Subgroups — D₃₅₃⋊#108 #36378800

Order 22592.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₅₃⋊M₁₆	C₂	1	2	yes	maximal
2	#26015063	C₂	1	2	yes	maximal, complemented
3	#26015062	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₃₅₃	C₂	1	1	yes	maximal, characteristic
5	#19150747	C₂²	1	4	yes	—
6	#19150746	—	2	2	no	—
7	#19150745	—	2	2	no	—
8	C₂×C₄×D₃₅₃	C₂²	1	1	yes	characteristic
9	C₂×#15667725	C₄	1	1	yes	characteristic
10	C₈×D₃₅₃	C₄	1	1	yes	characteristic
11	C₈×D₃₅₃	C₄	1	1	yes	characteristic
12	C₈×D₃₅₃	C₂²	1	1	yes	characteristic
13	C₈×D₃₅₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₃₅₃	C₄	1	1	yes	characteristic
15	#15667732	—	2	4	no	—
16	C₂²×D₃₅₃	Q₈	1	1	yes	characteristic
17	C₂×Dic₃₅₃	D₄	1	1	yes	characteristic
18	C₄×D₃₅₃	C₂×C₄	1	1	yes	characteristic
19	C₄×D₃₅₃	D₄	1	1	yes	characteristic
20	C₄×D₃₅₃	Q₈	1	1	yes	characteristic
21	C₄×D₃₅₃	C₂³	1	1	yes	characteristic
22	#15667725	C₂×C₄	1	1	yes	characteristic
23	#15667725	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₃₅₃	C₂×C₄	1	1	yes	characteristic
25	C₈×C₃₅₃	C₂×C₄	1	1	yes	characteristic
26	C₈×C₃₅₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃₅₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₃₅₃	—	2	2	no	—
29	C₂×D₃₅₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₃₅₃	C₂×Q₈	1	1	yes	characteristic
31	C₄×C₃₅₃	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₃₅₃	C₂²×C₄	1	1	yes	characteristic
33	Dic₃₅₃	C₄⋊C₄	1	1	yes	characteristic
34	Dic₃₅₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₃₅₃	—	2	1	no	—
36	C₂×C₃₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	D₃₅₃	—	2	1	no	—
38	D₃₅₃	#108	1	2	yes	complemented
39	C₃₅₃	C₂×#108	1	1	yes	characteristic, complemented, Sylow
40	C₂×#108	—	353	1	no	maximal, Sylow
41	C₂×M₁₆	—	353	2	no	—
42	C₂²×C₈	—	353	1	no	—
43	#108	—	353	2	no	—
44	#108	—	353	2	no	—
45	C₂²×C₄	—	353	1	no	—
46	M₁₆	—	353	4	no	—
47	M₁₆	—	706	2	no	—
48	C₂×C₈	—	353	1	no	—
49	C₂×C₈	—	353	1	no	—
50	C₂×C₈	—	353	1	no	—
51	C₂×C₈	—	353	1	no	—
52	C₂×C₈	—	353	1	no	—
53	C₂×C₈	—	706	2	no	—
54	C₂×C₈	#13083443	1	1	yes	characteristic
55	C₂³	—	353	1	no	—
56	C₂×C₄	—	353	1	no	—
57	C₂×C₄	—	353	1	no	—
58	C₂×C₄	—	353	1	no	—
59	C₂×C₄	—	353	1	no	—
60	C₂×C₄	—	353	1	no	—
61	C₂×C₄	C₂×#13083443	1	1	yes	characteristic
62	C₈	—	353	1	no	—
63	C₈	—	353	1	no	—
64	C₈	—	706	4	no	—
65	C₈	C₂×#13083443	1	1	yes	characteristic
66	C₈	C₂×#13083443	1	1	yes	characteristic
67	C₂²	—	353	1	no	—
68	C₂²	—	353	1	no	—
69	C₂²	—	706	2	no	—
70	C₂²	C₄⋊#13083443	1	1	yes	characteristic
71	C₄	—	353	1	no	—
72	C₄	—	353	1	no	—
73	C₄	C₄⋊#13083443	1	1	yes	characteristic
74	C₄	C₂²×#13083443	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	353	2	no	—
77	C₂	—	706	1	no	—
78	C₂	C₂×C₄⋊#13083443	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#13083443
commutator	C₄×C₃₅₃	C₂²×C₄
Frattini	C₄	C₂²×#13083443
Fitting	C₂×C₈×C₃₅₃	C₄
socle	C₂×C₃₅₃	C₂×C₄⋊C₄
prime radical	C₂²×D₃₅₃	Q₈
cosocle	C₄×D₃₅₃	C₂³
hypercenter	C₂×C₈	#13083443
hypocenter	C₃₅₃	C₂×#108
LCS	G ▷ C₄×C₃₅₃ ▷ C₂×C₃₅₃ ▷ C₃₅₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #26015063	C₂	semidirect
3. #26015062	C₂	semidirect
38. D₃₅₃	#108	semidirect
39. C₃₅₃	C₂×#108	semidirect

Maximal subgroups

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

subgroup	index
D₃₅₃⋊M₁₆	2
#26015063	2
#26015062	2
C₂×C₈×D₃₅₃	2
C₂×#108	353

Subgroups — D353⋊#108 #36378800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₅₃⋊#108 #36378800