Subgroups — C₂×#10588363 #11874912

Order 1152.

540 conjugacy classes of subgroups.

The subgroup lattice has 153 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63432	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#63378	C₂	1	2	yes	maximal
4	C₂×#63377	C₂	1	2	yes	maximal
5	#10588363	C₂	1	8	yes	maximal, direct product factor
6	C₂×#4683	—	3	1	no	maximal
7	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₉	C₂²	1	4	yes	—
11	C₂×Dic₉⋊C₄	—	2	4	no	—
12	#63432	—	2	4	no	—
13	#63432	C₂²	1	8	yes	—
14	C₄×C₈×C₉	C₂²	1	4	yes	—
15	#63378	C₂²	1	8	yes	—
16	#63377	C₂²	1	8	yes	—
17	C₂×#870	—	3	2	no	—
18	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
19	C₂×#818	—	3	2	no	—
20	C₂×#817	—	3	2	no	—
21	#4683	—	3	8	no	—
22	C₂²×C₄×C₉	D₄	1	2	yes	—
23	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₉	—	2	4	no	—
25	C₂×C₈×C₉	Q₈	1	4	yes	—
26	C₂×C₈×C₉	Q₈	1	4	yes	—
27	C₂×C₈×C₉	C₂³	1	2	yes	—
28	C₂×C₈×C₉	C₂³	1	2	yes	—
29	C₄²×C₉	D₄	1	2	yes	—
30	C₄²×C₉	C₂³	1	2	yes	—
31	C₄⋊Dic₉	—	2	4	no	—
32	C₄⋊Dic₉	C₂³	1	8	yes	—
33	Dic₉⋊C₄	—	2	16	no	—
34	C₂×#499	—	9	1	no	Sylow
35	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
36	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
37	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
38	C₂×C₄⋊Dic₃	—	3	4	no	—
39	C₂×Dic₃⋊C₄	—	6	4	no	—
40	#870	—	3	8	no	—
41	#870	—	6	4	no	—
42	C₃×C₄×C₈	C₂×D₃	1	4	yes	—
43	#818	—	3	8	no	—
44	#817	—	3	8	no	—
45	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₉	—	2	4	no	—
47	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
48	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
50	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
51	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
52	C₂×Dic₉	—	2	8	no	—
53	C₂×Dic₉	—	4	8	no	—
54	C₈×C₉	C₂×Q₈	1	4	yes	—
55	C₈×C₉	C₂×Q₈	1	4	yes	—
56	C₂×#125	—	9	2	no	—
57	#499	—	9	8	no	—
58	C₂×#107	—	9	2	no	—
59	C₂×#106	—	9	2	no	—
60	C₂×C₄×C₈	D₉	1	1	yes	characteristic
61	C₂²×C₃×C₄	D₁₂	1	2	yes	—
62	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
63	C₂²×Dic₃	—	6	4	no	—
64	C₂×C₃×C₈	Dic₆	1	4	yes	—
65	C₂×C₃×C₈	Dic₆	1	4	yes	—
66	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
67	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
68	C₃×C₄²	D₁₂	1	2	yes	—
69	C₃×C₄²	C₂²×D₃	1	2	yes	—
70	C₄⋊Dic₃	—	3	8	no	—
71	C₄⋊Dic₃	—	6	4	no	—
72	Dic₃⋊C₄	—	6	16	no	—
73	C₂²×C₉	C₄⋊Q₈	1	2	yes	—
74	C₂²×C₉	#135	1	4	yes	—
75	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
76	C₄×C₉	—	2	4	no	—
77	C₄×C₉	C₄⋊Q₈	1	2	yes	—
78	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
79	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
80	Dic₉	—	4	8	no	—
81	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
82	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
83	#125	—	9	8	no	—
84	#125	—	18	4	no	—
85	C₂×C₄⋊C₄	—	9	4	no	—
86	C₂×C₄⋊C₄	—	18	4	no	—
87	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
88	#107	—	9	8	no	—
89	#106	—	9	8	no	—
90	C₄×C₈	C₂×D₉	1	4	yes	—
91	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
92	C₂×C₃×C₄	—	2	4	no	—
93	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
94	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
95	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
96	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
97	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
98	C₂×Dic₃	—	6	8	no	—
99	C₂×Dic₃	—	12	8	no	—
100	C₃×C₈	C₂×Dic₆	1	4	yes	—
101	C₃×C₈	C₂×Dic₆	1	4	yes	—
102	C₂×C₉	#499	1	4	yes	complemented
103	C₂×C₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
104	C₂×C₉	C₂×#135	1	2	yes	—
105	C₂²×C₄	—	18	4	no	—
106	C₂²×C₄	D₃₆	1	2	yes	—
107	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
108	C₂×C₈	Dic₁₈	1	4	yes	—
109	C₂×C₈	Dic₁₈	1	4	yes	—
110	C₂×C₈	C₂²×D₉	1	2	yes	—
111	C₂×C₈	C₂²×D₉	1	2	yes	—
112	C₄⋊C₄	—	9	8	no	—
113	C₄⋊C₄	—	18	4	no	—
114	C₄⋊C₄	—	18	16	no	—
115	C₄²	D₃₆	1	2	yes	—
116	C₄²	C₂²×D₉	1	2	yes	—
117	C₂²×C₃	#869	1	2	yes	—
118	C₂²×C₃	#904	1	4	yes	—
119	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
120	C₃×C₄	—	2	4	no	—
121	C₃×C₄	#869	1	2	yes	—
122	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
123	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
124	Dic₃	—	12	8	no	—
125	C₉	C₂×#499	1	1	yes	characteristic, complemented, Sylow
126	C₂³	C₂×D₃₆	1	1	yes	characteristic
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	18	8	no	—
129	C₂×C₄	—	36	8	no	—
130	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
131	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
132	C₂×C₄	C₂×D₃₆	1	4	yes	—
133	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
134	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
135	C₈	C₂×Dic₁₈	1	4	yes	—
136	C₈	C₂×Dic₁₈	1	4	yes	—
137	C₂×C₃	#4683	1	4	yes	—
138	C₂×C₃	C₂×#869	1	1	yes	characteristic
139	C₂×C₃	C₂×#904	1	2	yes	—
140	C₂²	#63431	1	2	yes	—
141	C₂²	#63467	1	4	yes	—
142	C₂²	C₂²×D₃₆	1	1	yes	characteristic
143	C₄	—	2	4	no	—
144	C₄	—	36	8	no	—
145	C₄	#63431	1	2	yes	—
146	C₄	C₂²×Dic₁₈	1	1	yes	characteristic
147	C₄	C₂²×Dic₁₈	1	1	yes	characteristic
148	C₃	C₂×#4683	1	1	yes	characteristic
149	C₂	#10588363	1	4	yes	direct product factor
150	C₂	C₂×#63431	1	1	yes	characteristic
151	C₂	C₂×#63467	1	2	yes	—

	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×#499
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
5. #10588363	C₂	direct (N × H)
102. C₂×C₉	#499	semidirect
125. C₉	C₂×#499	semidirect
149. C₂	#10588363	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×#63432	2
C₂×C₄×C₈×C₉	2
C₂×#63378	2
C₂×#63377	2
#10588363	2
C₂×#4683	3

Subgroups — C2×#10588363 #11874912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588363 #11874912