Subgroups — #28377951

Order 13952.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295915	C₂	1	1	yes	maximal, characteristic
2	#20295867	C₂	1	1	yes	maximal, characteristic
3	#20294801	C₂	1	1	yes	maximal, characteristic
4	C₂×#13182032	C₄	1	2	yes	—
5	C₄×#11724786	C₄	1	1	yes	characteristic
6	C₄×#11724786	C₄	1	1	yes	characteristic
7	C₂×#13182004	C₄	1	1	yes	characteristic
8	C₈×Dic₁₀₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₀₉	C₄	1	1	yes	characteristic
10	C₂×#11724786	—	2	1	no	—
11	C₂×#11724786	—	2	1	no	—
12	#13182032	C₈	1	4	yes	complemented
13	C₂×#11724784	C₂×C₄	1	1	yes	characteristic
14	C₄×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
15	#13182004	—	2	1	no	—
16	C₂×C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₁₀₉	—	2	1	no	—
18	C₂×C₄×C₁₀₉	C₄²	1	1	yes	characteristic
19	C₂×Dic₁₀₉	M₁₆	1	1	yes	characteristic
20	C₂×Dic₁₀₉	M₁₆	1	1	yes	characteristic
21	#11724786	—	4	1	no	—
22	#11724786	—	4	1	no	—
23	C₈×C₁₀₉	M₁₆	1	1	yes	characteristic
24	C₈×C₁₀₉	M₁₆	1	1	yes	characteristic
25	#11724784	C₂×C₈	1	2	yes	—
26	C₂²×C₁₀₉	#97	1	1	yes	characteristic
27	C₄×C₁₀₉	C₄×C₈	1	1	yes	characteristic
28	C₄×C₁₀₉	#97	1	1	yes	characteristic
29	Dic₁₀₉	—	2	1	no	—
30	Dic₁₀₉	—	2	1	no	—
31	C₂×C₁₀₉	#322	1	1	yes	characteristic
32	C₂×C₁₀₉	#347	1	1	yes	characteristic
33	C₂×C₁₀₉	#347	1	1	yes	characteristic
34	#1313	—	109	1	no	maximal, Sylow
35	C₁₀₉	#1313	1	1	yes	characteristic, complemented, Sylow
36	#346	—	109	1	no	—
37	#346	—	109	1	no	—
38	#322	—	109	1	no	—
39	C₂×C₁₆	—	109	2	no	—
40	C₂×C₁₆	—	109	1	no	—
41	C₂×C₁₆	#89137	1	1	yes	characteristic
42	C₄×C₈	—	109	1	no	—
43	C₄×C₈	—	109	1	no	—
44	C₄×C₈	—	109	1	no	—
45	C₂×C₈	—	109	1	no	—
46	C₂×C₈	—	218	1	no	—
47	C₂×C₈	—	218	1	no	—
48	C₂×C₈	C₂×#89137	1	1	yes	characteristic
49	C₄²	—	109	1	no	—
50	C₁₆	—	2	1	no	—
51	C₁₆	—	109	4	no	—
52	C₁₆	—	218	1	no	—
53	C₂×C₄	—	109	1	no	—
54	C₂×C₄	—	109	1	no	—
55	C₂×C₄	C₄×#89137	1	1	yes	characteristic
56	C₈	—	109	2	no	—
57	C₈	—	436	1	no	—
58	C₈	—	436	1	no	—
59	C₈	#13182038	1	1	yes	characteristic
60	C₈	#13182039	1	1	yes	characteristic
61	C₂²	#16812753	1	1	yes	characteristic
62	C₄	—	218	1	no	—
63	C₄	—	218	1	no	—
64	C₄	C₈×#89137	1	1	yes	characteristic
65	C₄	#16812754	1	1	yes	characteristic
66	C₂	#11724786⋊C₈	1	1	yes	characteristic
67	C₂	#20295916	1	1	yes	characteristic
68	C₂	#20295917	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#89137
commutator	C₄×C₁₀₉	C₄×C₈
Frattini	C₂×C₈	C₂×#89137
Fitting	C₂×C₁₆×C₁₀₉	C₄
socle, prime radical	C₂²×C₁₀₉	#97
cosocle	C₈×Dic₁₀₉	C₂²
hypercenter	C₂×C₁₆	#89137
hypocenter	C₁₀₉	#1313
LCS	G ▷ C₄×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
12. #13182032	C₈	semidirect
35. C₁₀₉	#1313	semidirect

Maximal subgroups

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

subgroup	index
#20295915	2
#20295867	2
#20294801	2
#1313	109