Finite Group Databasebeta

← #25009998

Subgroups — #25009998

Order 11008.

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

normal subgroups only

This group has 372 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
2#19136673C212yesmaximal, complemented
3#19132632C211yesmaximal, characteristic, complemented
4#19132569C212yesmaximal, complemented
5C43×#1709C211yesmaximal, characteristic, complemented
6#14583700—22no—
7#14583340—22no—
8#14583166—22no—
9#14583066—22no—
10#14583017C2212yes—
11#14582720C2212yescomplemented
12#14582715—22no—
13C43×#494C2211yescharacteristic, complemented
14C43×#493C2211yescharacteristic
15C43×#486—22no—
16C82×C43C2211yescharacteristic, complemented
17#13063370—22no—
18#13063351—24no—
19#13063349—44no—
20#13063347D412yes—
21#13063344—42no—
22D8×D43—42no—
23#13063331—22no—
24#13063271—42no—
25#13063268—42no—
26#13063265—22no—
27#13063261D412yes—
28#13063253—22no—
29#13063242—22no—
30C2×Q16×C43—22no—
31C2×D8×C43—22no—
32C4⋊Q8×C43—21no—
33#127×C43D412yes—
34#102×C43—44no—
35C4×C8×C43—21no—
36C4×C8×C43C2311yescharacteristic
37C2×Q8×C43—41no—
38C2×D4×C43—22no—
39C2×D4×C43—42no—
40C2×C22⋊D43—82no—
41#10621900—44no—
42D4×D43—44no—
43#10621898—22no—
44Q16×C43—42no—
45Q16×C43—42no—
46D8×C43—42no—
47D8×C43—42no—
48C2×C8×C43—22no—
49C2×C8×C43C2×D412yes—
50C4⋊C4×C43—42no—
51C42×C43C2×D411yescharacteristic
52#10621883—44no—
53#10621882—44no—
54#10621877—22no—
55Dic172D812yes—
56D344D812yes—
57#10621873—22no—
58#10621872—42no—
59C8×D43—42no—
60C43⋊C16—42no—
61C23×C43—42no—
62C22×D43—82no—
63Q8×C43—82no—
64D4×C43—44no—
65D4×C43—84no—
66C2×C4×C43—21no—
67C2×C4×C43—81no—
68C2×C4×C43#12011yescharacteristic
69C22⋊D43—42no—
70C22⋊D43—84no—
71C2×Dic43—82no—
72D172—22no—
73C4×D43—42no—
74Dic86—22no—
75C8×C43—42no—
76C8×C43C2×D812yes—
77C8×C43AGL(1,ℤ/8)12yes—
78C43⋊C8—42no—
79#12312—431nomaximal, Sylow
80C22×C43—82no—
81C22×C43—162no—
82C22×C43#45311yescharacteristic
83C2×D43—42no—
84C2×D43—322no—
85C4×C43—22no—
86C4×C43—161no—
87C4×C43#44712yes—
88Dic43—42no—
89#3292—431no—
90#2214—432no—
91#1709D4311yescharacteristic, complemented
92#1357—431no—
93#1335—432no—
94C2×C43—21no—
95C2×C43—162no—
96C2×C43#161911yescharacteristic
97D43—82no—
98#576—862no—
99#510—862no—
100#494C2×D4311yescharacteristic, complemented
101#493C2×D4311yescharacteristic
102#486—22no—
103#472—862no—
104#453—862no—
105#443—432no—
106#364—432no—
107#362—862no—
108C82C2×D4311yescharacteristic, complemented
109C43#1231211yescharacteristic, complemented, Sylow
110H(5,𝔽2)—862no—
111AGL(1,ℤ/8)—864no—
112AGL(1,ℤ/8)—1724no—
113#135—432no—
114#135—1722no—
115C2×Q16—22no—
116C2×D8—22no—
117C2×D8—1722no—
118#131—862no—
119C4⋊Q8—21no—
120#127C22⋊D4312yes—
121Q32—1722no—
122SD32—1722no—
123M32—862no—
124#108—432no—
125#104—862no—
126#102—44no—
127#100—862no—
128C4×C8—21no—
129C4×C8C22×D4311yescharacteristic
130#41—862no—
131#41—1724no—
132C2×Q8—41no—
133C2×D4—22no—
134C2×D4—42no—
135C2×D4—3442no—
136C2×D4—1724no—
137Q16—42no—
138Q16—42no—
139Q16—432no—
140SD16—862no—
141SD16—1724no—
142D8—42no—
143D8—42no—
144D8—432no—
145D8—1724no—
146M16—862no—
147M16—1722no—
148C2×C8—22no—
149C2×C8—1722no—
150C2×C8D4×D4312yes—
151C4⋊C4—42no—
152C42C2×C22⋊D4311yescharacteristic
153C16—1722no—
154C23—42no—
155C23—3442no—
156Q8—82no—
157Q8—862no—
158D4—44no—
159D4—84no—
160D4—862no—
161D4—3444no—
162D4—1722no—
163C2×C4—21no—
164C2×C4—81no—
165C2×C4—3442no—
166C2×C4—1722no—
167C2×C4#1306329311yescharacteristic
168C8—42no—
169C8—1722no—
170C8D8×D4312yes—
171C8#1306334912yes—
172C22—82no—
173C22—162no—
174C22—13762no—
175C22—1722no—
176C22#1458306611yescharacteristic
177C4—22no—
178C4—161no—
179C4—1722no—
180C4#1458303112yes—
181C2—21no—
182C2—162no—
183C2—3442no—
184C2#1913364711yescharacteristic
subgroupG/H
centerC2#19133647
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1709C2
socleC2×C43#1619
prime radical#19146394C2
hypercenter#1709D43
hypocenterC43#12312
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1709

Complements

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

NH ≅ G/Ntype
2. #19136673C2semidirect
3. #19132632C2semidirect
4. #19132569C2semidirect
5. C43×#1709C2semidirect
11. #14582720C22semidirect
13. C43×#494C22semidirect
16. C82×C43C22semidirect
91. #1709D43semidirect
100. #494C2×D43semidirect
108. C82C2×D43semidirect
109. C43#12312semidirect

Maximal subgroups

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

subgroupindex
#191463942
#191366732
#191326322
#191325692
C43×#17092
#1231243