Finite Group Databasebeta

← #25011359

Subgroups — #25011359

Order 11008.

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

normal subgroups only

This group has 306 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#19136844C211yesmaximal, characteristic
2#19136822C211yesmaximal, characteristic, complemented
3#19136819C211yesmaximal, characteristic, complemented
4#19134202C211yesmaximal, characteristic, complemented
5#19134184C211yesmaximal, characteristic, complemented
6#19132514C211yesmaximal, characteristic, complemented
7C43×#2248C211yesmaximal, characteristic, complemented
8C2×#13063266—22no—
9#14583304C2211yescharacteristic
10#14583276C2211yescharacteristic
11#14583271—21no—
12#14583247—21no—
13#14583247—21no—
14#14583245—21no—
15#14582703—22no—
16#14582701—22no—
17C4×C43⋊C16C2211yescharacteristic
18C8×C43⋊C8C2211yescharacteristic
19C2×SD32×C43—22no—
20C43×#494C2211yescharacteristic
21C43×#493C2211yescharacteristic
22C4×C16×C43C2211yescharacteristic
23C2×#10621883—42no—
24C2×D344—21no—
25C2×D344—21no—
26#13063325—21no—
27#13063322—21no—
28#13063266—44no—
29C2×C43⋊C16D412yes—
30#13063259—21no—
31#13063259—21no—
32#13063246—42no—
33#13063245—42no—
34#13063245—42no—
35C4×C43⋊C8D411yescharacteristic
36C4×C43⋊C8D411yescharacteristic
37C2×Q16×C43—21no—
38C2×Q16×C43—21no—
39C2×D8×C43—21no—
40C2×D8×C43—21no—
41C4⋊Q8×C43—21no—
42#127×C43—21no—
43SD32×C43—44no—
44C2×C16×C43D412yes—
45C4×C8×C43C2311yescharacteristic
46C2×Q8×C43—41no—
47C2×D4×C43—41no—
48C2×D4×C43—41no—
49C2×D4×C43—41no—
50C2×D172—41no—
51C2×D172—41no—
52C2×D172—41no—
53C2×Dic86—41no—
54Q16×C43—42no—
55Q16×C43—42no—
56D8×C43—42no—
57D8×C43—42no—
58C2×C8×C43C2×D411yescharacteristic
59C2×C8×C43C2×D411yescharacteristic
60C4⋊C4×C43—41no—
61C4⋊C4×C43—41no—
62C42×C43C2×D411yescharacteristic
63#10621883—84no—
64C4⋊Dic43—41no—
65C4⋊Dic43—41no—
66C2×C43⋊C8D812yes—
67C2×C43⋊C8D812yes—
68D344—42no—
69D344—42no—
70C16×C43—22no—
71C43⋊C16—22no—
72C23×C43—81no—
73C22×D43—81no—
74Q8×C43—81no—
75Q8×C43—81no—
76D4×C43—81no—
77D4×C43—81no—
78D4×C43—82no—
79D4×C43—82no—
80C2×C4×C43—81no—
81C2×C4×C43#12711yescharacteristic
82C2×C4×C43C2×D811yescharacteristic
83C2×C4×C43C2×D811yescharacteristic
84C2×Dic43—81no—
85D172—81no—
86D172—81no—
87D172—82no—
88D172—82no—
89Dic86—82no—
90C8×C43AGL(1,ℤ/8)12yes—
91C8×C43AGL(1,ℤ/8)12yes—
92C43⋊C8—22no—
93C43⋊C8—22no—
94#12527—431nomaximal, Sylow
95C22×C43—161no—
96C22×C43—161no—
97C22×C43—161no—
98C22×C43#49311yescharacteristic
99C2×D43—161no—
100C2×D43—161no—
101C2×D43—161no—
102C4×C43—161no—
103C4×C43#49611yescharacteristic
104C4×C43#49611yescharacteristic
105C4×C43#50812yes—
106C4×C43#50912yes—
107Dic43—161no—
108#2248D4311yescharacteristic, complemented
109#2246—431no—
110#2241—431no—
111#2240—431no—
112#1709—431no—
113#1706—431no—
114#1312—431no—
115C2×C43—321no—
116C2×C43#172111yescharacteristic
117C2×C43#224911yescharacteristic
118C2×C43#225011yescharacteristic
119D43—321no—
120C2×SD32—22no—
121C2×D16—862no—
122#500—431no—
123#494C2×D4311yescharacteristic
124#493—431no—
125#493C2×D4311yescharacteristic
126#492—861no—
127#486—861no—
128#486—861no—
129#486—861no—
130#358—862no—
131#357—862no—
132C4×C16—431no—
133C4×C16C2×D4311yescharacteristic
134C82—431no—
135C43#1252711yescharacteristic, complemented, Sylow
136C2×Q16—21no—
137C2×Q16—21no—
138C2×SD16—1722no—
139C2×D8—21no—
140C2×D8—21no—
141C2×D8—861no—
142C2×D8—861no—
143C4⋊Q8—21no—
144C4⋊Q8—861no—
145#127—21no—
146#127—861no—
147SD32—44no—
148D16—1724no—
149C2×C16—432no—
150C2×C16C22⋊D4312yes—
151#107—861no—
152#107—861no—
153#102—1722no—
154#102—1722no—
155#102—1722no—
156C4×C8—431no—
157C4×C8—431no—
158C4×C8C22×D4311yescharacteristic
159C2×Q8—41no—
160C2×Q8—1721no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—1721no—
165C2×D4—1721no—
166C2×D4—1721no—
167Q16—42no—
168Q16—42no—
169SD16—3444no—
170D8—42no—
171D8—42no—
172D8—1722no—
173D8—1722no—
174C2×C8—432no—
175C2×C8—432no—
176C2×C8D4×D4311yescharacteristic
177C2×C8C2×C22⋊D4311yescharacteristic
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—1721no—
181C4⋊C4—1721no—
182C42D4×D4311yescharacteristic
183C16—22no—
184C16—862no—
185C23—81no—
186C23—3441no—
187Q8—81no—
188Q8—81no—
189Q8—3442no—
190D4—82no—
191D4—82no—
192D4—81no—
193D4—81no—
194D4—3442no—
195D4—3442no—
196D4—3441no—
197D4—3441no—
198C2×C4—81no—
199C2×C4—3441no—
200C2×C4#1306332111yescharacteristic
201C2×C4D8×D4311yescharacteristic
202C2×C4D8×D4311yescharacteristic
203C8—862no—
204C8—862no—
205C8#1306334912yes—
206C8#1306335112yes—
207C22—161no—
208C22—161no—
209C22—161no—
210C22—6881no—
211C22—6881no—
212C22—6881no—
213C22#1458327411yescharacteristic
214C4—161no—
215C4—6881no—
216C4#1458328611yescharacteristic
217C4#1458328711yescharacteristic
218C4#1458333012yes—
219C4#1458333612yes—
220C2—321no—
221C2—13761no—
222C2#1913426011yescharacteristic
223C2#1913685511yescharacteristic
224C2#1913686011yescharacteristic
subgroupG/H
centerC22#14583274
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2248C2
socleC22×C43#493
prime radical#19136844C2
hypercenter#2248D43
hypocenterC43#12527
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
2. #19136822C2semidirect
3. #19136819C2semidirect
4. #19134202C2semidirect
5. #19134184C2semidirect
6. #19132514C2semidirect
7. C43×#2248C2semidirect
108. #2248D43semidirect
135. C43#12527semidirect

Maximal subgroups

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

subgroupindex
#191368442
#191368222
#191368192
#191342022
#191341842
#191325142
C43×#22482
#1252743