Finite Group Databasebeta

← #19135770

Subgroups — #19135770

Order 5504.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#14583452C211yesmaximal, characteristic, complemented
2#14582915C211yesmaximal, characteristic
3C2×#13063251C211yesmaximal, characteristic
4#14582872C211yesmaximal, characteristic
5#14582660C211yesmaximal, characteristic, complemented
6#14582656C211yesmaximal, characteristic, complemented
7C43×#344C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063324—21no—
10#13063316—21no—
11#13063302—22no—
12C4×Dic86—22no—
13#13063284C2211yescharacteristic
14#13063284C2211yescharacteristic
15C2×C4×Dic43C2211yescharacteristic
16#13063251—21no—
17#13063251—21no—
18#13063251—22no—
19#13063239—22no—
20C2×M16×C43C2211yescharacteristic
21C2×M16×C43C2211yescharacteristic
22#117×C43C2211yescharacteristic
23C22×C4×C43C2311yescharacteristic
24C2×C22⋊D43—21no—
25C22×Dic43—21no—
26#10621898—21no—
27#10621898—21no—
28#10621898—21no—
29#10621898—21no—
30C2×D172Q811yescharacteristic, complemented
31C2×C4×D43—21no—
32C2×Dic86—22no—
33C2×Dic86Q811yescharacteristic, complemented
34M16×C43—21no—
35M16×C43—21no—
36M16×C43—21no—
37M16×C43—21no—
38C2×C8×C43—21no—
39C2×C8×C43—21no—
40C4⋊C4×C43—21no—
41C22⋊C4×C43D412yes—
42C42×C43—21no—
43C22⋊Dic43—21no—
44C22⋊Dic43—21no—
45C4⋊Dic43—22no—
46C4⋊Dic43—21no—
47C4⋊Dic43—21no—
48Dic43⋊C4—22no—
49Dic43⋊C4—22no—
50C4×Dic43—21no—
51C4×Dic43—21no—
52C4×Dic43D411yescharacteristic
53C4×Dic43D411yescharacteristic
54C4×Dic43D412yes—
55C23×C43C2×D411yescharacteristic
56C22×D43—21no—
57C2×C4×C43—22no—
58C2×C4×C43C2×D411yescharacteristic
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×Q811yescharacteristic
61C2×C4×C43#4111yescharacteristic
62C2×C4×C43#4111yescharacteristic
63C2×C4×C43#4111yescharacteristic
64C22⋊D43—41no—
65C22⋊D43—41no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68C2×Dic43—22no—
69C2×Dic43—21no—
70C2×Dic43—42no—
71C2×Dic43—41no—
72D172—21no—
73D172—21no—
74C4×D43—41no—
75C4×D43—41no—
76Dic86—21no—
77Dic86—21no—
78Dic86—44no—
79C8×C43—41no—
80C8×C43—41no—
81C22×C43—41no—
82C22×C43#12011yescharacteristic
83C22×C43C22⋊Q811yescharacteristic
84C22×C43#12411yescharacteristic
85C2×D43—41no—
86C2×D43—81no—
87C4×C43—42no—
88C4×C43C22⋊Q811yescharacteristic
89C4×C43C22⋊Q811yescharacteristic
90C4×C43#12411yescharacteristic
91C4×C43#12411yescharacteristic
92Dic43—22no—
93Dic43—42no—
94Dic43—41no—
95Dic43—41no—
96Dic43—81no—
97#2031—431nomaximal, Sylow
98C2×C43—21no—
99C2×C43—21no—
100C2×C43—21no—
101C2×C43#39311yescharacteristic
102D43—81no—
103#533—431no—
104#421—431no—
105C2×#104—431no—
106#410—431no—
107#344D4311yescharacteristic, complemented
108#339—431no—
109H(3,ℤ/4)—431no—
110C43#203111yescharacteristic, complemented, Sylow
111C2×#41—431no—
112C2×M16C2×D4311yescharacteristic
113C2×M16C2×D4311yescharacteristic
114C4⋊Q8—861no—
115#125—861no—
116C22⋊Q8—862no—
117C4×Q8—862no—
118#117—431no—
119#117—431no—
120#117C2×D4311yescharacteristic
121C2×C42—431no—
122#104—861no—
123#104—861no—
124#104—862no—
125#99—862no—
126#41—861no—
127#41—861no—
128#41—861no—
129#41—861no—
130C2×Q8—431no—
131C2×Q8—862no—
132C2×D4—431no—
133C2×D4—861no—
134C22×C4—861no—
135C22×C4—861no—
136C22×C4C22×D4311yescharacteristic
137M16—21no—
138M16—21no—
139M16—21no—
140M16—21no—
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—862no—
145C4⋊C4—862no—
146C4⋊C4—862no—
147C4⋊C4—861no—
148C4⋊C4—861no—
149C22⋊C4—861no—
150C22⋊C4—861no—
151C22⋊C4D17212yes—
152C42—21no—
153C42—431no—
154C42—431no—
155C42—432no—
156C42—861no—
157C42—861no—
158C23—861no—
159C23C2×D17211yescharacteristic
160Q8—861no—
161Q8—861no—
162Q8—1724no—
163D4—861no—
164D4—861no—
165D4—1721no—
166D4—1721no—
167C2×C4—22no—
168C2×C4—861no—
169C2×C4—861no—
170C2×C4—862no—
171C2×C4—861no—
172C2×C4—1722no—
173C2×C4—1721no—
174C2×C4—1721no—
175C2×C4—1721no—
176C2×C4#1062189811yescharacteristic
177C2×C4#1062189811yescharacteristic
178C2×C4D4×D4311yescharacteristic
179C2×C4D4×D4311yescharacteristic
180C2×C4#1062190011yescharacteristic
181C2×C4Q8×D4311yescharacteristic
182C8—41no—
183C8—41no—
184C22—41no—
185C22—3441no—
186C22—1721no—
187C22#1306329511yescharacteristic
188C22#1306330511yescharacteristic
189C22#1306331311yescharacteristic
190C4—42no—
191C4—862no—
192C4—3441no—
193C4—1721no—
194C4—1722no—
195C4—1721no—
196C4#1306330311yescharacteristic
197C4#1306330311yescharacteristic
198C4#1306331111yescharacteristic
199C4#1306331111yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—3441no—
204C2#1458281211yescharacteristic
subgroupG/H
centerC4#13063311
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#344C2
socleC2×C43#393
hypercenter#344D43
hypocenterC43#2031
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #14583452C2semidirect
5. #14582660C2semidirect
6. #14582656C2semidirect
7. C43×#344C2semidirect
30. C2×D172Q8semidirect
33. C2×Dic86Q8semidirect
107. #344D43semidirect
110. C43#2031semidirect