Finite Group Databasebeta

← #135×D467 #44470815

Subgroups — #135×D467 #44470815

Order 29888.

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×D467C212yesmaximal, complemented
2#28417976C211yesmaximal, characteristic, complemented
3#28417975C211yesmaximal, characteristic, complemented
4#28417974C212yesmaximal, complemented
5#28417973C212yesmaximal, complemented
6#28417972C211yesmaximal, characteristic, complemented
7Q16×D467C211yesmaximal, characteristic, complemented
8SD16×D467C212yesmaximal, complemented
9D8×D467C211yesmaximal, characteristic, complemented
10C2×C8×D467C211yesmaximal, characteristic, complemented
11#135×C467C211yesmaximal, characteristic, complemented
12#21418744C2212yescomplemented
13#21418743—22no—
14#21418743C2212yescomplemented
15#21418742—22no—
16#21418742C2212yescomplemented
17Q8×D467C2212yes—
18D4×D467—22no—
19D4×D467C2212yes—
20C2×C4×D467—22no—
21C2×C4×D467C2211yescharacteristic
22Dic1868C2211yescharacteristic, complemented
23#21418733C2212yescomplemented
24#21418732C2212yescomplemented
25#21418731C2212yescomplemented
26#21418730C2212yescomplemented
27D3736C2211yescharacteristic, complemented
28#21418728C2212yescomplemented
29C2×C467⋊C8C2211yescharacteristic, complemented
30C8×D467C2211yescharacteristic
31C8×D467C2211yescharacteristic
32C8×D467C2211yescharacteristic, complemented
33C8×D467C2211yescharacteristic, complemented
34#41×C467C2212yescomplemented
35Q16×C467C2211yescharacteristic, complemented
36SD16×C467C2212yescomplemented
37D8×C467C2211yescharacteristic, complemented
38C2×C8×C467C2211yescharacteristic, complemented
39C22×D467—22no—
40C22×D467D411yescharacteristic
41Dic934—22no—
42Dic934C2312yes—
43D1868—22no—
44D1868C2312yes—
45C22⋊D467—22no—
46C22⋊D467—22no—
47C22⋊D467—22no—
48C2×Dic467—22no—
49C2×Dic467D411yescharacteristic
50C4×D467—22no—
51C4×D467—22no—
52C4×D467—22no—
53C4×D467D411yescharacteristic
54C4×D467D411yescharacteristic
55C4×D467C2311yescharacteristic
56C4×D467C2311yescharacteristic
57C467⋊C8C2311yescharacteristic
58C467⋊C8C2311yescharacteristic
59Q8×C467C2312yes—
60D4×C467—22no—
61D4×C467C2312yes—
62C2×C4×C467—22no—
63C2×C4×C467C2311yescharacteristic
64C8×C467C2311yescharacteristic
65C8×C467C2311yescharacteristic
66C22×C467—22no—
67C22×C467C2×D411yescharacteristic
68C2×D467—22no—
69C2×D467—22no—
70C2×D467—44no—
71C2×D467C2×D411yescharacteristic
72C2×D467C2×D411yescharacteristic
73C4×C467—22no—
74C4×C467C2×D411yescharacteristic
75C4×C467C2411yescharacteristic
76Dic467—22no—
77Dic467C2×D411yescharacteristic
78Dic467C2×D411yescharacteristic
79C2×C467—21no—
80C2×C467—42no—
81C2×C467C22×D411yescharacteristic
82D467—21no—
83D467—42no—
84D467#13512yesdirect product factor
85C467C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—4671nomaximal, Sylow
87C2×#41—4672no—
88#135—4672no—
89#135—4671no—
90#135—4672no—
91#135—4671no—
92#135—4671no—
93#135D46711yescharacteristic, direct product factor
94C2×Q16—4671no—
95C2×SD16—4672no—
96C2×D8—4671no—
97C22×C8—4671no—
98#41—9342no—
99#41—9342no—
100#41—4672no—
101#41—4672no—
102#41—4672no—
103#41C2×D46712yescomplemented
104C2×Q8—4672no—
105C2×D4—9342no—
106C2×D4—4672no—
107C22×C4—9342no—
108C22×C4—4671no—
109Q16—4672no—
110Q16—4671no—
111Q16C2×D46711yescharacteristic, complemented
112SD16—4672no—
113SD16—4672no—
114SD16—4672no—
115SD16C2×D46712yescomplemented
116D8—4672no—
117D8—4671no—
118D8C2×D46711yescharacteristic, complemented
119C2×C8—4671no—
120C2×C8—4671no—
121C2×C8—4671no—
122C2×C8—4671no—
123C2×C8—4671no—
124C2×C8C2×D46711yescharacteristic, complemented
125C23—9342no—
126C23—4671no—
127Q8—9342no—
128Q8—4672no—
129Q8C22×D46712yes—
130D4—22no—
131D4—9342no—
132D4—9342no—
133D4—9342no—
134D4—9342no—
135D4—4672no—
136D4C22×D46712yes—
137C2×C4—22no—
138C2×C4—9342no—
139C2×C4—9342no—
140C2×C4—9342no—
141C2×C4—9342no—
142C2×C4—4671no—
143C2×C4—4671no—
144C2×C4—4671no—
145C2×C4—4671no—
146C2×C4—4671no—
147C2×C4C22×D46711yescharacteristic
148C8—4671no—
149C8—4671no—
150C8C22×D46711yescharacteristic
151C8C22×D46711yescharacteristic
152C22—22no—
153C22—18684no—
154C22—9342no—
155C22—9342no—
156C22—4671no—
157C22—4671no—
158C22D4×D46711yescharacteristic
159C4—22no—
160C4—9342no—
161C4—4671no—
162C4—4671no—
163C4D4×D46711yescharacteristic
164C4C23×D46711yescharacteristic
165C2—21no—
166C2—42no—
167C2—18682no—
168C2—9341no—
169C2—4672no—
170C2C2×D4×D46711yescharacteristic
subgroupG/H
centerC4D4×D467
commutator, cosocleC4×C467C24
FrattiniC4C23×D467
Fitting#135×C467C2
socleC2×C467C22×D4
hypercenter#135D467
hypocenterC467C2×#135
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D467C2semidirect
2. #28417976C2semidirect
3. #28417975C2semidirect
4. #28417974C2semidirect
5. #28417973C2semidirect
6. #28417972C2semidirect
7. Q16×D467C2semidirect
8. SD16×D467C2semidirect
9. D8×D467C2semidirect
10. C2×C8×D467C2semidirect
11. #135×C467C2semidirect
12. #21418744C22semidirect
14. #21418743C22semidirect
16. #21418742C22semidirect
22. Dic1868C22semidirect
23. #21418733C22semidirect
24. #21418732C22semidirect
25. #21418731C22semidirect
26. #21418730C22semidirect
27. D3736C22semidirect
28. #21418728C22semidirect
29. C2×C467⋊C8C22semidirect
32. C8×D467C22semidirect
33. C8×D467C22semidirect
34. #41×C467C22semidirect
35. Q16×C467C22semidirect
36. SD16×C467C22semidirect
37. D8×C467C22semidirect
38. C2×C8×C467C22semidirect
84. D467#135direct (N × H)
85. C467C2×#135semidirect
93. #135D467direct (N × H)
103. #41C2×D467semidirect
111. Q16C2×D467semidirect
115. SD16C2×D467semidirect
118. D8C2×D467semidirect
124. C2×C8C2×D467semidirect

Maximal subgroups

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

subgroupindex
#41×D4672
#284179762
#284179752
#284179742
#284179732
#284179722
Q16×D4672
SD16×D4672
D8×D4672
C2×C8×D4672
#135×C4672
C2×#135467