Finite Group Databasebeta

← #23763848

Subgroups — #23763848

Order 10112.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#19099074C211yesmaximal, characteristic
2C2×#14579089C212yesmaximal, complemented
3#19098527C211yesmaximal, characteristic, complemented
4#19098323C212yesmaximal, complemented
5C2×#117×C79C211yesmaximal, characteristic, complemented
6C2×#11929624C2211yescharacteristic
7C2×#11929608C2212yes—
8#14579144—21no—
9#14579140C412yescomplemented
10#14579135C412yescomplemented
11#14579130—21no—
12C4×C22⋊D79—22no—
13#14579120C2211yescharacteristic
14#14579089—24no—
15C22⋊(C79⋊C8)—22no—
16C23×C4×C79C2211yescharacteristic
17#117×C79—24no—
18C2×C4⋊C4×C79—21no—
19C2×C22⋊C4×C79—21no—
20C2×C42×C79C2212yes—
21#11929624—22no—
22#11929624—22no—
23C2×Dic158C2×C411yescharacteristic
24C2×D316C2×C411yescharacteristic
25C2×C22⋊D79—22no—
26C2×C22⋊D79—21no—
27C2×C4×D79—21no—
28#11929608—22no—
29#11929608—22no—
30C2×C79⋊C8—22no—
31C4⋊Dic79C2×C412yes—
32Dic79⋊C4—22no—
33C22⋊Dic79—22no—
34C22⋊Dic79—21no—
35(C2×D79)⋊C4—22no—
36C4×Dic79—21no—
37C24×C79D411yescharacteristic
38C22×C4×C79—22no—
39C22×C4×C79—22no—
40C22×C4×C79—22no—
41C22×C4×C79C2×C412yes—
42C22×C4×C79D411yescharacteristic
43C22×C4×C79D412yes—
44C22×C4×C79C2311yescharacteristic
45C4⋊C4×C79—24no—
46C22⋊C4×C79—24no—
47C42×C79—22no—
48C42×C79D414yescomplemented
49C23×C79—21no—
50C23×C79—21no—
51C23×C79—42no—
52C23×C79C22⋊C412yes—
53C23×C79C2×D411yescharacteristic
54C22×D79—21no—
55C2×C4×C79—21no—
56C2×C4×C79—21no—
57C2×C4×C79—24no—
58C2×C4×C79—24no—
59C2×C4×C79—24no—
60C2×C4×C79—44no—
61C2×C4×C79C22⋊C412yes—
62C2×C4×C79C22×C411yescharacteristic
63C2×C4×C79C2×D412yes—
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79#4112yes—
66C22⋊D79—44no—
67C22⋊D79—41no—
68C22⋊D79—41no—
69C2×Dic79—22no—
70C2×Dic79—21no—
71D316—22no—
72C4×D79—42no—
73Dic158—22no—
74C79⋊C8—42no—
75C22×C79—22no—
76C22×C79—22no—
77C22×C79—22no—
78C22×C79—22no—
79C22×C79—42no—
80C22×C79—42no—
81C22×C79C2×C22⋊C411yescharacteristic
82C22×C79#12011yescharacteristic
83C22×C79#12311yescharacteristic
84C2×D79—41no—
85C2×D79—42no—
86C4×C79—22no—
87C4×C79—44no—
88C4×C79C4×D412yes—
89C4×C79#12112yes—
90Dic79—41no—
91Dic79—42no—
92C2×C79—21no—
93C2×C79—21no—
94C2×C79—42no—
95C2×C79#38611yescharacteristic
96C2×C79#42112yes—
97D79—81no—
98#1897—791nomaximal, Sylow
99C79#189711yescharacteristic, complemented, Sylow
100#525—791no—
101C2×#117D7911yescharacteristic, complemented
102C2×#104—792no—
103#407—791no—
104#339—792no—
105C2×#41—791no—
106C23×C4C2×D7911yescharacteristic
107C2×M16—792no—
108#123—1581no—
109C22⋊Q8—792no—
110#121—792no—
111#120—1581no—
112C4×D4—1582no—
113#117—24no—
114#117—791no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D7912yes—
118#104—1584no—
119C22⋊C8—1582no—
120C24C22⋊D7911yescharacteristic
121#41—1582no—
122#41—1582no—
123C2×Q8—791no—
124C2×D4—791no—
125C2×D4—1582no—
126C2×D4—1581no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—1581no—
131C22×C4C4×D7912yes—
132C22×C4D31612yes—
133C22×C4C22⋊D7911yescharacteristic
134C22×C4C22×D7911yescharacteristic
135M16—1582no—
136M16—1582no—
137C2×C8—1582no—
138C4⋊C4—24no—
139C4⋊C4—792no—
140C4⋊C4—1582no—
141C22⋊C4—24no—
142C22⋊C4—1582no—
143C22⋊C4—1581no—
144C22⋊C4—1582no—
145C42—22no—
146C42—1581no—
147C42C22⋊D7914yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—1581no—
152C23(C2×D79)⋊C412yes—
153C23C2×C22⋊D7911yescharacteristic
154Q8—1582no—
155D4—3164no—
156D4—3161no—
157D4—3161no—
158D4—1582no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—3162no—
166C2×C4—1582no—
167C2×C4—1581no—
168C2×C4(C2×D79)⋊C412yes—
169C2×C4C2×C4×D7911yescharacteristic
170C2×C4C2×C22⋊D7912yes—
171C2×C4C2×D31611yescharacteristic
172C2×C4#1192962412yes—
173C8—3162no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—3161no—
181C22—3162no—
182C22C2×(C2×D79)⋊C411yescharacteristic
183C22#1457913011yescharacteristic
184C22#1457914411yescharacteristic
185C4—22no—
186C4—44no—
187C4—3161no—
188C4—3162no—
189C4C4×C22⋊D7912yes—
190C4#1457913512yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—6321no—
195C2#1909844211yescharacteristic
196C2#1909858112yes—
subgroupG/H
centerC2×C4C2×D316
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC2×#117×C79C2
socleC22×C79C2×C22⋊C4
prime radical#19099074C2
cosocleC22×C4×C79C23
hypercenterC2×#117D79
hypocenterC79#1897
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#14579089C2semidirect
3. #19098527C2semidirect
4. #19098323C2semidirect
5. C2×#117×C79C2semidirect
9. #14579140C4semidirect
10. #14579135C4semidirect
48. C42×C79D4semidirect
99. C79#1897semidirect
101. C2×#117D79semidirect
147. C42C22⋊D79semidirect