Finite Group Databasebeta

← #25003758

Subgroups — #25003758

Order 11008.

974 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
1C2×#14582915C211yesmaximal, characteristic
2#19143112C211yesmaximal, characteristic
3#19137083C211yesmaximal, characteristic
4#19137077C211yesmaximal, characteristic, complemented
5C2×#14582655C211yesmaximal, characteristic, complemented
6#19134288C211yesmaximal, characteristic, complemented
7C43×#1733C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×C4×Dic43C2211yescharacteristic
12#14582915—22no—
13#14582915C414yescomplemented
14C2×#13063251—22no—
15#14582907—21no—
16#14582903—21no—
17#14582898—22no—
18#14582893—22no—
19#14582804—21no—
20#14582800—21no—
21#14582795—22no—
22#14582776—22no—
23#14582771—22no—
24C4×Dic43⋊C4—22no—
25C4×(C2×D43)⋊C4—22no—
26#14582655—22no—
27#14582653—22no—
28C22×M16×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C2×#117×C43C2211yescharacteristic
31C43×#339—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—
47C23×Dic43D412yes—
48C22×C4×D43—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C22×C43⋊C8D412yes—
56#13063284—21no—
57#13063284—21no—
58#13063284C2×C412yes—
59#13063284D412yes—
60C2×C4⋊Dic43—21no—
61C2×Dic43⋊C4—24no—
62C2×C22⋊Dic43—21no—
63C2×(C2×D43)⋊C4—24no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43—21no—
69C2×C4×Dic43—21no—
70C2×C4×Dic43D412yes—
71#13063251—28no—
72#13063248—24no—
73#13063245—24no—
74C43⋊#95—24no—
75C43⋊#95—24no—
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×C43C2×C412yes—
83C22×C8×C43—21no—
84#117×C43—21no—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43—21no—
88#117×C43—21no—
89#117×C43—21no—
90#117×C43—21no—
91#117×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43D412yes—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C42×C43—21no—
97C2×C42×C43D412yes—
98C24×C43C2×D411yescharacteristic
99C23×D43—21no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43C22×C411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×Q811yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C2×C22⋊D43—22no—
117C2×C22⋊D43—22no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121C2×C22⋊D43—41no—
122C22×Dic43—21no—
123C22×Dic43—22no—
124C22×Dic43—22no—
125C22×Dic43—22no—
126C22×Dic43—22no—
127C22×Dic43—44no—
128#10621898—22no—
129#10621898—22no—
130#10621898—22no—
131#10621898—22no—
132#10621898—22no—
133#10621898—22no—
134#10621898—22no—
135#10621898—22no—
136#10621898—41no—
137#10621898—41no—
138#10621898—41no—
139#10621898—41no—
140#10621898—41no—
141#10621898—41no—
142#10621898—41no—
143#10621898—41no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172C4⋊C412yescomplemented
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—41no—
153C2×C4×D43—41no—
154C2×C4×D43—41no—
155C2×C4×D43—41no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86C4⋊C412yescomplemented
162M16×C43—22no—
163M16×C43—22no—
164M16×C43—41no—
165M16×C43—41no—
166C2×C8×C43—22no—
167C2×C8×C43—41no—
168C2×C8×C43—41no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C42×C43—22no—
178C42×C43—22no—
179C42×C43—41no—
180C42×C43—41no—
181C22⋊Dic43—22no—
182C22⋊Dic43—22no—
183(C2×D43)⋊C4—48no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186Dic43⋊C4—48no—
187C4×Dic43—22no—
188C4×Dic43—41no—
189C4×Dic43—41no—
190C4×Dic43—41no—
191C4×Dic43—41no—
192C4×Dic43C22⋊C414yescomplemented
193#10621877—41no—
194#10621877—41no—
195#10621877—41no—
196#10621877—41no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C23×C43—42no—
201C23×C43C4×D411yescharacteristic
202C23×C43#12011yescharacteristic
203C23×C43#12011yescharacteristic
204C23×C43#12111yescharacteristic
205C23×C43#12111yescharacteristic
206C23×C43C22⋊Q811yescharacteristic
207C23×C43#12411yescharacteristic
208C22×D43—22no—
209C22×D43—44no—
210C22×D43—41no—
211C22×D43—41no—
212C2×C4×C43—44no—
213C2×C4×C43—44no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43C2×C22⋊C411yescharacteristic
217C2×C4×C43C2×C4⋊C411yescharacteristic
218C2×C4×C43#11711yescharacteristic
219C2×C4×C43C4×D411yescharacteristic
220C2×C4×C43C4×D411yescharacteristic
221C2×C4×C43C4×D411yescharacteristic
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43C22⋊Q811yescharacteristic
230C2×C4×C43C22⋊Q811yescharacteristic
231C2×C4×C43C22⋊Q811yescharacteristic
232C2×C4×C43C22⋊Q811yescharacteristic
233C2×C4×C43C22⋊Q811yescharacteristic
234C2×C4×C43#12311yescharacteristic
235C2×C4×C43#12311yescharacteristic
236C2×C4×C43#12311yescharacteristic
237C2×C4×C43#12311yescharacteristic
238C2×C4×C43#12311yescharacteristic
239C2×C4×C43#12411yescharacteristic
240C2×C4×C43#12411yescharacteristic
241C2×C4×C43#12611yescharacteristic
242C2×C4×C43#12611yescharacteristic
243C2×C4×C43#12711yescharacteristic
244C22⋊D43—42no—
245C22⋊D43—42no—
246C22⋊D43—42no—
247C22⋊D43—42no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—22no—
252C2×Dic43—24no—
253C2×Dic43—44no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260D172—22no—
261D172—22no—
262D172—41no—
263D172—41no—
264C4×D43—42no—
265C4×D43—42no—
266C4×D43—42no—
267C4×D43—42no—
268Dic86—22no—
269Dic86—22no—
270Dic86—41no—
271Dic86—41no—
272C8×C43—42no—
273C43⋊C8—42no—
274#11083—431nomaximal, Sylow
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43#38511yescharacteristic
283C22×C43#38611yescharacteristic
284C22×C43#38811yescharacteristic
285C22×C43#39211yescharacteristic
286C22×C43#39311yescharacteristic
287C22×C43#39411yescharacteristic
288C22×C43#39611yescharacteristic
289C2×D43—44no—
290C2×D43—42no—
291C2×D43—82no—
292C2×D43—82no—
293C4×C43—82no—
294C4×C43—82no—
295C4×C43#38011yescharacteristic
296C4×C43#38511yescharacteristic
297C4×C43#38811yescharacteristic
298C4×C43#39011yescharacteristic
299C4×C43#39411yescharacteristic
300C4×C43#39611yescharacteristic
301C4×C43#39711yescharacteristic
302C4×C43#39911yescharacteristic
303Dic43—44no—
304Dic43—42no—
305Dic43—44no—
306C2×#421—431no—
307#2896—431no—
308#2297—431no—
309#2296—431no—
310#1733D4311yescharacteristic, complemented
311C2×H(3,ℤ/4)—431no—
312#1728—431no—
313C2×C43—21no—
314C2×C43—21no—
315C2×C43—21no—
316C2×C43—21no—
317C2×C43—21no—
318C2×C43—21no—
319C2×C43#143911yescharacteristic
320C2×C43#201012yes—
321D43—82no—
322C22×#41—431no—
323C22×M16—431no—
324C22×M16C2×D4311yescharacteristic
325C2×#117—431no—
326C2×#117C2×D4311yescharacteristic
327C2×#117C2×D4311yescharacteristic
328C22×C42—431no—
329#421—434no—
330#421—862no—
331C2×#104—862no—
332#419—861no—
333#418—861no—
334#417—862no—
335#416—862no—
336#391—861no—
337#390—861no—
338#389—862no—
339#386—862no—
340#385—862no—
341C4×C4⋊C4—862no—
342C4×C22⋊C4—862no—
343#339—22no—
344H(3,ℤ/4)—862no—
345#336—862no—
346C43#1108311yescharacteristic, complemented, Sylow
347C2×#41—432no—
348C2×#41—432no—
349C2×#41—861no—
350C2×#41—861no—
351C2×#41—861no—
352C2×#41—861no—
353C2×#41—861no—
354C2×#41—861no—
355C2×#41—861no—
356C2×#41—861no—
357C2×#41—861no—
358C2×#41—861no—
359C22×Q8—431no—
360C22×D4—431no—
361C22×D4—861no—
362C23×C4—432no—
363C23×C4—861no—
364C23×C4C22×D4311yescharacteristic
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—861no—
371C2×M16—861no—
372C2×M16—861no—
373C2×M16—861no—
374C2×M16—861no—
375C2×M16—861no—
376C2×M16C4×D4312yes—
377C22×C8—21no—
378C22×C8—432no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—432no—
388#117—432no—
389#117—861no—
390#117—861no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—864no—
394C2×C4⋊C4D17212yes—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—864no—
399C2×C42—21no—
400C2×C42—432no—
401C2×C42—861no—
402C2×C42—861no—
403C2×C42—861no—
404C2×C42—861no—
405C2×C42—861no—
406C2×C42—861no—
407C2×C42C22⋊D4312yes—
408#104—868no—
409#103—864no—
410#102—864no—
411#95—864no—
412#95—864no—
413C24—861no—
414C24D4×D4311yescharacteristic
415#41—862no—
416#41—862no—
417#41—862no—
418#41—862no—
419#41—862no—
420#41—862no—
421#41—862no—
422#41—862no—
423#41—1721no—
424#41—1721no—
425#41—1721no—
426#41—1721no—
427#41—1721no—
428#41—1721no—
429#41—1721no—
430#41—1721no—
431C2×Q8—432no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×D4—432no—
438C2×D4—862no—
439C2×D4—862no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—1721no—
446C2×D4—1721no—
447C2×D4—1721no—
448C2×D4—1721no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—861no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—1724no—
459C22×C4—1721no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4C2×C4×D4311yescharacteristic
464C22×C4C2×D17211yescharacteristic
465C22×C4#1062189811yescharacteristic
466C22×C4#1062189811yescharacteristic
467C22×C4#1062189811yescharacteristic
468C22×C4#1062189811yescharacteristic
469C22×C4D4×D4311yescharacteristic
470C22×C4D4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473C22×C4#1062190011yescharacteristic
474C22×C4Q8×D4311yescharacteristic
475C22×C4#1062190211yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477M16—22no—
478M16—22no—
479M16—41no—
480M16—41no—
481M16—1721no—
482M16—1721no—
483M16—1721no—
484M16—1721no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—862no—
489C2×C8—862no—
490C2×C8—862no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—1728no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—862no—
503C22⋊C4—862no—
504C22⋊C4—1728no—
505C42—22no—
506C42—22no—
507C42—41no—
508C42—41no—
509C42—434no—
510C42—862no—
511C42—1721no—
512C42—1721no—
513C42—1721no—
514C42—1721no—
515C23—42no—
516C23—862no—
517C23—1724no—
518C23—1721no—
519C23—1721no—
520C23#1306328711yescharacteristic
521C23#1306329311yescharacteristic
522C23#1306329511yescharacteristic
523C23#1306329811yescharacteristic
524C23#1306329811yescharacteristic
525C23#1306330311yescharacteristic
526C23#1306331111yescharacteristic
527Q8—862no—
528Q8—862no—
529Q8—1721no—
530Q8—1721no—
531D4—862no—
532D4—862no—
533D4—1722no—
534D4—1722no—
535D4—1722no—
536D4—1722no—
537D4—1721no—
538D4—1721no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—864no—
544C2×C4—864no—
545C2×C4—864no—
546C2×C4—862no—
547C2×C4—864no—
548C2×C4—1724no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4C22⋊C4×D4311yescharacteristic
560C2×C4C4⋊C4×D4311yescharacteristic
561C2×C4#1306328211yescharacteristic
562C2×C4(C22⋊D43)⋊C411yescharacteristic
563C2×C4C4×C22⋊D4311yescharacteristic
564C2×C4C4×D17211yescharacteristic
565C2×C4#1306329511yescharacteristic
566C2×C4#1306329711yescharacteristic
567C2×C4#1306329811yescharacteristic
568C2×C4#1306329811yescharacteristic
569C2×C4#1306329811yescharacteristic
570C2×C4#1306329911yescharacteristic
571C2×C4#1306330011yescharacteristic
572C2×C4#1306330111yescharacteristic
573C2×C4#1306330311yescharacteristic
574C2×C4#1306330311yescharacteristic
575C2×C4#1306330311yescharacteristic
576C2×C4#1306330511yescharacteristic
577C2×C4#1306330711yescharacteristic
578C2×C4#1306330811yescharacteristic
579C2×C4#1306331011yescharacteristic
580C2×C4#1306331011yescharacteristic
581C2×C4#1306331011yescharacteristic
582C2×C4#1306331111yescharacteristic
583C2×C4#1306331311yescharacteristic
584C2×C4#1306331911yescharacteristic
585C2×C4#1306332011yescharacteristic
586C2×C4#1306332111yescharacteristic
587C8—42no—
588C8—1722no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—3442no—
597C22—3442no—
598C22—1724no—
599C22—1722no—
600C22#1458277011yescharacteristic
601C22#1458277711yescharacteristic
602C22#1458278811yescharacteristic
603C22#1458280811yescharacteristic
604C22#1458281211yescharacteristic
605C22#1458281411yescharacteristic
606C22#1458282311yescharacteristic
607C4—82no—
608C4—82no—
609C4—1724no—
610C4—1722no—
611C4—1724no—
612C4#1458275811yescharacteristic
613C4#1458277311yescharacteristic
614C4#1458279011yescharacteristic
615C4#1458279911yescharacteristic
616C4#1458281711yescharacteristic
617C4#1458282111yescharacteristic
618C4#1458282811yescharacteristic
619C4#1458283411yescharacteristic
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—3442no—
627C2#1913283911yescharacteristic
628C2#1913566112yes—
subgroupG/H
centerC2×C4#13063321
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1733C2
socleC22×C43#392
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1733D43
hypocenterC43#11083
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #19137077C2semidirect
5. C2×#14582655C2semidirect
6. #19134288C2semidirect
7. C43×#1733C2semidirect
13. #14582915C4semidirect
149. C2×D172C4⋊C4semidirect
161. C2×Dic86C4⋊C4semidirect
192. C4×Dic43C22⋊C4semidirect
310. #1733D43semidirect
346. C43#11083semidirect

Maximal subgroups

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

subgroupindex
C2×#145829152
#191431122
#191370832
#191370772
C2×#145826552
#191342882
C43×#17332
#1108343