Subgroups — C₂²×#19150208 #36374556

Order 22336.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19150208	C₂	1	6	yes	maximal, direct product factor
2	C₂²×C₈×C₃₄₉	C₂	1	1	yes	maximal, characteristic
3	#19150208	C₂²	1	4	yes	direct product factor
4	C₂²×C₄×C₃₄₉	C₄	1	1	yes	characteristic
5	C₂×C₈×C₃₄₉	C₄	1	3	yes	—
6	C₂×C₈×C₃₄₉	C₂²	1	3	yes	—
7	C₂³×C₃₄₉	C₈	1	1	yes	characteristic
8	C₂×C₄×C₃₄₉	C₈	1	3	yes	—
9	C₂×C₄×C₃₄₉	C₂×C₄	1	3	yes	—
10	C₈×C₃₄₉	C₂×C₄	1	3	yes	—
11	C₈×C₃₄₉	C₂³	1	1	yes	characteristic
12	C₂²×C₃₄₉	C₁₆	1	4	yes	complemented
13	C₂²×C₃₄₉	C₂×C₈	1	3	yes	—
14	C₄×C₃₄₉	C₂×C₈	1	3	yes	—
15	C₄×C₃₄₉	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₃₄₉	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₃₄₉	C₂²×C₈	1	1	yes	characteristic
18	C₃₄₉	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	349	1	no	maximal, Sylow
20	C₂²×C₈	D₃₄₉	1	1	yes	characteristic
21	C₂×C₁₆	—	349	6	no	—
22	C₂²×C₄	Dic₃₄₉	1	1	yes	characteristic
23	C₂×C₈	Dic₃₄₉	1	3	yes	—
24	C₂×C₈	C₂×D₃₄₉	1	3	yes	—
25	C₁₆	—	349	4	no	—
26	C₂³	#14584095	1	1	yes	characteristic
27	C₂×C₄	#14584095	1	3	yes	—
28	C₂×C₄	C₂×Dic₃₄₉	1	3	yes	—
29	C₈	C₂×Dic₃₄₉	1	3	yes	—
30	C₈	C₂²×D₃₄₉	1	1	yes	characteristic
31	C₂²	#19150208	1	4	yes	direct product factor
32	C₂²	C₂×#14584095	1	3	yes	—
33	C₄	C₂×#14584095	1	3	yes	—
34	C₄	C₂²×Dic₃₄₉	1	1	yes	characteristic
35	C₂	C₂×#19150208	1	6	yes	direct product factor
36	C₂	C₂²×#14584095	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	D₃₄₉
commutator, hypocenter	C₃₄₉	C₂²×C₁₆
Frattini	C₈	C₂²×D₃₄₉
Fitting	C₂²×C₈×C₃₄₉	C₂
socle, prime radical	C₂³×C₃₄₉	C₈
cosocle	C₈×C₃₄₉	C₂³
LCS	G ▷ C₃₄₉
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#19150208	C₂	direct (N × H)
3. #19150208	C₂²	direct (N × H)
12. C₂²×C₃₄₉	C₁₆	semidirect
16. C₂×C₃₄₉	C₂×C₁₆	semidirect
18. C₃₄₉	C₂²×C₁₆	semidirect
31. C₂²	#19150208	direct (N × H)
35. C₂	C₂×#19150208	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19150208	2
C₂²×C₈×C₃₄₉	2
C₂²×C₁₆	349

Subgroups — C22×#19150208 #36374556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19150208 #36374556