11924031	C₄²	1	8	yes	complemented
44	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
45	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×#10596831	C₄²	1	1	yes	characteristic
47	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
48	C₈×D₇₃	C₂×C₈	1	4	yes	—
49	C₈×D₇₃	C₂²×C₄	1	4	yes	—
50	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
51	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
52	#11924003	C₄²	1	4	yes	complemented
53	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
54	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
55	C₄²×C₇₃	C₄²	1	1	yes	characteristic
56	C₁₆×C₇₃	C₄²	1	4	yes	complemented
57	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
58	C₂×#64408	—	2	8	no	—
59	C₂×#64408	C₄×C₈	1	8	yes	—
60	C₂×C₄×C₇₃	C₄×C₈	1	2	yes	—
61	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
62	C₂×Dic₇₃	C₄×C₈	1	2	yes	—
63	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
64	C₄×D₇₃	M₃₂	1	8	yes	—
65	C₄×D₇₃	C₂×C₄²	1	2	yes	—
66	C₄×D₇₃	C₂²×C₈	1	2	yes	—
67	#10596833	C₄×C₈	1	8	yes	—
68	C₈×C₇₃	C₄×C₈	1	2	yes	—
69	C₈×C₇₃	C₂×C₄²	1	2	yes	—
70	#10596831	C₄×C₈	1	2	yes	—
71	#10596831	C₂×C₄²	1	2	yes	—
72	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
73	C₂×D₇₃	C₂×C₄×C₈	1	2	yes	—
74	C₂×D₇₃	C₂×M₃₂	1	4	yes	—
75	#64408	—	2	8	no	—
76	C₄×C₇₃	#346	1	4	yes	complemented
77	C₄×C₇₃	C₄³	1	1	yes	characteristic
78	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
79	Dic₇₃	#346	1	4	yes	complemented
80	Dic₇₃	C₂×C₄×C₈	1	2	yes	—
81	C₄×#346	—	73	1	no	maximal, Sylow
82	C₂×C₇₃	C₄²×C₈	1	1	yes	characteristic
83	C₂×C₇₃	C₂×#346	1	2	yes	—
84	D₇₃	C₄×M₃₂	1	4	yes	—
85	C₂×#346	—	73	4	no	—
86	C₂×C₄×C₁₆	—	73	1	no	—
87	C₂×C₄×C₁₆	—	73	1	no	—
88	C₄²×C₈	—	73	1	no	—
89	C₇₃	C₄×#346	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₁₆	—	73	2	no	—
91	C₂²×C₁₆	—	73	2	no	—
92	C₂×C₄×C₈	—	73	2	no	—
93	C₂×C₄×C₈	—	73	2	no	—
94	C₂×C₄×C₈	—	73	1	no	—
95	C₂×C₄×C₈	—	73	1	no	—
96	C₄³	—	73	1	no	—
97	#346	—	73	16	no	—
98	C₄×C₁₆	—	73	2	no	—
99	C₄×C₁₆	—	73	2	no	—
100	C₄×C₁₆	—	73	2	no	—
101	C₄×C₁₆	—	73	1	no	—
102	C₄×C₁₆	#64408	1	1	yes	characteristic, complemented
103	C₂²×C₈	—	73	2	no	—
104	C₂²×C₈	—	73	1	no	—
105	C₂²×C₈	—	73	1	no	—
106	C₂×C₄²	—	73	2	no	—
107	C₂×C₄²	—	73	1	no	—
108	C₂×C₄²	—	73	4	no	—
109	C₂×C₁₆	—	73	4	no	—
110	C₂×C₁₆	—	73	8	no	—
111	C₂×C₁₆	—	73	2	no	—
112	C₂×C₁₆	—	73	8	no	—
113	C₂×C₁₆	C₂×#64408	1	2	yes	—
114	C₄×C₈	—	73	8	no	—
115	C₄×C₈	—	73	8	no	—
116	C₄×C₈	—	73	4	no	—
117	C₄×C₈	—	73	1	no	—
118	C₄×C₈	—	73	1	no	—
119	C₄×C₈	—	73	1	no	—
120	C₄×C₈	C₂×#64408	1	1	yes	characteristic
121	C₂²×C₄	—	73	2	no	—
122	C₂²×C₄	—	73	1	no	—
123	C₂²×C₄	—	73	4	no	—
124	C₂×C₈	—	73	4	no	—
125	C₂×C₈	—	73	4	no	—
126	C₂×C₈	—	73	4	no	—
127	C₂×C₈	—	73	1	no	—
128	C₂×C₈	—	73	1	no	—
129	C₂×C₈	—	73	4	no	—
130	C₂×C₈	—	73	4	no	—
131	C₂×C₈	C₄×#64408	1	1	yes	characteristic
132	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
133	C₄²	—	73	4	no	—
134	C₄²	—	73	4	no	—
135	C₄²	—	73	2	no	—
136	C₄²	—	73	1	no	—
137	C₄²	—	146	8	no	—
138	C₄²	C₄×#64408	1	1	yes	characteristic
139	C₁₆	—	73	8	no	—
140	C₁₆	—	73	4	no	—
141	C₁₆	C₄×#64408	1	4	yes	complemented
142	C₂³	—	73	1	no	—
143	C₂×C₄	—	73	1	no	—
144	C₂×C₄	—	73	2	no	—
145	C₂×C₄	—	73	8	no	—
146	C₂×C₄	—	73	2	no	—
147	C₂×C₄	—	73	2	no	—
148	C₂×C₄	—	73	8	no	—
149	C₂×C₄	—	146	8	no	—
150	C₂×C₄	C₈×#64408	1	2	yes	—
151	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
152	C₈	—	73	8	no	—
153	C₈	—	73	2	no	—
154	C₈	—	73	2	no	—
155	C₈	C₈×#64408	1	2	yes	—
156	C₈	C₂×C₄×#64408	1	2	yes	—
157	C₂²	—	73	2	no	—
158	C₂²	—	73	4	no	—
159	C₂²	C₂×C₈×#64408	1	1	yes	characteristic
160	C₄	—	73	2	no	—
161	C₄	—	73	4	no	—
162	C₄	—	146	8	no	—
163	C₄	#17989474	1	4	yes	direct product factor
164	C₄	C₄²×#64408	1	1	yes	characteristic
165	C₄	C₂×C₈×#64408	1	1	yes	characteristic
166	C₂	—	73	4	no	—
167	C₂	C₄×C₈×#64408	1	1	yes	characteristic
168	C₂	C₂×#17989474	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×#64408
commutator	C₂×C₇₃	C₄²×C₈
Frattini	C₂×C₈	C₂²×#64408
Fitting	C₄×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄×C₈
prime radical	C₂²×D₇₃	C₂²×C₈
cosocle	C₂×C₈×D₇₃	C₂³
hypercenter	C₄×C₁₆	#64408
hypocenter	C₇₃	C₄×#346
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
10. #17989474	C₄	direct (N × H)
11. #17989473	C₄	semidirect
12. C₄×#11924031	C₄	semidirect
15. C₄×#11924003	C₄	semidirect
16. C₁₆×Dic₇₃	C₄	semidirect
17. C₄×C₁₆×C₇₃	C₄	semidirect
43. #11924031	C₄²	semidirect
52. #11924003	C₄²	semidirect
56. C₁₆×C₇₃	C₄²	semidirect
76. C₄×C₇₃	#346	semidirect
79. Dic₇₃	#346	semidirect
89. C₇₃	C₄×#346	semidirect
102. C₄×C₁₆	#64408	semidirect
141. C₁₆	C₄×#64408	semidirect
163. C₄	#17989474	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×#17989474	2
C₄×#14556664	2
C₄×C₈×#64408	2
C₄×C₁₆×D₇₃	2
C₄×#346	73

Subgroups — C4×#17989474 #34012078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#17989474 #34012078