Subgroups — #37565609

Order 24256.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131328	C₂	1	1	yes	maximal, characteristic
2	#27131323	C₂	1	1	yes	maximal, characteristic, complemented
3	#27131253	C₂	1	4	yes	maximal, complemented
4	#97×C₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₅₁₆	—	2	2	no	—
6	C₂×D₁₅₁₆	C₂²	1	2	yes	—
7	C₄⋊Dic₃₇₉	C₂²	1	2	yes	—
8	Dic₃₇₉⋊C₄	—	2	2	no	—
9	C₂×C₈×C₃₇₉	C₂²	1	2	yes	—
10	C₄²×C₃₇₉	C₂²	1	1	yes	characteristic
11	C₂²×D₃₇₉	—	2	2	no	—
12	D₁₅₁₆	—	2	4	no	—
13	D₁₅₁₆	—	4	4	no	—
14	C₂×Dic₃₇₉	—	2	2	no	—
15	C₂×C₄×C₃₇₉	D₄	1	2	yes	—
16	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
17	C₈×C₃₇₉	—	2	2	no	—
18	C₂²×C₃₇₉	C₂×D₄	1	1	yes	characteristic
19	C₂×D₃₇₉	—	4	2	no	—
20	C₂×D₃₇₉	—	4	4	no	—
21	C₄×C₃₇₉	—	2	2	no	—
22	C₄×C₃₇₉	#41	1	2	yes	—
23	Dic₃₇₉	—	4	2	no	—
24	C₂×C₃₇₉	#124	1	1	yes	characteristic
25	C₂×C₃₇₉	AGL(1,ℤ/8)	1	2	yes	—
26	D₃₇₉	—	8	2	no	—
27	C₃₇₉	#490	1	1	yes	characteristic, complemented, Sylow
28	#490	—	379	1	no	maximal, Sylow
29	#127	—	379	1	no	—
30	#125	—	379	1	no	—
31	#102	—	379	4	no	—
32	#97	D₃₇₉	1	1	yes	characteristic, complemented
33	C₂×D₄	—	379	2	no	—
34	C₂×D₄	—	758	2	no	—
35	C₂×C₈	C₂×D₃₇₉	1	2	yes	—
36	C₄⋊C₄	—	379	2	no	—
37	C₄⋊C₄	—	758	2	no	—
38	C₄²	C₂×D₃₇₉	1	1	yes	characteristic
39	C₂³	—	758	2	no	—
40	D₄	—	1516	4	no	—
41	D₄	—	758	4	no	—
42	C₂×C₄	—	758	2	no	—
43	C₂×C₄	D₁₅₁₆	1	2	yes	—
44	C₂×C₄	C₂²×D₃₇₉	1	1	yes	characteristic
45	C₈	—	2	2	no	—
46	C₂²	—	1516	2	no	—
47	C₂²	—	1516	4	no	—
48	C₂²	C₂×D₁₅₁₆	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	1516	2	no	—
51	C₄	#20258606	1	2	yes	—
52	C₂	—	3032	2	no	—
53	C₂	#27131319	1	1	yes	characteristic
54	C₂	#27131359	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₅₁₆
commutator, cosocle	C₂×C₄×C₃₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₃₇₉
Fitting	#97×C₃₇₉	C₂
socle	C₂²×C₃₇₉	C₂×D₄
prime radical	#27131328	C₂
hypercenter	#97	D₃₇₉
hypocenter	C₃₇₉	#490
LCS	G ▷ C₂×C₄×C₃₇₉ ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. #27131323	C₂	semidirect
3. #27131253	C₂	semidirect
4. #97×C₃₇₉	C₂	semidirect
27. C₃₇₉	#490	semidirect
32. #97	D₃₇₉	semidirect

Maximal subgroups

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

subgroup	index
#27131328	2
#27131323	2
#27131253	2
#97×C₃₇₉	2
#490	379