Finite Group Databasebeta

← #23774608

Subgroups — #23774608

Order 10112.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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#19099120C211yesmaximal, characteristic
2C2×#14579153C211yesmaximal, characteristic
3#19098972C212yesmaximal, complemented
4#19098932C212yesmaximal, complemented
5#19098899C212yesmaximal
6#19098894C212yesmaximal
7#19098871C214yesmaximal, complemented
8#432×C79C211yesmaximal, characteristic
9#14579161C2211yescharacteristic
10#14579161C2211yescharacteristic
11#14579153—21no—
12#14579153—21no—
13#14579153—21no—
14#14579153C2212yes—
15#14579153C2212yes—
16#14579140—21no—
17#14579140C2212yes—
18C4×Dic158—21no—
19C4×Dic158C2212yes—
20#14579120—21no—
21C2×C4⋊Dic79C2211yescharacteristic
22C2×C4⋊Dic79C2211yescharacteristic
23C2×Dic79⋊C4—21no—
24C2×Dic79⋊C4—21no—
25#14579095C2214yes—
26#14579093C2214yes—
27#14579086C2214yes—
28#14579086C2214yes—
29C2×C42×C79C2211yescharacteristic
30C4⋊C8×C79C2212yes—
31C22⋊C8×C79C2212yes—
32#97×C79C2212yes—
33C2×Dic158—21no—
34C2×Dic158C2312yes—
35C22×Dic79—21no—
36C22×Dic79—21no—
37C4⋊Dic79—21no—
38C4⋊Dic79—21no—
39C4⋊Dic79—21no—
40C4⋊Dic79—21no—
41C4⋊Dic79—21no—
42C4⋊Dic79C2312yes—
43C4⋊Dic79C2312yes—
44C4⋊Dic79C2312yes—
45Dic79⋊C4—22no—
46Dic79⋊C4—22no—
47Dic79⋊C4—22no—
48Dic79⋊C4—22no—
49Dic79⋊C4—22no—
50Dic79⋊C4—22no—
51C22⋊Dic79—22no—
52C4×Dic79—22no—
53C22×C4×C79D411yescharacteristic
54C22×C4×C79D411yescharacteristic
55C22×C4×C79C2311yescharacteristic
56C2×C8×C79C2314yes—
57C42×C79D411yescharacteristic
58C42×C79D411yescharacteristic
59C42×C79C2311yescharacteristic
60C42×C79C2311yescharacteristic
61C23×C79C2×D411yescharacteristic
62C2×C4×C79—22no—
63C2×C4×C79—22no—
64C2×C4×C79—41no—
65C2×C4×C79C2×D411yescharacteristic
66C2×C4×C79C2×D411yescharacteristic
67C2×C4×C79C2×D411yescharacteristic
68C2×C4×C79C2×D411yescharacteristic
69C2×C4×C79C2×D411yescharacteristic
70C2×C4×C79C2411yescharacteristic
71C2×Dic79—22no—
72C2×Dic79—22no—
73C2×Dic79—22no—
74C2×Dic79—22no—
75C2×Dic79—42no—
76C2×Dic79—42no—
77Dic158—24no—
78Dic158—42no—
79C8×C79—24no—
80C22×C79—21no—
81C22×C79—21no—
82C22×C79#13712yes—
83C22×C79C22×D411yescharacteristic
84C4×C79—21no—
85C4×C79—21no—
86C4×C79—21no—
87C4×C79—21no—
88C4×C79—21no—
89C4×C792−1+412yes—
90Dic79—42no—
91Dic79—42no—
92Dic79—42no—
93Dic79—42no—
94C2×C79—22no—
95C2×C79#53611yescharacteristic
96C2×C79C2×#13711yescharacteristic
97C2×C79#57511yescharacteristic
98#3236—791nomaximal, Sylow
99C79#323611yescharacteristic, complemented, Sylow
100#533—791no—
101C2×#125—791no—
102#501—792no—
103#491—792no—
104#484—792no—
105#483—792no—
106#479—794no—
107#432D7911yescharacteristic
108C4⋊Q8—791no—
109C4⋊Q8—791no—
110#125—792no—
111#125—792no—
112#125—1581no—
113#125—1581no—
114#125—1581no—
115C22⋊Q8—792no—
116C22⋊Q8—1581no—
117C4×Q8—792no—
118C4×Q8—1581no—
119#117—1581no—
120C2×C4⋊C4—791no—
121C2×C4⋊C4—791no—
122C2×C4⋊C4—1581no—
123C2×C4⋊C4—1581no—
124C2×C42C2×D7911yescharacteristic
125#107—794no—
126#106—794no—
127C4⋊C8C2×D7912yes—
128#103—794no—
129#103—794no—
130C22⋊C8C2×D7912yes—
131#97C2×D7912yes—
132C2×Q8—792no—
133C2×Q8—1581no—
134C22×C4—1581no—
135C22×C4—1581no—
136C22×C4D31611yescharacteristic
137C22×C4D31611yescharacteristic
138C22×C4C22×D7911yescharacteristic
139C2×C8C22×D7914yes—
140C4⋊C4—792no—
141C4⋊C4—792no—
142C4⋊C4—792no—
143C4⋊C4—1582no—
144C4⋊C4—1582no—
145C4⋊C4—1582no—
146C4⋊C4—1582no—
147C4⋊C4—1582no—
148C4⋊C4—1582no—
149C4⋊C4—1581no—
150C4⋊C4—1581no—
151C4⋊C4—1581no—
152C4⋊C4—1581no—
153C4⋊C4—1581no—
154C22⋊C4—1582no—
155C42—1582no—
156C42D31611yescharacteristic
157C42D31611yescharacteristic
158C42C22×D7911yescharacteristic
159C42C22×D7911yescharacteristic
160C23C2×D31611yescharacteristic
161Q8—3162no—
162Q8—1584no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—3162no—
167C2×C4—3162no—
168C2×C4—1582no—
169C2×C4—1582no—
170C2×C4—1582no—
171C2×C4—1582no—
172C2×C4C2×D31611yescharacteristic
173C2×C4C2×D31611yescharacteristic
174C2×C4C2×D31611yescharacteristic
175C2×C4C2×D31611yescharacteristic
176C2×C4C2×D31611yescharacteristic
177C2×C4C23×D7911yescharacteristic
178C8—24no—
179C22—21no—
180C22—21no—
181C22#1457919412yes—
182C22C22×D31611yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—3162no—
189C4—3162no—
190C4—3162no—
191C4—3162no—
192C4#1457920812yes—
193C2—22no—
194C2#1909913911yescharacteristic
195C2C2×#1457919411yescharacteristic
196C2#1909936311yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#432×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#432D79
hypocenterC79#3236
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
3. #19098972C2semidirect
4. #19098932C2semidirect
7. #19098871C2semidirect
99. C79#3236semidirect