Finite Group Databasebeta

← #25010123

Subgroups — #25010123

Order 11008.

328 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 65 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#19147585C211yesmaximal, characteristic, complemented
2#19136627C211yesmaximal, characteristic
3#19133952C211yesmaximal, characteristic, complemented
4#19132644C211yesmaximal, characteristic, complemented
5#19132575C211yesmaximal, characteristic, complemented
6#19132557C211yesmaximal, characteristic, complemented
7C43×#2248C211yesmaximal, characteristic, complemented
8#14583623—21no—
9C2×#13063266—21no—
10#14583284—21no—
11#14583123—22no—
12#14583101—21no—
13#14583096—21no—
14C8×Dic86C2211yescharacteristic
15Q16×Dic43—21no—
16C4×D344C2211yescharacteristic
17C4⋊(C43⋊C16)C2211yescharacteristic
18#14582700—21no—
19#14582652C2211yescharacteristic
20#14582643—21no—
21C2×SD32×C43—22no—
22C43×#494C2211yescharacteristic
23C43×#493C2211yescharacteristic
24C4×C16×C43C2211yescharacteristic
25C2×#10621883—41no—
26C2×#10621884—22no—
27C2×D344D411yescharacteristic
28#13063320—42no—
29#13063314—22no—
30#13063305—41no—
31Q8×Dic43—22no—
32C4×Dic86D411yescharacteristic
33C4×D172—21no—
34#13063283—41no—
35#13063266—42no—
36C2×C43⋊C16—21no—
37#13063259D411yescharacteristic
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063249—22no—
42#13063247—21no—
43#13063246—41no—
44C8×Dic43—21no—
45C2×Q16×C43—21no—
46C2×Q16×C43D412yes—
47C2×D8×C43—21no—
48C2×D8×C43—21no—
49C4⋊Q8×C43—21no—
50#127×C43—21no—
51SD32×C43—44no—
52C2×C16×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—22no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43—41no—
58C2×D172—21no—
59C2×C4×D43—41no—
60C2×Dic86D811yescharacteristic
61Q16×C43—42no—
62Q16×C43—41no—
63Q16×C43—41no—
64D8×C43—42no—
65D8×C43—41no—
66D8×C43—41no—
67C2×C8×C43C2×D411yescharacteristic
68C2×C8×C43C2×D411yescharacteristic
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C42×C43C2×D411yescharacteristic
72#10621884—82no—
73#10621883—82no—
74(C2×D43)⋊C4—42no—
75(C2×D43)⋊C4—42no—
76(C2×D43)⋊C4—41no—
77C4⋊Dic43—21no—
78C4⋊Dic43—42no—
79C4⋊Dic43D811yescharacteristic
80Dic43⋊C4—21no—
81C4×Dic43—21no—
82C4×Dic43—42no—
83C2×C43⋊C8—21no—
84C2×C43⋊C8—41no—
85D344—21no—
86D344—21no—
87C16×C43—22no—
88C43⋊C16—41no—
89C23×C43—81no—
90C22×D43—41no—
91Q8×C43—42no—
92Q8×C43—42no—
93D4×C43—81no—
94D4×C43—81no—
95D4×C43—81no—
96D4×C43—81no—
97D4×C43—161no—
98C2×C4×C43—42no—
99C2×C4×C43#12011yescharacteristic
100C2×C4×C43C2×D811yescharacteristic
101C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
102C2×Dic43—21no—
103C2×Dic43—21no—
104C2×Dic43—41no—
105D172—41no—
106D172—41no—
107C4×D43—81no—
108C4×D43—81no—
109Dic86—21no—
110Dic86—21no—
111C8×C43—21no—
112C8×C43#13511yescharacteristic
113C8×C43AGL(1,ℤ/8)11yescharacteristic
114C43⋊C8—41no—
115C43⋊C8—81no—
116#12331—431nomaximal, Sylow
117C22×C43—161no—
118C22×C43—161no—
119C22×C43—161no—
120C22×C43#44711yescharacteristic
121C2×D43—81no—
122C2×D43—81no—
123C2×D43—81no—
124C4×C43—21no—
125C4×C43—82no—
126C4×C43#44911yescharacteristic
127C4×C43#45311yescharacteristic
128C4×C43#50811yescharacteristic
129C4×C43#50911yescharacteristic
130Dic43—41no—
131Dic43—41no—
132Dic43—81no—
133#3393—431no—
134#2248D4311yescharacteristic, complemented
135#2206—431no—
136#1668—431no—
137#1362—431no—
138Q8⋊C16—431no—
139#1331—431no—
140C2×C43—321no—
141C2×C43#162111yescharacteristic
142C2×C43#218611yescharacteristic
143C2×C43#219311yescharacteristic
144D43—161no—
145#556—861no—
146C2×SD32—22no—
147C2×D16—861no—
148#495—861no—
149#494C2×D4311yescharacteristic
150#493C2×D4311yescharacteristic
151#464—862no—
152#461—861no—
153#460—861no—
154C8×Q8—431no—
155C4×Q16—861no—
156C4×D8—431no—
157C4⋊C16—431no—
158#357—861no—
159C4×C16C2×D4311yescharacteristic
160#335—431no—
161#331—861no—
162C43#1233111yescharacteristic, complemented, Sylow
163C2×Q16—21no—
164C2×Q16C22⋊D4312yes—
165C2×SD16—862no—
166C2×SD16—1721no—
167C2×D8—21no—
168C2×D8—21no—
169C2×D8—431no—
170C4⋊Q8—21no—
171#127—21no—
172#126—1722no—
173#124—862no—
174C22⋊Q8—1721no—
175C4×Q8—431no—
176C4×Q8—862no—
177C4×D4—861no—
178#117—1721no—
179SD32—44no—
180D16—1722no—
181C2×C16—21no—
182C2×C16—861no—
183#107—431no—
184C4⋊C8—431no—
185C4⋊C8—861no—
186C4⋊C8—861no—
187#103—862no—
188#102—861no—
189#102—1721no—
190C4×C8—861no—
191C4×C8C22×D4311yescharacteristic
192C2×Q8—22no—
193C2×Q8—431no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—861no—
198C22×C4—1721no—
199Q16—42no—
200Q16—41no—
201Q16—41no—
202SD16—3442no—
203SD16—3442no—
204D8—42no—
205D8—41no—
206D8—41no—
207D8—861no—
208D8—861no—
209C2×C8—861no—
210C2×C8—1721no—
211C2×C8D4×D4311yescharacteristic
212C2×C8C2×C22⋊D4311yescharacteristic
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—431no—
216C4⋊C4—861no—
217C4⋊C4—861no—
218C4⋊C4—1722no—
219C22⋊C4—1722no—
220C22⋊C4—1722no—
221C22⋊C4—1721no—
222C42—861no—
223C42—1722no—
224C42D4×D4311yescharacteristic
225C16—22no—
226C16—1721no—
227C23—81no—
228C23—1721no—
229Q8—42no—
230Q8—42no—
231Q8—861no—
232Q8—861no—
233D4—81no—
234D4—81no—
235D4—81no—
236D4—81no—
237D4—161no—
238D4—1721no—
239D4—1721no—
240C2×C4—42no—
241C2×C4—861no—
242C2×C4—861no—
243C2×C4—3441no—
244C2×C4—3441no—
245C2×C4—1721no—
246C2×C4#1306329311yescharacteristic
247C2×C4D8×D4311yescharacteristic
248C2×C4#1306334911yescharacteristic
249C8—21no—
250C8—3441no—
251C8—1721no—
252C8#1306334411yescharacteristic
253C8#1306334911yescharacteristic
254C22—161no—
255C22—161no—
256C22—161no—
257C22—3441no—
258C22—3441no—
259C22—3441no—
260C22#1458303111yescharacteristic
261C4—21no—
262C4—82no—
263C4—3441no—
264C4—1721no—
265C4—1721no—
266C4#1458304111yescharacteristic
267C4#1458306611yescharacteristic
268C4#1458333011yescharacteristic
269C4#1458333611yescharacteristic
270C2—321no—
271C2—6881no—
272C2#1913365711yescharacteristic
273C2#1913651711yescharacteristic
274C2#1913655811yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2248C2
socleC22×C43#447
prime radical#19136627C2
hypercenter#2248D43
hypocenterC43#12331
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #19147585C2semidirect
3. #19133952C2semidirect
4. #19132644C2semidirect
5. #19132575C2semidirect
6. #19132557C2semidirect
7. C43×#2248C2semidirect
134. #2248D43semidirect
162. C43#12331semidirect

Maximal subgroups

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

subgroupindex
#191475852
#191366272
#191339522
#191326442
#191325752
#191325572
C43×#22482
#1233143