Subgroups — C₄×#15690911 #27159036

Order 12416.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690911	C₂	1	2	yes	maximal
2	C₄×#13095525	C₂	1	1	yes	maximal, characteristic
3	#15690911	C₄	1	4	yes	direct product factor
4	C₂×#13095525	C₄	1	1	yes	characteristic
5	C₂×#13095525	C₂²	1	1	yes	characteristic
6	C₄×#11715906	C₄	1	1	yes	characteristic
7	#13095525	C₈	1	2	yes	—
8	#13095525	C₂×C₄	1	2	yes	—
9	C₂×#11715906	C₈	1	1	yes	characteristic
10	C₂×#11715906	C₂×C₄	1	1	yes	characteristic
11	C₄×#87604	C₈	1	1	yes	characteristic
12	C₂×#87604	C₁₆	1	1	yes	characteristic
13	C₂×#87604	C₂×C₈	1	1	yes	characteristic
14	#11715906	C₁₆	1	2	yes	—
15	#11715906	C₄²	1	1	yes	characteristic
16	#11715906	C₂×C₈	1	1	yes	characteristic
17	C₄×D₉₇	C₁₆	1	1	yes	characteristic
18	C₂×D₉₇	C₂×C₁₆	1	1	yes	characteristic
19	#87604	C₃₂	1	2	yes	complemented
20	#87604	C₄×C₈	1	1	yes	characteristic
21	#87604	C₂×C₁₆	1	1	yes	characteristic
22	C₄×C₉₇	C₃₂	1	1	yes	characteristic, complemented
23	Dic₉₇	C₃₂	1	1	yes	characteristic, complemented
24	C₂×C₉₇	C₂×C₃₂	1	1	yes	characteristic
25	D₉₇	C₄×C₁₆	1	1	yes	characteristic
26	D₉₇	C₂×C₃₂	1	1	yes	characteristic
27	C₄×C₃₂	—	97	1	no	maximal, Sylow
28	C₉₇	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃₂	—	97	2	no	—
30	C₄×C₁₆	—	97	1	no	—
31	C₂×C₁₆	—	97	1	no	—
32	C₂×C₁₆	—	97	1	no	—
33	C₄×C₈	—	97	1	no	—
34	C₃₂	—	97	4	no	—
35	C₂×C₈	—	97	1	no	—
36	C₂×C₈	—	97	1	no	—
37	C₄²	—	97	1	no	—
38	C₁₆	—	97	2	no	—
39	C₁₆	—	97	2	no	—
40	C₂×C₄	—	97	1	no	—
41	C₂×C₄	—	97	1	no	—
42	C₂×C₄	—	97	1	no	—
43	C₈	—	97	1	no	—
44	C₈	—	97	1	no	—
45	C₈	—	97	2	no	—
46	C₂²	—	97	1	no	—
47	C₄	—	97	1	no	—
48	C₄	—	97	1	no	—
49	C₄	—	97	2	no	—
50	C₄	—	97	1	no	—
51	C₄	#15690911	1	1	yes	characteristic, direct product factor
52	C₂	—	97	1	no	—
53	C₂	—	97	1	no	—
54	C₂	C₂×#15690911	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	#15690911
commutator, hypocenter	C₉₇	C₄×C₃₂
Frattini	C₂	C₂×#15690911
Fitting	C₄×C₉₇	C₃₂
socle	C₂×C₉₇	C₂×C₃₂
prime radical	C₂×D₉₇	C₂×C₁₆
cosocle	C₂×#13095525	C₂²
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
3. #15690911	C₄	direct (N × H)
19. #87604	C₃₂	semidirect
22. C₄×C₉₇	C₃₂	semidirect
23. Dic₉₇	C₃₂	semidirect
28. C₉₇	C₄×C₃₂	semidirect
51. C₄	#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
C₄×#13095525	2
C₄×C₃₂	97

Subgroups — C4×#15690911 #27159036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15690911 #27159036