Finite Group Databasebeta

← #19134976

Subgroups — #19134976

Order 5504.

332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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#14583666C211yesmaximal, characteristic, complemented
2#14583445C211yesmaximal, characteristic
3#14582917C212yesmaximal, complemented
4#14582658C212yesmaximal, complemented
5C43×#410C211yesmaximal, characteristic, complemented
6C2×#10621898C2211yescharacteristic
7#13063332—24no—
8C2×#10621877—22no—
9C2×#10621877C2212yes—
10#13063323C411yescharacteristic, complemented
11#13063321C411yescharacteristic, complemented
12#13063314C411yescharacteristic, complemented
13#13063312C411yescharacteristic, complemented
14#13063297—22no—
15C4×C22⋊D43—22no—
16C2×C4×Dic43C2211yescharacteristic
17#13063253—24no—
18C2×#41×C43C2211yescharacteristic
19#117×C43C2212yes—
20#99×C43—22no—
21#41×C43—22no—
22#41×C43—22no—
23C2×Q8×C43C2×C411yescharacteristic
24C2×D4×C43C2×C411yescharacteristic
25C2×D4×C43D412yes—
26C22×C4×C43D412yes—
27C22×C4×C43C2311yescharacteristic
28C2×C22⋊D43—22no—
29C2×C22⋊D43—21no—
30C22×Dic43—21no—
31#10621898—22no—
32#10621898—22no—
33C2×D172C2×C411yescharacteristic
34C2×C4×D43—21no—
35C2×Dic86C2×C411yescharacteristic
36C4⋊C4×C43—22no—
37C22⋊C4×C43—22no—
38C42×C43—22no—
39C22⋊Dic43—22no—
40(C2×D43)⋊C4—22no—
41Dic43⋊C4—22no—
42C4×Dic43—21no—
43C4×Dic43C2×C411yescharacteristic
44C4×Dic43C2×C411yescharacteristic
45#10621877—24no—
46#10621877—22no—
47#10621877D414yescomplemented
48C2×C43⋊C8—24no—
49C2×C43⋊C8—22no—
50C23×C43C22⋊C412yes—
51C23×C43C2×D411yescharacteristic
52C22×D43—21no—
53Q8×C43—22no—
54D4×C43—24no—
55D4×C43—22no—
56C2×C4×C43—22no—
57C2×C4×C43—22no—
58C2×C4×C43—42no—
59C2×C4×C43C22⋊C412yes—
60C2×C4×C43C22×C411yescharacteristic
61C2×C4×C43C2×D411yescharacteristic
62C2×C4×C43C2×D412yes—
63C2×C4×C43#4112yes—
64C22⋊D43—44no—
65C22⋊D43—42no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68C2×Dic43—21no—
69C2×Dic43—42no—
70D172—22no—
71C4×D43—41no—
72C4×D43—41no—
73Dic86—22no—
74C43⋊C8—24no—
75C22×C43—22no—
76C22×C43—41no—
77C22×C43—42no—
78C22×C43C2×C22⋊C411yescharacteristic
79C22×C43#12112yes—
80C2×D43—42no—
81C2×D43—41no—
82C4×C43—22no—
83C4×C43—82no—
84C4×C43C4×D412yes—
85C4×C43#12011yescharacteristic
86C4×C43#12311yescharacteristic
87Dic43—22no—
88Dic43—41no—
89Dic43—41no—
90#1884—431nomaximal, Sylow
91C2×C43—21no—
92C2×C43—22no—
93C2×C43—42no—
94C2×C43#38611yescharacteristic
95D43—81no—
96#568—431no—
97#532—431no—
98#421—432no—
99#410D4311yescharacteristic, complemented
100#339—432no—
101C43#188411yescharacteristic, complemented, Sylow
102C2×#41—431no—
103C2×#41C2×D4311yescharacteristic
104#131—864no—
105C2×M16—432no—
106C2×M16—862no—
107C4⋊Q8—431no—
108#127—431no—
109#124—431no—
110#124—431no—
111#121—862no—
112C4×D4—862no—
113#117C2×D4312yes—
114C2×C42—431no—
115#104—864no—
116#99—22no—
117#41—22no—
118#41—22no—
119#41—862no—
120#41—862no—
121C2×Q8—431no—
122C2×Q8C4×D4311yescharacteristic
123C2×D4—431no—
124C2×D4—862no—
125C2×D4—861no—
126C2×D4C4×D4311yescharacteristic
127C2×D4C22⋊D4312yes—
128C22×C4—861no—
129C22×C4—861no—
130C22×C4D17212yes—
131C22×C4C22×D4311yescharacteristic
132M16—434no—
133M16—864no—
134M16—862no—
135C2×C8—864no—
136C2×C8—862no—
137C4⋊C4—22no—
138C4⋊C4—862no—
139C22⋊C4—22no—
140C22⋊C4—862no—
141C22⋊C4—862no—
142C42—22no—
143C42—431no—
144C42—431no—
145C42—861no—
146C23—861no—
147C23(C2×D43)⋊C412yes—
148C23C2×C22⋊D4311yescharacteristic
149Q8—22no—
150Q8—862no—
151D4—24no—
152D4—22no—
153D4—862no—
154D4—1724no—
155D4—1722no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—861no—
160C2×C4—861no—
161C2×C4—861no—
162C2×C4—1722no—
163C2×C4—1721no—
164C2×C4—1721no—
165C2×C4(C2×D43)⋊C412yes—
166C2×C4C2×C4×D4311yescharacteristic
167C2×C4C2×D17211yescharacteristic
168C2×C4D4×D4312yes—
169C2×C4#1062190012yes—
170C8—864no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—1722no—
175C22—1721no—
176C22C2×(C2×D43)⋊C411yescharacteristic
177C22#1306329712yes—
178C4—22no—
179C4—82no—
180C4—862no—
181C4—1721no—
182C4—1721no—
183C4(C22⋊D43)⋊C412yes—
184C4#1306329511yescharacteristic
185C4#1306330911yescharacteristic
186C2—22no—
187C2—21no—
188C2—42no—
189C2—3441no—
190C2#1458277611yescharacteristic
subgroupG/H
centerC4#13063295
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#410C2
socleC2×C43#386
hypercenter#410D43
hypocenterC43#1884
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #14583666C2semidirect
3. #14582917C2semidirect
4. #14582658C2semidirect
5. C43×#410C2semidirect
10. #13063323C4semidirect
11. #13063321C4semidirect
12. #13063314C4semidirect
13. #13063312C4semidirect
47. #10621877D4semidirect
99. #410D43semidirect
101. C43#1884semidirect