Group #11794608 — subgroups

Subgroups — #11794608

Order 1152.

324 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 82 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×#63383	C₂	1	3	yes	maximal
2	#10588799	C₂	1	3	yes	maximal, complemented
3	C₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	#68722	—	3	1	no	maximal
5	C₂²×D₃₆	C₂²	1	1	yes	characteristic
6	C₂×C₉×M₁₆	C₂²	1	3	yes	—
7	C₂×#3667	C₂²	1	3	yes	—
8	#63383	—	2	6	no	—
9	#63381	—	2	6	no	—
10	C₂×#823	—	3	3	no	—
11	#5124	—	3	3	no	—
12	C₃×#338	D₃	1	1	yes	characteristic
13	C₂³×D₉	Q₈	1	2	yes	—
14	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
15	C₂×D₃₆	—	2	3	no	—
16	C₂×D₃₆	—	2	3	no	—
17	C₉×M₁₆	—	2	3	no	—
18	C₉×M₁₆	—	2	3	no	—
19	C₂×C₈×C₉	—	2	3	no	—
20	#3667	—	2	3	no	—
21	#3667	D₄	1	6	yes	—
22	C₂×C₉⋊C₈	—	2	3	no	—
23	#2069	—	9	1	no	Sylow
24	C₂²×D₁₂	—	3	1	no	—
25	C₂×C₃×M₁₆	C₂×D₃	1	3	yes	—
26	C₂×#208	—	3	3	no	—
27	#823	—	6	6	no	—
28	#822	—	6	6	no	—
29	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
30	C₂²×D₉	—	2	6	no	—
31	C₂²×D₉	—	8	2	no	—
32	C₂×C₄×C₉	C₂×D₄	1	3	yes	—
33	C₂×C₄×C₉	#41	1	3	yes	—
34	D₃₆	—	4	3	no	—
35	D₃₆	—	4	1	no	—
36	C₈×C₉	—	4	3	no	—
37	C₉⋊C₈	—	2	6	no	—
38	#430	—	9	3	no	—
39	C₂×#100	—	9	3	no	—
40	#338	D₉	1	1	yes	characteristic, complemented
41	C₂³×D₃	—	3	2	no	—
42	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
43	C₂×D₁₂	—	6	3	no	—
44	C₂×D₁₂	—	6	3	no	—
45	C₃×M₁₆	—	2	3	no	—
46	C₃×M₁₆	—	2	3	no	—
47	C₂×C₃×C₈	—	2	3	no	—
48	#208	—	3	6	no	—
49	#208	—	6	3	no	—
50	C₂×C₃⋊C₈	—	6	3	no	—
51	C₂²×C₉	—	4	1	no	—
52	C₂²×C₉	C₂²⋊Q₈	1	3	yes	—
53	C₂×D₉	—	4	2	no	—
54	C₂×D₉	—	8	6	no	—
55	C₄×C₉	#121	1	3	yes	—
56	C₄×C₉	#126	1	1	yes	characteristic
57	C₂²×D₄	—	9	1	no	—
58	C₂×M₁₆	—	9	3	no	—
59	C₂×M₁₆	C₂×D₉	1	3	yes	—
60	#108	—	18	6	no	—
61	#100	—	18	6	no	—
62	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
63	C₂²×D₃	—	6	6	no	—
64	C₂²×D₃	—	24	2	no	—
65	C₂×C₃×C₄	#235	1	3	yes	—
66	C₂×C₃×C₄	D₃×D₄	1	3	yes	—
67	D₁₂	—	12	1	no	—
68	D₁₂	—	12	3	no	—
69	C₃×C₈	—	4	3	no	—
70	C₃⋊C₈	—	6	6	no	—
71	C₂×C₉	—	2	3	no	—
72	C₂×C₉	#396	1	1	yes	characteristic
73	D₉	—	8	2	no	—
74	C₂⁴	—	9	2	no	—
75	C₂×D₄	—	18	3	no	—
76	C₂×D₄	—	18	3	no	—
77	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
78	M₁₆	—	2	3	no	—
79	M₁₆	—	2	3	no	—
80	M₁₆	—	9	6	no	—
81	M₁₆	—	18	3	no	—
82	C₂×C₈	—	2	3	no	—
83	C₂×C₈	—	18	3	no	—
84	C₂²×C₃	—	4	1	no	—
85	C₂²×C₃	#896	1	3	yes	—
86	C₂×D₃	—	12	2	no	—
87	C₂×D₃	—	24	6	no	—
88	C₃×C₄	#876	1	1	yes	characteristic
89	C₃×C₄	#884	1	3	yes	—
90	C₉	#2069	1	1	yes	characteristic, complemented, Sylow
91	C₂³	—	18	6	no	—
92	C₂³	—	72	2	no	—
93	C₂³	Q₈×D₉	1	1	yes	characteristic
94	D₄	—	36	1	no	—
95	D₄	—	36	3	no	—
96	C₂×C₄	#3697	1	3	yes	—
97	C₂×C₄	D₄×D₉	1	3	yes	—
98	C₈	—	4	3	no	—
99	C₈	—	18	6	no	—
100	C₂×C₃	—	2	3	no	—
101	C₂×C₃	#4676	1	1	yes	characteristic
102	D₃	—	24	2	no	—
103	C₂²	—	4	1	no	—
104	C₂²	—	36	2	no	—
105	C₂²	—	72	6	no	—
106	C₂²	#63458	1	3	yes	—
107	C₄	#63438	1	1	yes	characteristic
108	C₄	#63446	1	3	yes	—
109	C₃	#68722	1	1	yes	characteristic
110	C₂	—	2	3	no	—
111	C₂	—	72	2	no	—
112	C₂	#10588356	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63383

C₂

yes

maximal

#10588799

C₂

yes

maximal, complemented

C₉×#338

C₂

yes

maximal, characteristic, complemented

#68722

—

maximal

C₂²×D₃₆

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₂×#3667

C₂²

yes

—

—

—

—

—

D₃

yes

characteristic

C₂³×D₉

Q₈

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂×D₃₆

—

C₂×D₃₆

—

C₉×M₁₆

—

C₉×M₁₆

—

C₂×C₈×C₉

—

#3667

—

#3667

D₄

yes

—

C₂×C₉⋊C₈

—

#2069

—

Sylow

C₂²×D₁₂

—

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂×#208

—

#823

—

#822

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂²×D₉

—

C₂²×D₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

#41

yes

—

D₃₆

—

D₃₆

—

C₈×C₉

—

C₉⋊C₈

—

#430

—

C₂×#100

—

#338

D₉

yes

characteristic, complemented

C₂³×D₃

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂×D₁₂

—

C₂×D₁₂

—

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

#208

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

C₂²⋊Q₈

yes

—

C₂×D₉

—

C₂×D₉

—

C₄×C₉

#121

yes

—

C₄×C₉

#126

yes

characteristic

C₂²×D₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₉

yes

—

#108

—

#100

—

C₂³×C₃

D₃×Q₈

yes

characteristic

C₂²×D₃

—

C₂²×D₃

—

C₂×C₃×C₄

#235

yes

—

C₂×C₃×C₄

D₃×D₄

yes

—

D₁₂

—

D₁₂

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

#396

yes

characteristic

D₉

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₂²×D₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂²×C₃

—

C₂²×C₃

#896

yes

—

C₂×D₃

—

C₂×D₃

—

C₃×C₄

#876

yes

characteristic

C₃×C₄

#884

yes

—

C₉

#2069

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

Q₈×D₉

yes

characteristic

D₄

—

D₄

—

C₂×C₄

#3697

yes

—

C₂×C₄

D₄×D₉

yes

—

C₈

—

C₈

—

100

C₂×C₃

—

101

C₂×C₃

#4676

yes

characteristic

102

D₃

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

#63458

yes

—

107

C₄

#63438

yes

characteristic

108

C₄

#63446

yes

—

109

C₃

#68722

yes

characteristic

110

C₂

—

111

C₂

—

112

C₂

#10588356

yes

characteristic

	subgroup	G/H
center	C₂	#10588356
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#338	C₂
socle	C₂×C₃	#4676
prime radical	C₂²×D₃₆	C₂²
hypercenter	#338	D₉
hypocenter	C₉	#2069
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

subgroup

G/H

center

C₂

#10588356

commutator, cosocle

C₂²×C₄×C₉

C₂³

Frattini

C₂²×C₃×C₄

C₂²×D₃

C₂

C₂×C₃

C₂²×D₃₆

C₂²

D₉

C₉

G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

N	H ≅ G/N	type
2. #10588799	C₂	semidirect
3. C₉×#338	C₂	semidirect
40. #338	D₉	semidirect
90. C₉	#2069	semidirect

H ≅ G/N

type

2. #10588799

C₂

semidirect

3. C₉×#338

C₂

semidirect

40. #338

D₉

semidirect

90. C₉

#2069

semidirect

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

subgroup	index
C₂×#63383	2
#10588799	2
C₉×#338	2
#68722	3

subgroup

index

Subgroups — #11794608

Conjugacy classes of subgroups

Complements

Maximal subgroups