Finite Group Databasebeta

← #24997556

Subgroups — #24997556

Order 11008.

468 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 85 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#19144721C212yesmaximal
2#19135534C211yesmaximal, characteristic
3#19133210C212yesmaximal
4#19132465C211yesmaximal, characteristic
5C43×#3249C211yesmaximal, characteristic
6C2×C4×Dic86C2211yescharacteristic
7#14583227—22no—
8#14583181—22no—
9#14583106—22no—
10#14583054—22no—
11#14583004—24no—
12#14582956C2212yes—
13C2×#13063236C2211yescharacteristic
14#14582653—22no—
15#14582641—24no—
16C43×#533C2212yes—
17C43×#477—22no—
18C43×#467—22no—
19C43×#462—22no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C22×Dic86D411yescharacteristic
22C2×#10621885—24no—
23C22×C43⋊C8—21no—
24C4×Dic86—22no—
25C4×Dic86—22no—
26C2×C4⋊Dic43D411yescharacteristic
27C2×Dic43⋊C4—21no—
28C2×C4×Dic43—21no—
29#13063256—24no—
30C4⋊(C43⋊C8)—22no—
31#13063249—24no—
32#13063248—24no—
33C22⋊(C43⋊C8)—22no—
34#13063236—22no—
35#13063236D414yes—
36C2×Q16×C43—22no—
37C22×C8×C43D412yes—
38C4⋊Q8×C43D412yes—
39C4⋊Q8×C43D412yes—
40#125×C43—22no—
41C22⋊Q8×C43—22no—
42C22⋊Q8×C43—22no—
43C4×Q8×C43—22no—
44C4×Q8×C43—22no—
45#117×C43—22no—
46C2×C42×C43C2311yescharacteristic
47#107×C43—22no—
48C4⋊C8×C43—22no—
49#103×C43—24no—
50C2×Q8×C43—22no—
51C2×Q8×C43—22no—
52C22×C4×C43C2×D411yescharacteristic
53C22×C4×C43C2×D411yescharacteristic
54C22×C4×C43#4111yescharacteristic
55C22×Dic43—21no—
56C22×Dic43—21no—
57C2×Dic86—22no—
58C2×Dic86—42no—
59Q16×C43—82no—
60C2×C8×C43—22no—
61C2×C8×C43—42no—
62C4⋊C4×C43—22no—
63C4⋊C4×C43—22no—
64C4⋊C4×C43—22no—
65C4⋊C4×C43—22no—
66C4⋊C4×C43—42no—
67C4⋊C4×C43—42no—
68C22⋊C4×C43—42no—
69C42×C43—42no—
70C42×C43C2×D412yes—
71C42×C43C2×D412yes—
72#10621885—48no—
73C4⋊Dic43—22no—
74Dic43⋊C4—42no—
75C4×Dic43—41no—
76C4×Dic43—41no—
77C2×C43⋊C8—22no—
78C2×C43⋊C8—24no—
79C2×C43⋊C8—41no—
80C2×C43⋊C8—41no—
81C23×C43#12111yescharacteristic
82Q8×C43—44no—
83Q8×C43—42no—
84Q8×C43—42no—
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—21no—
88C2×C4×C43—41no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43#12012yes—
92C2×C4×C43#12011yescharacteristic
93C2×C4×C43#12112yes—
94C2×C4×C43#12711yescharacteristic
95C2×Dic43—22no—
96C2×Dic43—41no—
97C2×Dic43—41no—
98C2×Dic43—41no—
99C2×Dic43—42no—
100Dic86—24no—
101Dic86—42no—
102C8×C43—42no—
103C43⋊C8—42no—
104C43⋊C8—44no—
105#10031—431nomaximal, Sylow
106C22×C43—21no—
107C22×C43—21no—
108C22×C43#39211yescharacteristic
109C22×C43#47312yes—
110C4×C43—21no—
111C4×C43—22no—
112C4×C43—22no—
113C4×C43—82no—
114C4×C43—82no—
115C4×C43#45511yescharacteristic
116C4×C43#45611yescharacteristic
117Dic43—42no—
118Dic43—81no—
119#3249D4311yescharacteristic
120#3113—432no—
121#1985—431no—
122#1531—432no—
123#1290—431no—
124C2×C43—22no—
125C2×C43#200711yescharacteristic
126C2×C43#201011yescharacteristic
127C2×C43#202011yescharacteristic
128#533C2×D4312yes—
129C2×C4×Q8—431no—
130#483—862no—
131#477—22no—
132#475—862no—
133#467—22no—
134#462—22no—
135#462—862no—
136#451—862no—
137#441—864no—
138#432—432no—
139C2×C4⋊C8C2×D4311yescharacteristic
140C2×#97—431no—
141#336—862no—
142#330—864no—
143C43#1003111yescharacteristic, complemented, Sylow
144C22×Q8—431no—
145C2×Q16—22no—
146C2×Q16—864no—
147C22×C8—861no—
148C22×C8C22⋊D4312yes—
149C4⋊Q8C22⋊D4312yes—
150C4⋊Q8C22⋊D4312yes—
151#125—22no—
152C22⋊Q8—22no—
153C22⋊Q8—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—862no—
157C4×Q8—862no—
158#117—22no—
159C2×C4⋊C4—431no—
160C2×C4⋊C4—861no—
161C2×C42—861no—
162C2×C42C22×D4311yescharacteristic
163#107—22no—
164#106—864no—
165C4⋊C8—22no—
166C4⋊C8—862no—
167#103—24no—
168#103—864no—
169#103—864no—
170C22⋊C8—862no—
171#97—434no—
172#97—862no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—862no—
176C2×Q8—1722no—
177C22×C4—861no—
178C22×C4—861no—
179C22×C4D4×D4311yescharacteristic
180C22×C4#1062190011yescharacteristic
181C22×C4C2×C22⋊D4311yescharacteristic
182Q16—82no—
183Q16—1728no—
184C2×C8—22no—
185C2×C8—42no—
186C2×C8—862no—
187C2×C8—864no—
188C2×C8—1721no—
189C2×C8—1721no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—862no—
197C4⋊C4—1722no—
198C22⋊C4—42no—
199C42—42no—
200C42—1721no—
201C42—1721no—
202C42D4×D4312yes—
203C42C2×C22⋊D4312yes—
204C23#1306329611yescharacteristic
205Q8—44no—
206Q8—42no—
207Q8—42no—
208Q8—864no—
209Q8—1722no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—862no—
217C2×C4—1721no—
218C2×C4—1722no—
219C2×C4—1721no—
220C2×C4—1721no—
221C2×C4#1306329312yes—
222C2×C4#1306329411yescharacteristic
223C2×C4#1306329712yes—
224C2×C4#1306332111yescharacteristic
225C8—42no—
226C8—1722no—
227C8—1724no—
228C22—21no—
229C22—21no—
230C22#1458280711yescharacteristic
231C22#1458317112yes—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—82no—
236C4—82no—
237C4—3441no—
238C4—1722no—
239C4#1458307711yescharacteristic
240C4#1458308211yescharacteristic
241C2—22no—
242C2#1913564211yescharacteristic
243C2#1913565911yescharacteristic
244C2#1913571411yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3249C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#3249D43
hypocenterC43#10031
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
143. C43#10031semidirect

Maximal subgroups

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

subgroupindex
#191447212
#191355342
#191332102
#191324652
C43×#32492
#1003143