Finite Group Databasebeta

← #25011375

Subgroups — #25011375

Order 11008.

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

normal subgroups only

This group has 284 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#19136852C211yesmaximal, characteristic
2#19136822C211yesmaximal, characteristic, complemented
3#19136819C211yesmaximal, characteristic
4#19134202C211yesmaximal, characteristic
5#19134189C211yesmaximal, characteristic, complemented
6#19132514C211yesmaximal, characteristic, complemented
7C43×#2247C211yesmaximal, characteristic, complemented
8C2×#13063268—22no—
9#14583304C2211yescharacteristic
10#14583295—21no—
11#14583276C2211yescharacteristic
12#14583251—21no—
13#14583247—21no—
14#14583247—21no—
15#14582703—22no—
16#14582701—22no—
17C4×C43⋊C16C2211yescharacteristic
18C8×C43⋊C8C2211yescharacteristic
19C2×Q32×C43—22no—
20C43×#494C2211yescharacteristic
21C43×#494C2211yescharacteristic
22C4×C16×C43C2211yescharacteristic
23C2×D344—21no—
24C2×D344—21no—
25#13063325—21no—
26#13063322—21no—
27#13063268—44no—
28C2×C43⋊C16D412yes—
29#13063259—21no—
30#13063259—21no—
31#13063256—42no—
32#13063248—42no—
33#13063245—42no—
34#13063245—42no—
35C4×C43⋊C8D411yescharacteristic
36C4×C43⋊C8D411yescharacteristic
37C2×Q16×C43—21no—
38C2×Q16×C43—21no—
39C2×Q16×C43—21no—
40C2×Q16×C43—21no—
41C4⋊Q8×C43—21no—
42C4⋊Q8×C43—21no—
43Q32×C43—44no—
44C2×C16×C43D412yes—
45C4×C8×C43C2311yescharacteristic
46C2×Q8×C43—41no—
47C2×Q8×C43—41no—
48C2×D172—41no—
49C2×D172—41no—
50C2×D172—41no—
51C2×Dic86—41no—
52Q16×C43—42no—
53Q16×C43—42no—
54Q16×C43—42no—
55Q16×C43—42no—
56C2×C8×C43C2×D411yescharacteristic
57C2×C8×C43C2×D411yescharacteristic
58C4⋊C4×C43—41no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—41no—
61C4⋊C4×C43—41no—
62C42×C43C2×D411yescharacteristic
63C4⋊Dic43—41no—
64C4⋊Dic43—41no—
65C2×C43⋊C8D812yes—
66C2×C43⋊C8D812yes—
67D344—42no—
68D344—42no—
69C16×C43—22no—
70C43⋊C16—22no—
71C22×D43—81no—
72Q8×C43—81no—
73Q8×C43—81no—
74Q8×C43—81no—
75Q8×C43—81no—
76C2×C4×C43—81no—
77C2×C4×C43—81no—
78C2×C4×C43#12711yescharacteristic
79C2×C4×C43C2×D811yescharacteristic
80C2×C4×C43C2×D811yescharacteristic
81C2×Dic43—81no—
82D172—81no—
83D172—81no—
84D172—82no—
85D172—82no—
86Dic86—82no—
87C8×C43AGL(1,ℤ/8)12yes—
88C8×C43AGL(1,ℤ/8)12yes—
89C43⋊C8—22no—
90C43⋊C8—22no—
91#12530—431nomaximal, Sylow
92C22×C43#49311yescharacteristic
93C2×D43—161no—
94C2×D43—161no—
95C2×D43—161no—
96C4×C43—161no—
97C4×C43—161no—
98C4×C43#49611yescharacteristic
99C4×C43#49611yescharacteristic
100C4×C43#50812yes—
101C4×C43#51012yes—
102Dic43—161no—
103#2248—431no—
104#2247D4311yescharacteristic, complemented
105#2241—431no—
106#2240—431no—
107#1709—431no—
108#1707—431no—
109#1312—431no—
110C2×C43#172111yescharacteristic
111C2×C43#224911yescharacteristic
112C2×C43#225111yescharacteristic
113D43—321no—
114C2×Q32—22no—
115C2×SD32—862no—
116#500—431no—
117#498—861no—
118#494C2×D4311yescharacteristic
119#494C2×D4311yescharacteristic
120#493—431no—
121#487—861no—
122#486—861no—
123#486—861no—
124#358—862no—
125#357—862no—
126C4×C16—431no—
127C4×C16C2×D4311yescharacteristic
128C82—431no—
129C43#1253011yescharacteristic, complemented, Sylow
130C2×Q16—21no—
131C2×Q16—21no—
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—861no—
135C2×D8—861no—
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138C4⋊Q8—861no—
139#127—861no—
140Q32—44no—
141SD32—1724no—
142C2×C16—432no—
143C2×C16C22⋊D4312yes—
144#107—861no—
145#107—861no—
146#106—1722no—
147#103—1722no—
148#102—1722no—
149#102—1722no—
150C4×C8—431no—
151C4×C8—431no—
152C4×C8C22×D4311yescharacteristic
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—1721no—
156C2×D4—1721no—
157C2×D4—1721no—
158C2×D4—1721no—
159Q16—42no—
160Q16—42no—
161Q16—42no—
162Q16—42no—
163D8—1722no—
164D8—1722no—
165C2×C8—432no—
166C2×C8—432no—
167C2×C8D4×D4311yescharacteristic
168C2×C8C2×C22⋊D4311yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—1721no—
174C4⋊C4—1721no—
175C42D4×D4311yescharacteristic
176C16—22no—
177C16—862no—
178C23—3441no—
179Q8—81no—
180Q8—81no—
181Q8—81no—
182Q8—81no—
183Q8—3442no—
184D4—3442no—
185D4—3442no—
186D4—3441no—
187D4—3441no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—3441no—
191C2×C4#1306332111yescharacteristic
192C2×C4D8×D4311yescharacteristic
193C2×C4D8×D4311yescharacteristic
194C8—862no—
195C8—862no—
196C8#1306334912yes—
197C8#1306335112yes—
198C22—6881no—
199C22—6881no—
200C22—6881no—
201C22#1458327411yescharacteristic
202C4—161no—
203C4—161no—
204C4—6881no—
205C4#1458328611yescharacteristic
206C4#1458328711yescharacteristic
207C4#1458333212yes—
208C4#1458334112yes—
209C2—13761no—
210C2#1913426011yescharacteristic
211C2#1913685711yescharacteristic
212C2#1913686311yescharacteristic
subgroupG/H
centerC22#14583274
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2247C2
socleC22×C43#493
prime radical#14583276C22
hypercenter#2247D43
hypocenterC43#12530
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2247

Complements

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

NH ≅ G/Ntype
2. #19136822C2semidirect
5. #19134189C2semidirect
6. #19132514C2semidirect
7. C43×#2247C2semidirect
104. #2247D43semidirect
129. C43#12530semidirect

Maximal subgroups

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

subgroupindex
#191368522
#191368222
#191368192
#191342022
#191341892
#191325142
C43×#22472
#1253043