Finite Group Databasebeta

← #25010758

Subgroups — #25010758

Order 11008.

234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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#19136729C211yesmaximal, characteristic
2#19136641C211yesmaximal, characteristic
3#19134193C211yesmaximal, characteristic, complemented
4#19133389C211yesmaximal, characteristic
5#19132658C211yesmaximal, characteristic, complemented
6#19132643C211yesmaximal, characteristic, complemented
7C43×#1364C211yesmaximal, characteristic, complemented
8C2×#13063270—21no—
9#14583295—21no—
10#14583279C2211yescharacteristic
11#14583249—21no—
12C4×D344C2211yescharacteristic
13#14582964—21no—
14#14582724—21no—
15C4⋊(C43⋊C16)C2211yescharacteristic
16#14582704—21no—
17#14582699—21no—
18#14582626—21no—
19C8×C43⋊C8C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×C4⋊C16C2211yescharacteristic
22C43×#335C2211yescharacteristic
23C2×Dic172—21no—
24C2×Dic172—21no—
25C2×D344D411yescharacteristic
26C2×C8×D43—41no—
27#13063325—21no—
28C4×D172—21no—
29#13063270—42no—
30C2×C43⋊C16—21no—
31#13063259D411yescharacteristic
32#13063256—42no—
33#13063249—41no—
34#13063249—41no—
35#13063247—21no—
36(C2×D43)⋊C8—41no—
37C4×C43⋊C8D411yescharacteristic
38C4×C43⋊C8D411yescharacteristic
39C4⋊Q8×C43—21no—
40C2×C16×C43—21no—
41#107×C43—21no—
42#107×C43—21no—
43C4⋊C8×C43—21no—
44C4×C8×C43C2311yescharacteristic
45C2×Q8×C43—41no—
46C2×D172—21no—
47C2×C4×D43—41no—
48C2×Dic86—41no—
49C2×C8×C43—41no—
50C2×C8×C43C2×D411yescharacteristic
51C2×C8×C43#4111yescharacteristic
52C4⋊C4×C43—41no—
53C4⋊C4×C43—41no—
54C42×C43C2×D411yescharacteristic
55(C2×D43)⋊C4—41no—
56C4⋊Dic43—21no—
57C4⋊Dic43—41no—
58C4⋊Dic43—41no—
59C2×C43⋊C8—21no—
60C2×C43⋊C8D811yescharacteristic
61C2×C43⋊C8D811yescharacteristic
62Dic172—41no—
63Dic172—41no—
64Dic172—81no—
65D344—21no—
66D344SD1612yes—
67C8×D43—82no—
68C16×C43—41no—
69C43⋊C16—41no—
70C22×D43—41no—
71Q8×C43—81no—
72Q8×C43—81no—
73C2×C4×C43—81no—
74C2×C4×C43#12111yescharacteristic
75C2×C4×C43C2×D811yescharacteristic
76C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
77C2×Dic43—41no—
78C2×Dic43—81no—
79D172—22no—
80D172—41no—
81C4×D43—81no—
82C4×D43—81no—
83Dic86—81no—
84Dic86—81no—
85C8×C43—21no—
86C8×C43—81no—
87C8×C43C2×SD1611yescharacteristic
88C8×C43#13511yescharacteristic
89C43⋊C8—22no—
90C43⋊C8—21no—
91C43⋊C8—21no—
92#12422—431nomaximal, Sylow
93C22×C43#45911yescharacteristic
94C2×D43—42no—
95C2×D43—81no—
96C2×D43—81no—
97C4×C43—21no—
98C4×C43—161no—
99C4×C43#46511yescharacteristic
100C4×C43#47111yescharacteristic
101C4×C43#50811yescharacteristic
102C4×C43#50911yescharacteristic
103Dic43—81no—
104Dic43—161no—
105#2224—431no—
106#2208—431no—
107#1707—431no—
108C8×D8—431no—
109#1367—431no—
110#1364D4311yescharacteristic, complemented
111#1362—431no—
112C2×C43#166511yescharacteristic
113C2×C43#221011yescharacteristic
114C2×C43#221411yescharacteristic
115D43—82no—
116C2×SD32—861no—
117#500C2×D4311yescharacteristic
118#498—861no—
119#494—431no—
120#487—861no—
121C4×D8—431no—
122C8×D4—861no—
123#366—861no—
124C4⋊C16—431no—
125C4⋊C16C2×D4311yescharacteristic
126#358—861no—
127#357—861no—
128#335C2×D4311yescharacteristic
129D4⋊C8—861no—
130C82—431no—
131C43#1242211yescharacteristic, complemented, Sylow
132C2×Q16—861no—
133C2×Q16—861no—
134C2×D8—431no—
135C22×C8—1721no—
136C4⋊Q8—21no—
137C4⋊Q8—861no—
138C4×D4—861no—
139SD32—1722no—
140C2×C16—21no—
141C2×C16—861no—
142#107—21no—
143#107—21no—
144#107—431no—
145#106—1722no—
146C4⋊C8—21no—
147#103—1721no—
148#103—1721no—
149#102—861no—
150C22⋊C8—1721no—
151C4×C8—431no—
152C4×C8—431no—
153C4×C8C22×D4311yescharacteristic
154C2×Q8—41no—
155C2×Q8—1721no—
156C2×D4—861no—
157C22×C4—1721no—
158Q16—3441no—
159Q16—1721no—
160Q16—1721no—
161D8—432no—
162D8—861no—
163C2×C8—41no—
164C2×C8—431no—
165C2×C8—431no—
166C2×C8—861no—
167C2×C8—3442no—
168C2×C8#1062189811yescharacteristic
169C2×C8D4×D4311yescharacteristic
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—861no—
173C4⋊C4—1721no—
174C4⋊C4—1721no—
175C22⋊C4—1721no—
176C42D4×D4311yescharacteristic
177C16—41no—
178C16—1721no—
179C23—1721no—
180Q8—81no—
181Q8—81no—
182Q8—3441no—
183Q8—3441no—
184D4—862no—
185D4—1721no—
186C2×C4—81no—
187C2×C4—3441no—
188C2×C4—3441no—
189C2×C4—3441no—
190C2×C4—1721no—
191C2×C4#1306329811yescharacteristic
192C2×C4D8×D4311yescharacteristic
193C2×C4#1306335211yescharacteristic
194C8—21no—
195C8—81no—
196C8—862no—
197C8—861no—
198C8—861no—
199C8SD16×D4311yescharacteristic
200C8#1306334811yescharacteristic
201C22—3441no—
202C22—3441no—
203C22—1722no—
204C22#1458309311yescharacteristic
205C4—21no—
206C4—161no—
207C4—3441no—
208C4—6881no—
209C4#1458313111yescharacteristic
210C4#1458316511yescharacteristic
211C4#1458333011yescharacteristic
212C4#1458333311yescharacteristic
213C2—3442no—
214C2#1913393911yescharacteristic
215C2#1913664911yescharacteristic
216C2#1913667511yescharacteristic
subgroupG/H
centerC22#14583093
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1364C2
socleC22×C43#459
prime radicalC2×D344D4
hypercenter#1364D43
hypocenterC43#12422
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
3. #19134193C2semidirect
5. #19132658C2semidirect
6. #19132643C2semidirect
7. C43×#1364C2semidirect
110. #1364D43semidirect
131. C43#12422semidirect

Maximal subgroups

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

subgroupindex
#191367292
#191366412
#191341932
#191333892
#191326582
#191326432
C43×#13642
#1242243