Finite Group Databasebeta

← D3×#4537 #11774929

Subgroups — D3×#4537 #11774929

Order 1152.

821 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#121C211yesmaximal, characteristic
2D3×C3⋊#95C211yesmaximal, characteristic, complemented
3D3×#830C211yesmaximal, characteristic, complemented
4#10589403C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8C2×#4537—31nomaximal
9D3×#327—31nomaximal
10C2×C3×D3×D4—21no—
11C2×C3×D3×D4C411yescharacteristic, complemented
12C22×C3×C4×D3C2211yescharacteristic
13C22×D3×Dic3—21no—
14C32×#121C2211yescharacteristic
15C3×#939—21no—
16C3×#938C411yescharacteristic, complemented
17C3×#930C2211yescharacteristic
18C3×#895C411yescharacteristic, complemented
19C3×D3×C4⋊C4C411yescharacteristic, complemented
20C3×#884—21no—
21C3×D3×C22⋊C4—21no—
22C2×D3×C3⋊C8—21no—
23#63658C2211yescharacteristic, complemented
24#63657C2211yescharacteristic, complemented
25C3×C3⋊#95C2211yescharacteristic, complemented
26C3×#830C2211yescharacteristic, complemented
27#63579—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29C2×C3×#121—31no—
30D3×#121D311yescharacteristic
31C2×C3⋊#95—31no—
32C2×#830—31no—
33D3×C22⋊C8—31no—
34D3×#95—31no—
35C3×#327—31no—
36#4537—31no—
37#4537—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4537D311yescharacteristic, direct product factor
42#4470—31no—
43#4451—31no—
44C23×C3×D3—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4C2×C411yescharacteristic, complemented
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C3×D3×D4—42no—
56C3×D3×D4—42no—
57C3×D3×D4—42no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C411yescharacteristic, complemented
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—42no—
62C2×C3×C4×D3C2×C411yescharacteristic
63C2×C3×C4×D3C2×C411yescharacteristic
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3D411yescharacteristic
66C2×D3×Dic3—24no—
67C2×D3×Dic3—42no—
68C2×D3×Dic3—42no—
69C32×C4⋊C4C2×C411yescharacteristic, complemented
70C32×C22⋊C4—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C3×#217—21no—
73C3×(C2×D3)⋊C4—21no—
74C3×(C2×D3)⋊C4—21no—
75C3×C4⋊Dic3C2×C411yescharacteristic, complemented
76C3×Dic3⋊C4—21no—
77C2×C3×C3⋊C8—21no—
78D3×C3⋊C8—42no—
79C2×#327—91noSylow
80C22×C3×D4—31no—
81C22×C3×D4—61no—
82C23×C3×C4—31no—
83C23×Dic3—61no—
84C2×D3×D4—21no—
85C2×D3×D4Dic311yescharacteristic, complemented
86C22×C4×D3—61no—
87C22×C4×D3C2×D311yescharacteristic
88C3×#121—21no—
89C3×#121—31no—
90C3×#121—31no—
91C3×#121—31no—
92C3×#121—61no—
93C3×#121—61no—
94C3×#121C2×D311yescharacteristic
95C3×#121C2×D311yescharacteristic
96C2×C3×C4⋊C4—31no—
97C2×C3×C22⋊C4—61no—
98#939—21no—
99#938Dic311yescharacteristic, complemented
100#930C2×D311yescharacteristic
101C22×C3⋊C8—61no—
102C2×D3×C8—61no—
103#895Dic311yescharacteristic, complemented
104D3×C4⋊C4Dic311yescharacteristic, complemented
105#884—21no—
106D3×C22⋊C4—21no—
107C3×C22⋊C8—31no—
108C3×#95—31no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113C3⋊#95—61no—
114C3⋊#95C2×D311yescharacteristic, complemented
115#830—31no—
116#830—31no—
117#830—61no—
118#830—61no—
119#830C2×D311yescharacteristic, complemented
120(C2×D3)⋊C8—61no—
121C23×C32—21no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—21no—
126C22×C3×D3—42no—
127C22×C3×D3—42no—
128C22×C3×D3—42no—
129C22×C3×D3C22⋊C411yescharacteristic
130C22×C3×D3C22⋊C411yescharacteristic
131C22×C3×D3D812yes—
132C22×C3×D3SD1612yes—
133C32×D4—41no—
134C32×D4—41no—
135C32×D4—41no—
136C2×C32×C4—21no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C3×#67—42no—
144C3×#67—41no—
145C3×#67—41no—
146C3×#67—42no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3C22⋊C411yescharacteristic
153C2×C3×Dic3C22⋊C411yescharacteristic
154C3×D12—41no—
155C3×D12—42no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3—41no—
159C3×C4×D3—41no—
160C3×C4×D3—42no—
161D3×Dic3—48no—
162C3⋊(C3⋊C8)—41no—
163C3×C3⋊C8—41no—
164C2×#121—31no—
165C2×C22⋊C8—91no—
166C2×#95—91no—
167#327—31no—
168#327—91no—
169#327—91no—
170#327—91no—
171C24×C3—31no—
172C24×C3—61no—
173C23×D3—21no—
174C23×D3#6711yescharacteristic
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—31no—
179C2×C3×D4—41no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—122no—
185C2×C3×D4—122no—
186C2×C3×D4—122no—
187C2×C3×D4C4×D311yescharacteristic, complemented
188C2×C3×D4C2×Dic311yescharacteristic, complemented
189C22×C3×C4—21no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4—122no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C2×#67—21no—
201C2×#67—21no—
202C2×#67—21no—
203C22×Dic3—21no—
204C22×Dic3—64no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—121no—
208C22×Dic3—122no—
209C22×Dic3—122no—
210C22×Dic3#6711yescharacteristic
211D3×D4—42no—
212D3×D4—42no—
213D3×D4—42no—
214C2×D12—21no—
215C2×D12C2×Dic311yescharacteristic, complemented
216C2×C4×D3—21no—
217C2×C4×D3—42no—
218C2×C4×D3—64no—
219C2×C4×D3—122no—
220C2×C4×D3—122no—
221C2×C4×D3C2×Dic311yescharacteristic
222C2×C4×D3C2×Dic311yescharacteristic
223C2×C4×D3#6711yescharacteristic
224C2×C4×D3#6711yescharacteristic
225C2×C3×C8—61no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4C4×D311yescharacteristic, complemented
230C3×C4⋊C4C2×Dic311yescharacteristic, complemented
231C3×C22⋊C4—21no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—41no—
234C3×C22⋊C4—61no—
235C3×C22⋊C4—61no—
236C3×C22⋊C4—61no—
237#217—21no—
238(C2×D3)⋊C4—21no—
239(C2×D3)⋊C4—21no—
240C4⋊Dic3C2×Dic311yescharacteristic, complemented
241Dic3⋊C4—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—121no—
246C2×C3⋊C8—122no—
247D3×C8—122no—
248C22×C32—21no—
249C22×C32—21no—
250C22×C32—41no—
251C22×C32—41no—
252C22×C32—41no—
253C22×C32C2×C22⋊C411yescharacteristic
254C22×C32C2×D811yescharacteristic
255C22×C32C2×SD1611yescharacteristic
256C2×C3×D3—21no—
257C2×C3×D3—21no—
258C2×C3×D3—24no—
259C2×C3×D3—24no—
260C2×C3×D3—41no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C2×C3×D3—84no—
264C2×C3×D3#9912yes—
265C2×C3×D3#10212yes—
266C2×C3×D3#10212yes—
267C2×C3×D3#10412yes—
268C32×C4—21no—
269C32×C4—21no—
270C32×C4—41no—
271C3⋊Dic3—42no—
272C3×Dic3—21no—
273C3×Dic3—21no—
274C3×Dic3—42no—
275C3×Dic3—41no—
276C22×D4—31no—
277C22×D4—61no—
278C23×C4—31no—
279C23×C4—181no—
280C22×C8—181no—
281#121—31no—
282#121—31no—
283#121—31no—
284#121—61no—
285#121—61no—
286#121D3211yescharacteristic
287C2×C4⋊C4—31no—
288C2×C22⋊C4—61no—
289C22⋊C8—31no—
290C22⋊C8—91no—
291C22⋊C8—181no—
292#95—31no—
293#95—91no—
294#95—181no—
295C23×C3—21no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—31no—
299C23×C3—31no—
300C23×C3—32no—
301C23×C3—32no—
302C23×C3—41no—
303C23×C3—62no—
304C23×C3—62no—
305C23×C3—61no—
306C23×C3—122no—
307C23×C3—122no—
308C23×C3—122no—
309C23×C3D3×D411yescharacteristic
310C23×C3C2×#6711yescharacteristic
311C22×D3—22no—
312C22×D3—22no—
313C22×D3—21no—
314C22×D3—42no—
315C22×D3—42no—
316C22×D3—42no—
317C22×D3#21312yes—
318C22×D3#21412yes—
319C22×D3#21711yescharacteristic
320C22×D3#21711yescharacteristic
321C3×D4—41no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—41no—
327C3×D4—81no—
328C3×D4—81no—
329C3×D4—81no—
330C3×D4—121no—
331C3×D4—122no—
332C3×D4—122no—
333C3×D4—122no—
334C3×D4—121no—
335C3×D4—121no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—31no—
341C2×C3×C4—31no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—61no—
349C2×C3×C4—81no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—122no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4C2×C4×D311yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C22×Dic311yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360#67—42no—
361#67—41no—
362#67—41no—
363#67—42no—
364C2×Dic3—22no—
365C2×Dic3—21no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368C2×Dic3—41no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—122no—
372C2×Dic3—128no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377C2×Dic3—241no—
378C2×Dic3—241no—
379C2×Dic3#21711yescharacteristic
380C2×Dic3#21711yescharacteristic
381D12—41no—
382D12—42no—
383C4×D3—22no—
384C4×D3—22no—
385C4×D3—41no—
386C4×D3—41no—
387C4×D3—42no—
388C4×D3—128no—
389C3×C8—121no—
390C3⋊C8—41no—
391C3⋊C8—121no—
392C3⋊C8—121no—
393C3⋊C8—241no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32—81no—
397C2×C32C2×#9911yescharacteristic
398C2×C32C2×#10211yescharacteristic
399C2×C32C2×#10411yescharacteristic
400C3×D3—22no—
401C3×D3—81no—
402C3×D3#32714yescomplemented
403C24—31no—
404C24—61no—
405C2×D4—21no—
406C2×D4—31no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—61no—
411C2×D4—122no—
412C2×D4—122no—
413C2×D4—122no—
414C2×D4D3×Dic311yescharacteristic, complemented
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—122no—
423C22×C4—184no—
424C22×C4—181no—
425C22×C4—362no—
426C22×C4—362no—
427C22×C4C2×D3211yescharacteristic
428C2×C8—61no—
429C2×C8—181no—
430C2×C8—362no—
431C4⋊C4—31no—
432C4⋊C4—61no—
433C4⋊C4D3×Dic311yescharacteristic, complemented
434C22⋊C4—21no—
435C22⋊C4—61no—
436C22⋊C4—61no—
437C22⋊C4—61no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—32no—
446C22×C3—32no—
447C22×C3—32no—
448C22×C3—32no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—64no—
458C22×C3—64no—
459C22×C3—61no—
460C22×C3—61no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3—81no—
464C22×C3—121no—
465C22×C3—121no—
466C22×C3—121no—
467C22×C3—244no—
468C22×C3D3×C22⋊C411yescharacteristic
469C22×C3D3×D811yescharacteristic
470C22×C3D3×SD1611yescharacteristic
471C22×C3C2×#21311yescharacteristic
472C22×C3C2×#21411yescharacteristic
473C22×C3C2×#21711yescharacteristic
474C2×D3—21no—
475C2×D3—21no—
476C2×D3—24no—
477C2×D3—24no—
478C2×D3—41no—
479C2×D3—41no—
480C2×D3—41no—
481C2×D3—84no—
482C2×D3#83212yes—
483C2×D3#83212yes—
484C2×D3#83412yes—
485C2×D3#83712yes—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—41no—
491C3×C4—41no—
492C3×C4—41no—
493C3×C4—41no—
494C3×C4—61no—
495C3×C4—61no—
496C3×C4—81no—
497C3×C4—122no—
498C3×C4—121no—
499Dic3—21no—
500Dic3—21no—
501Dic3—42no—
502Dic3—41no—
503Dic3—122no—
504Dic3—122no—
505Dic3—242no—
506C32C2×#32711yescharacteristic, complemented, Sylow
507C23—21no—
508C23—31no—
509C23—32no—
510C23—32no—
511C23—31no—
512C23—62no—
513C23—62no—
514C23—61no—
515C23—122no—
516C23—122no—
517C23—122no—
518C23D3×#6711yescharacteristic
519D4—41no—
520D4—41no—
521D4—41no—
522D4—121no—
523D4—122no—
524D4—122no—
525D4—122no—
526D4—121no—
527D4—121no—
528C2×C4—21no—
529C2×C4—31no—
530C2×C4—31no—
531C2×C4—41no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—61no—
536C2×C4—121no—
537C2×C4—121no—
538C2×C4—122no—
539C2×C4—121no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—182no—
543C2×C4—368no—
544C2×C4—361no—
545C2×C4—361no—
546C2×C4C2×D3×Dic311yescharacteristic
547C2×C4D3×#6711yescharacteristic
548C8—121no—
549C8—361no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—34no—
558C2×C3—41no—
559C2×C3—41no—
560C2×C3—62no—
561C2×C3—81no—
562C2×C3—81no—
563C2×C3—161no—
564C2×C3—241no—
565C2×C3D3×#9911yescharacteristic
566C2×C3D3×#10211yescharacteristic
567C2×C3D3×#10411yescharacteristic
568C2×C3C2×#83211yescharacteristic
569C2×C3C2×#83411yescharacteristic
570C2×C3C2×#83711yescharacteristic
571D3—22no—
572D3—81no—
573D3#453714yesdirect product factor
574C22—21no—
575C22—21no—
576C22—32no—
577C22—32no—
578C22—32no—
579C22—32no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—64no—
584C22—64no—
585C22—61no—
586C22—61no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22—244no—
591C22D3×#21311yescharacteristic
592C22D3×#21411yescharacteristic
593C22D3×#21711yescharacteristic
594C4—21no—
595C4—21no—
596C4—41no—
597C4—61no—
598C4—61no—
599C4—122no—
600C4—121no—
601C4—362no—
602C3—21no—
603C3D3×#32711yescharacteristic, complemented
604C3C2×#453711yescharacteristic, complemented
605C2—21no—
606C2—21no—
607C2—34no—
608C2—62no—
609C2—81no—
610C2—241no—
611C2D3×#83211yescharacteristic
612C2D3×#83411yescharacteristic
613C2D3×#83711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32C2×C22⋊C4
prime radicalC3×D3×#121C2
cosocleC22×C32×C4C23
hypercenter#121D32
hypocenterC32C2×#327
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. D3×C3⋊#95C2semidirect
3. D3×#830C2semidirect
4. #10589403C2semidirect
5. C3×#4537C2semidirect
6. #10589150C2semidirect
7. #10589149C2semidirect
11. C2×C3×D3×D4C4semidirect
16. C3×#938C4semidirect
18. C3×#895C4semidirect
19. C3×D3×C4⋊C4C4semidirect
23. #63658C22semidirect
24. #63657C22semidirect
25. C3×C3⋊#95C22semidirect
26. C3×#830C22semidirect
41. #4537D3direct (N × H)
47. C2×C32×D4C2×C4semidirect
59. C2×C3×D12C2×C4semidirect
69. C32×C4⋊C4C2×C4semidirect
75. C3×C4⋊Dic3C2×C4semidirect
85. C2×D3×D4Dic3semidirect
99. #938Dic3semidirect
103. #895Dic3semidirect
104. D3×C4⋊C4Dic3semidirect
114. C3⋊#95C2×D3semidirect
119. #830C2×D3semidirect
187. C2×C3×D4C4×D3semidirect
188. C2×C3×D4C2×Dic3semidirect
215. C2×D12C2×Dic3semidirect
229. C3×C4⋊C4C4×D3semidirect
230. C3×C4⋊C4C2×Dic3semidirect
240. C4⋊Dic3C2×Dic3semidirect
402. C3×D3#327semidirect
414. C2×D4D3×Dic3semidirect
433. C4⋊C4D3×Dic3semidirect
506. C32C2×#327semidirect
573. D3#4537direct (N × H)
603. C3D3×#327semidirect
604. C3C2×#4537semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1212
D3×C3⋊#952
D3×#8302
#105894032
C3×#45372
#105891502
#105891492
C2×#45373
D3×#3273