Finite Group Databasebeta

← SD32×D21 #13056550

Subgroups — SD32×D21 #13056550

Order 1344.

180 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 49 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
1Q16×D21C211yesmaximal, characteristic, complemented
2D8×D21C211yesmaximal, characteristic
3C3×C7×SD32C211yesmaximal, characteristic, complemented
4#10620667C211yesmaximal, characteristic, complemented
5#10620666C211yesmaximal, characteristic, complemented
6#10620639C211yesmaximal, characteristic, complemented
7C16×D21C211yesmaximal, characteristic, complemented
8D7×SD32—31nomaximal, Hall
9Q8×D21—21no—
10D4×D21—21no—
11C3×C7×Q16C2211yescharacteristic, complemented
12C3×C7×D8C2211yescharacteristic
13#66635—21no—
14#66632—21no—
15Dic84C2211yescharacteristic, complemented
16D168C2211yescharacteristic
17C8×D21C2211yescharacteristic
18C3×C7×C16C2211yescharacteristic, complemented
19C3⋊(C7⋊C16)C2211yescharacteristic, complemented
20D7×Q16—31no—
21D7×D8—31no—
22C7×SD32D311yescharacteristic, complemented
23#6402—31no—
24#6401—31no—
25#6374—31no—
26D7×C16—31no—
27D3×SD32—71nomaximal, Hall
28C22×D21—41no—
29C3×C7×Q8—21no—
30C3×C7×D4—21no—
31#4268—41no—
32D84—21no—
33C4×D21—41no—
34C4×D21D411yescharacteristic
35Dic42—21no—
36Dic42—41no—
37C3×C7×C8C2311yescharacteristic
38C3⋊(C7⋊C8)D411yescharacteristic
39Q8×D7—61no—
40D4×D7—61no—
41C7×Q16C2×D311yescharacteristic, complemented
42C7×D8C2×D311yescharacteristic
43#1144—61no—
44#1141—61no—
45Dic28—31no—
46D56—31no—
47C8×D7—31no—
48C7×C16C2×D311yescharacteristic, complemented
49C7⋊C16—31no—
50D3×Q16—71no—
51D3×D8—71no—
52C3×SD32D711yescharacteristic, complemented
53#828—71no—
54#827—71no—
55#800—71no—
56D3×C16—71no—
57C22×C3×C7—41no—
58C2×D21—41no—
59C2×D21—82no—
60C2×D21D811yescharacteristic
61C3×C4×C7—41no—
62C3×C4×C7C2×D411yescharacteristic
63Dic21—41no—
64Dic21D811yescharacteristic
65C2×SD32—211noSylow
66C22×D7—121no—
67C7×Q8—21no—
68C7×D4—21no—
69C22⋊D7—121no—
70D28—61no—
71C4×D7—31no—
72C4×D7—121no—
73Dic14—61no—
74Dic14—121no—
75C7×C8C22×D311yescharacteristic
76C7⋊C8—31no—
77D3×Q8—141no—
78D3×D4—141no—
79C3×Q16C2×D711yescharacteristic, complemented
80C3×D8C2×D711yescharacteristic
81#216—141no—
82#213—141no—
83Dic12—71no—
84D24—71no—
85D3×C8—71no—
86C3×C16C2×D711yescharacteristic, complemented
87C3⋊C16—71no—
88C2×C3×C7—81no—
89C2×C3×C7C2×D811yescharacteristic
90D21—81no—
91D21SD3212yesdirect product factor
92C2×Q16—211no—
93C2×D8—211no—
94SD32—211no—
95SD32—211no—
96SD32—211no—
97SD32D2111yescharacteristic, direct product factor
98C2×C16—211no—
99C22×C7—41no—
100C2×D7—31no—
101C2×D7—121no—
102C2×D7—242no—
103C4×C7—41no—
104C4×C7D3×D411yescharacteristic
105Dic7—31no—
106Dic7—121no—
107C22×D3—281no—
108C3×Q8—21no—
109C3×D4—21no—
110#67—281no—
111D12—141no—
112C4×D3—71no—
113C4×D3—281no—
114Dic6—141no—
115Dic6—281no—
116C3×C8C22×D711yescharacteristic
117C3⋊C8—71no—
118C3×C7C2×SD3211yescharacteristic, complemented, Hall
119C2×Q8—421no—
120C2×D4—421no—
121Q16—211no—
122Q16—421no—
123Q16C2×D2111yescharacteristic, complemented
124D8—211no—
125D8—421no—
126D8C2×D2111yescharacteristic
127C2×C8—211no—
128C16—211no—
129C16C2×D2111yescharacteristic, complemented
130C2×C7—81no—
131C2×C7D3×D811yescharacteristic
132D7—32no—
133D7—241no—
134C22×C3—41no—
135C2×D3—71no—
136C2×D3—281no—
137C2×D3—562no—
138C3×C4—41no—
139C3×C4D4×D711yescharacteristic
140Dic3—71no—
141Dic3—281no—
142C23—841no—
143Q8—21no—
144Q8—421no—
145Q8—841no—
146D4—21no—
147D4—421no—
148D4—841no—
149C2×C4—211no—
150C2×C4—841no—
151C8—211no—
152C8C22×D2111yescharacteristic
153C7D3×SD3211yescharacteristic, complemented, Sylow
154C2×C3—81no—
155C2×C3D7×D811yescharacteristic
156D3—72no—
157D3—561no—
158C22—41no—
159C22—211no—
160C22—841no—
161C22—1682no—
162C4—41no—
163C4—211no—
164C4—841no—
165C4D4×D2111yescharacteristic
166C3D7×SD3211yescharacteristic, complemented, Sylow
167C2—81no—
168C2—212no—
169C2—1681no—
170C2D8×D2111yescharacteristic
subgroupG/H
centerC2D8×D21
commutator, cosocleC3×C7×C8C23
FrattiniC8C22×D21
FittingC3×C7×SD32C2
socleC2×C3×C7C2×D8
prime radicalD8×D21C2
hypercenterSD32D21
hypocenterC3×C7C2×SD32
LCSG ▷ C3×C7×C8 ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. Q16×D21C2semidirect
3. C3×C7×SD32C2semidirect
4. #10620667C2semidirect
5. #10620666C2semidirect
6. #10620639C2semidirect
7. C16×D21C2semidirect
11. C3×C7×Q16C22semidirect
15. Dic84C22semidirect
18. C3×C7×C16C22semidirect
19. C3⋊(C7⋊C16)C22semidirect
22. C7×SD32D3semidirect
41. C7×Q16C2×D3semidirect
48. C7×C16C2×D3semidirect
52. C3×SD32D7semidirect
79. C3×Q16C2×D7semidirect
86. C3×C16C2×D7semidirect
91. D21SD32direct (N × H)
97. SD32D21direct (N × H)
118. C3×C7C2×SD32semidirect
123. Q16C2×D21semidirect
129. C16C2×D21semidirect
153. C7D3×SD32semidirect
166. C3D7×SD32semidirect

Maximal subgroups

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

subgroupindex
Q16×D212
D8×D212
C3×C7×SD322
#106206672
#106206662
#106206392
C16×D212
D7×SD323
D3×SD327