Subgroups — #38767152

Order 25472.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15691869	C₂	1	3	yes	maximal
2	#27163739	C₂	1	3	yes	maximal, complemented
3	C₈²×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15691869	C₄	1	6	yes	—
5	C₄²×D₁₉₉	C₂²	1	1	yes	characteristic
6	#20263865	C₄	1	6	yes	—
7	C₄×C₁₉₉⋊C₈	C₂²	1	3	yes	—
8	C₄×C₈×C₁₉₉	C₂²	1	3	yes	—
9	C₂×C₄×D₁₉₉	C₂×C₄	1	3	yes	—
10	#15691869	—	2	12	no	—
11	C₂×C₁₉₉⋊C₈	C₂×C₄	1	6	yes	—
12	C₄×Dic₁₉₉	C₂×C₄	1	3	yes	—
13	C₂×C₈×C₁₉₉	C₂×C₄	1	6	yes	—
14	C₄²×C₁₉₉	C₂³	1	1	yes	characteristic
15	C₂²×D₁₉₉	C₄²	1	1	yes	characteristic
16	C₂×Dic₁₉₉	C₄²	1	3	yes	—
17	C₄×D₁₉₉	—	2	6	no	—
18	C₁₉₉⋊C₈	—	2	6	no	—
19	C₂×C₄×C₁₉₉	C₂²×C₄	1	3	yes	—
20	C₈×C₁₉₉	M₁₆	1	12	yes	complemented
21	C₂²×C₁₉₉	C₂×C₄²	1	1	yes	characteristic
22	C₂×D₁₉₉	—	2	3	no	—
23	C₄×C₁₉₉	C₂×M₁₆	1	6	yes	—
24	Dic₁₉₉	—	2	3	no	—
25	C₂×C₁₉₉	C₄×M₁₆	1	3	yes	—
26	D₁₉₉	—	4	1	no	—
27	C₁₉₉	#1455	1	1	yes	characteristic, complemented, Sylow
28	#1455	—	199	1	no	maximal, Sylow
29	C₄×M₁₆	—	199	3	no	—
30	#322	—	199	3	no	—
31	C₈²	D₁₉₉	1	1	yes	characteristic, complemented
32	C₂×M₁₆	—	199	6	no	—
33	C₂×C₄²	—	199	1	no	—
34	#97	—	199	6	no	—
35	C₄×C₈	—	199	3	no	—
36	C₄×C₈	C₂×D₁₉₉	1	3	yes	—
37	C₂²×C₄	—	199	3	no	—
38	M₁₆	—	398	12	no	—
39	C₂×C₈	—	199	6	no	—
40	C₂×C₈	C₄×D₁₉₉	1	6	yes	—
41	C₄²	—	199	3	no	—
42	C₄²	C₂²×D₁₉₉	1	1	yes	characteristic
43	C₂³	—	199	1	no	—
44	C₂×C₄	—	398	6	no	—
45	C₂×C₄	—	199	3	no	—
46	C₂×C₄	C₂×C₄×D₁₉₉	1	3	yes	—
47	C₈	—	398	6	no	—
48	C₈	#15691869	1	12	yes	complemented
49	C₂²	—	398	3	no	—
50	C₂²	C₄²×D₁₉₉	1	1	yes	characteristic
51	C₄	—	398	3	no	—
52	C₄	C₂×#15691869	1	6	yes	—
53	C₂	—	796	1	no	—
54	C₂	C₄×#15691869	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₁₉₉
commutator, socle	C₂²×C₁₉₉	C₂×C₄²
Fitting	C₈²×C₁₉₉	C₂
prime radical	C₂²×D₁₉₉	C₄²
cosocle	C₄²×C₁₉₉	C₂³
hypercenter	C₈²	D₁₉₉
hypocenter	C₁₉₉	#1455
LCS	G ▷ C₂²×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #27163739	C₂	semidirect
3. C₈²×C₁₉₉	C₂	semidirect
20. C₈×C₁₉₉	M₁₆	semidirect
27. C₁₉₉	#1455	semidirect
31. C₈²	D₁₉₉	semidirect
48. C₈	#15691869	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15691869	2
#27163739	2
C₈²×C₁₉₉	2
#1455	199