Finite Group Databasebeta

← #23769100

Subgroups — #23769100

Order 10112.

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

normal subgroups only

This group has 476 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×#14579118C211yesmaximal, characteristic
2#19098501C211yesmaximal, characteristic, complemented
3#19098498C211yesmaximal, characteristic
4#19098494C211yesmaximal, characteristic, complemented
5#19098489C211yesmaximal, characteristic
6#19098458C212yesmaximal, complemented
7#19098453C212yesmaximal
8#19098444C212yesmaximal, complemented
9#19098434C212yesmaximal
10#19098409C211yesmaximal, characteristic, complemented
11C2×#125×C79C211yesmaximal, characteristic, complemented
12C22×C4×D79C2211yescharacteristic
13#14579118—24no—
14C2×Dic79⋊C4C2212yes—
15C2×Dic79⋊C4C2212yes—
16C2×Dic79⋊C4C2211yescharacteristic
17C2×Dic79⋊C4C2211yescharacteristic
18C2×(C2×D79)⋊C4C2212yes—
19C2×(C2×D79)⋊C4C2212yes—
20C2×(C2×D79)⋊C4C2211yescharacteristic
21C2×(C2×D79)⋊C4C2211yescharacteristic
22C2×C4×Dic79C2212yes—
23C2×C4×Dic79C2211yescharacteristic
24C79⋊#95C2212yes—
25C79⋊#95C2211yescharacteristic
26C79⋊#95C2211yescharacteristic
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31#125×C79—24no—
32C2×C4⋊C4×C79C2212yes—
33C2×C4⋊C4×C79C2212yes—
34C2×C4⋊C4×C79C2211yescharacteristic
35C2×C4⋊C4×C79C2211yescharacteristic
36C2×C42×C79C2211yescharacteristic
37C23×D79C2311yescharacteristic
38C22×Dic79C2312yes—
39C22×Dic79C2311yescharacteristic
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2312yes—
42C22×Dic79C2311yescharacteristic
43C2×C4×D79—22no—
44C2×C4×D79—22no—
45C2×C4×D79—22no—
46Dic79⋊C4—24no—
47Dic79⋊C4—24no—
48Dic79⋊C4—22no—
49Dic79⋊C4—22no—
50(C2×D79)⋊C4—24no—
51(C2×D79)⋊C4—24no—
52(C2×D79)⋊C4—22no—
53(C2×D79)⋊C4—22no—
54C4×Dic79—24no—
55C4×Dic79—22no—
56C22×C4×C79C2312yes—
57C22×C4×C79C2312yes—
58C22×C4×C79C2311yescharacteristic
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2311yescharacteristic
61C4⋊C4×C79—24no—
62C4⋊C4×C79—24no—
63C4⋊C4×C79—22no—
64C4⋊C4×C79—22no—
65C42×C79D414yes—
66C23×C79C2411yescharacteristic
67C22×D79—21no—
68C22×D79—22no—
69C22×D79—21no—
70C22×D79—22no—
71C22×D79#4112yes—
72C2×C4×C79—22no—
73C2×C4×C79—21no—
74C2×C4×C79—21no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79—22no—
81C2×C4×C79—22no—
82C2×C4×C79C2×D412yes—
83C2×C4×C79C2×D412yes—
84C2×C4×C79C2×D412yes—
85C2×Dic79—21no—
86C2×Dic79—22no—
87C2×Dic79—21no—
88C2×Dic79—22no—
89C2×Dic79—21no—
90C2×Dic79—21no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79#4114yes—
97C2×Dic79#4112yes—
98C4×D79—28no—
99C22×C79C22×D411yescharacteristic
100C22×C79C2×#4111yescharacteristic
101C22×C79C2×#4111yescharacteristic
102C22×C79C2×#4112yes—
103C22×C792−1+412yes—
104C2×D79—22no—
105C2×D79—24no—
106C2×D79—41no—
107C2×D79—41no—
108C2×D79—42no—
109C4×C79—22no—
110C4×C79—22no—
111C4×C79—22no—
112C4×C79—42no—
113C4×C79—42no—
114Dic79—22no—
115Dic79—24no—
116Dic79—41no—
117Dic79—41no—
118Dic79—42no—
119C2×C79#52511yescharacteristic
120C2×C79#53211yescharacteristic
121C2×C79#53611yescharacteristic
122C2×C79#55212yes—
123C2×C79#55212yes—
124D79—42no—
125#2611—791nomaximal, Sylow
126C79#261111yescharacteristic, complemented, Sylow
127C2×#125D7911yescharacteristic, complemented
128C2×#117—791no—
129#400—791no—
130#399—791no—
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—24no—
140#117—1584no—
141C2×C4⋊C4—791no—
142C2×C4⋊C4—791no—
143C2×C4⋊C4—792no—
144C2×C4⋊C4—792no—
145C2×C4⋊C4C2×D7912yes—
146C2×C4⋊C4C2×D7912yes—
147C2×C4⋊C4C2×D7911yescharacteristic
148C2×C4⋊C4C2×D7911yescharacteristic
149C2×C22⋊C4—791no—
150C2×C22⋊C4—791no—
151C2×C22⋊C4—792no—
152C2×C22⋊C4—792no—
153C2×C42—791no—
154C2×C42—792no—
155C2×C42C2×D7911yescharacteristic
156#95—792no—
157#95—791no—
158#95—791no—
159#95—792no—
160#95—792no—
161#95—792no—
162#95—792no—
163C24—791no—
164C22×C4—792no—
165C22×C4—791no—
166C22×C4—792no—
167C22×C4—791no—
168C22×C4—791no—
169C22×C4—1582no—
170C22×C4—1582no—
171C22×C4—1582no—
172C22×C4C22×D7912yes—
173C22×C4C22×D7912yes—
174C22×C4C22×D7911yescharacteristic
175C22×C4C22×D7911yescharacteristic
176C22×C4C22×D7911yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—1584no—
182C4⋊C4—1584no—
183C4⋊C4—1582no—
184C4⋊C4—1582no—
185C22⋊C4—1584no—
186C22⋊C4—1584no—
187C22⋊C4—1582no—
188C22⋊C4—1582no—
189C42—1584no—
190C42—1582no—
191C42C22⋊D7914yes—
192C23—792no—
193C23—1582no—
194C23—1581no—
195C23—1582no—
196C23—1581no—
197C23C23×D7911yescharacteristic
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—794no—
209C2×C4—792no—
210C2×C4—1588no—
211C2×C4—1582no—
212C2×C4—1582no—
213C2×C4—1582no—
214C2×C4—1582no—
215C2×C4—1582no—
216C2×C4—1581no—
217C2×C4—1581no—
218C2×C4—1582no—
219C2×C4—1581no—
220C2×C4—1582no—
221C2×C4—1581no—
222C2×C4C2×C22⋊D7912yes—
223C2×C4C2×C22⋊D7912yes—
224C2×C4C2×C22⋊D7912yes—
225C22—3161no—
226C22—3162no—
227C22—3161no—
228C22—1584no—
229C22—1582no—
230C22C22×C22⋊D7911yescharacteristic
231C22#41×D7911yescharacteristic
232C22#41×D7911yescharacteristic
233C22#41×D7912yes—
234C22#1457920912yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—3161no—
241C4—3162no—
242C4—3161no—
243C4—1584no—
244C4—1582no—
245C2—3162no—
246C2#1909907011yescharacteristic
247C2#1909910911yescharacteristic
248C2#1909913711yescharacteristic
249C2#1909924512yes—
250C2#1909924512yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×#125×C79C2
prime radicalC23×D79C23
hypercenterC2×#125D79
hypocenterC79#2611
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #19098501C2semidirect
4. #19098494C2semidirect
6. #19098458C2semidirect
8. #19098444C2semidirect
10. #19098409C2semidirect
11. C2×#125×C79C2semidirect
126. C79#2611semidirect
127. C2×#125D79semidirect