Subgroups — #11763833

Order 1088.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587563	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#3624	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#3624	C₂	1	1	yes	maximal, characteristic
4	#10587544	C₂	1	1	yes	maximal, characteristic, complemented
5	#10587542	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄⋊#3624	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#3624	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
9	C₂×#3624	C₂²	1	1	yes	characteristic
10	C₂×#3624	C₂²	1	1	yes	characteristic
11	C₂×#3624	C₂²	1	1	yes	characteristic
12	C₂×#3624	C₂²	1	1	yes	characteristic
13	C₂²⋊C₄×C₁₇	C₄	1	1	yes	characteristic
14	C₂²⋊Dic₁₇	C₄	1	1	yes	characteristic
15	#63225	C₄	1	1	yes	characteristic
16	#63225	C₄	1	1	yes	characteristic
17	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
18	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
19	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₁₇	—	2	1	no	—
23	C₂×Dic₁₇	—	2	1	no	—
24	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
26	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
27	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
28	#3624	—	2	1	no	—
29	#3624	—	2	1	no	—
30	#3624	—	2	1	no	—
31	#3624	—	2	1	no	—
32	C₂²×C₁₇	—	2	1	no	—
33	C₂²×C₁₇	—	2	1	no	—
34	C₂²×C₁₇	—	2	1	no	—
35	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₁₇	—	2	1	no	—
37	C₄×C₁₇	—	2	1	no	—
38	Dic₁₇	—	2	1	no	—
39	Dic₁₇	—	2	1	no	—
40	Dic₁₇	—	2	1	no	—
41	Dic₁₇	#41	1	1	yes	characteristic
42	Dic₁₇	#41	1	1	yes	characteristic
43	#433	—	17	1	no	maximal, Sylow
44	C₂×C₁₇	—	4	1	no	—
45	C₂×C₁₇	#117	1	1	yes	characteristic
46	C₂×C₁₇	#131	1	1	yes	characteristic
47	C₂×C₁₇	#131	1	1	yes	characteristic
48	#117	—	17	1	no	—
49	C₄⋊C₈	—	17	1	no	—
50	C₄⋊C₈	—	17	1	no	—
51	C₂²⋊C₈	—	17	1	no	—
52	C₂²⋊C₈	—	17	1	no	—
53	#97	—	17	1	no	—
54	C₄×C₈	—	17	1	no	—
55	C₁₇	#433	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	—	17	1	no	—
57	C₂×C₈	—	17	1	no	—
58	C₂×C₈	—	17	1	no	—
59	C₂×C₈	—	17	1	no	—
60	C₂×C₈	—	17	1	no	—
61	C₄⋊C₄	—	17	1	no	—
62	C₄⋊C₄	—	17	1	no	—
63	C₂²⋊C₄	—	17	1	no	—
64	C₂²⋊C₄	#595	1	1	yes	characteristic
65	C₄²	—	17	1	no	—
66	C₄²	—	17	1	no	—
67	C₂³	C₂×#595	1	1	yes	characteristic
68	C₂×C₄	—	17	1	no	—
69	C₂×C₄	—	17	1	no	—
70	C₂×C₄	—	17	1	no	—
71	C₂×C₄	—	17	1	no	—
72	C₂×C₄	—	34	1	no	—
73	C₂×C₄	—	34	1	no	—
74	C₂×C₄	C₂×#595	1	1	yes	characteristic
75	C₂×C₄	C₂×#595	1	1	yes	characteristic
76	C₈	—	34	1	no	—
77	C₈	—	34	1	no	—
78	C₈	—	34	1	no	—
79	C₈	—	34	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	C₂²×#595	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	2	1	no	—
86	C₄	—	17	1	no	—
87	C₄	—	17	1	no	—
88	C₄	—	34	1	no	—
89	C₄	—	34	1	no	—
90	C₄	—	34	1	no	—
91	C₂	—	4	1	no	—
92	C₂	#10587677	1	1	yes	characteristic
93	C₂	#10587678	1	1	yes	characteristic
94	C₂	#10587678	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄
Fitting	C₂²⋊C₄×C₁₇	C₄
prime radical	C₂³×C₁₇	C₂×C₄
cosocle	C₂×Dic₁₇	C₂³
hypercenter	C₂²⋊C₄	#595
hypocenter	C₁₇	#433
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
4. #10587544	C₂	semidirect
5. #10587542	C₂	semidirect
6. C₄⋊#3624	C₂	semidirect
7. C₄×#3624	C₂	semidirect
55. C₁₇	#433	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10587563	2
C₂²⋊#3624	2
#10587544	2
#10587542	2
C₄⋊#3624	2
C₄×#3624	2
#433	17