Finite Group Databasebeta

← #24991722

Subgroups — #24991722

Order 11008.

834 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137300C211yesmaximal, characteristic
2#19134530C211yesmaximal, characteristic, complemented
3C2×#14582633C211yesmaximal, characteristic
4#19132866C211yesmaximal, characteristic, complemented
5#19132475C211yesmaximal, characteristic, complemented
6#19132437C211yesmaximal, characteristic, complemented
7C2×C43×#448C211yesmaximal, characteristic
8C2×D4×Dic43—21no—
9C2×#13063249—21no—
10C2×#13063249—21no—
11C2×C22⋊(C43⋊C8)C2211yescharacteristic
12#14582792—21no—
13#14582785—21no—
14#14582779—21no—
15#14582779—21no—
16#14582774—21no—
17#14582759C2211yescharacteristic
18C2×C43⋊#95—21no—
19C2×C43⋊#95—21no—
20C2×C43⋊#95C2211yescharacteristic
21C2×C43⋊#95C2211yescharacteristic
22#14582633—22no—
23C23×Q8×C43C2211yescharacteristic
24C22×SD16×C43—21no—
25C2×#121×C43C2211yescharacteristic
26C43×#448—22no—
27C43×#448C414yescomplemented
28C2×#103×C43—21no—
29C2×C22⋊C8×C43C2211yescharacteristic
30C23×Dic43—21no—
31C23×Dic43—21no—
32C23×Dic43D411yescharacteristic
33C23×Dic43D411yescharacteristic
34C22×C43⋊C8—21no—
35D4×Dic43—42no—
36D4×Dic43—42no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43D411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C4×Dic43—21no—
45#13063249—42no—
46#13063249—42no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—42no—
57C43⋊#95—42no—
58C22×Q8×C43—21no—
59C22×Q8×C43—21no—
60C22×Q8×C43—21no—
61C22×Q8×C43—21no—
62C22×Q8×C43—21no—
63C22×Q8×C43—42no—
64C22×Q8×C43—42no—
65C22×Q8×C43C2×C412yescomplemented
66C22×D4×C43—21no—
67C22×D4×C43D411yescharacteristic
68C23×C4×C43—21no—
69C23×C4×C43C2311yescharacteristic
70C2×SD16×C43—24no—
71C2×SD16×C43—42no—
72C2×SD16×C43—42no—
73C22×C8×C43—21no—
74#121×C43—21no—
75#121×C43—21no—
76#121×C43C2×C412yes—
77#121×C43D412yes—
78C2×C4⋊C4×C43D411yescharacteristic
79C2×C22⋊C4×C43—21no—
80#103×C43—24no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43C2×C412yescomplemented
83C24×C43—21no—
84C24×C43C2×D411yescharacteristic
85C2×Q8×C43—22no—
86C2×Q8×C43—22no—
87C2×Q8×C43—22no—
88C2×Q8×C43—22no—
89C2×Q8×C43—22no—
90C2×Q8×C43—22no—
91C2×Q8×C43—44no—
92C2×Q8×C43—41no—
93C2×Q8×C43—41no—
94C2×Q8×C43—41no—
95C2×Q8×C43—41no—
96C2×Q8×C43—44no—
97C2×Q8×C43—44no—
98C2×Q8×C43—44no—
99C2×Q8×C43—41no—
100C2×Q8×C43—41no—
101C2×D4×C43—21no—
102C2×D4×C43—22no—
103C2×D4×C43—22no—
104C2×D4×C43—41no—
105C2×D4×C43—41no—
106C2×D4×C43—41no—
107C2×D4×C43—41no—
108C2×D4×C43—41no—
109C2×D4×C43—41no—
110C2×D4×C43C22⋊C412yes—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—21no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43C22×C411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C22×C4×C43#4111yescharacteristic
127C22×Dic43—22no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—41no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C22×Dic43—41no—
139C22×Dic43—41no—
140C22×Dic43—41no—
141C22×Dic43—41no—
142C22×Dic43—42no—
143C22×Dic43—41no—
144C22×Dic43—41no—
145C22×Dic43—41no—
146C22×Dic43—81no—
147C22×Dic43—81no—
148C22×Dic43SD1612yescomplemented
149SD16×C43—48no—
150C2×C8×C43—22no—
151C2×C8×C43—41no—
152C2×C8×C43—41no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43C22⋊C412yes—
155C22⋊C4×C43—22no—
156C22⋊C4×C43—22no—
157C22⋊Dic43—42no—
158C22⋊Dic43—41no—
159C22⋊Dic43—41no—
160C22⋊Dic43—81no—
161C22⋊Dic43—81no—
162C4⋊Dic43—42no—
163C4⋊Dic43—41no—
164C4⋊Dic43—41no—
165C4×Dic43—42no—
166C2×C43⋊C8—41no—
167C2×C43⋊C8—41no—
168C2×C43⋊C8—41no—
169C23×C43—21no—
170C23×C43—21no—
171C23×C43—21no—
172C23×C43—21no—
173C23×C43—22no—
174C23×C43—41no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43C4×D411yescharacteristic
181C23×C43#12011yescharacteristic
182C23×C43#12111yescharacteristic
183C23×C43C2×SD1611yescharacteristic
184C23×C43#13511yescharacteristic
185C23×C43AGL(1,ℤ/8)11yescharacteristic
186C23×C43#13711yescharacteristic
187Q8×C43—24no—
188Q8×C43—24no—
189Q8×C43—42no—
190Q8×C43—42no—
191Q8×C43—42no—
192Q8×C43—42no—
193Q8×C43—42no—
194Q8×C43—42no—
195D4×C43—42no—
196D4×C43—42no—
197D4×C43—42no—
198D4×C43—42no—
199D4×C43—42no—
200D4×C43—81no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—24no—
206C2×C4×C43—22no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43C2×C22⋊C411yescharacteristic
220C2×C4×C43C4×D411yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12311yescharacteristic
223C2×Dic43—22no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—81no—
241C2×Dic43—84no—
242C2×Dic43—81no—
243C2×Dic43—81no—
244C2×Dic43—81no—
245C2×Dic43—81no—
246C2×Dic43—81no—
247C8×C43—42no—
248C43⋊C8—81no—
249#9039—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43#38611yescharacteristic
270C22×C43C4×SD1611yescharacteristic
271C22×C43#44011yescharacteristic
272C22×C43#45011yescharacteristic
273C22×C43#45211yescharacteristic
274C22×C43#45511yescharacteristic
275C22×C43#45611yescharacteristic
276C22×C43B(4,𝔽2)11yescharacteristic
277C22×C43B(4,𝔽2)11yescharacteristic
278C22×C43#46111yescharacteristic
279C22×C43#46311yescharacteristic
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—42no—
285C4×C43—44no—
286Dic43—42no—
287Dic43—82no—
288Dic43—81no—
289Dic43—81no—
290Dic43—81no—
291C2×#448D4311yescharacteristic
292#2325—431no—
293#1787—431no—
294C2×#327—431no—
295#1446—431no—
296#1294—431no—
297#1280—431no—
298C2×C43—21no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—82no—
303C2×C43#160111yescharacteristic
304C2×C43#160311yescharacteristic
305C2×C43#160411yescharacteristic
306C2×C43#160611yescharacteristic
307C2×C43#187711yescharacteristic
308C2×C43#188211yescharacteristic
309C2×C43#188911yescharacteristic
310C23×Q8C2×D4311yescharacteristic
311C22×SD16—21no—
312C2×#121C2×D4311yescharacteristic
313C2×C4×D4—861no—
314#448—22no—
315#448Dic4314yescomplemented
316C2×#103—21no—
317C2×#103—861no—
318C2×#103—861no—
319C2×C22⋊C8—431no—
320C2×C22⋊C8C2×D4311yescharacteristic
321#388—861no—
322#387—861no—
323#386—861no—
324#386—861no—
325#385—861no—
326#380—431no—
327C2×#95—431no—
328C2×#95—431no—
329C2×#95—861no—
330C2×#95—861no—
331#327—862no—
332C43#903911yescharacteristic, complemented, Sylow
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8—42no—
339C22×Q8—42no—
340C22×Q8C2×Dic4312yescomplemented
341C22×D4—21no—
342C22×D4C22⋊D4311yescharacteristic
343C23×C4—21no—
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—861no—
347C23×C4—861no—
348C23×C4C22×D4311yescharacteristic
349C2×SD16—24no—
350C2×SD16—42no—
351C2×SD16—42no—
352C22×C8—21no—
353C22×C8—861no—
354#121—21no—
355#121—21no—
356#121C2×Dic4312yes—
357#121C22⋊D4312yes—
358C4×D4—1722no—
359C4×D4—1722no—
360C2×C4⋊C4—431no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—861no—
363C2×C4⋊C4C22⋊D4311yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—861no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—861no—
369C2×C42—861no—
370#103—24no—
371#103—1722no—
372#103—1722no—
373C22⋊C8—21no—
374C22⋊C8—861no—
375C22⋊C8—861no—
376C22⋊C8C2×Dic4312yescomplemented
377#95—861no—
378#95—861no—
379#95—861no—
380#95—861no—
381#95—861no—
382#95—861no—
383#95—861no—
384#95—1722no—
385#95—1722no—
386C24—21no—
387C24D4×D4311yescharacteristic
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—44no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—44no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4C22⋊Dic4312yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—432no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—862no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—3441no—
434C22×C4—3441no—
435C22×C4—1722no—
436C22×C4—1721no—
437C22×C4—1721no—
438C22×C4—1721no—
439C22×C4—1721no—
440C22×C4—1721no—
441C22×C4—1721no—
442C22×C4—1721no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4D4×D4311yescharacteristic
447C22×C4#1062190011yescharacteristic
448C22×C4#1062190011yescharacteristic
449C22×C4C22×Dic4311yescharacteristic
450C22×C4C2×C22⋊D4311yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452SD16—48no—
453C2×C8—22no—
454C2×C8—41no—
455C2×C8—41no—
456C2×C8—1721no—
457C2×C8—1721no—
458C2×C8—1721no—
459C4⋊C4—21no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4—1722no—
463C4⋊C4C22⋊Dic4312yes—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—3441no—
467C22⋊C4—3441no—
468C22⋊C4—1722no—
469C22⋊C4—1721no—
470C22⋊C4—1721no—
471C42—1722no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23D4×Dic4311yescharacteristic
484C23#1306329311yescharacteristic
485C23#1306329711yescharacteristic
486C23SD16×D4311yescharacteristic
487C23#1306334611yescharacteristic
488C23#1306335211yescharacteristic
489C23#1306335411yescharacteristic
490Q8—24no—
491Q8—24no—
492Q8—42no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496Q8—42no—
497Q8—42no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—42no—
502D4—42no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—862no—
523C2×C4—3441no—
524C2×C4—3441no—
525C2×C4—3441no—
526C2×C4—3441no—
527C2×C4—3444no—
528C2×C4—3441no—
529C2×C4—3441no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1722no—
546C2×C4C2×C22⋊Dic4311yescharacteristic
547C2×C4D4×Dic4311yescharacteristic
548C2×C4#1306329711yescharacteristic
549C2×C4#1306330611yescharacteristic
550C8—42no—
551C8—3441no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22#1458277911yescharacteristic
572C22SD16×Dic4311yescharacteristic
573C22#1458300011yescharacteristic
574C22#1458304811yescharacteristic
575C22#1458305811yescharacteristic
576C22#1458307511yescharacteristic
577C22#1458308011yescharacteristic
578C22#1458308511yescharacteristic
579C22#1458308511yescharacteristic
580C22#1458310211yescharacteristic
581C22#1458311611yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—44no—
587C4—42no—
588C4—3442no—
589C4—3441no—
590C4—3441no—
591C4—3441no—
592C4—1722no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—82no—
598C2#1913354511yescharacteristic
599C2#1913355511yescharacteristic
600C2#1913356211yescharacteristic
601C2#1913357211yescharacteristic
602C2#1913493111yescharacteristic
603C2#1913496611yescharacteristic
604C2#1913500411yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#448C2
socleC23×C43#120
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenterC2×#448D43
hypocenterC43#9039
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. #19134530C2semidirect
4. #19132866C2semidirect
5. #19132475C2semidirect
6. #19132437C2semidirect
27. C43×#448C4semidirect
65. C22×Q8×C43C2×C4semidirect
82. C22⋊C8×C43C2×C4semidirect
148. C22×Dic43SD16semidirect
315. #448Dic43semidirect
332. C43#9039semidirect
340. C22×Q8C2×Dic43semidirect
376. C22⋊C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191373002
#191345302
C2×#145826332
#191328662
#191324752
#191324372
C2×C43×#4482
#903943