Subgroups — #15778308

Order 3328.

318 conjugacy classes of subgroups.

The subgroup lattice has 184 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	#13114715	C₂	1	2	yes	maximal
4	#13112932	C₂	1	2	yes	maximal
5	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88059	C₂²	1	2	yes	—
10	#11718767	C₂²	1	2	yes	—
11	#11718762	—	2	2	no	—
12	C₄×C₁₃×C₁₆	C₄	1	4	yes	complemented
13	#11718115	—	2	2	no	—
14	#11718098	C₄	1	4	yes	complemented
15	#11718097	C₄	1	2	yes	complemented
16	#11718096	C₄	1	2	yes	complemented
17	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
20	#88180	—	2	2	no	—
21	C₂×#6099	—	2	2	no	—
22	C₂×C₁₃×C₁₆	—	2	1	no	—
23	C₂×C₁₃×C₁₆	—	2	1	no	—
24	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
25	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
26	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
27	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
28	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
29	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₃	Q₈	1	2	yes	—
31	#88059	—	2	2	no	—
32	#88059	C₂×C₄	1	4	yes	—
33	#88058	C₂×C₄	1	4	yes	—
34	#88057	—	2	2	no	—
35	#88055	—	4	2	no	—
36	C₈×Dic₁₃	—	4	2	no	—
37	#12670	—	13	1	no	maximal, Sylow
38	C₂²×C₄×C₁₃	—	2	1	no	—
39	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
41	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
42	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
43	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
49	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
50	C₄²×C₁₃	—	2	1	no	—
51	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
52	C₂²⋊Dic₁₃	—	4	2	no	—
53	C₄⋊Dic₁₃	—	2	4	no	—
54	C₄×Dic₁₃	—	4	2	no	—
55	#6099	—	2	4	no	—
56	#6099	—	4	2	no	—
57	C₂×#1055	—	4	2	no	—
58	C₁₃×C₁₆	—	2	2	no	—
59	C₁₃×C₁₆	C₄²	1	2	yes	—
60	C₁₃×C₁₆	C₄²	1	2	yes	—
61	C₂×#368	—	13	1	no	—
62	#2158	—	13	1	no	—
63	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
64	#1772	—	13	2	no	—
65	#1382	—	13	2	no	—
66	C₂³×C₁₃	#135	1	1	yes	characteristic
67	C₂×C₄×C₁₃	—	2	4	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
74	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
75	C₂×Dic₁₃	—	4	4	no	—
76	C₈×C₁₃	#107	1	2	yes	—
77	C₈×C₁₃	#107	1	2	yes	—
78	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
79	C₈×C₁₃	#117	1	1	yes	characteristic
80	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
81	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
82	#1055	—	4	4	no	—
83	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
84	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
85	C₂×#108	—	13	2	no	—
86	#427	—	13	2	no	—
87	#405	—	26	2	no	—
88	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
89	#368	—	13	4	no	—
90	#367	—	13	2	no	—
91	#366	—	13	2	no	—
92	C₄×C₁₆	Dic₁₃	1	4	yes	complemented
93	#339	—	26	2	no	—
94	C₂²×C₁₃	—	2	2	no	—
95	C₂²×C₁₃	#427	1	1	yes	characteristic
96	C₂²×C₁₃	C₄×D₈	1	1	yes	characteristic
97	C₂²×C₁₃	C₄×Q₁₆	1	1	yes	characteristic
98	C₄×C₁₃	—	2	4	no	—
99	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
100	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
101	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
102	C₄×C₁₃	C₄×Q₁₆	1	1	yes	characteristic
103	Dic₁₃	—	8	4	no	—
104	C₂×M₁₆	—	26	2	no	—
105	C₂²×C₈	D₅₂	1	1	yes	characteristic
106	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
107	#117	—	26	2	no	—
108	C₂×C₄²	D₅₂	1	1	yes	characteristic
109	C₂×C₁₆	—	2	1	no	—
110	C₂×C₁₆	—	2	1	no	—
111	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
112	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
113	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
114	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
115	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
116	#108	—	13	4	no	—
117	#108	—	26	2	no	—
118	#107	—	13	4	no	—
119	#106	—	26	2	no	—
120	#97	—	52	2	no	—
121	C₄×C₈	—	52	2	no	—
122	C₄×C₈	Dic₂₆	1	2	yes	—
123	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
124	C₂×C₁₃	—	2	1	no	—
125	C₂×C₁₃	—	2	1	no	—
126	C₂×C₁₃	C₄×#107	1	1	yes	characteristic
127	C₂×C₁₃	#2178	1	2	yes	—
128	C₂²×C₄	—	2	1	no	—
129	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
130	M₁₆	—	26	4	no	—
131	M₁₆	—	52	2	no	—
132	C₂×C₈	—	52	2	no	—
133	C₂×C₈	D₁₀₄	1	1	yes	characteristic
134	C₂×C₈	D₁₀₄	1	1	yes	characteristic
135	C₂×C₈	Dic₅₂	1	2	yes	—
136	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
137	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
138	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
139	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
140	C₂×C₈	#6127	1	1	yes	characteristic
141	C₂×C₈	#6127	1	1	yes	characteristic
142	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
143	C₄⋊C₄	—	26	4	no	—
144	C₂²⋊C₄	—	52	2	no	—
145	C₄²	—	2	1	no	—
146	C₄²	—	52	2	no	—
147	C₄²	C₄⋊Dic₁₃	1	2	yes	—
148	C₁₆	—	2	2	no	—
149	C₁₆	C₄×Dic₁₃	1	2	yes	—
150	C₁₆	C₄×Dic₁₃	1	2	yes	—
151	C₁₃	#12670	1	1	yes	characteristic, complemented, Sylow
152	C₂³	#88158	1	1	yes	characteristic
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	52	4	no	—
156	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
157	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
158	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
159	C₂×C₄	#88158	1	1	yes	characteristic
160	C₂×C₄	C₂×Dic₅₂	1	1	yes	characteristic
161	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
162	C₈	—	52	4	no	—
163	C₈	#88058	1	2	yes	—
164	C₈	#88058	1	2	yes	—
165	C₈	C₄×Dic₂₆	1	1	yes	characteristic
166	C₈	C₄×Dic₂₆	1	1	yes	characteristic
167	C₈	C₂×C₄×Dic₁₃	1	1	yes	characteristic
168	C₈	#88180	1	1	yes	characteristic
169	C₂²	—	2	2	no	—
170	C₂²	C₄×D₁₀₄	1	1	yes	characteristic
171	C₂²	C₄×Dic₅₂	1	1	yes	characteristic
172	C₂²	#11718767	1	1	yes	characteristic
173	C₄	—	2	4	no	—
174	C₄	—	104	4	no	—
175	C₄	C₄×D₁₀₄	1	1	yes	characteristic
176	C₄	C₄×Dic₅₂	1	1	yes	characteristic
177	C₄	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
178	C₄	C₂×#88058	1	1	yes	characteristic
179	C₂	—	2	1	no	—
180	C₂	—	2	1	no	—
181	C₂	C₄×#88058	1	1	yes	characteristic
182	C₂	#13116718	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₁₀₄
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle	C₂²×C₁₃	C₄×D₈
prime radical	C₂³×C₁₃	#135
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	#12670
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₄×C₁₃×C₁₆	C₄	semidirect
14. #11718098	C₄	semidirect
15. #11718097	C₄	semidirect
16. #11718096	C₄	semidirect
92. C₄×C₁₆	Dic₁₃	semidirect
151. C₁₃	#12670	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
#13114715	2
#13112932	2
C₂×C₄×C₁₃×C₁₆	2
#12670	13