Finite Group Databasebeta

← #23774187

Subgroups — #23774187

Order 10112.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#19099073C212yesmaximal, complemented
2#19098906C212yesmaximal, complemented
3#19098885C212yesmaximal, complemented
4#19098804C211yesmaximal, characteristic, complemented
5#19098790C212yesmaximal, complemented
6#19098726C212yesmaximal, complemented
7#19098705C212yesmaximal, complemented
8C2×(C2×D79)⋊C8C211yesmaximal, characteristic, complemented
9#466×C79C211yesmaximal, characteristic, complemented
10C2×#11929623C2212yes—
11C22×C4×D79C2211yescharacteristic
12C2×Dic316C2211yescharacteristic, complemented
13C2×#11929612C2212yescomplemented
14C22×C79⋊C8C2211yescharacteristic
15#14579143—22no—
16#14579141C2212yes—
17#14579140C2212yes—
18#14579132C2212yes—
19#14579129—22no—
20D4×Dic79—22no—
21(C22⋊D79)⋊C4—22no—
22#14579119C2212yes—
23#14579095C2211yescharacteristic, complemented
24#14579092C2212yescomplemented
25#14579086C2212yescomplemented
26#14579084C2212yescomplemented
27#14579082C2212yescomplemented
28(C2×D79)⋊C8C2212yes—
29(C2×D79)⋊C8C2212yes—
30C2×D8×C79C2211yescharacteristic, complemented
31C22×C8×C79C2211yescharacteristic
32#121×C79C2212yes—
33#107×C79C2211yescharacteristic, complemented
34#102×C79C2212yescomplemented
35C23×D79D411yescharacteristic
36#11929623—42no—
37#11929623—42no—
38C2×Dic158C2312yes—
39C2×C22⋊D79—22no—
40C2×C22⋊D79—22no—
41C22×Dic79—22no—
42C22×Dic79D411yescharacteristic
43C2×C4×D79—41no—
44C2×C4×D79—41no—
45C2×C4×D79D412yes—
46C2×C4×D79C2312yes—
47Dic316—41no—
48#11929612—42no—
49C2×C79⋊C8—41no—
50C2×C79⋊C8C2312yes—
51C4⋊Dic79—22no—
52C4⋊Dic79C2312yes—
53Dic79⋊C4—22no—
54C22⋊Dic79—22no—
55C22⋊Dic79—22no—
56(C2×D79)⋊C4—22no—
57(C2×D79)⋊C4—22no—
58C4×Dic79—22no—
59C2×D4×C79—22no—
60C2×D4×C79C2312yes—
61C22×C4×C79C2311yescharacteristic
62D8×C79—41no—
63C2×C8×C79—41no—
64C2×C8×C79C2311yescharacteristic
65C2×C8×C79C2311yescharacteristic
66C4⋊C4×C79C2312yes—
67C22⋊C4×C79—22no—
68C23×C79—22no—
69C23×C79C2×D411yescharacteristic
70C22×D79—22no—
71C22×D79—41no—
72C22×D79—41no—
73C22×D79C2×D412yes—
74D4×C79—22no—
75D4×C79—22no—
76D4×C79—44no—
77C2×C4×C79—21no—
78C2×C4×C79—21no—
79C2×C4×C79—22no—
80C2×C4×C79C2×D411yescharacteristic
81C2×C4×C79C2411yescharacteristic
82C22⋊D79—44no—
83C22⋊D79—44no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—41no—
87C2×Dic79—44no—
88C2×Dic79C2×D412yes—
89C4×D79—22no—
90C4×D79—22no—
91C4×D79—42no—
92Dic158—22no—
93Dic158—22no—
94C8×C79—21no—
95C8×C79—21no—
96C79⋊C8—22no—
97C22×C79—21no—
98C22×C79—21no—
99C22×C79—42no—
100C22×C79—42no—
101C22×C79—42no—
102C22×C79#13512yes—
103C22×C79C22×D411yescharacteristic
104C2×D79—22no—
105C2×D79—22no—
106C2×D79—22no—
107C2×D79—44no—
108C4×C79—21no—
109C4×C79—42no—
110C4×C79H(5,𝔽2)11yescharacteristic
111C4×C79H(5,𝔽2)11yescharacteristic
112Dic79—22no—
113Dic79—42no—
114Dic79—42no—
115C2×C79—22no—
116C2×C79—82no—
117C2×C79#53411yescharacteristic
118C2×C79C2×#13511yescharacteristic
119C2×C79#57511yescharacteristic
120D79—42no—
121#3191—791nomaximal, Sylow
122C79#319111yescharacteristic, complemented, Sylow
123#525—792no—
124#485—792no—
125#482—792no—
126#467—791no—
127#466D7911yescharacteristic, complemented
128#465—792no—
129#452—792no—
130#449—792no—
131C2×C22⋊C8—791no—
132C2×#41—792no—
133C23×C4—791no—
134C2×Q16—791no—
135C2×SD16—792no—
136C2×D8C2×D7911yescharacteristic, complemented
137C22×C8—791no—
138C22×C8C2×D7911yescharacteristic
139#123—1582no—
140C22⋊Q8—792no—
141C22⋊Q8—792no—
142#121—792no—
143#121C2×D7912yes—
144#120—1582no—
145C4×D4—1582no—
146C4×D4—1582no—
147#117—792no—
148#107—791no—
149#107C2×D7911yescharacteristic, complemented
150#106—792no—
151#103—792no—
152#103—792no—
153#102—792no—
154#102C2×D7912yescomplemented
155C22⋊C8—792no—
156C22⋊C8—792no—
157C24—791no—
158#41—3162no—
159#41—3162no—
160C2×Q8—792no—
161C2×D4—22no—
162C2×D4—1582no—
163C2×D4—1582no—
164C2×D4C22×D7912yes—
165C22×C4—3161no—
166C22×C4—3161no—
167C22×C4—791no—
168C22×C4—792no—
169C22×C4—792no—
170C22×C4—1582no—
171C22×C4C22×D7911yescharacteristic
172Q16—3161no—
173SD16—3162no—
174D8—41no—
175C2×C8—41no—
176C2×C8—3161no—
177C2×C8—792no—
178C2×C8C22×D7911yescharacteristic
179C2×C8C22×D7911yescharacteristic
180C4⋊C4—792no—
181C4⋊C4—1582no—
182C4⋊C4—1582no—
183C4⋊C4C22×D7912yes—
184C22⋊C4—22no—
185C22⋊C4—1582no—
186C22⋊C4—1582no—
187C22⋊C4—1582no—
188C22⋊C4—1582no—
189C42—1582no—
190C23—22no—
191C23—3161no—
192C23—3161no—
193C23—792no—
194C23—1582no—
195C23D4×D7911yescharacteristic
196Q8—1582no—
197Q8—1582no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—3164no—
202D4—3164no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—3162no—
207C2×C4—3164no—
208C2×C4—3161no—
209C2×C4—792no—
210C2×C4—1582no—
211C2×C4—1582no—
212C2×C4—1582no—
213C2×C4—1582no—
214C2×C4D4×D7911yescharacteristic
215C2×C4C23×D7911yescharacteristic
216C8—21no—
217C8—21no—
218C8—1582no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—3164no—
225C22—1582no—
226C22—1582no—
227C22—1582no—
228C22#1457918012yes—
229C22C2×D4×D7911yescharacteristic
230C4—21no—
231C4—42no—
232C4—3162no—
233C4—3162no—
234C4—1582no—
235C4#1457920611yescharacteristic
236C4#1457920711yescharacteristic
237C2—22no—
238C2—82no—
239C2—3162no—
240C2#1909912111yescharacteristic
241C2C2×#1457918011yescharacteristic
242C2#1909936011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#466×C79C2
socleC22×C79C22×D4
hypercenter#466D79
hypocenterC79#3191
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #19099073C2semidirect
2. #19098906C2semidirect
3. #19098885C2semidirect
4. #19098804C2semidirect
5. #19098790C2semidirect
6. #19098726C2semidirect
7. #19098705C2semidirect
8. C2×(C2×D79)⋊C8C2semidirect
9. #466×C79C2semidirect
12. C2×Dic316C22semidirect
13. C2×#11929612C22semidirect
23. #14579095C22semidirect
24. #14579092C22semidirect
25. #14579086C22semidirect
26. #14579084C22semidirect
27. #14579082C22semidirect
30. C2×D8×C79C22semidirect
33. #107×C79C22semidirect
34. #102×C79C22semidirect
122. C79#3191semidirect
127. #466D79semidirect
136. C2×D8C2×D79semidirect
149. #107C2×D79semidirect
154. #102C2×D79semidirect