Finite Group Databasebeta

← #23769743

Subgroups — #23769743

Order 10112.

568 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14579142C212yesmaximal
2C2×#14579138C212yesmaximal, complemented
3#19098497C212yesmaximal, complemented
4#19098491C212yesmaximal, complemented
5#19098483C211yesmaximal, characteristic, complemented
6#19098451C212yesmaximal, complemented
7#19098438C212yesmaximal, complemented
8#19098432C211yesmaximal, characteristic, complemented
9#394×C79C211yesmaximal, characteristic
10C22×Dic158C2211yescharacteristic
11C23×Dic79C2212yes—
12#14579142—28no—
13#14579138—28no—
14C2×C4⋊Dic79C2212yes—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×C22⋊Dic79C2212yes—
21C2×C22⋊Dic79C2212yes—
22C2×C22⋊Dic79C2212yes—
23C2×C4×Dic79C2211yescharacteristic
24C79⋊#95C2212yes—
25C79⋊#95C2212yes—
26C79⋊#95C2212yes—
27C79⋊#95C2211yescharacteristic
28C22×D4×C79C2211yescharacteristic
29C2×C4⋊C4×C79C2211yescharacteristic
30C2×C22⋊C4×C79C2212yes—
31C2×C22⋊C4×C79C2212yes—
32#95×C79C2211yescharacteristic
33C2×Dic158—24no—
34C2×Dic158—41no—
35C22×Dic79—24no—
36C22×Dic79—24no—
37C22×Dic79—42no—
38C22×Dic79C2312yes—
39C22×Dic79C2312yes—
40C22×Dic79C2312yes—
41C22×Dic79C2312yes—
42C4⋊Dic79—24no—
43C4⋊Dic79—41no—
44Dic79⋊C4—24no—
45Dic79⋊C4—24no—
46Dic79⋊C4—24no—
47Dic79⋊C4—24no—
48C22⋊Dic79—24no—
49C22⋊Dic79—24no—
50C22⋊Dic79D418yes—
51C4×Dic79—22no—
52C24×C79C2312yes—
53C2×D4×C79—24no—
54C2×D4×C79—41no—
55C22×C4×C79C2311yescharacteristic
56C22×C4×C79C2312yes—
57C22×C4×C79C2311yescharacteristic
58C22×C4×C79C2311yescharacteristic
59C4⋊C4×C79—41no—
60C22⋊C4×C79—24no—
61C22⋊C4×C79—24no—
62C23×C79—22no—
63C23×C79—22no—
64C23×C79—22no—
65C23×C79—22no—
66C23×C79—22no—
67C23×C79—22no—
68C23×C79C2×D414yes—
69C23×C79C2411yescharacteristic
70D4×C79—44no—
71C2×C4×C79—21no—
72C2×C4×C79—21no—
73C2×C4×C79—22no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—21no—
78C2×C4×C79—21no—
79C2×C4×C79—22no—
80C2×C4×C79#4112yes—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79—22no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—48no—
92C2×Dic79C2×D414yes—
93C2×Dic79C2×D414yes—
94Dic158—44no—
95C22×C79—24no—
96C22×C79—24no—
97C22×C79—24no—
98C22×C79—42no—
99C22×C79—42no—
100C22×C79—42no—
101C22×C79—42no—
102C22×C79C22×D412yes—
103C22×C79C2×#4111yescharacteristic
104C22×C79H(5,𝔽2)11yescharacteristic
105C22×C792−1+411yescharacteristic
106C22×C792−1+412yes—
107C4×C79—22no—
108C4×C79—41no—
109C4×C79—41no—
110C4×C79—42no—
111Dic79—24no—
112Dic79—24no—
113Dic79—42no—
114Dic79—42no—
115C2×C79—44no—
116C2×C79#53612yes—
117C2×C79#53911yescharacteristic
118C2×C79D4211yescharacteristic
119C2×C79#54712yes—
120C2×C79#56311yescharacteristic
121#2680—791nomaximal, Sylow
122C79#268011yescharacteristic, complemented, Sylow
123C2×#123—792no—
124C2×C22⋊Q8—792no—
125#398—792no—
126#397—792no—
127#395—791no—
128#394D7911yescharacteristic
129#388—792no—
130#385—792no—
131#384—791no—
132C22×Q8—791no—
133C22×D4C2×D7911yescharacteristic
134C23×C4—792no—
135#123—1588no—
136C22⋊Q8—1588no—
137C2×C4⋊C4—791no—
138C2×C4⋊C4—792no—
139C2×C4⋊C4—792no—
140C2×C4⋊C4—792no—
141C2×C4⋊C4—792no—
142C2×C4⋊C4—792no—
143C2×C4⋊C4C2×D7911yescharacteristic
144C2×C22⋊C4—792no—
145C2×C22⋊C4—792no—
146C2×C22⋊C4—792no—
147C2×C22⋊C4C2×D7912yes—
148C2×C22⋊C4C2×D7912yes—
149C2×C42—791no—
150#95—792no—
151#95—792no—
152#95—792no—
153#95—791no—
154#95C2×D7911yescharacteristic
155C24C22×D7912yes—
156C2×Q8—3161no—
157C2×Q8—1584no—
158C2×D4—24no—
159C2×D4—41no—
160C22×C4—3162no—
161C22×C4—792no—
162C22×C4—792no—
163C22×C4—792no—
164C22×C4—792no—
165C22×C4—1584no—
166C22×C4—1584no—
167C22×C4C22×D7912yes—
168C22×C4C22×D7911yescharacteristic
169C22×C4C22×D7911yescharacteristic
170C22×C4C22×D7911yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—3161no—
173C4⋊C4—1584no—
174C4⋊C4—1584no—
175C4⋊C4—1584no—
176C4⋊C4—1584no—
177C4⋊C4—1584no—
178C22⋊C4—24no—
179C22⋊C4—24no—
180C22⋊C4—798no—
181C22⋊C4—1584no—
182C22⋊C4—1584no—
183C42—1582no—
184C23—22no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—22no—
190C23D4×D7914yes—
191C23C23×D7911yescharacteristic
192Q8—3164no—
193D4—44no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—3168no—
204C2×C4—794no—
205C2×C4—794no—
206C2×C4—1582no—
207C2×C4—1582no—
208C2×C4—1582no—
209C2×C4—1582no—
210C2×C4—1582no—
211C2×C4—1582no—
212C2×C4—1582no—
213C2×C4—1582no—
214C2×C4—1582no—
215C2×C4—1582no—
216C2×C4#1192962312yes—
217C22—24no—
218C22—24no—
219C22—24no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C2×D4×D7912yes—
225C22C2×#1192962311yescharacteristic
226C22#1457920611yescharacteristic
227C22#1457920811yescharacteristic
228C22#1457920812yes—
229C4—22no—
230C4—41no—
231C4—41no—
232C4—42no—
233C4—3162no—
234C4—3162no—
235C4—1584no—
236C4—1584no—
237C2—44no—
238C2#1909913512yes—
239C2#1909915811yescharacteristic
240C2#1909919511yescharacteristic
241C2#1909921312yes—
242C2#1909931311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radicalC22×D4×C79C22
hypercenter#394D79
hypocenterC79#2680
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14579138C2semidirect
3. #19098497C2semidirect
4. #19098491C2semidirect
5. #19098483C2semidirect
6. #19098451C2semidirect
7. #19098438C2semidirect
8. #19098432C2semidirect
122. C79#2680semidirect