Finite Group Databasebeta

← #25169837

Subgroups — #25169837

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139192C211yesmaximal, characteristic
2#19137651C211yesmaximal, characteristic, complemented
3#19136142C211yesmaximal, characteristic, complemented
4#19135913C211yesmaximal, characteristic
5#19135842C211yesmaximal, characteristic, complemented
6#19135680C211yesmaximal, characteristic
7#19135449C211yesmaximal, characteristic
8#19135237C211yesmaximal, characteristic, complemented
9#19135216C211yesmaximal, characteristic
10#19135181C211yesmaximal, characteristic, complemented
11#19134949C211yesmaximal, characteristic
12#19134949C211yesmaximal, characteristic
13#19134611C211yesmaximal, characteristic, complemented
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1916C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31#14582828—21no—
32#14582825—21no—
33#14582805C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582795—21no—
40#14582789—21no—
41#14582788—21no—
42#14582782—21no—
43#14582782—21no—
44#14582765C2211yescharacteristic
45C4⋊C4×Dic43—21no—
46C4×C4⋊Dic43C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C4×C8×C43C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C2×#10621873—22no—
63C2×#10621873—22no—
64C2×#10621873—22no—
65C2×#10621873—41no—
66C2×#10621873—41no—
67C2×#10621873—41no—
68#13063325—22no—
69#13063325—22no—
70C4×Dic86—22no—
71C4×Dic86—22no—
72C4×Dic86—41no—
73C4×Dic86—41no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
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×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94#13063259—41no—
95#13063257—22no—
96#13063250—22no—
97#13063250—22no—
98#13063250—22no—
99#13063250—41no—
100#13063250—41no—
101#13063250—41no—
102#13063247—22no—
103#13063247—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—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C2×C4⋊C4×C43D411yescharacteristic
118C2×C4⋊C4×C43D411yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C4⋊C8×C43—41no—
123C4×C8×C43—41no—
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C23×D43—21no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86#4112yes—
158C2×Dic86#4112yes—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
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#4112yes—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—81no—
182(C2×D43)⋊C4—81no—
183(C2×D43)⋊C4—81no—
184(C2×D43)⋊C4—81no—
185C4⋊Dic43—24no—
186C4⋊Dic43—24no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43#4112yes—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—81no—
200C4×Dic43—42no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203C4×Dic43—81no—
204#10621873—44no—
205#10621873—44no—
206C23×C43C22×D411yescharacteristic
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
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#13512yes—
231C2×C4×C43#13712yes—
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
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—
259D172—41no—
260D172—41no—
261D172—41no—
262D172—41no—
263Dic86—22no—
264Dic86—22no—
265Dic86—22no—
266Dic86—22no—
267Dic86—41no—
268Dic86—41no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—22no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275#27069—431nomaximal, Sylow
276C22×C43#52511yescharacteristic
277C22×C43#54611yescharacteristic
278C22×C43#55011yescharacteristic
279C22×C43C2×#13511yescharacteristic
280C22×C43C2×#13711yescharacteristic
281C22×C43#57711yescharacteristic
282C22×C43#57711yescharacteristic
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C4×C43—22no—
291C4×C43—22no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43#52911yescharacteristic
297C4×C43#53811yescharacteristic
298C4×C43#55111yescharacteristic
299C4×C43#55311yescharacteristic
300Dic43—42no—
301Dic43—42no—
302Dic43—42no—
303Dic43—81no—
304Dic43—81no—
305Dic43—81no—
306Dic43—81no—
307#2513—431no—
308#2365—431no—
309#2097—431no—
310#2055—431no—
311#2043—431no—
312#2013—431no—
313#1968—431no—
314#1928—431no—
315#1925—431no—
316#1920—431no—
317#1916D4311yescharacteristic, complemented
318#1880—431no—
319#1880—431no—
320#1805—431no—
321C4×#103—431no—
322C2×C43#246711yescharacteristic
323C2×C43#310811yescharacteristic
324C2×C43#312611yescharacteristic
325C2×C43#330311yescharacteristic
326C2×C43#332011yescharacteristic
327C2×C43#339411yescharacteristic
328C2×C43#340011yescharacteristic
329D43—161no—
330C22×SD16—431no—
331C22×SD16—431no—
332C2×C4⋊Q8—431no—
333C2×C4×Q8—431no—
334C2×C4×Q8—431no—
335C2×#107—431no—
336C2×#106—431no—
337C2×C4⋊C8C2×D4311yescharacteristic
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#102—431no—
345C2×#102—431no—
346C2×C4×C8C2×D4311yescharacteristic
347#397—861no—
348#397—861no—
349#391—431no—
350#391—431no—
351#390—431no—
352#390—431no—
353#390—431no—
354#389—431no—
355#389—861no—
356#388—861no—
357#388—861no—
358#387—861no—
359#387—861no—
360#382—431no—
361C4×C4⋊C4—431no—
362C4×C4⋊C4—431no—
363C4×C4⋊C4—861no—
364C4×C4⋊C4C2×D4311yescharacteristic
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#336C2×D4311yescharacteristic
370#336C2×D4311yescharacteristic
371#336C2×D4311yescharacteristic
372#336C2×D4311yescharacteristic
373C43#2706911yescharacteristic, complemented, Sylow
374C22×Q8—431no—
375C22×Q8—431no—
376C22×D4—431no—
377C2×SD16—862no—
378C2×SD16—862no—
379C2×SD16—862no—
380C2×SD16—1721no—
381C2×SD16—1721no—
382C2×SD16—1721no—
383C22×C8C22×D4311yescharacteristic
384C22×C8C22×D4311yescharacteristic
385C22×C8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387C4⋊Q8—862no—
388C4⋊Q8—862no—
389C4×Q8—862no—
390C4×Q8—862no—
391C4×Q8—1721no—
392C4×Q8—1721no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4D17211yescharacteristic
404C2×C4⋊C4D17211yescharacteristic
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42C22×D4311yescharacteristic
416C2×C42C22×D4311yescharacteristic
417C2×C42C22×D4311yescharacteristic
418#107—1721no—
419#106—862no—
420C4⋊C8—41no—
421#103—862no—
422#103—862no—
423#103—862no—
424#103—1721no—
425#103—1721no—
426#103—1721no—
427#102—862no—
428#102—1721no—
429C4×C8—41no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95D17211yescharacteristic
440#95D17211yescharacteristic
441C24—861no—
442C2×Q8—432no—
443C2×Q8—432no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4C2×D17211yescharacteristic
468C22×C4C2×D17211yescharacteristic
469C22×C4C2×D17211yescharacteristic
470C22×C4C2×D17211yescharacteristic
471C22×C4C2×D17211yescharacteristic
472C22×C4C2×D17211yescharacteristic
473C22×C4C23×D4311yescharacteristic
474SD16—1724no—
475SD16—1724no—
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×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8#1062190212yes—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—432no—
491C4⋊C4—864no—
492C4⋊C4—864no—
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—861no—
502C4⋊C4—3441no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C22⋊C4—3441no—
506C22⋊C4—3441no—
507C22⋊C4—3441no—
508C22⋊C4—3441no—
509C22⋊C4—1722no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—3441no—
518C42—1722no—
519C42—1722no—
520C42—1722no—
521C23—1721no—
522C23—1721no—
523C23—1721no—
524C23—1721no—
525C23—1721no—
526C23—1721no—
527C23—1721no—
528C23C22×D17211yescharacteristic
529Q8—862no—
530Q8—862no—
531Q8—862no—
532Q8—862no—
533Q8—1721no—
534Q8—1721no—
535Q8—1721no—
536Q8—1721no—
537D4—1721no—
538D4—1721no—
539D4—1721no—
540D4—1721no—
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—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
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—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4#1306334712yes—
579C2×C4#1306335812yes—
580C2×C4#41×D4311yescharacteristic
581C2×C4#41×D4311yescharacteristic
582C2×C4#41×D4311yescharacteristic
583C2×C4C2×#1062190211yescharacteristic
584C2×C4#1306337011yescharacteristic
585C2×C4#1306337111yescharacteristic
586C8—22no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—3441no—
591C22—3441no—
592C22—3441no—
593C22—3441no—
594C22—3441no—
595C22—3441no—
596C22—3441no—
597C22#1458341111yescharacteristic
598C22#1458354411yescharacteristic
599C22#1458357111yescharacteristic
600C22C2×#1306334711yescharacteristic
601C22C2×#1306335811yescharacteristic
602C22#1458371111yescharacteristic
603C22#1458371111yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—3441no—
611C4—3441no—
612C4—3441no—
613C4—3441no—
614C4—1722no—
615C4—1722no—
616C4—1722no—
617C4#1458343411yescharacteristic
618C4#1458348511yescharacteristic
619C4#1458357611yescharacteristic
620C4#1458360011yescharacteristic
621C2—6881no—
622C2#1913864411yescharacteristic
623C2#1914467711yescharacteristic
624C2#1914488711yescharacteristic
625C2#1914652411yescharacteristic
626C2#1914676811yescharacteristic
627C2#1914759311yescharacteristic
628C2#1914765011yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1916C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1916D43
hypocenterC43#27069
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
2. #19137651C2semidirect
3. #19136142C2semidirect
5. #19135842C2semidirect
8. #19135237C2semidirect
10. #19135181C2semidirect
13. #19134611C2semidirect
14. C4×#13063250C2semidirect
15. C43×#1916C2semidirect
317. #1916D43semidirect
373. C43#27069semidirect

Maximal subgroups

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

subgroupindex
#191391922
#191376512
#191361422
#191359132
#191358422
#191356802
#191354492
#191352372
#191352162
#191351812
#191349492
#191346112
C4×#130632502
C43×#19162
#2706943