Finite Group Databasebeta

← #23776283

Subgroups — #23776283

Order 10112.

336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 133 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#19099293C212yesmaximal
2#19098967C212yesmaximal
3#19098857C214yesmaximal
4#19098855C212yesmaximal
5C8×Dic158C211yesmaximal, characteristic
6C4×Dic316C211yesmaximal, characteristic
7#19098657C212yesmaximal
8#500×C79C211yesmaximal, characteristic
9C2×Dic316C2211yescharacteristic
10#14579160—22no—
11#14579160C2214yes—
12#14579159—24no—
13C4×Dic158C2212yes—
14C4×Dic158C2211yescharacteristic
15#14579126—22no—
16#14579126C2214yes—
17#14579095C2211yescharacteristic
18#14579094C2214yes—
19C4⋊(C79⋊C8)C2211yescharacteristic
20Dic79⋊C8C2212yes—
21#14579086C2212yes—
22#14579084C2214yes—
23C8×Dic79C2212yes—
24C4⋊Q8×C79C2212yes—
25#107×C79C2212yes—
26#107×C79C2212yes—
27C4×C8×C79C2211yescharacteristic
28C2×Dic158—24no—
29C2×Dic158D411yescharacteristic
30C2×Dic158C2312yes—
31Dic316Q814yescomplemented
32C2×C79⋊C8C2312yes—
33C4⋊Dic79D411yescharacteristic
34C4⋊Dic79C2312yes—
35Dic79⋊C4—24no—
36Dic79⋊C4—24no—
37Dic79⋊C4—22no—
38Dic79⋊C4D412yes—
39C4×Dic79—24no—
40C4×Dic79—22no—
41C4×Dic79C2312yes—
42C2×Q8×C79—22no—
43C2×C8×C79C2311yescharacteristic
44C2×C8×C79C2311yescharacteristic
45C4⋊C4×C79—22no—
46C4⋊C4×C79C2314yes—
47C42×C79C2311yescharacteristic
48Q8×C79—82no—
49C2×C4×C79—24no—
50C2×C4×C79C2×D411yescharacteristic
51C2×C4×C79C2×D411yescharacteristic
52C2×C4×C79C2411yescharacteristic
53C2×Dic79—22no—
54C2×Dic79—22no—
55C2×Dic79C2×D412yes—
56C2×Dic79C2×D412yes—
57Dic158—22no—
58Dic158—84no—
59Dic158Q1614yescomplemented
60Dic158C2×Q814yes—
61C8×C79—21no—
62C8×C79C2×Q812yes—
63C79⋊C8—22no—
64C22×C79C22×D411yescharacteristic
65C4×C79—21no—
66C4×C79—44no—
67C4×C79C2×Q1612yes—
68C4×C79C22×Q811yescharacteristic
69C4×C792−1+411yescharacteristic
70Dic79—24no—
71Dic79—22no—
72Dic79—42no—
73Dic79C2×Q1614yes—
74C2×C79D4×Q811yescharacteristic
75C2×C79C22×Q1611yescharacteristic
76C2×C79#57611yescharacteristic
77Q8×Q16—791nomaximal, Sylow
78C79Q8×Q1611yescharacteristic, complemented, Sylow
79Q82—792no—
80#500—792no—
81#500D7911yescharacteristic
82#477—792no—
83#477—794no—
84C8×Q8—791no—
85C4×Q16—792no—
86C4×Q16—791no—
87C2×Q16—791no—
88C4⋊Q8—794no—
89C4⋊Q8—1582no—
90C4⋊Q8—1584no—
91C4⋊Q8C2×D7912yes—
92C4×Q8—791no—
93C4×Q8—794no—
94C4×Q8—792no—
95C4×Q8—1582no—
96#107—791no—
97#107—794no—
98#107C2×D7912yes—
99#107C2×D7912yes—
100C4⋊C8—792no—
101C4⋊C8—791no—
102#103—792no—
103#103—794no—
104C4×C8—792no—
105C4×C8C2×D7911yescharacteristic
106C2×Q8—22no—
107C2×Q8—791no—
108C2×Q8—792no—
109C2×Q8—1584no—
110Q16—794no—
111C2×C8—792no—
112C2×C8C22×D7911yescharacteristic
113C2×C8C22×D7911yescharacteristic
114C4⋊C4—22no—
115C4⋊C4—792no—
116C4⋊C4—791no—
117C4⋊C4—792no—
118C4⋊C4—1584no—
119C4⋊C4—1584no—
120C4⋊C4—1582no—
121C4⋊C4C22×D7914yes—
122C42—792no—
123C42—1584no—
124C42—1582no—
125C42C22×D7911yescharacteristic
126Q8—82no—
127Q8—794no—
128Q8—794no—
129Q8—6324no—
130Q8—1582no—
131C2×C4—24no—
132C2×C4—792no—
133C2×C4—792no—
134C2×C4—1582no—
135C2×C4—1582no—
136C2×C4D4×D7911yescharacteristic
137C2×C4D4×D7911yescharacteristic
138C2×C4C23×D7911yescharacteristic
139C8—21no—
140C8—1582no—
141C8Q8×D7912yes—
142C22C2×D4×D7911yescharacteristic
143C4—21no—
144C4—44no—
145C4—3162no—
146C4—794no—
147C4—1584no—
148C4—1582no—
149C4Q16×D7912yes—
150C4C2×Q8×D7911yescharacteristic
151C4#1457920911yescharacteristic
152C2#1909922811yescharacteristic
153C2C2×Q16×D7911yescharacteristic
154C2#1909936411yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#500×C79C2
socle, prime radicalC22×C79C22×D4
hypercenter#500D79
hypocenterC79Q8×Q16
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
31. Dic316Q8semidirect
59. Dic158Q16semidirect
78. C79Q8×Q16semidirect