Finite Group Databasebeta

← #25250061

Subgroups — #25250061

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583339C211yesmaximal, characteristic
2#19143512C211yesmaximal, characteristic
3#19143462C211yesmaximal, characteristic, complemented
4#19136483C218yesmaximal, complemented
5#19136367C211yesmaximal, characteristic, complemented
6C2×#14582716C211yesmaximal, characteristic, complemented
7#19136199C211yesmaximal, characteristic, complemented
8C43×#2145C211yesmaximal, characteristic
9C22×Dic172C2211yescharacteristic
10#14583666—21no—
11#14583376—21no—
12#14583339C414yescomplemented
13#14583339C2214yes—
14C2×#13063271C412yescomplemented
15C2×#13063269C412yescomplemented
16C2×#13063265C2211yescharacteristic
17#14583021C2214yes—
18#14583016—22no—
19#14583005C2214yescomplemented
20#14582993—22no—
21C2×#13063261C2211yescharacteristic
22#14582916—21no—
23#14582907—21no—
24#14582854C2211yescharacteristic
25#14582721C2214yescomplemented
26#14582716C2214yescomplemented
27#14582676C2214yescomplemented
28C2×#135×C43C2211yescharacteristic
29C2×M32×C43C2211yescharacteristic
30C43×#427C2211yescharacteristic
31C43×#360C2214yes—
32C22×Dic86—21no—
33C2×Dic172—21no—
34C2×Dic172—21no—
35C2×Dic172—21no—
36C2×Dic172C2×C412yes—
37C2×Dic172C2×C412yes—
38C2×Dic172C2312yes—
39#13063332—24no—
40#13063332—42no—
41C2×#10621877—21no—
42C2×#10621877—42no—
43C2×#10621877D411yescharacteristic
44C4×Dic86—42no—
45#13063290—24no—
46#13063284D411yescharacteristic
47#13063281—42no—
48#13063271C2×C418yes—
49#13063269C2×C418yes—
50#13063265C2×C412yes—
51#13063265C2312yes—
52C2×C43⋊C16C2×C412yes—
53#13063261—21no—
54#13063261C2312yes—
55#13063252—24no—
56#13063248—24no—
57#13063235C2312yes—
58C8×Dic43D412yes—
59C2×#41×C43—21no—
60#135×C43—21no—
61#135×C43—21no—
62#135×C43C2×C412yes—
63#135×C43C2312yes—
64C2×Q16×C43C2×C411yescharacteristic
65C2×SD16×C43—21no—
66C2×D8×C43C2×C411yescharacteristic
67C22×C8×C43C2311yescharacteristic
68#117×C43—21no—
69M32×C43—21no—
70M32×C43C2312yes—
71C2×C16×C43—21no—
72#107×C43—21no—
73#106×C43C2312yes—
74#41×C43—22no—
75#41×C43—22no—
76#41×C43—41no—
77#41×C43—41no—
78C2×Q8×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43C2×D411yescharacteristic
83C22×Dic43—41no—
84C2×Dic86—22no—
85C2×Dic86—22no—
86C2×Dic86—22no—
87C2×Dic86—41no—
88C2×Dic86—41no—
89C2×Dic86—41no—
90Q16×C43—21no—
91Q16×C43C22×C412yes—
92SD16×C43—22no—
93SD16×C43—22no—
94D8×C43—21no—
95D8×C43C22×C412yes—
96C2×C8×C43C22×C411yescharacteristic
97C2×C8×C43C22×C411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43#4111yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C2×C8×C43C2411yescharacteristic
102C4⋊C4×C43—22no—
103C22⋊C4×C43—41no—
104C42×C43—41no—
105C22⋊Dic43—21no—
106C4⋊Dic43—21no—
107Dic43⋊C4—44no—
108C4×Dic43—44no—
109C4×Dic43C2×D412yes—
110#10621877—21no—
111#10621877—21no—
112#10621877—22no—
113#10621877—44no—
114#10621877—41no—
115C2×C43⋊C8—44no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8C2×D412yes—
118Dic172—22no—
119Dic172—22no—
120Dic172—22no—
121Dic172C22×C414yes—
122C16×C43—22no—
123C43⋊C16C22×C414yes—
124C23×C43—41no—
125C23×C43AGL(1,ℤ/8)11yescharacteristic
126Q8×C43—22no—
127Q8×C43—41no—
128D4×C43—22no—
129D4×C43—42no—
130D4×C43—42no—
131D4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43C22×D411yescharacteristic
142C2×Dic43—22no—
143C2×Dic43—42no—
144C2×Dic43—42no—
145C2×Dic43—42no—
146Dic86—24no—
147Dic86—42no—
148Dic86—42no—
149Dic86—42no—
150C8×C43C4×D411yescharacteristic
151C8×C43C4×D411yescharacteristic
152C8×C43C23×C411yescharacteristic
153C8×C43C2×#4111yescharacteristic
154C43⋊C8—22no—
155C43⋊C8—42no—
156#33470—431nomaximal, Sylow
157C22×C43—41no—
158C22×C43—42no—
159C22×C43—161no—
160C22×C43#44211yescharacteristic
161C22×C43#44211yescharacteristic
162C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
163C4×C43—42no—
164C4×C43—82no—
165C4×C43#44211yescharacteristic
166C4×C43#44211yescharacteristic
167C4×C43C2×C4×D411yescharacteristic
168C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
169Dic43—42no—
170Dic43—44no—
171C2×#510—431no—
172#2957—431no—
173#2950—431no—
174#2180—438no—
175#2155—431no—
176C2×#362—431no—
177#2145D4311yescharacteristic
178#2110—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—82no—
183C2×C43C2×#44211yescharacteristic
184C2×#135C2×D4311yescharacteristic
185C22×Q16—431no—
186#568—861no—
187#519—861no—
188#510—434no—
189#510—434no—
190C2×Q32—432no—
191C2×SD32—432no—
192C2×M32—431no—
193C2×M32C2×D4311yescharacteristic
194#444—434no—
195#443—862no—
196#441—434no—
197C4×Q16—862no—
198C2×#108—431no—
199#427C2×D4311yescharacteristic
200#421—861no—
201#419—861no—
202#405—431no—
203#365—434no—
204#362—434no—
205#360C2×D4314yes—
206#347—434no—
207C43#3347011yescharacteristic, complemented, Sylow
208C2×#41—21no—
209C22×Q8—861no—
210#135—21no—
211#135—21no—
212#135C4×D4312yes—
213#135C22×D4312yes—
214C2×Q16—432no—
215C2×Q16—432no—
216C2×Q16—432no—
217C2×Q16—861no—
218C2×Q16—861no—
219C2×Q16—861no—
220C2×Q16C4×D4311yescharacteristic
221C2×SD16—21no—
222C2×D8C4×D4311yescharacteristic
223#131—864no—
224#131—1722no—
225C2×M16—431no—
226C2×M16—861no—
227C2×M16—1722no—
228C22×C8C22×D4311yescharacteristic
229C4×Q8—864no—
230C4×Q8—1722no—
231#117—21no—
232#117—431no—
233#117—1722no—
234Q32—438no—
235SD32—438no—
236M32—21no—
237M32—432no—
238M32—432no—
239M32C22×D4312yes—
240C2×C16—21no—
241C2×C16—432no—
242#108—432no—
243#108—861no—
244#107—21no—
245#106C22×D4312yes—
246#104—864no—
247#103—864no—
248#97—432no—
249C4×C8—432no—
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8—862no—
256C2×Q8—862no—
257C2×Q8—862no—
258C2×Q8—1721no—
259C2×Q8—1721no—
260C2×Q8—1721no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—41no—
264C22×C4—1721no—
265C22×C4D4×D4311yescharacteristic
266Q16—21no—
267Q16—434no—
268Q16—862no—
269Q16—862no—
270Q16—862no—
271Q16C2×C4×D4312yes—
272SD16—22no—
273SD16—22no—
274D8—21no—
275D8C2×C4×D4312yes—
276M16—861no—
277M16—861no—
278M16—862no—
279M16—1724no—
280M16—1721no—
281C2×C8—432no—
282C2×C8—1724no—
283C2×C8—1721no—
284C2×C8C2×C4×D4311yescharacteristic
285C2×C8C2×C4×D4311yescharacteristic
286C2×C8D4×D4311yescharacteristic
287C2×C8#1062190011yescharacteristic
288C2×C8#1062190011yescharacteristic
289C2×C8C23×D4311yescharacteristic
290C4⋊C4—22no—
291C4⋊C4—861no—
292C4⋊C4—1724no—
293C22⋊C4—41no—
294C22⋊C4—861no—
295C42—41no—
296C42—432no—
297C42—1724no—
298C16—22no—
299C16—434no—
300C23—41no—
301C23#1306334911yescharacteristic
302Q8—22no—
303Q8—41no—
304Q8—864no—
305Q8—1722no—
306Q8—1722no—
307Q8—1722no—
308D4—22no—
309D4—42no—
310D4—42no—
311D4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—862no—
317C2×C4—1722no—
318C2×C4—1722no—
319C2×C4—1722no—
320C2×C4(C22⋊D43)⋊C411yescharacteristic
321C2×C4(C22⋊D43)⋊C411yescharacteristic
322C2×C4#1306334911yescharacteristic
323C2×C4#1306335211yescharacteristic
324C2×C4#1306335211yescharacteristic
325C2×C4C2×D4×D4311yescharacteristic
326C8—862no—
327C8—1722no—
328C8(C22⋊D43)⋊C411yescharacteristic
329C8(C22⋊D43)⋊C411yescharacteristic
330C8C22×C4×D4311yescharacteristic
331C8C2×#1062190011yescharacteristic
332C22—41no—
333C22—42no—
334C22—161no—
335C22#1458300811yescharacteristic
336C22#1458300811yescharacteristic
337C22C2×#1306334911yescharacteristic
338C4—42no—
339C4—82no—
340C4—1722no—
341C4—1724no—
342C4#1458300811yescharacteristic
343C4#1458300811yescharacteristic
344C4C2×(C22⋊D43)⋊C411yescharacteristic
345C4C2×#1306335211yescharacteristic
346C2—21no—
347C2—21no—
348C2—21no—
349C2—82no—
350C2C2×#1458300811yescharacteristic
subgroupG/H
centerC2C2×#14583008
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2145C2
socleC2×C43C2×#442
prime radicalC2×#135×C43C22
cosocleC2×C8×C43C24
hypercenter#2145D43
hypocenterC43#33470
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #2145

Complements

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

NH ≅ G/Ntype
3. #19143462C2semidirect
4. #19136483C2semidirect
5. #19136367C2semidirect
6. C2×#14582716C2semidirect
7. #19136199C2semidirect
12. #14583339C4semidirect
14. C2×#13063271C4semidirect
15. C2×#13063269C4semidirect
19. #14583005C22semidirect
25. #14582721C22semidirect
26. #14582716C22semidirect
27. #14582676C22semidirect
207. C43#33470semidirect

Maximal subgroups

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

subgroupindex
C2×#145833392
#191435122
#191434622
#191364832
#191363672
C2×#145827162
#191361992
C43×#21452
#3347043