Finite Group Databasebeta

← #34057829

Subgroups — #34057829

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#23750427C212yesmaximal, complemented
2#23750062C214yesmaximal, complemented
3#23750060C212yesmaximal, complemented
4#23750058C212yesmaximal, complemented
5C2×D2384C211yesmaximal, characteristic, complemented
6D16×D149C212yesmaximal, complemented
7#23750041C211yesmaximal, characteristic, complemented
8#508×C149C211yesmaximal, characteristic, complemented
9#18011957—22no—
10#18011938—24no—
11#18011936—22no—
12#18011934C2214yescomplemented
13C2×D1192C2212yescomplemented
14D8×D149C2214yescomplemented
15#18011917C2211yescharacteristic
16#18011854C2214yescomplemented
17D2384C2212yescomplemented
18D2384C2212yescomplemented
19#18011852C2214yescomplemented
20#18011851C2211yescharacteristic, complemented
21#18011850C2212yescomplemented
22C16×D149C2212yescomplemented
23#135×C149C2212yescomplemented
24Q32×C149C2211yescharacteristic, complemented
25SD32×C149C2212yescomplemented
26D16×C149C2211yescharacteristic, complemented
27C2×C16×C149C2211yescharacteristic, complemented
28#14558737—24no—
29#14558736—42no—
30#14558736D411yescharacteristic
31C2×D596—22no—
32C2×D596—42no—
33D4×D149—24no—
34D4×D149—44no—
35#14558723—24no—
36D1192—22no—
37D1192C2314yes—
38#14558721—24no—
39#14558720D411yescharacteristic
40#14558719D412yes—
41C8×D149C2312yes—
42#14558711C2312yes—
43#41×C149—22no—
44Q16×C149C2312yes—
45SD16×C149—22no—
46D8×C149C2312yes—
47C2×C8×C149C2311yescharacteristic
48C16×C149C2311yescharacteristic
49C16×C149C2311yescharacteristic
50C22×D149—42no—
51C22×D149—44no—
52Dic298D811yescharacteristic
53D596—24no—
54D596—44no—
55D596—42no—
56D596D811yescharacteristic
57C22⋊D149—44no—
58C22⋊D149D812yes—
59C4×D149—44no—
60C4×D149C2×D412yes—
61#11924746C2×D412yes—
62Q8×C149—22no—
63D4×C149—22no—
64D4×C149—42no—
65C2×C4×C149—42no—
66C2×C4×C149C2×D411yescharacteristic
67C8×C149C2×D411yescharacteristic
68C8×C149C2411yescharacteristic
69C22×C149—42no—
70C22×C149C2×D811yescharacteristic
71C2×D149—44no—
72C2×D149—164no—
73C2×D149—162no—
74C2×D149C2×D812yes—
75C4×C149—42no—
76C4×C149C2×D811yescharacteristic
77C4×C149C22×D411yescharacteristic
78Dic149C2×D812yes—
79C2×C149—21no—
80C2×C149—82no—
81C2×C149C22×D811yescharacteristic
82D149—22no—
83D149—84no—
84C149#341511yescharacteristic, complemented, Sylow
85#3415—1491nomaximal, Sylow
86#576—1492no—
87#509—1492no—
88#509—1494no—
89#508—1492no—
90#508D14911yescharacteristic, complemented
91C2×D16—1492no—
92C2×D16—1491no—
93#504—1491no—
94H(5,𝔽2)—2982no—
95AGL(1,ℤ/8)—2984no—
96AGL(1,ℤ/8)—2982no—
97#135—1494no—
98#135C2×D14912yescomplemented
99C2×D8—1494no—
100C2×D8—1492no—
101#131—1491no—
102Q32C2×D14911yescharacteristic, complemented
103SD32—1494no—
104SD32C2×D14912yescomplemented
105D16—1494no—
106D16—1492no—
107D16—1492no—
108D16C2×D14911yescharacteristic, complemented
109M32—1491no—
110M32—1492no—
111C2×C16—1492no—
112C2×C16C2×D14911yescharacteristic, complemented
113#41—22no—
114#41—2984no—
115#41—5962no—
116#41—1491no—
117C2×D4—2984no—
118C2×D4—2982no—
119C2×D4—5962no—
120C2×D4—5964no—
121Q16C22×D14912yes—
122SD16—22no—
123SD16—2984no—
124D8—2984no—
125D8—2982no—
126D8—1494no—
127D8C22×D14912yes—
128M16—1491no—
129M16—1492no—
130C2×C8—1492no—
131C2×C8C22×D14911yescharacteristic
132C16—1492no—
133C16C22×D14911yescharacteristic
134C16C22×D14911yescharacteristic
135C23—5964no—
136C23—5962no—
137Q8—22no—
138Q8—1491no—
139D4—22no—
140D4—42no—
141D4—2984no—
142D4—5964no—
143D4—5964no—
144D4—5962no—
145D4—1492no—
146D4—1491no—
147C2×C4—42no—
148C2×C4—5964no—
149C2×C4—1492no—
150C2×C4D4×D14911yescharacteristic
151C8—1492no—
152C8D4×D14911yescharacteristic
153C8C23×D14911yescharacteristic
154C22—42no—
155C22—23842no—
156C22—23844no—
157C22—5964no—
158C22—1492no—
159C22D8×D14911yescharacteristic
160C4—42no—
161C4—1492no—
162C4D8×D14911yescharacteristic
163C4C2×D4×D14911yescharacteristic
164C2—21no—
165C2—82no—
166C2—2982no—
167C2—11924no—
168C2C2×D8×D14911yescharacteristic
subgroupG/H
centerC2C2×D8×D149
commutator, cosocleC8×C149C24
FrattiniC8C23×D149
Fitting#508×C149C2
socleC2×C149C22×D8
hypercenter#508D149
hypocenterC149#3415
LCSG ▷ C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #23750427C2semidirect
2. #23750062C2semidirect
3. #23750060C2semidirect
4. #23750058C2semidirect
5. C2×D2384C2semidirect
6. D16×D149C2semidirect
7. #23750041C2semidirect
8. #508×C149C2semidirect
12. #18011934C22semidirect
13. C2×D1192C22semidirect
14. D8×D149C22semidirect
16. #18011854C22semidirect
17. D2384C22semidirect
18. D2384C22semidirect
19. #18011852C22semidirect
20. #18011851C22semidirect
21. #18011850C22semidirect
22. C16×D149C22semidirect
23. #135×C149C22semidirect
24. Q32×C149C22semidirect
25. SD32×C149C22semidirect
26. D16×C149C22semidirect
27. C2×C16×C149C22semidirect
84. C149#3415semidirect
90. #508D149semidirect
98. #135C2×D149semidirect
102. Q32C2×D149semidirect
104. SD32C2×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
#237504272
#237500622
#237500602
#237500582
C2×D23842
D16×D1492
#237500412
#508×C1492
#3415149