Subgroups — #14643133

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068362	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622092	C₂	1	2	yes	maximal
4	C₂×#10622092	C₂	1	2	yes	maximal
5	C₄×C₁₁×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#97	C₄	1	4	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
8	C₄³×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₁⋊C₈	C₄	1	4	yes	—
10	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
13	#10622162	C₄	1	4	yes	—
14	#10622092	C₄	1	8	yes	complemented
15	#10622092	C₄	1	8	yes	complemented
16	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
17	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
21	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
22	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
23	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
24	C₁₁×#97	—	2	8	no	—
25	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
26	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
27	C₄×C₁₁⋊C₈	—	2	8	no	—
28	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
29	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
30	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
31	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
32	#7842	—	11	1	no	maximal, Sylow
33	C₂²×C₄×C₁₁	C₄²	1	4	yes	—
34	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₁	—	2	8	no	—
38	C₂×C₈×C₁₁	C₄²	1	8	yes	—
39	C₄²×C₁₁	—	2	4	no	—
40	C₄²×C₁₁	—	2	4	no	—
41	C₄²×C₁₁	M₁₆	1	8	yes	—
42	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
43	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
44	C₂×C₁₁⋊C₈	—	2	4	no	—
45	C₂×C₁₁⋊C₈	—	2	8	no	—
46	C₂×C₁₁⋊C₈	C₄²	1	4	yes	—
47	C₂×C₁₁⋊C₈	C₄²	1	8	yes	—
48	C₂×C₁₁⋊C₈	C₄²	1	4	yes	—
49	C₂×C₁₁⋊C₈	M₁₆	1	8	yes	—
50	#1744	—	11	1	no	—
51	C₄×#97	D₁₁	1	1	yes	characteristic
52	C₄²×C₈	—	11	1	no	—
53	C₂×#322	—	11	2	no	—
54	C₂×#322	—	11	2	no	—
55	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
56	C₂×C₄×C₁₁	—	2	4	no	—
57	C₂×C₄×C₁₁	—	2	4	no	—
58	C₂×C₄×C₁₁	#97	1	8	yes	—
59	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
60	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
61	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
62	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
63	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
64	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
65	C₂×C₄×C₁₁	#131	1	4	yes	—
66	C₈×C₁₁	—	2	8	no	—
67	C₁₁⋊C₈	—	2	4	no	—
68	C₁₁⋊C₈	—	2	8	no	—
69	C₁₁⋊C₈	#97	1	8	yes	complemented
70	C₂×#97	Dic₁₁	1	4	yes	—
71	C₂×C₄×C₈	—	11	1	no	—
72	C₂×C₄×C₈	—	11	1	no	—
73	C₂×C₄×C₈	—	11	2	no	—
74	C₂×C₄×C₈	—	11	4	no	—
75	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
76	C₄³	C₂×D₁₁	1	1	yes	characteristic
77	#336	—	11	4	no	—
78	#322	—	11	8	no	—
79	#322	—	11	8	no	—
80	C₂²×C₁₁	C₄³	1	1	yes	characteristic
81	C₂²×C₁₁	C₂×#97	1	2	yes	—
82	C₂²×C₁₁	C₄×M₁₆	1	2	yes	—
83	C₂²×C₁₁	#405	1	2	yes	—
84	C₄×C₁₁	—	2	8	no	—
85	C₄×C₁₁	C₂×#97	1	2	yes	—
86	C₄×C₁₁	C₄×M₁₆	1	4	yes	—
87	C₄×C₁₁	C₄×M₁₆	1	2	yes	—
88	C₄×C₁₁	#405	1	4	yes	—
89	C₂²×C₈	—	11	2	no	—
90	C₂²×C₈	—	11	4	no	—
91	C₂²×C₈	—	11	2	no	—
92	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
93	C₂×C₄²	C₄×D₁₁	1	2	yes	—
94	C₂×C₄²	C₄×D₁₁	1	2	yes	—
95	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
96	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
97	#97	—	2	8	no	—
98	C₄×C₈	—	11	4	no	—
99	C₄×C₈	—	11	4	no	—
100	C₄×C₈	—	11	4	no	—
101	C₄×C₈	—	11	4	no	—
102	C₄×C₈	—	22	8	no	—
103	C₄×C₈	C₄×D₁₁	1	4	yes	—
104	C₄×C₈	C₄×D₁₁	1	4	yes	—
105	C₂×C₁₁	#1451	1	4	yes	—
106	C₂×C₁₁	C₄×#97	1	1	yes	characteristic
107	C₂×C₁₁	C₄×#97	1	1	yes	characteristic
108	C₂×C₁₁	#1726	1	1	yes	characteristic
109	C₂²×C₄	C₄×Dic₁₁	1	4	yes	—
110	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
111	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
112	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
113	C₂×C₈	—	2	8	no	—
114	C₂×C₈	—	11	4	no	—
115	C₂×C₈	—	11	8	no	—
116	C₂×C₈	—	11	4	no	—
117	C₂×C₈	—	11	8	no	—
118	C₂×C₈	—	22	4	no	—
119	C₂×C₈	—	22	8	no	—
120	C₂×C₈	C₄×Dic₁₁	1	8	yes	—
121	C₄²	—	2	4	no	—
122	C₄²	—	2	4	no	—
123	C₄²	#4318	1	8	yes	—
124	C₄²	C₂×C₄×D₁₁	1	2	yes	—
125	C₄²	C₂×C₄×D₁₁	1	2	yes	—
126	C₁₁	#7842	1	1	yes	characteristic, complemented, Sylow
127	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
128	C₂×C₄	—	2	4	no	—
129	C₂×C₄	—	2	4	no	—
130	C₂×C₄	#66867	1	8	yes	—
131	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
132	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
133	C₂×C₄	C₄²×D₁₁	1	2	yes	—
134	C₂×C₄	M₁₆×D₁₁	1	4	yes	—
135	C₂×C₄	#66960	1	4	yes	—
136	C₂×C₄	C₂×#4318	1	4	yes	—
137	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
138	C₈	—	2	8	no	—
139	C₈	—	11	8	no	—
140	C₈	—	22	4	no	—
141	C₈	—	22	8	no	—
142	C₂²	C₂×#66867	1	2	yes	—
143	C₂²	C₄²×Dic₁₁	1	1	yes	characteristic
144	C₂²	M₁₆×Dic₁₁	1	2	yes	—
145	C₂²	#10622735	1	2	yes	—
146	C₄	—	2	8	no	—
147	C₄	D₁₁×#97	1	2	yes	—
148	C₄	#10622320	1	2	yes	—
149	C₄	#10622321	1	4	yes	—
150	C₄	C₄×#4318	1	4	yes	—
151	C₂	#13066903	1	4	yes	—
152	C₂	#97×Dic₁₁	1	1	yes	characteristic
153	C₂	C₄×#66867	1	1	yes	characteristic
154	C₂	#13068304	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₁
commutator	C₂²×C₁₁	C₄³
Fitting	C₄×C₁₁×#97	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₄×#97	D₁₁
hypocenter	C₁₁	#7842
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
14. #10622092	C₄	semidirect
15. #10622092	C₄	semidirect
69. C₁₁⋊C₈	#97	semidirect
126. C₁₁	#7842	semidirect

Maximal subgroups

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

subgroup	index
#13068362	2
C₄²×C₁₁⋊C₈	2
C₂×#10622092	2
C₄×C₁₁×#97	2
#7842	11