Finite Group Databasebeta

← #16840569

Subgroups — #16840569

Order 3904.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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#14519824C211yesmaximal, characteristic, complemented
2#14519823C211yesmaximal, characteristic, complemented
3#14519809C212yesmaximal, complemented
4#14519807C211yesmaximal, characteristic, complemented
5#14519802C211yesmaximal, characteristic, complemented
6#14519801C212yesmaximal, complemented
7#14519798C212yesmaximal, complemented
8C2×#11758190C211yesmaximal, characteristic, complemented
9SD16×D61C212yesmaximal, complemented
10#14519783C211yesmaximal, characteristic, complemented
11#135×C61C211yesmaximal, characteristic, complemented
12#41×C61C2211yescharacteristic
13#41×C61C2211yescharacteristic, complemented
14#11758226C2212yes—
15Q8×D61C2212yescomplemented
16#11758224—22no—
17#11758224C2212yescomplemented
18D4×D61—22no—
19D4×D61C2212yes—
20#11758222—21no—
21#11758222—21no—
22#11758222C2211yescharacteristic
23C2×D244—21no—
24C2×D244C2211yescharacteristic
25C2×Dic122—21no—
26C2×Dic122C2211yescharacteristic, complemented
27Q16×C61C2211yescharacteristic, complemented
28SD16×C61C2211yescharacteristic, complemented
29SD16×C61C2211yescharacteristic, complemented
30D8×C61C2211yescharacteristic, complemented
31C2×C8×C61C2211yescharacteristic, complemented
32#11758202C2212yescomplemented
33#11758201C2212yescomplemented
34#11758200C2212yescomplemented
35#11758199C2212yescomplemented
36#11758194C2211yescharacteristic, complemented
37#11758190C2212yescomplemented
38#11758190C2212yescomplemented
39#11758189C2212yescomplemented
40C8×D61C2212yescomplemented
41C22×D61—21no—
42C22×D61—22no—
43Q8×C61C2311yescharacteristic
44Q8×C61C2311yescharacteristic
45D4×C61—21no—
46D4×C61—21no—
47D4×C61C2311yescharacteristic
48D4×C61C2311yescharacteristic
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61C2311yescharacteristic
52C22⋊D61—22no—
53C22⋊D61—22no—
54C22⋊D61D412yes—
55C2×Dic61—21no—
56C2×Dic61—22no—
57D244—22no—
58D244—21no—
59D244D411yescharacteristic
60D244C2312yes—
61C4×D61—22no—
62C4×D61—22no—
63C4×D61C2312yes—
64Dic122—21no—
65Dic122—22no—
66Dic122D411yescharacteristic
67Dic122C2312yes—
68C8×C61C2311yescharacteristic
69C8×C61C2311yescharacteristic
70#92418C2312yes—
71C22×C61—21no—
72C22×C61—21no—
73C22×C61C2×D411yescharacteristic
74C2×D61—22no—
75C2×D61—82no—
76C2×D61—81no—
77C2×D61C2×D412yes—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61C2×D411yescharacteristic
81C4×C61C2411yescharacteristic
82Dic61—22no—
83Dic61C2×D412yes—
84C2×C61—21no—
85C2×C61—41no—
86C2×C61—41no—
87C2×C61C22×D411yescharacteristic
88D61—22no—
89D61—42no—
90#577—611nomaximal, Sylow
91C61#57711yescharacteristic, complemented, Sylow
922−1+4—611no—
93H(5,𝔽2)—611no—
94#137—611no—
95#137—612no—
96AGL(1,ℤ/8)—611no—
97AGL(1,ℤ/8)—612no—
98#135—612no—
99#135D6111yescharacteristic, complemented
100C2×SD16—612no—
101C2×SD16—611no—
102#131—611no—
103#41—611no—
104#41—612no—
105#41—612no—
106#41—1221no—
107#41—1221no—
108#41—1222no—
109#41C2×D6111yescharacteristic
110#41C2×D6111yescharacteristic, complemented
111C2×Q8—612no—
112C2×Q8—611no—
113C2×Q8—1221no—
114C2×D4—612no—
115C2×D4—611no—
116C2×D4—1221no—
117C2×D4—1222no—
118Q16—612no—
119Q16C2×D6111yescharacteristic, complemented
120SD16—612no—
121SD16—612no—
122SD16—612no—
123SD16—612no—
124SD16C2×D6111yescharacteristic, complemented
125SD16C2×D6111yescharacteristic, complemented
126D8—612no—
127D8C2×D6111yescharacteristic, complemented
128M16—611no—
129M16—612no—
130C2×C8—612no—
131C2×C8C2×D6111yescharacteristic, complemented
132C23—1222no—
133C23—1221no—
134Q8—611no—
135Q8—612no—
136Q8—1222no—
137Q8—1221no—
138Q8C22×D6111yescharacteristic
139Q8C22×D6111yescharacteristic
140D4—21no—
141D4—21no—
142D4—612no—
143D4—611no—
144D4—612no—
145D4—1222no—
146D4—1222no—
147D4—1222no—
148D4—1221no—
149D4C22×D6111yescharacteristic
150D4C22×D6111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—612no—
154C2×C4—1222no—
155C2×C4—1222no—
156C2×C4—1222no—
157C2×C4—1221no—
158C2×C4C22×D6111yescharacteristic
159C8—612no—
160C8C22×D6111yescharacteristic
161C8C22×D6111yescharacteristic
162C22—21no—
163C22—21no—
164C22—612no—
165C22—1222no—
166C22—4881no—
167C22—4882no—
168C22D4×D6111yescharacteristic
169C4—21no—
170C4—21no—
171C4—612no—
172C4—1222no—
173C4D4×D6111yescharacteristic
174C4C23×D6111yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—1222no—
179C2—2442no—
180C2C2×D4×D6111yescharacteristic
subgroupG/H
centerC2C2×D4×D61
commutator, cosocleC4×C61C24
FrattiniC4C23×D61
Fitting#135×C61C2
socleC2×C61C22×D4
hypercenter#135D61
hypocenterC61#577
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #14519824C2semidirect
2. #14519823C2semidirect
3. #14519809C2semidirect
4. #14519807C2semidirect
5. #14519802C2semidirect
6. #14519801C2semidirect
7. #14519798C2semidirect
8. C2×#11758190C2semidirect
9. SD16×D61C2semidirect
10. #14519783C2semidirect
11. #135×C61C2semidirect
13. #41×C61C22semidirect
15. Q8×D61C22semidirect
17. #11758224C22semidirect
26. C2×Dic122C22semidirect
27. Q16×C61C22semidirect
28. SD16×C61C22semidirect
29. SD16×C61C22semidirect
30. D8×C61C22semidirect
31. C2×C8×C61C22semidirect
32. #11758202C22semidirect
33. #11758201C22semidirect
34. #11758200C22semidirect
35. #11758199C22semidirect
36. #11758194C22semidirect
37. #11758190C22semidirect
38. #11758190C22semidirect
39. #11758189C22semidirect
40. C8×D61C22semidirect
91. C61#577semidirect
99. #135D61semidirect
110. #41C2×D61semidirect
119. Q16C2×D61semidirect
124. SD16C2×D61semidirect
125. SD16C2×D61semidirect
127. D8C2×D61semidirect
131. C2×C8C2×D61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145198242
#145198232
#145198092
#145198072
#145198022
#145198012
#145197982
C2×#117581902
SD16×D612
#145197832
#135×C612
#57761