Finite Group Databasebeta

← #23766204

Subgroups — #23766204

Order 10112.

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

normal subgroups only

This group has 428 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×#14579153C211yesmaximal, characteristic
2#19098458C212yesmaximal
3#19098448C212yesmaximal
4#19098447C212yesmaximal
5#19098446C212yesmaximal
6#19098444C212yesmaximal
7#19098431C211yesmaximal, characteristic
8C4×Dic79⋊C4C212yesmaximal
9C4×C4⋊C4×C79C211yesmaximal, characteristic
10#14579153C418yescomplemented
11C2×C4⋊Dic79C2211yescharacteristic
12C2×C4⋊Dic79C2211yescharacteristic
13C2×Dic79⋊C4C2212yes—
14C2×Dic79⋊C4C2212yes—
15C2×Dic79⋊C4C2212yes—
16C2×Dic79⋊C4C2212yes—
17C2×C4×Dic79C2212yes—
18C2×C4×Dic79C2212yes—
19C79⋊#95C2212yes—
20C79⋊#95C2212yes—
21C79⋊#95C2211yescharacteristic
22C79⋊#95C2212yes—
23C79⋊#95C2211yescharacteristic
24C79⋊#95C2212yes—
25C79⋊#95C2212yes—
26C79⋊#95C2212yes—
27C2×C4⋊C4×C79C2212yes—
28C2×C42×C79C2211yescharacteristic
29C2×C42×C79C2211yescharacteristic
30C2×C42×C79C2211yescharacteristic
31#95×C79C2212yes—
32C22×Dic79C2312yes—
33C22×Dic79C2312yes—
34C22×Dic79C2312yes—
35C22×Dic79C2312yes—
36C4⋊Dic79C2×C414yes—
37C4⋊Dic79C2×C414yes—
38Dic79⋊C4—24no—
39Dic79⋊C4—42no—
40Dic79⋊C4C2×C418yes—
41Dic79⋊C4C2×C418yes—
42C4×Dic79—24no—
43C4×Dic79—42no—
44C22×C4×C79C2312yes—
45C22×C4×C79C2311yescharacteristic
46C22×C4×C79C2311yescharacteristic
47C22×C4×C79C2311yescharacteristic
48C22×C4×C79C2312yes—
49C4⋊C4×C79—24no—
50C42×C79—41no—
51C42×C79—41no—
52C42×C79C2×C414yes—
53C23×C79C2411yescharacteristic
54C2×C4×C79—22no—
55C2×C4×C79—22no—
56C2×C4×C79—21no—
57C2×C4×C79—22no—
58C2×C4×C79—22no—
59C2×C4×C79—21no—
60C2×C4×C79—22no—
61C2×C4×C79—22no—
62C2×C4×C79—22no—
63C2×C4×C79C22×C412yes—
64C2×C4×C79C22×C412yes—
65C2×C4×C79C22×C412yes—
66C2×C4×C79#4114yes—
67C2×Dic79—22no—
68C2×Dic79—22no—
69C2×Dic79—22no—
70C2×Dic79—22no—
71C2×Dic79—22no—
72C2×Dic79—22no—
73C2×Dic79—22no—
74C2×Dic79—22no—
75C2×Dic79—22no—
76C2×Dic79—22no—
77C2×Dic79C22×C414yes—
78C2×Dic79C22×C414yes—
79C22×C79C23×C411yescharacteristic
80C22×C79C2×#4112yes—
81C22×C79H(5,𝔽2)11yescharacteristic
82C22×C792−1+412yes—
83C22×C792−1+411yescharacteristic
84C4×C79—22no—
85C4×C79—22no—
86C4×C79—22no—
87C4×C79—24no—
88C4×C79—42no—
89Dic79—24no—
90Dic79—24no—
91Dic79—42no—
92Dic79—42no—
93C2×C79C4×#4111yescharacteristic
94C2×C79#51911yescharacteristic
95C2×C79#52011yescharacteristic
96C2×C79#53912yes—
97C2×C79#54112yes—
98#2336—791nomaximal, Sylow
99C79#233611yescharacteristic, complemented, Sylow
100C2×#125—791no—
101#389—792no—
102#387—792no—
103#387—792no—
104#387—792no—
105#387—792no—
106#383—791no—
107C4×C4⋊C4—792no—
108C4×C4⋊C4D7911yescharacteristic
109#125—798no—
110C2×C4⋊C4—792no—
111C2×C4⋊C4—792no—
112C2×C4⋊C4—791no—
113C2×C4⋊C4—791no—
114C2×C4⋊C4—792no—
115C2×C4⋊C4—792no—
116C2×C4⋊C4C2×D7912yes—
117C2×C42—792no—
118C2×C42—792no—
119C2×C42C2×D7911yescharacteristic
120C2×C42C2×D7911yescharacteristic
121C2×C42C2×D7911yescharacteristic
122#95—792no—
123#95—792no—
124#95—791no—
125#95—792no—
126#95—791no—
127#95—792no—
128#95—792no—
129#95—792no—
130#95C2×D7912yes—
131C22×C4—792no—
132C22×C4—792no—
133C22×C4—792no—
134C22×C4—792no—
135C22×C4C22×D7912yes—
136C22×C4C22×D7911yescharacteristic
137C22×C4C22×D7911yescharacteristic
138C22×C4C22×D7911yescharacteristic
139C22×C4C22×D7912yes—
140C4⋊C4—24no—
141C4⋊C4—3162no—
142C4⋊C4—798no—
143C4⋊C4—798no—
144C4⋊C4—794no—
145C4⋊C4—794no—
146C4⋊C4—1584no—
147C42—41no—
148C42—41no—
149C42—3162no—
150C42—1584no—
151C42C4×D7914yes—
152C23C23×D7911yescharacteristic
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—794no—
163C2×C4—794no—
164C2×C4—1582no—
165C2×C4—1582no—
166C2×C4—1582no—
167C2×C4—1582no—
168C2×C4—1582no—
169C2×C4—1582no—
170C2×C4—1582no—
171C2×C4—1582no—
172C2×C4—1582no—
173C2×C4—1582no—
174C2×C4C2×C4×D7912yes—
175C2×C4C2×C4×D7912yes—
176C2×C4C2×C4×D7912yes—
177C2×C4#1192962414yes—
178C22C22×C4×D7911yescharacteristic
179C22C2×#1192962412yes—
180C22#1457920611yescharacteristic
181C22#1457920812yes—
182C22#1457920911yescharacteristic
183C4—24no—
184C4—22no—
185C4—22no—
186C4—22no—
187C4—42no—
188C4—3162no—
189C4—3162no—
190C4—1584no—
191C4—1584no—
192C2C4×#1192962411yescharacteristic
193C2#1909904011yescharacteristic
194C2#1909904411yescharacteristic
195C2#1909915512yes—
196C2#1909917112yes—
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
FittingC4×C4⋊C4×C79C2
socle, prime radical, cosocleC23×C79C24
hypercenterC4×C4⋊C4D79
hypocenterC79#2336
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
10. #14579153C4semidirect
99. C79#2336semidirect