Subgroups — C₄×#19149586 #36351783

Order 22144.

752 conjugacy classes of subgroups.

The subgroup lattice has 148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Dic₁₇₃	C₂	1	2	yes	maximal
2	C₂×#19149586	C₂	1	4	yes	maximal
3	C₂²×C₄²×C₁₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₁₇₃	C₂²	1	4	yes	—
5	C₂×C₄×Dic₁₇₃	—	2	4	no	—
6	C₂×C₄×Dic₁₇₃	—	2	4	no	—
7	C₂×C₄×Dic₁₇₃	C₄	1	8	yes	complemented
8	#19149586	C₄	1	16	yes	direct product factor
9	C₂³×C₄×C₁₇₃	C₂²	1	2	yes	—
10	C₂³×C₄×C₁₇₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₁₇₃	—	2	4	no	—
12	C₂×C₄²×C₁₇₃	C₄	1	4	yes	complemented
13	C₂²×Dic₁₇₃	—	2	4	no	—
14	C₂²×Dic₁₇₃	—	2	4	no	—
15	C₂²×Dic₁₇₃	—	2	8	no	—
16	C₂²×Dic₁₇₃	C₂×C₄	1	16	yes	—
17	C₂²×Dic₁₇₃	C₂×C₄	1	8	yes	—
18	C₄×Dic₁₇₃	—	2	16	no	—
19	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₁₇₃	—	2	4	no	—
21	C₂²×C₄×C₁₇₃	—	2	4	no	—
22	C₂²×C₄×C₁₇₃	C₂×C₄	1	8	yes	—
23	C₂²×C₄×C₁₇₃	C₂×C₄	1	4	yes	—
24	C₂²×C₄×C₁₇₃	C₂×C₄	1	4	yes	—
25	C₂²×C₄×C₁₇₃	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₇₃	D₄	1	4	yes	—
27	C₂²×C₄×C₁₇₃	D₄	1	2	yes	—
28	C₂²×C₄×C₁₇₃	Q₈	1	2	yes	—
29	C₄²×C₁₇₃	—	2	8	no	—
30	C₂×Dic₁₇₃	—	2	8	no	—
31	C₂×Dic₁₇₃	—	2	8	no	—
32	C₂×Dic₁₇₃	—	2	16	no	—
33	C₂×Dic₁₇₃	—	2	16	no	—
34	C₂×Dic₁₇₃	C₄²	1	16	yes	complemented
35	C₂³×C₁₇₃	C₂²×C₄	1	2	yes	—
36	C₂³×C₁₇₃	C₂²×C₄	1	4	yes	—
37	C₂³×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₂³×C₁₇₃	C₂×D₄	1	2	yes	—
39	C₂³×C₁₇₃	C₂×D₄	1	1	yes	characteristic
40	C₂³×C₁₇₃	C₂×Q₈	1	1	yes	characteristic
41	C₂³×C₁₇₃	#41	1	4	yes	—
42	C₂×C₄×C₁₇₃	—	2	4	no	—
43	C₂×C₄×C₁₇₃	—	2	4	no	—
44	C₂×C₄×C₁₇₃	—	2	16	no	—
45	C₂×C₄×C₁₇₃	C₄²	1	4	yes	—
46	C₂×C₄×C₁₇₃	C₄²	1	8	yes	complemented
47	C₂×C₄×C₁₇₃	C₂²⋊C₄	1	8	yes	—
48	C₂×C₄×C₁₇₃	C₂²⋊C₄	1	4	yes	—
49	C₂×C₄×C₁₇₃	C₄⋊C₄	1	8	yes	—
50	C₂×C₄×C₁₇₃	C₄⋊C₄	1	4	yes	—
51	C₂²×C₁₇₃	C₂×C₄²	1	1	yes	characteristic
52	C₂²×C₁₇₃	C₂×C₄²	1	4	yes	—
53	C₂²×C₁₇₃	C₂×C₄²	1	2	yes	—
54	C₂²×C₁₇₃	C₂×C₂²⋊C₄	1	2	yes	—
55	C₂²×C₁₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₁₇₃	C₂×C₄⋊C₄	1	2	yes	—
57	C₂²×C₁₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₁₇₃	#117	1	4	yes	—
59	C₂²×C₁₇₃	#117	1	2	yes	—
60	C₂²×C₁₇₃	C₄×D₄	1	8	yes	—
61	C₂²×C₁₇₃	C₄×D₄	1	4	yes	—
62	C₂²×C₁₇₃	C₄×Q₈	1	4	yes	—
63	C₄×C₁₇₃	—	2	8	no	—
64	C₄×C₁₇₃	#95	1	8	yes	complemented
65	Dic₁₇₃	—	2	16	no	—
66	C₂×C₁₇₃	C₄³	1	1	yes	characteristic
67	C₂×C₁₇₃	C₂×#95	1	1	yes	characteristic
68	C₂×C₁₇₃	#376	1	1	yes	characteristic
69	C₂×C₁₇₃	C₄×C₂²⋊C₄	1	2	yes	—
70	C₂×C₁₇₃	C₄×C₂²⋊C₄	1	4	yes	—
71	C₂×C₁₇₃	C₄×C₄⋊C₄	1	2	yes	—
72	C₂×C₁₇₃	C₄×C₄⋊C₄	1	4	yes	—
73	C₁₇₃	C₄×#95	1	1	yes	characteristic, complemented, Sylow
74	C₄×#95	—	173	1	no	maximal, Sylow
75	C₂²×C₄²	—	173	2	no	—
76	C₂²×C₄²	D₁₇₃	1	1	yes	characteristic
77	C₂×#95	—	173	4	no	—
78	C₂³×C₄	—	173	4	no	—
79	C₂³×C₄	C₂×D₁₇₃	1	2	yes	—
80	C₂³×C₄	C₂×D₁₇₃	1	1	yes	characteristic
81	C₂×C₄²	—	2	4	no	—
82	C₂×C₄²	—	346	4	no	—
83	C₂×C₄²	—	346	4	no	—
84	C₂×C₄²	—	173	8	no	—
85	C₂×C₄²	Dic₁₇₃	1	4	yes	complemented
86	#95	—	173	16	no	—
87	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
88	C₂²×C₄	—	2	4	no	—
89	C₂²×C₄	—	2	4	no	—
90	C₂²×C₄	—	346	4	no	—
91	C₂²×C₄	—	346	4	no	—
92	C₂²×C₄	—	346	8	no	—
93	C₂²×C₄	—	173	16	no	—
94	C₂²×C₄	—	173	8	no	—
95	C₂²×C₄	C₄×D₁₇₃	1	8	yes	—
96	C₂²×C₄	C₄×D₁₇₃	1	4	yes	—
97	C₂²×C₄	C₂×Dic₁₇₃	1	4	yes	—
98	C₂²×C₄	C₂×Dic₁₇₃	1	2	yes	—
99	C₂²×C₄	C₂²⋊D₁₇₃	1	4	yes	—
100	C₂²×C₄	D₆₉₂	1	2	yes	—
101	C₂²×C₄	Dic₃₄₆	1	2	yes	—
102	C₄²	—	2	8	no	—
103	C₄²	—	346	16	no	—
104	C₂³	C₂×C₄×D₁₇₃	1	2	yes	—
105	C₂³	C₂×C₄×D₁₇₃	1	4	yes	—
106	C₂³	C₂²×Dic₁₇₃	1	1	yes	characteristic
107	C₂³	C₂×C₂²⋊D₁₇₃	1	2	yes	—
108	C₂³	C₂×D₆₉₂	1	1	yes	characteristic
109	C₂³	C₂×Dic₃₄₆	1	1	yes	characteristic
110	C₂³	#14583826	1	4	yes	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	—	2	16	no	—
114	C₂×C₄	—	346	8	no	—
115	C₂×C₄	—	346	8	no	—
116	C₂×C₄	—	346	16	no	—
117	C₂×C₄	—	346	16	no	—
118	C₂×C₄	—	173	16	no	—
119	C₂×C₄	C₄×Dic₁₇₃	1	4	yes	—
120	C₂×C₄	C₄×Dic₁₇₃	1	8	yes	complemented
121	C₂×C₄	#14583803	1	8	yes	—
122	C₂×C₄	C₂²⋊Dic₁₇₃	1	4	yes	—
123	C₂×C₄	#14583805	1	8	yes	—
124	C₂×C₄	C₄⋊Dic₁₇₃	1	4	yes	—
125	C₂²	C₄²×D₁₇₃	1	4	yes	—
126	C₂²	C₂×C₄×Dic₁₇₃	1	1	yes	characteristic
127	C₂²	C₂×C₄×Dic₁₇₃	1	2	yes	—
128	C₂²	C₂×#14583803	1	2	yes	—
129	C₂²	C₂×C₂²⋊Dic₁₇₃	1	1	yes	characteristic
130	C₂²	C₂×#14583805	1	2	yes	—
131	C₂²	C₂×C₄⋊Dic₁₇₃	1	1	yes	characteristic
132	C₂²	#19149636	1	4	yes	—
133	C₂²	#19149638	1	2	yes	—
134	C₂²	C₄×C₂²⋊D₁₇₃	1	8	yes	—
135	C₂²	C₄×D₆₉₂	1	4	yes	—
136	C₂²	C₄×Dic₃₄₆	1	4	yes	—
137	C₄	—	2	8	no	—
138	C₄	—	346	16	no	—
139	C₄	#19149586	1	8	yes	direct product factor
140	C₂	C₄²×Dic₁₇₃	1	1	yes	characteristic
141	C₂	C₂×#19149586	1	1	yes	characteristic
142	C₂	#26011337	1	1	yes	characteristic
143	C₂	C₄×C₂²⋊Dic₁₇₃	1	2	yes	—
144	C₂	C₄×#14583803	1	4	yes	—
145	C₂	C₄×C₄⋊Dic₁₇₃	1	2	yes	—
146	C₂	C₄×#14583805	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂×D₁₇₃
commutator	C₂×C₁₇₃	C₄³
Frattini	C₂⁴	C₂²×D₁₇₃
Fitting	C₂²×C₄²×C₁₇₃	C₂
socle, prime radical, cosocle	C₂⁴×C₁₇₃	C₂³
hypercenter	C₂²×C₄²	D₁₇₃
hypocenter	C₁₇₃	C₄×#95
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
7. C₂×C₄×Dic₁₇₃	C₄	semidirect
8. #19149586	C₄	direct (N × H)
12. C₂×C₄²×C₁₇₃	C₄	semidirect
34. C₂×Dic₁₇₃	C₄²	semidirect
46. C₂×C₄×C₁₇₃	C₄²	semidirect
64. C₄×C₁₇₃	#95	semidirect
73. C₁₇₃	C₄×#95	semidirect
85. C₂×C₄²	Dic₁₇₃	semidirect
120. C₂×C₄	C₄×Dic₁₇₃	semidirect
139. C₄	#19149586	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×C₄×Dic₁₇₃	2
C₂×#19149586	2
C₂²×C₄²×C₁₇₃	2
C₄×#95	173

Subgroups — C4×#19149586 #36351783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19149586 #36351783