Finite Group Databasebeta

← #25000735

Subgroups — #25000735

Order 11008.

386 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 75 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#19133315C212yesmaximal, complemented
3#19133205C212yesmaximal, complemented
4#19132506C211yesmaximal, characteristic, complemented
5C43×#1849C211yesmaximal, characteristic, complemented
6#14583449C2212yes—
7#14583190—22no—
8#14583152—22no—
9#14583095—22no—
10#14582956C2212yes—
11#14582644—22no—
12#14582642—22no—
13#14582638—24no—
14C2×#108×C43—22no—
15C43×#423C2211yescharacteristic
16C43×#423C2211yescharacteristic
17C2×#97×C43C2211yescharacteristic
18C2×#10621898—22no—
19C2×D344—22no—
20#13063325D412yes—
21#13063322D412yes—
22#13063313—22no—
23#13063299—22no—
24#13063299—22no—
25C4×D172—22no—
26C4×D172—22no—
27#13063257—22no—
28C4⋊(C43⋊C8)—22no—
29#13063247—24no—
30C22⋊(C43⋊C8)—22no—
31#13063236—22no—
32C2×M16×C43—21no—
33C2×M16×C43D412yes—
34C22×C8×C43—21no—
35C2×C42×C43C2311yescharacteristic
36#108×C43—44no—
37C4⋊C8×C43—22no—
38C4⋊C8×C43—22no—
39#97×C43—21no—
40#97×C43D412yes—
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—
51M16×C43—42no—
52C2×C8×C43—22no—
53C2×C8×C43—22no—
54C2×C8×C43—22no—
55C2×C8×C43—22no—
56C2×C8×C43—41no—
57C42×C43C2×D411yescharacteristic
58C42×C43C2×D412yes—
59C42×C43#4111yescharacteristic
60(C2×D43)⋊C4—42no—
61(C2×D43)⋊C4—42no—
62C4⋊Dic43—22no—
63C4⋊Dic43—22no—
64C2×C43⋊C8—42no—
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#12111yescharacteristic
73C2×C4×C43#12112yes—
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—24no—
84C8×C43—42no—
85C8×C43—81no—
86C43⋊C8—82no—
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#1849D4311yescharacteristic, complemented
102#1557—432no—
103#1530—432no—
104#1307—431no—
105C2×C43—41no—
106C2×C43#203911yescharacteristic
107C2×C43#204812yes—
108D43—162no—
109#532—432no—
110#476—862no—
111#469—862no—
112#459—862no—
113#432—432no—
114C2×#108—22no—
115#423C2×D4311yescharacteristic
116#423C2×D4311yescharacteristic
117C2×#97C2×D4311yescharacteristic
118#332—862no—
119#331—862no—
120#329—864no—
121C43#1052411yescharacteristic, complemented, Sylow
122C2×#41—862no—
123C2×D8—862no—
124C2×M16—21no—
125C2×M16C22⋊D4312yes—
126C22×C8—21no—
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—44no—
136#106—862no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—862no—
140#102—864no—
141C22⋊C8—862no—
142#97—21no—
143#97—862no—
144#97D17212yes—
145#41—3444no—
146C2×Q8—862no—
147C2×D4—862no—
148C2×D4—862no—
149C2×D4—862no—
150C2×D4—1722no—
151C22×C4—1722no—
152C22×C4#1062190212yes—
153C22×C4C2×C22⋊D4311yescharacteristic
154D8—3442no—
155M16—42no—
156M16—42no—
157C2×C8—22no—
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—22no—
161C2×C8—41no—
162C2×C8—1722no—
163C4⋊C4—862no—
164C4⋊C4—862no—
165C22⋊C4—1722no—
166C22⋊C4—1722no—
167C42C2×D17211yescharacteristic
168C42#1062189811yescharacteristic
169C42D4×D4312yes—
170C23—1722no—
171C23#1306331411yescharacteristic
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#1306329311yescharacteristic
184C2×C4#1306329911yescharacteristic
185C2×C4#1306330012yes—
186C2×C4#1306331012yes—
187C8—24no—
188C8—42no—
189C8—81no—
190C8—3442no—
191C22—21no—
192C22—22no—
193C22—3442no—
194C22—3442no—
195C22—3442no—
196C22#1458281611yescharacteristic
197C4—21no—
198C4—22no—
199C4—22no—
200C4—3442no—
201C4#1458306611yescharacteristic
202C4#1458308111yescharacteristic
203C2—41no—
204C2—6882no—
205C2#1913581911yescharacteristic
206C2#1913587012yes—
subgroupG/H
centerC22#14582816
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1849C2
socleC22×C43#394
prime radical#19145976C2
hypercenter#1849D43
hypocenterC43#10524
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1849

Complements

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

NH ≅ G/Ntype
2. #19133315C2semidirect
3. #19133205C2semidirect
4. #19132506C2semidirect
5. C43×#1849C2semidirect
101. #1849D43semidirect
121. C43#10524semidirect

Maximal subgroups

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

subgroupindex
#191459762
#191333152
#191332052
#191325062
C43×#18492
#1052443