Finite Group Databasebeta

← #25003025

Subgroups — #25003025

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582915C211yesmaximal, characteristic
2C2×#14582901C211yesmaximal, characteristic
3C2×#14582872C211yesmaximal, characteristic
4#19136951C211yesmaximal, characteristic, complemented
5#19134315C211yesmaximal, characteristic, complemented
6C2×#14582656C211yesmaximal, characteristic, complemented
7C2×C43×#344C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12#14582915—22no—
13#14582915C414yescomplemented
14C2×#13063251—22no—
15#14582901—22no—
16#14582901—22no—
17C2×#13063250C412yescomplemented
18C2×#13063247C412yescomplemented
19#14582872—22no—
20#14582872C414yescomplemented
21C2×#13063239—22no—
22C4⋊C4×Dic43—22no—
23C4×C4⋊Dic43—22no—
24C22⋊C4×Dic43—22no—
25#14582662—22no—
26#14582656—22no—
27C22×M16×C43C2211yescharacteristic
28C22×M16×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C43×#344—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×#10621898C2×C412yes—
43C22×Dic86C2×C411yescharacteristic
44C22×D172C2×C411yescharacteristic
45C22×C22⋊D43—21no—
46C23×Dic43—21no—
47C22×C4×D43—21no—
48#13063284—21no—
49#13063284—21no—
50#13063284—21no—
51#13063284—21no—
52#13063284—21no—
53#13063284C2×C412yes—
54#13063284C2×C412yes—
55#13063284D412yes—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43—21no—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43C2×C412yes—
62C2×C4⋊Dic43D412yes—
63C2×C4⋊Dic43D412yes—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—24no—
68C2×C4×Dic43D412yes—
69#13063251—28no—
70#13063250—24no—
71#13063247—24no—
72#13063239—28no—
73C43⋊#95—24no—
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×C43C2×C412yes—
87C22×C8×C43—21no—
88C22×C8×C43C2×C412yes—
89#117×C43—21no—
90#117×C43—21no—
91#117×C43C2×C412yes—
92#117×C43D412yes—
93C2×C4⋊C4×C43—21no—
94C2×C22⋊C4×C43D412yes—
95C2×C42×C43—21no—
96C24×C43C2×D411yescharacteristic
97C23×D43—21no—
98C22×C4×C43—22no—
99C22×C4×C43C22×C411yescharacteristic
100C22×C4×C43C22×C411yescharacteristic
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
113C2×C22⋊D43—22no—
114C2×C22⋊D43—22no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C2×C22⋊D43—41no—
118C2×C22⋊D43—41no—
119C22×Dic43—21no—
120C22×Dic43—22no—
121C22×Dic43—22no—
122C22×Dic43—22no—
123C22×Dic43—22no—
124C22×Dic43—41no—
125C22×Dic43—82no—
126#10621898—22no—
127#10621898—22no—
128#10621898—22no—
129#10621898—22no—
130#10621898—22no—
131#10621898—22no—
132#10621898—22no—
133#10621898—22no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138#10621898—41no—
139#10621898—41no—
140#10621898—41no—
141#10621898—41no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172C4212yescomplemented
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—41no—
151C2×C4×D43—41no—
152C2×C4×D43—41no—
153C2×C4×D43—41no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86C4212yescomplemented
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—22no—
172C2×C8×C43—41no—
173C2×C8×C43—41no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43C22⋊C414yes—
178C42×C43—22no—
179C42×C43—22no—
180C22⋊Dic43—22no—
181C22⋊Dic43—22no—
182C22⋊Dic43—22no—
183C22⋊Dic43—41no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4⋊Dic43—22no—
189C4⋊Dic43—22no—
190C4⋊Dic43—41no—
191C4⋊Dic43C22⋊C414yes—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—41no—
195C4×Dic43—84no—
196C4×Dic43C22⋊C414yes—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C2×C22⋊C411yescharacteristic
200C23×C43C4×D411yescharacteristic
201C23×C43C4×D411yescharacteristic
202C23×C43#12011yescharacteristic
203C23×C43#12111yescharacteristic
204C23×C43#12111yescharacteristic
205C23×C43#12311yescharacteristic
206C22×D43—22no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—81no—
210C22×D43—81no—
211C2×C4×C43—24no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43C2×C4211yescharacteristic
215C2×C4×C43C2×C22⋊C411yescharacteristic
216C2×C4×C43C2×C22⋊C411yescharacteristic
217C2×C4×C43#11711yescharacteristic
218C2×C4×C43#11711yescharacteristic
219C2×C4×C43#11711yescharacteristic
220C2×C4×C43C4×D411yescharacteristic
221C2×C4×C43C4×D411yescharacteristic
222C2×C4×C43C4×D411yescharacteristic
223C2×C4×C43C4×D411yescharacteristic
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43C4×D411yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12311yescharacteristic
235C2×C4×C43#12311yescharacteristic
236C2×C4×C43#12411yescharacteristic
237C2×C4×C43#12411yescharacteristic
238C2×C4×C43#12411yescharacteristic
239C2×C4×C43#12611yescharacteristic
240C2×C4×C43#12611yescharacteristic
241C2×C4×C43#12711yescharacteristic
242C22⋊D43—42no—
243C22⋊D43—42no—
244C22⋊D43—42no—
245C22⋊D43—42no—
246C2×Dic43—22no—
247C2×Dic43—24no—
248C2×Dic43—24no—
249C2×Dic43—42no—
250C2×Dic43—44no—
251C2×Dic43—42no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—42no—
255C2×Dic43—82no—
256C2×Dic43—82no—
257C2×Dic43—81no—
258C2×Dic43—81no—
259D172—22no—
260D172—22no—
261D172—41no—
262D172—41no—
263C4×D43—42no—
264C4×D43—42no—
265C4×D43—42no—
266C4×D43—42no—
267Dic86—22no—
268Dic86—22no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—42no—
272C8×C43—42no—
273#10954—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43C4×C22⋊C411yescharacteristic
285C22×C43#38611yescharacteristic
286C22×C43#38611yescharacteristic
287C22×C43#38611yescharacteristic
288C22×C43#38811yescharacteristic
289C22×C43#38811yescharacteristic
290C22×C43#39011yescharacteristic
291C2×D43—42no—
292C2×D43—82no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—82no—
296C4×C43—44no—
297C4×C43C4×C22⋊C411yescharacteristic
298C4×C43C4×C22⋊C411yescharacteristic
299C4×C43#38811yescharacteristic
300C4×C43#38811yescharacteristic
301C4×C43#38811yescharacteristic
302C4×C43#38811yescharacteristic
303C4×C43#39011yescharacteristic
304C4×C43#39011yescharacteristic
305Dic43—44no—
306Dic43—44no—
307Dic43—42no—
308Dic43—82no—
309C2×#421—431no—
310C2×#417—431no—
311C2×#410—431no—
312#2274—431no—
313C2×#344D4311yescharacteristic, complemented
314#1736—431no—
315C2×H(3,ℤ/4)—431no—
316C2×C43—21no—
317C2×C43—21no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43#143711yescharacteristic
323C2×C43#190411yescharacteristic
324C2×C43#190511yescharacteristic
325D43—82no—
326C22×#41—431no—
327C22×M16C2×D4311yescharacteristic
328C22×M16C2×D4311yescharacteristic
329C2×#117—431no—
330C2×#117—431no—
331C2×#117C2×D4311yescharacteristic
332C22×C4⋊C4—431no—
333#421—434no—
334#421—862no—
335C2×#104—862no—
336#417—862no—
337#417—862no—
338C2×#103—432no—
339C2×#102—432no—
340#410—434no—
341#410—862no—
342C2×#99—862no—
343C4×C4⋊C4—862no—
344C4×C4⋊C4—862no—
345C4×C22⋊C4—862no—
346#344—22no—
347#340—862no—
348H(3,ℤ/4)—862no—
349C43#1095411yescharacteristic, complemented, Sylow
350C2×#41—432no—
351C2×#41—432no—
352C2×#41—861no—
353C2×#41—861no—
354C2×#41—861no—
355C2×#41—861no—
356C2×#41—861no—
357C2×#41—861no—
358C2×#41—861no—
359C2×#41—861no—
360C2×#41—861no—
361C2×#41—861no—
362C22×Q8—431no—
363C22×D4—431no—
364C22×D4—861no—
365C23×C4—861no—
366C23×C4—861no—
367C23×C4C22×D4311yescharacteristic
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16C4×D4312yes—
380C22×C8—21no—
381C22×C8C4×D4312yes—
382#117—21no—
383#117—21no—
384#117—432no—
385#117—432no—
386#117—432no—
387#117—861no—
388#117—861no—
389#117—861no—
390#117—861no—
391#117—861no—
392#117C4×D4312yes—
393#117C22⋊D4312yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—432no—
396C2×C4⋊C4—432no—
397C2×C4⋊C4—432no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4D17212yes—
406C2×C42—21no—
407C2×C42—432no—
408C2×C42—861no—
409C2×C42—864no—
410#104—868no—
411#103—864no—
412#102—864no—
413#99—868no—
414#95—864no—
415C24—861no—
416C24C2×D17211yescharacteristic
417#41—862no—
418#41—862no—
419#41—862no—
420#41—862no—
421#41—862no—
422#41—862no—
423#41—862no—
424#41—862no—
425#41—1721no—
426#41—1721no—
427#41—1721no—
428#41—1721no—
429#41—1721no—
430#41—1721no—
431#41—1721no—
432#41—1721no—
433C2×Q8—432no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×D4—432no—
440C2×D4—862no—
441C2×D4—862no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—1721no—
448C2×D4—1721no—
449C2×D4—1721no—
450C2×D4—1721no—
451C22×C4—22no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—861no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—3442no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4—1721no—
464C22×C4—1721no—
465C22×C4C2×C4×D4311yescharacteristic
466C22×C4C2×C4×D4311yescharacteristic
467C22×C4C2×C4×D4311yescharacteristic
468C22×C4#1062189811yescharacteristic
469C22×C4#1062189811yescharacteristic
470C22×C4D4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473C22×C4D4×D4311yescharacteristic
474C22×C4#1062190011yescharacteristic
475C22×C4#1062190011yescharacteristic
476C22×C4#1062190211yescharacteristic
477C22×C4#1062190211yescharacteristic
478C22×C4C2×C22⋊D4311yescharacteristic
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16—41no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—41no—
492C2×C8—41no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—434no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—1721no—
503C22⋊C4—22no—
504C22⋊C4—862no—
505C22⋊C4—862no—
506C22⋊C4—862no—
507C22⋊C4—1721no—
508C22⋊C4(C2×D43)⋊C414yes—
509C42—22no—
510C42—22no—
511C42—434no—
512C42—862no—
513C42—862no—
514C42—3444no—
515C42—1721no—
516C23—41no—
517C23—41no—
518C23—862no—
519C23—3441no—
520C23—3441no—
521C23—1721no—
522C23—1721no—
523C23C2×(C2×D43)⋊C411yescharacteristic
524C23C4×D17211yescharacteristic
525C23C4×D17211yescharacteristic
526C23#1306329511yescharacteristic
527C23#1306330011yescharacteristic
528C23#1306330011yescharacteristic
529C23#1306330911yescharacteristic
530Q8—862no—
531Q8—862no—
532Q8—1721no—
533Q8—1721no—
534D4—862no—
535D4—862no—
536D4—1722no—
537D4—1722no—
538D4—1722no—
539D4—1722no—
540D4—1721no—
541D4—1721no—
542C2×C4—24no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—862no—
546C2×C4—864no—
547C2×C4—864no—
548C2×C4—3441no—
549C2×C4—3441no—
550C2×C4—3442no—
551C2×C4—3442no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1724no—
555C2×C4—1722no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4C42×D4311yescharacteristic
563C2×C4C22⋊C4×D4311yescharacteristic
564C2×C4C22⋊C4×D4311yescharacteristic
565C2×C4#1306328211yescharacteristic
566C2×C4#1306328311yescharacteristic
567C2×C4#1306328311yescharacteristic
568C2×C4(C22⋊D43)⋊C411yescharacteristic
569C2×C4(C22⋊D43)⋊C411yescharacteristic
570C2×C4(C22⋊D43)⋊C411yescharacteristic
571C2×C4(C22⋊D43)⋊C411yescharacteristic
572C2×C4C4×C22⋊D4311yescharacteristic
573C2×C4C4×C22⋊D4311yescharacteristic
574C2×C4#1306328711yescharacteristic
575C2×C4#1306328711yescharacteristic
576C2×C4#1306328711yescharacteristic
577C2×C4#1306328711yescharacteristic
578C2×C4#1306329711yescharacteristic
579C2×C4#1306329711yescharacteristic
580C2×C4#1306329811yescharacteristic
581C2×C4#1306329811yescharacteristic
582C2×C4#1306331011yescharacteristic
583C2×C4#1306331011yescharacteristic
584C2×C4#1306331111yescharacteristic
585C2×C4#1306331111yescharacteristic
586C2×C4#1306331411yescharacteristic
587C2×C4#1306332011yescharacteristic
588C2×C4#1306332011yescharacteristic
589C2×C4#1306332111yescharacteristic
590C8—42no—
591C8—42no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—3442no—
603C22—3442no—
604C22—3441no—
605C22—3441no—
606C22—1722no—
607C22C4×(C2×D43)⋊C411yescharacteristic
608C22#1458277611yescharacteristic
609C22#1458277711yescharacteristic
610C22#1458277711yescharacteristic
611C22#1458279111yescharacteristic
612C22#1458279111yescharacteristic
613C22#1458280011yescharacteristic
614C4—44no—
615C4—3442no—
616C4—1724no—
617C4—1724no—
618C4—1722no—
619C4#1458274611yescharacteristic
620C4#1458274611yescharacteristic
621C4#1458278811yescharacteristic
622C4#1458278811yescharacteristic
623C4#1458278911yescharacteristic
624C4#1458278911yescharacteristic
625C4#1458279911yescharacteristic
626C4#1458279911yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—3442no—
634C2#1913283111yescharacteristic
635C2#1913508111yescharacteristic
636C2#1913508811yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC22×C43#386
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43#10954
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. #19136951C2semidirect
5. #19134315C2semidirect
6. C2×#14582656C2semidirect
7. C2×C43×#344C2semidirect
13. #14582915C4semidirect
17. C2×#13063250C4semidirect
18. C2×#13063247C4semidirect
20. #14582872C4semidirect
147. C2×D172C42semidirect
159. C2×Dic86C42semidirect
313. C2×#344D43semidirect
349. C43#10954semidirect

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×#145828722
#191369512
#191343152
C2×#145826562
C2×C43×#3442
#1095443