Subgroups — C₃×#553 #5883

Order 192.

238 conjugacy classes of subgroups.

The subgroup lattice has 158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#126	C₂	1	2	yes	maximal, complemented
2	C₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#123	C₂	1	2	yes	maximal, complemented
4	C₃×#121	C₂	1	2	yes	maximal, complemented
5	C₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×D₄	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	#553	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×D₄	C₂²	1	2	yes	—
14	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₄	C₂²	1	2	yes	—
17	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄	C₂²	1	2	yes	—
20	C₂²×C₃×C₄	C₂²	1	2	yes	—
21	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₃×C₄²	C₂²	1	2	yes	—
35	C₃×C₄²	C₂²	1	1	yes	characteristic
36	#126	C₂×C₃	1	2	yes	complemented
37	#125	C₂×C₃	1	1	yes	characteristic, complemented
38	#123	C₂×C₃	1	2	yes	complemented
39	#121	C₂×C₃	1	2	yes	complemented
40	#121	C₂×C₃	1	1	yes	characteristic, complemented
41	#121	C₂×C₃	1	1	yes	characteristic, complemented
42	C₄×D₄	C₂×C₃	1	2	yes	complemented
43	C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
44	C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
45	#117	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂³×C₃	C₂³	1	1	yes	characteristic
48	C₂³×C₃	C₂³	1	2	yes	—
49	C₂³×C₃	C₂³	1	1	yes	characteristic
50	C₃×D₄	—	2	4	no	—
51	C₃×D₄	—	2	2	no	—
52	C₃×D₄	—	2	2	no	—
53	C₃×D₄	—	4	2	no	—
54	C₂×C₃×C₄	—	2	2	no	—
55	C₂×C₃×C₄	—	2	2	no	—
56	C₂×C₃×C₄	—	4	2	no	—
57	C₂×C₃×C₄	—	4	2	no	—
58	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄	C₂³	1	2	yes	—
60	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄	C₂³	1	2	yes	—
62	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄	C₂³	1	2	yes	—
65	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
66	C₂×D₄	C₂²×C₃	1	2	yes	—
67	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×D₄	C₂²×C₃	1	2	yes	—
70	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₄	C₂²×C₃	1	2	yes	—
73	C₂²×C₄	C₂²×C₃	1	2	yes	—
74	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
75	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
76	C₄⋊C₄	C₂²×C₃	1	2	yes	—
77	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₄⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂²⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂²⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂²⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₄²	C₂²×C₃	1	2	yes	—
88	C₄²	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₃	—	2	1	no	—
90	C₂²×C₃	—	2	1	no	—
91	C₂²×C₃	—	2	1	no	—
92	C₂²×C₃	—	2	1	no	—
93	C₂²×C₃	—	2	2	no	—
94	C₂²×C₃	—	2	2	no	—
95	C₂²×C₃	—	2	2	no	—
96	C₂²×C₃	—	2	1	no	—
97	C₂²×C₃	#41	1	2	yes	—
98	C₂²×C₃	C₂⁴	1	1	yes	characteristic
99	C₃×C₄	—	2	1	no	—
100	C₃×C₄	—	2	1	no	—
101	C₃×C₄	—	2	2	no	—
102	C₃×C₄	—	2	1	no	—
103	C₃×C₄	—	2	1	no	—
104	C₃×C₄	—	2	2	no	—
105	C₃×C₄	—	2	2	no	—
106	C₃×C₄	#41	1	2	yes	—
107	C₂³	C₂³×C₃	1	1	yes	characteristic
108	C₂³	C₂³×C₃	1	2	yes	—
109	C₂³	C₂³×C₃	1	1	yes	characteristic
110	D₄	—	2	4	no	—
111	D₄	—	2	2	no	—
112	D₄	—	2	2	no	—
113	D₄	—	4	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
119	C₂×C₄	C₂³×C₃	1	2	yes	—
120	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
121	C₂×C₄	C₂³×C₃	1	2	yes	—
122	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
123	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
124	C₂×C₄	C₂³×C₃	1	2	yes	—
125	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
126	C₂×C₃	—	2	2	no	—
127	C₂×C₃	—	4	1	no	—
128	C₂×C₃	—	4	2	no	—
129	C₂×C₃	C₂×#41	1	1	yes	characteristic
130	C₂×C₃	C₂×#41	1	1	yes	characteristic
131	C₂×C₃	H(5,𝔽₂)	1	1	yes	characteristic
132	C₂²	—	2	1	no	—
133	C₂²	—	2	1	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	—	2	2	no	—
137	C₂²	—	2	2	no	—
138	C₂²	—	2	2	no	—
139	C₂²	—	2	1	no	—
140	C₂²	C₃×#41	1	2	yes	—
141	C₂²	C₂⁴×C₃	1	1	yes	characteristic
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	—	2	2	no	—
145	C₄	—	2	1	no	—
146	C₄	—	2	1	no	—
147	C₄	—	2	2	no	—
148	C₄	—	2	2	no	—
149	C₄	C₃×#41	1	2	yes	—
150	C₃	#553	1	1	yes	characteristic, direct product factor, Sylow
151	C₂	—	2	2	no	—
152	C₂	—	4	1	no	—
153	C₂	—	4	2	no	—
154	C₂	C₂×C₃×#41	1	1	yes	characteristic
155	C₂	C₂×C₃×#41	1	1	yes	characteristic
156	C₂	C₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#126	C₂	semidirect
2. C₃×#125	C₂	semidirect
3. C₃×#123	C₂	semidirect
4. C₃×#121	C₂	semidirect
5. C₃×#121	C₂	semidirect
6. C₃×#121	C₂	semidirect
7. C₃×C₄×D₄	C₂	semidirect
8. C₃×C₄×D₄	C₂	semidirect
9. C₃×C₄×D₄	C₂	semidirect
10. C₃×#117	C₂	semidirect
11. C₂×C₃×C₄⋊C₄	C₂	semidirect
12. #553	C₃	direct (N × H)
36. #126	C₂×C₃	semidirect
37. #125	C₂×C₃	semidirect
38. #123	C₂×C₃	semidirect
39. #121	C₂×C₃	semidirect
40. #121	C₂×C₃	semidirect
41. #121	C₂×C₃	semidirect
42. C₄×D₄	C₂×C₃	semidirect
43. C₄×D₄	C₂×C₃	semidirect
44. C₄×D₄	C₂×C₃	semidirect
45. #117	C₂×C₃	semidirect
46. C₂×C₄⋊C₄	C₂×C₃	semidirect
150. C₃	#553	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#126	2
C₃×#125	2
C₃×#123	2
C₃×#121	2
C₃×C₄×D₄	2
C₃×#117	2
C₂×C₃×C₄⋊C₄	2
#553	3

Subgroups — C3×#553 #5883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#553 #5883