Subgroups — #28363177

Order 13952.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20294781	C₂	1	6	yes	maximal
2	#376×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#11724784	C₂²	1	4	yes	—
4	C₂×C₄²×C₁₀₉	C₂²	1	3	yes	—
5	#95×C₁₀₉	C₄	1	4	yes	—
6	C₂×#11724784	—	2	12	no	—
7	C₂²×C₄×C₁₀₉	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
9	C₄²×C₁₀₉	—	2	6	no	—
10	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₀₉	—	2	6	no	—
12	C₂×C₄×C₁₀₉	—	2	12	no	—
13	C₂×C₄×C₁₀₉	#41	1	6	yes	—
14	#11724784	—	4	4	no	—
15	C₂²×C₁₀₉	#117	1	3	yes	—
16	C₂²×C₁₀₉	#131	1	4	yes	—
17	C₄×C₁₀₉	—	4	6	no	—
18	C₄×C₁₀₉	#126	1	4	yes	—
19	C₂×C₁₀₉	#383	1	1	yes	characteristic
20	C₂×C₁₀₉	#433	1	6	yes	—
21	#1840	—	109	1	no	maximal, Sylow
22	C₁₀₉	#1840	1	1	yes	characteristic, complemented, Sylow
23	#376	D₁₀₉	1	1	yes	characteristic
24	#336	—	109	6	no	—
25	C₂²×C₈	—	109	4	no	—
26	C₂×C₄²	C₂×D₁₀₉	1	3	yes	—
27	#95	Dic₁₀₉	1	4	yes	—
28	C₂²×C₄	C₂×Dic₁₀₉	1	6	yes	—
29	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
30	C₂×C₈	—	218	12	no	—
31	C₄²	—	2	6	no	—
32	C₂³	C₂²×Dic₁₀₉	1	1	yes	characteristic
33	C₂×C₄	—	2	6	no	—
34	C₂×C₄	—	2	12	no	—
35	C₂×C₄	#13182029	1	6	yes	—
36	C₈	—	436	4	no	—
37	C₂²	#16812658	1	3	yes	—
38	C₂²	#16812706	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	#16812693	1	4	yes	—
41	C₂	#20294894	1	1	yes	characteristic
42	C₂	#20295087	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₀₉
commutator, socle, prime radical	C₂³×C₁₀₉	C₂²×C₄
Fitting	#376×C₁₀₉	C₂
cosocle	C₂²×C₄×C₁₀₉	C₂³
hypercenter	#376	D₁₀₉
hypocenter	C₁₀₉	#1840
LCS	G ▷ C₂³×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

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

N	H ≅ G/N	type
22. C₁₀₉	#1840	semidirect

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