Finite Group Databasebeta

← D3×#4986 #11808515

Subgroups — D3×#4986 #11808515

Order 1152.

1275 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3#10592685C211yesmaximal, characteristic, complemented
4C3×#4986C211yesmaximal, characteristic, complemented
5D3×C3⋊#95C212yesmaximal
6D3×C3⋊#95C212yesmaximal
7D3×C3⋊#95C211yesmaximal, characteristic
8#10591343C212yesmaximal, complemented
9#10591341C212yesmaximal, complemented
10#10591226C211yesmaximal, characteristic, complemented
11#10591225C211yesmaximal, characteristic, complemented
12C2×#4986—31nomaximal
13D3×#400—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C22×D3×Dic3C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C3×D3×C4⋊C4—24no—
26C2×Dic3⋊Dic3C2212yes—
27D3×C4⋊Dic3—24no—
28#63658C2212yes—
29#63658C2212yes—
30#63658C2211yescharacteristic
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C22×C3×C4⋊C4—31no—
40C22×C4⋊Dic3—31no—
41C2×D3×C4⋊C4—31no—
42C2×D3×C4⋊C4D311yescharacteristic
43C3×#400—31no—
44C2×C3⋊#95—31no—
45C2×C3⋊#95—32no—
46C2×C3⋊#95—32no—
47#4986—31no—
48#4986—31no—
49#4986—31no—
50#4986—32no—
51#4986—32no—
52#4986—31no—
53#4986—61no—
54#4986D311yescharacteristic, direct product factor
55#4985—31no—
56D3×#95—32no—
57D3×#95—32no—
58D3×#95—31no—
59#4660—32no—
60#4659—31no—
61#4658—32no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—24no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—24no—
78C2×C3×C4×D3D414yes—
79C2×C3×C4×D3Q814yes—
80C2×D3×Dic3—24no—
81C2×D3×Dic3—28no—
82C2×D3×Dic3—24no—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C32×C4⋊C4—22no—
86C4⋊(C3⋊Dic3)—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—22no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91Dic3⋊Dic3—24no—
92C2×#400—91noSylow
93C23×C3×C4—31no—
94C23×C3×C4—31no—
95C23×C3×C4—31no—
96C23×Dic3—32no—
97C23×Dic3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—32no—
100C22×C4×D3C2×D311yescharacteristic
101C22×C4×D3C2×D311yescharacteristic
102C22×C4×D3C2×D311yescharacteristic
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C4⋊C4—64no—
109C2×C3×C4⋊C4C2×D311yescharacteristic
110C2×C3×C4⋊C4C2×D311yescharacteristic
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3—61no—
115C2×C4⋊Dic3—64no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4C2×D311yescharacteristic
120C2×Dic3⋊C4C2×D311yescharacteristic
121D3×C4⋊C4—24no—
122D3×C4⋊C4—64no—
123C3×#95—32no—
124C3×#95—31no—
125C3×#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95—31no—
129C3⋊#95—31no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—61no—
143C3⋊#95—62no—
144C3⋊#95—62no—
145C3⋊#95C2×D311yescharacteristic
146C3⋊#95C2×D312yes—
147C3⋊#95C2×D312yes—
148C23×C32C2411yescharacteristic
149C22×C3×D3C2×D412yes—
150C22×C3×D3C2×Q812yes—
151C22×C3×D3#4112yes—
152C22×C3×D3#4114yes—
153C22×C3×D3#4114yes—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—22no—
157C2×C32×C4—21no—
158C2×C32×C4—22no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×Q812yes—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—24no—
165C2×C3⋊Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—24no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×Q812yes—
178C3×C4×D3—28no—
179C3×C4×D3—28no—
180C3×C4×D3—44no—
181D3×Dic3—48no—
182D3×Dic3—48no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—91no—
185#400—31no—
186#400—92no—
187#400—91no—
188#400—92no—
189#400—91no—
190#400—91no—
191C2×#95—91no—
192C2×#95—92no—
193C2×#95—92no—
194C24×C3—31no—
195C23×D3C22×D311yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—34no—
202C22×C3×C4—34no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4—64no—
209C22×C3×C4—62no—
210C22×C3×C4—64no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—64no—
224C22×Dic3—64no—
225C22×Dic3—68no—
226C22×Dic3—64no—
227C22×Dic3—64no—
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D311yescharacteristic
232C22×Dic3C22×D311yescharacteristic
233C2×C4×D3—22no—
234C2×C4×D3—24no—
235C2×C4×D3—22no—
236C2×C4×D3—24no—
237C2×C4×D3—22no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—68no—
242C2×C4×D3—64no—
243C2×C4×D3Dic614yes—
244C2×C4×D3#6714yes—
245C3×C4⋊C4—22no—
246C3×C4⋊C4—22no—
247C3×C4⋊C4—42no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4—62no—
250C3×C4⋊C4—62no—
251C3×C4⋊C4—62no—
252C4⋊Dic3—22no—
253C4⋊Dic3—22no—
254C4⋊Dic3—64no—
255C4⋊Dic3—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3—122no—
258Dic3⋊C4—22no—
259Dic3⋊C4—22no—
260Dic3⋊C4—64no—
261C22×C32C22×D411yescharacteristic
262C22×C32C22×Q811yescharacteristic
263C22×C32C2×#4111yescharacteristic
264C22×C32C2×#4112yes—
265C22×C32C2×#4112yes—
266C2×C3×D3C22⋊Q814yes—
267C2×C3×D3#12314yes—
268C2×C3×D3#12414yes—
269C2×C3×D3#12518yes—
270C2×C3×D3#12618yes—
271C32×C4—22no—
272C32×C4—22no—
273C32×C4—41no—
274C3⋊Dic3—42no—
275C3⋊Dic3—42no—
276C3×Dic3—22no—
277C3×Dic3—22no—
278C3×Dic3—41no—
279C3×Dic3—42no—
280C3×Dic3—42no—
281C23×C4—31no—
282C23×C4—31no—
283C23×C4—31no—
284C23×C4—92no—
285C23×C4—92no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—64no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4—184no—
294C2×C4⋊C4D3211yescharacteristic
295#95—31no—
296#95—32no—
297#95—32no—
298#95—92no—
299#95—92no—
300#95—92no—
301#95—92no—
302#95—92no—
303#95—91no—
304#95—92no—
305#95—92no—
306C23×C3—21no—
307C23×C3—32no—
308C23×C3—32no—
309C23×C3—34no—
310C23×C3—32no—
311C23×C3—34no—
312C23×C3C23×D311yescharacteristic
313C23×C3C23×D311yescharacteristic
314C22×D3C2×Dic612yes—
315C22×D3#23512yes—
316C22×D3#23714yes—
317C22×D3#23914yes—
318C22×D3C2×#6712yes—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—42no—
336C2×C3×C4—41no—
337C2×C3×C4—42no—
338C2×C3×C4—68no—
339C2×C3×C4—68no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—61no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—64no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—124no—
351C2×C3×C4C2×Dic612yes—
352C2×C3×C4D3×D412yes—
353C2×C3×C4D3×Q812yes—
354C2×C3×C4C2×#6712yes—
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—21no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—24no—
363C2×Dic3—22no—
364C2×Dic3—21no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—64no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—64no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—124no—
380C2×Dic3—128no—
381C2×Dic3—128no—
382C2×Dic3C2×Dic612yes—
383C2×Dic3C2×#6712yes—
384C4×D3—28no—
385C4×D3—28no—
386C4×D3—44no—
387C4×D3—128no—
388C4×D3—128no—
389C2×C32C2×C22⋊Q811yescharacteristic
390C2×C32C2×#12311yescharacteristic
391C2×C32C2×#12411yescharacteristic
392C2×C32C2×#12512yes—
393C2×C32C2×#12612yes—
394C3×D3#40018yescomplemented
395C24—31no—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—34no—
399C22×C4—34no—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—31no—
403C22×C4—62no—
404C22×C4—62no—
405C22×C4—64no—
406C22×C4—62no—
407C22×C4—64no—
408C22×C4—92no—
409C22×C4—92no—
410C22×C4—184no—
411C22×C4—184no—
412C22×C4—184no—
413C22×C4—188no—
414C22×C4—184no—
415C22×C4C2×D3211yescharacteristic
416C22×C4C2×D3211yescharacteristic
417C22×C4C2×D3211yescharacteristic
418C4⋊C4—22no—
419C4⋊C4—62no—
420C4⋊C4—62no—
421C4⋊C4—62no—
422C4⋊C4—62no—
423C4⋊C4—184no—
424C4⋊C4—182no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—34no—
431C22×C3—34no—
432C22×C3—38no—
433C22×C3—38no—
434C22×C3—34no—
435C22×C3C22×Dic611yescharacteristic
436C22×C3C2×#23511yescharacteristic
437C22×C3C2×D3×D411yescharacteristic
438C22×C3C2×#23712yes—
439C22×C3C2×D3×Q811yescharacteristic
440C22×C3C2×#23912yes—
441C22×C3D3×#4111yescharacteristic
442C22×C3D3×#4112yes—
443C22×C3D3×#4112yes—
444C22×C3C22×#6711yescharacteristic
445C2×D3#89018yes—
446C2×D3#89818yes—
447C2×D3#92414yes—
448C2×D3#93514yes—
449C2×D3#94714yes—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—62no—
459C3×C4—62no—
460C3×C4—81no—
461C3×C4—121no—
462C3×C4—122no—
463C3×C4—122no—
464Dic3—22no—
465Dic3—22no—
466Dic3—42no—
467Dic3—42no—
468Dic3—41no—
469Dic3—122no—
470Dic3—122no—
471Dic3—122no—
472Dic3—122no—
473Dic3—242no—
474Dic3—242no—
475C32C2×#40011yescharacteristic, complemented, Sylow
476C23—32no—
477C23—32no—
478C23—34no—
479C23—34no—
480C23—32no—
481C23C22×D3211yescharacteristic
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—68no—
490C2×C4—68no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—61no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—64no—
499C2×C4—61no—
500C2×C4—62no—
501C2×C4—124no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—184no—
506C2×C4—182no—
507C2×C4—368no—
508C2×C4—368no—
509C2×C4D3×Dic612yes—
510C2×C4D3×#6712yes—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—22no—
514C2×C3—21no—
515C2×C3—22no—
516C2×C3—38no—
517C2×C3C2×#89012yes—
518C2×C3C2×#89812yes—
519C2×C3D3×C22⋊Q811yescharacteristic
520C2×C3D3×#12311yescharacteristic
521C2×C3D3×#12411yescharacteristic
522C2×C3D3×#12512yes—
523C2×C3D3×#12612yes—
524C2×C3C2×#92411yescharacteristic
525C2×C3C2×#93511yescharacteristic
526C2×C3C2×#94711yescharacteristic
527D3#498618yesdirect product factor
528C22—34no—
529C22—34no—
530C22—38no—
531C22—34no—
532C22—38no—
533C22C2×D3×Dic611yescharacteristic
534C22D3×#23511yescharacteristic
535C22D3×#23712yes—
536C22D3×#23912yes—
537C22C2×D3×#6711yescharacteristic
538C4—22no—
539C4—22no—
540C4—41no—
541C4—62no—
542C4—62no—
543C4—121no—
544C4—122no—
545C4—122no—
546C4—362no—
547C4—362no—
548C3—21no—
549C3D3×#40011yescharacteristic, complemented
550C3C2×#498611yescharacteristic, complemented
551C2—38no—
552C2D3×#89012yes—
553C2D3×#89812yes—
554C2D3×#92411yescharacteristic
555C2D3×#93511yescharacteristic
556C2D3×#94711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#400
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10592685C2semidirect
4. C3×#4986C2semidirect
8. #10591343C2semidirect
9. #10591341C2semidirect
10. #10591226C2semidirect
11. #10591225C2semidirect
54. #4986D3direct (N × H)
394. C3×D3#400semidirect
475. C32C2×#400semidirect
527. D3#4986direct (N × H)
549. C3D3×#400semidirect
550. C3C2×#4986semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×D3×C4⋊Dic32
#105926852
C3×#49862
D3×C3⋊#952
#105913432
#105913412
#105912262
#105912252
C2×#49863
D3×#4003