Finite Group Databasebeta

← #25009054

Subgroups — #25009054

Order 11008.

398 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 67 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#19136512C212yesmaximal, complemented
3#19132603C212yesmaximal, complemented
4#19132535C211yesmaximal, characteristic, complemented
5C43×#2056C211yesmaximal, characteristic, complemented
6#14583449—21no—
7C2×#13063268—22no—
8#14583180—22no—
9#14583135—21no—
10#14583135C2212yes—
11#14583095—22no—
12#14582703—22no—
13C22⋊(C43⋊C16)C2212yes—
14C22×Q16×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C2×#103×C43—21no—
17C43×#391—21no—
18C43×#340C2211yescharacteristic
19C2×#10621898—41no—
20C2×D344—21no—
21C2×D344D412yes—
22#13063325—21no—
23#13063322—21no—
24#13063313—41no—
25#13063299—22no—
26#13063299—41no—
27C4×D172—22no—
28C4×D172—41no—
29#13063268—44no—
30C2×C43⋊C16—22no—
31#13063259—21no—
32#13063259D412yes—
33#13063247—22no—
34#13063247—22no—
35C22×Q8×C43—21no—
36C2×Q16×C43—22no—
37C2×Q16×C43—42no—
38C22×C8×C43D411yescharacteristic
39C22×C8×C43C2311yescharacteristic
40C2×C4⋊C4×C43—21no—
41C2×C42×C43D411yescharacteristic
42C4⋊C8×C43—22no—
43#103×C43—42no—
44#95×C43—41no—
45#95×C43—41no—
46C2×Q8×C43—22no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C22×C4×C43—41no—
53C22×C4×C43—41no—
54C22×C4×C43D811yescharacteristic
55C22×C4×C43D811yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C2×C22⋊D43—42no—
58#10621898—82no—
59#10621898—82no—
60C2×D172—22no—
61C2×D172—41no—
62C2×D172—41no—
63C2×C4×D43—42no—
64C2×Dic86—41no—
65Q16×C43—24no—
66Q16×C43—42no—
67C2×C8×C43—21no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43C2×D412yes—
71C4⋊C4×C43—41no—
72C4⋊C4×C43—41no—
73C42×C43—21no—
74C42×C43—21no—
75(C2×D43)⋊C4—42no—
76(C2×D43)⋊C4—42no—
77C4⋊Dic43—22no—
78C4⋊Dic43—41no—
79D344—42no—
80D344—81no—
81C43⋊C16—42no—
82C23×C43C2×D811yescharacteristic
83C22×D43—42no—
84Q8×C43—42no—
85Q8×C43—42no—
86Q8×C43—81no—
87Q8×C43—81no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—41no—
94C2×C4×C43—42no—
95C2×C4×C43—81no—
96C2×C4×C43—81no—
97C2×C4×C43—81no—
98C2×C4×C43—81no—
99C2×C4×C43—81no—
100C2×C4×C43SD3212yescomplemented
101C2×C4×C43#12011yescharacteristic
102C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
103C22⋊D43—82no—
104C22⋊D43—82no—
105C2×Dic43—42no—
106D172—42no—
107D172—42no—
108D172—82no—
109D172—82no—
110C4×D43—84no—
111Dic86—82no—
112C8×C43—22no—
113C8×C43—41no—
114#12161—431nomaximal, Sylow
115C22×C43—21no—
116C22×C43—21no—
117C22×C43#44711yescharacteristic
118C22×C43C2×SD3211yescharacteristic
119C22×C43#50911yescharacteristic
120C2×D43—82no—
121C2×D43—82no—
122C2×D43—82no—
123C4×C43—21no—
124C4×C43—22no—
125C4×C43—41no—
126C4×C43—82no—
127C4×C43—161no—
128C4×C43#45411yescharacteristic
129C4×C43B(4,𝔽2)11yescharacteristic
130Dic43—82no—
131#3245—431no—
132#2185—432no—
133#2056D4311yescharacteristic, complemented
134#1347—432no—
135#1322—431no—
136C2×C43—21no—
137C2×C43—21no—
138C2×C43#159811yescharacteristic
139C2×C43#218711yescharacteristic
140C2×C43#219111yescharacteristic
141D43—162no—
142C22×Q16C2×D4311yescharacteristic
143#532—861no—
144C2×SD32—862no—
145#474—862no—
146#466—432no—
147#466—861no—
148#459—862no—
149C2×C4⋊C8C2×D4311yescharacteristic
150C2×#103—21no—
151#391—21no—
152#358—862no—
153C22⋊C16—432no—
154#340C2×D4311yescharacteristic
155C43#1216111yescharacteristic, complemented, Sylow
156C2×#41—1721no—
157C22×Q8—21no—
158C2×Q16—22no—
159C2×Q16—42no—
160C2×D8—432no—
161C2×D8—861no—
162C22×C8C22⋊D4311yescharacteristic
163C22×C8C22×D4311yescharacteristic
164C4⋊Q8—861no—
165#127—861no—
166#124—1721no—
167#121—862no—
168#121—1721no—
169C4×D4—862no—
170C4×D4—1721no—
171C2×C4⋊C4—21no—
172C2×C42C22⋊D4311yescharacteristic
173SD32—1724no—
174C2×C16—862no—
175#107—432no—
176#107—861no—
177C4⋊C8—22no—
178#103—42no—
179#102—862no—
180#102—862no—
181#95—41no—
182#95—41no—
183#41—3442no—
184#41—3442no—
185C2×Q8—22no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—1721no—
192C2×D4—862no—
193C2×D4—1721no—
194C2×D4—1721no—
195C2×D4—1722no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—1722no—
199C22×C4#1062188211yescharacteristic
200C22×C4#1062188211yescharacteristic
201C22×C4C2×C22⋊D4311yescharacteristic
202Q16—24no—
203Q16—42no—
204D8—3441no—
205D8—1722no—
206C2×C8—21no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8D4×D4312yes—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—862no—
213C4⋊C4—1721no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C42—21no—
217C42—21no—
218C16—1722no—
219C23—1722no—
220C23C2×#1062188211yescharacteristic
221Q8—42no—
222Q8—42no—
223Q8—81no—
224Q8—81no—
225Q8—3442no—
226D4—3442no—
227D4—3442no—
228D4—3442no—
229D4—3442no—
230D4—1722no—
231D4—1722no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—3444no—
245C2×C4—1722no—
246C2×C4#1306326812yescomplemented
247C2×C4#1306329311yescharacteristic
248C2×C4#1306335011yescharacteristic
249C8—22no—
250C8—41no—
251C22—21no—
252C22—21no—
253C22—3442no—
254C22—3442no—
255C22—3442no—
256C22#1458303211yescharacteristic
257C22C2×#1306326811yescharacteristic
258C22#1458333411yescharacteristic
259C4—22no—
260C4—21no—
261C4—41no—
262C4—82no—
263C4—161no—
264C4—3442no—
265C4#1458307111yescharacteristic
266C4#1458308511yescharacteristic
267C2—21no—
268C2—21no—
269C2—6882no—
270C2#1913352911yescharacteristic
271C2#1913652311yescharacteristic
272C2#1913654511yescharacteristic
subgroupG/H
centerC22#14583032
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#2056C2
socleC22×C43#447
prime radical#19145905C2
hypercenter#2056D43
hypocenterC43#12161
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2056

Complements

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

NH ≅ G/Ntype
2. #19136512C2semidirect
3. #19132603C2semidirect
4. #19132535C2semidirect
5. C43×#2056C2semidirect
100. C2×C4×C43SD32semidirect
133. #2056D43semidirect
155. C43#12161semidirect
246. C2×C4#13063268semidirect

Maximal subgroups

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

subgroupindex
#191459052
#191365122
#191326032
#191325352
C43×#20562
#1216143