Subgroups — C₃²×#1836 #11768885

Order 1152.

672 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic
2	C₃²×#384	C₂	1	1	yes	maximal, characteristic
3	C₃²×#382	C₂	1	1	yes	maximal, characteristic
4	C₃²×#340	C₂	1	4	yes	maximal
5	C₃×#1836	C₃	1	4	yes	maximal, direct product factor
6	C₂²×C₃²×C₈	C₂²	1	2	yes	—
7	C₂×C₃²×C₄⋊C₄	—	2	2	no	—
8	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
11	C₃²×#97	C₄	1	4	yes	complemented
12	C₃²×#95	—	2	2	no	—
13	C₂×C₃×#97	C₂×C₃	1	4	yes	—
14	C₃×#384	C₂×C₃	1	4	yes	—
15	C₃×#382	C₂×C₃	1	4	yes	—
16	C₃×#340	C₂×C₃	1	16	yes	—
17	C₂²×C₃²×C₄	—	2	2	no	—
18	C₂²×C₃²×C₄	—	2	2	no	—
19	C₂²×C₃²×C₄	D₄	1	2	yes	—
20	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
21	C₂×C₃²×C₈	—	2	2	no	—
22	C₂×C₃²×C₈	—	2	2	no	—
23	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
24	C₃²×C₄⋊C₄	—	2	4	no	—
25	C₃²×C₄⋊C₄	—	2	4	no	—
26	C₃²×C₄⋊C₄	—	4	4	no	—
27	C₃²×C₄²	C₂×C₄	1	2	yes	—
28	C₃²×C₄²	Q₈	1	2	yes	—
29	#1836	C₃²	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²×C₃×C₈	C₂²×C₃	1	8	yes	—
31	C₂×C₃×C₄⋊C₄	—	2	8	no	—
32	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
33	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
34	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
35	C₃×#97	C₃×C₄	1	16	yes	complemented
36	C₃×#95	—	2	8	no	—
37	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
38	C₂×C₃²×C₄	—	2	2	no	—
39	C₂×C₃²×C₄	—	2	2	no	—
40	C₂×C₃²×C₄	—	4	2	no	—
41	C₂×C₃²×C₄	—	4	2	no	—
42	C₂×C₃²×C₄	—	4	4	no	—
43	C₂×C₃²×C₄	—	4	2	no	—
44	C₂×C₃²×C₄	—	4	2	no	—
45	C₂×C₃²×C₄	C₄⋊C₄	1	4	yes	—
46	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₃²×C₄	#41	1	2	yes	—
49	C₂×C₃²×C₄	#41	1	2	yes	—
50	C₃²×C₈	—	2	4	no	—
51	C₂×#97	C₂×C₃²	1	1	yes	characteristic
52	#384	C₂×C₃²	1	1	yes	characteristic
53	#382	C₂×C₃²	1	1	yes	characteristic
54	#340	C₂×C₃²	1	4	yes	—
55	C₂²×C₃×C₄	—	2	8	no	—
56	C₂²×C₃×C₄	—	2	8	no	—
57	C₂²×C₃×C₄	C₃×D₄	1	8	yes	—
58	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
59	C₂×C₃×C₈	—	2	8	no	—
60	C₂×C₃×C₈	—	2	8	no	—
61	C₂×C₃×C₈	C₂×C₃×C₄	1	16	yes	—
62	C₃×C₄⋊C₄	—	2	16	no	—
63	C₃×C₄⋊C₄	—	2	16	no	—
64	C₃×C₄⋊C₄	—	4	16	no	—
65	C₃×C₄²	C₂×C₃×C₄	1	8	yes	—
66	C₃×C₄²	C₃×Q₈	1	8	yes	—
67	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₃²	#124	1	1	yes	characteristic
69	C₂²×C₃²	#124	1	1	yes	characteristic
70	C₂²×C₃²	AGL(1,ℤ/8)	1	2	yes	—
71	C₂²×C₃²	#137	1	2	yes	—
72	C₃²×C₄	—	2	4	no	—
73	C₃²×C₄	—	8	2	no	—
74	C₃²×C₄	—	8	2	no	—
75	C₃²×C₄	#117	1	2	yes	—
76	C₃²×C₄	#125	1	2	yes	—
77	C₂²×C₈	C₂²×C₃²	1	2	yes	—
78	C₂×C₄⋊C₄	—	2	2	no	—
79	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
80	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
81	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
82	#97	C₃²×C₄	1	4	yes	complemented
83	#95	—	2	2	no	—
84	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
85	C₂×C₃×C₄	—	2	8	no	—
86	C₂×C₃×C₄	—	2	8	no	—
87	C₂×C₃×C₄	—	4	8	no	—
88	C₂×C₃×C₄	—	4	8	no	—
89	C₂×C₃×C₄	—	4	16	no	—
90	C₂×C₃×C₄	—	4	8	no	—
91	C₂×C₃×C₄	—	4	8	no	—
92	C₂×C₃×C₄	C₃×C₄⋊C₄	1	16	yes	—
93	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
94	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
95	C₂×C₃×C₄	C₃×#41	1	8	yes	—
96	C₂×C₃×C₄	C₃×#41	1	8	yes	—
97	C₃×C₈	—	2	16	no	—
98	C₂×C₃²	#382	1	1	yes	characteristic
99	C₂×C₃²	#428	1	2	yes	—
100	C₂×C₃²	#489	1	2	yes	—
101	C₂×C₃²	#490	1	1	yes	characteristic
102	C₂×C₃²	#491	1	1	yes	characteristic
103	C₂²×C₄	—	2	2	no	—
104	C₂²×C₄	—	2	2	no	—
105	C₂²×C₄	C₃²×D₄	1	2	yes	—
106	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	C₂×C₃²×C₄	1	4	yes	—
110	C₄⋊C₄	—	2	4	no	—
111	C₄⋊C₄	—	2	4	no	—
112	C₄⋊C₄	—	4	4	no	—
113	C₄²	C₂×C₃²×C₄	1	2	yes	—
114	C₄²	C₃²×Q₈	1	2	yes	—
115	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
116	C₂²×C₃	C₃×#124	1	4	yes	—
117	C₂²×C₃	C₃×#124	1	4	yes	—
118	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	8	yes	—
119	C₂²×C₃	C₃×#137	1	8	yes	—
120	C₃×C₄	—	2	16	no	—
121	C₃×C₄	—	8	8	no	—
122	C₃×C₄	—	8	8	no	—
123	C₃×C₄	C₃×#117	1	8	yes	—
124	C₃×C₄	C₃×#125	1	8	yes	—
125	C₃²	#1836	1	1	yes	characteristic, direct product factor, Sylow
126	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	4	2	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	—	4	4	no	—
132	C₂×C₄	—	4	2	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	C₃²×C₄⋊C₄	1	4	yes	—
135	C₂×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
136	C₂×C₄	C₂×C₃²×Q₈	1	1	yes	characteristic
137	C₂×C₄	C₃²×#41	1	2	yes	—
138	C₂×C₄	C₃²×#41	1	2	yes	—
139	C₈	—	2	4	no	—
140	C₂×C₃	C₃×#382	1	4	yes	—
141	C₂×C₃	C₃×#428	1	8	yes	—
142	C₂×C₃	C₃×#489	1	8	yes	—
143	C₂×C₃	C₃×#490	1	4	yes	—
144	C₂×C₃	C₃×#491	1	4	yes	—
145	C₂²	C₂×C₃²×C₄⋊C₄	1	1	yes	characteristic
146	C₂²	C₃²×#124	1	1	yes	characteristic
147	C₂²	C₃²×#124	1	1	yes	characteristic
148	C₂²	C₃²×AGL(1,ℤ/8)	1	2	yes	—
149	C₂²	C₃²×#137	1	2	yes	—
150	C₄	—	2	4	no	—
151	C₄	—	8	2	no	—
152	C₄	—	8	2	no	—
153	C₄	C₃²×#117	1	2	yes	—
154	C₄	C₃²×#125	1	2	yes	—
155	C₃	C₃×#1836	1	4	yes	direct product factor
156	C₂	C₃²×#382	1	1	yes	characteristic
157	C₂	C₃²×#428	1	2	yes	—
158	C₂	C₃²×#489	1	2	yes	—
159	C₂	C₃²×#490	1	1	yes	characteristic
160	C₂	C₃²×#491	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃²	C₂×D₄
commutator	C₂×C₄	C₂²×C₃²×C₄
Frattini, cosocle	C₂²×C₄	C₂³×C₃²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃² ◁ C₂×C₃²×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃×#1836	C₃	direct (N × H)
11. C₃²×#97	C₄	semidirect
29. #1836	C₃²	direct (N × H)
35. C₃×#97	C₃×C₄	semidirect
82. #97	C₃²×C₄	semidirect
125. C₃²	#1836	direct (N × H)
155. C₃	C₃×#1836	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×C₃²×#97	2
C₃²×#384	2
C₃²×#382	2
C₃²×#340	2
C₃×#1836	3

Subgroups — C32×#1836 #11768885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1836 #11768885