Finite Group Databasebeta

← #13161955

Subgroups — #13161955

Order 1728.

746 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64147C211yesmaximal, characteristic
2C2×C3×#3754C211yesmaximal, characteristic, complemented
3#11723674C211yesmaximal, characteristic, complemented
4C2×#88809C211yesmaximal, characteristic, complemented
5C3×#63659C211yesmaximal, characteristic, complemented
6#11722080C211yesmaximal, characteristic, complemented
7#11722076C211yesmaximal, characteristic, complemented
8#10591502—31nomaximal
9#10591464—31nomaximal
10#10591462—31nomaximal
11C2×C33×D4C2211yescharacteristic
12C2×C3×#638—21no—
13C2×C3×C4×C3⋊D3C2211yescharacteristic
14C2×C3×#634C2211yescharacteristic
15C3×#3757—21no—
16C3×#3754—22no—
17C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
21#88815—21no—
22#88814—21no—
23#88809—22no—
24#64147D311yescharacteristic
25C2×#3754D311yescharacteristic, complemented
26C3×#938—31no—
27C3×#938—31no—
28C3×#938—61no—
29C2×C3×#214—31no—
30C2×C3×#214—31no—
31C2×C3×#214—61no—
32#63871—31no—
33#63857—31no—
34#63856—31no—
35C2×#3712—31no—
36C2×#3711—31no—
37C2×#3711—31no—
38#63659D311yescharacteristic, complemented
39C3×#832—31no—
40C3×#832—31no—
41C3×#832—61no—
42#63576—31no—
43#63575—31no—
44#63575—31no—
45#63567—31no—
46#63566—31no—
47#63565—31no—
48C23×C33—21no—
49C22×C3×C3⋊D3D411yescharacteristic
50C33×D4—21no—
51C33×D4—21no—
52C2×C33×C4C2311yescharacteristic
53C3×#638—42no—
54C2×C3×C3⋊Dic3—21no—
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×#634—21no—
61C3×#634—21no—
62C3×C3⋊(C3⋊C8)—21no—
63C3×C3⋊(C3⋊C8)D412yescomplemented
64#5174—91no—
65#5042—91no—
66#4780—91no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4—21no—
70C2×C32×D4—41no—
71C2×C32×D4C2×D311yescharacteristic
72C2×C32×D4C2×D311yescharacteristic
73C2×C32×D4C2×D311yescharacteristic
74C2×#638—21no—
75C2×C4×C3⋊D3C2×D311yescharacteristic
76C2×#634C2×D311yescharacteristic
77C2×C3×#67—61no—
78C2×C3×#67—61no—
79C2×C3×#67—62no—
80C2×C3×C4×D3—31no—
81C2×C3×C4×D3—31no—
82C2×C3×C4×D3—61no—
83C2×C3×Dic6—31no—
84C2×C3×Dic6—31no—
85C2×C3×Dic6—61no—
86#3757—21no—
87#3754—22no—
88C4⋊(C3⋊Dic3)C2×D311yescharacteristic
89C4⋊(C3⋊Dic3)C2×D311yescharacteristic
90C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
91C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
92C3×#217—61no—
93C3×#217—61no—
94C3×#217—62no—
95C3×#214—62no—
96C3×#214—62no—
97C3×#214—64no—
98C3×C4⋊Dic3—31no—
99C3×C4⋊Dic3—31no—
100C3×C4⋊Dic3—31no—
101C3×C4⋊Dic3—31no—
102C3×C4⋊Dic3—61no—
103C3×C4⋊Dic3—61no—
104C2×C3×C3⋊C8—31no—
105C2×C3×C3⋊C8—31no—
106C2×C3×C3⋊C8—31no—
107C2×C3×C3⋊C8—31no—
108C2×C3×C3⋊C8—61no—
109C2×C3×C3⋊C8—61no—
110#3724—61no—
111Dic3⋊Dic3—61no—
112Dic3⋊Dic3—61no—
113#3722—61no—
114(C2×D3)⋊Dic3—61no—
115(C2×D3)⋊Dic3—61no—
116#3712—62no—
117#3711—62no—
118#3711—62no—
119C22×C33—41no—
120C22×C33—41no—
121C22×C33—41no—
122C22×C33C2×D411yescharacteristic
123C2×C3×C3⋊D3—21no—
124C2×C3×C3⋊D3—21no—
125C2×C3×C3⋊D3—21no—
126C33×C4C2×D411yescharacteristic
127C33×C4#4111yescharacteristic
128C3×C3⋊Dic3—21no—
129C3×C3⋊Dic3—41no—
130C3×C3⋊Dic3—41no—
131C3×C3⋊Dic3—41no—
132C2×C3×SD16—91no—
133C3×#121—91no—
134#946—91no—
135#938—31no—
136#938—31no—
137#938—61no—
138C2×#214—31no—
139C2×#214—31no—
140C2×#214—61no—
141#924—91no—
142C2×#208—91no—
143C2×ΓL(1,𝔽25)—91no—
144C2×ΓL(1,𝔽25)—91no—
145#897—91no—
146C3×#102—91no—
147#835—91no—
148#832—31no—
149#832—31no—
150#832—61no—
151#818—91no—
152#816—91no—
153#810—91no—
154#807—91no—
155#807—91no—
156C23×C32—21no—
157C23×C32—22no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—41no—
161C23×C32—41no—
162C23×C32—42no—
163C22×C3⋊D3#6711yescharacteristic
164C22×C3×D3—31no—
165C22×C3×D3—31no—
166C22×C3×D3—61no—
167C32×D4—21no—
168C32×D4—21no—
169C32×D4—22no—
170C32×D4—22no—
171C32×D4—21no—
172C32×D4—21no—
173C32×D4—21no—
174C32×D4—21no—
175C32×D4—41no—
176C32×D4—41no—
177C32×D4—41no—
178C32×D4—41no—
179C32×D4—42no—
180C32×D4—42no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—41no—
185C2×C32×C4C22×D311yescharacteristic
186C2×C32×C4C22×D311yescharacteristic
187C2×C32×C4C22×D311yescharacteristic
188#638—42no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3#6711yescharacteristic
193C4×C3⋊D3—21no—
194C4×C3⋊D3—21no—
195#634—21no—
196#634—21no—
197C3×#67—124no—
198C3×#67—122no—
199C3×#67—122no—
200C2×C3×Dic3—31no—
201C2×C3×Dic3—31no—
202C2×C3×Dic3—61no—
203C2×C3×Dic3—62no—
204C2×C3×Dic3—61no—
205C2×C3×Dic3—61no—
206C2×C3×Dic3—61no—
207C2×C3×Dic3—61no—
208C2×C3×Dic3—61no—
209C2×C3×Dic3—61no—
210C2×C3×Dic3—121no—
211C2×C3×Dic3—121no—
212C3×C4×D3—61no—
213C3×C4×D3—61no—
214C3×C4×D3—61no—
215C3×C4×D3—61no—
216C3×C4×D3—121no—
217C3×C4×D3—121no—
218C3×Dic6—62no—
219C3×Dic6—61no—
220C3×Dic6—61no—
221C3×Dic6—61no—
222C3×Dic6—61no—
223C3×Dic6—121no—
224C3⋊(C3⋊C8)—21no—
225C3⋊(C3⋊C8)#6712yescomplemented
226C3×C3⋊C8—32no—
227C3×C3⋊C8—32no—
228C3×C3⋊C8—62no—
229C3×C3⋊C8—61no—
230C3×C3⋊C8—61no—
231C3×C3⋊C8—121no—
232#468—271noSylow
233C2×C33—81no—
234C2×C33#12111yescharacteristic
235C2×C33AGL(1,ℤ/8)11yescharacteristic
236C2×C33#13711yescharacteristic
237C3×C3⋊D3—41no—
238C2×C3×Q8—91no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—41no—
243C2×C3×D4—181no—
244C2×C3×D4D3211yescharacteristic
245C2×C3×D4D3211yescharacteristic
246C2×C3×D4D3211yescharacteristic
247C22×C3×C4—91no—
248C2×#67—61no—
249C2×#67—61no—
250C2×#67—62no—
251C2×C4×D3—31no—
252C2×C4×D3—31no—
253C2×C4×D3—61no—
254C2×Dic6—31no—
255C2×Dic6—31no—
256C2×Dic6—61no—
257C3×SD16—182no—
258C2×C3×C8—91no—
259C2×C3×C8—91no—
260C3×C4⋊C4—91no—
261C3×C4⋊C4—91no—
262C3×C22⋊C4—181no—
263#217—61no—
264#217—61no—
265#217—62no—
266#217—181no—
267#214—62no—
268#214—62no—
269#214—64no—
270(C2×D3)⋊C4—181no—
271(C2×D3)⋊C4—181no—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—181no—
279Dic3⋊C4—181no—
280Dic3⋊C4—181no—
281#208—182no—
282C2×C3⋊C8—31no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—61no—
287C2×C3⋊C8—61no—
288ΓL(1,𝔽25)—182no—
289ΓL(1,𝔽25)—182no—
290C22×C32—21no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—41no—
294C22×C32—42no—
295C22×C32—42no—
296C22×C32—42no—
297C22×C32—44no—
298C22×C32—41no—
299C22×C32—41no—
300C22×C32—41no—
301C22×C32—41no—
302C22×C32—41no—
303C22×C32—42no—
304C22×C32—42no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—81no—
310C22×C32—81no—
311C22×C32—81no—
312C22×C32—81no—
313C22×C32—82no—
314C22×C32—82no—
315C22×C32D3×D411yescharacteristic
316C22×C32D3×D411yescharacteristic
317C22×C32C2×#6711yescharacteristic
318C2×C3⋊D3—21no—
319C2×C3⋊D3—21no—
320C2×C3⋊D3—21no—
321C2×C3×D3—62no—
322C2×C3×D3—61no—
323C2×C3×D3—61no—
324C2×C3×D3—61no—
325C2×C3×D3—61no—
326C2×C3×D3—61no—
327C2×C3×D3—61no—
328C2×C3×D3—121no—
329C2×C3×D3—121no—
330C32×C4—21no—
331C32×C4—21no—
332C32×C4—21no—
333C32×C4—21no—
334C32×C4—21no—
335C32×C4—21no—
336C32×C4—41no—
337C32×C4—41no—
338C32×C4#23511yescharacteristic
339C32×C4D3×D411yescharacteristic
340C32×C4D3×D411yescharacteristic
341C32×C4#23711yescharacteristic
342C32×C4#23711yescharacteristic
343C32×C4C2×#6711yescharacteristic
344C3⋊Dic3—21no—
345C3⋊Dic3—41no—
346C3⋊Dic3—41no—
347C3⋊Dic3—41no—
348C3×Dic3—61no—
349C3×Dic3—61no—
350C3×Dic3—121no—
351C3×Dic3—122no—
352C3×Dic3—122no—
353C3×Dic3—121no—
354C3×Dic3—121no—
355C3×Dic3—121no—
356C3×Dic3—121no—
357C3×Dic3—121no—
358C3×Dic3—121no—
359C3×Dic3—241no—
360C2×SD16—91no—
361C2×M16—271no—
362C22⋊Q8—271no—
363#121—91no—
364#107—271no—
365#103—271no—
366#102—91no—
367C33#46811yescharacteristic, complemented, Sylow
368C23×C3—22no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—42no—
375C23×C3—91no—
376C22×D3—31no—
377C22×D3—31no—
378C22×D3—61no—
379C3×Q8—181no—
380C3×Q8—181no—
381C3×D4—22no—
382C3×D4—22no—
383C3×D4—21no—
384C3×D4—21no—
385C3×D4—21no—
386C3×D4—21no—
387C3×D4—21no—
388C3×D4—21no—
389C3×D4—41no—
390C3×D4—41no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—42no—
394C3×D4—42no—
395C3×D4—362no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—41no—
400C2×C3×C4—91no—
401C2×C3×C4—181no—
402C2×C3×C4—181no—
403C2×C3×C4—181no—
404C2×C3×C4—181no—
405C2×C3×C4—181no—
406C2×C3×C4C2×D3211yescharacteristic
407C2×C3×C4C2×D3211yescharacteristic
408C2×C3×C4C2×D3211yescharacteristic
409#67—124no—
410#67—122no—
411#67—122no—
412C2×Dic3—31no—
413C2×Dic3—31no—
414C2×Dic3—61no—
415C2×Dic3—62no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C4×D3—61no—
425C4×D3—61no—
426C4×D3—61no—
427C4×D3—61no—
428C4×D3—121no—
429C4×D3—121no—
430Dic6—62no—
431Dic6—61no—
432Dic6—61no—
433Dic6—61no—
434Dic6—61no—
435Dic6—121no—
436C3×C8—92no—
437C3×C8—181no—
438C3⋊C8—32no—
439C3⋊C8—32no—
440C3⋊C8—62no—
441C3⋊C8—61no—
442C3⋊C8—61no—
443C3⋊C8—121no—
444C2×C32—21no—
445C2×C32—21no—
446C2×C32—21no—
447C2×C32—21no—
448C2×C32—21no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—21no—
452C2×C32—21no—
453C2×C32—41no—
454C2×C32—41no—
455C2×C32—41no—
456C2×C32—82no—
457C2×C32—82no—
458C2×C32—82no—
459C2×C32—84no—
460C2×C32—81no—
461C2×C32—81no—
462C2×C32—81no—
463C2×C32#88411yescharacteristic
464C2×C32#91111yescharacteristic
465C2×C32#91411yescharacteristic
466C2×C32#91511yescharacteristic
467C2×C32#91511yescharacteristic
468C2×C32#93211yescharacteristic
469C2×C32#93811yescharacteristic
470C2×C32#93911yescharacteristic
471C2×C32#95111yescharacteristic
472C3⋊D3—41no—
473C3×D3—122no—
474C3×D3—121no—
475C3×D3—121no—
476C2×Q8—91no—
477C2×D4—181no—
478C2×D4#111311yescharacteristic
479C22×C4—91no—
480SD16—182no—
481M16—542no—
482C2×C8—91no—
483C2×C8—91no—
484C4⋊C4—91no—
485C4⋊C4—91no—
486C4⋊C4—541no—
487C22⋊C4—181no—
488C22⋊C4—541no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—44no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—81no—
509C22×C3—81no—
510C22×C3—81no—
511C22×C3—81no—
512C22×C3—82no—
513C22×C3—82no—
514C22×C3—181no—
515C22×C3—181no—
516C22×C3—181no—
517C22×C3D3×#6711yescharacteristic
518C22×C3D3×#6711yescharacteristic
519C22×C3#381111yescharacteristic
520C2×D3—62no—
521C2×D3—61no—
522C2×D3—61no—
523C2×D3—61no—
524C2×D3—61no—
525C2×D3—61no—
526C2×D3—61no—
527C2×D3—121no—
528C2×D3—121no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—41no—
536C3×C4—41no—
537C3×C4—181no—
538C3×C4—361no—
539C3×C4—361no—
540C3×C4—361no—
541C3×C4#380411yescharacteristic
542C3×C4#380411yescharacteristic
543C3×C4#380511yescharacteristic
544C3×C4D3×#6711yescharacteristic
545C3×C4D3×#6711yescharacteristic
546C3×C4#381111yescharacteristic
547Dic3—61no—
548Dic3—61no—
549Dic3—121no—
550Dic3—122no—
551Dic3—122no—
552Dic3—121no—
553Dic3—121no—
554Dic3—121no—
555Dic3—121no—
556Dic3—121no—
557Dic3—121no—
558Dic3—241no—
559C32—21no—
560C32—21no—
561C32—21no—
562C32—41no—
563C32#478011yescharacteristic, complemented
564C32#504211yescharacteristic, complemented
565C32#517411yescharacteristic, complemented
566C23—21no—
567C23—91no—
568Q8—181no—
569Q8—181no—
570D4—21no—
571D4—21no—
572D4—362no—
573C2×C4—91no—
574C2×C4—181no—
575C2×C4—181no—
576C2×C4—181no—
577C2×C4—181no—
578C2×C4—181no—
579C2×C4C2×#111311yescharacteristic
580C8—92no—
581C8—181no—
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—82no—
595C2×C3—82no—
596C2×C3—82no—
597C2×C3—84no—
598C2×C3—81no—
599C2×C3—81no—
600C2×C3—81no—
601C2×C3—361no—
602C2×C3#6392911yescharacteristic
603C2×C3#6392911yescharacteristic
604C2×C3#6393111yescharacteristic
605C2×C3#6393211yescharacteristic
606C2×C3#6393411yescharacteristic
607C2×C3#6393711yescharacteristic
608C2×C3#6395811yescharacteristic
609C2×C3#6397011yescharacteristic
610C2×C3#6397111yescharacteristic
611D3—122no—
612D3—121no—
613D3—121no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—181no—
618C22—181no—
619C22—181no—
620C22#8904911yescharacteristic
621C4—181no—
622C4—361no—
623C4—361no—
624C4—361no—
625C4#8904611yescharacteristic
626C4#8904911yescharacteristic
627C3—21no—
628C3—21no—
629C3—21no—
630C3—41no—
631C3#1059146211yescharacteristic, complemented
632C3#1059146411yescharacteristic, complemented
633C3#1059150211yescharacteristic, complemented
634C2—81no—
635C2—361no—
636C2#1172370511yescharacteristic
637C2#1172370611yescharacteristic
638C2#1172372511yescharacteristic
subgroupG/H
centerC22#89049
commutator, cosocleC2×C33×C4C23
FrattiniC2×C4C2×#1113
FittingC2×C33×D4C22
socleC22×C33C2×D4
prime radicalC3×#64147C2
hypercenterC2×D4#1113
hypocenterC33#468
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
2. C2×C3×#3754C2semidirect
3. #11723674C2semidirect
4. C2×#88809C2semidirect
5. C3×#63659C2semidirect
6. #11722080C2semidirect
7. #11722076C2semidirect
25. C2×#3754D3semidirect
38. #63659D3semidirect
63. C3×C3⋊(C3⋊C8)D4semidirect
225. C3⋊(C3⋊C8)#67semidirect
367. C33#468semidirect
563. C32#4780semidirect
564. C32#5042semidirect
565. C32#5174semidirect
631. C3#10591462semidirect
632. C3#10591464semidirect
633. C3#10591502semidirect

Maximal subgroups

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

subgroupindex
C3×#641472
C2×C3×#37542
#117236742
C2×#888092
C3×#636592
#117220802
#117220762
#105915023
#105914643
#105914623