Finite Group Databasebeta

← #23774243

Subgroups — #23774243

Order 10112.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#19099076C212yesmaximal, complemented
2#19098902C212yesmaximal, complemented
3#19098889C212yesmaximal, complemented
4#19098816C211yesmaximal, characteristic, complemented
5#19098811C212yesmaximal, complemented
6#19098724C212yesmaximal, complemented
7#19098711C212yesmaximal, complemented
8#19098526C211yesmaximal, characteristic, complemented
9#470×C79C211yesmaximal, characteristic, complemented
10C2×#11929625C2212yes—
11C22×C4×D79C2211yescharacteristic
12C2×#11929611C2212yescomplemented
13C2×D632C2211yescharacteristic, complemented
14C2×#11929608C2211yescharacteristic
15#14579146—22no—
16#14579137C2212yes—
17#14579136C2212yes—
18#14579135C2212yes—
19#14579131—22no—
20#14579123—22no—
21(C22⋊D79)⋊C4—22no—
22#14579119C2212yes—
23#14579094C2212yescomplemented
24#14579093C2211yescharacteristic, complemented
25#14579085C2212yescomplemented
26#14579083C2212yescomplemented
27#14579081C2212yescomplemented
28(C2×D79)⋊C8C2212yes—
29(C2×D79)⋊C8C2212yes—
30C2×Q16×C79C2211yescharacteristic, complemented
31C2×M16×C79C2211yescharacteristic
32C22⋊Q8×C79C2212yes—
33#106×C79C2211yescharacteristic, complemented
34#103×C79C2212yescomplemented
35C23×D79D411yescharacteristic
36#11929625—42no—
37#11929625—42no—
38C2×D316—22no—
39C2×D316—22no—
40C2×D316C2312yes—
41C2×C22⋊D79—22no—
42C22×Dic79D411yescharacteristic
43C2×C4×D79—22no—
44C2×C4×D79—41no—
45C2×C4×D79—41no—
46C2×C4×D79D412yes—
47C2×C4×D79C2312yes—
48#11929611—42no—
49D632—41no—
50#11929608—41no—
51C2×C79⋊C8C2312yes—
52C4⋊Dic79C2312yes—
53Dic79⋊C4—22no—
54(C2×D79)⋊C4—22no—
55(C2×D79)⋊C4—22no—
56(C2×D79)⋊C4—22no—
57(C2×D79)⋊C4—22no—
58C4×Dic79—22no—
59C2×Q8×C79C2312yes—
60C22×C4×C79C2311yescharacteristic
61Q16×C79—41no—
62M16×C79—41no—
63C2×C8×C79C2311yescharacteristic
64C2×C8×C79C2311yescharacteristic
65C4⋊C4×C79—22no—
66C4⋊C4×C79C2312yes—
67C22⋊C4×C79—22no—
68C23×C79C2×D411yescharacteristic
69C22×D79—22no—
70C22×D79—41no—
71C22×D79—42no—
72C22×D79C2×D412yes—
73Q8×C79—22no—
74Q8×C79—22no—
75C2×C4×C79—21no—
76C2×C4×C79—21no—
77C2×C4×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79C2×D411yescharacteristic
80C2×C4×C79C2411yescharacteristic
81C22⋊D79—44no—
82C2×Dic79—22no—
83C2×Dic79—41no—
84C2×Dic79C2×D412yes—
85D316—22no—
86D316—22no—
87D316—44no—
88D316—44no—
89C4×D79—22no—
90C4×D79—22no—
91C4×D79—42no—
92C4×D79—44no—
93C8×C79—21no—
94C8×C79—21no—
95C79⋊C8—22no—
96C22×C79—21no—
97C22×C79—22no—
98C22×C79C22×D411yescharacteristic
99C2×D79—22no—
100C2×D79—22no—
101C2×D79—22no—
102C2×D79—44no—
103C2×D79—42no—
104C2×D79—42no—
105C2×D79—42no—
106C4×C79—21no—
107C4×C79—42no—
108C4×C79—42no—
109C4×C79H(5,𝔽2)11yescharacteristic
110C4×C79H(5,𝔽2)11yescharacteristic
111Dic79—22no—
112Dic79—42no—
113C2×C79—41no—
114C2×C79#53411yescharacteristic
115C2×C79#57512yes—
116D79—42no—
117D79—82no—
118#3197—791nomaximal, Sylow
119C79#319711yescharacteristic, complemented, Sylow
120#525—792no—
121#485—792no—
122#482—792no—
123#470D7911yescharacteristic, complemented
124#469—791no—
125#468—792no—
126#452—792no—
127#449—792no—
128#407—791no—
129C2×#41—792no—
130C23×C4—791no—
131C2×Q16C2×D7911yescharacteristic, complemented
132C2×SD16—792no—
133C2×D8—791no—
134C2×M16—791no—
135C2×M16C2×D7911yescharacteristic
136#123—1582no—
137C22⋊Q8—792no—
138C22⋊Q8C2×D7912yes—
139#121—792no—
140#121—792no—
141#120—1582no—
142C4×D4—1582no—
143C4×D4—1582no—
144#117—792no—
145#107—792no—
146#106—791no—
147#106C2×D7911yescharacteristic, complemented
148#103—792no—
149#103C2×D7912yescomplemented
150#102—792no—
151#102—792no—
152C22⋊C8—792no—
153C22⋊C8—792no—
154C24—791no—
155#41—3162no—
156#41—3162no—
157C2×Q8C22×D7912yes—
158C2×D4—792no—
159C2×D4—1582no—
160C2×D4—1582no—
161C2×D4—1582no—
162C22×C4—3161no—
163C22×C4—3161no—
164C22×C4—791no—
165C22×C4—792no—
166C22×C4—792no—
167C22×C4—1582no—
168C22×C4C22×D7911yescharacteristic
169Q16—41no—
170SD16—3162no—
171D8—3161no—
172M16—41no—
173M16—3161no—
174C2×C8—792no—
175C2×C8C22×D7911yescharacteristic
176C2×C8C22×D7911yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—792no—
179C4⋊C4—1582no—
180C4⋊C4C22×D7912yes—
181C22⋊C4—22no—
182C22⋊C4—1582no—
183C22⋊C4—1582no—
184C22⋊C4—1582no—
185C22⋊C4—1582no—
186C42—1582no—
187C23—3161no—
188C23—3162no—
189C23—792no—
190C23—1582no—
191C23D4×D7911yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—3164no—
195D4—3164no—
196D4—3164no—
197D4—1582no—
198D4—1582no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—3162no—
204C2×C4—3164no—
205C2×C4—3161no—
206C2×C4—792no—
207C2×C4—1582no—
208C2×C4—1582no—
209C2×C4—1582no—
210C2×C4D4×D7911yescharacteristic
211C2×C4C23×D7911yescharacteristic
212C8—21no—
213C8—21no—
214C8—1582no—
215C22—22no—
216C22—21no—
217C22—3164no—
218C22—3162no—
219C22—3162no—
220C22—3162no—
221C22—1582no—
222C22—1582no—
223C22—1582no—
224C22C2×D4×D7911yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—3162no—
229C4—1582no—
230C4#1457920611yescharacteristic
231C4#1457920711yescharacteristic
232C2—41no—
233C2—3162no—
234C2—6322no—
235C2#1909912111yescharacteristic
236C2#1909936212yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#470×C79C2
socleC22×C79C22×D4
hypercenter#470D79
hypocenterC79#3197
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #19099076C2semidirect
2. #19098902C2semidirect
3. #19098889C2semidirect
4. #19098816C2semidirect
5. #19098811C2semidirect
6. #19098724C2semidirect
7. #19098711C2semidirect
8. #19098526C2semidirect
9. #470×C79C2semidirect
12. C2×#11929611C22semidirect
13. C2×D632C22semidirect
23. #14579094C22semidirect
24. #14579093C22semidirect
25. #14579085C22semidirect
26. #14579083C22semidirect
27. #14579081C22semidirect
30. C2×Q16×C79C22semidirect
33. #106×C79C22semidirect
34. #103×C79C22semidirect
119. C79#3197semidirect
123. #470D79semidirect
131. C2×Q16C2×D79semidirect
147. #106C2×D79semidirect
149. #103C2×D79semidirect