Finite Group Databasebeta

← #24999361

Subgroups — #24999361

Order 11008.

478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 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#19145986C212yesmaximal
2#19135573C212yesmaximal
3#19135571C211yesmaximal, characteristic
4C43⋊#1309C211yesmaximal, characteristic
5C43×#3255C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583184—22no—
8#14583181—22no—
9#14583155—24no—
10#14583109—22no—
11#14583106—22no—
12#14582923C2212yes—
13C42×Dic43C2211yescharacteristic
14#14582660—22no—
15#14582658—24no—
16C43×#533C2212yes—
17C43×#475—22no—
18C43×#470—22no—
19C43×#462—22no—
20C43×#423C2211yescharacteristic
21C2×#10621885—24no—
22C2×#10621877D414yes—
23#13063325D412yes—
24#13063317—21no—
25#13063304—22no—
26C4×Dic86—22no—
27#13063284—21no—
28C2×C4×Dic43—22no—
29C2×C4×Dic43—21no—
30#13063256—24no—
31C4⋊(C43⋊C8)—22no—
32C4⋊(C43⋊C8)—22no—
33#13063249—24no—
34#13063248—24no—
35C2×Q16×C43—22no—
36C2×M16×C43D412yes—
37C4⋊Q8×C43D412yes—
38C4⋊Q8×C43D412yes—
39#125×C43—22no—
40C22⋊Q8×C43—22no—
41C22⋊Q8×C43—22no—
42C4×Q8×C43—22no—
43C4×Q8×C43—22no—
44#117×C43—22no—
45C2×C42×C43C2311yescharacteristic
46#106×C43—22no—
47C4⋊C8×C43—22no—
48#103×C43—24no—
49C2×Q8×C43—22no—
50C2×Q8×C43—22no—
51C22×C4×C43C2×D412yes—
52C22×C4×C43C2×D411yescharacteristic
53C22×Dic43—41no—
54C2×Dic86—22no—
55Q16×C43—82no—
56M16×C43—42no—
57C2×C8×C43—22no—
58C4⋊C4×C43—22no—
59C4⋊C4×C43—22no—
60C4⋊C4×C43—22no—
61C4⋊C4×C43—22no—
62C4⋊C4×C43—42no—
63C4⋊C4×C43—42no—
64C22⋊C4×C43—42no—
65C42×C43—42no—
66C42×C43C2×D411yescharacteristic
67C42×C43C2×D412yes—
68C42×C43#4111yescharacteristic
69C22⋊Dic43—41no—
70#10621885—84no—
71C4⋊Dic43—22no—
72C4⋊Dic43—22no—
73Dic43⋊C4—42no—
74C4×Dic43—24no—
75C4×Dic43—22no—
76C4×Dic43—42no—
77C4×Dic43—41no—
78C4×Dic43—41no—
79#10621877—44no—
80C2×C43⋊C8—24no—
81C23×C43#12711yescharacteristic
82Q8×C43—42no—
83Q8×C43—42no—
84Q8×C43—42no—
85Q8×C43—42no—
86C2×C4×C43—22no—
87C2×C4×C43—21no—
88C2×C4×C43—22no—
89C2×C4×C43—21no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43#12012yes—
93C2×C4×C43#12011yescharacteristic
94C2×C4×C43#12111yescharacteristic
95C2×C4×C43#12112yes—
96C2×Dic43—44no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99Dic86—42no—
100Dic86—42no—
101C8×C43—42no—
102C43⋊C8—44no—
103#10303—431nomaximal, Sylow
104C22×C43—22no—
105C22×C43—21no—
106C22×C43#39211yescharacteristic
107C4×C43—22no—
108C4×C43—21no—
109C4×C43—82no—
110C4×C43—82no—
111C4×C43#45512yes—
112C4×C43#45511yescharacteristic
113C4×C43#45612yes—
114C4×C43#45611yescharacteristic
115Dic43—44no—
116Dic43—82no—
117#3255—432no—
118#3255D4311yescharacteristic
119#1994—431no—
120#1994—432no—
121#1309—431no—
122C2×C43—41no—
123C2×C43#200712yes—
124C2×C43#200711yescharacteristic
125#533—431no—
126#533C2×D4312yes—
127#475—22no—
128#475—862no—
129#475—862no—
130#470—22no—
131#470—864no—
132#462—22no—
133#462—862no—
134#462—862no—
135#423—432no—
136#423C2×D4311yescharacteristic
137C43—431no—
138#339—864no—
139#339—862no—
140C43#1030311yescharacteristic, complemented, Sylow
141C2×Q16—22no—
142C2×Q16—864no—
143C2×M16—434no—
144C2×M16C22⋊D4312yes—
145C4⋊Q8—432no—
146C4⋊Q8C22⋊D4312yes—
147C4⋊Q8C22⋊D4312yes—
148#125—22no—
149#125—861no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152C22⋊Q8—862no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—862no—
156#117—22no—
157#117—861no—
158C2×C42—862no—
159C2×C42—861no—
160C2×C42C22×D4311yescharacteristic
161#106—22no—
162#106—864no—
163C4⋊C8—22no—
164C4⋊C8—862no—
165C4⋊C8—862no—
166#103—24no—
167#103—864no—
168#103—864no—
169C2×Q8—22no—
170C2×Q8—22no—
171C2×Q8—862no—
172C22×C4—1721no—
173C22×C4D4×D4312yes—
174C22×C4C2×C22⋊D4311yescharacteristic
175Q16—82no—
176Q16—3444no—
177M16—42no—
178M16—1724no—
179C2×C8—22no—
180C2×C8—864no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—862no—
188C4⋊C4—862no—
189C4⋊C4—1722no—
190C22⋊C4—42no—
191C22⋊C4—1721no—
192C42—42no—
193C42—864no—
194C42—862no—
195C42—1722no—
196C42—1721no—
197C42—1721no—
198C42D4×D4311yescharacteristic
199C42#1062190011yescharacteristic
200C42C2×C22⋊D4312yes—
201C23#1306332111yescharacteristic
202Q8—42no—
203Q8—42no—
204Q8—42no—
205Q8—42no—
206Q8—1722no—
207Q8—1722no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—1722no—
215C2×C4—1724no—
216C2×C4—1722no—
217C2×C4#1306329312yes—
218C2×C4#1306329411yescharacteristic
219C2×C4#1306329611yescharacteristic
220C2×C4#1306329712yes—
221C8—42no—
222C8—1724no—
223C22—22no—
224C22—21no—
225C22#1458280711yescharacteristic
226C4—22no—
227C4—21no—
228C4—82no—
229C4—82no—
230C4—3442no—
231C4—1724no—
232C4#1458307512yes—
233C4#1458307711yescharacteristic
234C4#1458308012yes—
235C4#1458308211yescharacteristic
236C2—41no—
237C2#1913564012yes—
238C2#1913564211yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3255C2
socleC22×C43#392
prime radicalC23×C43#127
hypercenter#3255D43
hypocenterC43#10303
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
140. C43#10303semidirect

Maximal subgroups

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

subgroupindex
#191459862
#191355732
#191355712
C43⋊#13092
C43×#32552
#1030343