Finite Group Databasebeta

← #25115110

Subgroups — #25115110

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583022C211yesmaximal, characteristic
2#19143480C211yesmaximal, characteristic
3#19143472C211yesmaximal, characteristic
4#19143192C211yesmaximal, characteristic, complemented
5#19143187C211yesmaximal, characteristic, complemented
6#19135380C211yesmaximal, characteristic, complemented
7#19135375C211yesmaximal, characteristic, complemented
8#19134829C211yesmaximal, characteristic, complemented
9#19134829C211yesmaximal, characteristic, complemented
10#19134822C211yesmaximal, characteristic, complemented
11#19134822C211yesmaximal, characteristic, complemented
12#19134763C211yesmaximal, characteristic, complemented
13#19134656C211yesmaximal, characteristic, complemented
14#19134651C211yesmaximal, characteristic, complemented
15C43×#1773C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19#14583379C2211yescharacteristic
20#14583379C2211yescharacteristic
21#14583379C2211yescharacteristic
22#14583379C2211yescharacteristic
23#14583022C418yescomplemented
24#14583012—21no—
25#14583007—21no—
26#14583001—21no—
27#14583001—21no—
28C4×Dic172—21no—
29C4×#10621873—21no—
30C4×#10621873—21no—
31C4×D344—21no—
32C2×#13063261C2211yescharacteristic
33#14582942C2211yescharacteristic
34#14582942C2211yescharacteristic
35#14582942C2211yescharacteristic
36#14582942C2211yescharacteristic
37#14582940—21no—
38#14582940—21no—
39#14582938—21no—
40#14582938—21no—
41#14582936—21no—
42#14582934—21no—
43C2×#13063259C2211yescharacteristic
44C2×#13063259C2211yescharacteristic
45#107×D43—21no—
46C2×#13063257C2211yescharacteristic
47C2×#13063257C2211yescharacteristic
48#106×D43—21no—
49C2×#13063253C2211yescharacteristic
50C2×#13063253C2211yescharacteristic
51#14582901C2211yescharacteristic
52#14582901C2211yescharacteristic
53#14582901C2211yescharacteristic
54#14582901C2211yescharacteristic
55#14582769C2211yescharacteristic
56#14582765C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582667C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic
62C43×#427C2211yescharacteristic
63C43×#405C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C2×#97×C43C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C43×#339C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69C2×#10621898C2311yescharacteristic
70#13063347C2×C414yes—
71#13063347Q814yes—
72C2×Dic172D411yescharacteristic
73C2×#10621873D411yescharacteristic
74C2×#10621873D411yescharacteristic
75C2×D344D411yescharacteristic
76#13063331—22no—
77#13063331—22no—
78#13063331C2×C414yescomplemented
79#13063331C2×C414yescomplemented
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621872—21no—
83C2×#10621872—21no—
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×D172—21no—
91C4×D172—21no—
92C4×D172—21no—
93C4×D172—21no—
94(C22⋊D43)⋊C4—41no—
95(C22⋊D43)⋊C4—41no—
96(C22⋊D43)⋊C4—41no—
97(C22⋊D43)⋊C4—41no—
98#13063283—21no—
99#13063283—21no—
100#13063283—21no—
101#13063283—21no—
102C2×C4⋊Dic43—41no—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C4⋊C4×D43—21no—
108C4⋊C4×D43—21no—
109C4⋊C4×D43—21no—
110C4⋊C4×D43—21no—
111#13063261C2×C414yescomplemented
112#13063259—21no—
113#13063259—21no—
114#13063259—21no—
115#13063259—21no—
116#13063258—21no—
117#13063258—21no—
118#13063258—21no—
119#13063258—21no—
120#13063257—21no—
121#13063257—21no—
122#13063257—21no—
123#13063257—21no—
124#13063256—21no—
125#13063256—21no—
126#13063256—21no—
127#13063256—21no—
128#13063253C2×C414yescomplemented
129#13063253C2×C414yescomplemented
130#13063250—21no—
131#13063250—21no—
132#13063250—21no—
133#13063250—21no—
134#13063247—21no—
135#13063247—21no—
136#13063247—21no—
137#13063247—21no—
138C43⋊#95—41no—
139C2×M16×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143#117×C43C2311yescharacteristic
144#117×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#108×C43—22no—
147#107×C43D411yescharacteristic
148#107×C43D411yescharacteristic
149#106×C43D411yescharacteristic
150#106×C43D411yescharacteristic
151#97×C43—21no—
152#97×C43—21no—
153#97×C43C2×C414yescomplemented
154C4×C8×C43—21no—
155C4×C8×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—21no—
159C2×C22⋊D43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164#10621898—21no—
165#10621898—21no—
166#10621898—21no—
167#10621898—21no—
168#10621898C22×C412yes—
169#10621898C22×C412yes—
170#10621898C2×Q812yes—
171#10621898C2×Q812yes—
172C2×D172C2×D411yescharacteristic
173C2×D172C2×D411yescharacteristic
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—41no—
177C2×C4×D43—41no—
178C2×C4×D43—41no—
179C2×C4×D43—41no—
180C2×Dic86C2×D411yescharacteristic
181C2×Dic86C2×D411yescharacteristic
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43C22×C412yes—
189C2×C8×C43C22×C412yes—
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×Q812yes—
195C2×C8×C43#4112yes—
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43C22×C412yes—
206(C2×D43)⋊C4—41no—
207(C2×D43)⋊C4—41no—
208(C2×D43)⋊C4—41no—
209(C2×D43)⋊C4—41no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—82no—
219Dic43⋊C4—41no—
220Dic43⋊C4—41no—
221Dic43⋊C4—41no—
222Dic43⋊C4—41no—
223C4×Dic43—41no—
224C4×Dic43—41no—
225C4×Dic43—41no—
226C4×Dic43—41no—
227#10621877—21no—
228#10621877—21no—
229#10621877C22×C412yes—
230#10621877C22×C412yes—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233Dic172C4⋊C414yescomplemented
234D344C4⋊C414yescomplemented
235#10621873C4⋊C414yescomplemented
236#10621873C4⋊C414yescomplemented
237#10621872—24no—
238#10621872—24no—
239C8×D43—24no—
240C8×D43—24no—
241C23×C43H(5,𝔽2)11yescharacteristic
242C22×D43—21no—
243C22×D43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×Q811yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C432−1+411yescharacteristic
257C22⋊D43—22no—
258C22⋊D43—22no—
259C22⋊D43—22no—
260C22⋊D43—22no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—81no—
268C2×Dic43—81no—
269C2×Dic43—81no—
270C2×Dic43—81no—
271D172—21no—
272D172—21no—
273D172C2×C4⋊C412yes—
274D172C2×C4⋊C412yes—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—161no—
280C4×D43—161no—
281C4×D43—161no—
282C4×D43—161no—
283Dic86—21no—
284Dic86—21no—
285Dic86C2×C4⋊C412yes—
286Dic86C2×C4⋊C412yes—
287C8×C43—41no—
288C8×C43—41no—
289C8×C43C2×C4⋊C412yes—
290C8×C43C2×C4⋊C412yes—
291C8×C43C4×D412yes—
292C8×C43C4×D412yes—
293C43⋊C8—22no—
294C43⋊C8—22no—
295#22693—431nomaximal, Sylow
296C22×C43—21no—
297C22×C43—21no—
298C22×C43#52011yescharacteristic
299C22×C43D4211yescharacteristic
300C22×C43#55411yescharacteristic
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—41no—
307C4×C43—42no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43C22×C4⋊C411yescharacteristic
313C4×C43C2×C4×D411yescharacteristic
314C4×C43#54711yescharacteristic
315C4×C43D4×Q811yescharacteristic
316Dic43—22no—
317Dic43—22no—
318Dic43—81no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322C2×#444—431no—
323#2952—431no—
324#2951—431no—
325#2913—431no—
326#2912—431no—
327#1952—431no—
328#1951—431no—
329#1860—431no—
330#1860—431no—
331#1859—431no—
332#1859—431no—
333#1847—431no—
334#1816—431no—
335#1815—431no—
336#1773D4311yescharacteristic, complemented
337C2×C43—21no—
338C2×C43—21no—
339C2×C43D4×C4⋊C411yescharacteristic
340C2×C43#328811yescharacteristic
341C2×C43#328911yescharacteristic
342D43—42no—
343D43—42no—
344C2×#135—431no—
345C2×#131—431no—
346C2×#131—431no—
347#520—431no—
348#520—431no—
349#520—431no—
350#520—431no—
351#444—438no—
352#442—861no—
353#441—861no—
354#440—861no—
355#440—861no—
356C4×Q16—861no—
357C4×SD16—861no—
358C4×SD16—861no—
359C4×D8—861no—
360C2×#108—431no—
361C2×#108C2×D4311yescharacteristic
362#428—431no—
363#428—431no—
364#428—431no—
365#428—431no—
366#428—861no—
367#428—861no—
368#428—861no—
369#428—861no—
370#427—861no—
371#427—861no—
372#427C2×D4311yescharacteristic
373C2×#107—431no—
374C2×#107—431no—
375C2×#107—861no—
376C2×#106—431no—
377C2×#106—431no—
378C2×#106—861no—
379C2×#104—431no—
380C2×#104—431no—
381#417—431no—
382#417—431no—
383#417—431no—
384#417—431no—
385#405C2×D4311yescharacteristic
386#405C2×D4311yescharacteristic
387C2×#97C2×D4311yescharacteristic
388#384—431no—
389#382—431no—
390#343—431no—
391#343—431no—
392#343—431no—
393#343—431no—
394#339C2×D4311yescharacteristic
395#339C2×D4311yescharacteristic
396C43#2269311yescharacteristic, complemented, Sylow
397C2×#41—431no—
398C2×#41—431no—
399#135—434no—
400#135—434no—
401C2×Q16—431no—
402C2×SD16—431no—
403C2×SD16—431no—
404C2×D8—431no—
405#131—434no—
406#131—434no—
407#131—862no—
408#131—862no—
409C2×M16—431no—
410C2×M16—431no—
411C2×M16—861no—
412C2×M16—861no—
413C2×M16C22×D4311yescharacteristic
414C2×M16C22×D4311yescharacteristic
415C22×C8—861no—
416C22×C8—861no—
417C22×C8C22×D4311yescharacteristic
418C22×C8C22×D4311yescharacteristic
419C4×Q8—861no—
420C4×Q8—861no—
421C4×Q8—861no—
422C4×Q8—861no—
423C4×D4—861no—
424C4×D4—861no—
425C4×D4—861no—
426C4×D4—861no—
427C4×D4—1721no—
428C4×D4—1721no—
429C4×D4—1721no—
430C4×D4—1721no—
431#117—861no—
432#117—861no—
433#117—861no—
434#117—861no—
435#117C22×D4311yescharacteristic
436#117C22×D4311yescharacteristic
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—1721no—
446C2×C42C22×D4311yescharacteristic
447#108—22no—
448#108—434no—
449#107—861no—
450#107—861no—
451#107—861no—
452#107—861no—
453#107—861no—
454#107—861no—
455#107—861no—
456#107—861no—
457#107D17211yescharacteristic
458#107D17211yescharacteristic
459#106—861no—
460#106—861no—
461#106—861no—
462#106—861no—
463#106—861no—
464#106—861no—
465#106—861no—
466#106—861no—
467#106D17211yescharacteristic
468#106D17211yescharacteristic
469#104—434no—
470#104—434no—
471#103—861no—
472#103—861no—
473#103—861no—
474#103—861no—
475#102—861no—
476#102—861no—
477#102—861no—
478#102—861no—
479#97—21no—
480#97—21no—
481#97C4×D4314yescomplemented
482C4×C8—21no—
483C4×C8—21no—
484#95—1721no—
485#41—432no—
486#41—432no—
487#41—432no—
488#41—432no—
489#41—861no—
490#41—861no—
491#41—861no—
492#41—861no—
493C2×Q8—431no—
494C2×Q8—431no—
495C2×D4—431no—
496C2×D4—431no—
497C2×D4—861no—
498C2×D4—861no—
499C22×C4—21no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—1721no—
507C22×C4—1721no—
508C22×C4—1721no—
509C22×C4—1721no—
510C22×C4C23×D4311yescharacteristic
511Q16—434no—
512SD16—434no—
513SD16—434no—
514D8—434no—
515M16—21no—
516M16—21no—
517M16—21no—
518M16—21no—
519M16—432no—
520M16—432no—
521M16—861no—
522M16—861no—
523M16—864no—
524M16—864no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—864no—
530C2×C8—864no—
531C2×C8C2×C4×D4312yes—
532C2×C8C2×C4×D4312yes—
533C2×C8C2×D17211yescharacteristic
534C2×C8C2×D17211yescharacteristic
535C2×C8#1062189812yes—
536C2×C8D4×D4311yescharacteristic
537C2×C8D4×D4311yescharacteristic
538C2×C8Q8×D4312yes—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—3442no—
548C4⋊C4—1721no—
549C4⋊C4—1721no—
550C4⋊C4—1721no—
551C4⋊C4—1721no—
552C4⋊C4C2×D17211yescharacteristic
553C4⋊C4C2×D17211yescharacteristic
554C4⋊C4C2×D17211yescharacteristic
555C4⋊C4C2×D17211yescharacteristic
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—1721no—
559C22⋊C4—1721no—
560C22⋊C4—1721no—
561C22⋊C4—1721no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—1721no—
566C42—1721no—
567C42—1721no—
568C42—1721no—
569C42C2×C4×D4312yes—
570C23—861no—
571C23—861no—
572C23#1306337111yescharacteristic
573Q8—432no—
574Q8—432no—
575Q8—861no—
576Q8—861no—
577D4—432no—
578D4—432no—
579D4—862no—
580D4—862no—
581D4—862no—
582D4—862no—
583D4—861no—
584D4—861no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—3441no—
599C2×C4—3441no—
600C2×C4—3441no—
601C2×C4—3441no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—6881no—
607C2×C4—6881no—
608C2×C4—6881no—
609C2×C4—6881no—
610C2×C4C22×C4×D4311yescharacteristic
611C2×C4C2×D4×D4311yescharacteristic
612C2×C4C22×D17211yescharacteristic
613C2×C4C2×Q8×D4311yescharacteristic
614C2×C4C2×#1062189811yescharacteristic
615C2×C4#1306337211yescharacteristic
616C8—41no—
617C8—41no—
618C8—862no—
619C8—862no—
620C8C4⋊C4×D4312yes—
621C8C4⋊C4×D4312yes—
622C8C4×D17212yes—
623C8C4×D17212yes—
624C22—21no—
625C22—21no—
626C22—862no—
627C22—862no—
628C22—1721no—
629C22—1721no—
630C22—1721no—
631C22—1721no—
632C22#1458337911yescharacteristic
633C22D4×D17211yescharacteristic
634C22#1458360911yescharacteristic
635C4—42no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—862no—
641C4—862no—
642C4—3441no—
643C4—3441no—
644C4—3441no—
645C4—3441no—
646C4C2×C4⋊C4×D4311yescharacteristic
647C4C2×C4×D17211yescharacteristic
648C4#1458355411yescharacteristic
649C4Q8×D17211yescharacteristic
650C2—21no—
651C2—21no—
652C2—1722no—
653C2—1722no—
654C2C4⋊C4×D17211yescharacteristic
655C2#1914636211yescharacteristic
656C2#1914637111yescharacteristic
subgroupG/H
centerC22D4×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1773C2
socleC22×C43D42
prime radicalC2×#13063347C22
cosocleC22×C4×C43C24
hypercenter#1773D43
hypocenterC43#22693
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1773

Complements

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

NH ≅ G/Ntype
4. #19143192C2semidirect
5. #19143187C2semidirect
6. #19135380C2semidirect
7. #19135375C2semidirect
8. #19134829C2semidirect
9. #19134829C2semidirect
10. #19134822C2semidirect
11. #19134822C2semidirect
12. #19134763C2semidirect
13. #19134656C2semidirect
14. #19134651C2semidirect
15. C43×#1773C2semidirect
23. #14583022C4semidirect
78. #13063331C2×C4semidirect
79. #13063331C2×C4semidirect
111. #13063261C2×C4semidirect
128. #13063253C2×C4semidirect
129. #13063253C2×C4semidirect
153. #97×C43C2×C4semidirect
233. Dic172C4⋊C4semidirect
234. D344C4⋊C4semidirect
235. #10621873C4⋊C4semidirect
236. #10621873C4⋊C4semidirect
336. #1773D43semidirect
396. C43#22693semidirect
481. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830222
#191434802
#191434722
#191431922
#191431872
#191353802
#191353752
#191348292
#191348222
#191347632
#191346562
#191346512
C43×#17732
#2269343