Finite Group Databasebeta

← #25169767

Subgroups — #25169767

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139166C211yesmaximal, characteristic, complemented
2#19137656C211yesmaximal, characteristic
3#19135912C211yesmaximal, characteristic, complemented
4#19135828C211yesmaximal, characteristic
5#19135684C211yesmaximal, characteristic
6#19135447C211yesmaximal, characteristic, complemented
7#19135228C211yesmaximal, characteristic, complemented
8#19135221C211yesmaximal, characteristic, complemented
9#19135182C211yesmaximal, characteristic, complemented
10#19135155C211yesmaximal, characteristic, complemented
11#19134928C211yesmaximal, characteristic, complemented
12#19134927C211yesmaximal, characteristic, complemented
13#19134592C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2094C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063321C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×(C22⋊D43)⋊C4—21no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582838—21no—
31#14582837—21no—
32#14582805C2211yescharacteristic
33#14582804C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582799—21no—
37#14582798C2211yescharacteristic
38#14582785—21no—
39#14582780—21no—
40#14582776—21no—
41#14582775—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×Dic43⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#384C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43—21no—
63C23×Dic43—21no—
64C22×C4×D43—21no—
65C2×#10621873—22no—
66C2×#10621873—22no—
67C2×#10621873—41no—
68C2×#10621883—22no—
69C2×#10621883—41no—
70C2×#10621883—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063321—22no—
74#13063321—22no—
75C4×D172—22no—
76C4×D172—41no—
77D4×Dic43—22no—
78D4×Dic43—41no—
79(C22⋊D43)⋊C4—44no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4D411yescharacteristic
84C2×Dic43⋊C4D411yescharacteristic
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C4⋊(C43⋊C8)—41no—
94#13063250—22no—
95#13063248—41no—
96#13063247—22no—
97#13063246—22no—
98#13063245—41no—
99#13063245—41no—
100C8×Dic43—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×D4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#106×C43—22no—
124#106×C43—41no—
125#102×C43—22no—
126#102×C43—41no—
127C24×C43—21no—
128C23×D43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43#4112yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—24no—
143C2×C22⋊D43—42no—
144C2×C22⋊D43—42no—
145C2×C22⋊D43—81no—
146C2×C22⋊D43—81no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—81no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172#4112yes—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—81no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43#4112yes—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43—81no—
186C22⋊C4×C43—42no—
187C22⋊C4×C43—81no—
188C42×C43—21no—
189C42×C43—21no—
190C22⋊Dic43—42no—
191#10621883—44no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—81no—
199C4⋊Dic43#4112yes—
200Dic43⋊C4—41no—
201Dic43⋊C4SD1614yescomplemented
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—42no—
207C4×Dic43—81no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214#10621873—44no—
215C23×C43—22no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—41no—
233D4×C43—41no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43C2×SD1612yes—
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C22⋊D43—48no—
256C22⋊D43—84no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—84no—
277C2×Dic43C2×SD1612yes—
278C2×Dic43C2×SD1612yes—
279D172—22no—
280D172—22no—
281D172—41no—
282D172—41no—
283C4×D43—84no—
284Dic86—41no—
285Dic86—41no—
286Dic86—41no—
287Dic86—41no—
288C8×C43—22no—
289C8×C43—41no—
290C43⋊C8—41no—
291C43⋊C8—41no—
292#27064—431nomaximal, Sylow
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43#52511yescharacteristic
301C22×C43#54611yescharacteristic
302C22×C43#55011yescharacteristic
303C22×C43C22×SD1611yescharacteristic
304C22×C43#57511yescharacteristic
305C22×C43#57611yescharacteristic
306C22×C43#57711yescharacteristic
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C4×C43—22no—
315C4×C43—41no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43#52911yescharacteristic
320C4×C43#53811yescharacteristic
321C4×C43#55111yescharacteristic
322C4×C43#55311yescharacteristic
323Dic43—22no—
324Dic43—22no—
325Dic43—41no—
326Dic43—42no—
327Dic43—41no—
328Dic43—81no—
329Dic43—81no—
330#2511—431no—
331#2366—431no—
332#2094D4311yescharacteristic, complemented
333#2055—431no—
334#2041—431no—
335#2014—431no—
336#1968—431no—
337#1927—431no—
338#1926—431no—
339#1920—431no—
340#1916—431no—
341#1877—431no—
342#1877—431no—
343#1802—431no—
344C4×#102—431no—
345C2×C43—82no—
346C2×C43#246711yescharacteristic
347C2×C43#310111yescharacteristic
348C2×C43#311811yescharacteristic
349C2×C43#329511yescharacteristic
350C2×C43#331711yescharacteristic
351C2×C43#339211yescharacteristic
352C2×C43#340311yescharacteristic
353D43—82no—
354C22×SD16—431no—
355C22×SD16—431no—
356C2×#127—431no—
357C2×C4×D4—431no—
358C2×C4×D4—431no—
359C2×C4×D4—861no—
360C2×#106C2×D4311yescharacteristic
361C2×#106C2×D4311yescharacteristic
362C2×C4⋊C8—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×#102C2×D4311yescharacteristic
370C2×#102C2×D4311yescharacteristic
371C2×C4×C8—431no—
372#400—861no—
373#400—861no—
374#391—431no—
375#391—431no—
376#391—431no—
377#390—431no—
378#390—861no—
379#390C2×D4311yescharacteristic
380#389—431no—
381#387—861no—
382#387—861no—
383#386—861no—
384#386—861no—
385#384C2×D4311yescharacteristic
386C4×C4⋊C4—431no—
387C4×C4⋊C4—431no—
388C4×C4⋊C4—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#336—431no—
394#336—431no—
395#336—431no—
396#336C2×D4311yescharacteristic
397C43#2706411yescharacteristic, complemented, Sylow
398C22×Q8—431no—
399C22×D4—431no—
400C22×D4—861no—
401C22×D4—861no—
402C22×D4C22×D4311yescharacteristic
403C23×C4—861no—
404C23×C4—861no—
405C2×SD16—862no—
406C2×SD16—862no—
407C2×SD16—862no—
408C2×SD16—1721no—
409C2×SD16—1721no—
410C2×SD16—1721no—
411C22×C8—431no—
412C22×C8—431no—
413C22×C8C22×D4311yescharacteristic
414C22×C8C22×D4311yescharacteristic
415#127—862no—
416#127—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—1721no—
420C4×D4—1721no—
421C4×D4—1724no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42C22×D4311yescharacteristic
443#106—22no—
444#106—41no—
445C4⋊C8—1721no—
446#103—862no—
447#103—1721no—
448#102—22no—
449#102—41no—
450#102—862no—
451#102—862no—
452#102—1721no—
453#102—1721no—
454C4×C8—1721no—
455#95—431no—
456#95—431no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466C24—21no—
467C24—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—432no—
480C2×D4—864no—
481C2×D4—864no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—3441no—
488C2×D4—3441no—
489C2×D4—1722no—
490C2×D4—1722no—
491C2×D4#1062190212yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—3441no—
503C22×C4—3441no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511SD16—1724no—
512SD16—1724no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8#1062190012yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—81no—
533C4⋊C4—434no—
534C4⋊C4—432no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—3441no—
539C4⋊C4—1721no—
540C22⋊C4—42no—
541C22⋊C4—81no—
542C22⋊C4—3441no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C42—21no—
547C42—21no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42—861no—
552C42—3441no—
553C42—1722no—
554C23—22no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—862no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23C2×D4×D4311yescharacteristic
569Q8—1721no—
570Q8—1721no—
571Q8—1721no—
572Q8—1721no—
573D4—22no—
574D4—22no—
575D4—41no—
576D4—41no—
577D4—862no—
578D4—862no—
579D4—3444no—
580D4—1728no—
581D4—1721no—
582D4—1721no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—432no—
598C2×C4—432no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—862no—
610C2×C4—3444no—
611C2×C4—3444no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4SD16×D4312yes—
621C2×C4#41×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4C2×#1062190011yescharacteristic
624C2×C4C2×#1062190211yescharacteristic
625C2×C4#1306337011yescharacteristic
626C2×C4#1306337111yescharacteristic
627C8—22no—
628C8—41no—
629C8—1721no—
630C8—1721no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—3441no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22#1458341211yescharacteristic
646C22#1458354111yescharacteristic
647C22#1458356911yescharacteristic
648C22C2×SD16×D4311yescharacteristic
649C22#1458369511yescharacteristic
650C22#1458370311yescharacteristic
651C22#1458370511yescharacteristic
652C4—22no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—862no—
658C4—862no—
659C4—3441no—
660C4—3441no—
661C4—1721no—
662C4—1722no—
663C4—1721no—
664C4#1458343511yescharacteristic
665C4#1458348911yescharacteristic
666C4#1458357211yescharacteristic
667C4#1458359411yescharacteristic
668C2—82no—
669C2—3442no—
670C2#1913864911yescharacteristic
671C2#1914460511yescharacteristic
672C2#1914478411yescharacteristic
673C2#1914641711yescharacteristic
674C2#1914672411yescharacteristic
675C2#1914757311yescharacteristic
676C2#1914768011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2094C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenter#2094D43
hypocenterC43#27064
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
1. #19139166C2semidirect
3. #19135912C2semidirect
6. #19135447C2semidirect
7. #19135228C2semidirect
8. #19135221C2semidirect
9. #19135182C2semidirect
10. #19135155C2semidirect
11. #19134928C2semidirect
12. #19134927C2semidirect
13. #19134592C2semidirect
14. #102×Dic43C2semidirect
15. C43×#2094C2semidirect
201. Dic43⋊C4SD16semidirect
332. #2094D43semidirect
397. C43#27064semidirect

Maximal subgroups

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

subgroupindex
#191391662
#191376562
#191359122
#191358282
#191356842
#191354472
#191352282
#191352212
#191351822
#191351552
#191349282
#191349272
#191345922
#102×Dic432
C43×#20942
#2706443