Finite Group Databasebeta

← #24997575

Subgroups — #24997575

Order 11008.

584 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 103 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#19145041C211yesmaximal, characteristic
2#19144626C212yesmaximal, complemented
3#19132993C212yesmaximal, complemented
4#19132426C211yesmaximal, characteristic, complemented
5C43×#1985C211yesmaximal, characteristic, complemented
6C2×#13063347—22no—
7#14583449C2212yes—
8#14583293—22no—
9#14583288—22no—
10#14583217—22no—
11#14583184—22no—
12#14583099—22no—
13#14583038—22no—
14C4×#10621884—24no—
15#14582952C2212yes—
16#14582626—24no—
17C2×C4×Q8×C43C2211yescharacteristic
18C2×C4⋊C8×C43C2211yescharacteristic
19C2×#97×C43C2211yescharacteristic
20C43×#336—22no—
21C2×#10621898—22no—
22#13063347—44no—
23#13063347—44no—
24C2×Dic172—22no—
25C2×#10621873—24no—
26C2×#10621884—24no—
27C2×D344—22no—
28#13063325D412yes—
29#13063322D412yes—
30#13063313—22no—
31#13063299—22no—
32#13063299—22no—
33C4×D172—22no—
34C4×D172—22no—
35#13063256—24no—
36C4⋊(C43⋊C8)—22no—
37#13063249—24no—
38#13063245—24no—
39C22⋊(C43⋊C8)—22no—
40C4×C43⋊C8D414yes—
41C22×Q8×C43D411yescharacteristic
42C22×C8×C43—21no—
43C22×C8×C43D412yes—
44C4×Q8×C43—22no—
45C4×Q8×C43—22no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C42×C43—21no—
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43—22no—
51#97×C43—22no—
52C2×Q8×C43—22no—
53C2×Q8×C43—42no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43#4111yescharacteristic
59C2×C22⋊D43—42no—
60#10621898—44no—
61#10621898—44no—
62C2×D172—22no—
63C2×D172—22no—
64C2×D172—22no—
65C2×C4×D43—42no—
66C2×Dic86—22no—
67C2×C8×C43—22no—
68C2×C8×C43—22no—
69C2×C8×C43—41no—
70C2×C8×C43—42no—
71C2×C8×C43SD1614yescomplemented
72C4⋊C4×C43—22no—
73C4⋊C4×C43—42no—
74C42×C43—41no—
75C42×C43—41no—
76C42×C43C2×D412yes—
77C42×C43C2×D412yes—
78#10621884—48no—
79(C2×D43)⋊C4—42no—
80(C2×D43)⋊C4—42no—
81C4⋊Dic43—22no—
82C4⋊Dic43—22no—
83C2×C43⋊C8—24no—
84Dic172—44no—
85D344—44no—
86#10621873—48no—
87C23×C43#12111yescharacteristic
88C22×D43—42no—
89Q8×C43—24no—
90Q8×C43—42no—
91C2×C4×C43—22no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—42no—
97C2×C4×C43—41no—
98C2×C4×C43#12011yescharacteristic
99C2×C4×C43#12012yes—
100C2×C4×C43#12112yes—
101C2×C4×C43#12711yescharacteristic
102C2×C4×C43C2×SD1612yes—
103C2×C4×C43AGL(1,ℤ/8)12yes—
104C22⋊D43—84no—
105C2×Dic43—42no—
106D172—44no—
107D172—44no—
108D172—44no—
109C4×D43—82no—
110C4×D43—82no—
111Dic86—44no—
112C8×C43—24no—
113C8×C43—81no—
114C43⋊C8—44no—
115#10034—431nomaximal, Sylow
116C22×C43—21no—
117C22×C43—21no—
118C22×C43#39211yescharacteristic
119C22×C43#46012yes—
120C2×D43—82no—
121C2×D43—82no—
122C2×D43—82no—
123C4×C43—22no—
124C4×C43—22no—
125C4×C43—42no—
126C4×C43—81no—
127C4×C43#45012yes—
128C4×C43#49211yescharacteristic
129C4×C43#49611yescharacteristic
130Dic43—82no—
131#3150—431no—
132#3103—432no—
133#1985D4311yescharacteristic, complemented
134#1480—432no—
135#1275—431no—
136C2×C43—22no—
137C2×C43#201011yescharacteristic
138C2×C43#201411yescharacteristic
139C2×C43#201711yescharacteristic
140D43—162no—
141C2×#135—862no—
142#532—432no—
143C2×C4×Q8C2×D4311yescharacteristic
144#497—862no—
145#496—862no—
146#481—862no—
147#475—862no—
148#460—862no—
149#448—862no—
150C4×SD16—864no—
151#431—432no—
152C2×C4⋊C8C2×D4311yescharacteristic
153C2×#97C2×D4311yescharacteristic
154#336—22no—
155D4⋊C8—864no—
156C43#1003411yescharacteristic, complemented, Sylow
157C2×#41—862no—
158C22×Q8D17211yescharacteristic
159#135—1724no—
160#135—1724no—
161C2×Q16—862no—
162C2×SD16—864no—
163C2×SD16—864no—
164C2×D8—862no—
165C22×C8—21no—
166C22×C8C22⋊D4312yes—
167C4⋊Q8—432no—
168#127—432no—
169#124—862no—
170#121—862no—
171#121—862no—
172C4×Q8—22no—
173C4×Q8—22no—
174C4×D4—862no—
175C4×D4—862no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4D17211yescharacteristic
178C2×C42—21no—
179C2×C42C22×D4311yescharacteristic
180#106—864no—
181C4⋊C8—22no—
182C4⋊C8—862no—
183#103—864no—
184#102—864no—
185C22⋊C8—862no—
186#97—22no—
187C4×C8—434no—
188#41—1724no—
189#41—1724no—
190C2×Q8—22no—
191C2×Q8—42no—
192C2×Q8—862no—
193C2×D4—862no—
194C2×D4—862no—
195C2×D4—862no—
196C2×D4—1722no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—1722no—
200C22×C4C2×D17211yescharacteristic
201C22×C4#1062189811yescharacteristic
202C22×C4C2×C22⋊D4311yescharacteristic
203Q16—1724no—
204SD16—1728no—
205SD16—1728no—
206D8—1724no—
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—41no—
210C2×C8—42no—
211C2×C8—864no—
212C2×C8#1062188414yescomplemented
213C4⋊C4—22no—
214C4⋊C4—42no—
215C4⋊C4—862no—
216C4⋊C4—862no—
217C22⋊C4—1722no—
218C22⋊C4—1722no—
219C42—41no—
220C42—41no—
221C42D4×D4312yes—
222C42D4×D4312yes—
223C23—1722no—
224C23#1306329911yescharacteristic
225Q8—24no—
226Q8—42no—
227Q8—1724no—
228D4—3444no—
229D4—1724no—
230D4—1724no—
231D4—1724no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—3442no—
240C2×C4—3442no—
241C2×C4—1722no—
242C2×C4#1306329311yescharacteristic
243C2×C4#1306329512yes—
244C2×C4#1306329812yes—
245C2×C4#1306332111yescharacteristic
246C2×C4C2×#1062188412yes—
247C2×C4#1306335012yes—
248C8—24no—
249C8—81no—
250C8—1724no—
251C22—21no—
252C22—21no—
253C22—3442no—
254C22—3442no—
255C22—3442no—
256C22#1458280811yescharacteristic
257C22#1458309912yes—
258C4—22no—
259C4—22no—
260C4—42no—
261C4—81no—
262C4—3442no—
263C4#1458304912yes—
264C4#1458327311yescharacteristic
265C4#1458328911yescharacteristic
266C2—22no—
267C2—6882no—
268C2#1913566211yescharacteristic
269C2#1913568211yescharacteristic
270C2#1913569911yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1985C2
socleC22×C43#392
prime radical#19145041C2
hypercenter#1985D43
hypocenterC43#10034
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. #19144626C2semidirect
3. #19132993C2semidirect
4. #19132426C2semidirect
5. C43×#1985C2semidirect
71. C2×C8×C43SD16semidirect
133. #1985D43semidirect
156. C43#10034semidirect
212. C2×C8#10621884semidirect

Maximal subgroups

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

subgroupindex
#191450412
#191446262
#191329932
#191324262
C43×#19852
#1003443