Finite Group Databasebeta

← #23762737

Subgroups — #23762737

Order 10112.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#19099313C211yesmaximal, characteristic
2#19098972C211yesmaximal, characteristic, complemented
3#19098932C211yesmaximal, characteristic, complemented
4#19098922C211yesmaximal, characteristic
5#19098304C211yesmaximal, characteristic, complemented
6#19098304C211yesmaximal, characteristic, complemented
7#329×C79C211yesmaximal, characteristic
8#14579161C2211yescharacteristic
9#14579159—21no—
10#14579154—21no—
11#14579154—21no—
12#14579153C2211yescharacteristic
13#14579153C2211yescharacteristic
14#14579142—21no—
15#14579138—21no—
16#14579138—21no—
17#14579095—21no—
18#14579093—21no—
19#14579086—21no—
20#14579086—21no—
21#14579085—21no—
22#14579082—21no—
23#14579072C2211yescharacteristic
24#124×C79C2211yescharacteristic
25#97×C79C2211yescharacteristic
26#97×C79C2211yescharacteristic
27C2×Dic158—21no—
28C2×Dic158—21no—
29C22×Dic79—21no—
30C2×C79⋊C8—21no—
31C4⋊Dic79—21no—
32C4⋊Dic79—21no—
33C4⋊Dic79D411yescharacteristic
34C4⋊Dic79D411yescharacteristic
35C4⋊Dic79D411yescharacteristic
36C4⋊Dic79D411yescharacteristic
37Dic79⋊C4—21no—
38Dic79⋊C4—21no—
39Dic79⋊C4—21no—
40Dic79⋊C4—21no—
41Dic79⋊C4—21no—
42Dic79⋊C4—21no—
43C22⋊Dic79—21no—
44C22⋊Dic79—21no—
45C22⋊Dic79—21no—
46C4×Dic79—21no—
47C2×Q8×C79D411yescharacteristic
48C2×D4×C79D411yescharacteristic
49C2×C8×C79—21no—
50C2×C8×C79—21no—
51C22⋊C4×C79—21no—
52C22⋊C4×C79—21no—
53C42×C79C2311yescharacteristic
54C23×C79—21no—
55Q8×C79—41no—
56D4×C79—41no—
57C2×C4×C79—21no—
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79C2×D411yescharacteristic
61C2×Dic79—21no—
62C2×Dic79—21no—
63C2×Dic79—21no—
64C2×Dic79—21no—
65C2×Dic79—41no—
66C2×Dic79—81no—
67Dic158—42no—
68Dic158—81no—
69C8×C79—22no—
70C8×C79—41no—
71C79⋊C8—41no—
72C22×C79—41no—
73C22×C79—41no—
74C22×C79—41no—
75C22×C79#12011yescharacteristic
76C4×C79—21no—
77C4×C79—21no—
78C4×C79—21no—
79C4×C79—41no—
80Dic79—41no—
81Dic79—41no—
82Dic79—41no—
83Dic79—41no—
84Dic79—81no—
85C2×C79—81no—
86C2×C79#45411yescharacteristic
87C2×C79#45511yescharacteristic
88C2×C79#45611yescharacteristic
89#1664—791nomaximal, Sylow
90C79#166411yescharacteristic, complemented, Sylow
91#563—791no—
92#501—791no—
93#491—791no—
94#489—791no—
95#330—791no—
96#330—791no—
97#329D7911yescharacteristic
98C4⋊Q8—791no—
99C4⋊Q8—1581no—
100#126—1581no—
101#126—1581no—
102#125—791no—
103#125—791no—
104#124C2×D7911yescharacteristic
105#123—1581no—
106C22⋊Q8—1581no—
107C22⋊Q8—1581no—
108#107—1581no—
109#106—1581no—
110#103—1581no—
111#103—1581no—
112#103—1581no—
113#102—1581no—
114#97—791no—
115#97C2×D7911yescharacteristic
116#97C2×D7911yescharacteristic
117C2×Q8—1581no—
118C2×Q8—1581no—
119C2×Q8D31611yescharacteristic
120C2×D4D31611yescharacteristic
121C22×C4—1581no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—1581no—
125C4⋊C4—791no—
126C4⋊C4—791no—
127C4⋊C4—791no—
128C4⋊C4—791no—
129C4⋊C4—1581no—
130C4⋊C4—1581no—
131C4⋊C4—1581no—
132C4⋊C4—1581no—
133C4⋊C4—1581no—
134C4⋊C4—1581no—
135C4⋊C4—1581no—
136C4⋊C4—1581no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—1581no—
140C22⋊C4—1581no—
141C22⋊C4—1581no—
142C42—1581no—
143C42C22×D7911yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—3162no—
147Q8—6321no—
148D4—41no—
149C2×C4—21no—
150C2×C4—3161no—
151C2×C4—6321no—
152C2×C4—1581no—
153C2×C4—1581no—
154C2×C4—1581no—
155C2×C4—1581no—
156C2×C4D4×D7911yescharacteristic
157C2×C4D4×D7911yescharacteristic
158C2×C4C2×D31611yescharacteristic
159C8—22no—
160C8—41no—
161C8—3161no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1457913111yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—3161no—
171C4—3161no—
172C4—3161no—
173C4—3161no—
174C4—6321no—
175C2—81no—
176C2#1909873711yescharacteristic
177C2#1909874311yescharacteristic
178C2#1909874711yescharacteristic
subgroupG/H
centerC22#14579131
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#329×C79C2
socleC22×C79#120
prime radicalC2×D4×C79D4
hypercenter#329D79
hypocenterC79#1664
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #19098972C2semidirect
3. #19098932C2semidirect
5. #19098304C2semidirect
6. #19098304C2semidirect
90. C79#1664semidirect