Subgroups — C₂²×#11718255 #16794901

Order 3328.

942 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊#1057	C₂	1	2	yes	maximal
2	C₂×#11718255	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×#1057	—	2	2	no	—
5	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₂³×#1055	C₄	1	1	yes	characteristic
8	C₂×C₄⋊#1057	—	2	6	no	—
9	C₂×C₄⋊#1057	C₂²	1	12	yes	—
10	C₂×C₈×Dic₁₃	C₄	1	6	yes	—
11	C₂×C₈×Dic₁₃	C₂²	1	6	yes	—
12	#11718255	C₂²	1	16	yes	direct product factor
13	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂³×Dic₁₃	D₄	1	1	yes	characteristic
15	C₂³×Dic₁₃	Q₈	1	1	yes	characteristic
16	C₂²×#1057	—	2	12	no	—
17	C₂²×#1057	—	4	8	no	—
18	C₂²×C₈×C₁₃	—	2	4	no	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	6	yes	—
20	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
21	C₂×C₄×Dic₁₃	D₄	1	3	yes	—
22	C₂×C₄×Dic₁₃	Q₈	1	3	yes	—
23	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
24	C₂²×#1055	C₈	1	8	yes	complemented
25	C₂²×#1055	C₂×C₄	1	6	yes	—
26	C₄⋊#1057	—	2	12	no	—
27	C₄⋊#1057	C₂³	1	8	yes	—
28	C₈×Dic₁₃	C₂×C₄	1	12	yes	—
29	C₈×Dic₁₃	C₂³	1	4	yes	—
30	C₂²×#334	—	13	1	no	maximal, Sylow
31	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₃	C₄⋊C₄	1	3	yes	—
33	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
34	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
35	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
36	C₂²×Dic₁₃	—	2	4	no	—
37	C₂²×Dic₁₃	C₄⋊C₄	1	3	yes	—
38	C₂²×Dic₁₃	C₄⋊C₄	1	3	yes	—
39	C₂²×Dic₁₃	SD₁₆	1	8	yes	—
40	C₂²×Dic₁₃	C₂×D₄	1	3	yes	—
41	C₂²×Dic₁₃	C₂×Q₈	1	3	yes	—
42	C₂×#1057	—	2	8	no	—
43	C₂×#1057	—	4	24	no	—
44	C₂×C₈×C₁₃	—	2	12	no	—
45	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
46	C₄×Dic₁₃	C₄⋊C₄	1	6	yes	—
47	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
48	C₄×Dic₁₃	C₂×D₄	1	3	yes	—
49	C₄×Dic₁₃	C₂×Q₈	1	3	yes	—
50	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
51	C₂×#1055	C₂×C₈	1	24	yes	complemented
52	C₂×#1055	C₂²×C₄	1	4	yes	—
53	C₂²×C₄⋊C₈	—	13	2	no	—
54	C₂²×C₄×C₈	—	13	1	no	—
55	C₂×#334	—	13	12	no	—
56	C₂³×C₁₃	C₄⋊C₈	1	4	yes	—
57	C₂³×C₁₃	#106	1	4	yes	—
58	C₂³×C₁₃	#108	1	4	yes	—
59	C₂³×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
60	C₂×C₄×C₁₃	C₄⋊C₈	1	12	yes	—
61	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
62	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
63	C₂×C₄×C₁₃	C₂×M₁₆	1	6	yes	—
64	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
65	C₂×Dic₁₃	—	2	6	no	—
66	C₂×Dic₁₃	—	2	6	no	—
67	C₂×Dic₁₃	#106	1	12	yes	—
68	C₂×Dic₁₃	C₂×C₄⋊C₄	1	3	yes	—
69	C₂×Dic₁₃	C₂×C₄⋊C₄	1	3	yes	—
70	C₂×Dic₁₃	C₂×SD₁₆	1	12	yes	—
71	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
72	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
73	#1057	—	4	8	no	—
74	C₈×C₁₃	—	2	4	no	—
75	#1055	C₂²×C₈	1	8	yes	complemented
76	C₂³×C₈	—	13	1	no	—
77	C₂³×C₈	—	26	2	no	—
78	C₂³×C₈	#261	1	1	yes	characteristic
79	C₂²×C₄²	—	13	1	no	—
80	C₂×C₄⋊C₈	—	13	12	no	—
81	C₂×C₄⋊C₈	—	26	6	no	—
82	C₂×C₄×C₈	—	13	6	no	—
83	C₂×C₄×C₈	—	13	6	no	—
84	#334	—	13	16	no	—
85	C₂²×C₁₃	#334	1	16	yes	complemented
86	C₂²×C₁₃	C₂×C₄⋊C₈	1	6	yes	—
87	C₂²×C₁₃	C₂×#106	1	6	yes	—
88	C₂²×C₁₃	C₂×#108	1	6	yes	—
89	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
90	C₄×C₁₃	C₂×C₄⋊C₈	1	6	yes	—
91	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
92	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
93	Dic₁₃	—	2	3	no	—
94	Dic₁₃	—	2	1	no	—
95	Dic₁₃	C₂×#106	1	6	yes	—
96	Dic₁₃	C₂²×SD₁₆	1	2	yes	—
97	C₂³×C₄	—	13	1	no	—
98	C₂³×C₄	—	13	1	no	—
99	C₂³×C₄	C₂×#261	1	1	yes	characteristic
100	C₂²×C₈	—	2	4	no	—
101	C₂²×C₈	—	13	8	no	—
102	C₂²×C₈	—	13	6	no	—
103	C₂²×C₈	—	26	12	no	—
104	C₂²×C₈	—	52	8	no	—
105	C₂²×C₈	C₂×#261	1	6	yes	—
106	C₂×C₄²	—	13	3	no	—
107	C₂×C₄²	—	13	3	no	—
108	C₂×C₄²	—	13	3	no	—
109	C₂×C₄²	—	13	3	no	—
110	C₄⋊C₈	—	13	8	no	—
111	C₄⋊C₈	—	26	12	no	—
112	C₄×C₈	—	13	4	no	—
113	C₄×C₈	—	13	12	no	—
114	C₂×C₁₃	C₂×#334	1	12	yes	complemented
115	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
116	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
117	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
118	C₂⁴	C₄⋊#261	1	1	yes	characteristic
119	C₂²×C₄	—	13	8	no	—
120	C₂²×C₄	—	13	3	no	—
121	C₂²×C₄	—	13	3	no	—
122	C₂²×C₄	—	13	3	no	—
123	C₂²×C₄	—	13	3	no	—
124	C₂²×C₄	—	26	4	no	—
125	C₂²×C₄	D₁₃⋊C₈	1	4	yes	—
126	C₂²×C₄	C₄⋊#261	1	3	yes	—
127	C₂²×C₄	#6122	1	4	yes	—
128	C₂²×C₄	C₂²×#261	1	3	yes	—
129	C₂×C₈	—	2	12	no	—
130	C₂×C₈	—	13	24	no	—
131	C₂×C₈	—	13	4	no	—
132	C₂×C₈	—	26	8	no	—
133	C₂×C₈	—	52	24	no	—
134	C₂×C₈	C₂²×#261	1	4	yes	—
135	C₄²	—	13	3	no	—
136	C₄²	—	13	6	no	—
137	C₄²	—	13	3	no	—
138	C₄²	—	13	1	no	—
139	C₄²	—	13	3	no	—
140	C₁₃	C₂²×#334	1	1	yes	characteristic, complemented, Sylow
141	C₂³	#88101	1	4	yes	—
142	C₂³	#88104	1	4	yes	—
143	C₂³	#88112	1	4	yes	—
144	C₂³	C₂×C₄⋊#261	1	3	yes	—
145	C₂×C₄	—	13	12	no	—
146	C₂×C₄	—	13	12	no	—
147	C₂×C₄	—	13	1	no	—
148	C₂×C₄	—	13	3	no	—
149	C₂×C₄	—	13	3	no	—
150	C₂×C₄	—	13	1	no	—
151	C₂×C₄	—	26	6	no	—
152	C₂×C₄	—	26	6	no	—
153	C₂×C₄	#88112	1	12	yes	—
154	C₂×C₄	C₂×D₁₃⋊C₈	1	6	yes	—
155	C₂×C₄	C₂×C₄⋊#261	1	3	yes	—
156	C₂×C₄	C₂×#6122	1	6	yes	—
157	C₂×C₄	C₂³×#261	1	1	yes	characteristic
158	C₈	—	2	4	no	—
159	C₈	—	13	8	no	—
160	C₈	—	52	8	no	—
161	C₂²	#11718255	1	16	yes	direct product factor
162	C₂²	C₂×#88101	1	6	yes	—
163	C₂²	C₂×#88104	1	6	yes	—
164	C₂²	C₂×#88112	1	6	yes	—
165	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
166	C₄	—	13	2	no	—
167	C₄	—	13	6	no	—
168	C₄	—	26	3	no	—
169	C₄	—	26	1	no	—
170	C₄	C₂×#88112	1	6	yes	—
171	C₄	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
172	C₄	C₂²×#6122	1	1	yes	characteristic
173	C₂	C₂×#11718255	1	12	yes	direct product factor
174	C₂	C₂²×#88112	1	1	yes	characteristic
175	C₂	C₂²×#88101	1	1	yes	characteristic
176	C₂	C₂²×#88104	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₄⋊#261
commutator	C₄×C₁₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂³×C₈×C₁₃	C₄
socle, prime radical	C₂⁴×C₁₃	C₄⋊C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂³×C₈	#261
hypocenter	C₁₃	C₂²×#334
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#11718255	C₂	direct (N × H)
12. #11718255	C₂²	direct (N × H)
24. C₂²×#1055	C₈	semidirect
51. C₂×#1055	C₂×C₈	semidirect
75. #1055	C₂²×C₈	semidirect
85. C₂²×C₁₃	#334	semidirect
114. C₂×C₁₃	C₂×#334	semidirect
140. C₁₃	C₂²×#334	semidirect
161. C₂²	#11718255	direct (N × H)
173. C₂	C₂×#11718255	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×C₄⋊#1057	2
C₂×#11718255	2
C₂²×C₈×Dic₁₃	2
C₂²×#334	13

Subgroups — C22×#11718255 #16794901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718255 #16794901