Finite Group Databasebeta

← #23762654

Subgroups — #23762654

Order 10112.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#19099283C211yesmaximal, characteristic
2#19098966C211yesmaximal, characteristic, complemented
3#19098845C211yesmaximal, characteristic, complemented
4#19098310C211yesmaximal, characteristic, complemented
5#19098293C211yesmaximal, characteristic, complemented
6D4⋊(C79⋊C8)C211yesmaximal, characteristic
7#461×C79C211yesmaximal, characteristic
8#14579161C2211yescharacteristic
9#14579154—22no—
10#14579148—21no—
11#14579140—21no—
12C4×Dic158C2211yescharacteristic
13#14579126—21no—
14#14579120—21no—
15#14579094—22no—
16#14579092—21no—
17C4⋊(C79⋊C8)C2211yescharacteristic
18#14579084—21no—
19C4×C79⋊C8C2211yescharacteristic
20C2×SD16×C79—21no—
21C4⋊Q8×C79C2211yescharacteristic
22C4×D4×C79C2211yescharacteristic
23C4⋊C8×C79C2211yescharacteristic
24#103×C79—21no—
25C2×Dic158—21no—
26C2×Dic158D411yescharacteristic
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C4⋊Dic79—21no—
30C4⋊Dic79D411yescharacteristic
31C4⋊Dic79D412yes—
32Dic79⋊C4—22no—
33Dic79⋊C4—21no—
34C22⋊Dic79—22no—
35C22⋊Dic79—22no—
36C4×Dic79—22no—
37C4×Dic79—21no—
38C2×Q8×C79—21no—
39C2×D4×C79D411yescharacteristic
40C22×C4×C79—21no—
41SD16×C79—42no—
42C2×C8×C79—21no—
43C4⋊C4×C79—21no—
44C4⋊C4×C79—21no—
45C4⋊C4×C79D411yescharacteristic
46C22⋊C4×C79—21no—
47C42×C79C2311yescharacteristic
48C23×C79—21no—
49Q8×C79—41no—
50Q8×C79—41no—
51D4×C79—21no—
52D4×C79—21no—
53C2×C4×C79—21no—
54C2×C4×C79—41no—
55C2×C4×C79—41no—
56C2×C4×C79—41no—
57C2×C4×C79C2×D411yescharacteristic
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C2×Dic79—21no—
61C2×Dic79—21no—
62C2×Dic79—22no—
63Dic158—21no—
64Dic158—21no—
65Dic158—41no—
66Dic158—41no—
67C8×C79—41no—
68C79⋊C8—22no—
69C79⋊C8—41no—
70C22×C79—41no—
71C22×C79—41no—
72C22×C79—41no—
73C22×C79#12011yescharacteristic
74C4×C79—21no—
75C4×C79—41no—
76C4×C79—81no—
77C4×C79#13511yescharacteristic
78C4×C79#13511yescharacteristic
79C4×C79AGL(1,ℤ/8)11yescharacteristic
80C4×C79#13711yescharacteristic
81Dic79—42no—
82Dic79—41no—
83Dic79—41no—
84C2×C79—81no—
85C2×C79#44911yescharacteristic
86C2×C79#45211yescharacteristic
87C2×C79#45611yescharacteristic
88#1650—791nomaximal, Sylow
89C79#165011yescharacteristic, complemented, Sylow
90#556—791no—
91#500—791no—
92#475—791no—
93#461D7911yescharacteristic
94#332—791no—
95Q8⋊C8—791no—
96D4⋊C8—791no—
97C2×SD16—21no—
98C4⋊Q8—791no—
99C4⋊Q8C2×D7911yescharacteristic
100#126—1582no—
101#124—1581no—
102C22⋊Q8—1581no—
103C4×Q8—791no—
104C4×Q8—1581no—
105C4×D4C2×D7911yescharacteristic
106#117—1581no—
107#107—1582no—
108#106—1581no—
109C4⋊C8—791no—
110C4⋊C8C2×D7911yescharacteristic
111#103—21no—
112#103—1581no—
113C4×C8—791no—
114C2×Q8—21no—
115C2×Q8—791no—
116C2×Q8—1581no—
117C2×D4C22⋊D7911yescharacteristic
118C22×C4—21no—
119SD16—42no—
120C2×C8—21no—
121C2×C8—1581no—
122C2×C8—1581no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—791no—
126C4⋊C4—792no—
127C4⋊C4—1582no—
128C4⋊C4—1581no—
129C4⋊C4—1581no—
130C4⋊C4C22⋊D7911yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—1582no—
133C22⋊C4—1582no—
134C42—1582no—
135C42—1581no—
136C42C22×D7911yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—3161no—
141Q8—3161no—
142Q8—1581no—
143Q8—1581no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—1581no—
151C2×C4—1582no—
152C2×C4—1581no—
153C2×C4D4×D7911yescharacteristic
154C2×C4D4×D7911yescharacteristic
155C2×C4C2×C22⋊D7911yescharacteristic
156C8—41no—
157C8—3161no—
158C8—1582no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1457912911yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—3162no—
167C4—3161no—
168C4—3161no—
169C4#1457918111yescharacteristic
170C4#1457918211yescharacteristic
171C4#1457918711yescharacteristic
172C4#1457919011yescharacteristic
173C2—81no—
174C2#1909870611yescharacteristic
175C2#1909872211yescharacteristic
176C2#1909874411yescharacteristic
subgroupG/H
centerC22#14579129
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#461×C79C2
socleC22×C79#120
prime radicalC2×D4×C79D4
hypercenter#461D79
hypocenterC79#1650
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #19098966C2semidirect
3. #19098845C2semidirect
4. #19098310C2semidirect
5. #19098293C2semidirect
89. C79#1650semidirect