Finite Group Databasebeta

← #25010356

Subgroups — #25010356

Order 11008.

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

normal subgroups only

This group has 358 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#19134181C211yesmaximal, characteristic, complemented
3#19132636C211yesmaximal, characteristic, complemented
4#19132568C212yesmaximal, complemented
5C43×#3291C211yesmaximal, characteristic
6#14583297C2211yescharacteristic, complemented
7#14583295—21no—
8#14583271—21no—
9#14582723—22no—
10#14582720C2212yescomplemented
11#14582709—22no—
12C8×C43⋊C8C2211yescharacteristic, complemented
13C43×#577—22no—
14C43×#492C2211yescharacteristic
15C43×#471—22no—
16C43×#456—21no—
17C43×#453—21no—
18C43×#443C2212yes—
19C2×#10621883—42no—
20#13063325—21no—
21#13063265—22no—
22#13063257—22no—
23#13063256—42no—
24C4×C43⋊C8—21no—
252−1+4×C43—21no—
26H(5,𝔽2)×C43—21no—
27#137×C43—22no—
28#137×C43—42no—
29AGL(1,ℤ/8)×C43—22no—
30AGL(1,ℤ/8)×C43—42no—
31#135×C43—42no—
32#135×C43D412yes—
33C2×SD16×C43—22no—
34C2×SD16×C43—42no—
35#131×C43—22no—
36C4⋊Q8×C43D411yescharacteristic
37#127×C43D411yescharacteristic
38#108×C43D412yes—
39#104×C43—22no—
40#101×C43—21no—
41#100×C43—21no—
42C4×C8×C43C2311yescharacteristic
43#41×C43—22no—
44#41×C43—42no—
45#41×C43—42no—
46#41×C43—81no—
47C2×Q8×C43—21no—
48C2×Q8×C43—42no—
49C2×D4×C43—21no—
50C2×D4×C43—41no—
51C2×D4×C43—42no—
52C2×D4×C43—81no—
53C2×Dic86—41no—
54Q16×C43—42no—
55Q16×C43SD1612yescomplemented
56SD16×C43—22no—
57SD16×C43—42no—
58SD16×C43—42no—
59SD16×C43—42no—
60SD16×C43—42no—
61D8×C43—42no—
62D8×C43SD1612yescomplemented
63M16×C43—22no—
64M16×C43—42no—
65C2×C8×C43—42no—
66C2×C8×C43C2×D412yes—
67C4⋊C4×C43—41no—
68C42×C43C2×D411yescharacteristic
69#10621883—84no—
70C4⋊Dic43—41no—
71C4⋊Dic43—41no—
72C2×C43⋊C8—22no—
73C43⋊C16—42no—
74C23×C43—41no—
75C23×C43—81no—
76Q8×C43—22no—
77Q8×C43—42no—
78Q8×C43—81no—
79D4×C43—22no—
80D4×C43—42no—
81D4×C43—42no—
82D4×C43—82no—
83D4×C43—82no—
84D4×C43—81no—
85C2×C4×C43—21no—
86C2×C4×C43—42no—
87C2×C4×C43—41no—
88C2×C4×C43—81no—
89C2×C4×C43—82no—
90C2×C4×C43#12011yescharacteristic
91C2×Dic43—81no—
92Dic86—82no—
93C8×C43—42no—
94C8×C43C2×SD1612yes—
95C8×C43AGL(1,ℤ/8)12yes—
96C43⋊C8—24no—
97#12364—431nomaximal, Sylow
98C22×C43—42no—
99C22×C43—81no—
100C22×C43—161no—
101C22×C43—321no—
102C22×C43#45311yescharacteristic
103C4×C43—22no—
104C4×C43—42no—
105C4×C43—81no—
106C4×C43#45012yes—
107Dic43—161no—
108#3291D4311yescharacteristic
109#2230—432no—
110#1705—431no—
111#1359—431no—
112#1335—432no—
113C2×C43—21no—
114C2×C43—82no—
115C2×C43—161no—
116C2×C43#162911yescharacteristic
117#577—22no—
118#498—431no—
119#498—861no—
120#492—861no—
121#492C2×D4311yescharacteristic
122#471—22no—
123#456—21no—
124#453—21no—
125#443C2×D4312yes—
126#365—862no—
127#364—432no—
128#360—862no—
129C82—431no—
130C43#1236411yescharacteristic, complemented, Sylow
1312−1+4—21no—
132H(5,𝔽2)—21no—
133#137—22no—
134#137—42no—
135AGL(1,ℤ/8)—22no—
136AGL(1,ℤ/8)—42no—
137#135—42no—
138#135C22⋊D4312yes—
139C2×SD16—22no—
140C2×SD16—42no—
141C2×SD16—1722no—
142#131—22no—
143C4⋊Q8—861no—
144C4⋊Q8C22⋊D4311yescharacteristic
145#127C22⋊D4311yescharacteristic
146M32—862no—
147#108C22⋊D4312yes—
148#106—862no—
149#106—1722no—
150#104—22no—
151#101—21no—
152#100—21no—
153C4×C8—861no—
154C4×C8C22×D4311yescharacteristic
155#41—22no—
156#41—42no—
157#41—42no—
158#41—81no—
159C2×Q8—21no—
160C2×Q8—42no—
161C2×Q8—1721no—
162C2×D4—21no—
163C2×D4—41no—
164C2×D4—42no—
165C2×D4—81no—
166Q16—42no—
167Q16#1062188312yescomplemented
168SD16—22no—
169SD16—42no—
170SD16—42no—
171SD16—42no—
172SD16—42no—
173SD16—3444no—
174D8—42no—
175D8#1062188312yescomplemented
176M16—22no—
177M16—42no—
178C2×C8—42no—
179C2×C8—862no—
180C2×C8C2×C22⋊D4312yes—
181C4⋊C4—41no—
182C4⋊C4—1721no—
183C4⋊C4—1721no—
184C42C2×C22⋊D4311yescharacteristic
185C16—1722no—
186C23—41no—
187C23—81no—
188Q8—22no—
189Q8—42no—
190Q8—81no—
191Q8—3442no—
192D4—22no—
193D4—42no—
194D4—42no—
195D4—82no—
196D4—82no—
197D4—81no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—81no—
202C2×C4—82no—
203C2×C4—3441no—
204C2×C4#1306329411yescharacteristic
205C8—42no—
206C8—864no—
207C8C2×#1062188312yes—
208C8#1306335112yes—
209C22—42no—
210C22—81no—
211C22—161no—
212C22—321no—
213C22#1458306711yescharacteristic
214C4—22no—
215C4—42no—
216C4—81no—
217C4—6881no—
218C4#1458305012yes—
219C2—21no—
220C2—82no—
221C2—161no—
222C2#1913371111yescharacteristic
subgroupG/H
centerC2#19133711
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
Fitting, prime radicalC43×#3291C2
socleC2×C43#1629
hypercenter#3291D43
hypocenterC43#12364
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #3291

Complements

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

NH ≅ G/Ntype
1. #19136766C2semidirect
2. #19134181C2semidirect
3. #19132636C2semidirect
4. #19132568C2semidirect
6. #14583297C22semidirect
10. #14582720C22semidirect
12. C8×C43⋊C8C22semidirect
55. Q16×C43SD16semidirect
62. D8×C43SD16semidirect
130. C43#12364semidirect
167. Q16#10621883semidirect
175. D8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191367662
#191341812
#191326362
#191325682
C43×#32912
#1236443