Finite Group Databasebeta

← D3×#5700 #11910276

Subgroups — D3×#5700 #11910276

Order 1152.

2414 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#10596171C211yesmaximal, characteristic, complemented
2C3×#5700C211yesmaximal, characteristic, complemented
3C3×D3×#125C211yesmaximal, characteristic, complemented
4D3×#896C214yesmaximal, complemented
5D3×#895C214yesmaximal, complemented
6D3×#894C214yesmaximal, complemented
7#10594593C214yesmaximal, complemented
8#10594500C214yesmaximal, complemented
9#10594493C214yesmaximal, complemented
10D3×#875C212yesmaximal, complemented
11#10593953C212yesmaximal, complemented
12D3×#562—31nomaximal
13C2×#5700—31nomaximal
14C2×D3×D12C2214yes—
15C2×D3×D12C2212yes—
16C2×C4×D32C2214yes—
17C2×D3×Dic6C2212yes—
18C32×#125C2211yescharacteristic, complemented
19#64105C2214yescomplemented
20#64104C2214yescomplemented
21#64103C2214yescomplemented
22#64084C2212yescomplemented
23C3×#896C2214yescomplemented
24C3×#895C2214yescomplemented
25C3×#894C2214yescomplemented
26C3×D3×C4⋊C4C2212yes—
27C3×D3×C4⋊C4C2214yes—
28C3×#890C2212yescomplemented
29C3×#889C2214yescomplemented
30C3×#875C2212yescomplemented
31C3×C42×D3C2211yescharacteristic
32C3×#870C2211yescharacteristic, complemented
33D3×(C2×D3)⋊C4C2214yes—
34D3×(C2×D3)⋊C4C2214yes—
35D3×(C2×D3)⋊C4C2214yes—
36#63916C2214yescomplemented
37#63910C2214yescomplemented
38#63910C2214yescomplemented
39#63909C2214yescomplemented
40#63899C2214yescomplemented
41#63897C2214yescomplemented
42#63896C2214yescomplemented
43#63895C2214yescomplemented
44#63890C2214yescomplemented
45#63888C2214yescomplemented
46#63886C2214yescomplemented
47#63886C2214yescomplemented
48#63884C2214yescomplemented
49D3×Dic3⋊C4C2214yes—
50#63865C2214yescomplemented
51#63864C2212yescomplemented
52#63860C2212yescomplemented
53#63854C2214yescomplemented
54#63853C2214yescomplemented
55#63852C2214yescomplemented
56#63852C2214yescomplemented
57#63851C2214yescomplemented
58#63850C2214yescomplemented
59C3×#562—31no—
60C2×C3×#125—31no—
61#5700—31no—
62#5700—31no—
63#5700—34no—
64#5700—34no—
65#5700—34no—
66#5700—32no—
67#5700—61no—
68#5700D311yescharacteristic, direct product factor
69D3×#125D311yescharacteristic, complemented
70#5684—32no—
71D3×#124—32no—
72#5667—34no—
73D3×#123—34no—
74#5647—34no—
75D3×C22⋊Q8—34no—
76#5621—34no—
77D3×#121—34no—
78C2×#896—34no—
79C2×#895—34no—
80C2×#894—34no—
81C2×#875—32no—
82C22×D32C2314yes—
83C2×C4⋊(C3⋊D3)C2312yes—
84C2×C4⋊(C3⋊D3)C2314yes—
85C2×C4×C3⋊D3C2314yes—
86C2×#634C2312yes—
87C2×C3×D12C2314yes—
88C2×C3×D12C2312yes—
89C2×C3×C4×D3C2314yes—
90C2×C3×C4×D3C2312yes—
91C2×C3×C4×D3C2311yescharacteristic
92C2×C3×C4×D3C2314yes—
93C2×C3×Dic6C2312yes—
94C2×#627C2314yes—
95C2×#626C2314yes—
96C2×#626C2314yes—
97C2×#626C2314yes—
98C2×#624C2314yes—
99C2×D3×Dic3C2314yes—
100C2×D3×Dic3C2314yes—
101D3×D12—44no—
102D3×D12—48no—
103C4×D32—48no—
104D3×Dic6—44no—
105C32×C4⋊C4C2314yes—
106C32×C4⋊C4C2312yes—
107C32×C42C2311yescharacteristic
108#3752C2314yes—
109#3752C2314yes—
110#3752C2314yes—
111#3750C2314yes—
112C3×(C2×D3)⋊C4C2314yes—
113C3×(C2×D3)⋊C4C2314yes—
114C3×(C2×D3)⋊C4C2314yes—
115C3×C4⋊Dic3C2314yes—
116C3×C4⋊Dic3C2312yes—
117C3×Dic3⋊C4C2314yes—
118C3×Dic3⋊C4C2314yes—
119C3×Dic3⋊C4C2314yes—
120C3×Dic3⋊C4C2314yes—
121C3×C4×Dic3C2312yes—
122C3×C4×Dic3C2311yescharacteristic
123#3724C2314yes—
124Dic3⋊Dic3C2314yes—
125#3722C2314yes—
126#3722C2314yes—
127#3722C2314yes—
128(C2×D3)⋊Dic3C2314yes—
129(C2×D3)⋊Dic3C2314yes—
130(C2×D3)⋊Dic3C2314yes—
131C2×#562—91noSylow
132C2×D3×Q8—32no—
133C2×D3×D4—34no—
134C2×D3×D4—32no—
135C22×D12—32no—
136C22×D12—34no—
137C22×C4×D3—34no—
138C22×C4×D3—34no—
139C22×Dic6—32no—
140C3×#125—21no—
141C3×#125—34no—
142C3×#125—32no—
143C3×#125—31no—
144C3×#125C2×D311yescharacteristic, complemented
145C3×#125C2×D311yescharacteristic, complemented
146C3×#124—32no—
147C3×#123—34no—
148C3×C22⋊Q8—34no—
149C3×#121—34no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4—34no—
152C2×C3×C42—31no—
153#947—32no—
154#946—34no—
155#939—34no—
156#939—34no—
157#938—34no—
158#936—32no—
159#935—34no—
160#930—34no—
161#929—34no—
162C2×(C2×D3)⋊C4—34no—
163C2×(C2×D3)⋊C4—34no—
164C2×(C2×D3)⋊C4—34no—
165#924—34no—
166C2×Dic3⋊C4—34no—
167#897—34no—
168#896—34no—
169#896—34no—
170#896—34no—
171#896—34no—
172#896—34no—
173#896—34no—
174#896—34no—
175#896—34no—
176#896—34no—
177#896—64no—
178#896C2×D314yescomplemented
179#895—34no—
180#895—34no—
181#895—34no—
182#895—34no—
183#895—34no—
184#895—34no—
185#895—34no—
186#895—34no—
187#895—64no—
188#895C2×D314yescomplemented
189#894—34no—
190#894—34no—
191#894—34no—
192#894—34no—
193#894—34no—
194#894—34no—
195#894—34no—
196#894—34no—
197#894—34no—
198#894—64no—
199#894C2×D314yescomplemented
200D3×C4⋊C4—34no—
201D3×C4⋊C4C2×D312yes—
202D3×C4⋊C4C2×D314yes—
203#890C2×D312yescomplemented
204#889C2×D314yescomplemented
205#886—34no—
206#885—34no—
207#885—34no—
208#884—34no—
209#884—34no—
210#883—34no—
211#883—34no—
212D3×C22⋊C4—34no—
213D3×C22⋊C4—34no—
214D3×C22⋊C4—34no—
215#878—34no—
216#878—34no—
217#875—32no—
218#875—32no—
219#875—32no—
220#875—32no—
221#875—34no—
222#875—34no—
223#875—62no—
224#875C2×D312yescomplemented
225C42×D3C2×D311yescharacteristic
226#870C2×D311yescharacteristic, complemented
227C22×C3⋊D3C2414yes—
228C22×C3×D3C2414yes—
229C22×C3×D3C2411yescharacteristic
230C2×D32—28no—
231C2×D32—28no—
232C2×D32—28no—
233C2×C32×C4C2412yes—
234C2×C32×C4C2411yescharacteristic
235C2×C32×C4C2414yes—
236C2×C3⋊Dic3C2414yes—
237C4⋊(C3⋊D3)—42no—
238C4⋊(C3⋊D3)—44no—
239C4×C3⋊D3—44no—
240#634—42no—
241C2×C3×Dic3C2411yescharacteristic
242C2×C3×Dic3C2412yes—
243C2×C3×Dic3C2414yes—
244C2×C3×Dic3C2414yes—
245C3×D12—42no—
246C3×D12—44no—
247C3×C4×D3—24no—
248C3×C4×D3—28no—
249C3×C4×D3—22no—
250C3×C4×D3—44no—
251C3×Dic6—42no—
252#627—44no—
253#626—44no—
254#626—44no—
255#626—44no—
256#624—44no—
257D3×Dic3—28no—
258D3×Dic3—44no—
259#562—31no—
260#562—94no—
261#562—94no—
262#562—94no—
263#562—92no—
264#562—91no—
265C2×#125—31no—
266C2×#124—92no—
267C2×#123—94no—
268C2×C22⋊Q8—94no—
269C2×#121—94no—
270C23×D3—34no—
271C23×D3—34no—
272C2×C3×Q8—32no—
273C2×C3×D4—34no—
274C2×C3×D4—32no—
275C22×C3×C4—34no—
276C22×C3×C4—31no—
277C22×C3×C4—32no—
278C22×C3×C4—34no—
279C2×#67—34no—
280C2×#67—34no—
281C2×#67—34no—
282C22×Dic3—34no—
283C22×Dic3—34no—
284D3×Q8—124no—
285D3×D4—128no—
286D3×D4—124no—
287C2×D12—34no—
288C2×D12—34no—
289C2×D12—34no—
290C2×D12—32no—
291C2×D12—32no—
292C2×D12—34no—
293C2×D12—34no—
294C2×D12—62no—
295C2×D12—64no—
296C2×D12—124no—
297C2×D12—128no—
298C2×D12C22×D312yes—
299C2×D12C22×D314yes—
300C2×C4×D3—34no—
301C2×C4×D3—34no—
302C2×C4×D3—34no—
303C2×C4×D3—34no—
304C2×C4×D3—34no—
305C2×C4×D3—34no—
306C2×C4×D3—64no—
307C2×C4×D3—128no—
308C2×C4×D3—128no—
309C2×C4×D3C22×D311yescharacteristic
310C2×C4×D3C22×D312yes—
311C2×C4×D3C22×D314yes—
312C2×C4×D3C22×D314yes—
313C2×Dic6—32no—
314C2×Dic6—32no—
315C2×Dic6—34no—
316C2×Dic6—34no—
317C2×Dic6—62no—
318C2×Dic6—124no—
319C2×Dic6C22×D312yes—
320C3×C4⋊C4—22no—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—34no—
323C3×C4⋊C4—34no—
324C3×C4⋊C4—32no—
325C3×C4⋊C4—34no—
326C3×C4⋊C4—34no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4C22×D314yes—
329C3×C4⋊C4C22×D312yes—
330C3×C4⋊C4C22×D312yes—
331C3×C4⋊C4C22×D314yes—
332C3×C22⋊C4—34no—
333C3×C22⋊C4—34no—
334C3×C22⋊C4—34no—
335C3×C42—21no—
336C3×C42—32no—
337C3×C42—31no—
338C3×C42C22×D311yescharacteristic
339C3×C42C22×D311yescharacteristic
340#217—34no—
341#217—34no—
342#217—34no—
343(C2×D3)⋊C4—34no—
344(C2×D3)⋊C4—34no—
345(C2×D3)⋊C4—34no—
346(C2×D3)⋊C4—34no—
347(C2×D3)⋊C4—34no—
348(C2×D3)⋊C4—34no—
349(C2×D3)⋊C4—34no—
350(C2×D3)⋊C4—34no—
351(C2×D3)⋊C4—34no—
352(C2×D3)⋊C4—34no—
353(C2×D3)⋊C4—34no—
354(C2×D3)⋊C4—34no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—34no—
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—64no—
359(C2×D3)⋊C4—64no—
360(C2×D3)⋊C4—64no—
361(C2×D3)⋊C4C22×D314yes—
362(C2×D3)⋊C4C22×D314yes—
363(C2×D3)⋊C4C22×D314yes—
364C4⋊Dic3—34no—
365C4⋊Dic3C22×D312yes—
366C4⋊Dic3C22×D314yes—
367Dic3⋊C4—34no—
368Dic3⋊C4—34no—
369Dic3⋊C4—34no—
370Dic3⋊C4—34no—
371Dic3⋊C4—34no—
372Dic3⋊C4—64no—
373Dic3⋊C4C22×D314yes—
374Dic3⋊C4C22×D314yes—
375Dic3⋊C4C22×D314yes—
376Dic3⋊C4C22×D314yes—
377C4×Dic3C22×D311yescharacteristic
378C4×Dic3C22×D312yes—
379C22×C32C2511yescharacteristic
380C2×C3⋊D3—24no—
381C2×C3⋊D3—24no—
382C2×C3⋊D3—24no—
383C2×C3×D3—24no—
384C2×C3×D3—24no—
385C2×C3×D3—24no—
386C2×C3×D3H(5,𝔽2)14yes—
387C2×C3×D32−1+412yes—
388D32—416no—
389C32×C4—22no—
390C32×C4—24no—
391C32×C4—21no—
392C3⋊Dic3—24no—
393C3×Dic3—24no—
394C3×Dic3—24no—
395C3×Dic3—22no—
396C3×Dic3—21no—
397C22×Q8—92no—
398C22×D4—94no—
399C22×D4—92no—
400C23×C4—94no—
401#125—34no—
402#125—32no—
403#125—31no—
404#125D3211yescharacteristic, complemented
405#124—32no—
406#124—94no—
407#124—94no—
408#124—92no—
409#124—92no—
410#124—92no—
411#123—34no—
412#123—94no—
413#123—94no—
414#123—94no—
415#123—94no—
416#123—94no—
417#123—94no—
418#123—94no—
419C22⋊Q8—34no—
420C22⋊Q8—94no—
421C22⋊Q8—94no—
422C22⋊Q8—94no—
423C22⋊Q8—94no—
424C22⋊Q8—94no—
425C22⋊Q8—94no—
426C22⋊Q8—94no—
427#121—34no—
428#121—94no—
429#121—94no—
430#121—94no—
431#121—94no—
432#121—94no—
433#121—94no—
434#121—94no—
435C2×C4⋊C4—34no—
436C2×C4⋊C4—32no—
437C2×C4⋊C4—94no—
438C2×C22⋊C4—94no—
439C2×C22⋊C4—94no—
440C2×C22⋊C4—94no—
441C2×C42—31no—
442C23×C3—31no—
443C23×C3—34no—
444C22×D3—34no—
445C22×D3—34no—
446C22×D3—64no—
447C22×D3—68no—
448C22×D3—68no—
449C22×D3—68no—
450C22×D3—68no—
451C22×D3—68no—
452C22×D3—68no—
453C22×D3C23×D314yes—
454C22×D3C23×D311yescharacteristic
455C3×Q8—122no—
456C3×D4—122no—
457C3×D4—124no—
458C2×C3×C4—24no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—34no—
462C2×C3×C4—34no—
463C2×C3×C4—31no—
464C2×C3×C4—32no—
465C2×C3×C4—64no—
466C2×C3×C4—68no—
467C2×C3×C4—62no—
468C2×C3×C4—124no—
469C2×C3×C4C23×D312yes—
470C2×C3×C4C23×D311yescharacteristic
471C2×C3×C4C23×D314yes—
472C2×C3×C4C23×D314yes—
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D312yes—
475#67—124no—
476#67—124no—
477#67—124no—
478C2×Dic3—34no—
479C2×Dic3—34no—
480C2×Dic3—64no—
481C2×Dic3—68no—
482C2×Dic3—124no—
483C2×Dic3C23×D311yescharacteristic
484C2×Dic3C23×D312yes—
485C2×Dic3C23×D314yes—
486C2×Dic3C23×D314yes—
487D12—42no—
488D12—44no—
489D12—122no—
490D12—124no—
491D12—122no—
492D12—124no—
493D12—124no—
494D12—124no—
495D12—124no—
496D12—242no—
497D12—244no—
498C4×D3—22no—
499C4×D3—28no—
500C4×D3—24no—
501C4×D3—44no—
502C4×D3—68no—
503C4×D3—124no—
504C4×D3—124no—
505C4×D3—124no—
506C4×D3—124no—
507C4×D3—124no—
508C4×D3—244no—
509Dic6—42no—
510Dic6—124no—
511Dic6—124no—
512Dic6—122no—
513Dic6—122no—
514Dic6—242no—
515C2×C32C2×H(5,𝔽2)12yes—
516C2×C32C2×2−1+411yescharacteristic
517C3⋊D3—44no—
518C3×D3—44no—
519C3×D3#56214yescomplemented
520C24—94no—
521C2×Q8—32no—
522C2×Q8—94no—
523C2×Q8—92no—
524C2×Q8—364no—
525C2×D4—34no—
526C2×D4—32no—
527C2×D4—94no—
528C2×D4—94no—
529C2×D4—94no—
530C2×D4—94no—
531C2×D4—92no—
532C2×D4—368no—
533C2×D4—364no—
534C22×C4—31no—
535C22×C4—32no—
536C22×C4—34no—
537C22×C4—34no—
538C22×C4—94no—
539C22×C4—94no—
540C22×C4—94no—
541C22×C4—94no—
542C22×C4—368no—
543C4⋊C4—34no—
544C4⋊C4—34no—
545C4⋊C4—34no—
546C4⋊C4—34no—
547C4⋊C4—32no—
548C4⋊C4—34no—
549C4⋊C4—94no—
550C4⋊C4—94no—
551C4⋊C4—94no—
552C4⋊C4C2×D3214yes—
553C4⋊C4C2×D3212yes—
554C22⋊C4—34no—
555C22⋊C4—34no—
556C22⋊C4—34no—
557C22⋊C4—94no—
558C22⋊C4—94no—
559C22⋊C4—94no—
560C22⋊C4—94no—
561C22⋊C4—94no—
562C22⋊C4—94no—
563C22⋊C4—94no—
564C22⋊C4—94no—
565C22⋊C4—94no—
566C42—32no—
567C42—31no—
568C42C2×D3211yescharacteristic
569C22×C3—21no—
570C22×C3—34no—
571C22×C3—32no—
572C22×C3—64no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3C24×D311yescharacteristic
576C22×C3C24×D311yescharacteristic
577C2×D3—24no—
578C2×D3—24no—
579C2×D3—24no—
580C2×D3—64no—
581C2×D3—64no—
582C2×D3—64no—
583C2×D3—64no—
584C2×D3—64no—
585C2×D3—64no—
586C2×D3—124no—
587C2×D3—124no—
588C2×D3—124no—
589C2×D3—1216no—
590C2×D3—1216no—
591C2×D3#100712yes—
592C2×D3#100914yes—
593C3×C4—21no—
594C3×C4—22no—
595C3×C4—24no—
596C3×C4—22no—
597C3×C4—24no—
598C3×C4—21no—
599C3×C4—42no—
600C3×C4—44no—
601C3×C4—41no—
602C3×C4—64no—
603C3×C4—62no—
604C3×C4—64no—
605C3×C4—61no—
606Dic3—21no—
607Dic3—22no—
608Dic3—24no—
609Dic3—24no—
610Dic3—64no—
611Dic3—64no—
612Dic3—124no—
613C32C2×#56211yescharacteristic, complemented, Sylow
614C23—31no—
615C23—34no—
616C23—94no—
617C23—188no—
618C23—188no—
619C23—188no—
620Q8—122no—
621Q8—362no—
622Q8—364no—
623D4—124no—
624D4—122no—
625D4—364no—
626D4—362no—
627D4—364no—
628D4—364no—
629D4—364no—
630C2×C4—31no—
631C2×C4—32no—
632C2×C4—34no—
633C2×C4—34no—
634C2×C4—68no—
635C2×C4—64no—
636C2×C4—62no—
637C2×C4—94no—
638C2×C4—124no—
639C2×C4—188no—
640C2×C4—364no—
641C2×C4—364no—
642C2×C4—364no—
643C2×C4C22×D3211yescharacteristic
644C2×C4C22×D3212yes—
645C2×C4C22×D3214yes—
646C2×C3—21no—
647C2×C3—22no—
648C2×C3—34no—
649C2×C3—124no—
650C2×C3C2×#100711yescharacteristic
651C2×C3C2×#100912yes—
652C2×C3D3×H(5,𝔽2)12yes—
653C2×C3D3×2−1+411yescharacteristic
654D3—44no—
655D3—124no—
656D3—124no—
657D3—244no—
658D3#570014yesdirect product factor
659C22—32no—
660C22—34no—
661C22—64no—
662C22—64no—
663C22—64no—
664C22—184no—
665C22—184no—
666C22—184no—
667C22—3616no—
668C22C23×D3211yescharacteristic
669C4—21no—
670C4—24no—
671C4—22no—
672C4—61no—
673C4—64no—
674C4—62no—
675C4—64no—
676C4—184no—
677C3—21no—
678C3C2×#570011yescharacteristic, complemented
679C3D3×#56211yescharacteristic, complemented
680C2—34no—
681C2—124no—
682C2—364no—
683C2D3×#100711yescharacteristic
684C2D3×#100912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#125C22
hypercenter#125D32
hypocenterC32C2×#562
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #10596171C2semidirect
2. C3×#5700C2semidirect
3. C3×D3×#125C2semidirect
4. D3×#896C2semidirect
5. D3×#895C2semidirect
6. D3×#894C2semidirect
7. #10594593C2semidirect
8. #10594500C2semidirect
9. #10594493C2semidirect
10. D3×#875C2semidirect
11. #10593953C2semidirect
18. C32×#125C22semidirect
19. #64105C22semidirect
20. #64104C22semidirect
21. #64103C22semidirect
22. #64084C22semidirect
23. C3×#896C22semidirect
24. C3×#895C22semidirect
25. C3×#894C22semidirect
28. C3×#890C22semidirect
29. C3×#889C22semidirect
30. C3×#875C22semidirect
32. C3×#870C22semidirect
36. #63916C22semidirect
37. #63910C22semidirect
38. #63910C22semidirect
39. #63909C22semidirect
40. #63899C22semidirect
41. #63897C22semidirect
42. #63896C22semidirect
43. #63895C22semidirect
44. #63890C22semidirect
45. #63888C22semidirect
46. #63886C22semidirect
47. #63886C22semidirect
48. #63884C22semidirect
50. #63865C22semidirect
51. #63864C22semidirect
52. #63860C22semidirect
53. #63854C22semidirect
54. #63853C22semidirect
55. #63852C22semidirect
56. #63852C22semidirect
57. #63851C22semidirect
58. #63850C22semidirect
68. #5700D3direct (N × H)
69. D3×#125D3semidirect
144. C3×#125C2×D3semidirect
145. C3×#125C2×D3semidirect
178. #896C2×D3semidirect
188. #895C2×D3semidirect
199. #894C2×D3semidirect
203. #890C2×D3semidirect
204. #889C2×D3semidirect
224. #875C2×D3semidirect
226. #870C2×D3semidirect
404. #125D32semidirect
519. C3×D3#562semidirect
613. C32C2×#562semidirect
658. D3#5700direct (N × H)
678. C3C2×#5700semidirect
679. C3D3×#562semidirect

Maximal subgroups

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

subgroupindex
#105961712
C3×#57002
C3×D3×#1252
D3×#8962
D3×#8952
D3×#8942
#105945932
#105945002
#105944932
D3×#8752
#105939532
D3×#5623
C2×#57003