Finite Group Databasebeta

← #19134566

Subgroups — #19134566

Order 5504.

588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#13063371C211yesmaximal, characteristic
2#14582915C212yesmaximal, complemented
3#14582905C212yesmaximal, complemented
4#14582873C211yesmaximal, characteristic, complemented
5C43×#413C211yesmaximal, characteristic, complemented
6#13063371—24no—
7#13063371—24no—
8C2×#10621902—21no—
9C2×#10621898C412yescomplemented
10C2×#10621898C2211yescharacteristic
11C22×D172C412yescomplemented
12C22×D172C2211yescharacteristic
13C2×D4×D43—22no—
14C2×D4×D43—21no—
15#13063284C2212yescomplemented
16#13063251—24no—
17#13063247—24no—
18#13063240—22no—
19C2×#41×C43C2211yescharacteristic
20C2×M16×C43C2212yescomplemented
21#101×C43—21no—
22#100×C43—21no—
23C23×D43—22no—
24C23×D43—21no—
25#41×C43—22no—
26#41×C43—22no—
27C2×Q8×C43D411yescharacteristic
28C2×D4×C43D411yescharacteristic
29C2×D4×C43D412yes—
30C22×C4×C43C2×C412yes—
31C22×C4×C43C2311yescharacteristic
32C2×C22⋊D43—22no—
33C2×C22⋊D43—21no—
34#10621902—28no—
35D4×D43—28no—
36D4×D43—216no—
37#10621898—22no—
38#10621898—24no—
39#10621898—24no—
40#10621898D414yes—
41C2×D172—22no—
42C2×D172—21no—
43C2×D172—22no—
44C2×D172—24no—
45C2×D172—24no—
46C2×D172C2×C411yescharacteristic
47C2×D172C2×C412yes—
48C2×D172D414yes—
49C2×C4×D43—22no—
50C2×C4×D43—21no—
51C2×Dic86C2×C411yescharacteristic
52M16×C43—22no—
53M16×C43—22no—
54C2×C8×C43—22no—
55C22⋊Dic43—22no—
56C4⋊Dic43—22no—
57C4×Dic43—22no—
58C23×C43C22⋊C412yes—
59C23×C43C2×D411yescharacteristic
60C22×D43—22no—
61C22×D43—21no—
62C22×D43—28no—
63C22×D43—24no—
64C22×D43—82no—
65C22×D43—84no—
66Q8×C43—22no—
67D4×C43—24no—
68D4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43C22⋊C412yes—
72C2×C4×C43C22×C411yescharacteristic
73C2×C4×C43C2×D412yes—
74C2×C4×C43C2×D412yes—
75C2×C4×C43C2×D411yescharacteristic
76C22⋊D43—28no—
77C22⋊D43—24no—
78C2×Dic43—21no—
79C2×Dic43—42no—
80D172—28no—
81D172—21no—
82D172—22no—
83D172—24no—
84D172C22⋊C412yes—
85D172C22⋊C414yes—
86C4×D43—28no—
87C4×D43—24no—
88Dic86—21no—
89Dic86C22⋊C412yes—
90C8×C43—42no—
91C22×C43—22no—
92C22×C43—41no—
93C22×C43—42no—
94C22×C43C2×C22⋊C411yescharacteristic
95C22×C43#12012yes—
96C2×D43—22no—
97C2×D43—24no—
98C2×D43—44no—
99C2×D43—42no—
100C2×D43—84no—
101C2×D43—88no—
102C4×C43—22no—
103C4×C43C2×C22⋊C411yescharacteristic
104C4×C43C2×C22⋊C411yescharacteristic
105C4×C43#12012yes—
106Dic43—22no—
107Dic43—82no—
108#1795—431nomaximal, Sylow
109C2×C43—22no—
110C2×C43—21no—
111C2×C43—42no—
112C2×C43#37911yescharacteristic
113D43—44no—
114D43—42no—
115C2×H(5,𝔽2)—431no—
116#421—432no—
117#418—432no—
118#413D4311yescharacteristic, complemented
119#410—431no—
120C43#179511yescharacteristic, complemented, Sylow
121H(5,𝔽2)—864no—
122H(5,𝔽2)—864no—
123C2×#41—431no—
124C2×#41—432no—
125C2×#41—861no—
126C2×#41C2×D4311yescharacteristic
127C22×D4—431no—
128C22×D4—432no—
129C22×D4—862no—
130C22×D4—861no—
131C2×M16C2×D4312yescomplemented
132#117—432no—
133#104—864no—
134#102—864no—
135#101—21no—
136#100—21no—
137#99—862no—
138C24—862no—
139C24—861no—
140#41—22no—
141#41—22no—
142#41—434no—
143#41—864no—
144#41—864no—
145#41—868no—
146#41—862no—
147C2×Q8—431no—
148C2×Q8C22⋊D4311yescharacteristic
149C2×D4—432no—
150C2×D4—431no—
151C2×D4—434no—
152C2×D4—864no—
153C2×D4—864no—
154C2×D4—8616no—
155C2×D4—868no—
156C2×D4—862no—
157C2×D4—861no—
158C2×D4—862no—
159C2×D4—862no—
160C2×D4—861no—
161C2×D4D17212yes—
162C2×D4C22⋊D4311yescharacteristic
163C22×C4—862no—
164C22×C4—861no—
165C22×C4C4×D4312yes—
166C22×C4C22×D4311yescharacteristic
167M16—22no—
168M16—22no—
169C2×C8—22no—
170C4⋊C4—862no—
171C22⋊C4—862no—
172C42—862no—
173C23—868no—
174C23—864no—
175C23—862no—
176C23—861no—
177C23—3442no—
178C23—3444no—
179C23(C2×D43)⋊C412yes—
180C23C2×D17211yescharacteristic
181Q8—22no—
182Q8—432no—
183Q8—861no—
184D4—24no—
185D4—22no—
186D4—434no—
187D4—432no—
188D4—868no—
189D4—868no—
190D4—864no—
191D4—861no—
192D4—862no—
193D4—864no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—868no—
197C2×C4—861no—
198C2×C4—864no—
199C2×C4—1722no—
200C2×C4(C2×D43)⋊C412yes—
201C2×C4C2×C4×D4311yescharacteristic
202C2×C4D4×D4312yes—
203C2×C4D4×D4312yes—
204C2×C4C2×C22⋊D4311yescharacteristic
205C8—42no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22—864no—
210C22—862no—
211C22—3444no—
212C22—3448no—
213C22—1724no—
214C22—1722no—
215C22C2×(C2×D43)⋊C411yescharacteristic
216C22#1306329512yes—
217C4—22no—
218C4—862no—
219C4—3442no—
220C4C22⋊C4×D4311yescharacteristic
221C4C22⋊C4×D4311yescharacteristic
222C4#1306329312yes—
223C2—22no—
224C2—21no—
225C2—42no—
226C2—1724no—
227C2—1722no—
228C2#1458275411yescharacteristic
subgroupG/H
centerC2#14582754
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#413C2
socleC2×C43#379
hypercenter#413D43
hypocenterC43#1795
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #14582915C2semidirect
3. #14582905C2semidirect
4. #14582873C2semidirect
5. C43×#413C2semidirect
9. C2×#10621898C4semidirect
11. C22×D172C4semidirect
15. #13063284C22semidirect
20. C2×M16×C43C22semidirect
118. #413D43semidirect
120. C43#1795semidirect
131. C2×M16C2×D43semidirect