Finite Group Databasebeta

← D3×#4554 #11783398

Subgroups — D3×#4554 #11783398

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3C2×D3×#208C211yesmaximal, characteristic
4#10589420C211yesmaximal, characteristic, complemented
5C3×#4554C211yesmaximal, characteristic, complemented
6#10589168C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8C2×#4554—31nomaximal
9D3×#343—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×D3×Dic3C412yes—
12C2×C32×M16C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×D3×M16—22no—
19C3×D3×M16C414yescomplemented
20C2×C3×ΓL(1,𝔽25)—21no—
21C2×C3×D3×C8—21no—
22C2×Dic3⋊Dic3C412yes—
23D3×C4⋊Dic3—21no—
24D3×C4⋊Dic3—21no—
25D3×C4⋊Dic3—21no—
26D3×C4⋊Dic3—21no—
27C2×#3711—21no—
28D3×#208—22no—
29D3×#208C414yescomplemented
30C2×D3×C3⋊C8—21no—
31C22×C3×M16—31no—
32C22×C4⋊Dic3—31no—
33C22×#208—31no—
34C2×D3×M16—31no—
35C2×D3×M16D311yescharacteristic
36C2×D3×C4⋊C4—31no—
37C3×#343—31no—
38#4554—31no—
39#4554—31no—
40#4554—31no—
41#4554—31no—
42#4554—31no—
43#4554—61no—
44#4554D311yescharacteristic, direct product factor
45#4530—31no—
46C23×C3×D3C2×C411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2×C412yes—
49C22×C3×Dic3C2×C412yes—
50C22×C3×Dic3C2×C411yescharacteristic
51C2×C3×C4×D3C2×C412yes—
52C2×C3×C4×D3C2×C412yes—
53C2×C3×C4×D3D412yes—
54C2×C3×C4×D3D411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×C3×C4×D3D411yescharacteristic
58C2×C3×C4×D3Q812yes—
59C2×D3×Dic3—22no—
60C2×D3×Dic3—22no—
61C2×D3×Dic3—44no—
62C32×M16—21no—
63C32×M16C2×C412yescomplemented
64C2×C32×C8—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67#3748—21no—
68#3748C2×C412yescomplemented
69C2×C3⋊(C3⋊C8)—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208C2×C412yescomplemented
75C3×#208C2×C412yescomplemented
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C3×ΓL(1,𝔽25)—24no—
79C3×D3×C8—24no—
80Dic3⋊Dic3—22no—
81Dic3⋊Dic3—22no—
82#3711—24no—
83D3×C3⋊C8—24no—
84C2×#343—91noSylow
85C23×C3×C4—31no—
86C23×Dic3—32no—
87C22×C4×D3—32no—
88C22×C4×D3C2×D311yescharacteristic
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16—34no—
93C2×C3×M16—61no—
94C2×C3×M16—62no—
95C2×C3×M16C2×D311yescharacteristic
96C2×C3×M16C2×D311yescharacteristic
97C22×C3×C8—61no—
98C2×C3×C4⋊C4—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—32no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3—61no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3—61no—
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×Dic3⋊C4—32no—
109C2×#208—31no—
110C2×#208—31no—
111C2×#208—34no—
112C2×#208—61no—
113C2×#208—61no—
114C2×#208—62no—
115C2×#208C2×D311yescharacteristic
116C2×#208C2×D311yescharacteristic
117C22×C3⋊C8—61no—
118D3×M16—22no—
119D3×M16—34no—
120D3×M16—62no—
121D3×M16Dic314yescomplemented
122C2×ΓL(1,𝔽25)—21no—
123C2×ΓL(1,𝔽25)—61no—
124C2×D3×C8—21no—
125C2×D3×C8—61no—
126D3×C4⋊C4—61no—
127D3×C4⋊C4—61no—
128D3×C4⋊C4—61no—
129D3×C4⋊C4—61no—
130C23×C32C22×C411yescharacteristic
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3C4212yes—
134C22×C3×D3C22⋊C411yescharacteristic
135C22×C3×D3C22⋊C411yescharacteristic
136C22×C3×D3C4⋊C412yes—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×Q811yescharacteristic
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—42no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3C4212yes—
148C2×C3×Dic3C22⋊C411yescharacteristic
149C2×C3×Dic3C22⋊C411yescharacteristic
150C2×C3×Dic3C4⋊C412yes—
151C3×C4×D3C22⋊C412yes—
152C3×C4×D3C22⋊C412yes—
153C3×C4×D3C22⋊C412yes—
154C3×C4×D3C22⋊C412yes—
155C3×C4×D3C4⋊C412yes—
156C3×C4×D3C4⋊C412yes—
157C3×C4×D3C4⋊C412yes—
158C3×C4×D3C4⋊C412yes—
159D3×Dic3—44no—
160D3×Dic3—44no—
161C32×C8—22no—
162C3⋊(C3⋊C8)—22no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—22no—
165C22×M16—31no—
166C22×M16—91no—
167C22×C4⋊C4—91no—
168#343—31no—
169#343—91no—
170#343—91no—
171#343—91no—
172C24×C3—31no—
173C23×D3C4×D311yescharacteristic
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—32no—
181C22×C3×C4—31no—
182C22×C3×C4—31no—
183C22×C3×C4—32no—
184C22×C3×C4—32no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—62no—
190C22×Dic3—62no—
191C22×Dic3—62no—
192C22×Dic3—124no—
193C22×Dic3C4×D312yes—
194C22×Dic3C4×D311yescharacteristic
195C2×C4×D3—62no—
196C2×C4×D3—62no—
197C2×C4×D3—124no—
198C2×C4×D3Dic612yes—
199C2×C4×D3C4×D312yes—
200C2×C4×D3D1211yescharacteristic
201C2×C4×D3D1211yescharacteristic
202C2×C4×D3C2×Dic312yes—
203C2×C4×D3#6711yescharacteristic
204C2×C4×D3#6711yescharacteristic
205C2×C4×D3#6712yes—
206C3×M16—21no—
207C3×M16—21no—
208C3×M16—22no—
209C3×M16—32no—
210C3×M16—32no—
211C3×M16—41no—
212C3×M16—64no—
213C3×M16—61no—
214C3×M16—61no—
215C3×M16C4×D312yescomplemented
216C3×M16C2×Dic312yescomplemented
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—41no—
220C2×C3×C8—64no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C4⋊Dic3—62no—
228C4⋊Dic3—62no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—121no—
234C4⋊Dic3—121no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237#208—21no—
238#208—21no—
239#208—32no—
240#208—32no—
241#208—62no—
242#208—64no—
243#208—61no—
244#208—61no—
245#208—121no—
246#208C4×D312yescomplemented
247#208C2×Dic312yescomplemented
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—121no—
254ΓL(1,𝔽25)—24no—
255ΓL(1,𝔽25)—64no—
256D3×C8—24no—
257D3×C8—64no—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32C2×C4211yescharacteristic
261C22×C32C2×C22⋊C411yescharacteristic
262C22×C32C2×C4⋊C411yescharacteristic
263C2×C3×D3—21no—
264C2×C3×D3—21no—
265C2×C3×D3—24no—
266C2×C3×D3—24no—
267C2×C3×D3#9512yes—
268C2×C3×D3#9512yes—
269C2×C3×D3#10012yes—
270C2×C3×D3#10112yes—
271C32×C4C2×C22⋊C411yescharacteristic
272C32×C4C2×C22⋊C411yescharacteristic
273C32×C4C2×C4⋊C411yescharacteristic
274C32×C4C2×C4⋊C411yescharacteristic
275C3⋊Dic3—42no—
276C3×Dic3—42no—
277C3×Dic3#9512yes—
278C3×Dic3#9512yes—
279C23×C4—31no—
280C23×C4—92no—
281C2×M16—31no—
282C2×M16—31no—
283C2×M16—34no—
284C2×M16—61no—
285C2×M16—62no—
286C2×M16—94no—
287C2×M16—91no—
288C2×M16—181no—
289C2×M16—182no—
290C2×M16D3211yescharacteristic
291C22×C8—61no—
292C22×C8—181no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4—181no—
297C2×C4⋊C4—181no—
298C2×C4⋊C4—181no—
299C2×C4⋊C4—181no—
300C23×C3—21no—
301C23×C3—31no—
302C23×C3—32no—
303C23×C3—31no—
304C23×C3—32no—
305C23×C3—62no—
306C23×C3—62no—
307C23×C3C2×C4×D311yescharacteristic
308C23×C3C2×C4×D311yescharacteristic
309C22×D3—22no—
310C22×D3—22no—
311C22×D3C4×Dic312yes—
312C22×D3Dic3⋊C412yes—
313C22×D3(C2×D3)⋊C411yescharacteristic
314C22×D3(C2×D3)⋊C411yescharacteristic
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—31no—
323C2×C3×C4—31no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—62no—
334C2×C3×C4—122no—
335C2×C3×C4C2×Dic611yescharacteristic
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4C2×C4×D311yescharacteristic
338C2×C3×C4C2×C4×D311yescharacteristic
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×Q811yescharacteristic
344C2×C3×C4C22×Dic311yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×Dic3—22no—
348C2×Dic3—42no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—122no—
352C2×Dic3—124no—
353C2×Dic3—124no—
354C2×Dic3—122no—
355C2×Dic3—122no—
356C2×Dic3—242no—
357C2×Dic3C4×Dic312yes—
358C2×Dic3Dic3⋊C412yes—
359C2×Dic3(C2×D3)⋊C411yescharacteristic
360C2×Dic3(C2×D3)⋊C411yescharacteristic
361C4×D3—124no—
362C4×D3—124no—
363C4×D3Dic3⋊C412yes—
364C4×D3Dic3⋊C412yes—
365C4×D3C4⋊Dic312yes—
366C4×D3C4⋊Dic312yes—
367C4×D3(C2×D3)⋊C412yes—
368C4×D3(C2×D3)⋊C412yes—
369C4×D3#21712yes—
370C4×D3#21712yes—
371C3×C8—22no—
372C3×C8—22no—
373C3×C8—42no—
374C3×C8—62no—
375C3×C8—62no—
376C3⋊C8—22no—
377C3⋊C8—22no—
378C3⋊C8—62no—
379C3⋊C8—62no—
380C3⋊C8—122no—
381C2×C32—21no—
382C2×C32—21no—
383C2×C32C2×#9511yescharacteristic
384C2×C32C2×#10011yescharacteristic
385C2×C32C2×#10111yescharacteristic
386C3×D3—22no—
387C3×D3#34314yescomplemented
388C24—31no—
389C22×C4—31no—
390C22×C4—32no—
391C22×C4—32no—
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—32no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—92no—
400C22×C4—182no—
401C22×C4—182no—
402C22×C4—364no—
403C22×C4C2×D3211yescharacteristic
404M16—21no—
405M16—32no—
406M16—32no—
407M16—64no—
408M16—61no—
409M16—61no—
410M16—92no—
411M16—184no—
412M16—181no—
413M16D3×Dic312yescomplemented
414C2×C8—21no—
415C2×C8—64no—
416C2×C8—61no—
417C2×C8—61no—
418C2×C8—184no—
419C2×C8—181no—
420C4⋊C4—61no—
421C4⋊C4—61no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—32no—
434C22×C3—32no—
435C22×C3—32no—
436C22×C3—32no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—64no—
440C22×C3—64no—
441C22×C3—61no—
442C22×C3—61no—
443C22×C3C42×D311yescharacteristic
444C22×C3D3×C22⋊C411yescharacteristic
445C22×C3D3×C4⋊C411yescharacteristic
446C22×C3C2×C4×Dic311yescharacteristic
447C22×C3C2×Dic3⋊C411yescharacteristic
448C22×C3C2×(C2×D3)⋊C411yescharacteristic
449C2×D3—21no—
450C2×D3—21no—
451C2×D3—24no—
452C2×D3—24no—
453C2×D3#82312yes—
454C2×D3#82412yes—
455C2×D3C3⋊#9512yes—
456C2×D3C3⋊#9512yes—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—32no—
462C3×C4—32no—
463C3×C4—122no—
464C3×C4D3×C22⋊C411yescharacteristic
465C3×C4D3×C22⋊C411yescharacteristic
466C3×C4D3×C4⋊C411yescharacteristic
467C3×C4D3×C4⋊C411yescharacteristic
468C3×C4C2×Dic3⋊C411yescharacteristic
469C3×C4C2×C4⋊Dic311yescharacteristic
470C3×C4C2×(C2×D3)⋊C411yescharacteristic
471C3×C4C2×#21711yescharacteristic
472Dic3—42no—
473Dic3—122no—
474Dic3—122no—
475Dic3—242no—
476Dic3C3⋊#9512yes—
477Dic3C3⋊#9512yes—
478C32C2×#34311yescharacteristic, complemented, Sylow
479C23—31no—
480C23—32no—
481C23—32no—
482C23—31no—
483C23—62no—
484C23—62no—
485C23C4×D3211yescharacteristic
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—31no—
489C2×C4—31no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—62no—
499C2×C4—122no—
500C2×C4—182no—
501C2×C4—364no—
502C2×C4—364no—
503C2×C4—362no—
504C2×C4D3×Dic611yescharacteristic
505C2×C4C4×D3211yescharacteristic
506C2×C4D3×D1211yescharacteristic
507C2×C4C2×D3×Dic311yescharacteristic
508C2×C4D3×#6711yescharacteristic
509C2×C4D3×#6711yescharacteristic
510C8—22no—
511C8—62no—
512C8—62no—
513C8—182no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—34no—
522C2×C3—41no—
523C2×C3—41no—
524C2×C3—62no—
525C2×C3D3×#9511yescharacteristic
526C2×C3D3×#10011yescharacteristic
527C2×C3D3×#10111yescharacteristic
528C2×C3C2×#82311yescharacteristic
529C2×C3C2×#82411yescharacteristic
530C2×C3C2×C3⋊#9511yescharacteristic
531D3—22no—
532D3#455414yesdirect product factor
533C22—21no—
534C22—21no—
535C22—32no—
536C22—32no—
537C22—32no—
538C22—32no—
539C22—64no—
540C22—64no—
541C22—61no—
542C22—61no—
543C22C4×D3×Dic311yescharacteristic
544C22D3×Dic3⋊C411yescharacteristic
545C22D3×(C2×D3)⋊C411yescharacteristic
546C4—32no—
547C4—32no—
548C4—122no—
549C4—362no—
550C4D3×Dic3⋊C411yescharacteristic
551C4D3×C4⋊Dic311yescharacteristic
552C4D3×(C2×D3)⋊C411yescharacteristic
553C4D3×#21711yescharacteristic
554C3—21no—
555C3D3×#34311yescharacteristic, complemented
556C3C2×#455411yescharacteristic, complemented
557C2—21no—
558C2—21no—
559C2—34no—
560C2—62no—
561C2D3×#82311yescharacteristic
562C2D3×#82411yescharacteristic
563C2D3×C3⋊#9511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32C2×#343
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10589420C2semidirect
5. C3×#4554C2semidirect
6. #10589168C2semidirect
7. #10589167C2semidirect
19. C3×D3×M16C4semidirect
29. D3×#208C4semidirect
44. #4554D3direct (N × H)
63. C32×M16C2×C4semidirect
68. #3748C2×C4semidirect
74. C3×#208C2×C4semidirect
75. C3×#208C2×C4semidirect
121. D3×M16Dic3semidirect
215. C3×M16C4×D3semidirect
216. C3×M16C2×Dic3semidirect
246. #208C4×D3semidirect
247. #208C2×Dic3semidirect
387. C3×D3#343semidirect
413. M16D3×Dic3semidirect
478. C32C2×#343semidirect
532. D3#4554direct (N × H)
555. C3D3×#343semidirect
556. C3C2×#4554semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
C2×D3×C4⋊Dic32
C2×D3×#2082
#105894202
C3×#45542
#105891682
#105891672
C2×#45543
D3×#3433