Subgroups — C₂²×#11718081 #16015939

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6090	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88058	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718081	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₁₃×#107	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
7	C₂²×C₄⋊Dic₁₃	—	2	1	no	—
8	C₂×C₁₃×#107	—	2	3	no	—
9	C₂×C₁₃×#107	C₂²	1	6	yes	—
10	C₂×#88058	—	2	3	no	—
11	C₂×#88058	C₂²	1	6	yes	—
12	C₂²×#6090	C₄	1	8	yes	complemented
13	C₂²×#6090	C₂²	1	6	yes	—
14	#11718081	C₂²	1	16	yes	direct product factor
15	C₂³×C₄×C₁₃	—	4	1	no	—
16	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
17	C₂³×Dic₁₃	—	4	1	no	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
19	C₂²×C₈×C₁₃	D₄	1	3	yes	—
20	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
21	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
22	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
23	C₂×C₁₃×C₄⋊C₄	—	4	3	no	—
24	C₂×C₄⋊Dic₁₃	—	2	6	no	—
25	C₂×C₄⋊Dic₁₃	—	4	3	no	—
26	C₁₃×#107	—	2	6	no	—
27	C₁₃×#107	C₂³	1	4	yes	—
28	#88058	—	2	6	no	—
29	#88058	C₂³	1	4	yes	—
30	C₂×#6090	C₂×C₄	1	24	yes	complemented
31	C₂×#6090	C₂³	1	4	yes	—
32	C₂²×#366	—	13	1	no	maximal, Sylow
33	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	—	4	6	no	—
35	C₂²×C₄×C₁₃	—	8	4	no	—
36	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
37	C₂²×C₄×C₁₃	D₈	1	3	yes	—
38	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
39	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
40	C₂²×Dic₁₃	—	4	6	no	—
41	C₂²×Dic₁₃	—	8	4	no	—
42	C₂×C₈×C₁₃	C₄⋊C₄	1	12	yes	—
43	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
44	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
45	C₂×C₈×C₁₃	C₂×Q₈	1	6	yes	—
46	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
47	C₁₃×C₄⋊C₄	—	2	4	no	—
48	C₁₃×C₄⋊C₄	—	4	6	no	—
49	C₄⋊Dic₁₃	—	2	4	no	—
50	C₄⋊Dic₁₃	—	4	6	no	—
51	#6090	C₂²×C₄	1	8	yes	complemented
52	C₂³×C₁₆	—	13	1	no	—
53	C₂²×#107	—	13	1	no	—
54	C₂²×#107	D₁₃	1	1	yes	characteristic
55	C₂×#366	—	13	12	no	—
56	C₂³×C₁₃	#107	1	4	yes	—
57	C₂³×C₁₃	D₁₆	1	4	yes	—
58	C₂³×C₁₃	Q₃₂	1	4	yes	—
59	C₂³×C₁₃	C₂×D₈	1	3	yes	—
60	C₂×C₄×C₁₃	—	4	4	no	—
61	C₂×C₄×C₁₃	—	8	12	no	—
62	C₂×C₄×C₁₃	#107	1	12	yes	—
63	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
64	C₂×C₄×C₁₃	C₂×D₈	1	3	yes	—
65	C₂×C₄×C₁₃	C₂×Q₁₆	1	6	yes	—
66	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
67	C₂×Dic₁₃	—	4	4	no	—
68	C₂×Dic₁₃	—	8	12	no	—
69	C₈×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
70	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
71	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
72	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
73	C₂²×C₄⋊C₄	—	2	1	no	—
74	C₂²×C₄⋊C₄	—	26	1	no	—
75	C₂²×C₁₆	—	13	8	no	—
76	C₂²×C₁₆	—	13	6	no	—
77	C₂×#107	—	2	3	no	—
78	C₂×#107	—	13	6	no	—
79	C₂×#107	—	26	3	no	—
80	C₂×#107	C₂×D₁₃	1	6	yes	—
81	#366	—	13	16	no	—
82	C₂²×C₁₃	#366	1	16	yes	complemented
83	C₂²×C₁₃	C₂×#107	1	6	yes	—
84	C₂²×C₁₃	C₂×D₁₆	1	6	yes	—
85	C₂²×C₁₃	C₂×Q₃₂	1	6	yes	—
86	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
87	C₄×C₁₃	—	8	4	no	—
88	C₄×C₁₃	C₂×#107	1	6	yes	—
89	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
90	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
91	Dic₁₃	—	8	4	no	—
92	C₂³×C₄	—	4	1	no	—
93	C₂³×C₄	—	52	1	no	—
94	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
95	C₂²×C₈	Dic₂₆	1	4	yes	—
96	C₂²×C₈	C₄×D₁₃	1	4	yes	—
97	C₂²×C₈	C₂²⋊D₁₃	1	3	yes	—
98	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
99	C₂×C₄⋊C₄	—	2	6	no	—
100	C₂×C₄⋊C₄	—	4	3	no	—
101	C₂×C₄⋊C₄	—	26	6	no	—
102	C₂×C₄⋊C₄	—	52	3	no	—
103	C₂×C₁₆	—	13	24	no	—
104	C₂×C₁₆	—	13	4	no	—
105	#107	—	2	6	no	—
106	#107	—	13	4	no	—
107	#107	—	26	6	no	—
108	#107	C₂²×D₁₃	1	4	yes	—
109	C₂×C₁₃	C₂×#366	1	12	yes	complemented
110	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
111	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
112	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
113	C₂⁴	#6104	1	1	yes	characteristic
114	C₂²×C₄	—	4	6	no	—
115	C₂²×C₄	—	8	4	no	—
116	C₂²×C₄	—	52	6	no	—
117	C₂²×C₄	—	104	4	no	—
118	C₂²×C₄	#6101	1	4	yes	—
119	C₂²×C₄	#6104	1	3	yes	—
120	C₂²×C₄	#6107	1	4	yes	—
121	C₂²×C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
122	C₂×C₈	#6101	1	12	yes	—
123	C₂×C₈	C₂×Dic₂₆	1	6	yes	—
124	C₂×C₈	C₂×C₄×D₁₃	1	6	yes	—
125	C₂×C₈	C₂×C₂²⋊D₁₃	1	3	yes	—
126	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
127	C₄⋊C₄	—	2	4	no	—
128	C₄⋊C₄	—	4	6	no	—
129	C₄⋊C₄	—	26	4	no	—
130	C₄⋊C₄	—	52	6	no	—
131	C₁₆	—	13	8	no	—
132	C₁₃	C₂²×#366	1	1	yes	characteristic, complemented, Sylow
133	C₂³	#88047	1	4	yes	—
134	C₂³	#88066	1	4	yes	—
135	C₂³	#88069	1	4	yes	—
136	C₂³	C₂×#6104	1	3	yes	—
137	C₂×C₄	—	4	4	no	—
138	C₂×C₄	—	8	12	no	—
139	C₂×C₄	—	52	4	no	—
140	C₂×C₄	—	104	12	no	—
141	C₂×C₄	#88047	1	12	yes	—
142	C₂×C₄	C₂×#6101	1	6	yes	—
143	C₂×C₄	C₂×#6104	1	3	yes	—
144	C₂×C₄	C₂×#6107	1	6	yes	—
145	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
146	C₈	C₂×#6101	1	6	yes	—
147	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
148	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
149	C₂²	#11718081	1	16	yes	direct product factor
150	C₂²	C₂×#88047	1	6	yes	—
151	C₂²	C₂×#88066	1	6	yes	—
152	C₂²	C₂×#88069	1	6	yes	—
153	C₂²	C₂²×#6104	1	1	yes	characteristic
154	C₄	—	8	4	no	—
155	C₄	—	104	4	no	—
156	C₄	C₂×#88047	1	6	yes	—
157	C₄	C₂²×#6101	1	1	yes	characteristic
158	C₄	C₂²×#6107	1	1	yes	characteristic
159	C₂	C₂×#11718081	1	12	yes	direct product factor
160	C₂	C₂²×#88047	1	1	yes	characteristic
161	C₂	C₂²×#88066	1	1	yes	characteristic
162	C₂	C₂²×#88069	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	#6104
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×#107	C₂
socle, prime radical	C₂⁴×C₁₃	D₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×#107	D₁₃
hypocenter	C₁₃	C₂²×#366
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×#107

Complements

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

N	H ≅ G/N	type
3. C₂×#11718081	C₂	direct (N × H)
12. C₂²×#6090	C₄	semidirect
14. #11718081	C₂²	direct (N × H)
30. C₂×#6090	C₂×C₄	semidirect
51. #6090	C₂²×C₄	semidirect
82. C₂²×C₁₃	#366	semidirect
109. C₂×C₁₃	C₂×#366	semidirect
132. C₁₃	C₂²×#366	semidirect
149. C₂²	#11718081	direct (N × H)
159. C₂	C₂×#11718081	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#6090	2
C₂²×#88058	2
C₂×#11718081	2
C₂²×C₁₃×#107	2
C₂²×#366	13

Subgroups — C22×#11718081 #16015939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718081 #16015939