Finite Group Databasebeta

← #24984089

Subgroups — #24984089

Order 11008.

268 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 39 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#19132531C211yesmaximal, characteristic, complemented
2#19132482C211yesmaximal, characteristic, complemented
3C43×#2010C211yesmaximal, characteristic
4C2×C22⋊(C43⋊C8)—21no—
5#14582681—21no—
6C43×#575C411yescharacteristic
7C43×#525—21no—
8C43×#421—21no—
9C43×#407C2211yescharacteristic
10C43×H(3,ℤ/4)C411yescharacteristic
11C22×C43⋊C8—41no—
12#13063265—41no—
13C22⋊(C43⋊C8)—22no—
14C22⋊(C43⋊C8)—41no—
15C2×#41×C43—21no—
16C23×C4×C43D411yescharacteristic
17#137×C43—41no—
18AGL(1,ℤ/8)×C43—41no—
19#135×C43—41no—
20C2×M16×C43C2×C411yescharacteristic
21C2×M16×C43D411yescharacteristic
22#123×C43—41no—
23C22⋊Q8×C43—41no—
24#121×C43—41no—
25#120×C43—41no—
26C4×D4×C43—42no—
27#117×C43—21no—
28#104×C43—42no—
29C22⋊C8×C43—41no—
30C24×C43SD1611yescharacteristic
31#41×C43—41no—
32#41×C43—41no—
33#41×C43—41no—
34#41×C43—41no—
35C2×Q8×C43—21no—
36C2×D4×C43—21no—
37C2×D4×C43—42no—
38C2×D4×C43—41no—
39C22×C4×C43—21no—
40C22×C4×C43—21no—
41C22×C4×C43—41no—
42C22×C4×C43—41no—
43C22×C4×C43—41no—
44C22×C4×C43C22⋊C411yescharacteristic
45C22×C4×C43D811yescharacteristic
46Q16×C43—41no—
47SD16×C43—42no—
48D8×C43—41no—
49M16×C43—41no—
50M16×C43—41no—
51C2×C8×C43—21no—
52C2×C8×C43—21no—
53C4⋊C4×C43—41no—
54C4⋊C4×C43—42no—
55C22⋊C4×C43—42no—
56C22⋊C4×C43—42no—
57C22⋊C4×C43—41no—
58C42×C43—22no—
59C2×C43⋊C8—42no—
60C2×C43⋊C8—81no—
61C2×C43⋊C8—81no—
62C43⋊C16—81no—
63C23×C43—21no—
64C23×C43—41no—
65C23×C43—42no—
66C23×C43—41no—
67C23×C43#10211yescharacteristic
68Q8×C43—41no—
69Q8×C43—41no—
70D4×C43—41no—
71D4×C43—41no—
72D4×C43—81no—
73D4×C43—84no—
74D4×C43—81no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43—42no—
82C2×C4×C43—41no—
83C2×C4×C43—81no—
84C2×C4×C43—81no—
85C2×C4×C43—81no—
86C2×C4×C43#9911yescharacteristic
87C2×C4×C43#10411yescharacteristic
88C8×C43—41no—
89C8×C43—41no—
90C43⋊C8—82no—
91#7397—431nomaximal, Sylow
92C22×C43—22no—
93C22×C43—21no—
94C22×C43—41no—
95C22×C43—41no—
96C22×C43—42no—
97C22×C43—41no—
98C22×C43—81no—
99C22×C43—82no—
100C22×C43—81no—
101C22×C43#32711yescharacteristic
102C4×C43—21no—
103C4×C43—41no—
104C4×C43—82no—
105C4×C43—81no—
106C4×C43AΣL(1,𝔽16)11yescharacteristic
107C4×C43#35311yescharacteristic
108#2010D4311yescharacteristic
109#1320—431no—
110#1298—431no—
111C2×C43—21no—
112C2×C43—41no—
113C2×C43—42no—
114C2×C43—161no—
115C2×C43#134311yescharacteristic
116#575Dic4311yescharacteristic
117#525—21no—
118#421—21no—
119#407C2×D4311yescharacteristic
120C2×C22⋊C8—861no—
121#349—861no—
122H(3,ℤ/4)Dic4311yescharacteristic
123C43#739711yescharacteristic, complemented, Sylow
124C2×#41—21no—
125C23×C4C22⋊D4311yescharacteristic
126#137—41no—
127AGL(1,ℤ/8)—41no—
128#135—41no—
129C2×M16C2×Dic4311yescharacteristic
130C2×M16C22⋊D4311yescharacteristic
131C22×C8—1721no—
132#123—41no—
133C22⋊Q8—41no—
134#121—41no—
135#120—41no—
136C4×D4—42no—
137#117—21no—
138M32—1721no—
139#104—42no—
140C22⋊C8—41no—
141C22⋊C8—862no—
142C22⋊C8—1721no—
143C24#1062188311yescharacteristic
144#41—41no—
145#41—41no—
146#41—41no—
147#41—41no—
148C2×Q8—21no—
149C2×D4—21no—
150C2×D4—42no—
151C2×D4—41no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4#1062188211yescharacteristic
158C22×C4C22⋊Dic4311yescharacteristic
159Q16—41no—
160SD16—42no—
161D8—41no—
162M16—41no—
163M16—41no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—3441no—
167C2×C8—3441no—
168C2×C8—1722no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C22⋊C4—41no—
174C42—22no—
175C16—3441no—
176C23—21no—
177C23—41no—
178C23—42no—
179C23—41no—
180C23#1306324611yescharacteristic
181Q8—41no—
182Q8—41no—
183D4—41no—
184D4—41no—
185D4—81no—
186D4—84no—
187D4—81no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4#1306324011yescharacteristic
200C2×C4#1306325211yescharacteristic
201C8—41no—
202C8—41no—
203C8—3442no—
204C22—22no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—41no—
210C22—81no—
211C22—82no—
212C22—81no—
213C22#1458263311yescharacteristic
214C4—21no—
215C4—41no—
216C4—82no—
217C4—81no—
218C4#1458268611yescharacteristic
219C4#1458269211yescharacteristic
220C2—21no—
221C2—41no—
222C2—42no—
223C2—161no—
224C2#1913259211yescharacteristic
subgroupG/H
centerC4#14582692
commutatorC2×M16×C43C2×C4
Frattini#407C2×D43
Fitting, prime radicalC43×#2010C2
socleC2×C43#1343
cosocleC43×#407C22
hypercenter#2010D43
hypocenterC43#7397
LCSG ▷ C2×M16×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #407 ◁ #2010

Complements

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

NH ≅ G/Ntype
1. #19132531C2semidirect
2. #19132482C2semidirect
123. C43#7397semidirect

Maximal subgroups

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

subgroupindex
#191325312
#191324822
C43×#20102
#739743