Finite Group Databasebeta

← #25010997

Subgroups — #25010997

Order 11008.

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

normal subgroups only

This group has 196 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#19136768C211yesmaximal, characteristic, complemented
2#19136668C211yesmaximal, characteristic
3#19136438C211yesmaximal, characteristic, complemented
4#19132663C211yesmaximal, characteristic, complemented
5#19132656C211yesmaximal, characteristic, complemented
6#19132632C211yesmaximal, characteristic, complemented
7C43×#2244C211yesmaximal, characteristic, complemented
8#14583335—21no—
9#14583315—21no—
10#14583017C2211yescharacteristic
11#14582721—21no—
12#14582720C2211yescharacteristic
13#14582720C2211yescharacteristic
14#14582720C2211yescharacteristic
15#14582712—21no—
16#14582708—21no—
17#14582682—21no—
18C43×#499C2211yescharacteristic
19C43×#493C2211yescharacteristic
20C43×#357—21no—
21C43×#357—21no—
22C43×#346C2211yescharacteristic
23#13063347D411yescharacteristic
24#13063331—21no—
25#13063269—41no—
26#13063266—41no—
27#13063265—21no—
28#13063265—21no—
29#13063265—21no—
30#13063264—41no—
31C16×D43—41no—
32#13063261D411yescharacteristic
33#13063253—21no—
34C2×D8×C43—21no—
35C2×D8×C43—21no—
36#127×C43—21no—
37#125×C43—21no—
38C2×C16×C43D411yescharacteristic
39C2×C16×C43D411yescharacteristic
40#107×C43—21no—
41#106×C43—21no—
42C4×C8×C43C2311yescharacteristic
43C2×D4×C43—41no—
44C2×D4×C43—81no—
45#10621898—21no—
46D8×C43—41no—
47D8×C43—41no—
48D8×C43—41no—
49D8×C43—41no—
50C2×C8×C43C2×D411yescharacteristic
51C2×C8×C43C2×D411yescharacteristic
52C4⋊C4×C43—41no—
53C4⋊C4×C43—81no—
54C42×C43#4111yescharacteristic
55#10621877—21no—
56Dic172SD1611yescharacteristic
57D344SD1611yescharacteristic
58#10621873—21no—
59#10621872—41no—
60C8×D43—41no—
61C16×C43—21no—
62C16×C43—21no—
63C43⋊C16—41no—
64C43⋊C16—41no—
65C43⋊C16—41no—
66C23×C43—81no—
67D4×C43—81no—
68D4×C43—81no—
69D4×C43—162no—
70C2×C4×C43—21no—
71C2×C4×C43—81no—
72C2×C4×C43#12111yescharacteristic
73C22⋊D43—41no—
74D172—21no—
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—162no—
84C22×C43—161no—
85C22×C43#47211yescharacteristic
86C2×D43—41no—
87C4×C43—41no—
88C4×C43—161no—
89C4×C43#46311yescharacteristic
90C4×C43#46511yescharacteristic
91Dic43—41no—
92#2244D4311yescharacteristic, complemented
93#2231—431no—
94#2213—431no—
95#2171—431no—
96#1369—431no—
97#1366—431no—
98#1357—431no—
99C2×C43—21no—
100C2×C43—321no—
101C2×C43#167711yescharacteristic
102D43—81no—
103#509—861no—
104#504—861no—
105#499C2×D4311yescharacteristic
106#493C2×D4311yescharacteristic
107#443—431no—
108#365—861no—
109#364—431no—
110#364—431no—
111#364—431no—
112#361—861no—
113#360—861no—
114#357—21no—
115#357—21no—
116#350—861no—
117#346C2×D4311yescharacteristic
118C43#1246511yescharacteristic, complemented, Sylow
119#135—431no—
120C2×D8—21no—
121C2×D8—21no—
122#131—861no—
123#127—21no—
124#125—21no—
125SD32—1721no—
126D16—1721no—
127M32—861no—
128M32—861no—
129M32—861no—
130M32—1721no—
131C2×C16—1721no—
132C2×C16C22⋊D4311yescharacteristic
133C2×C16C22⋊D4311yescharacteristic
134#108—431no—
135#107—21no—
136#106—21no—
137#104—861no—
138C4×C8C22×D4311yescharacteristic
139#41—861no—
140C2×D4—41no—
141C2×D4—81no—
142Q16—431no—
143SD16—861no—
144D8—41no—
145D8—41no—
146D8—41no—
147D8—41no—
148D8—431no—
149M16—861no—
150M16—1721no—
151C2×C8—1721no—
152C2×C8D4×D4311yescharacteristic
153C2×C8C2×C22⋊D4311yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—81no—
156C42#1062190011yescharacteristic
157C16—21no—
158C16—21no—
159C16—1721no—
160C16—1721no—
161C16—1721no—
162C23—81no—
163Q8—861no—
164D4—81no—
165D4—81no—
166D4—162no—
167D4—861no—
168D4—1721no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—1721no—
172C2×C4#1306329611yescharacteristic
173C8—1721no—
174C8SD16×D4311yescharacteristic
175C8#1306334511yescharacteristic
176C8#1306334611yescharacteristic
177C8#1306335011yescharacteristic
178C22—162no—
179C22—161no—
180C22—1721no—
181C22#1458316611yescharacteristic
182C4—41no—
183C4—161no—
184C4—1721no—
185C4#1458311111yescharacteristic
186C4#1458312511yescharacteristic
187C2—21no—
188C2—321no—
189C2—3441no—
190C2#1913400111yescharacteristic
subgroupG/H
centerC2#19134001
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2244C2
socleC2×C43#1677
prime radical#19136668C2
hypercenter#2244D43
hypocenterC43#12465
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2244

Complements

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

NH ≅ G/Ntype
1. #19136768C2semidirect
3. #19136438C2semidirect
4. #19132663C2semidirect
5. #19132656C2semidirect
6. #19132632C2semidirect
7. C43×#2244C2semidirect
92. #2244D43semidirect
118. C43#12465semidirect

Maximal subgroups

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

subgroupindex
#191367682
#191366682
#191364382
#191326632
#191326562
#191326322
C43×#22442
#1246543