Finite Group Databasebeta

← #25004169

Subgroups — #25004169

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582881C211yesmaximal, characteristic
2C2×#14582872C211yesmaximal, characteristic
3#19137085C211yesmaximal, characteristic
4C2×#14582659C211yesmaximal, characteristic, complemented
5C2×#14582656C211yesmaximal, characteristic, complemented
6C2×#14582655C211yesmaximal, characteristic, complemented
7C2×C43×#339C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582881—22no—
13#14582881—22no—
14C2×#13063243—21no—
15C2×#13063241—21no—
16#14582872—22no—
17#14582872—22no—
18C2×#13063239—22no—
19#14582805—21no—
20#14582801—21no—
21#14582778—22no—
22C4×(C2×D43)⋊C4C414yescomplemented
23#14582659—22no—
24#14582656—22no—
25#14582655—22no—
26C22×M16×C43C2211yescharacteristic
27C2×#117×C43C2211yescharacteristic
28C22×C42×C43C2211yescharacteristic
29C43×#339—22no—
30C2×#10621898—21no—
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×#10621898—21no—
42C22×Dic86D411yescharacteristic
43C22×D172D411yescharacteristic
44C22×C22⋊D43D412yes—
45C22×C4×D43C2×C412yes—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877D412yes—
52C22×C43⋊C8—21no—
53#13063284—21no—
54#13063284—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284—21no—
59#13063284—21no—
60#13063284D412yes—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C22⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×(C2×D43)⋊C4—24no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43C2×C412yes—
68#13063243—24no—
69#13063241—24no—
70#13063239—28no—
71C43⋊#95—24no—
72C23×C4×C43—21no—
73C23×C4×C43C2311yescharacteristic
74C2×M16×C43—21no—
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43D412yes—
80C22×C8×C43—21no—
81#117×C43—21no—
82#117×C43—21no—
83#117×C43—21no—
84#117×C43D412yes—
85C2×C4⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C42×C43—21no—
88C2×C42×C43—21no—
89C2×C42×C43—21no—
90C2×C42×C43—21no—
91C2×C42×C43—21no—
92C2×C42×C43—21no—
93C2×C42×C43C2×C412yes—
94C24×C43C2×D411yescharacteristic
95C23×D43C22⋊C412yes—
96C22×C4×C43—22no—
97C22×C4×C43—44no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43C22×C411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C2×C22⋊D43—22no—
116C2×C22⋊D43—22no—
117C2×C22⋊D43—22no—
118C2×C22⋊D43—22no—
119C2×C22⋊D43—22no—
120C2×C22⋊D43—22no—
121C22×Dic43—22no—
122C22×Dic43—41no—
123C22×Dic43C22⋊C412yes—
124#10621898—41no—
125#10621898—41no—
126#10621898—41no—
127#10621898—41no—
128#10621898—41no—
129#10621898—41no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138#10621898—41no—
139#10621898—41no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—41no—
161M16×C43—41no—
162C2×C8×C43—22no—
163C2×C8×C43—41no—
164C2×C8×C43—41no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—41no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—41no—
169C42×C43—22no—
170C42×C43—22no—
171C42×C43—22no—
172C42×C43—41no—
173C42×C43—41no—
174C42×C43—41no—
175C22⋊Dic43—22no—
176C22⋊Dic43—41no—
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179(C2×D43)⋊C4—48no—
180C4⋊Dic43—22no—
181C4⋊Dic43—41no—
182C4⋊Dic43—41no—
183C4⋊Dic43—41no—
184C4×Dic43—22no—
185C4×Dic43—22no—
186C4×Dic43—22no—
187C4×Dic43—41no—
188#10621877—22no—
189#10621877—22no—
190#10621877—41no—
191#10621877—41no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—41no—
194C2×C43⋊C8—41no—
195C23×C43—42no—
196C23×C43C2×C22⋊C411yescharacteristic
197C23×C43#12011yescharacteristic
198C23×C43#12111yescharacteristic
199C23×C43#12111yescharacteristic
200C23×C43#12311yescharacteristic
201C23×C43#12311yescharacteristic
202C23×C43#12311yescharacteristic
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—44no—
207C2×C4×C43—24no—
208C2×C4×C43—42no—
209C2×C4×C43—44no—
210C2×C4×C43—44no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—82no—
214C2×C4×C43#11711yescharacteristic
215C2×C4×C43#11711yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43C4×D411yescharacteristic
218C2×C4×C43C4×D411yescharacteristic
219C2×C4×C43C4×D411yescharacteristic
220C2×C4×C43#12011yescharacteristic
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×C43#12311yescharacteristic
228C2×C4×C43#12311yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C2×C4×C43#12311yescharacteristic
232C2×C4×C43#12311yescharacteristic
233C2×C4×C43#12311yescharacteristic
234C2×C4×C43#12411yescharacteristic
235C2×C4×C43#12411yescharacteristic
236C2×C4×C43#12411yescharacteristic
237C2×C4×C43#12411yescharacteristic
238C2×C4×C43#12611yescharacteristic
239C2×C4×C43#12611yescharacteristic
240C2×C4×C43#12611yescharacteristic
241C2×C4×C43#12611yescharacteristic
242C22⋊D43—42no—
243C22⋊D43—42no—
244C22⋊D43—42no—
245C22⋊D43—42no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—44no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—82no—
253D172—41no—
254D172—41no—
255D172—41no—
256D172—41no—
257C4×D43—42no—
258C4×D43—42no—
259C4×D43—42no—
260C4×D43—42no—
261Dic86—41no—
262Dic86—41no—
263Dic86—41no—
264Dic86—41no—
265C8×C43—42no—
266C43⋊C8—42no—
267#11148—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43#38111yescharacteristic
276C22×C43#38611yescharacteristic
277C22×C43#38611yescharacteristic
278C22×C43#39411yescharacteristic
279C22×C43#39411yescharacteristic
280C22×C43#39711yescharacteristic
281C22×C43#39711yescharacteristic
282C2×D43—44no—
283C2×D43—42no—
284C2×D43—82no—
285C2×D43—82no—
286C4×C43—44no—
287C4×C43—82no—
288C4×C43#38811yescharacteristic
289C4×C43#38811yescharacteristic
290C4×C43#38811yescharacteristic
291C4×C43#38811yescharacteristic
292C4×C43#39411yescharacteristic
293C4×C43#39411yescharacteristic
294C4×C43#39711yescharacteristic
295C4×C43#39711yescharacteristic
296Dic43—42no—
297Dic43—82no—
298Dic43—82no—
299C2×#413—431no—
300C2×#410—431no—
301#2297—431no—
302C2×#339—431no—
303C2×#339D4311yescharacteristic, complemented
304C2×H(3,ℤ/4)—431no—
305C2×H(3,ℤ/4)—431no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43#144011yescharacteristic
313C2×C43#182712yes—
314D43—82no—
315C22×#41—431no—
316C22×M16—431no—
317C22×M16C2×D4311yescharacteristic
318C2×#117—431no—
319C2×#117—431no—
320C2×#117C2×D4311yescharacteristic
321C22×C42C2×D4311yescharacteristic
322#413—862no—
323#413—862no—
324C2×#101—861no—
325C2×#100—861no—
326#410—862no—
327#410—862no—
328C2×#99—862no—
329#391—861no—
330#390—861no—
331#386—862no—
332C4×C22⋊C4—434no—
333#339—22no—
334#339—862no—
335H(3,ℤ/4)—862no—
336H(3,ℤ/4)—862no—
337C43#1114811yescharacteristic, complemented, Sylow
338C2×#41—861no—
339C2×#41—861no—
340C2×#41—861no—
341C2×#41—861no—
342C2×#41—861no—
343C2×#41—861no—
344C2×#41—861no—
345C2×#41—861no—
346C2×#41—861no—
347C2×#41—861no—
348C2×#41—861no—
349C2×#41—861no—
350C22×Q8—431no—
351C22×D4—432no—
352C22×D4—431no—
353C23×C4—21no—
354C23×C4—432no—
355C23×C4C22×D4311yescharacteristic
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×M16C22⋊D4312yes—
368C22×C8—21no—
369C22×C8—861no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—432no—
374#117—861no—
375#117—861no—
376#117—861no—
377#117—861no—
378#117—861no—
379#117—861no—
380#117—861no—
381#117D17212yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—864no—
388C2×C22⋊C4—861no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—432no—
396C2×C42—861no—
397C2×C42C4×D4312yes—
398#101—864no—
399#100—864no—
400#99—868no—
401#95—864no—
402C24—432no—
403C24D4×D4311yescharacteristic
404#41—1721no—
405#41—1721no—
406#41—1721no—
407#41—1721no—
408#41—1721no—
409#41—1721no—
410#41—1721no—
411#41—1721no—
412#41—1721no—
413#41—1721no—
414#41—1721no—
415#41—1721no—
416#41—1721no—
417#41—1721no—
418#41—1721no—
419#41—1721no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×D4—862no—
427C2×D4—862no—
428C2×D4—862no—
429C2×D4—862no—
430C2×D4—862no—
431C2×D4—862no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—861no—
437C2×D4—861no—
438C22×C4—22no—
439C22×C4—44no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—432no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—1721no—
452C22×C4C2×C4×D4311yescharacteristic
453C22×C4C2×D17211yescharacteristic
454C22×C4#1062189811yescharacteristic
455C22×C4#1062189811yescharacteristic
456C22×C4#1062189811yescharacteristic
457C22×C4#1062189811yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4#1062190011yescharacteristic
462C22×C4#1062190011yescharacteristic
463C22×C4#1062190211yescharacteristic
464C22×C4#1062190211yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466M16—22no—
467M16—22no—
468M16—41no—
469M16—41no—
470M16—862no—
471M16—862no—
472M16—1721no—
473M16—1721no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—862no—
478C2×C8—1721no—
479C2×C8—1721no—
480C4⋊C4—22no—
481C4⋊C4—41no—
482C4⋊C4—862no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C22⋊C4—22no—
487C22⋊C4—41no—
488C22⋊C4—862no—
489C22⋊C4—1728no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C42—22no—
494C42—22no—
495C42—22no—
496C42—41no—
497C42—41no—
498C42—41no—
499C42—862no—
500C42—862no—
501C42—862no—
502C42—1721no—
503C23—42no—
504C23—862no—
505C23—862no—
506C23—862no—
507C23—1724no—
508C23C22⋊C4×D4311yescharacteristic
509C23#1306329511yescharacteristic
510C23#1306329611yescharacteristic
511C23#1306329811yescharacteristic
512C23#1306330711yescharacteristic
513C23#1306331011yescharacteristic
514C23#1306331011yescharacteristic
515Q8—1721no—
516Q8—1721no—
517Q8—1721no—
518Q8—1721no—
519D4—1722no—
520D4—1722no—
521D4—1722no—
522D4—1722no—
523D4—1721no—
524D4—1721no—
525D4—1721no—
526D4—1721no—
527C2×C4—24no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—82no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—3442no—
538C2×C4—1724no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4#1306328211yescharacteristic
546C2×C4#1306328311yescharacteristic
547C2×C4(C22⋊D43)⋊C411yescharacteristic
548C2×C4C4×C22⋊D4311yescharacteristic
549C2×C4#1306328711yescharacteristic
550C2×C4C4×D17211yescharacteristic
551C2×C4#1306329311yescharacteristic
552C2×C4#1306329711yescharacteristic
553C2×C4#1306329811yescharacteristic
554C2×C4#1306329811yescharacteristic
555C2×C4#1306329911yescharacteristic
556C2×C4#1306330011yescharacteristic
557C2×C4#1306330011yescharacteristic
558C2×C4#1306330711yescharacteristic
559C2×C4#1306330711yescharacteristic
560C2×C4#1306330811yescharacteristic
561C2×C4#1306330911yescharacteristic
562C2×C4#1306331011yescharacteristic
563C2×C4#1306331011yescharacteristic
564C2×C4#1306331011yescharacteristic
565C2×C4#1306331111yescharacteristic
566C2×C4#1306331111yescharacteristic
567C2×C4#1306331311yescharacteristic
568C2×C4#1306331411yescharacteristic
569C2×C4#1306331911yescharacteristic
570C2×C4#1306332011yescharacteristic
571C2×C4#1306332011yescharacteristic
572C2×C4#1306332011yescharacteristic
573C8—42no—
574C8—1722no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—3442no—
583C22—3442no—
584C22—1722no—
585C22—1724no—
586C22#1458276111yescharacteristic
587C22#1458277511yescharacteristic
588C22#1458277711yescharacteristic
589C22#1458281511yescharacteristic
590C22#1458281711yescharacteristic
591C22#1458282511yescharacteristic
592C22#1458282811yescharacteristic
593C4—44no—
594C4—82no—
595C4—3442no—
596C4—3442no—
597C4—1722no—
598C4#1458278811yescharacteristic
599C4#1458278911yescharacteristic
600C4#1458279011yescharacteristic
601C4#1458279111yescharacteristic
602C4#1458281411yescharacteristic
603C4#1458281611yescharacteristic
604C4#1458282611yescharacteristic
605C4#1458282811yescharacteristic
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—3442no—
613C2#1913284311yescharacteristic
614C2#1913469812yes—
subgroupG/H
centerC2×C4#13063283
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#339C2
socleC22×C43#381
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#339D43
hypocenterC43#11148
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#14582659C2semidirect
5. C2×#14582656C2semidirect
6. C2×#14582655C2semidirect
7. C2×C43×#339C2semidirect
22. C4×(C2×D43)⋊C4C4semidirect
303. C2×#339D43semidirect
337. C43#11148semidirect

Maximal subgroups

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

subgroupindex
C2×#145828812
C2×#145828722
#191370852
C2×#145826592
C2×#145826562
C2×#145826552
C2×C43×#3392
#1114843