Subgroups — C₂×#10588362 #11874945

Order 1152.

636 conjugacy classes of subgroups.

The subgroup lattice has 159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63431	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#63378	C₂	1	4	yes	maximal
4	#10588362	C₂	1	8	yes	maximal, direct product factor
5	C₂×#4682	—	3	1	no	maximal
6	C₂²×Dic₁₈	—	2	2	no	—
7	C₂²×C₈×C₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₉	—	2	2	no	—
10	C₂×C₄⋊Dic₉	C₂²	1	4	yes	—
11	#63431	—	2	4	no	—
12	#63431	C₂²	1	8	yes	—
13	C₄×C₈×C₉	C₂²	1	4	yes	—
14	#63378	C₂²	1	16	yes	—
15	C₂×#869	—	3	2	no	—
16	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
17	C₂×#818	—	3	4	no	—
18	#4682	—	3	8	no	—
19	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₉	—	2	4	no	—
23	C₂×Dic₁₈	—	2	8	no	—
24	C₂×Dic₁₈	—	4	8	no	—
25	C₂×C₈×C₉	Q₈	1	8	yes	complemented
26	C₂×C₈×C₉	C₂³	1	4	yes	—
27	C₄²×C₉	D₄	1	2	yes	—
28	C₄²×C₉	C₂³	1	2	yes	—
29	C₄⋊Dic₉	—	2	4	no	—
30	C₄⋊Dic₉	—	2	8	no	—
31	C₄⋊Dic₉	C₂³	1	8	yes	—
32	C₂×#500	—	9	1	no	Sylow
33	C₂²×Dic₆	—	6	2	no	—
34	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
35	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
36	C₂×C₄⋊Dic₃	—	3	4	no	—
37	C₂×C₄⋊Dic₃	—	6	2	no	—
38	#869	—	3	8	no	—
39	#869	—	6	4	no	—
40	C₃×C₄×C₈	C₂×D₃	1	4	yes	—
41	#818	—	3	16	no	—
42	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₉	D₈	1	4	yes	—
44	C₂×C₄×C₉	Q₁₆	1	4	yes	—
45	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
49	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₉	—	2	8	no	—
51	C₂×Dic₉	—	4	8	no	—
52	Dic₁₈	—	4	16	no	—
53	C₈×C₉	C₂×Q₈	1	8	yes	complemented
54	C₂×C₄⋊Q₈	—	9	2	no	—
55	#500	—	9	8	no	—
56	C₂×#107	—	9	4	no	—
57	C₂×C₄×C₈	D₉	1	1	yes	characteristic
58	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
59	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
60	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
61	C₂²×Dic₃	—	6	4	no	—
62	C₂×Dic₆	—	6	8	no	—
63	C₂×Dic₆	—	12	8	no	—
64	C₂×C₃×C₈	Dic₆	1	8	yes	—
65	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
66	C₃×C₄²	D₁₂	1	2	yes	—
67	C₃×C₄²	C₂²×D₃	1	2	yes	—
68	C₄⋊Dic₃	—	3	8	no	—
69	C₄⋊Dic₃	—	6	8	no	—
70	C₄⋊Dic₃	—	6	4	no	—
71	C₂²×C₉	C₄⋊Q₈	1	2	yes	—
72	C₂²×C₉	C₂×D₈	1	2	yes	—
73	C₂²×C₉	C₂×Q₁₆	1	2	yes	—
74	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
75	C₄×C₉	C₄⋊Q₈	1	2	yes	—
76	C₄×C₉	C₂×D₈	1	4	yes	—
77	C₄×C₉	C₂×Q₁₆	1	4	yes	—
78	C₄×C₉	C₂²×Q₈	1	2	yes	—
79	Dic₉	—	4	8	no	—
80	C₂²×Q₈	—	18	2	no	—
81	C₂²×C₈	C₂×D₉	1	2	yes	—
82	C₄⋊Q₈	—	9	8	no	—
83	C₄⋊Q₈	—	18	4	no	—
84	C₂×C₄⋊C₄	—	9	4	no	—
85	C₂×C₄⋊C₄	—	18	2	no	—
86	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
87	#107	—	9	16	no	—
88	C₄×C₈	C₂×D₉	1	4	yes	—
89	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
90	C₂×C₃×C₄	D₂₄	1	4	yes	—
91	C₂×C₃×C₄	Dic₁₂	1	4	yes	—
92	C₂×C₃×C₄	C₂×Dic₆	1	4	yes	—
93	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
94	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
95	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
96	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
97	C₂×Dic₃	—	6	8	no	—
98	C₂×Dic₃	—	12	8	no	—
99	Dic₆	—	12	16	no	—
100	C₃×C₈	C₂×Dic₆	1	8	yes	—
101	C₂×C₉	#500	1	4	yes	complemented
102	C₂×C₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
103	C₂×C₉	C₂²×D₈	1	1	yes	characteristic
104	C₂×C₉	C₂²×Q₁₆	1	1	yes	characteristic
105	C₂×Q₈	—	18	8	no	—
106	C₂×Q₈	—	36	8	no	—
107	C₂²×C₄	—	18	4	no	—
108	C₂²×C₄	D₃₆	1	1	yes	characteristic
109	C₂²×C₄	D₃₆	1	1	yes	characteristic
110	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
111	C₂×C₈	Dic₁₈	1	8	yes	complemented
112	C₂×C₈	C₂²×D₉	1	4	yes	—
113	C₄⋊C₄	—	9	8	no	—
114	C₄⋊C₄	—	18	4	no	—
115	C₄⋊C₄	—	18	8	no	—
116	C₄²	D₃₆	1	2	yes	—
117	C₄²	C₂²×D₉	1	2	yes	—
118	C₂²×C₃	#869	1	2	yes	—
119	C₂²×C₃	C₂×D₂₄	1	2	yes	—
120	C₂²×C₃	C₂×Dic₁₂	1	2	yes	—
121	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
122	C₃×C₄	#869	1	2	yes	—
123	C₃×C₄	C₂×D₂₄	1	4	yes	—
124	C₃×C₄	C₂×Dic₁₂	1	4	yes	—
125	C₃×C₄	C₂²×Dic₆	1	2	yes	—
126	Dic₃	—	12	8	no	—
127	C₉	C₂×#500	1	1	yes	characteristic, complemented, Sylow
128	C₂³	C₂×D₃₆	1	1	yes	characteristic
129	Q₈	—	36	16	no	—
130	C₂×C₄	—	18	8	no	—
131	C₂×C₄	—	36	8	no	—
132	C₂×C₄	Dic₃₆	1	4	yes	—
133	C₂×C₄	D₇₂	1	4	yes	—
134	C₂×C₄	C₂×Dic₁₈	1	4	yes	—
135	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
136	C₂×C₄	C₂×D₃₆	1	2	yes	—
137	C₂×C₄	C₂×D₃₆	1	2	yes	—
138	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
139	C₈	C₂×Dic₁₈	1	8	yes	complemented
140	C₂×C₃	#4682	1	4	yes	—
141	C₂×C₃	C₂×#869	1	1	yes	characteristic
142	C₂×C₃	C₂²×D₂₄	1	1	yes	characteristic
143	C₂×C₃	C₂²×Dic₁₂	1	1	yes	characteristic
144	C₂²	#63431	1	2	yes	—
145	C₂²	C₂×Dic₃₆	1	2	yes	—
146	C₂²	C₂×D₇₂	1	2	yes	—
147	C₂²	C₂²×D₃₆	1	1	yes	characteristic
148	C₄	—	36	8	no	—
149	C₄	#63431	1	2	yes	—
150	C₄	C₂×Dic₃₆	1	4	yes	—
151	C₄	C₂×D₇₂	1	4	yes	—
152	C₄	C₂²×Dic₁₈	1	2	yes	—
153	C₃	C₂×#4682	1	1	yes	characteristic
154	C₂	#10588362	1	4	yes	direct product factor
155	C₂	C₂×#63431	1	1	yes	characteristic
156	C₂	C₂²×Dic₃₆	1	1	yes	characteristic
157	C₂	C₂²×D₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₆
commutator, cosocle	C₂×C₄×C₉	C₂⁴
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₄×C₈×C₉	C₂
socle, prime radical	C₂³×C₃	C₂×D₁₂
hypercenter	C₂×C₄×C₈	D₉
hypocenter	C₉	C₂×#500
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #10588362	C₂	direct (N × H)
25. C₂×C₈×C₉	Q₈	semidirect
53. C₈×C₉	C₂×Q₈	semidirect
101. C₂×C₉	#500	semidirect
111. C₂×C₈	Dic₁₈	semidirect
127. C₉	C₂×#500	semidirect
139. C₈	C₂×Dic₁₈	semidirect
154. C₂	#10588362	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×#63431	2
C₂×C₄×C₈×C₉	2
C₂×#63378	2
#10588362	2
C₂×#4682	3

Subgroups — C2×#10588362 #11874945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588362 #11874945