Subgroups — #37565605

Order 24256.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131330	C₂	1	1	yes	maximal, characteristic, complemented
2	#27131320	C₂	1	1	yes	maximal, characteristic
3	#27131255	C₂	1	1	yes	maximal, characteristic, complemented
4	#27131253	C₂	1	1	yes	maximal, characteristic
5	#27131251	C₂	1	1	yes	maximal, characteristic
6	#27131241	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₇₅₈	—	2	1	no	—
9	C₂×D₁₅₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₃₇₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₃₇₉	C₂²	1	1	yes	characteristic
12	Dic₃₇₉⋊C₄	—	2	1	no	—
13	(C₂×D₃₇₉)⋊C₄	—	2	1	no	—
14	(C₂×D₃₇₉)⋊C₄	—	2	1	no	—
15	C₄×Dic₃₇₉	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₃₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₃₇₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₃₇₉	C₂²	1	1	yes	characteristic
19	C₂²×D₃₇₉	—	2	1	no	—
20	Dic₇₅₈	—	4	2	no	—
21	D₁₅₁₆	—	2	1	no	—
22	D₁₅₁₆	—	2	1	no	—
23	C₂×Dic₃₇₉	—	2	1	no	—
24	C₂×Dic₃₇₉	D₄	1	1	yes	characteristic
25	C₂×Dic₃₇₉	D₄	1	1	yes	characteristic
26	C₃₇₉⋊C₈	—	2	1	no	—
27	Q₈×C₃₇₉	—	2	1	no	—
28	Q₈×C₃₇₉	—	2	1	no	—
29	C₂×C₄×C₃₇₉	—	2	1	no	—
30	C₂×C₄×C₃₇₉	—	2	1	no	—
31	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
32	C₈×C₃₇₉	—	2	1	no	—
33	C₂²×C₃₇₉	C₂×D₄	1	1	yes	characteristic
34	C₂×D₃₇₉	—	4	1	no	—
35	C₂×D₃₇₉	—	4	1	no	—
36	C₂×D₃₇₉	—	4	1	no	—
37	C₄×C₃₇₉	—	4	1	no	—
38	C₄×C₃₇₉	—	4	1	no	—
39	C₄×C₃₇₉	#41	1	1	yes	characteristic
40	C₄×C₃₇₉	#41	1	1	yes	characteristic
41	Dic₃₇₉	—	2	1	no	—
42	Dic₃₇₉	—	2	1	no	—
43	Dic₃₇₉	—	4	1	no	—
44	C₂×C₃₇₉	#124	1	1	yes	characteristic
45	C₂×C₃₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
46	C₂×C₃₇₉	#137	1	1	yes	characteristic
47	D₃₇₉	—	8	1	no	—
48	C₃₇₉	#489	1	1	yes	characteristic, complemented, Sylow
49	#489	—	379	1	no	maximal, Sylow
50	C₄⋊Q₈	—	379	1	no	—
51	#124	—	379	1	no	—
52	#103	—	379	1	no	—
53	#103	D₃₇₉	1	1	yes	characteristic, complemented
54	#102	—	379	1	no	—
55	#102	—	379	1	no	—
56	#97	—	379	1	no	—
57	C₂×Q₈	—	758	1	no	—
58	C₂×Q₈	C₂×D₃₇₉	1	1	yes	characteristic
59	C₂×D₄	—	379	1	no	—
60	C₂×C₈	—	379	1	no	—
61	C₂×C₈	C₂×D₃₇₉	1	1	yes	characteristic
62	C₄⋊C₄	—	379	1	no	—
63	C₄⋊C₄	—	758	1	no	—
64	C₄⋊C₄	C₂×D₃₇₉	1	1	yes	characteristic
65	C₂²⋊C₄	—	758	1	no	—
66	C₂²⋊C₄	—	758	1	no	—
67	C₄²	—	379	1	no	—
68	C₂³	—	758	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	1516	2	no	—
72	D₄	—	758	1	no	—
73	D₄	—	758	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	379	1	no	—
77	C₂×C₄	—	379	1	no	—
78	C₂×C₄	—	758	1	no	—
79	C₂×C₄	C₂²×D₃₇₉	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	758	1	no	—
82	C₂²	—	1516	1	no	—
83	C₂²	—	1516	1	no	—
84	C₂²	—	1516	1	no	—
85	C₂²	D₄×D₃₇₉	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	1516	1	no	—
89	C₄	—	758	1	no	—
90	C₄	—	758	1	no	—
91	C₄	#20258605	1	1	yes	characteristic
92	C₄	#20258606	1	1	yes	characteristic
93	C₂	—	3032	1	no	—
94	C₂	#27131317	1	1	yes	characteristic
95	C₂	#27131358	1	1	yes	characteristic
96	C₂	#27131363	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₇₉
commutator, cosocle	C₂×C₄×C₃₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₃₇₉
Fitting	#103×C₃₇₉	C₂
socle	C₂²×C₃₇₉	C₂×D₄
prime radical	C₂×D₁₅₁₆	C₂²
hypercenter	#103	D₃₇₉
hypocenter	C₃₇₉	#489
LCS	G ▷ C₂×C₄×C₃₇₉ ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
1. #27131330	C₂	semidirect
3. #27131255	C₂	semidirect
6. #27131241	C₂	semidirect
7. #103×C₃₇₉	C₂	semidirect
48. C₃₇₉	#489	semidirect
53. #103	D₃₇₉	semidirect

Maximal subgroups

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

subgroup	index
#27131330	2
#27131320	2
#27131255	2
#27131253	2
#27131251	2
#27131241	2
#103×C₃₇₉	2
#489	379