Finite Group Databasebeta

← #23772909

Subgroups — #23772909

Order 10112.

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

normal subgroups only

This group has 494 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×#14579187C211yesmaximal, characteristic
2#19099137C211yesmaximal, characteristic, complemented
3#19099038C211yesmaximal, characteristic, complemented
4#19098780C214yesmaximal, complemented
5#19098766C214yesmaximal, complemented
6#19098589C211yesmaximal, characteristic, complemented
7#19098572C211yesmaximal, characteristic, complemented
8#19098560C211yesmaximal, characteristic, complemented
9C22×SD16×C79C211yesmaximal, characteristic, complemented
10C2×#11929624C2211yescharacteristic
11#14579187—24no—
12C2×#11929612C2212yes—
13C2×#11929609C2212yes—
14C2×#11929608C2211yescharacteristic
15#14579159C2212yescomplemented
16#14579150C2212yescomplemented
17#14579144—22no—
18#14579137—22no—
19D4×Dic79—22no—
20D4×Dic79C2214yes—
21#14579120C2211yescharacteristic
22#14579120C2211yescharacteristic
23C2×C22⋊Dic79—22no—
24Dic79⋊C8C2214yescomplemented
25#14579086C2212yescomplemented
26#14579085C2214yescomplemented
27#14579083C2212yescomplemented
28C22×Q8×C79C2211yescharacteristic
29C22×D4×C79C2211yescharacteristic
30C2×SD16×C79—24no—
31C2×SD16×C79C2214yes—
32C22×C8×C79C2211yescharacteristic
33#11929624—22no—
34#11929624—22no—
35C2×Dic158C2311yescharacteristic
36C2×D316C2311yescharacteristic
37C2×C22⋊D79—21no—
38C22×Dic79—24no—
39C2×C4×D79—21no—
40#11929612—24no—
41#11929609—24no—
42#11929608—22no—
43C2×C79⋊C8C2312yes—
44C4⋊Dic79D412yes—
45C4⋊Dic79C2312yes—
46Dic79⋊C4—24no—
47C22⋊Dic79—24no—
48C22⋊Dic79—21no—
49C22⋊Dic79D412yes—
50(C2×D79)⋊C4—24no—
51C4×Dic79—21no—
52C4×Dic79C2312yes—
53C24×C79—21no—
54C2×Q8×C79—21no—
55C2×Q8×C79—22no—
56C2×Q8×C79—22no—
57C2×Q8×C79C2312yes—
58C2×D4×C79—21no—
59C2×D4×C79—22no—
60C2×D4×C79D414yes—
61C2×D4×C79C2312yes—
62C22×C4×C79—21no—
63C22×C4×C79C2311yescharacteristic
64SD16×C79—28no—
65C2×C8×C79—22no—
66C2×C8×C79C2312yes—
67C23×C79—22no—
68C23×C79—24no—
69C23×C79—82no—
70C23×C79C2×D411yescharacteristic
71C22×D79—21no—
72Q8×C79—22no—
73Q8×C79—22no—
74Q8×C79—42no—
75D4×C79—24no—
76D4×C79—22no—
77D4×C79C2×D414yes—
78C2×C4×C79—22no—
79C2×C4×C79—42no—
80C2×C4×C79C2×D411yescharacteristic
81C2×C4×C79C2×D412yes—
82C2×C4×C79#4112yes—
83C2×C4×C79C2411yescharacteristic
84C22⋊D79—42no—
85C2×Dic79—22no—
86C2×Dic79—21no—
87C2×Dic79—84no—
88C2×Dic79C2×D414yes—
89D316—21no—
90D316—21no—
91C4×D79—42no—
92Dic158—21no—
93Dic158—21no—
94C8×C79—22no—
95C79⋊C8—22no—
96C22×C79—22no—
97C22×C79—24no—
98C22×C79—44no—
99C22×C79—84no—
100C22×C79#12112yes—
101C22×C79C22×D411yescharacteristic
102C2×D79—41no—
103C2×D79—42no—
104C4×C79—42no—
105C4×C79#12112yes—
106C4×C79C22×D411yescharacteristic
107C4×C79C2×#4111yescharacteristic
108Dic79—24no—
109Dic79—41no—
110Dic79—42no—
111C2×C79—22no—
112C2×C79—44no—
113C2×C79C2×#12111yescharacteristic
114C2×C79#57712yes—
115D79—81no—
116#3042—791nomaximal, Sylow
117C79#304211yescharacteristic, complemented, Sylow
118C2×AGL(1,ℤ/8)—791no—
119C22×SD16D7911yescharacteristic, complemented
120#536—791no—
121#518—791no—
122#463—794no—
123#461—794no—
124#424—791no—
125#419—791no—
126#416—791no—
127C2×#41—791no—
128C22×Q8C2×D7911yescharacteristic
129C22×D4C2×D7911yescharacteristic
130AGL(1,ℤ/8)—1584no—
131C2×SD16—24no—
132C2×SD16—792no—
133C2×SD16C2×D7914yes—
134C2×D8—792no—
135C2×M16—791no—
136C22×C8C2×D7911yescharacteristic
137C4⋊Q8—792no—
138#124—792no—
139#123—1582no—
140C22⋊Q8—1582no—
141C4×D4—794no—
142C4×D4—1582no—
143#117—791no—
144#117—791no—
145C2×C22⋊C4—1582no—
146C4⋊C8—794no—
147#103—794no—
148#103—792no—
149#102—792no—
150C24—21no—
151#41—1582no—
152#41—1582no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—791no—
157C2×Q8C22×D7912yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—791no—
161C2×D4—1581no—
162C2×D4C22⋊D7914yes—
163C2×D4C22×D7912yes—
164C22×C4—21no—
165C22×C4—1581no—
166C22×C4—1584no—
167C22×C4C22×D7911yescharacteristic
168SD16—28no—
169SD16—1584no—
170D8—1584no—
171M16—1582no—
172C2×C8—22no—
173C2×C8—792no—
174C2×C8C22×D7912yes—
175C4⋊C4—792no—
176C4⋊C4—792no—
177C4⋊C4—1584no—
178C22⋊C4—792no—
179C22⋊C4—1584no—
180C22⋊C4—1584no—
181C22⋊C4—1581no—
182C42—792no—
183C42—1581no—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—1581no—
188C23D4×D7911yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—1581no—
193Q8—1581no—
194D4—22no—
195D4—24no—
196D4—3162no—
197D4—1581no—
198D4—1581no—
199D4C2×C22⋊D7914yes—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—3162no—
203C2×C4—794no—
204C2×C4—6324no—
205C2×C4—1582no—
206C2×C4—1581no—
207C2×C4D4×D7911yescharacteristic
208C2×C4C2×C22⋊D7912yes—
209C2×C4#1192962312yes—
210C2×C4C23×D7911yescharacteristic
211C8—22no—
212C8—1582no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—3161no—
218C22—3162no—
219C22#1457913312yes—
220C22C2×D4×D7911yescharacteristic
221C4—42no—
222C4—3161no—
223C4—3162no—
224C4—1584no—
225C4#1457913312yes—
226C4C22×C22⋊D7911yescharacteristic
227C4C2×#1192962311yescharacteristic
228C2—22no—
229C2—44no—
230C2—6321no—
231C2C2×#1457913311yescharacteristic
232C2#1909936912yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC22×SD16×C79C2
socleC22×C79C22×D4
prime radicalC2×#14579187C2
hypercenterC22×SD16D79
hypocenterC79#3042
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. #19099137C2semidirect
3. #19099038C2semidirect
4. #19098780C2semidirect
5. #19098766C2semidirect
6. #19098589C2semidirect
7. #19098572C2semidirect
8. #19098560C2semidirect
9. C22×SD16×C79C2semidirect
15. #14579159C22semidirect
16. #14579150C22semidirect
24. Dic79⋊C8C22semidirect
25. #14579086C22semidirect
26. #14579085C22semidirect
27. #14579083C22semidirect
117. C79#3042semidirect
119. C22×SD16D79semidirect