Finite Group Databasebeta

← #19139845

Subgroups — #19139845

Order 5504.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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#14582816C211yesmaximal, characteristic
2#14582812C212yesmaximal, complemented
3#14582804C211yesmaximal, characteristic, complemented
4#14582789C212yesmaximal, complemented
5#14582777C212yesmaximal
6#14582766C212yesmaximal, complemented
7#14582761C212yesmaximal, complemented
8#14582746C212yesmaximal, complemented
9C43×#400C211yesmaximal, characteristic, complemented
10C22×Dic86C2211yescharacteristic
11C22×D172C2211yescharacteristic
12C22×C4×D43C2212yes—
13C2×(C2×D43)⋊C4C2212yes—
14C2×(C2×D43)⋊C4C2212yes—
15C2×(C2×D43)⋊C4C2212yes—
16C2×(C2×D43)⋊C4C2212yes—
17C2×(C2×D43)⋊C4C2212yes—
18C2×C4×Dic43C2212yes—
19C2×C4×Dic43C2211yescharacteristic
20C43⋊#95C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C2×C4⋊C4×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28#95×C43C2212yes—
29#95×C43C2211yescharacteristic
30#95×C43C2212yes—
31C23×D43C2312yes—
32C22×C4×C43C2312yes—
33C22×C4×C43C2311yescharacteristic
34C22×C4×C43C2312yes—
35C22×C4×C43C2311yescharacteristic
36C22×C4×C43C2311yescharacteristic
37C22×Dic43C2312yes—
38C22×Dic43C2312yes—
39C22×Dic43C2312yes—
40C2×D172—24no—
41C2×D172—41no—
42C2×C4×D43—24no—
43C2×C4×D43—24no—
44C2×C4×D43—42no—
45C2×Dic86—22no—
46C2×Dic86—41no—
47C2×Dic86—41no—
48C4⋊C4×C43—41no—
49C4⋊C4×C43—41no—
50(C2×D43)⋊C4—24no—
51(C2×D43)⋊C4—24no—
52(C2×D43)⋊C4—24no—
53(C2×D43)⋊C4—42no—
54(C2×D43)⋊C4—42no—
55C4×Dic43—24no—
56C4×Dic43—41no—
57C23×C43C2411yescharacteristic
58C22×D43—22no—
59C22×D43—22no—
60C22×D43—22no—
61C22×D43—22no—
62C22×D43—22no—
63C22×D43—22no—
64C22×D43#4114yes—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—22no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43#4112yes—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43#4114yes—
87D172—44no—
88C4×D43—48no—
89Dic86—44no—
90C22×C43C2×#4112yes—
91C22×C43C2×#4112yes—
92C22×C43C2×#4111yescharacteristic
93C22×C43H(5,𝔽2)11yescharacteristic
94C22×C43H(5,𝔽2)11yescharacteristic
95C2×D43—24no—
96C2×D43—24no—
97C2×D43—24no—
98C2×D43—42no—
99C2×D43—42no—
100C2×D43—42no—
101C2×D43—42no—
102C4×C43—22no—
103C4×C43—42no—
104C4×C43—41no—
105C4×C43—41no—
106C4×C43—42no—
107Dic43—24no—
108Dic43—42no—
109Dic43—42no—
110#2572—431nomaximal, Sylow
111C2×C43#52912yes—
112C2×C43#53811yescharacteristic
113C2×C43#55112yes—
114C2×C43#55111yescharacteristic
115C2×C43#55511yescharacteristic
116D43—44no—
117#400D4311yescharacteristic, complemented
118#394—431no—
119#393—432no—
120#391—431no—
121#388—432no—
122#386—432no—
123#383—432no—
124#381—432no—
125C4×C22⋊C4—432no—
126C43#257211yescharacteristic, complemented, Sylow
127C22×Q8—431no—
128C22×D4—431no—
129C23×C4—432no—
130C2×C4⋊C4C2×D4311yescharacteristic
131C2×C4⋊C4C2×D4311yescharacteristic
132C2×C22⋊C4—432no—
133C2×C22⋊C4—432no—
134C2×C22⋊C4—432no—
135C2×C22⋊C4—432no—
136C2×C22⋊C4—432no—
137C2×C42—432no—
138C2×C42—431no—
139#95—432no—
140#95—432no—
141#95—432no—
142#95—431no—
143#95—432no—
144#95—432no—
145#95C2×D4312yes—
146#95C2×D4311yescharacteristic
147#95C2×D4312yes—
148C24—432no—
149C2×Q8—862no—
150C2×Q8—1721no—
151C2×Q8—1721no—
152C2×D4—864no—
153C2×D4—1721no—
154C22×C4—432no—
155C22×C4—432no—
156C22×C4—432no—
157C22×C4—864no—
158C22×C4—864no—
159C22×C4—1722no—
160C22×C4C22×D4311yescharacteristic
161C22×C4C22×D4312yes—
162C22×C4C22×D4311yescharacteristic
163C22×C4C22×D4312yes—
164C22×C4C22×D4311yescharacteristic
165C4⋊C4—41no—
166C4⋊C4—41no—
167C22⋊C4—864no—
168C22⋊C4—864no—
169C22⋊C4—864no—
170C22⋊C4—1722no—
171C22⋊C4—1722no—
172C42—864no—
173C42—1721no—
174C23—434no—
175C23—862no—
176C23—862no—
177C23—862no—
178C23—862no—
179C23—862no—
180C23—862no—
181C23C23×D4311yescharacteristic
182Q8—1724no—
183D4—1724no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—434no—
197C2×C4—862no—
198C2×C4—862no—
199C2×C4—862no—
200C2×C4—862no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4—862no—
205C2×C4—1728no—
206C2×C4#1062190212yes—
207C22—864no—
208C22—864no—
209C22—864no—
210C22—1722no—
211C22—1722no—
212C22—1722no—
213C22—1722no—
214C22#41×D4312yes—
215C22#41×D4312yes—
216C22C2×#1062190211yescharacteristic
217C22#1306337011yescharacteristic
218C22#1306337111yescharacteristic
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—42no—
224C4—864no—
225C4—1722no—
226C4—1722no—
227C2—1724no—
228C2#1458343412yes—
229C2#1458348911yescharacteristic
230C2#1458357412yes—
231C2#1458357711yescharacteristic
232C2#1458361111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2572
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #14582812C2semidirect
3. #14582804C2semidirect
4. #14582789C2semidirect
6. #14582766C2semidirect
7. #14582761C2semidirect
8. #14582746C2semidirect
9. C43×#400C2semidirect
117. #400D43semidirect
126. C43#2572semidirect