Finite Group Databasebeta

← #25000736

Subgroups — #25000736

Order 11008.

386 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 73 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#19145976C211yesmaximal, characteristic
2#19134769C211yesmaximal, characteristic, complemented
3#19133318C212yesmaximal, complemented
4#19133207C212yesmaximal, complemented
5C43×#1307C211yesmaximal, characteristic, complemented
6#14583449C2212yes—
7#14583190—22no—
8#14583152—22no—
9#14583095—22no—
10C2×#13063260—22no—
11#14582923C2211yescharacteristic
12C2×#13063236C2211yescharacteristic
13#14582646—22no—
14#14582642—22no—
15#14582638—24no—
16C43×#432C2212yes—
17C43×#423C2211yescharacteristic
18C2×#10621898—22no—
19C2×D344—22no—
20C2×#10621877—21no—
21C22×C43⋊C8—21no—
22#13063325D412yes—
23#13063322D412yes—
24#13063313—22no—
25#13063299—22no—
26#13063299—22no—
27C4×D172—22no—
28C4×D172—22no—
29#13063260—44no—
30#13063257—22no—
31C4⋊(C43⋊C8)—22no—
32#13063247—24no—
33#13063236—21no—
34#13063236D412yes—
35C2×M16×C43D412yes—
36C2×C42×C43C2311yescharacteristic
37C4⋊C8×C43—22no—
38C4⋊C8×C43—22no—
39C22⋊C8×C43—22no—
40#97×C43—22no—
41C22×C4×C43C2×D411yescharacteristic
42C22×C4×C43#4112yes—
43C2×C22⋊D43—42no—
44#10621898—84no—
45C2×D172—22no—
46C2×D172—22no—
47C2×D172—22no—
48C2×C4×D43—42no—
49C2×Dic86—22no—
50M16×C43—42no—
51C2×C8×C43—22no—
52C2×C8×C43—42no—
53C42×C43C2×D412yes—
54C42×C43C2×D411yescharacteristic
55C42×C43#4111yescharacteristic
56(C2×D43)⋊C4—42no—
57(C2×D43)⋊C4—42no—
58C4⋊Dic43—22no—
59C4⋊Dic43—22no—
60#10621877—42no—
61C2×C43⋊C8—22no—
62C2×C43⋊C8—22no—
63C2×C43⋊C8—22no—
64C2×C43⋊C8—41no—
65D344—82no—
66C23×C43#12411yescharacteristic
67C22×D43—42no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—42no—
71C2×C4×C43#12011yescharacteristic
72C2×C4×C43#12112yes—
73C2×C4×C43#12111yescharacteristic
74C2×C4×C43#12312yes—
75C22⋊D43—84no—
76C2×Dic43—42no—
77D172—42no—
78D172—42no—
79D172—82no—
80D172—82no—
81C4×D43—84no—
82Dic86—82no—
83C8×C43—42no—
84C8×C43—82no—
85C43⋊C8—24no—
86C43⋊C8—81no—
87#10524—431nomaximal, Sylow
88C22×C43—22no—
89C22×C43—21no—
90C22×C43#39411yescharacteristic
91C2×D43—82no—
92C2×D43—82no—
93C2×D43—82no—
94C4×C43—22no—
95C4×C43—22no—
96C4×C43—21no—
97C4×C43#45311yescharacteristic
98C4×C43#45611yescharacteristic
99Dic43—82no—
100#3253—431no—
101#1849—431no—
102#1557—432no—
103#1530—432no—
104#1307D4311yescharacteristic, complemented
105C2×C43—41no—
106C2×C43#203911yescharacteristic
107C2×C43#204812yes—
108D43—162no—
109#532—432no—
110#476—862no—
111#469—862no—
112#459—862no—
113#432C2×D4312yes—
114C2×#108—862no—
115#423—431no—
116#423C2×D4311yescharacteristic
117C2×#97—431no—
118#332—862no—
119#331—862no—
120#329—864no—
121C43#1052411yescharacteristic, complemented, Sylow
122C2×#41—862no—
123C2×D8—862no—
124C2×M16—861no—
125C2×M16D17212yes—
126C22×C8—861no—
127C4⋊Q8—432no—
128#127—432no—
129#124—862no—
130#121—862no—
131#121—862no—
132C4×D4—862no—
133C4×D4—862no—
134C2×C42C22×D4311yescharacteristic
135#108—1724no—
136#106—862no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—862no—
140#102—864no—
141C22⋊C8—22no—
142#97—22no—
143#97—432no—
144#97—861no—
145#41—3444no—
146C2×Q8—862no—
147C2×D4—862no—
148C2×D4—862no—
149C2×D4—862no—
150C2×D4—1722no—
151C22×C4—1722no—
152C22×C4C2×D17211yescharacteristic
153C22×C4#1062189812yes—
154D8—3442no—
155M16—42no—
156M16—1722no—
157C2×C8—22no—
158C2×C8—42no—
159C2×C8—862no—
160C2×C8—862no—
161C2×C8—862no—
162C2×C8—1721no—
163C4⋊C4—862no—
164C4⋊C4—862no—
165C22⋊C4—1722no—
166C22⋊C4—1722no—
167C42D4×D4312yes—
168C42D4×D4311yescharacteristic
169C42#1062190211yescharacteristic
170C23—1722no—
171C23#1306331311yescharacteristic
172Q8—3442no—
173D4—3442no—
174D4—3442no—
175D4—3444no—
176D4—1722no—
177D4—1722no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—3444no—
182C2×C4—1722no—
183C2×C4#1306329511yescharacteristic
184C2×C4#1306329812yes—
185C2×C4#1306330011yescharacteristic
186C2×C4#1306331012yes—
187C8—42no—
188C8—82no—
189C8—864no—
190C8—3441no—
191C22—21no—
192C22—22no—
193C22—3442no—
194C22—3442no—
195C22—3442no—
196C22#1458281711yescharacteristic
197C4—21no—
198C4—22no—
199C4—22no—
200C4—3442no—
201C4#1458306911yescharacteristic
202C4#1458308411yescharacteristic
203C2—41no—
204C2—6882no—
205C2#1913582011yescharacteristic
206C2#1913587112yes—
subgroupG/H
centerC22#14582817
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1307C2
socleC22×C43#394
prime radical#19145976C2
hypercenter#1307D43
hypocenterC43#10524
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
2. #19134769C2semidirect
3. #19133318C2semidirect
4. #19133207C2semidirect
5. C43×#1307C2semidirect
104. #1307D43semidirect
121. C43#10524semidirect

Maximal subgroups

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

subgroupindex
#191459762
#191347692
#191333182
#191332072
C43×#13072
#1052443