Finite Group Databasebeta

← #25124136

Subgroups — #25124136

Order 11008.

1482 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583477C211yesmaximal, characteristic
2C2×#14582942C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic, complemented
4C2×#14582893C211yesmaximal, characteristic, complemented
5C2×#14582866C211yesmaximal, characteristic, complemented
6#19135798C212yesmaximal, complemented
7#19135791C212yesmaximal, complemented
8#19135784C212yesmaximal, complemented
9#19135777C212yesmaximal, complemented
10C2×#14582661C211yesmaximal, characteristic, complemented
11C43×#2311C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C23×C43⋊C8C2211yescharacteristic
15#14583477—24no—
16#14583477—24no—
17C2×#13063304C2212yes—
18C2×#13063301—21no—
19C2×#13063299C2212yes—
20C2×#13063297—22no—
21C2×#13063296—21no—
22C22×C4⋊Dic43C2211yescharacteristic
23#14582942—24no—
24C2×#13063258C2212yes—
25C2×#13063256C2212yes—
26#14582898—24no—
27#14582893—24no—
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2212yes—
30C2×#13063248C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2212yes—
33C2×#13063245C2211yescharacteristic
34#14582866—24no—
35C2×C22⋊(C43⋊C8)C2212yes—
36C2×C22⋊(C43⋊C8)C2212yes—
37#14582661C2212yes—
38#14582661C2212yes—
39C22×#41×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C22×C4⋊C4×C43C2211yescharacteristic
42C43×#391—21no—
43C43×#390—21no—
44C43×#386—22no—
45C43×#380C2212yes—
46C43×#380C2212yes—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898D414yes—
53C22×Dic86C2311yescharacteristic
54C22×D172C2311yescharacteristic
55C22×C22⋊D43—21no—
56C22×C22⋊D43—22no—
57C23×Dic43—21no—
58C22×C4×D43—21no—
59C2×#10621877—22no—
60C2×#10621877—22no—
61C2×#10621877D414yescomplemented
62C22×C43⋊C8—22no—
63C22×C43⋊C8—22no—
64C22×C43⋊C8—22no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2312yes—
68#13063304—24no—
69#13063304—24no—
70#13063301—28no—
71#13063299—24no—
72#13063299—24no—
73#13063297—216no—
74#13063296—28no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—22no—
77C2×C4⋊Dic43D414yes—
78C2×C4⋊Dic43C2312yes—
79C2×Dic43⋊C4—22no—
80C2×C22⋊Dic43—22no—
81C2×(C2×D43)⋊C4—22no—
82#13063258—24no—
83#13063256—24no—
84#13063248—22no—
85#13063248—22no—
86#13063248—24no—
87#13063245—22no—
88#13063245—22no—
89#13063245—24no—
90C22⋊(C43⋊C8)—24no—
91C22⋊(C43⋊C8)—24no—
92C2×#41×C43—22no—
93C2×#41×C43—22no—
94C2×#41×C43—22no—
95C2×#41×C43—22no—
96C2×#41×C43—22no—
97C2×#41×C43—22no—
98C22×Q8×C43D411yescharacteristic
99C22×D4×C43D411yescharacteristic
100C22×D4×C43D412yes—
101C23×C4×C43—21no—
102C23×C4×C43C2312yes—
103C23×C4×C43C2311yescharacteristic
104#117×C43—22no—
105#117×C43—22no—
106C2×C4⋊C4×C43—22no—
107C2×C4⋊C4×C43—22no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2312yes—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—22no—
114C2×C22⋊C4×C43—22no—
115C2×C42×C43—21no—
116#95×C43—22no—
117#95×C43—22no—
118C24×C43C2×D412yes—
119C24×C43C2×D411yescharacteristic
120C23×D43—21no—
121#41×C43—44no—
122#41×C43—44no—
123#41×C43—44no—
124#41×C43—44no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43—22no—
131C2×D4×C43—24no—
132C2×D4×C43—24no—
133C2×D4×C43—24no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—42no—
144C22×C4×C43—81no—
145C22×C4×C43—81no—
146C22×C4×C43C2×D412yes—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43#4112yes—
152C22×C4×C43#4112yes—
153C22×C4×C43#4112yes—
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—28no—
156C2×C22⋊D43—24no—
157C2×C22⋊D43—42no—
158C2×C22⋊D43—42no—
159C2×C22⋊D43—82no—
160C2×C22⋊D43—82no—
161C22×Dic43—24no—
162C22×Dic43—22no—
163C22×Dic43—21no—
164C22×Dic43—81no—
165C22×Dic43—81no—
166#10621898—28no—
167#10621898—28no—
168#10621898—44no—
169#10621898—44no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172C2×D412yes—
176C2×C4×D43—24no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86C2×D412yes—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—42no—
192C22⋊C4×C43—42no—
193C22⋊C4×C43—82no—
194C22⋊C4×C43—82no—
195C42×C43—42no—
196C22⋊Dic43—28no—
197(C2×D43)⋊C4—28no—
198C4⋊Dic43—24no—
199C4⋊Dic43—22no—
200C4⋊Dic43C2×D414yes—
201Dic43⋊C4—28no—
202#10621877—28no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—44no—
212C2×C43⋊C8C2×D414yes—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43#12012yes—
225C23×C43#12112yes—
226C23×C43#12312yes—
227C23×C43C22×D411yescharacteristic
228C22×D43—22no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235Q8×C43—44no—
236D4×C43—48no—
237D4×C43—44no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
248C2×C4×C43—41no—
249C2×C4×C43—42no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—84no—
255C2×C4×C43#12012yes—
256C2×C4×C43#12112yes—
257C2×C4×C43#12114yes—
258C2×C4×C43#12114yes—
259C2×C4×C43#12314yes—
260C2×C4×C43#12312yes—
261C2×C4×C43#12414yes—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C22⋊D43—48no—
269C22⋊D43—88no—
270C2×Dic43—22no—
271C2×Dic43—24no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—84no—
277D172—22no—
278D172—22no—
279D172—41no—
280D172—41no—
281C4×D43—48no—
282Dic86—22no—
283Dic86—22no—
284Dic86—41no—
285Dic86—41no—
286C43⋊C8—24no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#23485—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43#39414yes—
304C22×C43C2×#12011yescharacteristic
305C22×C43C2×#12111yescharacteristic
306C22×C43C2×#12311yescharacteristic
307C22×C43#57611yescharacteristic
308C22×C43#57711yescharacteristic
309C22×C43#57711yescharacteristic
310C22×C43#57811yescharacteristic
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C4×C43—42no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43—82no—
322C4×C43#39414yes—
323C4×C43C2×#12111yescharacteristic
324C4×C43C2×#12111yescharacteristic
325C4×C43C2×#12311yescharacteristic
326C4×C43C2×#12411yescharacteristic
327Dic43—42no—
328Dic43—44no—
329C2×#537—431no—
330C2×#428—431no—
331C2×#417—431no—
332C2×#416—431no—
333C2×#408—431no—
334#2311D4311yescharacteristic, complemented
335#2036—432no—
336#2035—432no—
337#2034—432no—
338#2033—432no—
339C2×#340—431no—
340C2×C43—24no—
341C2×C43—82no—
342C2×C43C2×#39411yescharacteristic
343C2×C43#301211yescharacteristic
344C2×C43#301311yescharacteristic
345C2×C43#306211yescharacteristic
346C2×C43#306311yescharacteristic
347C2×C43#309811yescharacteristic
348C2×C43#309911yescharacteristic
349D43—82no—
350C22×#41—431no—
351C22×#41C2×D4311yescharacteristic
352C22×M16—431no—
353C23×C8—431no—
354#537—864no—
355#537—864no—
356C2×C22⋊Q8—432no—
357C2×C22⋊Q8—861no—
358C2×#121—432no—
359C2×#121—861no—
360C2×#121—862no—
361C2×#117C2×D4311yescharacteristic
362C22×C4⋊C4—431no—
363C22×C4⋊C4C2×D4311yescharacteristic
364#428—864no—
365C2×#107—432no—
366C2×#106—432no—
367#417—864no—
368#416—864no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103—432no—
372C2×#102—431no—
373C2×#102—431no—
374C2×#102—432no—
375#408—864no—
376C2×C22⋊C8—432no—
377C2×C22⋊C8—432no—
378#391—21no—
379#390—21no—
380#386—22no—
381#380C2×D4312yes—
382#380C2×D4312yes—
383#340—432no—
384#340—432no—
385C43#2348511yescharacteristic, complemented, Sylow
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—22no—
389C2×#41—22no—
390C2×#41—22no—
391C2×#41—22no—
392C2×#41—434no—
393C2×#41—862no—
394C2×#41—862no—
395C2×#41—862no—
396C2×#41—862no—
397C2×#41—862no—
398C22×Q8—431no—
399C22×Q8C22⋊D4311yescharacteristic
400C22×D4—431no—
401C22×D4—862no—
402C22×D4—861no—
403C22×D4C22⋊D4312yes—
404C22×D4C22⋊D4311yescharacteristic
405C23×C4—21no—
406C23×C4—861no—
407C23×C4—861no—
408C23×C4C22×D4312yes—
409C23×C4C22×D4311yescharacteristic
410C2×M16—434no—
411C2×M16—862no—
412C2×M16—862no—
413C22×C8—432no—
414C22×C8—431no—
415C22×C8—431no—
416C22×C8—862no—
417C22×C8—862no—
418C22×C8—862no—
419C22⋊Q8—864no—
420C22⋊Q8—864no—
421C22⋊Q8—868no—
422#121—864no—
423#121—864no—
424#121—868no—
425#121—8616no—
426#117—22no—
427#117—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—434no—
432C2×C4⋊C4—432no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—862no—
436C2×C4⋊C4C22×D4312yes—
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—862no—
443C2×C22⋊C4—862no—
444C2×C42—21no—
445#107—864no—
446#106—864no—
447#103—864no—
448#103—862no—
449#103—862no—
450#102—864no—
451#102—862no—
452#102—862no—
453C22⋊C8—864no—
454C22⋊C8—864no—
455#95—22no—
456#95—22no—
457C24—861no—
458C24C2×C22⋊D4312yes—
459C24C2×C22⋊D4311yescharacteristic
460#41—44no—
461#41—44no—
462#41—44no—
463#41—44no—
464#41—868no—
465#41—868no—
466#41—1724no—
467#41—1724no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—432no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—432no—
484C2×D4—868no—
485C2×D4—864no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—3442no—
492C2×D4—3442no—
493C2×D4—1722no—
494C2×D4—1722no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—42no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—864no—
508C22×C4—862no—
509C22×C4—861no—
510C22×C4—864no—
511C22×C4—3441no—
512C22×C4—3441no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4#1062189812yes—
516C22×C4#1062189812yes—
517C22×C4D4×D4312yes—
518C22×C4D4×D4312yes—
519C22×C4D4×D4312yes—
520C22×C4#1062190012yes—
521C22×C4C2×C22⋊D4312yes—
522C22×C4C2×C22⋊D4311yescharacteristic
523C22×C4C23×D4311yescharacteristic
524M16—868no—
525C2×C8—434no—
526C2×C8—862no—
527C2×C8—862no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—1724no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—22no—
541C4⋊C4—42no—
542C4⋊C4—434no—
543C4⋊C4—868no—
544C4⋊C4—864no—
545C4⋊C4—862no—
546C22⋊C4—42no—
547C22⋊C4—82no—
548C22⋊C4—82no—
549C22⋊C4—868no—
550C22⋊C4—868no—
551C42—42no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—862no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23#1306329312yes—
571C23#1306329712yes—
572C23#1306330812yes—
573C23C22×C22⋊D4311yescharacteristic
574Q8—44no—
575Q8—862no—
576Q8—862no—
577Q8—1721no—
578Q8—1721no—
579D4—48no—
580D4—44no—
581D4—862no—
582D4—862no—
583D4—3448no—
584D4—1728no—
585D4—1721no—
586D4—1721no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—84no—
604C2×C4—864no—
605C2×C4—862no—
606C2×C4—3444no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1728no—
612C2×C4#1306329312yes—
613C2×C4#1306329712yes—
614C2×C4#1306329814yes—
615C2×C4#1306329814yes—
616C2×C4#1306330714yes—
617C2×C4#1306330812yes—
618C2×C4#1306331114yes—
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4C2×D4×D4311yescharacteristic
621C2×C4C2×D4×D4311yescharacteristic
622C2×C4C2×#1062190011yescharacteristic
623C2×C4C2×#1062189811yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C8—864no—
626C8—1721no—
627C8—1721no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—3441no—
642C22—3441no—
643C22—3441no—
644C22—3441no—
645C22—1722no—
646C22—1722no—
647C22—1722no—
648C22#1458281414yes—
649C22C2×#1306329311yescharacteristic
650C22C2×#1306329711yescharacteristic
651C22C2×#1306330811yescharacteristic
652C22#1458370211yescharacteristic
653C22#1458370711yescharacteristic
654C22#1458371011yescharacteristic
655C22#1458371411yescharacteristic
656C4—42no—
657C4—82no—
658C4—81no—
659C4—81no—
660C4—1722no—
661C4—1724no—
662C4#1458281414yes—
663C4C2×#1306329811yescharacteristic
664C4C2×#1306329811yescharacteristic
665C4C2×#1306330711yescharacteristic
666C4C2×#1306331111yescharacteristic
667C2—24no—
668C2—82no—
669C2—3442no—
670C2C2×#1458281411yescharacteristic
671C2#1914389611yescharacteristic
672C2#1914390711yescharacteristic
673C2#1914427111yescharacteristic
674C2#1914428211yescharacteristic
675C2#1914457311yescharacteristic
676C2#1914458411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2311C2
socleC23×C43C22×D4
prime radicalC2×#14583477C2
hypercenter#2311D43
hypocenterC43#23485
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#14582942C2semidirect
3. C2×#14582898C2semidirect
4. C2×#14582893C2semidirect
5. C2×#14582866C2semidirect
6. #19135798C2semidirect
7. #19135791C2semidirect
8. #19135784C2semidirect
9. #19135777C2semidirect
10. C2×#14582661C2semidirect
11. C43×#2311C2semidirect
61. C2×#10621877D4semidirect
334. #2311D43semidirect
385. C43#23485semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
C2×#145829422
C2×#145828982
C2×#145828932
C2×#145828662
#191357982
#191357912
#191357842
#191357772
C2×#145826612
C43×#23112
#2348543