Subgroups — #15671553

Order 2944.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092807	C₂	1	1	yes	maximal, characteristic
2	#13092214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#124	C₂²	1	1	yes	characteristic
5	C₂×#67274	—	2	1	no	—
6	C₂×#67272	—	2	1	no	—
7	#10625045	C₄	1	1	yes	characteristic, complemented
8	C₂₃×#99	—	2	1	no	—
9	#10625018	—	2	1	no	—
10	#10624985	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₂₃	D₄	1	1	yes	characteristic
12	C₂×D₄×C₂₃	D₄	1	1	yes	characteristic
13	C₂×D₉₂	—	2	1	no	—
14	C₂×D₉₂	—	4	1	no	—
15	C₂²⋊C₄×C₂₃	—	4	1	no	—
16	C₂²⋊C₄×C₂₃	—	4	1	no	—
17	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
18	#67274	—	4	2	no	—
19	#67272	—	4	2	no	—
20	#67267	—	4	1	no	—
21	C₂×C₂₃⋊C₈	—	2	1	no	—
22	C₂³×C₂₃	—	2	1	no	—
23	C₂²×D₂₃	—	4	1	no	—
24	Q₈×C₂₃	—	4	1	no	—
25	D₄×C₂₃	—	4	1	no	—
26	C₂×C₄×C₂₃	—	2	1	no	—
27	C₂×C₄×C₂₃	—	2	1	no	—
28	C₂×C₄×C₂₃	—	8	1	no	—
29	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
30	D₉₂	—	4	1	no	—
31	D₉₂	—	4	1	no	—
32	D₉₂	—	8	2	no	—
33	C₂₃⋊C₈	—	2	2	no	—
34	C₂₃⋊C₈	—	8	1	no	—
35	#1406	—	23	1	no	maximal, Sylow
36	C₂²×C₂₃	—	4	1	no	—
37	C₂²×C₂₃	—	8	1	no	—
38	C₂²×C₂₃	#99	1	1	yes	characteristic
39	C₂×D₂₃	—	8	2	no	—
40	C₂×D₂₃	—	8	1	no	—
41	C₄×C₂₃	—	2	1	no	—
42	C₄×C₂₃	—	4	1	no	—
43	C₄×C₂₃	—	4	1	no	—
44	C₄×C₂₃	—	16	1	no	—
45	#496	—	23	1	no	—
46	#355	—	23	1	no	—
47	#354	D₂₃	1	1	yes	characteristic, complemented
48	C₂×C₂₃	—	2	1	no	—
49	C₂×C₂₃	—	8	1	no	—
50	C₂×C₂₃	#353	1	1	yes	characteristic
51	D₂₃	—	16	1	no	—
52	C₂×SD₁₆	—	46	1	no	—
53	C₂×D₈	—	46	1	no	—
54	#127	—	23	1	no	—
55	#124	C₂×D₂₃	1	1	yes	characteristic
56	#101	—	46	1	no	—
57	#99	—	2	1	no	—
58	#97	—	23	1	no	—
59	C₂₃	#1406	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	D₉₂	1	1	yes	characteristic
61	C₂×D₄	—	46	1	no	—
62	C₂×D₄	—	92	1	no	—
63	C₂×D₄	C₂²⋊D₂₃	1	1	yes	characteristic
64	SD₁₆	—	92	2	no	—
65	D₈	—	92	2	no	—
66	M₁₆	—	92	1	no	—
67	C₂×C₈	—	46	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₄²	C₄×D₂₃	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	92	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	92	1	no	—
76	D₄	—	92	1	no	—
77	D₄	—	184	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	8	1	no	—
81	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
82	C₈	—	46	2	no	—
83	C₈	—	184	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	184	2	no	—
87	C₂²	—	184	1	no	—
88	C₂²	#10624988	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	16	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	368	1	no	—
96	C₂	#13092209	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092209
commutator	C₄²×C₂₃	C₂×C₄
Frattini	#124	C₂×D₂₃
Fitting	C₂₃×#354	C₂
socle	C₂×C₂₃	#353
prime radical	#13092807	C₂
cosocle	C₂₃×#124	C₂²
hypercenter	#354	D₂₃
hypocenter	C₂₃	#1406
LCS	G ▷ C₄²×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
2. #13092214	C₂	semidirect
3. C₂₃×#354	C₂	semidirect
7. #10625045	C₄	semidirect
10. #10624985	C₄	semidirect
47. #354	D₂₃	semidirect
59. C₂₃	#1406	semidirect

Maximal subgroups

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

subgroup	index
#13092807	2
#13092214	2
C₂₃×#354	2
#1406	23