Group #19151817 — subgroups

Subgroups — #19151817

Order 5696.

112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 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	C₂×#13083564	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13083562	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
5	#15667936	C₂	1	1	yes	maximal, characteristic, complemented
6	#15667933	C₂	1	1	yes	maximal, characteristic
7	#124×C₈₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₇₈	C₂²	1	1	yes	characteristic
9	#13083564	—	2	2	no	—
10	#13083562	—	2	2	no	—
11	C₂×#10623494	C₂²	1	1	yes	characteristic
12	C₂×#10623494	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
14	#13083553	—	2	1	no	—
15	C₄×Dic₈₉	—	2	1	no	—
16	C₂×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²⋊C₄×C₈₉	—	2	1	no	—
19	C₂²⋊C₄×C₈₉	—	2	1	no	—
20	C₄²×C₈₉	C₂²	1	1	yes	characteristic
21	C₂³×C₈₉	—	2	1	no	—
22	Q₈×C₈₉	—	2	1	no	—
23	Q₈×C₈₉	—	2	1	no	—
24	D₄×C₈₉	—	2	1	no	—
25	D₄×C₈₉	—	2	1	no	—
26	C₂×C₄×C₈₉	—	2	1	no	—
27	C₂×C₄×C₈₉	D₄	1	1	yes	characteristic
28	C₂×C₄×C₈₉	D₄	1	1	yes	characteristic
29	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
30	C₂×Dic₈₉	—	2	1	no	—
31	C₂×Dic₈₉	—	2	1	no	—
32	Dic₁₇₈	—	2	1	no	—
33	Dic₁₇₈	D₄	1	2	yes	—
34	#10623494	—	2	1	no	—
35	#10623494	—	2	1	no	—
36	C₂²×C₈₉	—	4	1	no	—
37	C₂²×C₈₉	—	4	1	no	—
38	C₂²×C₈₉	—	4	1	no	—
39	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
40	C₄×C₈₉	—	2	1	no	—
41	C₄×C₈₉	—	2	1	no	—
42	C₄×C₈₉	—	4	1	no	—
43	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
44	C₄×C₈₉	#41	1	1	yes	characteristic
45	Dic₈₉	—	2	2	no	—
46	Dic₈₉	—	4	1	no	—
47	C₂×C₈₉	—	8	1	no	—
48	C₂×C₈₉	#121	1	1	yes	characteristic
49	C₂×C₈₉	#135	1	1	yes	characteristic
50	C₂×C₈₉	#137	1	1	yes	characteristic
51	C₈₉	#464	1	1	yes	characteristic, complemented, Sylow
52	#464	—	89	1	no	maximal, Sylow
53	C₂×Q₁₆	—	89	1	no	—
54	C₂×SD₁₆	—	89	1	no	—
55	#124	D₈₉	1	1	yes	characteristic
56	C₄×Q₈	—	89	1	no	—
57	C₄⋊C₈	—	89	1	no	—
58	#103	—	89	1	no	—
59	#102	—	89	1	no	—
60	C₂×Q₈	—	89	1	no	—
61	C₂×Q₈	C₂×D₈₉	1	1	yes	characteristic
62	C₂×D₄	C₂×D₈₉	1	1	yes	characteristic
63	Q₁₆	—	178	2	no	—
64	SD₁₆	—	178	2	no	—
65	C₂×C₈	—	89	1	no	—
66	C₂×C₈	—	89	1	no	—
67	C₄⋊C₄	—	89	1	no	—
68	C₄⋊C₄	—	178	1	no	—
69	C₂²⋊C₄	—	2	1	no	—
70	C₂²⋊C₄	—	2	1	no	—
71	C₄²	—	178	1	no	—
72	C₄²	C₂×D₈₉	1	1	yes	characteristic
73	C₂³	—	2	1	no	—
74	Q₈	—	2	1	no	—
75	Q₈	—	2	1	no	—
76	Q₈	—	89	2	no	—
77	Q₈	—	178	1	no	—
78	D₄	—	2	1	no	—
79	D₄	—	2	1	no	—
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	178	1	no	—
82	C₂×C₄	—	178	1	no	—
83	C₂×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
84	C₂×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
85	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
86	C₈	—	178	1	no	—
87	C₈	—	178	1	no	—
88	C₂²	—	4	1	no	—
89	C₂²	—	4	1	no	—
90	C₂²	—	4	1	no	—
91	C₂²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	2	1	no	—
94	C₄	—	4	1	no	—
95	C₄	—	356	1	no	—
96	C₄	—	178	2	no	—
97	C₄	D₄×D₈₉	1	1	yes	characteristic
98	C₄	#13083573	1	1	yes	characteristic
99	C₂	—	8	1	no	—
100	C₂	#15667983	1	1	yes	characteristic
101	C₂	#15668032	1	1	yes	characteristic
102	C₂	#15668042	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13083564

C₂

yes

maximal, characteristic, complemented

C₂×#13083562

C₂

yes

maximal, characteristic

C₄×Dic₁₇₈

C₂

yes

maximal, characteristic, complemented

C₄⋊#10623494

C₂

yes

maximal, characteristic, complemented

#15667936

C₂

yes

maximal, characteristic, complemented

#15667933

C₂

yes

maximal, characteristic

#124×C₈₉

C₂

yes

maximal, characteristic

C₂×Dic₁₇₈

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#10623494

C₂²

yes

characteristic

C₄⋊Dic₈₉

C₂²

yes

characteristic

#13083553

—

C₄×Dic₈₉

—

C₂×Q₈×C₈₉

C₂²

yes

characteristic

C₂×D₄×C₈₉

C₂²

yes

characteristic

C₂²⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

C₂²

yes

characteristic

C₂³×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

D₄

yes

characteristic

C₂×C₄×C₈₉

D₄

yes

characteristic

C₂×C₄×C₈₉

C₂³

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

D₄

yes

—

#10623494

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×D₄

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

C₂×D₄

yes

characteristic

C₄×C₈₉

#41

yes

characteristic

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

C₈₉

yes

characteristic, complemented, Sylow

#464

—

maximal, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

#124

D₈₉

yes

characteristic

C₄×Q₈

—

C₄⋊C₈

—

#103

—

#102

—

C₂×Q₈

—

C₂×Q₈

C₂×D₈₉

yes

characteristic

C₂×D₄

C₂×D₈₉

yes

characteristic

Q₁₆

—

178

—

SD₁₆

—

178

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

178

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

178

—

C₄²

C₂×D₈₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

178

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

C₂²⋊D₈₉

yes

characteristic

C₂×C₄

C₂²⋊D₈₉

yes

characteristic

C₂×C₄

C₂²×D₈₉

yes

characteristic

C₈

—

178

—

C₈

—

178

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂×C₂²⋊D₈₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

356

—

C₄

—

178

—

C₄

D₄×D₈₉

yes

characteristic

C₄

#13083573

yes

characteristic

C₂

—

100

C₂

#15667983

yes

characteristic

101

C₂

#15668032

yes

characteristic

102

C₂

#15668042

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	#124×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	#124	D₈₉
hypocenter	C₈₉	#464
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

subgroup

G/H

center

C₂²

C₂×C₂²⋊D₈₉

commutator

C₂×C₄×C₈₉

C₂³

Frattini

C₂×C₄

C₂²×D₈₉

Fitting

#124×C₈₉

C₂

socle

C₂²×C₈₉

C₂×D₄

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #124

N	H ≅ G/N	type
1. C₂×#13083564	C₂	semidirect
3. C₄×Dic₁₇₈	C₂	semidirect
4. C₄⋊#10623494	C₂	semidirect
5. #15667936	C₂	semidirect
51. C₈₉	#464	semidirect

H ≅ G/N

type

1. C₂×#13083564

C₂

semidirect

3. C₄×Dic₁₇₈

C₂

semidirect

4. C₄⋊#10623494

C₂

semidirect

5. #15667936

C₂

semidirect

51. C₈₉

#464

semidirect

Subgroups — #19151817

Conjugacy classes of subgroups

Complements