Finite Group Databasebeta

← #19135074

Subgroups — #19135074

Order 5504.

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

normal subgroups only

This group has 324 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
1C2×#13063353C211yesmaximal, characteristic
2#14583665C211yesmaximal, characteristic, complemented
3#14582917C211yesmaximal, characteristic, complemented
4#14582903C211yesmaximal, characteristic, complemented
5C2×#13063241C211yesmaximal, characteristic, complemented
6C43⋊#338C211yesmaximal, characteristic, complemented
7C43×#344C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×D172C2211yescharacteristic
10#13063353—22no—
11#13063353—22no—
12C2×#10621873C412yescomplemented
13C2×D344C412yescomplemented
14#13063333—22no—
15#13063331—22no—
16C2×#10621877C2211yescharacteristic
17C2×#10621877C2211yescharacteristic
18M16×D43—22no—
19#13063253—22no—
20#13063245—22no—
21#13063241—22no—
22C2×M16×C43C2211yescharacteristic
23C2×M16×C43C2211yescharacteristic
24#117×C43C2211yescharacteristic
25C23×D43—21no—
26C22×C4×C43C2311yescharacteristic
27C2×C22⋊D43—21no—
28#10621898—21no—
29#10621898—21no—
30#10621898D412yes—
31#10621898D412yes—
32C2×D172—21no—
33C2×D172—21no—
34C2×D172—21no—
35C2×D172—21no—
36C2×D172—21no—
37C2×D172C2×C412yes—
38C2×D172C2×C411yescharacteristic
39C2×C4×D43—21no—
40C2×Dic86C2×C411yescharacteristic
41M16×C43—21no—
42M16×C43—21no—
43M16×C43—21no—
44M16×C43D412yes—
45C2×C8×C43—21no—
46C2×C8×C43C2×C412yes—
47C4⋊C4×C43—21no—
48C22⋊C4×C43—21no—
49C42×C43—21no—
50#10621877—21no—
51#10621877—21no—
52#10621877—21no—
53#10621877—21no—
54C2×C43⋊C8—21no—
55C2×C43⋊C8D412yes—
56D344—24no—
57#10621873—24no—
58#10621872—24no—
59C8×D43—24no—
60C23×C43#4111yescharacteristic
61C22×D43—21no—
62C22×D43—22no—
63C22×D43—41no—
64C22×D43—41no—
65C22×D43—82no—
66C2×C4×C43—41no—
67C2×C4×C43C22×C411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43#4111yescharacteristic
73C22⋊D43—22no—
74C22⋊D43—22no—
75C2×Dic43—21no—
76D172—22no—
77D172—21no—
78D172—22no—
79D172—41no—
80D172—41no—
81D172C22⋊C412yes—
82C4×D43—22no—
83C4×D43—22no—
84Dic86—21no—
85Dic86C22⋊C412yes—
86C8×C43—22no—
87C8×C43—22no—
88C43⋊C8—22no—
89C43⋊C8—41no—
90C22×C43—41no—
91C22×C43C4×D411yescharacteristic
92C22×C43#12111yescharacteristic
93C22×C43#12311yescharacteristic
94C2×D43—22no—
95C2×D43—42no—
96C2×D43—81no—
97C2×D43—82no—
98C2×D43—82no—
99C2×D43—82no—
100C4×C43—81no—
101C4×C43C2×C22⋊C411yescharacteristic
102C4×C43C4×D411yescharacteristic
103C4×C43#12011yescharacteristic
104C4×C43#12111yescharacteristic
105Dic43—22no—
106#1903—431nomaximal, Sylow
107C2×C43—21no—
108C2×C43—21no—
109C2×C43—21no—
110C2×C43#38611yescharacteristic
111D43—42no—
112D43—82no—
113C2×AGL(1,ℤ/8)—431no—
114#568—431no—
115#421—431no—
116#418—431no—
117C2×#100—431no—
118#344D4311yescharacteristic, complemented
119#338—431no—
120C43#190311yescharacteristic, complemented, Sylow
121C2×#41—431no—
122C22×D4—431no—
123AGL(1,ℤ/8)—862no—
124AGL(1,ℤ/8)—862no—
125C2×SD16—432no—
126C2×D8—432no—
127#131—862no—
128#131—862no—
129C2×M16—431no—
130C2×M16—431no—
131C2×M16—862no—
132C2×M16C2×D4311yescharacteristic
133C2×M16C2×D4311yescharacteristic
134#117C2×D4311yescharacteristic
135#104—862no—
136#102—862no—
137#100—862no—
138C24—861no—
139#41—432no—
140#41—432no—
141#41—861no—
142#41—861no—
143C2×Q8—431no—
144C2×D4—431no—
145C2×D4—432no—
146C2×D4—861no—
147C2×D4—861no—
148C2×D4—861no—
149C2×D4—861no—
150C2×D4—861no—
151C2×D4—861no—
152C22×C4—861no—
153C22×C4C22×D4311yescharacteristic
154SD16—864no—
155D8—864no—
156M16—21no—
157M16—21no—
158M16—21no—
159M16—864no—
160M16—861no—
161M16—861no—
162M16—861no—
163M16—861no—
164M16D17212yes—
165C2×C8—21no—
166C2×C8—432no—
167C2×C8—864no—
168C2×C8—861no—
169C2×C8C4×D4312yes—
170C4⋊C4—21no—
171C22⋊C4—21no—
172C42—21no—
173C23—861no—
174C23—862no—
175C23—3442no—
176C23—1721no—
177C23—1721no—
178C23#1062189811yescharacteristic
179Q8—432no—
180Q8—861no—
181D4—432no—
182D4—862no—
183D4—862no—
184D4—862no—
185D4—861no—
186D4—862no—
187D4—1721no—
188D4—1721no—
189C2×C4—41no—
190C2×C4—861no—
191C2×C4—862no—
192C2×C4—862no—
193C2×C4C2×C4×D4311yescharacteristic
194C2×C4C2×D17211yescharacteristic
195C2×C4D4×D4311yescharacteristic
196C2×C4D4×D4311yescharacteristic
197C2×C4D4×D4311yescharacteristic
198C2×C4#1062190211yescharacteristic
199C8—22no—
200C8—22no—
201C8—862no—
202C8—1721no—
203C22—41no—
204C22—862no—
205C22—3442no—
206C22—3442no—
207C22—3442no—
208C22—3441no—
209C22—1722no—
210C22C4×D17211yescharacteristic
211C22#1306329811yescharacteristic
212C22#1306331011yescharacteristic
213C4—81no—
214C4—862no—
215C4C22⋊C4×D4311yescharacteristic
216C4#1306328711yescharacteristic
217C4#1306329511yescharacteristic
218C4#1306330011yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—3442no—
223C2—1722no—
224C2#1458277711yescharacteristic
subgroupG/H
centerC2#14582777
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#344C2
socleC2×C43#386
hypercenter#344D43
hypocenterC43#1903
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #14583665C2semidirect
3. #14582917C2semidirect
4. #14582903C2semidirect
5. C2×#13063241C2semidirect
6. C43⋊#338C2semidirect
7. C43×#344C2semidirect
12. C2×#10621873C4semidirect
13. C2×D344C4semidirect
118. #344D43semidirect
120. C43#1903semidirect