Subgroups — C₄×#11718081 #15778319

Order 3328.

366 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718081	C₂	1	2	yes	maximal
2	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic
3	C₄×#88058	C₂	1	1	yes	maximal, characteristic
4	#13112927	C₂	1	2	yes	maximal
5	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#107	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
9	C₂×#88058	C₂²	1	2	yes	—
10	C₂²×#6090	C₂²	1	1	yes	characteristic
11	C₂²×#6090	C₂²	1	1	yes	characteristic
12	C₄×C₄⋊Dic₁₃	—	2	1	no	—
13	C₁₃×#340	—	2	1	no	—
14	#11718143	—	2	1	no	—
15	#11718081	C₄	1	8	yes	direct product factor
16	C₄×#6090	C₄	1	4	yes	complemented
17	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
20	C₂×C₄²×C₁₃	—	4	1	no	—
21	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₃	—	2	2	no	—
23	C₂×C₄×Dic₁₃	—	4	1	no	—
24	C₁₃×#107	—	2	2	no	—
25	C₁₃×#107	C₂×C₄	1	4	yes	—
26	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₄×C₈×C₁₃	Q₈	1	2	yes	—
28	C₁₃×#95	—	4	1	no	—
29	#88071	—	4	1	no	—
30	#88058	—	2	2	no	—
31	#88058	C₂×C₄	1	4	yes	—
32	C₂×#6090	—	2	2	no	—
33	C₂×#6090	C₂×C₄	1	2	yes	—
34	C₂×#6090	C₂×C₄	1	2	yes	—
35	C₂×#6090	C₂×C₄	1	4	yes	—
36	C₄×#366	—	13	1	no	maximal, Sylow
37	C₂²×C₄×C₁₃	—	4	2	no	—
38	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×Dic₁₃	—	4	2	no	—
42	C₂×C₈×C₁₃	—	2	2	no	—
43	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
46	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₈×C₁₃	#41	1	2	yes	—
48	C₁₃×C₄⋊C₄	—	2	4	no	—
49	C₁₃×C₄⋊C₄	—	4	2	no	—
50	C₄²×C₁₃	—	8	2	no	—
51	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
52	C₄²×C₁₃	Q₁₆	1	2	yes	—
53	C₄⋊Dic₁₃	—	2	4	no	—
54	C₄⋊Dic₁₃	—	4	2	no	—
55	C₄×Dic₁₃	—	8	2	no	—
56	#6090	—	2	2	no	—
57	#6090	C₄²	1	4	yes	complemented
58	C₂×#366	—	13	2	no	—
59	C₂×C₄×C₁₆	—	13	1	no	—
60	C₄×#107	—	13	1	no	—
61	C₄×#107	D₁₃	1	1	yes	characteristic
62	#1380	—	13	2	no	—
63	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	4	4	no	—
66	C₂×C₄×C₁₃	—	8	2	no	—
67	C₂×C₄×C₁₃	—	8	2	no	—
68	C₂×C₄×C₁₃	#107	1	2	yes	—
69	C₂×C₄×C₁₃	#107	1	2	yes	—
70	C₂×C₄×C₁₃	D₁₆	1	2	yes	—
71	C₂×C₄×C₁₃	Q₃₂	1	2	yes	—
72	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
74	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#135	1	2	yes	—
76	C₂×Dic₁₃	—	4	4	no	—
77	C₂×Dic₁₃	—	8	2	no	—
78	C₂×Dic₁₃	—	8	2	no	—
79	C₈×C₁₃	—	2	2	no	—
80	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
81	C₈×C₁₃	#117	1	1	yes	characteristic
82	C₈×C₁₃	C₄×Q₈	1	2	yes	—
83	C₂²×C₁₆	—	13	1	no	—
84	C₂²×C₁₆	—	13	1	no	—
85	C₂×#107	—	13	2	no	—
86	C₂×#107	C₂×D₁₃	1	2	yes	—
87	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
88	C₄×C₄⋊C₄	—	2	1	no	—
89	C₄×C₄⋊C₄	—	26	1	no	—
90	#366	—	13	8	no	—
91	C₄×C₁₆	—	13	4	no	—
92	#340	—	2	1	no	—
93	#340	—	26	1	no	—
94	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
95	C₂²×C₁₃	C₄×D₈	1	2	yes	—
96	C₂²×C₁₃	C₂×D₁₆	1	1	yes	characteristic
97	C₂²×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
98	C₂²×C₁₃	#508	1	2	yes	—
99	C₄×C₁₃	—	2	2	no	—
100	C₄×C₁₃	—	8	4	no	—
101	C₄×C₁₃	#366	1	4	yes	complemented
102	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
103	C₄×C₁₃	#427	1	1	yes	characteristic
104	C₄×C₁₃	C₄×Q₁₆	1	2	yes	—
105	Dic₁₃	—	8	4	no	—
106	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
107	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
108	C₂×C₄⋊C₄	—	2	2	no	—
109	C₂×C₄⋊C₄	—	26	2	no	—
110	C₂×C₄²	—	4	1	no	—
111	C₂×C₄²	—	52	1	no	—
112	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
113	C₂×C₁₆	—	13	2	no	—
114	C₂×C₁₆	—	13	4	no	—
115	C₂×C₁₆	—	13	2	no	—
116	C₂×C₁₆	—	26	2	no	—
117	#107	—	2	2	no	—
118	#107	—	13	4	no	—
119	#107	—	26	2	no	—
120	#107	C₄×D₁₃	1	4	yes	—
121	C₄×C₈	Dic₂₆	1	2	yes	—
122	C₄×C₈	C₄×D₁₃	1	2	yes	—
123	#95	—	4	1	no	—
124	#95	—	52	1	no	—
125	C₂×C₁₃	C₄×#107	1	1	yes	characteristic
126	C₂×C₁₃	C₂×#366	1	1	yes	characteristic
127	C₂×C₁₃	#2158	1	1	yes	characteristic
128	C₂×C₁₃	C₄×D₁₆	1	2	yes	—
129	C₂×C₁₃	C₄×Q₃₂	1	2	yes	—
130	C₂²×C₄	—	4	2	no	—
131	C₂²×C₄	—	52	2	no	—
132	C₂²×C₄	#6104	1	1	yes	characteristic
133	C₂²×C₄	#6104	1	1	yes	characteristic
134	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	#6101	1	2	yes	—
137	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
138	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
139	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
140	C₂×C₈	#6127	1	2	yes	—
141	C₄⋊C₄	—	2	4	no	—
142	C₄⋊C₄	—	4	2	no	—
143	C₄⋊C₄	—	26	4	no	—
144	C₄⋊C₄	—	52	2	no	—
145	C₄²	—	8	2	no	—
146	C₄²	—	104	2	no	—
147	C₄²	#6101	1	2	yes	—
148	C₄²	#6107	1	2	yes	—
149	C₁₆	—	13	4	no	—
150	C₁₆	—	26	2	no	—
151	C₁₃	C₄×#366	1	1	yes	characteristic, complemented, Sylow
152	C₂³	C₂×#6104	1	1	yes	characteristic
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	4	4	no	—
155	C₂×C₄	—	8	2	no	—
156	C₂×C₄	—	8	2	no	—
157	C₂×C₄	—	52	4	no	—
158	C₂×C₄	—	104	2	no	—
159	C₂×C₄	—	104	2	no	—
160	C₂×C₄	#88047	1	2	yes	—
161	C₂×C₄	#88047	1	2	yes	—
162	C₂×C₄	#88066	1	2	yes	—
163	C₂×C₄	#88069	1	2	yes	—
164	C₂×C₄	C₂×#6101	1	1	yes	characteristic
165	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
166	C₂×C₄	C₂×#6107	1	1	yes	characteristic
167	C₂×C₄	#88204	1	2	yes	—
168	C₈	—	2	2	no	—
169	C₈	C₄×Dic₂₆	1	2	yes	—
170	C₈	C₄²×D₁₃	1	1	yes	characteristic
171	C₈	#88126	1	1	yes	characteristic
172	C₂²	C₂×#88047	1	1	yes	characteristic
173	C₂²	C₄×#6104	1	2	yes	—
174	C₂²	C₂×#88066	1	1	yes	characteristic
175	C₂²	C₂×#88069	1	1	yes	characteristic
176	C₂²	#11718855	1	2	yes	—
177	C₄	—	2	2	no	—
178	C₄	—	8	4	no	—
179	C₄	—	104	4	no	—
180	C₄	#11718081	1	4	yes	direct product factor
181	C₄	C₄×#6101	1	1	yes	characteristic
182	C₄	#11718659	1	1	yes	characteristic
183	C₄	C₄×#6107	1	2	yes	—
184	C₂	C₄×#88047	1	1	yes	characteristic
185	C₂	C₂×#11718081	1	1	yes	characteristic
186	C₂	#13116618	1	1	yes	characteristic
187	C₂	C₄×#88066	1	2	yes	—
188	C₂	C₄×#88069	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	#6104
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₄×C₁₃×#107	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₄×#107	D₁₃
hypocenter	C₁₃	C₄×#366
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
15. #11718081	C₄	direct (N × H)
16. C₄×#6090	C₄	semidirect
57. #6090	C₄²	semidirect
101. C₄×C₁₃	#366	semidirect
151. C₁₃	C₄×#366	semidirect
180. C₄	#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
C₂×#11718081	2
C₂×C₄×#6090	2
C₄×#88058	2
#13112927	2
C₄×C₁₃×#107	2
C₄×#366	13

Subgroups — C4×#11718081 #15778319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718081 #15778319