Finite Group Databasebeta

← #24991823

Subgroups — #24991823

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145155C211yesmaximal, characteristic
2#19143544C211yesmaximal, characteristic, complemented
3#19135513C211yesmaximal, characteristic
4#19132995C211yesmaximal, characteristic
5#19132436C211yesmaximal, characteristic, complemented
6#19132431C211yesmaximal, characteristic, complemented
7C43×#1503C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583295C411yescharacteristic, complemented
10#14583273C411yescharacteristic, complemented
11#14583249C411yescharacteristic, complemented
12#14583247C411yescharacteristic, complemented
13#14583130—22no—
14#14583030—21no—
15#14583030—22no—
16Q8×C43⋊C8—21no—
17C4×#10621884—22no—
18#14582926—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063253—21no—
21C2×#13063253—21no—
22#14582855—21no—
23C4×#10621877C2211yescharacteristic
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582628—21no—
26#14582628—21no—
27C43×#533C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#328—22no—
31C2×#10621898—21no—
32C2×#10621884—22no—
33C2×#10621877D411yescharacteristic
34C2×#10621877D411yescharacteristic
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37#13063325C2×C411yescharacteristic
38#13063322C2×C411yescharacteristic
39#13063313—21no—
40#13063299—21no—
41#13063299—21no—
42C4×D172—21no—
43C4×D172—21no—
44#13063256—22no—
45C4⋊(C43⋊C8)—22no—
46C4⋊(C43⋊C8)—22no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)D411yescharacteristic
49C4⋊(C43⋊C8)D411yescharacteristic
50#13063253—42no—
51#13063253—42no—
52#13063249—22no—
53#13063245—22no—
54#13063236—22no—
55#13063236—21no—
56C4×C43⋊C8—22no—
57C4×C43⋊C8—21no—
58C4×C43⋊C8—21no—
59C4×C43⋊C8C2×C411yescharacteristic
60C4×C43⋊C8C2×C411yescharacteristic
61C4⋊Q8×C43C2×C411yescharacteristic
62C4⋊Q8×C43C2×C411yescharacteristic
63#125×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43D412yes—
66C4×Q8×C43—21no—
67C4×Q8×C43D412yes—
68#117×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C42×C43—21no—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C4×C8×C43—21no—
75#95×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43C22⋊C412yes—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C2×C22⋊D43—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87C2×D172—21no—
88C2×D172—21no—
89C2×D172—21no—
90C2×C4×D43—41no—
91C2×Dic86—21no—
92C2×C8×C43—41no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43C22⋊C412yes—
101C22⋊C4×C43—22no—
102C42×C43—22no—
103C42×C43—41no—
104C42×C43—41no—
105C42×C43C22×C411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43#4111yescharacteristic
109#10621884—44no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—41no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114#10621877—21no—
115#10621877—21no—
116#10621877—21no—
117#10621877SD1612yescomplemented
118C2×C43⋊C8—21no—
119C2×C43⋊C8—21no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—42no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C23×C43#12111yescharacteristic
128C22×D43—41no—
129Q8×C43—42no—
130Q8×C43—41no—
131Q8×C43—41no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43C2×C22⋊C411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43C4×D411yescharacteristic
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12311yescharacteristic
146C2×C4×C43C2×SD1611yescharacteristic
147C2×C4×C43#13511yescharacteristic
148C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C43#13711yescharacteristic
150C22⋊D43—81no—
151C22⋊D43—81no—
152C2×Dic43—41no—
153D172—42no—
154D172—41no—
155D172—41no—
156D172—41no—
157D172—41no—
158C4×D43—81no—
159C4×D43—81no—
160Dic86—41no—
161Dic86—41no—
162C8×C43—81no—
163C43⋊C8—22no—
164C43⋊C8—22no—
165C43⋊C8—41no—
166C43⋊C8—41no—
167C43⋊C8—41no—
168C43⋊C8—41no—
169#9054—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#38611yescharacteristic
173C22×C43#46011yescharacteristic
174C22×C43#46411yescharacteristic
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—42no—
182C4×C43—42no—
183C4×C43—82no—
184C4×C43C4×SD1611yescharacteristic
185C4×C43#44011yescharacteristic
186C4×C43#44311yescharacteristic
187C4×C43#44411yescharacteristic
188C4×C43#44811yescharacteristic
189C4×C43#44911yescharacteristic
190Dic43—81no—
191#3167—431no—
192#2962—431no—
193#1980—431no—
194#1503D4311yescharacteristic, complemented
195#1480—431no—
196#1279—431no—
197#1278—431no—
198C2×C43—21no—
199C2×C43—21no—
200C2×C43#187611yescharacteristic
201C2×C43#188011yescharacteristic
202C2×C43#188411yescharacteristic
203D43—161no—
204#533C2×D4311yescharacteristic
205#532—431no—
206#498—431no—
207#492—431no—
208#487—431no—
209#486—431no—
210#465—862no—
211#446—861no—
212#446—862no—
213C8×Q8—861no—
214C4×SD16—862no—
215#431C2×D4311yescharacteristic
216#424—861no—
217C2×C4⋊C8—431no—
218C2×#104—861no—
219C2×#104—861no—
220#405—861no—
221C4×M16—431no—
222C2×C4×C8—431no—
223C4×C4⋊C4C2×D4311yescharacteristic
224#328—22no—
225D4⋊C8—861no—
226D4⋊C8—861no—
227C43#905411yescharacteristic, complemented, Sylow
228C2×#41—861no—
229C2×SD16—862no—
230C2×M16—431no—
231C2×M16—431no—
232C22×C8—861no—
233C22×C8—861no—
234C4⋊Q8—431no—
235C4⋊Q8C4×D4311yescharacteristic
236C4⋊Q8C4×D4311yescharacteristic
237#127—431no—
238#125—21no—
239#124—861no—
240C22⋊Q8—21no—
241C22⋊Q8C22⋊D4312yes—
242#121—861no—
243#121—861no—
244C4×Q8—21no—
245C4×Q8D17212yes—
246C4×D4—861no—
247C4×D4—861no—
248#117—21no—
249C2×C4⋊C4—21no—
250C2×C42—21no—
251C2×C42C22×D4311yescharacteristic
252#106—862no—
253C4⋊C8—21no—
254C4⋊C8—431no—
255C4⋊C8—431no—
256C4⋊C8—862no—
257C4⋊C8—862no—
258C4⋊C8—861no—
259#104—1722no—
260#104—1722no—
261#103—862no—
262#102—862no—
263C22⋊C8—21no—
264#97—862no—
265#97—861no—
266C4×C8—21no—
267C4×C8—431no—
268C4×C8—431no—
269C4×C8—862no—
270C4×C8—861no—
271C4×C8—861no—
272#95—21no—
273#41—1721no—
274#41—1721no—
275#41—1721no—
276#41—1721no—
277C2×Q8—21no—
278C2×Q8—861no—
279C2×Q8(C2×D43)⋊C412yes—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4—1721no—
284C22×C4—41no—
285C22×C4—1721no—
286C22×C4D4×D4311yescharacteristic
287C22×C4#1062190011yescharacteristic
288C22×C4C2×C22⋊D4311yescharacteristic
289SD16—1724no—
290M16—432no—
291M16—861no—
292M16—861no—
293M16—861no—
294C2×C8—41no—
295C2×C8—861no—
296C2×C8—861no—
297C2×C8—861no—
298C2×C8—861no—
299C2×C8—861no—
300C2×C8—861no—
301C2×C8—1722no—
302C2×C8—1721no—
303C2×C8—1721no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4(C2×D43)⋊C412yes—
314C22⋊C4—22no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C42—22no—
318C42—41no—
319C42—41no—
320C42C2×C4×D4311yescharacteristic
321C42C2×D17211yescharacteristic
322C42D4×D4311yescharacteristic
323C42#1062190011yescharacteristic
324C23—1721no—
325C23#1306329711yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—1721no—
330Q8—1721no—
331D4—3441no—
332D4—3441no—
333D4—1722no—
334D4—1721no—
335D4—1721no—
336D4—1721no—
337D4—1721no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—3441no—
347C2×C4—3441no—
348C2×C4—1721no—
349C2×C4C2×(C2×D43)⋊C411yescharacteristic
350C2×C4(C22⋊D43)⋊C411yescharacteristic
351C2×C4(C22⋊D43)⋊C411yescharacteristic
352C2×C4#1306329511yescharacteristic
353C2×C4#1306329711yescharacteristic
354C2×C4#1306330911yescharacteristic
355C2×C4SD16×D4311yescharacteristic
356C2×C4#1306334811yescharacteristic
357C2×C4#1306335211yescharacteristic
358C2×C4#1306335711yescharacteristic
359C8—81no—
360C8—862no—
361C8—862no—
362C8—1721no—
363C8—1721no—
364C8—1721no—
365C8—1721no—
366C22—21no—
367C22—21no—
368C22—3441no—
369C22—3441no—
370C22—3441no—
371C22#1458277611yescharacteristic
372C22#1458309711yescharacteristic
373C22#1458312311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—82no—
380C4—3441no—
381C4#1458298411yescharacteristic
382C4#1458300211yescharacteristic
383C4#1458301311yescharacteristic
384C4#1458301811yescharacteristic
385C4#1458303911yescharacteristic
386C4#1458304711yescharacteristic
387C2—21no—
388C2—21no—
389C2—6881no—
390C2#1913492011yescharacteristic
391C2#1913494811yescharacteristic
392C2#1913497611yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1503C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1503D43
hypocenterC43#9054
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. #19143544C2semidirect
5. #19132436C2semidirect
6. #19132431C2semidirect
7. C43×#1503C2semidirect
9. #14583295C4semidirect
10. #14583273C4semidirect
11. #14583249C4semidirect
12. #14583247C4semidirect
117. #10621877SD16semidirect
194. #1503D43semidirect
227. C43#9054semidirect

Maximal subgroups

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

subgroupindex
#191451552
#191435442
#191355132
#191329952
#191324362
#191324312
C43×#15032
#905443