Finite Group Databasebeta

← #23776533

Subgroups — #23776533

Order 10112.

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

normal subgroups only

This group has 364 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#135×D79C212yesmaximal, complemented
2#19099005C212yesmaximal, complemented
3#19099002C212yesmaximal, complemented
4#19099000C212yesmaximal, complemented
5#19098997C212yesmaximal, complemented
6#19098995C211yesmaximal, characteristic, complemented
7#19098993C212yesmaximal, complemented
8C2×#14579100C211yesmaximal, characteristic, complemented
9#508×C79C211yesmaximal, characteristic, complemented
10#41×D79—22no—
11#14579184C2212yes—
12#14579183C2212yescomplemented
13#14579182—22no—
14#14579181—22no—
15#14579180C2212yes—
16Q16×D79C2212yescomplemented
17SD16×D79—22no—
18D8×D79C2212yescomplemented
19C2×C8×D79C2211yescharacteristic
20Dic632C2211yescharacteristic, complemented
21#14579107C2212yescomplemented
22#14579106C2212yescomplemented
23#14579105C2212yescomplemented
24#14579104C2212yescomplemented
25D1264C2211yescharacteristic, complemented
26#14579102C2212yescomplemented
27#14579100C2212yescomplemented
28#14579100C2212yescomplemented
29C2×C79⋊C16C2211yescharacteristic, complemented
30#135×C79C2212yescomplemented
31Q32×C79C2211yescharacteristic, complemented
32SD32×C79C2212yescomplemented
33D16×C79C2211yescharacteristic, complemented
34C2×C16×C79C2211yescharacteristic, complemented
35#11929625—22no—
36#11929624—22no—
37#11929624—42no—
38#11929623—22no—
39#11929623—42no—
40Q8×D79—22no—
41D4×D79—22no—
42D4×D79—42no—
43C2×C4×D79—42no—
44C2×C4×D79D411yescharacteristic
45Dic316C2312yes—
46#11929614—22no—
47#11929613—22no—
48#11929612—22no—
49#11929611—22no—
50D632C2312yes—
51#11929609—22no—
52C2×C79⋊C8D411yescharacteristic
53C8×D79D412yes—
54C8×D79C2312yes—
55C79⋊C16C2312yes—
56#41×C79—22no—
57Q16×C79C2312yes—
58SD16×C79—22no—
59D8×C79C2312yes—
60C2×C8×C79C2311yescharacteristic
61C16×C79C2311yescharacteristic
62C16×C79C2311yescharacteristic
63C22×D79—42no—
64C22×D79D811yescharacteristic
65Q8×C79—22no—
66D4×C79—22no—
67D4×C79—42no—
68C2×C4×C79—42no—
69C2×C4×C79C2×D411yescharacteristic
70C22⋊D79—42no—
71C22⋊D79—42no—
72C22⋊D79—42no—
73C2×Dic79—42no—
74C2×Dic79D811yescharacteristic
75D316—22no—
76D316—42no—
77C4×D79—42no—
78C4×D79—42no—
79C4×D79—42no—
80C4×D79D812yes—
81C4×D79C2×D412yes—
82Dic158—22no—
83Dic158—42no—
84C8×C79C2×D411yescharacteristic
85C8×C79C2411yescharacteristic
86C79⋊C8C2×D412yes—
87C22×C79—42no—
88C22×C79C2×D811yescharacteristic
89C2×D79—41no—
90C2×D79—42no—
91C2×D79—84no—
92C2×D79C2×D812yes—
93C4×C79—42no—
94C4×C79C2×D811yescharacteristic
95C4×C79C22×D411yescharacteristic
96Dic79—42no—
97Dic79C2×D812yes—
98C2×C79—21no—
99C2×C79—82no—
100C2×C79C22×D811yescharacteristic
101D79—22no—
102D79—82no—
103#3414—791nomaximal, Sylow
104C79#341411yescharacteristic, complemented, Sylow
105C2×#135—792no—
106#510—792no—
107#510—792no—
108#509—792no—
109#509—792no—
110#508—792no—
111#508—791no—
112#508D7911yescharacteristic, complemented
113C2×M32—791no—
114C2×#41—1582no—
115#135—792no—
116#135—792no—
117#135—792no—
118#135—1582no—
119#135—1582no—
120#135C2×D7912yescomplemented
121C2×Q16—792no—
122C2×SD16—1582no—
123C2×D8—792no—
124C22×C8—791no—
125Q32—792no—
126Q32—791no—
127Q32C2×D7911yescharacteristic, complemented
128SD32—792no—
129SD32—792no—
130SD32—792no—
131SD32C2×D7912yescomplemented
132D16—792no—
133D16—791no—
134D16C2×D7911yescharacteristic, complemented
135M32—792no—
136M32—792no—
137C2×C16—791no—
138C2×C16C2×D7911yescharacteristic, complemented
139#41—22no—
140#41—3162no—
141#41—3162no—
142#41—1582no—
143#41—1582no—
144#41—1582no—
145C2×Q8—1582no—
146C2×D4—3162no—
147C2×D4—1582no—
148C22×C4—3162no—
149C22×C4—791no—
150Q16—792no—
151Q16—1582no—
152Q16C22×D7912yes—
153SD16—22no—
154SD16—1582no—
155SD16—1582no—
156SD16—1582no—
157D8—792no—
158D8—1582no—
159D8C22×D7912yes—
160C2×C8—791no—
161C2×C8—792no—
162C2×C8—792no—
163C2×C8C22×D7911yescharacteristic
164C16—792no—
165C16C22×D7911yescharacteristic
166C16C22×D7911yescharacteristic
167C23—3162no—
168C23—791no—
169Q8—22no—
170Q8—3162no—
171Q8—1582no—
172D4—22no—
173D4—42no—
174D4—3162no—
175D4—3162no—
176D4—3162no—
177D4—3162no—
178D4—1582no—
179C2×C4—42no—
180C2×C4—3162no—
181C2×C4—3162no—
182C2×C4—3162no—
183C2×C4—3162no—
184C2×C4—791no—
185C2×C4—792no—
186C2×C4—792no—
187C2×C4D4×D7911yescharacteristic
188C8—792no—
189C8D4×D7911yescharacteristic
190C8C23×D7911yescharacteristic
191C22—42no—
192C22—3161no—
193C22—3162no—
194C22—792no—
195C22—6324no—
196C22D8×D7911yescharacteristic
197C4—42no—
198C4—3162no—
199C4—792no—
200C4D8×D7911yescharacteristic
201C4C2×D4×D7911yescharacteristic
202C2—21no—
203C2—82no—
204C2—6322no—
205C2—1582no—
206C2C2×D8×D7911yescharacteristic
subgroupG/H
centerC4D8×D79
commutator, cosocleC8×C79C24
FrattiniC8C23×D79
Fitting#508×C79C2
socleC2×C79C22×D8
hypercenter#508D79
hypocenterC79#3414
LCSG ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D79C2semidirect
2. #19099005C2semidirect
3. #19099002C2semidirect
4. #19099000C2semidirect
5. #19098997C2semidirect
6. #19098995C2semidirect
7. #19098993C2semidirect
8. C2×#14579100C2semidirect
9. #508×C79C2semidirect
12. #14579183C22semidirect
16. Q16×D79C22semidirect
18. D8×D79C22semidirect
20. Dic632C22semidirect
21. #14579107C22semidirect
22. #14579106C22semidirect
23. #14579105C22semidirect
24. #14579104C22semidirect
25. D1264C22semidirect
26. #14579102C22semidirect
27. #14579100C22semidirect
28. #14579100C22semidirect
29. C2×C79⋊C16C22semidirect
30. #135×C79C22semidirect
31. Q32×C79C22semidirect
32. SD32×C79C22semidirect
33. D16×C79C22semidirect
34. C2×C16×C79C22semidirect
104. C79#3414semidirect
112. #508D79semidirect
120. #135C2×D79semidirect
127. Q32C2×D79semidirect
131. SD32C2×D79semidirect
134. D16C2×D79semidirect
138. C2×C16C2×D79semidirect