Finite Group Databasebeta

← #25009968

Subgroups — #25009968

Order 11008.

274 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 53 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#19146065C211yesmaximal, characteristic
2#19136815C211yesmaximal, characteristic, complemented
3#19136807C211yesmaximal, characteristic
4#19136176C211yesmaximal, characteristic, complemented
5#19132588C211yesmaximal, characteristic, complemented
6#19132547C211yesmaximal, characteristic, complemented
7C43×#1341C211yesmaximal, characteristic
8#14583516—21no—
9#14583187—21no—
10#14583183—21no—
11#14583157C2211yescharacteristic
12#14583126—21no—
13#14583120—21no—
14#14583112—21no—
15#14582948C2211yescharacteristic
16#14582927C2211yescharacteristic
17#14582722—21no—
18#14582721—21no—
19#14582716—21no—
20#14582712—21no—
21#14582681C2211yescharacteristic
22#14582671—21no—
23#14582663—21no—
24C43×#469C2211yescharacteristic
25C43×#349C2211yescharacteristic
26C43×#338C2211yescharacteristic
27C2×Dic172D411yescharacteristic
28C2×#10621883—21no—
29C2×#10621877—21no—
30C22×C43⋊C8D411yescharacteristic
31#13063324—21no—
32#13063318—41no—
33#13063312—21no—
34#13063312—41no—
35#13063306—41no—
36#13063304—21no—
37#13063302—41no—
38#13063290—21no—
39D4×Dic43—21no—
40#13063284D411yescharacteristic
41#13063265—21no—
42#13063261—21no—
43#13063261—21no—
44#13063257D411yescharacteristic
45#13063256—21no—
46Dic43⋊C8—21no—
47Dic43⋊C8—21no—
48#13063250—21no—
49#13063248—21no—
50#13063246—21no—
51C2×D8×C43D411yescharacteristic
52C2×M16×C43—21no—
53C2×M16×C43C2311yescharacteristic
54#121×C43—21no—
55M32×C43—21no—
56#106×C43D411yescharacteristic
57#102×C43—21no—
58C2×D4×C43—21no—
59C2×D4×C43—41no—
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—41no—
62C2×Dic86—21no—
63C2×Dic86—41no—
64D8×C43—41no—
65M16×C43—41no—
66M16×C43—41no—
67M16×C43—41no—
68C2×C8×C43—41no—
69C2×C8×C43C2×D411yescharacteristic
70C2×C8×C43C2×D411yescharacteristic
71C4⋊C4×C43—21no—
72C22⋊C4×C43—41no—
73C22⋊Dic43—41no—
74C22⋊Dic43—41no—
75C22⋊Dic43—41no—
76C22⋊Dic43—41no—
77C22⋊Dic43SD1611yescharacteristic
78C22⋊Dic43SD1611yescharacteristic
79#10621883—81no—
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82Dic43⋊C4—41no—
83Dic43⋊C4—41no—
84Dic43⋊C4—41no—
85C4×Dic43—21no—
86C4×Dic43—41no—
87#10621877—41no—
88#10621877—41no—
89C2×C43⋊C8—21no—
90C2×C43⋊C8—41no—
91C2×C43⋊C8—41no—
92Dic172—41no—
93C16×C43—41no—
94C43⋊C16—41no—
95C23×C43—41no—
96C23×C43C2×SD1611yescharacteristic
97D4×C43—41no—
98D4×C43—41no—
99D4×C43—161no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—41no—
103C2×C4×C43#12011yescharacteristic
104C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
105C2×Dic43—21no—
106C2×Dic43—21no—
107C2×Dic43—41no—
108C2×Dic43—41no—
109C2×Dic43—161no—
110Dic86—41no—
111Dic86—41no—
112Dic86—161no—
113C8×C43—21no—
114C8×C43—21no—
115C8×C43—81no—
116C43⋊C8—41no—
117C43⋊C8—81no—
118#12306—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—41no—
121C22×C43—81no—
122C22×C43—81no—
123C22×C43—81no—
124C22×C43#45011yescharacteristic
125C4×C43—21no—
126C4×C43—81no—
127C4×C43#45411yescharacteristic
128C4×C43#45811yescharacteristic
129Dic43—41no—
130Dic43—41no—
131Dic43—81no—
132Dic43—81no—
133#3263—431no—
134#2239—431no—
135#2238—431no—
136#2103—431no—
137#1342—431no—
138#1341D4311yescharacteristic
139#1328—431no—
140C2×C43—21no—
141C2×C43—41no—
142C2×C43—161no—
143C2×C43#161611yescharacteristic
144#542—861no—
145#476—861no—
146#475—861no—
147#470—431no—
148#469C2×D4311yescharacteristic
149#465—861no—
150#464—861no—
151#463—861no—
152#430—431no—
153#424—431no—
154#365—861no—
155#365—861no—
156#362—861no—
157#361—861no—
158#349—431no—
159#349C2×D4311yescharacteristic
160#344—861no—
161#341—861no—
162#338C2×D4311yescharacteristic
163C43#1230611yescharacteristic, complemented, Sylow
164C2×Q16—431no—
165C2×SD16—861no—
166C2×D8D17211yescharacteristic
167C2×M16—21no—
168C2×M16—861no—
169C2×M16C22×D4311yescharacteristic
170C22×C8—431no—
171C4⋊Q8—861no—
172#126—1721no—
173#124—861no—
174#124—1721no—
175#123—1721no—
176C22⋊Q8—861no—
177C22⋊Q8—1721no—
178#121—21no—
179C4×Q8—861no—
180C4×D4—861no—
181#117—431no—
182M32—21no—
183M32—861no—
184#108—861no—
185#108—861no—
186#106—431no—
187#106—861no—
188#106D17211yescharacteristic
189C4⋊C8—861no—
190C4⋊C8—861no—
191#103—861no—
192#103—861no—
193#102—21no—
194#102—861no—
195C2×Q8—861no—
196C2×Q8—1721no—
197C2×D4—21no—
198C2×D4—41no—
199C22×C4—1721no—
200C22×C4D4×D4311yescharacteristic
201Q16—1721no—
202SD16—3441no—
203D8—41no—
204M16—41no—
205M16—41no—
206M16—41no—
207M16—1721no—
208M16—1721no—
209C2×C8—41no—
210C2×C8—861no—
211C2×C8—1721no—
212C2×C8—1721no—
213C2×C8C2×D17211yescharacteristic
214C2×C8D4×D4311yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—861no—
217C4⋊C4—861no—
218C4⋊C4—1721no—
219C4⋊C4—1721no—
220C4⋊C4—1721no—
221C22⋊C4—41no—
222C22⋊C4—431no—
223C22⋊C4—431no—
224C22⋊C4—1721no—
225C22⋊C4—1721no—
226C22⋊C4—1721no—
227C22⋊C4—1721no—
228C42—861no—
229C42—1721no—
230C16—41no—
231C16—1721no—
232C23—41no—
233C23SD16×D4311yescharacteristic
234Q8—1721no—
235Q8—1721no—
236Q8—6881no—
237D4—41no—
238D4—41no—
239D4—161no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—861no—
244C2×C4—861no—
245C2×C4—1721no—
246C2×C4—1721no—
247C2×C4—6881no—
248C2×C4#1306329511yescharacteristic
249C2×C4#1306334911yescharacteristic
250C8—21no—
251C8—21no—
252C8—81no—
253C8—3441no—
254C8—1721no—
255C22—21no—
256C22—41no—
257C22—81no—
258C22—81no—
259C22—81no—
260C22#1458305111yescharacteristic
261C4—21no—
262C4—81no—
263C4—3441no—
264C4—3441no—
265C4—1721no—
266C4—1721no—
267C4#1458307311yescharacteristic
268C4#1458309011yescharacteristic
269C2—21no—
270C2—41no—
271C2—161no—
272C2#1913363311yescharacteristic
subgroupG/H
centerC2#19133633
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#1341C2
socleC2×C43#1616
prime radicalC43×#469C22
hypercenter#1341D43
hypocenterC43#12306
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1341

Complements

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

NH ≅ G/Ntype
2. #19136815C2semidirect
4. #19136176C2semidirect
5. #19132588C2semidirect
6. #19132547C2semidirect
163. C43#12306semidirect

Maximal subgroups

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

subgroupindex
#191460652
#191368152
#191368072
#191361762
#191325882
#191325472
C43×#13412
#1230643