Finite Group Databasebeta

← #19133657

Subgroups — #19133657

Order 5504.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#14583569C211yesmaximal, characteristic, complemented
2#14583096C211yesmaximal, characteristic, complemented
3#14583091C211yesmaximal, characteristic, complemented
4#14582643C211yesmaximal, characteristic, complemented
5#14582631C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic, complemented
7C43×#493C211yesmaximal, characteristic, complemented
8C2×#10621900—21no—
9C2×#10621883—21no—
10C2×#10621882—21no—
11#13063321—21no—
12#13063297—22no—
13#13063296—21no—
14C4×Dic86C2211yescharacteristic
15C4×D172C2211yescharacteristic
16D4×Dic43—21no—
17C4⋊(C43⋊C8)C2211yescharacteristic
18C4⋊(C43⋊C8)C2211yescharacteristic
19#13063246—21no—
20#13063246—21no—
21C2×D8×C43—22no—
22#127×C43C2211yescharacteristic
23#127×C43C2211yescharacteristic
24C4×C8×C43C2211yescharacteristic
25C2×D4×C43—21no—
26C2×D4×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43—21no—
29C2×D4×C43—21no—
30C2×D4×C43D412yes—
31C2×C22⋊D43—22no—
32C2×C22⋊D43—22no—
33C22×Dic43—22no—
34#10621900—42no—
35#10621900—42no—
36C2×D172D411yescharacteristic
37C2×C4×D43—21no—
38C2×Dic86D411yescharacteristic
39D8×C43—44no—
40C2×C8×C43—21no—
41C42×C43C2311yescharacteristic
42C22⋊Dic43—22no—
43#10621883—42no—
44#10621882—42no—
45(C2×D43)⋊C4—21no—
46C4⋊Dic43D411yescharacteristic
47C4⋊Dic43D411yescharacteristic
48Dic43⋊C4—21no—
49C4×Dic43—21no—
50C2×C43⋊C8—21no—
51C2×C43⋊C8—21no—
52C23×C43—22no—
53C23×C43—41no—
54C22×D43—21no—
55D4×C43—42no—
56D4×C43—42no—
57D4×C43—41no—
58D4×C43—41no—
59D4×C43—41no—
60D4×C43—41no—
61D4×C43—41no—
62D4×C43—41no—
63D4×C43—41no—
64D4×C43—41no—
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C22⋊D43—44no—
69C22⋊D43—82no—
70C2×Dic43—21no—
71C2×Dic43—21no—
72C2×Dic43—21no—
73C2×Dic43—44no—
74D172—21no—
75D172—21no—
76C4×D43—41no—
77C4×D43—41no—
78Dic86—21no—
79Dic86D812yescomplemented
80C8×C43—22no—
81C43⋊C8—41no—
82C43⋊C8—41no—
83C22×C43—42no—
84C22×C43—42no—
85C22×C43—42no—
86C22×C43—81no—
87C22×C43—81no—
88C22×C43—81no—
89C22×C43#12011yescharacteristic
90C2×D43—41no—
91C2×D43—41no—
92C2×D43—41no—
93C4×C43—21no—
94C4×C43C2×D811yescharacteristic
95C4×C43#13511yescharacteristic
96C4×C43AGL(1,ℤ/8)11yescharacteristic
97C4×C43AGL(1,ℤ/8)11yescharacteristic
98Dic43—22no—
99Dic43—41no—
100Dic43—41no—
101#1621—431nomaximal, Sylow
102C2×C43—82no—
103C2×C43—161no—
104C2×C43#44711yescharacteristic
105C2×C43#44911yescharacteristic
106C2×C43#45311yescharacteristic
107D43—81no—
108#550—431no—
109#493D4311yescharacteristic, complemented
110#460—431no—
111#459—431no—
112#331—431no—
113Q8⋊C8—431no—
114D4⋊C8—431no—
115C43#162111yescharacteristic, complemented, Sylow
116C2×#41—861no—
117C2×SD16—861no—
118C2×D8—22no—
119C2×D8—861no—
120#127—861no—
121#127C2×D4311yescharacteristic
122#127C2×D4311yescharacteristic
123#121—861no—
124#121—862no—
125C4×Q8—431no—
126C4×D4—431no—
127C4×D4—861no—
128C4⋊C8—431no—
129C4⋊C8—431no—
130#102—861no—
131#102—861no—
132C4×C8C2×D4311yescharacteristic
133#41—1722no—
134#41—1722no—
135C2×Q8—431no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—431no—
142C2×D4—862no—
143C2×D4—862no—
144C2×D4C22⋊D4312yes—
145C22×C4—862no—
146C22×C4—861no—
147SD16—1722no—
148D8—44no—
149D8—1722no—
150C2×C8—21no—
151C2×C8—861no—
152C2×C8—861no—
153C4⋊C4—431no—
154C4⋊C4—431no—
155C4⋊C4—861no—
156C22⋊C4—862no—
157C22⋊C4—861no—
158C42—861no—
159C42C22×D4311yescharacteristic
160C23—22no—
161C23—41no—
162C23—861no—
163Q8—432no—
164Q8—861no—
165D4—42no—
166D4—42no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—861no—
176D4—861no—
177D4—3442no—
178D4—1724no—
179C2×C4—861no—
180C2×C4—861no—
181C2×C4—861no—
182C2×C4—1724no—
183C2×C4—1721no—
184C2×C4—1721no—
185C2×C4D4×D4311yescharacteristic
186C2×C4D4×D4311yescharacteristic
187C2×C4C2×C22⋊D4311yescharacteristic
188C8—22no—
189C8—1721no—
190C8—1721no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—1721no—
198C22—1721no—
199C22—1721no—
200C22#1306329311yescharacteristic
201C4—21no—
202C4—862no—
203C4—1721no—
204C4—1721no—
205C4D8×D4311yescharacteristic
206C4#1306334411yescharacteristic
207C4#1306334911yescharacteristic
208C4#1306334911yescharacteristic
209C2—82no—
210C2—161no—
211C2—3441no—
212C2#1458303111yescharacteristic
213C2#1458304111yescharacteristic
214C2#1458306611yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#493C2
socleC22×C43#120
hypercenter#493D43
hypocenterC43#1621
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #14583569C2semidirect
2. #14583096C2semidirect
3. #14583091C2semidirect
4. #14582643C2semidirect
5. #14582631C2semidirect
6. #14582628C2semidirect
7. C43×#493C2semidirect
79. Dic86D8semidirect
109. #493D43semidirect
115. C43#1621semidirect