Subgroups — C₂²×#11718085 #16015970

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 186 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×#88059	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718085	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₁₃×#108	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×M₁₆	—	2	1	no	—
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6099	—	2	1	no	—
8	C₂×C₁₃×#108	—	2	3	no	—
9	C₂×C₁₃×#108	C₂²	1	6	yes	—
10	C₂×#88059	—	2	3	no	—
11	C₂×#88059	C₂²	1	6	yes	—
12	C₂²×#6090	C₄	1	6	yes	—
13	C₂²×#6090	C₄	1	2	yes	—
14	C₂²×#6090	C₂²	1	6	yes	—
15	#11718085	C₂²	1	16	yes	direct product factor
16	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₁₃×M₁₆	—	2	6	no	—
18	C₂×C₁₃×M₁₆	—	4	3	no	—
19	C₂²×C₈×C₁₃	—	4	1	no	—
20	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	D₄	1	3	yes	—
23	C₂²×C₈×C₁₃	Q₈	1	3	yes	—
24	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
26	C₂×#6099	—	2	6	no	—
27	C₂×#6099	—	4	3	no	—
28	C₂²×#1055	—	4	1	no	—
29	C₁₃×#108	—	2	6	no	—
30	C₁₃×#108	C₂³	1	4	yes	—
31	#88059	—	2	6	no	—
32	#88059	C₂³	1	4	yes	—
33	C₂×#6090	C₂×C₄	1	12	yes	—
34	C₂×#6090	C₂×C₄	1	12	yes	—
35	C₂×#6090	C₂³	1	4	yes	—
36	C₂²×#368	—	13	1	no	maximal, Sylow
37	C₂⁴×C₁₃	Q₁₆	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₄⋊C₄	1	3	yes	—
39	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	D₈	1	3	yes	—
41	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	Q₁₆	1	3	yes	—
43	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
44	C₁₃×M₁₆	—	2	4	no	—
45	C₁₃×M₁₆	—	4	6	no	—
46	C₂×C₈×C₁₃	—	4	6	no	—
47	C₂×C₈×C₁₃	C₄⋊C₄	1	6	yes	—
48	C₂×C₈×C₁₃	C₄⋊C₄	1	3	yes	—
49	C₂×C₈×C₁₃	C₄⋊C₄	1	3	yes	—
50	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
51	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
52	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
53	C₂×C₈×C₁₃	C₂×Q₈	1	3	yes	—
54	C₂×C₈×C₁₃	C₂×Q₈	1	3	yes	—
55	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
56	#6099	—	2	4	no	—
57	#6099	—	4	6	no	—
58	C₂×#1055	—	4	6	no	—
59	#6090	C₂²×C₄	1	8	yes	—
60	C₂³×C₁₆	—	13	1	no	—
61	C₂²×#108	—	13	1	no	—
62	C₂²×#108	D₁₃	1	1	yes	characteristic
63	C₂×#368	—	13	12	no	—
64	C₂³×C₁₃	—	2	4	no	—
65	C₂³×C₁₃	#107	1	3	yes	—
66	C₂³×C₁₃	#107	1	1	yes	characteristic
67	C₂³×C₁₃	C₂×Q₁₆	1	3	yes	—
68	C₂×C₄×C₁₃	#107	1	6	yes	—
69	C₂×C₄×C₁₃	#107	1	3	yes	—
70	C₂×C₄×C₁₃	#107	1	3	yes	—
71	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
72	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
73	C₂×C₄×C₁₃	C₂×D₈	1	3	yes	—
74	C₂×C₄×C₁₃	C₂×D₈	1	3	yes	—
75	C₂×C₄×C₁₃	C₂×Q₁₆	1	3	yes	—
76	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
77	C₈×C₁₃	—	4	4	no	—
78	C₈×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
79	C₈×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
80	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
81	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
82	#1055	—	4	4	no	—
83	C₂²×M₁₆	—	2	1	no	—
84	C₂²×M₁₆	—	26	1	no	—
85	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
86	C₂²×C₁₆	—	13	2	no	—
87	C₂²×C₁₆	—	13	6	no	—
88	C₂²×C₁₆	—	13	6	no	—
89	C₂×#108	—	2	3	no	—
90	C₂×#108	—	13	6	no	—
91	C₂×#108	—	26	3	no	—
92	C₂×#108	C₂×D₁₃	1	6	yes	—
93	#368	—	13	16	no	—
94	C₂²×C₁₃	—	2	6	no	—
95	C₂²×C₁₃	—	2	6	no	—
96	C₂²×C₁₃	#368	1	4	yes	complemented
97	C₂²×C₁₃	C₂×#107	1	3	yes	—
98	C₂²×C₁₃	C₂×#107	1	3	yes	—
99	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
100	C₄×C₁₃	C₂×#107	1	3	yes	—
101	C₄×C₁₃	C₂×#107	1	3	yes	—
102	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
103	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
104	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
105	C₂×M₁₆	—	2	6	no	—
106	C₂×M₁₆	—	4	3	no	—
107	C₂×M₁₆	—	26	6	no	—
108	C₂×M₁₆	—	52	3	no	—
109	C₂²×C₈	—	4	1	no	—
110	C₂²×C₈	—	52	1	no	—
111	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
112	C₂²×C₈	Dic₂₆	1	3	yes	—
113	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
114	C₂²×C₈	C₄×D₁₃	1	3	yes	—
115	C₂²×C₈	C₂²⋊D₁₃	1	3	yes	—
116	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
117	C₂×C₁₆	—	13	12	no	—
118	C₂×C₁₆	—	13	12	no	—
119	C₂×C₁₆	—	13	4	no	—
120	#108	—	2	6	no	—
121	#108	—	13	4	no	—
122	#108	—	26	6	no	—
123	#108	C₂²×D₁₃	1	4	yes	—
124	C₂×C₁₃	—	2	1	no	—
125	C₂×C₁₃	—	2	3	no	—
126	C₂×C₁₃	C₂×#368	1	6	yes	complemented
127	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
128	C₂⁴	#6107	1	1	yes	characteristic
129	C₂²×C₄	#6101	1	1	yes	characteristic
130	C₂²×C₄	#6101	1	3	yes	—
131	C₂²×C₄	#6104	1	3	yes	—
132	C₂²×C₄	#6104	1	1	yes	characteristic
133	C₂²×C₄	#6107	1	3	yes	—
134	C₂²×C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
135	M₁₆	—	2	4	no	—
136	M₁₆	—	4	6	no	—
137	M₁₆	—	26	4	no	—
138	M₁₆	—	52	6	no	—
139	C₂×C₈	—	4	6	no	—
140	C₂×C₈	—	52	6	no	—
141	C₂×C₈	#6101	1	6	yes	—
142	C₂×C₈	#6101	1	3	yes	—
143	C₂×C₈	#6101	1	3	yes	—
144	C₂×C₈	C₂×Dic₂₆	1	3	yes	—
145	C₂×C₈	C₂×Dic₂₆	1	3	yes	—
146	C₂×C₈	C₂×C₄×D₁₃	1	3	yes	—
147	C₂×C₈	C₂×C₄×D₁₃	1	3	yes	—
148	C₂×C₈	C₂×C₂²⋊D₁₃	1	3	yes	—
149	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
150	C₁₆	—	13	8	no	—
151	C₁₃	C₂²×#368	1	1	yes	characteristic, complemented, Sylow
152	C₂³	—	2	4	no	—
153	C₂³	#88047	1	3	yes	—
154	C₂³	#88047	1	1	yes	characteristic
155	C₂³	C₂×#6107	1	3	yes	—
156	C₂×C₄	#88047	1	6	yes	—
157	C₂×C₄	#88047	1	3	yes	—
158	C₂×C₄	#88047	1	3	yes	—
159	C₂×C₄	C₂×#6101	1	3	yes	—
160	C₂×C₄	C₂×#6101	1	3	yes	—
161	C₂×C₄	C₂×#6104	1	3	yes	—
162	C₂×C₄	C₂×#6104	1	3	yes	—
163	C₂×C₄	C₂×#6107	1	3	yes	—
164	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
165	C₈	—	4	4	no	—
166	C₈	—	52	4	no	—
167	C₈	C₂×#6101	1	3	yes	—
168	C₈	C₂×#6101	1	3	yes	—
169	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
170	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
171	C₂²	—	2	6	no	—
172	C₂²	—	2	6	no	—
173	C₂²	#11718085	1	4	yes	direct product factor
174	C₂²	C₂×#88047	1	3	yes	—
175	C₂²	C₂×#88047	1	3	yes	—
176	C₂²	C₂²×#6107	1	1	yes	characteristic
177	C₄	C₂×#88047	1	3	yes	—
178	C₄	C₂×#88047	1	3	yes	—
179	C₄	C₂²×#6101	1	1	yes	characteristic
180	C₄	C₂²×#6104	1	1	yes	characteristic
181	C₂	—	2	1	no	—
182	C₂	—	2	3	no	—
183	C₂	C₂×#11718085	1	6	yes	direct product factor
184	C₂	C₂²×#88047	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#6104
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×#108	C₂
socle	C₂³×C₁₃	#107
prime radical	C₂⁴×C₁₃	Q₁₆
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×#108	D₁₃
hypocenter	C₁₃	C₂²×#368
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
3. C₂×#11718085	C₂	direct (N × H)
15. #11718085	C₂²	direct (N × H)
96. C₂²×C₁₃	#368	semidirect
126. C₂×C₁₃	C₂×#368	semidirect
151. C₁₃	C₂²×#368	semidirect
173. C₂²	#11718085	direct (N × H)
183. C₂	C₂×#11718085	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×#88059	2
C₂×#11718085	2
C₂²×C₁₃×#108	2
C₂²×#368	13

Subgroups — C22×#11718085 #16015970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718085 #16015970