Subgroups — C₂²⋊#22552719 #45692519

Order 33516.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#22552719	—	4	1	no	maximal, Hall
3	C₂×C₇²×C₁₉⋊C₃	—	3	1	no	—
4	C₂²⋊#11924781	—	7	8	no	maximal
5	C₂²×C₇²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₇²×C₁₉⋊C₃	A₄	1	1	yes	characteristic
7	C₂×C₇²×C₁₉	—	3	1	no	—
8	C₂²⋊#89204	—	19	1	no	maximal, Hall
9	C₂²×C₇×C₁₉⋊C₃	ΓL(1,𝔽₈)	1	8	yes	—
10	#11924781	—	28	8	no	—
11	C₇²×C₁₉	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
12	C₂×C₇×C₁₉⋊C₃	—	3	8	no	—
13	C₂²⋊#4296	—	49	1	no	Hall
14	C₂²×C₃×C₇²	—	19	1	no	—
15	C₂²×C₇×C₁₉	C₇⋊C₉	1	8	yes	complemented
16	#89204	—	76	1	no	Hall
17	C₇×C₁₉⋊C₃	C₂²⋊ΓL(1,𝔽₈)	1	8	yes	—
18	C₂×C₃×C₇²	—	57	1	no	—
19	C₂×C₇×C₁₉	—	3	8	no	—
20	C₂²⋊(C₇⋊C₉)	—	133	8	no	—
21	C₂²×C₁₉⋊C₃	#3861	1	1	yes	characteristic
22	C₂²×C₇²	#4296	1	1	yes	characteristic, complemented, Hall
23	#4296	—	196	1	no	Hall
24	C₃×C₇²	—	19	1	no	—
25	C₇×C₁₉	C₂²⋊(C₇⋊C₉)	1	8	yes	complemented
26	C₂×C₁₉⋊C₃	—	3	1	no	—
27	C₂×C₇²	—	3	1	no	—
28	C₂²×C₃×C₇	—	19	8	no	—
29	C₂²×C₁₉	#89204	1	1	yes	characteristic, complemented, Hall
30	C₇⋊C₉	—	532	8	no	—
31	C₁₉⋊C₃	C₂²⋊#3861	1	1	yes	characteristic
32	C₇²	C₂²⋊#4296	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₇	—	57	8	no	—
34	C₂×C₁₉	—	3	1	no	—
35	C₂²⋊C₉	—	931	1	no	Hall
36	C₂²×C₇	#11924781	1	8	yes	complemented
37	C₃×C₇	—	19	8	no	—
38	C₁₉	C₂²⋊#89204	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₇	—	3	8	no	—
40	C₂²×C₃	—	19	1	no	—
41	C₉	—	3724	1	no	Sylow
42	C₇	C₂²⋊#11924781	1	8	yes	complemented
43	C₂×C₃	—	57	1	no	—
44	C₂²	#22552719	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	19	1	no	—
46	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂²×C₇²×C₁₉	C₉
prime radical, cosocle	C₂²×C₇²×C₁₉⋊C₃	C₃
LCS	G ▷ C₂²×C₇²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
5. C₂²×C₇²×C₁₉	C₉	semidirect
11. C₇²×C₁₉	C₂²⋊C₉	semidirect
15. C₂²×C₇×C₁₉	C₇⋊C₉	semidirect
22. C₂²×C₇²	#4296	semidirect
25. C₇×C₁₉	C₂²⋊(C₇⋊C₉)	semidirect
29. C₂²×C₁₉	#89204	semidirect
32. C₇²	C₂²⋊#4296	semidirect
36. C₂²×C₇	#11924781	semidirect
38. C₁₉	C₂²⋊#89204	semidirect
42. C₇	C₂²⋊#11924781	semidirect
44. C₂²	#22552719	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₇²×C₁₉⋊C₃	3
#22552719	4
C₂²⋊#11924781	7
C₂²⋊#89204	19

Subgroups — C22⋊#22552719 #45692519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#22552719 #45692519