Subgroups — C₂²⋊#15690911 #27159037

Order 12416.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690911	C₂	1	2	yes	maximal, complemented
2	C₂²×#13095525	C₂	1	1	yes	maximal, characteristic
3	#15690911	—	2	2	no	—
4	C₂×#13095525	—	2	2	no	—
5	C₂×#13095525	C₄	1	1	yes	characteristic
6	C₂×#13095525	C₂²	1	1	yes	characteristic
7	C₂²×#11715906	C₄	1	1	yes	characteristic
8	#13095525	—	2	1	no	—
9	#13095525	D₄	1	2	yes	—
10	C₂×#11715906	—	2	1	no	—
11	C₂×#11715906	—	2	1	no	—
12	C₂×#11715906	C₈	1	1	yes	characteristic
13	C₂×#11715906	C₂×C₄	1	1	yes	characteristic
14	C₂²×#87604	C₈	1	1	yes	characteristic
15	C₂²×D₉₇	C₁₆	1	1	yes	characteristic
16	C₂×#87604	—	2	1	no	—
17	C₂×#87604	—	2	1	no	—
18	C₂×#87604	C₁₆	1	1	yes	characteristic
19	C₂×#87604	C₂×C₈	1	1	yes	characteristic
20	#11715906	—	2	1	no	—
21	#11715906	C₂²⋊C₄	1	1	yes	characteristic
22	#11715906	M₁₆	1	1	yes	characteristic
23	C₂²×C₉₇	C₃₂	1	1	yes	characteristic, complemented
24	C₂×D₉₇	—	2	1	no	—
25	C₂×D₉₇	—	2	1	no	—
26	C₂×D₉₇	C₃₂	1	1	yes	characteristic, complemented
27	C₂×D₉₇	C₂×C₁₆	1	1	yes	characteristic
28	#87604	—	2	1	no	—
29	#87604	C₂²⋊C₈	1	1	yes	characteristic
30	#87604	M₃₂	1	1	yes	characteristic
31	C₂×C₉₇	—	2	1	no	—
32	C₂×C₉₇	C₂×C₃₂	1	1	yes	characteristic
33	D₉₇	—	2	1	no	—
34	D₉₇	C₂²⋊C₁₆	1	1	yes	characteristic
35	D₉₇	M₆₄	1	1	yes	characteristic
36	C₂²⋊C₃₂	—	97	1	no	maximal, Sylow
37	C₉₇	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₁₆	—	97	1	no	—
39	C₂×C₃₂	—	97	2	no	—
40	C₂²×C₈	—	97	1	no	—
41	C₂×C₁₆	—	97	1	no	—
42	C₂×C₁₆	—	97	1	no	—
43	C₂×C₁₆	—	194	2	no	—
44	C₃₂	—	194	2	no	—
45	C₂²×C₄	—	97	1	no	—
46	C₂×C₈	—	97	1	no	—
47	C₂×C₈	—	97	1	no	—
48	C₂×C₈	—	194	1	no	—
49	C₂×C₈	—	194	1	no	—
50	C₁₆	—	97	2	no	—
51	C₁₆	—	194	1	no	—
52	C₂³	—	97	1	no	—
53	C₂×C₄	—	97	1	no	—
54	C₂×C₄	—	97	1	no	—
55	C₂×C₄	—	194	1	no	—
56	C₂×C₄	—	194	1	no	—
57	C₈	—	97	1	no	—
58	C₈	—	97	1	no	—
59	C₈	—	194	1	no	—
60	C₂²	—	97	1	no	—
61	C₂²	—	97	1	no	—
62	C₂²	—	194	1	no	—
63	C₂²	—	194	1	no	—
64	C₂²	#15690911	1	1	yes	characteristic, complemented
65	C₄	—	97	1	no	—
66	C₄	—	97	1	no	—
67	C₄	—	194	1	no	—
68	C₂	—	2	1	no	—
69	C₂	—	97	1	no	—
70	C₂	—	97	1	no	—
71	C₂	—	194	1	no	—
72	C₂	C₂×#15690911	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#15690911	C₂	semidirect
23. C₂²×C₉₇	C₃₂	semidirect
26. C₂×D₉₇	C₃₂	semidirect
37. C₉₇	C₂²⋊C₃₂	semidirect
64. C₂²	#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
C₂²×#13095525	2
C₂²⋊C₃₂	97

Subgroups — C22⋊#15690911 #27159037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#15690911 #27159037