Subgroups — C₃²×#1846 #11768895

Order 1152.

744 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×#107	C₂	1	2	yes	maximal
2	C₂×C₃²×#106	C₂	1	2	yes	maximal
3	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	C₃²×#382	C₂	1	2	yes	maximal
5	C₃×#1846	C₃	1	4	yes	maximal, direct product factor
6	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₃²×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
10	C₃²×#107	—	2	4	no	—
11	C₃²×#106	—	2	4	no	—
12	C₃²×C₄×C₈	C₄	1	4	yes	complemented
13	C₃²×#95	—	2	4	no	—
14	C₂×C₃×#107	C₂×C₃	1	8	yes	—
15	C₂×C₃×#106	C₂×C₃	1	8	yes	—
16	C₂×C₃×C₄×C₈	C₂×C₃	1	4	yes	—
17	C₃×#382	C₂×C₃	1	8	yes	—
18	C₂²×C₃²×C₄	—	2	4	no	—
19	C₂²×C₃²×C₄	D₄	1	2	yes	—
20	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
21	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
22	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
23	C₂×C₃²×C₈	D₄	1	2	yes	—
24	C₂×C₃²×C₈	D₄	1	2	yes	—
25	C₂×C₃²×C₈	Q₈	1	2	yes	—
26	C₂×C₃²×C₈	Q₈	1	2	yes	—
27	C₃²×C₄⋊C₄	—	2	4	no	—
28	C₃²×C₄⋊C₄	—	2	4	no	—
29	C₃²×C₄²	C₂×C₄	1	2	yes	—
30	C₃²×C₄²	Q₈	1	2	yes	—
31	#1846	C₃²	1	1	yes	characteristic, direct product factor, Sylow
32	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
33	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
34	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	16	yes	—
35	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
36	C₃×#107	—	2	16	no	—
37	C₃×#106	—	2	16	no	—
38	C₃×C₄×C₈	C₃×C₄	1	16	yes	complemented
39	C₃×#95	—	2	16	no	—
40	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
41	C₂×C₃²×C₄	—	2	4	no	—
42	C₂×C₃²×C₄	—	4	4	no	—
43	C₂×C₃²×C₄	—	4	8	no	—
44	C₂×C₃²×C₄	C₄⋊C₄	1	4	yes	—
45	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
47	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
48	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
51	C₃²×C₈	C₄⋊C₄	1	4	yes	—
52	C₃²×C₈	C₄⋊C₄	1	4	yes	—
53	C₂×#107	C₂×C₃²	1	2	yes	—
54	C₂×#106	C₂×C₃²	1	2	yes	—
55	C₂×C₄×C₈	C₂×C₃²	1	1	yes	characteristic
56	#382	C₂×C₃²	1	2	yes	—
57	C₂²×C₃×C₄	—	2	16	no	—
58	C₂²×C₃×C₄	C₃×D₄	1	8	yes	—
59	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
60	C₂×C₃×C₈	C₂×C₃×C₄	1	8	yes	—
61	C₂×C₃×C₈	C₂×C₃×C₄	1	8	yes	—
62	C₂×C₃×C₈	C₃×D₄	1	8	yes	—
63	C₂×C₃×C₈	C₃×D₄	1	8	yes	—
64	C₂×C₃×C₈	C₃×Q₈	1	8	yes	—
65	C₂×C₃×C₈	C₃×Q₈	1	8	yes	—
66	C₃×C₄⋊C₄	—	2	16	no	—
67	C₃×C₄⋊C₄	—	2	16	no	—
68	C₃×C₄²	C₂×C₃×C₄	1	8	yes	—
69	C₃×C₄²	C₃×Q₈	1	8	yes	—
70	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂²×C₃²	#127	1	1	yes	characteristic
72	C₂²×C₃²	C₄⋊Q₈	1	1	yes	characteristic
73	C₂²×C₃²	#135	1	4	yes	—
74	C₃²×C₄	—	2	4	no	—
75	C₃²×C₄	—	8	4	no	—
76	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
78	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
79	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
80	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
81	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
82	C₂×C₄⋊C₄	C₂²×C₃²	1	4	yes	—
83	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
84	#107	—	2	4	no	—
85	#106	—	2	4	no	—
86	C₄×C₈	C₃²×C₄	1	4	yes	complemented
87	#95	—	2	4	no	—
88	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
89	C₂×C₃×C₄	—	2	16	no	—
90	C₂×C₃×C₄	—	4	16	no	—
91	C₂×C₃×C₄	—	4	32	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×D₄	1	4	yes	—
95	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
96	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
97	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
98	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
99	C₃×C₈	C₃×C₄⋊C₄	1	16	yes	—
100	C₃×C₈	C₃×C₄⋊C₄	1	16	yes	—
101	C₂×C₃²	#384	1	1	yes	characteristic
102	C₂×C₃²	#427	1	2	yes	—
103	C₂×C₃²	#495	1	2	yes	—
104	C₂×C₃²	#499	1	2	yes	—
105	C₂²×C₄	—	2	4	no	—
106	C₂²×C₄	C₃²×D₄	1	2	yes	—
107	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
108	C₂×C₈	C₂×C₃²×C₄	1	2	yes	—
109	C₂×C₈	C₂×C₃²×C₄	1	2	yes	—
110	C₂×C₈	C₃²×D₄	1	2	yes	—
111	C₂×C₈	C₃²×D₄	1	2	yes	—
112	C₂×C₈	C₃²×Q₈	1	2	yes	—
113	C₂×C₈	C₃²×Q₈	1	2	yes	—
114	C₄⋊C₄	—	2	4	no	—
115	C₄⋊C₄	—	2	4	no	—
116	C₄²	C₂×C₃²×C₄	1	2	yes	—
117	C₄²	C₃²×Q₈	1	2	yes	—
118	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
119	C₂²×C₃	C₃×#127	1	4	yes	—
120	C₂²×C₃	C₃×C₄⋊Q₈	1	4	yes	—
121	C₂²×C₃	C₃×#135	1	16	yes	—
122	C₃×C₄	—	2	16	no	—
123	C₃×C₄	—	8	16	no	—
124	C₃×C₄	C₂×C₃×C₄⋊C₄	1	4	yes	—
125	C₃×C₄	C₂×C₃×C₄⋊C₄	1	4	yes	—
126	C₃×C₄	C₃×C₄⋊Q₈	1	4	yes	—
127	C₃×C₄	C₃×C₄⋊Q₈	1	4	yes	—
128	C₃²	#1846	1	1	yes	characteristic, direct product factor, Sylow
129	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
130	C₂×C₄	—	2	4	no	—
131	C₂×C₄	—	4	4	no	—
132	C₂×C₄	—	4	8	no	—
133	C₂×C₄	C₃²×C₄⋊C₄	1	4	yes	—
134	C₂×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
135	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
136	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
137	C₂×C₄	C₂×C₃²×Q₈	1	1	yes	characteristic
138	C₂×C₄	C₂×C₃²×Q₈	1	1	yes	characteristic
139	C₂×C₄	C₂×C₃²×Q₈	1	1	yes	characteristic
140	C₈	C₃²×C₄⋊C₄	1	4	yes	—
141	C₈	C₃²×C₄⋊C₄	1	4	yes	—
142	C₂×C₃	C₃×#384	1	4	yes	—
143	C₂×C₃	C₃×#427	1	8	yes	—
144	C₂×C₃	C₃×#495	1	8	yes	—
145	C₂×C₃	C₃×#499	1	8	yes	—
146	C₂²	C₂×C₃²×C₄⋊C₄	1	1	yes	characteristic
147	C₂²	C₃²×#127	1	1	yes	characteristic
148	C₂²	C₃²×C₄⋊Q₈	1	1	yes	characteristic
149	C₂²	C₃²×#135	1	4	yes	—
150	C₄	—	2	4	no	—
151	C₄	—	8	4	no	—
152	C₄	C₂×C₃²×C₄⋊C₄	1	1	yes	characteristic
153	C₄	C₂×C₃²×C₄⋊C₄	1	1	yes	characteristic
154	C₄	C₃²×C₄⋊Q₈	1	1	yes	characteristic
155	C₄	C₃²×C₄⋊Q₈	1	1	yes	characteristic
156	C₃	C₃×#1846	1	4	yes	direct product factor
157	C₂	C₃²×#384	1	1	yes	characteristic
158	C₂	C₃²×#427	1	2	yes	—
159	C₂	C₃²×#495	1	2	yes	—
160	C₂	C₃²×#499	1	2	yes	—

	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×#1846	C₃	direct (N × H)
12. C₃²×C₄×C₈	C₄	semidirect
31. #1846	C₃²	direct (N × H)
38. C₃×C₄×C₈	C₃×C₄	semidirect
86. C₄×C₈	C₃²×C₄	semidirect
128. C₃²	#1846	direct (N × H)
156. C₃	C₃×#1846	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×#107	2
C₂×C₃²×#106	2
C₂×C₃²×C₄×C₈	2
C₃²×#382	2
C₃×#1846	3

Subgroups — C32×#1846 #11768895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1846 #11768895