Finite Group Databasebeta

← #23772283

Subgroups — #23772283

Order 10112.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C2×#14579183C211yesmaximal, characteristic
2#19099044C212yesmaximal, complemented
3#19098674C212yesmaximal, complemented
4#19098669C212yesmaximal, complemented
5#19098650C214yesmaximal, complemented
6#19098562C212yesmaximal, complemented
7#19098518C211yesmaximal, characteristic, complemented
8C2×#106×C79C211yesmaximal, characteristic, complemented
9C2×#11929624C2212yes—
10#14579183C418yescomplemented
11C2×Dic316C2211yescharacteristic
12C2×#11929613C2212yes—
13C2×D632C2211yescharacteristic
14C2×#11929608C2211yescharacteristic
15#14579126C2214yes—
16#14579123C2214yes—
17C4×C22⋊D79—24no—
18#14579120C2211yescharacteristic
19#14579119—22no—
20C4⋊C4×D79—22no—
21#14579084C2214yes—
22#14579081C2214yes—
23#14579071C2212yes—
24C8×Dic79C2212yes—
25C22×C8×C79C2211yescharacteristic
26C2×C4⋊C4×C79C2212yes—
27#106×C79C2212yes—
28#106×C79C2212yes—
29#11929624—24no—
30#11929624C2×C418yescomplemented
31C2×Dic158C2312yes—
32C2×D316C2312yes—
33C2×C22⋊D79—22no—
34C2×C4×D79—24no—
35C2×C4×D79—22no—
36Dic316C2×C414yescomplemented
37#11929613C2×C418yescomplemented
38D632C2×C414yescomplemented
39#11929608—22no—
40C2×C79⋊C8C2312yes—
41C4⋊Dic79D412yes—
42Dic79⋊C4—24no—
43C22⋊Dic79D412yes—
44(C2×D79)⋊C4—24no—
45C4×Dic79—24no—
46C4×Dic79C2312yes—
47C22×C4×C79—22no—
48C22×C4×C79C2311yescharacteristic
49C2×C8×C79C2×C414yescomplemented
50C2×C8×C79C2311yescharacteristic
51C2×C8×C79C2311yescharacteristic
52C4⋊C4×C79—22no—
53C4⋊C4×C79C2314yes—
54C23×C79C2×D411yescharacteristic
55C22×D79—22no—
56C2×C4×C79—24no—
57C2×C4×C79—82no—
58C2×C4×C79C22×C412yes—
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79#4112yes—
61C2×C4×C79C2411yescharacteristic
62C22⋊D79—28no—
63C2×Dic79—22no—
64C2×Dic79C2×D414yes—
65D316—22no—
66D316C22×C414yes—
67C4×D79—28no—
68C4×D79—84no—
69Dic158—22no—
70Dic158C22×C414yes—
71C8×C79C22×C412yes—
72C8×C79C22×C412yes—
73C79⋊C8—22no—
74C22×C79—22no—
75C22×C79C4×D412yes—
76C22×C79C22×D411yescharacteristic
77C2×D79—24no—
78C2×D79—42no—
79C2×D79—42no—
80C4×C79—44no—
81C4×C79C4×D412yes—
82C4×C79C23×C411yescharacteristic
83C4×C79C2×#4111yescharacteristic
84Dic79—24no—
85Dic79—24no—
86C2×C79—22no—
87C2×C79C2×C4×D411yescharacteristic
88C2×C79#57712yes—
89D79—44no—
90#2952—791nomaximal, Sylow
91C79#295211yescharacteristic, complemented, Sylow
92C2×#135—791no—
93#520—792no—
94#442—792no—
95#441—792no—
96C4×SD16—794no—
97C2×#106D7911yescharacteristic, complemented
98#417—792no—
99#405—791no—
100C2×#41—792no—
101#135—798no—
102C2×Q16—791no—
103C2×SD16—792no—
104C2×D8—791no—
105C2×M16—791no—
106C22×C8C2×D7911yescharacteristic
107C4×Q8—794no—
108C4×D4—794no—
109C4×D4—1584no—
110#117—791no—
111#117—1582no—
112C2×C4⋊C4—1582no—
113C2×C4⋊C4C2×D7912yes—
114#106C2×D7912yes—
115#106C2×D7912yes—
116#103—794no—
117#102—794no—
118#97—792no—
119C4×C8—792no—
120#41—798no—
121#41—1584no—
122C2×Q8—792no—
123C2×D4—792no—
124C2×D4—1582no—
125C22×C4—22no—
126C22×C4—1584no—
127C22×C4—1582no—
128C22×C4C22×D7911yescharacteristic
129Q16—794no—
130SD16—798no—
131D8—794no—
132M16—1582no—
133C2×C8—792no—
134C2×C8C4×D7914yescomplemented
135C2×C8C22×D7911yescharacteristic
136C2×C8C22×D7911yescharacteristic
137C4⋊C4—22no—
138C4⋊C4—792no—
139C4⋊C4—1584no—
140C4⋊C4C22×D7914yes—
141C22⋊C4—792no—
142C22⋊C4—1584no—
143C42—792no—
144C42—1584no—
145C23—1582no—
146C23D4×D7911yescharacteristic
147Q8—794no—
148Q8—1582no—
149D4—794no—
150D4—1588no—
151D4—1582no—
152C2×C4—24no—
153C2×C4—82no—
154C2×C4—794no—
155C2×C4—6324no—
156C2×C4—1582no—
157C2×C4—1588no—
158C2×C4C2×C4×D7912yes—
159C2×C4D4×D7911yescharacteristic
160C2×C4#1192962512yes—
161C2×C4C23×D7911yescharacteristic
162C8—1582no—
163C8C2×C4×D7912yes—
164C8C2×C4×D7912yes—
165C22—22no—
166C22—3162no—
167C22—3162no—
168C22—1584no—
169C22#1457912312yes—
170C22C2×D4×D7911yescharacteristic
171C4—44no—
172C4—1584no—
173C4—1584no—
174C4#1457912312yes—
175C4C22×C4×D7911yescharacteristic
176C4C2×#1192962511yescharacteristic
177C2—22no—
178C2—3164no—
179C2C2×#1457912311yescharacteristic
180C2#1909936912yes—
subgroupG/H
centerC22C2×D4×D79
commutatorC4×C79C23×C4
FrattiniC2×C4C23×D79
FittingC2×#106×C79C2
socleC22×C79C22×D4
prime radicalC2×#14579183C2
cosocleC2×C4×C79C24
hypercenterC2×#106D79
hypocenterC79#2952
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. #19099044C2semidirect
3. #19098674C2semidirect
4. #19098669C2semidirect
5. #19098650C2semidirect
6. #19098562C2semidirect
7. #19098518C2semidirect
8. C2×#106×C79C2semidirect
10. #14579183C4semidirect
30. #11929624C2×C4semidirect
36. Dic316C2×C4semidirect
37. #11929613C2×C4semidirect
38. D632C2×C4semidirect
49. C2×C8×C79C2×C4semidirect
91. C79#2952semidirect
97. C2×#106D79semidirect
134. C2×C8C4×D79semidirect