Group #34175366 — subgroups

Subgroups — #34175366

Order 20224.

148 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23765216	C₂	1	2	yes	maximal
2	C₇₉×#2151	C₂	1	1	yes	maximal, characteristic
3	#19098384	—	2	2	no	—
4	#19098345	—	2	2	no	—
5	#19098341	C₄	1	4	yes	—
6	C₂×M₃₂×C₇₉	C₄	1	1	yes	characteristic
7	C₂²×C₁₆×C₇₉	C₄	1	1	yes	characteristic
8	#405×C₇₉	C₂²	1	1	yes	characteristic
9	C₄⋊C₁₆×C₇₉	—	2	2	no	—
10	#14579101	—	2	4	no	—
11	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
12	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
13	#117×C₇₉	Q₈	1	1	yes	characteristic
14	M₃₂×C₇₉	—	4	1	no	—
15	C₂×C₁₆×C₇₉	—	2	1	no	—
16	C₂×C₁₆×C₇₉	—	2	1	no	—
17	C₂×C₁₆×C₇₉	—	4	1	no	—
18	#97×C₇₉	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₇₉	D₄	1	2	yes	—
20	C₇₉⋊C₁₆	—	4	4	no	—
21	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
22	M₁₆×C₇₉	—	4	1	no	—
23	C₂×C₈×C₇₉	—	2	1	no	—
24	C₂×C₈×C₇₉	—	2	1	no	—
25	C₂×C₈×C₇₉	C₄²	1	1	yes	characteristic
26	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
27	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₄⋊C₄×C₇₉	—	2	1	no	—
29	C₂²⋊C₄×C₇₉	—	2	1	no	—
30	C₄²×C₇₉	C₄⋊C₄	1	2	yes	—
31	C₁₆×C₇₉	—	4	1	no	—
32	C₁₆×C₇₉	—	4	1	no	—
33	C₂³×C₇₉	#108	1	1	yes	characteristic
34	C₂×C₄×C₇₉	—	2	1	no	—
35	C₂×C₄×C₇₉	—	2	1	no	—
36	C₂×C₄×C₇₉	—	2	2	no	—
37	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
38	C₂×C₄×C₇₉	#108	1	1	yes	characteristic
39	C₈×C₇₉	—	2	2	no	—
40	C₈×C₇₉	—	2	1	no	—
41	C₈×C₇₉	#100	1	1	yes	characteristic
42	C₈×C₇₉	#101	1	1	yes	characteristic
43	C₂²×C₇₉	—	2	1	no	—
44	C₂²×C₇₉	—	4	1	no	—
45	C₂²×C₇₉	#341	1	1	yes	characteristic
46	C₄×C₇₉	—	2	1	no	—
47	C₄×C₇₉	—	4	2	no	—
48	C₄×C₇₉	H(3,ℤ/4)	1	1	yes	characteristic
49	C₄×C₇₉	#343	1	1	yes	characteristic
50	#7240	—	79	1	no	maximal, Sylow
51	C₂×C₇₉	—	2	1	no	—
52	C₂×C₇₉	—	4	1	no	—
53	C₂×C₇₉	#1290	1	1	yes	characteristic
54	#2166	—	79	2	no	—
55	#2151	D₇₉	1	1	yes	characteristic
56	C₇₉	#7240	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₃₂	Dic₇₉	1	1	yes	characteristic
58	C₂²×C₁₆	Dic₇₉	1	1	yes	characteristic
59	#405	C₂×D₇₉	1	1	yes	characteristic
60	#364	—	158	2	no	—
61	C₄⋊C₁₆	—	2	2	no	—
62	#349	—	158	2	no	—
63	#347	—	79	4	no	—
64	C₂×M₁₆	D₃₁₆	1	1	yes	characteristic
65	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
66	#117	Dic₁₅₈	1	1	yes	characteristic
67	M₃₂	—	4	1	no	—
68	M₃₂	—	158	4	no	—
69	C₂×C₁₆	—	2	1	no	—
70	C₂×C₁₆	—	2	1	no	—
71	C₂×C₁₆	—	4	1	no	—
72	#97	C₄×D₇₉	1	2	yes	—
73	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
74	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
75	M₁₆	—	4	1	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	C₄×Dic₇₉	1	1	yes	characteristic
79	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
80	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
81	C₄⋊C₄	—	2	1	no	—
82	C₂²⋊C₄	—	2	1	no	—
83	C₄²	Dic₇₉⋊C₄	1	2	yes	—
84	C₁₆	—	4	1	no	—
85	C₁₆	—	4	1	no	—
86	C₁₆	—	316	4	no	—
87	C₂³	#14579097	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
92	C₂×C₄	#14579097	1	1	yes	characteristic
93	C₈	—	2	2	no	—
94	C₈	—	2	1	no	—
95	C₈	#14579078	1	1	yes	characteristic
96	C₈	#14579080	1	1	yes	characteristic
97	C₂²	—	2	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	#19098328	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	#19098320	1	1	yes	characteristic
103	C₄	#19098332	1	1	yes	characteristic
104	C₂	—	2	1	no	—
105	C₂	—	4	1	no	—
106	C₂	#23761270	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23765216

C₂

yes

maximal

C₇₉×#2151

C₂

yes

maximal, characteristic

#19098384

—

#19098345

—

#19098341

C₄

yes

—

C₂×M₃₂×C₇₉

C₄

yes

characteristic

C₂²×C₁₆×C₇₉

C₄

yes

characteristic

#405×C₇₉

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₉

—

#14579101

—

C₂×M₁₆×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

#117×C₇₉

Q₈

yes

characteristic

M₃₂×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

—

#97×C₇₉

C₂×C₄

yes

—

C₄×C₈×C₇₉

D₄

yes

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

C₄⋊C₄

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₄²

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₄⋊C₄

yes

—

C₁₆×C₇₉

—

C₁₆×C₇₉

—

C₂³×C₇₉

#108

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

yes

C₈×C₇₉

yes

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#341

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

D₇₉

yes

characteristic

C₇₉

#7240

yes

characteristic, complemented, Sylow

C₂×M₃₂

Dic₇₉

yes

characteristic

C₂²×C₁₆

Dic₇₉

yes

characteristic

#405

C₂×D₇₉

yes

characteristic

#364

—

158

—

C₄⋊C₁₆

—

#349

—

158

—

#347

—

C₂×M₁₆

D₃₁₆

yes

characteristic

C₂²×C₈

C₂×Dic₇₉

yes

characteristic

#117

Dic₁₅₈

yes

characteristic

M₃₂

—

M₃₂

—

158

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

C₄×D₇₉

yes

—

C₄×C₈

C₂²⋊D₇₉

yes

—

C₂²×C₄

C₄⋊Dic₇₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×Dic₇₉

yes

characteristic

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

C₂×C₈

C₂²⋊Dic₇₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

Dic₇₉⋊C₄

yes

—

C₁₆

—

C₁₆

—

C₁₆

—

316

—

C₂³

#14579097

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₇₉⋊#95

yes

characteristic

C₂×C₄

#14579097

yes

characteristic

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

C₂²

#19098328

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

#19098320

yes

characteristic

103

C₄

#19098332

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

#23761270

yes

characteristic

	subgroup	G/H
center	C₄	#19098320
commutator	C₂×C₈×C₇₉	C₄²
Frattini	#405	C₂×D₇₉
Fitting	C₇₉×#2151	C₂
socle	C₂×C₇₉	#1290
prime radical	C₂³×C₇₉	#108
cosocle	#405×C₇₉	C₂²
hypercenter	#2151	D₇₉
hypocenter	C₇₉	#7240
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #2151

subgroup

G/H

center

C₄

#19098320

commutator

C₂×C₈×C₇₉

C₄²

Frattini

#405

C₂×D₇₉

Fitting

C₇₉×#2151

C₂

C₂×C₇₉

C₂³×C₇₉

#405×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #2151

N	H ≅ G/N	type
56. C₇₉	#7240	semidirect

H ≅ G/N

type

56. C₇₉

#7240

semidirect

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

subgroup	index
#23765216	2
C₇₉×#2151	2
#7240	79

subgroup

index

#23765216

C₇₉×#2151

#7240

Subgroups — #34175366

Conjugacy classes of subgroups

Complements

Maximal subgroups