Finite Group Databasebeta

← D3×#5197 #11861052

Subgroups — D3×#5197 #11861052

Order 1152.

980 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#135C211yesmaximal, characteristic
2D3×#948C212yesmaximal, complemented
3#10592896C211yesmaximal, characteristic, complemented
4C3×#5197C211yesmaximal, characteristic, complemented
5#10591676C212yesmaximal, complemented
6#10591674C212yesmaximal, complemented
7D3×#837C212yesmaximal, complemented
8#10590920C211yesmaximal, characteristic, complemented
9#10590916C211yesmaximal, characteristic, complemented
10D3×#819C211yesmaximal, characteristic, complemented
11D3×#815C211yesmaximal, characteristic, complemented
12C2×#5197—31nomaximal
13D3×#444—31nomaximal
14C3×D3×#41C2212yes—
15C32×#135C2211yescharacteristic
16#64157C2212yescomplemented
17C3×#950C2212yes—
18C3×#948C2212yescomplemented
19C3×#919C411yescharacteristic, complemented
20C3×D3×Q16C411yescharacteristic, complemented
21C3×#916C412yescomplemented
22C3×D3×SD16C412yescomplemented
23C3×#912C411yescharacteristic, complemented
24C3×D3×D8C411yescharacteristic, complemented
25C3×#904C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C4×D3×Dic3C2211yescharacteristic
28#63815—22no—
29#63815C2212yescomplemented
30#63814—22no—
31#63814C2212yescomplemented
32D3×#208—22no—
33D3×#208C2212yes—
34C2×D3×C3⋊C8—22no—
35C2×D3×C3⋊C8C2211yescharacteristic
36#63664C2212yescomplemented
37#63646C2211yescharacteristic, complemented
38#63642C2211yescharacteristic, complemented
39C3×#837C2212yescomplemented
40C3×#819C2211yescharacteristic, complemented
41C3×#815C2211yescharacteristic, complemented
42#63577C2212yescomplemented
43#63569C2212yescomplemented
44#63568C2212yescomplemented
45#63555C2211yescharacteristic, complemented
46#63554C2211yescharacteristic, complemented
47C2×C3×#135—31no—
48C2×#948—32no—
49D3×#135D311yescharacteristic
50D3×#131—32no—
51C3×#444—31no—
52C2×#837—32no—
53#5197—31no—
54#5197—31no—
55#5197—32no—
56#5197—32no—
57#5197—31no—
58#5197—31no—
59#5197—61no—
60#5197D311yescharacteristic, direct product factor
61#5145—32no—
62C2×#819—31no—
63C2×#815—31no—
64#4894—31no—
65D3×#108—31no—
66#4823—32no—
67D3×#104—32no—
68#4717—31no—
69D3×#97—31no—
70C32×#41C2312yes—
71C3×#239C2×C412yes—
72C3×D3×Q8C2×C412yes—
73C3×#237—22no—
74C3×#237C2×C412yes—
75C3×D3×D4—22no—
76C3×D3×D4C2×C412yes—
77C3×#235—22no—
78C3×#235C2312yes—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3C2311yescharacteristic
81C2×D3×Dic3—21no—
82C32×Q16C2×C411yescharacteristic, complemented
83C32×SD16C2×C412yescomplemented
84C32×D8C2×C411yescharacteristic, complemented
85C2×C32×C8C2311yescharacteristic
86C4×C3⋊Dic3C2311yescharacteristic
87#3748—22no—
88#3748C2312yes—
89C2×C3⋊(C3⋊C8)—22no—
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91C3×#216C2×C412yescomplemented
92C3×#215C2×C412yescomplemented
93C3×#214C2×C412yescomplemented
94C3×#213C2×C412yescomplemented
95C3×C4×Dic3C2311yescharacteristic
96C3×#208—22no—
97C3×#208C2312yes—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101C3×Dic12C2×C411yescharacteristic, complemented
102C3×D24C2×C411yescharacteristic, complemented
103C3×#204C2×C412yescomplemented
104C3×D3×C8C2×C411yescharacteristic
105C3×D3×C8C2×C411yescharacteristic
106C3×D3×C8C2×C411yescharacteristic
107C3×D3×C8C2×C411yescharacteristic
108Dic32—21no—
109#3711—22no—
110#3711—22no—
111#3711—22no—
112D3×C3⋊C8—22no—
113D3×C3⋊C8—22no—
114D3×C3⋊C8—22no—
115D3×C3⋊C8D412yes—
116D3×C3⋊C8D412yes—
117C2×#444—91noSylow
118C2×C3×#41—32no—
119D3×#41C2×D312yes—
120C3×#135—21no—
121C3×#135—32no—
122C3×#135—31no—
123C3×#135—32no—
124C3×#135—31no—
125C3×#135—31no—
126C3×#135C2×D311yescharacteristic
127C3×#135C2×D311yescharacteristic
128C2×C3×Q16—31no—
129C2×C3×SD16—32no—
130C2×C3×D8—31no—
131C3×#131—32no—
132C22×C3×C8—31no—
133#950C2×D312yes—
134#948—32no—
135#948—32no—
136#948—32no—
137#948—32no—
138#948—62no—
139#948—62no—
140#948—62no—
141#948C2×D312yescomplemented
142C2×C4×Dic3—31no—
143C2×#208—32no—
144C2×#208—62no—
145C22×C3⋊C8—31no—
146C22×C3⋊C8—62no—
147#919Dic311yescharacteristic, complemented
148D3×Q16Dic311yescharacteristic, complemented
149#916Dic312yescomplemented
150D3×SD16Dic312yescomplemented
151#912Dic311yescharacteristic, complemented
152D3×D8Dic311yescharacteristic, complemented
153#907—32no—
154#907—62no—
155D3×M16—32no—
156D3×M16—62no—
157#904C2×D311yescharacteristic
158#901—32no—
159#901—62no—
160C2×D3×C8—31no—
161C2×D3×C8—62no—
162C2×D3×C8C2×D311yescharacteristic
163C42×D3—31no—
164C3×#108—31no—
165C3×#104—32no—
166C3×#97—31no—
167#837—32no—
168#837—32no—
169#837—32no—
170#837—32no—
171#837—62no—
172#837C2×D312yescomplemented
173#825—32no—
174#822—32no—
175#819—31no—
176#819—31no—
177#819—32no—
178#819—61no—
179#819C2×D311yescharacteristic, complemented
180#815—31no—
181#815—31no—
182#815—31no—
183#815—31no—
184#815—31no—
185#815—61no—
186#815C2×D311yescharacteristic, complemented
187#805—32no—
188#803—31no—
189C22×C3×D3—22no—
190C22×C3×D3#4111yescharacteristic
191C32×Q8C22×C412yes—
192C32×D4—22no—
193C32×D4C22×C412yes—
194C2×C32×C4—22no—
195C2×C32×C4C2411yescharacteristic
196C2×C3⋊Dic3—21no—
197C3×#67—22no—
198C3×#67—22no—
199C3×#67—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3#4111yescharacteristic
203C3×D12—22no—
204C3×D12C22×C412yes—
205C3×C4×D3—22no—
206C3×C4×D3—22no—
207C3×C4×D3—22no—
208C3×C4×D3C22×C411yescharacteristic
209C3×C4×D3C22×C411yescharacteristic
210C3×C4×D3C2×D411yescharacteristic
211C3×C4×D3C2×D411yescharacteristic
212C3×Dic6—22no—
213C3×Dic6C22×C412yes—
214D3×Dic3—42no—
215C32×C8C22×C411yescharacteristic
216C32×C8C22×C411yescharacteristic
217C3⋊(C3⋊C8)—22no—
218C3⋊(C3⋊C8)C2×D412yes—
219C3×C3⋊C8—22no—
220C3×C3⋊C8C22×C411yescharacteristic
221C3×C3⋊C8C22×C411yescharacteristic
222C3×C3⋊C8C2×D412yes—
223C2×#135—31no—
224C2×#131—92no—
225#444—31no—
226#444—91no—
227#444—92no—
228#444—91no—
229#444—92no—
230#444—91no—
231C2×#108—91no—
232C2×#104—92no—
233C2×#97—91no—
234C3×#41—22no—
235C3×#41—32no—
236C3×#41—32no—
237C3×#41—32no—
238C3×#41—62no—
239C3×#41—62no—
240C3×#41C22×D312yes—
241C3×#41C22×D312yes—
242C2×C3×Q8—32no—
243C2×C3×D4—32no—
244C2×C3×D4—62no—
245C22×C3×C4—31no—
246C22×C3×C4—62no—
247C22×Dic3—61no—
248#239C2×Dic312yes—
249D3×Q8C2×Dic312yes—
250#237—22no—
251#237C2×Dic312yes—
252D3×D4—22no—
253D3×D4C2×Dic312yes—
254#235—22no—
255#235C22×D312yes—
256C2×C4×D3—22no—
257C2×C4×D3—61no—
258C2×C4×D3C22×D311yescharacteristic
259C3×Q16—21no—
260C3×Q16—32no—
261C3×Q16—31no—
262C3×Q16C4×D311yescharacteristic, complemented
263C3×Q16C2×Dic311yescharacteristic, complemented
264C3×SD16—22no—
265C3×SD16—32no—
266C3×SD16—32no—
267C3×SD16—32no—
268C3×SD16C4×D312yescomplemented
269C3×SD16C2×Dic312yescomplemented
270C3×D8—21no—
271C3×D8—32no—
272C3×D8—31no—
273C3×D8C4×D311yescharacteristic, complemented
274C3×D8C2×Dic311yescharacteristic, complemented
275C3×M16—32no—
276C3×M16—62no—
277C2×C3×C8—21no—
278C2×C3×C8—31no—
279C2×C3×C8—31no—
280C2×C3×C8—31no—
281C2×C3×C8—31no—
282C2×C3×C8—31no—
283C2×C3×C8—31no—
284C2×C3×C8—62no—
285C2×C3×C8C22×D311yescharacteristic
286C2×C3×C8C22×D311yescharacteristic
287C3×C42—31no—
288#216C2×Dic312yescomplemented
289#215C2×Dic312yescomplemented
290#214C2×Dic312yescomplemented
291#213C2×Dic312yescomplemented
292C4×Dic3—31no—
293C4×Dic3—31no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3C22×D311yescharacteristic
298#208—22no—
299#208—32no—
300#208—32no—
301#208—62no—
302#208—62no—
303#208—62no—
304#208—62no—
305#208—62no—
306#208—62no—
307#208—122no—
308#208C22×D312yes—
309C2×C3⋊C8—22no—
310C2×C3⋊C8—31no—
311C2×C3⋊C8—31no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—32no—
314C2×C3⋊C8—61no—
315C2×C3⋊C8—62no—
316C2×C3⋊C8—62no—
317C2×C3⋊C8—62no—
318C2×C3⋊C8—62no—
319C2×C3⋊C8—62no—
320C2×C3⋊C8—122no—
321C2×C3⋊C8C22×D311yescharacteristic
322C2×C3⋊C8C22×D311yescharacteristic
323Dic12C2×Dic311yescharacteristic, complemented
324D24C2×Dic311yescharacteristic, complemented
325#204C2×Dic312yescomplemented
326ΓL(1,𝔽25)—62no—
327ΓL(1,𝔽25)—62no—
328ΓL(1,𝔽25)—62no—
329D3×C8—32no—
330D3×C8—32no—
331D3×C8—62no—
332D3×C8—62no—
333D3×C8—62no—
334D3×C8C2×Dic311yescharacteristic
335D3×C8C2×Dic311yescharacteristic
336D3×C8C2×Dic311yescharacteristic
337D3×C8C2×Dic311yescharacteristic
338C22×C32—22no—
339C22×C32C2×#4111yescharacteristic
340C2×C3×D3—22no—
341C2×C3×D3—22no—
342C2×C3×D3—44no—
343C2×C3×D3C4×D411yescharacteristic
344C2×C3×D3C4×D411yescharacteristic
345C32×C4—22no—
346C32×C4C23×C411yescharacteristic
347C32×C4C22×D411yescharacteristic
348C3⋊Dic3—41no—
349C3×Dic3—22no—
350C3×Dic3—41no—
351C3×Dic3C4×D411yescharacteristic
352C3×Dic3C4×D411yescharacteristic
353C2×#41—32no—
354#135—32no—
355#135—31no—
356#135—32no—
357#135—31no—
358#135—31no—
359#135D3211yescharacteristic
360C2×Q16—31no—
361C2×SD16—32no—
362C2×D8—31no—
363#131—32no—
364#131—92no—
365#131—92no—
366#131—92no—
367#131—182no—
368#131—182no—
369C2×M16—92no—
370C2×M16—182no—
371C22×C8—31no—
372C22×C8—91no—
373C22×C8—182no—
374C2×C42—91no—
375#108—31no—
376#108—92no—
377#108—91no—
378#104—32no—
379#104—92no—
380#104—92no—
381#104—92no—
382#97—31no—
383#97—91no—
384#97—91no—
385#97—91no—
386C23×C3—31no—
387C23×C3—62no—
388C22×D3—22no—
389C22×D3#23711yescharacteristic
390C3×Q8—22no—
391C3×Q8—32no—
392C3×Q8—62no—
393C3×Q8C2×C4×D312yes—
394C3×Q8C22×Dic312yes—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—32no—
399C3×D4—42no—
400C3×D4—62no—
401C3×D4—62no—
402C3×D4—62no—
403C3×D4—62no—
404C3×D4C2×C4×D312yes—
405C3×D4C22×Dic312yes—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—21no—
409C2×C3×C4—31no—
410C2×C3×C4—31no—
411C2×C3×C4—31no—
412C2×C3×C4—31no—
413C2×C3×C4—31no—
414C2×C3×C4—42no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—61no—
420C2×C3×C4C23×D311yescharacteristic
421C2×C3×C4C23×D311yescharacteristic
422#67—22no—
423#67—22no—
424#67—22no—
425C2×Dic3—22no—
426C2×Dic3—21no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—121no—
430C2×Dic3—122no—
431C2×Dic3#23711yescharacteristic
432D12—22no—
433D12C22×Dic312yes—
434C4×D3—22no—
435C4×D3—22no—
436C4×D3—22no—
437C4×D3—122no—
438C4×D3D3×D411yescharacteristic
439C4×D3D3×D411yescharacteristic
440C4×D3C22×Dic311yescharacteristic
441C4×D3C22×Dic311yescharacteristic
442Dic6—22no—
443Dic6C22×Dic312yes—
444C3×C8—21no—
445C3×C8—21no—
446C3×C8—31no—
447C3×C8—31no—
448C3×C8—32no—
449C3×C8—62no—
450C3×C8C2×C4×D311yescharacteristic
451C3×C8C2×C4×D311yescharacteristic
452C3×C8C22×Dic311yescharacteristic
453C3×C8C22×Dic311yescharacteristic
454C3⋊C8—22no—
455C3⋊C8—32no—
456C3⋊C8—32no—
457C3⋊C8—62no—
458C3⋊C8—62no—
459C3⋊C8—62no—
460C3⋊C8—122no—
461C3⋊C8D3×D412yes—
462C3⋊C8C22×Dic311yescharacteristic
463C3⋊C8C22×Dic311yescharacteristic
464C2×C32—21no—
465C2×C32—42no—
466C2×C32C2×C4×D411yescharacteristic
467C3×D3—21no—
468C3×D3—42no—
469C3×D3#44412yescomplemented
470#41—32no—
471#41—32no—
472#41—32no—
473#41—62no—
474#41—62no—
475#41C2×D3212yes—
476C2×Q8—32no—
477C2×D4—32no—
478C2×D4—62no—
479C22×C4—31no—
480C22×C4—62no—
481C22×C4—181no—
482Q16—32no—
483Q16—31no—
484Q16D3×Dic311yescharacteristic, complemented
485SD16—32no—
486SD16—32no—
487SD16—32no—
488SD16D3×Dic312yescomplemented
489D8—32no—
490D8—31no—
491D8D3×Dic311yescharacteristic, complemented
492M16—32no—
493M16—62no—
494M16—92no—
495M16—182no—
496M16—182no—
497M16—182no—
498M16—182no—
499C2×C8—31no—
500C2×C8—31no—
501C2×C8—31no—
502C2×C8—31no—
503C2×C8—31no—
504C2×C8—31no—
505C2×C8—62no—
506C2×C8—92no—
507C2×C8—92no—
508C2×C8—91no—
509C2×C8—182no—
510C2×C8—182no—
511C2×C8—182no—
512C2×C8—182no—
513C2×C8C2×D3211yescharacteristic
514C42—31no—
515C42—91no—
516C42—181no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—21no—
520C22×C3—31no—
521C22×C3—31no—
522C22×C3—42no—
523C22×C3—62no—
524C22×C3—62no—
525C22×C3—124no—
526C22×C3C2×#23711yescharacteristic
527C22×C3D3×#4111yescharacteristic
528C2×D3—22no—
529C2×D3—22no—
530C2×D3—44no—
531C2×D3D4×Dic311yescharacteristic
532C2×D3D4×Dic311yescharacteristic
533C3×C4—22no—
534C3×C4—22no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—31no—
538C3×C4—31no—
539C3×C4—42no—
540C3×C4—62no—
541C3×C4—121no—
542C3×C4C22×C4×D311yescharacteristic
543C3×C4C2×D3×D411yescharacteristic
544C3×C4C2×D3×D411yescharacteristic
545C3×C4C23×Dic311yescharacteristic
546Dic3—22no—
547Dic3—41no—
548Dic3—121no—
549Dic3—121no—
550Dic3—241no—
551Dic3D4×Dic311yescharacteristic
552Dic3D4×Dic311yescharacteristic
553C32C2×#44411yescharacteristic, complemented, Sylow
554C23—31no—
555C23—62no—
556Q8—32no—
557Q8—62no—
558Q8C2×D3×Dic312yes—
559D4—22no—
560D4—32no—
561D4—62no—
562D4—62no—
563D4—62no—
564D4—62no—
565D4C2×D3×Dic312yes—
566C2×C4—22no—
567C2×C4—31no—
568C2×C4—31no—
569C2×C4—31no—
570C2×C4—31no—
571C2×C4—31no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—61no—
577C2×C4—181no—
578C2×C4—362no—
579C2×C4C22×D3211yescharacteristic
580C8—32no—
581C8—31no—
582C8—31no—
583C8—62no—
584C8—92no—
585C8—182no—
586C8C2×D3×Dic311yescharacteristic
587C8C2×D3×Dic311yescharacteristic
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—32no—
592C2×C3—41no—
593C2×C3—42no—
594C2×C3—42no—
595C2×C3—61no—
596C2×C3—82no—
597C2×C3—122no—
598C2×C3C4×D3×D411yescharacteristic
599C2×C3C2×D4×Dic311yescharacteristic
600D3—21no—
601D3—42no—
602D3#519712yesdirect product factor
603C22—22no—
604C22—31no—
605C22—31no—
606C22—62no—
607C22—62no—
608C22—124no—
609C22D3×#23711yescharacteristic
610C4—22no—
611C4—31no—
612C4—31no—
613C4—62no—
614C4—121no—
615C4—361no—
616C4D32×D411yescharacteristic
617C4C22×D3×Dic311yescharacteristic
618C3—21no—
619C3D3×#44411yescharacteristic, complemented
620C3C2×#519711yescharacteristic, complemented
621C2—21no—
622C2—32no—
623C2—42no—
624C2—61no—
625C2—122no—
626C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32C2×C4×D4
prime radicalC3×D3×#135C2
cosocleC2×C32×C4C24
hypercenter#135D32
hypocenterC32C2×#444
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
2. D3×#948C2semidirect
3. #10592896C2semidirect
4. C3×#5197C2semidirect
5. #10591676C2semidirect
6. #10591674C2semidirect
7. D3×#837C2semidirect
8. #10590920C2semidirect
9. #10590916C2semidirect
10. D3×#819C2semidirect
11. D3×#815C2semidirect
16. #64157C22semidirect
18. C3×#948C22semidirect
19. C3×#919C4semidirect
20. C3×D3×Q16C4semidirect
21. C3×#916C4semidirect
22. C3×D3×SD16C4semidirect
23. C3×#912C4semidirect
24. C3×D3×D8C4semidirect
29. #63815C22semidirect
31. #63814C22semidirect
36. #63664C22semidirect
37. #63646C22semidirect
38. #63642C22semidirect
39. C3×#837C22semidirect
40. C3×#819C22semidirect
41. C3×#815C22semidirect
42. #63577C22semidirect
43. #63569C22semidirect
44. #63568C22semidirect
45. #63555C22semidirect
46. #63554C22semidirect
60. #5197D3direct (N × H)
82. C32×Q16C2×C4semidirect
83. C32×SD16C2×C4semidirect
84. C32×D8C2×C4semidirect
91. C3×#216C2×C4semidirect
92. C3×#215C2×C4semidirect
93. C3×#214C2×C4semidirect
94. C3×#213C2×C4semidirect
101. C3×Dic12C2×C4semidirect
102. C3×D24C2×C4semidirect
103. C3×#204C2×C4semidirect
141. #948C2×D3semidirect
147. #919Dic3semidirect
148. D3×Q16Dic3semidirect
149. #916Dic3semidirect
150. D3×SD16Dic3semidirect
151. #912Dic3semidirect
152. D3×D8Dic3semidirect
172. #837C2×D3semidirect
179. #819C2×D3semidirect
186. #815C2×D3semidirect
262. C3×Q16C4×D3semidirect
263. C3×Q16C2×Dic3semidirect
268. C3×SD16C4×D3semidirect
269. C3×SD16C2×Dic3semidirect
273. C3×D8C4×D3semidirect
274. C3×D8C2×Dic3semidirect
288. #216C2×Dic3semidirect
289. #215C2×Dic3semidirect
290. #214C2×Dic3semidirect
291. #213C2×Dic3semidirect
323. Dic12C2×Dic3semidirect
324. D24C2×Dic3semidirect
325. #204C2×Dic3semidirect
469. C3×D3#444semidirect
484. Q16D3×Dic3semidirect
488. SD16D3×Dic3semidirect
491. D8D3×Dic3semidirect
553. C32C2×#444semidirect
602. D3#5197direct (N × H)
619. C3D3×#444semidirect
620. C3C2×#5197semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1352
D3×#9482
#105928962
C3×#51972
#105916762
#105916742
D3×#8372
#105909202
#105909162
D3×#8192
D3×#8152
C2×#51973
D3×#4443