Finite Group Databasebeta

← #25009944

Subgroups — #25009944

Order 11008.

310 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 59 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#19136812C212yesmaximal, complemented
2#19136148C211yesmaximal, characteristic
3#19132583C212yesmaximal, complemented
4#19132533C211yesmaximal, characteristic
5C43×#3202C211yesmaximal, characteristic
6#14582948C2211yescharacteristic
7#14582925—21no—
8#14582916—21no—
9#14582721—22no—
10#14582715—22no—
11#14582681C2212yes—
12#14582656C2211yescharacteristic
13C43×#536—21no—
14C43×#485—22no—
15C43×#470C2212yes—
16C43×#467—21no—
17C43×#451—22no—
18C43×#408C2211yescharacteristic
19C2×#10621877—21no—
20#13063284—21no—
21#13063265—22no—
22#13063261—22no—
23Dic43⋊C8—42no—
24#13063252—42no—
25C2×#41×C43D411yescharacteristic
26C22×Q8×C43—21no—
27C2×Q16×C43—21no—
28C2×Q16×C43D412yes—
29C2×M16×C43C2311yescharacteristic
30C22×C8×C43D411yescharacteristic
31C4⋊Q8×C43—41no—
32#124×C43—41no—
33#123×C43—41no—
34#123×C43—41no—
35C22⋊Q8×C43—22no—
36C22⋊Q8×C43—22no—
37#117×C43—21no—
38#107×C43—21no—
39#106×C43D412yes—
40#103×C43—22no—
41#103×C43—22no—
42C22⋊C8×C43—22no—
43#41×C43—41no—
44#41×C43—41no—
45C2×Q8×C43—22no—
46C2×Q8×C43—41no—
47C2×Q8×C43—81no—
48C2×Q8×C43—81no—
49C2×Q8×C43SD1611yescharacteristic
50C2×D4×C43—21no—
51C2×D4×C43SD1611yescharacteristic
52C22×C4×C43—21no—
53C22×C4×C43—41no—
54C22×C4×C43C2×D411yescharacteristic
55Q16×C43—42no—
56Q16×C43—81no—
57M16×C43—41no—
58C2×C8×C43—21no—
59C2×C8×C43—41no—
60C2×C8×C43C2×D412yes—
61C4⋊C4×C43—22no—
62C4⋊C4×C43—42no—
63C4⋊C4×C43—42no—
64C22⋊C4×C43—41no—
65C22⋊C4×C43—42no—
66C22⋊C4×C43—42no—
67C42×C43—41no—
68C22⋊Dic43—41no—
69C4⋊Dic43—41no—
70C4×Dic43—22no—
71#10621877—41no—
72#10621877—41no—
73C2×C43⋊C8—41no—
74C43⋊C16—42no—
75C23×C43—21no—
76C23×C43AGL(1,ℤ/8)11yescharacteristic
77Q8×C43—41no—
78Q8×C43—42no—
79Q8×C43—42no—
80Q8×C43—82no—
81D4×C43—41no—
82D4×C43—81no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—82no—
91C2×C4×C43#12011yescharacteristic
92C2×C4×C43C2×SD1611yescharacteristic
93C2×Dic43—42no—
94C8×C43—22no—
95C8×C43—41no—
96C43⋊C8—81no—
97#12302—431nomaximal, Sylow
98C22×C43—21no—
99C22×C43—41no—
100C22×C43—42no—
101C22×C43—41no—
102C22×C43#45011yescharacteristic
103C4×C43—21no—
104C4×C43—41no—
105C4×C43—82no—
106C4×C43—82no—
107C4×C43#45311yescharacteristic
108C4×C43#45811yescharacteristic
109Dic43—82no—
110#3202D4311yescharacteristic
111#2239—432no—
112#2098—431no—
113#1340—432no—
114#1321—431no—
115C2×C43—21no—
116C2×C43—41no—
117C2×C43—81no—
118C2×C43#161311yescharacteristic
119#536—21no—
120#485—22no—
121#470C2×D4312yes—
122#467—21no—
123#451—22no—
124#430—431no—
125#424—861no—
126#421—861no—
127#408C2×D4311yescharacteristic
128#365—862no—
129#362—862no—
130#349—432no—
131H(3,ℤ/4)—431no—
132C43#1230211yescharacteristic, complemented, Sylow
133C2×#41C22⋊D4311yescharacteristic
134C22×Q8—21no—
135C2×Q16—21no—
136C2×Q16C22⋊D4312yes—
137C2×M16—861no—
138C2×M16C22×D4311yescharacteristic
139C22×C8C22⋊D4311yescharacteristic
140C4⋊Q8—41no—
141#124—41no—
142#123—41no—
143#123—41no—
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146#117—21no—
147#117—861no—
148M32—862no—
149#108—862no—
150#107—21no—
151#106C22⋊D4312yes—
152C4⋊C8—1722no—
153#104—1722no—
154#103—22no—
155#103—22no—
156C22⋊C8—22no—
157#41—41no—
158#41—41no—
159C2×Q8—22no—
160C2×Q8—41no—
161C2×Q8—81no—
162C2×Q8—81no—
163C2×Q8#1062188311yescharacteristic
164C2×D4—21no—
165C2×D4#1062188311yescharacteristic
166C22×C4—21no—
167C22×C4—41no—
168C22×C4C2×C22⋊D4311yescharacteristic
169Q16—42no—
170Q16—81no—
171M16—41no—
172M16—1721no—
173M16—1721no—
174C2×C8—21no—
175C2×C8—41no—
176C2×C8—1721no—
177C2×C8C2×C22⋊D4312yes—
178C4⋊C4—22no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—1721no—
182C22⋊C4—41no—
183C22⋊C4—42no—
184C22⋊C4—42no—
185C22⋊C4—1721no—
186C42—41no—
187C42—862no—
188C16—1722no—
189C23—21no—
190C23#1306335111yescharacteristic
191Q8—41no—
192Q8—42no—
193Q8—42no—
194Q8—82no—
195D4—41no—
196D4—81no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—82no—
205C2×C4—1722no—
206C2×C4#1306329411yescharacteristic
207C2×C4C2×#1062188311yescharacteristic
208C8—22no—
209C8—41no—
210C8—3441no—
211C22—21no—
212C22—41no—
213C22—42no—
214C22—41no—
215C22#1458305011yescharacteristic
216C4—21no—
217C4—41no—
218C4—82no—
219C4—82no—
220C4—3442no—
221C4#1458306711yescharacteristic
222C4#1458308911yescharacteristic
223C2—21no—
224C2—41no—
225C2—81no—
226C2#1913361511yescharacteristic
subgroupG/H
centerC2#19133615
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#3202C2
socleC2×C43#1613
prime radicalC2×#41×C43D4
hypercenter#3202D43
hypocenterC43#12302
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3202

Complements

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

NH ≅ G/Ntype
1. #19136812C2semidirect
3. #19132583C2semidirect
132. C43#12302semidirect

Maximal subgroups

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

subgroupindex
#191368122
#191361482
#191325832
#191325332
C43×#32022
#1230243