Finite Group Databasebeta

← #25009980

Subgroups — #25009980

Order 11008.

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

normal subgroups only

This group has 274 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#19145989C211yesmaximal, characteristic
2#19136815C212yesmaximal
3#19136170C211yesmaximal, characteristic
4#19132584C212yesmaximal
5C43×#1327C211yesmaximal, characteristic
6#14583456—21no—
7#14583185—22no—
8#14583157—21no—
9#14583157C2212yes—
10#14583110—22no—
11#14582948C2211yescharacteristic
12#14582722—22no—
13#14582716—22no—
14#14582671—21no—
15#14582659—21no—
16#14582656C2211yescharacteristic
17C43×#423C2211yescharacteristic
18C43×#349C2212yes—
19C2×Dic172—21no—
20C2×Dic172D412yes—
21C2×#10621877—21no—
22#13063325—21no—
23#13063325—21no—
24#13063317—41no—
25#13063304—22no—
26#13063304—41no—
27C4×Dic86—22no—
28C4×Dic86—41no—
29#13063284—21no—
30#13063284—41no—
31#13063261—22no—
32#13063257—21no—
33#13063257D412yes—
34#13063250—22no—
35#13063250—22no—
36C2×M16×C43D411yescharacteristic
37C2×M16×C43C2311yescharacteristic
38C2×C42×C43D411yescharacteristic
39M32×C43—22no—
40C4⋊C8×C43—22no—
41C22×C4×C43—21no—
42C22×C4×C43C2×D411yescharacteristic
43C2×Dic86—22no—
44C2×Dic86—41no—
45M16×C43—41no—
46M16×C43—41no—
47C2×C8×C43—21no—
48C2×C8×C43C2×D412yes—
49C42×C43—21no—
50C42×C43SD1611yescharacteristic
51C42×C43SD1611yescharacteristic
52C22⋊Dic43—42no—
53C22⋊Dic43—41no—
54C4⋊Dic43—22no—
55C4⋊Dic43—41no—
56C4⋊Dic43—41no—
57C4⋊Dic43—41no—
58C4⋊Dic43—41no—
59Dic43⋊C4—42no—
60Dic43⋊C4—42no—
61C4×Dic43—42no—
62C4×Dic43—41no—
63#10621877—41no—
64#10621877—41no—
65C2×C43⋊C8—41no—
66Dic172—42no—
67Dic172—81no—
68C16×C43—42no—
69C23×C43AGL(1,ℤ/8)11yescharacteristic
70C2×C4×C43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43—42no—
75C2×C4×C43#12011yescharacteristic
76C2×C4×C43C2×SD1611yescharacteristic
77C2×Dic43—42no—
78C2×Dic43—42no—
79C2×Dic43—81no—
80Dic86—42no—
81Dic86—42no—
82Dic86—82no—
83C8×C43—22no—
84C8×C43—41no—
85C43⋊C8—81no—
86#12308—431nomaximal, Sylow
87C22×C43—21no—
88C22×C43—41no—
89C22×C43#45011yescharacteristic
90C4×C43—22no—
91C4×C43—21no—
92C4×C43—41no—
93C4×C43#45411yescharacteristic
94C4×C43#45811yescharacteristic
95Dic43—82no—
96Dic43—82no—
97Dic43—161no—
98#3255—431no—
99#2239—432no—
100#2102—431no—
101#1340—432no—
102#1327D4311yescharacteristic
103C2×C43—21no—
104C2×C43—41no—
105C2×C43#161611yescharacteristic
106#533—861no—
107#475—862no—
108#470—432no—
109#470—861no—
110#462—862no—
111#430—431no—
112#423C2×D4311yescharacteristic
113#365—862no—
114#362—862no—
115#349C2×D4312yes—
116#344—861no—
117#339—861no—
118H(3,ℤ/4)—431no—
119C43#1230811yescharacteristic, complemented, Sylow
120C2×Q16—432no—
121C2×Q16—861no—
122C2×M16—861no—
123C2×M16D17211yescharacteristic
124C2×M16C22×D4311yescharacteristic
125C4⋊Q8—861no—
126C4⋊Q8—861no—
127#125—1721no—
128C22⋊Q8—862no—
129C22⋊Q8—1721no—
130C4×Q8—862no—
131C4×Q8—1721no—
132#117—861no—
133#117—1721no—
134C2×C42D17211yescharacteristic
135M32—22no—
136#108—862no—
137#106—432no—
138#106—861no—
139C4⋊C8—22no—
140#103—862no—
141#103—862no—
142C2×Q8—862no—
143C2×Q8—1721no—
144C22×C4—21no—
145C22×C4C2×D17211yescharacteristic
146Q16—3441no—
147Q16—1722no—
148M16—41no—
149M16—41no—
150M16—1721no—
151M16—1721no—
152C2×C8—21no—
153C2×C8—1721no—
154C2×C8D4×D4312yes—
155C4⋊C4—862no—
156C4⋊C4—1721no—
157C4⋊C4—1721no—
158C4⋊C4—1721no—
159C4⋊C4—1722no—
160C4⋊C4—1721no—
161C4⋊C4—1722no—
162C22⋊C4—1721no—
163C22⋊C4—1722no—
164C42—21no—
165C42—1721no—
166C42—1722no—
167C42#1062187311yescharacteristic
168C42#1062187311yescharacteristic
169C16—42no—
170C23#1306335311yescharacteristic
171Q8—3442no—
172Q8—1722no—
173Q8—1722no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—3441no—
180C2×C4—1722no—
181C2×C4—1722no—
182C2×C4#1306329511yescharacteristic
183C2×C4C2×#1062187311yescharacteristic
184C8—22no—
185C8—41no—
186C8—3441no—
187C22—21no—
188C22—41no—
189C22#1458305211yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—3442no—
194C4—3442no—
195C4—6881no—
196C4#1458307411yescharacteristic
197C4#1458309011yescharacteristic
198C2—21no—
199C2—41no—
200C2#1913363411yescharacteristic
subgroupG/H
centerC2#19133634
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#1327C2
socleC2×C43#1616
prime radicalC23×C43AGL(1,ℤ/8)
hypercenter#1327D43
hypocenterC43#12308
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
119. C43#12308semidirect

Maximal subgroups

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

subgroupindex
#191459892
#191368152
#191361702
#191325842
C43×#13272
#1230843