Subgroups — #28412505

Order 14656.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301055	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊#14270087	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#14270087	C₂	1	1	yes	maximal, characteristic
4	C₂²⋊#14270087	C₂	1	1	yes	maximal, characteristic
5	#20301043	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#14270087	C₂	1	1	yes	maximal, characteristic, complemented
7	#20300944	C₂	1	1	yes	maximal, characteristic
8	C₂×#14270087	C₂²	1	1	yes	characteristic
9	C₂×#14270087	C₂²	1	1	yes	characteristic
10	C₂×#14270087	C₂²	1	1	yes	characteristic
11	C₂×#14270087	C₂²	1	1	yes	characteristic
12	C₂²×Dic₂₂₉	C₂²	1	1	yes	characteristic
13	#16814645	C₄	1	1	yes	characteristic
14	#16814645	C₄	1	1	yes	characteristic
15	C₂²⋊Dic₂₂₉	C₄	1	1	yes	characteristic
16	C₄×Dic₂₂₉	C₂²	1	1	yes	characteristic
17	C₄×Dic₂₂₉	C₂²	1	1	yes	characteristic
18	C₂²⋊C₄×C₂₂₉	C₄	1	1	yes	characteristic
19	#14270087	—	2	1	no	—
20	#14270087	—	2	1	no	—
21	#14270087	—	2	1	no	—
22	#14270087	—	2	1	no	—
23	C₂×Dic₂₂₉	—	2	1	no	—
24	C₂×Dic₂₂₉	—	2	1	no	—
25	C₂×Dic₂₂₉	C₂×C₄	1	1	yes	characteristic
26	C₂×Dic₂₂₉	C₂×C₄	1	1	yes	characteristic
27	C₂×Dic₂₂₉	C₂×C₄	1	1	yes	characteristic
28	C₂×Dic₂₂₉	C₂³	1	1	yes	characteristic
29	C₂³×C₂₂₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₂₂₉	—	2	1	no	—
33	C₂²×C₂₂₉	—	2	1	no	—
34	C₂²×C₂₂₉	—	2	1	no	—
35	C₂²×C₂₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₂₂₉	—	2	1	no	—
37	C₄×C₂₂₉	—	2	1	no	—
38	Dic₂₂₉	—	2	1	no	—
39	Dic₂₂₉	—	2	1	no	—
40	Dic₂₂₉	—	2	1	no	—
41	Dic₂₂₉	#41	1	1	yes	characteristic
42	Dic₂₂₉	#41	1	1	yes	characteristic
43	C₂×C₂₂₉	—	4	1	no	—
44	C₂×C₂₂₉	#117	1	1	yes	characteristic
45	C₂×C₂₂₉	#131	1	1	yes	characteristic
46	C₂×C₂₂₉	#131	1	1	yes	characteristic
47	C₂₂₉	#433	1	1	yes	characteristic, complemented, Sylow
48	#433	—	229	1	no	maximal, Sylow
49	#117	—	229	1	no	—
50	C₄⋊C₈	—	229	1	no	—
51	C₄⋊C₈	—	229	1	no	—
52	C₂²⋊C₈	—	229	1	no	—
53	C₂²⋊C₈	—	229	1	no	—
54	#97	—	229	1	no	—
55	C₄×C₈	—	229	1	no	—
56	C₂²×C₄	—	229	1	no	—
57	C₂×C₈	—	229	1	no	—
58	C₂×C₈	—	229	1	no	—
59	C₂×C₈	—	229	1	no	—
60	C₂×C₈	—	229	1	no	—
61	C₄⋊C₄	—	229	1	no	—
62	C₄⋊C₄	—	229	1	no	—
63	C₂²⋊C₄	—	229	1	no	—
64	C₂²⋊C₄	#11745021	1	1	yes	characteristic
65	C₄²	—	229	1	no	—
66	C₄²	—	229	1	no	—
67	C₂³	C₂×#11745021	1	1	yes	characteristic
68	C₂×C₄	—	458	1	no	—
69	C₂×C₄	—	458	1	no	—
70	C₂×C₄	—	229	1	no	—
71	C₂×C₄	—	229	1	no	—
72	C₂×C₄	—	229	1	no	—
73	C₂×C₄	—	229	1	no	—
74	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
75	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
76	C₈	—	458	1	no	—
77	C₈	—	458	1	no	—
78	C₈	—	458	1	no	—
79	C₈	—	458	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	C₂²×#11745021	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	2	1	no	—
86	C₄	—	458	1	no	—
87	C₄	—	458	1	no	—
88	C₄	—	458	1	no	—
89	C₄	—	229	1	no	—
90	C₄	—	229	1	no	—
91	C₂	—	4	1	no	—
92	C₂	#20301067	1	1	yes	characteristic
93	C₂	#20301075	1	1	yes	characteristic
94	C₂	#20301075	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#11745021
commutator, socle	C₂²×C₂₂₉	C₂²×C₄
Fitting	C₂²⋊C₄×C₂₂₉	C₄
prime radical	C₂³×C₂₂₉	C₂×C₄
cosocle	C₂×Dic₂₂₉	C₂³
hypercenter	C₂²⋊C₄	#11745021
hypocenter	C₂₂₉	#433
LCS	G ▷ C₂²×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. #20301055	C₂	semidirect
2. C₄⋊#14270087	C₂	semidirect
5. #20301043	C₂	semidirect
6. C₄×#14270087	C₂	semidirect
47. C₂₂₉	#433	semidirect

Maximal subgroups

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

subgroup	index
#20301055	2
C₄⋊#14270087	2
C₂²⋊#14270087	2
#20301043	2
C₄×#14270087	2
#20300944	2
#433	229