Finite Group Databasebeta

← #25003977

Subgroups — #25003977

Order 11008.

870 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×#14582947C211yesmaximal, characteristic, complemented
2C2×#14582917C211yesmaximal, characteristic
3C2×#14582898C211yesmaximal, characteristic
4C2×#14582881C211yesmaximal, characteristic
5C2×#14582669C211yesmaximal, characteristic, complemented
6C2×#14582668C211yesmaximal, characteristic, complemented
7C43×#1736C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12#14582947—22no—
13#14582947—22no—
14C2×#13063260—22no—
15#14582917—22no—
16#14582917C414yescomplemented
17C2×#13063253—22no—
18#14582898—22no—
19#14582898—22no—
20C2×#13063248—21no—
21C2×#13063245—21no—
22#14582881—22no—
23#14582881—22no—
24C2×#13063243—21no—
25C2×#13063241—21no—
26#14582669—22no—
27#14582668—22no—
28C22×M16×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C22×C4⋊C4×C43C2211yescharacteristic
31C43×#340—22no—
32C2×#10621898—21no—
33C2×#10621898—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898C2×C412yes—
43C2×#10621898Q812yes—
44C22×Dic86D411yescharacteristic
45C22×D172D411yescharacteristic
46C22×C22⋊D43—21no—
47C22×C4×D43—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877C2×C412yes—
62C2×#10621877D412yes—
63C2×#10621877D412yes—
64C2×#10621877D412yes—
65C2×#10621877D412yes—
66C22×C43⋊C8—21no—
67C22×C43⋊C8—21no—
68C22×C43⋊C8—21no—
69#13063260—28no—
70#13063253—28no—
71#13063248—24no—
72#13063245—24no—
73#13063243—24no—
74#13063241—24no—
75C23×C4×C43—21no—
76C23×C4×C43C2311yescharacteristic
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43D412yes—
83C22×C8×C43—21no—
84#117×C43—21no—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43C2×C412yes—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43D412yes—
95C2×C22⋊C4×C43—21no—
96C2×C42×C43—21no—
97C24×C43#4111yescharacteristic
98C23×D43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—82no—
104C22×C4×C43C22×C411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×Q811yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×C4×C43#4111yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C2×C22⋊D43—22no—
119C2×C22⋊D43—22no—
120C2×C22⋊D43—41no—
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C2×C22⋊D43—41no—
124C22×Dic43—21no—
125#10621898—22no—
126#10621898—22no—
127#10621898—22no—
128#10621898—22no—
129#10621898—22no—
130#10621898—22no—
131#10621898—22no—
132#10621898—22no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138#10621898—41no—
139#10621898—41no—
140#10621898—41no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172C4⋊C412yes—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—41no—
150C2×C4×D43—41no—
151C2×C4×D43—41no—
152C2×C4×D43—41no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86C4⋊C412yes—
159M16×C43—22no—
160M16×C43—22no—
161M16×C43—41no—
162M16×C43—41no—
163C2×C8×C43—22no—
164C2×C8×C43—41no—
165C2×C8×C43—41no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—41no—
174C42×C43—22no—
175C42×C43—41no—
176#10621877—22no—
177#10621877—22no—
178#10621877—22no—
179#10621877—22no—
180#10621877—22no—
181#10621877—22no—
182#10621877—22no—
183#10621877—41no—
184#10621877—41no—
185#10621877—41no—
186#10621877—41no—
187#10621877C22⋊C414yes—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—41no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—41no—
196C2×C43⋊C8—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C4×D411yescharacteristic
200C23×C43#12111yescharacteristic
201C23×C43C22⋊Q811yescharacteristic
202C23×C43#12311yescharacteristic
203C23×C43#12411yescharacteristic
204C23×C43#12411yescharacteristic
205C23×C43#12611yescharacteristic
206C22×D43—22no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—81no—
210C22×D43—81no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—81no—
214C2×C4×C43—81no—
215C2×C4×C43—82no—
216C2×C4×C43—82no—
217C2×C4×C43—82no—
218C2×C4×C43C2×C22⋊C411yescharacteristic
219C2×C4×C43C2×C4⋊C411yescharacteristic
220C2×C4×C43#11711yescharacteristic
221C2×C4×C43C4×D411yescharacteristic
222C2×C4×C43C4×D411yescharacteristic
223C2×C4×C43C4×D411yescharacteristic
224C2×C4×C43#12011yescharacteristic
225C2×C4×C43#12011yescharacteristic
226C2×C4×C43#12011yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43C22⋊Q811yescharacteristic
235C2×C4×C43C22⋊Q811yescharacteristic
236C2×C4×C43C22⋊Q811yescharacteristic
237C2×C4×C43C22⋊Q811yescharacteristic
238C2×C4×C43C22⋊Q811yescharacteristic
239C2×C4×C43#12311yescharacteristic
240C2×C4×C43#12311yescharacteristic
241C2×C4×C43#12311yescharacteristic
242C2×C4×C43#12311yescharacteristic
243C2×C4×C43#12411yescharacteristic
244C2×C4×C43#12611yescharacteristic
245C2×C4×C43#12711yescharacteristic
246C22⋊D43—42no—
247C22⋊D43—42no—
248C22⋊D43—42no—
249C22⋊D43—42no—
250C2×Dic43—22no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253D172—22no—
254D172—22no—
255D172—41no—
256D172—41no—
257C4×D43—42no—
258C4×D43—42no—
259C4×D43—42no—
260C4×D43—42no—
261Dic86—22no—
262Dic86—22no—
263Dic86—41no—
264Dic86—41no—
265C8×C43—42no—
266C43⋊C8—24no—
267C43⋊C8—42no—
268C43⋊C8—42no—
269#11120—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43#38511yescharacteristic
281C22×C43#38811yescharacteristic
282C22×C43#39011yescharacteristic
283C22×C43#39311yescharacteristic
284C22×C43#39411yescharacteristic
285C22×C43#39611yescharacteristic
286C22×C43#39711yescharacteristic
287C2×D43—42no—
288C2×D43—82no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—82no—
292C4×C43—82no—
293C4×C43—82no—
294C4×C43#38011yescharacteristic
295C4×C43#38511yescharacteristic
296C4×C43#38611yescharacteristic
297C4×C43#38811yescharacteristic
298C4×C43#39211yescharacteristic
299C4×C43#39411yescharacteristic
300C4×C43#39611yescharacteristic
301C4×C43#39911yescharacteristic
302Dic43—42no—
303C2×#430—431no—
304C2×#421—431no—
305C2×#417—431no—
306C2×#413—431no—
307C2×#344—431no—
308C2×#343—431no—
309#1736D4311yescharacteristic, complemented
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—21no—
313C2×C43—21no—
314C2×C43—21no—
315C2×C43—21no—
316C2×C43#143911yescharacteristic
317C2×C43#204811yescharacteristic
318C2×C43#204911yescharacteristic
319D43—82no—
320C22×#41—431no—
321C22×M16—431no—
322C22×M16—431no—
323C22×M16—431no—
324C22×M16C2×D4311yescharacteristic
325C2×#117C2×D4311yescharacteristic
326C22×C4⋊C4C2×D4311yescharacteristic
327#430—862no—
328#430—862no—
329C2×#108—862no—
330#421—434no—
331#421—862no—
332C2×#104—862no—
333#417—862no—
334#417—862no—
335C2×#103—861no—
336C2×#102—861no—
337#413—862no—
338#413—862no—
339C2×#101—861no—
340C2×#100—861no—
341#344—862no—
342#343—862no—
343#340—22no—
344C43#1112011yescharacteristic, complemented, Sylow
345C2×#41—432no—
346C2×#41—432no—
347C2×#41—861no—
348C2×#41—861no—
349C2×#41—861no—
350C2×#41—861no—
351C2×#41—861no—
352C2×#41—861no—
353C2×#41—861no—
354C2×#41—861no—
355C2×#41—861no—
356C2×#41—861no—
357C22×Q8—431no—
358C22×D4—431no—
359C22×D4—861no—
360C23×C4—21no—
361C23×C4—861no—
362C23×C4C22×D4311yescharacteristic
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—432no—
369C2×M16—432no—
370C2×M16—432no—
371C2×M16—432no—
372C2×M16—432no—
373C2×M16—861no—
374C2×M16—861no—
375C2×M16—861no—
376C2×M16—861no—
377C2×M16—861no—
378C2×M16—861no—
379C2×M16—861no—
380C2×M16—861no—
381C2×M16—861no—
382C2×M16—861no—
383C2×M16—861no—
384C2×M16—861no—
385C2×M16—861no—
386C2×M16D17212yes—
387C22×C8—21no—
388C22×C8—861no—
389C22×C8—861no—
390C22×C8—861no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117C4×D4312yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C22⋊D4312yes—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404#108—868no—
405#104—868no—
406#103—864no—
407#102—864no—
408#101—864no—
409#100—864no—
410C24—861no—
411C24#1062190011yescharacteristic
412#41—862no—
413#41—862no—
414#41—862no—
415#41—862no—
416#41—862no—
417#41—862no—
418#41—862no—
419#41—862no—
420#41—1721no—
421#41—1721no—
422#41—1721no—
423#41—1721no—
424#41—1721no—
425#41—1721no—
426#41—1721no—
427#41—1721no—
428C2×Q8—432no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×D4—432no—
435C2×D4—862no—
436C2×D4—862no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—1721no—
443C2×D4—1721no—
444C2×D4—1721no—
445C2×D4—1721no—
446C22×C4—22no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—82no—
451C22×C4—861no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—1721no—
455C22×C4—1721no—
456C22×C4—1721no—
457C22×C4—1721no—
458C22×C4C2×C4×D4311yescharacteristic
459C22×C4C2×D17211yescharacteristic
460C22×C4#1062189811yescharacteristic
461C22×C4#1062189811yescharacteristic
462C22×C4#1062189811yescharacteristic
463C22×C4#1062189811yescharacteristic
464C22×C4D4×D4311yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4Q8×D4311yescharacteristic
470C22×C4#1062190211yescharacteristic
471C22×C4C2×C22⋊D4311yescharacteristic
472M16—22no—
473M16—22no—
474M16—41no—
475M16—41no—
476M16—434no—
477M16—862no—
478M16—862no—
479M16—862no—
480M16—862no—
481M16—862no—
482M16—862no—
483M16—862no—
484M16—1721no—
485M16—1721no—
486M16—1721no—
487M16—1721no—
488C2×C8—22no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—862no—
492C2×C8—862no—
493C2×C8—862no—
494C2×C8—862no—
495C2×C8—862no—
496C2×C8—1721no—
497C2×C8—1721no—
498C2×C8—1721no—
499C2×C8—1721no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C22⋊C4—22no—
507C22⋊C4—41no—
508C42—22no—
509C42—41no—
510C23—41no—
511C23—41no—
512C23—862no—
513C23—3441no—
514C23—3441no—
515C23—1721no—
516C23—1721no—
517C23(C22⋊D43)⋊C411yescharacteristic
518C23#1306329711yescharacteristic
519C23#1306330511yescharacteristic
520C23#1306330711yescharacteristic
521C23#1306331111yescharacteristic
522C23#1306331111yescharacteristic
523C23#1306332011yescharacteristic
524Q8—862no—
525Q8—862no—
526Q8—1721no—
527Q8—1721no—
528D4—862no—
529D4—862no—
530D4—1722no—
531D4—1722no—
532D4—1722no—
533D4—1722no—
534D4—1721no—
535D4—1721no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—81no—
541C2×C4—81no—
542C2×C4—82no—
543C2×C4—862no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1722no—
547C2×C4—1722no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4C22⋊C4×D4311yescharacteristic
551C2×C4C4⋊C4×D4311yescharacteristic
552C2×C4#1306328211yescharacteristic
553C2×C4C4×C22⋊D4311yescharacteristic
554C2×C4#1306328711yescharacteristic
555C2×C4C4×D17211yescharacteristic
556C2×C4#1306329311yescharacteristic
557C2×C4#1306329511yescharacteristic
558C2×C4#1306329511yescharacteristic
559C2×C4#1306329811yescharacteristic
560C2×C4#1306329811yescharacteristic
561C2×C4#1306329811yescharacteristic
562C2×C4#1306329811yescharacteristic
563C2×C4#1306329811yescharacteristic
564C2×C4#1306329911yescharacteristic
565C2×C4#1306330011yescharacteristic
566C2×C4#1306330111yescharacteristic
567C2×C4#1306330311yescharacteristic
568C2×C4#1306330311yescharacteristic
569C2×C4#1306330311yescharacteristic
570C2×C4#1306330311yescharacteristic
571C2×C4#1306330811yescharacteristic
572C2×C4#1306331011yescharacteristic
573C2×C4#1306331011yescharacteristic
574C2×C4#1306331011yescharacteristic
575C2×C4#1306331311yescharacteristic
576C2×C4#1306331911yescharacteristic
577C2×C4#1306332111yescharacteristic
578C8—42no—
579C8—864no—
580C8—1722no—
581C8—1722no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—3442no—
593C22—3442no—
594C22—3441no—
595C22—3441no—
596C22—1722no—
597C22#1458277311yescharacteristic
598C22#1458278811yescharacteristic
599C22#1458279911yescharacteristic
600C22#1458281211yescharacteristic
601C22#1458281411yescharacteristic
602C22#1458282111yescharacteristic
603C22#1458282811yescharacteristic
604C4—82no—
605C4—82no—
606C4—1722no—
607C4#1458275811yescharacteristic
608C4#1458277011yescharacteristic
609C4#1458277711yescharacteristic
610C4#1458279011yescharacteristic
611C4#1458280811yescharacteristic
612C4#1458281711yescharacteristic
613C4#1458282311yescharacteristic
614C4#1458283411yescharacteristic
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—21no—
621C2—3442no—
622C2#1913283911yescharacteristic
623C2#1913586611yescharacteristic
624C2#1913587311yescharacteristic
subgroupG/H
centerC22#14582814
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1736C2
socleC22×C43#394
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1736D43
hypocenterC43#11120
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
1. C2×#14582947C2semidirect
5. C2×#14582669C2semidirect
6. C2×#14582668C2semidirect
7. C43×#1736C2semidirect
16. #14582917C4semidirect
309. #1736D43semidirect
344. C43#11120semidirect

Maximal subgroups

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

subgroupindex
C2×#145829472
C2×#145829172
C2×#145828982
C2×#145828812
C2×#145826692
C2×#145826682
C43×#17362
#1112043