Finite Group Databasebeta

← #19135081

Subgroups — #19135081

Order 5504.

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

normal subgroups only

This group has 346 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#14583373C211yesmaximal, characteristic, complemented
3#14582915C211yesmaximal, characteristic, complemented
4#14582905C211yesmaximal, characteristic, complemented
5#14582872C211yesmaximal, characteristic, complemented
6#14582656C211yesmaximal, characteristic, complemented
7C43×#344C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×D172C2211yescharacteristic
10#13063353—22no—
11#13063353—22no—
12C2×#10621873C412yescomplemented
13C2×D344C412yescomplemented
14C4×D172—22no—
15#13063287—22no—
16#13063284C2211yescharacteristic
17#13063284C2211yescharacteristic
18C22⋊C4×D43—22no—
19#13063251—22no—
20#13063247—22no—
21#13063239—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#10621898—21no—
31#10621898—21no—
32C2×D172—21no—
33C2×D172—21no—
34C2×D172—21no—
35C2×D172C2×C412yes—
36C2×D172C2×C411yescharacteristic, complemented
37C2×D172D412yes—
38C2×D172D412yes—
39C2×C4×D43—21no—
40C2×C4×D43—24no—
41C2×Dic86C2×C411yescharacteristic, complemented
42M16×C43—21no—
43M16×C43—21no—
44M16×C43—21no—
45M16×C43—21no—
46C2×C8×C43—21no—
47C2×C8×C43C2×C412yescomplemented
48C4⋊C4×C43—21no—
49C22⋊C4×C43D412yes—
50C42×C43—21no—
51C22⋊Dic43—21no—
52C22⋊Dic43—21no—
53(C2×D43)⋊C4—24no—
54C4⋊Dic43—21no—
55C4⋊Dic43—21no—
56C4×Dic43—21no—
57C4×Dic43D412yes—
58D344—24no—
59#10621873—24no—
60C23×C43C2×D411yescharacteristic
61C22×D43—22no—
62C22×D43—22no—
63C22×D43—22no—
64C22×D43—21no—
65C22×D43—82no—
66C2×C4×C43—22no—
67C2×C4×C43C22×C411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43#4111yescharacteristic
72C2×C4×C43#4111yescharacteristic
73C22⋊D43—41no—
74C22⋊D43—41no—
75C2×Dic43—21no—
76C2×Dic43—22no—
77C2×Dic43—41no—
78D172—21no—
79D172—22no—
80D172—21no—
81D172—22no—
82D172—22no—
83D172C22⋊C414yes—
84C4×D43—41no—
85C4×D43—41no—
86C4×D43—84no—
87Dic86—21no—
88Dic86—21no—
89C8×C43—22no—
90C8×C43—41no—
91C22×C43—41no—
92C22×C43C4×D411yescharacteristic
93C22×C43#12011yescharacteristic
94C22×C43#12111yescharacteristic
95C2×D43—24no—
96C2×D43—44no—
97C2×D43—41no—
98C2×D43—82no—
99C2×D43—82no—
100C2×D43—81no—
101C4×C43—42no—
102C4×C43C2×C22⋊C411yescharacteristic
103C4×C43C4×D411yescharacteristic
104C4×C43#12111yescharacteristic
105C4×C43#12311yescharacteristic
106Dic43—42no—
107Dic43—41no—
108Dic43—81no—
109#1904—431nomaximal, Sylow
110C2×C43—21no—
111C2×C43—21no—
112C2×C43—21no—
113C2×C43#38611yescharacteristic
114D43—44no—
115D43—81no—
116C2×AGL(1,ℤ/8)—431no—
117#518—431no—
118#421—431no—
119#418—431no—
120#410—431no—
121#344D4311yescharacteristic, complemented
122H(3,ℤ/4)—431no—
123C43#190411yescharacteristic, complemented, Sylow
124C2×#41—431no—
125C22×D4—431no—
126AGL(1,ℤ/8)—862no—
127AGL(1,ℤ/8)—862no—
128C2×SD16—432no—
129C2×D8—432no—
130C2×M16C2×D4311yescharacteristic
131C2×M16C2×D4311yescharacteristic
132C4×D4—862no—
133C4×D4—862no—
134#117—431no—
135#117—431no—
136#117C2×D4311yescharacteristic
137C2×C22⋊C4—862no—
138#104—862no—
139#102—862no—
140#99—862no—
141C24—861no—
142#41—861no—
143#41—861no—
144#41—861no—
145#41—861no—
146C2×Q8—431no—
147C2×D4—432no—
148C2×D4—431no—
149C2×D4—432no—
150C2×D4—432no—
151C2×D4—861no—
152C2×D4—861no—
153C2×D4—861no—
154C2×D4—861no—
155C22×C4—864no—
156C22×C4—861no—
157C22×C4C22×D4311yescharacteristic
158SD16—864no—
159D8—864no—
160M16—21no—
161M16—21no—
162M16—21no—
163M16—21no—
164C2×C8—21no—
165C2×C8C4×D4312yescomplemented
166C4⋊C4—21no—
167C4⋊C4—861no—
168C4⋊C4—861no—
169C22⋊C4—864no—
170C22⋊C4—861no—
171C22⋊C4—861no—
172C22⋊C4D17212yes—
173C42—21no—
174C42—432no—
175C42—861no—
176C23—862no—
177C23—862no—
178C23—862no—
179C23—861no—
180C23—3442no—
181C23C2×D17211yescharacteristic
182Q8—861no—
183Q8—861no—
184D4—434no—
185D4—861no—
186D4—862no—
187D4—861no—
188D4—862no—
189D4—862no—
190D4—1721no—
191D4—1721no—
192C2×C4—22no—
193C2×C4—861no—
194C2×C4—862no—
195C2×C4—3444no—
196C2×C4—1721no—
197C2×C4—1721no—
198C2×C4—1721no—
199C2×C4C2×C4×D4311yescharacteristic
200C2×C4#1062189811yescharacteristic
201C2×C4D4×D4311yescharacteristic
202C2×C4D4×D4311yescharacteristic
203C2×C4D4×D4311yescharacteristic
204C2×C4#1062190211yescharacteristic
205C8—22no—
206C8—41no—
207C22—41no—
208C22—864no—
209C22—3441no—
210C22—3442no—
211C22—3442no—
212C22—1724no—
213C22—1721no—
214C22C4×D17211yescharacteristic
215C22#1306329511yescharacteristic
216C22#1306330011yescharacteristic
217C4—42no—
218C4—3441no—
219C4—1722no—
220C4—1721no—
221C4C22⋊C4×D4311yescharacteristic
222C4#1306328711yescharacteristic
223C4#1306329811yescharacteristic
224C4#1306331011yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—3441no—
229C2—1724no—
230C2#1458277711yescharacteristic
subgroupG/H
centerC2#14582777
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#344C2
socleC2×C43#386
hypercenter#344D43
hypocenterC43#1904
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. #14583373C2semidirect
3. #14582915C2semidirect
4. #14582905C2semidirect
5. #14582872C2semidirect
6. #14582656C2semidirect
7. C43×#344C2semidirect
12. C2×#10621873C4semidirect
13. C2×D344C4semidirect
36. C2×D172C2×C4semidirect
41. C2×Dic86C2×C4semidirect
47. C2×C8×C43C2×C4semidirect
121. #344D43semidirect
123. C43#1904semidirect
165. C2×C8C4×D43semidirect