Finite Group Databasebeta

← #25003779

Subgroups — #25003779

Order 11008.

866 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582925C211yesmaximal, characteristic, complemented
2C2×#14582915C211yesmaximal, characteristic
3C2×#14582896C211yesmaximal, characteristic
4C2×#14582881C211yesmaximal, characteristic
5C2×#14582670C211yesmaximal, characteristic, complemented
6C2×#14582656C211yesmaximal, characteristic, complemented
7C2×C43×#341C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582925—22no—
13#14582925—22no—
14C2×Dic43⋊C8—22no—
15#14582915—22no—
16#14582915C414yescomplemented
17C2×#13063251—22no—
18#14582896—22no—
19#14582896—22no—
20C2×#13063250—21no—
21C2×#13063247—21no—
22#14582881—22no—
23#14582881—22no—
24C2×#13063243—21no—
25C2×#13063241—21no—
26#14582670—22no—
27#14582656—22no—
28C22×M16×C43C2211yescharacteristic
29C22×M16×C43C2211yescharacteristic
30C23×C8×C43C2211yescharacteristic
31C43×#341—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×#10621877D412yes—
54C22×C43⋊C8—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284—21no—
59#13063284—21no—
60#13063284C2×C412yes—
61#13063284D412yes—
62#13063284D412yes—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43D412yes—
69Dic43⋊C8—28no—
70#13063251—28no—
71#13063250—24no—
72#13063247—24no—
73#13063243—24no—
74#13063241—24no—
75C23×C4×C43C2311yescharacteristic
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
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×C43C2×C412yes—
87C2×M16×C43D412yes—
88C22×C8×C43—21no—
89C22×C8×C43—21no—
90C22×C8×C43—21no—
91C22×C8×C43—21no—
92C22×C8×C43—21no—
93C22×C8×C43—21no—
94C22×C8×C43—21no—
95C22×C8×C43—21no—
96C22×C8×C43D412yes—
97C24×C43#4111yescharacteristic
98C23×D43—21no—
99C22×C4×C43C22×C411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×Q811yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C2×C22⋊D43—22no—
114C2×C22⋊D43—22no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C2×C22⋊D43—41no—
118C2×C22⋊D43—41no—
119C22×Dic43—22no—
120C22×Dic43—21no—
121C22×Dic43—41no—
122#10621898—22no—
123#10621898—22no—
124#10621898—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—22no—
128#10621898—22no—
129#10621898—22no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172C4⋊C412yes—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—41no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86C4⋊C412yes—
156M16×C43—22no—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—41no—
161M16×C43—41no—
162M16×C43—41no—
163M16×C43—41no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C2×C8×C43—22no—
169C2×C8×C43—41no—
170C2×C8×C43—41no—
171C2×C8×C43—41no—
172C2×C8×C43—41no—
173C2×C8×C43—41no—
174C2×C8×C43—41no—
175C2×C8×C43—41no—
176C2×C8×C43—41no—
177C22⋊Dic43—22no—
178C22⋊Dic43—22no—
179C22⋊Dic43—22no—
180C22⋊Dic43—41no—
181C4⋊Dic43—22no—
182C4⋊Dic43—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43—41no—
185C4×Dic43—22no—
186C4×Dic43—22no—
187C4×Dic43—41no—
188C4×Dic43C22⋊C414yes—
189#10621877—22no—
190#10621877—22no—
191#10621877—41no—
192#10621877—41no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—41no—
196C23×C43—42no—
197C23×C43C4×D411yescharacteristic
198C23×C43#12111yescharacteristic
199C23×C43C22⋊Q811yescharacteristic
200C23×C43#12311yescharacteristic
201C23×C43#12311yescharacteristic
202C23×C43#12311yescharacteristic
203C23×C43#12611yescharacteristic
204C22×D43—22no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—82no—
208C2×C4×C43C2×C22⋊C411yescharacteristic
209C2×C4×C43C2×C4⋊C411yescharacteristic
210C2×C4×C43#11711yescharacteristic
211C2×C4×C43C4×D411yescharacteristic
212C2×C4×C43C4×D411yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43C22⋊Q811yescharacteristic
225C2×C4×C43C22⋊Q811yescharacteristic
226C2×C4×C43C22⋊Q811yescharacteristic
227C2×C4×C43C22⋊Q811yescharacteristic
228C2×C4×C43C22⋊Q811yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C2×C4×C43#12411yescharacteristic
232C2×C4×C43#12411yescharacteristic
233C2×C4×C43#12411yescharacteristic
234C2×C4×C43#12611yescharacteristic
235C2×C4×C43#12711yescharacteristic
236C22⋊D43—42no—
237C22⋊D43—42no—
238C22⋊D43—42no—
239C22⋊D43—42no—
240C2×Dic43—22no—
241C2×Dic43—24no—
242C2×Dic43—44no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246C2×Dic43—82no—
247D172—22no—
248D172—22no—
249D172—41no—
250D172—41no—
251C4×D43—42no—
252C4×D43—42no—
253C4×D43—42no—
254C4×D43—42no—
255Dic86—22no—
256Dic86—22no—
257Dic86—41no—
258Dic86—41no—
259C8×C43—42no—
260C8×C43—42no—
261C8×C43—42no—
262C43⋊C8—42no—
263#11086—431nomaximal, Sylow
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43#38511yescharacteristic
272C22×C43#38611yescharacteristic
273C22×C43#38811yescharacteristic
274C22×C43#39411yescharacteristic
275C22×C43#39611yescharacteristic
276C22×C43#39711yescharacteristic
277C22×C43#39911yescharacteristic
278C2×D43—42no—
279C2×D43—82no—
280C2×D43—82no—
281C2×D43—82no—
282C4×C43#38011yescharacteristic
283C4×C43#38511yescharacteristic
284C4×C43#38811yescharacteristic
285C4×C43#39011yescharacteristic
286C4×C43#39211yescharacteristic
287C4×C43#39311yescharacteristic
288C4×C43#39411yescharacteristic
289C4×C43#39611yescharacteristic
290Dic43—44no—
291Dic43—42no—
292Dic43—82no—
293C2×#424—431no—
294C2×#421—431no—
295C2×#416—431no—
296C2×#413—431no—
297C2×#344—431no—
298C2×#341D4311yescharacteristic, complemented
299C2×H(3,ℤ/4)—431no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43#143911yescharacteristic
307C2×C43#208012yes—
308D43—82no—
309C22×#41—431no—
310C22×M16—431no—
311C22×M16C2×D4311yescharacteristic
312C22×M16C2×D4311yescharacteristic
313C23×C8C2×D4311yescharacteristic
314C2×#117—431no—
315C2×#117—431no—
316#424—862no—
317#424—862no—
318C2×C4⋊C8—862no—
319#421—434no—
320#421—862no—
321C2×#104—862no—
322#416—862no—
323#416—862no—
324C2×#103—861no—
325C2×#102—861no—
326#413—862no—
327#413—862no—
328C2×#101—861no—
329C2×#100—861no—
330#344—862no—
331#341—22no—
332H(3,ℤ/4)—862no—
333C43#1108611yescharacteristic, complemented, Sylow
334C2×#41—432no—
335C2×#41—432no—
336C2×#41—861no—
337C2×#41—861no—
338C2×#41—861no—
339C2×#41—861no—
340C2×#41—861no—
341C2×#41—861no—
342C2×#41—861no—
343C2×#41—861no—
344C2×#41—861no—
345C2×#41—861no—
346C22×Q8—431no—
347C22×D4—431no—
348C22×D4—861no—
349C23×C4—861no—
350C23×C4C22×D4311yescharacteristic
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—432no—
362C2×M16—861no—
363C2×M16—861no—
364C2×M16—861no—
365C2×M16—861no—
366C2×M16—861no—
367C2×M16C4×D4312yes—
368C2×M16C22⋊D4312yes—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—861no—
378C22×C8D17212yes—
379#117—432no—
380#117—432no—
381#117—432no—
382#117—861no—
383#117—861no—
384#117—861no—
385#117—861no—
386#117—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—432no—
392C2×C42—861no—
393C4⋊C8—868no—
394#104—868no—
395#103—864no—
396#102—864no—
397#101—864no—
398#100—864no—
399C24—861no—
400C24#1062190211yescharacteristic
401#41—862no—
402#41—862no—
403#41—862no—
404#41—862no—
405#41—862no—
406#41—862no—
407#41—862no—
408#41—862no—
409#41—1721no—
410#41—1721no—
411#41—1721no—
412#41—1721no—
413#41—1721no—
414#41—1721no—
415#41—1721no—
416#41—1721no—
417C2×Q8—432no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×D4—432no—
424C2×D4—862no—
425C2×D4—862no—
426C2×D4—861no—
427C2×D4—861no—
428C2×D4—861no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—1721no—
432C2×D4—1721no—
433C2×D4—1721no—
434C2×D4—1721no—
435C22×C4—862no—
436C22×C4—861no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—1721no—
440C22×C4—1721no—
441C22×C4—1721no—
442C22×C4—1721no—
443C22×C4—1721no—
444C22×C4C2×C4×D4311yescharacteristic
445C22×C4C2×D17211yescharacteristic
446C22×C4#1062189811yescharacteristic
447C22×C4#1062189811yescharacteristic
448C22×C4#1062189811yescharacteristic
449C22×C4#1062189811yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4#1062190011yescharacteristic
456C22×C4Q8×D4311yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—862no—
467M16—862no—
468M16—1721no—
469M16—1721no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—862no—
484C2×C8—1721no—
485C2×C8—1721no—
486C4⋊C4—862no—
487C4⋊C4—862no—
488C4⋊C4—862no—
489C4⋊C4—1721no—
490C22⋊C4—862no—
491C22⋊C4—862no—
492C22⋊C4—862no—
493C22⋊C4—1721no—
494C42—434no—
495C42—862no—
496C42—862no—
497C42—1721no—
498C23—42no—
499C23—862no—
500C23—3442no—
501C23—1721no—
502C23—1721no—
503C23#1306328711yescharacteristic
504C23#1306330011yescharacteristic
505C23#1306330111yescharacteristic
506C23#1306331011yescharacteristic
507C23#1306331011yescharacteristic
508C23#1306331011yescharacteristic
509C23#1306332011yescharacteristic
510Q8—862no—
511Q8—862no—
512Q8—1721no—
513Q8—1721no—
514D4—862no—
515D4—862no—
516D4—1722no—
517D4—1722no—
518D4—1722no—
519D4—1722no—
520D4—1721no—
521D4—1721no—
522C2×C4—862no—
523C2×C4—864no—
524C2×C4—3442no—
525C2×C4—1722no—
526C2×C4—1724no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1722no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4C22⋊C4×D4311yescharacteristic
534C2×C4C4⋊C4×D4311yescharacteristic
535C2×C4#1306328211yescharacteristic
536C2×C4(C22⋊D43)⋊C411yescharacteristic
537C2×C4C4×C22⋊D4311yescharacteristic
538C2×C4C4×D17211yescharacteristic
539C2×C4#1306329311yescharacteristic
540C2×C4#1306329511yescharacteristic
541C2×C4#1306329511yescharacteristic
542C2×C4#1306329711yescharacteristic
543C2×C4#1306329811yescharacteristic
544C2×C4#1306329811yescharacteristic
545C2×C4#1306329811yescharacteristic
546C2×C4#1306329811yescharacteristic
547C2×C4#1306329811yescharacteristic
548C2×C4#1306329911yescharacteristic
549C2×C4#1306330311yescharacteristic
550C2×C4#1306330311yescharacteristic
551C2×C4#1306330311yescharacteristic
552C2×C4#1306330311yescharacteristic
553C2×C4#1306330511yescharacteristic
554C2×C4#1306330711yescharacteristic
555C2×C4#1306330811yescharacteristic
556C2×C4#1306331111yescharacteristic
557C2×C4#1306331111yescharacteristic
558C2×C4#1306331311yescharacteristic
559C2×C4#1306331911yescharacteristic
560C2×C4#1306332111yescharacteristic
561C8—42no—
562C8—42no—
563C8—42no—
564C8—1722no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—3442no—
573C22—3442no—
574C22—3442no—
575C22—1722no—
576C22#1458277011yescharacteristic
577C22#1458277711yescharacteristic
578C22#1458278811yescharacteristic
579C22#1458281711yescharacteristic
580C22#1458282111yescharacteristic
581C22#1458282811yescharacteristic
582C22#1458283411yescharacteristic
583C4—3442no—
584C4—1724no—
585C4—1722no—
586C4#1458275811yescharacteristic
587C4#1458277311yescharacteristic
588C4#1458279011yescharacteristic
589C4#1458279911yescharacteristic
590C4#1458280811yescharacteristic
591C4#1458281211yescharacteristic
592C4#1458281411yescharacteristic
593C4#1458282311yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—3442no—
601C2#1913283911yescharacteristic
602C2#1913605112yes—
subgroupG/H
centerC2×C4#13063311
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#341C2
socleC22×C43#397
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#341D43
hypocenterC43#11086
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
1. C2×#14582925C2semidirect
5. C2×#14582670C2semidirect
6. C2×#14582656C2semidirect
7. C2×C43×#341C2semidirect
16. #14582915C4semidirect
298. C2×#341D43semidirect
333. C43#11086semidirect

Maximal subgroups

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

subgroupindex
C2×#145829252
C2×#145829152
C2×#145828962
C2×#145828812
C2×#145826702
C2×#145826562
C2×C43×#3412
#1108643