Finite Group Databasebeta

← #19136608

Subgroups — #19136608

Order 5504.

226 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 45 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#14583088C212yesmaximal
2#14583076C211yesmaximal, characteristic
3#14582694C211yesmaximal, characteristic, complemented
4#14582689C212yesmaximal, complemented
5C43×#563C211yesmaximal, characteristic, complemented
6#13063370C2211yescharacteristic
7#13063356—21no—
8#13063308—22no—
9#13063253—21no—
10#13063242C2211yescharacteristic
11#13063240C2212yes—
12#13063239—22no—
13C4⋊Q8×C43—21no—
14#126×C43—22no—
15#125×C43—21no—
16#124×C43C2211yescharacteristic
17#123×C43C2212yes—
18C22⋊Q8×C43—22no—
19C2×Q8×C43—21no—
20C2×Q8×C43D411yescharacteristic
21C2×D4×C43C2311yescharacteristic
22C22×C4×C43D412yes—
23C2×C22⋊D43—22no—
24#10621900—41no—
25D4×D43—41no—
26#10621898—21no—
27C4⋊C4×C43—21no—
28C4⋊C4×C43—22no—
29C4⋊C4×C43—22no—
30C4⋊C4×C43—21no—
31C4⋊C4×C43—22no—
32C22⋊C4×C43—22no—
33C22⋊C4×C43—22no—
34C22⋊C4×C43D412yes—
35C42×C43—21no—
36C42×C43D411yescharacteristic
37C22⋊Dic43—22no—
38#10621885—41no—
39#10621884—41no—
40(C2×D43)⋊C4—42no—
41Dic43⋊C4—42no—
42#10621877—21no—
43C23×C43C2×D412yes—
44C22×D43—22no—
45Q8×C43—41no—
46Q8×C43—81no—
47D4×C43—41no—
48C2×C4×C43—21no—
49C2×C4×C43—22no—
50C2×C4×C43—21no—
51C2×C4×C43—22no—
52C2×C4×C43—42no—
53C2×C4×C43C2×D411yescharacteristic
54C22⋊D43—42no—
55C22⋊D43—41no—
56C2×Dic43—22no—
57C2×Dic43—42no—
58D172—21no—
59C4×D43—41no—
60Dic86—21no—
61C43⋊C8—41no—
62C22×C43—22no—
63C22×C43—42no—
64C22×C43#12011yescharacteristic
65C2×D43—41no—
66C2×D43—82no—
67C4×C43—21no—
68C4×C43—42no—
69C4×C43—41no—
70C4×C43—42no—
71C4×C43—41no—
72Dic43—41no—
73Dic43—82no—
74#2201—431nomaximal, Sylow
75C2×C43—21no—
76C2×C43—42no—
77C2×C43B(4,𝔽2)11yescharacteristic
78D43—81no—
79#563D4311yescharacteristic, complemented
80#458—432no—
81#455—431no—
82#354—431no—
83#352—432no—
84C43#220111yescharacteristic, complemented, Sylow
85H(5,𝔽2)—431no—
86#137—861no—
87C4⋊Q8—21no—
88#126—22no—
89#125—21no—
90#124C2×D4311yescharacteristic
91#123—862no—
92#123C2×D4312yes—
93C22⋊Q8—22no—
94#104—861no—
95#100—431no—
96#99—432no—
97#99—862no—
98#41—861no—
99#41—1721no—
100C2×Q8—21no—
101C2×Q8C22⋊D4311yescharacteristic
102C2×D4—862no—
103C2×D4—1721no—
104C2×D4C22×D4311yescharacteristic
105C22×C4C22⋊D4312yes—
106Q16—1721no—
107SD16—1721no—
108M16—861no—
109C4⋊C4—21no—
110C4⋊C4—22no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—22no—
114C4⋊C4—1722no—
115C22⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—862no—
118C22⋊C4—1722no—
119C22⋊C4C22⋊D4312yes—
120C42—21no—
121C42C22⋊D4311yescharacteristic
122C23—862no—
123C23C2×C22⋊D4312yes—
124Q8—41no—
125Q8—81no—
126Q8—861no—
127D4—41no—
128D4—861no—
129D4—1722no—
130D4—1721no—
131C2×C4—21no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—862no—
137C2×C4—1721no—
138C2×C4—1722no—
139C2×C4C2×C22⋊D4311yescharacteristic
140C8—1721no—
141C22—22no—
142C22—42no—
143C22—3442no—
144C22—1721no—
145C22#1306329411yescharacteristic
146C4—21no—
147C4—42no—
148C4—41no—
149C4—42no—
150C4—41no—
151C4—3442no—
152C4—1721no—
153C2—21no—
154C2—42no—
155C2—3441no—
156C2#1458308611yescharacteristic
subgroupG/H
centerC2#14583086
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×#563C2
socleC2×C43B(4,𝔽2)
hypercenter#563D43
hypocenterC43#2201
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #563

Complements

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

NH ≅ G/Ntype
3. #14582694C2semidirect
4. #14582689C2semidirect
5. C43×#563C2semidirect
79. #563D43semidirect
84. C43#2201semidirect