Finite Group Databasebeta

← #24997588

Subgroups — #24997588

Order 11008.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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#19145119C211yesmaximal, characteristic, complemented
2#19144604C212yesmaximal
3#19135393C211yesmaximal, characteristic
4#19132999C212yesmaximal, complemented
5C43×#1275C211yesmaximal, characteristic, complemented
6#14583456C2212yes—
7C2×C4×D172C2211yescharacteristic
8#14583308—22no—
9#14583308—22no—
10#14583230—22no—
11#14583190—22no—
12#14583105—22no—
13#14583052—22no—
14C4×#10621873—24no—
15#14582937—22no—
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×(C2×D43)⋊C8—22no—
18#14582631—24no—
19C43×#431C2212yes—
20C2×#97×C43C2211yescharacteristic
21C22×D172D411yescharacteristic
22C22×C4×D43—21no—
23C2×#10621873—24no—
24C22×C43⋊C8—21no—
25#13063325D412yes—
26#13063325D412yes—
27#13063317—22no—
28#13063304—22no—
29#13063304—22no—
30C4×Dic86—22no—
31C4×Dic86—22no—
32C4×D172—22no—
33C4×D172—22no—
34#13063284—22no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×(C2×D43)⋊C4—21no—
37#13063259—22no—
38#13063259—22no—
39#13063257—24no—
40#13063257—24no—
41C4⋊(C43⋊C8)—22no—
42#13063250—24no—
43#13063247—24no—
44(C2×D43)⋊C8—44no—
45C22×C8×C43D412yes—
46C2×C42×C43C2311yescharacteristic
47C4⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49#97×C43—22no—
50C4×C8×C43D414yes—
51C23×D43—21no—
52C22×C4×C43C2×D411yescharacteristic
53C22×C4×C43C2×D411yescharacteristic
54C22×C4×C43#4111yescharacteristic
55C22×Dic43—21no—
56C2×D172—22no—
57C2×D172—42no—
58C2×C4×D43—41no—
59C2×C4×D43—41no—
60C2×C4×D43—42no—
61C2×C4×D43—42no—
62C2×Dic86—22no—
63C2×Dic86—22no—
64C2×C8×C43—22no—
65C2×C8×C43—22no—
66C2×C8×C43—24no—
67C2×C8×C43SD1614yescomplemented
68C42×C43C2×D412yes—
69C42×C43C2×D412yes—
70C22⋊Dic43—42no—
71(C2×D43)⋊C4—42no—
72C4⋊Dic43—22no—
73C4⋊Dic43—22no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76C4⋊Dic43—22no—
77Dic43⋊C4—42no—
78Dic43⋊C4—42no—
79C4×Dic43—42no—
80C2×C43⋊C8—41no—
81C2×C43⋊C8—42no—
82#10621873—48no—
83C23×C43#12111yescharacteristic
84C22×D43—22no—
85C22×D43—41no—
86C22×D43—42no—
87C22×D43—41no—
88C22×D43—42no—
89C2×C4×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43#12012yes—
92C2×C4×C43#12011yescharacteristic
93C2×C4×C43#12112yes—
94C2×C4×C43#12711yescharacteristic
95C2×C4×C43C2×SD1612yes—
96C2×C4×C43#13712yes—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—41no—
100C2×Dic43—42no—
101D172—24no—
102D172—42no—
103C4×D43—82no—
104C4×D43—81no—
105C4×D43—81no—
106Dic86—44no—
107Dic86—44no—
108C8×C43—24no—
109C8×C43—44no—
110C43⋊C8—81no—
111#10036—431nomaximal, Sylow
112C22×C43—21no—
113C22×C43—21no—
114C22×C43#39211yescharacteristic
115C22×C43#46112yes—
116C2×D43—44no—
117C2×D43—42no—
118C2×D43—82no—
119C2×D43—81no—
120C2×D43—81no—
121C4×C43—22no—
122C4×C43—22no—
123C4×C43#44812yes—
124C4×C43#49211yescharacteristic
125C4×C43#49711yescharacteristic
126Dic43—82no—
127Dic43—81no—
128Dic43—82no—
129#3162—431no—
130#3101—432no—
131#1955—431no—
132#1481—432no—
133#1275D4311yescharacteristic, complemented
134C2×C43—22no—
135C2×C43#201011yescharacteristic
136C2×C43#201311yescharacteristic
137C2×C43#201711yescharacteristic
138D43—82no—
139#533—432no—
140C2×C4×D4—431no—
141#501—862no—
142#501—862no—
143#483—862no—
144#476—862no—
145#461—862no—
146#450—862no—
147C4×SD16—864no—
148#431C2×D4312yes—
149#427—862no—
150C2×C4⋊C8—431no—
151C2×C22⋊C8—862no—
152C2×#97C2×D4311yescharacteristic
153Q8⋊C8—864no—
154C43#1003611yescharacteristic, complemented, Sylow
155C22×D4—431no—
156C23×C4—861no—
157C2×SD16—864no—
158C22×C8—861no—
159C22×C8D17212yes—
160C4⋊Q8—432no—
161C4⋊Q8—432no—
162#125—862no—
163C22⋊Q8—862no—
164C22⋊Q8—862no—
165C4×Q8—862no—
166C4×Q8—862no—
167C4×D4—862no—
168C4×D4—862no—
169#117—862no—
170C2×C4⋊C4—431no—
171C2×C22⋊C4—861no—
172C2×C42C22×D4311yescharacteristic
173#107—862no—
174#107—862no—
175#106—864no—
176#106—864no—
177C4⋊C8—22no—
178C4⋊C8—862no—
179#103—864no—
180#102—864no—
181C22⋊C8—22no—
182C22⋊C8—1724no—
183#97—22no—
184C4×C8D17214yes—
185C24—861no—
186C2×Q8—862no—
187C2×Q8—862no—
188C2×D4—862no—
189C2×D4—1722no—
190C22×C4—861no—
191C22×C4—1721no—
192C22×C4—1721no—
193C22×C4—1722no—
194C22×C4—1722no—
195C22×C4C2×D17211yescharacteristic
196C22×C4D4×D4311yescharacteristic
197C22×C4#1062190211yescharacteristic
198SD16—1728no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—24no—
202C2×C8—1721no—
203C2×C8—1722no—
204C2×C8#1062187314yescomplemented
205C4⋊C4—862no—
206C4⋊C4—862no—
207C4⋊C4—862no—
208C4⋊C4—862no—
209C4⋊C4—862no—
210C4⋊C4—1722no—
211C4⋊C4—1722no—
212C22⋊C4—1722no—
213C22⋊C4—1722no—
214C42—1722no—
215C42C2×D17212yes—
216C42D4×D4312yes—
217C23—862no—
218C23—1721no—
219C23—1722no—
220C23—1721no—
221C23—1722no—
222C23#1306330011yescharacteristic
223Q8—1724no—
224Q8—1724no—
225D4—864no—
226D4—1722no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—3442no—
230C2×C4—3441no—
231C2×C4—3441no—
232C2×C4—1722no—
233C2×C4—1722no—
234C2×C4—1721no—
235C2×C4—1722no—
236C2×C4#1306329512yes—
237C2×C4#1306329511yescharacteristic
238C2×C4#1306330012yes—
239C2×C4#1306332211yescharacteristic
240C2×C4C2×#1062187312yes—
241C2×C4#1306335812yes—
242C8—24no—
243C8—44no—
244C8—3441no—
245C22—21no—
246C22—21no—
247C22—3442no—
248C22—3441no—
249C22—3441no—
250C22—1724no—
251C22—1722no—
252C22#1458280911yescharacteristic
253C22#1458310512yes—
254C4—22no—
255C4—22no—
256C4—3442no—
257C4—3441no—
258C4—3442no—
259C4#1458304012yes—
260C4#1458327211yescharacteristic
261C4#1458329311yescharacteristic
262C2—22no—
263C2—3442no—
264C2#1913566311yescharacteristic
265C2#1913568011yescharacteristic
266C2#1913570011yescharacteristic
subgroupG/H
centerC2×C4#13063322
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1275C2
socleC22×C43#392
prime radicalC22×D172D4
hypercenter#1275D43
hypocenterC43#10036
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
1. #19145119C2semidirect
4. #19132999C2semidirect
5. C43×#1275C2semidirect
67. C2×C8×C43SD16semidirect
133. #1275D43semidirect
154. C43#10036semidirect
204. C2×C8#10621873semidirect

Maximal subgroups

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

subgroupindex
#191451192
#191446042
#191353932
#191329992
C43×#12752
#1003643