Finite Group Databasebeta

← #24997542

Subgroups — #24997542

Order 11008.

512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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#19144718C212yesmaximal, complemented
3#19135534C211yesmaximal, characteristic, complemented
4#19133207C212yesmaximal, complemented
5C43×#1290C211yesmaximal, characteristic, complemented
6#14583449C2212yes—
7C2×C4×Dic86C2211yescharacteristic
8#14583213—22no—
9#14583195—22no—
10#14583180—22no—
11#14583135—22no—
12#14583100—22no—
13#14583095—22no—
14#14583040—22no—
15#14583001—24no—
16C2×#13063236C2211yescharacteristic
17#14582653—22no—
18#14582638—24no—
19C43×#432C2212yes—
20C2×C4⋊C8×C43C2211yescharacteristic
21C2×#10621898—22no—
22C22×Dic86D411yescharacteristic
23C2×#10621873—24no—
24C2×D344—22no—
25C22×C43⋊C8—21no—
26#13063325D412yes—
27#13063322D412yes—
28#13063313—22no—
29#13063299—22no—
30#13063299—22no—
31C4×Dic86—22no—
32C4×Dic86—22no—
33C4×D172—22no—
34C4×D172—22no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×C4×Dic43—21no—
38#13063259—22no—
39#13063259—24no—
40#13063250—24no—
41#13063247—24no—
42#13063247—24no—
43#13063236—22no—
44C22×C8×C43D412yes—
45C2×C42×C43C2311yescharacteristic
46C4⋊C8×C43—22no—
47C4⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49#97×C43D414yes—
50C22×C4×C43C2×D411yescharacteristic
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43#4111yescharacteristic
53C2×C22⋊D43—42no—
54C22×Dic43—21no—
55C22×Dic43—21no—
56#10621898—84no—
57C2×D172—22no—
58C2×D172—22no—
59C2×D172—22no—
60C2×C4×D43—42no—
61C2×Dic86—22no—
62C2×Dic86—22no—
63C2×Dic86—42no—
64C2×C8×C43—24no—
65C2×C8×C43—22no—
66C2×C8×C43—42no—
67C42×C43C2×D412yes—
68C42×C43C2×D412yes—
69(C2×D43)⋊C4—42no—
70(C2×D43)⋊C4—42no—
71C4⋊Dic43—22no—
72C4⋊Dic43—22no—
73C4⋊Dic43—22no—
74Dic43⋊C4—42no—
75C4×Dic43—41no—
76C4×Dic43—41no—
77C2×C43⋊C8—22no—
78C2×C43⋊C8—41no—
79C2×C43⋊C8—41no—
80D344—82no—
81#10621873—48no—
82C23×C43#12111yescharacteristic
83C22×D43—42no—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—41no—
88C2×C4×C43#12012yes—
89C2×C4×C43#12011yescharacteristic
90C2×C4×C43#12112yes—
91C2×C4×C43#12711yescharacteristic
92C22⋊D43—84no—
93C2×Dic43—22no—
94C2×Dic43—41no—
95C2×Dic43—41no—
96C2×Dic43—41no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99D172—44no—
100D172—42no—
101D172—42no—
102D172—82no—
103C4×D43—84no—
104Dic86—24no—
105Dic86—42no—
106Dic86—82no—
107C8×C43—44no—
108C8×C43—42no—
109C43⋊C8—42no—
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#45511yescharacteristic
122C4×C43#45611yescharacteristic
123Dic43—42no—
124Dic43—82no—
125Dic43—81no—
126#3245—431no—
127#3112—432no—
128#1985—431no—
129#1530—432no—
130#1290D4311yescharacteristic, complemented
131C2×C43—22no—
132C2×C43#200711yescharacteristic
133C2×C43#201011yescharacteristic
134C2×C43#201811yescharacteristic
135D43—162no—
136#532—432no—
137C2×C4×Q8—431no—
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#432C2×D4312yes—
147C2×C4⋊C8C2×D4311yescharacteristic
148C2×#97—431no—
149#336—862no—
150#329—864no—
151C43#1002811yescharacteristic, complemented, Sylow
152C2×#41—862no—
153C22×Q8—431no—
154C2×SD16—864no—
155C2×D8—862no—
156C22×C8—861no—
157C22×C8D17212yes—
158C4⋊Q8—432no—
159#127—432no—
160#124—862no—
161#121—862no—
162#121—862no—
163C4×Q8—862no—
164C4×Q8—862no—
165C4×D4—862no—
166C4×D4—862no—
167C2×C4⋊C4—431no—
168C2×C4⋊C4—861no—
169C2×C42—861no—
170C2×C42C22×D4311yescharacteristic
171#107—864no—
172#107—862no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175#103—864no—
176#102—864no—
177#102—864no—
178C22⋊C8—22no—
179#97—862no—
180#97D17214yes—
181#41—3444no—
182C2×Q8—862no—
183C2×Q8—862no—
184C2×Q8—1722no—
185C2×D4—862no—
186C2×D4—862no—
187C2×D4—862no—
188C2×D4—1722no—
189C22×C4—861no—
190C22×C4—861no—
191C22×C4—1722no—
192C22×C4C2×D17211yescharacteristic
193C22×C4D4×D4311yescharacteristic
194C22×C4#1062190211yescharacteristic
195SD16—1728no—
196D8—3442no—
197C2×C8—24no—
198C2×C8—22no—
199C2×C8—42no—
200C2×C8—862no—
201C2×C8—1721no—
202C2×C8—1721no—
203C4⋊C4—862no—
204C4⋊C4—862no—
205C4⋊C4—862no—
206C4⋊C4—1722no—
207C22⋊C4—1722no—
208C22⋊C4—1722no—
209C42—1721no—
210C42—1721no—
211C42C2×D17212yes—
212C42D4×D4312yes—
213C23—1722no—
214C23#1306330011yescharacteristic
215Q8—864no—
216Q8—3442no—
217Q8—1722no—
218D4—3442no—
219D4—3444no—
220D4—1724no—
221D4—1722no—
222D4—1722no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—862no—
228C2×C4—3444no—
229C2×C4—1721no—
230C2×C4—1722no—
231C2×C4—1722no—
232C2×C4—1721no—
233C2×C4—1721no—
234C2×C4#1306329512yes—
235C2×C4#1306329511yescharacteristic
236C2×C4#1306330012yes—
237C2×C4#1306332211yescharacteristic
238C8—44no—
239C8—42no—
240C8—1722no—
241C22—21no—
242C22—21no—
243C22—3442no—
244C22—3442no—
245C22—3442no—
246C22#1458280911yescharacteristic
247C22#1458317012yes—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—3442no—
252C4—3441no—
253C4—1722no—
254C4#1458307911yescharacteristic
255C4#1458308411yescharacteristic
256C2—22no—
257C2—6882no—
258C2#1913564411yescharacteristic
259C2#1913566311yescharacteristic
260C2#1913570511yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1290C2
socleC22×C43#392
prime radical#19145905C2
hypercenter#1290D43
hypocenterC43#10028
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
2. #19144718C2semidirect
3. #19135534C2semidirect
4. #19133207C2semidirect
5. C43×#1290C2semidirect
130. #1290D43semidirect
151. C43#10028semidirect

Maximal subgroups

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

subgroupindex
#191459052
#191447182
#191355342
#191332072
C43×#12902
#1002843