Subgroups — C₂²×#11718098 #16015971

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88059	C₂	1	2	yes	maximal
2	C₂×#11718098	C₂	1	12	yes	maximal, direct product factor
3	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₂²×#6099	—	2	2	no	—
6	C₂²×C₁₃×C₁₆	C₄	1	6	yes	—
7	C₂²×C₁₃×C₁₆	C₄	1	2	yes	—
8	C₂²×C₁₃×C₁₆	C₂²	1	6	yes	—
9	C₂×#88059	—	2	6	no	—
10	C₂×#88059	C₂²	1	12	yes	—
11	#11718098	C₂²	1	16	yes	direct product factor
12	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
14	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	D₄	1	3	yes	—
16	C₂²×C₈×C₁₃	Q₈	1	3	yes	—
17	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
19	C₂×#6099	—	2	12	no	—
20	C₂×#6099	—	4	6	no	—
21	C₂²×#1055	—	4	2	no	—
22	C₂×C₁₃×C₁₆	C₂×C₄	1	12	yes	—
23	C₂×C₁₃×C₁₆	C₂×C₄	1	12	yes	—
24	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
25	#88059	—	2	12	no	—
26	#88059	C₂³	1	8	yes	—
27	C₂²×#368	—	13	1	no	maximal, Sylow
28	C₂⁴×C₁₃	Q₁₆	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	C₄⋊C₄	1	3	yes	—
30	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₃	D₈	1	3	yes	—
32	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	Q₁₆	1	3	yes	—
34	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
35	C₂×C₈×C₁₃	C₄⋊C₄	1	6	yes	—
36	C₂×C₈×C₁₃	C₄⋊C₄	1	3	yes	—
37	C₂×C₈×C₁₃	C₄⋊C₄	1	3	yes	—
38	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
39	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
40	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
41	C₂×C₈×C₁₃	C₂×Q₈	1	3	yes	—
42	C₂×C₈×C₁₃	C₂×Q₈	1	3	yes	—
43	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
44	#6099	—	2	8	no	—
45	#6099	—	4	12	no	—
46	C₂×#1055	—	4	12	no	—
47	C₁₃×C₁₆	C₂²×C₄	1	8	yes	—
48	C₂³×C₁₆	D₁₃	1	1	yes	characteristic
49	C₂²×#108	—	13	2	no	—
50	C₂×#368	—	13	12	no	—
51	C₂³×C₁₃	—	2	4	no	—
52	C₂³×C₁₃	#107	1	3	yes	—
53	C₂³×C₁₃	#107	1	1	yes	characteristic
54	C₂³×C₁₃	C₂×Q₁₆	1	3	yes	—
55	C₂×C₄×C₁₃	#107	1	6	yes	—
56	C₂×C₄×C₁₃	#107	1	3	yes	—
57	C₂×C₄×C₁₃	#107	1	3	yes	—
58	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
59	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
60	C₂×C₄×C₁₃	C₂×D₈	1	3	yes	—
61	C₂×C₄×C₁₃	C₂×D₈	1	3	yes	—
62	C₂×C₄×C₁₃	C₂×Q₁₆	1	3	yes	—
63	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
64	C₈×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
65	C₈×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
66	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
67	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
68	#1055	—	4	8	no	—
69	C₂²×M₁₆	—	26	2	no	—
70	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
71	C₂²×C₁₆	Dic₁₃	1	2	yes	—
72	C₂²×C₁₆	Dic₁₃	1	6	yes	—
73	C₂²×C₁₆	C₂×D₁₃	1	6	yes	—
74	C₂×#108	—	13	12	no	—
75	C₂×#108	—	26	6	no	—
76	#368	—	13	16	no	—
77	C₂²×C₁₃	—	2	6	no	—
78	C₂²×C₁₃	—	2	6	no	—
79	C₂²×C₁₃	#368	1	4	yes	complemented
80	C₂²×C₁₃	C₂×#107	1	3	yes	—
81	C₂²×C₁₃	C₂×#107	1	3	yes	—
82	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
83	C₄×C₁₃	C₂×#107	1	3	yes	—
84	C₄×C₁₃	C₂×#107	1	3	yes	—
85	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
86	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
87	C₂³×C₄	D₅₂	1	1	yes	characteristic
88	C₂×M₁₆	—	26	12	no	—
89	C₂×M₁₆	—	52	6	no	—
90	C₂²×C₈	—	52	2	no	—
91	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
92	C₂²×C₈	Dic₂₆	1	3	yes	—
93	C₂²×C₈	D₅₂	1	3	yes	—
94	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
95	C₂²×C₈	C₂×Dic₁₃	1	3	yes	—
96	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
97	C₂×C₁₆	C₂×Dic₁₃	1	12	yes	—
98	C₂×C₁₆	C₂×Dic₁₃	1	12	yes	—
99	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
100	#108	—	13	8	no	—
101	#108	—	26	12	no	—
102	C₂×C₁₃	—	2	1	no	—
103	C₂×C₁₃	—	2	3	no	—
104	C₂×C₁₃	C₂×#368	1	6	yes	complemented
105	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
106	C₂⁴	Dic₅₂	1	1	yes	characteristic
107	C₂²×C₄	D₁₀₄	1	3	yes	—
108	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
109	C₂²×C₄	Dic₅₂	1	3	yes	—
110	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
111	C₂²×C₄	C₄⋊Dic₁₃	1	3	yes	—
112	C₂²×C₄	C₂×D₅₂	1	3	yes	—
113	M₁₆	—	26	8	no	—
114	M₁₆	—	52	12	no	—
115	C₂×C₈	—	52	12	no	—
116	C₂×C₈	C₄⋊Dic₁₃	1	6	yes	—
117	C₂×C₈	C₄⋊Dic₁₃	1	3	yes	—
118	C₂×C₈	C₄⋊Dic₁₃	1	3	yes	—
119	C₂×C₈	C₂×Dic₂₆	1	3	yes	—
120	C₂×C₈	C₂×Dic₂₆	1	3	yes	—
121	C₂×C₈	C₂×D₅₂	1	3	yes	—
122	C₂×C₈	C₂²×Dic₁₃	1	3	yes	—
123	C₂×C₈	C₂²×Dic₁₃	1	3	yes	—
124	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
125	C₁₆	C₂²×Dic₁₃	1	8	yes	—
126	C₁₃	C₂²×#368	1	1	yes	characteristic, complemented, Sylow
127	C₂³	—	2	4	no	—
128	C₂³	#88058	1	3	yes	—
129	C₂³	#88058	1	1	yes	characteristic
130	C₂³	C₂×Dic₅₂	1	3	yes	—
131	C₂×C₄	#88058	1	6	yes	—
132	C₂×C₄	#88058	1	3	yes	—
133	C₂×C₄	#88058	1	3	yes	—
134	C₂×C₄	C₂×D₁₀₄	1	3	yes	—
135	C₂×C₄	C₂×D₁₀₄	1	3	yes	—
136	C₂×C₄	C₂×Dic₅₂	1	3	yes	—
137	C₂×C₄	C₂×C₄⋊Dic₁₃	1	3	yes	—
138	C₂×C₄	C₂×C₄⋊Dic₁₃	1	3	yes	—
139	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
140	C₈	—	52	8	no	—
141	C₈	C₂×C₄⋊Dic₁₃	1	3	yes	—
142	C₈	C₂×C₄⋊Dic₁₃	1	3	yes	—
143	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
144	C₈	C₂³×Dic₁₃	1	1	yes	characteristic
145	C₂²	—	2	6	no	—
146	C₂²	—	2	6	no	—
147	C₂²	#11718098	1	4	yes	direct product factor
148	C₂²	C₂×#88058	1	3	yes	—
149	C₂²	C₂×#88058	1	3	yes	—
150	C₂²	C₂²×Dic₅₂	1	1	yes	characteristic
151	C₄	C₂×#88058	1	3	yes	—
152	C₄	C₂×#88058	1	3	yes	—
153	C₄	C₂²×D₁₀₄	1	1	yes	characteristic
154	C₄	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
155	C₂	—	2	1	no	—
156	C₂	—	2	3	no	—
157	C₂	C₂×#11718098	1	6	yes	direct product factor
158	C₂	C₂²×#88058	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₁₀₄
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂³×C₁₃×C₁₆	C₂
socle	C₂³×C₁₃	#107
prime radical	C₂⁴×C₁₃	Q₁₆
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂³×C₁₆	D₁₃
hypocenter	C₁₃	C₂²×#368
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#11718098	C₂	direct (N × H)
11. #11718098	C₂²	direct (N × H)
79. C₂²×C₁₃	#368	semidirect
104. C₂×C₁₃	C₂×#368	semidirect
126. C₁₃	C₂²×#368	semidirect
147. C₂²	#11718098	direct (N × H)
157. C₂	C₂×#11718098	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88059	2
C₂×#11718098	2
C₂³×C₁₃×C₁₆	2
C₂²×#368	13

Subgroups — C22×#11718098 #16015971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718098 #16015971