Finite Group Databasebeta

← #25003822

Subgroups — #25003822

Order 11008.

910 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143112C211yesmaximal, characteristic
2C2×#14582898C211yesmaximal, characteristic
3C2×#14582872C211yesmaximal, characteristic
4C2×#14582669C211yesmaximal, characteristic, complemented
5#19134314C211yesmaximal, characteristic, complemented
6#19134304C211yesmaximal, characteristic, complemented
7C43×#2317C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582907—21no—
13#14582903—21no—
14#14582898—22no—
15#14582898—22no—
16#14582898—21no—
17#14582898—21no—
18#14582893—22no—
19C2×#13063248—21no—
20C2×#13063245—21no—
21#14582872—22no—
22#14582872C414yescomplemented
23C2×#13063239—22no—
24#14582669—22no—
25#14582661—22no—
26#14582658—22no—
27C2×#117×C43C2211yescharacteristic
28C2×#117×C43C2211yescharacteristic
29C22×C4⋊C4×C43C2211yescharacteristic
30C43×#389—22no—
31C43×#385—22no—
32C43×#384—21no—
33C43×#382—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898C2×C412yes—
45C2×#10621898Q812yes—
46C22×Dic86D411yescharacteristic
47C22×D172D411yescharacteristic
48C22×C22⋊D43—21no—
49C22×C4×D43—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877D412yes—
62C22×C43⋊C8—21no—
63C22×C43⋊C8D412yes—
64#13063284—21no—
65#13063284—21no—
66#13063284—21no—
67#13063284C2×C412yes—
68C2×C4⋊Dic43—21no—
69C2×C22⋊Dic43—21no—
70C2×C4×Dic43—21no—
71#13063248—24no—
72#13063248—22no—
73#13063248—22no—
74#13063245—24no—
75#13063245—22no—
76#13063245—22no—
77#13063239—28no—
78C23×C4×C43—21no—
79C23×C4×C43C2311yescharacteristic
80#117×C43—21no—
81#117×C43—21no—
82#117×C43—21no—
83#117×C43—21no—
84#117×C43—21no—
85#117×C43—21no—
86#117×C43C2×C412yes—
87#117×C43D412yes—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—24no—
95C2×C4⋊C4×C43D412yes—
96C2×C4⋊C4×C43D411yescharacteristic
97C2×C4⋊C4×C43D411yescharacteristic
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43D412yes—
100C2×C42×C43—21no—
101C2×C42×C43—21no—
102#95×C43—24no—
103C24×C43C2×D411yescharacteristic
104C23×D43—21no—
105C22×C4×C43—22no—
106C22×C4×C43—21no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—41no—
110C22×C4×C43—41no—
111C22×C4×C43—82no—
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
126C2×C22⋊D43—22no—
127C2×C22⋊D43—22no—
128C2×C22⋊D43—41no—
129C2×C22⋊D43—41no—
130C2×C22⋊D43—41no—
131C2×C22⋊D43—41no—
132C22×Dic43—21no—
133C22×Dic43—41no—
134#10621898—22no—
135#10621898—22no—
136#10621898—22no—
137#10621898—22no—
138#10621898—22no—
139#10621898—22no—
140#10621898—22no—
141#10621898—22no—
142#10621898—41no—
143#10621898—41no—
144#10621898—41no—
145#10621898—41no—
146#10621898—41no—
147#10621898—41no—
148#10621898—41no—
149#10621898—41no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C4⋊C412yescomplemented
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—41no—
159C2×C4×D43—41no—
160C2×C4×D43—41no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86C4⋊C412yescomplemented
168C4⋊C4×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—84no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43C22⋊C414yes—
183C42×C43—22no—
184C42×C43—22no—
185C42×C43—41no—
186C42×C43—41no—
187C22⋊Dic43—22no—
188C22⋊Dic43—41no—
189C4⋊Dic43—22no—
190C4⋊Dic43—41no—
191C4×Dic43—22no—
192C4×Dic43—41no—
193#10621877—22no—
194#10621877—22no—
195#10621877—41no—
196#10621877—41no—
197#10621877—41no—
198#10621877—41no—
199#10621877—41no—
200#10621877—41no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—41no—
206C2×C43⋊C8—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43C2×C22⋊C411yescharacteristic
210C23×C43#12011yescharacteristic
211C23×C43#12111yescharacteristic
212C23×C43C22⋊Q811yescharacteristic
213C23×C43#12311yescharacteristic
214C23×C43#12411yescharacteristic
215C23×C43#12711yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—81no—
220C22×D43—81no—
221C2×C4×C43—24no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—44no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—42no—
230C2×C4×C43—82no—
231C2×C4×C43—82no—
232C2×C4×C43C2×C4⋊C411yescharacteristic
233C2×C4×C43#11711yescharacteristic
234C2×C4×C43C4×D411yescharacteristic
235C2×C4×C43C4×D411yescharacteristic
236C2×C4×C43C4×D411yescharacteristic
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43#12011yescharacteristic
239C2×C4×C43#12011yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43C22⋊Q811yescharacteristic
248C2×C4×C43C22⋊Q811yescharacteristic
249C2×C4×C43C22⋊Q811yescharacteristic
250C2×C4×C43C22⋊Q811yescharacteristic
251C2×C4×C43C22⋊Q811yescharacteristic
252C2×C4×C43#12311yescharacteristic
253C2×C4×C43#12311yescharacteristic
254C2×C4×C43#12311yescharacteristic
255C2×C4×C43#12311yescharacteristic
256C2×C4×C43#12411yescharacteristic
257C2×C4×C43#12411yescharacteristic
258C2×C4×C43#12611yescharacteristic
259C2×C4×C43#12611yescharacteristic
260C22⋊D43—42no—
261C22⋊D43—42no—
262C22⋊D43—42no—
263C22⋊D43—42no—
264C2×Dic43—22no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—42no—
268C2×Dic43—81no—
269C2×Dic43—81no—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274C4×D43—42no—
275C4×D43—42no—
276C4×D43—42no—
277C4×D43—42no—
278Dic86—22no—
279Dic86—22no—
280Dic86—41no—
281Dic86—41no—
282C43⋊C8—42no—
283C43⋊C8—42no—
284#11093—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43#38011yescharacteristic
296C22×C43#38611yescharacteristic
297C22×C43#39011yescharacteristic
298C22×C43#39211yescharacteristic
299C22×C43#39311yescharacteristic
300C22×C43#39711yescharacteristic
301C22×C43#39911yescharacteristic
302C2×D43—42no—
303C2×D43—82no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—82no—
307C4×C43—44no—
308C4×C43—81no—
309C4×C43—82no—
310C4×C43—81no—
311C4×C43#38511yescharacteristic
312C4×C43#38511yescharacteristic
313C4×C43#38811yescharacteristic
314C4×C43#38811yescharacteristic
315C4×C43#39411yescharacteristic
316C4×C43#39411yescharacteristic
317C4×C43#39611yescharacteristic
318C4×C43#39611yescharacteristic
319Dic43—42no—
320Dic43—82no—
321#2896—431no—
322C2×#417—431no—
323C2×#410—431no—
324#2317D4311yescharacteristic, complemented
325C2×#344—431no—
326#1736—431no—
327#1733—431no—
328C2×C43—21no—
329C2×C43—21no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—21no—
333C2×C43—21no—
334C2×C43#143911yescharacteristic
335C2×C43#200811yescharacteristic
336C2×C43#200911yescharacteristic
337D43—82no—
338C22×#41—431no—
339C22×M16—431no—
340C22×M16—431no—
341C2×#117—431no—
342C2×#117C2×D4311yescharacteristic
343C2×#117C2×D4311yescharacteristic
344C22×C4⋊C4C2×D4311yescharacteristic
345#419—861no—
346#418—861no—
347#417—862no—
348#417—862no—
349#417—861no—
350#417—861no—
351#416—862no—
352C2×#103—861no—
353C2×#102—861no—
354#410—434no—
355#410—862no—
356C2×#99—862no—
357#389—22no—
358#385—22no—
359#384—21no—
360#382—21no—
361#344—862no—
362#340—862no—
363#339—862no—
364C43#1109311yescharacteristic, complemented, Sylow
365C2×#41—432no—
366C2×#41—432no—
367C2×#41—861no—
368C2×#41—861no—
369C2×#41—861no—
370C2×#41—861no—
371C2×#41—861no—
372C2×#41—861no—
373C2×#41—861no—
374C2×#41—861no—
375C2×#41—861no—
376C2×#41—861no—
377C22×Q8—431no—
378C22×D4—431no—
379C22×D4—861no—
380C23×C4—21no—
381C23×C4—861no—
382C23×C4C22×D4311yescharacteristic
383C2×M16—432no—
384C2×M16—861no—
385C2×M16—861no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—861no—
389C2×M16—861no—
390C2×M16—861no—
391C2×M16—861no—
392C2×M16—861no—
393C2×M16—861no—
394C2×M16—861no—
395C22×C8—432no—
396C22×C8—861no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—432no—
404#117—861no—
405#117—861no—
406#117—861no—
407#117C4×D4312yes—
408#117D17212yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4C22⋊D4312yes—
418C2×C4⋊C4C22⋊D4311yescharacteristic
419C2×C4⋊C4C22⋊D4311yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4C22⋊D4312yes—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—861no—
426#103—864no—
427#103—862no—
428#103—862no—
429#102—864no—
430#102—862no—
431#102—862no—
432#99—868no—
433#95—24no—
434C24—861no—
435C24C2×C22⋊D4311yescharacteristic
436#41—862no—
437#41—862no—
438#41—862no—
439#41—862no—
440#41—862no—
441#41—862no—
442#41—862no—
443#41—862no—
444#41—1721no—
445#41—1721no—
446#41—1721no—
447#41—1721no—
448#41—1721no—
449#41—1721no—
450#41—1721no—
451#41—1721no—
452C2×Q8—432no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×D4—432no—
459C2×D4—862no—
460C2×D4—862no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—1721no—
467C2×D4—1721no—
468C2×D4—1721no—
469C2×D4—1721no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—82no—
477C22×C4—861no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—1721no—
481C22×C4—1721no—
482C22×C4—1721no—
483C22×C4—1721no—
484C22×C4—1721no—
485C22×C4C2×C4×D4311yescharacteristic
486C22×C4C2×D17211yescharacteristic
487C22×C4#1062189811yescharacteristic
488C22×C4#1062189811yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4#1062190011yescharacteristic
493C22×C4Q8×D4311yescharacteristic
494C22×C4#1062190211yescharacteristic
495C22×C4#1062190211yescharacteristic
496C22×C4#1062190211yescharacteristic
497C22×C4C2×C22⋊D4311yescharacteristic
498C22×C4C2×C22⋊D4311yescharacteristic
499M16—862no—
500M16—862no—
501M16—1721no—
502M16—1721no—
503M16—1721no—
504M16—1721no—
505M16—1721no—
506M16—1721no—
507C2×C8—862no—
508C2×C8—862no—
509C2×C8—862no—
510C2×C8—862no—
511C2×C8—1721no—
512C2×C8—1721no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—84no—
524C4⋊C4—862no—
525C4⋊C4—1721no—
526C22⋊C4—22no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—862no—
530C22⋊C4—1721no—
531C22⋊C4(C2×D43)⋊C414yes—
532C42—22no—
533C42—22no—
534C42—41no—
535C42—41no—
536C42—862no—
537C42—1721no—
538C23—41no—
539C23—41no—
540C23—862no—
541C23—3441no—
542C23—3441no—
543C23—1721no—
544C23—1721no—
545C23C2×(C2×D43)⋊C411yescharacteristic
546C23#1306329411yescharacteristic
547C23#1306329611yescharacteristic
548C23#1306330111yescharacteristic
549C23#1306330811yescharacteristic
550C23#1306331411yescharacteristic
551C23#1306332111yescharacteristic
552Q8—862no—
553Q8—862no—
554Q8—1721no—
555Q8—1721no—
556D4—862no—
557D4—862no—
558D4—1722no—
559D4—1722no—
560D4—1722no—
561D4—1722no—
562D4—1721no—
563D4—1721no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—862no—
576C2×C4—3441no—
577C2×C4—3441no—
578C2×C4—1722no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4C4⋊C4×D4311yescharacteristic
586C2×C4#1306328311yescharacteristic
587C2×C4C4×C22⋊D4311yescharacteristic
588C2×C4C4×C22⋊D4311yescharacteristic
589C2×C4#1306328711yescharacteristic
590C2×C4#1306328711yescharacteristic
591C2×C4#1306329311yescharacteristic
592C2×C4#1306329311yescharacteristic
593C2×C4#1306329711yescharacteristic
594C2×C4#1306329711yescharacteristic
595C2×C4#1306329911yescharacteristic
596C2×C4#1306329911yescharacteristic
597C2×C4#1306330011yescharacteristic
598C2×C4#1306330011yescharacteristic
599C2×C4#1306330011yescharacteristic
600C2×C4#1306330111yescharacteristic
601C2×C4#1306330111yescharacteristic
602C2×C4#1306330311yescharacteristic
603C2×C4#1306330311yescharacteristic
604C2×C4#1306330511yescharacteristic
605C2×C4#1306331011yescharacteristic
606C2×C4#1306331011yescharacteristic
607C2×C4#1306331011yescharacteristic
608C2×C4#1306331011yescharacteristic
609C2×C4#1306331411yescharacteristic
610C2×C4#1306331411yescharacteristic
611C2×C4#1306332011yescharacteristic
612C2×C4#1306332011yescharacteristic
613C8—1722no—
614C8—1722no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—3442no—
626C22—3442no—
627C22—3441no—
628C22—3441no—
629C22—1722no—
630C22#1458275611yescharacteristic
631C22#1458277811yescharacteristic
632C22#1458280011yescharacteristic
633C22#1458280711yescharacteristic
634C22#1458281011yescharacteristic
635C22#1458282511yescharacteristic
636C22#1458283411yescharacteristic
637C4—44no—
638C4—82no—
639C4—81no—
640C4—81no—
641C4—3442no—
642C4—1722no—
643C4#1458277011yescharacteristic
644C4#1458277011yescharacteristic
645C4#1458278911yescharacteristic
646C4#1458278911yescharacteristic
647C4#1458281611yescharacteristic
648C4#1458281611yescharacteristic
649C4#1458282111yescharacteristic
650C4#1458282111yescharacteristic
651C2—21no—
652C2—21no—
653C2—21no—
654C2—21no—
655C2—21no—
656C2—21no—
657C2—3442no—
658C2#1913283711yescharacteristic
659C2#1913564811yescharacteristic
660C2#1913565511yescharacteristic
subgroupG/H
centerC22#14582807
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2317C2
socleC22×C43#392
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#2317D43
hypocenterC43#11093
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2317

Complements

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

NH ≅ G/Ntype
4. C2×#14582669C2semidirect
5. #19134314C2semidirect
6. #19134304C2semidirect
7. C43×#2317C2semidirect
22. #14582872C4semidirect
155. C2×D172C4⋊C4semidirect
167. C2×Dic86C4⋊C4semidirect
324. #2317D43semidirect
364. C43#11093semidirect

Maximal subgroups

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

subgroupindex
#191431122
C2×#145828982
C2×#145828722
C2×#145826692
#191343142
#191343042
C43×#23172
#1109343