Subgroups — C₂×#26015053 #36378771

Order 22592.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19150746	C₂	1	2	yes	maximal
2	#26015053	C₂	1	4	yes	maximal, direct product factor
3	C₂²×Dic₇₀₆	C₂	1	1	yes	maximal, characteristic
4	#19150746	—	2	2	no	—
5	#19150746	C₂²	1	4	yes	—
6	C₂×#15667732	—	2	2	no	—
7	C₂×Dic₇₀₆	—	2	2	no	—
8	C₂×Dic₇₀₆	—	2	2	no	—
9	C₂×Dic₇₀₆	C₄	1	2	yes	—
10	C₂×Dic₇₀₆	C₂²	1	2	yes	—
11	C₂²×Dic₃₅₃	C₄	1	1	yes	characteristic
12	C₂²×Dic₃₅₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₃₅₃	C₄	1	1	yes	characteristic
14	#15667732	—	2	4	no	—
15	Dic₇₀₆	—	2	4	no	—
16	Dic₇₀₆	—	2	4	no	—
17	C₂×Dic₃₅₃	—	2	1	no	—
18	C₂×Dic₃₅₃	—	2	1	no	—
19	C₂×Dic₃₅₃	C₂×C₄	1	2	yes	—
20	C₂×Dic₃₅₃	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₃₅₃	D₄	1	2	yes	—
22	C₂×Dic₃₅₃	D₄	1	2	yes	—
23	C₂×Dic₃₅₃	C₂³	1	1	yes	characteristic
24	C₂³×C₃₅₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₅₃	—	2	1	no	—
26	C₂×C₄×C₃₅₃	—	2	1	no	—
27	C₂×C₄×C₃₅₃	C₂×C₄	1	2	yes	—
28	C₂²×C₃₅₃	—	2	2	no	—
29	C₂²×C₃₅₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₃₅₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₃₅₃	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₃₅₃	—	2	2	no	—
33	Dic₃₅₃	—	2	2	no	—
34	Dic₃₅₃	C₂²⋊C₄	1	2	yes	—
35	Dic₃₅₃	C₂×D₄	1	2	yes	—
36	C₂×C₃₅₃	—	2	1	no	—
37	C₂×C₃₅₃	—	2	1	no	—
38	C₂×C₃₅₃	#101	1	2	yes	complemented
39	C₂×C₃₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₃₅₃	C₂×#101	1	1	yes	characteristic, complemented, Sylow
41	C₂×#101	—	353	1	no	maximal, Sylow
42	C₂²×Q₈	—	353	1	no	—
43	C₂×M₁₆	—	353	2	no	—
44	#101	—	353	4	no	—
45	C₂×Q₈	—	353	2	no	—
46	C₂×Q₈	—	353	2	no	—
47	C₂×Q₈	—	706	2	no	—
48	C₂×Q₈	—	706	2	no	—
49	C₂²×C₄	—	353	1	no	—
50	C₂²×C₄	—	353	1	no	—
51	C₂²×C₄	#13083443	1	1	yes	characteristic
52	M₁₆	—	353	4	no	—
53	M₁₆	—	706	2	no	—
54	C₂×C₈	—	706	2	no	—
55	C₂³	C₂×#13083443	1	1	yes	characteristic
56	Q₈	—	706	4	no	—
57	Q₈	—	706	4	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	353	2	no	—
61	C₂×C₄	—	353	2	no	—
62	C₂×C₄	—	353	1	no	—
63	C₂×C₄	—	353	1	no	—
64	C₂×C₄	—	353	2	no	—
65	C₂×C₄	—	706	1	no	—
66	C₂×C₄	—	706	1	no	—
67	C₂×C₄	C₂×#13083443	1	2	yes	—
68	C₈	—	706	4	no	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂²⋊#13083443	1	1	yes	characteristic
71	C₂²	C₂²⋊#13083443	1	1	yes	characteristic
72	C₂²	C₂²×#13083443	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	353	2	no	—
75	C₄	—	353	2	no	—
76	C₄	—	706	2	no	—
77	C₂	—	2	1	no	—
78	C₂	—	2	1	no	—
79	C₂	#26015053	1	2	yes	direct product factor
80	C₂	C₂×C₂²⋊#13083443	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#13083443
commutator	C₂²×C₃₅₃	C₂²×C₄
Frattini	C₂²	C₂²×#13083443
Fitting	C₂²×C₄×C₃₅₃	C₄
socle	C₂²×C₃₅₃	C₂²⋊C₄
prime radical	C₂³×C₃₅₃	C₂×C₄
cosocle	C₂×Dic₃₅₃	C₂³
hypercenter	C₂²×C₄	#13083443
hypocenter	C₃₅₃	C₂×#101
LCS	G ▷ C₂²×C₃₅₃ ▷ C₂×C₃₅₃ ▷ C₃₅₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #26015053	C₂	direct (N × H)
38. C₂×C₃₅₃	#101	semidirect
40. C₃₅₃	C₂×#101	semidirect
79. C₂	#26015053	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19150746	2
#26015053	2
C₂²×Dic₇₀₆	2
C₂×#101	353

Subgroups — C2×#26015053 #36378771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26015053 #36378771