Subgroups — #15779375

Order 3328.

266 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718098	C₂	1	1	yes	maximal, characteristic
2	#13116620	C₂	1	1	yes	maximal, characteristic
3	#13116609	C₂	1	2	yes	maximal
4	#13114960	C₂	1	2	yes	maximal
5	C₁₃×#2108	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×#405	C₂²	1	1	yes	characteristic
9	C₂×#88059	C₂²	1	2	yes	—
10	#11718767	C₂²	1	2	yes	—
11	C₁₃×#346	C₄	1	2	yes	complemented
12	C₄×C₁₃×C₁₆	C₄	1	2	yes	complemented
13	#11718148	—	2	2	no	—
14	#11718123	—	2	2	no	—
15	#11718105	—	2	4	no	—
16	#11718098	—	2	1	no	—
17	#11718098	—	2	1	no	—
18	#11718097	—	2	1	no	—
19	#11718096	—	2	1	no	—
20	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
22	C₁₃×#117	D₄	1	1	yes	characteristic
23	#88180	—	2	2	no	—
24	C₂×#6099	—	2	2	no	—
25	C₁₃×M₃₂	D₄	1	2	yes	—
26	C₁₃×M₃₂	Q₈	1	2	yes	—
27	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
29	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
31	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
32	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
33	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
34	C₁₃×#97	Q₈	1	2	yes	—
35	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
36	#88059	—	2	2	no	—
37	#88059	—	2	2	no	—
38	#88058	—	2	2	no	—
39	#88057	—	2	2	no	—
40	#12911	—	13	1	no	maximal, Sylow
41	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
42	C₁₃×M₁₆	—	2	1	no	—
43	C₁₃×M₁₆	—	2	1	no	—
44	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
45	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₁₃×C₂²⋊C₄	—	2	1	no	—
53	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
54	C₂²⋊Dic₁₃	—	4	2	no	—
55	C₄⋊Dic₁₃	—	4	2	no	—
56	C₄×Dic₁₃	—	4	2	no	—
57	#6099	—	4	2	no	—
58	#6099	—	4	2	no	—
59	C₂×#1055	—	4	2	no	—
60	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
61	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
62	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
63	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
64	C₁₃×C₁₆	C₄⋊C₄	1	4	yes	—
65	C₂×#368	—	13	1	no	—
66	#2158	—	13	1	no	—
67	#2155	—	13	2	no	—
68	#2108	D₁₃	1	1	yes	characteristic
69	#1833	—	13	2	no	—
70	C₂³×C₁₃	#135	1	1	yes	characteristic
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
78	C₂×Dic₁₃	—	8	2	no	—
79	C₈×C₁₃	—	2	2	no	—
80	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
83	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
84	#1055	—	8	2	no	—
85	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
86	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
87	C₂×#108	—	13	2	no	—
88	#427	—	13	2	no	—
89	#405	C₂×D₁₃	1	1	yes	characteristic
90	#368	—	26	1	no	—
91	#368	—	26	1	no	—
92	#367	—	26	1	no	—
93	#366	—	26	1	no	—
94	#365	—	26	4	no	—
95	#346	Dic₁₃	1	2	yes	complemented
96	C₄×C₁₆	Dic₁₃	1	2	yes	complemented
97	#344	—	26	2	no	—
98	H(3,ℤ/4)	—	26	2	no	—
99	C₂²×C₁₃	—	4	1	no	—
100	C₂²×C₁₃	#427	1	1	yes	characteristic
101	C₂²×C₁₃	#495	1	1	yes	characteristic
102	C₂²×C₁₃	#499	1	1	yes	characteristic
103	C₄×C₁₃	—	4	2	no	—
104	C₄×C₁₃	#384	1	1	yes	characteristic
105	C₄×C₁₃	#427	1	1	yes	characteristic
106	C₄×C₁₃	#495	1	1	yes	characteristic
107	C₄×C₁₃	#499	1	1	yes	characteristic
108	Dic₁₃	—	16	2	no	—
109	C₂×M₁₆	—	26	2	no	—
110	C₂×M₁₆	D₅₂	1	1	yes	characteristic
111	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
112	#117	—	26	2	no	—
113	#117	D₅₂	1	1	yes	characteristic
114	M₃₂	Dic₂₆	1	2	yes	—
115	M₃₂	D₅₂	1	2	yes	—
116	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
117	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
118	C₂×C₁₆	D₅₂	1	1	yes	characteristic
119	C₂×C₁₆	D₅₂	1	1	yes	characteristic
120	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
121	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
122	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
123	#108	—	26	2	no	—
124	#108	—	26	2	no	—
125	#107	—	26	2	no	—
126	#106	—	26	2	no	—
127	#97	Dic₂₆	1	2	yes	—
128	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
129	C₂×C₁₃	—	2	1	no	—
130	C₂×C₁₃	—	2	1	no	—
131	C₂×C₁₃	—	2	1	no	—
132	C₂×C₁₃	#1846	1	1	yes	characteristic
133	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
134	M₁₆	—	2	1	no	—
135	M₁₆	—	2	1	no	—
136	M₁₆	—	52	2	no	—
137	M₁₆	—	52	2	no	—
138	C₂×C₈	—	52	2	no	—
139	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
140	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
141	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
142	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
143	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
144	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
145	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
146	C₄⋊C₄	—	2	1	no	—
147	C₄⋊C₄	—	52	2	no	—
148	C₂²⋊C₄	—	2	1	no	—
149	C₂²⋊C₄	—	52	2	no	—
150	C₄²	—	52	2	no	—
151	C₄²	C₄⋊Dic₁₃	1	2	yes	—
152	C₁₆	C₄⋊Dic₁₃	1	1	yes	characteristic
153	C₁₆	C₄⋊Dic₁₃	1	1	yes	characteristic
154	C₁₆	C₄⋊Dic₁₃	1	1	yes	characteristic
155	C₁₆	C₄⋊Dic₁₃	1	1	yes	characteristic
156	C₁₆	C₄⋊Dic₁₃	1	4	yes	—
157	C₁₃	#12911	1	1	yes	characteristic, complemented, Sylow
158	C₂³	#88158	1	1	yes	characteristic
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	104	2	no	—
161	C₂×C₄	#88123	1	1	yes	characteristic
162	C₂×C₄	#88128	1	1	yes	characteristic
163	C₂×C₄	#88158	1	1	yes	characteristic
164	C₂×C₄	#88158	1	1	yes	characteristic
165	C₂×C₄	#88158	1	1	yes	characteristic
166	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
167	C₈	—	2	2	no	—
168	C₈	—	104	2	no	—
169	C₈	#88123	1	1	yes	characteristic
170	C₈	#88123	1	1	yes	characteristic
171	C₈	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
172	C₈	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
173	C₂²	—	4	1	no	—
174	C₂²	#11718344	1	1	yes	characteristic
175	C₂²	#11718357	1	1	yes	characteristic
176	C₂²	#11718767	1	1	yes	characteristic
177	C₄	—	4	2	no	—
178	C₄	—	208	2	no	—
179	C₄	#11718344	1	1	yes	characteristic
180	C₄	#11718357	1	1	yes	characteristic
181	C₄	#11718596	1	1	yes	characteristic
182	C₄	#11718767	1	1	yes	characteristic
183	C₂	—	2	1	no	—
184	C₂	—	2	1	no	—
185	C₂	—	2	1	no	—
186	C₂	#13115000	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718767
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#2108	C₂
socle	C₂×C₁₃	#1846
prime radical	C₂³×C₁₃	#135
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#2108	D₁₃
hypocenter	C₁₃	#12911
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #117 ◁ #405 ◁ #2108

Complements

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

N	H ≅ G/N	type
11. C₁₃×#346	C₄	semidirect
12. C₄×C₁₃×C₁₆	C₄	semidirect
95. #346	Dic₁₃	semidirect
96. C₄×C₁₆	Dic₁₃	semidirect
157. C₁₃	#12911	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718098	2
#13116620	2
#13116609	2
#13114960	2
C₁₃×#2108	2
#12911	13