Finite Group Databasebeta

← #25079815

Subgroups — #25079815

Order 11008.

678 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145907C211yesmaximal, characteristic, complemented
2#19145021C211yesmaximal, characteristic
3#19143530C211yesmaximal, characteristic, complemented
4#19134087C212yesmaximal, complemented
5#19134077C212yesmaximal, complemented
6#19133945C212yesmaximal, complemented
7#19133941C212yesmaximal, complemented
8C2×#14582649C211yesmaximal, characteristic, complemented
9#19133272C211yesmaximal, characteristic, complemented
10#19133270C211yesmaximal, characteristic, complemented
11C43×#3246C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13C2×#13063345—21no—
14#14583449C2211yescharacteristic
15#14583281—21no—
16#14583281—21no—
17#14583278C2211yescharacteristic
18#14583275C2211yescharacteristic
19#14583273C2211yescharacteristic
20#14583271C2211yescharacteristic
21#14583186—21no—
22#14583184C2212yes—
23#14583130—22no—
24#14583101—21no—
25#14583099C2212yes—
26#14583030—21no—
27#14583030C2212yes—
28Q8×C43⋊C8—21no—
29Q8×C43⋊C8C2212yes—
30#14582926—21no—
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582855—21no—
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582649C2212yes—
36#14582649C2212yes—
37#14582645C2212yes—
38#14582644C2212yes—
39#14582643C2212yes—
40#14582642C2212yes—
41C43×#533C2211yescharacteristic
42C43×#532C2211yescharacteristic
43C43×#476—21no—
44C43×#475C2212yes—
45C43×#465—22no—
46C43×#461—21no—
47C43×#460C2212yes—
48C2×C4⋊C8×C43C2211yescharacteristic
49C2×#10621898—21no—
50#13063345—44no—
51#13063345—44no—
52C2×#10621885—21no—
53C2×#10621885—21no—
54C2×#10621883—21no—
55C2×#10621883—21no—
56C2×#10621884—22no—
57C2×#10621884—21no—
58C2×#10621884—21no—
59C2×#10621882—21no—
60C2×#10621882—21no—
61C2×#10621877—21no—
62C22×C43⋊C8—21no—
63C22×C43⋊C8D411yescharacteristic
64C22×C43⋊C8D411yescharacteristic
65#13063325C2311yescharacteristic
66#13063322C2311yescharacteristic
67#13063313—21no—
68#13063299—21no—
69#13063299—21no—
70C4×D172—21no—
71C4×D172—21no—
72#13063256—22no—
73C4⋊(C43⋊C8)—21no—
74C4⋊(C43⋊C8)—21no—
75C4⋊(C43⋊C8)—22no—
76C4⋊(C43⋊C8)—22no—
77C4⋊(C43⋊C8)C2312yes—
78C4⋊(C43⋊C8)C2312yes—
79#13063249—22no—
80#13063245—22no—
81#13063236—22no—
82C4×C43⋊C8—22no—
83C4×C43⋊C8D411yescharacteristic
84C4×C43⋊C8D411yescharacteristic
85C4×C43⋊C8C2311yescharacteristic
86C4×C43⋊C8C2311yescharacteristic
87C2×#41×C43—21no—
88C2×SD16×C43—22no—
89C22×C8×C43—21no—
90C4⋊Q8×C43D411yescharacteristic
91C4⋊Q8×C43D411yescharacteristic
92C4⋊Q8×C43C2311yescharacteristic
93#127×C43C2311yescharacteristic
94#125×C43—21no—
95#124×C43—21no—
96C22⋊Q8×C43—21no—
97C22⋊Q8×C43D412yes—
98#121×C43—21no—
99#121×C43—21no—
100C4×Q8×C43—21no—
101C4×Q8×C43C2312yes—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104#117×C43—21no—
105C2×C42×C43C2311yescharacteristic
106#106×C43—22no—
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2312yes—
109#103×C43—22no—
110#102×C43—22no—
111#41×C43—42no—
112#41×C43—42no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×Q8×C43C2×D412yes—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C2×C22⋊D43—41no—
125#10621898—42no—
126#10621898—42no—
127C2×D172—21no—
128C2×D172—21no—
129C2×D172—21no—
130C2×C4×D43—41no—
131C2×Dic86—21no—
132SD16×C43—82no—
133C2×C8×C43—22no—
134C2×C8×C43—81no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43C2×D412yes—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C42×C43—22no—
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C42×C43#4111yescharacteristic
150C42×C43C2411yescharacteristic
151#10621885—42no—
152#10621885—42no—
153#10621884—42no—
154#10621884—42no—
155#10621884—82no—
156#10621883—42no—
157#10621883—42no—
158#10621882—42no—
159#10621882—42no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164#10621877—42no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—22no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8—81no—
169C2×C43⋊C8SD1614yescomplemented
170C2×C43⋊C8C2×D411yescharacteristic
171C2×C43⋊C8C2×D411yescharacteristic
172C2×C43⋊C8C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174C23×C43—41no—
175C23×C43#12111yescharacteristic
176C22×D43—41no—
177Q8×C43—22no—
178Q8×C43—22no—
179Q8×C43—42no—
180Q8×C43—41no—
181Q8×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—41no—
186D4×C43—81no—
187D4×C43—82no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—82no—
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43C2×SD1612yes—
199C2×C4×C43AGL(1,ℤ/8)12yes—
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C2×#4111yescharacteristic
203C22⋊D43—82no—
204C2×Dic43—41no—
205D172—41no—
206D172—41no—
207D172—41no—
208D172—41no—
209D172—81no—
210C4×D43—82no—
211Dic86—41no—
212Dic86—41no—
213C8×C43—42no—
214C43⋊C8—21no—
215C43⋊C8—21no—
216C43⋊C8—42no—
217C43⋊C8—42no—
218C43⋊C8C2×SD1612yes—
219C43⋊C8C2×SD1612yes—
220#19205—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43#46012yes—
227C22×C43C2×#12111yescharacteristic
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—42no—
235C4×C43—42no—
236C4×C43—81no—
237C4×C43#46012yes—
238C4×C43C22×SD1611yescharacteristic
239C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
240C4×C43#57711yescharacteristic
241C4×C43#57711yescharacteristic
242Dic43—81no—
243#3246—431no—
244#3246D4311yescharacteristic, complemented
245#3147—431no—
246#2960—431no—
247#1690—432no—
248#1688—432no—
249#1666—432no—
250#1666—432no—
251C2×#334—431no—
252#1547—431no—
253#1547—431no—
254C2×C43—22no—
255C2×C43—161no—
256C2×C43C2×#46011yescharacteristic
257C2×C43#306011yescharacteristic
258C2×C43#306711yescharacteristic
259D43—161no—
260C2×#135—861no—
261C2×#135—861no—
262#533C2×D4311yescharacteristic
263#532—431no—
264#532C2×D4311yescharacteristic
265#495—861no—
266#495—861no—
267#494—431no—
268#493—431no—
269#492—431no—
270#492—431no—
271#476—21no—
272#476—861no—
273#475—432no—
274#475C2×D4312yes—
275#465—22no—
276#465—862no—
277#461—21no—
278#461—861no—
279#460—432no—
280#460C2×D4312yes—
281#446—432no—
282#446—861no—
283C8×Q8—432no—
284C8×Q8—861no—
285#424—861no—
286#423—431no—
287C2×C4⋊C8—431no—
288C2×C4⋊C8C2×D4311yescharacteristic
289#405—861no—
290C2×C4×C8—431no—
291#334—432no—
292#334—432no—
293#332—432no—
294#332—432no—
295#331—432no—
296#331—432no—
297C43#1920511yescharacteristic, complemented, Sylow
298C2×#41—21no—
299C2×#41—861no—
300#135—1724no—
301#135—1724no—
302C2×Q16—861no—
303C2×Q16—861no—
304C2×SD16—22no—
305C2×SD16—861no—
306C2×SD16—861no—
307C2×SD16—861no—
308C2×SD16—861no—
309C2×SD16—862no—
310C2×D8—861no—
311C2×D8—861no—
312C2×M16—861no—
313C22×C8—21no—
314C22×C8—431no—
315C22×C8—431no—
316C22×C8—861no—
317C4⋊Q8—431no—
318C4⋊Q8C22⋊D4311yescharacteristic
319C4⋊Q8C22⋊D4311yescharacteristic
320C4⋊Q8C22×D4311yescharacteristic
321#127—431no—
322#127C22×D4311yescharacteristic
323#125—21no—
324#124—21no—
325#124—861no—
326C22⋊Q8—21no—
327C22⋊Q8C22⋊D4312yes—
328#121—21no—
329#121—21no—
330#121—861no—
331#121—861no—
332C4×Q8—21no—
333C4×Q8C22×D4312yes—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—861no—
337C4×D4—861no—
338#117—21no—
339C2×C42C22×D4311yescharacteristic
340#106—22no—
341#106—862no—
342C4⋊C8—21no—
343C4⋊C8—432no—
344C4⋊C8—432no—
345C4⋊C8—862no—
346C4⋊C8—862no—
347C4⋊C8—861no—
348C4⋊C8—861no—
349C4⋊C8C22×D4312yes—
350#103—22no—
351#103—862no—
352#102—22no—
353#102—862no—
354#97—862no—
355C4×C8—431no—
356C4×C8—431no—
357C4×C8—431no—
358C4×C8—431no—
359C4×C8—862no—
360#41—42no—
361#41—42no—
362#41—1722no—
363#41—1722no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—861no—
367C2×Q8C2×C22⋊D4312yes—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—41no—
372C2×D4—861no—
373C2×D4—861no—
374C2×D4—861no—
375C2×D4—1721no—
376C22×C4—41no—
377C22×C4—1721no—
378C22×C4D4×D4311yescharacteristic
379C22×C4#1062190011yescharacteristic
380C22×C4C2×C22⋊D4311yescharacteristic
381Q16—1722no—
382Q16—1722no—
383SD16—82no—
384SD16—3442no—
385SD16—1722no—
386SD16—1722no—
387SD16—1722no—
388SD16—1722no—
389D8—1722no—
390D8—1722no—
391M16—1722no—
392C2×C8—22no—
393C2×C8—81no—
394C2×C8—434no—
395C2×C8—431no—
396C2×C8—431no—
397C2×C8—431no—
398C2×C8—431no—
399C2×C8—862no—
400C2×C8—862no—
401C2×C8—862no—
402C2×C8—3441no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—861no—
411C4⋊C4—861no—
412C4⋊C4C2×C22⋊D4312yes—
413C22⋊C4—22no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—1721no—
417C22⋊C4—1721no—
418C42—22no—
419C42D4×D4311yescharacteristic
420C42#1062190011yescharacteristic
421C42C2×C22⋊D4311yescharacteristic
422C42C23×D4311yescharacteristic
423C23—41no—
424C23—1721no—
425C23#1306329711yescharacteristic
426Q8—22no—
427Q8—22no—
428Q8—42no—
429Q8—41no—
430Q8—41no—
431Q8—1721no—
432Q8—1721no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4—3441no—
440D4—3442no—
441D4—1721no—
442D4—1721no—
443D4—1721no—
444D4—1721no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—82no—
452C2×C4—3442no—
453C2×C4—1721no—
454C2×C4#1306329711yescharacteristic
455C2×C4#1306329711yescharacteristic
456C2×C4#1306329711yescharacteristic
457C2×C4SD16×D4312yes—
458C2×C4#1306335212yes—
459C2×C4C2×D4×D4311yescharacteristic
460C2×C4C22×C22⋊D4311yescharacteristic
461C2×C4C2×#1062190011yescharacteristic
462C8—42no—
463C8—432no—
464C8—432no—
465C8—861no—
466C8—861no—
467C8—1722no—
468C8—1722no—
469C22—21no—
470C22—21no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—3441no—
475C22—3441no—
476C22—3441no—
477C22#1458309712yes—
478C22C2×#1306329711yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—42no—
484C4—81no—
485C4—3441no—
486C4#1458309712yes—
487C4C2×SD16×D4311yescharacteristic
488C4C2×#1306335211yescharacteristic
489C4#1458370711yescharacteristic
490C4#1458371011yescharacteristic
491C2—22no—
492C2—161no—
493C2—6881no—
494C2C2×#1458309711yescharacteristic
495C2#1914425411yescharacteristic
496C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3246C2
socleC22×C43C2×#121
prime radical#19145021C2
hypercenter#3246D43
hypocenterC43#19205
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3246

Complements

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

NH ≅ G/Ntype
1. #19145907C2semidirect
3. #19143530C2semidirect
4. #19134087C2semidirect
5. #19134077C2semidirect
6. #19133945C2semidirect
7. #19133941C2semidirect
8. C2×#14582649C2semidirect
9. #19133272C2semidirect
10. #19133270C2semidirect
11. C43×#3246C2semidirect
169. C2×C43⋊C8SD16semidirect
244. #3246D43semidirect
297. C43#19205semidirect

Maximal subgroups

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

subgroupindex
#191459072
#191450212
#191435302
#191340872
#191340772
#191339452
#191339412
C2×#145826492
#191332722
#191332702
C43×#32462
#1920543