Subgroups — C₄⋊#15690911 #27159038

Order 12416.

62 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	—	2	2	no	—
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	—	2	1	no	—
8	#13095525	D₄	1	1	yes	characteristic
9	#13095525	Q₈	1	1	yes	characteristic
10	C₂×#11715906	C₈	1	1	yes	characteristic
11	C₂×#11715906	C₂×C₄	1	1	yes	characteristic
12	C₄×#87604	C₈	1	1	yes	characteristic
13	C₂×#87604	C₁₆	1	1	yes	characteristic
14	C₂×#87604	C₂×C₈	1	1	yes	characteristic
15	#11715906	—	2	1	no	—
16	#11715906	C₄⋊C₄	1	1	yes	characteristic
17	#11715906	M₁₆	1	1	yes	characteristic
18	C₄×D₉₇	C₁₆	1	1	yes	characteristic
19	C₂×D₉₇	C₂×C₁₆	1	1	yes	characteristic
20	#87604	—	2	1	no	—
21	#87604	C₄⋊C₈	1	1	yes	characteristic
22	#87604	M₃₂	1	1	yes	characteristic
23	C₄×C₉₇	C₃₂	1	1	yes	characteristic, complemented
24	Dic₉₇	C₃₂	1	1	yes	characteristic, complemented
25	C₂×C₉₇	C₂×C₃₂	1	1	yes	characteristic
26	D₉₇	C₄⋊C₁₆	1	1	yes	characteristic
27	D₉₇	M₆₄	1	1	yes	characteristic
28	C₄⋊C₃₂	—	97	1	no	maximal, Sylow
29	C₉₇	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃₂	—	97	2	no	—
31	C₄×C₁₆	—	97	1	no	—
32	C₂×C₁₆	—	97	1	no	—
33	C₂×C₁₆	—	97	1	no	—
34	C₄×C₈	—	97	1	no	—
35	C₃₂	—	194	2	no	—
36	C₂×C₈	—	97	1	no	—
37	C₂×C₈	—	97	1	no	—
38	C₄²	—	97	1	no	—
39	C₁₆	—	97	1	no	—
40	C₁₆	—	97	1	no	—
41	C₁₆	—	194	1	no	—
42	C₂×C₄	—	97	1	no	—
43	C₂×C₄	—	97	1	no	—
44	C₂×C₄	—	97	1	no	—
45	C₈	—	97	1	no	—
46	C₈	—	97	1	no	—
47	C₈	—	194	1	no	—
48	C₂²	—	97	1	no	—
49	C₄	—	97	1	no	—
50	C₄	—	97	1	no	—
51	C₄	—	97	1	no	—
52	C₄	—	194	1	no	—
53	C₄	#15690911	1	1	yes	characteristic, complemented
54	C₂	—	97	1	no	—
55	C₂	—	97	1	no	—
56	C₂	C₂×#15690911	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
23. C₄×C₉₇	C₃₂	semidirect
24. Dic₉₇	C₃₂	semidirect
29. C₉₇	C₄⋊C₃₂	semidirect
53. C₄	#15690911	semidirect

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 #27159038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#15690911 #27159038