Finite Group Databasebeta

← #25100154

Subgroups — #25100154

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582946C211yesmaximal, characteristic
2#19143182C211yesmaximal, characteristic
3C2×#14582940C211yesmaximal, characteristic
4#428×D43C211yesmaximal, characteristic
5#19143011C211yesmaximal, characteristic
6#19135379C211yesmaximal, characteristic, complemented
7#19135378C211yesmaximal, characteristic, complemented
8#19135377C211yesmaximal, characteristic, complemented
9#19135376C211yesmaximal, characteristic, complemented
10#19135375C211yesmaximal, characteristic, complemented
11#19135374C211yesmaximal, characteristic, complemented
12#19135372C211yesmaximal, characteristic, complemented
13#19134332C211yesmaximal, characteristic
14#343×D43C211yesmaximal, characteristic
15C43×#1952C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21#117×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582946C418yescomplemented
24C2×#13063261C2211yescharacteristic
25C2×#13063260C2211yescharacteristic
26C2×#13063260C2211yescharacteristic
27#14582942C2211yescharacteristic
28#14582942C2211yescharacteristic
29#14582941C2211yescharacteristic
30#14582941C2211yescharacteristic
31#14582940—21no—
32#14582940—21no—
33#14582940—21no—
34#14582940—21no—
35#14582940—21no—
36#14582940—21no—
37#14582939C2211yescharacteristic
38#14582939C2211yescharacteristic
39#14582938—21no—
40#14582938—21no—
41#14582936—21no—
42#14582934—21no—
43C2×#13063258C2211yescharacteristic
44#107×D43—21no—
45C2×#13063257C2211yescharacteristic
46C2×#13063256C2211yescharacteristic
47#106×D43—21no—
48#14582857C2211yescharacteristic
49#14582856—21no—
50#14582855C2211yescharacteristic
51#14582854C2211yescharacteristic
52#14582853—21no—
53#14582851—21no—
54C4×#10621872—21no—
55#14582668C2211yescharacteristic
56#14582668C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582667C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic
62C43×#428C2211yescharacteristic
63C43×#428C2211yescharacteristic
64C2×#107×C43C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#343C2211yescharacteristic
68C22×C4×D43—21no—
69C22×C4×D43C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C2×#10621872C2×C414yes—
77C2×#10621872D411yescharacteristic
78C2×#10621872D411yescharacteristic
79C2×#10621872D411yescharacteristic
80C2×#10621872D411yescharacteristic
81C2×#10621872Q814yes—
82M16×D43—22no—
83M16×D43—22no—
84M16×D43—22no—
85M16×D43C2×C414yes—
86M16×D43C2×C414yes—
87M16×D43Q814yes—
88C22×C43⋊C8C2311yescharacteristic
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91C2×C8×D43—21no—
92#13063284C2311yescharacteristic
93#13063283—21no—
94#13063283—21no—
95#13063283—21no—
96#13063283—21no—
97#13063283D411yescharacteristic
98#13063283D411yescharacteristic
99#13063282—21no—
100#13063281—21no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43—21no—
106C4⋊C4×D43—21no—
107C4⋊C4×D43—21no—
108C4⋊C4×D43D411yescharacteristic
109C4⋊C4×D43D411yescharacteristic
110C2×(C2×D43)⋊C4—21no—
111C22⋊C4×D43—21no—
112C2×C4×Dic43—21no—
113C42×D43—21no—
114#13063261C2×C414yescomplemented
115#13063260C2×C414yescomplemented
116#13063260C2×C414yescomplemented
117#13063259—21no—
118#13063259—21no—
119#13063258—21no—
120#13063258—21no—
121#13063258—21no—
122#13063258—21no—
123#13063258—21no—
124#13063258—21no—
125#13063257—21no—
126#13063257—21no—
127#13063257—21no—
128#13063257—21no—
129#13063256—21no—
130#13063256—21no—
131#13063256—21no—
132#13063256—21no—
133#13063256—21no—
134#13063256—21no—
135#13063236—21no—
136#13063235—21no—
137#13063235—21no—
138C4×C43⋊C8—21no—
139C8×Dic43—21no—
140C8×Dic43—21no—
141C2×M16×C43C2311yescharacteristic
142C2×M16×C43C2311yescharacteristic
143C2×M16×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145#117×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148#108×C43C2×C414yescomplemented
149#107×C43—21no—
150#107×C43—21no—
151#107×C43—21no—
152#107×C43—21no—
153#106×C43—21no—
154#106×C43—21no—
155#97×C43—21no—
156C4×C8×C43—21no—
157C23×D43#4111yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C2411yescharacteristic
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43#4111yescharacteristic
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—41no—
167C2×C4×D43—41no—
168C2×C4×D43—82no—
169C2×C4×D43C22×C412yes—
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×Q812yes—
175C2×C4×D43C2×Q812yes—
176C2×C4×D43#4112yes—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43C22×C412yes—
181M16×C43C22×C412yes—
182M16×C43C2×Q812yes—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43C22×C412yes—
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C2×C8×C43C2×Q812yes—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C22⋊C4×C43—21no—
197C42×C43—21no—
198C22⋊Dic43—21no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43C2×D411yescharacteristic
208C4⋊Dic43C2×D411yescharacteristic
209Dic43⋊C4—21no—
210Dic43⋊C4—21no—
211Dic43⋊C4—41no—
212Dic43⋊C4—41no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—41no—
217C4×Dic43—41no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877C22×C412yes—
222#10621877C22×C412yes—
223#10621877C2×Q812yes—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C22×C412yes—
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230C2×C43⋊C8C2×Q812yes—
231#10621872—24no—
232#10621872—24no—
233#10621872—24no—
234#10621872C4⋊C414yes—
235#10621872C4⋊C414yes—
236#10621872C4⋊C414yes—
237#10621872C4⋊C414yes—
238C8×D43—24no—
239C8×D43—24no—
240C8×D43—24no—
241C23×C43C2×#4111yescharacteristic
242C22×D43—41no—
243C22×D43—41no—
244C22×D43C4×Q812yes—
245C22×D43#12111yescharacteristic
246C22×D43#12111yescharacteristic
247C22×D43#12512yes—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—81no—
253C2×C4×C43—81no—
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×Q811yescharacteristic
258C2×C4×C43C22×Q811yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—81no—
265C2×Dic43—81no—
266C2×Dic43C4×Q812yes—
267C2×Dic43#12111yescharacteristic
268C2×Dic43#12111yescharacteristic
269C2×Dic43#12512yes—
270C4×D43—81no—
271C4×D43—81no—
272C4×D43—82no—
273C4×D43—82no—
274C4×D43C2×C4⋊C412yes—
275C4×D43C2×C4⋊C412yes—
276C4×D43C4×D412yes—
277C4×D43C4×D412yes—
278C4×D43C22⋊Q812yes—
279C4×D43C22⋊Q812yes—
280C4×D43C4⋊Q812yes—
281C4×D43C4⋊Q812yes—
282C8×C43—22no—
283C8×C43—22no—
284C8×C43—22no—
285C8×C43C2×C4⋊C412yes—
286C8×C43C2×C4⋊C412yes—
287C43⋊C8—22no—
288C43⋊C8—22no—
289C43⋊C8—22no—
290C43⋊C8C2×C4⋊C412yes—
291C43⋊C8C2×C4⋊C412yes—
292#21182—431nomaximal, Sylow
293C22×C43—21no—
294C22×C43—21no—
295C22×C43C2×C4×Q811yescharacteristic
296C22×C43C2×#12111yescharacteristic
297C22×C43C2×#12511yescharacteristic
298C2×D43—21no—
299C2×D43—21no—
300C2×D43—21no—
301C2×D43—21no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43#38912yes—
305C2×D43#38912yes—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43C22×C4⋊C411yescharacteristic
311C4×C43C2×C4×D411yescharacteristic
312C4×C43C2×C22⋊Q811yescharacteristic
313C4×C43C2×C4⋊Q811yescharacteristic
314Dic43—41no—
315Dic43—41no—
316Dic43—81no—
317Dic43—81no—
318Dic43#38912yes—
319Dic43#38912yes—
320C2×#430—431no—
321#2911—431no—
322C2×#428—431no—
323C2×#428—431no—
324#2873—431no—
325#1952—431no—
326#1952—431no—
327#1952—431no—
328#1952D4311yescharacteristic, complemented
329#1951—431no—
330#1951—431no—
331#1951—431no—
332#1951—431no—
333#1742—431no—
334C2×#343—431no—
335C2×C43—21no—
336C2×C43—21no—
337C2×C43C2×#38911yescharacteristic
338C2×C43#306811yescharacteristic
339C2×C43#306911yescharacteristic
340D43—22no—
341D43—22no—
342C22×M16—431no—
343C22×M16—431no—
344C22×M16—431no—
345C22×M16—431no—
346C2×#117—431no—
347C2×#117—431no—
348C22×C4⋊C4—431no—
349#430—438no—
350C2×#108—431no—
351C2×#108—431no—
352C2×#108—431no—
353C2×#108C2×D4311yescharacteristic
354#428—431no—
355#428—431no—
356#428—431no—
357#428—431no—
358#428—431no—
359#428—431no—
360#428—861no—
361#428—861no—
362#428—861no—
363#428—861no—
364#428—861no—
365#428—861no—
366#428—861no—
367#428—861no—
368#428C2×D4311yescharacteristic
369#428C2×D4311yescharacteristic
370#427—861no—
371#427—861no—
372C2×#107—431no—
373C2×#107—861no—
374C2×#107C2×D4311yescharacteristic
375C2×#106—431no—
376C2×#106—431no—
377C2×#106—861no—
378#405—431no—
379#405—431no—
380#405—431no—
381#405—861no—
382#405—861no—
383#405C2×D4311yescharacteristic
384C4×M16—861no—
385C4×M16—861no—
386#343—431no—
387#343—431no—
388#343—431no—
389#343—431no—
390#343—431no—
391#343—431no—
392#343C2×D4311yescharacteristic
393#343C2×D4311yescharacteristic
394C43#2118211yescharacteristic, complemented, Sylow
395C23×C4—431no—
396C23×C4—861no—
397C2×M16—434no—
398C2×M16—431no—
399C2×M16—431no—
400C2×M16—431no—
401C2×M16—431no—
402C2×M16—434no—
403C2×M16—431no—
404C2×M16—431no—
405C2×M16—431no—
406C2×M16—434no—
407C2×M16—434no—
408C2×M16—434no—
409C2×M16—861no—
410C2×M16—861no—
411C2×M16—861no—
412C2×M16—862no—
413C2×M16—862no—
414C2×M16—862no—
415C2×M16C22×D4311yescharacteristic
416C2×M16C22×D4311yescharacteristic
417C2×M16C22×D4311yescharacteristic
418C22×C8—431no—
419C22×C8—861no—
420C22×C8—861no—
421C22×C8—861no—
422C22×C8C22×D4311yescharacteristic
423#117—431no—
424#117—431no—
425#117—431no—
426#117—861no—
427#117—861no—
428#117—861no—
429#117—861no—
430#117—861no—
431#117—861no—
432#117C22×D4311yescharacteristic
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4C22×D4311yescharacteristic
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C42—861no—
447C2×C42—861no—
448#108—434no—
449#108—434no—
450#108—434no—
451#108C4×D4314yescomplemented
452#107—21no—
453#107—21no—
454#107—21no—
455#107—21no—
456#107—861no—
457#107—861no—
458#107—861no—
459#107—861no—
460#107—861no—
461#107—861no—
462#107—861no—
463#107—861no—
464#106—21no—
465#106—21no—
466#106—861no—
467#106—861no—
468#106—861no—
469#106—861no—
470#106—861no—
471#106—861no—
472#106—861no—
473#106—861no—
474#106—861no—
475#106—861no—
476#97—21no—
477#97—861no—
478#97—861no—
479#97—861no—
480C4×C8—21no—
481C4×C8—861no—
482C4×C8—861no—
483C4×C8—861no—
484C24—431no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—431no—
488C22×C4—432no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—432no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—3442no—
501C22×C4—1721no—
502C22×C4—1721no—
503C22×C4C23×D4311yescharacteristic
504M16—21no—
505M16—21no—
506M16—21no—
507M16—434no—
508M16—434no—
509M16—434no—
510M16—434no—
511M16—432no—
512M16—432no—
513M16—432no—
514M16—864no—
515M16—864no—
516M16—864no—
517M16—861no—
518M16—861no—
519M16—861no—
520M16C2×C4×D4312yes—
521M16C2×C4×D4312yes—
522M16Q8×D4312yes—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—432no—
527C2×C8—431no—
528C2×C8—431no—
529C2×C8—432no—
530C2×C8—864no—
531C2×C8—864no—
532C2×C8—864no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8C2×C4×D4312yes—
537C2×C8D4×D4311yescharacteristic
538C2×C8D4×D4311yescharacteristic
539C2×C8Q8×D4312yes—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—431no—
545C4⋊C4—431no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—1721no—
553C4⋊C4—1721no—
554C4⋊C4D4×D4311yescharacteristic
555C4⋊C4D4×D4311yescharacteristic
556C22⋊C4—21no—
557C22⋊C4—861no—
558C22⋊C4—861no—
559C22⋊C4—861no—
560C22⋊C4—1721no—
561C22⋊C4—1721no—
562C42—21no—
563C42—861no—
564C42—861no—
565C42—861no—
566C42—1721no—
567C42—1721no—
568C23—431no—
569C23—431no—
570C23—432no—
571C23—432no—
572C23—1721no—
573C23—1721no—
574C23#41×D4311yescharacteristic
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—432no—
582C2×C4—431no—
583C2×C4—431no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—3441no—
596C2×C4—3441no—
597C2×C4—3442no—
598C2×C4—3442no—
599C2×C4—3441no—
600C2×C4—3441no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4C22×C4×D4311yescharacteristic
604C2×C4C2×D4×D4311yescharacteristic
605C2×C4C2×D4×D4311yescharacteristic
606C2×C4C2×Q8×D4311yescharacteristic
607C2×C4C2×Q8×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C8—22no—
610C8—22no—
611C8—22no—
612C8—432no—
613C8—432no—
614C8—862no—
615C8—862no—
616C8—862no—
617C8C4⋊C4×D4312yes—
618C8C4⋊C4×D4312yes—
619C22—21no—
620C22—21no—
621C22—432no—
622C22—432no—
623C22—861no—
624C22—861no—
625C22—861no—
626C22—861no—
627C22—1722no—
628C22—1722no—
629C22C4×Q8×D4311yescharacteristic
630C22#121×D4311yescharacteristic
631C22#125×D4311yescharacteristic
632C4—41no—
633C4—41no—
634C4—81no—
635C4—81no—
636C4—432no—
637C4—432no—
638C4—3441no—
639C4—3441no—
640C4—1721no—
641C4—1721no—
642C4C2×C4⋊C4×D4311yescharacteristic
643C4C4×D4×D4311yescharacteristic
644C4C22⋊Q8×D4311yescharacteristic
645C4C4⋊Q8×D4311yescharacteristic
646C2—21no—
647C2—21no—
648C2—862no—
649C2—862no—
650C2#389×D4311yescharacteristic
651C2#1914432111yescharacteristic
652C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1952C2
socleC22×C43C2×#121
prime radicalC23×D43#41
cosocleC22×C4×C43C24
hypercenter#1952D43
hypocenterC43#21182
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
6. #19135379C2semidirect
7. #19135378C2semidirect
8. #19135377C2semidirect
9. #19135376C2semidirect
10. #19135375C2semidirect
11. #19135374C2semidirect
12. #19135372C2semidirect
15. C43×#1952C2semidirect
23. #14582946C4semidirect
114. #13063261C2×C4semidirect
115. #13063260C2×C4semidirect
116. #13063260C2×C4semidirect
148. #108×C43C2×C4semidirect
328. #1952D43semidirect
394. C43#21182semidirect
451. #108C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829462
#191431822
C2×#145829402
#428×D432
#191430112
#191353792
#191353782
#191353772
#191353762
#191353752
#191353742
#191353722
#191343322
#343×D432
C43×#19522
#2118243