Finite Group Databasebeta

← #19133529

Subgroups — #19133529

Order 5504.

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

normal subgroups only

This group has 310 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#14583480C211yesmaximal, characteristic, complemented
2#14583033C212yesmaximal, complemented
3#14582632C212yesmaximal, complemented
4#14582625C211yesmaximal, characteristic, complemented
5C43×#394C211yesmaximal, characteristic, complemented
6C2×#10621898—21no—
7C2×#10621882—22no—
8#13063305—22no—
9#13063300—22no—
10#13063299—21no—
11#13063299C2212yes—
12#13063246—22no—
13C22⋊(C43⋊C8)C2212yes—
14C22×D4×C43C2211yescharacteristic
15C2×C4⋊C4×C43C2211yescharacteristic
16C2×C22⋊C4×C43—21no—
17C2×C22⋊C4×C43—21no—
18#95×C43C2211yescharacteristic
19C24×C43—21no—
20C2×D4×C43—22no—
21C2×D4×C43—42no—
22C22×C4×C43—21no—
23C22×C4×C43D411yescharacteristic
24C22×C4×C43D411yescharacteristic
25C22×C4×C43C2311yescharacteristic
26C2×C22⋊D43—22no—
27#10621898—42no—
28#10621898—42no—
29C2×D172—21no—
30C2×D172—21no—
31C2×D172D412yes—
32C2×C4×D43—22no—
33C2×Dic86—21no—
34C4⋊C4×C43—22no—
35C22⋊C4×C43—42no—
36C22⋊C4×C43—42no—
37#10621882—44no—
38(C2×D43)⋊C4—22no—
39(C2×D43)⋊C4—22no—
40C4⋊Dic43—21no—
41C4⋊Dic43D412yes—
42C2×C43⋊C8—22no—
43C23×C43—22no—
44C23×C43—41no—
45C23×C43—41no—
46C23×C43—41no—
47C23×C43—41no—
48C23×C43—41no—
49C23×C43—41no—
50C23×C43C2×D411yescharacteristic
51C22×D43—22no—
52D4×C43—24no—
53D4×C43—42no—
54C2×C4×C43—21no—
55C2×C4×C43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—41no—
58C2×C4×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43—41no—
61C2×C4×C43—41no—
62C2×C4×C43D812yescomplemented
63C2×C4×C43C2×D412yes—
64C22⋊D43—42no—
65C22⋊D43—42no—
66C2×Dic43—22no—
67D172—42no—
68D172—42no—
69D172—81no—
70C4×D43—44no—
71Dic86—42no—
72C43⋊C8—42no—
73C22×C43—21no—
74C22×C43—21no—
75C22×C43—42no—
76C22×C43—42no—
77C22×C43—42no—
78C22×C43—81no—
79C22×C43—81no—
80C22×C43—81no—
81C22×C43—81no—
82C22×C43#12011yescharacteristic
83C22×C43C2×D811yescharacteristic
84C22×C43AGL(1,ℤ/8)11yescharacteristic
85C2×D43—42no—
86C2×D43—42no—
87C2×D43—42no—
88C4×C43—22no—
89C4×C43—22no—
90C4×C43—41no—
91C4×C43—81no—
92Dic43—42no—
93#1598—431nomaximal, Sylow
94C2×C43—21no—
95C2×C43—21no—
96C2×C43—82no—
97C2×C43#44711yescharacteristic
98C2×C43#45411yescharacteristic
99C2×C43B(4,𝔽2)11yescharacteristic
100D43—82no—
101#537—431no—
102#447—432no—
103#394D4311yescharacteristic, complemented
104#327—432no—
105#324—431no—
106C43#159811yescharacteristic, complemented, Sylow
107C2×#41—861no—
108C22×D4C2×D4311yescharacteristic
109C2×D8—862no—
110C22⋊Q8—862no—
111#121—432no—
112#121—862no—
113#121—861no—
114C2×C4⋊C4C2×D4311yescharacteristic
115C2×C22⋊C4—21no—
116C2×C22⋊C4—21no—
117#102—862no—
118C22⋊C8—432no—
119#95C2×D4311yescharacteristic
120C24—21no—
121#41—1722no—
122#41—1722no—
123C2×Q8—861no—
124C2×D4—22no—
125C2×D4—42no—
126C2×D4—432no—
127C2×D4—861no—
128C2×D4—861no—
129C2×D4—862no—
130C22×C4—21no—
131C22×C4—862no—
132C22×C4C22⋊D4311yescharacteristic
133C22×C4C22⋊D4311yescharacteristic
134C22×C4C22×D4311yescharacteristic
135D8—1724no—
136C2×C8—862no—
137C4⋊C4—22no—
138C4⋊C4—432no—
139C4⋊C4—861no—
140C22⋊C4—42no—
141C22⋊C4—42no—
142C22⋊C4—862no—
143C22⋊C4—862no—
144C23—22no—
145C23—41no—
146C23—41no—
147C23—41no—
148C23—41no—
149C23—41no—
150C23—41no—
151C23—862no—
152C23C2×C22⋊D4311yescharacteristic
153Q8—1722no—
154D4—24no—
155D4—42no—
156D4—3441no—
157D4—1722no—
158D4—1722no—
159D4—1722no—
160D4—1722no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—862no—
170C2×C4—1724no—
171C2×C4#1062188212yescomplemented
172C2×C4D4×D4312yes—
173C8—1722no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—1722no—
184C22—1722no—
185C22—1722no—
186C22#1306329311yescharacteristic
187C22C2×#1062188211yescharacteristic
188C22#1306335011yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—81no—
193C4—1722no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—3442no—
198C2#1458303211yescharacteristic
199C2#1458307111yescharacteristic
200C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#394C2
socleC22×C43#120
hypercenter#394D43
hypocenterC43#1598
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #14583480C2semidirect
2. #14583033C2semidirect
3. #14582632C2semidirect
4. #14582625C2semidirect
5. C43×#394C2semidirect
62. C2×C4×C43D8semidirect
103. #394D43semidirect
106. C43#1598semidirect
171. C2×C4#10621882semidirect