Finite Group Databasebeta

← #23762732

Subgroups — #23762732

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#19099317C211yesmaximal, characteristic
2#19098931C211yesmaximal, characteristic, complemented
3#19098925C211yesmaximal, characteristic
4#19098305C211yesmaximal, characteristic, complemented
5#19098304C211yesmaximal, characteristic, complemented
6#19098302C211yesmaximal, characteristic
7#501×C79C211yesmaximal, characteristic, complemented
8#14579160—21no—
9#14579156—21no—
10#14579156—21no—
11#14579153C2211yescharacteristic
12#14579149C2211yescharacteristic
13#14579146—21no—
14#14579141—21no—
15#14579139—21no—
16#14579085—21no—
17#14579085—21no—
18#14579084—21no—
19#14579081—21no—
20#14579072C2211yescharacteristic
21#14579072C2211yescharacteristic
22C4⋊Q8×C79C2211yescharacteristic
23#125×C79C2211yescharacteristic
24#107×C79—21no—
25#106×C79—21no—
26#97×C79C2211yescharacteristic
27C2×Dic158—21no—
28C2×Dic158D411yescharacteristic
29C2×D316D411yescharacteristic
30C2×C4×D79—21no—
31C2×C79⋊C8—21no—
32C2×C79⋊C8—21no—
33C4⋊Dic79—21no—
34C4⋊Dic79D411yescharacteristic
35C4⋊Dic79D411yescharacteristic
36Dic79⋊C4—21no—
37Dic79⋊C4—21no—
38Dic79⋊C4—21no—
39(C2×D79)⋊C4—21no—
40(C2×D79)⋊C4—21no—
41(C2×D79)⋊C4—21no—
42(C2×D79)⋊C4—21no—
43(C2×D79)⋊C4—21no—
44C4×Dic79—21no—
45C2×Q8×C79—21no—
46C2×C8×C79—21no—
47C4⋊C4×C79—21no—
48C4⋊C4×C79—21no—
49C4⋊C4×C79—21no—
50C4⋊C4×C79—21no—
51C4⋊C4×C79D411yescharacteristic
52C4⋊C4×C79D411yescharacteristic
53C42×C79C2311yescharacteristic
54C22×D79—21no—
55Q8×C79—42no—
56C2×C4×C79—21no—
57C2×C4×C79—21no—
58C2×C4×C79—41no—
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79C2×D411yescharacteristic
61C2×C4×C79C2×D411yescharacteristic
62C2×Dic79—21no—
63C2×Dic79—21no—
64C2×Dic79—21no—
65D316—41no—
66C4×D79—81no—
67Dic158—41no—
68Dic158—81no—
69C8×C79—22no—
70C79⋊C8—41no—
71C79⋊C8—41no—
72C22×C79#12011yescharacteristic
73C2×D79—41no—
74C2×D79—41no—
75C2×D79—41no—
76C4×C79—21no—
77C4×C79—21no—
78C4×C79—21no—
79C4×C79—41no—
80C4×C79—41no—
81C4×C79—81no—
82Dic79—41no—
83Dic79—41no—
84Dic79—41no—
85C2×C79#45411yescharacteristic
86C2×C79#45511yescharacteristic
87C2×C79#45611yescharacteristic
88D79—81no—
89#1664—791nomaximal, Sylow
90C79#166411yescharacteristic, complemented, Sylow
91#563—791no—
92#501D7911yescharacteristic, complemented
93#491—791no—
94#489—791no—
95#330—791no—
96#330—791no—
97#329—791no—
98C4⋊Q8—1581no—
99C4⋊Q8C2×D7911yescharacteristic
100#126—1581no—
101#126—1581no—
102#125—791no—
103#125C2×D7911yescharacteristic
104#124—791no—
105#123—1581no—
106C22⋊Q8—1581no—
107C22⋊Q8—1581no—
108#107—21no—
109#106—21no—
110#103—1581no—
111#103—1581no—
112#103—1581no—
113#102—1581no—
114#97—791no—
115#97—791no—
116#97C2×D7911yescharacteristic
117C2×Q8—21no—
118C2×Q8—791no—
119C2×Q8—1581no—
120C2×D4—791no—
121C22×C4—1581no—
122C2×C8—21no—
123C2×C8—1581no—
124C2×C8—1581no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—791no—
130C4⋊C4—791no—
131C4⋊C4—1581no—
132C4⋊C4—1581no—
133C4⋊C4—1581no—
134C4⋊C4—1581no—
135C4⋊C4C22⋊D7911yescharacteristic
136C4⋊C4C22⋊D7911yescharacteristic
137C22⋊C4—1581no—
138C22⋊C4—1581no—
139C22⋊C4—1581no—
140C22⋊C4—1581no—
141C22⋊C4—1581no—
142C42—1581no—
143C42C22×D7911yescharacteristic
144C23—1581no—
145Q8—42no—
146Q8—3161no—
147Q8—6321no—
148D4—3161no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—6321no—
153C2×C4—1581no—
154C2×C4—1581no—
155C2×C4—1581no—
156C2×C4D4×D7911yescharacteristic
157C2×C4D4×D7911yescharacteristic
158C2×C4C2×C22⋊D7911yescharacteristic
159C8—22no—
160C8—3161no—
161C8—3161no—
162C22—3161no—
163C22—3161no—
164C22—3161no—
165C22#1457912911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—3161no—
173C4—3161no—
174C4—3161no—
175C2—6321no—
176C2#1909873411yescharacteristic
177C2#1909873911yescharacteristic
178C2#1909874511yescharacteristic
subgroupG/H
centerC22#14579129
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#501×C79C2
socleC22×C79#120
prime radicalC2×D316D4
hypercenter#501D79
hypocenterC79#1664
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #19098931C2semidirect
4. #19098305C2semidirect
5. #19098304C2semidirect
7. #501×C79C2semidirect
90. C79#1664semidirect
92. #501D79semidirect