Finite Group Databasebeta

← #25003636

Subgroups — #25003636

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582905C211yesmaximal, characteristic
2C2×#14582905C211yesmaximal, characteristic
3#19137219C211yesmaximal, characteristic, complemented
4C2×#14582800C211yesmaximal, characteristic
5C2×#14582660C211yesmaximal, characteristic, complemented
6C2×#14582660C211yesmaximal, characteristic, complemented
7C2×C43×#343C211yesmaximal, characteristic, complemented
8C23×D172C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×(C2×D43)⋊C4—22no—
12C22×C4×Dic43C2211yescharacteristic
13#14582905—22no—
14#14582905—22no—
15#14582905—22no—
16#14582905C414yescomplemented
17C2×#13063247—21no—
18C2×#13063247—21no—
19C2×#13063247—22no—
20#14582800—22no—
21#14582800—22no—
22#14582795—22no—
23#14582772—22no—
24#14582768—21no—
25#14582764—21no—
26#14582660—22no—
27#14582660—22no—
28C22×M16×C43C2211yescharacteristic
29C22×M16×C43C2211yescharacteristic
30C22×C4⋊C4×C43C2211yescharacteristic
31C43×#343—22no—
32C24×D43—21no—
33C22×D172—21no—
34C22×D172—21no—
35C22×D172—21no—
36C22×D172—21no—
37C22×D172—21no—
38C22×D172—21no—
39C22×D172—21no—
40C22×D172—21no—
41C22×D172—21no—
42C22×D172—21no—
43C22×D172—21no—
44C22×D172C2×C412yes—
45C22×D172D412yes—
46C22×D172Q812yes—
47C23×Dic43—21no—
48#13063284—21no—
49#13063284—21no—
50#13063284—21no—
51#13063284—21no—
52#13063284—21no—
53#13063284—21no—
54#13063284C2×C412yes—
55#13063284D412yes—
56C2×C4⋊Dic43D411yescharacteristic
57C2×C4⋊Dic43D411yescharacteristic
58C2×C4⋊Dic43D412yes—
59C2×Dic43⋊C4—24no—
60C2×C22⋊Dic43—21no—
61C2×C22⋊Dic43—21no—
62C2×(C2×D43)⋊C4—28no—
63C2×(C2×D43)⋊C4—48no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43—21no—
69C2×C4×Dic43—21no—
70C2×C4×Dic43—21no—
71C2×C4×Dic43D412yes—
72#13063247—24no—
73#13063247—24no—
74#13063247—28no—
75C43⋊#95—24no—
76C23×C4×C43D412yes—
77C23×C4×C43C2311yescharacteristic
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—
90C22×C8×C43—21no—
91C22×C8×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C24×C43C2×D411yescharacteristic
99C23×D43—22no—
100C23×D43—22no—
101C23×D43—22no—
102C23×D43—44no—
103C23×D43—44no—
104C23×D43—41no—
105C23×D43—41no—
106C23×D43—41no—
107C23×D43—41no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—44no—
112C22×C4×C43C22×C411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×Q811yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C22×C4×C43#4111yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C22×Dic43—24no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—42no—
132C22×Dic43—41no—
133C22×Dic43—41no—
134C2×D172—22no—
135C2×D172—22no—
136C2×D172—22no—
137C2×D172—22no—
138C2×D172—22no—
139C2×D172—22no—
140C2×D172—22no—
141C2×D172—22no—
142C2×D172—22no—
143C2×D172—22no—
144C2×D172—22no—
145C2×D172—22no—
146C2×D172—22no—
147C2×D172—22no—
148C2×D172—22no—
149C2×D172—41no—
150C2×D172—41no—
151C2×D172—41no—
152C2×D172—41no—
153C2×D172—41no—
154C2×D172—41no—
155C2×D172—41no—
156C2×D172—41no—
157C2×D172—41no—
158C2×D172—41no—
159C2×D172—41no—
160C2×D172—41no—
161C2×D172C4⋊C414yescomplemented
162M16×C43—22no—
163M16×C43—22no—
164M16×C43—22no—
165M16×C43—22no—
166M16×C43—41no—
167M16×C43—41no—
168M16×C43—41no—
169M16×C43—41no—
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C2×C8×C43—41no—
173C2×C8×C43—41no—
174C2×C8×C43—41no—
175C2×C8×C43—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C22⋊Dic43—22no—
181C22⋊Dic43—22no—
182C22⋊Dic43—41no—
183C22⋊Dic43—41no—
184(C2×D43)⋊C4—416no—
185C4⋊Dic43—22no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C22⋊C414yescomplemented
191Dic43⋊C4—84no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—22no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198C4×Dic43—41no—
199C4×Dic43—41no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43C4×D411yescharacteristic
203C23×C43#12011yescharacteristic
204C23×C43#12011yescharacteristic
205C23×C43#12111yescharacteristic
206C23×C43#12111yescharacteristic
207C23×C43C22⋊Q811yescharacteristic
208C23×C43#12411yescharacteristic
209C22×D43—24no—
210C22×D43—44no—
211C22×D43—48no—
212C22×D43—44no—
213C22×D43—48no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43—84no—
221C22×D43—82no—
222C22×D43—82no—
223C22×D43—84no—
224C22×D43—82no—
225C22×D43—82no—
226C2×C4×C43—44no—
227C2×C4×C43—42no—
228C2×C4×C43—44no—
229C2×C4×C43—82no—
230C2×C4×C43C2×C22⋊C411yescharacteristic
231C2×C4×C43C2×C4⋊C411yescharacteristic
232C2×C4×C43#11711yescharacteristic
233C2×C4×C43C4×D411yescharacteristic
234C2×C4×C43C4×D411yescharacteristic
235C2×C4×C43C4×D411yescharacteristic
236C2×C4×C43#12011yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43C22⋊Q811yescharacteristic
244C2×C4×C43C22⋊Q811yescharacteristic
245C2×C4×C43C22⋊Q811yescharacteristic
246C2×C4×C43C22⋊Q811yescharacteristic
247C2×C4×C43C22⋊Q811yescharacteristic
248C2×C4×C43#12311yescharacteristic
249C2×C4×C43#12311yescharacteristic
250C2×C4×C43#12311yescharacteristic
251C2×C4×C43#12311yescharacteristic
252C2×C4×C43#12311yescharacteristic
253C2×C4×C43#12411yescharacteristic
254C2×C4×C43#12411yescharacteristic
255C2×C4×C43#12611yescharacteristic
256C2×C4×C43#12611yescharacteristic
257C2×C4×C43#12711yescharacteristic
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—44no—
261C2×Dic43—42no—
262C2×Dic43—44no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270D172—24no—
271D172—24no—
272D172—42no—
273D172—42no—
274D172—42no—
275D172—42no—
276D172—42no—
277D172—42no—
278C8×C43—42no—
279C8×C43—42no—
280#11063—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43#38511yescharacteristic
290C22×C43#38611yescharacteristic
291C22×C43#38811yescharacteristic
292C22×C43#39211yescharacteristic
293C22×C43#39311yescharacteristic
294C22×C43#39411yescharacteristic
295C22×C43#39611yescharacteristic
296C22×C43#45312yes—
297C22×C43#45412yes—
298C2×D43—48no—
299C2×D43—44no—
300C2×D43—84no—
301C2×D43—84no—
302C2×D43—84no—
303C2×D43—84no—
304C2×D43—82no—
305C2×D43—82no—
306C2×D43—84no—
307C4×C43—82no—
308C4×C43#38011yescharacteristic
309C4×C43#38511yescharacteristic
310C4×C43#38811yescharacteristic
311C4×C43#39011yescharacteristic
312C4×C43#39411yescharacteristic
313C4×C43#39611yescharacteristic
314C4×C43#39711yescharacteristic
315C4×C43#39911yescharacteristic
316Dic43—44no—
317Dic43—44no—
318Dic43—81no—
319Dic43—81no—
320C2×#418—431no—
321C2×#418—431no—
322#2317—431no—
323C2×#390—431no—
324C2×#343D4311yescharacteristic, complemented
325C2×#339—431no—
326C2×#339—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—21no—
330C2×C43—21no—
331C2×C43#143911yescharacteristic
332C2×C43#188312yes—
333C2×C43#200211yescharacteristic
334C2×C43#200311yescharacteristic
335C2×C43#202712yes—
336D43—84no—
337C23×D4—431no—
338C22×M16C2×D4311yescharacteristic
339C22×M16C2×D4311yescharacteristic
340C2×#117—431no—
341C2×#117—431no—
342C22×C4⋊C4C2×D4311yescharacteristic
343C22×C22⋊C4—862no—
344C22×C42—431no—
345#418—434no—
346#418—862no—
347#418—862no—
348#418—862no—
349C2×#102—862no—
350C2×#102—861no—
351C2×#102—861no—
352#390—862no—
353#390—862no—
354#389—862no—
355#385—862no—
356#384—861no—
357#382—861no—
358#343—22no—
359#339—862no—
360#339—862no—
361C43#1106311yescharacteristic, complemented, Sylow
362C25—861no—
363C22×D4—432no—
364C22×D4—432no—
365C22×D4—432no—
366C22×D4—861no—
367C22×D4—861no—
368C22×D4—861no—
369C22×D4—861no—
370C22×D4—861no—
371C22×D4—861no—
372C22×D4—861no—
373C22×D4—861no—
374C22×D4—861no—
375C22×D4—861no—
376C22×D4—861no—
377C23×C4—861no—
378C23×C4D17212yes—
379C23×C4C22×D4311yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16—21no—
390C2×M16C4×D4312yes—
391C2×M16C22⋊D4312yes—
392C22×C8—21no—
393C22×C8—21no—
394#117—432no—
395#117—432no—
396#117—861no—
397#117—861no—
398#117—861no—
399#117—861no—
400#117—861no—
401#117—861no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—432no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—864no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—868no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—1728no—
416C2×C42—432no—
417C2×C42—861no—
418C2×C42—861no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42—861no—
423C2×C42—861no—
424#102—868no—
425#102—864no—
426#102—864no—
427#95—864no—
428C24—862no—
429C24—862no—
430C24—862no—
431C24—1724no—
432C24—1724no—
433C24—1721no—
434C24—1721no—
435C24—1721no—
436C24—1721no—
437C24C2×D17211yescharacteristic
438C2×D4—434no—
439C2×D4—862no—
440C2×D4—862no—
441C2×D4—862no—
442C2×D4—862no—
443C2×D4—862no—
444C2×D4—862no—
445C2×D4—862no—
446C2×D4—862no—
447C2×D4—862no—
448C2×D4—862no—
449C2×D4—862no—
450C2×D4—862no—
451C2×D4—862no—
452C2×D4—862no—
453C2×D4—862no—
454C2×D4—1721no—
455C2×D4—1721no—
456C2×D4—1721no—
457C2×D4—1721no—
458C2×D4—1721no—
459C2×D4—1721no—
460C2×D4—1721no—
461C2×D4—1721no—
462C2×D4—1721no—
463C2×D4—1721no—
464C2×D4—1721no—
465C2×D4—1721no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—44no—
470C22×C4—864no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—1722no—
476C22×C4—1721no—
477C22×C4—1721no—
478C22×C4C2×C4×D4311yescharacteristic
479C22×C4#1062189811yescharacteristic
480C22×C4#1062189811yescharacteristic
481C22×C4#1062189811yescharacteristic
482C22×C4#1062189811yescharacteristic
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485C22×C4D4×D4311yescharacteristic
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4#1062190011yescharacteristic
489C22×C4Q8×D4311yescharacteristic
490C22×C4#1062190211yescharacteristic
491C22×C4C2×C22⋊D4311yescharacteristic
492M16—22no—
493M16—22no—
494M16—22no—
495M16—22no—
496M16—41no—
497M16—41no—
498M16—41no—
499M16—41no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—434no—
511C4⋊C4—862no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—3444no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—17216no—
520C22⋊C4—1721no—
521C22⋊C4—1721no—
522C42—862no—
523C42—862no—
524C42—862no—
525C42—862no—
526C42—1721no—
527C42—1721no—
528C42—1721no—
529C42—1721no—
530C23—22no—
531C23—22no—
532C23—864no—
533C23—3444no—
534C23—3442no—
535C23—3442no—
536C23—3444no—
537C23—3442no—
538C23—3442no—
539C23—1724no—
540C23—1728no—
541C23—1724no—
542C23—1728no—
543C23—1722no—
544C23—1722no—
545C23—1722no—
546C23—1722no—
547C23—1722no—
548C23—1722no—
549C23C4×D17211yescharacteristic
550C23#1306329511yescharacteristic
551C23#1306329511yescharacteristic
552C23#1306329911yescharacteristic
553C23#1306330011yescharacteristic
554C23#1306330511yescharacteristic
555C23#1306331311yescharacteristic
556D4—864no—
557D4—864no—
558D4—1722no—
559D4—1722no—
560D4—1722no—
561D4—1722no—
562D4—1722no—
563D4—1722no—
564C2×C4—44no—
565C2×C4—42no—
566C2×C4—44no—
567C2×C4—82no—
568C2×C4—864no—
569C2×C4—864no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1724no—
575C2×C4—1722no—
576C2×C4—1724no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4C22⋊C4×D4311yescharacteristic
581C2×C4C4⋊C4×D4311yescharacteristic
582C2×C4#1306328211yescharacteristic
583C2×C4(C22⋊D43)⋊C411yescharacteristic
584C2×C4C4×C22⋊D4311yescharacteristic
585C2×C4#1306328711yescharacteristic
586C2×C4#1306329311yescharacteristic
587C2×C4#1306329711yescharacteristic
588C2×C4#1306329811yescharacteristic
589C2×C4#1306329811yescharacteristic
590C2×C4#1306329811yescharacteristic
591C2×C4#1306329811yescharacteristic
592C2×C4#1306329811yescharacteristic
593C2×C4#1306330111yescharacteristic
594C2×C4#1306330311yescharacteristic
595C2×C4#1306330311yescharacteristic
596C2×C4#1306330311yescharacteristic
597C2×C4#1306330311yescharacteristic
598C2×C4#1306330711yescharacteristic
599C2×C4#1306330811yescharacteristic
600C2×C4#1306331011yescharacteristic
601C2×C4#1306331011yescharacteristic
602C2×C4#1306331011yescharacteristic
603C2×C4#1306331111yescharacteristic
604C2×C4#1306331111yescharacteristic
605C2×C4#1306331911yescharacteristic
606C2×C4#1306332011yescharacteristic
607C2×C4#1306332111yescharacteristic
608C8—42no—
609C8—42no—
610C22—22no—
611C22—22no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—22no—
617C22—22no—
618C22—3444no—
619C22—3444no—
620C22—3444no—
621C22—3444no—
622C22—3442no—
623C22—3442no—
624C22—3444no—
625C22—1728no—
626C22—1724no—
627C22#1458277311yescharacteristic
628C22#1458277711yescharacteristic
629C22#1458279011yescharacteristic
630C22#1458280811yescharacteristic
631C22#1458281211yescharacteristic
632C22#1458281711yescharacteristic
633C22#1458282111yescharacteristic
634C22#1458306912yes—
635C22#1458307412yes—
636C4—82no—
637C4—3441no—
638C4—3441no—
639C4—1724no—
640C4—1724no—
641C4#1458275811yescharacteristic
642C4#1458277011yescharacteristic
643C4#1458278811yescharacteristic
644C4#1458279911yescharacteristic
645C4#1458281411yescharacteristic
646C4#1458282311yescharacteristic
647C4#1458282811yescharacteristic
648C4#1458283411yescharacteristic
649C2—21no—
650C2—21no—
651C2—21no—
652C2—21no—
653C2—3444no—
654C2#1913283911yescharacteristic
655C2#1913497012yes—
656C2#1913561211yescharacteristic
657C2#1913561911yescharacteristic
658C2#1913575212yes—
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#343C2
socleC23×C43#120
prime radicalC23×D172C22
cosocleC23×C4×C43C23
hypercenterC2×#343D43
hypocenterC43#11063
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
3. #19137219C2semidirect
5. C2×#14582660C2semidirect
6. C2×#14582660C2semidirect
7. C2×C43×#343C2semidirect
16. #14582905C4semidirect
161. C2×D172C4⋊C4semidirect
190. C4⋊Dic43C22⋊C4semidirect
324. C2×#343D43semidirect
361. C43#11063semidirect

Maximal subgroups

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

subgroupindex
C2×#145829052
#191372192
C2×#145828002
C2×#145826602
C2×C43×#3432
#1106343