Finite Group Databasebeta

← #135×D311 #34092472

Subgroups — #135×D311 #34092472

Order 19904.

266 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 101 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#41×D311C212yesmaximal, complemented
2#23755731C211yesmaximal, characteristic, complemented
3#23755730C211yesmaximal, characteristic, complemented
4#23755729C212yesmaximal, complemented
5#23755728C212yesmaximal, complemented
6#23755727C211yesmaximal, characteristic, complemented
7Q16×D311C211yesmaximal, characteristic, complemented
8SD16×D311C212yesmaximal, complemented
9D8×D311C211yesmaximal, characteristic, complemented
10C2×C8×D311C211yesmaximal, characteristic, complemented
11#135×C311C211yesmaximal, characteristic, complemented
12#19097316C2212yescomplemented
13#19097315—22no—
14#19097315C2212yescomplemented
15#19097314—22no—
16#19097314C2212yescomplemented
17Q8×D311C2212yes—
18D4×D311—22no—
19D4×D311C2212yes—
20C2×C4×D311—22no—
21C2×C4×D311C2211yescharacteristic
22Dic1244C2211yescharacteristic, complemented
23#19097305C2212yescomplemented
24#19097304C2212yescomplemented
25#19097303C2212yescomplemented
26#19097302C2212yescomplemented
27D2488C2211yescharacteristic, complemented
28#19097300C2212yescomplemented
29C2×C311⋊C8C2211yescharacteristic, complemented
30C8×D311C2211yescharacteristic
31C8×D311C2211yescharacteristic
32C8×D311C2211yescharacteristic, complemented
33C8×D311C2211yescharacteristic, complemented
34#41×C311C2212yescomplemented
35Q16×C311C2211yescharacteristic, complemented
36SD16×C311C2212yescomplemented
37D8×C311C2211yescharacteristic, complemented
38C2×C8×C311C2211yescharacteristic, complemented
39C22×D311—22no—
40C22×D311D411yescharacteristic
41Dic622—22no—
42Dic622C2312yes—
43D1244—22no—
44D1244C2312yes—
45C22⋊D311—22no—
46C22⋊D311—22no—
47C22⋊D311—22no—
48C2×Dic311—22no—
49C2×Dic311D411yescharacteristic
50C4×D311—22no—
51C4×D311—22no—
52C4×D311—22no—
53C4×D311D411yescharacteristic
54C4×D311D411yescharacteristic
55C4×D311C2311yescharacteristic
56C4×D311C2311yescharacteristic
57C311⋊C8C2311yescharacteristic
58C311⋊C8C2311yescharacteristic
59Q8×C311C2312yes—
60D4×C311—22no—
61D4×C311C2312yes—
62C2×C4×C311—22no—
63C2×C4×C311C2311yescharacteristic
64C8×C311C2311yescharacteristic
65C8×C311C2311yescharacteristic
66C22×C311—22no—
67C22×C311C2×D411yescharacteristic
68C2×D311—22no—
69C2×D311—22no—
70C2×D311—44no—
71C2×D311C2×D411yescharacteristic
72C2×D311C2×D411yescharacteristic
73C4×C311—22no—
74C4×C311C2×D411yescharacteristic
75C4×C311C2411yescharacteristic
76Dic311—22no—
77Dic311C2×D411yescharacteristic
78Dic311C2×D411yescharacteristic
79C2×C311—21no—
80C2×C311—42no—
81C2×C311C22×D411yescharacteristic
82D311—21no—
83D311—42no—
84D311#13512yesdirect product factor
85C311C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—3111nomaximal, Sylow
87C2×#41—3112no—
88#135—3112no—
89#135—3111no—
90#135—3112no—
91#135—3111no—
92#135—3111no—
93#135D31111yescharacteristic, direct product factor
94C2×Q16—3111no—
95C2×SD16—3112no—
96C2×D8—3111no—
97C22×C8—3111no—
98#41—3112no—
99#41—3112no—
100#41—3112no—
101#41—6222no—
102#41—6222no—
103#41C2×D31112yescomplemented
104C2×Q8—3112no—
105C2×D4—3112no—
106C2×D4—6222no—
107C22×C4—3111no—
108C22×C4—6222no—
109Q16—3112no—
110Q16—3111no—
111Q16C2×D31111yescharacteristic, complemented
112SD16—3112no—
113SD16—3112no—
114SD16—3112no—
115SD16C2×D31112yescomplemented
116D8—3112no—
117D8—3111no—
118D8C2×D31111yescharacteristic, complemented
119C2×C8—3111no—
120C2×C8—3111no—
121C2×C8—3111no—
122C2×C8—3111no—
123C2×C8—3111no—
124C2×C8C2×D31111yescharacteristic, complemented
125C23—3111no—
126C23—6222no—
127Q8—3112no—
128Q8—6222no—
129Q8C22×D31112yes—
130D4—22no—
131D4—3112no—
132D4—6222no—
133D4—6222no—
134D4—6222no—
135D4—6222no—
136D4C22×D31112yes—
137C2×C4—22no—
138C2×C4—3111no—
139C2×C4—3111no—
140C2×C4—3111no—
141C2×C4—3111no—
142C2×C4—3111no—
143C2×C4—6222no—
144C2×C4—6222no—
145C2×C4—6222no—
146C2×C4—6222no—
147C2×C4C22×D31111yescharacteristic
148C8—3111no—
149C8—3111no—
150C8C22×D31111yescharacteristic
151C8C22×D31111yescharacteristic
152C22—22no—
153C22—3111no—
154C22—3111no—
155C22—6222no—
156C22—6222no—
157C22—12444no—
158C22D4×D31111yescharacteristic
159C4—22no—
160C4—3111no—
161C4—3111no—
162C4—6222no—
163C4D4×D31111yescharacteristic
164C4C23×D31111yescharacteristic
165C2—21no—
166C2—42no—
167C2—3112no—
168C2—6221no—
169C2—12442no—
170C2C2×D4×D31111yescharacteristic
subgroupG/H
centerC4D4×D311
commutator, cosocleC4×C311C24
FrattiniC4C23×D311
Fitting#135×C311C2
socleC2×C311C22×D4
hypercenter#135D311
hypocenterC311C2×#135
LCSG ▷ C4×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D311C2semidirect
2. #23755731C2semidirect
3. #23755730C2semidirect
4. #23755729C2semidirect
5. #23755728C2semidirect
6. #23755727C2semidirect
7. Q16×D311C2semidirect
8. SD16×D311C2semidirect
9. D8×D311C2semidirect
10. C2×C8×D311C2semidirect
11. #135×C311C2semidirect
12. #19097316C22semidirect
14. #19097315C22semidirect
16. #19097314C22semidirect
22. Dic1244C22semidirect
23. #19097305C22semidirect
24. #19097304C22semidirect
25. #19097303C22semidirect
26. #19097302C22semidirect
27. D2488C22semidirect
28. #19097300C22semidirect
29. C2×C311⋊C8C22semidirect
32. C8×D311C22semidirect
33. C8×D311C22semidirect
34. #41×C311C22semidirect
35. Q16×C311C22semidirect
36. SD16×C311C22semidirect
37. D8×C311C22semidirect
38. C2×C8×C311C22semidirect
84. D311#135direct (N × H)
85. C311C2×#135semidirect
93. #135D311direct (N × H)
103. #41C2×D311semidirect
111. Q16C2×D311semidirect
115. SD16C2×D311semidirect
118. D8C2×D311semidirect
124. C2×C8C2×D311semidirect

Maximal subgroups

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

subgroupindex
#41×D3112
#237557312
#237557302
#237557292
#237557282
#237557272
Q16×D3112
SD16×D3112
D8×D3112
C2×C8×D3112
#135×C3112
C2×#135311