Finite Group Databasebeta

← #25159531

Subgroups — #25159531

Order 11008.

804 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583207C211yesmaximal, characteristic, complemented
2C2×#14582941C211yesmaximal, characteristic
3#19138319C211yesmaximal, characteristic
4#19137620C211yesmaximal, characteristic
5#19136142C211yesmaximal, characteristic, complemented
6#19136088C211yesmaximal, characteristic, complemented
7#19135989C211yesmaximal, characteristic, complemented
8#19135934C211yesmaximal, characteristic, complemented
9#19135365C211yesmaximal, characteristic, complemented
10#19135174C211yesmaximal, characteristic, complemented
11#19135028C211yesmaximal, characteristic
12#19134900C211yesmaximal, characteristic
13#19134866C211yesmaximal, characteristic, complemented
14#19134796C211yesmaximal, characteristic
15C43×#1851C211yesmaximal, characteristic
16C2×#13063317C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21#14583207—24no—
22#14582941—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063259C2211yescharacteristic
25C2×#13063259C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33#14582841—21no—
34#14582833—21no—
35#14582805C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582793—21no—
40#14582787—21no—
41#14582781—21no—
42#14582771—21no—
43#14582765C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582757—21no—
46C4×C4⋊Dic43C2211yescharacteristic
47#14582750—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C23×Dic43—21no—
63#13063317—22no—
64#13063317—41no—
65#13063304—22no—
66#13063304Q814yes—
67C4×Dic86—22no—
68C4×Dic86—41no—
69#13063284—22no—
70#13063284—41no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—41no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94#13063259—22no—
95#13063259—22no—
96#13063259—22no—
97#13063257—22no—
98#13063257—41no—
99#13063257D414yes—
100#13063250—22no—
101#13063250—22no—
102#13063250—22no—
103#13063250—41no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C23×C4×C43C2311yescharacteristic
114C2×M16×C43—22no—
115C2×M16×C43—22no—
116C2×M16×C43—22no—
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C2×C22⋊C4×C43D411yescharacteristic
122C2×C22⋊C4×C43D411yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C4⋊C8×C43—22no—
126C4⋊C8×C43—22no—
127C22⋊C8×C43—22no—
128#95×C43D411yescharacteristic
129#95×C43D411yescharacteristic
130C24×C43C2×D411yescharacteristic
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×Q812yes—
141C22×C4×C43#4112yes—
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—81no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86C2×Q812yes—
160M16×C43—28no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D412yes—
172C2×C8×C43#4112yes—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C22⋊Dic43—24no—
180C22⋊Dic43—42no—
181C22⋊Dic43—42no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—42no—
194C4⋊Dic43C2×D412yes—
195C4⋊Dic43C2×D412yes—
196C4⋊Dic43C2×Q812yes—
197Dic43⋊C4—24no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202Dic43⋊C4—81no—
203Dic43⋊C4—81no—
204C4×Dic43—42no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43C22⋊Q812yes—
214C23×C43C22×D411yescharacteristic
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43C22⋊Q812yes—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×Q811yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—84no—
265Dic86—22no—
266Dic86—22no—
267Dic86—41no—
268Dic86—41no—
269C8×C43—22no—
270C8×C43—22no—
271C8×C43—41no—
272C8×C43—41no—
273#26367—431nomaximal, Sylow
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43C2×C22⋊Q811yescharacteristic
282C22×C43D4211yescharacteristic
283C22×C43#54711yescharacteristic
284C22×C43#57511yescharacteristic
285C22×C43#57511yescharacteristic
286C22×C43#57711yescharacteristic
287C22×C43#57811yescharacteristic
288C4×C43—22no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43#52511yescharacteristic
294C4×C43#53911yescharacteristic
295C4×C43D4×Q811yescharacteristic
296C4×C43#55411yescharacteristic
297Dic43—42no—
298Dic43—42no—
299Dic43—42no—
300Dic43—42no—
301Dic43—81no—
302Dic43—81no—
303Dic43—81no—
304Dic43—81no—
305C2×#479—431no—
306C2×#428—431no—
307#2442—431no—
308#2362—431no—
309#2097—431no—
310#2087—431no—
311#2068—431no—
312#2059—431no—
313#1949—431no—
314#1919—431no—
315#1894—431no—
316#1872—431no—
317#1865—431no—
318#1854—431no—
319#1851D4311yescharacteristic
320C2×C43—42no—
321C2×C43#244911yescharacteristic
322C2×C43#308011yescharacteristic
323C2×C43#308211yescharacteristic
324C2×C43#326911yescharacteristic
325C2×C43#327511yescharacteristic
326C2×C43#334911yescharacteristic
327C2×C43#335111yescharacteristic
328C22×M16C2×D4311yescharacteristic
329C2×#125—431no—
330C2×C22⋊Q8—431no—
331C2×C4×Q8—431no—
332C2×#117—431no—
333C22×C4⋊C4—431no—
334#479—864no—
335#428—864no—
336C2×#107—431no—
337C2×#107—431no—
338C2×#107—431no—
339C2×#106—431no—
340C2×#106—431no—
341C2×#106—431no—
342C2×C4⋊C8C2×D4311yescharacteristic
343C2×C4⋊C8C2×D4311yescharacteristic
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×C22⋊C8C2×D4311yescharacteristic
349#400—861no—
350#398—861no—
351#391—431no—
352#389—431no—
353#389—431no—
354#389—431no—
355#388—861no—
356#388—861no—
357#387—861no—
358#385—861no—
359#382—431no—
360#380—431no—
361#380—861no—
362C4×C4⋊C4—431no—
363C4×C4⋊C4—861no—
364C4×C22⋊C4C2×D4311yescharacteristic
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#336C2×D4311yescharacteristic
372#336C2×D4311yescharacteristic
373C43#2636711yescharacteristic, complemented, Sylow
374C22×Q8—431no—
375C23×C4—861no—
376C23×C4C22×D4311yescharacteristic
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384#125—862no—
385#125—1721no—
386C22⋊Q8—434no—
387C22⋊Q8—862no—
388C4×Q8—862no—
389C4×Q8—1721no—
390#117—862no—
391#117—1721no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—1721no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4D17211yescharacteristic
413C2×C22⋊C4D17211yescharacteristic
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418C2×C42C22×D4311yescharacteristic
419#107—862no—
420#107—862no—
421#107—862no—
422#106—434no—
423#106—862no—
424#106—1721no—
425C4⋊C8—22no—
426C4⋊C8—22no—
427#103—862no—
428#103—862no—
429#103—862no—
430#103—1721no—
431C22⋊C8—22no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95D17211yescharacteristic
442#95D17211yescharacteristic
443C24C2×D17211yescharacteristic
444C2×Q8—432no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—3441no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4C2×D17211yescharacteristic
466C22×C4C2×D17211yescharacteristic
467C22×C4C2×D17211yescharacteristic
468C22×C4C2×D17211yescharacteristic
469C22×C4C2×D17211yescharacteristic
470C22×C4#1062190012yes—
471C22×C4Q8×D4312yes—
472C22×C4C23×D4311yescharacteristic
473M16—28no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8D4×D4312yes—
485C2×C8#1062190012yes—
486C4⋊C4—432no—
487C4⋊C4—432no—
488C4⋊C4—432no—
489C4⋊C4—864no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—3441no—
502C4⋊C4—3441no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C4⋊C4—1722no—
507C4⋊C4—1722no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—864no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—1722no—
518C42—1722no—
519C42—1722no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23#1306330512yes—
527C23C22×D17211yescharacteristic
528Q8—862no—
529Q8—862no—
530Q8—1721no—
531Q8—1721no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—3444no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4#1306330512yes—
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4C2×Q8×D4311yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062190011yescharacteristic
580C2×C4#1306337111yescharacteristic
581C2×C4#1306337211yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#1306330511yescharacteristic
594C22D4×D17211yescharacteristic
595C22#1458355311yescharacteristic
596C22#1458369911yescharacteristic
597C22#1458369911yescharacteristic
598C22#1458371111yescharacteristic
599C22#1458371611yescharacteristic
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—3441no—
606C4—3441no—
607C4—3441no—
608C4—3441no—
609C4—1722no—
610C4—1722no—
611C4—1722no—
612C4—1722no—
613C4#1458340511yescharacteristic
614C4#1458349311yescharacteristic
615C4#1458356211yescharacteristic
616C4#1458360711yescharacteristic
617C2—42no—
618C2#1913840211yescharacteristic
619C2#1914441811yescharacteristic
620C2#1914443811yescharacteristic
621C2#1914615511yescharacteristic
622C2#1914623111yescharacteristic
623C2#1914712711yescharacteristic
624C2#1914715711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1851C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1851D43
hypocenterC43#26367
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#14583207C2semidirect
5. #19136142C2semidirect
6. #19136088C2semidirect
7. #19135989C2semidirect
8. #19135934C2semidirect
9. #19135365C2semidirect
10. #19135174C2semidirect
13. #19134866C2semidirect
373. C43#26367semidirect

Maximal subgroups

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

subgroupindex
C2×#145832072
C2×#145829412
#191383192
#191376202
#191361422
#191360882
#191359892
#191359342
#191353652
#191351742
#191350282
#191349002
#191348662
#191347962
C43×#18512
#2636743