Finite Group Databasebeta

← #25010366

Subgroups — #25010366

Order 11008.

364 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 67 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#19136766C212yesmaximal, complemented
2#19134221C211yesmaximal, characteristic, complemented
3#19132632C211yesmaximal, characteristic, complemented
4#19132571C212yesmaximal, complemented
5C43×#3292C211yesmaximal, characteristic
6#14583297C2211yescharacteristic, complemented
7#14583271—21no—
8#14583245—21no—
9#14582723—22no—
10#14582720C2212yescomplemented
11#14582709—22no—
12#14582620C2211yescharacteristic, complemented
13C43×#576—22no—
14C43×#493C2211yescharacteristic
15C43×#472—22no—
16C43×#453—21no—
17C43×#453—21no—
18C43×#443C2212yes—
19C2×#10621883—42no—
20#13063325—21no—
21#13063265—22no—
22#13063257—22no—
23#13063246—42no—
24C4×C43⋊C8—21no—
25H(5,𝔽2)×C43—21no—
26H(5,𝔽2)×C43—21no—
27AGL(1,ℤ/8)×C43—22no—
28AGL(1,ℤ/8)×C43—22no—
29AGL(1,ℤ/8)×C43—42no—
30AGL(1,ℤ/8)×C43—42no—
31#135×C43—42no—
32#135×C43D412yes—
33C2×D8×C43—22no—
34C2×D8×C43—42no—
35#131×C43—22no—
36#127×C43D411yescharacteristic
37#127×C43D411yescharacteristic
38#108×C43D412yes—
39#104×C43—22no—
40#100×C43—21no—
41#100×C43—21no—
42C4×C8×C43C2311yescharacteristic
43#41×C43—22no—
44#41×C43—42no—
45#41×C43—42no—
46C2×D4×C43—21no—
47C2×D4×C43—21no—
48C2×D4×C43—41no—
49C2×D4×C43—41no—
50C2×D4×C43—42no—
51C2×D4×C43—42no—
52C2×D4×C43—81no—
53C2×D4×C43—81no—
54C2×Dic86—41no—
55Q16×C43SD1612yescomplemented
56SD16×C43—22no—
57SD16×C43—42no—
58SD16×C43—42no—
59D8×C43—42no—
60D8×C43—42no—
61D8×C43—42no—
62D8×C43—42no—
63D8×C43SD1612yescomplemented
64M16×C43—22no—
65M16×C43—42no—
66C2×C8×C43—42no—
67C2×C8×C43C2×D412yes—
68C42×C43C2×D411yescharacteristic
69#10621883—84no—
70C4⋊Dic43—41no—
71C4⋊Dic43—41no—
72C2×C43⋊C8—22no—
73C43⋊C16—42no—
74C23×C43—41no—
75C23×C43—41no—
76C23×C43—81no—
77C23×C43—81no—
78Q8×C43—22no—
79D4×C43—22no—
80D4×C43—42no—
81D4×C43—42no—
82D4×C43—42no—
83D4×C43—82no—
84D4×C43—82no—
85D4×C43—82no—
86D4×C43—82no—
87C2×C4×C43—21no—
88C2×C4×C43—42no—
89C2×C4×C43—81no—
90C2×C4×C43—81no—
91C2×C4×C43#12011yescharacteristic
92C2×Dic43—81no—
93Dic86—82no—
94C8×C43—42no—
95C8×C43C2×SD1612yes—
96C8×C43AGL(1,ℤ/8)12yes—
97C43⋊C8—42no—
98#12366—431nomaximal, Sylow
99C22×C43—42no—
100C22×C43—81no—
101C22×C43—81no—
102C22×C43—161no—
103C22×C43—161no—
104C22×C43—321no—
105C22×C43—321no—
106C22×C43#45311yescharacteristic
107C4×C43—22no—
108C4×C43—42no—
109C4×C43#45012yes—
110Dic43—161no—
111#3292D4311yescharacteristic
112#2230—432no—
113#1715—431no—
114#1357—431no—
115#1336—432no—
116C2×C43—21no—
117C2×C43—82no—
118C2×C43—161no—
119C2×C43—161no—
120C2×C43#162911yescharacteristic
121#576—22no—
122#498—431no—
123#493C2×D4311yescharacteristic
124#492—861no—
125#486—861no—
126#472—22no—
127#453—21no—
128#453—21no—
129#443C2×D4312yes—
130#365—862no—
131#364—432no—
132#360—862no—
133#322—431no—
134C43#1236611yescharacteristic, complemented, Sylow
135H(5,𝔽2)—21no—
136H(5,𝔽2)—21no—
137AGL(1,ℤ/8)—22no—
138AGL(1,ℤ/8)—22no—
139AGL(1,ℤ/8)—42no—
140AGL(1,ℤ/8)—42no—
141#135—42no—
142#135C22⋊D4312yes—
143C2×SD16—1722no—
144C2×D8—22no—
145C2×D8—42no—
146#131—22no—
147C4⋊Q8—861no—
148#127C22⋊D4311yescharacteristic
149#127C22⋊D4311yescharacteristic
150M32—862no—
151#108C22⋊D4312yes—
152#106—862no—
153#104—22no—
154#102—1722no—
155#100—21no—
156#100—21no—
157C4×C8—861no—
158C4×C8C22×D4311yescharacteristic
159#41—22no—
160#41—42no—
161#41—42no—
162C2×Q8—1721no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—42no—
168C2×D4—42no—
169C2×D4—81no—
170C2×D4—81no—
171Q16#1062188312yescomplemented
172SD16—22no—
173SD16—42no—
174SD16—42no—
175SD16—3444no—
176D8—42no—
177D8—42no—
178D8—42no—
179D8—42no—
180D8#1062188312yescomplemented
181M16—22no—
182M16—42no—
183C2×C8—42no—
184C2×C8—862no—
185C2×C8C2×C22⋊D4312yes—
186C4⋊C4—1721no—
187C4⋊C4—1721no—
188C42C2×C22⋊D4311yescharacteristic
189C16—1722no—
190C23—41no—
191C23—41no—
192C23—81no—
193C23—81no—
194Q8—22no—
195Q8—3442no—
196D4—22no—
197D4—42no—
198D4—42no—
199D4—42no—
200D4—82no—
201D4—82no—
202D4—82no—
203D4—82no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—81no—
207C2×C4—81no—
208C2×C4—3441no—
209C2×C4#1306329411yescharacteristic
210C8—42no—
211C8—1722no—
212C8C2×#1062188312yes—
213C8#1306335112yes—
214C22—42no—
215C22—81no—
216C22—81no—
217C22—161no—
218C22—161no—
219C22—321no—
220C22—321no—
221C22#1458306711yescharacteristic
222C4—22no—
223C4—42no—
224C4—6881no—
225C4#1458305012yes—
226C2—21no—
227C2—82no—
228C2—161no—
229C2—161no—
230C2#1913371111yescharacteristic
subgroupG/H
centerC2#19133711
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
Fitting, prime radicalC43×#3292C2
socleC2×C43#1629
hypercenter#3292D43
hypocenterC43#12366
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #3292

Complements

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

NH ≅ G/Ntype
1. #19136766C2semidirect
2. #19134221C2semidirect
3. #19132632C2semidirect
4. #19132571C2semidirect
6. #14583297C22semidirect
10. #14582720C22semidirect
12. #14582620C22semidirect
55. Q16×C43SD16semidirect
63. D8×C43SD16semidirect
134. C43#12366semidirect
171. Q16#10621883semidirect
180. D8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191367662
#191342212
#191326322
#191325712
C43×#32922
#1236643