Finite Group Databasebeta

← #25010132

Subgroups — #25010132

Order 11008.

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

normal subgroups only

This group has 362 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#19147569C211yesmaximal, characteristic
2#19136852C211yesmaximal, characteristic, complemented
3#19133962C211yesmaximal, characteristic, complemented
4#19132642C211yesmaximal, characteristic, complemented
5#19132573C211yesmaximal, characteristic, complemented
6#19132556C211yesmaximal, characteristic, complemented
7C43×#2208C211yesmaximal, characteristic, complemented
8#14583570—21no—
9C2×#13063268—22no—
10#14583276C2211yescharacteristic
11#14583274—21no—
12#14583181—21no—
13#14583094—21no—
14#14583093—22no—
15C8×Dic86C2211yescharacteristic
16#14582981—21no—
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582645—21no—
20C2×SD32×C43—21no—
21C43×#494C2211yescharacteristic
22C4×D8×C43C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#358—21no—
25C2×#10621898—41no—
26C2×D344—21no—
27C2×D344D412yes—
28C2×#10621882—22no—
29#13063322—21no—
30#13063321—22no—
31#13063299—41no—
32#13063298—42no—
33C4×Dic86D411yescharacteristic
34#13063287—22no—
35#13063268—44no—
36C2×C43⋊C16—21no—
37#13063256—41no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063248—41no—
42#13063245—22no—
43C8×Dic43—21no—
44C2×Q16×C43—21no—
45C2×Q16×C43—21no—
46C2×D8×C43D411yescharacteristic
47C4⋊Q8×C43—21no—
48C4×D4×C43—21no—
49SD32×C43—42no—
50C2×C16×C43—21no—
51#107×C43D411yescharacteristic
52#102×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—41no—
55C2×D4×C43—21no—
56C22×C4×C43—41no—
57C2×C22⋊D43—42no—
58C2×C22⋊D43—42no—
59#10621898—82no—
60#10621898—82no—
61C2×D172—22no—
62C2×D172—41no—
63C2×D172—41no—
64C2×C4×D43—42no—
65C2×Dic86D811yescharacteristic
66Q16×C43—42no—
67Q16×C43—41no—
68Q16×C43—41no—
69D8×C43—21no—
70D8×C43—21no—
71C2×C8×C43C2×D411yescharacteristic
72C2×C8×C43C2×D411yescharacteristic
73C4⋊C4×C43—21no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C22⋊C4×C43—41no—
77C42×C43C2×D411yescharacteristic
78#10621882—82no—
79(C2×D43)⋊C4—42no—
80C4⋊Dic43D811yescharacteristic
81Dic43⋊C4—21no—
82C4×Dic43—21no—
83C2×C43⋊C8—21no—
84C2×C43⋊C8—41no—
85D344—42no—
86D344—41no—
87D344—41no—
88C16×C43—41no—
89C43⋊C16—22no—
90C23×C43—41no—
91C22×D43—42no—
92Q8×C43—81no—
93Q8×C43—81no—
94D4×C43—41no—
95D4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43—81no—
98C2×C4×C43—81no—
99C2×C4×C43—81no—
100C2×C4×C43#12011yescharacteristic
101C2×C4×C43C2×D811yescharacteristic
102C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
103C22⋊D43—84no—
104C22⋊D43—162no—
105C2×Dic43—21no—
106C2×Dic43—21no—
107D172—42no—
108D172—42no—
109D172—81no—
110D172—81no—
111D172—161no—
112C4×D43—84no—
113Dic86—21no—
114Dic86SD3212yescomplemented
115C8×C43—21no—
116C8×C43#13511yescharacteristic
117C8×C43AGL(1,ℤ/8)11yescharacteristic
118C43⋊C8—41no—
119C43⋊C8—81no—
120#12332—431nomaximal, Sylow
121C22×C43—81no—
122C22×C43—81no—
123C22×C43—81no—
124C22×C43#44711yescharacteristic
125C2×D43—82no—
126C2×D43—82no—
127C2×D43—82no—
128C4×C43—21no—
129C4×C43—81no—
130C4×C43—161no—
131C4×C43#44911yescharacteristic
132C4×C43#45311yescharacteristic
133C4×C43C2×SD3211yescharacteristic
134C4×C43#50911yescharacteristic
135Dic43—22no—
136Dic43—41no—
137#3391—431no—
138#2248—431no—
139#2208D4311yescharacteristic, complemented
140#1670—431no—
141#1361—431no—
142Q8⋊C16—431no—
143#1331—431no—
144C2×C43—161no—
145C2×C43#162111yescharacteristic
146C2×C43#218711yescharacteristic
147C2×C43#219411yescharacteristic
148D43—162no—
149#550—861no—
150C2×SD32—21no—
151C2×SD32—862no—
152#494C2×D4311yescharacteristic
153#493—431no—
154#493—861no—
155#475—861no—
156#459—862no—
157#459—861no—
158C8×Q8—431no—
159C4×D8—861no—
160C4×D8C2×D4311yescharacteristic
161C4⋊C16C2×D4311yescharacteristic
162#358—21no—
163C4×C16—431no—
164#335—431no—
165#332—861no—
166C43#1233211yescharacteristic, complemented, Sylow
167C2×#41—1721no—
168C2×Q16—21no—
169C2×Q16—21no—
170C2×D8—432no—
171C2×D8—862no—
172C2×D8—861no—
173C2×D8C22⋊D4311yescharacteristic
174C4⋊Q8—21no—
175#127—862no—
176#127—861no—
177#121—1722no—
178#121—1721no—
179C4×Q8—431no—
180C4×D4—21no—
181C4×D4—862no—
182SD32—42no—
183SD32—1724no—
184C2×C16—21no—
185C2×C16—861no—
186#107C22⋊D4311yescharacteristic
187#106—1721no—
188C4⋊C8—431no—
189C4⋊C8—861no—
190C4⋊C8—861no—
191#103—1721no—
192#102—21no—
193#102—862no—
194C4×C8—861no—
195C4×C8C22×D4311yescharacteristic
196#41—3442no—
197#41—3442no—
198C2×Q8—41no—
199C2×Q8—431no—
200C2×D4—21no—
201C2×D4—862no—
202C2×D4—1722no—
203C2×D4—1722no—
204C2×D4—1721no—
205C2×D4—1721no—
206C22×C4—41no—
207C22×C4—1722no—
208Q16—42no—
209Q16—41no—
210Q16—41no—
211D8—21no—
212D8—21no—
213D8—3442no—
214D8—1722no—
215D8—1721no—
216D8—1721no—
217C2×C8—861no—
218C2×C8—1721no—
219C2×C8D4×D4311yescharacteristic
220C2×C8C2×C22⋊D4311yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—431no—
225C4⋊C4—861no—
226C22⋊C4—41no—
227C22⋊C4—1722no—
228C42—861no—
229C42D4×D4311yescharacteristic
230C16—41no—
231C16—862no—
232C23—41no—
233C23—1722no—
234Q8—81no—
235Q8—81no—
236Q8—432no—
237Q8—861no—
238D4—41no—
239D4—41no—
240D4—3444no—
241D4—3441no—
242D4—3441no—
243D4—1722no—
244D4—1722no—
245D4—6881no—
246D4—6882no—
247C2×C4—41no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—861no—
252C2×C4—861no—
253C2×C4—3444no—
254C2×C4#1306329311yescharacteristic
255C2×C4D8×D4311yescharacteristic
256C2×C4#1306334911yescharacteristic
257C8—21no—
258C8—3441no—
259C8—1721no—
260C8#1306334511yescharacteristic
261C8#1306335111yescharacteristic
262C22—81no—
263C22—81no—
264C22—81no—
265C22—3442no—
266C22—3442no—
267C22—3442no—
268C22#1458303111yescharacteristic
269C4—21no—
270C4—81no—
271C4—161no—
272C4—862no—
273C4—1721no—
274C4#1458304211yescharacteristic
275C4#1458306511yescharacteristic
276C4SD32×D4311yescharacteristic
277C4#1458333611yescharacteristic
278C2—161no—
279C2—6882no—
280C2#1913365911yescharacteristic
281C2#1913652211yescharacteristic
282C2#1913656311yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2208C2
socleC22×C43#447
prime radical#19147569C2
hypercenter#2208D43
hypocenterC43#12332
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #19136852C2semidirect
3. #19133962C2semidirect
4. #19132642C2semidirect
5. #19132573C2semidirect
6. #19132556C2semidirect
7. C43×#2208C2semidirect
114. Dic86SD32semidirect
139. #2208D43semidirect
166. C43#12332semidirect

Maximal subgroups

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

subgroupindex
#191475692
#191368522
#191339622
#191326422
#191325732
#191325562
C43×#22082
#1233243