Finite Group Databasebeta

← #23765874

Subgroups — #23765874

Order 10112.

500 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 217 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#19098468C212yesmaximal
3#19098459C212yesmaximal
4#19098445C214yesmaximal
5C4×Dic79⋊C4C212yesmaximal
6#19098409C212yesmaximal
7C42×Dic79C211yesmaximal, characteristic
8C4×C4⋊C4×C79C211yesmaximal, characteristic
9C22×Dic158C2211yescharacteristic
10C4×Dic158C418yescomplemented
11C2×C4⋊Dic79C2211yescharacteristic
12C2×Dic79⋊C4C2214yes—
13C2×Dic79⋊C4C2212yes—
14C2×C4×Dic79C2211yescharacteristic
15C2×C4×Dic79C2212yes—
16C2×C4×Dic79C2212yes—
17C2×C4×Dic79C2212yes—
18C2×C4×Dic79C2211yescharacteristic
19C79⋊#95C2214yes—
20C79⋊#95C2214yes—
21C79⋊#95C2214yes—
22C2×C4⋊C4×C79C2212yes—
23C2×C42×C79C2212yes—
24C2×C42×C79C2211yescharacteristic
25#95×C79C2212yes—
26C2×Dic158—24no—
27C2×Dic158C2×C414yes—
28C22×Dic79C2312yes—
29C22×Dic79C2312yes—
30C22×Dic79C2312yes—
31C22×Dic79C2312yes—
32C4⋊Dic79C2×C414yes—
33Dic79⋊C4—28no—
34Dic79⋊C4C2×C418yes—
35C4×Dic79—24no—
36C4×Dic79—22no—
37C4×Dic79—24no—
38C4×Dic79C2×C418yes—
39C4×Dic79Q814yescomplemented
40C22×C4×C79C2314yes—
41C22×C4×C79C2311yescharacteristic
42C22×C4×C79C2311yescharacteristic
43C22×C4×C79C2311yescharacteristic
44C4⋊C4×C79—24no—
45C42×C79—24no—
46C42×C79C2×C414yes—
47C23×C79C2411yescharacteristic
48C2×C4×C79—22no—
49C2×C4×C79—24no—
50C2×C4×C79—24no—
51C2×C4×C79—24no—
52C2×C4×C79C22×C412yes—
53C2×C4×C79C22×C412yes—
54C2×C4×C79C22×C412yes—
55C2×C4×C79C2×Q812yes—
56C2×C4×C79#4112yes—
57C2×C4×C79#4114yes—
58C2×Dic79—22no—
59C2×Dic79—22no—
60C2×Dic79—22no—
61C2×Dic79—22no—
62C2×Dic79—24no—
63C2×Dic79—24no—
64C2×Dic79C22×C414yes—
65C2×Dic79C22×C414yes—
66C2×Dic79C2×Q814yes—
67C2×Dic79#4114yes—
68Dic158—28no—
69C22×C79C23×C411yescharacteristic
70C22×C79C22×Q811yescharacteristic
71C22×C79C2×#4112yes—
72C22×C79C2×#4111yescharacteristic
73C22×C79C2×#4112yes—
74C4×C79—22no—
75C4×C79—44no—
76C4×C79#11714yes—
77C4×C79C4×Q814yes—
78Dic79—24no—
79Dic79—24no—
80Dic79—24no—
81Dic79—24no—
82C2×C79C2×#11711yescharacteristic
83C2×C79C2×C4×Q811yescharacteristic
84C2×C79C4×#4111yescharacteristic
85C2×C79#52912yes—
86C2×C79#53312yes—
87#2295—791nomaximal, Sylow
88C79#229511yescharacteristic, complemented, Sylow
89C2×C4×Q8—791no—
90#391—792no—
91#389—792no—
92#387—794no—
93C4×C4⋊C4—792no—
94C4×C4⋊C4D7911yescharacteristic
95#376—792no—
96C43—791no—
97C22×Q8—791no—
98C4×Q8—798no—
99C2×C4⋊C4—792no—
100C2×C4⋊C4—791no—
101C2×C4⋊C4—794no—
102C2×C4⋊C4C2×D7912yes—
103C2×C42—792no—
104C2×C42—791no—
105C2×C42—792no—
106C2×C42—792no—
107C2×C42—791no—
108C2×C42C2×D7912yes—
109C2×C42C2×D7911yescharacteristic
110#95—794no—
111#95—794no—
112#95—794no—
113#95C2×D7912yes—
114C2×Q8—794no—
115C2×Q8—1584no—
116C22×C4—792no—
117C22×C4—792no—
118C22×C4—792no—
119C22×C4—792no—
120C22×C4C22×D7914yes—
121C22×C4C22×D7911yescharacteristic
122C22×C4C22×D7911yescharacteristic
123C22×C4C22×D7911yescharacteristic
124C4⋊C4—24no—
125C4⋊C4—798no—
126C4⋊C4—794no—
127C4⋊C4—1588no—
128C42—24no—
129C42—798no—
130C42—794no—
131C42—1584no—
132C42—1582no—
133C42—1584no—
134C42C4×D7914yes—
135C23C23×D7911yescharacteristic
136Q8—1588no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4—24no—
140C2×C4—24no—
141C2×C4—794no—
142C2×C4—794no—
143C2×C4—794no—
144C2×C4—794no—
145C2×C4—1582no—
146C2×C4—1584no—
147C2×C4—1582no—
148C2×C4—1582no—
149C2×C4—1582no—
150C2×C4—1584no—
151C2×C4C2×C4×D7912yes—
152C2×C4C2×C4×D7912yes—
153C2×C4C2×C4×D7912yes—
154C2×C4Q8×D7912yes—
155C2×C4#1192962312yes—
156C2×C4#1192962414yes—
157C22C22×C4×D7911yescharacteristic
158C22C2×Q8×D7911yescharacteristic
159C22#41×D7912yes—
160C22C2×#1192962311yescharacteristic
161C22C2×#1192962412yes—
162C4—22no—
163C4—44no—
164C4—1584no—
165C4—1584no—
166C4—1584no—
167C4—1584no—
168C4#1457911814yes—
169C4#1457912614yes—
170C2C2×#1457911811yescharacteristic
171C2C2×#1457912611yescharacteristic
172C2#1909903111yescharacteristic
173C2#1909909512yes—
174C2#1909911712yes—
subgroupG/H
centerC22×C4C22×D79
commutatorC22×C79C23×C4
FrattiniC23C23×D79
FittingC4×C4⋊C4×C79C2
socle, prime radical, cosocleC23×C79C24
hypercenterC4×C4⋊C4D79
hypocenterC79#2295
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
10. C4×Dic158C4semidirect
39. C4×Dic79Q8semidirect
88. C79#2295semidirect