Finite Group Databasebeta

← #25009995

Subgroups — #25009995

Order 11008.

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

normal subgroups only

This group has 366 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#19136671C212yesmaximal, complemented
2#19134202C211yesmaximal, characteristic, complemented
3#19132634C211yesmaximal, characteristic, complemented
4#19132568C212yesmaximal, complemented
5C43×#3293C211yesmaximal, characteristic, complemented
6#14583334—22no—
7#14583276C2211yescharacteristic
8#14583247—22no—
9#14582720C2212yes—
10#14582711—22no—
11C8×C43⋊C8C2211yescharacteristic
12C43×#578—22no—
13C43×#494C2211yescharacteristic
14C43×#473—22no—
15C43×#456—22no—
16C43×#443C2212yes—
17C2×D344—22no—
18#13063322—21no—
19#13063268—42no—
20#13063266—42no—
21#13063265—22no—
22#13063245—44no—
23C4×C43⋊C8—21no—
242−1+4×C43—22no—
25#137×C43—24no—
26#137×C43—44no—
27#135×C43—42no—
28#135×C43D412yes—
29C2×Q16×C43—22no—
30C2×Q16×C43—42no—
31#131×C43—22no—
32C4⋊Q8×C43D412yes—
33#108×C43D412yes—
34#104×C43—22no—
35#101×C43—22no—
36C4×C8×C43C2311yescharacteristic
37#41×C43—22no—
38#41×C43—44no—
39#41×C43—82no—
40C2×Q8×C43—22no—
41C2×Q8×C43—44no—
42C2×D172—42no—
43C2×D172—41no—
44Q16×C43—44no—
45Q16×C43—42no—
46Q16×C43—42no—
47Q16×C43D812yes—
48SD16×C43—22no—
49SD16×C43—44no—
50D8×C43D812yes—
51M16×C43—22no—
52M16×C43—42no—
53C2×C8×C43—42no—
54C2×C8×C43C2×D412yes—
55C4⋊C4×C43—42no—
56C42×C43C2×D411yescharacteristic
57C2×C43⋊C8—22no—
58D344—42no—
59D344—42no—
60C43⋊C16—42no—
61C22×D43—81no—
62Q8×C43—22no—
63Q8×C43—44no—
64Q8×C43—82no—
65D4×C43—22no—
66D4×C43—42no—
67D4×C43—82no—
68C2×C4×C43—21no—
69C2×C4×C43—42no—
70C2×C4×C43—42no—
71C2×C4×C43—84no—
72C2×C4×C43#12011yescharacteristic
73D172—84no—
74D172—82no—
75C8×C43—42no—
76C8×C43C2×D812yes—
77C8×C43AGL(1,ℤ/8)12yes—
78C43⋊C8—42no—
79#12311—431nomaximal, Sylow
80C22×C43—42no—
81C22×C43#45311yescharacteristic
82C2×D43—162no—
83C2×D43—161no—
84C4×C43—22no—
85C4×C43—42no—
86C4×C43—82no—
87C4×C43#44712yes—
88#3293D4311yescharacteristic, complemented
89#2213—432no—
90#1709—431no—
91#1358—431no—
92#1335—432no—
93C2×C43—21no—
94C2×C43—82no—
95C2×C43#161911yescharacteristic
96D43—321no—
97#578—22no—
98#509—862no—
99#494C2×D4311yescharacteristic
100#493—431no—
101#486—862no—
102#473—22no—
103#456—22no—
104#443C2×D4312yes—
105#364—432no—
106#361—862no—
107C82—431no—
108C43#1231111yescharacteristic, complemented, Sylow
1092−1+4—22no—
110#137—24no—
111#137—44no—
112#135—42no—
113#135C22⋊D4312yes—
114C2×Q16—22no—
115C2×Q16—42no—
116C2×D8—862no—
117#131—22no—
118C4⋊Q8C22⋊D4312yes—
119#127—861no—
120SD32—1722no—
121D16—1722no—
122M32—862no—
123#108C22⋊D4312yes—
124#104—22no—
125#102—1724no—
126#101—22no—
127C4×C8—861no—
128C4×C8C22×D4311yescharacteristic
129#41—22no—
130#41—44no—
131#41—82no—
132C2×Q8—22no—
133C2×Q8—44no—
134C2×D4—1722no—
135C2×D4—1721no—
136Q16—44no—
137Q16—42no—
138Q16—42no—
139Q16#1062188212yes—
140SD16—22no—
141SD16—44no—
142D8—1722no—
143D8—1722no—
144D8#1062188212yes—
145M16—22no—
146M16—42no—
147C2×C8—42no—
148C2×C8—862no—
149C2×C8C2×C22⋊D4312yes—
150C4⋊C4—42no—
151C42C2×C22⋊D4311yescharacteristic
152C16—1722no—
153C23—3441no—
154Q8—22no—
155Q8—44no—
156Q8—82no—
157D4—22no—
158D4—42no—
159D4—82no—
160D4—3444no—
161D4—3442no—
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—84no—
166C2×C4#1306329411yescharacteristic
167C8—42no—
168C8—1722no—
169C8C2×#1062188212yes—
170C8#1306335112yes—
171C22—42no—
172C22—6882no—
173C22—6881no—
174C22#1458306711yescharacteristic
175C4—22no—
176C4—42no—
177C4—82no—
178C4#1458303312yes—
179C2—21no—
180C2—82no—
181C2—13761no—
182C2#1913364911yescharacteristic
subgroupG/H
centerC2#19133649
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#3293C2
socleC2×C43#1619
hypercenter#3293D43
hypocenterC43#12311
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #3293

Complements

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

NH ≅ G/Ntype
1. #19136671C2semidirect
2. #19134202C2semidirect
3. #19132634C2semidirect
4. #19132568C2semidirect
5. C43×#3293C2semidirect
88. #3293D43semidirect
108. C43#12311semidirect

Maximal subgroups

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

subgroupindex
#191366712
#191342022
#191326342
#191325682
C43×#32932
#1231143