Finite Group Databasebeta

← #25000474

Subgroups — #25000474

Order 11008.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583180C211yesmaximal, characteristic
2#19135396C211yesmaximal, characteristic, complemented
3#19135388C211yesmaximal, characteristic
4#19134592C211yesmaximal, characteristic
5C2×#14582649C211yesmaximal, characteristic, complemented
6C2×#14582646C211yesmaximal, characteristic, complemented
7C43×#1296C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C2×C4×D172C2211yescharacteristic
10#14583180—22no—
11#14583180—22no—
12C2×#13063259—21no—
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063248—21no—
15C2×#13063248—21no—
16C2×#13063247—21no—
17C2×#13063245—21no—
18C2×(C2×D43)⋊C8—21no—
19C2×(C2×D43)⋊C8—21no—
20C2×C4×C43⋊C8C2211yescharacteristic
21#14582661—21no—
22#14582649—22no—
23#14582646—22no—
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C43×#384C2211yescharacteristic
27C22×Dic86—21no—
28C22×D172D411yescharacteristic
29C22×C4×D43—21no—
30C22×C43⋊C8—21no—
31C22×C43⋊C8D411yescharacteristic
32C22×C43⋊C8D411yescharacteristic
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325D412yes—
37C4×D172—21no—
38C4×D172—21no—
39C4×D172—21no—
40C4×D172—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43D411yescharacteristic
44C2×(C2×D43)⋊C4—21no—
45#13063259—24no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48#13063248—42no—
49#13063248—42no—
50#13063247—24no—
51#13063245—42no—
52(C2×D43)⋊C8—42no—
53(C2×D43)⋊C8—42no—
54C4×C43⋊C8—21no—
55C4×C43⋊C8—21no—
56C22×C8×C43—21no—
57C22×C8×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C42×C43C2311yescharacteristic
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43D412yes—
66C23×D43—21no—
67C22×C4×C43—41no—
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43#4111yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—41no—
73C2×D172—21no—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172SD1612yes—
79C2×C4×D43—41no—
80C2×C4×D43—41no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×C4×D43—41no—
84C2×C4×D43—41no—
85C2×Dic86—22no—
86C2×Dic86—41no—
87C2×Dic86—41no—
88C2×Dic86—41no—
89C2×Dic86—41no—
90C2×Dic86—41no—
91C2×C8×C43—22no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—81no—
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105C42×C43#4111yescharacteristic
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—41no—
108C4⋊Dic43—22no—
109C4⋊Dic43—21no—
110C4⋊Dic43—22no—
111C4⋊Dic43—21no—
112C4⋊Dic43—41no—
113C4⋊Dic43—41no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—21no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—21no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8D812yes—
123C23×C43#12111yescharacteristic
124C22×D43—22no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43—41no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43—41no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43#12011yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43#12311yescharacteristic
140C2×C4×C43#12311yescharacteristic
141C2×C4×C43#12411yescharacteristic
142C2×C4×C43C2×D811yescharacteristic
143C2×C4×C43C2×SD1611yescharacteristic
144C2×C4×C43#13511yescharacteristic
145C2×C4×C43#13511yescharacteristic
146C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C43#13711yescharacteristic
149C2×C4×C43#13711yescharacteristic
150C2×Dic43—42no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—81no—
155C2×Dic43—81no—
156D172—22no—
157D172—22no—
158D172—41no—
159D172—41no—
160C4×D43—81no—
161C4×D43—81no—
162C4×D43—81no—
163C4×D43—81no—
164Dic86—42no—
165Dic86—42no—
166Dic86—81no—
167Dic86—81no—
168C8×C43—42no—
169C8×C43—81no—
170C43⋊C8—22no—
171C43⋊C8—41no—
172C43⋊C8—81no—
173#10484—431nomaximal, Sylow
174C22×C43#39411yescharacteristic
175C22×C43#45911yescharacteristic
176C22×C43#46311yescharacteristic
177C22×C43#46511yescharacteristic
178C22×C43#47011yescharacteristic
179C22×C43#47111yescharacteristic
180C22×C43#47311yescharacteristic
181C2×D43—42no—
182C2×D43—42no—
183C2×D43—42no—
184C2×D43—81no—
185C2×D43—81no—
186C2×D43—81no—
187C2×D43—81no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—161no—
191C4×C43#44811yescharacteristic
192C4×C43#45211yescharacteristic
193C4×C43#45911yescharacteristic
194C4×C43#46311yescharacteristic
195C4×C43#46611yescharacteristic
196C4×C43#46911yescharacteristic
197C4×C43#48311yescharacteristic
198C4×C43#48511yescharacteristic
199Dic43—82no—
200Dic43—81no—
201C2×#474—431no—
202#1956—431no—
203#1954—431no—
204#1802—431no—
205C2×#334—431no—
206C2×#332—431no—
207#1296D4311yescharacteristic, complemented
208C2×C43#166511yescharacteristic
209C2×C43#167911yescharacteristic
210C2×C43#168911yescharacteristic
211C2×C43#170311yescharacteristic
212C2×C43#203511yescharacteristic
213C2×C43#205211yescharacteristic
214C2×C43#205411yescharacteristic
215D43—82no—
216C2×C4⋊Q8—431no—
217C2×C4×D4—431no—
218#474—862no—
219#474—862no—
220C2×#107—861no—
221C2×C4⋊C8—431no—
222C2×C4⋊C8C2×D4311yescharacteristic
223C2×C4⋊C8C2×D4311yescharacteristic
224C2×#103—861no—
225C2×#103—861no—
226C2×#102—861no—
227C2×#102—861no—
228C2×C22⋊C8—861no—
229C2×C22⋊C8—861no—
230C2×C4×C8—431no—
231#384C2×D4311yescharacteristic
232#340—861no—
233#334—862no—
234#332—862no—
235C43#1048411yescharacteristic, complemented, Sylow
236C22×Q8—861no—
237C22×D4—431no—
238C23×C4—861no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—431no—
242C22×C8—431no—
243C22×C8—861no—
244C4⋊Q8—432no—
245C4⋊Q8—861no—
246C4⋊Q8—861no—
247C4⋊Q8—861no—
248C4×D4—861no—
249C4×D4—861no—
250C4×D4—861no—
251C4×D4—861no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4—861no—
257C2×C4⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C42C22×D4311yescharacteristic
260#107—864no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—861no—
265C4⋊C8—861no—
266C4⋊C8D17212yes—
267#103—1722no—
268#103—1722no—
269#102—864no—
270#102—1722no—
271C22⋊C8—1722no—
272C22⋊C8—1722no—
273C4×C8—861no—
274C4×C8—861no—
275C24—861no—
276C2×Q8—862no—
277C2×Q8—1721no—
278C2×Q8—1721no—
279C2×Q8—1721no—
280C2×Q8—1721no—
281C2×Q8—1721no—
282C2×D4—432no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—861no—
288C22×C4—41no—
289C22×C4—861no—
290C22×C4—1721no—
291C22×C4—1721no—
292C22×C4—1721no—
293C22×C4—1721no—
294C22×C4—1721no—
295C22×C4—1721no—
296C22×C4—1721no—
297C22×C4#1062189811yescharacteristic
298C22×C4D4×D4311yescharacteristic
299C22×C4D4×D4311yescharacteristic
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—432no—
307C2×C8—861no—
308C2×C8—861no—
309C2×C8—861no—
310C2×C8—861no—
311C2×C8—861no—
312C2×C8—1721no—
313C2×C8—1721no—
314C2×C8—1721no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—81no—
320C4⋊C4—862no—
321C4⋊C4—861no—
322C4⋊C4—861no—
323C4⋊C4—862no—
324C4⋊C4—1721no—
325C4⋊C4—1721no—
326C22⋊C4—1721no—
327C22⋊C4—1721no—
328C42C2×D17211yescharacteristic
329C42#1062189811yescharacteristic
330C42D4×D4311yescharacteristic
331C42#1062190211yescharacteristic
332C23—862no—
333C23—1721no—
334C23—1721no—
335C23—1721no—
336C23—1721no—
337C23—1721no—
338C23—1721no—
339C23#1306329811yescharacteristic
340Q8—3441no—
341Q8—3441no—
342Q8—1722no—
343Q8—1722no—
344D4—862no—
345D4—862no—
346D4—1721no—
347D4—1721no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—3441no—
354C2×C4—3441no—
355C2×C4—3441no—
356C2×C4—3441no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—1721no—
360C2×C4—1722no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4#1306329511yescharacteristic
364C2×C4#1306329811yescharacteristic
365C2×C4#1306330011yescharacteristic
366C2×C4#1306331011yescharacteristic
367C2×C4#1306331011yescharacteristic
368C2×C4#1306331311yescharacteristic
369C2×C4D8×D4311yescharacteristic
370C2×C4SD16×D4311yescharacteristic
371C2×C4#1306334411yescharacteristic
372C2×C4#1306334811yescharacteristic
373C2×C4#1306335211yescharacteristic
374C2×C4#1306335211yescharacteristic
375C2×C4#1306335411yescharacteristic
376C2×C4#1306335711yescharacteristic
377C8—42no—
378C8—81no—
379C8—862no—
380C8—3441no—
381C8—1721no—
382C22—3441no—
383C22—3441no—
384C22—3441no—
385C22—3441no—
386C22—1722no—
387C22—1722no—
388C22—1722no—
389C22#1458281711yescharacteristic
390C22#1458309311yescharacteristic
391C22#1458311711yescharacteristic
392C22#1458312711yescharacteristic
393C22#1458315611yescharacteristic
394C22#1458316111yescharacteristic
395C22#1458317311yescharacteristic
396C4—21no—
397C4—21no—
398C4—161no—
399C4—3441no—
400C4—3442no—
401C4#1458303911yescharacteristic
402C4#1458306211yescharacteristic
403C4#1458309311yescharacteristic
404C4#1458311711yescharacteristic
405C4#1458313611yescharacteristic
406C4#1458315311yescharacteristic
407C4#1458323111yescharacteristic
408C4#1458324211yescharacteristic
409C2—3442no—
410C2#1913393511yescharacteristic
411C2#1913402111yescharacteristic
412C2#1913408311yescharacteristic
413C2#1913417311yescharacteristic
414C2#1913579411yescharacteristic
415C2#1913589711yescharacteristic
416C2#1913590711yescharacteristic
subgroupG/H
centerC23#13063298
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1296C2
socleC23×C43#121
prime radicalC22×D172D4
hypercenter#1296D43
hypocenterC43#10484
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #19135396C2semidirect
5. C2×#14582649C2semidirect
6. C2×#14582646C2semidirect
7. C43×#1296C2semidirect
207. #1296D43semidirect
235. C43#10484semidirect

Maximal subgroups

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

subgroupindex
C2×#145831802
#191353962
#191353882
#191345922
C2×#145826492
C2×#145826462
C43×#12962
#1048443