Finite Group Databasebeta

← #19140375

Subgroups — #19140375

Order 5504.

526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#13063308C211yesmaximal, characteristic
2#14582837C212yesmaximal, complemented
3#14582834C212yesmaximal, complemented
4#14582830C212yesmaximal, complemented
5#14582825C212yesmaximal, complemented
6#14582778C212yesmaximal
7#14582772C212yesmaximal, complemented
8#14582762C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C43C211yesmaximal, characteristic, complemented
10C22×C22⋊D43C2211yescharacteristic
11#13063308—24no—
12C2×Dic43⋊C4C2211yescharacteristic
13C2×Dic43⋊C4C2211yescharacteristic
14C2×Dic43⋊C4C2214yes—
15C2×C22⋊Dic43C2211yescharacteristic
16C2×C22⋊Dic43C2212yes—
17C2×(C2×D43)⋊C4C2211yescharacteristic
18C2×(C2×D43)⋊C4C2211yescharacteristic
19C2×(C2×D43)⋊C4C2214yes—
20C43⋊#95C2212yes—
21C43⋊#95C2214yes—
22C43⋊#95C2214yes—
23C43⋊#95C2212yes—
24C23×C4×C43C2211yescharacteristic
25C23×C4×C43C2212yes—
26C2×C4⋊C4×C43—24no—
27C2×C4⋊C4×C43C2212yes—
28C2×C4⋊C4×C43C2212yes—
29C24×C43C2311yescharacteristic
30C23×D43C2311yescharacteristic
31C22×C4×C43—24no—
32C22×C4×C43—24no—
33C22×C4×C43—44no—
34C22×C4×C43D414yes—
35C22×C4×C43C2314yes—
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—22no—
39C2×C22⋊D43—24no—
40C22×Dic43C2311yescharacteristic
41C22×Dic43C2314yes—
42C22×Dic43C2311yescharacteristic
43C22×Dic43C2311yescharacteristic
44C4⋊C4×C43—24no—
45C4⋊C4×C43—24no—
46C22⋊Dic43—22no—
47C22⋊Dic43—24no—
48(C2×D43)⋊C4—22no—
49(C2×D43)⋊C4—22no—
50(C2×D43)⋊C4—44no—
51Dic43⋊C4—22no—
52Dic43⋊C4—22no—
53Dic43⋊C4—44no—
54C23×C43—22no—
55C23×C43—22no—
56C23×C43C2×D412yes—
57C23×C43#4114yes—
58C23×C43C2411yescharacteristic
59C22×D43—21no—
60C22×D43—22no—
61C22×D43—22no—
62C22×D43—22no—
63C2×C4×C43—28no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—24no—
67C2×C4×C43—24no—
68C2×C4×C43—24no—
69C2×C4×C43—48no—
70C2×C4×C43C2×D412yes—
71C2×C4×C43C2×D412yes—
72C22⋊D43—44no—
73C2×Dic43—21no—
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—24no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—24no—
80C2×Dic43—22no—
81C2×Dic43—24no—
82C22×C43—22no—
83C22×C43—22no—
84C22×C43—28no—
85C22×C43#12314yes—
86C22×C43C22×D411yescharacteristic
87C22×C43C2×#4112yes—
88C22×C43H(5,𝔽2)12yes—
89C22×C432−1+412yes—
90C2×D43—41no—
91C2×D43—41no—
92C2×D43—41no—
93C2×D43—44no—
94C4×C43—22no—
95C4×C43—22no—
96C4×C43—44no—
97Dic43—41no—
98Dic43—41no—
99Dic43—41no—
100Dic43—44no—
101#2623—431nomaximal, Sylow
102C2×C43—24no—
103C2×C43C2×#12311yescharacteristic
104C2×C43#53511yescharacteristic
105C2×C43#53611yescharacteristic
106C2×C43#53914yes—
107D43—81no—
108C2×#123—431no—
109C22×C4⋊C4D4311yescharacteristic, complemented
110#400—432no—
111#399—432no—
112#398—432no—
113#397—432no—
114#386—432no—
115#385—432no—
116#381—431no—
117C43#262311yescharacteristic, complemented, Sylow
118C22×D4—431no—
119C23×C4C2×D4311yescharacteristic
120C23×C4C2×D4312yes—
121#123—864no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—431no—
124C2×C4⋊C4—431no—
125C2×C4⋊C4—434no—
126C2×C4⋊C4C2×D4312yes—
127C2×C4⋊C4C2×D4312yes—
128C2×C22⋊C4—431no—
129C2×C22⋊C4—432no—
130C2×C22⋊C4—431no—
131C2×C22⋊C4—431no—
132C2×C22⋊C4—434no—
133#95—432no—
134#95—432no—
135#95—434no—
136#95—434no—
137C24—431no—
138C24C22×D4311yescharacteristic
139C2×D4—864no—
140C2×D4—862no—
141C22×C4—24no—
142C22×C4—24no—
143C22×C4—44no—
144C22×C4—431no—
145C22×C4—434no—
146C22×C4—431no—
147C22×C4—431no—
148C22×C4C22⋊D4314yes—
149C22×C4C22×D4314yes—
150C22×C4C22×D4311yescharacteristic
151C22×C4C22×D4311yescharacteristic
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—862no—
155C4⋊C4—862no—
156C4⋊C4—1724no—
157C22⋊C4—864no—
158C22⋊C4—862no—
159C22⋊C4—862no—
160C22⋊C4—862no—
161C22⋊C4—1724no—
162C23—22no—
163C23—22no—
164C23—861no—
165C23—862no—
166C23—862no—
167C23—862no—
168C23#1062189814yes—
169C23C2×C22⋊D4312yes—
170C23C23×D4311yescharacteristic
171D4—1724no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—48no—
179C2×C4—861no—
180C2×C4—861no—
181C2×C4—861no—
182C2×C4—864no—
183C2×C4—862no—
184C2×C4—864no—
185C2×C4—862no—
186C2×C4—862no—
187C2×C4—864no—
188C2×C4C2×C22⋊D4312yes—
189C2×C4C2×C22⋊D4312yes—
190C22—22no—
191C22—22no—
192C22—28no—
193C22—1721no—
194C22—1721no—
195C22—1721no—
196C22—1724no—
197C22#1306330814yes—
198C22C22×C22⋊D4311yescharacteristic
199C22C2×#1062189812yes—
200C22#1306337012yes—
201C22#1306337312yes—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—1721no—
206C4—1721no—
207C4—1721no—
208C4—1724no—
209C2—24no—
210C2—3441no—
211C2C2×#1306330811yescharacteristic
212C2#1458346611yescharacteristic
213C2#1458347311yescharacteristic
214C2#1458349614yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC22×C4⋊C4×C43C2
hypercenterC22×C4⋊C4D43
hypocenterC43#2623
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14582837C2semidirect
3. #14582834C2semidirect
4. #14582830C2semidirect
5. #14582825C2semidirect
7. #14582772C2semidirect
8. #14582762C2semidirect
9. C22×C4⋊C4×C43C2semidirect
109. C22×C4⋊C4D43semidirect
117. C43#2623semidirect