Finite Group Databasebeta

← #19136539

Subgroups — #19136539

Order 5504.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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#14583696C211yesmaximal, characteristic, complemented
2#14583335C211yesmaximal, characteristic, complemented
3#14583149C211yesmaximal, characteristic, complemented
4#14582710C211yesmaximal, characteristic, complemented
5#14582709C211yesmaximal, characteristic, complemented
6#14582680C211yesmaximal, characteristic, complemented
7C43×#509C211yesmaximal, characteristic, complemented
8#41×D43—21no—
9#13063357—21no—
10#13063354—21no—
11#13063352—21no—
12#13063349—21no—
13#13063347C2211yescharacteristic
14#13063345—21no—
15C2×#10621872C2211yescharacteristic
16#13063296—21no—
17#13063269—21no—
18#13063266—21no—
19#13063265C2211yescharacteristic, complemented
20#13063257C2211yescharacteristic, complemented
21#13063246—21no—
22#135×C43C2211yescharacteristic
23C2×D8×C43C2211yescharacteristic, complemented
24SD32×C43—21no—
25D16×C43—21no—
26M32×C43C2211yescharacteristic, complemented
27#41×C43—21no—
28C2×D4×C43—21no—
29C2×C22⋊D43—41no—
30#10621902—21no—
31Q8×D43—21no—
32#10621900—21no—
33#10621900—41no—
34D4×D43—21no—
35D4×D43—41no—
36#10621898—21no—
37#10621898—41no—
38C2×C4×D43—41no—
39C2×C4×D43D411yescharacteristic
40Q16×C43D411yescharacteristic, complemented
41SD16×C43—21no—
42D8×C43—21no—
43D8×C43—21no—
44D8×C43D411yescharacteristic, complemented
45C2×C8×C43C2311yescharacteristic
46C22⋊Dic43—41no—
47#10621885—21no—
48#10621884—21no—
49#10621883—21no—
50#10621882—21no—
51C4⋊Dic43—21no—
52C2×C43⋊C8D411yescharacteristic
53Dic172D411yescharacteristic, complemented
54D344D411yescharacteristic, complemented
55#10621873—21no—
56#10621872—21no—
57#10621872—21no—
58C16×C43—21no—
59C43⋊C16—21no—
60C23×C43—41no—
61C22×D43—41no—
62C22×D43D811yescharacteristic
63Q8×C43—21no—
64D4×C43—21no—
65D4×C43—41no—
66D4×C43—41no—
67D4×C43—41no—
68C2×C4×C43—41no—
69C2×C4×C43C2×D411yescharacteristic
70C22⋊D43—41no—
71C22⋊D43—41no—
72C22⋊D43—41no—
73C22⋊D43—82no—
74C2×Dic43—41no—
75C2×Dic43—41no—
76C2×Dic43D811yescharacteristic
77D172—21no—
78D172—41no—
79C4×D43—21no—
80C4×D43—21no—
81C4×D43—41no—
82C4×D43—41no—
83C4×D43—41no—
84Dic86—21no—
85Dic86—41no—
86C8×C43C2×D411yescharacteristic
87C8×C43C2×D411yescharacteristic
88C43⋊C8—21no—
89C22×C43—41no—
90C22×C43—81no—
91C22×C43—81no—
92C22×C43—81no—
93C22×C43C2×D811yescharacteristic
94C2×D43—21no—
95C2×D43—41no—
96C2×D43—41no—
97C2×D43—82no—
98C4×C43—41no—
99C4×C43#12011yescharacteristic
100C4×C43AGL(1,ℤ/8)11yescharacteristic
101Dic43—21no—
102Dic43—41no—
103Dic43—81no—
104#2190—431nomaximal, Sylow
105C2×C43—21no—
106C2×C43—81no—
107C2×C43—161no—
108C2×C43#44711yescharacteristic
109D43—41no—
110D43—81no—
111#575—431no—
112#509—431no—
113#509D4311yescharacteristic, complemented
114#469—431no—
115#360—431no—
116#360—431no—
117#349—431no—
118C43#219011yescharacteristic, complemented, Sylow
119C2×#41—861no—
120#137—861no—
121#137—861no—
122AGL(1,ℤ/8)—861no—
123AGL(1,ℤ/8)—861no—
124#135—431no—
125#135—861no—
126#135C2×D4311yescharacteristic
127C2×D8C2×D4311yescharacteristic, complemented
128C2×M16—431no—
129#121—861no—
130SD32—21no—
131SD32—861no—
132D16—21no—
133D16—861no—
134M32—431no—
135M32C2×D4311yescharacteristic, complemented
136#106—431no—
137#102—861no—
138#41—21no—
139#41—861no—
140#41—861no—
141#41—861no—
142#41—1721no—
143#41—1721no—
144C2×Q8—861no—
145C2×D4—21no—
146C2×D4—861no—
147C2×D4—1721no—
148C2×D4—1721no—
149C22×C4—431no—
150C22×C4—1721no—
151Q16—431no—
152Q16—861no—
153Q16C22⋊D4311yescharacteristic, complemented
154SD16—21no—
155SD16—861no—
156SD16—861no—
157SD16—861no—
158D8—21no—
159D8—21no—
160D8—431no—
161D8—861no—
162D8C22⋊D4311yescharacteristic, complemented
163M16—861no—
164M16—861no—
165C2×C8—431no—
166C2×C8C22×D4311yescharacteristic
167C4⋊C4—861no—
168C22⋊C4—1721no—
169C16—21no—
170C16—861no—
171C23—41no—
172C23—431no—
173C23—1721no—
174Q8—21no—
175Q8—861no—
176Q8—1721no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—861no—
182D4—3442no—
183D4—1721no—
184D4—1721no—
185D4—1721no—
186D4—1721no—
187C2×C4—41no—
188C2×C4—431no—
189C2×C4—861no—
190C2×C4—861no—
191C2×C4—1721no—
192C2×C4—1721no—
193C2×C4—1721no—
194C2×C4—1721no—
195C2×C4—1721no—
196C2×C4D4×D4311yescharacteristic
197C8—861no—
198C8D4×D4311yescharacteristic
199C8C2×C22⋊D4311yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—861no—
205C22—3442no—
206C22—1721no—
207C22—1721no—
208C22D8×D4311yescharacteristic
209C4—41no—
210C4—861no—
211C4—3441no—
212C4—1721no—
213C4#1306329311yescharacteristic
214C4#1306334911yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—3441no—
219C2—1721no—
220C2#1458303111yescharacteristic
subgroupG/H
centerC2#14583031
commutatorC2×C8×C43C23
FrattiniC2×C8C22×D43
FittingC43×#509C2
socleC2×C43#447
hypercenter#509D43
hypocenterC43#2190
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #14583696C2semidirect
2. #14583335C2semidirect
3. #14583149C2semidirect
4. #14582710C2semidirect
5. #14582709C2semidirect
6. #14582680C2semidirect
7. C43×#509C2semidirect
19. #13063265C22semidirect
20. #13063257C22semidirect
23. C2×D8×C43C22semidirect
26. M32×C43C22semidirect
40. Q16×C43D4semidirect
44. D8×C43D4semidirect
53. Dic172D4semidirect
54. D344D4semidirect
113. #509D43semidirect
118. C43#2190semidirect
127. C2×D8C2×D43semidirect
135. M32C2×D43semidirect
153. Q16C22⋊D43semidirect
162. D8C22⋊D43semidirect