Finite Group Databasebeta

← D3×#93759 #72254963

Subgroups — D3×#93759 #72254963

Order 3072.

746 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72245577C211yesmaximal, characteristic, complemented
2#72245562C211yesmaximal, characteristic, complemented
3#72245517C211yesmaximal, characteristic, complemented
4C3×#93759C211yesmaximal, characteristic, complemented
5D3×#7456C211yesmaximal, characteristic, complemented
6D3×#12047C211yesmaximal, characteristic
7D3×#7053C211yesmaximal, characteristic, complemented
8C2×#93759—31nomaximal, Sylow
9D3×#2178C411yescharacteristic
10D3×#2170—21no—
11D3×#1422—21no—
12#10706949C2211yescharacteristic
13#10706948C411yescharacteristic
14#10706947C411yescharacteristic
15#10706946—21no—
16#10706945—21no—
17D3×#1373C411yescharacteristic
18D3×#1335—21no—
19D3×#1312—21no—
20D3×#1311C2211yescharacteristic
21#10682855C2211yescharacteristic, complemented
22#10682854—21no—
23#10681804—21no—
24#10681803C2211yescharacteristic, complemented
25C3×#12047C2211yescharacteristic
26C3×#7456C2211yescharacteristic, complemented
27C3×#7053C2211yescharacteristic, complemented
28C2×#12047—31no—
29C2×#7456—31no—
30C2×#7053—31no—
31#93759—31no—
32#93759—31no—
33#93759—31no—
34#93759D311yescharacteristic, direct product factor
35D3×#508C811yescharacteristic
36D3×#504—41no—
37D3×#443—21no—
38C3×#2178C2×C411yescharacteristic
39C3×#2170—21no—
40#71511C811yescharacteristic
41#71452—41no—
42#70923—21no—
43#70921—21no—
44D3×M64—41no—
45D3×#368C811yescharacteristic
46#69357C811yescharacteristic
47D3×#364—21no—
48#69300—21no—
49D3×#359—21no—
50#69238—21no—
51D3×#350—41no—
52#69122—41no—
53#69067C2×C411yescharacteristic
54#69056—21no—
55C4×D3×C16—22no—
56C4×D3×C16C2×C411yescharacteristic
57C4×D3×C16D411yescharacteristic
58D3×C82D411yescharacteristic
59C3×#1422—21no—
60C3×#1373C2×C411yescharacteristic
61C3×#1335—21no—
62C3×#1312—21no—
63C3×#1311C2311yescharacteristic
64#67766—21no—
65#67599—41no—
66#67568—21no—
67#67566—21no—
68#67510—21no—
69#67502C2×C411yescharacteristic
70#67499—22no—
71#67498C2×C411yescharacteristic
72#67498D411yescharacteristic
73#67441—21no—
74#67438—21no—
75#67437D411yescharacteristic
76C2×#2178—31no—
77C2×#2170—61no—
78C2×#1422—61no—
79#12047—31no—
80#12047—31no—
81#12047—31no—
82#12047—61no—
83#12047—61no—
84#12047C2×D311yescharacteristic
85C2×#1373—31no—
86C2×#1335—61no—
87C2×#1312—61no—
88C2×#1311—31no—
89#7456—31no—
90#7456—61no—
91#7456C2×D311yescharacteristic, complemented
92#7053—31no—
93#7053—61no—
94#7053C2×D311yescharacteristic, complemented
95D3×#135—21no—
96D3×#131—41no—
97C3×#508C2×C811yescharacteristic
98C3×#504—41no—
99C3×#443—21no—
100#5196—21no—
101#5194—21no—
102#5144—41no—
103#5140—41no—
104#4919C1611yescharacteristic, complemented
105D3×Q32C1611yescharacteristic, complemented
106#4916—21no—
107D3×SD32—21no—
108#4912C1611yescharacteristic, complemented
109D3×D16C1611yescharacteristic, complemented
110#4907—41no—
111#4907—81no—
112D3×M32—41no—
113D3×M32—81no—
114#4904C2×C811yescharacteristic
115#4901—41no—
116#4901—81no—
117C2×D3×C16—42no—
118C2×D3×C16—81no—
119C2×D3×C16C2×C811yescharacteristic
120C2×D3×C16M1611yescharacteristic
121C2×D3×C16D811yescharacteristic
122C2×D3×C16SD1611yescharacteristic
123#4895—21no—
124D3×#108—21no—
125#4824—41no—
126D3×#104—41no—
127#4700—21no—
128C4×D3×C8—21no—
129C4×D3×C8C22⋊C411yescharacteristic
130C3×M64—41no—
131C3×#368C2×C811yescharacteristic
132C3×#364—21no—
133C3×#359—21no—
134C3×#350—41no—
135C3×C4×C16—22no—
136C3×C4×C16C22×C411yescharacteristic
137C3×C4×C16C2×D411yescharacteristic
138C3×C82C2×D411yescharacteristic
139#4567—21no—
140#4561—41no—
141#4515—41no—
142#4511—41no—
143#4510—21no—
144#4508—41no—
145#4506C2×C811yescharacteristic
146Dic3×C16—42no—
147Dic3×C16C2×C811yescharacteristic
148Dic3×C16M1611yescharacteristic
149Dic3×C16D811yescharacteristic
150Dic3×C16SD1611yescharacteristic
151#4499—41no—
152#4497—21no—
153#4493—21no—
154#4463—21no—
155C4×C3⋊C16—22no—
156C4×C3⋊C16C22⋊C411yescharacteristic
157C4×C3⋊C16C22⋊C411yescharacteristic
158C8×C3⋊C8—21no—
159C8×C3⋊C8C22⋊C411yescharacteristic
160#4447—81no—
161D3×C32—81no—
162C2×#508—31no—
163C2×#504—121no—
164C2×#443—61no—
165C2×M64—121no—
166#2178—31no—
167#2178—31no—
168#2178—31no—
169#2178—61no—
170#2178—61no—
171#2178C4×D311yescharacteristic
172#2170—21no—
173#2170—61no—
174#2170—61no—
175#2170—61no—
176#2170—121no—
177#2170—121no—
178C2×#368—31no—
179C2×#364—61no—
180C2×#359—61no—
181C2×#350—121no—
182C2×C4×C16—31no—
183C2×C4×C16—31no—
184C2×C4×C16—62no—
185C2×C82—31no—
186#1422—21no—
187#1422—61no—
188#1422—121no—
189#1373—31no—
190#1373—61no—
191#1373C4×D311yescharacteristic
192#1335—21no—
193#1335—61no—
194#1335—61no—
195#1335—61no—
196#1312—21no—
197#1312—62no—
198#1312—61no—
199#1311—31no—
200#1311—31no—
201#1311—31no—
202#1311C22×D311yescharacteristic
203D3×#41—41no—
204C3×#135—21no—
205C3×#131—41no—
206#950—41no—
207#948—41no—
208#919—21no—
209D3×Q16—21no—
210#916—41no—
211D3×SD16—41no—
212#912—21no—
213D3×D8—21no—
214#907—41no—
215#907—81no—
216D3×M16—41no—
217D3×M16—81no—
218#904—21no—
219#901—41no—
220#901—81no—
221C2×D3×C8—22no—
222C2×D3×C8—81no—
223C2×D3×C8C22⋊C811yescharacteristic
224C2×D3×C8#10211yescharacteristic
225C42×D3#10411yescharacteristic
226C3×Q32C2×C1611yescharacteristic, complemented
227C3×SD32—21no—
228C3×D16C2×C1611yescharacteristic, complemented
229C3×M32—41no—
230C3×M32—81no—
231C2×C3×C16—42no—
232C2×C3×C16—81no—
233C2×C3×C16C22×C811yescharacteristic
234C2×C3×C16C2×M1611yescharacteristic
235C2×C3×C16C2×D811yescharacteristic
236C2×C3×C16C2×SD1611yescharacteristic
237C3×#108—21no—
238C3×#104—41no—
239C3×C4×C8—21no—
240C3×C4×C8C2×C22⋊C411yescharacteristic
241#837—41no—
242#829—21no—
243#828—21no—
244#827—21no—
245#826—21no—
246#825—41no—
247#822—41no—
248#819—21no—
249C8×Dic3—22no—
250C8×Dic3C22⋊C811yescharacteristic
251C8×Dic3#10211yescharacteristic
252#812—41no—
253#812—81no—
254C2×C3⋊C16—42no—
255C2×C3⋊C16—81no—
256C2×C3⋊C16C22⋊C811yescharacteristic
257C2×C3⋊C16C22⋊C811yescharacteristic
258C2×C3⋊C16#10211yescharacteristic
259C2×C3⋊C16#10211yescharacteristic
260#805—41no—
261C4×C3⋊C8—21no—
262C4×C3⋊C8#10411yescharacteristic
263Dic24C2×C1611yescharacteristic, complemented
264#800—21no—
265D48C2×C1611yescharacteristic, complemented
266#798—81no—
267#798—81no—
268#798—81no—
269D3×C16—21no—
270D3×C16—21no—
271D3×C16—21no—
272D3×C16—21no—
273D3×C16—21no—
274D3×C16—21no—
275D3×C16—81no—
276D3×C16—81no—
277D3×C16—84no—
278D3×C16—81no—
279D3×C16C2×C1611yescharacteristic
280D3×C16C2×C1611yescharacteristic
281D3×C16M3211yescharacteristic
282D3×C16M3211yescharacteristic
283C3×C32—81no—
284C3⋊C32—81no—
285C2×#135—61no—
286C2×#131—121no—
287#508—31no—
288#508—31no—
289#508—31no—
290#508—61no—
291#508—61no—
292#508D3×C811yescharacteristic
293C2×Q32—31no—
294C2×SD32—61no—
295C2×D16—31no—
296#504—41no—
297#504—121no—
298#504—121no—
299#504—121no—
300#504—241no—
301#504—241no—
302C2×M32—121no—
303C2×M32—241no—
304C22×C16—31no—
305C22×C16—31no—
306C22×C16—31no—
307C22×C16—31no—
308C22×C16—122no—
309C22×C16—241no—
310#443—21no—
311#443—61no—
312#443—61no—
313#443—61no—
314#443—121no—
315#443—121no—
316C2×#108—61no—
317C2×#104—121no—
318C2×C4×C8—31no—
319C2×C4×C8—61no—
320M64—41no—
321M64—121no—
322M64—241no—
323C2×C32—241no—
324#368—31no—
325#368—61no—
326#368D3×C811yescharacteristic
327#364—21no—
328#364—61no—
329#364—121no—
330#359—21no—
331#359—61no—
332#359—61no—
333#359—61no—
334#350—41no—
335#350—121no—
336#350—121no—
337#350—121no—
338C4×C16—22no—
339C4×C16—31no—
340C4×C16—31no—
341C4×C16—31no—
342C4×C16—31no—
343C4×C16—31no—
344C4×C16—31no—
345C4×C16—62no—
346C4×C16—122no—
347C4×C16C2×C4×D311yescharacteristic
348C4×C16D3×D411yescharacteristic
349C82—31no—
350C82—61no—
351C82D3×D411yescharacteristic
352C3×#41—41no—
353#239—41no—
354D3×Q8—41no—
355#237—41no—
356#237—81no—
357D3×D4—41no—
358D3×D4—81no—
359#235—41no—
360#235—81no—
361C2×C4×D3—21no—
362C2×C4×D3—81no—
363C2×C4×D3D4⋊C811yescharacteristic
364C3×Q16—21no—
365C3×SD16—41no—
366C3×D8—21no—
367C3×M16—41no—
368C3×M16—81no—
369C2×C3×C8—22no—
370C2×C3×C8—81no—
371C2×C3×C8C2×C22⋊C811yescharacteristic
372C2×C3×C8C2×#10211yescharacteristic
373C3×C42C2×#10411yescharacteristic
374#216—41no—
375#215—41no—
376#214—41no—
377#213—41no—
378C4×Dic3—21no—
379C4×Dic3D4⋊C811yescharacteristic
380#208—41no—
381#208—81no—
382C2×C3⋊C8—22no—
383C2×C3⋊C8—81no—
384C2×C3⋊C8D4⋊C811yescharacteristic
385C2×C3⋊C8D4⋊C811yescharacteristic
386Dic12—21no—
387D24—21no—
388#204—41no—
389ΓL(1,𝔽25)—81no—
390ΓL(1,𝔽25)—81no—
391ΓL(1,𝔽25)—81no—
392D3×C8—44no—
393D3×C8—81no—
394D3×C8—81no—
395D3×C8—81no—
396D3×C8C22⋊C1611yescharacteristic
397D3×C8C22⋊C1611yescharacteristic
398D3×C8#35011yescharacteristic
399D3×C8#35011yescharacteristic
400D3×C8#36011yescharacteristic
401D3×C8#36011yescharacteristic
402D3×C8#36111yescharacteristic
403D3×C8#36111yescharacteristic
404C3×C16—21no—
405C3×C16—21no—
406C3×C16—21no—
407C3×C16—82no—
408C3×C16—81no—
409C3×C16C22×C1611yescharacteristic
410C3×C16C2×M3211yescharacteristic
411C3⋊C16—21no—
412C3⋊C16—21no—
413C3⋊C16—21no—
414C3⋊C16—82no—
415C3⋊C16—81no—
416C3⋊C16C22⋊C1611yescharacteristic
417C3⋊C16C22⋊C1611yescharacteristic
418C2×#41—121no—
419#135—21no—
420#135—61no—
421#135—61no—
422#135—61no—
423#135—121no—
424#135—121no—
425C2×Q16—61no—
426C2×SD16—121no—
427C2×D8—61no—
428#131—41no—
429#131—121no—
430#131—121no—
431#131—121no—
432#131—241no—
433#131—241no—
434C2×M16—121no—
435C2×M16—241no—
436C22×C8—31no—
437C22×C8—31no—
438C22×C8—62no—
439C22×C8—241no—
440C2×C42—31no—
441Q32—31no—
442Q32—61no—
443Q32D3×C1611yescharacteristic, complemented
444SD32—21no—
445SD32—61no—
446SD32—61no—
447SD32—61no—
448D16—31no—
449D16—61no—
450D16D3×C1611yescharacteristic, complemented
451M32—41no—
452M32—81no—
453M32—121no—
454M32—241no—
455M32—241no—
456M32—241no—
457M32—241no—
458C2×C16—31no—
459C2×C16—31no—
460C2×C16—31no—
461C2×C16—31no—
462C2×C16—31no—
463C2×C16—31no—
464C2×C16—31no—
465C2×C16—31no—
466C2×C16—42no—
467C2×C16—61no—
468C2×C16—61no—
469C2×C16—61no—
470C2×C16—61no—
471C2×C16—61no—
472C2×C16—61no—
473C2×C16—81no—
474C2×C16—122no—
475C2×C16—241no—
476C2×C16—241no—
477C2×C16—241no—
478C2×C16—241no—
479C2×C16—244no—
480C2×C16C2×D3×C811yescharacteristic
481C2×C16D3×M1611yescharacteristic
482C2×C16D3×D811yescharacteristic
483C2×C16D3×SD1611yescharacteristic
484#108—21no—
485#108—61no—
486#108—121no—
487#104—41no—
488#104—121no—
489#104—121no—
490#104—121no—
491C4×C8—21no—
492C4×C8—31no—
493C4×C8—31no—
494C4×C8—31no—
495C4×C8—62no—
496C4×C8—61no—
497C4×C8D3×C22⋊C411yescharacteristic
498C32—81no—
499C32—241no—
500C22×D3—81no—
501C22×D3#133611yescharacteristic
502C3×Q8—41no—
503C3×D4—41no—
504C3×D4—81no—
505C2×C3×C4—21no—
506C2×C3×C4—81no—
507C2×C3×C4C2×D4⋊C811yescharacteristic
508#67—81no—
509#67—81no—
510#67—81no—
511C2×Dic3—21no—
512C2×Dic3—81no—
513C2×Dic3#133611yescharacteristic
514D12—41no—
515D12—81no—
516C4×D3—24no—
517C4×D3—81no—
518C4×D3—81no—
519C4×D3—81no—
520C4×D3D4⋊C1611yescharacteristic
521C4×D3D4⋊C1611yescharacteristic
522C4×D3#133311yescharacteristic
523C4×D3#133311yescharacteristic
524Dic6—41no—
525Dic6—81no—
526C3×C8—42no—
527C3×C8—81no—
528C3×C8C2×C22⋊C1611yescharacteristic
529C3×C8C2×#35011yescharacteristic
530C3×C8C2×#36011yescharacteristic
531C3×C8C2×#36111yescharacteristic
532C3⋊C8—42no—
533C3⋊C8—81no—
534C3⋊C8D4⋊C1611yescharacteristic
535C3⋊C8D4⋊C1611yescharacteristic
536C3⋊C8#133311yescharacteristic
537C3⋊C8#133311yescharacteristic
538#41—41no—
539#41—121no—
540#41—121no—
541#41—121no—
542#41—241no—
543#41—241no—
544C2×Q8—121no—
545C2×D4—121no—
546C2×D4—241no—
547C22×C4—31no—
548C22×C4—61no—
549C22×C4—241no—
550Q16—21no—
551Q16—61no—
552Q16—121no—
553SD16—41no—
554SD16—121no—
555SD16—121no—
556SD16—121no—
557D8—21no—
558D8—61no—
559D8—121no—
560M16—41no—
561M16—81no—
562M16—121no—
563M16—241no—
564M16—241no—
565M16—241no—
566M16—241no—
567C2×C8—22no—
568C2×C8—31no—
569C2×C8—31no—
570C2×C8—31no—
571C2×C8—31no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8—31no—
578C2×C8—62no—
579C2×C8—81no—
580C2×C8—124no—
581C2×C8—241no—
582C2×C8—241no—
583C2×C8—241no—
584C2×C8—241no—
585C2×C8D3×C22⋊C811yescharacteristic
586C2×C8D3×#10211yescharacteristic
587C42—31no—
588C42—61no—
589C42D3×#10411yescharacteristic
590C16—21no—
591C16—21no—
592C16—21no—
593C16—31no—
594C16—31no—
595C16—61no—
596C16—61no—
597C16—61no—
598C16—82no—
599C16—81no—
600C16—242no—
601C16—241no—
602C16C2×D3×C1611yescharacteristic
603C16D3×M3211yescharacteristic
604C22×C3—81no—
605C22×C3C2×#133611yescharacteristic
606C2×D3—22no—
607C2×D3—81no—
608C2×D3—162no—
609C2×D3#707011yescharacteristic
610C2×D3#707011yescharacteristic
611C3×C4—22no—
612C3×C4—81no—
613C3×C4C2×D4⋊C1611yescharacteristic
614C3×C4C2×#133311yescharacteristic
615Dic3—22no—
616Dic3—81no—
617Dic3#707011yescharacteristic
618Dic3#707011yescharacteristic
619C23—31no—
620C23—241no—
621Q8—41no—
622Q8—121no—
623Q8—241no—
624D4—41no—
625D4—81no—
626D4—121no—
627D4—241no—
628D4—241no—
629D4—241no—
630D4—241no—
631C2×C4—21no—
632C2×C4—31no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—64no—
638C2×C4—61no—
639C2×C4—81no—
640C2×C4—241no—
641C2×C4—241no—
642C2×C4—241no—
643C2×C4—241no—
644C2×C4D3×D4⋊C811yescharacteristic
645C8—31no—
646C8—31no—
647C8—31no—
648C8—31no—
649C8—42no—
650C8—81no—
651C8—122no—
652C8—241no—
653C8D3×C22⋊C1611yescharacteristic
654C8D3×#35011yescharacteristic
655C8D3×#36011yescharacteristic
656C8D3×#36111yescharacteristic
657C2×C3—21no—
658C2×C3—161no—
659C2×C3C2×#707011yescharacteristic
660D3—21no—
661D3—161no—
662D3#9375912yesdirect product factor
663C22—31no—
664C22—31no—
665C22—62no—
666C22—81no—
667C22—241no—
668C22—482no—
669C22D3×#133611yescharacteristic
670C4—22no—
671C4—31no—
672C4—31no—
673C4—62no—
674C4—81no—
675C4—241no—
676C4D3×D4⋊C1611yescharacteristic
677C4D3×#133311yescharacteristic
678C3C2×#9375911yescharacteristic, complemented, Sylow
679C2—21no—
680C2—32no—
681C2—61no—
682C2—161no—
683C2—481no—
684C2D3×#707011yescharacteristic
subgroupG/H
centerC4D3×#1333
commutatorC3×C16C22×C16
Frattini#1311C22×D3
FittingC3×#93759C2
socleC2×C3C2×#7070
prime radicalD3×#508C8
cosocleC3×#1311C23
hypercenter#93759D3
hypocenterC3C2×#93759
LCSG ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C16 ◁ #1311 ◁ #93759

Complements

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

NH ≅ G/Ntype
1. #72245577C2semidirect
2. #72245562C2semidirect
3. #72245517C2semidirect
4. C3×#93759C2semidirect
5. D3×#7456C2semidirect
7. D3×#7053C2semidirect
21. #10682855C22semidirect
24. #10681803C22semidirect
26. C3×#7456C22semidirect
27. C3×#7053C22semidirect
34. #93759D3direct (N × H)
91. #7456C2×D3semidirect
94. #7053C2×D3semidirect
104. #4919C16semidirect
105. D3×Q32C16semidirect
108. #4912C16semidirect
109. D3×D16C16semidirect
226. C3×Q32C2×C16semidirect
228. C3×D16C2×C16semidirect
263. Dic24C2×C16semidirect
265. D48C2×C16semidirect
443. Q32D3×C16semidirect
450. D16D3×C16semidirect
662. D3#93759direct (N × H)
678. C3C2×#93759semidirect

Maximal subgroups

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

subgroupindex
#722455772
#722455622
#722455172
C3×#937592
D3×#74562
D3×#120472
D3×#70532
C2×#937593