Finite Group Databasebeta

← #25001926

Subgroups — #25001926

Order 11008.

1226 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
1C2×#14583665C211yesmaximal, characteristic
2C2×#14582872C211yesmaximal, characteristic
3#19137183C211yesmaximal, characteristic
4#19134316C211yesmaximal, characteristic, complemented
5#19134315C211yesmaximal, characteristic, complemented
6C2×#14582655C211yesmaximal, characteristic, complemented
7C2×C43×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9#14583665—22no—
10#14583665—22no—
11#14583665—22no—
12#14583665C414yescomplemented
13C2×#13063333—22no—
14C2×#13063331—22no—
15C22×#10621877C2211yescharacteristic
16C2×M16×D43—22no—
17C2×#13063284C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19#14582872—22no—
20#14582872C414yescomplemented
21C2×#13063239—22no—
22#14582805C412yescomplemented
23#14582801C412yescomplemented
24#14582776—22no—
25#14582756—22no—
26#14582662—22no—
27#14582661—22no—
28#14582655—22no—
29C22×M16×C43C2211yescharacteristic
30C2×#117×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic
32C43×H(3,ℤ/4)—22no—
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—
43C2×#10621898D412yes—
44C2×#10621898Q812yes—
45C22×Dic86C2×C411yescharacteristic
46C22×D172C2×C411yescharacteristic
47C22×C22⋊D43D412yes—
48C23×Dic43—21no—
49C22×C4×D43D412yes—
50#13063333—28no—
51#13063333—28no—
52#13063331—28no—
53#13063331—28no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877C2×C412yes—
59C2×#10621877D412yes—
60C2×#10621872—24no—
61M16×D43—28no—
62M16×D43—28no—
63C22×C43⋊C8D412yes—
64C2×C8×D43—24no—
65#13063284—21no—
66#13063284—21no—
67#13063284—21no—
68#13063284C2×C412yes—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2×C412yes—
76C2×C22⋊Dic43—21no—
77C2×(C2×D43)⋊C4—24no—
78C2×C4×Dic43—21no—
79#13063239—28no—
80C43⋊#95—24no—
81C23×C4×C43C2311yescharacteristic
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C2×M16×C43—21no—
86C2×M16×C43C2×C412yes—
87C2×M16×C43D412yes—
88C22×C8×C43D412yes—
89#117×C43—21no—
90#117×C43—21no—
91#117×C43—21no—
92#117×C43—21no—
93#117×C43—21no—
94#117×C43—21no—
95#117×C43—21no—
96#117×C43C2×C412yes—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C42×C43—21no—
102C2×C42×C43C2×C412yes—
103C24×C43C2×D411yescharacteristic
104C23×D43C22⋊C412yes—
105C22×C4×C43—22no—
106C22×C4×C43—41no—
107C22×C4×C43C22×C411yescharacteristic
108C22×C4×C43C22×C411yescharacteristic
109C22×C4×C43C22×C411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×Q811yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×C4×C43#4111yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C2×C22⋊D43—22no—
122C2×C22⋊D43—22no—
123C2×C22⋊D43—22no—
124C2×C22⋊D43—22no—
125C2×C22⋊D43C22⋊C414yes—
126C2×C22⋊D43C4⋊C414yes—
127C22×Dic43—22no—
128C22×Dic43—41no—
129C22×Dic43—41no—
130C22×Dic43—41no—
131C22×Dic43—82no—
132C22×Dic43C22⋊C412yes—
133#10621898—22no—
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—22no—
143#10621898—22no—
144#10621898—22no—
145#10621898—22no—
146#10621898—22no—
147#10621898—22no—
148#10621898—22no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C4212yes—
154C2×D172C4⋊C412yes—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43C22⋊C414yes—
160C2×C4×D43C4⋊C414yes—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86C4212yes—
166C2×Dic86C4⋊C412yes—
167M16×C43—22no—
168M16×C43—22no—
169M16×C43—22no—
170M16×C43—22no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C2×C8×C43C22⋊C414yescomplemented
174C4⋊C4×C43—22no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C42×C43—22no—
183C42×C43—22no—
184C42×C43—22no—
185C42×C43—41no—
186C22⋊Dic43—22no—
187C22⋊Dic43—41no—
188(C2×D43)⋊C4—84no—
189C4⋊Dic43—22no—
190C4⋊Dic43—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43—41no—
193C4⋊Dic43—41no—
194C4⋊Dic43—41no—
195C4×Dic43—22no—
196C4×Dic43—41no—
197#10621877—22no—
198#10621877—22no—
199#10621877—22no—
200#10621877—22no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8C22⋊C414yescomplemented
204#10621872—216no—
205C8×D43—216no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43C2×C22⋊C411yescharacteristic
209C23×C43C2×C22⋊C411yescharacteristic
210C23×C43C2×C4⋊C411yescharacteristic
211C23×C43#12111yescharacteristic
212C23×C43#12111yescharacteristic
213C23×C43#12111yescharacteristic
214C23×C43#12111yescharacteristic
215C22×D43—22no—
216C22×D43—22no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43#9514yes—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—81no—
225C2×C4×C43—81no—
226C2×C4×C43C2×C4211yescharacteristic
227C2×C4×C43C2×C22⋊C411yescharacteristic
228C2×C4×C43C2×C22⋊C411yescharacteristic
229C2×C4×C43C2×C22⋊C411yescharacteristic
230C2×C4×C43C2×C4⋊C411yescharacteristic
231C2×C4×C43C2×C4⋊C411yescharacteristic
232C2×C4×C43#11711yescharacteristic
233C2×C4×C43#11711yescharacteristic
234C2×C4×C43C4×D411yescharacteristic
235C2×C4×C43C4×D411yescharacteristic
236C2×C4×C43C4×D411yescharacteristic
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43C4×D411yescharacteristic
239C2×C4×C43C4×D411yescharacteristic
240C2×C4×C43C4×D411yescharacteristic
241C2×C4×C43C4×D411yescharacteristic
242C2×C4×C43#12011yescharacteristic
243C2×C4×C43#12011yescharacteristic
244C2×C4×C43#12011yescharacteristic
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43C22⋊Q811yescharacteristic
247C2×C4×C43C22⋊Q811yescharacteristic
248C2×C4×C43C22⋊Q811yescharacteristic
249C2×C4×C43C22⋊Q811yescharacteristic
250C2×C4×C43#12311yescharacteristic
251C2×C4×C43#12311yescharacteristic
252C2×C4×C43#12311yescharacteristic
253C2×C4×C43#12311yescharacteristic
254C22⋊D43—24no—
255C22⋊D43—24no—
256C22⋊D43—24no—
257C22⋊D43—24no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—44no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—81no—
264C2×Dic43—81no—
265C2×Dic43—82no—
266C2×Dic43—82no—
267C2×Dic43#9514yes—
268D172—22no—
269D172—22no—
270D172—22no—
271D172—22no—
272C4×D43—24no—
273C4×D43—24no—
274C4×D43—24no—
275C4×D43—24no—
276Dic86—22no—
277Dic86—22no—
278Dic86—22no—
279Dic86—22no—
280C8×C43—24no—
281C43⋊C8—24no—
282#10742—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43C2×#9511yescharacteristic
294C22×C43#38011yescharacteristic
295C22×C43#38011yescharacteristic
296C22×C43#38611yescharacteristic
297C22×C43#38611yescharacteristic
298C22×C43#38611yescharacteristic
299C22×C43#38611yescharacteristic
300C2×D43—24no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—44no—
304C2×D43—82no—
305C4×C43—82no—
306C4×C43—82no—
307C4×C43C4×C22⋊C411yescharacteristic
308C4×C43C4×C22⋊C411yescharacteristic
309C4×C43#37911yescharacteristic
310C4×C43#38111yescharacteristic
311C4×C43#38511yescharacteristic
312C4×C43#38511yescharacteristic
313C4×C43#38511yescharacteristic
314C4×C43#38511yescharacteristic
315Dic43—24no—
316Dic43—82no—
317Dic43—82no—
318C2×#568—431no—
319C2×#410—431no—
320#2311—431no—
321#1736—431no—
322#1736—431no—
323C2×H(3,ℤ/4)—431no—
324C2×H(3,ℤ/4)D4311yescharacteristic, complemented
325C2×C43—21no—
326C2×C43—21no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—21no—
330C2×C43—21no—
331C2×C43C22⋊#9511yescharacteristic
332C2×C43#190911yescharacteristic
333C2×C43#191011yescharacteristic
334D43—44no—
335C22×#41—431no—
336#568—434no—
337#568—862no—
338#568—862no—
339#568—862no—
340C2×#131—862no—
341C2×#131—862no—
342C22×M16—431no—
343C22×M16—862no—
344C22×M16C2×D4311yescharacteristic
345C2×#117—431no—
346C2×#117C2×D4311yescharacteristic
347C2×#117C2×D4311yescharacteristic
348C22×C4⋊C4—431no—
349#410—434no—
350#410—862no—
351C2×#99—862no—
352#391—432no—
353#390—432no—
354#386—862no—
355#380—862no—
356#340—862no—
357#340—862no—
358H(3,ℤ/4)—22no—
359H(3,ℤ/4)—862no—
360C43#1074211yescharacteristic, complemented, Sylow
361C2×#41—432no—
362C2×#41—432no—
363C2×#41—432no—
364C2×#41—432no—
365C2×#41—861no—
366C2×#41—861no—
367C2×#41—861no—
368C2×#41—861no—
369C2×#41—861no—
370C2×#41—861no—
371C2×#41—861no—
372C2×#41—861no—
373C22×Q8—431no—
374C22×D4—432no—
375C22×D4—431no—
376C23×C4—432no—
377C23×C4—861no—
378C23×C4C22×D4311yescharacteristic
379#131—868no—
380#131—868no—
381#131—868no—
382#131—868no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—432no—
388C2×M16—432no—
389C2×M16—864no—
390C2×M16—868no—
391C2×M16—868no—
392C2×M16—861no—
393C2×M16—861no—
394C2×M16—861no—
395C2×M16—861no—
396C2×M16C4×D4312yes—
397C2×M16C22⋊D4312yes—
398C22×C8—432no—
399C22×C8—864no—
400C22×C8D17212yes—
401#117—21no—
402#117—21no—
403#117—21no—
404#117—21no—
405#117—21no—
406#117—21no—
407#117—21no—
408#117—432no—
409#117—861no—
410#117—861no—
411#117—861no—
412#117C4×D4312yes—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—432no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—864no—
426C2×C42—21no—
427C2×C42—861no—
428C2×C42C4×D4312yes—
429#99—868no—
430#95—864no—
431C24—432no—
432C24D4×D4311yescharacteristic
433#41—862no—
434#41—862no—
435#41—862no—
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—862no—
445#41—862no—
446#41—862no—
447#41—862no—
448#41—862no—
449C2×Q8—432no—
450C2×Q8—432no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×D4—434no—
456C2×D4—434no—
457C2×D4—432no—
458C2×D4—432no—
459C2×D4—862no—
460C2×D4—862no—
461C2×D4—862no—
462C2×D4—862no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C22×C4—22no—
468C22×C4—41no—
469C22×C4—432no—
470C22×C4—434no—
471C22×C4—434no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—3442no—
478C22×C4—1721no—
479C22×C4—1721no—
480C22×C4—1721no—
481C22×C4C2×C4×D4311yescharacteristic
482C22×C4C2×C4×D4311yescharacteristic
483C22×C4C2×C4×D4311yescharacteristic
484C22×C4C2×D17211yescharacteristic
485C22×C4#1062189811yescharacteristic
486C22×C4#1062189811yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4D4×D4311yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4#1062190011yescharacteristic
492C22×C4Q8×D4311yescharacteristic
493C22×C4#1062190211yescharacteristic
494C22×C4C2×C22⋊D4311yescharacteristic
495M16—22no—
496M16—22no—
497M16—22no—
498M16—22no—
499M16—8616no—
500M16—862no—
501M16—862no—
502M16—862no—
503M16—862no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—434no—
507C2×C8—8616no—
508C2×C8—862no—
509C2×C8—862no—
510C2×C8(C2×D43)⋊C414yescomplemented
511C4⋊C4—22no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—1721no—
519C4⋊C4—1721no—
520C4⋊C4—1721no—
521C22⋊C4—22no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—862no—
526C22⋊C4—3444no—
527C22⋊C4—1721no—
528C42—22no—
529C42—22no—
530C42—22no—
531C42—41no—
532C42—862no—
533C42—1721no—
534C23—41no—
535C23—41no—
536C23—434no—
537C23—862no—
538C23—862no—
539C23—1722no—
540C23—1722no—
541C23C22⋊C4×D4311yescharacteristic
542C23C22⋊C4×D4311yescharacteristic
543C23C4⋊C4×D4311yescharacteristic
544C23#1306329611yescharacteristic
545C23#1306329811yescharacteristic
546C23#1306329811yescharacteristic
547C23#1306330011yescharacteristic
548Q8—862no—
549Q8—862no—
550Q8—862no—
551Q8—862no—
552D4—864no—
553D4—864no—
554D4—864no—
555D4—864no—
556D4—862no—
557D4—862no—
558D4—862no—
559D4—862no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—434no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—864no—
570C2×C4—864no—
571C2×C4—864no—
572C2×C4—864no—
573C2×C4—3442no—
574C2×C4—3442no—
575C2×C4—3441no—
576C2×C4—3441no—
577C2×C4—1724no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4C42×D4311yescharacteristic
581C2×C4C22⋊C4×D4311yescharacteristic
582C2×C4C22⋊C4×D4311yescharacteristic
583C2×C4C2×(C2×D43)⋊C411yescharacteristic
584C2×C4C4⋊C4×D4311yescharacteristic
585C2×C4C4⋊C4×D4311yescharacteristic
586C2×C4#1306328211yescharacteristic
587C2×C4#1306328311yescharacteristic
588C2×C4(C22⋊D43)⋊C411yescharacteristic
589C2×C4(C22⋊D43)⋊C411yescharacteristic
590C2×C4C4×C22⋊D4311yescharacteristic
591C2×C4C4×C22⋊D4311yescharacteristic
592C2×C4#1306328711yescharacteristic
593C2×C4#1306328711yescharacteristic
594C2×C4C4×D17211yescharacteristic
595C2×C4C4×D17211yescharacteristic
596C2×C4#1306329311yescharacteristic
597C2×C4#1306329311yescharacteristic
598C2×C4#1306329511yescharacteristic
599C2×C4#1306329511yescharacteristic
600C2×C4#1306330111yescharacteristic
601C2×C4#1306330311yescharacteristic
602C2×C4#1306330311yescharacteristic
603C2×C4#1306330511yescharacteristic
604C2×C4#1306330711yescharacteristic
605C2×C4#1306330711yescharacteristic
606C2×C4#1306331011yescharacteristic
607C2×C4#1306331011yescharacteristic
608C8—24no—
609C8—864no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—864no—
621C22—3442no—
622C22—1724no—
623C22—1722no—
624C22—1722no—
625C22#95×D4311yescharacteristic
626C22#1458275611yescharacteristic
627C22#1458275811yescharacteristic
628C22#1458277511yescharacteristic
629C22#1458277511yescharacteristic
630C22#1458277711yescharacteristic
631C22#1458277711yescharacteristic
632C4—82no—
633C4—82no—
634C4—864no—
635C4—3442no—
636C4—3442no—
637C4#1458274611yescharacteristic
638C4C4×(C2×D43)⋊C411yescharacteristic
639C4#1458275411yescharacteristic
640C4#1458276111yescharacteristic
641C4#1458277011yescharacteristic
642C4#1458277011yescharacteristic
643C4#1458277311yescharacteristic
644C4#1458277311yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—21no—
650C2—21no—
651C2—1724no—
652C2(C2×D43)⋊#9511yescharacteristic
653C2#1913511611yescharacteristic
654C2#1913512111yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC22×C43#386
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43#10742
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #19134316C2semidirect
5. #19134315C2semidirect
6. C2×#14582655C2semidirect
7. C2×C43×H(3,ℤ/4)C2semidirect
12. #14583665C4semidirect
20. #14582872C4semidirect
22. #14582805C4semidirect
23. #14582801C4semidirect
173. C2×C8×C43C22⋊C4semidirect
203. C2×C43⋊C8C22⋊C4semidirect
324. C2×H(3,ℤ/4)D43semidirect
360. C43#10742semidirect
510. C2×C8(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
C2×#145828722
#191371832
#191343162
#191343152
C2×#145826552
C2×C43×H(3,ℤ/4)2
#1074243