Finite Group Databasebeta

← #23766694

Subgroups — #23766694

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×Dic158C212yesmaximal
2#19098497C212yesmaximal
3#19098496C212yesmaximal
4#19098484C212yesmaximal
5#19098483C212yesmaximal
6C4×Dic79⋊C4C212yesmaximal
7C4×C4⋊Dic79C211yesmaximal, characteristic
8#19098409C211yesmaximal, characteristic
9C4×C4⋊C4×C79C211yesmaximal, characteristic
10C22×Dic158C2212yes—
11C4×Dic158—28no—
12C2×C4⋊Dic79C2212yes—
13C2×C4⋊Dic79C2212yes—
14C2×Dic79⋊C4C2212yes—
15C2×Dic79⋊C4C2212yes—
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×C4×Dic79C2212yes—
19C2×C4×Dic79C2211yescharacteristic
20C2×C4×Dic79C2211yescharacteristic
21C79⋊#95C2212yes—
22C79⋊#95C2212yes—
23C79⋊#95C2211yescharacteristic
24C79⋊#95C2211yescharacteristic
25C79⋊#95C2212yes—
26C79⋊#95C2212yes—
27C2×C4⋊C4×C79C2212yes—
28C2×C42×C79C2212yes—
29C2×C42×C79C2211yescharacteristic
30#95×C79C2211yescharacteristic
31#95×C79C2211yescharacteristic
32C2×Dic158—24no—
33C2×Dic158—24no—
34C2×Dic158—24no—
35C22×Dic79C2312yes—
36C22×Dic79C2312yes—
37C22×Dic79C2312yes—
38C22×Dic79C2312yes—
39C4⋊Dic79—24no—
40C4⋊Dic79—24no—
41Dic79⋊C4—24no—
42Dic79⋊C4—24no—
43Dic79⋊C4—24no—
44Dic79⋊C4—24no—
45C4×Dic79—24no—
46C4×Dic79D414yes—
47C4×Dic79Q814yescomplemented
48C22×C4×C79C2312yes—
49C22×C4×C79C2311yescharacteristic
50C22×C4×C79C2311yescharacteristic
51C22×C4×C79C2312yes—
52C22×C4×C79C2311yescharacteristic
53C4⋊C4×C79—24no—
54C42×C79—24no—
55C42×C79Q814yescomplemented
56C23×C79C2411yescharacteristic
57C2×C4×C79—22no—
58C2×C4×C79—22no—
59C2×C4×C79—22no—
60C2×C4×C79—22no—
61C2×C4×C79—22no—
62C2×C4×C79—22no—
63C2×C4×C79—22no—
64C2×C4×C79C2×D412yes—
65C2×C4×C79C2×Q812yes—
66C2×C4×C79C2×Q812yes—
67C2×C4×C79C2×Q812yes—
68C2×C4×C79C2×Q812yes—
69C2×C4×C79#4114yes—
70C2×Dic79—22no—
71C2×Dic79—22no—
72C2×Dic79—22no—
73C2×Dic79—22no—
74C2×Dic79—22no—
75C2×Dic79—22no—
76C2×Dic79—22no—
77C2×Dic79—22no—
78C2×Dic79—22no—
79C2×Dic79C2×D414yes—
80C2×Dic79C2×Q814yes—
81C2×Dic79#4114yes—
82Dic158—216no—
83C22×C79C22×D411yescharacteristic
84C22×C79C22×Q811yescharacteristic
85C22×C79C22×Q811yescharacteristic
86C22×C79C2×#4112yes—
87C22×C79C2×#4112yes—
88C4×C79—24no—
89C4×C79—22no—
90C4×C79—22no—
91C4×C79—42no—
92C4×C79C4⋊Q814yes—
93Dic79—24no—
94Dic79—24no—
95Dic79—24no—
96Dic79—42no—
97C2×C79#52512yes—
98C2×C79C2×C4⋊Q811yescharacteristic
99C2×C79#53311yescharacteristic
100C2×C79#53312yes—
101C2×C79#53311yescharacteristic
102#2399—791nomaximal, Sylow
103C79#239911yescharacteristic, complemented, Sylow
104C2×C4×Q8—792no—
105#398—792no—
106#398—792no—
107#395—792no—
108#395—792no—
109C4×C4⋊C4—791no—
110C4×C4⋊C4—792no—
111C4×C4⋊C4D7911yescharacteristic
112#376—791no—
113C22×Q8—792no—
114C4×Q8—1588no—
115C2×C4⋊C4—792no—
116C2×C4⋊C4—792no—
117C2×C4⋊C4—792no—
118C2×C4⋊C4—792no—
119C2×C4⋊C4—792no—
120C2×C4⋊C4—792no—
121C2×C4⋊C4C2×D7912yes—
122C2×C42—791no—
123C2×C42—791no—
124C2×C42—792no—
125C2×C42C2×D7912yes—
126C2×C42C2×D7911yescharacteristic
127#95—792no—
128#95—792no—
129#95—792no—
130#95—791no—
131#95—792no—
132#95—791no—
133#95C2×D7911yescharacteristic
134#95C2×D7911yescharacteristic
135C2×Q8—1584no—
136C2×Q8—1584no—
137C2×Q8—1584no—
138C22×C4—792no—
139C22×C4—792no—
140C22×C4—792no—
141C22×C4—792no—
142C22×C4C22×D7912yes—
143C22×C4C22×D7911yescharacteristic
144C22×C4C22×D7911yescharacteristic
145C22×C4C22×D7912yes—
146C22×C4C22×D7911yescharacteristic
147C4⋊C4—24no—
148C4⋊C4—1584no—
149C4⋊C4—1584no—
150C4⋊C4—1584no—
151C4⋊C4—1584no—
152C4⋊C4—1584no—
153C4⋊C4—1584no—
154C42—24no—
155C42—794no—
156C42—794no—
157C42—1584no—
158C42Dic15814yescomplemented
159C23C23×D7911yescharacteristic
160Q8—15816no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—794no—
169C2×C4—794no—
170C2×C4—794no—
171C2×C4—1582no—
172C2×C4—1582no—
173C2×C4—1582no—
174C2×C4—1582no—
175C2×C4—1582no—
176C2×C4—1582no—
177C2×C4—1582no—
178C2×C4—1582no—
179C2×C4—1582no—
180C2×C4D4×D7912yes—
181C2×C4Q8×D7912yes—
182C2×C4C2×Dic15812yes—
183C2×C4C2×Dic15812yes—
184C2×C4C2×Dic15812yes—
185C2×C4#1192962414yes—
186C22C2×D4×D7911yescharacteristic
187C22C2×Q8×D7911yescharacteristic
188C22C22×Dic15811yescharacteristic
189C22#41×D7912yes—
190C22C2×#1192962412yes—
191C4—24no—
192C4—22no—
193C4—22no—
194C4—42no—
195C4—3162no—
196C4—1584no—
197C4—1584no—
198C4—1584no—
199C4#1457916014yes—
200C2#1909907212yes—
201C2C2×#1457916011yescharacteristic
202C2#1909911611yescharacteristic
203C2#1909911712yes—
204C2#1909912011yescharacteristic
subgroupG/H
centerC22×C4C22×D79
commutator, socle, prime radical, cosocleC23×C79C24
FrattiniC23C23×D79
FittingC4×C4⋊C4×C79C2
hypercenterC4×C4⋊C4D79
hypocenterC79#2399
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
47. C4×Dic79Q8semidirect
55. C42×C79Q8semidirect
103. C79#2399semidirect
158. C42Dic158semidirect