Finite Group Databasebeta

← C3×#82539 #11868935

Subgroups — C3×#82539 #11868935

Order 1152.

965 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#518C211yesmaximal, characteristic
2C3×#5519C211yesmaximal, characteristic, complemented
3C3×#5215C211yesmaximal, characteristic
4C2×C3×#832C211yesmaximal, characteristic
5C3×#5009C212yesmaximal, complemented
6C3×#5009C212yesmaximal, complemented
7C3×#5008C212yesmaximal, complemented
8C3×#5007C212yesmaximal, complemented
9C3×#4999C211yesmaximal, characteristic, complemented
10C3×#4998C211yesmaximal, characteristic, complemented
11C3×#4995C211yesmaximal, characteristic, complemented
12C3×#3081—31nomaximal
13#82539C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C32×C4×D4—21no—
16C32×C4×D4—21no—
17C32×C4×D4C2212yes—
18C32×C4×D4C2212yes—
19C32×#117C2211yescharacteristic
20C32×#117C2211yescharacteristic
21C2×C32×C22⋊C4—22no—
22C3×#926C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#890—21no—
27C3×#888—21no—
28C3×#878—22no—
29C3×#870C2212yescomplemented
30C3×#869C2212yescomplemented
31C3×#832C2212yes—
32C3×#832C2212yes—
33C3×#832C2212yes—
34C3×#832C2212yes—
35C3×#808C2212yescomplemented
36C3×#808C2211yescharacteristic, complemented
37C3×#808C2211yescharacteristic, complemented
38C3×#807C2212yescomplemented
39C3×#807C2211yescharacteristic, complemented
40C3×#807C2211yescharacteristic, complemented
41C3×C4⋊(C3⋊C8)C2212yescomplemented
42C3×C4⋊(C3⋊C8)C2212yescomplemented
43C3×#544—31no—
44C3×#518—21no—
45C3×#518D311yescharacteristic
46C3×#518C2×C311yescharacteristic
47#5519C2×C311yescharacteristic, complemented
48C3×#478—32no—
49C3×#478—32no—
50C3×#476—32no—
51C3×#474—32no—
52C3×#428—31no—
53C3×#427—31no—
54C3×#424—31no—
55C3×#418—31no—
56C2×C3×#102—31no—
57#5215C2×C311yescharacteristic
58C2×#832C2×C311yescharacteristic
59#5009C2×C312yescomplemented
60#5009C2×C312yescomplemented
61#5008C2×C312yescomplemented
62#5007C2×C312yescomplemented
63#4999C2×C311yescharacteristic, complemented
64#4998C2×C311yescharacteristic, complemented
65#4995C2×C311yescharacteristic, complemented
66C24×C32—21no—
67C2×C32×D4—21no—
68C2×C32×D4—22no—
69C2×C32×D4Q814yescomplemented
70C2×C32×D4C2312yes—
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4C2311yescharacteristic
74C22×C3×Dic3—21no—
75C2×C3×Dic6—22no—
76C32×C4⋊C4D411yescharacteristic
77C32×C4⋊C4D411yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C4⋊C4C2311yescharacteristic
80C32×C22⋊C4—21no—
81C32×C22⋊C4—22no—
82C32×C22⋊C4—22no—
83C32×C22⋊C4D412yes—
84C32×C42—21no—
85C32×C42C2312yes—
86C3×#217—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—21no—
95C3×#208—22no—
96C2×C3×C3⋊C8—22no—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100#3081—31noSylow
101C22×C3×D4—21no—
102C22×C3×D4C2×D311yescharacteristic
103C22×C3×D4C22×C311yescharacteristic
104C2×C3×M16—31no—
105C22×C3×C8—31no—
106C3×C4⋊Q8—32no—
107C3×C4⋊Q8—61no—
108C3×#125—32no—
109C3×#125—61no—
110C3×C22⋊Q8—62no—
111C3×C4×D4—22no—
112C3×C4×D4—22no—
113C3×C4×D4—21no—
114C3×C4×D4—21no—
115C3×C4×D4—21no—
116C3×C4×D4—21no—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C3×C4×D4C2×D312yes—
120C3×C4×D4C2×D312yes—
121C3×C4×D4C22×C312yes—
122C3×C4×D4C22×C312yes—
123C3×#117—21no—
124C3×#117—21no—
125C3×#117—31no—
126C3×#117C2×D311yescharacteristic
127C3×#117C2×D311yescharacteristic
128C3×#117C22×C311yescharacteristic
129C3×#117C22×C311yescharacteristic
130C2×C3×C4⋊C4—31no—
131C2×C3×C22⋊C4—24no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134#926C22×C311yescharacteristic
135C2×C4⋊Dic3C22×C311yescharacteristic
136C2×#208C22×C311yescharacteristic
137C22×C3⋊C8C22×C311yescharacteristic
138#890—21no—
139#888—21no—
140#878—22no—
141#870C22×C312yescomplemented
142#869C22×C312yescomplemented
143C3×#107—31no—
144C3×#107—31no—
145C3×#107—32no—
146C3×#106—31no—
147C3×#106—31no—
148C3×#106—32no—
149C3×C4⋊C8—32no—
150C3×C4⋊C8—32no—
151C3×#102—32no—
152C3×#102—32no—
153C3×#102—32no—
154C3×#102—32no—
155#832C22×C312yes—
156#832C22×C312yes—
157#832C22×C312yes—
158#832C22×C312yes—
159#808C22×C312yescomplemented
160#808C22×C311yescharacteristic, complemented
161#808C22×C311yescharacteristic, complemented
162#807C22×C312yescomplemented
163#807C22×C311yescharacteristic, complemented
164#807C22×C311yescharacteristic, complemented
165C4⋊(C3⋊C8)C22×C312yescomplemented
166C4⋊(C3⋊C8)C22×C312yescomplemented
167C23×C32—22no—
168C23×C32—24no—
169C23×C32—81no—
170C23×C32—81no—
171C23×C32C2×D411yescharacteristic
172C32×D4—24no—
173C32×D4—22no—
174C32×D4C2×Q814yes—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—82no—
178C2×C32×C4—82no—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×Q812yes—
183C2×C32×C4#4112yes—
184C2×C32×C4C2411yescharacteristic
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—81no—
189C3×Dic6—82no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—22no—
193#544—31no—
194#518C3×D311yescharacteristic
195#478—32no—
196#478—32no—
197#476—32no—
198#474—32no—
199#428—31no—
200#427—31no—
201#424—31no—
202#418—31no—
203C2×#102—31no—
204C24×C3—22no—
205C24×C3—21no—
206C24×C3—21no—
207C2×C3×Q8—62no—
208C2×C3×D4—22no—
209C2×C3×D4—24no—
210C2×C3×D4—22no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—22no—
214C2×C3×D4—24no—
215C2×C3×D4—22no—
216C2×C3×D4Dic614yescomplemented
217C2×C3×D4C3×Q814yescomplemented
218C2×C3×D4C22×D312yes—
219C2×C3×D4C23×C312yes—
220C22×C3×C4—24no—
221C22×C3×C4—24no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—21no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C23×C311yescharacteristic
230C22×Dic3—21no—
231C2×Dic6—22no—
232C3×M16—62no—
233C2×C3×C8—31no—
234C2×C3×C8—32no—
235C2×C3×C8—31no—
236C2×C3×C8—62no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—32no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4#6711yescharacteristic
249C3×C4⋊C4#6711yescharacteristic
250C3×C4⋊C4C3×D411yescharacteristic
251C3×C4⋊C4C3×D411yescharacteristic
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C4⋊C4C22×D311yescharacteristic
254C3×C4⋊C4C23×C311yescharacteristic
255C3×C4⋊C4C23×C311yescharacteristic
256C3×C22⋊C4—22no—
257C3×C22⋊C4—24no—
258C3×C22⋊C4—24no—
259C3×C22⋊C4—21no—
260C3×C22⋊C4—21no—
261C3×C22⋊C4—22no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—22no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4#6712yes—
268C3×C22⋊C4C3×D412yes—
269C3×C42—22no—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42—22no—
273C3×C42—61no—
274C3×C42C22×D312yes—
275C3×C42C23×C312yes—
276#217—21no—
277C4⋊Dic3—22no—
278C4⋊Dic3—21no—
279C4⋊Dic3C23×C311yescharacteristic
280C4⋊Dic3C23×C312yes—
281C4⋊Dic3C23×C311yescharacteristic
282Dic3⋊C4—22no—
283Dic3⋊C4—22no—
284C4×Dic3—21no—
285#208—22no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8C23×C311yescharacteristic
288C2×C3⋊C8C23×C312yes—
289C2×C3⋊C8C23×C311yescharacteristic
290C22×C32—24no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—42no—
294C22×C32—42no—
295C22×C32—84no—
296C22×C32C22⋊Q812yes—
297C22×C32C22×D411yescharacteristic
298C32×C4—22no—
299C32×C4—22no—
300C32×C4—41no—
301C32×C4—41no—
302C32×C4C22⋊Q812yes—
303C32×C4C22×Q811yescharacteristic
304C32×C4C2×#4111yescharacteristic
305C3×Dic3—41no—
306C3×Dic3—42no—
307C3×Dic3—41no—
308C22×D4C2×C3×D311yescharacteristic
309C2×M16—31no—
310C22×C8—31no—
311C4⋊Q8—32no—
312C4⋊Q8—61no—
313#125—32no—
314#125—61no—
315C22⋊Q8—62no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4C2×C3×D312yes—
319C4×D4C2×C3×D312yes—
320#117—31no—
321#117C2×C3×D311yescharacteristic
322#117C2×C3×D311yescharacteristic
323C2×C4⋊C4—31no—
324C2×C22⋊C4—22no—
325#107—31no—
326#107—31no—
327#107—32no—
328#106—31no—
329#106—31no—
330#106—32no—
331C4⋊C8—32no—
332C4⋊C8—32no—
333#102—32no—
334#102—32no—
335#102—32no—
336#102—32no—
337C23×C3—24no—
338C23×C3—28no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—21no—
344C23×C3—81no—
345C23×C3—81no—
346C23×C3—81no—
347C23×C3—81no—
348C23×C3—82no—
349C23×C3—82no—
350C23×C3C2×#6711yescharacteristic
351C23×C3C2×C3×D411yescharacteristic
352C3×Q8—242no—
353C3×D4—28no—
354C3×D4—24no—
355C3×D4—24no—
356C3×D4—24no—
357C3×D4—22no—
358C3×D4—22no—
359C3×D4—24no—
360C3×D4C2×Dic614yes—
361C3×D4C2×C3×Q814yes—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—62no—
377C2×C3×C4—82no—
378C2×C3×C4—82no—
379C2×C3×C4—82no—
380C2×C3×C4—82no—
381C2×C3×C4—84no—
382C2×C3×C4—84no—
383C2×C3×C4—241no—
384C2×C3×C4C2×Dic612yes—
385C2×C3×C4#23512yes—
386C2×C3×C4C2×#6712yes—
387C2×C3×C4C2×#6712yes—
388C2×C3×C4C2×#6711yescharacteristic
389C2×C3×C4C2×C3×D412yes—
390C2×C3×C4C2×C3×D412yes—
391C2×C3×C4C2×C3×D411yescharacteristic
392C2×C3×C4C2×C3×Q812yes—
393C2×C3×C4C3×#4112yes—
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C24×C311yescharacteristic
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—22no—
399C2×Dic3—81no—
400Dic6—82no—
401C3×C8—61no—
402C3×C8—61no—
403C3×C8—62no—
404C3⋊C8—21no—
405C3⋊C8—21no—
406C3⋊C8—22no—
407C2×C32—22no—
408C2×C32—44no—
409C2×C32C2×C22⋊Q811yescharacteristic
410C2×C32#57611yescharacteristic
411C2×C32#57711yescharacteristic
412C24—21no—
413C2×Q8—62no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4C3×Dic614yescomplemented
417C2×D4C22×C3×D312yes—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—61no—
421C22×C4C22×C3×D311yescharacteristic
422M16—62no—
423C2×C8—31no—
424C2×C8—32no—
425C2×C8—31no—
426C2×C8—62no—
427C4⋊C4—32no—
428C4⋊C4—31no—
429C4⋊C4—31no—
430C4⋊C4—61no—
431C4⋊C4—62no—
432C4⋊C4—62no—
433C4⋊C4—62no—
434C4⋊C4C3×#6711yescharacteristic
435C4⋊C4C3×#6711yescharacteristic
436C4⋊C4C22×C3×D311yescharacteristic
437C4⋊C4C22×C3×D311yescharacteristic
438C22⋊C4—21no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—61no—
442C22⋊C4C3×#6712yes—
443C42—21no—
444C42—61no—
445C42C22×C3×D312yes—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—28no—
451C22×C3—24no—
452C22×C3—24no—
453C22×C3—22no—
454C22×C3—21no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—44no—
458C22×C3—44no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—84no—
464C22×C3—84no—
465C22×C3—88no—
466C22×C3#92412yes—
467C22×C3C3×C22⋊Q812yes—
468C22×C3C22×#6711yescharacteristic
469C22×C3C22×C3×D411yescharacteristic
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—22no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—42no—
480C3×C4—42no—
481C3×C4—41no—
482C3×C4—41no—
483C3×C4—41no—
484C3×C4—41no—
485C3×C4—122no—
486C3×C4—121no—
487C3×C4—121no—
488C3×C4#92412yes—
489C3×C4C3×C22⋊Q812yes—
490C3×C4C22×Dic611yescharacteristic
491C3×C4C2×#23511yescharacteristic
492C3×C4C22×C3×Q811yescharacteristic
493C3×C4C2×C3×#4111yescharacteristic
494Dic3—41no—
495Dic3—42no—
496Dic3—41no—
497C32#308111yescharacteristic, complemented, Sylow
498C23—22no—
499C23—24no—
500C23—81no—
501C23—81no—
502C23C2×C3×#6711yescharacteristic
503Q8—242no—
504D4—24no—
505D4—22no—
506D4C2×C3×Dic614yes—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—62no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4—241no—
515C2×C4C2×C3×Dic612yes—
516C2×C4C3×#23512yes—
517C2×C4C2×C3×#6712yes—
518C2×C4C2×C3×#6712yes—
519C2×C4C2×C3×#6711yescharacteristic
520C2×C4C23×C3×D311yescharacteristic
521C8—61no—
522C8—61no—
523C8—62no—
524C2×C3—22no—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—42no—
530C2×C3—48no—
531C2×C3—44no—
532C2×C3—44no—
533C2×C3C2×#92411yescharacteristic
534C2×C3#583511yescharacteristic
535C2×C3#583611yescharacteristic
536C2×C3C2×C3×C22⋊Q811yescharacteristic
537C2×C3C3×#57611yescharacteristic
538C2×C3C3×#57711yescharacteristic
539C22—21no—
540C22—21no—
541C22—24no—
542C22—42no—
543C22—42no—
544C22—84no—
545C22C3×#92412yes—
546C22C22×C3×#6711yescharacteristic
547C4—22no—
548C4—22no—
549C4—41no—
550C4—41no—
551C4—122no—
552C4—121no—
553C4—121no—
554C4C3×#92412yes—
555C4C22×C3×Dic611yescharacteristic
556C4C2×C3×#23511yescharacteristic
557C3—21no—
558C3#8253911yescharacteristic, direct product factor
559C3C3×#308111yescharacteristic, complemented
560C2—22no—
561C2—44no—
562C2C2×C3×#92411yescharacteristic
563C2C3×#583511yescharacteristic
564C2C3×#583611yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#518C2
socleC22×C32C22×D4
prime radicalC22×C32×D4C22
hypercenterC3×#518D3
hypocenterC3C3×#3081
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#518

Complements

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

NH ≅ G/Ntype
2. C3×#5519C2semidirect
5. C3×#5009C2semidirect
6. C3×#5009C2semidirect
7. C3×#5008C2semidirect
8. C3×#5007C2semidirect
9. C3×#4999C2semidirect
10. C3×#4998C2semidirect
11. C3×#4995C2semidirect
13. #82539C3direct (N × H)
29. C3×#870C22semidirect
30. C3×#869C22semidirect
35. C3×#808C22semidirect
36. C3×#808C22semidirect
37. C3×#808C22semidirect
38. C3×#807C22semidirect
39. C3×#807C22semidirect
40. C3×#807C22semidirect
41. C3×C4⋊(C3⋊C8)C22semidirect
42. C3×C4⋊(C3⋊C8)C22semidirect
47. #5519C2×C3semidirect
59. #5009C2×C3semidirect
60. #5009C2×C3semidirect
61. #5008C2×C3semidirect
62. #5007C2×C3semidirect
63. #4999C2×C3semidirect
64. #4998C2×C3semidirect
65. #4995C2×C3semidirect
69. C2×C32×D4Q8semidirect
141. #870C22×C3semidirect
142. #869C22×C3semidirect
159. #808C22×C3semidirect
160. #808C22×C3semidirect
161. #808C22×C3semidirect
162. #807C22×C3semidirect
163. #807C22×C3semidirect
164. #807C22×C3semidirect
165. C4⋊(C3⋊C8)C22×C3semidirect
166. C4⋊(C3⋊C8)C22×C3semidirect
216. C2×C3×D4Dic6semidirect
217. C2×C3×D4C3×Q8semidirect
416. C2×D4C3×Dic6semidirect
497. C32#3081semidirect
558. C3#82539direct (N × H)
559. C3C3×#3081semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
C3×#55192
C3×#52152
C2×C3×#8322
C3×#50092
C3×#50082
C3×#50072
C3×#49992
C3×#49982
C3×#49952
C3×#30813
#825393