Subgroups — C₂²×#15690900 #27158964

Order 12416.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690900	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#13095514	C₂	1	1	yes	maximal, characteristic
3	#15690900	C₂²	1	4	yes	direct product factor
4	C₂×#13095514	C₄	1	3	yes	—
5	C₂×#13095514	C₂²	1	3	yes	—
6	C₂²×#11715895	C₄	1	1	yes	characteristic
7	#13095514	C₂×C₄	1	3	yes	—
8	#13095514	C₂³	1	1	yes	characteristic
9	C₂×#11715895	C₈	1	3	yes	—
10	C₂×#11715895	C₂×C₄	1	3	yes	—
11	C₂²×C₄×C₉₇	C₈	1	1	yes	characteristic
12	C₂³×C₉₇	C₁₆	1	1	yes	characteristic
13	C₂×C₄×C₉₇	C₁₆	1	3	yes	—
14	C₂×C₄×C₉₇	C₂×C₈	1	3	yes	—
15	#11715895	C₂×C₈	1	3	yes	—
16	#11715895	C₂²×C₄	1	1	yes	characteristic
17	C₂²×C₉₇	C₃₂	1	4	yes	complemented
18	C₂²×C₉₇	C₂×C₁₆	1	3	yes	—
19	C₄×C₉₇	C₂×C₁₆	1	3	yes	—
20	C₄×C₉₇	C₂²×C₈	1	1	yes	characteristic
21	C₂×C₉₇	C₂×C₃₂	1	6	yes	complemented
22	C₂×C₉₇	C₂²×C₁₆	1	1	yes	characteristic
23	C₂²×C₃₂	—	97	1	no	maximal, Sylow
24	C₉₇	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
25	C₂²×C₁₆	—	97	1	no	—
26	C₂×C₃₂	—	97	6	no	—
27	C₂²×C₈	—	97	1	no	—
28	C₂×C₁₆	—	97	3	no	—
29	C₂×C₁₆	—	97	3	no	—
30	C₃₂	—	97	4	no	—
31	C₂²×C₄	#11715906	1	1	yes	characteristic
32	C₂×C₈	—	97	3	no	—
33	C₂×C₈	—	97	3	no	—
34	C₁₆	—	97	3	no	—
35	C₁₆	—	97	1	no	—
36	C₂³	#13095523	1	1	yes	characteristic
37	C₂×C₄	#13095523	1	3	yes	—
38	C₂×C₄	C₂×#11715906	1	3	yes	—
39	C₈	—	97	1	no	—
40	C₈	—	97	3	no	—
41	C₂²	#15690900	1	4	yes	direct product factor
42	C₂²	C₂×#13095523	1	3	yes	—
43	C₄	C₂×#13095523	1	3	yes	—
44	C₄	C₂²×#11715906	1	1	yes	characteristic
45	C₂	C₂×#15690900	1	6	yes	direct product factor
46	C₂	C₂²×#13095523	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	#11715906
commutator, hypocenter	C₉₇	C₂²×C₃₂
Frattini	C₄	C₂²×#11715906
Fitting	C₂²×C₄×C₉₇	C₈
socle, prime radical	C₂³×C₉₇	C₁₆
cosocle	#13095514	C₂³
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#15690900	C₂	direct (N × H)
3. #15690900	C₂²	direct (N × H)
17. C₂²×C₉₇	C₃₂	semidirect
21. C₂×C₉₇	C₂×C₃₂	semidirect
24. C₉₇	C₂²×C₃₂	semidirect
41. C₂²	#15690900	direct (N × H)
45. C₂	C₂×#15690900	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×#15690900	2
C₂²×#13095514	2
C₂²×C₃₂	97

Subgroups — C22×#15690900 #27158964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15690900 #27158964