Finite Group Databasebeta

← #46830972

Subgroups — #46830972

Order 34624.

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

normal subgroups only

This group has 262 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#41×D541C212yesmaximal, complemented
2#31772660C212yesmaximal, complemented
3#31772657C212yesmaximal, complemented
4#31772655C212yesmaximal, complemented
5#31772652C212yesmaximal, complemented
6#31772650C211yesmaximal, characteristic, complemented
7#31772648C212yesmaximal, complemented
8C2×#22575819C211yesmaximal, characteristic, complemented
9#135×C541C211yesmaximal, characteristic, complemented
10#22575837C2212yes—
11#22575836—22no—
12#22575836C2212yescomplemented
13#22575835—22no—
14#22575835C2212yes—
15Q8×D541C2212yescomplemented
16D4×D541—22no—
17D4×D541C2212yescomplemented
18C2×C4×D541—22no—
19C2×C4×D541C2211yescharacteristic
20Dic2164C2211yescharacteristic, complemented
21#22575826C2212yescomplemented
22#22575825C2212yescomplemented
23#22575824C2212yescomplemented
24#22575823C2212yescomplemented
25D4328C2211yescharacteristic, complemented
26#22575821C2212yescomplemented
27#22575819C2212yescomplemented
28#22575819C2212yescomplemented
29C2×#16864513C2211yescharacteristic, complemented
30#41×C541C2212yescomplemented
31Q16×C541C2211yescharacteristic, complemented
32SD16×C541C2212yescomplemented
33D8×C541C2211yescharacteristic, complemented
34C2×C8×C541C2211yescharacteristic, complemented
35C22×D541—22no—
36C22×D541D411yescharacteristic
37Dic1082—22no—
38Dic1082C2312yes—
39D2164—22no—
40D2164C2312yes—
41C22⋊D541—22no—
42C22⋊D541—22no—
43C22⋊D541—22no—
44C2×Dic541—22no—
45C2×Dic541D411yescharacteristic
46C4×D541—22no—
47C4×D541—22no—
48C4×D541—22no—
49C4×D541D412yes—
50C4×D541C2312yes—
51#16864513C2312yes—
52Q8×C541C2312yes—
53D4×C541—22no—
54D4×C541C2312yes—
55C2×C4×C541—22no—
56C2×C4×C541C2311yescharacteristic
57C8×C541C2311yescharacteristic
58C8×C541C2311yescharacteristic
59C22×C541—22no—
60C22×C541C2×D411yescharacteristic
61C2×D541—22no—
62C2×D541—41no—
63C2×D541—44no—
64C2×D541C2×D412yes—
65C4×C541—22no—
66C4×C541C2×D411yescharacteristic
67C4×C541C2411yescharacteristic
68Dic541—22no—
69Dic541C2×D412yes—
70C2×C541—21no—
71C2×C541—42no—
72C2×C541C22×D411yescharacteristic
73D541—22no—
74D541—42no—
75C541#57511yescharacteristic, complemented, Sylow
76#575—5411nomaximal, Sylow
77C2×#41—5412no—
78#137—5412no—
79#137—5412no—
80AGL(1,ℤ/8)—5412no—
81AGL(1,ℤ/8)—5412no—
82#135—5412no—
83#135—5411no—
84#135D54111yescharacteristic, complemented
85C2×M16—5411no—
86#41—5412no—
87#41—5412no—
88#41—5412no—
89#41—10822no—
90#41—10822no—
91#41C2×D54112yescomplemented
92C2×Q8—5412no—
93C2×D4—5412no—
94C2×D4—10822no—
95C22×C4—5411no—
96C22×C4—10822no—
97Q16—5412no—
98Q16—5411no—
99Q16C2×D54111yescharacteristic, complemented
100SD16—5412no—
101SD16—5412no—
102SD16—5412no—
103SD16C2×D54112yescomplemented
104D8—5412no—
105D8—5411no—
106D8C2×D54111yescharacteristic, complemented
107M16—5412no—
108M16—5412no—
109C2×C8—5411no—
110C2×C8C2×D54111yescharacteristic, complemented
111C23—5411no—
112C23—10822no—
113Q8—5412no—
114Q8—10822no—
115Q8C22×D54112yes—
116D4—22no—
117D4—5412no—
118D4—10822no—
119D4—10822no—
120D4—10822no—
121D4—10822no—
122D4C22×D54112yes—
123C2×C4—22no—
124C2×C4—5411no—
125C2×C4—5412no—
126C2×C4—5412no—
127C2×C4—10822no—
128C2×C4—10822no—
129C2×C4—10822no—
130C2×C4—10822no—
131C2×C4C22×D54111yescharacteristic
132C8—5412no—
133C8C22×D54111yescharacteristic
134C8C22×D54111yescharacteristic
135C22—22no—
136C22—5412no—
137C22—10822no—
138C22—21641no—
139C22—21644no—
140C22D4×D54111yescharacteristic
141C4—22no—
142C4—5412no—
143C4—10822no—
144C4D4×D54111yescharacteristic
145C4C23×D54111yescharacteristic
146C2—21no—
147C2—42no—
148C2—10822no—
149C2—21642no—
150C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC4D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
Fitting#135×C541C2
socleC2×C541C22×D4
hypercenter#135D541
hypocenterC541#575
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. #31772660C2semidirect
3. #31772657C2semidirect
4. #31772655C2semidirect
5. #31772652C2semidirect
6. #31772650C2semidirect
7. #31772648C2semidirect
8. C2×#22575819C2semidirect
9. #135×C541C2semidirect
12. #22575836C22semidirect
15. Q8×D541C22semidirect
17. D4×D541C22semidirect
20. Dic2164C22semidirect
21. #22575826C22semidirect
22. #22575825C22semidirect
23. #22575824C22semidirect
24. #22575823C22semidirect
25. D4328C22semidirect
26. #22575821C22semidirect
27. #22575819C22semidirect
28. #22575819C22semidirect
29. C2×#16864513C22semidirect
30. #41×C541C22semidirect
31. Q16×C541C22semidirect
32. SD16×C541C22semidirect
33. D8×C541C22semidirect
34. C2×C8×C541C22semidirect
75. C541#575semidirect
84. #135D541semidirect
91. #41C2×D541semidirect
99. Q16C2×D541semidirect
103. SD16C2×D541semidirect
106. D8C2×D541semidirect
110. 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
#317726602
#317726572
#317726552
#317726522
#317726502
#317726482
C2×#225758192
#135×C5412
#575541