Finite Group Databasebeta

← #23766691

Subgroups — #23766691

Order 10112.

504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 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×C4×Dic158C211yesmaximal, characteristic
2#19098494C212yesmaximal
3#19098493C212yesmaximal
4#19098483C212yesmaximal
5#19098482C212yesmaximal
6C4×Dic79⋊C4C214yesmaximal
7#19098409C211yesmaximal, characteristic
8C2×C4×Q8×C79C211yesmaximal, characteristic
9C22×Dic158C2211yescharacteristic
10C4×Dic158—24no—
11C2×C4⋊Dic79C2211yescharacteristic
12C2×Dic79⋊C4C2214yes—
13C2×Dic79⋊C4C2214yes—
14C2×Dic79⋊C4C2212yes—
15C2×C4×Dic79C2212yes—
16C2×C4×Dic79C2212yes—
17C79⋊#95C2212yes—
18C79⋊#95C2212yes—
19C79⋊#95C2214yes—
20C79⋊#95C2214yes—
21C22×Q8×C79C2211yescharacteristic
22C4×Q8×C79—24no—
23C2×C4⋊C4×C79C2212yes—
24C2×C4⋊C4×C79C2211yescharacteristic
25C2×C42×C79C2212yes—
26C2×C42×C79C2211yescharacteristic
27C2×Dic158—24no—
28C2×Dic158—22no—
29C22×Dic79C2312yes—
30C22×Dic79C2314yes—
31C22×Dic79C2312yes—
32C4⋊Dic79—22no—
33Dic79⋊C4—28no—
34Dic79⋊C4—24no—
35Dic79⋊C4—28no—
36C4×Dic79—24no—
37C4×Dic79Q818yescomplemented
38C2×Q8×C79—22no—
39C2×Q8×C79—24no—
40C22×C4×C79C2312yes—
41C22×C4×C79C2311yescharacteristic
42C22×C4×C79C2311yescharacteristic
43C22×C4×C79C2312yes—
44C22×C4×C79C2311yescharacteristic
45C4⋊C4×C79—24no—
46C4⋊C4×C79—22no—
47C42×C79—24no—
48C42×C79D414yes—
49C23×C79C2411yescharacteristic
50Q8×C79—28no—
51C2×C4×C79—22no—
52C2×C4×C79—22no—
53C2×C4×C79—22no—
54C2×C4×C79—22no—
55C2×C4×C79—22no—
56C2×C4×C79—24no—
57C2×C4×C79C2×D412yes—
58C2×C4×C79C2×D412yes—
59C2×C4×C79C2×D412yes—
60C2×C4×C79C2×Q814yes—
61C2×C4×C79#4114yes—
62C2×Dic79—22no—
63C2×Dic79—24no—
64C2×Dic79—24no—
65C2×Dic79—22no—
66C2×Dic79—22no—
67C2×Dic79—24no—
68C2×Dic79C2×Q818yes—
69C2×Dic79#4114yes—
70Dic158—28no—
71C22×C79C22×D411yescharacteristic
72C22×C79C22×Q812yes—
73C22×C79C2×#4112yes—
74C22×C79C2×#4112yes—
75C4×C79—22no—
76C4×C79—22no—
77C4×C79—24no—
78C4×C79—42no—
79C4×C79C4⋊Q814yes—
80Dic79—24no—
81Dic79—28no—
82Dic79—42no—
83C2×C79#52511yescharacteristic
84C2×C79#52511yescharacteristic
85C2×C79C2×C4⋊Q811yescharacteristic
86C2×C79#53314yes—
87#2399—791nomaximal, Sylow
88C79#239911yescharacteristic, complemented, Sylow
89C2×C4×Q8—791no—
90C2×C4×Q8D7911yescharacteristic
91#398—792no—
92#398—792no—
93#395—792no—
94#395—792no—
95C4×C4⋊C4—794no—
96#376—791no—
97C22×Q8—791no—
98C22×Q8C2×D7911yescharacteristic
99C4×Q8—24no—
100C4×Q8—1584no—
101C2×C4⋊C4—792no—
102C2×C4⋊C4—791no—
103C2×C4⋊C4—794no—
104C2×C4⋊C4—794no—
105C2×C4⋊C4C2×D7912yes—
106C2×C4⋊C4C2×D7911yescharacteristic
107C2×C42—792no—
108C2×C42—792no—
109C2×C42C2×D7912yes—
110C2×C42C2×D7911yescharacteristic
111#95—792no—
112#95—792no—
113#95—794no—
114#95—794no—
115C2×Q8—22no—
116C2×Q8—24no—
117C2×Q8—1584no—
118C2×Q8—1582no—
119C22×C4—794no—
120C22×C4—792no—
121C22×C4—792no—
122C22×C4C22×D7912yes—
123C22×C4C22×D7911yescharacteristic
124C22×C4C22×D7911yescharacteristic
125C22×C4C22×D7912yes—
126C22×C4C22×D7911yescharacteristic
127C4⋊C4—24no—
128C4⋊C4—22no—
129C4⋊C4—1588no—
130C4⋊C4—1584no—
131C4⋊C4—1582no—
132C4⋊C4—1588no—
133C42—24no—
134C42—798no—
135C42—1584no—
136C42C22⋊D7914yes—
137C23C23×D7911yescharacteristic
138Q8—28no—
139Q8—1588no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—22no—
146C2×C4—798no—
147C2×C4—794no—
148C2×C4—1584no—
149C2×C4—1582no—
150C2×C4—1584no—
151C2×C4—1582no—
152C2×C4—1584no—
153C2×C4—1582no—
154C2×C4C2×C22⋊D7912yes—
155C2×C4C2×C22⋊D7912yes—
156C2×C4C2×C22⋊D7912yes—
157C2×C4Q8×D7914yes—
158C2×C4#1192962414yes—
159C22C22×C22⋊D7911yescharacteristic
160C22C2×Q8×D7912yes—
161C22#41×D7912yes—
162C22C2×#1192962412yes—
163C4—22no—
164C4—22no—
165C4—24no—
166C4—42no—
167C4—3162no—
168C4—1584no—
169C4—1588no—
170C4#1457915914yes—
171C2#1909907011yescharacteristic
172C2#1909907411yescharacteristic
173C2C2×#1457915911yescharacteristic
174C2#1909911714yes—
subgroupG/H
centerC22×C4C22×D79
commutator, socle, prime radical, cosocleC23×C79C24
FrattiniC23C23×D79
FittingC2×C4×Q8×C79C2
hypercenterC2×C4×Q8D79
hypocenterC79#2399
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
37. C4×Dic79Q8semidirect
88. C79#2399semidirect