Finite Group Databasebeta

← #25011003

Subgroups — #25011003

Order 11008.

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

normal subgroups only

This group has 196 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#19136838C211yesmaximal, characteristic, complemented
2#19136768C211yesmaximal, characteristic, complemented
3#19136672C211yesmaximal, characteristic
4#19136436C211yesmaximal, characteristic, complemented
5#19132662C211yesmaximal, characteristic, complemented
6#19132631C211yesmaximal, characteristic, complemented
7C43×#1366C211yesmaximal, characteristic, complemented
8#14583337—21no—
9#14583317—21no—
10#14583276C2211yescharacteristic
11#14583017C2211yescharacteristic
12#14582721—21no—
13#14582720C2211yescharacteristic
14#14582713—21no—
15#14582708—21no—
16#14582699—21no—
17#14582699—21no—
18#14582684—21no—
19#14582675C2211yescharacteristic
20C43×#499C2211yescharacteristic
21C43×#364C2211yescharacteristic
22C43×#364C2211yescharacteristic
23#13063347D411yescharacteristic
24C2×D344—21no—
25C2×D344—21no—
26#13063331—21no—
27#13063322—21no—
28#13063270—41no—
29D688—41no—
30#13063265—21no—
31#13063264—41no—
32C2×C43⋊C16D411yescharacteristic
33C2×C43⋊C16D411yescharacteristic
34C16×D43—41no—
35#13063261D411yescharacteristic
36#13063253—21no—
37#125×C43—21no—
38M32×C43—21no—
39M32×C43—21no—
40#107×C43—21no—
41#106×C43—21no—
42C4×C8×C43C2311yescharacteristic
43#10621898—21no—
44C2×D172—41no—
45C2×D172—81no—
46C2×C8×C43C2×D411yescharacteristic
47C2×C8×C43C2×D411yescharacteristic
48C4⋊C4×C43—41no—
49C4⋊C4×C43—81no—
50C42×C43#4111yescharacteristic
51#10621877—21no—
52Dic172SD1611yescharacteristic
53D344—41no—
54D344—41no—
55D344—41no—
56D344—41no—
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—
66C22×D43—81no—
67C2×C4×C43—21no—
68C2×C4×C43—81no—
69C2×C4×C43#12111yescharacteristic
70C22⋊D43—41no—
71D172—21no—
72D172—81no—
73D172—81no—
74D172—162no—
75C4×D43—41no—
76Dic86—21no—
77C8×C43C2×SD1611yescharacteristic
78C8×C43#13511yescharacteristic
79C8×C43#13511yescharacteristic
80C8×C43AGL(1,ℤ/8)11yescharacteristic
81C43⋊C8—41no—
82#12465—431nomaximal, Sylow
83C22×C43#47211yescharacteristic
84C2×D43—41no—
85C2×D43—162no—
86C2×D43—161no—
87C4×C43—41no—
88C4×C43—161no—
89C4×C43#46311yescharacteristic
90C4×C43#46511yescharacteristic
91Dic43—41no—
92#2244—431no—
93#2231—431no—
94#2213—431no—
95#2171—431no—
96#1369—431no—
97#1366D4311yescharacteristic, complemented
98#1357—431no—
99C2×C43—21no—
100C2×C43#167711yescharacteristic
101D43—81no—
102D43—321no—
103#509—861no—
104#504—861no—
105#499C2×D4311yescharacteristic
106#493—431no—
107#443—431no—
108#365—861no—
109#364—431no—
110#364C2×D4311yescharacteristic
111#364C2×D4311yescharacteristic
112#361—861no—
113#360—861no—
114#357—861no—
115#357—861no—
116#350—861no—
117#346—431no—
118C43#1246511yescharacteristic, complemented, Sylow
119#135—431no—
120C2×D8—861no—
121C2×D8—861no—
122#131—861no—
123#127—861no—
124#125—21no—
125SD32—1721no—
126D16—1721no—
127M32—21no—
128M32—21no—
129M32—861no—
130M32—1721no—
131C2×C16—431no—
132C2×C16—431no—
133C2×C16—1721no—
134#108—431no—
135#107—21no—
136#106—21no—
137#104—861no—
138C4×C8C22×D4311yescharacteristic
139#41—861no—
140C2×D4—3441no—
141C2×D4—1721no—
142Q16—431no—
143SD16—861no—
144D8—431no—
145D8—1721no—
146D8—1721no—
147D8—1721no—
148D8—1721no—
149M16—861no—
150M16—1721no—
151C2×C8—1721no—
152C2×C8D4×D4311yescharacteristic
153C2×C8D4×D4311yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—81no—
156C42#1062189811yescharacteristic
157C16—41no—
158C16—41no—
159C16—861no—
160C16—861no—
161C16—1721no—
162C23—3441no—
163Q8—861no—
164D4—861no—
165D4—3441no—
166D4—3441no—
167D4—1721no—
168D4—6882no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—1721no—
172C2×C4#1306329811yescharacteristic
173C8—1721no—
174C8SD16×D4311yescharacteristic
175C8#1306334811yescharacteristic
176C8#1306334811yescharacteristic
177C8#1306335211yescharacteristic
178C22—1721no—
179C22—6882no—
180C22—6881no—
181C22#1458316811yescharacteristic
182C4—41no—
183C4—161no—
184C4—1721no—
185C4#1458311711yescharacteristic
186C4#1458313111yescharacteristic
187C2—21no—
188C2—3441no—
189C2—13761no—
190C2#1913400711yescharacteristic
subgroupG/H
centerC2#19134007
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1366C2
socleC2×C43#1677
prime radical#19136672C2
hypercenter#1366D43
hypocenterC43#12465
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
1. #19136838C2semidirect
2. #19136768C2semidirect
4. #19136436C2semidirect
5. #19132662C2semidirect
6. #19132631C2semidirect
7. C43×#1366C2semidirect
97. #1366D43semidirect
118. C43#12465semidirect

Maximal subgroups

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

subgroupindex
#191368382
#191367682
#191366722
#191364362
#191326622
#191326312
C43×#13662
#1246543