Finite Group Databasebeta

← #25015686

Subgroups — #25015686

Order 11008.

370 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 99 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#19145119C211yesmaximal, characteristic
2#19136315C212yesmaximal
3#19132702C212yesmaximal
4#19132679C211yesmaximal, characteristic
5C43×#1971C211yesmaximal, characteristic
6#14583456—21no—
7C2×#13063265C2212yes—
8#14583308—24no—
9#14582937—21no—
10#14582937C2212yes—
11#14582703—24no—
12C22×Q16×C43C2211yescharacteristic
13C2×#106×C43C2211yescharacteristic
14C2×#103×C43—21no—
15C2×#97×C43C2211yescharacteristic
16C43×#391—21no—
17#13063325—22no—
18#13063317—22no—
19#13063304—42no—
20C4×Dic86—42no—
21#13063284—22no—
22#13063265—22no—
23#13063265—22no—
24C2×C43⋊C16—22no—
25#13063259—22no—
26#13063259D414yes—
27#13063257—22no—
28#13063257—22no—
29C22×Q8×C43—21no—
30C2×Q16×C43—22no—
31C2×Q16×C43—22no—
32C2×Q16×C43—21no—
33C2×Q16×C43Q812yescomplemented
34C22×C8×C43D411yescharacteristic
35C22×C8×C43C2311yescharacteristic
36C2×C4⋊C4×C43—21no—
37C2×C42×C43D411yescharacteristic
38#106×C43—22no—
39#103×C43—42no—
40#97×C43—22no—
41#95×C43—42no—
42C2×Q8×C43—22no—
43C2×Q8×C43—41no—
44C2×Q8×C43—41no—
45C2×Q8×C43—41no—
46C2×Q8×C43—41no—
47C2×Q8×C43—41no—
48C22×C4×C43—41no—
49C22×C4×C43—41no—
50C22×C4×C43D812yes—
51C22×C4×C43C2×D411yescharacteristic
52C2×Dic86—42no—
53Q16×C43—24no—
54Q16×C43—42no—
55C2×C8×C43—21no—
56C2×C8×C43—21no—
57C2×C8×C43SD1612yes—
58C2×C8×C43C2×D412yes—
59C2×C8×C43C2×Q811yescharacteristic
60C2×C8×C43#4111yescharacteristic
61C2×C8×C43#4112yes—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—41no—
64C42×C43—21no—
65C42×C43—21no—
66C22⋊Dic43—42no—
67C4⋊Dic43—24no—
68C4⋊Dic43—42no—
69Dic43⋊C4—44no—
70C4×Dic43—42no—
71C43⋊C16—42no—
72C23×C43C2×D811yescharacteristic
73Q8×C43—42no—
74Q8×C43—42no—
75Q8×C43—81no—
76Q8×C43—81no—
77C2×C4×C43—22no—
78C2×C4×C43—42no—
79C2×C4×C43—42no—
80C2×C4×C43—81no—
81C2×C4×C43—81no—
82C2×C4×C43—82no—
83C2×C4×C43—81no—
84C2×C4×C43#12011yescharacteristic
85C2×C4×C43C22⋊Q811yescharacteristic
86C2×C4×C43#12411yescharacteristic
87C2×C4×C43C2×SD1611yescharacteristic
88C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
89C2×C4×C43#13711yescharacteristic
90C2×Dic43—44no—
91Dic86—84no—
92C8×C43—22no—
93C8×C43C22⋊Q812yes—
94C8×C43#12412yes—
95#13368—431nomaximal, Sylow
96C22×C43—22no—
97C22×C43#44711yescharacteristic
98C22×C43#47411yescharacteristic
99C22×C43#48611yescharacteristic
100C4×C43—42no—
101C4×C43—82no—
102C4×C43—161no—
103C4×C43#39311yescharacteristic
104C4×C43#44811yescharacteristic
105C4×C43#47611yescharacteristic
106C4×C43#48911yescharacteristic
107Dic43—84no—
108#3162—431no—
109#2141—432no—
110#1971D4311yescharacteristic
111#1386—432no—
112#1377—431no—
113C2×C43—21no—
114C2×C43—21no—
115C2×C43#202311yescharacteristic
116C2×C43#219112yes—
117C22×Q16C2×D4311yescharacteristic
118#533—861no—
119C2×M32—432no—
120#501—864no—
121#427—432no—
122#427—861no—
123C2×#106C2×D4311yescharacteristic
124C2×#103—21no—
125C2×#97C2×D4311yescharacteristic
126#391—21no—
127#358—864no—
128C43#1336811yescharacteristic, complemented, Sylow
129C22×Q8—21no—
130C2×Q16—21no—
131C2×Q16—22no—
132C2×Q16—22no—
133C2×Q16Dic8612yescomplemented
134C22×C8C22⋊D4311yescharacteristic
135C22×C8C22×D4311yescharacteristic
136C4⋊Q8—862no—
137#125—862no—
138C22⋊Q8—1722no—
139C4×Q8—1722no—
140#117—862no—
141C2×C4⋊C4—21no—
142C2×C42C22⋊D4311yescharacteristic
143M32—862no—
144M32—862no—
145C2×C16—862no—
146#107—434no—
147#107—862no—
148#106—22no—
149#106—862no—
150#106—862no—
151#103—42no—
152#97—22no—
153#95—42no—
154C2×Q8—22no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—1722no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4#1062188212yes—
164C22×C4C2×C22⋊D4311yescharacteristic
165Q16—24no—
166Q16—42no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8#1062188312yes—
170C2×C8C2×Dic8611yescharacteristic
171C2×C8#1062189811yescharacteristic
172C2×C8D4×D4312yes—
173C2×C8#1062190012yes—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—864no—
177C4⋊C4—1724no—
178C4⋊C4—1722no—
179C22⋊C4—1722no—
180C42—21no—
181C42—21no—
182C42—1722no—
183C16—1722no—
184C23C2×#1062188211yescharacteristic
185Q8—42no—
186Q8—42no—
187Q8—81no—
188Q8—81no—
189Q8—3444no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—1724no—
198C2×C4#1306329311yescharacteristic
199C2×C4#1306330411yescharacteristic
200C2×C4#1306331211yescharacteristic
201C2×C4C2×#1062188311yescharacteristic
202C2×C4#1306335011yescharacteristic
203C2×C4#1306335511yescharacteristic
204C8—22no—
205C8#1306330212yes—
206C8#1306331112yes—
207C22—22no—
208C22#1458303211yescharacteristic
209C22#1458317911yescharacteristic
210C22#1458324511yescharacteristic
211C4—42no—
212C4—82no—
213C4—161no—
214C4—3444no—
215C4#1458281111yescharacteristic
216C4#1458303711yescharacteristic
217C4#1458318911yescharacteristic
218C4#1458325811yescharacteristic
219C2—21no—
220C2—21no—
221C2#1913573111yescharacteristic
222C2#1913654512yes—
subgroupG/H
centerC22#14583032
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1971C2
socleC22×C43#447
prime radicalC23×C43C2×D8
hypercenter#1971D43
hypocenterC43#13368
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #1971

Complements

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

NH ≅ G/Ntype
33. C2×Q16×C43Q8semidirect
128. C43#13368semidirect
133. C2×Q16Dic86semidirect

Maximal subgroups

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

subgroupindex
#191451192
#191363152
#191327022
#191326792
C43×#19712
#1336843