Finite Group Databasebeta

← #13155967

Subgroups — #13155967

Order 1728.

746 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88810C211yesmaximal, characteristic, complemented
2C2×#88789C211yesmaximal, characteristic, complemented
3C3×#63911C211yesmaximal, characteristic, complemented
4C3×#63894C211yesmaximal, characteristic, complemented
5Dic3⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#11722033C211yesmaximal, characteristic, complemented
7C3×#63562C211yesmaximal, characteristic, complemented
8#10591429—31nomaximal
9#10590547—31nomaximal
10#10590347—31nomaximal
11C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×D12C2211yescharacteristic
14C2×C3×#626—21no—
15C2×C3×#626—21no—
16C2×C3×#624—21no—
17C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
19C32×C4⋊Dic3C2211yescharacteristic
20C32×C4×Dic3C2211yescharacteristic
21#88810—22no—
22#88789—22no—
23C3×#3722—21no—
24C2×#3753—31no—
25C3×#940—31no—
26C3×#893—31no—
27C3×#874—31no—
28C3×C4×D12—31no—
29#63911D311yescharacteristic, complemented
30#63894D311yescharacteristic, complemented
31C2×#3714—31no—
32C2×#3714—31no—
33C2×#3713—31no—
34C2×#3713—31no—
35C2×#3713—31no—
36C2×#3713—61no—
37#63636—31no—
38C4⋊(C3⋊(C3⋊C8))—31no—
39C3×#832—31no—
40C3×#809—31no—
41Dic3⋊(C3⋊C8)—31no—
42Dic3⋊(C3⋊C8)—31no—
43Dic3⋊(C3⋊C8)—61no—
44#63562—31no—
45#63562—31no—
46#63562—61no—
47#63562D311yescharacteristic, complemented
48C22×C3×C3⋊D3—21no—
49C22×C3×C3⋊D3—21no—
50C22×C32×D3—21no—
51C2×C33×C4C2311yescharacteristic
52C3×C4⋊(C3⋊D3)—21no—
53C3×C4⋊(C3⋊D3)—21no—
54C3×C4⋊(C3⋊D3)—21no—
55C3×C4⋊(C3⋊D3)D412yescomplemented
56C2×C32×Dic3—21no—
57C2×C32×Dic3D411yescharacteristic
58C2×C32×Dic3D411yescharacteristic
59C32×D12—21no—
60C32×D12—21no—
61C3×#626—42no—
62C3×#626—42no—
63C3×#624—42no—
64C3⋊(C3⋊(C3⋊C8))—21no—
65C3×C3⋊(C3⋊C8)—21no—
66#5072—91no—
67#5015—91no—
68#4786—91no—
69C2×C32×D4—31no—
70C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
71C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
72C2×C3×#67—61no—
73C2×C3×#67—61no—
74C2×C3×D12—21no—
75C2×C3×D12—31no—
76C2×C3×D12—31no—
77C2×C3×D12—31no—
78C2×C3×D12—31no—
79C2×C3×D12—61no—
80C2×C3×D12—61no—
81C2×C3×D12—61no—
82C2×C3×D12—61no—
83C2×C3×D12C2×D311yescharacteristic
84C2×C3×D12C2×D311yescharacteristic
85C2×C3×C4×D3—61no—
86C2×C3×C4×D3—61no—
87C2×#626—21no—
88C2×#626—21no—
89C2×#624—21no—
90C32×C4⋊C4—31no—
91C32×C42—31no—
92#3753—62no—
93C2×C3⋊(C3⋊C8)—31no—
94C2×C3⋊(C3⋊C8)—31no—
95C2×C3⋊(C3⋊C8)—31no—
96C2×C3⋊(C3⋊C8)—61no—
97C2×C3⋊(C3⋊C8)—61no—
98C2×C3⋊(C3⋊C8)—61no—
99C2×C3⋊(C3⋊C8)—121no—
100C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
101C3×(C2×D3)⋊C4—61no—
102C3×(C2×D3)⋊C4—61no—
103C3×C4⋊Dic3—21no—
104C3×C4⋊Dic3C2×D311yescharacteristic
105C3×C4⋊Dic3C2×D311yescharacteristic
106C3×C4×Dic3—21no—
107C3×C4×Dic3C2×D311yescharacteristic
108C3×C4×Dic3C2×D311yescharacteristic
109C2×C3×C3⋊C8—31no—
110C2×C3×C3⋊C8—31no—
111C2×C3×C3⋊C8—61no—
112#3722—21no—
113#3714—62no—
114#3714—62no—
115#3713—62no—
116#3713—62no—
117#3713—62no—
118#3713—64no—
119C22×C33C2×D411yescharacteristic
120C2×C3×C3⋊D3—22no—
121C2×C3×C3⋊D3—41no—
122C2×C3×C3⋊D3—41no—
123C2×C3×C3⋊D3—41no—
124C2×C3×C3⋊D3—41no—
125C2×C3×C3⋊D3—41no—
126C2×C32×D3—41no—
127C2×C32×D3—41no—
128C2×C32×D3—41no—
129C33×C4C2×D411yescharacteristic
130C33×C4#4111yescharacteristic
131C32×Dic3—21no—
132C32×Dic3—41no—
133C32×Dic3D812yescomplemented
134C3×#127—91no—
135C3×C4×D4—91no—
136#940—31no—
137C2×#213—91no—
138C2×#213—91no—
139C2×#213—91no—
140C2×#213—91no—
141C2×#213—91no—
142C2×#213—181no—
143C2×D24—91no—
144#893—31no—
145#874—31no—
146C4×D12—31no—
147C3×#102—91no—
148#832—31no—
149#832—91no—
150Dic3⋊C8—91no—
151#809—31no—
152#809—91no—
153#809—91no—
154#809—181no—
155C4⋊(C3⋊C8)—91no—
156C4⋊(C3⋊C8)—91no—
157C4⋊(C3⋊C8)—181no—
158C23×C32—61no—
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3—21no—
163C22×C3×D3—41no—
164C22×C3×D3—61no—
165C22×C3×D3—61no—
166C22×C3×D3—61no—
167C22×C3×D3—61no—
168C22×C3×D3—121no—
169C22×C3×D3—121no—
170C32×D4—61no—
171C32×D4—61no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—31no—
176C2×C32×C4—31no—
177C2×C32×C4—41no—
178C2×C32×C4—61no—
179C2×C32×C4C22×D311yescharacteristic
180C2×C32×C4C22×D311yescharacteristic
181C2×C32×C4C22×D311yescharacteristic
182C4⋊(C3⋊D3)—21no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)—21no—
185C4⋊(C3⋊D3)D1212yescomplemented
186C3×#67—122no—
187C3×#67—122no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3#6711yescharacteristic
194C2×C3×Dic3#6711yescharacteristic
195C2×C3×Dic3#6711yescharacteristic
196C2×C3×Dic3#6711yescharacteristic
197C3×D12—22no—
198C3×D12—21no—
199C3×D12—21no—
200C3×D12—21no—
201C3×D12—21no—
202C3×D12—32no—
203C3×D12—32no—
204C3×D12—41no—
205C3×D12—62no—
206C3×D12—62no—
207C3×D12—61no—
208C3×D12—61no—
209C3×D12—61no—
210C3×D12—61no—
211C3×D12—61no—
212C3×D12—61no—
213C3×D12—121no—
214C3×D12—121no—
215C3×D12—122no—
216C3×D12—122no—
217C3×C4×D3—122no—
218C3×C4×D3—122no—
219#626—42no—
220#626—42no—
221#624—42no—
222C3⋊(C3⋊C8)—21no—
223C3⋊(C3⋊C8)—61no—
224C3⋊(C3⋊C8)—62no—
225C3⋊(C3⋊C8)—61no—
226C3⋊(C3⋊C8)—61no—
227C3⋊(C3⋊C8)—121no—
228C3⋊(C3⋊C8)—121no—
229C3⋊(C3⋊C8)—122no—
230C3×C3⋊C8—61no—
231C3×C3⋊C8—61no—
232C3×C3⋊C8—121no—
233#459—271noSylow
234C2×C33#12111yescharacteristic
235C2×C33C2×D811yescharacteristic
236C2×C33AGL(1,ℤ/8)11yescharacteristic
237C3×C3⋊D3—42no—
238C3×C3⋊D3—81no—
239C32×D3—81no—
240C2×C3×D4—31no—
241C2×C3×D4—31no—
242C2×C3×D4—61no—
243C2×C3×D4—91no—
244C2×C3×D4—91no—
245C2×C3×D4—181no—
246C2×C3×D4—181no—
247C22×C3×C4—181no—
248C2×#67—61no—
249C2×#67—61no—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—31no—
253C2×D12—31no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12D3211yescharacteristic
259C2×C4×D3—61no—
260C2×C4×D3—61no—
261C2×C3×C8—91no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—61no—
265C3×C22⋊C4—181no—
266C3×C42—31no—
267C3×C42—31no—
268C3×C42—61no—
269#213—182no—
270#213—182no—
271#213—182no—
272#213—182no—
273#213—182no—
274#213—184no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277C4⋊Dic3D3211yescharacteristic
278C4×Dic3D3211yescharacteristic
279C2×C3⋊C8—31no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—61no—
282C2×C3⋊C8—91no—
283C2×C3⋊C8—91no—
284C2×C3⋊C8—91no—
285C2×C3⋊C8—181no—
286C2×C3⋊C8—181no—
287C2×C3⋊C8—181no—
288C2×C3⋊C8—361no—
289D24—182no—
290C22×C32—21no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—41no—
294C22×C32—121no—
295C22×C32—121no—
296C22×C32—121no—
297C22×C32D3×D411yescharacteristic
298C22×C32C2×#6711yescharacteristic
299C22×C32C2×#6711yescharacteristic
300C2×C3⋊D3—22no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3⋊D3—41no—
304C2×C3⋊D3—41no—
305C2×C3⋊D3—41no—
306C2×C3×D3—42no—
307C2×C3×D3—41no—
308C2×C3×D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3—41no—
311C2×C3×D3—41no—
312C2×C3×D3—41no—
313C2×C3×D3—62no—
314C2×C3×D3—62no—
315C2×C3×D3—81no—
316C2×C3×D3—81no—
317C2×C3×D3—122no—
318C2×C3×D3—121no—
319C2×C3×D3—121no—
320C2×C3×D3—121no—
321C2×C3×D3—121no—
322C2×C3×D3—122no—
323C2×C3×D3—121no—
324C2×C3×D3—121no—
325C2×C3×D3—121no—
326C2×C3×D3—121no—
327C2×C3×D3—121no—
328C2×C3×D3—121no—
329C2×C3×D3—241no—
330C2×C3×D3—241no—
331C2×C3×D3—241no—
332C2×C3×D3—241no—
333C32×C4—21no—
334C32×C4—21no—
335C32×C4—21no—
336C32×C4—21no—
337C32×C4—21no—
338C32×C4—21no—
339C32×C4—32no—
340C32×C4—41no—
341C32×C4—41no—
342C32×C4—61no—
343C32×C4—121no—
344C32×C4C2×D1211yescharacteristic
345C32×C4#23511yescharacteristic
346C32×C4#23511yescharacteristic
347C32×C4D3×D411yescharacteristic
348C32×C4D3×D411yescharacteristic
349C32×C4#23711yescharacteristic
350C3×Dic3—21no—
351C3×Dic3—21no—
352C3×Dic3—22no—
353C3×Dic3—41no—
354C3×Dic3—41no—
355C3×Dic3—41no—
356C3×Dic3—81no—
357C3×Dic3#21312yescomplemented
358C3×Dic3#21312yescomplemented
359C2×D8—271no—
360C2×D8—271no—
361#127—91no—
362C4×D4—91no—
363C4⋊C8—271no—
364#102—91no—
365#102—271no—
366C33#45911yescharacteristic, complemented, Sylow
367C23×C3—61no—
368C23×C3—61no—
369C23×C3—121no—
370C23×C3—181no—
371C23×C3—181no—
372C22×D3—21no—
373C22×D3—61no—
374C22×D3—61no—
375C22×D3—61no—
376C22×D3—61no—
377C22×D3—121no—
378C22×D3—121no—
379C3×D4—62no—
380C3×D4—61no—
381C3×D4—61no—
382C3×D4—61no—
383C3×D4—61no—
384C3×D4—92no—
385C3×D4—121no—
386C3×D4—181no—
387C3×D4—181no—
388C3×D4—181no—
389C3×D4—362no—
390C3×D4—362no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—41no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—121no—
404C2×C3×C4—362no—
405C2×C3×C4C2×D3211yescharacteristic
406C2×C3×C4C2×D3211yescharacteristic
407C2×C3×C4C2×D3211yescharacteristic
408#67—122no—
409#67—122no—
410C2×Dic3—21no—
411C2×Dic3#62511yescharacteristic
412C2×Dic3#62511yescharacteristic
413D12—21no—
414D12—21no—
415D12—32no—
416D12—32no—
417D12—62no—
418D12—62no—
419D12—61no—
420D12—61no—
421D12—61no—
422D12—61no—
423D12—61no—
424D12—61no—
425D12—121no—
426D12—121no—
427D12—122no—
428D12—122no—
429C4×D3—122no—
430C4×D3—122no—
431C3×C8—181no—
432C3⋊C8—61no—
433C3⋊C8—61no—
434C3⋊C8—121no—
435C3⋊C8—182no—
436C3⋊C8—181no—
437C3⋊C8—181no—
438C3⋊C8—181no—
439C3⋊C8—361no—
440C3⋊C8—361no—
441C3⋊C8—362no—
442C2×C32—21no—
443C2×C32—21no—
444C2×C32—21no—
445C2×C32—21no—
446C2×C32—21no—
447C2×C32—21no—
448C2×C32—21no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—41no—
452C2×C32—41no—
453C2×C32—41no—
454C2×C32—241no—
455C2×C32#88411yescharacteristic
456C2×C32D3×D811yescharacteristic
457C2×C32#91411yescharacteristic
458C2×C32#93011yescharacteristic
459C2×C32C2×#21311yescharacteristic
460C2×C32C2×#21311yescharacteristic
461C2×C32#93211yescharacteristic
462C2×C32#93811yescharacteristic
463C2×C32#94911yescharacteristic
464C3⋊D3—42no—
465C3⋊D3—81no—
466C3×D3—82no—
467C3×D3—81no—
468C3×D3—81no—
469C3×D3—122no—
470C3×D3—122no—
471C3×D3—242no—
472C3×D3—242no—
473C3×D3—241no—
474C3×D3—241no—
475C2×D4—31no—
476C2×D4—91no—
477C2×D4—91no—
478C2×D4—181no—
479C2×D4—181no—
480C22×C4—181no—
481D8—542no—
482D8—542no—
483C2×C8—91no—
484C2×C8—271no—
485C4⋊C4—31no—
486C22⋊C4—181no—
487C42—31no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—41no—
492C22×C3—122no—
493C22×C3—121no—
494C22×C3—121no—
495C22×C3—121no—
496C22×C3—121no—
497C22×C3—121no—
498C22×C3—121no—
499C22×C3—182no—
500C22×C3—241no—
501C22×C3—241no—
502C22×C3—361no—
503C22×C3—361no—
504C22×C3—361no—
505C22×C3—361no—
506C22×C3—361no—
507C22×C3C2×#62511yescharacteristic
508C22×C3D3×#6711yescharacteristic
509C22×C3D3×#6711yescharacteristic
510C2×D3—41no—
511C2×D3—41no—
512C2×D3—41no—
513C2×D3—62no—
514C2×D3—62no—
515C2×D3—122no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—122no—
521C2×D3—121no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—241no—
528C2×D3—241no—
529C2×D3—241no—
530C2×D3—241no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—32no—
538C3×C4—32no—
539C3×C4—41no—
540C3×C4—41no—
541C3×C4—62no—
542C3×C4—61no—
543C3×C4—61no—
544C3×C4—121no—
545C3×C4—121no—
546C3×C4—121no—
547C3×C4—241no—
548C3×C4#379511yescharacteristic
549C3×C4#379811yescharacteristic
550C3×C4D3×D1211yescharacteristic
551C3×C4D3×D1211yescharacteristic
552C3×C4#380411yescharacteristic
553C3×C4#381111yescharacteristic
554Dic3—21no—
555Dic3—41no—
556Dic3#371312yescomplemented
557C32—21no—
558C32—21no—
559C32—21no—
560C32—41no—
561C32#478611yescharacteristic, complemented
562C32#501511yescharacteristic, complemented
563C32#507211yescharacteristic, complemented
564C23—61no—
565C23—181no—
566C23—181no—
567D4—61no—
568D4—61no—
569D4—92no—
570D4—181no—
571D4—181no—
572D4—181no—
573D4—362no—
574D4—362no—
575C2×C4—31no—
576C2×C4—31no—
577C2×C4—61no—
578C2×C4—362no—
579C2×C4D3311yescharacteristic
580C8—181no—
581C8—541no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—41no—
592C2×C3—41no—
593C2×C3—41no—
594C2×C3—242no—
595C2×C3—241no—
596C2×C3—241no—
597C2×C3—362no—
598C2×C3—721no—
599C2×C3C2×#371311yescharacteristic
600C2×C3#6382311yescharacteristic
601C2×C3#6390611yescharacteristic
602C2×C3#6390811yescharacteristic
603C2×C3D3×#21311yescharacteristic
604C2×C3D3×#21311yescharacteristic
605C2×C3#6393411yescharacteristic
606C2×C3#6393911yescharacteristic
607C2×C3#6395811yescharacteristic
608D3—81no—
609D3—122no—
610D3—122no—
611D3—242no—
612D3—242no—
613D3—241no—
614D3—241no—
615C22—121no—
616C22—121no—
617C22—121no—
618C22—182no—
619C22—361no—
620C22—361no—
621C22—361no—
622C22—361no—
623C22—361no—
624C22D3×#62511yescharacteristic
625C4—32no—
626C4—61no—
627C4—121no—
628C4#8895511yescharacteristic
629C4#8896011yescharacteristic
630C3—21no—
631C3—21no—
632C3—21no—
633C3—41no—
634C3#1059034711yescharacteristic, complemented
635C3#1059054711yescharacteristic, complemented
636C3#1059142911yescharacteristic, complemented
637C2—241no—
638C2—362no—
639C2—721no—
640C2D3×#371311yescharacteristic
641C2#1172286711yescharacteristic
642C2#1172295711yescharacteristic
subgroupG/H
centerC22D3×#625
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. C2×#88789C2semidirect
3. C3×#63911C2semidirect
4. C3×#63894C2semidirect
5. Dic3⋊(C3⋊(C3⋊C8))C2semidirect
6. #11722033C2semidirect
7. C3×#63562C2semidirect
29. #63911D3semidirect
30. #63894D3semidirect
47. #63562D3semidirect
55. C3×C4⋊(C3⋊D3)D4semidirect
133. C32×Dic3D8semidirect
185. C4⋊(C3⋊D3)D12semidirect
357. C3×Dic3#213semidirect
358. C3×Dic3#213semidirect
366. C33#459semidirect
556. Dic3#3713semidirect
561. C32#4786semidirect
562. C32#5015semidirect
563. C32#5072semidirect
634. C3#10590347semidirect
635. C3#10590547semidirect
636. C3#10591429semidirect

Maximal subgroups

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

subgroupindex
C2×#888102
C2×#887892
C3×#639112
C3×#638942
Dic3⋊(C3⋊(C3⋊C8))2
#117220332
C3×#635622
#105914293
#105905473
#105903473