Subgroups — #26038804

Order 11456.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19153110	C₂	1	1	yes	maximal, characteristic
2	#19153105	C₂	1	1	yes	maximal, characteristic, complemented
3	#19153035	C₂	1	4	yes	maximal, complemented
4	#97×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₇₁₆	—	2	2	no	—
6	C₂×D₇₁₆	C₂²	1	2	yes	—
7	C₄⋊Dic₁₇₉	C₂²	1	2	yes	—
8	Dic₁₇₉⋊C₄	—	2	2	no	—
9	C₂×C₈×C₁₇₉	C₂²	1	2	yes	—
10	C₄²×C₁₇₉	C₂²	1	1	yes	characteristic
11	C₂²×D₁₇₉	—	2	2	no	—
12	D₇₁₆	—	2	4	no	—
13	D₇₁₆	—	4	4	no	—
14	C₂×Dic₁₇₉	—	2	2	no	—
15	C₂×C₄×C₁₇₉	D₄	1	2	yes	—
16	C₂×C₄×C₁₇₉	C₂³	1	1	yes	characteristic
17	C₈×C₁₇₉	—	2	2	no	—
18	C₂²×C₁₇₉	C₂×D₄	1	1	yes	characteristic
19	C₂×D₁₇₉	—	4	2	no	—
20	C₂×D₁₇₉	—	4	4	no	—
21	C₄×C₁₇₉	—	2	2	no	—
22	C₄×C₁₇₉	#41	1	2	yes	—
23	Dic₁₇₉	—	4	2	no	—
24	C₂×C₁₇₉	#124	1	1	yes	characteristic
25	C₂×C₁₇₉	AGL(1,ℤ/8)	1	2	yes	—
26	D₁₇₉	—	8	2	no	—
27	C₁₇₉	#490	1	1	yes	characteristic, complemented, Sylow
28	#490	—	179	1	no	maximal, Sylow
29	#127	—	179	1	no	—
30	#125	—	179	1	no	—
31	#102	—	179	4	no	—
32	#97	D₁₇₉	1	1	yes	characteristic, complemented
33	C₂×D₄	—	358	2	no	—
34	C₂×D₄	—	179	2	no	—
35	C₂×C₈	C₂×D₁₇₉	1	2	yes	—
36	C₄⋊C₄	—	358	2	no	—
37	C₄⋊C₄	—	179	2	no	—
38	C₄²	C₂×D₁₇₉	1	1	yes	characteristic
39	C₂³	—	358	2	no	—
40	D₄	—	358	4	no	—
41	D₄	—	716	4	no	—
42	C₂×C₄	—	358	2	no	—
43	C₂×C₄	D₇₁₆	1	2	yes	—
44	C₂×C₄	C₂²×D₁₇₉	1	1	yes	characteristic
45	C₈	—	2	2	no	—
46	C₂²	—	716	2	no	—
47	C₂²	—	716	4	no	—
48	C₂²	C₂×D₇₁₆	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	716	2	no	—
51	C₄	#15668259	1	2	yes	—
52	C₂	—	1432	2	no	—
53	C₂	#19153101	1	1	yes	characteristic
54	C₂	#19153141	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₇₁₆
commutator, cosocle	C₂×C₄×C₁₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₇₉
Fitting	#97×C₁₇₉	C₂
socle	C₂²×C₁₇₉	C₂×D₄
prime radical	#19153110	C₂
hypercenter	#97	D₁₇₉
hypocenter	C₁₇₉	#490
LCS	G ▷ C₂×C₄×C₁₇₉ ▷ C₂×C₁₇₉ ▷ C₁₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. #19153105	C₂	semidirect
3. #19153035	C₂	semidirect
4. #97×C₁₇₉	C₂	semidirect
27. C₁₇₉	#490	semidirect
32. #97	D₁₇₉	semidirect

Maximal subgroups

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

subgroup	index
#19153110	2
#19153105	2
#19153035	2
#97×C₁₇₉	2
#490	179