Finite Group Databasebeta

← #25010417

Subgroups — #25010417

Order 11008.

344 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 73 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
1D4×Dic172C211yesmaximal, characteristic
2#19136824C211yesmaximal, characteristic, complemented
3#19136744C211yesmaximal, characteristic, complemented
4#19132643C211yesmaximal, characteristic, complemented
5#19132558C211yesmaximal, characteristic, complemented
6D4⋊(C43⋊C16)C211yesmaximal, characteristic
7C43×#1675C211yesmaximal, characteristic
8C22×Dic172—21no—
9D4×Dic86—21no—
10#14583279C2211yescharacteristic
11#14583140—21no—
12#14583110—21no—
13#14583057—22no—
14C4×Dic172C2211yescharacteristic
15#14582724—21no—
16C4⋊(C43⋊C16)C2211yescharacteristic
17#14582702—22no—
18#14582702—21no—
19C4×C43⋊C16C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×#476—21no—
22C8×D4×C43C2211yescharacteristic
23C43×#335C2211yescharacteristic
24C43×#333—21no—
25C22×Dic86—22no—
26C2×Dic172—22no—
27C2×Dic172—21no—
28C2×Dic172—42no—
29C2×Dic172—42no—
30C2×Dic172D411yescharacteristic
31C2×Dic172D412yes—
32#13063325—21no—
33#13063324—41no—
34#13063304—22no—
35#13063302—42no—
36C4×Dic86—21no—
37D4×Dic43—41no—
38C2×C43⋊C16—21no—
39C2×C43⋊C16—21no—
40#13063259D411yescharacteristic
41#13063250—22no—
42#13063250—21no—
43C22×C8×C43—21no—
44C4⋊Q8×C43—21no—
45C4×D4×C43D411yescharacteristic
46#107×C43—21no—
47#107×C43—21no—
48#106×C43—41no—
49C4⋊C8×C43—21no—
50C4⋊C8×C43D411yescharacteristic
51#102×C43—41no—
52C22⋊C8×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—41no—
55C2×D4×C43D811yescharacteristic
56C22×C4×C43—21no—
57C22×Dic43—42no—
58C2×Dic86—21no—
59C2×Dic86—22no—
60C2×Dic86—44no—
61C2×Dic86—42no—
62C2×Dic86—82no—
63C2×C8×C43—21no—
64C2×C8×C43—41no—
65C2×C8×C43—41no—
66C2×C8×C43—41no—
67C2×C8×C43C2×D411yescharacteristic
68C2×C8×C43C2×D411yescharacteristic
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43D811yescharacteristic
72C22⋊C4×C43—21no—
73C42×C43C2×D411yescharacteristic
74C22⋊Dic43—42no—
75C4⋊Dic43—21no—
76C4⋊Dic43—41no—
77C4⋊Dic43—41no—
78Dic43⋊C4—42no—
79Dic43⋊C4—41no—
80C4×Dic43—41no—
81Dic172—21no—
82Dic172—42no—
83Dic172—44no—
84Dic172—41no—
85Dic172—41no—
86Dic172SD1612yes—
87C43⋊C16—41no—
88C43⋊C16—41no—
89C23×C43—21no—
90Q8×C43—161no—
91D4×C43—21no—
92D4×C43Q3212yes—
93C2×C4×C43—21no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—81no—
97C2×C4×C43#12011yescharacteristic
98C2×C4×C43C2×D811yescharacteristic
99C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
100C2×Dic43—41no—
101C2×Dic43—41no—
102C2×Dic43—42no—
103C2×Dic43—84no—
104Dic86—22no—
105Dic86—41no—
106Dic86—42no—
107Dic86—42no—
108Dic86—84no—
109C8×C43—21no—
110C8×C43—41no—
111C8×C43—81no—
112C8×C43C2×SD1611yescharacteristic
113C8×C43AGL(1,ℤ/8)11yescharacteristic
114#12374—431nomaximal, Sylow
115C22×C43—22no—
116C22×C43—41no—
117C22×C43—41no—
118C22×C43#44711yescharacteristic
119C4×C43—21no—
120C4×C43—41no—
121C4×C43—161no—
122C4×C43#45011yescharacteristic
123C4×C43#45511yescharacteristic
124C4×C43C2×Q3211yescharacteristic
125C4×C43#51011yescharacteristic
126Dic43—42no—
127Dic43—82no—
128Dic43—81no—
129D4×Q16—431no—
130#2241—431no—
131#2227—431no—
132#1675D4311yescharacteristic
133#1362—431no—
134#1332—431no—
135D4⋊C16—431no—
136C2×C43—42no—
137C2×C43#163911yescharacteristic
138C2×C43#218811yescharacteristic
139C2×C43#219311yescharacteristic
140C22×Q16—861no—
141D4×Q8—861no—
142#500C2×D4311yescharacteristic
143#494—431no—
144#476—21no—
145#467—861no—
146#462—861no—
147#451—862no—
148C4×Q16—431no—
149C8×D4C2×D4311yescharacteristic
150#366—861no—
151C4⋊C16—431no—
152#358—861no—
153#358—862no—
154C4×C16—431no—
155#335C2×D4311yescharacteristic
156#333—21no—
157C43#1237411yescharacteristic, complemented, Sylow
158C22×Q8—862no—
159C2×Q16—431no—
160C2×Q16—432no—
161C2×Q16—862no—
162C2×Q16—861no—
163C2×Q16—1722no—
164C2×Q16—1722no—
165C22×C8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—861no—
168C4⋊Q8—1721no—
169C22⋊Q8—862no—
170C22⋊Q8—1722no—
171C4×Q8—861no—
172C4×D4—1721no—
173C4×D4C22⋊D4311yescharacteristic
174C2×C16—861no—
175C2×C16—861no—
176#107—21no—
177#107—21no—
178#107—431no—
179#106—41no—
180C4⋊C8—21no—
181C4⋊C8C22⋊D4311yescharacteristic
182#103—862no—
183#103—861no—
184#102—41no—
185C22⋊C8—21no—
186C4×C8C22×D4311yescharacteristic
187C2×Q8—41no—
188C2×Q8—861no—
189C2×Q8—862no—
190C2×Q8—3442no—
191C2×Q8—1722no—
192C2×Q8—1724no—
193C2×D4#1062188211yescharacteristic
194C22×C4—21no—
195C22×C4—1722no—
196Q16—432no—
197Q16—861no—
198Q16—1722no—
199Q16—1724no—
200Q16—1721no—
201Q16—1721no—
202C2×C8—21no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8D4×D4311yescharacteristic
207C2×C8D4×D4311yescharacteristic
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—861no—
211C4⋊C4—1722no—
212C4⋊C4—1721no—
213C4⋊C4—1721no—
214C4⋊C4—1721no—
215C4⋊C4#1062188211yescharacteristic
216C22⋊C4—21no—
217C22⋊C4—1722no—
218C42—1721no—
219C42C2×C22⋊D4311yescharacteristic
220C16—1721no—
221C16—1721no—
222C23—21no—
223Q8—161no—
224Q8—862no—
225Q8—3444no—
226Q8—1722no—
227Q8—1722no—
228Q8—1721no—
229D4—21no—
230D4#1306327112yes—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4—3444no—
236C2×C4—1721no—
237C2×C4—1722no—
238C2×C4—1721no—
239C2×C4#1306329311yescharacteristic
240C2×C4C2×#1062188211yescharacteristic
241C2×C4#1306335011yescharacteristic
242C8—21no—
243C8—41no—
244C8—81no—
245C8SD16×D4311yescharacteristic
246C8#1306335211yescharacteristic
247C22—22no—
248C22—41no—
249C22—41no—
250C22#1458303211yescharacteristic
251C4—21no—
252C4—41no—
253C4—161no—
254C4—3441no—
255C4—3442no—
256C4—1722no—
257C4#1458304811yescharacteristic
258C4#1458307511yescharacteristic
259C4C2×#1306327111yescharacteristic
260C4#1458333911yescharacteristic
261C2—42no—
262C2#1913377211yescharacteristic
263C2#1913652811yescharacteristic
264C2#1913655711yescharacteristic
subgroupG/H
centerC22#14583032
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1675C2
socleC22×C43#447
prime radicalC2×D4×C43D8
hypercenter#1675D43
hypocenterC43#12374
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1675

Complements

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

NH ≅ G/Ntype
2. #19136824C2semidirect
3. #19136744C2semidirect
4. #19132643C2semidirect
5. #19132558C2semidirect
157. C43#12374semidirect

Maximal subgroups

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

subgroupindex
D4×Dic1722
#191368242
#191367442
#191326432
#191325582
D4⋊(C43⋊C16)2
C43×#16752
#1237443