Finite Group Databasebeta

← #25079427

Subgroups — #25079427

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144988C211yesmaximal, characteristic, complemented
2C2×#14583189C211yesmaximal, characteristic, complemented
3D4×#10621877C211yesmaximal, characteristic, complemented
4#19134168C212yesmaximal, complemented
5#19134126C212yesmaximal, complemented
6#19134044C212yesmaximal, complemented
7#19134002C212yesmaximal, complemented
8#19133348C211yesmaximal, characteristic, complemented
9#19133275C211yesmaximal, characteristic, complemented
10#19133272C211yesmaximal, characteristic, complemented
11C43×#3100C211yesmaximal, characteristic
12C22×#10621877—21no—
13C2×#13063325C2211yescharacteristic
14#14583258—22no—
15#14583249C2212yescomplemented
16#14583245C2212yescomplemented
17#14583189—21no—
18#14583189—21no—
19#14583189C2212yes—
20#14583189C2212yes—
21#14582977C2212yes—
22#14582971—22no—
23D4×C43⋊C8C2212yes—
24C2×#13063256—21no—
25#14582923C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27#14582900—21no—
28#14582900—21no—
29C2×#13063246—21no—
30#14582863—21no—
31C4×#10621877C2211yescharacteristic
32#14582651C2212yescomplemented
33#14582649C2212yescomplemented
34#14582647C2212yescomplemented
35#14582647C2212yescomplemented
36#14582645C2212yescomplemented
37#14582643C2212yescomplemented
38C43×#532C2211yescharacteristic
39C2×C4×D4×C43C2211yescharacteristic
40C43×#480—21no—
41C43×#474C2211yescharacteristic
42C43×#474C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#459C2211yescharacteristic
45C43×#447—21no—
46C4×D8×C43—21no—
47C4×D8×C43—21no—
48C43×#431C2211yescharacteristic
49C22×Dic86—21no—
50C2×#10621877—21no—
51C2×#10621877—22no—
52C2×#10621877—44no—
53C2×#10621877D411yescharacteristic
54C2×#10621877D411yescharacteristic
55C22×C43⋊C8—21no—
56C22×C43⋊C8—22no—
57#13063325—21no—
58#13063325—21no—
59#13063325—21no—
60#13063325C2312yes—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63#13063256—22no—
64#13063256—22no—
65C4⋊(C43⋊C8)—21no—
66C4⋊(C43⋊C8)—21no—
67C4⋊(C43⋊C8)C2312yes—
68C4⋊(C43⋊C8)C2312yes—
69#13063249—22no—
70#13063249—22no—
71#13063246—22no—
72#13063246—22no—
73#13063246—22no—
74#13063246—22no—
75C22⋊(C43⋊C8)—22no—
76C22⋊(C43⋊C8)—22no—
77#13063236D412yes—
78C4×C43⋊C8C2312yes—
79C2×#41×C43—21no—
80C22×D4×C43D411yescharacteristic
81C23×C4×C43—21no—
82C2×D8×C43—21no—
83C2×D8×C43—21no—
84C4⋊Q8×C43C2311yescharacteristic
85#127×C43C2311yescharacteristic
86#124×C43—21no—
87#121×C43—21no—
88#121×C43—21no—
89C4×D4×C43—21no—
90C4×D4×C43—21no—
91C4×D4×C43—21no—
92C4×D4×C43—21no—
93C4×D4×C43D411yescharacteristic
94C4×D4×C43D411yescharacteristic
95C4×D4×C43C2311yescharacteristic
96C4×D4×C43C2311yescharacteristic
97C2×C4⋊C4×C43D411yescharacteristic
98C2×C22⋊C4×C43—21no—
99C2×C42×C43C2311yescharacteristic
100#107×C43—21no—
101#107×C43—21no—
102C4⋊C8×C43C2311yescharacteristic
103C4⋊C8×C43C2311yescharacteristic
104#102×C43—21no—
105#102×C43—21no—
106#102×C43—21no—
107#102×C43—21no—
108C22⋊C8×C43—21no—
109C4×C8×C43—21no—
110C24×C43—21no—
111#41×C43—42no—
112#41×C43—42no—
113C2×Q8×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—22no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—41no—
120C2×D4×C43—41no—
121C2×D4×C43C2×D411yescharacteristic
122C2×D4×C43C2×D411yescharacteristic
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—41no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43#4111yescharacteristic
134C22×Dic43—41no—
135C2×Dic86—22no—
136C2×Dic86—41no—
137C2×Dic86—82no—
138D8×C43—42no—
139D8×C43—42no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43C2×D411yescharacteristic
146C4⋊C4×C43C2×D411yescharacteristic
147C22⋊C4×C43—21no—
148C22⋊C4×C43—21no—
149C22⋊C4×C43—21no—
150C22⋊C4×C43—21no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C42×C43#4111yescharacteristic
156C42×C43C2411yescharacteristic
157C4⋊Dic43—22no—
158C4⋊Dic43—22no—
159C4⋊Dic43—41no—
160C4⋊Dic43—41no—
161#10621877—22no—
162#10621877—22no—
163#10621877—44no—
164#10621877—42no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—22no—
167C2×C43⋊C8—44no—
168C2×C43⋊C8—42no—
169C2×C43⋊C8C2×D412yes—
170C2×C43⋊C8C2×D412yes—
171C23×C43—21no—
172C23×C43—21no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—41no—
176C23×C43—81no—
177C23×C43#12111yescharacteristic
178Q8×C43—41no—
179Q8×C43—41no—
180D4×C43—21no—
181D4×C43—21no—
182D4×C43—21no—
183D4×C43—42no—
184D4×C43—41no—
185D4×C43—41no—
186D4×C43—41no—
187D4×C43—41no—
188D4×C43—81no—
189D4×C43—82no—
190D4×C43#13712yes—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—41no—
196C2×C4×C43—42no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—41no—
204C2×C4×C43—82no—
205C2×C4×C43#12111yescharacteristic
206C2×C4×C43#12111yescharacteristic
207C2×C4×C43#12111yescharacteristic
208C2×C4×C43#13512yes—
209C2×C4×C43AGL(1,ℤ/8)12yes—
210C2×C4×C43C22×D411yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C2×C4×C43C2×#4111yescharacteristic
213C2×Dic43—42no—
214C2×Dic43—82no—
215Dic86—82no—
216Dic86—82no—
217C8×C43—41no—
218C8×C43—41no—
219C43⋊C8—22no—
220C43⋊C8—22no—
221C43⋊C8—42no—
222C43⋊C8—42no—
223#19168—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—22no—
227C22×C43—41no—
228C22×C43—41no—
229C22×C43—41no—
230C22×C43—41no—
231C22×C43—41no—
232C22×C43—84no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43#46312yes—
237C22×C43C2×#12111yescharacteristic
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—41no—
242C4×C43—41no—
243C4×C43—81no—
244C4×C43#46312yes—
245C4×C43C2×#13511yescharacteristic
246C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C43C2×#13711yescharacteristic
248C4×C43#57511yescharacteristic
249Dic43—82no—
250#3141—431no—
251#3100D4311yescharacteristic
252C2×#476—431no—
253D4×M16—431no—
254#1703—432no—
255#1697—432no—
256#1683—432no—
257#1677—432no—
258#1565—431no—
259#1548—431no—
260#1547—431no—
261C2×C43—22no—
262C2×C43—42no—
263C2×C43—81no—
264C2×C43—161no—
265C2×C43C2×#46311yescharacteristic
266C2×C43#305611yescharacteristic
267C2×C43#306811yescharacteristic
268C22×M16—861no—
269#532C2×D4311yescharacteristic
270C2×C4⋊Q8—431no—
271C2×C4×D4C2×D4311yescharacteristic
272#489—862no—
273#487—432no—
274#486—432no—
275#480—21no—
276#476—432no—
277#476—432no—
278#476—861no—
279#476—861no—
280#474C2×D4311yescharacteristic
281#474C2×D4311yescharacteristic
282#459C2×D4311yescharacteristic
283#459C2×D4311yescharacteristic
284#447—21no—
285C4×D8—21no—
286C4×D8—21no—
287#436—432no—
288#435—862no—
289C8×D4—432no—
290#431C2×D4311yescharacteristic
291C2×#106—861no—
292#423—431no—
293C2×C4⋊C8—431no—
294#417—861no—
295#417—861no—
296C2×#102—861no—
297#407—861no—
298C4×M16—431no—
299#335—432no—
300#334—432no—
301#333—432no—
302#333—432no—
303#332—432no—
304#331—432no—
305C43#1916811yescharacteristic, complemented, Sylow
306C2×#41—21no—
307C22×Q8—861no—
308C22×D4C22⋊D4311yescharacteristic
309C23×C4—21no—
310C2×D8—21no—
311C2×D8—21no—
312C2×M16—431no—
313C2×M16—431no—
314C2×M16—862no—
315C2×M16—861no—
316C2×M16—1724no—
317C22×C8—862no—
318C22×C8—861no—
319C4⋊Q8—432no—
320C4⋊Q8—861no—
321C4⋊Q8—861no—
322C4⋊Q8—861no—
323C4⋊Q8C22×D4311yescharacteristic
324#127C22×D4311yescharacteristic
325#124—21no—
326#121—21no—
327#121—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4C22⋊D4311yescharacteristic
333C4×D4C22⋊D4311yescharacteristic
334C4×D4C22×D4311yescharacteristic
335C4×D4C22×D4311yescharacteristic
336C2×C4⋊C4—861no—
337C2×C4⋊C4—861no—
338C2×C4⋊C4C22⋊D4311yescharacteristic
339C2×C22⋊C4—21no—
340C2×C42C22×D4311yescharacteristic
341#107—21no—
342#107—21no—
343#106—862no—
344#106—862no—
345C4⋊C8—432no—
346C4⋊C8—432no—
347C4⋊C8—861no—
348C4⋊C8—861no—
349C4⋊C8C22×D4311yescharacteristic
350C4⋊C8C22×D4311yescharacteristic
351#103—862no—
352#103—862no—
353#102—21no—
354#102—21no—
355#102—21no—
356#102—21no—
357#102—862no—
358#102—862no—
359#102—862no—
360#102—862no—
361C22⋊C8—21no—
362C22⋊C8—862no—
363C22⋊C8—862no—
364#97—432no—
365C4×C8—21no—
366C4×C8—432no—
367C24—21no—
368#41—42no—
369#41—42no—
370C2×Q8—21no—
371C2×Q8—862no—
372C2×Q8—3442no—
373C2×Q8—1721no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4C2×C22⋊D4311yescharacteristic
382C2×D4C2×C22⋊D4311yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—41no—
391C22×C4—1721no—
392C22×C4D4×D4311yescharacteristic
393C22×C4#1062190011yescharacteristic
394C22×C4C2×C22⋊D4311yescharacteristic
395D8—42no—
396D8—42no—
397M16—862no—
398M16—862no—
399M16—1724no—
400M16—1722no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—432no—
404C2×C8—432no—
405C2×C8—862no—
406C2×C8—862no—
407C2×C8—1724no—
408C2×C8—1722no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—862no—
413C4⋊C4—862no—
414C4⋊C4—1721no—
415C4⋊C4—1721no—
416C4⋊C4C2×C22⋊D4311yescharacteristic
417C4⋊C4C2×C22⋊D4311yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C42D4×D4311yescharacteristic
425C42#1062190011yescharacteristic
426C42C2×C22⋊D4311yescharacteristic
427C42C23×D4311yescharacteristic
428C23—21no—
429C23—21no—
430C23—42no—
431C23—42no—
432C23—41no—
433C23—81no—
434C23#1306329711yescharacteristic
435Q8—41no—
436Q8—41no—
437Q8—3442no—
438Q8—3442no—
439D4—21no—
440D4—21no—
441D4—21no—
442D4—42no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—41no—
447D4—81no—
448D4—82no—
449D4#1306335512yes—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—82no—
464C2×C4—3442no—
465C2×C4—1722no—
466C2×C4#1306329711yescharacteristic
467C2×C4#1306329711yescharacteristic
468C2×C4#1306329711yescharacteristic
469C2×C4#1306334412yes—
470C2×C4#1306334912yes—
471C2×C4C2×D4×D4311yescharacteristic
472C2×C4C22×C22⋊D4311yescharacteristic
473C2×C4C2×#1062190011yescharacteristic
474C8—41no—
475C8—41no—
476C8—862no—
477C8—862no—
478C8—1722no—
479C8—1722no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—84no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22#1458311212yes—
493C22C2×#1306329711yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—41no—
498C4—41no—
499C4—81no—
500C4—3442no—
501C4#1458311212yes—
502C4C2×#1306334411yescharacteristic
503C4C2×#1306334911yescharacteristic
504C4C2×#1306335511yescharacteristic
505C4#1458369711yescharacteristic
506C2—22no—
507C2—42no—
508C2—81no—
509C2—161no—
510C2C2×#1458311211yescharacteristic
511C2#1914422711yescharacteristic
512C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3100C2
socleC22×C43C2×#121
hypercenter#3100D43
hypocenterC43#19168
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #19144988C2semidirect
2. C2×#14583189C2semidirect
3. D4×#10621877C2semidirect
4. #19134168C2semidirect
5. #19134126C2semidirect
6. #19134044C2semidirect
7. #19134002C2semidirect
8. #19133348C2semidirect
9. #19133275C2semidirect
10. #19133272C2semidirect
15. #14583249C22semidirect
16. #14583245C22semidirect
32. #14582651C22semidirect
33. #14582649C22semidirect
34. #14582647C22semidirect
35. #14582647C22semidirect
36. #14582645C22semidirect
37. #14582643C22semidirect
305. C43#19168semidirect

Maximal subgroups

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

subgroupindex
#191449882
C2×#145831892
D4×#106218772
#191341682
#191341262
#191340442
#191340022
#191333482
#191332752
#191332722
C43×#31002
#1916843