Finite Group Databasebeta

← #19135012

Subgroups — #19135012

Order 5504.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#14583665C211yesmaximal, characteristic, complemented
2#14583411C211yesmaximal, characteristic
3#14582881C211yesmaximal, characteristic, complemented
4#14582862C211yesmaximal, characteristic, complemented
5#14582862C211yesmaximal, characteristic, complemented
6#14582669C211yesmaximal, characteristic, complemented
7C43×#344C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×C4×D43C2211yescharacteristic
10#13063333—22no—
11#13063331—22no—
12C2×#10621877C2211yescharacteristic
13C2×#10621877C2211yescharacteristic
14M16×D43—22no—
15#13063309C412yes—
16#13063305—21no—
17#13063300—21no—
18#13063295C412yes—
19C4×D172—22no—
20#13063243—21no—
21#13063241—21no—
22(C2×D43)⋊C8—22no—
23(C2×D43)⋊C8—22no—
24C2×M16×C43C2211yescharacteristic
25C2×M16×C43C2211yescharacteristic
26#117×C43C2211yescharacteristic
27C23×D43C2×C411yescharacteristic
28C22×C4×C43C2311yescharacteristic
29C2×C22⋊D43C2×C412yes—
30C22×Dic43C2×C411yescharacteristic
31#10621898—21no—
32#10621898—21no—
33#10621898—21no—
34#10621898—21no—
35C2×D172—22no—
36C2×D172D411yescharacteristic
37C2×C4×D43—21no—
38C2×C4×D43—21no—
39C2×C4×D43—21no—
40C2×C4×D43—21no—
41C2×C4×D43—21no—
42C2×C4×D43—21no—
43C2×C4×D43D412yes—
44C2×Dic86D411yescharacteristic
45M16×C43—21no—
46M16×C43—21no—
47M16×C43—21no—
48M16×C43—21no—
49C2×C8×C43—21no—
50C2×C8×C43D412yescomplemented
51C4⋊C4×C43—21no—
52C22⋊C4×C43C2×C412yes—
53C42×C43—21no—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4—22no—
56C4⋊Dic43—22no—
57#10621877—21no—
58#10621877—21no—
59#10621877—21no—
60#10621877—21no—
61C2×C43⋊C8—21no—
62C2×C43⋊C8D412yescomplemented
63#10621872—24no—
64C8×D43—24no—
65C23×C43C22×C411yescharacteristic
66C22×D43—21no—
67C22×D43—21no—
68C22×D43—21no—
69C22×D43—42no—
70C22×D43C22⋊C412yes—
71C2×C4×C43—22no—
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43#4111yescharacteristic
77C2×C4×C43#4111yescharacteristic
78C22⋊D43—22no—
79C22⋊D43—22no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43C22⋊C412yes—
84D172—21no—
85D172—21no—
86D172—44no—
87C4×D43—22no—
88C4×D43—22no—
89C4×D43—41no—
90C4×D43—41no—
91C4×D43—41no—
92C4×D43—41no—
93Dic86—21no—
94Dic86—21no—
95C8×C43—22no—
96C8×C43—41no—
97C43⋊C8—22no—
98C43⋊C8—41no—
99C22×C43—41no—
100C22×C43C2×C22⋊C411yescharacteristic
101C22×C43C4×D411yescharacteristic
102C22×C43C4×D411yescharacteristic
103C2×D43—22no—
104C2×D43—22no—
105C2×D43—22no—
106C2×D43—22no—
107C2×D43—41no—
108C2×D43—41no—
109C2×D43—41no—
110C2×D43—41no—
111C2×D43—42no—
112C4×C43—42no—
113C4×C43#12011yescharacteristic
114C4×C43#12111yescharacteristic
115C4×C43#12111yescharacteristic
116C4×C43#12311yescharacteristic
117Dic43—22no—
118Dic43—41no—
119#1891—431nomaximal, Sylow
120C2×C43—21no—
121C2×C43—21no—
122C2×C43—21no—
123C2×C43#38611yescharacteristic
124D43—42no—
125D43—42no—
126#568—431no—
127#525—431no—
128#413—431no—
129#407—431no—
130#407—431no—
131#344—431no—
132#344D4311yescharacteristic, complemented
133C43#189111yescharacteristic, complemented, Sylow
134C2×#41—431no—
135C23×C4—431no—
136#131—862no—
137#131—862no—
138C2×M16—431no—
139C2×M16—431no—
140C2×M16—862no—
141C2×M16C2×D4311yescharacteristic
142C2×M16C2×D4311yescharacteristic
143#123—432no—
144C22⋊Q8—861no—
145#121—861no—
146#120—432no—
147C4×D4—862no—
148#117C2×D4311yescharacteristic
149#101—861no—
150#100—861no—
151C22⋊C8—862no—
152C22⋊C8—862no—
153C24—431no—
154#41—861no—
155#41—861no—
156#41—861no—
157#41—861no—
158C2×Q8—431no—
159C2×D4—432no—
160C2×D4—431no—
161C2×D4—862no—
162C22×C4—432no—
163C22×C4—431no—
164C22×C4—861no—
165C22×C4—861no—
166C22×C4—861no—
167C22×C4—861no—
168C22×C4—861no—
169C22×C4—861no—
170C22×C4C22×D4311yescharacteristic
171M16—21no—
172M16—21no—
173M16—21no—
174M16—21no—
175M16—864no—
176M16—861no—
177M16—861no—
178M16—861no—
179M16—861no—
180C2×C8—21no—
181C2×C8—432no—
182C2×C8—864no—
183C2×C8—861no—
184C2×C8D17212yescomplemented
185C4⋊C4—21no—
186C4⋊C4—862no—
187C22⋊C4—862no—
188C22⋊C4—862no—
189C22⋊C4C4×D4312yes—
190C42—21no—
191C23—432no—
192C23—861no—
193C23—861no—
194C23—861no—
195C23—1722no—
196C23C2×C4×D4311yescharacteristic
197Q8—861no—
198Q8—861no—
199D4—862no—
200D4—862no—
201D4—861no—
202D4—861no—
203D4—1724no—
204C2×C4—22no—
205C2×C4—432no—
206C2×C4—862no—
207C2×C4—862no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—861no—
211C2×C4—1721no—
212C2×C4—1721no—
213C2×C4—1721no—
214C2×C4—1721no—
215C2×C4C2×D17211yescharacteristic
216C2×C4#1062189811yescharacteristic
217C2×C4D4×D4311yescharacteristic
218C2×C4D4×D4311yescharacteristic
219C2×C4D4×D4311yescharacteristic
220C2×C4#1062190211yescharacteristic
221C8—22no—
222C8—41no—
223C8—862no—
224C8—1721no—
225C22—41no—
226C22—862no—
227C22—862no—
228C22—862no—
229C22—862no—
230C22—1722no—
231C22—1721no—
232C22—1721no—
233C22—1721no—
234C22—1721no—
235C22C22⋊C4×D4311yescharacteristic
236C22#1306328711yescharacteristic
237C22C4×D17211yescharacteristic
238C4—42no—
239C4—862no—
240C4—1721no—
241C4#1306329511yescharacteristic
242C4#1306329811yescharacteristic
243C4#1306330011yescharacteristic
244C4#1306331011yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—1722no—
249C2—1722no—
250C2#1458277711yescharacteristic
subgroupG/H
centerC4#13063295
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#344C2
socleC2×C43#386
hypercenter#344D43
hypocenterC43#1891
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #14583665C2semidirect
3. #14582881C2semidirect
4. #14582862C2semidirect
5. #14582862C2semidirect
6. #14582669C2semidirect
7. C43×#344C2semidirect
50. C2×C8×C43D4semidirect
62. C2×C43⋊C8D4semidirect
132. #344D43semidirect
133. C43#1891semidirect
184. C2×C8D172semidirect