Finite Group Databasebeta

← #19135949

Subgroups — #19135949

Order 5504.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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#14583525C211yesmaximal, characteristic
2#14582774C212yesmaximal
3#14582771C211yesmaximal, characteristic
4#14582665C212yesmaximal
5C43×#342C211yesmaximal, characteristic
6C23×Dic43C2211yescharacteristic
7#13063304—21no—
8#13063304—21no—
9#13063302—22no—
10#13063302—22no—
11C2×C4⋊Dic43—22no—
12C2×Dic43⋊C4—21no—
13C2×C22⋊Dic43C2212yes—
14C2×C22⋊Dic43C2211yescharacteristic
15C43⋊#95—21no—
16C43⋊#95—22no—
17C2×C22⋊C4×C43C2211yescharacteristic
18C2×C22⋊C4×C43C2212yes—
19C24×C43C2311yescharacteristic
20C22×C4×C43—22no—
21C22×C4×C43D411yescharacteristic
22C22×C4×C43D411yescharacteristic
23C22×Dic43—21no—
24C22×Dic43—21no—
25C22×Dic43—22no—
26C22×Dic43—42no—
27C22×Dic43D412yes—
28C22×Dic43D412yes—
29C2×Dic86—21no—
30C2×Dic86—21no—
31C22⋊C4×C43—22no—
32C22⋊C4×C43—22no—
33C22⋊C4×C43Q814yescomplemented
34C22⋊Dic43—22no—
35C22⋊Dic43—22no—
36C22⋊Dic43—21no—
37C22⋊Dic43Q812yescomplemented
38C4⋊Dic43—21no—
39C4⋊Dic43—21no—
40C4⋊Dic43—44no—
41Dic43⋊C4—22no—
42Dic43⋊C4—22no—
43Dic43⋊C4—42no—
44C23×C43—41no—
45C23×C43—41no—
46C23×C43C2×D411yescharacteristic
47C23×C43C2×D412yes—
48C23×C43C2×Q812yes—
49C23×C43C2×Q811yescharacteristic
50C23×C43#4111yescharacteristic
51C2×C4×C43—21no—
52C2×C4×C43—21no—
53C2×C4×C43—24no—
54C2×C4×C43—42no—
55C2×C4×C43—42no—
56C2×C4×C43—41no—
57C2×C4×C43—41no—
58C2×Dic43—22no—
59C2×Dic43—24no—
60C2×Dic43—22no—
61C2×Dic43—22no—
62C2×Dic43—22no—
63C2×Dic43—41no—
64C2×Dic43—41no—
65C2×Dic43—41no—
66C2×Dic43—42no—
67C2×Dic43—41no—
68C2×Dic43—42no—
69C2×Dic43—42no—
70Dic86—81no—
71Dic86—81no—
72C22×C43—21no—
73C22×C43—22no—
74C22×C43—21no—
75C22×C43—22no—
76C22×C43—42no—
77C22×C43—41no—
78C22×C43—41no—
79C22×C43#12011yescharacteristic
80C22×C43C22⋊Q812yes—
81C22×C43C22⋊Q811yescharacteristic
82C22×C43C4⋊Q812yes—
83C22×C43C4⋊Q811yescharacteristic
84C4×C43—44no—
85C4×C43—41no—
86C4×C43—41no—
87Dic43—42no—
88Dic43—42no—
89Dic43—42no—
90Dic43—42no—
91#2062—431nomaximal, Sylow
92C2×C43—21no—
93C2×C43—22no—
94C2×C43—22no—
95C2×C43—21no—
96C2×C43#39511yescharacteristic
97C2×C43B(4,𝔽2)11yescharacteristic
98C2×C43#45811yescharacteristic
99#543—431no—
100#385—431no—
101#385—432no—
102#342—432no—
103#342D4311yescharacteristic
104C43#206211yescharacteristic, complemented, Sylow
105C23×C4—431no—
106C22⋊Q8—862no—
107C22⋊Q8—862no—
108C22⋊Q8—861no—
109C22⋊Q8—861no—
110C2×C4⋊C4—862no—
111C2×C4⋊C4—861no—
112C2×C22⋊C4—431no—
113C2×C22⋊C4—432no—
114C2×C22⋊C4C2×D4311yescharacteristic
115C2×C22⋊C4C2×D4312yes—
116#95—862no—
117#95—861no—
118C24C22×D4311yescharacteristic
119C2×Q8—861no—
120C2×Q8—861no—
121C22×C4—22no—
122C22×C4—432no—
123C22×C4—432no—
124C22×C4—861no—
125C22×C4—861no—
126C22×C4—862no—
127C22×C4—1722no—
128C22×C4D17211yescharacteristic
129C22×C4D17211yescharacteristic
130C4⋊C4—862no—
131C4⋊C4—862no—
132C4⋊C4—861no—
133C4⋊C4—861no—
134C4⋊C4—1722no—
135C4⋊C4—1724no—
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—432no—
139C22⋊C4—862no—
140C22⋊C4—862no—
141C22⋊C4—861no—
142C22⋊C4Dic8614yescomplemented
143C23—41no—
144C23—41no—
145C23C2×Dic8612yes—
146C23C2×D17211yescharacteristic
147C23D4×D4312yes—
148C23#1062190011yescharacteristic
149C23Q8×D4311yescharacteristic
150Q8—3441no—
151Q8—3441no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—24no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—862no—
160C2×C4—864no—
161C2×C4—862no—
162C2×C4—862no—
163C2×C4—862no—
164C2×C4—1721no—
165C2×C4—1721no—
166C2×C4—1722no—
167C2×C4—1721no—
168C2×C4—1721no—
169C2×C4—1722no—
170C2×C4—1722no—
171C22—21no—
172C22—22no—
173C22—21no—
174C22—22no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22#1306329511yescharacteristic
179C22#1306330212yes—
180C22#1306330511yescharacteristic
181C22#1306332412yes—
182C22#1306332511yescharacteristic
183C4—44no—
184C4—41no—
185C4—41no—
186C4—1722no—
187C4—1722no—
188C4—1722no—
189C4—1722no—
190C2—22no—
191C2—21no—
192C2—22no—
193C2—21no—
194C2#1458282011yescharacteristic
195C2#1458308711yescharacteristic
196C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC24×C43C23
FrattiniC24C22×D43
FittingC43×#342C2
socleC22×C43#120
hypercenter#342D43
hypocenterC43#2062
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
33. C22⋊C4×C43Q8semidirect
37. C22⋊Dic43Q8semidirect
104. C43#2062semidirect
142. C22⋊C4Dic86semidirect