Group #22618200 — subgroups

Subgroups — #22618200

Order 9344.

348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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	#17988526	C₂	1	3	yes	maximal
2	#17988520	C₂	1	6	yes	maximal
3	#17988507	C₂	1	3	yes	maximal
4	#17988455	C₂	1	2	yes	maximal
5	#384×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₇₃	C₂²	1	3	yes	—
8	C₂×#11924007	C₂²	1	6	yes	—
9	#14556498	C₂²	1	6	yes	—
10	#14556498	C₂²	1	6	yes	—
11	#14556498	C₂²	1	3	yes	—
12	#14556498	C₂²	1	3	yes	—
13	C₂×C₄⋊C₄×C₇₃	C₂²	1	3	yes	—
14	C₂×C₄⋊C₄×C₇₃	C₂²	1	3	yes	—
15	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₄₆	—	4	3	no	—
17	C₂²×Dic₇₃	C₂³	1	6	yes	—
18	C₂²×Dic₇₃	C₂³	1	2	yes	—
19	C₄⋊Dic₇₃	—	4	3	no	—
20	#11924007	—	4	6	no	—
21	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
23	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
24	C₄⋊C₄×C₇₃	—	4	3	no	—
25	C₄⋊C₄×C₇₃	—	4	3	no	—
26	C₄²×C₇₃	Q₈	1	4	yes	complemented
27	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₇₃	—	2	3	no	—
29	C₂×C₄×C₇₃	—	2	3	no	—
30	C₂×C₄×C₇₃	—	2	6	no	—
31	C₂×C₄×C₇₃	—	2	3	no	—
32	C₂×C₄×C₇₃	—	2	3	no	—
33	C₂×C₄×C₇₃	C₂×Q₈	1	6	yes	—
34	C₂×Dic₇₃	—	2	6	no	—
35	C₂×Dic₇₃	—	2	6	no	—
36	C₂×Dic₇₃	—	2	12	no	—
37	Dic₁₄₆	—	4	4	no	—
38	C₂²×C₇₃	C₂²×Q₈	1	1	yes	characteristic
39	C₂²×C₇₃	H(5,𝔽₂)	1	3	yes	—
40	C₂²×C₇₃	2₋¹⁺⁴	1	3	yes	—
41	C₄×C₇₃	—	2	6	no	—
42	C₄×C₇₃	—	4	1	no	—
43	C₄×C₇₃	—	4	3	no	—
44	Dic₇₃	—	4	2	no	—
45	Dic₇₃	—	4	6	no	—
46	C₂×C₇₃	#544	1	3	yes	—
47	C₂×C₇₃	#560	1	1	yes	characteristic
48	C₂×C₇₃	#563	1	3	yes	—
49	#2843	—	73	1	no	maximal, Sylow
50	C₇₃	#2843	1	1	yes	characteristic, complemented, Sylow
51	#400	—	73	3	no	—
52	#398	—	73	6	no	—
53	#395	—	73	3	no	—
54	#384	D₇₃	1	1	yes	characteristic
55	#383	—	73	2	no	—
56	C₂²×Q₈	—	73	1	no	—
57	C₂×C₄⋊C₄	—	73	6	no	—
58	C₂×C₄⋊C₄	—	73	3	no	—
59	C₂×C₄⋊C₄	C₂×D₇₃	1	3	yes	—
60	C₂×C₄⋊C₄	C₂×D₇₃	1	3	yes	—
61	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
62	#95	—	73	6	no	—
63	#95	—	73	6	no	—
64	#95	—	73	3	no	—
65	#95	—	73	3	no	—
66	C₂×Q₈	—	292	3	no	—
67	C₂²×C₄	—	73	6	no	—
68	C₂²×C₄	—	73	2	no	—
69	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
70	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
71	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
72	C₄⋊C₄	—	4	3	no	—
73	C₄⋊C₄	—	4	3	no	—
74	C₄⋊C₄	—	292	6	no	—
75	C₄⋊C₄	—	292	3	no	—
76	C₄²	Dic₁₄₆	1	4	yes	complemented
77	C₂³	C₂³×D₇₃	1	1	yes	characteristic
78	Q₈	—	292	4	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	6	no	—
82	C₂×C₄	—	2	3	no	—
83	C₂×C₄	—	2	3	no	—
84	C₂×C₄	—	146	6	no	—
85	C₂×C₄	—	146	6	no	—
86	C₂×C₄	—	146	12	no	—
87	C₂×C₄	C₂×Dic₁₄₆	1	6	yes	—
88	C₂²	C₂²×Dic₁₄₆	1	1	yes	characteristic
89	C₂²	#14556636	1	3	yes	—
90	C₂²	#14556639	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	4	1	no	—
93	C₄	—	4	3	no	—
94	C₄	—	292	2	no	—
95	C₄	—	292	6	no	—
96	C₂	#17989218	1	3	yes	—
97	C₂	#17989324	1	1	yes	characteristic
98	C₂	#17989336	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988526

C₂

yes

maximal

#17988520

C₂

yes

maximal

#17988507

C₂

yes

maximal

#17988455

C₂

yes

maximal

#384×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

C₂×C₄⋊C₄×C₇₃

C₂²

yes

—

C₂×C₄⋊C₄×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

Q₈

yes

complemented

C₂³×C₇₃

C₂⁴

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

C₂²×C₇₃

C₂²×Q₈

yes

characteristic

C₂²×C₇₃

H(5,𝔽₂)

yes

—

C₂²×C₇₃

2₋¹⁺⁴

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#544

yes

—

C₂×C₇₃

#560

yes

characteristic

C₂×C₇₃

#563

yes

—

#2843

—

maximal, Sylow

C₇₃

#2843

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic

#383

—

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

—

C₂×C₄²

C₂×D₇₃

yes

—

—

—

—

C₂×Q₈

—

292

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄²

Dic₁₄₆

yes

complemented

C₂³

C₂³×D₇₃

yes

characteristic

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×Dic₁₄₆

yes

—

C₂²

C₂²×Dic₁₄₆

yes

characteristic

C₂²

#14556636

yes

—

C₂²

#14556639

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

292

—

C₄

—

292

—

C₂

#17989218

yes

—

C₂

#17989324

yes

characteristic

C₂

#17989336

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Fitting	#384×C₇₃	C₂
hypercenter	#384	D₇₃
hypocenter	C₇₃	#2843
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂⁴

Fitting

#384×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
26. C₄²×C₇₃	Q₈	semidirect
50. C₇₃	#2843	semidirect
76. C₄²	Dic₁₄₆	semidirect

H ≅ G/N

type

26. C₄²×C₇₃

Q₈

semidirect

50. C₇₃

#2843

semidirect

76. C₄²

Dic₁₄₆

semidirect

Subgroups — #22618200

Conjugacy classes of subgroups

Complements