Finite Group Databasebeta

← #13161949

Subgroups — #13161949

Order 1728.

810 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64147C211yesmaximal, characteristic, complemented
2C2×C3×#3753C211yesmaximal, characteristic, complemented
3#11723696C211yesmaximal, characteristic, complemented
4C2×#88808C211yesmaximal, characteristic, complemented
5C3×#63659C211yesmaximal, characteristic, complemented
6#11722080C211yesmaximal, characteristic, complemented
7#11722075C211yesmaximal, characteristic, complemented
8#10591498—31nomaximal
9#10591455—31nomaximal
10#10591449—31nomaximal
11C2×C33×D4C2211yescharacteristic
12C2×C3×#638—21no—
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×C4×C3⋊D3C2211yescharacteristic
15C2×#6295—21no—
16C3×#3757—21no—
17C3×#3753—22no—
18C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
22#88814—21no—
23#88808—22no—
24#64147D311yescharacteristic, complemented
25C2×#3753D311yescharacteristic, complemented
26C3×#938—31no—
27C3×#938—31no—
28C3×#938—61no—
29C2×C3×#213—31no—
30C2×C3×#213—31no—
31C2×C3×#213—61no—
32#63916—31no—
33#63909—31no—
34#63908—31no—
35C2×#3710—31no—
36C2×D3×C3⋊C8—31no—
37C2×D3×C3⋊C8—31no—
38#63659D311yescharacteristic, complemented
39C3×#832—31no—
40C3×#832—31no—
41C3×#832—61no—
42#63576—31no—
43#63575—31no—
44#63575—31no—
45#63564—31no—
46#63563—31no—
47#63562—31no—
48C23×C33—21no—
49C22×C3×C3⋊D3—21no—
50C22×C3×C3⋊D3D411yescharacteristic
51C33×D4—21no—
52C33×D4—21no—
53C2×C33×C4C2311yescharacteristic
54C3×#638—42no—
55C2×C3×C3⋊Dic3—21no—
56C2×C3×C3⋊Dic3—21no—
57C2×C3×C3⋊Dic3D411yescharacteristic
58C3×C4⋊(C3⋊D3)—21no—
59C3×C4⋊(C3⋊D3)—21no—
60C3×C4×C3⋊D3—21no—
61C3×C4×C3⋊D3—21no—
62#6295—42no—
63C3×C3⋊(C3⋊C8)—21no—
64C3×C3⋊(C3⋊C8)D412yescomplemented
65#5157—91no—
66#5038—91no—
67#4775—91no—
68C2×C32×D4—21no—
69C2×C32×D4—21no—
70C2×C32×D4—21no—
71C2×C32×D4—41no—
72C2×C32×D4C2×D311yescharacteristic
73C2×C32×D4C2×D311yescharacteristic
74C2×C32×D4C2×D311yescharacteristic
75C2×#638—21no—
76C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
77C2×C4×C3⋊D3C2×D311yescharacteristic
78C2×C3×#67—61no—
79C2×C3×#67—61no—
80C2×C3×#67—62no—
81C2×C3×D12—31no—
82C2×C3×D12—31no—
83C2×C3×D12—61no—
84C2×C3×C4×D3—31no—
85C2×C3×C4×D3—31no—
86C2×C3×C4×D3—61no—
87C2×#626—61no—
88C2×#626—61no—
89C2×#625—61no—
90#3757—21no—
91#3753—22no—
92C4⋊(C3⋊Dic3)C2×D311yescharacteristic
93C4⋊(C3⋊Dic3)C2×D311yescharacteristic
94C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
95C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
96C3×#217—61no—
97C3×#217—61no—
98C3×#217—62no—
99C3×#213—62no—
100C3×#213—62no—
101C3×#213—64no—
102C3×C4⋊Dic3—31no—
103C3×C4⋊Dic3—31no—
104C3×C4⋊Dic3—31no—
105C3×C4⋊Dic3—31no—
106C3×C4⋊Dic3—61no—
107C3×C4⋊Dic3—61no—
108C2×C3×C3⋊C8—31no—
109C2×C3×C3⋊C8—31no—
110C2×C3×C3⋊C8—31no—
111C2×C3×C3⋊C8—31no—
112C2×C3×C3⋊C8—61no—
113C2×C3×C3⋊C8—61no—
114#3722—61no—
115(C2×D3)⋊Dic3—61no—
116(C2×D3)⋊Dic3—61no—
117#3710—62no—
118D3×C3⋊C8—62no—
119D3×C3⋊C8—62no—
120C22×C33—41no—
121C22×C33—41no—
122C22×C33—41no—
123C22×C33C2×D411yescharacteristic
124C2×C3×C3⋊D3—21no—
125C2×C3×C3⋊D3—21no—
126C2×C3×C3⋊D3—41no—
127C2×C3×C3⋊D3—41no—
128C2×C3×C3⋊D3—41no—
129C2×C3×C3⋊D3D812yescomplemented
130C33×C4C2×D411yescharacteristic
131C33×C4#4111yescharacteristic
132C3×C3⋊Dic3—21no—
133C3×C3⋊Dic3—41no—
134C3×C3⋊Dic3—41no—
135C2×C3×D8—91no—
136C3×#121—91no—
137#938—31no—
138#938—31no—
139#938—61no—
140#938—91no—
141C2×#213—31no—
142C2×#213—31no—
143C2×#213—61no—
144#930—91no—
145C22×C3⋊C8—91no—
146C2×D3×C8—91no—
147C2×D3×C8—91no—
148#895—91no—
149C3×#102—91no—
150#832—31no—
151#832—31no—
152#832—61no—
153#832—91no—
154#821—91no—
155#818—91no—
156#809—91no—
157#807—91no—
158#807—91no—
159C23×C32—21no—
160C23×C32—22no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—41no—
164C23×C32—41no—
165C23×C32—42no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3#6711yescharacteristic
168C22×C3×D3—31no—
169C22×C3×D3—31no—
170C22×C3×D3—61no—
171C22×C3×D3—61no—
172C22×C3×D3—61no—
173C22×C3×D3—121no—
174C32×D4—21no—
175C32×D4—21no—
176C32×D4—22no—
177C32×D4—22no—
178C32×D4—21no—
179C32×D4—21no—
180C32×D4—21no—
181C32×D4—21no—
182C32×D4—41no—
183C32×D4—41no—
184C32×D4—41no—
185C32×D4—41no—
186C32×D4—42no—
187C32×D4—42no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—41no—
192C2×C32×C4C22×D311yescharacteristic
193C2×C32×C4C22×D311yescharacteristic
194C2×C32×C4C22×D311yescharacteristic
195#638—42no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3#6711yescharacteristic
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)—21no—
201C4×C3⋊D3—21no—
202C4×C3⋊D3—21no—
203C3×#67—122no—
204C3×#67—122no—
205C3×#67—124no—
206C2×C3×Dic3—31no—
207C2×C3×Dic3—31no—
208C2×C3×Dic3—61no—
209C2×C3×Dic3—62no—
210C2×C3×Dic3—61no—
211C2×C3×Dic3—61no—
212C2×C3×Dic3—61no—
213C2×C3×Dic3—61no—
214C2×C3×Dic3—121no—
215C3×D12—62no—
216C3×D12—61no—
217C3×D12—61no—
218C3×D12—61no—
219C3×D12—61no—
220C3×D12—121no—
221C3×C4×D3—61no—
222C3×C4×D3—61no—
223C3×C4×D3—61no—
224C3×C4×D3—61no—
225C3×C4×D3—121no—
226C3×C4×D3—121no—
227#626—122no—
228#626—122no—
229#625—122no—
230C3⋊(C3⋊C8)—21no—
231C3⋊(C3⋊C8)#6712yescomplemented
232C3×C3⋊C8—32no—
233C3×C3⋊C8—32no—
234C3×C3⋊C8—62no—
235C3×C3⋊C8—61no—
236C3×C3⋊C8—61no—
237C3×C3⋊C8—121no—
238#466—271noSylow
239C2×C33—81no—
240C2×C33#12111yescharacteristic
241C2×C33C2×D811yescharacteristic
242C2×C33#13511yescharacteristic
243C3×C3⋊D3—22no—
244C3×C3⋊D3—81no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—41no—
249C2×C3×D4—91no—
250C2×C3×D4—181no—
251C2×C3×D4D3211yescharacteristic
252C2×C3×D4D3211yescharacteristic
253C2×C3×D4D3211yescharacteristic
254C22×C3×C4—91no—
255C2×#67—61no—
256C2×#67—61no—
257C2×#67—62no—
258C2×#67—181no—
259C2×#67—181no—
260C2×D12—31no—
261C2×D12—31no—
262C2×D12—61no—
263C2×D12—181no—
264C2×C4×D3—31no—
265C2×C4×D3—31no—
266C2×C4×D3—61no—
267C3×D8—182no—
268C2×C3×C8—91no—
269C2×C3×C8—91no—
270C3×C4⋊C4—91no—
271C3×C4⋊C4—91no—
272C3×C22⋊C4—181no—
273#217—61no—
274#217—61no—
275#217—62no—
276#217—181no—
277#213—62no—
278#213—62no—
279#213—64no—
280(C2×D3)⋊C4—181no—
281(C2×D3)⋊C4—181no—
282C4⋊Dic3—31no—
283C4⋊Dic3—31no—
284C4⋊Dic3—31no—
285C4⋊Dic3—31no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—31no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8—61no—
294C2×C3⋊C8—182no—
295D3×C8—182no—
296D3×C8—182no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—41no—
301C22×C32—42no—
302C22×C32—42no—
303C22×C32—42no—
304C22×C32—44no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32—42no—
311C22×C32—42no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32—81no—
317C22×C32—81no—
318C22×C32—81no—
319C22×C32—81no—
320C22×C32—82no—
321C22×C32—82no—
322C22×C32D3×D411yescharacteristic
323C22×C32D3×D411yescharacteristic
324C22×C32C2×#6711yescharacteristic
325C2×C3⋊D3—21no—
326C2×C3⋊D3—21no—
327C2×C3⋊D3—41no—
328C2×C3⋊D3—41no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3#21312yescomplemented
331C2×C3×D3—32no—
332C2×C3×D3—32no—
333C2×C3×D3—62no—
334C2×C3×D3—61no—
335C2×C3×D3—61no—
336C2×C3×D3—61no—
337C2×C3×D3—61no—
338C2×C3×D3—121no—
339C2×C3×D3—121no—
340C2×C3×D3—122no—
341C2×C3×D3—121no—
342C2×C3×D3—121no—
343C2×C3×D3—121no—
344C2×C3×D3—121no—
345C2×C3×D3—121no—
346C2×C3×D3—121no—
347C2×C3×D3—241no—
348C2×C3×D3—241no—
349C32×C4—21no—
350C32×C4—21no—
351C32×C4—21no—
352C32×C4—21no—
353C32×C4—21no—
354C32×C4—21no—
355C32×C4—41no—
356C32×C4—41no—
357C32×C4#23511yescharacteristic
358C32×C4D3×D411yescharacteristic
359C32×C4D3×D411yescharacteristic
360C32×C4#23711yescharacteristic
361C32×C4#23711yescharacteristic
362C32×C4C2×#6711yescharacteristic
363C3⋊Dic3—21no—
364C3⋊Dic3—41no—
365C3⋊Dic3—41no—
366C3×Dic3—61no—
367C3×Dic3—61no—
368C3×Dic3—121no—
369C3×Dic3—122no—
370C3×Dic3—121no—
371C3×Dic3—121no—
372C3×Dic3—121no—
373C3×Dic3—121no—
374C3×Dic3—241no—
375C2×D8—91no—
376C22×C8—271no—
377#121—91no—
378#121—271no—
379#107—271no—
380#102—91no—
381#102—271no—
382C33#46611yescharacteristic, complemented, Sylow
383C23×C3—22no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—42no—
390C23×C3—91no—
391C23×C3—181no—
392C22×D3—31no—
393C22×D3—31no—
394C22×D3—61no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—121no—
398C3×D4—22no—
399C3×D4—22no—
400C3×D4—21no—
401C3×D4—21no—
402C3×D4—21no—
403C3×D4—21no—
404C3×D4—21no—
405C3×D4—21no—
406C3×D4—41no—
407C3×D4—41no—
408C3×D4—41no—
409C3×D4—41no—
410C3×D4—42no—
411C3×D4—42no—
412C3×D4—181no—
413C3×D4—181no—
414C3×D4—362no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—41no—
419C2×C3×C4—91no—
420C2×C3×C4—181no—
421C2×C3×C4—181no—
422C2×C3×C4—181no—
423C2×C3×C4—181no—
424C2×C3×C4C2×D3211yescharacteristic
425C2×C3×C4C2×D3211yescharacteristic
426C2×C3×C4C2×D3211yescharacteristic
427#67—122no—
428#67—122no—
429#67—124no—
430#67—362no—
431#67—362no—
432C2×Dic3—31no—
433C2×Dic3—31no—
434C2×Dic3—61no—
435C2×Dic3—62no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—121no—
441D12—62no—
442D12—61no—
443D12—61no—
444D12—61no—
445D12—61no—
446D12—121no—
447D12—362no—
448C4×D3—61no—
449C4×D3—61no—
450C4×D3—61no—
451C4×D3—61no—
452C4×D3—121no—
453C4×D3—121no—
454C3×C8—92no—
455C3×C8—181no—
456C3⋊C8—32no—
457C3⋊C8—32no—
458C3⋊C8—62no—
459C3⋊C8—61no—
460C3⋊C8—61no—
461C3⋊C8—121no—
462C2×C32—21no—
463C2×C32—21no—
464C2×C32—21no—
465C2×C32—21no—
466C2×C32—21no—
467C2×C32—21no—
468C2×C32—21no—
469C2×C32—21no—
470C2×C32—21no—
471C2×C32—41no—
472C2×C32—41no—
473C2×C32—41no—
474C2×C32—82no—
475C2×C32—82no—
476C2×C32—82no—
477C2×C32—84no—
478C2×C32—81no—
479C2×C32—81no—
480C2×C32—81no—
481C2×C32#88411yescharacteristic
482C2×C32D3×D811yescharacteristic
483C2×C32D3×D811yescharacteristic
484C2×C32#91211yescharacteristic
485C2×C32#91611yescharacteristic
486C2×C32C2×#21311yescharacteristic
487C2×C32#93811yescharacteristic
488C2×C32#93911yescharacteristic
489C2×C32#95011yescharacteristic
490C3⋊D3—22no—
491C3⋊D3—81no—
492C3×D3—62no—
493C3×D3—62no—
494C3×D3—122no—
495C3×D3—242no—
496C3×D3—241no—
497C3×D3—241no—
498C2×D4—91no—
499C2×D4—181no—
500C2×D4—541no—
501C2×D4#111311yescharacteristic
502C22×C4—91no—
503D8—182no—
504C2×C8—91no—
505C2×C8—91no—
506C2×C8—542no—
507C4⋊C4—91no—
508C4⋊C4—91no—
509C22⋊C4—181no—
510C22⋊C4—541no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—44no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—81no—
531C22×C3—81no—
532C22×C3—81no—
533C22×C3—81no—
534C22×C3—82no—
535C22×C3—82no—
536C22×C3—92no—
537C22×C3—181no—
538C22×C3—181no—
539C22×C3—361no—
540C22×C3—361no—
541C22×C3—361no—
542C22×C3D3×#6711yescharacteristic
543C22×C3D3×#6711yescharacteristic
544C22×C3#381111yescharacteristic
545C2×D3—32no—
546C2×D3—32no—
547C2×D3—62no—
548C2×D3—61no—
549C2×D3—61no—
550C2×D3—61no—
551C2×D3—61no—
552C2×D3—121no—
553C2×D3—121no—
554C2×D3—122no—
555C2×D3—121no—
556C2×D3—121no—
557C2×D3—121no—
558C2×D3—121no—
559C2×D3—121no—
560C2×D3—121no—
561C2×D3—241no—
562C2×D3—241no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—41no—
570C3×C4—41no—
571C3×C4—181no—
572C3×C4—361no—
573C3×C4—361no—
574C3×C4#380411yescharacteristic
575C3×C4#380411yescharacteristic
576C3×C4#380511yescharacteristic
577C3×C4D3×#6711yescharacteristic
578C3×C4D3×#6711yescharacteristic
579C3×C4#381111yescharacteristic
580Dic3—61no—
581Dic3—61no—
582Dic3—121no—
583Dic3—122no—
584Dic3—121no—
585Dic3—121no—
586Dic3—121no—
587Dic3—121no—
588Dic3—241no—
589C32—21no—
590C32—21no—
591C32—21no—
592C32—41no—
593C32#477511yescharacteristic, complemented
594C32#503811yescharacteristic, complemented
595C32#515711yescharacteristic, complemented
596C23—21no—
597C23—91no—
598C23—181no—
599D4—21no—
600D4—21no—
601D4—181no—
602D4—181no—
603D4—362no—
604D4—1082no—
605C2×C4—91no—
606C2×C4—181no—
607C2×C4—181no—
608C2×C4—181no—
609C2×C4—181no—
610C2×C4C2×#111311yescharacteristic
611C8—92no—
612C8—181no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—41no—
623C2×C3—41no—
624C2×C3—41no—
625C2×C3—82no—
626C2×C3—82no—
627C2×C3—82no—
628C2×C3—84no—
629C2×C3—81no—
630C2×C3—81no—
631C2×C3—81no—
632C2×C3—182no—
633C2×C3—721no—
634C2×C3D3×#21311yescharacteristic
635C2×C3D3×#21311yescharacteristic
636C2×C3#6392611yescharacteristic
637C2×C3#6393311yescharacteristic
638C2×C3#6393511yescharacteristic
639C2×C3#6393611yescharacteristic
640C2×C3#6395811yescharacteristic
641C2×C3#6397011yescharacteristic
642C2×C3#6397111yescharacteristic
643D3—62no—
644D3—62no—
645D3—122no—
646D3—242no—
647D3—241no—
648D3—241no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—92no—
653C22—181no—
654C22—181no—
655C22—361no—
656C22—361no—
657C22—361no—
658C22#8904911yescharacteristic
659C4—181no—
660C4—361no—
661C4—361no—
662C4#8904611yescharacteristic
663C4#8904911yescharacteristic
664C3—21no—
665C3—21no—
666C3—21no—
667C3—41no—
668C3#1059144911yescharacteristic, complemented
669C3#1059145511yescharacteristic, complemented
670C3#1059149811yescharacteristic, complemented
671C2—81no—
672C2—182no—
673C2—721no—
674C2#1172370211yescharacteristic
675C2#1172370711yescharacteristic
676C2#1172372511yescharacteristic
subgroupG/H
centerC22#89049
commutator, cosocleC2×C33×C4C23
FrattiniC2×C4C2×#1113
FittingC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×D4#1113
hypocenterC33#466
LCSG ▷ C2×C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64147C2semidirect
2. C2×C3×#3753C2semidirect
3. #11723696C2semidirect
4. C2×#88808C2semidirect
5. C3×#63659C2semidirect
6. #11722080C2semidirect
7. #11722075C2semidirect
24. #64147D3semidirect
25. C2×#3753D3semidirect
38. #63659D3semidirect
64. C3×C3⋊(C3⋊C8)D4semidirect
129. C2×C3×C3⋊D3D8semidirect
231. C3⋊(C3⋊C8)#67semidirect
330. C2×C3⋊D3#213semidirect
382. C33#466semidirect
593. C32#4775semidirect
594. C32#5038semidirect
595. C32#5157semidirect
668. C3#10591449semidirect
669. C3#10591455semidirect
670. C3#10591498semidirect

Maximal subgroups

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

subgroupindex
C3×#641472
C2×C3×#37532
#117236962
C2×#888082
C3×#636592
#117220802
#117220752
#105914983
#105914553
#105914493