Finite Group Databasebeta

← #19135551

Subgroups — #19135551

Order 5504.

260 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 99 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×#13063316C211yesmaximal, characteristic
2C2×Dic43⋊C8C211yesmaximal, characteristic
3C4⋊C4×Dic43C211yesmaximal, characteristic
4#14582662C211yesmaximal, characteristic
5#14582661C211yesmaximal, characteristic
6#14582661C211yesmaximal, characteristic
7C43×#340C211yesmaximal, characteristic
8C22×C43⋊C8C2211yescharacteristic
9#13063316—22no—
10#13063316C414yescomplemented
11C2×C4⋊Dic43—21no—
12C2×C4⋊Dic43C2211yescharacteristic
13C2×C4⋊Dic43C2211yescharacteristic
14C2×Dic43⋊C4—21no—
15C2×C4×Dic43—21no—
16C2×C4×Dic43C2211yescharacteristic
17Dic43⋊C8—22no—
18C43⋊#95—21no—
19C22×C8×C43C2211yescharacteristic
20C2×C4⋊C4×C43C2211yescharacteristic
21C2×C4⋊C4×C43C2211yescharacteristic
22C22×C4×C43—21no—
23C22×C4×C43—21no—
24C22×C4×C43C2311yescharacteristic
25C22×Dic43—21no—
26C22×Dic43—21no—
27C22×Dic43D411yescharacteristic
28C22×Dic43D411yescharacteristic
29C2×C8×C43—21no—
30C2×C8×C43—21no—
31C2×C8×C43—21no—
32C4⋊C4×C43—21no—
33C4⋊C4×C43—21no—
34C4⋊C4×C43C2×C412yes—
35C4⋊C4×C43Q812yes—
36C4⋊Dic43—21no—
37C4⋊Dic43—21no—
38C4⋊Dic43—24no—
39C4⋊Dic43C2×C412yes—
40C4⋊Dic43Q812yes—
41Dic43⋊C4—24no—
42C4×Dic43—42no—
43C4×Dic43C2×C412yes—
44C4×Dic43D412yes—
45C2×C43⋊C8—21no—
46C2×C43⋊C8—21no—
47C2×C43⋊C8—21no—
48C23×C43C2×D411yescharacteristic
49C2×C4×C43—22no—
50C2×C4×C43—22no—
51C2×C4×C43—41no—
52C2×C4×C43—41no—
53C2×C4×C43—41no—
54C2×C4×C43—41no—
55C2×C4×C43C22×C411yescharacteristic
56C2×C4×C43C2×D411yescharacteristic
57C2×C4×C43C2×Q811yescharacteristic
58C2×C4×C43C2×Q811yescharacteristic
59C2×C4×C43#4111yescharacteristic
60C2×C4×C43#4111yescharacteristic
61C2×Dic43—21no—
62C2×Dic43—21no—
63C2×Dic43—21no—
64C2×Dic43—21no—
65C2×Dic43—22no—
66C2×Dic43—22no—
67C2×Dic43—41no—
68C2×Dic43—41no—
69C2×Dic43—41no—
70C2×Dic43—41no—
71C2×Dic43C22⋊C412yes—
72C2×Dic43C22⋊C412yes—
73C8×C43—41no—
74C43⋊C8—41no—
75C22×C43C2×C22⋊C411yescharacteristic
76C22×C43C22⋊Q811yescharacteristic
77C22×C43C22⋊Q811yescharacteristic
78C22×C43#13511yescharacteristic
79C22×C43#13511yescharacteristic
80C22×C43AGL(1,ℤ/8)11yescharacteristic
81C22×C43#13711yescharacteristic
82C4×C43—42no—
83C4×C43—42no—
84C4×C43C4×Q811yescharacteristic
85C4×C43C4×Q811yescharacteristic
86C4×C43#12411yescharacteristic
87C4×C43C4⋊Q811yescharacteristic
88Dic43—22no—
89Dic43—22no—
90Dic43—42no—
91Dic43—42no—
92#1989—431nomaximal, Sylow
93C2×C43#39111yescharacteristic
94C2×C43#41611yescharacteristic
95C2×C43#41711yescharacteristic
96C2×C43#47811yescharacteristic
97C2×C43#47811yescharacteristic
98C2×C43#47911yescharacteristic
99C2×C43#47911yescharacteristic
100C2×#125—431no—
101C2×C4⋊C8—431no—
102C4×C4⋊C4—431no—
103#340—431no—
104#340—431no—
105#340—431no—
106#340D4311yescharacteristic
107C43#198911yescharacteristic, complemented, Sylow
108C22×C8—431no—
109C22×C8C2×D4311yescharacteristic
110#125—434no—
111#125—862no—
112C2×C4⋊C4—431no—
113C2×C4⋊C4—431no—
114C2×C4⋊C4—861no—
115C2×C4⋊C4—861no—
116C2×C4⋊C4C2×D4311yescharacteristic
117C2×C4⋊C4C2×D4311yescharacteristic
118C2×C42—431no—
119C2×C42—861no—
120C4⋊C8—862no—
121#95—861no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—431no—
125C22×C4—431no—
126C22×C4—861no—
127C22×C4—861no—
128C22×C4C22×D4311yescharacteristic
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—861no—
133C2×C8—861no—
134C2×C8—861no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—432no—
138C4⋊C4—432no—
139C4⋊C4—864no—
140C4⋊C4—864no—
141C4⋊C4—861no—
142C4⋊C4—861no—
143C4⋊C4Dic8612yes—
144C4⋊C4C4×D4312yes—
145C42—432no—
146C42—432no—
147C42—1722no—
148C23D4×D4311yescharacteristic
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—432no—
156C2×C4—432no—
157C2×C4—861no—
158C2×C4—861no—
159C2×C4—861no—
160C2×C4—861no—
161C2×C4—862no—
162C2×C4—862no—
163C2×C4—1721no—
164C2×C4—1721no—
165C2×C4—1721no—
166C2×C4—1721no—
167C2×C4C2×Dic8611yescharacteristic
168C2×C4C2×C4×D4311yescharacteristic
169C2×C4#1062189811yescharacteristic
170C2×C4D4×D4311yescharacteristic
171C2×C4#1062190011yescharacteristic
172C2×C4Q8×D4311yescharacteristic
173C8—41no—
174C8—1721no—
175C22C22⋊C4×D4311yescharacteristic
176C22#1306330211yescharacteristic
177C22#1306330311yescharacteristic
178C22#1306334411yescharacteristic
179C22#1306334611yescharacteristic
180C22#1306335211yescharacteristic
181C22#1306335711yescharacteristic
182C4—42no—
183C4—42no—
184C4—862no—
185C4—862no—
186C4—1722no—
187C4—1722no—
188C4#1306329011yescharacteristic
189C4C4×Dic8611yescharacteristic
190C4#1306331111yescharacteristic
191C4#1306332411yescharacteristic
192C2#1458280311yescharacteristic
193C2#1458289211yescharacteristic
194C2#1458289911yescharacteristic
195C2#1458319711yescharacteristic
196C2#1458319811yescharacteristic
197C2#1458320411yescharacteristic
198C2#1458320511yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#340C2
socleC23×C43C2×D4
hypercenter#340D43
hypocenterC43#1989
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
10. #13063316C4semidirect
107. C43#1989semidirect