Finite Group Databasebeta

← #19133580

Subgroups — #19133580

Order 5504.

280 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 53 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#14583461C211yesmaximal, characteristic
2#14583212C212yesmaximal, complemented
3#14582632C212yesmaximal, complemented
4#14582623C211yesmaximal, characteristic, complemented
5C43×#397C211yesmaximal, characteristic, complemented
6C22×C22⋊D43—21no—
7#13063309—22no—
8#13063299—21no—
9#13063299C2212yes—
10#13063295—22no—
11#13063258—22no—
12#13063245—22no—
13C22⋊(C43⋊C8)C2212yescomplemented
14C2×C4⋊C4×C43C2211yescharacteristic, complemented
15C2×C22⋊C4×C43—21no—
16C2×C22⋊C4×C43C2211yescharacteristic
17#95×C43—21no—
18#95×C43C2211yescharacteristic, complemented
19C24×C43D411yescharacteristic
20C23×D43—21no—
21C22×C4×C43—21no—
22C22×C4×C43—21no—
23C22×C4×C43D411yescharacteristic
24C22×C4×C43C2311yescharacteristic
25C2×C22⋊D43—22no—
26C2×C22⋊D43—22no—
27C2×C22⋊D43—42no—
28C2×C22⋊D43—42no—
29C22×Dic43—21no—
30C2×D172—21no—
31C2×D172D412yes—
32C4⋊C4×C43—22no—
33C22⋊C4×C43—22no—
34C22⋊C4×C43—42no—
35(C2×D43)⋊C4—22no—
36(C2×D43)⋊C4—22no—
37C4⋊Dic43—21no—
38C4⋊Dic43D412yes—
39C2×C43⋊C8—22no—
40C23×C43—21no—
41C23×C43—21no—
42C23×C43—41no—
43C23×C43—41no—
44C23×C43D812yes—
45C23×C43C2×D411yescharacteristic
46C22×D43—22no—
47C22×D43—42no—
48C22×D43—81no—
49C22×D43—81no—
50C2×C4×C43—21no—
51C2×C4×C43—41no—
52C2×C4×C43—41no—
53C2×C4×C43—41no—
54C2×C4×C43—41no—
55C2×C4×C43—41no—
56C2×C4×C43—41no—
57C2×C4×C43—41no—
58C2×C4×C43—41no—
59C2×C4×C43C2×D412yes—
60C22⋊D43—44no—
61C22⋊D43—42no—
62C22⋊D43—42no—
63C2×Dic43—22no—
64C2×Dic43—42no—
65D172—42no—
66D172—81no—
67C43⋊C8—42no—
68C22×C43—21no—
69C22×C43—21no—
70C22×C43—22no—
71C22×C43—42no—
72C22×C43—41no—
73C22×C43—41no—
74C22×C43—81no—
75C22×C43#12011yescharacteristic
76C22×C43C2×D811yescharacteristic
77C22×C43AGL(1,ℤ/8)11yescharacteristic
78C2×D43—42no—
79C2×D43—42no—
80C2×D43—42no—
81C2×D43—84no—
82C4×C43—22no—
83C4×C43—41no—
84C4×C43—81no—
85C4×C43—81no—
86Dic43—42no—
87#1607—431nomaximal, Sylow
88C2×C43—21no—
89C2×C43—21no—
90C2×C43—42no—
91C2×C43#44711yescharacteristic
92C2×C43#45511yescharacteristic
93C2×C43#45811yescharacteristic
94D43—82no—
95#534—431no—
96#480—432no—
97#397D4311yescharacteristic, complemented
98#327—432no—
99#323—431no—
100C43#160711yescharacteristic, complemented, Sylow
101C22×D4—861no—
102#123—862no—
103#121—432no—
104#121—861no—
105#120—862no—
106C2×C4⋊C4C2×D4311yescharacteristic, complemented
107C2×C22⋊C4—21no—
108C2×C22⋊C4C2×D4311yescharacteristic
109#107—862no—
110#102—862no—
111C22⋊C8—432no—
112#95—21no—
113#95C2×D4311yescharacteristic, complemented
114C24—861no—
115C24C22⋊D4311yescharacteristic
116C2×D4—432no—
117C2×D4—861no—
118C2×D4—862no—
119C2×D4—862no—
120C2×D4—1722no—
121C2×D4—1722no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—861no—
125C22×C4C22⋊D4311yescharacteristic
126C22×C4C22×D4311yescharacteristic
127C2×C8—862no—
128C4⋊C4—22no—
129C4⋊C4—432no—
130C4⋊C4—861no—
131C22⋊C4—22no—
132C22⋊C4—42no—
133C22⋊C4—862no—
134C22⋊C4—862no—
135C23—21no—
136C23—21no—
137C23—41no—
138C23—41no—
139C23—862no—
140C23—3441no—
141C23—3441no—
142C23—1722no—
143C23#1062188212yes—
144C23C2×C22⋊D4311yescharacteristic
145D4—3441no—
146D4—1722no—
147D4—1724no—
148D4—1722no—
149D4—1722no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—862no—
160C2×C4—1722no—
161C2×C4D4×D4312yes—
162C8—1722no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—81no—
170C22—3444no—
171C22—1722no—
172C22—1722no—
173C22—1722no—
174C22#1306329311yescharacteristic
175C22C2×#1062188211yescharacteristic
176C22#1306335011yescharacteristic
177C4—22no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—1722no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—3442no—
186C2#1458303211yescharacteristic
187C2#1458307611yescharacteristic
188C2#1458308811yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#397C2
socleC22×C43#120
hypercenter#397D43
hypocenterC43#1607
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #14583212C2semidirect
3. #14582632C2semidirect
4. #14582623C2semidirect
5. C43×#397C2semidirect
13. C22⋊(C43⋊C8)C22semidirect
14. C2×C4⋊C4×C43C22semidirect
18. #95×C43C22semidirect
97. #397D43semidirect
100. C43#1607semidirect
106. C2×C4⋊C4C2×D43semidirect
113. #95C2×D43semidirect