Finite Group Databasebeta

← #19133713

Subgroups — #19133713

Order 5504.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D172C211yesmaximal, characteristic
2#14583272C211yesmaximal, characteristic, complemented
3#14583190C211yesmaximal, characteristic, complemented
4#14583189C211yesmaximal, characteristic, complemented
5#14582642C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic, complemented
7C43×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×D172—21no—
9C2×D4×D43—21no—
10C2×#10621873—22no—
11#13063325C2211yescharacteristic, complemented
12#13063322C2211yescharacteristic
13#13063300—21no—
14#13063299—21no—
15#13063295—22no—
16C4×D172C2211yescharacteristic
17#13063257—21no—
18#13063256—21no—
19C4⋊(C43⋊C8)C2211yescharacteristic, complemented
20#13063247—21no—
21#13063246—21no—
22C4×D4×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic, complemented
24C4×C8×C43C2211yescharacteristic, complemented
25C23×D43—22no—
26C2×D4×C43D411yescharacteristic
27C22×C4×C43—21no—
28C2×C22⋊D43—22no—
29D4×D43—42no—
30D4×D43—42no—
31C2×D172—22no—
32C2×D172—21no—
33C2×D172—21no—
34C2×D172—42no—
35C2×D172—42no—
36C2×D172D411yescharacteristic
37C2×D172D412yes—
38C2×C4×D43—21no—
39C2×Dic86—21no—
40C2×C8×C43—21no—
41C2×C8×C43—21no—
42C4⋊C4×C43D411yescharacteristic
43C22⋊C4×C43—21no—
44C42×C43C2311yescharacteristic
45(C2×D43)⋊C4—22no—
46(C2×D43)⋊C4—21no—
47C4⋊Dic43—21no—
48C4⋊Dic43—21no—
49C4⋊Dic43D411yescharacteristic
50C2×C43⋊C8—21no—
51#10621873—44no—
52C23×C43—21no—
53C22×D43—21no—
54C22×D43—22no—
55C22×D43—44no—
56C22×D43—44no—
57C22×D43—82no—
58D4×C43—21no—
59D4×C43SD1612yescomplemented
60C2×C4×C43—21no—
61C2×C4×C43—41no—
62C2×C4×C43—41no—
63C2×C4×C43C2×D411yescharacteristic
64C2×C4×C43C2×D411yescharacteristic
65C2×C4×C43C2×D411yescharacteristic
66C22⋊D43—44no—
67C2×Dic43—21no—
68C2×Dic43—41no—
69D172—21no—
70D172—42no—
71D172—44no—
72D172—41no—
73D172—41no—
74D172—41no—
75D172—41no—
76D172SD1612yescomplemented
77C4×D43—41no—
78C4×D43—41no—
79Dic86—42no—
80C8×C43—22no—
81C8×C43—41no—
82C43⋊C8—41no—
83C22×C43—22no—
84C22×C43—41no—
85C22×C43—41no—
86C22×C43#12011yescharacteristic
87C2×D43—22no—
88C2×D43—41no—
89C2×D43—41no—
90C2×D43—42no—
91C2×D43—42no—
92C2×D43—42no—
93C2×D43—88no—
94C4×C43—21no—
95C4×C43—41no—
96C4×C43C2×SD1611yescharacteristic
97C4×C43C2×SD1611yescharacteristic
98C4×C43AGL(1,ℤ/8)11yescharacteristic
99C4×C43AGL(1,ℤ/8)11yescharacteristic
100Dic43—41no—
101Dic43—81no—
102#1629—431nomaximal, Sylow
103C2×C43—42no—
104C2×C43#45011yescharacteristic
105C2×C43#45011yescharacteristic
106C2×C43#45311yescharacteristic
107D43—42no—
108D43—82no—
109D42—431no—
110#492—431no—
111#476—431no—
112#476—431no—
113#331—431no—
114D4⋊C8—431no—
115D4⋊C8D4311yescharacteristic, complemented
116C43#162911yescharacteristic, complemented, Sylow
117C22×D4—861no—
118C22×D4—861no—
119C2×SD16—862no—
120C4⋊Q8—431no—
121#127—431no—
122#121—861no—
123#121—861no—
124#120—862no—
125C4×D4—431no—
126C4×D4C2×D4311yescharacteristic
127#106—861no—
128#106—861no—
129C4⋊C8—431no—
130C4⋊C8C2×D4311yescharacteristic, complemented
131#102—861no—
132#102—861no—
133C4×C8C2×D4311yescharacteristic, complemented
134C24—862no—
135C2×Q8—861no—
136C2×D4—431no—
137C2×D4—432no—
138C2×D4—862no—
139C2×D4—862no—
140C2×D4—861no—
141C2×D4—861no—
142C2×D4—1722no—
143C2×D4—1722no—
144C2×D4—1722no—
145C2×D4—1722no—
146C2×D4D17211yescharacteristic
147C22×C4—21no—
148C22×C4—861no—
149SD16—1724no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—861no—
153C4⋊C4—431no—
154C4⋊C4—861no—
155C4⋊C4—861no—
156C4⋊C4D17211yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—862no—
159C22⋊C4—861no—
160C42C22×D4311yescharacteristic
161C23—21no—
162C23—861no—
163C23—862no—
164C23—3442no—
165C23—1724no—
166C23—1724no—
167Q8—1722no—
168D4—21no—
169D4—432no—
170D4—861no—
171D4—1722no—
172D4—1724no—
173D4—1724no—
174D4—1721no—
175D4—1721no—
176D4—1721no—
177D4—1721no—
178D4#1062187312yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—861no—
183C2×C4—1721no—
184C2×C4—1721no—
185C2×C4—1721no—
186C2×C4C2×D17211yescharacteristic
187C2×C4D4×D4311yescharacteristic
188C2×C4D4×D4311yescharacteristic
189C8—22no—
190C8—41no—
191C8—1721no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—862no—
196C22—3448no—
197C22—1722no—
198C22—1722no—
199C22—1722no—
200C22—1721no—
201C22—1721no—
202C22#1306329511yescharacteristic
203C4—21no—
204C4—41no—
205C4—3441no—
206C4—1721no—
207C4SD16×D4311yescharacteristic
208C4C2×#1062187311yescharacteristic
209C4#1306334911yescharacteristic
210C4#1306335311yescharacteristic
211C2—42no—
212C2—3442no—
213C2—1722no—
214C2#1458305111yescharacteristic
215C2#1458305211yescharacteristic
216C2#1458306811yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×D4⋊C8C2
socleC22×C43#120
hypercenterD4⋊C8D43
hypocenterC43#1629
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
2. #14583272C2semidirect
3. #14583190C2semidirect
4. #14583189C2semidirect
5. #14582642C2semidirect
6. #14582628C2semidirect
7. C43×D4⋊C8C2semidirect
11. #13063325C22semidirect
19. C4⋊(C43⋊C8)C22semidirect
23. C4⋊C8×C43C22semidirect
24. C4×C8×C43C22semidirect
59. D4×C43SD16semidirect
76. D172SD16semidirect
115. D4⋊C8D43semidirect
116. C43#1629semidirect
130. C4⋊C8C2×D43semidirect
133. C4×C8C2×D43semidirect
178. D4#10621873semidirect