Finite Group Databasebeta

← #19135721

Subgroups — #19135721

Order 5504.

638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 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#14583461C211yesmaximal, characteristic, complemented
2C2×#13063294C212yesmaximal, complemented
3C2×#13063239C212yesmaximal, complemented
4#14582666C211yesmaximal, characteristic, complemented
5C43×#379C211yesmaximal, characteristic, complemented
6C22×C22⋊D43—22no—
7C22×C22⋊D43C2212yes—
8#13063309—22no—
9#13063299—22no—
10#13063295—22no—
11#13063294—24no—
12#13063294—24no—
13C2×C22⋊Dic43—22no—
14C2×C22⋊Dic43C2212yes—
15#13063239—24no—
16C25×C43C2211yescharacteristic
17C2×C22⋊C4×C43—22no—
18C2×C22⋊C4×C43C2211yescharacteristic
19C2×C22⋊C4×C43C2211yescharacteristic
20C24×C43—21no—
21C24×C43—22no—
22C24×C43—22no—
23C24×C43—21no—
24C24×C43—44no—
25C24×C43D412yescomplemented
26C24×C43C2311yescharacteristic
27C23×D43D412yescomplemented
28C22×C4×C43—21no—
29C22×C4×C43D412yescomplemented
30C2×C22⋊D43—28no—
31C2×C22⋊D43—22no—
32C2×C22⋊D43—22no—
33C2×C22⋊D43—22no—
34C2×C22⋊D43—22no—
35C2×C22⋊D43—22no—
36C2×C22⋊D43—22no—
37C2×C22⋊D43—48no—
38C22×Dic43—22no—
39C22×Dic43D412yescomplemented
40C2×D172—22no—
41C22⋊C4×C43—22no—
42C22⋊C4×C43—22no—
43C22⋊C4×C43—44no—
44C22⋊Dic43—28no—
45C22⋊Dic43—22no—
46C22⋊Dic43D414yescomplemented
47(C2×D43)⋊C4—24no—
48C4⋊Dic43—22no—
49C23×C43—24no—
50C23×C43—28no—
51C23×C43—24no—
52C23×C43—22no—
53C23×C43—44no—
54C23×C43—42no—
55C23×C43—44no—
56C23×C43—42no—
57C23×C43—44no—
58C23×C43—48no—
59C23×C43—41no—
60C23×C43—42no—
61C23×C43—41no—
62C23×C43C2×D411yescharacteristic
63C23×C43C2×D412yes—
64C23×C43C2×D412yes—
65C23×C43C2×D411yescharacteristic
66C23×C43#4111yescharacteristic
67C22×D43—22no—
68C22×D43—22no—
69C22×D43—22no—
70C22×D43—44no—
71C2×C4×C43—22no—
72C2×C4×C43—42no—
73C2×C4×C43—42no—
74C2×C4×C43—41no—
75C22⋊D43—416no—
76C22⋊D43—42no—
77C22⋊D43—42no—
78C22⋊D43—42no—
79C22⋊D43—42no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—24no—
83C2×Dic43—22no—
84C2×Dic43—44no—
85D172—82no—
86C22×C43—24no—
87C22×C43—22no—
88C22×C43—24no—
89C22×C43—28no—
90C22×C43—41no—
91C22×C43—42no—
92C22×C43—41no—
93C22×C43—44no—
94C22×C43—44no—
95C22×C43—48no—
96C22×C43—42no—
97C22×C43—42no—
98C22×C43—44no—
99C22×C43#12011yescharacteristic
100C22×C43#12012yes—
101C22×C43#12112yes—
102C22×C43#12111yescharacteristic
103C22×C43#12711yescharacteristic
104C2×D43—44no—
105C2×D43—42no—
106C2×D43—44no—
107C2×D43—82no—
108C4×C43—42no—
109C4×C43—81no—
110Dic43—44no—
111Dic43—42no—
112#2021—431nomaximal, Sylow
113C2×C43—22no—
114C2×C43—21no—
115C2×C43—22no—
116C2×C43—21no—
117C2×C43—44no—
118C2×C43#39211yescharacteristic
119C2×C43B(4,𝔽2)12yes—
120D43—82no—
121#534—431no—
122C2×#120—432no—
123C2×#99—432no—
124#379D4311yescharacteristic, complemented
125#342—431no—
126C43#202111yescharacteristic, complemented, Sylow
127C25C2×D4311yescharacteristic
128C22×D4—432no—
129C22×D4—862no—
130#123—862no—
131#121—862no—
132#120—862no—
133#120—864no—
134#120—864no—
135C2×C22⋊C4—22no—
136C2×C22⋊C4—432no—
137C2×C22⋊C4—862no—
138C2×C22⋊C4C2×D4311yescharacteristic
139C2×C22⋊C4C2×D4311yescharacteristic
140#99—864no—
141C24—22no—
142C24—21no—
143C24—21no—
144C24—22no—
145C24—44no—
146C24—432no—
147C24D17212yescomplemented
148C24C22×D4311yescharacteristic
149C2×D4—862no—
150C2×D4—868no—
151C2×D4—862no—
152C2×D4—862no—
153C2×D4—862no—
154C2×D4—862no—
155C2×D4—862no—
156C2×D4—862no—
157C2×D4—1728no—
158C22×C4—21no—
159C22×C4—432no—
160C22×C4—862no—
161C22×C4C22⋊D4312yescomplemented
162C4⋊C4—862no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—44no—
166C22⋊C4—434no—
167C22⋊C4—864no—
168C22⋊C4—868no—
169C22⋊C4—862no—
170C23—24no—
171C23—28no—
172C23—24no—
173C23—22no—
174C23—42no—
175C23—44no—
176C23—42no—
177C23—44no—
178C23—48no—
179C23—44no—
180C23—41no—
181C23—42no—
182C23—41no—
183C23—862no—
184C23—862no—
185C23—862no—
186C23—1724no—
187C23C2×D17211yescharacteristic
188C23#1062189811yescharacteristic
189C23D4×D4312yes—
190C23D4×D4312yes—
191C23C2×C22⋊D4311yescharacteristic
192D4—3442no—
193D4—17216no—
194D4—1722no—
195D4—1722no—
196D4—1722no—
197D4—1722no—
198C2×C4—22no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—862no—
203C2×C4—864no—
204C2×C4—862no—
205C2×C4—862no—
206C2×C4—1724no—
207C22—22no—
208C22—24no—
209C22—28no—
210C22—24no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—44no—
215C22—44no—
216C22—42no—
217C22—48no—
218C22—42no—
219C22—44no—
220C22—3442no—
221C22—1724no—
222C22—1722no—
223C22—1724no—
224C22#1306329311yescharacteristic
225C22#1306329512yes—
226C22#1306329812yes—
227C22#1306329911yescharacteristic
228C22#1306332111yescharacteristic
229C4—42no—
230C4—81no—
231C4—1724no—
232C4—1722no—
233C2—21no—
234C2—22no—
235C2—21no—
236C2—22no—
237C2—44no—
238C2—3442no—
239C2#1458280811yescharacteristic
240C2#1458308512yes—
subgroupG/H
centerC22#13063293
commutatorC24×C43C23
FrattiniC24C22×D43
FittingC43×#379C2
socleC22×C43#120
hypercenter#379D43
hypocenterC43#2021
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #14583461C2semidirect
2. C2×#13063294C2semidirect
3. C2×#13063239C2semidirect
4. #14582666C2semidirect
5. C43×#379C2semidirect
25. C24×C43D4semidirect
27. C23×D43D4semidirect
29. C22×C4×C43D4semidirect
39. C22×Dic43D4semidirect
46. C22⋊Dic43D4semidirect
124. #379D43semidirect
126. C43#2021semidirect
147. C24D172semidirect
161. C22×C4C22⋊D43semidirect