Finite Group Databasebeta

← #25011006

Subgroups — #25011006

Order 11008.

186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 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#19136840C211yesmaximal, characteristic, complemented
2#19136772C211yesmaximal, characteristic
3#19136673C211yesmaximal, characteristic
4#19136436C211yesmaximal, characteristic
5#19132662C211yesmaximal, characteristic, complemented
6#19132657C211yesmaximal, characteristic, complemented
7C43×#1358C211yesmaximal, characteristic, complemented
8#14583340—21no—
9#14583317—21no—
10#14583301C2211yescharacteristic
11#14583017C2211yescharacteristic
12#14582722—21no—
13#14582720C2211yescharacteristic
14#14582715—21no—
15#14582710—21no—
16#14582703—21no—
17#14582703—21no—
18#14582684—21no—
19#14582675C2211yescharacteristic
20C43×#494C2211yescharacteristic
21C43×#364C2211yescharacteristic
22C43×#364C2211yescharacteristic
23#13063347D411yescharacteristic
24#13063331—21no—
25#13063317—21no—
26#13063271—41no—
27#13063268—41no—
28#13063265—21no—
29#13063264—41no—
30C2×C43⋊C16D411yescharacteristic
31C2×C43⋊C16D411yescharacteristic
32C16×D43—41no—
33#13063261D411yescharacteristic
34#13063259—21no—
35#13063257—21no—
36#13063253—21no—
37C2×Q16×C43—21no—
38C2×Q16×C43—21no—
39C4⋊Q8×C43—21no—
40M32×C43—21no—
41M32×C43—21no—
42C4×C8×C43C2311yescharacteristic
43C2×Q8×C43—41no—
44#10621898—21no—
45Q16×C43—41no—
46Q16×C43—41no—
47Q16×C43—41no—
48Q16×C43—41no—
49C2×C8×C43C2×D411yescharacteristic
50C2×C8×C43C2×D411yescharacteristic
51C4⋊C4×C43—81no—
52C42×C43#4111yescharacteristic
53C4⋊Dic43—41no—
54Dic43⋊C4—81no—
55#10621877—21no—
56Dic172SD1611yescharacteristic
57D344SD1611yescharacteristic
58#10621873—21no—
59#10621872—41no—
60C8×D43—41no—
61C16×C43—41no—
62C16×C43—41no—
63C43⋊C16—21no—
64C43⋊C16—21no—
65C43⋊C16—41no—
66Q8×C43—81no—
67Q8×C43—81no—
68C2×C4×C43—21no—
69C2×C4×C43—81no—
70C2×C4×C43#12111yescharacteristic
71C22⋊D43—41no—
72C2×Dic43—81no—
73D172—21no—
74C4×D43—41no—
75Dic86—21no—
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—161no—
86C4×C43#46311yescharacteristic
87C4×C43#46511yescharacteristic
88Dic43—41no—
89Dic43—161no—
90#2245—431no—
91#2231—431no—
92#2214—431no—
93#2171—431no—
94#1369—431no—
95#1366—431no—
96#1358D4311yescharacteristic, complemented
97C2×C43—21no—
98C2×C43#167711yescharacteristic
99D43—81no—
100#510—861no—
101#504—861no—
102#499—431no—
103#494C2×D4311yescharacteristic
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#346—431no—
115C43#1246611yescharacteristic, complemented, Sylow
116#135—431no—
117C2×Q16—21no—
118C2×Q16—21no—
119#131—861no—
120C4⋊Q8—21no—
121#125—861no—
122Q32—1721no—
123SD32—1721no—
124M32—21no—
125M32—21no—
126M32—861no—
127M32—1721no—
128C2×C16—431no—
129C2×C16—431no—
130C2×C16—1721no—
131#108—431no—
132#107—861no—
133#106—861no—
134#104—861no—
135C4×C8C22×D4311yescharacteristic
136#41—861no—
137C2×Q8—41no—
138Q16—41no—
139Q16—41no—
140Q16—41no—
141Q16—41no—
142Q16—431no—
143SD16—861no—
144D8—431no—
145M16—861no—
146M16—1721no—
147C2×C8—1721no—
148C2×C8D4×D4311yescharacteristic
149C2×C8D4×D4311yescharacteristic
150C4⋊C4—81no—
151C4⋊C4—3441no—
152C4⋊C4—1721no—
153C42#1062189811yescharacteristic
154C16—41no—
155C16—41no—
156C16—861no—
157C16—861no—
158C16—1721no—
159Q8—81no—
160Q8—81no—
161Q8—861no—
162D4—861no—
163D4—1721no—
164C2×C4—21no—
165C2×C4—81no—
166C2×C4—3441no—
167C2×C4—1721no—
168C2×C4#1306329811yescharacteristic
169C8—1721no—
170C8SD16×D4311yescharacteristic
171C8#1306334411yescharacteristic
172C8#1306334611yescharacteristic
173C8#1306334911yescharacteristic
174C22—1721no—
175C22#1458316811yescharacteristic
176C4—41no—
177C4—161no—
178C4—1721no—
179C4—6881no—
180C4#1458311311yescharacteristic
181C4#1458312711yescharacteristic
182C2—21no—
183C2—3441no—
184C2#1913400311yescharacteristic
subgroupG/H
centerC2#19134003
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1358C2
socleC2×C43#1677
prime radical#13063347D4
hypercenter#1358D43
hypocenterC43#12466
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
1. #19136840C2semidirect
5. #19132662C2semidirect
6. #19132657C2semidirect
7. C43×#1358C2semidirect
96. #1358D43semidirect
115. C43#12466semidirect

Maximal subgroups

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

subgroupindex
#191368402
#191367722
#191366732
#191364362
#191326622
#191326572
C43×#13582
#1246643