Finite Group Databasebeta

← #25009988

Subgroups — #25009988

Order 11008.

406 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 59 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#19146394C211yesmaximal, characteristic, complemented
2#19136668C212yesmaximal, complemented
3#19132632C211yesmaximal, characteristic, complemented
4#19132569C212yesmaximal, complemented
5C43×#1712C211yesmaximal, characteristic, complemented
6#14583700—22no—
7#14583335—22no—
8#14583166—22no—
9#14583066—22no—
10#14583017C2212yes—
11#14582720C2212yescomplemented
12#14582712—22no—
13C43×#493—22no—
14C43×#493C2211yescharacteristic
15C43×#493C2211yescharacteristic, complemented
16C82×C43C2211yescharacteristic, complemented
17#13063370—22no—
18#13063351—24no—
19#13063349—44no—
20#13063347D412yes—
21#13063344—42no—
22D8×D43—42no—
23#13063331—22no—
24#13063269—42no—
25#13063266—42no—
26#13063265—22no—
27#13063261D412yes—
28#13063253—22no—
29#13063242—22no—
30C2×D8×C43—22no—
31C2×D8×C43—22no—
32C2×D8×C43—44no—
33#127×C43—21no—
34#127×C43D412yes—
35C4×C8×C43—21no—
36C4×C8×C43C2311yescharacteristic
37C2×D4×C43—22no—
38C2×D4×C43—42no—
39C2×D4×C43—42no—
40C2×D4×C43—41no—
41C2×C22⋊D43—82no—
42#10621900—44no—
43D4×D43—44no—
44#10621898—22no—
45D8×C43—42no—
46D8×C43—42no—
47D8×C43—42no—
48D8×C43—42no—
49D8×C43—88no—
50C2×C8×C43—22no—
51C2×C8×C43C2×D412yes—
52C42×C43C2×D411yescharacteristic
53#10621883—44no—
54#10621882—44no—
55#10621877—22no—
56Dic172D812yescomplemented
57D344D812yescomplemented
58#10621873—22no—
59#10621872—42no—
60C8×D43—42no—
61C43⋊C16—42no—
62C23×C43—42no—
63C23×C43—81no—
64C22×D43—82no—
65D4×C43—44no—
66D4×C43—84no—
67D4×C43—84no—
68D4×C43—82no—
69C2×C4×C43—21no—
70C2×C4×C43#12011yescharacteristic
71C22⋊D43—42no—
72C22⋊D43—84no—
73C2×Dic43—82no—
74D172—22no—
75C4×D43—42no—
76Dic86—22no—
77C8×C43—24no—
78C8×C43C2×D812yes—
79C8×C43AGL(1,ℤ/8)12yes—
80C43⋊C8—42no—
81#12310—431nomaximal, Sylow
82C22×C43—82no—
83C22×C43—162no—
84C22×C43—162no—
85C22×C43—161no—
86C22×C43#45311yescharacteristic
87C2×D43—42no—
88C2×D43—322no—
89C4×C43—22no—
90C4×C43#44712yes—
91Dic43—42no—
92#3292—431no—
93#2213—432no—
94#1712D4311yescharacteristic, complemented
95#1357—431no—
96#1335—432no—
97C2×C43—21no—
98C2×C43—162no—
99C2×C43—321no—
100C2×C43#161911yescharacteristic
101D43—82no—
102#576—862no—
103#509—862no—
104#493—22no—
105#493C2×D4311yescharacteristic
106#493C2×D4311yescharacteristic, complemented
107#472—862no—
108#453—862no—
109#443—432no—
110#364—432no—
111#361—862no—
112C82C2×D4311yescharacteristic, complemented
113C43#1231011yescharacteristic, complemented, Sylow
114H(5,𝔽2)—862no—
115AGL(1,ℤ/8)—864no—
116AGL(1,ℤ/8)—1724no—
117#135—432no—
118#135—1722no—
119C2×D8—22no—
120C2×D8—22no—
121C2×D8—44no—
122C2×D8—1722no—
123#131—862no—
124#127—21no—
125#127C22⋊D4312yes—
126SD32—1722no—
127D16—1722no—
128M32—862no—
129#108—432no—
130#104—862no—
131#100—862no—
132C4×C8—21no—
133C4×C8C22×D4311yescharacteristic
134#41—862no—
135#41—1724no—
136C2×D4—22no—
137C2×D4—42no—
138C2×D4—42no—
139C2×D4—41no—
140C2×D4—3442no—
141C2×D4—1724no—
142Q16—432no—
143SD16—862no—
144SD16—1724no—
145D8—42no—
146D8—42no—
147D8—42no—
148D8—42no—
149D8—88no—
150D8—432no—
151D8—1724no—
152M16—862no—
153M16—1722no—
154C2×C8—22no—
155C2×C8—1722no—
156C2×C8D4×D4312yes—
157C42C2×C22⋊D4311yescharacteristic
158C16—1722no—
159C23—42no—
160C23—81no—
161C23—3442no—
162Q8—862no—
163D4—44no—
164D4—84no—
165D4—84no—
166D4—82no—
167D4—862no—
168D4—3444no—
169D4—1722no—
170C2×C4—21no—
171C2×C4—3442no—
172C2×C4—1722no—
173C2×C4#1306329311yescharacteristic
174C8—24no—
175C8—1722no—
176C8D8×D4312yes—
177C8#1306334912yes—
178C22—82no—
179C22—162no—
180C22—162no—
181C22—161no—
182C22—13762no—
183C22—1722no—
184C22#1458306611yescharacteristic
185C4—22no—
186C4—1722no—
187C4#1458303112yes—
188C2—21no—
189C2—162no—
190C2—321no—
191C2—3442no—
192C2#1913364711yescharacteristic
subgroupG/H
centerC2#19133647
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1712C2
socleC2×C43#1619
hypercenter#1712D43
hypocenterC43#12310
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1712

Complements

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

NH ≅ G/Ntype
1. #19146394C2semidirect
2. #19136668C2semidirect
3. #19132632C2semidirect
4. #19132569C2semidirect
5. C43×#1712C2semidirect
11. #14582720C22semidirect
15. C43×#493C22semidirect
16. C82×C43C22semidirect
56. Dic172D8semidirect
57. D344D8semidirect
94. #1712D43semidirect
106. #493C2×D43semidirect
112. C82C2×D43semidirect
113. C43#12310semidirect

Maximal subgroups

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

subgroupindex
#191463942
#191366682
#191326322
#191325692
C43×#17122
#1231043