Finite Group Databasebeta

← #28376169

Subgroups — #28376169

Order 13952.

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#20295827C212yesmaximal, complemented
2#20295462C212yesmaximal, complemented
3#20295460C214yesmaximal, complemented
4#20295458C211yesmaximal, characteristic, complemented
5#20295455C212yesmaximal, complemented
6D16×D109C212yesmaximal, complemented
7#20295442C211yesmaximal, characteristic, complemented
8C2×D16×C109C211yesmaximal, characteristic, complemented
9#16812744—22no—
10#16812725—22no—
11#16812723—24no—
12#16812721C2212yescomplemented
13#16812718C2214yescomplemented
14D8×D109C2214yescomplemented
15#16812705C2211yescharacteristic
16Dic872C2211yescharacteristic, complemented
17#16812644C2212yescomplemented
18#16812643C2214yescomplemented
19D1744C2211yescharacteristic, complemented
20#16812640C2214yescomplemented
21#16812639C2211yescharacteristic, complemented
22#16812638C2212yescomplemented
23C16×D109C2212yescomplemented
24C2×D8×C109C2212yescomplemented
25D16×C109C2212yescomplemented
26D16×C109C2212yescomplemented
27C2×C16×C109C2211yescharacteristic, complemented
28#13182029—22no—
29#13182029D411yescharacteristic
30#13182028—24no—
31#13182028—42no—
32C2×C22⋊D109—44no—
33D4×D109—24no—
34D4×D109—42no—
35Dic436C2312yes—
36#13182018—22no—
37#13182017—24no—
38D872C2312yes—
39#13182014—24no—
40#13182013D411yescharacteristic
41#13182012D412yes—
42C8×D109C2312yes—
43#13182004C2312yes—
44C2×D4×C109—22no—
45D8×C109—22no—
46D8×C109C2314yes—
47C2×C8×C109C2311yescharacteristic
48C16×C109C2311yescharacteristic
49C16×C109C2311yescharacteristic
50C23×C109—42no—
51C22×D109—44no—
52D4×C109—24no—
53D4×C109—42no—
54C2×C4×C109C2×D411yescharacteristic
55C22⋊D109—42no—
56C22⋊D109—44no—
57C22⋊D109—44no—
58C22⋊D109D812yes—
59C2×Dic109—44no—
60D436—22no—
61D436D811yescharacteristic
62C4×D109—42no—
63C4×D109C2×D412yes—
64Dic218—22no—
65Dic218D811yescharacteristic
66C8×C109C2×D411yescharacteristic
67C8×C109C2411yescharacteristic
68#11724784C2×D412yes—
69C22×C109—44no—
70C22×C109—162no—
71C22×C109C2×D811yescharacteristic
72C2×D109—42no—
73C2×D109—164no—
74C2×D109C2×D812yes—
75C4×C109C2×D811yescharacteristic
76C4×C109C22×D411yescharacteristic
77Dic109—42no—
78Dic109C2×D812yes—
79C2×C109—21no—
80C2×C109—84no—
81C2×C109C22×D811yescharacteristic
82D109—22no—
83D109—82no—
84#3415—1091nomaximal, Sylow
85C109#341511yescharacteristic, complemented, Sylow
86#576—1092no—
87#509—1092no—
88#509—1094no—
89#508—1092no—
90#508—1091no—
91C2×D16—1092no—
92C2×D16D10911yescharacteristic, complemented
93#504—1091no—
94H(5,𝔽2)—2182no—
95AGL(1,ℤ/8)—2184no—
96AGL(1,ℤ/8)—2182no—
97#135—1094no—
98#135—1092no—
99C2×D8—1094no—
100C2×D8C2×D10912yescomplemented
101#131—1091no—
102Q32—1091no—
103SD32—1094no—
104SD32—1092no—
105D16—1094no—
106D16—1091no—
107D16C2×D10912yescomplemented
108D16C2×D10912yescomplemented
109M32—1091no—
110M32—1092no—
111C2×C16—1092no—
112C2×C16C2×D10911yescharacteristic, complemented
113#41—1091no—
114#41—4362no—
115#41—2184no—
116#41—2182no—
117C2×D4—22no—
118C2×D4—4362no—
119C2×D4—4364no—
120C2×D4—2184no—
121Q16—1092no—
122SD16—2184no—
123SD16—2182no—
124D8—22no—
125D8—1092no—
126D8—2184no—
127D8C22×D10914yes—
128M16—1091no—
129M16—1092no—
130C2×C8—1092no—
131C2×C8C22×D10911yescharacteristic
132C16—1092no—
133C16C22×D10911yescharacteristic
134C16C22×D10911yescharacteristic
135C23—42no—
136C23—4364no—
137Q8—1091no—
138Q8—2182no—
139D4—24no—
140D4—42no—
141D4—1092no—
142D4—1091no—
143D4—4364no—
144D4—4364no—
145D4—4362no—
146D4—2182no—
147C2×C4—1092no—
148C2×C4—4364no—
149C2×C4—4362no—
150C2×C4D4×D10911yescharacteristic
151C8—1092no—
152C8D4×D10911yescharacteristic
153C8C23×D10911yescharacteristic
154C22—44no—
155C22—162no—
156C22—1092no—
157C22—4362no—
158C22—17444no—
159C22D8×D10911yescharacteristic
160C4—1092no—
161C4—4362no—
162C4D8×D10911yescharacteristic
163C4C2×D4×D10911yescharacteristic
164C2—21no—
165C2—84no—
166C2—8722no—
167C2—2182no—
168C2C2×D8×D10911yescharacteristic
subgroupG/H
centerC2C2×D8×D109
commutator, cosocleC8×C109C24
FrattiniC8C23×D109
FittingC2×D16×C109C2
socleC2×C109C22×D8
hypercenterC2×D16D109
hypocenterC109#3415
LCSG ▷ C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #20295827C2semidirect
2. #20295462C2semidirect
3. #20295460C2semidirect
4. #20295458C2semidirect
5. #20295455C2semidirect
6. D16×D109C2semidirect
7. #20295442C2semidirect
8. C2×D16×C109C2semidirect
12. #16812721C22semidirect
13. #16812718C22semidirect
14. D8×D109C22semidirect
16. Dic872C22semidirect
17. #16812644C22semidirect
18. #16812643C22semidirect
19. D1744C22semidirect
20. #16812640C22semidirect
21. #16812639C22semidirect
22. #16812638C22semidirect
23. C16×D109C22semidirect
24. C2×D8×C109C22semidirect
25. D16×C109C22semidirect
26. D16×C109C22semidirect
27. C2×C16×C109C22semidirect
85. C109#3415semidirect
92. C2×D16D109semidirect
100. C2×D8C2×D109semidirect
107. D16C2×D109semidirect
108. D16C2×D109semidirect
112. C2×C16C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202958272
#202954622
#202954602
#202954582
#202954552
D16×D1092
#202954422
C2×D16×C1092
#3415109