Finite Group Databasebeta

← #25000740

Subgroups — #25000740

Order 11008.

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

normal subgroups only

This group has 370 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×#1838C211yesmaximal, characteristic, complemented
6#14583449C2212yes—
7#14583190—22no—
8#14583152—22no—
9#14583095—22no—
10#14582956C2212yes—
11#14582644—22no—
12#14582642—22no—
13#14582638—24no—
14C43×#423C2211yescharacteristic
15C43×#423C2211yescharacteristic
16C2×#97×C43C2211yescharacteristic
17C43×#341—22no—
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
36C4⋊C8×C43—22no—
37C4⋊C8×C43—22no—
38#97×C43—21no—
39#97×C43D412yes—
40C22×C4×C43C2×D411yescharacteristic
41C22×C4×C43#4112yes—
42C2×C22⋊D43—42no—
43#10621898—84no—
44C2×D172—22no—
45C2×D172—22no—
46C2×D172—22no—
47C2×C4×D43—42no—
48C2×Dic86—22no—
49M16×C43—42no—
50M16×C43—42no—
51C2×C8×C43—22no—
52C2×C8×C43—22no—
53C2×C8×C43—41no—
54C2×C8×C43—41no—
55C2×C8×C43—41no—
56C42×C43C2×D411yescharacteristic
57C42×C43C2×D412yes—
58C42×C43#4111yescharacteristic
59(C2×D43)⋊C4—42no—
60(C2×D43)⋊C4—42no—
61C4⋊Dic43—22no—
62C4⋊Dic43—22no—
63C2×C43⋊C8—42no—
64D344—82no—
65C23×C43#12411yescharacteristic
66C22×D43—42no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—42no—
70C2×C4×C43#12011yescharacteristic
71C2×C4×C43#12111yescharacteristic
72C2×C4×C43#12112yes—
73C2×C4×C43#12312yes—
74C22⋊D43—84no—
75C2×Dic43—42no—
76D172—42no—
77D172—42no—
78D172—82no—
79D172—82no—
80C4×D43—84no—
81Dic86—82no—
82C8×C43—42no—
83C8×C43—42no—
84C8×C43—81no—
85C43⋊C8—82no—
86#10525—431nomaximal, Sylow
87C22×C43—22no—
88C22×C43—21no—
89C22×C43#39411yescharacteristic
90C2×D43—82no—
91C2×D43—82no—
92C2×D43—82no—
93C4×C43—22no—
94C4×C43—22no—
95C4×C43—21no—
96C4×C43#45411yescharacteristic
97C4×C43#45511yescharacteristic
98Dic43—82no—
99#3253—431no—
100#1838D4311yescharacteristic, complemented
101#1557—432no—
102#1530—432no—
103#1307—431no—
104C2×C43—41no—
105C2×C43#204011yescharacteristic
106C2×C43#204812yes—
107D43—162no—
108#532—432no—
109#476—862no—
110#469—862no—
111#459—862no—
112#432—432no—
113#423C2×D4311yescharacteristic
114#423C2×D4311yescharacteristic
115C2×#97C2×D4311yescharacteristic
116#341—22no—
117#332—862no—
118#331—862no—
119#329—864no—
120C43#1052511yescharacteristic, complemented, Sylow
121C2×#41—862no—
122C2×D8—862no—
123C2×M16—21no—
124C2×M16C22⋊D4312yes—
125C22×C8—21no—
126C4⋊Q8—432no—
127#127—432no—
128#124—862no—
129#121—862no—
130#121—862no—
131C4×D4—862no—
132C4×D4—862no—
133C2×C42C22×D4311yescharacteristic
134#106—862no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—862no—
138#102—864no—
139C22⋊C8—862no—
140#97—21no—
141#97—862no—
142#97D17212yes—
143#41—3444no—
144C2×Q8—862no—
145C2×D4—862no—
146C2×D4—862no—
147C2×D4—862no—
148C2×D4—1722no—
149C22×C4—1722no—
150C22×C4#1062190212yes—
151C22×C4C2×C22⋊D4311yescharacteristic
152D8—3442no—
153M16—42no—
154M16—42no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—1722no—
161C4⋊C4—862no—
162C4⋊C4—862no—
163C22⋊C4—1722no—
164C22⋊C4—1722no—
165C42C2×D17211yescharacteristic
166C42#1062189811yescharacteristic
167C42D4×D4312yes—
168C23—1722no—
169C23#1306331411yescharacteristic
170Q8—3442no—
171D4—3442no—
172D4—3442no—
173D4—3444no—
174D4—1722no—
175D4—1722no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—3444no—
180C2×C4—1722no—
181C2×C4#1306329311yescharacteristic
182C2×C4#1306329911yescharacteristic
183C2×C4#1306330012yes—
184C2×C4#1306331012yes—
185C8—42no—
186C8—42no—
187C8—81no—
188C8—3442no—
189C22—21no—
190C22—22no—
191C22—3442no—
192C22—3442no—
193C22—3442no—
194C22#1458281611yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—3442no—
199C4#1458307111yescharacteristic
200C4#1458307611yescharacteristic
201C2—41no—
202C2—6882no—
203C2#1913582411yescharacteristic
204C2#1913587012yes—
subgroupG/H
centerC22#14582816
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1838C2
socleC22×C43#394
prime radical#19145976C2
hypercenter#1838D43
hypocenterC43#10525
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1838

Complements

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

NH ≅ G/Ntype
2. #19133315C2semidirect
3. #19133205C2semidirect
4. #19132506C2semidirect
5. C43×#1838C2semidirect
100. #1838D43semidirect
120. C43#10525semidirect

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×#18382
#1052543