Finite Group Databasebeta

← #25010127

Subgroups — #25010127

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#19136852C211yesmaximal, characteristic, complemented
3#19136631C211yesmaximal, characteristic
4#19133956C211yesmaximal, characteristic, complemented
5#19132573C211yesmaximal, characteristic, complemented
6#19132555C211yesmaximal, characteristic, complemented
7C43×#1362C211yesmaximal, characteristic, complemented
8#14583623—21no—
9C2×#13063268—22no—
10C2×D688—21no—
11#14583284—21no—
12#14583276C2211yescharacteristic
13#14583123—22no—
14#14583101—21no—
15#14583100—21no—
16C8×Dic86C2211yescharacteristic
17Q16×Dic43—21no—
18C4×D344C2211yescharacteristic
19#14582701—21no—
20C4×C43⋊C16C2211yescharacteristic
21#14582642—21no—
22C43×#494C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×#10621873—41no—
26C2×#10621884—22no—
27C2×D344—21no—
28C2×D344—21no—
29C2×D344D411yescharacteristic
30#13063322—21no—
31#13063320—42no—
32#13063314—22no—
33#13063305—41no—
34Q8×Dic43—22no—
35C4×Dic86D411yescharacteristic
36C4×D172—21no—
37#13063283—41no—
38#13063268—44no—
39D688—42no—
40C2×C43⋊C16—21no—
41#13063259D411yescharacteristic
42C4⋊(C43⋊C8)D411yescharacteristic
43Dic43⋊C8—21no—
44#13063249—22no—
45#13063247—21no—
46#13063247—41no—
47C8×Dic43—21no—
48C2×Q16×C43—21no—
49C2×Q16×C43D412yes—
50C4⋊Q8×C43—21no—
51C2×C16×C43—21no—
52C4⋊C8×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—22no—
55C2×D172—21no—
56C2×D172—41no—
57C2×D172—41no—
58C2×D172—41no—
59C2×C4×D43—41no—
60C2×Dic86D811yescharacteristic
61Q16×C43—42no—
62Q16×C43—41no—
63Q16×C43—41no—
64C2×C8×C43—41no—
65C2×C8×C43C2×D411yescharacteristic
66C2×C8×C43C2×D411yescharacteristic
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C42×C43C2×D411yescharacteristic
70#10621884—82no—
71(C2×D43)⋊C4—42no—
72(C2×D43)⋊C4—42no—
73(C2×D43)⋊C4—41no—
74C4⋊Dic43—21no—
75C4⋊Dic43—42no—
76C4⋊Dic43D811yescharacteristic
77Dic43⋊C4—21no—
78C4×Dic43—21no—
79C4×Dic43—42no—
80C2×C43⋊C8—21no—
81D344—21no—
82D344—21no—
83D344—42no—
84D344—41no—
85D344—41no—
86#10621873—82no—
87C16×C43—41no—
88C43⋊C16—22no—
89C22×D43—41no—
90C22×D43—81no—
91Q8×C43—42no—
92Q8×C43—42no—
93C2×C4×C43—42no—
94C2×C4×C43#12011yescharacteristic
95C2×C4×C43C2×D811yescharacteristic
96C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
97C2×Dic43—21no—
98C2×Dic43—21no—
99C2×Dic43—41no—
100D172—41no—
101D172—41no—
102D172—81no—
103D172—81no—
104D172—81no—
105D172—81no—
106D172—161no—
107C4×D43—81no—
108C4×D43—81no—
109Dic86—21no—
110Dic86—21no—
111C8×C43—21no—
112C8×C43—81no—
113C8×C43#13511yescharacteristic
114C8×C43AGL(1,ℤ/8)11yescharacteristic
115C43⋊C8—41no—
116#12331—431nomaximal, Sylow
117C22×C43#44711yescharacteristic
118C2×D43—81no—
119C2×D43—81no—
120C2×D43—81no—
121C2×D43—161no—
122C2×D43—161no—
123C2×D43—161no—
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#2248—431no—
135#2206—431no—
136#1668—431no—
137#1362D4311yescharacteristic, complemented
138Q8⋊C16—431no—
139#1331—431no—
140C2×C43#162111yescharacteristic
141C2×C43#218611yescharacteristic
142C2×C43#219311yescharacteristic
143D43—161no—
144D43—321no—
145#556—861no—
146C2×SD32—862no—
147C2×D16—861no—
148#495—861no—
149#494C2×D4311yescharacteristic
150#493—431no—
151#464—862no—
152#461—861no—
153#460—861no—
154C8×Q8—431no—
155C4×Q16—861no—
156C4×D8—431no—
157C4⋊C16C2×D4311yescharacteristic
158#357—861no—
159C4×C16—431no—
160#335C2×D4311yescharacteristic
161#331—861no—
162C43#1233111yescharacteristic, complemented, Sylow
163C2×Q16—21no—
164C2×Q16D17212yes—
165C2×SD16—862no—
166C2×SD16—1721no—
167C2×D8—431no—
168C2×D8—861no—
169C2×D8—861no—
170C4⋊Q8—21no—
171#127—861no—
172#126—1722no—
173#124—862no—
174C22⋊Q8—1721no—
175C4×Q8—431no—
176C4×Q8—862no—
177C4×D4—861no—
178#117—1721no—
179SD32—1724no—
180D16—1722no—
181C2×C16—21no—
182C2×C16—861no—
183#107—431no—
184C4⋊C8—21no—
185C4⋊C8—431no—
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—861no—
195C2×D4—1721no—
196C2×D4—1721no—
197C2×D4—1721no—
198C22×C4—1721no—
199Q16—42no—
200Q16—41no—
201Q16—41no—
202SD16—3442no—
203SD16—3442no—
204D8—861no—
205D8—861no—
206D8—1722no—
207D8—1721no—
208D8—1721no—
209C2×C8—41no—
210C2×C8—861no—
211C2×C8C2×D17211yescharacteristic
212C2×C8D4×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—41no—
226C16—862no—
227C23—3441no—
228C23—1721no—
229Q8—42no—
230Q8—42no—
231Q8—861no—
232Q8—861no—
233D4—3441no—
234D4—3441no—
235D4—3441no—
236D4—3441no—
237D4—1721no—
238D4—1721no—
239D4—6881no—
240C2×C4—42no—
241C2×C4—861no—
242C2×C4—861no—
243C2×C4—3441no—
244C2×C4—3441no—
245C2×C4—1721no—
246C2×C4#1306329511yescharacteristic
247C2×C4D8×D4311yescharacteristic
248C2×C4#1306335211yescharacteristic
249C8—21no—
250C8—81no—
251C8—1721no—
252C8#1306334611yescharacteristic
253C8#1306334911yescharacteristic
254C22—3441no—
255C22—3441no—
256C22—3441no—
257C22—6881no—
258C22—6881no—
259C22—6881no—
260C22#1458303411yescharacteristic
261C4—21no—
262C4—82no—
263C4—3441no—
264C4—1721no—
265C4—1721no—
266C4#1458304511yescharacteristic
267C4#1458306911yescharacteristic
268C4#1458333211yescharacteristic
269C4#1458333611yescharacteristic
270C2—13761no—
271C2—6881no—
272C2#1913366111yescharacteristic
273C2#1913652111yescharacteristic
274C2#1913656211yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1362C2
socleC22×C43#447
prime radical#19136631C2
hypercenter#1362D43
hypocenterC43#12331
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #19147585C2semidirect
2. #19136852C2semidirect
4. #19133956C2semidirect
5. #19132573C2semidirect
6. #19132555C2semidirect
7. C43×#1362C2semidirect
137. #1362D43semidirect
162. C43#12331semidirect

Maximal subgroups

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

subgroupindex
#191475852
#191368522
#191366312
#191339562
#191325732
#191325552
C43×#13622
#1233143