Subgroups — #15779359

Order 3328.

342 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718097	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718081	C₂	1	2	yes	maximal
3	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#13114999	C₂	1	2	yes	maximal
5	C₂×C₁₃×#367	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#107	C₂²	1	2	yes	—
8	C₂×#88058	C₂²	1	2	yes	—
9	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂²×#6090	C₂²	1	1	yes	characteristic
11	#11718638	—	2	2	no	—
12	C₂×#88048	—	2	2	no	—
13	C₁₃×#367	—	2	2	no	—
14	#11718097	—	2	2	no	—
15	C₁₆×Dic₁₃	C₄	1	4	yes	complemented
16	#11718081	—	2	4	no	—
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
19	C₂×C₄⋊Dic₁₃	—	2	2	no	—
20	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
21	C₂²×#1055	D₄	1	1	yes	characteristic
22	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
23	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
24	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
25	C₁₃×#107	—	2	2	no	—
26	C₁₃×#107	—	2	2	no	—
27	#88071	—	4	4	no	—
28	#88058	—	2	2	no	—
29	#88058	—	2	2	no	—
30	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
31	C₈×Dic₁₃	Q₈	1	2	yes	—
32	C₂×#6090	C₂×C₄	1	2	yes	—
33	C₂×#6090	D₄	1	2	yes	—
34	C₂×#6090	Q₈	1	2	yes	—
35	#88048	—	4	4	no	—
36	#12907	—	13	1	no	maximal, Sylow
37	C₂²×C₄×C₁₃	—	4	2	no	—
38	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂²×Dic₁₃	—	4	2	no	—
40	C₂²×Dic₁₃	D₈	1	2	yes	—
41	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
47	C₁₃×C₄⋊C₄	—	4	2	no	—
48	C₁₃×C₄⋊C₄	—	4	2	no	—
49	C₄⋊Dic₁₃	—	4	2	no	—
50	C₄⋊Dic₁₃	—	4	2	no	—
51	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
52	C₄×Dic₁₃	Q₁₆	1	2	yes	—
53	C₂×#1055	C₄⋊C₄	1	2	yes	—
54	C₂×#1055	D₈	1	2	yes	—
55	C₂×#1055	Q₁₆	1	2	yes	—
56	C₁₃×C₁₆	C₄⋊C₄	1	4	yes	—
57	#6090	C₄⋊C₄	1	4	yes	—
58	C₂×#367	—	13	1	no	—
59	C₂×#367	D₁₃	1	1	yes	characteristic
60	C₂×#366	—	13	2	no	—
61	C₂×C₄×C₁₆	—	13	1	no	—
62	#1846	—	13	2	no	—
63	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	—	8	2	no	—
65	C₂×C₄×C₁₃	—	8	4	no	—
66	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
72	C₂×Dic₁₃	—	2	4	no	—
73	C₂×Dic₁₃	—	8	2	no	—
74	C₂×Dic₁₃	—	8	4	no	—
75	C₂×Dic₁₃	#107	1	4	yes	—
76	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
78	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
79	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
80	#1055	#107	1	4	yes	—
81	C₂²×C₁₆	—	13	1	no	—
82	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
83	C₂×#107	—	13	2	no	—
84	C₂×#107	C₂×D₁₃	1	2	yes	—
85	C₂×#106	—	26	2	no	—
86	C₂×C₄×C₈	—	13	1	no	—
87	#382	—	26	2	no	—
88	#367	—	2	2	no	—
89	#367	—	26	2	no	—
90	#366	—	26	4	no	—
91	C₄×C₁₆	—	13	4	no	—
92	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
93	C₂²×C₁₃	#493	1	1	yes	characteristic
94	C₂²×C₁₃	#500	1	1	yes	characteristic
95	C₂²×C₁₃	#508	1	4	yes	—
96	C₄×C₁₃	—	16	2	no	—
97	C₄×C₁₃	#384	1	1	yes	characteristic
98	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
99	C₄×C₁₃	#494	1	1	yes	characteristic
100	C₄×C₁₃	#500	1	1	yes	characteristic
101	Dic₁₃	—	2	4	no	—
102	Dic₁₃	—	16	2	no	—
103	C₂²×C₈	—	13	1	no	—
104	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
105	C₂×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄⋊C₄	—	26	2	no	—
107	C₂×C₄²	—	13	1	no	—
108	C₂×C₁₆	—	13	2	no	—
109	C₂×C₁₆	—	13	2	no	—
110	C₂×C₁₆	—	13	2	no	—
111	C₂×C₁₆	Dic₂₆	1	2	yes	—
112	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
113	C₂×C₁₆	C₂²⋊D₁₃	1	2	yes	—
114	#107	—	2	2	no	—
115	#107	—	2	2	no	—
116	#107	—	26	2	no	—
117	#107	—	26	2	no	—
118	#106	—	52	4	no	—
119	C₄×C₈	—	13	2	no	—
120	C₄×C₈	—	13	2	no	—
121	#95	—	52	4	no	—
122	C₂×C₁₃	#1845	1	1	yes	characteristic
123	C₂×C₁₃	#2158	1	2	yes	—
124	C₂×C₁₃	#2249	1	2	yes	—
125	C₂×C₁₃	#2253	1	2	yes	—
126	C₂²×C₄	—	4	2	no	—
127	C₂²×C₄	—	13	2	no	—
128	C₂²×C₄	—	52	2	no	—
129	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
130	C₂×C₈	—	13	2	no	—
131	C₂×C₈	—	13	2	no	—
132	C₂×C₈	—	13	2	no	—
133	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
134	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
135	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
136	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
137	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
138	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
139	C₄⋊C₄	—	4	2	no	—
140	C₄⋊C₄	—	4	2	no	—
141	C₄⋊C₄	—	52	2	no	—
142	C₄⋊C₄	—	52	2	no	—
143	C₄²	—	13	2	no	—
144	C₄²	—	13	2	no	—
145	C₁₆	—	13	4	no	—
146	C₁₆	#6101	1	4	yes	—
147	C₁₃	#12907	1	1	yes	characteristic, complemented, Sylow
148	C₂³	D₈×D₁₃	1	1	yes	characteristic
149	C₂×C₄	—	8	2	no	—
150	C₂×C₄	—	8	4	no	—
151	C₂×C₄	—	13	4	no	—
152	C₂×C₄	—	26	4	no	—
153	C₂×C₄	—	104	2	no	—
154	C₂×C₄	—	104	4	no	—
155	C₂×C₄	#88142	1	1	yes	characteristic
156	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
157	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
158	C₂×C₄	Q₁₆×D₁₃	1	1	yes	characteristic
159	C₂×C₄	Q₁₆×D₁₃	1	1	yes	characteristic
160	C₂×C₄	#88194	1	1	yes	characteristic
161	C₈	—	13	4	no	—
162	C₈	#88142	1	1	yes	characteristic
163	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
164	C₈	C₂×#6101	1	1	yes	characteristic
165	C₈	#88198	1	1	yes	characteristic
166	C₂²	#11718535	1	1	yes	characteristic
167	C₂²	D₁₃×#107	1	1	yes	characteristic
168	C₂²	#11718577	1	4	yes	—
169	C₂²	#11718812	1	1	yes	characteristic
170	C₄	—	16	2	no	—
171	C₄	—	26	4	no	—
172	C₄	—	208	2	no	—
173	C₄	#11718535	1	1	yes	characteristic
174	C₄	D₁₃×#107	1	1	yes	characteristic
175	C₄	#11718637	1	1	yes	characteristic
176	C₄	#11718842	1	1	yes	characteristic
177	C₂	#13114994	1	1	yes	characteristic
178	C₂	#13116619	1	2	yes	—
179	C₂	#13117096	1	2	yes	—
180	C₂	#13117114	1	2	yes	—

	subgroup	G/H
center	C₂³	D₈×D₁₃
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#367	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#367	D₁₃
hypocenter	C₁₃	#12907
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#367

Complements

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

N	H ≅ G/N	type
15. C₁₆×Dic₁₃	C₄	semidirect
147. C₁₃	#12907	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718097	2
C₂×#11718081	2
C₂×C₁₆×Dic₁₃	2
#13114999	2
C₂×C₁₃×#367	2
#12907	13