Finite Group Databasebeta

← #25146102

Subgroups — #25146102

Order 11008.

850 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×#14583102C211yesmaximal, characteristic
2C2×#14583023C211yesmaximal, characteristic, complemented
3#19139809C211yesmaximal, characteristic, complemented
4#19139515C211yesmaximal, characteristic
5#19135975C211yesmaximal, characteristic, complemented
6#19135972C211yesmaximal, characteristic, complemented
7#19135911C211yesmaximal, characteristic
8#19135451C211yesmaximal, characteristic
9#19135448C211yesmaximal, characteristic
10#19135395C211yesmaximal, characteristic, complemented
11#19135357C211yesmaximal, characteristic, complemented
12#19135274C211yesmaximal, characteristic, complemented
13#19135272C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic
15C43×#2055C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063323C2211yescharacteristic
18C2×#13063302—21no—
19C2×C4×Dic86C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21#14583102—24no—
22#14583023—24no—
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36#14582841—21no—
37#14582840—21no—
38#14582822—21no—
39#14582822—21no—
40#14582806C2211yescharacteristic
41#14582805C2211yescharacteristic
42#14582804C2211yescharacteristic
43#14582803—21no—
44#14582802C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582797C2211yescharacteristic
47#14582768C2211yescharacteristic
48#14582763—21no—
49#14582757—21no—
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063323—22no—
70#13063323—22no—
71#13063302—44no—
72C4×Dic86—22no—
73C4×Dic86—22no—
74D4×Dic43—22no—
75D4×Dic43—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43D411yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4D411yescharacteristic
87C2×Dic43⋊C4D411yescharacteristic
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063257—41no—
95#13063256—41no—
96Dic43⋊C8—22no—
97Dic43⋊C8D414yes—
98#13063250—22no—
99#13063250—41no—
100#13063249—22no—
101#13063249—22no—
102#13063248—22no—
103#13063246—22no—
104C4×C43⋊C8—22no—
105C8×Dic43—22no—
106C8×Dic43—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C22×Q8×C43C2311yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C2×SD16×C43—22no—
119C2×SD16×C43—22no—
120C2×SD16×C43—41no—
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
128C4⋊C8×C43—22no—
129#103×C43—41no—
130#102×C43—22no—
131#95×C43—21no—
132#95×C43—21no—
133C24×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43#4112yes—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×Dic86—22no—
164C2×Dic86—22no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86SD1614yescomplemented
172SD16×C43—44no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D412yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—81no—
185C42×C43—21no—
186C42×C43—21no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—81no—
190#10621883—44no—
191C4⋊Dic43—22no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—42no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205Dic43⋊C4—81no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—42no—
209C4×Dic43C2×D412yes—
210C4×Dic43#4112yes—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8C2×D412yes—
216C2×C43⋊C8#4112yes—
217C23×C43—22no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43C22×D411yescharacteristic
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—41no—
232D4×C43—41no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43C2×SD1612yes—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×C4×C432−1+411yescharacteristic
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—84no—
274C2×Dic43#12112yes—
275C2×Dic43#12112yes—
276C2×Dic43C2×SD1612yes—
277C2×Dic43C2×SD1612yes—
278C2×Dic43#13512yes—
279Dic86—28no—
280Dic86—41no—
281Dic86—41no—
282Dic86—41no—
283Dic86—41no—
284C8×C43—22no—
285C8×C43—41no—
286C43⋊C8—22no—
287C43⋊C8—22no—
288#25293—431nomaximal, Sylow
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43C2×#12111yescharacteristic
297C22×C43#54811yescharacteristic
298C22×C43#55011yescharacteristic
299C22×C43C22×SD1611yescharacteristic
300C22×C43C2×#13511yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57811yescharacteristic
303C4×C43—22no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43#52911yescharacteristic
309C4×C43#54211yescharacteristic
310C4×C43#54611yescharacteristic
311C4×C43#54811yescharacteristic
312Dic43—22no—
313Dic43—22no—
314Dic43—41no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318Dic43—81no—
319Dic43#46514yes—
320C2×#461—431no—
321C2×C8×Q8—431no—
322#2568—431no—
323#2538—431no—
324#2066—431no—
325#2066—431no—
326#2055—431no—
327#2055D4311yescharacteristic
328#1968—431no—
329#1968—431no—
330#1956—431no—
331#1948—431no—
332#1933—431no—
333#1933—431no—
334C4×#102—431no—
335C2×C43—82no—
336C2×C43#242611yescharacteristic
337C2×C43C2×#46511yescharacteristic
338C2×C43#306311yescharacteristic
339C2×C43#335911yescharacteristic
340C2×C43#336011yescharacteristic
341C2×C43#339211yescharacteristic
342C2×C43#339311yescharacteristic
343C22×SD16—431no—
344C22×SD16C2×D4311yescharacteristic
345C2×C4⋊Q8—431no—
346C2×C22⋊Q8—861no—
347C2×C4×Q8—431no—
348C2×C4×D4—431no—
349#461—864no—
350C8×Q8—864no—
351C2×#106—431no—
352C2×#106—431no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8—431no—
355C2×C4⋊C8C2×D4311yescharacteristic
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#103C2×D4311yescharacteristic
362C2×#102—431no—
363C2×#102C2×D4311yescharacteristic
364C2×C4×C8—431no—
365C2×C4×C8—431no—
366C2×C4×C8—431no—
367#400—861no—
368#400—861no—
369#396—861no—
370#396—861no—
371#391—431no—
372#391—431no—
373#391—431no—
374#391—861no—
375#391C2×D4311yescharacteristic
376#390—431no—
377#390C2×D4311yescharacteristic
378#389—431no—
379#389—431no—
380#384—431no—
381#382—861no—
382#380—861no—
383C4×C4⋊C4—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340C2×D4311yescharacteristic
388C43#2529311yescharacteristic, complemented, Sylow
389C22×Q8—431no—
390C22×Q8—431no—
391C22×Q8C22×D4311yescharacteristic
392C22×D4C22×D4311yescharacteristic
393C23×C4—861no—
394C2×SD16—22no—
395C2×SD16—22no—
396C2×SD16—41no—
397C2×SD16—862no—
398C2×SD16—862no—
399C2×SD16—1721no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404C4⋊Q8—862no—
405C4⋊Q8—862no—
406C22⋊Q8—1724no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×D4—862no—
410C4×D4—862no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434#106—1721no—
435#106—1721no—
436C4⋊C8—22no—
437C4⋊C8—434no—
438C4⋊C8—862no—
439#103—41no—
440#103—862no—
441#103—862no—
442#103—862no—
443#103—862no—
444#103—1721no—
445#102—22no—
446#102—862no—
447C4×C8—862no—
448C4×C8—862no—
449C4×C8—862no—
450#95—21no—
451#95—21no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461C24—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—434no—
469C2×Q8—862no—
470C2×Q8—862no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4#1062190012yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500SD16—44no—
501SD16—1724no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—432no—
508C2×C8—432no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8D4×D4312yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—3441no—
528C4⋊C4—1722no—
529C4⋊C4—1722no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C22⋊C4—42no—
534C22⋊C4—81no—
535C22⋊C4—3441no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C42—21no—
539C42—21no—
540C42—432no—
541C42—432no—
542C42—861no—
543C42—861no—
544C42—1722no—
545C23—22no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C2×D4×D4311yescharacteristic
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—41no—
557Q8—868no—
558Q8—1721no—
559Q8—1721no—
560Q8—1721no—
561Q8—1721no—
562D4—22no—
563D4—22no—
564D4—41no—
565D4—41no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—3444no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4SD16×D4312yes—
606C2×C4C2×D4×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4C2×#1062190011yescharacteristic
610C2×C4#1306337011yescharacteristic
611C2×C4#1306337211yescharacteristic
612C8—22no—
613C8—41no—
614C8—862no—
615C8—862no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22#121×D4311yescharacteristic
624C22#1458355511yescharacteristic
625C22#1458356711yescharacteristic
626C22C2×SD16×D4311yescharacteristic
627C22#135×D4311yescharacteristic
628C22#1458370911yescharacteristic
629C22#1458371511yescharacteristic
630C4—22no—
631C4—41no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—434no—
636C4—862no—
637C4—862no—
638C4—3441no—
639C4—3441no—
640C4—3441no—
641C4—3441no—
642C4—1721no—
643C4#1458342611yescharacteristic
644C4#1458351711yescharacteristic
645C4#1458353611yescharacteristic
646C4#1458355711yescharacteristic
647C2—82no—
648C2#1913815411yescharacteristic
649C2#465×D4311yescharacteristic
650C2#1914428111yescharacteristic
651C2#1914723211yescharacteristic
652C2#1914723911yescharacteristic
653C2#1914757511yescharacteristic
654C2#1914757811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2055C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2055D43
hypocenterC43#25293
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. C2×#14583023C2semidirect
3. #19139809C2semidirect
5. #19135975C2semidirect
6. #19135972C2semidirect
10. #19135395C2semidirect
11. #19135357C2semidirect
12. #19135274C2semidirect
13. #19135272C2semidirect
171. C2×Dic86SD16semidirect
388. C43#25293semidirect

Maximal subgroups

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

subgroupindex
C2×#145831022
C2×#145830232
#191398092
#191395152
#191359752
#191359722
#191359112
#191354512
#191354482
#191353952
#191353572
#191352742
#191352722
#102×Dic432
C43×#20552
#2529343