Finite Group Databasebeta

← #25123467

Subgroups — #25123467

Order 11008.

2014 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063358C211yesmaximal, characteristic, complemented
2C2×#14583477C211yesmaximal, characteristic
3C2×#14583470C211yesmaximal, characteristic, complemented
4C2×#14582896C211yesmaximal, characteristic, complemented
5C22×#13063250C211yesmaximal, characteristic, complemented
6#19135605C214yesmaximal, complemented
7#19135600C214yesmaximal, complemented
8#19134315C211yesmaximal, characteristic, complemented
9C2×C43×#408C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11C23×Dic86C2211yescharacteristic
12C2×#13063358—24no—
13C2×#13063358—24no—
14C2×#13063358—24no—
15C22×Dic172C2212yes—
16C22×#10621873C2212yes—
17#14583477—24no—
18#14583477—24no—
19#14583470—24no—
20#14583470—24no—
21C2×#13063323—21no—
22C2×#13063312—21no—
23C2×#13063306—22no—
24C2×#13063304C2214yes—
25C2×#13063304C2212yes—
26C2×#13063301—21no—
27C2×#13063299C2212yes—
28C2×#13063297—22no—
29C2×#13063296—21no—
30C2×#13063284C2211yescharacteristic
31C22×C4⋊Dic43C2211yescharacteristic
32#14582896—24no—
33C2×#13063250—24no—
34C2×#13063250C2214yes—
35C2×#13063250C2212yes—
36C2×#13063247C2212yes—
37#14582662C2214yes—
38C22×#41×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C23×C8×C43C2211yescharacteristic
41C43×#408—24no—
42C2×C22⋊C8×C43C2214yes—
43C2×#10621898—22no—
44C2×#10621898—22no—
45C2×#10621898—22no—
46C2×#10621898—22no—
47C2×#10621898—22no—
48C2×#10621898D414yes—
49C22×Dic86—22no—
50C22×Dic86—22no—
51C22×Dic86—22no—
52C22×Dic86—22no—
53C22×Dic86—21no—
54C22×Dic86—22no—
55C22×Dic86D414yescomplemented
56C22×Dic86C2312yes—
57C22×Dic86C2311yescharacteristic
58C22×D172C2311yescharacteristic
59C22×C22⋊D43—21no—
60C22×C22⋊D43—22no—
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C4×D43—21no—
64#13063358—232no—
65C2×Dic172—24no—
66C2×Dic172—24no—
67C2×Dic172—24no—
68C2×#10621873—24no—
69C2×#10621873—24no—
70C2×#10621873—24no—
71#13063323—28no—
72#13063312—28no—
73#13063306—216no—
74#13063304—28no—
75#13063304—24no—
76#13063304—28no—
77#13063304—24no—
78#13063301—28no—
79#13063299—24no—
80#13063299—24no—
81#13063297—216no—
82#13063296—28no—
83#13063284—22no—
84#13063284D414yescomplemented
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—22no—
87C2×C4⋊Dic43D414yes—
88C2×C4⋊Dic43C2312yes—
89C2×C4⋊Dic43C2312yes—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—24no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—22no—
94C2×C22⋊Dic43—24no—
95C2×(C2×D43)⋊C4—22no—
96C2×C4×Dic43—21no—
97#13063250—28no—
98#13063250—24no—
99#13063247—24no—
100C2×#41×C43—22no—
101C2×#41×C43—22no—
102C2×#41×C43—22no—
103C2×#41×C43—22no—
104C2×#41×C43—22no—
105C2×#41×C43—22no—
106C22×Q8×C43D411yescharacteristic
107C22×D4×C43D411yescharacteristic
108C22×D4×C43D412yes—
109C23×C4×C43C2312yes—
110C23×C4×C43C2311yescharacteristic
111C2×M16×C43—22no—
112C2×M16×C43—22no—
113C2×M16×C43D414yescomplemented
114C22×C8×C43—22no—
115C22×C8×C43—22no—
116C22×C8×C43—22no—
117C22×C8×C43C2312yes—
118C22×C8×C43C2312yes—
119C22⋊C8×C43—28no—
120C24×C43C2×D412yes—
121C24×C43C2×D411yescharacteristic
122C23×D43—21no—
123#41×C43—44no—
124#41×C43—44no—
125#41×C43—44no—
126#41×C43—44no—
127C2×Q8×C43—22no—
128C2×Q8×C43—22no—
129C2×Q8×C43—22no—
130C2×D4×C43—22no—
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43—24no—
134C2×D4×C43—24no—
135C2×D4×C43—24no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43C2×D412yes—
143C22×C4×C43C2×D412yes—
144C22×C4×C43C2×D412yes—
145C22×C4×C43C2×D412yes—
146C22×C4×C43C2×D412yes—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43#4112yes—
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—28no—
152C2×C22⋊D43—24no—
153C2×C22⋊D43—42no—
154C2×C22⋊D43—42no—
155C2×C22⋊D43—84no—
156C22×Dic43—24no—
157C22×Dic43—24no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—21no—
161C22×Dic43—22no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43—82no—
165#10621898—28no—
166#10621898—28no—
167#10621898—44no—
168#10621898—44no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172C2×D412yes—
175C2×C4×D43—24no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×Dic86—28no—
179C2×Dic86—28no—
180C2×Dic86—22no—
181C2×Dic86—21no—
182C2×Dic86—22no—
183C2×Dic86—22no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—22no—
187C2×Dic86—21no—
188C2×Dic86—24no—
189C2×Dic86—22no—
190C2×Dic86—21no—
191C2×Dic86—42no—
192C2×Dic86—44no—
193C2×Dic86—42no—
194C2×Dic86—44no—
195C2×Dic86C2×D414yes—
196C2×Dic86C2×D412yes—
197M16×C43—28no—
198C2×C8×C43—22no—
199C2×C8×C43—22no—
200C2×C8×C43—22no—
201C2×C8×C43—22no—
202C2×C8×C43—22no—
203C2×C8×C43—44no—
204C2×C8×C43C2×D414yes—
205C22⋊Dic43—28no—
206C22⋊Dic43—216no—
207C22⋊Dic43—24no—
208(C2×D43)⋊C4—28no—
209C4⋊Dic43—24no—
210C4⋊Dic43—22no—
211C4⋊Dic43—22no—
212C4⋊Dic43C2×D414yes—
213C4⋊Dic43C2×D414yes—
214Dic43⋊C4—28no—
215Dic43⋊C4—216no—
216C4×Dic43—24no—
217Dic172—216no—
218#10621873—216no—
219C23×C43—22no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43—24no—
225C23×C43—24no—
226C23×C43#12012yes—
227C23×C43#12012yes—
228C23×C43#12112yes—
229C23×C43C22×D411yescharacteristic
230C22×D43—22no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—42no—
234C22×D43—42no—
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#12014yes—
246C2×C4×C43#12012yes—
247C2×C4×C43#12012yes—
248C2×C4×C43#12114yes—
249C2×C4×C43#12114yes—
250C2×C4×C43#12112yes—
251C2×C4×C43#12714yes—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C22⋊D43—48no—
259C22⋊D43—88no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—22no—
263C2×Dic43—24no—
264C2×Dic43—42no—
265C2×Dic43—41no—
266C2×Dic43—42no—
267C2×Dic43—41no—
268C2×Dic43—42no—
269C2×Dic43—44no—
270C2×Dic43—42no—
271C2×Dic43—48no—
272C2×Dic43—84no—
273D172—22no—
274D172—22no—
275D172—41no—
276D172—41no—
277C4×D43—48no—
278Dic86—24no—
279Dic86—22no—
280Dic86—24no—
281Dic86—22no—
282Dic86—42no—
283Dic86—41no—
284Dic86—42no—
285Dic86—41no—
286Dic86—48no—
287C8×C43—24no—
288C8×C43—42no—
289#23394—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—24no—
293C22×C43—24no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—44no—
298C22×C43—44no—
299C22×C43#39214yes—
300C22×C43C2×#12011yescharacteristic
301C22×C43C2×#12011yescharacteristic
302C22×C43C2×#12111yescharacteristic
303C22×C43#57712yes—
304C22×C43#57812yes—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—82no—
309C2×D43—82no—
310C4×C43—42no—
311C4×C43#39214yes—
312C4×C43C2×#12011yescharacteristic
313C4×C43C2×#12111yescharacteristic
314C4×C43C2×#12111yescharacteristic
315C4×C43C2×#12711yescharacteristic
316Dic43—44no—
317Dic43—42no—
318Dic43—44no—
319Dic43—44no—
320C22×#137—431no—
321C2×#537—431no—
322C2×#536—431no—
323C2×#416—431no—
324C22×#103—431no—
325C2×#408D4311yescharacteristic, complemented
326#2001—434no—
327#2000—434no—
328#1736—431no—
329C2×C43—24no—
330C2×C43—82no—
331C2×C43C2×#39211yescharacteristic
332C2×C43#300911yescharacteristic
333C2×C43#301111yescharacteristic
334C2×C43#301312yes—
335C2×C43#306312yes—
336D43—82no—
337C22×#41—431no—
338C22×#41C2×D4311yescharacteristic
339C23×Q8—431no—
340C2×#137—864no—
341C2×#137—864no—
342C2×#137—864no—
343C22×Q16—432no—
344C22×SD16—432no—
345C22×M16C2×D4311yescharacteristic
346C23×C8C2×D4311yescharacteristic
347#537—864no—
348#537—864no—
349#536—864no—
350#536—864no—
351C2×C4⋊Q8—861no—
352C2×#124—861no—
353C2×#123—862no—
354C2×C22⋊Q8—434no—
355C2×C22⋊Q8—432no—
356C2×C22⋊Q8—861no—
357C2×#121—432no—
358C2×#121—861no—
359C2×#121—862no—
360C2×#117—431no—
361C22×C4⋊C4—431no—
362#416—864no—
363C2×#103—434no—
364C2×#103—432no—
365C2×#103—864no—
366C2×#102—432no—
367#408—24no—
368C2×C22⋊C8C2×D4314yes—
369#340—434no—
370C43#2339411yescharacteristic, complemented, Sylow
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—434no—
378C2×#41—862no—
379C2×#41—862no—
380C2×#41—862no—
381C2×#41—862no—
382C2×#41—862no—
383C22×Q8—434no—
384C22×Q8—432no—
385C22×Q8—431no—
386C22×Q8—861no—
387C22×Q8—862no—
388C22×Q8—862no—
389C22×Q8—862no—
390C22×Q8—862no—
391C22×Q8—862no—
392C22×Q8D17211yescharacteristic
393C22×D4—431no—
394C22×D4—862no—
395C22×D4—861no—
396C22×D4D17212yes—
397C22×D4D17211yescharacteristic
398C23×C4—861no—
399C23×C4—861no—
400C23×C4—861no—
401C23×C4C22×D4312yes—
402C23×C4C22×D4311yescharacteristic
403#137—8632no—
404C2×Q16—864no—
405C2×Q16—864no—
406C2×Q16—864no—
407C2×SD16—864no—
408C2×SD16—864no—
409C2×SD16—864no—
410C2×M16—22no—
411C2×M16—22no—
412C2×M16C22⋊D4314yescomplemented
413C22×C8—22no—
414C22×C8—22no—
415C22×C8—22no—
416C22×C8C22×D4312yes—
417C22×C8C22×D4312yes—
418C4⋊Q8—868no—
419#124—868no—
420#123—8616no—
421C22⋊Q8—868no—
422C22⋊Q8—864no—
423C22⋊Q8—868no—
424C22⋊Q8—864no—
425C22⋊Q8—868no—
426#121—864no—
427#121—864no—
428#121—868no—
429#121—8616no—
430#117—434no—
431#117—862no—
432C2×C4⋊C4—434no—
433C2×C4⋊C4—432no—
434C2×C4⋊C4—432no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—862no—
437C2×C4⋊C4—864no—
438C2×C4⋊C4—862no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—862no—
441C2×C22⋊C4—864no—
442C2×C22⋊C4—862no—
443C2×C42—861no—
444#103—868no—
445#103—864no—
446#102—864no—
447C22⋊C8—28no—
448C24—861no—
449C24C2×D17212yes—
450C24C2×D17211yescharacteristic
451#41—44no—
452#41—44no—
453#41—44no—
454#41—44no—
455#41—868no—
456#41—868no—
457#41—1724no—
458#41—1724no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—434no—
463C2×Q8—432no—
464C2×Q8—864no—
465C2×Q8—862no—
466C2×Q8—861no—
467C2×Q8—868no—
468C2×Q8—868no—
469C2×Q8—862no—
470C2×Q8—861no—
471C2×Q8—862no—
472C2×Q8—861no—
473C2×Q8—862no—
474C2×Q8—861no—
475C2×Q8—862no—
476C2×Q8—861no—
477C2×Q8—1722no—
478C2×Q8—1724no—
479C2×Q8—1722no—
480C2×Q8—1724no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—432no—
488C2×D4—868no—
489C2×D4—864no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—3444no—
496C2×D4—1722no—
497C2×D4—1722no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—864no—
505C22×C4—864no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—861no—
509C22×C4—862no—
510C22×C4—864no—
511C22×C4—3442no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4—1722no—
516C22×C4C2×D17212yes—
517C22×C4C2×D17211yescharacteristic
518C22×C4#1062189812yes—
519C22×C4D4×D4312yes—
520C22×C4D4×D4312yes—
521C22×C4D4×D4312yes—
522C22×C4D4×D4312yes—
523C22×C4C2×C22⋊D4312yes—
524C22×C4C23×D4311yescharacteristic
525Q16—8616no—
526SD16—8616no—
527M16—28no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—44no—
534C2×C8C2×C22⋊D4314yes—
535C4⋊C4—434no—
536C4⋊C4—434no—
537C4⋊C4—868no—
538C4⋊C4—8616no—
539C4⋊C4—864no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C22⋊C4—868no—
543C22⋊C4—868no—
544C22⋊C4—8616no—
545C22⋊C4—864no—
546C42—864no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—24no—
553C23—24no—
554C23—862no—
555C23—1721no—
556C23—1721no—
557C23—1722no—
558C23—1722no—
559C23#1306329512yes—
560C23#1306329512yes—
561C23#1306329912yes—
562C23C22×D17211yescharacteristic
563Q8—44no—
564Q8—864no—
565Q8—862no—
566Q8—864no—
567Q8—862no—
568Q8—1728no—
569Q8—1722no—
570Q8—1721no—
571Q8—1722no—
572Q8—1721no—
573D4—48no—
574D4—44no—
575D4—862no—
576D4—862no—
577D4—3448no—
578D4—1728no—
579D4—1721no—
580D4—1721no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—864no—
589C2×C4—864no—
590C2×C4—862no—
591C2×C4—864no—
592C2×C4—3444no—
593C2×C4—1728no—
594C2×C4—1721no—
595C2×C4—1722no—
596C2×C4—1721no—
597C2×C4—1722no—
598C2×C4—1724no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1728no—
602C2×C4#1306329314yes—
603C2×C4#1306329512yes—
604C2×C4#1306329512yes—
605C2×C4#1306329814yes—
606C2×C4#1306329814yes—
607C2×C4#1306329912yes—
608C2×C4#1306332114yes—
609C2×C4C2×D4×D4311yescharacteristic
610C2×C4C2×D4×D4311yescharacteristic
611C2×C4C2×D4×D4311yescharacteristic
612C2×C4C2×D4×D4311yescharacteristic
613C2×C4C22×C22⋊D4311yescharacteristic
614C2×C4C2×#1062189811yescharacteristic
615C8—24no—
616C8—42no—
617C22—24no—
618C22—22no—
619C22—22no—
620C22—24no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—44no—
625C22—42no—
626C22—3442no—
627C22—3442no—
628C22—1722no—
629C22—1722no—
630C22—1722no—
631C22#1458280814yes—
632C22C2×#1306329511yescharacteristic
633C22C2×#1306329511yescharacteristic
634C22C2×#1306329911yescharacteristic
635C22#1458371112yes—
636C22#1458371612yes—
637C4—42no—
638C4—1724no—
639C4—1724no—
640C4—1722no—
641C4—1724no—
642C4#1458280814yes—
643C4C2×#1306329311yescharacteristic
644C4C2×#1306329811yescharacteristic
645C4C2×#1306329811yescharacteristic
646C4C2×#1306332111yescharacteristic
647C2—24no—
648C2—82no—
649C2—3442no—
650C2C2×#1458280811yescharacteristic
651C2#1914387411yescharacteristic
652C2#1914389211yescharacteristic
653C2#1914391312yes—
654C2#1914428612yes—
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#408C2
socleC23×C43C22×D4
prime radicalC2×#14583477C2
hypercenterC2×#408D43
hypocenterC43#23394
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C22×#13063358C2semidirect
3. C2×#14583470C2semidirect
4. C2×#14582896C2semidirect
5. C22×#13063250C2semidirect
6. #19135605C2semidirect
7. #19135600C2semidirect
8. #19134315C2semidirect
9. C2×C43×#408C2semidirect
55. C22×Dic86D4semidirect
84. #13063284D4semidirect
113. C2×M16×C43D4semidirect
325. C2×#408D43semidirect
370. C43#23394semidirect
412. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633582
C2×#145834772
C2×#145834702
C2×#145828962
C22×#130632502
#191356052
#191356002
#191343152
C2×C43×#4082
#2339443