Finite Group Databasebeta

← #23768971

Subgroups — #23768971

Order 10112.

492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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#19098494C211yesmaximal, characteristic, complemented
3#19098489C211yesmaximal, characteristic
4#19098482C211yesmaximal, characteristic, complemented
5#19098474C211yesmaximal, characteristic
6#19098454C212yesmaximal
7#19098447C212yesmaximal, complemented
8#19098444C212yesmaximal, complemented
9#19098434C212yesmaximal
10#19098431C211yesmaximal, characteristic, complemented
11C2×C4×Q8×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×Dic79C2211yescharacteristic
23C79⋊#95C2212yes—
24C79⋊#95C2212yes—
25C79⋊#95C2211yescharacteristic
26C79⋊#95C2211yescharacteristic
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C22×Q8×C79C2211yescharacteristic
32C4×Q8×C79—24no—
33C2×C4⋊C4×C79C2212yes—
34C2×C4⋊C4×C79C2211yescharacteristic
35C2×C42×C79C2212yes—
36C2×C42×C79C2211yescharacteristic
37C23×D79C2311yescharacteristic
38C22×Dic79C2312yes—
39C22×Dic79C2312yes—
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2311yescharacteristic
43C2×C4×D79—22no—
44C2×C4×D79—22no—
45C2×C4×D79—22no—
46Dic79⋊C4—24no—
47Dic79⋊C4—22no—
48Dic79⋊C4—22no—
49Dic79⋊C4—24no—
50(C2×D79)⋊C4—24no—
51(C2×D79)⋊C4—22no—
52(C2×D79)⋊C4—22no—
53(C2×D79)⋊C4—24no—
54C4×Dic79—22no—
55C2×Q8×C79—22no—
56C2×Q8×C79—24no—
57C22×C4×C79C2312yes—
58C22×C4×C79C2311yescharacteristic
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2311yescharacteristic
61C22×C4×C79C2312yes—
62C4⋊C4×C79—24no—
63C4⋊C4×C79—22no—
64C42×C79—24no—
65C42×C79D414yes—
66C23×C79C2411yescharacteristic
67C22×D79—21no—
68C22×D79—22no—
69C22×D79—21no—
70C22×D79—22no—
71C22×D79#4112yes—
72Q8×C79—28no—
73C2×C4×C79—22no—
74C2×C4×C79—21no—
75C2×C4×C79—21no—
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×C4×C79#4114yes—
86C2×Dic79—21no—
87C2×Dic79—21no—
88C2×Dic79—21no—
89C2×Dic79—21no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79#4112yes—
99C4×D79—28no—
100C22×C79C22×D411yescharacteristic
101C22×C79C2×#4111yescharacteristic
102C22×C79C2×#4111yescharacteristic
103C22×C79C2×#4112yes—
104C22×C792−1+412yes—
105C2×D79—22no—
106C2×D79—24no—
107C2×D79—41no—
108C2×D79—41no—
109C2×D79—42no—
110C4×C79—22no—
111C4×C79—22no—
112C4×C79—24no—
113C4×C79—22no—
114C4×C79—42no—
115Dic79—22no—
116Dic79—41no—
117Dic79—41no—
118Dic79—42no—
119Dic79—42no—
120C2×C79#52511yescharacteristic
121C2×C79#52511yescharacteristic
122C2×C79#53611yescharacteristic
123C2×C79#55212yes—
124C2×C79#55612yes—
125D79—42no—
126#2599—791nomaximal, Sylow
127C79#259911yescharacteristic, complemented, Sylow
128C2×C4×Q8D7911yescharacteristic, complemented
129C2×#117—791no—
130#398—791no—
131#397—791no—
132#395—791no—
133#393—791no—
134#388—792no—
135#387—792no—
136#387—792no—
137#385—792no—
138#383—791no—
139C22×Q8C2×D7911yescharacteristic
140C23×C4—791no—
141C4×Q8—24no—
142#117—1584no—
143C2×C4⋊C4—791no—
144C2×C4⋊C4—791no—
145C2×C4⋊C4—792no—
146C2×C4⋊C4—792no—
147C2×C4⋊C4C2×D7912yes—
148C2×C4⋊C4C2×D7911yescharacteristic
149C2×C22⋊C4—791no—
150C2×C22⋊C4—791no—
151C2×C22⋊C4—792no—
152C2×C22⋊C4—792no—
153C2×C42—791no—
154C2×C42C2×D7912yes—
155C2×C42C2×D7911yescharacteristic
156#95—792no—
157#95—792no—
158#95—791no—
159#95—791no—
160#95—792no—
161#95—792no—
162#95—792no—
163#95—792no—
164C24—791no—
165C2×Q8—22no—
166C2×Q8—24no—
167C22×C4—791no—
168C22×C4—792no—
169C22×C4—792no—
170C22×C4—791no—
171C22×C4—791no—
172C22×C4—1582no—
173C22×C4—1582no—
174C22×C4—1582no—
175C22×C4C22×D7912yes—
176C22×C4C22×D7911yescharacteristic
177C22×C4C22×D7911yescharacteristic
178C22×C4C22×D7911yescharacteristic
179C22×C4C22×D7912yes—
180C4⋊C4—24no—
181C4⋊C4—22no—
182C4⋊C4—1584no—
183C4⋊C4—1582no—
184C4⋊C4—1582no—
185C4⋊C4—1584no—
186C22⋊C4—1584no—
187C22⋊C4—1582no—
188C22⋊C4—1582no—
189C22⋊C4—1584no—
190C42—24no—
191C42—1582no—
192C42C22⋊D7914yes—
193C23—792no—
194C23—1581no—
195C23—1582no—
196C23—1582no—
197C23—1581no—
198C23C23×D7911yescharacteristic
199Q8—28no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—792no—
210C2×C4—1588no—
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—1581no—
220C2×C4—1581no—
221C2×C4—1581no—
222C2×C4—1581no—
223C2×C4C2×C22⋊D7912yes—
224C2×C4C2×C22⋊D7912yes—
225C2×C4C2×C22⋊D7912yes—
226C2×C4#1192962414yes—
227C22—3161no—
228C22—3162no—
229C22—3161no—
230C22—1584no—
231C22—1582no—
232C22C22×C22⋊D7911yescharacteristic
233C22#41×D7911yescharacteristic
234C22#41×D7911yescharacteristic
235C22C2×#1192962412yes—
236C22#1457920912yes—
237C4—22no—
238C4—22no—
239C4—22no—
240C4—24no—
241C4—42no—
242C4—3161no—
243C4—3162no—
244C4—3162no—
245C4—3161no—
246C4—1582no—
247C2—3162no—
248C2#1909907011yescharacteristic
249C2#1909907411yescharacteristic
250C2#1909913711yescharacteristic
251C2#1909925412yes—
252C2#1909928512yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×C4×Q8×C79C2
prime radicalC23×D79C23
hypercenterC2×C4×Q8D79
hypocenterC79#2599
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #19098494C2semidirect
4. #19098482C2semidirect
7. #19098447C2semidirect
8. #19098444C2semidirect
10. #19098431C2semidirect
11. C2×C4×Q8×C79C2semidirect
127. C79#2599semidirect
128. C2×C4×Q8D79semidirect