Group #22625022 — subgroups

Subgroups — #22625022

Order 9344.

158 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 40 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	#17989573	C₂	1	2	yes	maximal
2	#17988553	C₂	1	1	yes	maximal, characteristic
3	D₇₃⋊M₁₆	—	2	2	no	—
4	#14556652	—	2	2	no	—
5	#14556651	C₄	1	4	yes	—
6	C₂×#11924028	C₂²	1	1	yes	characteristic
7	C₂×#11924012	C₄	1	1	yes	characteristic
8	#14556503	—	2	2	no	—
9	C₂²×C₈×C₇₃	C₄	1	1	yes	characteristic
10	#11924038	—	4	2	no	—
11	#11924037	—	2	4	no	—
12	#11924036	—	4	2	no	—
13	#11924028	—	4	1	no	—
14	#11924028	—	4	1	no	—
15	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
16	C₂×D₂₉₂	Q₈	1	1	yes	characteristic
17	C₂×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×D₇₃	D₄	1	2	yes	—
19	#11924012	—	4	1	no	—
20	C₂×#10596831	—	2	1	no	—
21	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₃	—	2	1	no	—
23	C₂×C₈×C₇₃	—	4	1	no	—
24	C₂³×C₇₃	C₄²	1	1	yes	characteristic
25	C₂²×D₇₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	—	2	1	no	—
28	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂²⋊D₇₃	—	4	2	no	—
31	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
32	D₂₉₂	—	4	1	no	—
33	C₄×D₇₃	—	2	2	no	—
34	C₄×D₇₃	—	2	2	no	—
35	Dic₁₄₆	—	4	1	no	—
36	#10596833	—	4	4	no	—
37	C₈×C₇₃	—	4	1	no	—
38	#10596831	—	4	1	no	—
39	C₂²×C₇₃	—	2	1	no	—
40	C₂²×C₇₃	—	4	1	no	—
41	C₂²×C₇₃	#95	1	1	yes	characteristic
42	C₂×D₇₃	—	2	2	no	—
43	C₂×D₇₃	—	4	2	no	—
44	C₄×C₇₃	—	2	1	no	—
45	C₄×C₇₃	#99	1	1	yes	characteristic
46	C₄×C₇₃	#99	1	1	yes	characteristic
47	Dic₇₃	—	2	2	no	—
48	C₂×C₇₃	—	2	1	no	—
49	C₂×C₇₃	—	4	1	no	—
50	C₂×C₇₃	#342	1	1	yes	characteristic
51	D₇₃	—	4	2	no	—
52	#1392	—	73	1	no	maximal, Sylow
53	C₇₃	#1392	1	1	yes	characteristic, complemented, Sylow
54	#413	—	73	2	no	—
55	#408	—	73	1	no	—
56	C₂×#41	—	73	1	no	—
57	C₂×M₁₆	—	73	1	no	—
58	C₂×M₁₆	—	146	2	no	—
59	C₂²×C₈	#64408	1	1	yes	characteristic
60	#101	—	146	2	no	—
61	#100	—	73	4	no	—
62	C₂²⋊C₈	—	146	2	no	—
63	#41	—	292	1	no	—
64	#41	—	292	1	no	—
65	C₂×Q₈	—	73	1	no	—
66	C₂×D₄	—	73	2	no	—
67	C₂×D₄	—	73	1	no	—
68	C₂²×C₄	—	73	2	no	—
69	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
70	M₁₆	—	292	2	no	—
71	M₁₆	—	292	1	no	—
72	M₁₆	—	146	4	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	4	1	no	—
75	C₂×C₈	—	292	2	no	—
76	C₂×C₈	—	146	1	no	—
77	C₂³	—	73	2	no	—
78	C₂³	C₄×#64408	1	1	yes	characteristic
79	Q₈	—	292	1	no	—
80	D₄	—	292	1	no	—
81	D₄	—	292	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	73	2	no	—
85	C₂×C₄	—	146	2	no	—
86	C₂×C₄	—	146	2	no	—
87	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
88	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
89	C₈	—	4	1	no	—
90	C₈	—	292	4	no	—
91	C₈	—	292	1	no	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	—	292	2	no	—
95	C₂²	—	146	2	no	—
96	C₂²	(C₂×#64408)⋊C₄	1	1	yes	characteristic
97	C₄	—	2	1	no	—
98	C₄	—	146	2	no	—
99	C₄	#14556649	1	1	yes	characteristic
100	C₄	#14556650	1	1	yes	characteristic
101	C₂	—	2	1	no	—
102	C₂	—	4	1	no	—
103	C₂	—	292	2	no	—
104	C₂	#17989465	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989573

C₂

yes

maximal

#17988553

C₂

yes

maximal, characteristic

D₇₃⋊M₁₆

—

#14556652

—

#14556651

C₄

yes

—

C₂×#11924028

C₂²

yes

characteristic

C₂×#11924012

C₄

yes

characteristic

#14556503

—

C₂²×C₈×C₇₃

C₄

yes

—

—

—

—

—

C₂×Dic₁₄₆

D₄

yes

characteristic

C₂×D₂₉₂

Q₈

yes

characteristic

C₂×C₂²⋊D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

D₄

yes

—

#11924012

—

C₂×#10596831

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂³×C₇₃

C₄²

yes

characteristic

C₂²×D₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#95

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#342

yes

characteristic

D₇₃

—

#1392

—

maximal, Sylow

C₇₃

#1392

yes

characteristic, complemented, Sylow

#413

—

#408

—

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂²×C₈

#64408

yes

characteristic

#101

—

146

—

#100

—

C₂²⋊C₈

—

146

—

#41

—

292

—

#41

—

292

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

292

—

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

292

—

C₂×C₈

—

146

—

C₂³

—

C₂³

C₄×#64408

yes

characteristic

Q₈

—

292

—

D₄

—

292

—

D₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

292

—

C₈

—

292

—

C₂²

—

C₂²

—

C₂²

—

292

—

C₂²

—

146

—

C₂²

(C₂×#64408)⋊C₄

yes

characteristic

C₄

—

C₄

—

146

—

C₄

#14556649

yes

characteristic

100

C₄

#14556650

yes

characteristic

101

C₂

—

102

C₂

—

103

C₂

—

292

—

104

C₂

#17989465

yes

characteristic

	subgroup	G/H
center	C₄	#14556649
commutator	C₂³×C₇₃	C₄²
Frattini	C₂²×C₄	C₂×#64408
Fitting	C₂²×C₈×C₇₃	C₄
socle	C₂×C₇₃	#342
hypercenter	C₂²×C₈	#64408
hypocenter	C₇₃	#1392
LCS	G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₄

#14556649

commutator

C₂³×C₇₃

C₄²

Frattini

C₂²×C₄

C₂×#64408

Fitting

C₂²×C₈×C₇₃

C₄

C₂×C₇₃

C₂²×C₈

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
53. C₇₃	#1392	semidirect

H ≅ G/N

type

53. C₇₃

#1392

semidirect

Subgroups — #22625022

Conjugacy classes of subgroups

Complements