Finite Group Databasebeta

← #23773331

Subgroups — #23773331

Order 10112.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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
2#19098904C214yesmaximal, complemented
3#19098887C214yesmaximal, complemented
4#19098603C212yesmaximal, complemented
5#19098562C212yesmaximal, complemented
6#19098527C211yesmaximal, characteristic, complemented
7C2×#117×C79C211yesmaximal, characteristic, complemented
8C2×#11929624C2211yescharacteristic
9C2×#11929608C2212yes—
10#14579144—21no—
11#14579140C2212yes—
12#14579135C2212yes—
13#14579130—21no—
14C4×C22⋊D79—22no—
15#14579120C2211yescharacteristic
16#14579094C2214yescomplemented
17#14579092C2214yescomplemented
18#14579084C2214yescomplemented
19#14579081C2214yescomplemented
20C22⋊(C79⋊C8)C2214yes—
21C23×C4×C79C2211yescharacteristic
22#117×C79—22no—
23#117×C79C2214yes—
24C2×C4⋊C4×C79C2212yes—
25C2×C22⋊C4×C79—21no—
26C2×C42×C79—21no—
27#11929624—24no—
28C2×Dic158C2311yescharacteristic
29C2×D316C2311yescharacteristic
30C2×C22⋊D79—21no—
31C2×C22⋊D79—22no—
32C2×C4×D79—21no—
33#11929608—24no—
34C2×C79⋊C8C2314yes—
35C4⋊Dic79C2312yes—
36Dic79⋊C4—22no—
37C22⋊Dic79—21no—
38C22⋊Dic79—22no—
39(C2×D79)⋊C4—22no—
40C4×Dic79—21no—
41C24×C79D411yescharacteristic
42C22×C4×C79—24no—
43C22×C4×C79—22no—
44C22×C4×C79D411yescharacteristic
45C22×C4×C79D412yes—
46C22×C4×C79C2312yes—
47C22×C4×C79C2311yescharacteristic
48C4⋊C4×C79—22no—
49C4⋊C4×C79C2314yes—
50C22⋊C4×C79—24no—
51C42×C79—24no—
52C23×C79—22no—
53C23×C79—42no—
54C23×C79C2×D412yes—
55C23×C79C2×D411yescharacteristic
56C22×D79—21no—
57C2×C4×C79—22no—
58C2×C4×C79—24no—
59C2×C4×C79—24no—
60C2×C4×C79—24no—
61C2×C4×C79—44no—
62C2×C4×C79C2×D412yes—
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79#4114yes—
65C2×C4×C79C2411yescharacteristic
66C22⋊D79—44no—
67C22⋊D79—42no—
68C2×Dic79—22no—
69C2×Dic79—21no—
70D316—22no—
71C4×D79—42no—
72Dic158—22no—
73C79⋊C8—24no—
74C22×C79—22no—
75C22×C79—22no—
76C22×C79—22no—
77C22×C79—22no—
78C22×C79—44no—
79C22×C79#12312yes—
80C22×C79C22×D411yescharacteristic
81C2×D79—41no—
82C2×D79—42no—
83C4×C79—22no—
84C4×C79—44no—
85C4×C79#12312yes—
86C4×C79C2×#4112yes—
87Dic79—41no—
88Dic79—42no—
89C2×C79—22no—
90C2×C79—42no—
91C2×C79C2×#12311yescharacteristic
92C2×C79#57512yes—
93D79—81no—
94#3093—791nomaximal, Sylow
95C79#309311yescharacteristic, complemented, Sylow
96#525—791no—
97C2×#117D7911yescharacteristic, complemented
98#485—794no—
99#482—794no—
100#428—792no—
101#417—792no—
102#407—791no—
103C2×#41—791no—
104C23×C4C2×D7911yescharacteristic
105C2×M16—792no—
106#123—1581no—
107C22⋊Q8—792no—
108#121—792no—
109#120—1581no—
110C4×D4—1582no—
111#117—22no—
112#117—791no—
113#117C2×D7914yes—
114C2×C4⋊C4C2×D7912yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—794no—
118#106—794no—
119#103—794no—
120#102—794no—
121C22⋊C8—794no—
122C24C22⋊D7911yescharacteristic
123#41—1584no—
124C2×Q8—791no—
125C2×D4—791no—
126C2×D4—1582no—
127C2×D4—1581no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—1581no—
131C22×C4C22⋊D7911yescharacteristic
132C22×C4C22⋊D7912yes—
133C22×C4C22×D7912yes—
134C22×C4C22×D7911yescharacteristic
135M16—1584no—
136C2×C8—794no—
137C4⋊C4—22no—
138C4⋊C4—792no—
139C4⋊C4—1582no—
140C4⋊C4C22×D7914yes—
141C22⋊C4—24no—
142C22⋊C4—1581no—
143C22⋊C4—1582no—
144C22⋊C4—1582no—
145C42—24no—
146C42—1581no—
147C23—22no—
148C23—42no—
149C23—1581no—
150C23C2×C22⋊D7912yes—
151C23C2×C22⋊D7911yescharacteristic
152Q8—1582no—
153D4—3164no—
154D4—3162no—
155D4—1582no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—3162no—
162C2×C4—1582no—
163C2×C4—1581no—
164C2×C4C2×C22⋊D7912yes—
165C2×C4C2×C22⋊D7911yescharacteristic
166C2×C4#1192962414yes—
167C2×C4C23×D7911yescharacteristic
168C8—1584no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—3161no—
175C22—3162no—
176C22#1457914412yes—
177C22C22×C22⋊D7911yescharacteristic
178C4—22no—
179C4—44no—
180C4—3161no—
181C4—3162no—
182C4#1457914412yes—
183C4C2×#1192962412yes—
184C2—22no—
185C2—42no—
186C2—6321no—
187C2C2×#1457914411yescharacteristic
188C2#1909936112yes—
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×#117×C79C2
socleC22×C79C22×D4
prime radical#19099074C2
hypercenterC2×#117D79
hypocenterC79#3093
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #19098904C2semidirect
3. #19098887C2semidirect
4. #19098603C2semidirect
5. #19098562C2semidirect
6. #19098527C2semidirect
7. C2×#117×C79C2semidirect
16. #14579094C22semidirect
17. #14579092C22semidirect
18. #14579084C22semidirect
19. #14579081C22semidirect
95. C79#3093semidirect
97. C2×#117D79semidirect