Finite Group Databasebeta

← #25003737

Subgroups — #25003737

Order 11008.

902 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582922C211yesmaximal, characteristic, complemented
2C2×#14582915C211yesmaximal, characteristic
3C22×#13063251C211yesmaximal, characteristic
4#19143039C211yesmaximal, characteristic
5C2×#14582671C211yesmaximal, characteristic, complemented
6C2×#14582660C211yesmaximal, characteristic, complemented
7C43×#1738C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×C4×Dic43C2211yescharacteristic
12#14582922—22no—
13#14582922—22no—
14C2×Dic43⋊C8—22no—
15#14582915—22no—
16#14582915—22no—
17C2×#13063251—22no—
18C2×#13063251—22no—
19C2×#13063251—22no—
20C2×#13063251C412yescomplemented
21C2×#13063251C412yescomplemented
22#14582867—22no—
23#14582865—22no—
24#14582862—22no—
25#14582671—22no—
26#14582660—22no—
27C22×M16×C43C2211yescharacteristic
28C22×M16×C43C2211yescharacteristic
29C22×M16×C43C2211yescharacteristic
30C43×#341—22no—
31C2×#10621898—21no—
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×#10621898C2×C412yes—
42C2×#10621898D412yes—
43C22×Dic86Q811yescharacteristic
44C22×D172Q811yescharacteristic
45C22×C22⋊D43—21no—
46C23×Dic43—21no—
47C22×C4×D43—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C22×C43⋊C8D412yes—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284D412yes—
59C2×C4⋊Dic43—21no—
60C2×C22⋊Dic43—21no—
61C2×C4×Dic43—21no—
62C2×C4×Dic43—21no—
63C2×C4×Dic43—21no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43C2×C411yescharacteristic
66C2×C4×Dic43C2×C411yescharacteristic
67C2×C4×Dic43D412yes—
68C2×C4×Dic43D412yes—
69Dic43⋊C8—28no—
70#13063251—28no—
71#13063251—24no—
72#13063251—24no—
73(C2×D43)⋊C8—28no—
74C23×C4×C43C2311yescharacteristic
75C2×M16×C43—21no—
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×C43—21no—
87C2×M16×C43—21no—
88C2×M16×C43—21no—
89C2×M16×C43—21no—
90C2×M16×C43C2×C412yes—
91C2×M16×C43D412yes—
92C2×M16×C43D412yes—
93C22×C8×C43—21no—
94C22×C8×C43—21no—
95C22×C8×C43—21no—
96C24×C43#4111yescharacteristic
97C23×D43—21no—
98C22×C4×C43C22×C411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
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×Q811yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C2×C22⋊D43—22no—
113C2×C22⋊D43—22no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C2×C22⋊D43—41no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—22no—
121C22×Dic43—21no—
122C22×Dic43—22no—
123C22×Dic43—44no—
124C22×Dic43—41no—
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—22no—
162M16×C43—22no—
163M16×C43—22no—
164M16×C43—22no—
165M16×C43—41no—
166M16×C43—41no—
167M16×C43—41no—
168M16×C43—41no—
169M16×C43—41no—
170M16×C43—41no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—41no—
175C2×C8×C43—41no—
176C2×C8×C43—41no—
177C2×C8×C43—41no—
178C2×C8×C43—41no—
179C2×C8×C43—41no—
180C22⋊Dic43—22no—
181C22⋊Dic43—41no—
182C4⋊Dic43—22no—
183C4⋊Dic43—41no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—22no—
187C4×Dic43—22no—
188C4×Dic43—22no—
189C4×Dic43—41no—
190C4×Dic43C22⋊C412yes—
191C4×Dic43C22⋊C412yes—
192#10621877—41no—
193#10621877—41no—
194#10621877—41no—
195#10621877—41no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C23×C43—42no—
200C23×C43C4×D411yescharacteristic
201C23×C43#12111yescharacteristic
202C23×C43C22⋊Q811yescharacteristic
203C23×C43#12311yescharacteristic
204C23×C43#12311yescharacteristic
205C23×C43#12311yescharacteristic
206C23×C43#12611yescharacteristic
207C22×D43—22no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—82no—
211C2×C4×C43C2×C22⋊C411yescharacteristic
212C2×C4×C43C2×C4⋊C411yescharacteristic
213C2×C4×C43#11711yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43#12011yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43C22⋊Q811yescharacteristic
228C2×C4×C43C22⋊Q811yescharacteristic
229C2×C4×C43C22⋊Q811yescharacteristic
230C2×C4×C43C22⋊Q811yescharacteristic
231C2×C4×C43C22⋊Q811yescharacteristic
232C2×C4×C43#12311yescharacteristic
233C2×C4×C43#12311yescharacteristic
234C2×C4×C43#12411yescharacteristic
235C2×C4×C43#12411yescharacteristic
236C2×C4×C43#12411yescharacteristic
237C2×C4×C43#12611yescharacteristic
238C2×C4×C43#12711yescharacteristic
239C22⋊D43—42no—
240C22⋊D43—42no—
241C22⋊D43—42no—
242C22⋊D43—42no—
243C2×Dic43—24no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—44no—
248C2×Dic43—44no—
249C2×Dic43—42no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—42no—
253C2×Dic43—82no—
254D172—22no—
255D172—22no—
256D172—41no—
257D172—41no—
258C4×D43—42no—
259C4×D43—42no—
260C4×D43—42no—
261C4×D43—42no—
262Dic86—22no—
263Dic86—22no—
264Dic86—41no—
265Dic86—41no—
266C8×C43—42no—
267C8×C43—42no—
268C8×C43—42no—
269C43⋊C8—42no—
270#11080—431nomaximal, Sylow
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43#38511yescharacteristic
279C22×C43#38611yescharacteristic
280C22×C43#38811yescharacteristic
281C22×C43#39411yescharacteristic
282C22×C43#39611yescharacteristic
283C22×C43#39711yescharacteristic
284C22×C43#39911yescharacteristic
285C2×D43—44no—
286C2×D43—42no—
287C2×D43—82no—
288C2×D43—82no—
289C4×C43#38011yescharacteristic
290C4×C43#38511yescharacteristic
291C4×C43#38811yescharacteristic
292C4×C43#39011yescharacteristic
293C4×C43#39211yescharacteristic
294C4×C43#39311yescharacteristic
295C4×C43#39411yescharacteristic
296C4×C43#39611yescharacteristic
297Dic43—24no—
298Dic43—42no—
299Dic43—42no—
300Dic43—82no—
301C2×#423—431no—
302C2×#421—431no—
303C22×#104—431no—
304#2879—431no—
305C2×#344—431no—
306#1738D4311yescharacteristic, complemented
307C2×#339—431no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—21no—
313C2×C43—21no—
314C2×C43#143911yescharacteristic
315C2×C43#186112yes—
316D43—82no—
317C22×#41—431no—
318C22×M16—431no—
319C22×M16C2×D4311yescharacteristic
320C22×M16C2×D4311yescharacteristic
321C22×M16C2×D4311yescharacteristic
322C2×#117—431no—
323C22×C42—431no—
324#423—862no—
325#423—862no—
326C2×C4⋊C8—862no—
327#421—862no—
328#421—862no—
329C2×#104—432no—
330C2×#104—432no—
331C2×#104—862no—
332C2×#104—862no—
333C2×#104—862no—
334#408—862no—
335#408—862no—
336#407—862no—
337#344—862no—
338#341—22no—
339#339—862no—
340C43#1108011yescharacteristic, complemented, Sylow
341C2×#41—432no—
342C2×#41—432no—
343C2×#41—861no—
344C2×#41—861no—
345C2×#41—861no—
346C2×#41—861no—
347C2×#41—861no—
348C2×#41—861no—
349C2×#41—861no—
350C2×#41—861no—
351C2×#41—861no—
352C2×#41—861no—
353C22×Q8—431no—
354C22×D4—431no—
355C22×D4—861no—
356C23×C4—861no—
357C23×C4—861no—
358C23×C4C22×D4311yescharacteristic
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—861no—
375C2×M16—861no—
376C2×M16—861no—
377C2×M16—861no—
378C2×M16—861no—
379C2×M16—861no—
380C2×M16C4×D4312yes—
381C2×M16D17212yes—
382C2×M16C22⋊D4312yes—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—432no—
387#117—432no—
388#117—861no—
389#117—861no—
390#117—861no—
391C2×C4⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—432no—
396C2×C42—432no—
397C2×C42—861no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42—861no—
401C4⋊C8—868no—
402#104—864no—
403#104—864no—
404#104—868no—
405C22⋊C8—868no—
406C24—861no—
407C24#1062190211yescharacteristic
408#41—862no—
409#41—862no—
410#41—862no—
411#41—862no—
412#41—862no—
413#41—862no—
414#41—862no—
415#41—862no—
416#41—1721no—
417#41—1721no—
418#41—1721no—
419#41—1721no—
420#41—1721no—
421#41—1721no—
422#41—1721no—
423#41—1721no—
424C2×Q8—432no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×D4—432no—
431C2×D4—862no—
432C2×D4—862no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—861no—
437C2×D4—861no—
438C2×D4—1721no—
439C2×D4—1721no—
440C2×D4—1721no—
441C2×D4—1721no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—862no—
445C22×C4—861no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—1724no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4—1721no—
453C22×C4—1721no—
454C22×C4—1721no—
455C22×C4C2×C4×D4311yescharacteristic
456C22×C4C2×D17211yescharacteristic
457C22×C4#1062189811yescharacteristic
458C22×C4#1062189811yescharacteristic
459C22×C4#1062189811yescharacteristic
460C22×C4#1062189811yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4D4×D4311yescharacteristic
463C22×C4D4×D4311yescharacteristic
464C22×C4D4×D4311yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4#1062190011yescharacteristic
467C22×C4Q8×D4311yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—41no—
476M16—41no—
477M16—41no—
478M16—41no—
479M16—41no—
480M16—41no—
481M16—1721no—
482M16—1721no—
483M16—1721no—
484M16—1721no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—862no—
495C2×C8—862no—
496C2×C8—862no—
497C4⋊C4—862no—
498C4⋊C4—1721no—
499C22⋊C4—862no—
500C22⋊C4—1721no—
501C42—432no—
502C42—432no—
503C42—861no—
504C42—861no—
505C42—862no—
506C42—862no—
507C42—862no—
508C42—1721no—
509C23—42no—
510C23—862no—
511C23—3442no—
512C23—1721no—
513C23—1721no—
514C23#1306328711yescharacteristic
515C23#1306330011yescharacteristic
516C23#1306330111yescharacteristic
517C23#1306331011yescharacteristic
518C23#1306331011yescharacteristic
519C23#1306331011yescharacteristic
520C23#1306332011yescharacteristic
521Q8—862no—
522Q8—862no—
523Q8—1721no—
524Q8—1721no—
525D4—862no—
526D4—862no—
527D4—1722no—
528D4—1722no—
529D4—1722no—
530D4—1722no—
531D4—1721no—
532D4—1721no—
533C2×C4—864no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—3442no—
538C2×C4—1724no—
539C2×C4—1724no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4—1722no—
547C2×C4—1722no—
548C2×C4C22⋊C4×D4311yescharacteristic
549C2×C4C4⋊C4×D4311yescharacteristic
550C2×C4#1306328211yescharacteristic
551C2×C4(C22⋊D43)⋊C411yescharacteristic
552C2×C4C4×C22⋊D4311yescharacteristic
553C2×C4C4×D17211yescharacteristic
554C2×C4#1306329311yescharacteristic
555C2×C4#1306329511yescharacteristic
556C2×C4#1306329511yescharacteristic
557C2×C4#1306329711yescharacteristic
558C2×C4#1306329811yescharacteristic
559C2×C4#1306329811yescharacteristic
560C2×C4#1306329811yescharacteristic
561C2×C4#1306329811yescharacteristic
562C2×C4#1306329811yescharacteristic
563C2×C4#1306329911yescharacteristic
564C2×C4#1306330311yescharacteristic
565C2×C4#1306330311yescharacteristic
566C2×C4#1306330311yescharacteristic
567C2×C4#1306330311yescharacteristic
568C2×C4#1306330511yescharacteristic
569C2×C4#1306330711yescharacteristic
570C2×C4#1306330811yescharacteristic
571C2×C4#1306331111yescharacteristic
572C2×C4#1306331111yescharacteristic
573C2×C4#1306331311yescharacteristic
574C2×C4#1306331911yescharacteristic
575C2×C4#1306332111yescharacteristic
576C8—42no—
577C8—42no—
578C8—42no—
579C8—1722no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—3442no—
588C22—3442no—
589C22—1724no—
590C22—1722no—
591C22#1458277011yescharacteristic
592C22#1458277711yescharacteristic
593C22#1458278811yescharacteristic
594C22#1458281711yescharacteristic
595C22#1458282111yescharacteristic
596C22#1458282811yescharacteristic
597C22#1458283411yescharacteristic
598C4—864no—
599C4—3442no—
600C4—1722no—
601C4—1722no—
602C4#1458275811yescharacteristic
603C4#1458277311yescharacteristic
604C4#1458279011yescharacteristic
605C4#1458279911yescharacteristic
606C4#1458280811yescharacteristic
607C4#1458281211yescharacteristic
608C4#1458281411yescharacteristic
609C4#1458282311yescharacteristic
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—3442no—
617C2#1913283911yescharacteristic
618C2#1913483212yes—
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1738C2
socleC22×C43#385
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1738D43
hypocenterC43#11080
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1738

Complements

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

NH ≅ G/Ntype
1. C2×#14582922C2semidirect
5. C2×#14582671C2semidirect
6. C2×#14582660C2semidirect
7. C43×#1738C2semidirect
20. C2×#13063251C4semidirect
21. C2×#13063251C4semidirect
306. #1738D43semidirect
340. C43#11080semidirect

Maximal subgroups

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

subgroupindex
C2×#145829222
C2×#145829152
C22×#130632512
#191430392
C2×#145826712
C2×#145826602
C43×#17382
#1108043