Finite Group Databasebeta

← #23769091

Subgroups — #23769091

Order 10112.

476 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14579152C211yesmaximal, characteristic, complemented
2C2×#14579117C211yesmaximal, characteristic
3#19098501C211yesmaximal, characteristic, complemented
4#19098495C211yesmaximal, characteristic, complemented
5#19098488C211yesmaximal, characteristic
6#19098459C212yesmaximal, complemented
7#19098451C212yesmaximal
8#19098449C212yesmaximal, complemented
9#19098438C212yesmaximal
10#19098408C211yesmaximal, characteristic, complemented
11#399×C79C211yesmaximal, characteristic
12C23×Dic79C2211yescharacteristic
13#14579152—24no—
14#14579117—24no—
15C2×C4⋊Dic79C2212yes—
16C2×C4⋊Dic79C2212yes—
17C2×C4⋊Dic79C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×C22⋊Dic79C2212yes—
22C2×C22⋊Dic79C2211yescharacteristic
23C2×C4×Dic79C2212yes—
24C2×C4×Dic79C2211yescharacteristic
25C2×C4×Dic79C2211yescharacteristic
26C79⋊#95C2212yes—
27C79⋊#95C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2212yes—
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C22⋊C4×C79C2212yes—
35C2×C22⋊C4×C79C2211yescharacteristic
36#95×C79C2211yescharacteristic
37C22×Dic79—22no—
38C22×Dic79—22no—
39C22×Dic79—22no—
40C22×Dic79C2312yes—
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2312yes—
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2311yescharacteristic
46C4⋊Dic79—24no—
47C4⋊Dic79—24no—
48C4⋊Dic79—22no—
49Dic79⋊C4—22no—
50Dic79⋊C4—24no—
51Dic79⋊C4—22no—
52C22⋊Dic79—22no—
53C22⋊Dic79—24no—
54C4×Dic79—22no—
55C4×Dic79—24no—
56C4×Dic79D414yes—
57C24×C79C2311yescharacteristic
58C22×C4×C79C2311yescharacteristic
59C22×C4×C79C2312yes—
60C22×C4×C79C2311yescharacteristic
61C22×C4×C79C2312yes—
62C4⋊C4×C79—22no—
63C4⋊C4×C79—24no—
64C22⋊C4×C79—22no—
65C22⋊C4×C79—24no—
66C23×C79—21no—
67C23×C79—21no—
68C23×C79—22no—
69C23×C79—22no—
70C23×C79#4112yes—
71C23×C79C2411yescharacteristic
72C2×C4×C79—22no—
73C2×C4×C79—22no—
74C2×C4×C79—22no—
75C2×C4×C79—21no—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79C2×D412yes—
81C2×C4×C79#4114yes—
82C2×Dic79—28no—
83C2×Dic79—21no—
84C2×Dic79—22no—
85C2×Dic79—21no—
86C2×Dic79—21no—
87C2×Dic79—21no—
88C2×Dic79—21no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79C2×D412yes—
97C2×Dic79C2×D412yes—
98C2×Dic79#4112yes—
99C22×C79—22no—
100C22×C79—24no—
101C22×C79—41no—
102C22×C79—41no—
103C22×C79—42no—
104C22×C79C22×D411yescharacteristic
105C22×C79C2×#4111yescharacteristic
106C22×C79C2×#4112yes—
107C22×C79C2×#4111yescharacteristic
108C22×C792−1+412yes—
109C4×C79—22no—
110C4×C79—24no—
111C4×C79—41no—
112C4×C79—42no—
113Dic79—22no—
114Dic79—22no—
115Dic79—22no—
116Dic79—42no—
117Dic79—41no—
118Dic79—42no—
119C2×C79—42no—
120C2×C79#52511yescharacteristic
121C2×C79#53211yescharacteristic
122C2×C79#53611yescharacteristic
123C2×C79#55212yes—
124C2×C79#55212yes—
125#2611—791nomaximal, Sylow
126C79#261111yescharacteristic, complemented, Sylow
127C2×#125—791no—
128C2×#117—791no—
129#400—791no—
130#399D7911yescharacteristic
131#398—791no—
132#397—791no—
133#389—792no—
134#388—792no—
135#387—792no—
136#385—792no—
137#376—791no—
138C23×C4—791no—
139#125—1584no—
140#117—1584no—
141C2×C4⋊C4—791no—
142C2×C4⋊C4—791no—
143C2×C4⋊C4—792no—
144C2×C4⋊C4—792no—
145C2×C4⋊C4—791no—
146C2×C4⋊C4—792no—
147C2×C4⋊C4C2×D7911yescharacteristic
148C2×C4⋊C4C2×D7912yes—
149C2×C22⋊C4—791no—
150C2×C22⋊C4—792no—
151C2×C22⋊C4C2×D7911yescharacteristic
152C2×C22⋊C4C2×D7912yes—
153C2×C42—791no—
154C2×C42—791no—
155C2×C42—792no—
156#95—792no—
157#95—791no—
158#95—792no—
159#95—792no—
160#95—792no—
161#95—792no—
162#95C2×D7911yescharacteristic
163C24C22×D7911yescharacteristic
164C22×C4—791no—
165C22×C4—791no—
166C22×C4—791no—
167C22×C4—792no—
168C22×C4—791no—
169C22×C4—792no—
170C22×C4—1582no—
171C22×C4—1582no—
172C22×C4—1582no—
173C22×C4C22×D7911yescharacteristic
174C22×C4C22×D7912yes—
175C22×C4C22×D7911yescharacteristic
176C22×C4C22×D7912yes—
177C4⋊C4—22no—
178C4⋊C4—24no—
179C4⋊C4—1582no—
180C4⋊C4—1584no—
181C4⋊C4—1584no—
182C4⋊C4—1584no—
183C4⋊C4—1582no—
184C4⋊C4—1582no—
185C22⋊C4—22no—
186C22⋊C4—24no—
187C22⋊C4—1582no—
188C22⋊C4—1584no—
189C42—794no—
190C42—1582no—
191C42—1584no—
192C23—21no—
193C23—22no—
194C23—22no—
195C23—21no—
196C23#1192962512yes—
197C23C23×D7911yescharacteristic
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—792no—
207C2×C4—792no—
208C2×C4—792no—
209C2×C4—1582no—
210C2×C4—1582no—
211C2×C4—1582no—
212C2×C4—1582no—
213C2×C4—1582no—
214C2×C4—1582no—
215C2×C4—1581no—
216C2×C4—1582no—
217C2×C4—1588no—
218C2×C4—1581no—
219C2×C4—1582no—
220C2×C4—1581no—
221C2×C4—1581no—
222C2×C4—1581no—
223C2×C4D4×D7912yes—
224C2×C4#1192962314yes—
225C22—24no—
226C22—22no—
227C22—42no—
228C22—41no—
229C22—41no—
230C22C2×D4×D7911yescharacteristic
231C22#41×D7911yescharacteristic
232C22C2×#1192962312yes—
233C22C2×#1192962511yescharacteristic
234C22#1457920812yes—
235C4—24no—
236C4—22no—
237C4—42no—
238C4—41no—
239C4—3162no—
240C4—3162no—
241C4—3161no—
242C4—1582no—
243C4—1582no—
244C4—1582no—
245C2—42no—
246C2#1909907611yescharacteristic
247C2#1909911111yescharacteristic
248C2#1909913511yescharacteristic
249C2#1909925012yes—
250C2#1909925512yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#399×C79C2
prime radicalC24×C79C23
hypercenter#399D79
hypocenterC79#2611
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14579152C2semidirect
3. #19098501C2semidirect
4. #19098495C2semidirect
6. #19098459C2semidirect
8. #19098449C2semidirect
10. #19098408C2semidirect
126. C79#2611semidirect