Finite Group Databasebeta

← #24990571

Subgroups — #24990571

Order 11008.

764 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137208C211yesmaximal, characteristic
2#19134783C211yesmaximal, characteristic, complemented
3C2×#14582622C211yesmaximal, characteristic
4#19132837C211yesmaximal, characteristic
5#19132475C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1852C211yesmaximal, characteristic, complemented
8C22×(C2×D43)⋊C4—21no—
9C22×(C2×D43)⋊C4C2211yescharacteristic
10C2×C22⋊C4×D43—21no—
11C2×#13063258—21no—
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13#14582773—21no—
14#14582773—21no—
15#14582770—21no—
16#14582770—21no—
17#14582759C2211yescharacteristic
18#14582757—21no—
19C2×C43⋊#95—21no—
20C2×C43⋊#95C2211yescharacteristic
21#14582661—21no—
22#14582622C414yescomplemented
23C22×C4⋊C4×C43C2211yescharacteristic
24C2×#107×C43—21no—
25C2×C22⋊C8×C43C2211yescharacteristic
26C43×#380C2211yescharacteristic
27C43×#340—21no—
28C24×D43D411yescharacteristic
29C23×Dic43—21no—
30C23×Dic43D411yescharacteristic
31C22×C4×D43—21no—
32C22×C4×D43—21no—
33C22×C43⋊C8—21no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×C22⋊Dic43—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—42no—
46C2×(C2×D43)⋊C4—42no—
47C2×(C2×D43)⋊C4—42no—
48C2×(C2×D43)⋊C4C2×C412yes—
49C2×(C2×D43)⋊C4Q812yes—
50C22⋊C4×D43—42no—
51C22⋊C4×D43—42no—
52#13063258—42no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)C2×C412yescomplemented
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—42no—
61C23×C4×C43—21no—
62C23×C4×C43C2311yescharacteristic
63C22×C8×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—42no—
67C2×C4⋊C4×C43D411yescharacteristic
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C22⋊C4×C43—21no—
70#107×C43—42no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43C2×C412yescomplemented
73#95×C43—21no—
74C24×C43C2×D411yescharacteristic
75C23×D43—21no—
76C23×D43—21no—
77C23×D43—21no—
78C23×D43—21no—
79C23×D43—41no—
80C23×D43—41no—
81C23×D43—41no—
82C23×D43—41no—
83C23×D43C4⋊C412yes—
84C23×D43D812yes—
85C23×D43Q1612yes—
86C22×C4×C43—22no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×Q811yescharacteristic
101C22×C4×C43#4111yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×Dic43—22no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—41no—
109C22×Dic43—41no—
110C22×Dic43—41no—
111C22×Dic43—41no—
112C22×Dic43—41no—
113C22×Dic43—41no—
114C22×Dic43—41no—
115C22×Dic43—41no—
116C22×Dic43C4⋊C412yes—
117C2×C4×D43—42no—
118C2×C4×D43—42no—
119C2×C4×D43—81no—
120C2×C4×D43—81no—
121C2×C4×D43—81no—
122C2×C4×D43—81no—
123C2×C8×C43—22no—
124C2×C8×C43—41no—
125C2×C8×C43—41no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43—41no—
129C4⋊C4×C43—41no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C22⋊C4×C43—41no—
134C22⋊Dic43—41no—
135C22⋊Dic43—41no—
136(C2×D43)⋊C4—22no—
137(C2×D43)⋊C4—22no—
138(C2×D43)⋊C4—22no—
139(C2×D43)⋊C4—22no—
140(C2×D43)⋊C4—42no—
141(C2×D43)⋊C4—42no—
142(C2×D43)⋊C4—48no—
143C4⋊Dic43—41no—
144C4⋊Dic43—41no—
145Dic43⋊C4—81no—
146Dic43⋊C4—81no—
147C2×C43⋊C8—22no—
148C2×C43⋊C8—41no—
149C2×C43⋊C8—41no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43C2×C4⋊C411yescharacteristic
155C23×C43#12011yescharacteristic
156C23×C43#12311yescharacteristic
157C23×C43C2×D811yescharacteristic
158C23×C43C2×Q1611yescharacteristic
159C23×C43AGL(1,ℤ/8)11yescharacteristic
160C23×C43#13711yescharacteristic
161C22×D43—22no—
162C22×D43—22no—
163C22×D43—22no—
164C22×D43—22no—
165C22×D43—22no—
166C22×D43—22no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171C22×D43—42no—
172C22×D43—42no—
173C22×D43—42no—
174C22×D43—42no—
175C22×D43—42no—
176C22×D43—42no—
177C22×D43—81no—
178C22×D43—81no—
179C22×D43—81no—
180C22×D43—81no—
181C22×D43—81no—
182C22×D43—81no—
183C22×D43#10714yescomplemented
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—42no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—42no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—81no—
202C2×C4×C43—81no—
203C2×C4×C43—81no—
204C2×C4×C43—81no—
205C2×C4×C43C4×D411yescharacteristic
206C2×C4×C43C4×D411yescharacteristic
207C2×C4×C43C22⋊Q811yescharacteristic
208C2×C4×C43C22⋊Q811yescharacteristic
209C2×Dic43—22no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—42no—
213C2×Dic43—42no—
214C2×Dic43—42no—
215C2×Dic43—42no—
216C2×Dic43—41no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—81no—
223C2×Dic43—81no—
224C2×Dic43—81no—
225C2×Dic43—81no—
226C2×Dic43—81no—
227C4×D43—84no—
228C4×D43—84no—
229C8×C43—42no—
230C43⋊C8—42no—
231#8853—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43#38511yescharacteristic
245C22×C43C2×#10711yescharacteristic
246C22×C43#42811yescharacteristic
247C22×C43#44711yescharacteristic
248C22×C43#45111yescharacteristic
249C22×C43#45311yescharacteristic
250C22×C43#45511yescharacteristic
251C22×C43B(4,𝔽2)11yescharacteristic
252C22×C43#45811yescharacteristic
253C22×C43#48011yescharacteristic
254C22×C43#48411yescharacteristic
255C2×D43—24no—
256C2×D43—42no—
257C2×D43—42no—
258C2×D43—42no—
259C2×D43—42no—
260C2×D43—42no—
261C2×D43—42no—
262C2×D43—44no—
263C2×D43—82no—
264C2×D43—82no—
265C2×D43—82no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—81no—
271C4×C43—82no—
272C4×C43—81no—
273Dic43—42no—
274Dic43—82no—
275Dic43—81no—
276Dic43—81no—
277#2315—431no—
278#1852—431no—
279#1852D4311yescharacteristic, complemented
280C2×#323—431no—
281#1439—431no—
282#1294—431no—
283#1294—431no—
284C2×C43—21no—
285C2×C43—21no—
286C2×C43—21no—
287C2×C43—21no—
288C2×C43#159511yescharacteristic
289C2×C43#160211yescharacteristic
290C2×C43#160711yescharacteristic
291C2×C43#161411yescharacteristic
292C2×C43#185211yescharacteristic
293C2×C43#185611yescharacteristic
294C2×C43#186711yescharacteristic
295D43—44no—
296C22×C4⋊C4C2×D4311yescharacteristic
297C22×C22⋊C4—431no—
298C22×C22⋊C4—861no—
299C22×C22⋊C4—861no—
300C2×#107—21no—
301C2×#107—861no—
302C2×C22⋊C8—431no—
303C2×C22⋊C8C2×D4311yescharacteristic
304#385—861no—
305#385—861no—
306#385—861no—
307#385—861no—
308#380—431no—
309#380—861no—
310#380C2×D4311yescharacteristic
311C2×#95—431no—
312C2×#95—861no—
313#340—21no—
314#340—861no—
315#323—434no—
316C43#885311yescharacteristic, complemented, Sylow
317C25—431no—
318C23×C4—21no—
319C23×C4—431no—
320C23×C4—861no—
321C23×C4—861no—
322C23×C4—861no—
323C23×C4C22×D4311yescharacteristic
324C22×C8—21no—
325C22×C8—861no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—431no—
330C2×C4⋊C4—431no—
331C2×C4⋊C4—861no—
332C2×C4⋊C4—861no—
333C2×C4⋊C4C22⋊D4311yescharacteristic
334C2×C4⋊C4C22⋊D4311yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—432no—
337C2×C22⋊C4—432no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—861no—
340C2×C22⋊C4—861no—
341C2×C22⋊C4—861no—
342C2×C22⋊C4—861no—
343C2×C22⋊C4—861no—
344C2×C22⋊C4—861no—
345C2×C22⋊C4—1722no—
346C2×C22⋊C4—1722no—
347C2×C22⋊C4—1722no—
348C2×C22⋊C4—1722no—
349C2×C22⋊C4—1722no—
350#107—42no—
351#107—1722no—
352C22⋊C8—21no—
353C22⋊C8—432no—
354C22⋊C8—861no—
355C22⋊C8C4×D4312yescomplemented
356#95—21no—
357#95—861no—
358#95—861no—
359#95—861no—
360#95—861no—
361#95—861no—
362#95—1722no—
363C24—432no—
364C24—432no—
365C24—432no—
366C24—861no—
367C24—861no—
368C24—861no—
369C24—861no—
370C24—1721no—
371C24—1721no—
372C24—1721no—
373C24—1721no—
374C24D4×D4311yescharacteristic
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—432no—
387C22×C4—861no—
388C22×C4—861no—
389C22×C4—862no—
390C22×C4—861no—
391C22×C4—861no—
392C22×C4—3441no—
393C22×C4—3441no—
394C22×C4—3441no—
395C22×C4—3441no—
396C22×C4—1722no—
397C22×C4—1722no—
398C22×C4—1721no—
399C22×C4—1721no—
400C22×C4—1721no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4—1721no—
404C22×C4—1721no—
405C22×C4—1721no—
406C22×C4C2×C4×D4311yescharacteristic
407C22×C4#1062189811yescharacteristic
408C22×C4D4×D4311yescharacteristic
409C22×C4Q8×D4311yescharacteristic
410C22×C4#1062190211yescharacteristic
411C22×C4C2×C22⋊D4311yescharacteristic
412C2×C8—22no—
413C2×C8—41no—
414C2×C8—41no—
415C2×C8—862no—
416C2×C8—1721no—
417C2×C8—1721no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—3441no—
425C4⋊C4—3441no—
426C4⋊C4—1721no—
427C4⋊C4—1721no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—862no—
431C22⋊C4—862no—
432C22⋊C4—862no—
433C22⋊C4—862no—
434C22⋊C4—1722no—
435C22⋊C4—1722no—
436C22⋊C4—1728no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—434no—
444C23—862no—
445C23—862no—
446C23—862no—
447C23—862no—
448C23—862no—
449C23—862no—
450C23—3441no—
451C23—3441no—
452C23—3441no—
453C23—3441no—
454C23—3441no—
455C23—3441no—
456C23—1722no—
457C23—1722no—
458C23—1722no—
459C23—1722no—
460C23—1722no—
461C23—1722no—
462C23—1721no—
463C23—1721no—
464C23—1721no—
465C23—1721no—
466C23C4⋊C4×D4311yescharacteristic
467C23#1306329311yescharacteristic
468C23#1306331011yescharacteristic
469C23D8×D4311yescharacteristic
470C23Q16×D4311yescharacteristic
471C23#1306334911yescharacteristic
472C23#1306335711yescharacteristic
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4—862no—
495C2×C4—3444no—
496C2×C4—3444no—
497C2×C4—3441no—
498C2×C4—3441no—
499C2×C4—3441no—
500C2×C4—3441no—
501C2×C4—3441no—
502C2×C4—1722no—
503C2×C4—1722no—
504C2×C4—1722no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1722no—
514C2×C4C4×C22⋊D4311yescharacteristic
515C2×C4#1306328711yescharacteristic
516C2×C4#1306330111yescharacteristic
517C2×C4#1306330311yescharacteristic
518C8—42no—
519C8—1722no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—864no—
533C22—3442no—
534C22—3442no—
535C22—3442no—
536C22—1724no—
537C22—1722no—
538C22—1722no—
539C22—1722no—
540C22—1722no—
541C22—1722no—
542C22—1722no—
543C22#1458277011yescharacteristic
544C22#107×D4311yescharacteristic
545C22#1458294011yescharacteristic
546C22#1458303111yescharacteristic
547C22#1458305311yescharacteristic
548C22#1458306511yescharacteristic
549C22#1458307511yescharacteristic
550C22#1458308511yescharacteristic
551C22#1458308811yescharacteristic
552C22#1458321411yescharacteristic
553C22#1458323611yescharacteristic
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—82no—
559C4—81no—
560C4—81no—
561C4—3442no—
562C4—3441no—
563C4—3441no—
564C4—1722no—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—1724no—
570C2#1913351111yescharacteristic
571C2#1913355011yescharacteristic
572C2#1913357911yescharacteristic
573C2#1913361811yescharacteristic
574C2#1913478111yescharacteristic
575C2#1913480311yescharacteristic
576C2#1913487411yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1852C2
socleC23×C43#120
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1852D43
hypocenterC43#8853
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. #19134783C2semidirect
5. #19132475C2semidirect
6. #19132473C2semidirect
7. C43×#1852C2semidirect
22. #14582622C4semidirect
54. C22⋊(C43⋊C8)C2×C4semidirect
72. C22⋊C8×C43C2×C4semidirect
183. C22×D43#107semidirect
279. #1852D43semidirect
316. C43#8853semidirect
355. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191372082
#191347832
C2×#145826222
#191328372
#191324752
#191324732
C43×#18522
#885343