Finite Group Databasebeta

← #25003751

Subgroups — #25003751

Order 11008.

898 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×#14582922C211yesmaximal, characteristic, complemented
2C22×#13063251C211yesmaximal, characteristic
3#19143115C211yesmaximal, characteristic
4C2×#14582881C211yesmaximal, characteristic
5#19134333C211yesmaximal, characteristic, complemented
6C2×#14582660C211yesmaximal, characteristic, complemented
7C2×C43×#338C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×C4×Dic43C2211yescharacteristic
12#14582922—22no—
13#14582922—22no—
14C2×Dic43⋊C8—22no—
15C2×#13063251—21no—
16C2×#13063251—21no—
17C2×#13063251—22no—
18C2×#13063251C414yescomplemented
19#14582909—21no—
20#14582905—21no—
21#14582901—22no—
22#14582896—22no—
23#14582881—22no—
24#14582881—22no—
25C2×#13063243—21no—
26C2×#13063241—21no—
27#14582667—22no—
28#14582660—21no—
29#14582660—21no—
30C22×M16×C43C2211yescharacteristic
31C22×M16×C43C2211yescharacteristic
32C22×M16×C43C2211yescharacteristic
33C43×#338—22no—
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×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898C2×C412yes—
45C2×#10621898Q812yes—
46C22×Dic86D411yescharacteristic
47C22×D172D411yescharacteristic
48C22×C22⋊D43—21no—
49C23×Dic43—21no—
50C22×C4×D43—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877D412yes—
57C22×C43⋊C8—21no—
58#13063284—21no—
59#13063284—21no—
60#13063284—21no—
61#13063284—21no—
62C2×C4⋊Dic43D412yes—
63C2×C22⋊Dic43—21no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43C2×C412yes—
69C2×C4×Dic43D411yescharacteristic
70C2×C4×Dic43D411yescharacteristic
71C2×C4×Dic43D412yes—
72Dic43⋊C8—28no—
73#13063251—24no—
74#13063251—24no—
75#13063250—24no—
76#13063247—24no—
77#13063243—24no—
78#13063241—24no—
79C23×C4×C43C2311yescharacteristic
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C2×M16×C43—21no—
86C2×M16×C43—21no—
87C2×M16×C43—21no—
88C2×M16×C43—21no—
89C2×M16×C43—21no—
90C2×M16×C43—21no—
91C2×M16×C43—21no—
92C2×M16×C43—21no—
93C2×M16×C43—21no—
94C2×M16×C43—21no—
95C2×M16×C43—21no—
96C2×M16×C43C2×C412yes—
97C2×M16×C43D412yes—
98C22×C8×C43—21no—
99C22×C8×C43—21no—
100C22×C8×C43D412yes—
101C24×C43#4111yescharacteristic
102C23×D43—21no—
103C22×C4×C43C22×C411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
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×Q811yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×C4×C43#4111yescharacteristic
117C2×C22⋊D43—22no—
118C2×C22⋊D43—22no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C22×Dic43—22no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—22no—
127C22×Dic43—21no—
128C22×Dic43—22no—
129C22×Dic43—44no—
130#10621898—22no—
131#10621898—22no—
132#10621898—22no—
133#10621898—22no—
134#10621898—22no—
135#10621898—22no—
136#10621898—22no—
137#10621898—22no—
138#10621898—41no—
139#10621898—41no—
140#10621898—41no—
141#10621898—41no—
142#10621898—41no—
143#10621898—41no—
144#10621898—41no—
145#10621898—41no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172C4⋊C412yes—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—41no—
155C2×C4×D43—41no—
156C2×C4×D43—41no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C4⋊C412yes—
164M16×C43—22no—
165M16×C43—22no—
166M16×C43—22no—
167M16×C43—22no—
168M16×C43—41no—
169M16×C43—41no—
170M16×C43—41no—
171M16×C43—41no—
172M16×C43—41no—
173M16×C43—41no—
174M16×C43—41no—
175M16×C43—41no—
176C2×C8×C43—22no—
177C2×C8×C43—22no—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C2×C8×C43—41no—
182C2×C8×C43—41no—
183C2×C8×C43—41no—
184C2×C8×C43—41no—
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187C4⋊Dic43—22no—
188C4⋊Dic43—22no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—41no—
194C4×Dic43—41no—
195C4×Dic43C22⋊C412yes—
196C4×Dic43C22⋊C412yes—
197#10621877—22no—
198#10621877—22no—
199#10621877—41no—
200#10621877—41no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—41no—
203C2×C43⋊C8—41no—
204C23×C43—42no—
205C23×C43C4×D411yescharacteristic
206C23×C43#12111yescharacteristic
207C23×C43C22⋊Q811yescharacteristic
208C23×C43#12311yescharacteristic
209C23×C43#12311yescharacteristic
210C23×C43#12311yescharacteristic
211C23×C43#12611yescharacteristic
212C22×D43—22no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—82no—
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#12011yescharacteristic
224C2×C4×C43#12011yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43C22⋊Q811yescharacteristic
233C2×C4×C43C22⋊Q811yescharacteristic
234C2×C4×C43C22⋊Q811yescharacteristic
235C2×C4×C43C22⋊Q811yescharacteristic
236C2×C4×C43C22⋊Q811yescharacteristic
237C2×C4×C43#12311yescharacteristic
238C2×C4×C43#12311yescharacteristic
239C2×C4×C43#12411yescharacteristic
240C2×C4×C43#12411yescharacteristic
241C2×C4×C43#12411yescharacteristic
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—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—44no—
253C2×Dic43—44no—
254C2×Dic43—42no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—42no—
258C2×Dic43—82no—
259D172—22no—
260D172—22no—
261D172—41no—
262D172—41no—
263C4×D43—42no—
264C4×D43—42no—
265C4×D43—42no—
266C4×D43—42no—
267Dic86—22no—
268Dic86—22no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—42no—
272C8×C43—42no—
273C8×C43—42no—
274C43⋊C8—42no—
275#11082—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43#38511yescharacteristic
284C22×C43#38611yescharacteristic
285C22×C43#38811yescharacteristic
286C22×C43#39411yescharacteristic
287C22×C43#39611yescharacteristic
288C22×C43#39711yescharacteristic
289C22×C43#39911yescharacteristic
290C2×D43—42no—
291C2×D43—82no—
292C2×D43—82no—
293C2×D43—82no—
294C4×C43#38011yescharacteristic
295C4×C43#38511yescharacteristic
296C4×C43#38811yescharacteristic
297C4×C43#39011yescharacteristic
298C4×C43#39211yescharacteristic
299C4×C43#39311yescharacteristic
300C4×C43#39411yescharacteristic
301C4×C43#39611yescharacteristic
302Dic43—24no—
303Dic43—42no—
304Dic43—42no—
305Dic43—82no—
306C2×#423—431no—
307C22×#104—431no—
308#2896—431no—
309C2×#413—431no—
310#1742—431no—
311C2×#339—431no—
312C2×#338D4311yescharacteristic, complemented
313C2×C43—21no—
314C2×C43—21no—
315C2×C43—21no—
316C2×C43—21no—
317C2×C43—21no—
318C2×C43—21no—
319C2×C43#143911yescharacteristic
320C2×C43#205012yes—
321D43—82no—
322C22×#41—431no—
323C22×M16—431no—
324C22×M16C2×D4311yescharacteristic
325C22×M16C2×D4311yescharacteristic
326C22×M16C2×D4311yescharacteristic
327C2×#117—431no—
328C22×C42—431no—
329#423—862no—
330#423—862no—
331C2×C4⋊C8—862no—
332C2×#104—434no—
333C2×#104—861no—
334C2×#104—861no—
335C2×#104—862no—
336#419—861no—
337#418—861no—
338#417—862no—
339#416—862no—
340#413—862no—
341#413—862no—
342C2×#101—861no—
343C2×#100—861no—
344#343—862no—
345#339—861no—
346#339—861no—
347#338—22no—
348C43#1108211yescharacteristic, complemented, Sylow
349C2×#41—432no—
350C2×#41—432no—
351C2×#41—861no—
352C2×#41—861no—
353C2×#41—861no—
354C2×#41—861no—
355C2×#41—861no—
356C2×#41—861no—
357C2×#41—861no—
358C2×#41—861no—
359C2×#41—861no—
360C2×#41—861no—
361C22×Q8—431no—
362C22×D4—431no—
363C22×D4—861no—
364C23×C4—861no—
365C23×C4—861no—
366C23×C4C22×D4311yescharacteristic
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—432no—
384C2×M16—861no—
385C2×M16—861no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—861no—
389C2×M16C4×D4312yes—
390C2×M16C22⋊D4312yes—
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—861no—
394C22×C8D17212yes—
395#117—861no—
396#117—861no—
397#117—861no—
398#117—861no—
399C2×C4⋊C4—432no—
400C2×C22⋊C4—861no—
401C2×C42—432no—
402C2×C42—431no—
403C2×C42—431no—
404C2×C42—432no—
405C2×C42—861no—
406C2×C42—861no—
407C2×C42—861no—
408C2×C42—861no—
409C4⋊C8—868no—
410#104—864no—
411#104—864no—
412#103—864no—
413#102—864no—
414#101—864no—
415#100—864no—
416C24—861no—
417C24#1062190211yescharacteristic
418#41—862no—
419#41—862no—
420#41—862no—
421#41—862no—
422#41—862no—
423#41—862no—
424#41—862no—
425#41—862no—
426#41—1721no—
427#41—1721no—
428#41—1721no—
429#41—1721no—
430#41—1721no—
431#41—1721no—
432#41—1721no—
433#41—1721no—
434C2×Q8—432no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×D4—432no—
441C2×D4—862no—
442C2×D4—862no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—1721no—
449C2×D4—1721no—
450C2×D4—1721no—
451C2×D4—1721no—
452C22×C4—861no—
453C22×C4—862no—
454C22×C4—861no—
455C22×C4—862no—
456C22×C4—861no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—1724no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4—1721no—
464C22×C4—1721no—
465C22×C4C2×C4×D4311yescharacteristic
466C22×C4C2×D17211yescharacteristic
467C22×C4#1062189811yescharacteristic
468C22×C4#1062189811yescharacteristic
469C22×C4#1062189811yescharacteristic
470C22×C4#1062189811yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4D4×D4311yescharacteristic
476C22×C4#1062190011yescharacteristic
477C22×C4Q8×D4311yescharacteristic
478C22×C4C2×C22⋊D4311yescharacteristic
479M16—22no—
480M16—22no—
481M16—22no—
482M16—22no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16—41no—
487M16—41no—
488M16—41no—
489M16—41no—
490M16—41no—
491M16—862no—
492M16—862no—
493M16—1721no—
494M16—1721no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—862no—
505C2×C8—1721no—
506C2×C8—1721no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C42—432no—
512C42—432no—
513C42—862no—
514C42—862no—
515C42—861no—
516C42—861no—
517C42—1721no—
518C42—1721no—
519C23—42no—
520C23—862no—
521C23—3442no—
522C23—1721no—
523C23—1721no—
524C23#1306328711yescharacteristic
525C23#1306330011yescharacteristic
526C23#1306330111yescharacteristic
527C23#1306331011yescharacteristic
528C23#1306331011yescharacteristic
529C23#1306331011yescharacteristic
530C23#1306332011yescharacteristic
531Q8—862no—
532Q8—862no—
533Q8—1721no—
534Q8—1721no—
535D4—862no—
536D4—862no—
537D4—1722no—
538D4—1722no—
539D4—1722no—
540D4—1722no—
541D4—1721no—
542D4—1721no—
543C2×C4—864no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—3442no—
548C2×C4—1724no—
549C2×C4—1724no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4C22⋊C4×D4311yescharacteristic
559C2×C4C4⋊C4×D4311yescharacteristic
560C2×C4#1306328211yescharacteristic
561C2×C4(C22⋊D43)⋊C411yescharacteristic
562C2×C4C4×C22⋊D4311yescharacteristic
563C2×C4C4×D17211yescharacteristic
564C2×C4#1306329311yescharacteristic
565C2×C4#1306329511yescharacteristic
566C2×C4#1306329511yescharacteristic
567C2×C4#1306329711yescharacteristic
568C2×C4#1306329811yescharacteristic
569C2×C4#1306329811yescharacteristic
570C2×C4#1306329811yescharacteristic
571C2×C4#1306329811yescharacteristic
572C2×C4#1306329811yescharacteristic
573C2×C4#1306329911yescharacteristic
574C2×C4#1306330311yescharacteristic
575C2×C4#1306330311yescharacteristic
576C2×C4#1306330311yescharacteristic
577C2×C4#1306330311yescharacteristic
578C2×C4#1306330511yescharacteristic
579C2×C4#1306330711yescharacteristic
580C2×C4#1306330811yescharacteristic
581C2×C4#1306331111yescharacteristic
582C2×C4#1306331111yescharacteristic
583C2×C4#1306331311yescharacteristic
584C2×C4#1306331911yescharacteristic
585C2×C4#1306332111yescharacteristic
586C8—42no—
587C8—42no—
588C8—42no—
589C8—1722no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—3442no—
598C22—3442no—
599C22—3442no—
600C22—1722no—
601C22#1458277011yescharacteristic
602C22#1458277711yescharacteristic
603C22#1458278811yescharacteristic
604C22#1458281711yescharacteristic
605C22#1458282111yescharacteristic
606C22#1458282811yescharacteristic
607C22#1458283411yescharacteristic
608C4—864no—
609C4—3442no—
610C4—1722no—
611C4—1722no—
612C4#1458275811yescharacteristic
613C4#1458277311yescharacteristic
614C4#1458279011yescharacteristic
615C4#1458279911yescharacteristic
616C4#1458280811yescharacteristic
617C4#1458281211yescharacteristic
618C4#1458281411yescharacteristic
619C4#1458282311yescharacteristic
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—3442no—
627C2#1913283911yescharacteristic
628C2#1913588312yes—
subgroupG/H
centerC2×C4#13063313
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#338C2
socleC22×C43#394
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#338D43
hypocenterC43#11082
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#338

Complements

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

NH ≅ G/Ntype
1. C2×#14582922C2semidirect
5. #19134333C2semidirect
6. C2×#14582660C2semidirect
7. C2×C43×#338C2semidirect
18. C2×#13063251C4semidirect
312. C2×#338D43semidirect
348. C43#11082semidirect

Maximal subgroups

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

subgroupindex
C2×#145829222
C22×#130632512
#191431152
C2×#145828812
#191343332
C2×#145826602
C2×C43×#3382
#1108243