Finite Group Databasebeta

← #34057828

Subgroups — #34057828

Order 19072.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#23750426C212yesmaximal, complemented
2#23750061C212yesmaximal, complemented
3#23750059C214yesmaximal, complemented
4#23750057C211yesmaximal, characteristic, complemented
5#23750054C212yesmaximal, complemented
6D16×D149C212yesmaximal, complemented
7#23750041C211yesmaximal, characteristic, complemented
8C2×D16×C149C211yesmaximal, characteristic, complemented
9#18011956—22no—
10#18011937—22no—
11#18011935—24no—
12#18011933C2212yescomplemented
13#18011930C2214yescomplemented
14D8×D149C2214yescomplemented
15#18011917C2211yescharacteristic
16Dic1192C2211yescharacteristic, complemented
17#18011856C2212yescomplemented
18#18011855C2214yescomplemented
19D2384C2211yescharacteristic, complemented
20#18011852C2214yescomplemented
21#18011851C2211yescharacteristic, complemented
22#18011850C2212yescomplemented
23C16×D149C2212yescomplemented
24C2×D8×C149C2212yescomplemented
25D16×C149C2212yescomplemented
26D16×C149C2212yescomplemented
27C2×C16×C149C2211yescharacteristic, complemented
28#14558736—22no—
29#14558736D411yescharacteristic
30#14558735—24no—
31#14558735—42no—
32C2×C22⋊D149—44no—
33D4×D149—24no—
34D4×D149—42no—
35Dic596C2312yes—
36#14558725—22no—
37#14558724—24no—
38D1192C2312yes—
39#14558721—24no—
40#14558720D411yescharacteristic
41#14558719D412yes—
42C8×D149C2312yes—
43#14558711C2312yes—
44C2×D4×C149—22no—
45D8×C149—22no—
46D8×C149C2314yes—
47C2×C8×C149C2311yescharacteristic
48C16×C149C2311yescharacteristic
49C16×C149C2311yescharacteristic
50C22×D149—44no—
51Dic298—22no—
52Dic298D811yescharacteristic
53D596—22no—
54D596D811yescharacteristic
55C22⋊D149—42no—
56C22⋊D149—44no—
57C22⋊D149—44no—
58C22⋊D149D812yes—
59C2×Dic149—44no—
60C4×D149—42no—
61C4×D149C2×D412yes—
62#11924746C2×D412yes—
63C23×C149—42no—
64D4×C149—24no—
65D4×C149—42no—
66C2×C4×C149C2×D411yescharacteristic
67C8×C149C2×D411yescharacteristic
68C8×C149C2411yescharacteristic
69C22×C149—44no—
70C22×C149—162no—
71C22×C149C2×D811yescharacteristic
72C2×D149—42no—
73C2×D149—164no—
74C2×D149C2×D812yes—
75C4×C149C2×D811yescharacteristic
76C4×C149C22×D411yescharacteristic
77Dic149—42no—
78Dic149C2×D812yes—
79C2×C149—21no—
80C2×C149—84no—
81C2×C149C22×D811yescharacteristic
82D149—22no—
83D149—82no—
84C149#341511yescharacteristic, complemented, Sylow
85#3415—1491nomaximal, Sylow
86#576—1492no—
87#509—1492no—
88#509—1494no—
89#508—1492no—
90#508—1491no—
91C2×D16—1492no—
92C2×D16D14911yescharacteristic, complemented
93#504—1491no—
94H(5,𝔽2)—2982no—
95AGL(1,ℤ/8)—2984no—
96AGL(1,ℤ/8)—2982no—
97#135—1494no—
98#135—1492no—
99C2×D8—1494no—
100C2×D8C2×D14912yescomplemented
101#131—1491no—
102Q32—1491no—
103SD32—1494no—
104SD32—1492no—
105D16—1494no—
106D16—1491no—
107D16C2×D14912yescomplemented
108D16C2×D14912yescomplemented
109M32—1491no—
110M32—1492no—
111C2×C16—1492no—
112C2×C16C2×D14911yescharacteristic, complemented
113#41—2984no—
114#41—2982no—
115#41—5962no—
116#41—1491no—
117C2×D4—22no—
118C2×D4—2984no—
119C2×D4—5962no—
120C2×D4—5964no—
121Q16—1492no—
122SD16—2984no—
123SD16—2982no—
124D8—22no—
125D8—2984no—
126D8—1492no—
127D8C22×D14914yes—
128M16—1491no—
129M16—1492no—
130C2×C8—1492no—
131C2×C8C22×D14911yescharacteristic
132C16—1492no—
133C16C22×D14911yescharacteristic
134C16C22×D14911yescharacteristic
135C23—42no—
136C23—5964no—
137Q8—2982no—
138Q8—1491no—
139D4—24no—
140D4—42no—
141D4—2982no—
142D4—5964no—
143D4—5962no—
144D4—5964no—
145D4—1492no—
146D4—1491no—
147C2×C4—5964no—
148C2×C4—5962no—
149C2×C4—1492no—
150C2×C4D4×D14911yescharacteristic
151C8—1492no—
152C8D4×D14911yescharacteristic
153C8C23×D14911yescharacteristic
154C22—44no—
155C22—162no—
156C22—23844no—
157C22—5962no—
158C22—1492no—
159C22D8×D14911yescharacteristic
160C4—5962no—
161C4—1492no—
162C4D8×D14911yescharacteristic
163C4C2×D4×D14911yescharacteristic
164C2—21no—
165C2—84no—
166C2—2982no—
167C2—11922no—
168C2C2×D8×D14911yescharacteristic
subgroupG/H
centerC2C2×D8×D149
commutator, cosocleC8×C149C24
FrattiniC8C23×D149
FittingC2×D16×C149C2
socleC2×C149C22×D8
hypercenterC2×D16D149
hypocenterC149#3415
LCSG ▷ C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #23750426C2semidirect
2. #23750061C2semidirect
3. #23750059C2semidirect
4. #23750057C2semidirect
5. #23750054C2semidirect
6. D16×D149C2semidirect
7. #23750041C2semidirect
8. C2×D16×C149C2semidirect
12. #18011933C22semidirect
13. #18011930C22semidirect
14. D8×D149C22semidirect
16. Dic1192C22semidirect
17. #18011856C22semidirect
18. #18011855C22semidirect
19. D2384C22semidirect
20. #18011852C22semidirect
21. #18011851C22semidirect
22. #18011850C22semidirect
23. C16×D149C22semidirect
24. C2×D8×C149C22semidirect
25. D16×C149C22semidirect
26. D16×C149C22semidirect
27. C2×C16×C149C22semidirect
84. C149#3415semidirect
92. C2×D16D149semidirect
100. C2×D8C2×D149semidirect
107. D16C2×D149semidirect
108. D16C2×D149semidirect
112. C2×C16C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504262
#237500612
#237500592
#237500572
#237500542
D16×D1492
#237500412
C2×D16×C1492
#3415149