Finite Group Databasebeta

← #13155973

Subgroups — #13155973

Order 1728.

780 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88810C211yesmaximal, characteristic, complemented
2Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C3×#63911C211yesmaximal, characteristic, complemented
4C2×C3×#3714C211yesmaximal, characteristic, complemented
5#11722034C211yesmaximal, characteristic, complemented
6#11722032C211yesmaximal, characteristic, complemented
7C3×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10591428—31nomaximal
9#10590753—31nomaximal
10#10590355—31nomaximal
11C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×D12C2211yescharacteristic
14C2×Dic3×C3⋊D3—21no—
15C2×C3×#626—21no—
16C2×C3×#626—21no—
17C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
18C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
19C32×C4×Dic3C2211yescharacteristic
20C2×C32×C3⋊C8C2211yescharacteristic
21#88810—22no—
22#88803—21no—
23C3×#3714—22no—
24C4×C4⋊(C3⋊D3)—31no—
25C3×#940—31no—
26C2×C3×#213—31no—
27C2×C3×D24—31no—
28C3×#874—31no—
29#63911D311yescharacteristic, complemented
30Dic3×D12—31no—
31Dic3×D12—31no—
32Dic3×D12—61no—
33C2×#3714—31no—
34C2×#3714—31no—
35C2×#3714D311yescharacteristic, complemented
36C2×#3713—31no—
37#63659—31no—
38#63648—31no—
39C3×Dic3⋊C8—31no—
40C3×C4⋊(C3⋊C8)—31no—
41Dic3⋊(C3⋊C8)D311yescharacteristic, complemented
42#63563—31no—
43#63563—31no—
44#63563—31no—
45#63563—31no—
46#63563—61no—
47#63563—61no—
48C22×C3×C3⋊D3—21no—
49C22×C3×C3⋊D3—21no—
50C22×C32×D3—21no—
51C2×C33×C4C2311yescharacteristic
52C2×C3⋊(C3⋊Dic3)—21no—
53C3×C4⋊(C3⋊D3)—21no—
54C3×C4⋊(C3⋊D3)—21no—
55C3×C4⋊(C3⋊D3)—21no—
56C3×C4⋊(C3⋊D3)D412yescomplemented
57C2×C32×Dic3D411yescharacteristic
58C2×C32×Dic3D411yescharacteristic
59C32×D12—21no—
60C32×D12—21no—
61Dic3×C3⋊D3—42no—
62C3×#626—42no—
63C3×#626—42no—
64C3×C3⋊(C3⋊C8)—21no—
65C32×C3⋊C8—21no—
66#5150—91no—
67#5072—91no—
68#4843—91no—
69C2×C32×D4—31no—
70C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
71C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
72C2×C4×C3⋊D3—61no—
73C2×C3×#67—61no—
74C2×C3×#67—61no—
75C2×C3×D12—21no—
76C2×C3×D12—31no—
77C2×C3×D12—31no—
78C2×C3×D12—31no—
79C2×C3×D12—31no—
80C2×C3×D12—61no—
81C2×C3×D12—61no—
82C2×C3×D12—61no—
83C2×C3×D12—61no—
84C2×C3×D12C2×D311yescharacteristic
85C2×C3×D12C2×D311yescharacteristic
86C2×#626—21no—
87C2×#626—21no—
88C2×D3×Dic3—62no—
89C2×D3×Dic3—61no—
90C2×D3×Dic3—61no—
91C2×C32×C8—31no—
92C32×C42—31no—
93#3752—61no—
94C4⋊(C3⋊Dic3)—31no—
95C4⋊(C3⋊Dic3)—31no—
96C4⋊(C3⋊Dic3)—31no—
97C4⋊(C3⋊Dic3)—61no—
98C4⋊(C3⋊Dic3)—61no—
99C4⋊(C3⋊Dic3)—61no—
100C4⋊(C3⋊Dic3)—121no—
101C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
102C3×#213—62no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3C2×D311yescharacteristic
105C3×C4×Dic3C2×D311yescharacteristic
106C2×C3×C3⋊C8—21no—
107C2×C3×C3⋊C8—31no—
108C2×C3×C3⋊C8—31no—
109C2×C3×C3⋊C8—61no—
110C2×C3×C3⋊C8C2×D311yescharacteristic
111C2×C3×C3⋊C8C2×D311yescharacteristic
112C3×D24—62no—
113(C2×D3)⋊Dic3—62no—
114(C2×D3)⋊Dic3—61no—
115(C2×D3)⋊Dic3—61no—
116#3714—22no—
117#3714—62no—
118#3714—62no—
119#3713—62no—
120C22×C33C2×D411yescharacteristic
121C2×C3×C3⋊D3—22no—
122C2×C3×C3⋊D3—41no—
123C2×C3×C3⋊D3—41no—
124C2×C3×C3⋊D3—41no—
125C2×C3×C3⋊D3—41no—
126C2×C3×C3⋊D3—41no—
127C2×C32×D3—41no—
128C2×C32×D3—41no—
129C2×C32×D3—41no—
130C33×C4C2×D411yescharacteristic
131C33×C4#4111yescharacteristic
132C3⋊(C3⋊Dic3)—41no—
133C32×Dic3—21no—
134C32×Dic3D812yescomplemented
135C2×C3×D8—91no—
136C3×#127—91no—
137#940—31no—
138D4×Dic3—91no—
139C2×#213—31no—
140C2×#213—91no—
141C2×#213—91no—
142C2×D24—31no—
143C2×D24—91no—
144#874—31no—
145C4×D12—91no—
146C4×D12—91no—
147C4×D12—181no—
148C3×C4⋊C8—91no—
149#832—91no—
150#832—91no—
151#832—91no—
152#832—181no—
153#821—91no—
154#821—91no—
155#821—91no—
156#821—181no—
157Dic3⋊C8—31no—
158C4⋊(C3⋊C8)—31no—
159C23×C32—61no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C22×C3×D3—41no—
165C22×C3×D3—62no—
166C22×C3×D3—61no—
167C22×C3×D3—61no—
168C22×C3×D3—61no—
169C22×C3×D3—61no—
170C22×C3×D3—121no—
171C32×D4—61no—
172C32×D4—61no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—31no—
177C2×C32×C4—31no—
178C2×C32×C4—41no—
179C2×C32×C4C22×D311yescharacteristic
180C2×C32×C4C22×D311yescharacteristic
181C2×C32×C4C22×D311yescharacteristic
182C2×C3⋊Dic3—61no—
183C2×C3⋊Dic3—62no—
184C2×C3⋊Dic3—61no—
185C2×C3⋊Dic3—61no—
186C2×C3⋊Dic3—121no—
187C2×C3⋊Dic3—121no—
188C2×C3⋊Dic3—122no—
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)#6712yescomplemented
193C4×C3⋊D3—122no—
194C3×#67—122no—
195C3×#67—122no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3D1211yescharacteristic
199C2×C3×Dic3D1211yescharacteristic
200C2×C3×Dic3#6711yescharacteristic
201C2×C3×Dic3#6711yescharacteristic
202C3×D12—22no—
203C3×D12—21no—
204C3×D12—21no—
205C3×D12—21no—
206C3×D12—21no—
207C3×D12—32no—
208C3×D12—32no—
209C3×D12—41no—
210C3×D12—62no—
211C3×D12—62no—
212C3×D12—62no—
213C3×D12—61no—
214C3×D12—61no—
215C3×D12—61no—
216C3×D12—61no—
217C3×D12—61no—
218C3×D12—61no—
219C3×D12—121no—
220C3×D12—122no—
221C3×D12—122no—
222#626—42no—
223#626—42no—
224D3×Dic3—124no—
225D3×Dic3—122no—
226D3×Dic3—122no—
227C32×C8—61no—
228C3⋊(C3⋊C8)—21no—
229C3×C3⋊C8—21no—
230C3×C3⋊C8—21no—
231C3×C3⋊C8—41no—
232C3×C3⋊C8—61no—
233C3×C3⋊C8—61no—
234C3×C3⋊C8—121no—
235#459—271noSylow
236C2×C33#12111yescharacteristic
237C2×C33C2×D811yescharacteristic
238C2×C33AGL(1,ℤ/8)11yescharacteristic
239C3×C3⋊D3—42no—
240C3×C3⋊D3—81no—
241C32×D3—81no—
242C2×C3×D4—31no—
243C2×C3×D4—31no—
244C2×C3×D4—61no—
245C2×C3×D4—91no—
246C2×C3×D4—91no—
247C2×C3×D4—181no—
248C2×C3×D4—181no—
249C2×#67—61no—
250C2×#67—61no—
251C22×Dic3—181no—
252C2×D12—31no—
253C2×D12—31no—
254C2×D12—31no—
255C2×D12—31no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—61no—
259C2×D12—61no—
260C2×D12D3211yescharacteristic
261C2×C4×D3—181no—
262C2×C4×D3—181no—
263C2×C4×D3—182no—
264C3×D8—182no—
265C2×C3×C8—31no—
266C2×C3×C8—31no—
267C2×C3×C8—61no—
268C2×C3×C8—91no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—61no—
272#217—181no—
273#213—62no—
274#213—182no—
275#213—182no—
276(C2×D3)⋊C4—181no—
277(C2×D3)⋊C4—181no—
278(C2×D3)⋊C4—182no—
279C4⋊Dic3—91no—
280C4⋊Dic3—91no—
281C4⋊Dic3—91no—
282C4⋊Dic3—181no—
283C4⋊Dic3—181no—
284C4⋊Dic3—181no—
285C4⋊Dic3—361no—
286C4×Dic3D3211yescharacteristic
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—61no—
290C2×C3⋊C8D3211yescharacteristic
291D24—62no—
292D24—182no—
293C22×C32—21no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32—41no—
297C22×C32—121no—
298C22×C32—121no—
299C22×C32—121no—
300C22×C32C2×D1211yescharacteristic
301C22×C32D3×D411yescharacteristic
302C22×C32C2×#6711yescharacteristic
303C2×C3⋊D3—22no—
304C2×C3⋊D3—41no—
305C2×C3⋊D3—41no—
306C2×C3⋊D3—41no—
307C2×C3⋊D3—41no—
308C2×C3⋊D3—41no—
309C2×C3×D3—42no—
310C2×C3×D3—41no—
311C2×C3×D3—41no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—64no—
317C2×C3×D3—62no—
318C2×C3×D3—62no—
319C2×C3×D3—81no—
320C2×C3×D3—81no—
321C2×C3×D3—122no—
322C2×C3×D3—122no—
323C2×C3×D3—121no—
324C2×C3×D3—121no—
325C2×C3×D3—121no—
326C2×C3×D3—121no—
327C2×C3×D3—122no—
328C2×C3×D3—121no—
329C2×C3×D3—121no—
330C2×C3×D3—121no—
331C2×C3×D3—121no—
332C2×C3×D3—121no—
333C2×C3×D3—121no—
334C2×C3×D3—241no—
335C2×C3×D3—241no—
336C32×C4—21no—
337C32×C4—21no—
338C32×C4—21no—
339C32×C4—21no—
340C32×C4—21no—
341C32×C4—21no—
342C32×C4—32no—
343C32×C4—41no—
344C32×C4—41no—
345C32×C4—61no—
346C32×C4D3×D411yescharacteristic
347C32×C4D3×D411yescharacteristic
348C32×C4#23711yescharacteristic
349C32×C4#23711yescharacteristic
350C32×C4#23911yescharacteristic
351C32×C4C2×#6711yescharacteristic
352C3⋊Dic3—121no—
353C3⋊Dic3—122no—
354C3⋊Dic3—121no—
355C3⋊Dic3—121no—
356C3⋊Dic3—241no—
357C3⋊Dic3—241no—
358C3⋊Dic3—242no—
359C3×Dic3—21no—
360C3×Dic3—21no—
361C3×Dic3—22no—
362C3×Dic3—41no—
363C3×Dic3D2412yescomplemented
364C3×Dic3#21312yescomplemented
365C2×D8—91no—
366C2×D8—271no—
367#127—91no—
368C4×D4—271no—
369C4⋊C8—91no—
370#102—271no—
371#102—271no—
372C33#45911yescharacteristic, complemented, Sylow
373C23×C3—61no—
374C23×C3—61no—
375C23×C3—121no—
376C23×C3—181no—
377C23×C3—181no—
378C22×D3—21no—
379C22×D3—62no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—121no—
385C3×D4—62no—
386C3×D4—61no—
387C3×D4—61no—
388C3×D4—61no—
389C3×D4—61no—
390C3×D4—92no—
391C3×D4—121no—
392C3×D4—181no—
393C3×D4—181no—
394C3×D4—181no—
395C3×D4—362no—
396C3×D4—362no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—31no—
401C2×C3×C4—31no—
402C2×C3×C4—31no—
403C2×C3×C4—31no—
404C2×C3×C4—41no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4C2×D3211yescharacteristic
408C2×C3×C4C2×D3211yescharacteristic
409C2×C3×C4C2×D3211yescharacteristic
410#67—122no—
411#67—122no—
412C2×Dic3—182no—
413C2×Dic3—181no—
414C2×Dic3—181no—
415C2×Dic3—181no—
416C2×Dic3—361no—
417C2×Dic3—361no—
418C2×Dic3—362no—
419C2×Dic3—362no—
420C2×Dic3#62611yescharacteristic
421C2×Dic3#62611yescharacteristic
422D12—21no—
423D12—21no—
424D12—32no—
425D12—32no—
426D12—62no—
427D12—62no—
428D12—62no—
429D12—61no—
430D12—61no—
431D12—61no—
432D12—61no—
433D12—61no—
434D12—61no—
435D12—121no—
436D12—122no—
437D12—122no—
438C4×D3—362no—
439C4×D3—362no—
440C4×D3—364no—
441C3×C8—61no—
442C3×C8—61no—
443C3×C8—121no—
444C3×C8—181no—
445C3⋊C8—21no—
446C3⋊C8—61no—
447C3⋊C8—61no—
448C3⋊C8—121no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—21no—
452C2×C32—21no—
453C2×C32—21no—
454C2×C32—21no—
455C2×C32—21no—
456C2×C32—21no—
457C2×C32—21no—
458C2×C32—41no—
459C2×C32—41no—
460C2×C32—41no—
461C2×C32—241no—
462C2×C32#89511yescharacteristic
463C2×C32C2×D2411yescharacteristic
464C2×C32#90811yescharacteristic
465C2×C32D3×D811yescharacteristic
466C2×C32#91111yescharacteristic
467C2×C32C2×#21311yescharacteristic
468C2×C32#93211yescharacteristic
469C2×C32#93811yescharacteristic
470C2×C32#93911yescharacteristic
471C3⋊D3—42no—
472C3⋊D3—81no—
473C3×D3—82no—
474C3×D3—81no—
475C3×D3—81no—
476C3×D3—124no—
477C3×D3—122no—
478C3×D3—122no—
479C3×D3—242no—
480C3×D3—241no—
481C3×D3—241no—
482C2×D4—31no—
483C2×D4—91no—
484C2×D4—91no—
485C2×D4—181no—
486C2×D4—181no—
487C22×C4—541no—
488D8—182no—
489D8—542no—
490C2×C8—31no—
491C2×C8—91no—
492C4⋊C4—271no—
493C22⋊C4—541no—
494C42—31no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—41no—
499C22×C3—122no—
500C22×C3—121no—
501C22×C3—121no—
502C22×C3—121no—
503C22×C3—121no—
504C22×C3—121no—
505C22×C3—121no—
506C22×C3—182no—
507C22×C3—241no—
508C22×C3—241no—
509C22×C3—361no—
510C22×C3—361no—
511C22×C3—361no—
512C22×C3—361no—
513C22×C3—361no—
514C22×C3D3×D1211yescharacteristic
515C22×C3C2×#62611yescharacteristic
516C22×C3D3×#6711yescharacteristic
517C2×D3—41no—
518C2×D3—41no—
519C2×D3—41no—
520C2×D3—64no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—122no—
524C2×D3—122no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3—122no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—121no—
534C2×D3—121no—
535C2×D3—121no—
536C2×D3—241no—
537C2×D3—241no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—32no—
545C3×C4—32no—
546C3×C4—41no—
547C3×C4—41no—
548C3×C4—62no—
549C3×C4—61no—
550C3×C4—61no—
551C3×C4—121no—
552C3×C4#379611yescharacteristic
553C3×C4#379611yescharacteristic
554C3×C4#380211yescharacteristic
555C3×C4#380511yescharacteristic
556C3×C4D3×#6711yescharacteristic
557C3×C4D3×#6711yescharacteristic
558Dic3—21no—
559Dic3—362no—
560Dic3—361no—
561Dic3—361no—
562Dic3—361no—
563Dic3—721no—
564Dic3—721no—
565Dic3—722no—
566Dic3#371412yescomplemented
567C32—21no—
568C32—21no—
569C32—21no—
570C32—41no—
571C32#484311yescharacteristic, complemented
572C32#507211yescharacteristic, complemented
573C32#515011yescharacteristic, complemented
574C23—61no—
575C23—181no—
576C23—181no—
577D4—61no—
578D4—61no—
579D4—92no—
580D4—181no—
581D4—181no—
582D4—181no—
583D4—362no—
584D4—362no—
585C2×C4—31no—
586C2×C4—31no—
587C2×C4—541no—
588C2×C4—1082no—
589C2×C4D3311yescharacteristic
590C8—61no—
591C8—181no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—41no—
602C2×C3—41no—
603C2×C3—41no—
604C2×C3—242no—
605C2×C3—241no—
606C2×C3—241no—
607C2×C3—362no—
608C2×C3—721no—
609C2×C3D3×D2411yescharacteristic
610C2×C3#6379511yescharacteristic
611C2×C3C2×#371411yescharacteristic
612C2×C3#6383011yescharacteristic
613C2×C3#6388611yescharacteristic
614C2×C3#6391611yescharacteristic
615C2×C3D3×#21311yescharacteristic
616C2×C3#6393211yescharacteristic
617C2×C3#6397011yescharacteristic
618D3—81no—
619D3—124no—
620D3—122no—
621D3—122no—
622D3—242no—
623D3—241no—
624D3—241no—
625C22—121no—
626C22—121no—
627C22—121no—
628C22—182no—
629C22—361no—
630C22—361no—
631C22—361no—
632C22—361no—
633C22—361no—
634C22D3×#62611yescharacteristic
635C4—32no—
636C4—61no—
637C4—1081no—
638C4#8895311yescharacteristic
639C4#8896411yescharacteristic
640C3—21no—
641C3—21no—
642C3—21no—
643C3—41no—
644C3#1059035511yescharacteristic, complemented
645C3#1059075311yescharacteristic, complemented
646C3#1059142811yescharacteristic, complemented
647C2—241no—
648C2—362no—
649C2—721no—
650C2D3×#371411yescharacteristic
651C2#1172286911yescharacteristic
652C2#1172296211yescharacteristic
subgroupG/H
centerC22D3×#626
commutator, Fitting, cosocleC2×C33×C4C23
Frattini, hypercenterC2×C4D33
socleC22×C33C2×D4
hypocenterC33#459
LCSG ▷ C2×C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88810C2semidirect
2. Dic3×C4⋊(C3⋊D3)C2semidirect
3. C3×#63911C2semidirect
4. C2×C3×#3714C2semidirect
5. #11722034C2semidirect
6. #11722032C2semidirect
7. C3×Dic3⋊(C3⋊C8)C2semidirect
29. #63911D3semidirect
35. C2×#3714D3semidirect
41. Dic3⋊(C3⋊C8)D3semidirect
56. C3×C4⋊(C3⋊D3)D4semidirect
134. C32×Dic3D8semidirect
192. C4⋊(C3⋊D3)#67semidirect
363. C3×Dic3D24semidirect
364. C3×Dic3#213semidirect
372. C33#459semidirect
566. Dic3#3714semidirect
571. C32#4843semidirect
572. C32#5072semidirect
573. C32#5150semidirect
644. C3#10590355semidirect
645. C3#10590753semidirect
646. C3#10591428semidirect

Maximal subgroups

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

subgroupindex
C2×#888102
Dic3×C4⋊(C3⋊D3)2
C3×#639112
C2×C3×#37142
#117220342
#117220322
C3×Dic3⋊(C3⋊C8)2
#105914283
#105907533
#105903553