Finite Group Databasebeta

← #19133859

Subgroups — #19133859

Order 5504.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#14583564C211yesmaximal, characteristic
2#14583295C211yesmaximal, characteristic, complemented
3#14583185C211yesmaximal, characteristic, complemented
4#14583105C211yesmaximal, characteristic
5#14582629C211yesmaximal, characteristic, complemented
6#14582626C211yesmaximal, characteristic
7C43×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D43—21no—
9C2×#10621873—21no—
10#13063325C2211yescharacteristic
11#13063324—21no—
12#13063303—22no—
13#13063301—21no—
14C4×Dic86C2211yescharacteristic
15C4×D172C2211yescharacteristic
16#13063287—21no—
17#13063257—21no—
18#13063256—22no—
19#13063250—21no—
20#13063250—21no—
21C4×C43⋊C8C2211yescharacteristic
22C4⋊Q8×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4⋊C8×C43C2211yescharacteristic
25C2×Q8×C43—21no—
26Q8×D43—42no—
27Q8×D43—42no—
28C2×D172D411yescharacteristic
29C2×C4×D43—22no—
30C2×C4×D43—21no—
31C2×Dic86—22no—
32C2×Dic86—21no—
33C2×Dic86D411yescharacteristic
34C2×C8×C43—21no—
35C2×C8×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43D412yes—
38C42×C43C2311yescharacteristic
39(C2×D43)⋊C4—22no—
40(C2×D43)⋊C4—21no—
41C4⋊Dic43—21no—
42C4⋊Dic43—21no—
43C4⋊Dic43D411yescharacteristic
44C4⋊Dic43D411yescharacteristic
45Dic43⋊C4—22no—
46Dic43⋊C4—21no—
47C4×Dic43—21no—
48C2×C43⋊C8—21no—
49#10621873—42no—
50C22×D43—21no—
51Q8×C43—41no—
52Q8×C43—41no—
53C2×C4×C43—22no—
54C2×C4×C43C2×D411yescharacteristic
55C2×C4×C43C2×D411yescharacteristic
56C2×C4×C43C2×D411yescharacteristic
57C2×Dic43—21no—
58C2×Dic43—21no—
59C2×Dic43—21no—
60C2×Dic43—41no—
61D172—21no—
62D172SD1612yes—
63C4×D43—44no—
64C4×D43—41no—
65C4×D43—41no—
66Dic86—21no—
67Dic86—44no—
68Dic86—41no—
69Dic86—41no—
70Dic86SD1612yescomplemented
71C8×C43—41no—
72C8×C43—41no—
73C43⋊C8—22no—
74C22×C43#12011yescharacteristic
75C2×D43—22no—
76C2×D43—41no—
77C2×D43—41no—
78C4×C43—21no—
79C4×C43—42no—
80C4×C43C2×SD1611yescharacteristic
81C4×C43C2×SD1611yescharacteristic
82C4×C43AGL(1,ℤ/8)11yescharacteristic
83C4×C43#13711yescharacteristic
84Dic43—22no—
85Dic43—41no—
86Dic43—41no—
87Dic43—81no—
88#1651—431nomaximal, Sylow
89C2×C43#44811yescharacteristic
90C2×C43#45011yescharacteristic
91C2×C43#45611yescharacteristic
92D43—42no—
93D4×Q8—431no—
94#498—431no—
95#475—431no—
96#461—431no—
97#332D4311yescharacteristic, complemented
98Q8⋊C8—431no—
99D4⋊C8—431no—
100C43#165111yescharacteristic, complemented, Sylow
101C22×Q8—861no—
102C2×SD16—861no—
103C4⋊Q8—431no—
104C4⋊Q8—861no—
105C4⋊Q8C2×D4311yescharacteristic
106C22⋊Q8—861no—
107C22⋊Q8—862no—
108C4×Q8—431no—
109C4×D4—431no—
110C4×D4—861no—
111#106—861no—
112#106—862no—
113C4⋊C8C2×D4311yescharacteristic
114C4⋊C8C2×D4311yescharacteristic
115#103—861no—
116#103—861no—
117C4×C8—431no—
118C2×Q8—21no—
119C2×Q8—431no—
120C2×Q8—862no—
121C2×Q8—861no—
122C2×Q8—1722no—
123C2×Q8—1722no—
124C2×D4—431no—
125C22×C4—862no—
126C22×C4—861no—
127SD16—1722no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—861no—
131C4⋊C4—21no—
132C4⋊C4—431no—
133C4⋊C4—431no—
134C4⋊C4—862no—
135C4⋊C4—861no—
136C4⋊C4—861no—
137C4⋊C4—861no—
138C4⋊C4D17212yes—
139C22⋊C4—862no—
140C22⋊C4—861no—
141C42—861no—
142C42C22×D4311yescharacteristic
143C23—861no—
144Q8—41no—
145Q8—41no—
146Q8—432no—
147Q8—861no—
148Q8—1724no—
149Q8—1721no—
150Q8—1721no—
151D4—432no—
152D4—861no—
153C2×C4—22no—
154C2×C4—861no—
155C2×C4—861no—
156C2×C4—861no—
157C2×C4—1724no—
158C2×C4—1721no—
159C2×C4—1721no—
160C2×C4—1721no—
161C2×C4C2×D17211yescharacteristic
162C2×C4D4×D4311yescharacteristic
163C2×C4D4×D4311yescharacteristic
164C8—41no—
165C8—41no—
166C8—862no—
167C22—862no—
168C22—1721no—
169C22—1721no—
170C22#1306329511yescharacteristic
171C4—21no—
172C4—42no—
173C4—862no—
174C4—3441no—
175C4—1721no—
176C4—1721no—
177C4SD16×D4311yescharacteristic
178C4SD16×D4311yescharacteristic
179C4#1306334911yescharacteristic
180C4#1306335711yescharacteristic
181C2—1722no—
182C2#1458303911yescharacteristic
183C2#1458305111yescharacteristic
184C2#1458308411yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#332C2
socleC22×C43#120
hypercenter#332D43
hypocenterC43#1651
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. #14583295C2semidirect
3. #14583185C2semidirect
5. #14582629C2semidirect
7. C43×#332C2semidirect
70. Dic86SD16semidirect
97. #332D43semidirect
100. C43#1651semidirect