Finite Group Databasebeta

← #19135043

Subgroups — #19135043

Order 5504.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#14583410C211yesmaximal, characteristic
2C2×#13063253C212yesmaximal, complemented
3#14582863C211yesmaximal, characteristic, complemented
4#14582659C212yesmaximal, complemented
5C2×#117×C43C211yesmaximal, characteristic, complemented
6C2×#10621898C2211yescharacteristic
7C2×#10621877C2212yes—
8#13063308—21no—
9#13063304C412yescomplemented
10#13063299C412yescomplemented
11#13063294—21no—
12C4×C22⋊D43—22no—
13#13063284C2211yescharacteristic
14#13063253—24no—
15C22⋊(C43⋊C8)—22no—
16C23×C4×C43C2211yescharacteristic
17#117×C43—24no—
18C2×C4⋊C4×C43—21no—
19C2×C22⋊C4×C43—21no—
20C2×C42×C43C2212yes—
21C24×C43D411yescharacteristic
22C22×C4×C43—22no—
23C22×C4×C43—22no—
24C22×C4×C43—22no—
25C22×C4×C43C2×C412yes—
26C22×C4×C43D412yes—
27C22×C4×C43D411yescharacteristic
28C22×C4×C43C2311yescharacteristic
29C2×C22⋊D43—22no—
30C2×C22⋊D43—21no—
31#10621898—22no—
32#10621898—22no—
33C2×D172C2×C411yescharacteristic
34C2×C4×D43—21no—
35C2×Dic86C2×C411yescharacteristic
36C4⋊C4×C43—24no—
37C22⋊C4×C43—24no—
38C42×C43—22no—
39C42×C43D414yescomplemented
40C22⋊Dic43—22no—
41C22⋊Dic43—21no—
42(C2×D43)⋊C4—22no—
43C4⋊Dic43C2×C412yes—
44Dic43⋊C4—22no—
45C4×Dic43—21no—
46#10621877—22no—
47#10621877—22no—
48C2×C43⋊C8—22no—
49C23×C43—21no—
50C23×C43—21no—
51C23×C43—42no—
52C23×C43C22⋊C412yes—
53C23×C43C2×D411yescharacteristic
54C22×D43—21no—
55C2×C4×C43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—24no—
58C2×C4×C43—24no—
59C2×C4×C43—24no—
60C2×C4×C43—44no—
61C2×C4×C43C22⋊C412yes—
62C2×C4×C43C22×C411yescharacteristic
63C2×C4×C43C2×D411yescharacteristic
64C2×C4×C43C2×D412yes—
65C2×C4×C43#4112yes—
66C22⋊D43—44no—
67C22⋊D43—41no—
68C22⋊D43—41no—
69C2×Dic43—22no—
70C2×Dic43—21no—
71D172—22no—
72C4×D43—42no—
73Dic86—22no—
74C43⋊C8—42no—
75C22×C43—22no—
76C22×C43—22no—
77C22×C43—22no—
78C22×C43—22no—
79C22×C43—42no—
80C22×C43—42no—
81C22×C43C2×C22⋊C411yescharacteristic
82C22×C43#12011yescharacteristic
83C22×C43#12311yescharacteristic
84C2×D43—41no—
85C2×D43—42no—
86C4×C43—22no—
87C4×C43—44no—
88C4×C43C4×D412yes—
89C4×C43#12112yes—
90Dic43—41no—
91Dic43—42no—
92#1897—431nomaximal, Sylow
93C2×C43—21no—
94C2×C43—21no—
95C2×C43—42no—
96C2×C43#38611yescharacteristic
97C2×C43#42112yes—
98D43—81no—
99#525—431no—
100C2×#117D4311yescharacteristic, complemented
101C2×#104—432no—
102#407—431no—
103#339—432no—
104C43#189711yescharacteristic, complemented, Sylow
105C2×#41—431no—
106C23×C4C2×D4311yescharacteristic
107C2×M16—432no—
108#123—861no—
109C22⋊Q8—432no—
110#121—432no—
111#120—861no—
112C4×D4—862no—
113#117—24no—
114#117—431no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D4312yes—
118#104—864no—
119C22⋊C8—862no—
120C24C22⋊D4311yescharacteristic
121#41—862no—
122#41—862no—
123C2×Q8—431no—
124C2×D4—431no—
125C2×D4—862no—
126C2×D4—861no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—861no—
131C22×C4C4×D4312yes—
132C22×C4D17212yes—
133C22×C4C22⋊D4311yescharacteristic
134C22×C4C22×D4311yescharacteristic
135M16—862no—
136M16—862no—
137C2×C8—862no—
138C4⋊C4—24no—
139C4⋊C4—432no—
140C4⋊C4—862no—
141C22⋊C4—24no—
142C22⋊C4—862no—
143C22⋊C4—861no—
144C22⋊C4—862no—
145C42—22no—
146C42—861no—
147C42C22⋊D4314yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—861no—
152C23(C2×D43)⋊C412yes—
153C23C2×C22⋊D4311yescharacteristic
154Q8—862no—
155D4—862no—
156D4—1724no—
157D4—1721no—
158D4—1721no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—862no—
166C2×C4—861no—
167C2×C4—1722no—
168C2×C4(C2×D43)⋊C412yes—
169C2×C4C2×C4×D4311yescharacteristic
170C2×C4C2×D17211yescharacteristic
171C2×C4#1062189812yes—
172C2×C4C2×C22⋊D4312yes—
173C8—1722no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—1722no—
181C22—1721no—
182C22C2×(C2×D43)⋊C411yescharacteristic
183C22#1306329411yescharacteristic
184C22#1306330811yescharacteristic
185C4—22no—
186C4—44no—
187C4—1722no—
188C4—1721no—
189C4C4×C22⋊D4312yes—
190C4#1306329912yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—3441no—
195C2#1458277811yescharacteristic
196C2#1458291712yes—
subgroupG/H
centerC2×C4C2×D172
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC2×#117×C43C2
socleC22×C43C2×C22⋊C4
hypercenterC2×#117D43
hypocenterC43#1897
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#13063253C2semidirect
3. #14582863C2semidirect
4. #14582659C2semidirect
5. C2×#117×C43C2semidirect
9. #13063304C4semidirect
10. #13063299C4semidirect
39. C42×C43D4semidirect
100. C2×#117D43semidirect
104. C43#1897semidirect
147. C42C22⋊D43semidirect