Finite Group Databasebeta

← #34061007

Subgroups — #34061007

Order 19072.

220 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D149⋊M32C211yesmaximal, characteristic, complemented
2D149⋊#108C211yesmaximal, characteristic, complemented
3#23750540C214yesmaximal, complemented
4C2×#18011934C211yesmaximal, characteristic
5D149⋊M16—21no—
6#18011986—21no—
7#18011985—21no—
8D149⋊C16C2212yescomplemented
9#18011982C2212yescomplemented
10#18011981—21no—
11C2×#14558737—21no—
12#18011934—21no—
13#18011934—21no—
14#18011934C412yes—
15#18011934C2212yes—
16C2×#14558723—21no—
17C2×D1192C411yescharacteristic
18C2×C8×D149C2211yescharacteristic
19C2×Q16×C149C411yescharacteristic
20#14558746—22no—
21#14558745—41no—
22D149⋊C8—41no—
23#14558739—22no—
24#14558737—22no—
25#14558737—22no—
26#14558737—41no—
27#14558737—41no—
28C2×D596—21no—
29C2×D596—41no—
30C2×C4×D149—41no—
31C2×C4×D149D411yescharacteristic
32#14558723—22no—
33#14558723—22no—
34D1192—21no—
35D1192C2×C412yes—
36C2×#11924746D411yescharacteristic
37C8×D149C2×C411yescharacteristic
38C8×D149D411yescharacteristic
39C8×D149D411yescharacteristic
40C8×D149C2311yescharacteristic
41C2×Q8×C149—21no—
42Q16×C149—21no—
43Q16×C149C2×C412yes—
44C2×C8×C149C2×C411yescharacteristic
45#11924753—42no—
46C22×D149—41no—
47C22×D149SD1611yescharacteristic
48D596—22no—
49D596—42no—
50D596—42no—
51D596—41no—
52C2×Dic149D811yescharacteristic
53C4×D149—42no—
54C4×D149—42no—
55C4×D149C22⋊C411yescharacteristic
56C4×D149D811yescharacteristic
57C4×D149SD1611yescharacteristic
58C4×D149C2×D411yescharacteristic
59#11924746C22⋊C411yescharacteristic
60#11924746C2×D411yescharacteristic
61Q8×C149—22no—
62Q8×C149—41no—
63C2×C4×C149—41no—
64C2×C4×C149C22⋊C411yescharacteristic
65C8×C149C22⋊C411yescharacteristic
66C8×C149C22×C411yescharacteristic
67C22×C149#10211yescharacteristic
68C2×D149—41no—
69C2×D149—42no—
70C2×D149—82no—
71C2×D149#10211yescharacteristic
72C2×D149C2×SD1611yescharacteristic
73C4×C149—42no—
74C4×C149#10211yescharacteristic
75C4×C149C2×C22⋊C411yescharacteristic
76Dic149#10211yescharacteristic
77Dic149C2×D811yescharacteristic
78C2×C149—21no—
79C2×C149C2×#10211yescharacteristic
80D149—21no—
81D149—21no—
82D149—82no—
83C149#214311yescharacteristic, complemented, Sylow
84#2143—1491nomaximal, Sylow
85C2×#135—1491no—
86C2×M32—1491no—
87C2×#108—1491no—
88#359—1494no—
89C2×#41—2981no—
90#135—2981no—
91#135—2981no—
92#135—1492no—
93#135—1492no—
94C2×Q16#1059701011yescharacteristic
95C2×SD16—2981no—
96C2×D8—1491no—
97C2×M16—2981no—
98C22×C8—1491no—
99M32—2981no—
100M32—2981no—
101C2×C16—1492no—
102#108—2981no—
103#108—1492no—
104#41—2982no—
105#41—2982no—
106#41—5961no—
107#41—5961no—
108C2×Q8—21no—
109C2×D4—2981no—
110C2×D4—5961no—
111C22×C4—5961no—
112C22×C4—1491no—
113Q16—21no—
114Q16C2×#1059701012yes—
115SD16—2982no—
116SD16—2982no—
117D8—2981no—
118D8—1492no—
119M16—2982no—
120M16—5961no—
121C2×C8—5961no—
122C2×C8—1491no—
123C2×C8—1491no—
124C2×C8—1491no—
125C2×C8—1491no—
126C2×C8—1491no—
127C2×C8C2×#1059701011yescharacteristic
128C16—2982no—
129C23—5961no—
130C23—1491no—
131Q8—22no—
132Q8—41no—
133D4—2982no—
134D4—5962no—
135D4—5962no—
136D4—5961no—
137C2×C4—41no—
138C2×C4—5962no—
139C2×C4—5962no—
140C2×C4—1491no—
141C2×C4—1491no—
142C2×C4—1491no—
143C2×C4—1491no—
144C2×C4—1491no—
145C2×C4C22⋊#1059701011yescharacteristic
146C8—5962no—
147C8—1491no—
148C8—1491no—
149C8C22⋊#1059701011yescharacteristic
150C8C22×#1059701011yescharacteristic
151C22—5961no—
152C22—5962no—
153C22—1491no—
154C22—1491no—
155C22—11922no—
156C22#1801197311yescharacteristic
157C4—42no—
158C4—1491no—
159C4—1491no—
160C4#1801197311yescharacteristic
161C4C2×C22⋊#1059701011yescharacteristic
162C2—21no—
163C2—2981no—
164C2—2981no—
165C2—11922no—
166C2C2×#1801197311yescharacteristic
subgroupG/H
centerC2C2×#18011973
commutatorC8×C149C22×C4
FrattiniC8C22×#10597010
FittingC2×Q16×C149C4
socleC2×C149C2×#102
prime radicalC2×#18011934C2
cosocleC8×D149C23
hypercenterC2×Q16#10597010
hypocenterC149#2143
LCSG ▷ C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. D149⋊M32C2semidirect
2. D149⋊#108C2semidirect
3. #23750540C2semidirect
8. D149⋊C16C22semidirect
9. #18011982C22semidirect
83. C149#2143semidirect

Maximal subgroups

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

subgroupindex
D149⋊M322
D149⋊#1082
#237505402
C2×#180119342
#2143149