Group #34060191 — subgroups

Subgroups — D₁₄₉⋊#333 #34060191

Order 19072.

256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 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	D₁₄₉⋊(C₄⋊C₈)	C₂	1	2	yes	maximal
2	#23750485	C₂	1	4	yes	maximal, complemented
3	C₄⋊Q₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×D₁₄₉⋊C₈	—	2	2	no	—
5	#18011978	C₂²	1	4	yes	—
6	C₄⋊#11924753	—	2	2	no	—
7	C₂×Q₈×D₁₄₉	C₄	1	2	yes	—
8	#18011911	C₄	1	1	yes	characteristic
9	#18011910	—	2	2	no	—
10	#18011909	C₂²	1	2	yes	—
11	C₄⋊C₄×D₁₄₉	—	2	2	no	—
12	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
13	C₄⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
14	D₁₄₉⋊C₈	—	4	4	no	—
15	C₂×#11924753	—	2	4	no	—
16	C₂×Dic₂₉₈	—	2	2	no	—
17	C₂×Dic₂₉₈	C₂×C₄	1	2	yes	—
18	Q₈×D₁₄₉	—	4	4	no	—
19	C₂×C₄×D₁₄₉	—	2	2	no	—
20	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×D₁₄₉	D₄	1	2	yes	—
22	C₄⋊Dic₁₄₉	—	2	2	no	—
23	#14558715	—	2	4	no	—
24	C₄×Dic₁₄₉	D₄	1	2	yes	—
25	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
26	C₂×Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
27	C₄⋊C₄×C₁₄₉	—	2	2	no	—
28	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
29	#11924753	—	4	4	no	—
30	C₂²×D₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
31	Dic₂₉₈	—	4	4	no	—
32	Dic₂₉₈	—	4	2	no	—
33	C₂×Dic₁₄₉	—	2	2	no	—
34	C₂×Dic₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×Dic₁₄₉	C₂×D₄	1	2	yes	—
36	C₄×D₁₄₉	—	2	2	no	—
37	C₄×D₁₄₉	—	4	4	no	—
38	C₄×D₁₄₉	SD₁₆	1	4	yes	—
39	C₄×D₁₄₉	Q₁₆	1	4	yes	—
40	Q₈×C₁₄₉	—	4	2	no	—
41	C₂×C₄×C₁₄₉	—	2	2	no	—
42	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
43	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
44	C₂²×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×D₁₄₉	#100	1	2	yes	—
46	C₂×D₁₄₉	#103	1	4	yes	—
47	C₄×C₁₄₉	—	2	1	no	—
48	C₄×C₁₄₉	—	4	2	no	—
49	C₄×C₁₄₉	#103	1	4	yes	—
50	Dic₁₄₉	—	2	1	no	—
51	Dic₁₄₉	—	4	2	no	—
52	Dic₁₄₉	C₂×SD₁₆	1	2	yes	—
53	Dic₁₄₉	C₂×Q₁₆	1	2	yes	—
54	C₂×C₁₄₉	C₂×#100	1	1	yes	characteristic
55	C₂×C₁₄₉	C₂×#103	1	2	yes	—
56	D₁₄₉	#333	1	4	yes	complemented
57	C₁₄₉	C₂×#333	1	1	yes	characteristic, complemented, Sylow
58	C₂×#333	—	149	1	no	maximal, Sylow
59	C₂×C₄⋊Q₈	—	149	1	no	—
60	C₂×C₄⋊C₈	—	149	2	no	—
61	#333	—	149	4	no	—
62	C₂²×Q₈	—	149	2	no	—
63	C₂²×C₈	—	298	2	no	—
64	C₄⋊Q₈	—	298	2	no	—
65	C₄⋊Q₈	—	149	2	no	—
66	C₄⋊Q₈	—	149	1	no	—
67	C₄⋊Q₈	#10597010	1	1	yes	characteristic
68	C₂×C₄⋊C₄	—	298	2	no	—
69	C₂×C₄²	—	149	1	no	—
70	C₄⋊C₈	—	298	2	no	—
71	C₄⋊C₈	—	149	4	no	—
72	C₂×Q₈	—	298	2	no	—
73	C₂×Q₈	—	596	4	no	—
74	C₂×Q₈	—	149	2	no	—
75	C₂×Q₈	C₂×#10597010	1	2	yes	—
76	C₂²×C₄	—	298	2	no	—
77	C₂²×C₄	—	149	1	no	—
78	C₂²×C₄	—	149	2	no	—
79	C₂×C₈	—	298	4	no	—
80	C₂×C₈	—	596	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	298	4	no	—
83	C₄⋊C₄	—	298	2	no	—
84	C₄²	—	149	2	no	—
85	C₄²	—	149	1	no	—
86	C₄²	C₂×#10597010	1	1	yes	characteristic
87	C₂³	—	149	1	no	—
88	Q₈	—	4	2	no	—
89	Q₈	—	596	2	no	—
90	Q₈	—	596	4	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	298	2	no	—
93	C₂×C₄	—	298	2	no	—
94	C₂×C₄	—	596	4	no	—
95	C₂×C₄	—	149	1	no	—
96	C₂×C₄	—	149	2	no	—
97	C₂×C₄	—	149	4	no	—
98	C₂×C₄	—	149	4	no	—
99	C₂×C₄	C₂²⋊#10597010	1	2	yes	—
100	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
101	C₈	—	596	4	no	—
102	C₂²	—	149	2	no	—
103	C₂²	—	149	4	no	—
104	C₂²	C₂×C₂²⋊#10597010	1	1	yes	characteristic
105	C₄	—	2	1	no	—
106	C₄	—	4	2	no	—
107	C₄	—	298	1	no	—
108	C₄	—	596	2	no	—
109	C₄	—	149	2	no	—
110	C₄	—	149	2	no	—
111	C₄	#18011974	1	4	yes	—
112	C₂	—	149	4	no	—
113	C₂	D₁₄₉⋊#100	1	1	yes	characteristic
114	C₂	C₂×#18011974	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

D₁₄₉⋊(C₄⋊C₈)

C₂

yes

maximal

#23750485

C₂

yes

maximal, complemented

C₄⋊Q₈×D₁₄₉

C₂

yes

maximal, characteristic

C₂×D₁₄₉⋊C₈

—

#18011978

C₂²

yes

—

C₄⋊#11924753

—

C₂×Q₈×D₁₄₉

C₄

yes

—

#18011911

C₄

yes

characteristic

#18011910

—

#18011909

C₂²

yes

—

C₄⋊C₄×D₁₄₉

—

C₄²×D₁₄₉

C₂²

yes

characteristic

C₄⋊Q₈×C₁₄₉

C₄

yes

characteristic

D₁₄₉⋊C₈

—

C₂×#11924753

—

C₂×Dic₂₉₈

—

C₂×Dic₂₉₈

C₂×C₄

yes

—

Q₈×D₁₄₉

—

C₂×C₄×D₁₄₉

—

C₂×C₄×D₁₄₉

C₂×C₄

yes

characteristic

C₂×C₄×D₁₄₉

D₄

yes

—

C₄⋊Dic₁₄₉

—

#14558715

—

C₄×Dic₁₄₉

D₄

yes

—

C₄×Dic₁₄₉

C₂³

yes

characteristic

C₂×Q₈×C₁₄₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₄₉

—

C₄²×C₁₄₉

C₂×C₄

yes

characteristic

#11924753

—

C₂²×D₁₄₉

C₂²⋊C₄

yes

characteristic

Dic₂₉₈

—

Dic₂₉₈

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₄₉

C₂×D₄

yes

—

C₄×D₁₄₉

—

C₄×D₁₄₉

—

C₄×D₁₄₉

SD₁₆

yes

—

C₄×D₁₄₉

Q₁₆

yes

—

Q₈×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₄₉

C₂²×C₄

yes

characteristic

C₂²×C₁₄₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₁₄₉

#100

yes

—

C₂×D₁₄₉

#103

yes

—

C₄×C₁₄₉

—

C₄×C₁₄₉

—

C₄×C₁₄₉

#103

yes

—

Dic₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

C₂×SD₁₆

yes

—

Dic₁₄₉

C₂×Q₁₆

yes

—

C₂×C₁₄₉

C₂×#100

yes

characteristic

C₂×C₁₄₉

C₂×#103

yes

—

D₁₄₉

#333

yes

complemented

C₁₄₉

C₂×#333

yes

characteristic, complemented, Sylow

C₂×#333

—

149

maximal, Sylow

C₂×C₄⋊Q₈

—

149

—

C₂×C₄⋊C₈

—

149

—

#333

—

149

—

C₂²×Q₈

—

149

—

C₂²×C₈

—

298

—

C₄⋊Q₈

—

298

—

C₄⋊Q₈

—

149

—

C₄⋊Q₈

—

149

—

C₄⋊Q₈

#10597010

yes

characteristic

C₂×C₄⋊C₄

—

298

—

C₂×C₄²

—

149

—

C₄⋊C₈

—

298

—

C₄⋊C₈

—

149

—

C₂×Q₈

—

298

—

C₂×Q₈

—

596

—

C₂×Q₈

—

149

—

C₂×Q₈

C₂×#10597010

yes

—

C₂²×C₄

—

298

—

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂×C₈

—

298

—

C₂×C₈

—

596

—

C₄⋊C₄

—

C₄⋊C₄

—

298

—

C₄⋊C₄

—

298

—

C₄²

—

149

—

C₄²

—

149

—

C₄²

C₂×#10597010

yes

characteristic

C₂³

—

149

—

Q₈

—

Q₈

—

596

—

Q₈

—

596

—

C₂×C₄

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

596

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

C₂²⋊#10597010

yes

—

100

C₂×C₄

C₂²×#10597010

yes

characteristic

101

C₈

—

596

—

102

C₂²

—

149

—

103

C₂²

—

149

—

104

C₂²

C₂×C₂²⋊#10597010

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

298

—

108

C₄

—

596

—

109

C₄

—

149

—

110

C₄

—

149

—

111

C₄

#18011974

yes

—

112

C₂

—

149

—

113

C₂

D₁₄₉⋊#100

yes

characteristic

114

C₂

C₂×#18011974

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#10597010
commutator	C₂×C₄×C₁₄₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#10597010
Fitting	C₄⋊Q₈×C₁₄₉	C₄
socle	C₂²×C₁₄₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₄₉	C₂²⋊C₄
cosocle	C₄×Dic₁₄₉	C₂³
hypercenter	C₄⋊Q₈	#10597010
hypocenter	C₁₄₉	C₂×#333
LCS	G ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

subgroup

G/H

center

C₂²

C₂×C₂²⋊#10597010

commutator

C₂×C₄×C₁₄₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#10597010

Fitting

C₄⋊Q₈×C₁₄₉

C₄

socle

C₂²×C₁₄₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₁₄₉

C₂²⋊C₄

cosocle

C₄×Dic₁₄₉

C₂³

C₄⋊Q₈

C₁₄₉

G ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₁₄₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

N	H ≅ G/N	type
2. #23750485	C₂	semidirect
56. D₁₄₉	#333	semidirect
57. C₁₄₉	C₂×#333	semidirect

H ≅ G/N

type

2. #23750485

C₂

semidirect

56. D₁₄₉

#333

semidirect

57. C₁₄₉

C₂×#333

semidirect

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

subgroup	index
D₁₄₉⋊(C₄⋊C₈)	2
#23750485	2
C₄⋊Q₈×D₁₄₉	2
C₂×#333	149

subgroup

index

D₁₄₉⋊(C₄⋊C₈)

#23750485

C₄⋊Q₈×D₁₄₉

C₂×#333

149

Subgroups — D₁₄₉⋊#333 #34060191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D149⋊#333 #34060191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₄₉⋊#333 #34060191