Finite Group Databasebeta

← #25009967

Subgroups — #25009967

Order 11008.

274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 59 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#19136812C211yesmaximal, characteristic, complemented
2#19136807C211yesmaximal, characteristic
3#19136175C211yesmaximal, characteristic, complemented
4#19132589C211yesmaximal, characteristic, complemented
5#19132586C211yesmaximal, characteristic
6#19132548C211yesmaximal, characteristic, complemented
7C43×#3263C211yesmaximal, characteristic
8#14582948C2211yescharacteristic
9#14582721—21no—
10#14582721—21no—
11#14582715—21no—
12#14582712—21no—
13#14582681C2211yescharacteristic
14#14582681C2211yescharacteristic
15#14582669—21no—
16#14582664—21no—
17C43⋊#338C2211yescharacteristic
18C43×#542—21no—
19C43×#476—21no—
20C43×#475—21no—
21C43×#470C2211yescharacteristic
22C43×#469C2211yescharacteristic
23C43×#465—21no—
24C43×#464—21no—
25C43×#463—21no—
26C43×#424C2211yescharacteristic
27C2×#10621877—21no—
28C2×#10621877—21no—
29#13063265—21no—
30#13063265—21no—
31#13063261—21no—
32#13063261—21no—
33C2×Q16×C43D411yescharacteristic
34C2×SD16×C43—21no—
35C2×D8×C43D411yescharacteristic
36C2×M16×C43C2311yescharacteristic
37C22×C8×C43D411yescharacteristic
38C4⋊Q8×C43—21no—
39#126×C43—41no—
40#124×C43—21no—
41#124×C43—41no—
42#123×C43—41no—
43C22⋊Q8×C43—21no—
44C22⋊Q8×C43—41no—
45#121×C43—21no—
46C4×Q8×C43—21no—
47C4×D4×C43—21no—
48#117×C43D411yescharacteristic
49#106×C43—21no—
50#106×C43D411yescharacteristic
51#106×C43D411yescharacteristic
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54#103×C43—21no—
55#103×C43—21no—
56#102×C43—21no—
57#102×C43—21no—
58C2×Q8×C43—21no—
59C2×Q8×C43—41no—
60C2×D4×C43—21no—
61C2×D4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43C2×D411yescharacteristic
64Q16×C43—41no—
65SD16×C43—81no—
66D8×C43—41no—
67M16×C43—41no—
68C2×C8×C43—21no—
69C2×C8×C43—41no—
70C2×C8×C43C2×D411yescharacteristic
71C2×C8×C43C2×D411yescharacteristic
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C22⋊C4×C43—41no—
79C22⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43SD1611yescharacteristic
84C22⋊C4×C43SD1611yescharacteristic
85C42×C43—21no—
86C42×C43—41no—
87#10621877—41no—
88#10621877—41no—
89#10621877—41no—
90#10621877—41no—
91C2×C43⋊C8—41no—
92C2×C43⋊C8—41no—
93C43⋊C16—41no—
94C43⋊C16—41no—
95C23×C43—41no—
96C23×C43C2×SD1611yescharacteristic
97Q8×C43—41no—
98Q8×C43—41no—
99Q8×C43—161no—
100D4×C43—41no—
101D4×C43—41no—
102D4×C43—161no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—161no—
111C2×C4×C43#12011yescharacteristic
112C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
113C8×C43—21no—
114C8×C43—21no—
115C8×C43—41no—
116C43⋊C8—81no—
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—41no—
127C4×C43—41no—
128C4×C43—81no—
129C4×C43—81no—
130C4×C43—81no—
131C4×C43#45411yescharacteristic
132C4×C43#45811yescharacteristic
133#3263D4311yescharacteristic
134#2239—431no—
135#2238—431no—
136#2103—431no—
137#1342—431no—
138#1341—431no—
139#1328—431no—
140C2×C43—21no—
141C2×C43—41no—
142C2×C43—161no—
143C2×C43#161611yescharacteristic
144#542—21no—
145#476—21no—
146#475—21no—
147#470C2×D4311yescharacteristic
148#469C2×D4311yescharacteristic
149#465—21no—
150#464—21no—
151#463—21no—
152#430—431no—
153#424C2×D4311yescharacteristic
154#365—861no—
155#365—861no—
156#362—861no—
157#361—861no—
158#349—431no—
159#349—431no—
160#344—861no—
161#341—861no—
162#338—431no—
163C43#1230611yescharacteristic, complemented, Sylow
164C2×Q16C22⋊D4311yescharacteristic
165C2×SD16—21no—
166C2×D8C22⋊D4311yescharacteristic
167C2×M16—861no—
168C2×M16—861no—
169C2×M16C22×D4311yescharacteristic
170C22×C8C22⋊D4311yescharacteristic
171C4⋊Q8—21no—
172#126—41no—
173#124—21no—
174#124—41no—
175#123—41no—
176C22⋊Q8—21no—
177C22⋊Q8—41no—
178#121—21no—
179C4×Q8—21no—
180C4×D4—21no—
181#117C22⋊D4311yescharacteristic
182M32—861no—
183M32—861no—
184#108—861no—
185#108—861no—
186#106—21no—
187#106C22⋊D4311yescharacteristic
188#106C22⋊D4311yescharacteristic
189C4⋊C8—21no—
190C4⋊C8—21no—
191#103—21no—
192#103—21no—
193#102—21no—
194#102—21no—
195C2×Q8—21no—
196C2×Q8—41no—
197C2×D4—21no—
198C2×D4—41no—
199C22×C4—41no—
200C22×C4C2×C22⋊D4311yescharacteristic
201Q16—41no—
202SD16—81no—
203D8—41no—
204M16—41no—
205M16—1721no—
206M16—1721no—
207M16—1721no—
208M16—1721no—
209C2×C8—21no—
210C2×C8—41no—
211C2×C8—1721no—
212C2×C8—1721no—
213C2×C8C2×C22⋊D4311yescharacteristic
214C2×C8C2×C22⋊D4311yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4#1062188311yescharacteristic
227C22⋊C4#1062188311yescharacteristic
228C42—21no—
229C42—41no—
230C16—1721no—
231C16—1721no—
232C23—41no—
233C23C2×#1062188311yescharacteristic
234Q8—41no—
235Q8—41no—
236Q8—161no—
237D4—41no—
238D4—41no—
239D4—161no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—161no—
248C2×C4#1306329411yescharacteristic
249C2×C4#1306335111yescharacteristic
250C8—21no—
251C8—21no—
252C8—41no—
253C8—3441no—
254C8—3441no—
255C22—21no—
256C22—41no—
257C22—81no—
258C22—81no—
259C22—81no—
260C22#1458305011yescharacteristic
261C4—21no—
262C4—41no—
263C4—41no—
264C4—81no—
265C4—81no—
266C4—81no—
267C4#1458307211yescharacteristic
268C4#1458308911yescharacteristic
269C2—21no—
270C2—41no—
271C2—161no—
272C2#1913363211yescharacteristic
subgroupG/H
centerC2#19133632
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#3263C2
socleC2×C43#1616
prime radicalC43×#469C22
hypercenter#3263D43
hypocenterC43#12306
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3263

Complements

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

NH ≅ G/Ntype
1. #19136812C2semidirect
3. #19136175C2semidirect
4. #19132589C2semidirect
6. #19132548C2semidirect
163. C43#12306semidirect

Maximal subgroups

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

subgroupindex
#191368122
#191368072
#191361752
#191325892
#191325862
#191325482
C43×#32632
#1230643