Finite Group Databasebeta

← #24985387

Subgroups — #24985387

Order 11008.

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

normal subgroups only

This group has 492 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#19141525C211yesmaximal, characteristic
2#19135920C212yesmaximal, complemented
3#19132419C212yesmaximal, complemented
4#19132416C211yesmaximal, characteristic
5C43×#2013C211yesmaximal, characteristic
6C2×#13063306—21no—
7C2×#13063258—22no—
8#14582829—21no—
9#14582824—22no—
10#14582797C2212yes—
11#14582774—22no—
12#14582661—22no—
13#14582654C2212yes—
14C22×SD16×C43—21no—
15C2×C4⋊Q8×C43C2211yescharacteristic
16C2×#103×C43—21no—
17C43×#390C2211yescharacteristic
18C43×#336C2211yescharacteristic
19C23×Dic43—21no—
20C22×C43⋊C8—22no—
21#13063306—42no—
22#13063306—42no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43D412yes—
25C2×C4⋊Dic43D412yes—
26C2×Dic43⋊C4—22no—
27C2×C22⋊Dic43—21no—
28C2×C22⋊Dic43—22no—
29#13063258—44no—
30C43⋊#95—21no—
31C43⋊#95—22no—
32C43⋊#95—22no—
33C22×Q8×C43—21no—
34C22×D4×C43D411yescharacteristic
35C2×SD16×C43—42no—
36C2×SD16×C43—42no—
37C2×SD16×C43—42no—
38C22×C8×C43—21no—
39C4⋊Q8×C43—42no—
40C2×C4⋊C4×C43—22no—
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C22⋊C4×C43—22no—
43C2×C42×C43C2311yescharacteristic
44#103×C43—42no—
45C24×C43—21no—
46C2×Q8×C43—22no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×D4×C43—21no—
53C2×D4×C43—41no—
54C2×D4×C43—41no—
55C2×D4×C43D812yes—
56C22×C4×C43—21no—
57C22×C4×C43—41no—
58C22×C4×C43C2×D412yes—
59C22×C4×C43C2×D411yescharacteristic
60C22×Dic43—22no—
61C22×Dic43—22no—
62C22×Dic43—42no—
63C22×Dic43—81no—
64C22×Dic43—81no—
65SD16×C43—48no—
66C2×C8×C43—22no—
67C2×C8×C43—41no—
68C2×C8×C43—41no—
69C4⋊C4×C43—24no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—42no—
72C22⋊C4×C43—42no—
73C22⋊C4×C43—42no—
74C42×C43—41no—
75C22⋊Dic43—42no—
76C22⋊Dic43—44no—
77C4⋊Dic43—22no—
78C4⋊Dic43—22no—
79C4⋊Dic43—42no—
80C4⋊Dic43—81no—
81Dic43⋊C4—42no—
82Dic43⋊C4—42no—
83C2×C43⋊C8—24no—
84C2×C43⋊C8—42no—
85C2×C43⋊C8—42no—
86C23×C43—22no—
87C23×C43—42no—
88C23×C43—41no—
89C23×C43—42no—
90C23×C43—41no—
91C23×C43#12011yescharacteristic
92Q8×C43—42no—
93Q8×C43—42no—
94Q8×C43—81no—
95Q8×C43—81no—
96D4×C43—42no—
97D4×C43—81no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—42no—
103C2×C4×C43—41no—
104C2×C4×C43—42no—
105C2×C4×C43—81no—
106C2×C4×C43—81no—
107C2×C4×C43C2×D811yescharacteristic
108C2×C4×C43#13512yes—
109C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C43#13712yes—
111C2×Dic43—42no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117C2×Dic43—84no—
118C8×C43—42no—
119C43⋊C8—44no—
120#7751—431nomaximal, Sylow
121C22×C43—42no—
122C22×C43—44no—
123C22×C43—82no—
124C22×C43—81no—
125C22×C43—81no—
126C22×C43#44711yescharacteristic
127C22×C43#45212yes—
128C22×C43#45311yescharacteristic
129C22×C43#45612yes—
130C22×C43B(4,𝔽2)11yescharacteristic
131C4×C43—21no—
132C4×C43—21no—
133C4×C43—22no—
134C4×C43—22no—
135C4×C43—82no—
136C4×C43—81no—
137Dic43—82no—
138Dic43—82no—
139#2724—431no—
140#2057—432no—
141#2013D4311yescharacteristic
142#1271—432no—
143#1270—431no—
144C2×C43—82no—
145C2×C43#159511yescharacteristic
146C2×C43#160312yes—
147C2×C43#163011yescharacteristic
148C2×C43#164712yes—
149C2×C43#166011yescharacteristic
150C22×SD16—21no—
151C2×C4⋊Q8C2×D4311yescharacteristic
152C2×#123—861no—
153C2×#107—862no—
154C2×#103—21no—
155#398—861no—
156#397—862no—
157#390C2×D4311yescharacteristic
158#389—432no—
159#385—862no—
160#340—862no—
161#336—432no—
162#336C2×D4311yescharacteristic
163C43#775111yescharacteristic, complemented, Sylow
164C22×Q8—21no—
165C22×D4C22⋊D4311yescharacteristic
166C23×C4—861no—
167C2×SD16—42no—
168C2×SD16—42no—
169C2×SD16—42no—
170C22×C8—21no—
171C22×C8—862no—
172C4⋊Q8—42no—
173#123—1722no—
174#123—1722no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—432no—
177C2×C4⋊C4—432no—
178C2×C4⋊C4—861no—
179C2×C4⋊C4—862no—
180C2×C4⋊C4C22⋊D4311yescharacteristic
181C2×C22⋊C4—22no—
182C2×C22⋊C4—862no—
183C2×C22⋊C4—861no—
184C2×C42C22×D4311yescharacteristic
185#107—1724no—
186#103—42no—
187#95—862no—
188#95—861no—
189#95—862no—
190C24—21no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4#1062188212yes—
201C22×C4—21no—
202C22×C4—41no—
203C22×C4—862no—
204C22×C4—862no—
205C22×C4—3441no—
206C22×C4—3441no—
207C22×C4—1722no—
208C22×C4D4×D4312yes—
209C22×C4C2×C22⋊D4311yescharacteristic
210SD16—48no—
211C2×C8—22no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—864no—
215C2×C8—1722no—
216C2×C8—1722no—
217C4⋊C4—24no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—862no—
221C4⋊C4—862no—
222C4⋊C4—3441no—
223C4⋊C4—1722no—
224C4⋊C4—1722no—
225C4⋊C4—1722no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—1722no—
229C22⋊C4—1724no—
230C42—41no—
231C23—22no—
232C23—42no—
233C23—41no—
234C23—42no—
235C23—41no—
236C23#1306329311yescharacteristic
237Q8—42no—
238Q8—42no—
239Q8—81no—
240Q8—81no—
241D4—42no—
242D4—81no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—3444no—
253C2×C4—1722no—
254C2×C4—1722no—
255C2×C4—1722no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4C2×#1062188211yescharacteristic
260C2×C4#1306334612yes—
261C2×C4#1306335011yescharacteristic
262C2×C4#1306335412yes—
263C8—42no—
264C8—1724no—
265C22—42no—
266C22—44no—
267C22—81no—
268C22—82no—
269C22—81no—
270C22#1458303211yescharacteristic
271C22#1458305812yes—
272C22#1458306611yescharacteristic
273C22#1458308012yes—
274C22#1458308511yescharacteristic
275C4—21no—
276C4—21no—
277C4—22no—
278C4—22no—
279C4—81no—
280C4—82no—
281C4—3442no—
282C4—3442no—
283C2—82no—
284C2#1913351211yescharacteristic
285C2#1913355512yes—
286C2#1913371411yescharacteristic
287C2#1913382812yes—
288C2#1913390411yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2013C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#2013D43
hypocenterC43#7751
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2013

Complements

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

NH ≅ G/Ntype
2. #19135920C2semidirect
3. #19132419C2semidirect
163. C43#7751semidirect

Maximal subgroups

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

subgroupindex
#191415252
#191359202
#191324192
#191324162
C43×#20132
#775143