Finite Group Databasebeta

← #46830763

Subgroups — #46830763

Order 34624.

250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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#31772621C212yesmaximal, complemented
2#31772614C212yesmaximal, complemented
3#31772610C212yesmaximal, complemented
4#31772607C211yesmaximal, characteristic, complemented
5#31772602C211yesmaximal, characteristic, complemented
6#31772601C212yesmaximal, complemented
7#31772597C212yesmaximal, complemented
8C4×C22⋊D541C212yesmaximal, complemented
9C2×C22⋊C4×C541C211yesmaximal, characteristic, complemented
10C2×Dic1082C2211yescharacteristic, complemented
11C2×D2164C2211yescharacteristic, complemented
12C2×C22⋊D541C2212yes—
13C2×C22⋊D541C2212yes—
14C2×C22⋊D541C2212yes—
15C2×C4×D541C2212yescomplemented
16C4⋊Dic541C2211yescharacteristic, complemented
17C4⋊Dic541C2211yescharacteristic, complemented
18#22575815C2212yescomplemented
19#22575815C2212yescomplemented
20C22⋊Dic541C2212yes—
21C22⋊Dic541C2212yes—
22C22⋊Dic541C2212yes—
23#22575813C2212yescomplemented
24#22575813C2212yescomplemented
25C4×Dic541C2212yescomplemented
26C24×C541C2211yescharacteristic
27C22×C4×C541C2211yescharacteristic
28C22×C4×C541C2211yescharacteristic
29C22⋊C4×C541C2212yes—
30C22⋊C4×C541C2212yes—
31C22×D541C2312yes—
32Dic1082—41no—
33D2164—41no—
34C22⋊D541—24no—
35C22⋊D541—42no—
36C22⋊D541—42no—
37C2×Dic541C2312yes—
38C2×Dic541C2312yes—
39C2×Dic541C2312yes—
40C4×D541—42no—
41C23×C541—22no—
42C23×C541—41no—
43C23×C541—41no—
44C23×C541C2312yes—
45C23×C541C2311yescharacteristic
46C2×C4×C541—41no—
47C2×C4×C541—41no—
48C2×C4×C541C2312yes—
49C2×C4×C541C2311yescharacteristic
50C2×C4×C541C2311yescharacteristic
51C22×C541—21no—
52C22×C541—21no—
53C22×C541—22no—
54C22×C541—22no—
55C22×C541—22no—
56C22×C541—44no—
57C22×C541#4112yes—
58C22×C541C2411yescharacteristic
59C2×D541—22no—
60C2×D541—22no—
61C2×D541—22no—
62C4×C541—22no—
63C4×C541—21no—
64C4×C541—21no—
65Dic541—22no—
66Dic541—22no—
67Dic541—22no—
68C2×C541—22no—
69C2×C541—42no—
70C2×C541C2×#4111yescharacteristic
71C2×C541H(5,𝔽2)11yescharacteristic
72C2×C541H(5,𝔽2)11yescharacteristic
73D541—42no—
74C541#53811yescharacteristic, complemented, Sylow
75#538—5411nomaximal, Sylow
76#126—5412no—
77#124—5412no—
78#123—5412no—
79C22⋊Q8—5411no—
80#121—5411no—
81#121—5412no—
82#120—5412no—
83C4×D4—5412no—
84C2×C22⋊C4D54111yescharacteristic, complemented
85C24C2×D54111yescharacteristic
86C2×Q8—5411no—
87C2×D4—5412no—
88C2×D4—5412no—
89C2×D4—5412no—
90C2×D4—5411no—
91C22×C4—5412no—
92C22×C4C2×D54111yescharacteristic
93C22×C4C2×D54111yescharacteristic
94C4⋊C4—5412no—
95C4⋊C4—5412no—
96C4⋊C4—5411no—
97C4⋊C4—5411no—
98C22⋊C4—5412no—
99C22⋊C4—5412no—
100C22⋊C4—5412no—
101C22⋊C4—5412no—
102C22⋊C4—5412no—
103C22⋊C4C2×D54112yes—
104C22⋊C4C2×D54112yes—
105C42—5412no—
106C23—22no—
107C23—41no—
108C23—41no—
109C23—5412no—
110C23C22×D54112yes—
111C23C22×D54111yescharacteristic
112Q8—21641no—
113D4—10824no—
114D4—21641no—
115D4—21642no—
116D4—21642no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—5412no—
120C2×C4—5412no—
121C2×C4—5412no—
122C2×C4—21642no—
123C2×C4C22×D54112yes—
124C2×C4C22×D54111yescharacteristic
125C2×C4C22×D54111yescharacteristic
126C22—21no—
127C22—21no—
128C22—22no—
129C22—22no—
130C22—22no—
131C22—44no—
132C22—10822no—
133C22—10822no—
134C22—10822no—
135C22#2257583612yes—
136C22C23×D54111yescharacteristic
137C4—22no—
138C4—21no—
139C4—21no—
140C4—10822no—
141C4—10822no—
142C4—10822no—
143C2—22no—
144C2—42no—
145C2—21642no—
146C2C2×#2257583611yescharacteristic
147C2#3177267311yescharacteristic
148C2#3177267311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D541
commutator, socle, cosocleC22×C541C24
FittingC2×C22⋊C4×C541C2
hypercenterC2×C22⋊C4D541
hypocenterC541#538
LCSG ▷ C22×C541 ▷ C541
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #31772621C2semidirect
2. #31772614C2semidirect
3. #31772610C2semidirect
4. #31772607C2semidirect
5. #31772602C2semidirect
6. #31772601C2semidirect
7. #31772597C2semidirect
8. C4×C22⋊D541C2semidirect
9. C2×C22⋊C4×C541C2semidirect
10. C2×Dic1082C22semidirect
11. C2×D2164C22semidirect
15. C2×C4×D541C22semidirect
16. C4⋊Dic541C22semidirect
17. C4⋊Dic541C22semidirect
18. #22575815C22semidirect
19. #22575815C22semidirect
23. #22575813C22semidirect
24. #22575813C22semidirect
25. C4×Dic541C22semidirect
74. C541#538semidirect
84. C2×C22⋊C4D541semidirect

Maximal subgroups

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

subgroupindex
#317726212
#317726142
#317726102
#317726072
#317726022
#317726012
#317725972
C4×C22⋊D5412
C2×C22⋊C4×C5412
#538541