Finite Group Databasebeta

← #135×D541 #46830953

Subgroups — #135×D541 #46830953

Order 34624.

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×D541C212yesmaximal, complemented
2#31772651C211yesmaximal, characteristic, complemented
3#31772650C211yesmaximal, characteristic, complemented
4#31772649C212yesmaximal, complemented
5#31772648C212yesmaximal, complemented
6#31772647C211yesmaximal, characteristic, complemented
7Q16×D541C211yesmaximal, characteristic, complemented
8SD16×D541C212yesmaximal, complemented
9D8×D541C211yesmaximal, characteristic, complemented
10C2×C8×D541C211yesmaximal, characteristic, complemented
11#135×C541C211yesmaximal, characteristic, complemented
12#22575837C2212yescomplemented
13#22575836—22no—
14#22575836C2212yescomplemented
15#22575835—22no—
16#22575835C2212yescomplemented
17Q8×D541C2212yes—
18D4×D541—22no—
19D4×D541C2212yes—
20C2×C4×D541—22no—
21C2×C4×D541C2211yescharacteristic
22Dic2164C2211yescharacteristic, complemented
23#22575826C2212yescomplemented
24#22575825C2212yescomplemented
25#22575824C2212yescomplemented
26#22575823C2212yescomplemented
27D4328C2211yescharacteristic, complemented
28#22575821C2212yescomplemented
29C2×#16864513C2211yescharacteristic, complemented
30C8×D541C2211yescharacteristic
31C8×D541C2211yescharacteristic
32C8×D541C2211yescharacteristic, complemented
33C8×D541C2211yescharacteristic, complemented
34#41×C541C2212yescomplemented
35Q16×C541C2211yescharacteristic, complemented
36SD16×C541C2212yescomplemented
37D8×C541C2211yescharacteristic, complemented
38C2×C8×C541C2211yescharacteristic, complemented
39C22×D541—22no—
40C22×D541D411yescharacteristic
41Dic1082—22no—
42Dic1082C2312yes—
43D2164—22no—
44D2164C2312yes—
45C22⋊D541—22no—
46C22⋊D541—22no—
47C22⋊D541—22no—
48C2×Dic541—22no—
49C2×Dic541D411yescharacteristic
50C4×D541—22no—
51C4×D541—22no—
52C4×D541—22no—
53C4×D541D411yescharacteristic
54C4×D541D411yescharacteristic
55C4×D541C2311yescharacteristic
56C4×D541C2311yescharacteristic
57#16864513C2311yescharacteristic
58#16864513C2311yescharacteristic
59Q8×C541C2312yes—
60D4×C541—22no—
61D4×C541C2312yes—
62C2×C4×C541—22no—
63C2×C4×C541C2311yescharacteristic
64C8×C541C2311yescharacteristic
65C8×C541C2311yescharacteristic
66C22×C541—22no—
67C22×C541C2×D411yescharacteristic
68C2×D541—22no—
69C2×D541—22no—
70C2×D541—44no—
71C2×D541C2×D411yescharacteristic
72C2×D541C2×D411yescharacteristic
73C4×C541—22no—
74C4×C541C2×D411yescharacteristic
75C4×C541C2411yescharacteristic
76Dic541—22no—
77Dic541C2×D411yescharacteristic
78Dic541C2×D411yescharacteristic
79C2×C541—21no—
80C2×C541—42no—
81C2×C541C22×D411yescharacteristic
82D541—21no—
83D541—42no—
84D541#13512yesdirect product factor
85C541C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—5411nomaximal, Sylow
87C2×#41—5412no—
88#135—5412no—
89#135—5411no—
90#135—5412no—
91#135—5411no—
92#135—5411no—
93#135D54111yescharacteristic, direct product factor
94C2×Q16—5411no—
95C2×SD16—5412no—
96C2×D8—5411no—
97C22×C8—5411no—
98#41—5412no—
99#41—5412no—
100#41—5412no—
101#41—10822no—
102#41—10822no—
103#41C2×D54112yescomplemented
104C2×Q8—5412no—
105C2×D4—5412no—
106C2×D4—10822no—
107C22×C4—5411no—
108C22×C4—10822no—
109Q16—5412no—
110Q16—5411no—
111Q16C2×D54111yescharacteristic, complemented
112SD16—5412no—
113SD16—5412no—
114SD16—5412no—
115SD16C2×D54112yescomplemented
116D8—5412no—
117D8—5411no—
118D8C2×D54111yescharacteristic, complemented
119C2×C8—5411no—
120C2×C8—5411no—
121C2×C8—5411no—
122C2×C8—5411no—
123C2×C8—5411no—
124C2×C8C2×D54111yescharacteristic, complemented
125C23—5411no—
126C23—10822no—
127Q8—5412no—
128Q8—10822no—
129Q8C22×D54112yes—
130D4—22no—
131D4—5412no—
132D4—10822no—
133D4—10822no—
134D4—10822no—
135D4—10822no—
136D4C22×D54112yes—
137C2×C4—22no—
138C2×C4—5411no—
139C2×C4—5411no—
140C2×C4—5411no—
141C2×C4—5411no—
142C2×C4—5411no—
143C2×C4—10822no—
144C2×C4—10822no—
145C2×C4—10822no—
146C2×C4—10822no—
147C2×C4C22×D54111yescharacteristic
148C8—5411no—
149C8—5411no—
150C8C22×D54111yescharacteristic
151C8C22×D54111yescharacteristic
152C22—22no—
153C22—5411no—
154C22—5411no—
155C22—10822no—
156C22—10822no—
157C22—21644no—
158C22D4×D54111yescharacteristic
159C4—22no—
160C4—5411no—
161C4—5411no—
162C4—10822no—
163C4D4×D54111yescharacteristic
164C4C23×D54111yescharacteristic
165C2—21no—
166C2—42no—
167C2—5412no—
168C2—10821no—
169C2—21642no—
170C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC4D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
Fitting#135×C541C2
socleC2×C541C22×D4
hypercenter#135D541
hypocenterC541C2×#135
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D541C2semidirect
2. #31772651C2semidirect
3. #31772650C2semidirect
4. #31772649C2semidirect
5. #31772648C2semidirect
6. #31772647C2semidirect
7. Q16×D541C2semidirect
8. SD16×D541C2semidirect
9. D8×D541C2semidirect
10. C2×C8×D541C2semidirect
11. #135×C541C2semidirect
12. #22575837C22semidirect
14. #22575836C22semidirect
16. #22575835C22semidirect
22. Dic2164C22semidirect
23. #22575826C22semidirect
24. #22575825C22semidirect
25. #22575824C22semidirect
26. #22575823C22semidirect
27. D4328C22semidirect
28. #22575821C22semidirect
29. C2×#16864513C22semidirect
32. C8×D541C22semidirect
33. C8×D541C22semidirect
34. #41×C541C22semidirect
35. Q16×C541C22semidirect
36. SD16×C541C22semidirect
37. D8×C541C22semidirect
38. C2×C8×C541C22semidirect
84. D541#135direct (N × H)
85. C541C2×#135semidirect
93. #135D541direct (N × H)
103. #41C2×D541semidirect
111. Q16C2×D541semidirect
115. SD16C2×D541semidirect
118. D8C2×D541semidirect
124. C2×C8C2×D541semidirect

Maximal subgroups

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

subgroupindex
#41×D5412
#317726512
#317726502
#317726492
#317726482
#317726472
Q16×D5412
SD16×D5412
D8×D5412
C2×C8×D5412
#135×C5412
C2×#135541