Finite Group Databasebeta

← #23762568

Subgroups — #23762568

Order 10112.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic158C211yesmaximal, characteristic
2#19098914C211yesmaximal, characteristic, complemented
3#19098859C211yesmaximal, characteristic, complemented
4#19098853C211yesmaximal, characteristic
5#19098310C211yesmaximal, characteristic, complemented
6#19098295C211yesmaximal, characteristic, complemented
7D4⋊C8×C79C211yesmaximal, characteristic
8C22×Dic158—21no—
9#14579161C2211yescharacteristic
10#14579161C2211yescharacteristic
11#14579160—21no—
12#14579140—21no—
13#14579138—22no—
14C4×Dic158C2211yescharacteristic
15D4×Dic79—21no—
16#14579095—21no—
17#14579092—21no—
18C4⋊(C79⋊C8)C2211yescharacteristic
19#14579086—21no—
20#14579086—22no—
21#14579082—21no—
22C4×D4×C79C2211yescharacteristic
23C4⋊C8×C79C2211yescharacteristic
24C4×C8×C79C2211yescharacteristic
25C2×Dic158—22no—
26C2×Dic158—21no—
27C2×Dic158—21no—
28C2×Dic158—42no—
29C2×Dic158—42no—
30C2×Dic158D411yescharacteristic
31C22×Dic79—22no—
32C2×C79⋊C8—21no—
33C4⋊Dic79—21no—
34C4⋊Dic79—21no—
35C4⋊Dic79—21no—
36C4⋊Dic79D412yes—
37C4⋊Dic79D411yescharacteristic
38Dic79⋊C4—22no—
39Dic79⋊C4—21no—
40C22⋊Dic79—22no—
41C4×Dic79—21no—
42C2×D4×C79D411yescharacteristic
43C22×C4×C79—21no—
44C2×C8×C79—21no—
45C2×C8×C79—21no—
46C4⋊C4×C79D411yescharacteristic
47C22⋊C4×C79—21no—
48C42×C79C2311yescharacteristic
49C23×C79—21no—
50D4×C79—21no—
51D4×C79Q1612yes—
52C2×C4×C79—21no—
53C2×C4×C79—41no—
54C2×C4×C79—41no—
55C2×C4×C79C2×D411yescharacteristic
56C2×C4×C79C2×D411yescharacteristic
57C2×C4×C79C2×D411yescharacteristic
58C2×Dic79—21no—
59C2×Dic79—21no—
60C2×Dic79—22no—
61C2×Dic79—44no—
62C2×Dic79—41no—
63Dic158—21no—
64Dic158—44no—
65Dic158—41no—
66Dic158—41no—
67Dic158—42no—
68Dic158SD1612yes—
69C8×C79—41no—
70C8×C79—41no—
71C79⋊C8—41no—
72C22×C79—22no—
73C22×C79—41no—
74C22×C79—41no—
75C22×C79#12011yescharacteristic
76C4×C79—21no—
77C4×C79—41no—
78C4×C79C2×SD1611yescharacteristic
79C4×C79C2×Q1611yescharacteristic
80C4×C79AGL(1,ℤ/8)11yescharacteristic
81C4×C79#13711yescharacteristic
82Dic79—22no—
83Dic79—42no—
84Dic79—41no—
85Dic79—81no—
86C2×C79—42no—
87C2×C79#45011yescharacteristic
88C2×C79#45111yescharacteristic
89C2×C79#45411yescharacteristic
90#1637—791nomaximal, Sylow
91C79#163711yescharacteristic, complemented, Sylow
92D4×Q8—791no—
93#487—791no—
94#477—791no—
95#476—791no—
96#332—791no—
97Q8⋊C8—791no—
98D4⋊C8D7911yescharacteristic
99C22×Q8—1581no—
100C4⋊Q8—791no—
101C4⋊Q8—791no—
102C4⋊Q8—1581no—
103C22⋊Q8—1582no—
104C22⋊Q8—1581no—
105C4×Q8—791no—
106C4×D4—1581no—
107C4×D4C2×D7911yescharacteristic
108#107—1581no—
109#106—1581no—
110C4⋊C8—791no—
111C4⋊C8C2×D7911yescharacteristic
112#103—1582no—
113#103—1581no—
114#102—1581no—
115C4×C8C2×D7911yescharacteristic
116C2×Q8—3162no—
117C2×Q8—3162no—
118C2×Q8—791no—
119C2×Q8—1582no—
120C2×Q8—1581no—
121C2×Q8—1581no—
122C2×D4D31611yescharacteristic
123C22×C4—21no—
124C22×C4—1582no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—1581no—
128C4⋊C4—792no—
129C4⋊C4—791no—
130C4⋊C4—1582no—
131C4⋊C4—1581no—
132C4⋊C4—1581no—
133C4⋊C4—1581no—
134C4⋊C4—1581no—
135C4⋊C4D31611yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—1582no—
138C42—1581no—
139C42C22×D7911yescharacteristic
140C23—21no—
141Q8—3162no—
142Q8—3164no—
143Q8—3161no—
144Q8—3161no—
145Q8—792no—
146Q8—1581no—
147D4—21no—
148D4Dic31612yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—3164no—
153C2×C4—3161no—
154C2×C4—1581no—
155C2×C4—1582no—
156C2×C4—1581no—
157C2×C4D4×D7911yescharacteristic
158C2×C4D4×D7911yescharacteristic
159C2×C4C2×D31611yescharacteristic
160C8—41no—
161C8—41no—
162C8—3161no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1457913111yescharacteristic
167C4—21no—
168C4—41no—
169C4—3162no—
170C4—3161no—
171C4—6321no—
172C4—1582no—
173C4SD16×D7911yescharacteristic
174C4C2×Dic31611yescharacteristic
175C4#1457918511yescharacteristic
176C4#1457919411yescharacteristic
177C2—42no—
178C2#1909871511yescharacteristic
179C2#1909872111yescharacteristic
180C2#1909873711yescharacteristic
subgroupG/H
centerC22#14579131
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
FittingD4⋊C8×C79C2
socleC22×C79#120
prime radicalC2×D4×C79D4
hypercenterD4⋊C8D79
hypocenterC79#1637
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #19098914C2semidirect
3. #19098859C2semidirect
5. #19098310C2semidirect
6. #19098295C2semidirect
91. C79#1637semidirect