Subgroups — #28417342

Order 14912.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21418594	C₂	1	2	yes	maximal
2	#21418523	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#11745400	—	2	2	no	—
4	C₂×Dic₄₆₆	C₄	1	1	yes	characteristic, complemented
5	C₂×D₉₃₂	C₂²	1	1	yes	characteristic
6	#16836571	—	2	2	no	—
7	C₄²×C₂₃₃	C₄	1	1	yes	characteristic, complemented
8	C₂×#11745400	—	4	2	no	—
9	C₂²×D₂₃₃	D₄	1	2	yes	—
10	Dic₄₆₆	—	4	1	no	—
11	D₉₃₂	—	4	1	no	—
12	C₂×Dic₂₃₃	—	2	1	no	—
13	C₂×C₄×C₂₃₃	—	2	1	no	—
14	C₂×C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₂₃₃	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₂₃₃	—	2	2	no	—
17	C₂×D₂₃₃	—	4	2	no	—
18	#11745400	—	8	2	no	—
19	C₄×C₂₃₃	—	2	1	no	—
20	C₄×C₂₃₃	—	4	1	no	—
21	Dic₂₃₃	—	4	1	no	—
22	C₂×C₂₃₃	—	2	1	no	—
23	C₂×C₂₃₃	#99	1	1	yes	characteristic
24	D₂₃₃	—	4	2	no	—
25	C₂₃₃	#354	1	1	yes	characteristic, complemented, Sylow
26	#354	—	233	1	no	maximal, Sylow
27	#124	—	233	1	no	—
28	#99	—	233	2	no	—
29	C₂×Q₈	—	233	1	no	—
30	C₂×D₄	—	233	1	no	—
31	C₂²⋊C₄	—	466	2	no	—
32	C₂²⋊C₄	—	466	2	no	—
33	C₄²	#11745400	1	1	yes	characteristic, complemented
34	C₂³	—	233	2	no	—
35	Q₈	—	932	1	no	—
36	D₄	—	932	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	932	2	no	—
39	C₂×C₄	—	466	1	no	—
40	C₂×C₄	C₂×#11745400	1	1	yes	characteristic
41	C₂²	—	932	2	no	—
42	C₂²	—	466	2	no	—
43	C₂²	C₂²⋊#11745400	1	1	yes	characteristic
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₄	—	1864	2	no	—
47	C₄	—	932	1	no	—
48	C₂	—	2	1	no	—
49	C₂	—	932	2	no	—
50	C₂	#21418594	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21418594
commutator	C₂×C₄×C₂₃₃	C₂×C₄
Frattini	C₂×C₄	C₂×#11745400
Fitting	C₄²×C₂₃₃	C₄
socle	C₂×C₂₃₃	#99
prime radical, cosocle	C₂×D₉₃₂	C₂²
hypercenter	C₄²	#11745400
hypocenter	C₂₃₃	#354
LCS	G ▷ C₂×C₄×C₂₃₃ ▷ C₂²×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
4. C₂×Dic₄₆₆	C₄	semidirect
7. C₄²×C₂₃₃	C₄	semidirect
25. C₂₃₃	#354	semidirect
33. C₄²	#11745400	semidirect

Maximal subgroups

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

subgroup	index
#21418594	2
#21418523	2
#354	233