Finite Group Databasebeta

← #19133831

Subgroups — #19133831

Order 5504.

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

normal subgroups only

This group has 240 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#14583552C211yesmaximal, characteristic
2#14583302C211yesmaximal, characteristic, complemented
3#14583180C211yesmaximal, characteristic, complemented
4#14583105C211yesmaximal, characteristic, complemented
5#14582626C211yesmaximal, characteristic, complemented
6#14582626C211yesmaximal, characteristic, complemented
7C43×#332C211yesmaximal, characteristic, complemented
8C2×#10621902—21no—
9C2×#10621873—21no—
10#13063325C2211yescharacteristic
11#13063310—22no—
12#13063301—21no—
13#13063300—21no—
14C4×D172C2211yescharacteristic
15C4×D172C2211yescharacteristic
16C4⋊C4×D43—21no—
17#13063259—21no—
18#13063258—22no—
19#13063250—21no—
20#13063247—21no—
21C4×C43⋊C8C2211yescharacteristic
22C4⋊Q8×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4⋊C8×C43C2211yescharacteristic
25C2×Q8×C43—21no—
26#10621902—42no—
27#10621902—42no—
28C2×D172—22no—
29C2×D172D411yescharacteristic
30C2×D172D411yescharacteristic
31C2×C4×D43—22no—
32C2×C4×D43—21no—
33C2×C4×D43—21no—
34C2×Dic86—21no—
35C2×C8×C43—21no—
36C2×C8×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43D412yes—
39C42×C43C2311yescharacteristic
40(C2×D43)⋊C4—22no—
41(C2×D43)⋊C4—21no—
42(C2×D43)⋊C4—21no—
43C4⋊Dic43—21no—
44C4⋊Dic43—21no—
45C4⋊Dic43D411yescharacteristic
46C4⋊Dic43D411yescharacteristic
47Dic43⋊C4—22no—
48C2×C43⋊C8—21no—
49#10621873—42no—
50C22×D43—21no—
51C22×D43—21no—
52Q8×C43—41no—
53Q8×C43—41no—
54C2×C4×C43—22no—
55C2×C4×C43C2×D411yescharacteristic
56C2×C4×C43C2×D411yescharacteristic
57C2×C4×C43C2×D411yescharacteristic
58C2×Dic43—21no—
59C2×Dic43—21no—
60C2×Dic43—41no—
61D172—21no—
62D172—21no—
63D172—21no—
64D172—44no—
65D172D812yes—
66C4×D43—44no—
67C4×D43—41no—
68C4×D43—41no—
69C4×D43—41no—
70C4×D43—41no—
71Dic86—41no—
72Dic86—41no—
73C8×C43—41no—
74C8×C43—41no—
75C43⋊C8—22no—
76C22×C43#12011yescharacteristic
77C2×D43—22no—
78C2×D43—41no—
79C2×D43—41no—
80C2×D43—41no—
81C2×D43—41no—
82C2×D43—41no—
83C4×C43—21no—
84C4×C43—42no—
85C4×C43C2×D811yescharacteristic
86C4×C43#13511yescharacteristic
87C4×C43AGL(1,ℤ/8)11yescharacteristic
88C4×C43#13711yescharacteristic
89Dic43—41no—
90Dic43—41no—
91Dic43—81no—
92#1647—431nomaximal, Sylow
93C2×C43#44711yescharacteristic
94C2×C43#45211yescharacteristic
95C2×C43#45611yescharacteristic
96D43—42no—
97D43—81no—
98#547—431no—
99#500—431no—
100#474—431no—
101#461—431no—
102#332D4311yescharacteristic, complemented
103D4⋊C8—431no—
104D4⋊C8—431no—
105C43#164711yescharacteristic, complemented, Sylow
106C2×#41—861no—
107C2×SD16—861no—
108C4⋊Q8—431no—
109C4⋊Q8C2×D4311yescharacteristic
110#123—862no—
111C22⋊Q8—861no—
112#121—861no—
113C4×D4—431no—
114C4×D4—431no—
115C2×C4⋊C4—861no—
116#107—861no—
117#107—862no—
118C4⋊C8C2×D4311yescharacteristic
119C4⋊C8C2×D4311yescharacteristic
120#103—861no—
121#102—861no—
122C4×C8—431no—
123#41—1722no—
124#41—1722no—
125C2×Q8—21no—
126C2×Q8—861no—
127C2×D4—431no—
128C2×D4—431no—
129C2×D4—862no—
130C22×C4—862no—
131C22×C4—861no—
132C22×C4—861no—
133SD16—1722no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—861no—
137C4⋊C4—21no—
138C4⋊C4—431no—
139C4⋊C4—431no—
140C4⋊C4—862no—
141C4⋊C4—861no—
142C4⋊C4—861no—
143C4⋊C4D17212yes—
144C22⋊C4—862no—
145C22⋊C4—861no—
146C22⋊C4—861no—
147C42C22×D4311yescharacteristic
148C23—861no—
149C23—861no—
150Q8—41no—
151Q8—41no—
152Q8—1721no—
153Q8—1721no—
154D4—432no—
155D4—861no—
156D4—861no—
157D4—861no—
158D4—1724no—
159C2×C4—22no—
160C2×C4—861no—
161C2×C4—861no—
162C2×C4—1724no—
163C2×C4—1721no—
164C2×C4—1721no—
165C2×C4—1721no—
166C2×C4—1721no—
167C2×C4—1721no—
168C2×C4C2×D17211yescharacteristic
169C2×C4D4×D4311yescharacteristic
170C2×C4D4×D4311yescharacteristic
171C8—41no—
172C8—41no—
173C8—862no—
174C22—862no—
175C22—1721no—
176C22—1721no—
177C22—1721no—
178C22—1721no—
179C22—1721no—
180C22#1306329511yescharacteristic
181C4—21no—
182C4—42no—
183C4—3441no—
184C4—1721no—
185C4—1721no—
186C4D8×D4311yescharacteristic
187C4#1306334611yescharacteristic
188C4#1306335211yescharacteristic
189C4#1306335711yescharacteristic
190C2—3441no—
191C2—1722no—
192C2#1458303411yescharacteristic
193C2#1458306411yescharacteristic
194C2#1458308411yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#332C2
socleC22×C43#120
hypercenter#332D43
hypocenterC43#1647
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #14583302C2semidirect
3. #14583180C2semidirect
4. #14583105C2semidirect
5. #14582626C2semidirect
6. #14582626C2semidirect
7. C43×#332C2semidirect
102. #332D43semidirect
105. C43#1647semidirect