Finite Group Databasebeta

← #19136547

Subgroups — #19136547

Order 5504.

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

normal subgroups only

This group has 216 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
2#14583342C211yesmaximal, characteristic, complemented
3#14583339C211yesmaximal, characteristic, complemented
4#14583158C211yesmaximal, characteristic, complemented
5#14582708C211yesmaximal, characteristic, complemented
6#14582680C211yesmaximal, characteristic, complemented
7C43×#360C211yesmaximal, characteristic, complemented
8#41×D43—21no—
9#13063357—21no—
10#13063354—21no—
11#13063352—21no—
12#13063349—21no—
13#13063347C2211yescharacteristic
14#13063345—21no—
15C2×Dic172C2211yescharacteristic, complemented
16C2×#10621872C2211yescharacteristic
17#13063305—21no—
18Dic344—21no—
19#13063271—21no—
20#13063270—21no—
21#13063269—21no—
22#13063265C2211yescharacteristic, complemented
23#13063248—21no—
24#135×C43C2211yescharacteristic
25M32×C43C2211yescharacteristic, complemented
26#106×C43C2211yescharacteristic, complemented
27#41×C43—21no—
28#10621902—21no—
29Q8×D43—21no—
30#10621900—21no—
31#10621900—41no—
32D4×D43—21no—
33D4×D43—41no—
34#10621898—21no—
35#10621898—41no—
36C2×C4×D43—41no—
37C2×C4×D43D411yescharacteristic
38C2×Dic86—21no—
39Q16×C43D411yescharacteristic
40SD16×C43—21no—
41D8×C43D411yescharacteristic
42C2×C8×C43C2311yescharacteristic
43C4⋊C4×C43—21no—
44#10621885—21no—
45#10621884—21no—
46#10621883—21no—
47#10621882—21no—
48(C2×D43)⋊C4—41no—
49C4⋊Dic43—41no—
50C2×C43⋊C8D411yescharacteristic
51Dic172—21no—
52Dic172—21no—
53Dic172D411yescharacteristic
54D344D411yescharacteristic
55#10621873—21no—
56#10621872—21no—
57#10621872—21no—
58C16×C43—21no—
59C43⋊C16—21no—
60C22×D43—41no—
61C22×D43D811yescharacteristic
62Q8×C43—21no—
63D4×C43—21no—
64D4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43C2×D411yescharacteristic
68C22⋊D43—41no—
69C22⋊D43—41no—
70C22⋊D43—41no—
71C2×Dic43—41no—
72C2×Dic43—41no—
73C2×Dic43D811yescharacteristic
74D172—21no—
75D172—41no—
76C4×D43—21no—
77C4×D43—21no—
78C4×D43—41no—
79C4×D43—41no—
80C4×D43—41no—
81Dic86—21no—
82Dic86—41no—
83Dic86—41no—
84Dic86—41no—
85C8×C43C2×D411yescharacteristic
86C8×C43C2×D411yescharacteristic
87C43⋊C8—21no—
88C22×C43—41no—
89C22×C43C2×D811yescharacteristic
90C2×D43—21no—
91C2×D43—41no—
92C2×D43—41no—
93C2×D43—82no—
94C4×C43—41no—
95C4×C43—81no—
96C4×C43#12011yescharacteristic
97C4×C43AGL(1,ℤ/8)11yescharacteristic
98Dic43—21no—
99Dic43—41no—
100Dic43—81no—
101#2191—431nomaximal, Sylow
102C2×C43—21no—
103C2×C43—81no—
104C2×C43#44711yescharacteristic
105D43—41no—
106D43—81no—
107#575—431no—
108#510—431no—
109#510—431no—
110#470—431no—
111#360—431no—
112#360D4311yescharacteristic, complemented
113#349—431no—
114C43#219111yescharacteristic, complemented, Sylow
115C2×#41—861no—
116#137—861no—
117#137—861no—
118AGL(1,ℤ/8)—861no—
119AGL(1,ℤ/8)—861no—
120#135—431no—
121#135—861no—
122#135C2×D4311yescharacteristic
123C2×Q16—431no—
124C2×M16—431no—
125C22⋊Q8—861no—
126Q32—861no—
127Q32—861no—
128SD32—861no—
129SD32—861no—
130M32—431no—
131M32C2×D4311yescharacteristic, complemented
132#106C2×D4311yescharacteristic, complemented
133#103—861no—
134#41—21no—
135#41—861no—
136#41—861no—
137#41—861no—
138#41—1721no—
139#41—1721no—
140C2×Q8—861no—
141C2×Q8—861no—
142C2×D4—861no—
143C2×D4—1721no—
144C22×C4—431no—
145C22×C4—1721no—
146Q16—431no—
147Q16—861no—
148Q16—861no—
149Q16—861no—
150Q16D17211yescharacteristic
151SD16—21no—
152SD16—861no—
153SD16—861no—
154SD16—861no—
155D8—431no—
156D8—861no—
157D8D17211yescharacteristic
158M16—861no—
159M16—861no—
160C2×C8—431no—
161C2×C8C22×D4311yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—1721no—
164C22⋊C4—1721no—
165C16—21no—
166C16—861no—
167C23—431no—
168C23—1721no—
169Q8—21no—
170Q8—861no—
171Q8—1721no—
172Q8—1721no—
173Q8—1721no—
174D4—21no—
175D4—41no—
176D4—861no—
177D4—1721no—
178D4—1721no—
179D4—1721no—
180D4—1721no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—431no—
184C2×C4—861no—
185C2×C4—861no—
186C2×C4—1721no—
187C2×C4—1721no—
188C2×C4—1721no—
189C2×C4—1721no—
190C2×C4—1721no—
191C2×C4D4×D4311yescharacteristic
192C8—861no—
193C8C2×D17211yescharacteristic
194C8D4×D4311yescharacteristic
195C22—41no—
196C22—861no—
197C22—3442no—
198C22—1721no—
199C22—1721no—
200C22D8×D4311yescharacteristic
201C4—41no—
202C4—81no—
203C4—861no—
204C4—3441no—
205C4—1721no—
206C4#1306329511yescharacteristic
207C4#1306335211yescharacteristic
208C2—21no—
209C2—81no—
210C2—3441no—
211C2—1721no—
212C2#1458303411yescharacteristic
subgroupG/H
centerC2#14583034
commutatorC2×C8×C43C23
FrattiniC2×C8C22×D43
FittingC43×#360C2
socleC2×C43#447
hypercenter#360D43
hypocenterC43#2191
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #14583342C2semidirect
3. #14583339C2semidirect
4. #14583158C2semidirect
5. #14582708C2semidirect
6. #14582680C2semidirect
7. C43×#360C2semidirect
15. C2×Dic172C22semidirect
22. #13063265C22semidirect
25. M32×C43C22semidirect
26. #106×C43C22semidirect
112. #360D43semidirect
114. C43#2191semidirect
131. M32C2×D43semidirect
132. #106C2×D43semidirect