Finite Group Databasebeta

Subgroups — #13114901

Order 1664.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88155	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88059	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718627	C₂	1	2	yes	maximal
5	#11718122	C₂	1	2	yes	maximal, complemented
6	C₂×#6127	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×#6099	C₂²	1	2	yes	—
10	C₂×#6099	C₂²	1	1	yes	characteristic
11	#88155	—	2	2	no	—
12	#88155	C₄	1	4	yes	complemented
13	C₂×#6094	—	2	1	no	—
14	C₂×C₈×D₁₃	—	2	1	no	—
15	C₁₃×#107	—	2	1	no	—
16	C₁₃×#107	—	2	1	no	—
17	#88059	—	2	2	no	—
18	#88050	—	2	2	no	—
19	#88049	—	2	2	no	—
20	C₂²×C₄×C₁₃	—	2	2	no	—
21	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₂²⋊D₁₃	—	2	1	no	—
23	#6127	—	2	1	no	—
24	#6127	—	2	1	no	—
25	#6127	C₂×C₄	1	2	yes	—
26	#6127	Q₈	1	2	yes	—
27	C₂×D₅₂	D₄	1	1	yes	characteristic
28	C₂×C₄×D₁₃	—	2	1	no	—
29	C₂×Dic₂₆	D₄	1	1	yes	characteristic
30	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₁₃	D₄	1	2	yes	—
32	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
33	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
34	C₁₃×C₄⋊C₄	—	2	2	no	—
35	C₁₃×C₄⋊C₄	—	2	2	no	—
36	#6099	—	2	1	no	—
37	#6099	—	2	2	no	—
38	#6099	—	2	2	no	—
39	#6099	C₂×C₄	1	2	yes	—
40	C₂×#1055	—	2	1	no	—
41	C₂×#1055	—	2	2	no	—
42	#6094	—	2	4	no	—
43	C₈×D₁₃	—	2	4	no	—
44	#1816	—	13	1	no	maximal, Sylow
45	C₂³×C₁₃	#41	1	1	yes	characteristic
46	C₂²×D₁₃	—	2	1	no	—
47	C₂×C₄×C₁₃	—	4	2	no	—
48	C₂×C₄×C₁₃	—	8	2	no	—
49	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
55	C₂²⋊D₁₃	—	2	2	no	—
56	C₂²⋊D₁₃	—	2	2	no	—
57	C₂×Dic₁₃	—	2	1	no	—
58	D₅₂	—	2	1	no	—
59	D₅₂	C₄⋊C₄	1	2	yes	—
60	C₄×D₁₃	—	2	2	no	—
61	C₄×D₁₃	—	2	2	no	—
62	Dic₂₆	—	2	1	no	—
63	Dic₂₆	C₄⋊C₄	1	2	yes	—
64	C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
65	C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
66	#1055	—	2	2	no	—
67	#1055	—	4	2	no	—
68	C₂×#131	—	13	1	no	—
69	C₂×#108	—	13	1	no	—
70	C₂×#107	D₁₃	1	1	yes	characteristic, complemented
71	#417	—	13	2	no	—
72	#343	—	13	2	no	—
73	C₂²×C₁₃	—	2	1	no	—
74	C₂²×C₁₃	—	2	1	no	—
75	C₂²×C₁₃	#117	1	1	yes	characteristic
76	C₂²×C₁₃	#121	1	1	yes	characteristic
77	C₂²×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
78	C₂×D₁₃	—	2	2	no	—
79	C₂×D₁₃	—	4	1	no	—
80	C₂×D₁₃	—	4	1	no	—
81	C₄×C₁₃	—	8	2	no	—
82	C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₄×C₁₃	#121	1	1	yes	characteristic
85	C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
86	Dic₁₃	—	2	2	no	—
87	C₂×#41	—	13	1	no	—
88	#131	—	13	4	no	—
89	#131	—	26	2	no	—
90	C₂×M₁₆	—	13	1	no	—
91	C₂×M₁₆	—	13	2	no	—
92	C₂×M₁₆	—	26	1	no	—
93	C₂²×C₈	—	26	1	no	—
94	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
95	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
96	#108	—	26	2	no	—
97	#107	—	2	1	no	—
98	#107	—	2	1	no	—
99	#103	—	26	2	no	—
100	#102	—	26	2	no	—
101	C₂×C₁₃	—	2	1	no	—
102	C₂×C₁₃	—	2	1	no	—
103	C₂×C₁₃	#380	1	1	yes	characteristic
104	C₂×C₁₃	#472	1	1	yes	characteristic
105	C₂×C₁₃	#473	1	1	yes	characteristic
106	D₁₃	—	4	2	no	—
107	#41	—	13	2	no	—
108	#41	—	13	2	no	—
109	#41	—	26	1	no	—
110	#41	—	26	1	no	—
111	C₂×Q₈	—	13	1	no	—
112	C₂×D₄	—	13	1	no	—
113	C₂×D₄	—	26	1	no	—
114	C₂²×C₄	—	2	2	no	—
115	C₂²×C₄	—	26	1	no	—
116	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
117	M₁₆	—	13	2	no	—
118	M₁₆	—	26	1	no	—
119	M₁₆	—	26	4	no	—
120	M₁₆	—	26	2	no	—
121	M₁₆	—	26	2	no	—
122	C₂×C₈	—	26	1	no	—
123	C₂×C₈	—	26	4	no	—
124	C₂×C₈	—	26	2	no	—
125	C₂×C₈	C₄×D₁₃	1	2	yes	—
126	C₂×C₈	D₅₂	1	2	yes	—
127	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
128	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
129	C₄⋊C₄	—	2	2	no	—
130	C₄⋊C₄	—	2	2	no	—
131	C₁₃	#1816	1	1	yes	characteristic, complemented, Sylow
132	C₂³	—	26	1	no	—
133	C₂³	#6129	1	1	yes	characteristic
134	Q₈	—	13	2	no	—
135	Q₈	—	26	1	no	—
136	D₄	—	13	2	no	—
137	D₄	—	26	2	no	—
138	D₄	—	26	2	no	—
139	D₄	—	26	1	no	—
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	8	2	no	—
142	C₂×C₄	—	26	1	no	—
143	C₂×C₄	—	26	2	no	—
144	C₂×C₄	—	26	2	no	—
145	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
146	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
147	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
148	C₂×C₄	Q₈×D₁₃	1	1	yes	characteristic
149	C₂×C₄	#6131	1	1	yes	characteristic
150	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
151	C₈	—	26	2	no	—
152	C₈	—	52	2	no	—
153	C₈	#6103	1	2	yes	—
154	C₈	#6103	1	2	yes	—
155	C₂²	—	2	1	no	—
156	C₂²	—	2	1	no	—
157	C₂²	—	26	2	no	—
158	C₂²	—	52	1	no	—
159	C₂²	—	52	1	no	—
160	C₂²	#88146	1	1	yes	characteristic
161	C₂²	#88151	1	1	yes	characteristic
162	C₂²	#88192	1	1	yes	characteristic
163	C₄	—	8	2	no	—
164	C₄	—	26	2	no	—
165	C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
166	C₄	#88149	1	1	yes	characteristic
167	C₄	C₂×#6103	1	1	yes	characteristic
168	C₄	#88200	1	1	yes	characteristic
169	C₂	—	2	1	no	—
170	C₂	—	2	1	no	—
171	C₂	—	52	2	no	—
172	C₂	#11718648	1	1	yes	characteristic
173	C₂	#11718821	1	1	yes	characteristic
174	C₂	#11718853	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88192
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#107	C₂
socle	C₂²×C₁₃	#121
prime radical	C₂×#6127	C₂²
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×#107	D₁₃
hypocenter	C₁₃	#1816
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#107

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#107	C₂	semidirect
3. C₂×#88059	C₂	semidirect
5. #11718122	C₂	semidirect
12. #88155	C₄	semidirect
70. C₂×#107	D₁₃	semidirect
131. C₁₃	#1816	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88155	2
C₂×C₁₃×#107	2
C₂×#88059	2
#11718627	2
#11718122	2
#1816	13