Finite Group Databasebeta

← #25199589

Subgroups — #25199589

Order 11008.

724 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#19137278C211yesmaximal, characteristic
2#19137275C211yesmaximal, characteristic
3#19136033C211yesmaximal, characteristic
4#19135801C211yesmaximal, characteristic
5#19135793C211yesmaximal, characteristic
6#19135606C211yesmaximal, characteristic
7#19135236C211yesmaximal, characteristic, complemented
8#19135228C211yesmaximal, characteristic, complemented
9#19135190C211yesmaximal, characteristic, complemented
10#19134937C211yesmaximal, characteristic, complemented
11#19134935C211yesmaximal, characteristic, complemented
12#19134864C211yesmaximal, characteristic, complemented
13#19134862C211yesmaximal, characteristic, complemented
14#19134665C211yesmaximal, characteristic
15C43×#1920C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C2×#13063305C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582804C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582797—21no—
36#14582795—21no—
37#14582791—21no—
38#14582790—21no—
39#14582789—21no—
40#14582788—21no—
41#14582784—21no—
42#14582782—21no—
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C2×Dic172—22no—
63C2×Dic172—22no—
64C2×Dic172—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063305—22no—
68#13063305—22no—
69#13063305—22no—
70#13063305—22no—
71C4×Dic86—41no—
72C4×Dic86—41no—
73#13063290—41no—
74#13063290—41no—
75#13063282—41no—
76#13063282—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4D411yescharacteristic
85C2×Dic43⋊C4D411yescharacteristic
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×(C2×D43)⋊C4D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96#13063258—22no—
97#13063256—41no—
98#13063250—22no—
99#13063250—41no—
100#13063248—22no—
101#13063248—22no—
102#13063248—22no—
103#13063248—41no—
104(C2×D43)⋊C8—41no—
105(C2×D43)⋊C8—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#106×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—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—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43#4112yes—
173C4⋊C4×C43#4112yes—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—81no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—41no—
180(C2×D43)⋊C4—41no—
181(C2×D43)⋊C4—81no—
182(C2×D43)⋊C4—81no—
183C4⋊Dic43—24no—
184C4⋊Dic43—24no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—81no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C4×Dic43—81no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205Dic172—44no—
206C23×C43C22×D411yescharacteristic
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
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—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×C43—41no—
231C2×C4×C43—41no—
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—21no—
239C2×Dic43—21no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
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—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—41no—
263Dic86—22no—
264Dic86—22no—
265Dic86—22no—
266Dic86—22no—
267Dic86—41no—
268Dic86—41no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—41no—
272C8×C43—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275#29425—431nomaximal, Sylow
276C22×C43#52511yescharacteristic
277C22×C43#52511yescharacteristic
278C22×C43#53411yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57811yescharacteristic
282C22×C43#57811yescharacteristic
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—41no—
290C4×C43—42no—
291C4×C43—42no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43#55111yescharacteristic
297C4×C43#55311yescharacteristic
298C4×C43#55311yescharacteristic
299C4×C43#55911yescharacteristic
300Dic43—42no—
301Dic43—42no—
302Dic43—41no—
303Dic43—41no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307#2323—431no—
308#2323—431no—
309#2077—431no—
310#2036—431no—
311#2035—431no—
312#2001—431no—
313#1928—431no—
314#1927—431no—
315#1921—431no—
316#1920D4311yescharacteristic, complemented
317#1878—431no—
318#1878—431no—
319#1865—431no—
320#1865—431no—
321#1818—431no—
322C2×C43#260011yescharacteristic
323C2×C43#312011yescharacteristic
324C2×C43#312111yescharacteristic
325C2×C43#312511yescharacteristic
326C2×C43#312711yescharacteristic
327C2×C43#320111yescharacteristic
328C2×C43#320111yescharacteristic
329D43—81no—
330C22×Q16—431no—
331C2×C22⋊Q8—431no—
332C2×C22⋊Q8—431no—
333C2×C4×Q8—431no—
334C2×C4×Q8—431no—
335C2×#117—431no—
336C2×#107—431no—
337C2×#106—431no—
338C2×#106C2×D4311yescharacteristic
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×C22⋊C8—431no—
346C2×C22⋊C8—431no—
347#391—431no—
348#391—431no—
349#389—431no—
350#389—861no—
351#389—861no—
352#389C2×D4311yescharacteristic
353#388—861no—
354#388—861no—
355#388—861no—
356#388—861no—
357#387—861no—
358#387—861no—
359#380—431no—
360#380—431no—
361C4×C4⋊C4—431no—
362C4×C4⋊C4C2×D4311yescharacteristic
363#340—431no—
364#340—431no—
365#340—431no—
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368#340C2×D4311yescharacteristic
369#336—431no—
370#336—431no—
371#336—431no—
372#336C2×D4311yescharacteristic
373C43#2942511yescharacteristic, complemented, Sylow
374C22×Q8—431no—
375C22×Q8—431no—
376C23×C4—431no—
377C2×Q16—862no—
378C2×Q16—862no—
379C2×Q16—1721no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384C22⋊Q8—862no—
385C22⋊Q8—862no—
386C22⋊Q8—862no—
387C22⋊Q8—862no—
388C4×Q8—1721no—
389C4×Q8—1721no—
390C4×Q8—1721no—
391C4×Q8—1721no—
392#117—1721no—
393#117—1721no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—431no—
409C2×C22⋊C4—431no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—21no—
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42—861no—
419C2×C42C22×D4311yescharacteristic
420#107—862no—
421#106—22no—
422#106—1721no—
423#103—862no—
424#103—862no—
425#103—862no—
426#103—862no—
427#103—1721no—
428#103—1721no—
429C22⋊C8—1721no—
430C22⋊C8—1721no—
431#95—21no—
432#95—21no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441C24—431no—
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—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473C22×C4C23×D4311yescharacteristic
474Q16—1724no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—81no—
494C4⋊C4—864no—
495C4⋊C4—864no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—3441no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4#1062189812yes—
506C4⋊C4#1062190212yes—
507C22⋊C4—864no—
508C22⋊C4—864no—
509C22⋊C4—3441no—
510C22⋊C4—3441no—
511C22⋊C4—1721no—
512C22⋊C4—1721no—
513C42—21no—
514C42—21no—
515C42—81no—
516C42—861no—
517C42—861no—
518C42—3441no—
519C42—1722no—
520C42—1722no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23—861no—
525C23—861no—
526C23—861no—
527C23—861no—
528C23C2×D4×D4311yescharacteristic
529Q8—862no—
530Q8—862no—
531Q8—862no—
532Q8—862no—
533Q8—1721no—
534Q8—1721no—
535Q8—1721no—
536Q8—1721no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—862no—
556C2×C4—861no—
557C2×C4—862no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
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—1721no—
579C2×C4—1721no—
580C2×C4#41×D4311yescharacteristic
581C2×C4#41×D4311yescharacteristic
582C2×C4C2×#1062189811yescharacteristic
583C2×C4C2×#1062190211yescharacteristic
584C2×C4#1306337111yescharacteristic
585C2×C4#1306337111yescharacteristic
586C8—41no—
587C8—41no—
588C8—1721no—
589C8—1721no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22—1721no—
594C22—1721no—
595C22—1721no—
596C22—1721no—
597C22#1458340811yescharacteristic
598C22#1458341211yescharacteristic
599C22#1458346011yescharacteristic
600C22#1458370511yescharacteristic
601C22#1458370911yescharacteristic
602C22#1458371311yescharacteristic
603C22#1458371511yescharacteristic
604C4—41no—
605C4—41no—
606C4—42no—
607C4—42no—
608C4—81no—
609C4—81no—
610C4—3441no—
611C4—3441no—
612C4—1721no—
613C4—1721no—
614C4—1721no—
615C4—1722no—
616C4—1722no—
617C4#1458357411yescharacteristic
618C4#1458359311yescharacteristic
619C4#1458360211yescharacteristic
620C4#1458363411yescharacteristic
621C2—3441no—
622C2#1914018411yescharacteristic
623C2#1914481311yescharacteristic
624C2#1914482011yescharacteristic
625C2#1914487711yescharacteristic
626C2#1914489711yescharacteristic
627C2#1914547511yescharacteristic
628C2#1914548411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1920C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1920D43
hypocenterC43#29425
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
7. #19135236C2semidirect
8. #19135228C2semidirect
9. #19135190C2semidirect
10. #19134937C2semidirect
11. #19134935C2semidirect
12. #19134864C2semidirect
13. #19134862C2semidirect
15. C43×#1920C2semidirect
316. #1920D43semidirect
373. C43#29425semidirect

Maximal subgroups

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

subgroupindex
#191372782
#191372752
#191360332
#191358012
#191357932
#191356062
#191352362
#191352282
#191351902
#191349372
#191349352
#191348642
#191348622
#191346652
C43×#19202
#2942543