Finite Group Databasebeta

← #25011008

Subgroups — #25011008

Order 11008.

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

normal subgroups only

This group has 186 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#19136841C211yesmaximal, characteristic, complemented
2#19136772C211yesmaximal, characteristic
3#19136677C211yesmaximal, characteristic
4#19136438C211yesmaximal, characteristic
5#19132655C211yesmaximal, characteristic, complemented
6#19132633C211yesmaximal, characteristic, complemented
7C43×#1369C211yesmaximal, characteristic, complemented
8#14583342—21no—
9#14583315—21no—
10#14583301C2211yescharacteristic
11#14583279C2211yescharacteristic
12#14583017C2211yescharacteristic
13#14582722—21no—
14#14582720C2211yescharacteristic
15#14582716—21no—
16#14582710—21no—
17#14582704—21no—
18#14582704—21no—
19#14582682—21no—
20C43×#364C2211yescharacteristic
21C43×#364C2211yescharacteristic
22C43×#346C2211yescharacteristic
23#13063347D411yescharacteristic
24C2×Dic172—21no—
25C2×Dic172—21no—
26#13063331—21no—
27#13063325—21no—
28#13063317—21no—
29Dic344—41no—
30#13063270—41no—
31#13063265—21no—
32#13063264—41no—
33C16×D43—41no—
34#13063261D411yescharacteristic
35#13063259—21no—
36#13063257—21no—
37#13063253—21no—
38M32×C43—21no—
39M32×C43—21no—
40C2×C16×C43D411yescharacteristic
41C2×C16×C43D411yescharacteristic
42C4×C8×C43C2311yescharacteristic
43#10621898—21no—
44C2×Dic86—41no—
45C2×C8×C43C2×D411yescharacteristic
46C2×C8×C43C2×D411yescharacteristic
47C42×C43#4111yescharacteristic
48C4⋊Dic43—41no—
49C4⋊Dic43—81no—
50Dic43⋊C4—81no—
51#10621877—21no—
52Dic172—41no—
53Dic172—41no—
54Dic172—41no—
55Dic172—41no—
56Dic172SD1611yescharacteristic
57D344SD1611yescharacteristic
58#10621873—21no—
59#10621872—41no—
60C8×D43—41no—
61C16×C43—21no—
62C16×C43—21no—
63C16×C43—41no—
64C16×C43—41no—
65C43⋊C16—41no—
66C2×C4×C43—21no—
67C2×C4×C43#12111yescharacteristic
68C22⋊D43—41no—
69C2×Dic43—81no—
70C2×Dic43—81no—
71D172—21no—
72C4×D43—41no—
73Dic86—21no—
74Dic86—81no—
75Dic86—81no—
76C8×C43C2×SD1611yescharacteristic
77C8×C43#13511yescharacteristic
78C8×C43#13511yescharacteristic
79C8×C43AGL(1,ℤ/8)11yescharacteristic
80C43⋊C8—41no—
81#12466—431nomaximal, Sylow
82C22×C43#47211yescharacteristic
83C2×D43—41no—
84C4×C43—41no—
85C4×C43#46311yescharacteristic
86C4×C43#46511yescharacteristic
87Dic43—41no—
88Dic43—161no—
89Dic43—161no—
90#2245—431no—
91#2231—431no—
92#2214—431no—
93#2171—431no—
94#1369D4311yescharacteristic, complemented
95#1366—431no—
96#1358—431no—
97C2×C43—21no—
98C2×C43#167711yescharacteristic
99D43—81no—
100#510—861no—
101#504—861no—
102#499—431no—
103#494—431no—
104#443—431no—
105#365—861no—
106#364—431no—
107#364C2×D4311yescharacteristic
108#364C2×D4311yescharacteristic
109#362—861no—
110#360—861no—
111#358—861no—
112#358—861no—
113#350—861no—
114#346C2×D4311yescharacteristic
115C43#1246611yescharacteristic, complemented, Sylow
116#135—431no—
117C2×Q16—861no—
118C2×Q16—861no—
119#131—861no—
120C4⋊Q8—861no—
121#125—861no—
122Q32—1721no—
123SD32—1721no—
124M32—21no—
125M32—21no—
126M32—861no—
127M32—1721no—
128C2×C16—1721no—
129C2×C16D17211yescharacteristic
130C2×C16D17211yescharacteristic
131#108—431no—
132#107—861no—
133#106—861no—
134#104—861no—
135C4×C8C22×D4311yescharacteristic
136#41—861no—
137C2×Q8—1721no—
138Q16—431no—
139Q16—1721no—
140Q16—1721no—
141Q16—1721no—
142Q16—1721no—
143SD16—861no—
144D8—431no—
145M16—861no—
146M16—1721no—
147C2×C8—1721no—
148C2×C8C2×D17211yescharacteristic
149C2×C8D4×D4311yescharacteristic
150C4⋊C4—3441no—
151C4⋊C4—3441no—
152C4⋊C4—1721no—
153C42#1062190211yescharacteristic
154C16—21no—
155C16—21no—
156C16—41no—
157C16—41no—
158C16—1721no—
159Q8—861no—
160Q8—3441no—
161Q8—3441no—
162D4—861no—
163D4—1721no—
164C2×C4—21no—
165C2×C4—3441no—
166C2×C4—3441no—
167C2×C4—1721no—
168C2×C4#1306330011yescharacteristic
169C8—1721no—
170C8SD16×D4311yescharacteristic
171C8#1306334611yescharacteristic
172C8#1306334711yescharacteristic
173C8#1306335311yescharacteristic
174C22—1721no—
175C22#1458317011yescharacteristic
176C4—41no—
177C4—1721no—
178C4—6881no—
179C4—6881no—
180C4#1458311511yescharacteristic
181C4#1458312911yescharacteristic
182C2—21no—
183C2—3441no—
184C2#1913400511yescharacteristic
subgroupG/H
centerC2#19134005
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1369C2
socleC2×C43#1677
prime radical#13063347D4
hypercenter#1369D43
hypocenterC43#12466
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1369

Complements

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

NH ≅ G/Ntype
1. #19136841C2semidirect
5. #19132655C2semidirect
6. #19132633C2semidirect
7. C43×#1369C2semidirect
94. #1369D43semidirect
115. C43#12466semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191368412
#191367722
#191366772
#191364382
#191326552
#191326332
C43×#13692
#1246643