Finite Group Databasebeta

← #24997541

Subgroups — #24997541

Order 11008.

512 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 83 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#19145905C211yesmaximal, characteristic
2#19144717C212yesmaximal, complemented
3#19133205C212yesmaximal, complemented
4#19132465C211yesmaximal, characteristic, complemented
5C43×#1985C211yesmaximal, characteristic, complemented
6#14583449C2212yes—
7#14583212—22no—
8#14583194—22no—
9#14583180—22no—
10#14583135—22no—
11#14583099—22no—
12#14583095—22no—
13#14583038—22no—
14#14582997—24no—
15#14582956C2212yes—
16#14582638—24no—
17C2×C4×Q8×C43C2211yescharacteristic
18C2×C4⋊C8×C43C2211yescharacteristic
19C2×#97×C43C2211yescharacteristic
20C43×#336—22no—
21C2×#10621898—22no—
22C2×#10621884—24no—
23C2×D344—22no—
24#13063325D412yes—
25#13063322D412yes—
26#13063313—22no—
27#13063299—22no—
28#13063299—22no—
29C4×D172—22no—
30C4×D172—22no—
31#13063259—22no—
32#13063258—24no—
33C4⋊(C43⋊C8)—22no—
34#13063249—24no—
35#13063247—24no—
36#13063245—24no—
37C22⋊(C43⋊C8)—22no—
38#13063236D414yes—
39C22×Q8×C43D411yescharacteristic
40C22×C8×C43—21no—
41C22×C8×C43D412yes—
42C4×Q8×C43—22no—
43C4×Q8×C43—22no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C42×C43—21no—
47C2×C42×C43C2311yescharacteristic
48C4⋊C8×C43—22no—
49#97×C43—22no—
50C2×Q8×C43—22no—
51C2×Q8×C43—42no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43C2×D411yescharacteristic
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43#4111yescharacteristic
57C2×C22⋊D43—42no—
58#10621898—84no—
59C2×D172—22no—
60C2×D172—22no—
61C2×D172—22no—
62C2×C4×D43—42no—
63C2×Dic86—22no—
64C2×C8×C43—22no—
65C2×C8×C43—22no—
66C2×C8×C43—41no—
67C2×C8×C43—41no—
68C2×C8×C43—42no—
69C4⋊C4×C43—22no—
70C4⋊C4×C43—42no—
71C42×C43—41no—
72C42×C43—41no—
73C42×C43C2×D412yes—
74C42×C43C2×D412yes—
75#10621884—48no—
76(C2×D43)⋊C4—42no—
77(C2×D43)⋊C4—42no—
78C4⋊Dic43—22no—
79C4⋊Dic43—22no—
80C2×C43⋊C8—24no—
81D344—82no—
82C23×C43#12111yescharacteristic
83C22×D43—42no—
84Q8×C43—24no—
85Q8×C43—42no—
86C2×C4×C43—22no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—42no—
95C2×C4×C43#12011yescharacteristic
96C2×C4×C43#12012yes—
97C2×C4×C43#12112yes—
98C2×C4×C43#12711yescharacteristic
99C22⋊D43—84no—
100C2×Dic43—42no—
101D172—44no—
102D172—42no—
103D172—42no—
104D172—82no—
105C4×D43—84no—
106Dic86—82no—
107C8×C43—42no—
108C8×C43—42no—
109C43⋊C8—44no—
110#10028—431nomaximal, Sylow
111C22×C43—21no—
112C22×C43—21no—
113C22×C43#39211yescharacteristic
114C22×C43#47212yes—
115C2×D43—82no—
116C2×D43—82no—
117C2×D43—82no—
118C4×C43—21no—
119C4×C43—22no—
120C4×C43—22no—
121C4×C43—42no—
122C4×C43—81no—
123C4×C43#45511yescharacteristic
124C4×C43#45611yescharacteristic
125Dic43—82no—
126#3245—431no—
127#3112—432no—
128#1985D4311yescharacteristic, complemented
129#1530—432no—
130#1290—431no—
131C2×C43—22no—
132C2×C43#200711yescharacteristic
133C2×C43#201011yescharacteristic
134C2×C43#201811yescharacteristic
135D43—162no—
136#532—432no—
137C2×C4×Q8C2×D4311yescharacteristic
138#480—862no—
139#477—862no—
140#474—862no—
141#466—862no—
142#460—862no—
143#459—862no—
144#448—862no—
145#440—864no—
146#432—432no—
147C2×C4⋊C8C2×D4311yescharacteristic
148C2×#97C2×D4311yescharacteristic
149#336—22no—
150#329—864no—
151C43#1002811yescharacteristic, complemented, Sylow
152C2×#41—862no—
153C22×Q8D17211yescharacteristic
154C2×SD16—864no—
155C2×D8—862no—
156C22×C8—21no—
157C22×C8C22⋊D4312yes—
158C4⋊Q8—432no—
159#127—432no—
160#124—862no—
161#121—862no—
162#121—862no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×D4—862no—
166C4×D4—862no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4D17211yescharacteristic
169C2×C42—21no—
170C2×C42C22×D4311yescharacteristic
171#107—864no—
172#107—862no—
173C4⋊C8—22no—
174C4⋊C8—862no—
175#103—864no—
176#102—864no—
177#102—864no—
178C22⋊C8—862no—
179#97—22no—
180#97—434no—
181#41—3444no—
182C2×Q8—22no—
183C2×Q8—42no—
184C2×Q8—862no—
185C2×D4—862no—
186C2×D4—862no—
187C2×D4—862no—
188C2×D4—1722no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—1722no—
192C22×C4C2×D17211yescharacteristic
193C22×C4#1062189811yescharacteristic
194C22×C4C2×C22⋊D4311yescharacteristic
195SD16—1728no—
196D8—3442no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—42no—
202C2×C8—864no—
203C4⋊C4—22no—
204C4⋊C4—42no—
205C4⋊C4—862no—
206C4⋊C4—862no—
207C22⋊C4—1722no—
208C22⋊C4—1722no—
209C42—41no—
210C42—41no—
211C42D4×D4312yes—
212C42D4×D4312yes—
213C23—1722no—
214C23#1306329911yescharacteristic
215Q8—24no—
216Q8—42no—
217Q8—3442no—
218D4—3442no—
219D4—3444no—
220D4—1724no—
221D4—1722no—
222D4—1722no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—3444no—
233C2×C4—1722no—
234C2×C4#1306329311yescharacteristic
235C2×C4#1306329512yes—
236C2×C4#1306329812yes—
237C2×C4#1306332111yescharacteristic
238C8—42no—
239C8—42no—
240C8—1724no—
241C22—21no—
242C22—21no—
243C22—3442no—
244C22—3442no—
245C22—3442no—
246C22#1458280811yescharacteristic
247C22#1458316912yes—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—42no—
252C4—81no—
253C4—3442no—
254C4#1458307611yescharacteristic
255C4#1458308111yescharacteristic
256C2—22no—
257C2—6882no—
258C2#1913564111yescharacteristic
259C2#1913566211yescharacteristic
260C2#1913570411yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1985C2
socleC22×C43#392
prime radical#19145905C2
hypercenter#1985D43
hypocenterC43#10028
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. #19144717C2semidirect
3. #19133205C2semidirect
4. #19132465C2semidirect
5. C43×#1985C2semidirect
128. #1985D43semidirect
151. C43#10028semidirect

Maximal subgroups

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

subgroupindex
#191459052
#191447172
#191332052
#191324652
C43×#19852
#1002843