Finite Group Databasebeta

← #25196669

Subgroups — #25196669

Order 11008.

760 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142906C211yesmaximal, characteristic
2#19137125C211yesmaximal, characteristic
3#19136146C211yesmaximal, characteristic, complemented
4#19135933C211yesmaximal, characteristic, complemented
5#19135747C211yesmaximal, characteristic, complemented
6#19135190C211yesmaximal, characteristic, complemented
7#19135176C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic
9#19135027C211yesmaximal, characteristic
10#19134864C211yesmaximal, characteristic, complemented
11#19134850C211yesmaximal, characteristic, complemented
12#19134627C211yesmaximal, characteristic
13#19134627C211yesmaximal, characteristic
14#19134287C211yesmaximal, characteristic
15C43×#2101C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063317C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×C42×D43C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30#14582805C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582784—21no—
34#14582784—21no—
35#14582782—21no—
36#14582773—21no—
37#14582773—21no—
38#14582770—21no—
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44#14582746—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#382C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C2×#10621872—22no—
64C2×#10621872—22no—
65C2×#10621872—22no—
66C2×#10621872—22no—
67C2×#10621872—41no—
68C2×#10621872—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063317—41no—
72#13063317—41no—
73#13063305—22no—
74#13063305Q814yes—
75#13063290—41no—
76#13063290—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊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×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C42×D43—41no—
96C42×D43—41no—
97#13063258—22no—
98#13063258—41no—
99#13063256—22no—
100#13063256—41no—
101#13063250—41no—
102#13063250—41no—
103#13063248—22no—
104#13063248—22no—
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
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124C23×D43C2×D411yescharacteristic
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—22no—
144C2×C4×D43—41no—
145C2×C4×D43—41no—
146C2×C4×D43—41no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43C2×Q812yes—
150C2×C4×D43#4112yes—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86C2×Q812yes—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43C2×Q812yes—
172C42×C43—21no—
173C42×C43—21no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178C4⋊Dic43—24no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—42no—
186C4⋊Dic43—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—41no—
193C4×Dic43—41no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8#4112yes—
201C2×C43⋊C8#4112yes—
202#10621872—44no—
203#10621872—44no—
204C23×C43C22×D411yescharacteristic
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43C22⋊Q812yes—
212C2×C4×C43—22no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C22×Q811yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—22no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
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×Dic43C22⋊Q812yes—
256C2×Dic43#13712yes—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—44no—
262C4×D43—44no—
263Dic86—22no—
264Dic86—22no—
265Dic86—41no—
266Dic86—41no—
267C8×C43—41no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—22no—
271#29164—431nomaximal, Sylow
272C22×C43C2×C22⋊Q811yescharacteristic
273C22×C43#53211yescharacteristic
274C22×C43#53411yescharacteristic
275C22×C43C2×#13711yescharacteristic
276C22×C43#57511yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57511yescharacteristic
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—22no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C4×C43—42no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43#55111yescharacteristic
293C4×C43#55111yescharacteristic
294C4×C43#55411yescharacteristic
295C4×C43#55411yescharacteristic
296Dic43—22no—
297Dic43—22no—
298Dic43—42no—
299Dic43—41no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303#2851—431no—
304C4×C22⋊Q8—431no—
305#2101D4311yescharacteristic, complemented
306#2097—431no—
307#2059—431no—
308#2026—431no—
309#1921—431no—
310#1919—431no—
311#1894—431no—
312#1894—431no—
313#1865—431no—
314#1863—431no—
315#1809—431no—
316#1809—431no—
317#1728—431no—
318C2×C43#256411yescharacteristic
319C2×C43#307811yescharacteristic
320C2×C43#308011yescharacteristic
321C2×C43#317211yescharacteristic
322C2×C43#318311yescharacteristic
323C2×C43#319611yescharacteristic
324C2×C43#319711yescharacteristic
325D43—42no—
326C22×M16—431no—
327C22×M16—431no—
328C2×#125—431no—
329C2×C22⋊Q8—431no—
330C2×C4×Q8—431no—
331C22×C42—431no—
332C2×#107—431no—
333C2×#107—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340#391—431no—
341#389—431no—
342#389—431no—
343#389C2×D4311yescharacteristic
344#387—861no—
345#387—861no—
346#387—861no—
347#385—861no—
348#385—861no—
349#385—861no—
350#382C2×D4311yescharacteristic
351#380—431no—
352#380—431no—
353#380—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—861no—
356C4×C22⋊C4—861no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340C2×D4311yescharacteristic
362#340C2×D4311yescharacteristic
363#340C2×D4311yescharacteristic
364#340C2×D4311yescharacteristic
365#336—431no—
366#336—431no—
367#336—431no—
368#336C2×D4311yescharacteristic
369C43#2916411yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—431no—
374C2×M16—862no—
375C2×M16—862no—
376C2×M16—862no—
377C2×M16—862no—
378C2×M16—1721no—
379C2×M16—1721no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384#125—1721no—
385#125—1721no—
386C22⋊Q8—434no—
387C22⋊Q8—862no—
388C4×Q8—1721no—
389C4×Q8—1721no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—1721no—
414C2×C42—1721no—
415C2×C42C22×D4311yescharacteristic
416#107—862no—
417#107—1721no—
418#106—862no—
419#106—1721no—
420#103—862no—
421#103—862no—
422#103—1721no—
423#103—1721no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435C24—431no—
436C2×Q8—432no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—432no—
449C22×C4—432no—
450C22×C4—431no—
451C22×C4—862no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4—1721no—
464C22×C4—1721no—
465C22×C4D4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4C23×D4311yescharacteristic
468M16—1724no—
469M16—1724no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—432no—
477C2×C8—432no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—864no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C4⋊C4Q8×D4312yes—
503C22⋊C4—864no—
504C22⋊C4—1722no—
505C22⋊C4—1722no—
506C22⋊C4—1722no—
507C42—21no—
508C42—21no—
509C42—861no—
510C42—861no—
511C42—1721no—
512C42—1721no—
513C42—1722no—
514C42—1722no—
515C23—432no—
516C23—861no—
517C23—861no—
518C23—861no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23C2×D4×D4311yescharacteristic
523Q8—862no—
524Q8—862no—
525Q8—1721no—
526Q8—1721no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—432no—
546C2×C4—432no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—1724no—
560C2×C4—1724no—
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×C4C2×Q8×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4#1306337111yescharacteristic
577C2×C4#1306337111yescharacteristic
578C8—41no—
579C8—41no—
580C8—862no—
581C8—862no—
582C22—862no—
583C22—862no—
584C22—862no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22C22⋊Q8×D4311yescharacteristic
590C22#1458344811yescharacteristic
591C22#1458346011yescharacteristic
592C22#137×D4311yescharacteristic
593C22#1458369511yescharacteristic
594C22#1458369611yescharacteristic
595C22#1458369611yescharacteristic
596C4—41no—
597C4—41no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—862no—
603C4—862no—
604C4—3441no—
605C4—3441no—
606C4—3441no—
607C4—1722no—
608C4—1721no—
609C4#1458357411yescharacteristic
610C4#1458357411yescharacteristic
611C4#1458360511yescharacteristic
612C4#1458360511yescharacteristic
613C2—1722no—
614C2#1913977811yescharacteristic
615C2#1914439811yescharacteristic
616C2#1914441211yescharacteristic
617C2#1914520411yescharacteristic
618C2#1914532311yescharacteristic
619C2#1914542911yescharacteristic
620C2#1914543511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2101C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2101D43
hypocenterC43#29164
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
3. #19136146C2semidirect
4. #19135933C2semidirect
5. #19135747C2semidirect
6. #19135190C2semidirect
7. #19135176C2semidirect
10. #19134864C2semidirect
11. #19134850C2semidirect
15. C43×#2101C2semidirect
305. #2101D43semidirect
369. C43#29164semidirect

Maximal subgroups

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

subgroupindex
#191429062
#191371252
#191361462
#191359332
#191357472
#191351902
#191351762
#191350272
#191348642
#191348502
#191346272
#191342872
C43×#21012
#2916443