Finite Group Databasebeta

← #13153908

Subgroups — #13153908

Order 1728.

1170 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D4×C9C211yesmaximal, characteristic, complemented
2#11721839C211yesmaximal, characteristic
3#11721835C211yesmaximal, characteristic, complemented
4C4×#6233C211yesmaximal, characteristic, complemented
5C4×#6233C211yesmaximal, characteristic, complemented
6#11721815C211yesmaximal, characteristic, complemented
7C2×C4×C3⋊Dic9C211yesmaximal, characteristic, complemented
8#11721754C211yesmaximal, characteristic, complemented
9#11721745C211yesmaximal, characteristic, complemented
10#11721732C211yesmaximal, characteristic, complemented
11#11721731C211yesmaximal, characteristic, complemented
12#11721725C211yesmaximal, characteristic, complemented
13#11721724C211yesmaximal, characteristic, complemented
14#11721709C211yesmaximal, characteristic, complemented
15C4×#6226C211yesmaximal, characteristic, complemented
16#10596009—31nomaximal
17#10589640—33nomaximal
18C2×C3×D4×C9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic
23C22×C3⋊Dic9C2211yescharacteristic
24C22×C3⋊Dic9C2211yescharacteristic
25C2×C4×C3⋊D9C2211yescharacteristic
26C2×#6226C2211yescharacteristic
27C3×C9×C4⋊C4C2211yescharacteristic
28C3×C9×C22⋊C4C2211yescharacteristic
29C3×C9×C22⋊C4C2211yescharacteristic
30C3×C42×C9C2211yescharacteristic
31#88551C2211yescharacteristic
32#88551C2211yescharacteristic
33#88551C2211yescharacteristic
34#88551C2211yescharacteristic
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37#88536C2211yescharacteristic
38#88536C2211yescharacteristic
39C4⋊(C3⋊Dic9)C2211yescharacteristic
40C4⋊(C3⋊Dic9)C2211yescharacteristic
41C4⋊(C3⋊Dic9)C2211yescharacteristic
42#88534C2211yescharacteristic
43#88534C2211yescharacteristic
44#88534C2211yescharacteristic
45#88534C2211yescharacteristic
46#88534C2211yescharacteristic
47#88534C2211yescharacteristic
48C4×C3⋊Dic9C2211yescharacteristic
49C4×C3⋊Dic9C2211yescharacteristic
50C4×C3⋊Dic9C2211yescharacteristic
51C4×C3⋊Dic9C2211yescharacteristic
52C4×C3⋊Dic9C2211yescharacteristic
53C32×C4×D4D311yescharacteristic
54#64148—31no—
55#64144—31no—
56C4×#638—31no—
57C4×#638—31no—
58#64135—31no—
59C2×C4×C3⋊Dic3—31no—
60#64107—31no—
61#64098—31no—
62#64095—31no—
63#64094—31no—
64#64088—31no—
65#64087—31no—
66#64081—31no—
67C4×#634—31no—
68C4×D4×C9D313yescomplemented
69#63501—33no—
70#63497—33no—
71C4×#611—33no—
72C4×#611—33no—
73#63488—33no—
74C2×C4×Dic9—33no—
75#63460—33no—
76#63451—33no—
77#63448—33no—
78#63447—33no—
79#63441—33no—
80#63440—33no—
81#63434—33no—
82C4×Dic18—33no—
83C23×C3×C9C2311yescharacteristic
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C3×D4×C9—22no—
87C2×C3×C4×C9—22no—
88C2×C3×C4×C9—22no—
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94#6233—22no—
95#6233—22no—
96C2×C3⋊Dic9—22no—
97C2×C3⋊Dic9—22no—
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C4×C3⋊D9—22no—
106#6226—22no—
107#5538—93no—
108#5538—91no—
109C2×C32×D4C2×D311yescharacteristic
110C22×C32×C4C2×D311yescharacteristic
111C22×C32×C4C2×D311yescharacteristic
112C2×#638—31no—
113C2×#638—31no—
114C22×C3⋊Dic3—31no—
115C22×C3⋊Dic3—31no—
116C2×C4×C3⋊D3—31no—
117C2×#634—31no—
118C32×C4⋊C4C2×D311yescharacteristic
119C32×C22⋊C4C2×D311yescharacteristic
120C32×C22⋊C4C2×D311yescharacteristic
121C32×C42C2×D311yescharacteristic
122#3757—31no—
123#3757—31no—
124#3757—31no—
125#3757—31no—
126#3752—31no—
127#3752—31no—
128#3752—31no—
129#3752—31no—
130C4⋊(C3⋊Dic3)—31no—
131C4⋊(C3⋊Dic3)—31no—
132C4⋊(C3⋊Dic3)—31no—
133#3750—31no—
134#3750—31no—
135#3750—31no—
136#3750—31no—
137#3750—31no—
138#3750—31no—
139C4×C3⋊Dic3—31no—
140C4×C3⋊Dic3—31no—
141C4×C3⋊Dic3—31no—
142C4×C3⋊Dic3—31no—
143C4×C3⋊Dic3—31no—
144C2×D4×C9C2×D313yes—
145C22×C4×C9C2×D313yes—
146C22×C4×C9C2×D313yes—
147C2×#611—33no—
148C2×#611—33no—
149C22×Dic9—33no—
150C22×Dic9—33no—
151C2×C4×D9—33no—
152C2×Dic18—33no—
153C9×C4⋊C4C2×D313yes—
154C9×C22⋊C4C2×D313yes—
155C9×C22⋊C4C2×D313yes—
156C42×C9C2×D313yes—
157#3676—33no—
158#3676—33no—
159#3676—33no—
160#3676—33no—
161(C2×D9)⋊C4—33no—
162(C2×D9)⋊C4—33no—
163(C2×D9)⋊C4—33no—
164(C2×D9)⋊C4—33no—
165C4⋊Dic9—33no—
166C4⋊Dic9—33no—
167C4⋊Dic9—33no—
168Dic9⋊C4—33no—
169Dic9⋊C4—33no—
170Dic9⋊C4—33no—
171Dic9⋊C4—33no—
172Dic9⋊C4—33no—
173Dic9⋊C4—33no—
174C4×Dic9—33no—
175C4×Dic9—33no—
176C4×Dic9—33no—
177C4×Dic9—33no—
178C4×Dic9—33no—
179C22×C3×C9—21no—
180C22×C3×C9—21no—
181C22×C3×C9—21no—
182C22×C3×C9—21no—
183C22×C3×C9—21no—
184C22×C3×C9#4112yes—
185C22×C3×C9C2411yescharacteristic
186C2×C3⋊D9—21no—
187C2×C3⋊D9—21no—
188C2×C3⋊D9—21no—
189C3×C4×C9—21no—
190C3×C4×C9—21no—
191C3×C4×C9—21no—
192C3×C4×C9—21no—
193C3×C4×C9#4112yes—
194C3⋊Dic9—21no—
195C3⋊Dic9—21no—
196C3⋊Dic9—21no—
197C3⋊Dic9—21no—
198C3⋊Dic9—21no—
199C3⋊Dic9—21no—
200C3⋊Dic9#4112yes—
201C3×C4×D4D913yescomplemented
202C3×C4×D4C3⋊D311yescharacteristic
203#939—93no—
204#939—91no—
205#935—93no—
206#935—91no—
207C4×#67—93no—
208C4×#67—93no—
209C4×#67—91no—
210C4×#67—91no—
211#926—93no—
212#926—91no—
213C2×C4×Dic3—93no—
214C2×C4×Dic3—91no—
215#898—93no—
216#898—91no—
217#889—93no—
218#889—91no—
219#886—93no—
220#886—91no—
221#885—93no—
222#885—91no—
223#879—93no—
224#879—91no—
225#878—93no—
226#878—91no—
227#872—93no—
228#872—91no—
229C4×Dic6—93no—
230C4×Dic6—91no—
231C23×C32C22×D311yescharacteristic
232C23×C32C22×D311yescharacteristic
233C22×C3⋊D3—31no—
234C32×D4—22no—
235C2×C32×C4—22no—
236C2×C32×C4—22no—
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D311yescharacteristic
240C2×C32×C4C22×D311yescharacteristic
241C2×C32×C4C22×D311yescharacteristic
242#638—62no—
243#638—62no—
244C2×C3⋊Dic3—31no—
245C2×C3⋊Dic3—31no—
246C2×C3⋊Dic3—31no—
247C2×C3⋊Dic3—31no—
248C2×C3⋊Dic3—31no—
249C2×C3⋊Dic3—31no—
250C2×C3⋊Dic3—31no—
251C2×C3⋊Dic3—62no—
252C2×C3⋊Dic3—62no—
253C4×C3⋊D3—62no—
254#634—62no—
255C23×C9C22×D313yes—
256C23×C9C22×D313yes—
257C22×D9—33no—
258D4×C9—26no—
259C2×C4×C9—26no—
260C2×C4×C9—26no—
261C2×C4×C9C22×D313yes—
262C2×C4×C9C22×D313yes—
263C2×C4×C9C22×D313yes—
264C2×C4×C9C22×D313yes—
265C2×C4×C9C22×D313yes—
266#611—66no—
267#611—66no—
268C2×Dic9—33no—
269C2×Dic9—33no—
270C2×Dic9—33no—
271C2×Dic9—33no—
272C2×Dic9—33no—
273C2×Dic9—33no—
274C2×Dic9—33no—
275C2×Dic9—66no—
276C2×Dic9—66no—
277C4×D9—66no—
278Dic18—66no—
279#529—271noSylow
280C2×C3×C9—22no—
281C2×C3×C9—41no—
282C2×C3×C9C2×#4111yescharacteristic
283C2×C3×C9C2×#4111yescharacteristic
284C2×C3×C9C2×#4111yescharacteristic
285C3⋊D9—41no—
286C2×C3×D4C2×D913yes—
287C2×C3×D4C2×C3⋊D311yescharacteristic
288C22×C3×C4C2×D913yes—
289C22×C3×C4C2×D913yes—
290C22×C3×C4C2×C3⋊D311yescharacteristic
291C22×C3×C4C2×C3⋊D311yescharacteristic
292C2×#67—93no—
293C2×#67—93no—
294C2×#67—91no—
295C2×#67—91no—
296C22×Dic3—93no—
297C22×Dic3—93no—
298C22×Dic3—91no—
299C22×Dic3—91no—
300C2×C4×D3—93no—
301C2×C4×D3—91no—
302C2×Dic6—93no—
303C2×Dic6—91no—
304C3×C4⋊C4C2×D913yes—
305C3×C4⋊C4C2×C3⋊D311yescharacteristic
306C3×C22⋊C4C2×D913yes—
307C3×C22⋊C4C2×D913yes—
308C3×C22⋊C4C2×C3⋊D311yescharacteristic
309C3×C22⋊C4C2×C3⋊D311yescharacteristic
310C3×C42C2×D913yes—
311C3×C42C2×C3⋊D311yescharacteristic
312#217—93no—
313#217—93no—
314#217—93no—
315#217—93no—
316#217—91no—
317#217—91no—
318#217—91no—
319#217—91no—
320(C2×D3)⋊C4—93no—
321(C2×D3)⋊C4—93no—
322(C2×D3)⋊C4—93no—
323(C2×D3)⋊C4—93no—
324(C2×D3)⋊C4—91no—
325(C2×D3)⋊C4—91no—
326(C2×D3)⋊C4—91no—
327(C2×D3)⋊C4—91no—
328C4⋊Dic3—93no—
329C4⋊Dic3—93no—
330C4⋊Dic3—93no—
331C4⋊Dic3—91no—
332C4⋊Dic3—91no—
333C4⋊Dic3—91no—
334Dic3⋊C4—93no—
335Dic3⋊C4—93no—
336Dic3⋊C4—93no—
337Dic3⋊C4—93no—
338Dic3⋊C4—93no—
339Dic3⋊C4—93no—
340Dic3⋊C4—91no—
341Dic3⋊C4—91no—
342Dic3⋊C4—91no—
343Dic3⋊C4—91no—
344Dic3⋊C4—91no—
345Dic3⋊C4—91no—
346C4×Dic3—93no—
347C4×Dic3—93no—
348C4×Dic3—93no—
349C4×Dic3—93no—
350C4×Dic3—93no—
351C4×Dic3—91no—
352C4×Dic3—91no—
353C4×Dic3—91no—
354C4×Dic3—91no—
355C4×Dic3—91no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32#23512yes—
362C22×C32C23×D311yescharacteristic
363C2×C3⋊D3—61no—
364C2×C3⋊D3—61no—
365C2×C3⋊D3—61no—
366C32×C4—21no—
367C32×C4—21no—
368C32×C4—21no—
369C32×C4—21no—
370C32×C4#23712yes—
371C3⋊Dic3—32no—
372C3⋊Dic3—61no—
373C3⋊Dic3—61no—
374C3⋊Dic3—61no—
375C3⋊Dic3—61no—
376C3⋊Dic3—61no—
377C3⋊Dic3—61no—
378C22×C9—23no—
379C22×C9—23no—
380C22×C9—23no—
381C22×C9—23no—
382C22×C9—23no—
383C22×C9#23516yes—
384C22×C9C23×D313yes—
385C2×D9—63no—
386C2×D9—63no—
387C2×D9—63no—
388C4×C9—23no—
389C4×C9—23no—
390C4×C9—23no—
391C4×C9—23no—
392C4×C9#23716yes—
393Dic9—36no—
394Dic9—63no—
395Dic9—63no—
396Dic9—63no—
397Dic9—63no—
398Dic9—63no—
399Dic9—63no—
400#126—271no—
401#126—271no—
402#125—271no—
403#124—271no—
404#123—271no—
405#123—271no—
406C22⋊Q8—271no—
407#121—271no—
408C4×Q8—271no—
409C4×D4—271no—
410C4×D4—271no—
411C4×D4C3⋊D911yescharacteristic, complemented
412#117—271no—
413#117—271no—
414C2×C42—271no—
415C3×C9#52911yescharacteristic, complemented, Sylow
416C23×C3C22×D913yes—
417C23×C3C22×D913yes—
418C23×C3C22×C3⋊D311yescharacteristic
419C23×C3C22×C3⋊D311yescharacteristic
420C22×D3—91no—
421C22×D3—93no—
422C3×D4—26no—
423C3×D4—22no—
424C2×C3×C4—26no—
425C2×C3×C4—26no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4C22×D913yes—
429C2×C3×C4C22×D913yes—
430C2×C3×C4C22×D913yes—
431C2×C3×C4C22×D913yes—
432C2×C3×C4C22×D913yes—
433C2×C3×C4C22×C3⋊D311yescharacteristic
434C2×C3×C4C22×C3⋊D311yescharacteristic
435C2×C3×C4C22×C3⋊D311yescharacteristic
436C2×C3×C4C22×C3⋊D311yescharacteristic
437C2×C3×C4C22×C3⋊D311yescharacteristic
438#67—182no—
439#67—186no—
440#67—186no—
441#67—182no—
442C2×Dic3—91no—
443C2×Dic3—93no—
444C2×Dic3—91no—
445C2×Dic3—91no—
446C2×Dic3—91no—
447C2×Dic3—91no—
448C2×Dic3—91no—
449C2×Dic3—91no—
450C2×Dic3—93no—
451C2×Dic3—93no—
452C2×Dic3—93no—
453C2×Dic3—93no—
454C2×Dic3—93no—
455C2×Dic3—93no—
456C2×Dic3—182no—
457C2×Dic3—186no—
458C2×Dic3—186no—
459C2×Dic3—182no—
460C4×D3—186no—
461C4×D3—182no—
462Dic6—182no—
463Dic6—186no—
464C2×C32—22no—
465C2×C32—41no—
466C2×C32C2×#23511yescharacteristic
467C2×C32C2×#23711yescharacteristic
468C2×C32D3×#4111yescharacteristic
469C3⋊D3—121no—
470C2×C9—26no—
471C2×C9—43no—
472C2×C9C2×#23513yes—
473C2×C9C2×#23713yes—
474C2×C9D3×#4113yes—
475D9—123no—
476C2×Q8—271no—
477C2×D4—271no—
478C2×D4—271no—
479C2×D4C2×C3⋊D911yescharacteristic
480C22×C4—271no—
481C22×C4—271no—
482C22×C4—271no—
483C22×C4C2×C3⋊D911yescharacteristic
484C22×C4C2×C3⋊D911yescharacteristic
485C4⋊C4—271no—
486C4⋊C4—271no—
487C4⋊C4—271no—
488C4⋊C4—271no—
489C4⋊C4—271no—
490C4⋊C4—271no—
491C4⋊C4—271no—
492C4⋊C4—271no—
493C4⋊C4—271no—
494C4⋊C4C2×C3⋊D911yescharacteristic
495C22⋊C4—271no—
496C22⋊C4—271no—
497C22⋊C4—271no—
498C22⋊C4—271no—
499C22⋊C4—271no—
500C22⋊C4—271no—
501C22⋊C4—271no—
502C22⋊C4—271no—
503C22⋊C4C2×C3⋊D911yescharacteristic
504C22⋊C4C2×C3⋊D911yescharacteristic
505C42—271no—
506C42—271no—
507C42—271no—
508C42—271no—
509C42—271no—
510C42C2×C3⋊D911yescharacteristic
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—23no—
514C22×C3—23no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—23no—
519C22×C3—23no—
520C22×C3—23no—
521C22×C3#369716yes—
522C22×C3C23×D913yes—
523C22×C3#382812yes—
524C22×C3C23×C3⋊D311yescharacteristic
525C2×D3—181no—
526C2×D3—181no—
527C2×D3—181no—
528C2×D3—183no—
529C2×D3—183no—
530C2×D3—183no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—23no—
536C3×C4—23no—
537C3×C4—23no—
538C3×C4—23no—
539C3×C4#369916yes—
540C3×C4#383012yes—
541Dic3—92no—
542Dic3—96no—
543Dic3—181no—
544Dic3—181no—
545Dic3—181no—
546Dic3—181no—
547Dic3—181no—
548Dic3—181no—
549Dic3—183no—
550Dic3—183no—
551Dic3—183no—
552Dic3—183no—
553Dic3—183no—
554Dic3—183no—
555C32#553811yescharacteristic
556C9#553813yescomplemented
557C23—271no—
558C23C22×C3⋊D911yescharacteristic
559C23C22×C3⋊D911yescharacteristic
560Q8—542no—
561D4—22no—
562D4—542no—
563D4—542no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—271no—
567C2×C4—271no—
568C2×C4—271no—
569C2×C4—271no—
570C2×C4—271no—
571C2×C4—271no—
572C2×C4—271no—
573C2×C4—542no—
574C2×C4—542no—
575C2×C4—542no—
576C2×C4C22×C3⋊D911yescharacteristic
577C2×C4C22×C3⋊D911yescharacteristic
578C2×C4C22×C3⋊D911yescharacteristic
579C2×C4C22×C3⋊D911yescharacteristic
580C2×C4C22×C3⋊D911yescharacteristic
581C2×C3—22no—
582C2×C3—26no—
583C2×C3—41no—
584C2×C3—43no—
585C2×C3C2×#369713yes—
586C2×C3C2×#369913yes—
587C2×C3#41×D913yes—
588C2×C3C2×#382811yescharacteristic
589C2×C3C2×#383011yescharacteristic
590C2×C3#41×C3⋊D311yescharacteristic
591D3—361no—
592D3—363no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—541no—
599C22—541no—
600C22—541no—
601C22#8873612yes—
602C22C23×C3⋊D911yescharacteristic
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—272no—
608C4—541no—
609C4—541no—
610C4—541no—
611C4—541no—
612C4—541no—
613C4—541no—
614C4#8874212yes—
615C3#1058964013yescomplemented
616C3#1059600911yescharacteristic
617C2—22no—
618C2—41no—
619C2—1081no—
620C2C2×#8873611yescharacteristic
621C2C2×#8874211yescharacteristic
622C2#41×C3⋊D911yescharacteristic
subgroupG/H
centerC2×C4C22×C3⋊D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C23×C3⋊D3
FittingC3×C4×D4×C9C2
socleC22×C32C23×D3
prime radical#11721839C2
hypercenterC4×D4C3⋊D9
hypocenterC3×C9#529
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×C4×D4×C9C2semidirect
3. #11721835C2semidirect
4. C4×#6233C2semidirect
5. C4×#6233C2semidirect
6. #11721815C2semidirect
7. C2×C4×C3⋊Dic9C2semidirect
8. #11721754C2semidirect
9. #11721745C2semidirect
10. #11721732C2semidirect
11. #11721731C2semidirect
12. #11721725C2semidirect
13. #11721724C2semidirect
14. #11721709C2semidirect
15. C4×#6226C2semidirect
68. C4×D4×C9D3semidirect
201. C3×C4×D4D9semidirect
411. C4×D4C3⋊D9semidirect
415. C3×C9#529semidirect
556. C9#5538semidirect
615. C3#10589640semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D4×C92
#117218392
#117218352
C4×#62332
#117218152
C2×C4×C3⋊Dic92
#117217542
#117217452
#117217322
#117217312
#117217252
#117217242
#117217092
C4×#62262
#105960093
#105896403