Finite Group Databasebeta

← #23766365

Subgroups — #23766365

Order 10112.

464 conjugacy classes of subgroups; only the 233 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 233 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#19098470C212yesmaximal
2#19098449C214yesmaximal
3#19098431C212yesmaximal
4#19098429C211yesmaximal, characteristic
5C4⋊C4×Dic79C212yesmaximal
6C4×C4⋊Dic79C211yesmaximal, characteristic
7#19098409C212yesmaximal
8C2×C4×Q8×C79C211yesmaximal, characteristic
9C2×C4⋊Dic79C2212yes—
10C2×C4⋊Dic79C2212yes—
11C2×C4×Dic79C2214yes—
12C2×C4×Dic79C2212yes—
13C79⋊#95C2211yescharacteristic
14C79⋊#95C2212yes—
15C79⋊#95C2214yes—
16C79⋊#95C2211yescharacteristic
17C79⋊#95C2214yes—
18C79⋊#95C2212yes—
19C79⋊#95C2214yes—
20C22×Q8×C79C2211yescharacteristic
21C4×Q8×C79C418yescomplemented
22C2×C4⋊C4×C79C2211yescharacteristic
23C2×C4⋊C4×C79C2212yes—
24C2×C42×C79C2212yes—
25C2×C42×C79C2211yescharacteristic
26C22×Dic79C2314yes—
27C22×Dic79C2312yes—
28C22×Dic79C2312yes—
29C4⋊Dic79—24no—
30C4⋊Dic79—24no—
31C4×Dic79—28no—
32C4×Dic79—24no—
33C2×Q8×C79—22no—
34C2×Q8×C79—22no—
35C2×Q8×C79C2×C414yes—
36C22×C4×C79C2311yescharacteristic
37C22×C4×C79C2312yes—
38C22×C4×C79C2311yescharacteristic
39C22×C4×C79C2312yes—
40C22×C4×C79C2311yescharacteristic
41C4⋊C4×C79C2×C418yes—
42C4⋊C4×C79C2×C414yes—
43C42×C79C2×C418yes—
44C42×C79C2×C414yes—
45C23×C79C2411yescharacteristic
46Q8×C79—28no—
47C2×C4×C79—24no—
48C2×C4×C79—22no—
49C2×C4×C79—22no—
50C2×C4×C79—22no—
51C2×C4×C79—22no—
52C2×C4×C79C22×C412yes—
53C2×C4×C79C22×C414yes—
54C2×C4×C79C22×C412yes—
55C2×C4×C79C22×C414yes—
56C2×C4×C79C22×C412yes—
57C2×C4×C79#4112yes—
58C2×C4×C79#4112yes—
59C2×Dic79—22no—
60C2×Dic79—22no—
61C2×Dic79—24no—
62C2×Dic79—22no—
63C2×Dic79—22no—
64C2×Dic79—24no—
65C2×Dic79—22no—
66C2×Dic79—24no—
67C2×Dic79#4114yes—
68C22×C79C23×C411yescharacteristic
69C22×C79C2×#4112yes—
70C22×C79C2×#4111yescharacteristic
71C22×C79C2×#4111yescharacteristic
72C22×C792−1+412yes—
73C4×C79—24no—
74C4×C79—24no—
75C4×C79—22no—
76C4×C79—22no—
77C4×C79#11714yes—
78Dic79—24no—
79Dic79—42no—
80Dic79—44no—
81C2×C79C2×#11711yescharacteristic
82C2×C79C4×#4111yescharacteristic
83C2×C79#51911yescharacteristic
84C2×C79#55212yes—
85C2×C79#55612yes—
86#2356—791nomaximal, Sylow
87C79#235611yescharacteristic, complemented, Sylow
88C2×C4×Q8D7911yescharacteristic
89#391—792no—
90#387—794no—
91#383—792no—
92#382—791no—
93C4×C4⋊C4—792no—
94C4×C4⋊C4—791no—
95#376—792no—
96C22×Q8C2×D7911yescharacteristic
97C4×Q8Dic7918yescomplemented
98C2×C4⋊C4—792no—
99C2×C4⋊C4—792no—
100C2×C4⋊C4C2×D7911yescharacteristic
101C2×C4⋊C4C2×D7912yes—
102C2×C42—794no—
103C2×C42—792no—
104C2×C42C2×D7912yes—
105C2×C42C2×D7911yescharacteristic
106#95—791no—
107#95—792no—
108#95—794no—
109#95—791no—
110#95—794no—
111#95—792no—
112#95—794no—
113C2×Q8—22no—
114C2×Q8—22no—
115C2×Q8C2×Dic7914yes—
116C22×C4—792no—
117C22×C4—794no—
118C22×C4—792no—
119C22×C4C22×D7911yescharacteristic
120C22×C4C22×D7912yes—
121C22×C4C22×D7912yes—
122C22×C4C22×D7911yescharacteristic
123C22×C4C22×D7911yescharacteristic
124C4⋊C4—1584no—
125C4⋊C4—1584no—
126C4⋊C4C2×Dic7918yes—
127C4⋊C4C2×Dic7914yes—
128C42—1588no—
129C42—1584no—
130C42C2×Dic7918yes—
131C42C2×Dic7914yes—
132C23C23×D7911yescharacteristic
133Q8—28no—
134C2×C4—24no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—794no—
140C2×C4—1584no—
141C2×C4—1582no—
142C2×C4—1582no—
143C2×C4—1584no—
144C2×C4—1582no—
145C2×C4—1584no—
146C2×C4—1582no—
147C2×C4—1582no—
148C2×C4C22×Dic7912yes—
149C2×C4C22×Dic7914yes—
150C2×C4C22×Dic7912yes—
151C2×C4C22×Dic7914yes—
152C2×C4C22×Dic7912yes—
153C2×C4#1192962412yes—
154C2×C4#1192962412yes—
155C22C23×Dic7911yescharacteristic
156C22#41×D7912yes—
157C22C2×#1192962411yescharacteristic
158C22C2×#1192962411yescharacteristic
159C22#1457920912yes—
160C4—24no—
161C4—24no—
162C4—22no—
163C4—22no—
164C4—3162no—
165C4—3164no—
166C4—1584no—
167C4#1457912014yes—
168C2C2×#1457912011yescharacteristic
169C2#41×Dic7911yescharacteristic
170C2#1909904111yescharacteristic
171C2#1909925412yes—
172C2#1909928512yes—
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
FittingC2×C4×Q8×C79C2
socle, prime radical, cosocleC23×C79C24
hypercenterC2×C4×Q8D79
hypocenterC79#2356
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
21. C4×Q8×C79C4semidirect
87. C79#2356semidirect
97. C4×Q8Dic79semidirect