Finite Group Databasebeta

← #24985441

Subgroups — #24985441

Order 11008.

424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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#19142583C211yesmaximal, characteristic
2#19135929C212yesmaximal
3#19135694C211yesmaximal, characteristic
4#19132419C212yesmaximal
5C43×#1272C211yesmaximal, characteristic
6C22×#10621885—21no—
7C2×#13063325C2211yescharacteristic
8C2×#13063257—22no—
9C2×#13063248—21no—
10#14582838—21no—
11#14582831—22no—
12#14582806—21no—
13#14582797C2212yes—
14#14582786—22no—
15#14582662—22no—
16#14582654C2211yescharacteristic
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86—21no—
20C2×#10621885—42no—
21C2×#10621885—42no—
22C2×#10621885—42no—
23C22×C43⋊C8—21no—
24#13063325—42no—
25C2×C4⋊Dic43—22no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43D412yes—
29C2×C4⋊Dic43D412yes—
30C2×Dic43⋊C4—22no—
31C2×C4×Dic43—21no—
32#13063257—44no—
33#13063248—42no—
34C43⋊#95—21no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C22×Q8×C43D411yescharacteristic
39C22×C8×C43—22no—
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C42×C43C2311yescharacteristic
42#95×C43—22no—
43C2×Q8×C43—21no—
44C2×Q8×C43—41no—
45C2×Q8×C43—41no—
46C2×Q8×C43SD1612yes—
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43C2×D411yescharacteristic
50C22×C4×C43C2×D412yes—
51C22×Dic43—22no—
52C22×Dic43—22no—
53C22×Dic43—41no—
54C2×Dic86—22no—
55C2×Dic86—41no—
56C2×Dic86—41no—
57C2×Dic86—41no—
58C2×Dic86—41no—
59C2×Dic86—41no—
60C2×C8×C43—24no—
61C2×C8×C43—42no—
62C2×C8×C43—42no—
63C4⋊C4×C43—41no—
64C42×C43—41no—
65#10621885—48no—
66C4⋊Dic43—24no—
67C4⋊Dic43—22no—
68C4⋊Dic43—22no—
69C4⋊Dic43—42no—
70C4⋊Dic43—42no—
71C4⋊Dic43—81no—
72C4⋊Dic43—81no—
73Dic43⋊C4—42no—
74Dic43⋊C4—42no—
75C4×Dic43—81no—
76C2×C43⋊C8—22no—
77C2×C43⋊C8—41no—
78C2×C43⋊C8—41no—
79C23×C43#12011yescharacteristic
80Q8×C43—42no—
81Q8×C43—81no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—42no—
91C2×C4×C43C2×SD1611yescharacteristic
92C2×C4×C43#13512yes—
93C2×C4×C43#13712yes—
94C2×C4×C43#13711yescharacteristic
95C2×Dic43—42no—
96C2×Dic43—42no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—42no—
101C2×Dic43—42no—
102C2×Dic43—81no—
103C2×Dic43—81no—
104Dic86—42no—
105Dic86—42no—
106Dic86—81no—
107Dic86—81no—
108C8×C43—44no—
109C43⋊C8—42no—
110#7760—431nomaximal, Sylow
111C22×C43#44811yescharacteristic
112C22×C43#45212yes—
113C22×C43#45311yescharacteristic
114C22×C43#45612yes—
115C22×C43B(4,𝔽2)11yescharacteristic
116C4×C43—21no—
117C4×C43—21no—
118C4×C43—22no—
119C4×C43—22no—
120C4×C43—42no—
121C4×C43—81no—
122Dic43—82no—
123Dic43—82no—
124Dic43—82no—
125#2809—431no—
126#2058—432no—
127#2016—431no—
128#1272D4311yescharacteristic
129#1271—432no—
130C2×C43#159611yescharacteristic
131C2×C43#160312yes—
132C2×C43#163411yescharacteristic
133C2×C43#165312yes—
134C2×C43#166011yescharacteristic
135C22×Q16—861no—
136C2×C4⋊Q8—431no—
137C2×#106—862no—
138C2×#103—861no—
139#400—861no—
140#398—862no—
141#391—861no—
142#391C2×D4311yescharacteristic
143#389—432no—
144#387—862no—
145#340—862no—
146#336—431no—
147#336C2×D4312yes—
148C43#776011yescharacteristic, complemented, Sylow
149C22×Q8—861no—
150C22×Q8D17211yescharacteristic
151C2×Q16—1722no—
152C2×Q16—1722no—
153C2×Q16—1722no—
154C22×C8—22no—
155C22×C8—861no—
156C4⋊Q8—1722no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4—432no—
159C2×C4⋊C4—862no—
160C2×C4⋊C4—861no—
161C2×C4⋊C4—861no—
162C2×C4⋊C4—862no—
163C2×C4⋊C4D17211yescharacteristic
164C2×C42—861no—
165C2×C42C22×D4311yescharacteristic
166#106—1724no—
167#103—1722no—
168#95—22no—
169#95—861no—
170#95—862no—
171#95—862no—
172#95—862no—
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—862no—
177C2×Q8—1721no—
178C2×Q8—1721no—
179C2×Q8—1721no—
180C2×Q8—1721no—
181C2×Q8—1721no—
182C2×Q8#1062187312yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—862no—
186C22×C4—862no—
187C22×C4—1721no—
188C22×C4C2×D17211yescharacteristic
189C22×C4D4×D4312yes—
190Q16—1728no—
191C2×C8—24no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—862no—
195C2×C8—1721no—
196C2×C8—1721no—
197C4⋊C4—41no—
198C4⋊C4—864no—
199C4⋊C4—862no—
200C4⋊C4—862no—
201C4⋊C4—3441no—
202C4⋊C4—3441no—
203C4⋊C4—1722no—
204C4⋊C4—1722no—
205C4⋊C4—1722no—
206C4⋊C4—1722no—
207C42—41no—
208C42—3441no—
209C23#1306329511yescharacteristic
210Q8—42no—
211Q8—81no—
212Q8—3441no—
213Q8—3441no—
214Q8—1722no—
215Q8—1722no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—3441no—
226C2×C4—3441no—
227C2×C4—1722no—
228C2×C4—1722no—
229C2×C4—1722no—
230C2×C4—1722no—
231C2×C4—1722no—
232C2×C4—1722no—
233C2×C4—1722no—
234C2×C4C2×#1062187311yescharacteristic
235C2×C4#1306334612yes—
236C2×C4#1306335712yes—
237C2×C4#1306335811yescharacteristic
238C8—44no—
239C8—1722no—
240C22#1458304011yescharacteristic
241C22#1458306412yes—
242C22#1458306911yescharacteristic
243C22#1458308312yes—
244C22#1458308711yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—42no—
250C4—81no—
251C4—3442no—
252C4—3442no—
253C4—3442no—
254C2#1913352011yescharacteristic
255C2#1913356112yes—
256C2#1913374111yescharacteristic
257C2#1913387412yes—
258C2#1913390711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socle, prime radicalC23×C43#120
hypercenter#1272D43
hypocenterC43#7760
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
148. C43#7760semidirect

Maximal subgroups

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

subgroupindex
#191425832
#191359292
#191356942
#191324192
C43×#12722
#776043