Finite Group Databasebeta

← #25010389

Subgroups — #25010389

Order 11008.

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

normal subgroups only

This group has 350 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#19136734C211yesmaximal, characteristic, complemented
4#19132643C211yesmaximal, characteristic, complemented
5#19132558C211yesmaximal, characteristic, complemented
6D4⋊(C43⋊C16)C211yesmaximal, characteristic
7C43×#1673C211yesmaximal, characteristic
8C22×Dic172—21no—
9D4×Dic86—21no—
10#14583279C2211yescharacteristic
11#14583140—21no—
12#14583110—21no—
13#14583057—22no—
14C4×Dic172C2211yescharacteristic
15#14582726—21no—
16C4⋊(C43⋊C16)C2211yescharacteristic
17#14582702—22no—
18#14582702—21no—
19C4×C43⋊C16C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×#461—21no—
22C8×D4×C43C2211yescharacteristic
23C43×#335C2211yescharacteristic
24C43×#332—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—
43C2×SD16×C43—41no—
44C22×C8×C43—21no—
45C4⋊Q8×C43—21no—
46C4×D4×C43D411yescharacteristic
47#107×C43—21no—
48#107×C43—21no—
49C4⋊C8×C43—21no—
50C4⋊C8×C43D411yescharacteristic
51#103×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—
63SD16×C43—82no—
64C2×C8×C43—21no—
65C2×C8×C43—41no—
66C2×C8×C43—41no—
67C2×C8×C43—41no—
68C2×C8×C43C2×D411yescharacteristic
69C2×C8×C43C2×D411yescharacteristic
70C4⋊C4×C43—41no—
71C4⋊C4×C43—41no—
72C4⋊C4×C43D811yescharacteristic
73C22⋊C4×C43—21no—
74C42×C43C2×D411yescharacteristic
75C22⋊Dic43—42no—
76C4⋊Dic43—21no—
77C4⋊Dic43—41no—
78C4⋊Dic43—41no—
79Dic43⋊C4—42no—
80Dic43⋊C4—41no—
81C4×Dic43—41no—
82Dic172—21no—
83Dic172—42no—
84Dic172—44no—
85Dic172—41no—
86Dic172—41no—
87Dic172SD1612yescomplemented
88C43⋊C16—41no—
89C43⋊C16—41no—
90C23×C43—21no—
91Q8×C43—81no—
92Q8×C43—81no—
93D4×C43—21no—
94D4×C43SD3212yes—
95C2×C4×C43—21no—
96C2×C4×C43—41no—
97C2×C4×C43—41no—
98C2×C4×C43—81no—
99C2×C4×C43#12011yescharacteristic
100C2×C4×C43C2×D811yescharacteristic
101C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
102C2×Dic43—41no—
103C2×Dic43—41no—
104C2×Dic43—42no—
105C2×Dic43—84no—
106Dic86—22no—
107Dic86—41no—
108Dic86—42no—
109Dic86—42no—
110Dic86—84no—
111C8×C43—21no—
112C8×C43—41no—
113C8×C43—81no—
114C8×C43C2×SD1611yescharacteristic
115C8×C43AGL(1,ℤ/8)11yescharacteristic
116#12370—431nomaximal, Sylow
117C22×C43—22no—
118C22×C43—41no—
119C22×C43—41no—
120C22×C43#44711yescharacteristic
121C4×C43—21no—
122C4×C43—41no—
123C4×C43—161no—
124C4×C43#45011yescharacteristic
125C4×C43#45511yescharacteristic
126C4×C43C2×SD3211yescharacteristic
127C4×C43#51011yescharacteristic
128Dic43—42no—
129Dic43—82no—
130Dic43—81no—
131D4×Q16—431no—
132#2241—431no—
133#2225—431no—
134#1673D4311yescharacteristic
135#1362—431no—
136#1332—431no—
137D4⋊C16—431no—
138C2×C43—42no—
139C2×C43#163911yescharacteristic
140C2×C43#218511yescharacteristic
141C2×C43#219511yescharacteristic
142C22×Q16—861no—
143D4×Q8—861no—
144#500C2×D4311yescharacteristic
145#494—431no—
146#467—861no—
147#462—861no—
148#461—21no—
149#451—862no—
150C4×Q16—431no—
151C8×D4C2×D4311yescharacteristic
152#367—861no—
153C4⋊C16—431no—
154#358—861no—
155#358—862no—
156C4×C16—431no—
157#335C2×D4311yescharacteristic
158#332—21no—
159C43#1237011yescharacteristic, complemented, Sylow
160C22×Q8—862no—
161C2×Q16—431no—
162C2×Q16—432no—
163C2×Q16—862no—
164C2×Q16—861no—
165C2×Q16—1722no—
166C2×Q16—1722no—
167C2×SD16—41no—
168C22×C8—21no—
169C4⋊Q8—21no—
170C4⋊Q8—861no—
171C4⋊Q8—1721no—
172C22⋊Q8—862no—
173C22⋊Q8—1722no—
174C4×Q8—861no—
175C4×D4—1721no—
176C4×D4C22⋊D4311yescharacteristic
177C2×C16—861no—
178C2×C16—861no—
179#107—21no—
180#107—21no—
181#107—431no—
182C4⋊C8—21no—
183C4⋊C8C22⋊D4311yescharacteristic
184#103—41no—
185#103—862no—
186#103—861no—
187C22⋊C8—21no—
188C4×C8C22×D4311yescharacteristic
189C2×Q8—41no—
190C2×Q8—861no—
191C2×Q8—862no—
192C2×Q8—3442no—
193C2×Q8—1722no—
194C2×Q8—1724no—
195C2×D4#1062188211yescharacteristic
196C22×C4—21no—
197C22×C4—1722no—
198Q16—432no—
199Q16—861no—
200Q16—1722no—
201Q16—1724no—
202Q16—1721no—
203Q16—1721no—
204SD16—82no—
205C2×C8—21no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8D4×D4311yescharacteristic
210C2×C8D4×D4311yescharacteristic
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—861no—
214C4⋊C4—1722no—
215C4⋊C4—1721no—
216C4⋊C4—1721no—
217C4⋊C4—1721no—
218C4⋊C4#1062188211yescharacteristic
219C22⋊C4—21no—
220C22⋊C4—1722no—
221C42—1721no—
222C42C2×C22⋊D4311yescharacteristic
223C16—1721no—
224C16—1721no—
225C23—21no—
226Q8—81no—
227Q8—81no—
228Q8—862no—
229Q8—3444no—
230Q8—1722no—
231Q8—1722no—
232Q8—1721no—
233D4—21no—
234D4#1306326912yes—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—81no—
239C2×C4—3444no—
240C2×C4—1721no—
241C2×C4—1722no—
242C2×C4—1721no—
243C2×C4#1306329311yescharacteristic
244C2×C4C2×#1062188211yescharacteristic
245C2×C4#1306335011yescharacteristic
246C8—21no—
247C8—41no—
248C8—81no—
249C8SD16×D4311yescharacteristic
250C8#1306335211yescharacteristic
251C22—22no—
252C22—41no—
253C22—41no—
254C22#1458303211yescharacteristic
255C4—21no—
256C4—41no—
257C4—161no—
258C4—3441no—
259C4—3442no—
260C4—1722no—
261C4#1458304811yescharacteristic
262C4#1458307511yescharacteristic
263C4C2×#1306326911yescharacteristic
264C4#1458333911yescharacteristic
265C2—42no—
266C2#1913377211yescharacteristic
267C2#1913651111yescharacteristic
268C2#1913657111yescharacteristic
subgroupG/H
centerC22#14583032
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1673C2
socleC22×C43#447
prime radicalC2×D4×C43D8
hypercenter#1673D43
hypocenterC43#12370
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1673

Complements

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

NH ≅ G/Ntype
2. #19136824C2semidirect
3. #19136734C2semidirect
4. #19132643C2semidirect
5. #19132558C2semidirect
87. Dic172SD16semidirect
159. C43#12370semidirect

Maximal subgroups

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

subgroupindex
D4×Dic1722
#191368242
#191367342
#191326432
#191325582
D4⋊(C43⋊C16)2
C43×#16732
#1237043