Finite Group Databasebeta

← #19136621

Subgroups — #19136621

Order 5504.

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

normal subgroups only

This group has 236 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#14583081C211yesmaximal, characteristic, complemented
2#14583071C212yesmaximal, complemented
3#14582698C211yesmaximal, characteristic, complemented
4#14582696C212yesmaximal, complemented
5C43×#555C211yesmaximal, characteristic, complemented
6#13063373C2211yescharacteristic
7#13063356—21no—
8#13063351—22no—
9#13063253—22no—
10#13063253—21no—
11#13063244C2212yes—
12#13063244C2211yescharacteristic
13C4⋊Q8×C43C2211yescharacteristic
14#124×C43—21no—
15#124×C43C2212yes—
16#121×C43—22no—
17C4×D4×C43—21no—
18#117×C43—22no—
19C2×Q8×C43D411yescharacteristic
20C2×Q8×C43C2311yescharacteristic
21C2×D4×C43—21no—
22C2×D4×C43—21no—
23C2×D4×C43D412yes—
24C22×C4×C43—22no—
25#10621902—41no—
26Q8×D43—41no—
27#10621898—22no—
28#10621898—21no—
29C4⋊C4×C43—21no—
30C4⋊C4×C43—22no—
31C22⋊C4×C43—22no—
32C22⋊C4×C43—22no—
33C22⋊C4×C43—22no—
34C42×C43—21no—
35C42×C43D412yes—
36C42×C43D411yescharacteristic
37#10621885—41no—
38#10621884—41no—
39#10621883—42no—
40#10621882—42no—
41#10621877—22no—
42#10621877—21no—
43C23×C43—22no—
44Q8×C43—41no—
45Q8×C43—41no—
46D4×C43—42no—
47D4×C43—42no—
48D4×C43—81no—
49C2×C4×C43—21no—
50C2×C4×C43—22no—
51C2×C4×C43—21no—
52C2×C4×C43—44no—
53C2×C4×C43C2×D411yescharacteristic
54C2×C4×C43C2×D412yes—
55C22⋊D43—41no—
56D172—22no—
57D172—21no—
58C4×D43—42no—
59C4×D43—41no—
60Dic86—22no—
61Dic86—21no—
62C43⋊C8—42no—
63C43⋊C8—41no—
64C22×C43—42no—
65C22×C43—42no—
66C22×C43—42no—
67C22×C43#12011yescharacteristic
68C2×D43—41no—
69C4×C43—22no—
70C4×C43—22no—
71C4×C43—21no—
72C4×C43—42no—
73C4×C43—41no—
74Dic43—41no—
75#2204—431nomaximal, Sylow
76C2×C43—21no—
77C2×C43—82no—
78C2×C43B(4,𝔽2)11yescharacteristic
79D43—81no—
80#555D4311yescharacteristic, complemented
81#456—431no—
82#454—432no—
83#356—431no—
84#355—432no—
85C43#220411yescharacteristic, complemented, Sylow
862−1+4—431no—
87#137—861no—
88AGL(1,ℤ/8)—862no—
89C4⋊Q8C2×D4311yescharacteristic
90#124—21no—
91#124C2×D4312yes—
92#121—22no—
93C4×D4—21no—
94#117—22no—
95#104—862no—
96#104—861no—
97#101—431no—
98#101—432no—
99#41—862no—
100#41—861no—
101#41—1721no—
102C2×Q8—1721no—
103C2×Q8C22⋊D4311yescharacteristic
104C2×Q8C22×D4311yescharacteristic
105C2×D4—21no—
106C2×D4—21no—
107C2×D4C22⋊D4312yes—
108C22×C4—22no—
109Q16—1721no—
110SD16—1722no—
111SD16—1721no—
112D8—1722no—
113M16—862no—
114M16—861no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C42—21no—
121C42C22⋊D4312yes—
122C42C22⋊D4311yescharacteristic
123C23—22no—
124Q8—41no—
125Q8—41no—
126Q8—862no—
127Q8—861no—
128D4—42no—
129D4—42no—
130D4—81no—
131D4—862no—
132D4—861no—
133D4—1721no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—44no—
138C2×C4—1722no—
139C2×C4—1721no—
140C2×C4C2×C22⋊D4311yescharacteristic
141C2×C4C2×C22⋊D4312yes—
142C8—1722no—
143C8—1721no—
144C22—42no—
145C22—42no—
146C22—42no—
147C22—1721no—
148C22#1306329411yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—42no—
153C4—41no—
154C4—1721no—
155C2—21no—
156C2—82no—
157C2—3441no—
158C2#1458308611yescharacteristic
subgroupG/H
centerC2#14583086
commutatorC2×Q8×C43C23
FrattiniC2×Q8C22×D43
FittingC43×#555C2
socleC2×C43B(4,𝔽2)
hypercenter#555D43
hypocenterC43#2204
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #14583081C2semidirect
2. #14583071C2semidirect
3. #14582698C2semidirect
4. #14582696C2semidirect
5. C43×#555C2semidirect
80. #555D43semidirect
85. C43#2204semidirect