Finite Group Databasebeta

← #19138865

Subgroups — #19138865

Order 5504.

672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×(C2×D43)⋊C4C211yesmaximal, characteristic
2#14582834C212yesmaximal, complemented
3#14582825C212yesmaximal, complemented
4#14582790C214yesmaximal, complemented
5#14582771C212yesmaximal, complemented
6#14582762C211yesmaximal, characteristic, complemented
7#14582754C212yesmaximal
8C2×#117×C43C211yesmaximal, characteristic, complemented
9C24×D43C2211yescharacteristic
10C23×Dic43C2211yescharacteristic
11C2×Dic43⋊C4C2214yescomplemented
12C2×C22⋊Dic43C2212yes—
13C2×(C2×D43)⋊C4—24no—
14C2×(C2×D43)⋊C4C2212yes—
15C2×(C2×D43)⋊C4C2214yes—
16C2×(C2×D43)⋊C4C2212yes—
17C2×(C2×D43)⋊C4C2214yes—
18C43⋊#95C2212yescomplemented
19C43⋊#95C2214yescomplemented
20C43⋊#95C2212yescomplemented
21C23×C4×C43C2211yescharacteristic
22#117×C43—24no—
23C2×C4⋊C4×C43C2211yescharacteristic, complemented
24C2×C4⋊C4×C43C2211yescharacteristic, complemented
25C2×C22⋊C4×C43C2212yes—
26C2×C42×C43C2212yescomplemented
27C24×C43C2311yescharacteristic
28C23×D43—22no—
29C23×D43—24no—
30C23×D43—24no—
31C23×D43—42no—
32C23×D43C2312yes—
33C22×C4×C43—24no—
34C22×C4×C43D414yes—
35C22×C4×C43C2312yes—
36C22×C4×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×Dic43—22no—
40C22×Dic43—42no—
41C22×Dic43C2314yes—
42C22×Dic43C2312yes—
43C4⋊C4×C43—22no—
44C4⋊C4×C43—22no—
45C22⋊C4×C43—24no—
46C42×C43—24no—
47C22⋊Dic43—24no—
48(C2×D43)⋊C4—24no—
49(C2×D43)⋊C4—24no—
50(C2×D43)⋊C4—28no—
51(C2×D43)⋊C4—44no—
52Dic43⋊C4—44no—
53C23×C43—22no—
54C23×C43—22no—
55C23×C43C2×D412yes—
56C23×C43#4114yes—
57C23×C43C2411yescharacteristic
58C22×D43—28no—
59C22×D43—22no—
60C22×D43—22no—
61C22×D43—24no—
62C22×D43—24no—
63C22×D43—416no—
64C22×D43—44no—
65C22×D43—44no—
66C22×D43#4114yes—
67C2×C4×C43—28no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—24no—
73C2×C4×C43—24no—
74C2×C4×C43C2×D412yes—
75C2×C4×C43C2×D412yes—
76C2×Dic43—22no—
77C2×Dic43—24no—
78C2×Dic43—24no—
79C2×Dic43—24no—
80C2×Dic43—24no—
81C2×Dic43—44no—
82C22×C43—22no—
83C22×C43—22no—
84C22×C43—28no—
85C22×C43#12314yes—
86C22×C43C22×D411yescharacteristic
87C22×C43C2×#4112yes—
88C22×C43C2×#4112yes—
89C22×C43H(5,𝔽2)12yes—
90C2×D43—24no—
91C2×D43—28no—
92C2×D43—416no—
93C2×D43—42no—
94C2×D43—42no—
95C2×D43—44no—
96C4×C43—22no—
97C4×C43—22no—
98C4×C43—42no—
99C4×C43—42no—
100Dic43—42no—
101Dic43—44no—
102#2482—431nomaximal, Sylow
103C2×C43—24no—
104C2×C43C2×#12311yescharacteristic
105C2×C43#52511yescharacteristic
106C2×C43#53511yescharacteristic
107C2×C43#55114yes—
108D43—44no—
109C2×#117D4311yescharacteristic, complemented
110C22×C22⋊C4—431no—
111#399—432no—
112#397—432no—
113#388—434no—
114#385—432no—
115#381—431no—
116#379—432no—
117C43#248211yescharacteristic, complemented, Sylow
118C25—431no—
119C23×C4—431no—
120C23×C4C2×D4311yescharacteristic
121#117—24no—
122C2×C4⋊C4—434no—
123C2×C4⋊C4C2×D4311yescharacteristic, complemented
124C2×C4⋊C4C2×D4311yescharacteristic, complemented
125C2×C22⋊C4—432no—
126C2×C22⋊C4—432no—
127C2×C22⋊C4—432no—
128C2×C22⋊C4—434no—
129C2×C22⋊C4—434no—
130C2×C22⋊C4—864no—
131C2×C22⋊C4C2×D4312yes—
132C2×C42C2×D4312yescomplemented
133#95—432no—
134#95—432no—
135#95—434no—
136C24—432no—
137C24—864no—
138C24—862no—
139C24—864no—
140C24—1722no—
141C24C22×D4311yescharacteristic
142C22×C4—24no—
143C22×C4—434no—
144C22×C4—432no—
145C22×C4—862no—
146C22×C4—1722no—
147C22×C4C22⋊D4314yes—
148C22×C4C22×D4312yes—
149C22×C4C22×D4312yes—
150C22×C4C22×D4311yescharacteristic
151C22×C4C22×D4311yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—1724no—
155C22⋊C4—24no—
156C22⋊C4—868no—
157C22⋊C4—864no—
158C22⋊C4—864no—
159C22⋊C4—864no—
160C22⋊C4—1724no—
161C42—24no—
162C23—22no—
163C23—22no—
164C23—434no—
165C23—868no—
166C23—862no—
167C23—862no—
168C23—864no—
169C23—864no—
170C23—17216no—
171C23—1724no—
172C23—1724no—
173C23#1062189814yes—
174C23C2×C22⋊D4312yes—
175C23C23×D4311yescharacteristic
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—24no—
183C2×C4—862no—
184C2×C4—864no—
185C2×C4—864no—
186C2×C4—864no—
187C2×C4—864no—
188C2×C4—1724no—
189C2×C4C2×C22⋊D4312yes—
190C2×C4C2×C22⋊D4312yes—
191C22—28no—
192C22—22no—
193C22—22no—
194C22—868no—
195C22—864no—
196C22—17216no—
197C22—1724no—
198C22—1722no—
199C22—1722no—
200C22#1306330814yes—
201C22C22×C22⋊D4311yescharacteristic
202C22#41×D4312yes—
203C22C2×#1062189812yes—
204C22#1306337112yes—
205C4—22no—
206C4—22no—
207C4—42no—
208C4—42no—
209C4—1724no—
210C4—1722no—
211C2—24no—
212C2—1724no—
213C2C2×#1306330811yescharacteristic
214C2#1458340611yescharacteristic
215C2#1458346311yescharacteristic
216C2#1458357314yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#117×C43C2
hypercenterC2×#117D43
hypocenterC43#2482
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14582834C2semidirect
3. #14582825C2semidirect
4. #14582790C2semidirect
5. #14582771C2semidirect
6. #14582762C2semidirect
8. C2×#117×C43C2semidirect
11. C2×Dic43⋊C4C22semidirect
18. C43⋊#95C22semidirect
19. C43⋊#95C22semidirect
20. C43⋊#95C22semidirect
23. C2×C4⋊C4×C43C22semidirect
24. C2×C4⋊C4×C43C22semidirect
26. C2×C42×C43C22semidirect
109. C2×#117D43semidirect
117. C43#2482semidirect
123. C2×C4⋊C4C2×D43semidirect
124. C2×C4⋊C4C2×D43semidirect
132. C2×C42C2×D43semidirect