Finite Group Databasebeta

← #25010000

Subgroups — #25010000

Order 11008.

372 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 67 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#19136676C212yesmaximal, complemented
2#19134200C211yesmaximal, characteristic, complemented
3#19132632C211yesmaximal, characteristic, complemented
4#19132568C212yesmaximal, complemented
5C43×#3292C211yesmaximal, characteristic
6#14583339—22no—
7#14583279C2211yescharacteristic, complemented
8#14583245—22no—
9#14582720C2212yescomplemented
10#14582714—22no—
11C8×C43⋊C8C2211yescharacteristic, complemented
12C43×#576—22no—
13C43×#493C2211yescharacteristic
14C43×#472—22no—
15C43×#453—22no—
16C43×#443C2212yes—
17C2×Dic172—22no—
18#13063325—21no—
19#13063271—42no—
20#13063269—42no—
21#13063265—22no—
22#13063246—44no—
23C4×C43⋊C8—21no—
24H(5,𝔽2)×C43—22no—
25AGL(1,ℤ/8)×C43—24no—
26AGL(1,ℤ/8)×C43—44no—
27#135×C43—42no—
28#135×C43D412yes—
29C2×D8×C43—22no—
30C2×D8×C43—42no—
31#131×C43—22no—
32#127×C43D412yes—
33#108×C43D412yes—
34#104×C43—22no—
35#100×C43—22no—
36C4×C8×C43C2311yescharacteristic
37#41×C43—22no—
38#41×C43—44no—
39C2×D4×C43—22no—
40C2×D4×C43—42no—
41C2×D4×C43—44no—
42C2×D4×C43—82no—
43C2×Dic86—41no—
44Q16×C43D812yes—
45SD16×C43—22no—
46SD16×C43—44no—
47D8×C43—44no—
48D8×C43—42no—
49D8×C43—42no—
50D8×C43D812yes—
51M16×C43—22no—
52M16×C43—42no—
53C2×C8×C43—42no—
54C2×C8×C43C2×D412yes—
55C42×C43C2×D411yescharacteristic
56C4⋊Dic43—42no—
57C2×C43⋊C8—22no—
58Dic172—42no—
59Dic172—42no—
60C43⋊C16—42no—
61C23×C43—42no—
62C23×C43—82no—
63Q8×C43—22no—
64D4×C43—22no—
65D4×C43—42no—
66D4×C43—44no—
67D4×C43—84no—
68D4×C43—84no—
69C2×C4×C43—21no—
70C2×C4×C43—42no—
71C2×C4×C43—82no—
72C2×C4×C43#12011yescharacteristic
73C2×Dic43—81no—
74Dic86—82no—
75C8×C43—42no—
76C8×C43C2×D812yes—
77C8×C43AGL(1,ℤ/8)12yes—
78C43⋊C8—42no—
79#12312—431nomaximal, Sylow
80C22×C43—42no—
81C22×C43—82no—
82C22×C43—162no—
83C22×C43—322no—
84C22×C43#45311yescharacteristic
85C4×C43—22no—
86C4×C43—42no—
87C4×C43#44712yes—
88Dic43—161no—
89#3292D4311yescharacteristic
90#2214—432no—
91#1709—431no—
92#1357—431no—
93#1335—432no—
94C2×C43—21no—
95C2×C43—82no—
96C2×C43—162no—
97C2×C43#161911yescharacteristic
98#576—22no—
99#510—862no—
100#494—431no—
101#493C2×D4311yescharacteristic
102#486—862no—
103#472—22no—
104#453—22no—
105#443C2×D4312yes—
106#364—432no—
107#362—862no—
108C82—431no—
109C43#1231211yescharacteristic, complemented, Sylow
110H(5,𝔽2)—22no—
111AGL(1,ℤ/8)—24no—
112AGL(1,ℤ/8)—44no—
113#135—42no—
114#135C22⋊D4312yes—
115C2×Q16—862no—
116C2×D8—22no—
117C2×D8—42no—
118#131—22no—
119C4⋊Q8—861no—
120#127C22⋊D4312yes—
121Q32—1722no—
122SD32—1722no—
123M32—862no—
124#108C22⋊D4312yes—
125#104—22no—
126#102—1724no—
127#100—22no—
128C4×C8—861no—
129C4×C8C22×D4311yescharacteristic
130#41—22no—
131#41—44no—
132C2×Q8—1721no—
133C2×D4—22no—
134C2×D4—42no—
135C2×D4—44no—
136C2×D4—82no—
137Q16—1722no—
138Q16—1722no—
139Q16#1062188212yes—
140SD16—22no—
141SD16—44no—
142D8—44no—
143D8—42no—
144D8—42no—
145D8#1062188212yes—
146M16—22no—
147M16—42no—
148C2×C8—42no—
149C2×C8—862no—
150C2×C8C2×C22⋊D4312yes—
151C4⋊C4—1722no—
152C42C2×C22⋊D4311yescharacteristic
153C16—1722no—
154C23—42no—
155C23—82no—
156Q8—22no—
157Q8—3442no—
158D4—22no—
159D4—42no—
160D4—44no—
161D4—84no—
162D4—84no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—82no—
166C2×C4—3441no—
167C2×C4#1306329411yescharacteristic
168C8—42no—
169C8—1722no—
170C8C2×#1062188212yes—
171C8#1306335112yes—
172C22—42no—
173C22—82no—
174C22—162no—
175C22—322no—
176C22#1458306711yescharacteristic
177C4—22no—
178C4—42no—
179C4—6881no—
180C4#1458303312yes—
181C2—21no—
182C2—82no—
183C2—162no—
184C2#1913364911yescharacteristic
subgroupG/H
centerC2#19133649
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
Fitting, prime radicalC43×#3292C2
socleC2×C43#1619
hypercenter#3292D43
hypocenterC43#12312
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #3292

Complements

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

NH ≅ G/Ntype
1. #19136676C2semidirect
2. #19134200C2semidirect
3. #19132632C2semidirect
4. #19132568C2semidirect
7. #14583279C22semidirect
9. #14582720C22semidirect
11. C8×C43⋊C8C22semidirect
109. C43#12312semidirect

Maximal subgroups

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

subgroupindex
#191366762
#191342002
#191326322
#191325682
C43×#32922
#1231243