Finite Group Databasebeta

← #25004196

Subgroups — #25004196

Order 11008.

826 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×#14582915C211yesmaximal, characteristic
2C2×#14582901C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic
4C2×#14582671C211yesmaximal, characteristic, complemented
5C2×#14582667C211yesmaximal, characteristic, complemented
6#19134315C211yesmaximal, characteristic, complemented
7C43×#1738C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12#14582915—22no—
13#14582915—22no—
14C2×#13063251—22no—
15#14582901—22no—
16#14582901—22no—
17C2×#13063250—21no—
18C2×#13063247—21no—
19#14582881—22no—
20#14582881C414yescomplemented
21C2×#13063243—21no—
22C2×#13063241—21no—
23#14582671—22no—
24#14582667—22no—
25#14582662—22no—
26C22×M16×C43C2211yescharacteristic
27C22×M16×C43C2211yescharacteristic
28C22×M16×C43C2211yescharacteristic
29C43×#341—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×#10621898C2×C412yes—
41C2×#10621898D412yes—
42C22×Dic86D411yescharacteristic
43C22×D172D411yescharacteristic
44C22×C22⋊D43—21no—
45C23×Dic43—21no—
46C22×C4×D43—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877C2×C412yes—
53C22×C43⋊C8—21no—
54#13063284—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284D412yes—
58C2×C4⋊Dic43—21no—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43D412yes—
65C2×C22⋊Dic43—21no—
66C2×C4×Dic43—21no—
67#13063251—28no—
68#13063250—24no—
69#13063247—24no—
70#13063243—24no—
71#13063241—24no—
72C23×C4×C43C2311yescharacteristic
73C2×M16×C43—21no—
74C2×M16×C43—21no—
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×C43C2×C412yes—
89C2×M16×C43D412yes—
90C2×M16×C43D412yes—
91C22×C8×C43—21no—
92C22×C8×C43—21no—
93C22×C8×C43—21no—
94C24×C43#4111yescharacteristic
95C23×D43—21no—
96C22×C4×C43C22×C411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C2×C22⋊D43—22no—
111C2×C22⋊D43—22no—
112C2×C22⋊D43—41no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C22×Dic43—22no—
117C22×Dic43—21no—
118C22×Dic43—41no—
119C22×Dic43—41no—
120C22×Dic43—41no—
121C22×Dic43—82no—
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×D172C22⋊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×Dic86C22⋊C412yes—
156M16×C43—22no—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—22no—
161M16×C43—22no—
162M16×C43—41no—
163M16×C43—41no—
164M16×C43—41no—
165M16×C43—41no—
166M16×C43—41no—
167M16×C43—41no—
168C2×C8×C43—22no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
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—41no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43—22no—
182C4⋊Dic43—41no—
183C4⋊Dic43—41no—
184C4⋊Dic43—41no—
185C4×Dic43—22no—
186C4×Dic43—41no—
187#10621877—22no—
188#10621877—22no—
189#10621877—41no—
190#10621877—41no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—41no—
193C2×C43⋊C8—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43#11711yescharacteristic
197C23×C43#12111yescharacteristic
198C23×C43#12311yescharacteristic
199C23×C43#12311yescharacteristic
200C23×C43#12311yescharacteristic
201C23×C43#12411yescharacteristic
202C23×C43#12611yescharacteristic
203C22×D43—22no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—81no—
207C22×D43—81no—
208C2×C4×C43C2×C22⋊C411yescharacteristic
209C2×C4×C43#11711yescharacteristic
210C2×C4×C43C4×D411yescharacteristic
211C2×C4×C43C4×D411yescharacteristic
212C2×C4×C43C4×D411yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12111yescharacteristic
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#12311yescharacteristic
224C2×C4×C43#12311yescharacteristic
225C2×C4×C43#12311yescharacteristic
226C2×C4×C43#12311yescharacteristic
227C2×C4×C43#12311yescharacteristic
228C2×C4×C43#12311yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12411yescharacteristic
231C2×C4×C43#12411yescharacteristic
232C2×C4×C43#12411yescharacteristic
233C2×C4×C43#12611yescharacteristic
234C2×C4×C43#12611yescharacteristic
235C2×C4×C43#12611yescharacteristic
236C22⋊D43—42no—
237C22⋊D43—42no—
238C22⋊D43—42no—
239C22⋊D43—42no—
240C2×Dic43—22no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—81no—
246C2×Dic43—81no—
247C2×Dic43—82no—
248C2×Dic43—82no—
249C2×Dic43—82no—
250D172—22no—
251D172—22no—
252D172—41no—
253D172—41no—
254C4×D43—42no—
255C4×D43—42no—
256C4×D43—42no—
257C4×D43—42no—
258Dic86—22no—
259Dic86—22no—
260Dic86—41no—
261Dic86—41no—
262C8×C43—42no—
263C8×C43—42no—
264C8×C43—42no—
265C43⋊C8—42no—
266#11152—431nomaximal, Sylow
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43#38111yescharacteristic
278C22×C43#38811yescharacteristic
279C22×C43#38811yescharacteristic
280C22×C43#39411yescharacteristic
281C22×C43#39411yescharacteristic
282C22×C43#39711yescharacteristic
283C22×C43#39711yescharacteristic
284C2×D43—42no—
285C2×D43—82no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—82no—
289C4×C43#38611yescharacteristic
290C4×C43#38611yescharacteristic
291C4×C43#38811yescharacteristic
292C4×C43#38811yescharacteristic
293C4×C43#39411yescharacteristic
294C4×C43#39411yescharacteristic
295C4×C43#39711yescharacteristic
296C4×C43#39711yescharacteristic
297Dic43—42no—
298Dic43—82no—
299Dic43—82no—
300C2×#421—431no—
301C2×#417—431no—
302C2×#413—431no—
303C2×#344—431no—
304C2×#343—431no—
305#1738D4311yescharacteristic, complemented
306#1736—431no—
307C2×C43—21no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—21no—
313C2×C43#144011yescharacteristic
314C2×C43#204811yescharacteristic
315C2×C43#204911yescharacteristic
316D43—82no—
317C22×#41—431no—
318C22×M16—431no—
319C22×M16C2×D4311yescharacteristic
320C22×M16C2×D4311yescharacteristic
321C22×M16C2×D4311yescharacteristic
322C2×#117—431no—
323C22×C4⋊C4—431no—
324#421—862no—
325#421—862no—
326C2×#104—862no—
327#417—862no—
328#417—862no—
329C2×#103—861no—
330C2×#102—861no—
331#413—434no—
332#413—862no—
333C2×#101—861no—
334C2×#100—861no—
335#344—862no—
336#343—862no—
337#341—22no—
338#340—862no—
339C43#1115211yescharacteristic, complemented, Sylow
340C2×#41—432no—
341C2×#41—432no—
342C2×#41—861no—
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—
352C22×Q8—431no—
353C22×D4—431no—
354C22×D4—861no—
355C23×C4—861no—
356C23×C4—861no—
357C23×C4C22×D4311yescharacteristic
358C2×M16—21no—
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—432no—
374C2×M16—861no—
375C2×M16—861no—
376C2×M16—861no—
377C2×M16—861no—
378C2×M16—861no—
379C2×M16C4×D4312yes—
380C2×M16D17212yes—
381C2×M16C22⋊D4312yes—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—861no—
386#117—432no—
387#117—861no—
388#117—861no—
389#117—861no—
390C2×C4⋊C4—432no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C42—861no—
399#104—868no—
400#103—864no—
401#102—864no—
402#101—864no—
403#100—864no—
404C24—861no—
405C24#1062190211yescharacteristic
406#41—862no—
407#41—862no—
408#41—862no—
409#41—862no—
410#41—862no—
411#41—862no—
412#41—862no—
413#41—862no—
414#41—1721no—
415#41—1721no—
416#41—1721no—
417#41—1721no—
418#41—1721no—
419#41—1721no—
420#41—1721no—
421#41—1721no—
422C2×Q8—432no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×D4—432no—
429C2×D4—862no—
430C2×D4—862no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—1721no—
437C2×D4—1721no—
438C2×D4—1721no—
439C2×D4—1721no—
440C22×C4—861no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—3442no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1721no—
450C22×C4—1721no—
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×C4D4×D4311yescharacteristic
462C22×C4#1062190011yescharacteristic
463C22×C4#1062190011yescharacteristic
464C22×C4#1062190211yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466M16—22no—
467M16—22no—
468M16—22no—
469M16—22no—
470M16—22no—
471M16—22no—
472M16—41no—
473M16—41no—
474M16—41no—
475M16—41no—
476M16—41no—
477M16—41no—
478M16—862no—
479M16—862no—
480M16—1721no—
481M16—1721no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—862no—
492C2×C8—1721no—
493C2×C8—1721no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—1721no—
498C4⋊C4—1721no—
499C4⋊C4—1721no—
500C22⋊C4—862no—
501C22⋊C4—1721no—
502C42—862no—
503C42—1721no—
504C23—41no—
505C23—41no—
506C23—862no—
507C23—3441no—
508C23—3441no—
509C23—1721no—
510C23—1721no—
511C23#1306328311yescharacteristic
512C23#1306330011yescharacteristic
513C23#1306331011yescharacteristic
514C23#1306331011yescharacteristic
515C23#1306331011yescharacteristic
516C23#1306331411yescharacteristic
517C23#1306332011yescharacteristic
518Q8—862no—
519Q8—862no—
520Q8—1721no—
521Q8—1721no—
522D4—862no—
523D4—862no—
524D4—1722no—
525D4—1722no—
526D4—1722no—
527D4—1722no—
528D4—1721no—
529D4—1721no—
530C2×C4—862no—
531C2×C4—3442no—
532C2×C4—3442no—
533C2×C4—3441no—
534C2×C4—3441no—
535C2×C4—3442no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4C22⋊C4×D4311yescharacteristic
545C2×C4#1306328211yescharacteristic
546C2×C4(C22⋊D43)⋊C411yescharacteristic
547C2×C4C4×C22⋊D4311yescharacteristic
548C2×C4#1306328711yescharacteristic
549C2×C4C4×D17211yescharacteristic
550C2×C4#1306329311yescharacteristic
551C2×C4#1306329511yescharacteristic
552C2×C4#1306329611yescharacteristic
553C2×C4#1306329711yescharacteristic
554C2×C4#1306329811yescharacteristic
555C2×C4#1306329811yescharacteristic
556C2×C4#1306329811yescharacteristic
557C2×C4#1306329911yescharacteristic
558C2×C4#1306330011yescharacteristic
559C2×C4#1306330711yescharacteristic
560C2×C4#1306330711yescharacteristic
561C2×C4#1306330711yescharacteristic
562C2×C4#1306330811yescharacteristic
563C2×C4#1306330911yescharacteristic
564C2×C4#1306331011yescharacteristic
565C2×C4#1306331011yescharacteristic
566C2×C4#1306331111yescharacteristic
567C2×C4#1306331111yescharacteristic
568C2×C4#1306331311yescharacteristic
569C2×C4#1306331911yescharacteristic
570C2×C4#1306332011yescharacteristic
571C2×C4#1306332011yescharacteristic
572C8—42no—
573C8—42no—
574C8—42no—
575C8—1722no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—3442no—
587C22—3442no—
588C22—3441no—
589C22—3441no—
590C22—1722no—
591C22#1458276111yescharacteristic
592C22#1458278911yescharacteristic
593C22#1458279111yescharacteristic
594C22#1458281611yescharacteristic
595C22#1458281711yescharacteristic
596C22#1458282511yescharacteristic
597C22#1458282811yescharacteristic
598C4—3442no—
599C4—3442no—
600C4—1722no—
601C4#1458277511yescharacteristic
602C4#1458277711yescharacteristic
603C4#1458278811yescharacteristic
604C4#1458279011yescharacteristic
605C4#1458281411yescharacteristic
606C4#1458281511yescharacteristic
607C4#1458282611yescharacteristic
608C4#1458282811yescharacteristic
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—3442no—
616C2#1913284311yescharacteristic
617C2#1913587011yescharacteristic
618C2#1913587711yescharacteristic
subgroupG/H
centerC22#14582816
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1738C2
socleC22×C43#394
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1738D43
hypocenterC43#11152
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1738

Complements

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

NH ≅ G/Ntype
4. C2×#14582671C2semidirect
5. C2×#14582667C2semidirect
6. #19134315C2semidirect
7. C43×#1738C2semidirect
20. #14582881C4semidirect
305. #1738D43semidirect
339. C43#11152semidirect

Maximal subgroups

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

subgroupindex
C2×#145829152
C2×#145829012
C2×#145828812
C2×#145826712
C2×#145826672
#191343152
C43×#17382
#1115243