Finite Group Databasebeta

← #23769040

Subgroups — #23769040

Order 10112.

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

normal subgroups only

This group has 470 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×C4×Dic158C211yesmaximal, characteristic, complemented
2#19098502C211yesmaximal, characteristic, complemented
3#19098499C211yesmaximal, characteristic
4#19098483C211yesmaximal, characteristic, complemented
5#19098475C211yesmaximal, characteristic
6#19098458C212yesmaximal, complemented
7#19098457C212yesmaximal
8#19098451C212yesmaximal
9#19098444C212yesmaximal, complemented
10#19098409C211yesmaximal, characteristic, complemented
11C2×#126×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13C4×Dic158—24no—
14C2×C4⋊Dic79C2211yescharacteristic
15C2×Dic79⋊C4C2212yes—
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×C22⋊Dic79C2212yes—
19C2×C22⋊Dic79C2212yes—
20C2×C4×Dic79C2212yes—
21C2×C4×Dic79C2212yes—
22C79⋊#95C2212yes—
23C79⋊#95C2211yescharacteristic
24C79⋊#95C2211yescharacteristic
25C79⋊#95C2212yes—
26C79⋊#95C2212yes—
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29#126×C79—24no—
30C2×C4⋊C4×C79C2211yescharacteristic
31C2×C4⋊C4×C79C2211yescharacteristic
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C22⋊C4×C79C2211yescharacteristic
34C2×C22⋊C4×C79C2211yescharacteristic
35C2×C22⋊C4×C79C2211yescharacteristic
36C2×C42×C79C2211yescharacteristic
37C2×Dic158—24no—
38C2×Dic158—22no—
39C22×Dic79C2312yes—
40C22×Dic79C2312yes—
41C22×Dic79C2312yes—
42C22×Dic79C2312yes—
43C4⋊Dic79—22no—
44Dic79⋊C4—24no—
45Dic79⋊C4—24no—
46Dic79⋊C4—24no—
47C22⋊Dic79—24no—
48C22⋊Dic79—24no—
49C4×Dic79—24no—
50C4×Dic79—24no—
51C24×C79C2311yescharacteristic
52C22×C4×C79C2311yescharacteristic
53C22×C4×C79C2311yescharacteristic
54C22×C4×C79C2311yescharacteristic
55C22×C4×C79C2311yescharacteristic
56C22×C4×C79C2311yescharacteristic
57C22×C4×C79C2311yescharacteristic
58C4⋊C4×C79—22no—
59C4⋊C4×C79—22no—
60C4⋊C4×C79—22no—
61C22⋊C4×C79—22no—
62C22⋊C4×C79—22no—
63C22⋊C4×C79—22no—
64C42×C79D414yes—
65C23×C79—21no—
66C23×C79—22no—
67C23×C79—22no—
68C23×C79—21no—
69C23×C79—21no—
70C23×C79C2411yescharacteristic
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—21no—
74C2×C4×C79—21no—
75C2×C4×C79—21no—
76C2×C4×C79—21no—
77C2×C4×C79—21no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79—21no—
81C2×C4×C79—21no—
82C2×C4×C79C2×D412yes—
83C2×C4×C79C2×D412yes—
84C2×C4×C79C2×D412yes—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79—22no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—22no—
95C2×Dic79#4114yes—
96C2×Dic79#4114yes—
97Dic158—28no—
98C22×C79—41no—
99C22×C79—41no—
100C22×C79—41no—
101C22×C79—42no—
102C22×C79—42no—
103C22×C79C22×D411yescharacteristic
104C22×C79C2×#4112yes—
105C22×C79C2×#4112yes—
106C22×C792−1+411yescharacteristic
107C22×C792−1+411yescharacteristic
108C4×C79—22no—
109C4×C79—22no—
110C4×C79—22no—
111C4×C79—41no—
112C4×C79—41no—
113C4×C79—41no—
114Dic79—24no—
115Dic79—24no—
116Dic79—42no—
117Dic79—42no—
118C2×C79—81no—
119C2×C79#52511yescharacteristic
120C2×C79#53211yescharacteristic
121C2×C79#53611yescharacteristic
122C2×C79#55212yes—
123C2×C79#55612yes—
124#2604—791nomaximal, Sylow
125C79#260411yescharacteristic, complemented, Sylow
126C2×#126D7911yescharacteristic
127C2×C4×Q8—791no—
128#400—791no—
129#399—791no—
130#395—791no—
131#393—791no—
132#389—792no—
133#388—792no—
134#388—792no—
135#387—792no—
136#376—791no—
137C22×Q8—791no—
138#126—24no—
139C4×Q8—1584no—
140C2×C4⋊C4—792no—
141C2×C4⋊C4—791no—
142C2×C4⋊C4—792no—
143C2×C4⋊C4—792no—
144C2×C4⋊C4C2×D7911yescharacteristic
145C2×C4⋊C4C2×D7911yescharacteristic
146C2×C4⋊C4C2×D7911yescharacteristic
147C2×C22⋊C4—792no—
148C2×C22⋊C4—792no—
149C2×C22⋊C4C2×D7911yescharacteristic
150C2×C22⋊C4C2×D7911yescharacteristic
151C2×C22⋊C4C2×D7911yescharacteristic
152C2×C42—792no—
153C2×C42—792no—
154C2×C42C2×D7911yescharacteristic
155#95—792no—
156#95—791no—
157#95—791no—
158#95—792no—
159#95—792no—
160#95—792no—
161#95—792no—
162C24C22×D7911yescharacteristic
163C2×Q8—1584no—
164C2×Q8—1582no—
165C22×C4—792no—
166C22×C4—792no—
167C22×C4—792no—
168C22×C4—792no—
169C22×C4C22×D7911yescharacteristic
170C22×C4C22×D7911yescharacteristic
171C22×C4C22×D7911yescharacteristic
172C22×C4C22×D7911yescharacteristic
173C22×C4C22×D7911yescharacteristic
174C22×C4C22×D7911yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—1584no—
179C4⋊C4—1584no—
180C4⋊C4—1584no—
181C4⋊C4—1582no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—22no—
185C22⋊C4—1584no—
186C22⋊C4—1584no—
187C42—1584no—
188C42—1584no—
189C42C22⋊D7914yes—
190C23—22no—
191C23—22no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23C23×D7911yescharacteristic
196Q8—1588no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—794no—
209C2×C4—794no—
210C2×C4—1582no—
211C2×C4—1582no—
212C2×C4—1582no—
213C2×C4—1582no—
214C2×C4—1582no—
215C2×C4—1582no—
216C2×C4—1582no—
217C2×C4—1582no—
218C2×C4—1582no—
219C2×C4—1582no—
220C2×C4C2×C22⋊D7912yes—
221C2×C4C2×C22⋊D7912yes—
222C2×C4C2×C22⋊D7912yes—
223C22—42no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22C22×C22⋊D7911yescharacteristic
229C22#41×D7912yes—
230C22#41×D7912yes—
231C22#1457920811yescharacteristic
232C22#1457920811yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—41no—
237C4—41no—
238C4—41no—
239C4—3162no—
240C4—3162no—
241C4—1584no—
242C4—1584no—
243C2—81no—
244C2#1909907011yescharacteristic
245C2#1909910911yescharacteristic
246C2#1909913411yescharacteristic
247C2#1909924912yes—
248C2#1909928012yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×#126×C79C2
prime radicalC24×C79C23
hypercenterC2×#126D79
hypocenterC79#2604
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic158C2semidirect
2. #19098502C2semidirect
4. #19098483C2semidirect
6. #19098458C2semidirect
9. #19098444C2semidirect
10. #19098409C2semidirect
125. C79#2604semidirect