Subgroups — C₂²×#15690911 #27159043

Order 12416.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690911	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#13095525	C₂	1	1	yes	maximal, characteristic
3	#15690911	C₂²	1	4	yes	direct product factor
4	C₂×#13095525	C₄	1	3	yes	—
5	C₂×#13095525	C₂²	1	3	yes	—
6	C₂²×#11715906	C₄	1	1	yes	characteristic
7	#13095525	C₂×C₄	1	3	yes	—
8	#13095525	C₂³	1	1	yes	characteristic
9	C₂×#11715906	C₈	1	3	yes	—
10	C₂×#11715906	C₂×C₄	1	3	yes	—
11	C₂²×#87604	C₈	1	1	yes	characteristic
12	C₂²×D₉₇	C₁₆	1	1	yes	characteristic
13	C₂×#87604	C₁₆	1	3	yes	—
14	C₂×#87604	C₂×C₈	1	3	yes	—
15	#11715906	C₂×C₈	1	3	yes	—
16	#11715906	C₂²×C₄	1	1	yes	characteristic
17	C₂²×C₉₇	C₃₂	1	1	yes	characteristic, complemented
18	C₂×D₉₇	C₃₂	1	3	yes	complemented
19	C₂×D₉₇	C₂×C₁₆	1	3	yes	—
20	#87604	C₂×C₁₆	1	3	yes	—
21	#87604	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₉₇	C₂×C₃₂	1	3	yes	complemented
23	D₉₇	C₂×C₃₂	1	3	yes	complemented
24	D₉₇	C₂²×C₁₆	1	1	yes	characteristic
25	C₂²×C₃₂	—	97	1	no	maximal, Sylow
26	C₉₇	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₁₆	—	97	1	no	—
28	C₂×C₃₂	—	97	6	no	—
29	C₂²×C₈	—	97	1	no	—
30	C₂×C₁₆	—	97	3	no	—
31	C₂×C₁₆	—	97	3	no	—
32	C₃₂	—	97	4	no	—
33	C₂²×C₄	—	97	1	no	—
34	C₂×C₈	—	97	3	no	—
35	C₂×C₈	—	97	3	no	—
36	C₁₆	—	97	1	no	—
37	C₁₆	—	97	3	no	—
38	C₂³	—	97	1	no	—
39	C₂×C₄	—	97	3	no	—
40	C₂×C₄	—	97	3	no	—
41	C₈	—	97	1	no	—
42	C₈	—	97	3	no	—
43	C₂²	—	97	3	no	—
44	C₂²	—	97	3	no	—
45	C₂²	#15690911	1	1	yes	characteristic, direct product factor
46	C₄	—	97	1	no	—
47	C₄	—	97	3	no	—
48	C₂	—	97	1	no	—
49	C₂	—	97	3	no	—
50	C₂	C₂×#15690911	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	#15690911
commutator, hypocenter	C₉₇	C₂²×C₃₂
Frattini	C₁	G
Fitting, socle	C₂²×C₉₇	C₃₂
prime radical	C₂²×D₉₇	C₁₆
cosocle	#13095525	C₂³
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×#15690911	C₂	direct (N × H)
3. #15690911	C₂²	direct (N × H)
17. C₂²×C₉₇	C₃₂	semidirect
18. C₂×D₉₇	C₃₂	semidirect
22. C₂×C₉₇	C₂×C₃₂	semidirect
23. D₉₇	C₂×C₃₂	semidirect
26. C₉₇	C₂²×C₃₂	semidirect
45. C₂²	#15690911	direct (N × H)
50. C₂	C₂×#15690911	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×#15690911	2
C₂²×#13095525	2
C₂²×C₃₂	97

Subgroups — C22×#15690911 #27159043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15690911 #27159043