Finite Group Databasebeta

← #19133680

Subgroups — #19133680

Order 5504.

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

normal subgroups only

This group has 240 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#14583614C211yesmaximal, characteristic, complemented
2#14583272C211yesmaximal, characteristic, complemented
3#14583095C211yesmaximal, characteristic, complemented
4#14583094C211yesmaximal, characteristic, complemented
5#14582647C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic, complemented
7C43×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10621873—22no—
9C2×D344—21no—
10C2×#10621882—21no—
11#13063325C2211yescharacteristic
12#13063322C2211yescharacteristic
13#13063311—22no—
14#13063299—21no—
15#13063296—21no—
16C4×D172C2211yescharacteristic
17#13063284—21no—
18#13063283—21no—
19C4⋊(C43⋊C8)C2211yescharacteristic
20#13063247—21no—
21#13063245—21no—
22C4×D4×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4×C8×C43C2211yescharacteristic
25C2×D4×C43D411yescharacteristic
26C22×C4×C43—21no—
27C2×C22⋊D43—22no—
28C2×D172—21no—
29C2×D172—21no—
30C2×D172—21no—
31C2×D172D411yescharacteristic
32C2×C4×D43—21no—
33C2×Dic86D412yes—
34C2×C8×C43—21no—
35C2×C8×C43—21no—
36C4⋊C4×C43D411yescharacteristic
37C22⋊C4×C43—21no—
38C42×C43C2311yescharacteristic
39C22⋊Dic43—22no—
40#10621882—42no—
41(C2×D43)⋊C4—22no—
42(C2×D43)⋊C4—21no—
43C4⋊Dic43—21no—
44C4⋊Dic43—21no—
45C4⋊Dic43D411yescharacteristic
46C4×Dic43—22no—
47C2×C43⋊C8—21no—
48D344—42no—
49#10621873—44no—
50C23×C43—21no—
51C22×D43—21no—
52C22×D43—41no—
53D4×C43—21no—
54D4×C43—21no—
55C2×C4×C43—21no—
56C2×C4×C43—41no—
57C2×C4×C43—41no—
58C2×C4×C43C2×D411yescharacteristic
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×D411yescharacteristic
61C22⋊D43—82no—
62C2×Dic43—21no—
63C2×Dic43—22no—
64D172—21no—
65D172—21no—
66D172—42no—
67D172—41no—
68D172—41no—
69D172—41no—
70D172—41no—
71C4×D43—41no—
72C4×D43—41no—
73Dic86—42no—
74C8×C43—22no—
75C8×C43—41no—
76C43⋊C8—41no—
77C22×C43—41no—
78C22×C43—41no—
79C22×C43—41no—
80C22×C43#12011yescharacteristic
81C2×D43—41no—
82C2×D43—41no—
83C2×D43—41no—
84C2×D43—81no—
85C2×D43—81no—
86C2×D43—81no—
87C4×C43—21no—
88C4×C43—41no—
89C4×C43#13511yescharacteristic
90C4×C43#13511yescharacteristic
91C4×C43AGL(1,ℤ/8)11yescharacteristic
92C4×C43AGL(1,ℤ/8)11yescharacteristic
93Dic43—41no—
94Dic43—42no—
95#1624—431nomaximal, Sylow
96C2×C43—81no—
97C2×C43#44911yescharacteristic
98C2×C43#44911yescharacteristic
99C2×C43#45311yescharacteristic
100D43—81no—
101D43—161no—
102#555—431no—
103#492—431no—
104#459—431no—
105#459—431no—
106#333—431no—
107D4⋊C8—431no—
108D4⋊C8D4311yescharacteristic, complemented
109C43#162411yescharacteristic, complemented, Sylow
110C2×SD16—862no—
111C2×D8—861no—
112C2×D8—861no—
113C4⋊Q8—431no—
114#127—431no—
115#124—862no—
116#121—861no—
117#121—861no—
118C4×D4—431no—
119C4×D4C2×D4311yescharacteristic
120#117—861no—
121#117—861no—
122C4⋊C8—431no—
123C4⋊C8C2×D4311yescharacteristic
124#102—861no—
125#102—861no—
126C4×C8C2×D4311yescharacteristic
127C2×Q8—432no—
128C2×D4—431no—
129C2×D4—862no—
130C2×D4—861no—
131C2×D4—861no—
132C2×D4—861no—
133C2×D4D17211yescharacteristic
134C22×C4—21no—
135C22×C4—861no—
136SD16—1724no—
137D8—1722no—
138D8—1722no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—861no—
142C4⋊C4—431no—
143C4⋊C4—861no—
144C4⋊C4—861no—
145C4⋊C4D17211yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—862no—
148C22⋊C4—862no—
149C22⋊C4—861no—
150C42—862no—
151C42C22×D4311yescharacteristic
152C23—21no—
153C23—861no—
154C23—1721no—
155Q8—1722no—
156D4—21no—
157D4—21no—
158D4—861no—
159D4—861no—
160D4—3442no—
161D4—1722no—
162D4—1721no—
163D4—1721no—
164D4—1721no—
165D4—1721no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—861no—
170C2×C4—862no—
171C2×C4—1721no—
172C2×C4—1721no—
173C2×C4C2×D17211yescharacteristic
174C2×C4D4×D4311yescharacteristic
175C2×C4D4×D4311yescharacteristic
176C8—22no—
177C8—41no—
178C8—1721no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—3441no—
183C22—3441no—
184C22—3441no—
185C22—1721no—
186C22—1721no—
187C22—1721no—
188C22#1306329511yescharacteristic
189C4—21no—
190C4—41no—
191C4—1721no—
192C4—1722no—
193C4#1306334611yescharacteristic
194C4#1306334711yescharacteristic
195C4#1306334911yescharacteristic
196C4#1306335311yescharacteristic
197C2—81no—
198C2—3441no—
199C2—6881no—
200C2#1458304511yescharacteristic
201C2#1458304611yescharacteristic
202C2#1458306811yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×D4⋊C8C2
socleC22×C43#120
hypercenterD4⋊C8D43
hypocenterC43#1624
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #14583614C2semidirect
2. #14583272C2semidirect
3. #14583095C2semidirect
4. #14583094C2semidirect
5. #14582647C2semidirect
6. #14582628C2semidirect
7. C43×D4⋊C8C2semidirect
108. D4⋊C8D43semidirect
109. C43#1624semidirect