Finite Group Databasebeta

← C3×#74681 #11807509

Subgroups — C3×#74681 #11807509

Order 1152.

1247 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#935C211yesmaximal, characteristic
2C32×#386C211yesmaximal, characteristic
3C3×#5221C211yesmaximal, characteristic
4C3×C4×#217C212yesmaximal, complemented
5C3×#4944C212yesmaximal, complemented
6C3×#4944C212yesmaximal, complemented
7C3×Dic3×C22⋊C4C212yesmaximal, complemented
8C3×#4655C212yesmaximal, complemented
9C3×#4649C212yesmaximal, complemented
10C3×#2374—31nomaximal
11#74681C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C2×C32×C22⋊C4C2212yes—
16C2×C32×C22⋊C4C2211yescharacteristic
17C2×C3×#217C2212yes—
18C2×C3×#217C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2211yescharacteristic
21C3×#935C418yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C32×#95C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C2×C3×#123—31no—
35C2×#935C2×C311yescharacteristic
36C3×#390—31no—
37C3×#388—32no—
38C3×#388—32no—
39C3×#387—32no—
40C3×#386—21no—
41C3×#386D311yescharacteristic
42C3×#386C2×C311yescharacteristic
43C3×C4×C4⋊C4—32no—
44C3×C4×C22⋊C4—32no—
45C3×C4×C22⋊C4—32no—
46#5221C2×C311yescharacteristic
47C4×#217C2×C312yescomplemented
48#4944C2×C312yescomplemented
49#4944C2×C312yescomplemented
50Dic3×C22⋊C4C2×C312yescomplemented
51#4655C2×C312yescomplemented
52#4649C2×C312yescomplemented
53C24×C32C2311yescharacteristic
54C24×C32C2311yescharacteristic
55C2×C32×D4—41no—
56C2×C32×D4—41no—
57C2×C32×D4C2×C414yes—
58C22×C32×C4—24no—
59C22×C32×C4—41no—
60C22×C32×C4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C3×Dic3—41no—
64C22×C3×Dic3—41no—
65C22×C3×Dic3C2×C414yescomplemented
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C32×C22⋊C4—24no—
71C32×C22⋊C4—41no—
72C3×#217—24no—
73C3×#217—24no—
74C3×#217C2×C418yes—
75C3×#217C2×C414yescomplemented
76C3×C4⋊Dic3—41no—
77C3×Dic3⋊C4—24no—
78C3×Dic3⋊C4C2×C418yescomplemented
79C3×C4×Dic3—24no—
80C3×C4×Dic3—41no—
81C3×C4×Dic3—42no—
82C3×C4×Dic3—42no—
83#2374—31noSylow
84C22×C3×D4—21no—
85C22×C3×D4C2×D311yescharacteristic
86C22×C3×D4C22×C311yescharacteristic
87C23×C3×C4—21no—
88C23×C3×C4—31no—
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C22×C311yescharacteristic
91C23×Dic3C22×C311yescharacteristic
92C3×#123—38no—
93C2×C3×C4⋊C4—32no—
94C2×C3×C4⋊C4—32no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—32no—
99C2×C3×C22⋊C4—31no—
100C2×C3×C22⋊C4—32no—
101C2×C3×C22⋊C4—32no—
102C2×C3×C22⋊C4C2×D312yes—
103C2×C3×C22⋊C4C2×D311yescharacteristic
104C2×C3×C22⋊C4C22×C312yes—
105C2×C3×C22⋊C4C22×C311yescharacteristic
106C2×C3×C42—32no—
107C2×C3×C42—32no—
108C2×C3×C42—32no—
109C2×C3×C42—31no—
110C2×#217C22×C312yes—
111C2×#217C22×C312yes—
112C2×#217C22×C312yes—
113C2×#217C22×C311yescharacteristic
114#935C3×C418yescomplemented
115C2×C4⋊Dic3C22×C311yescharacteristic
116C2×Dic3⋊C4C22×C312yes—
117C2×Dic3⋊C4C22×C312yes—
118C2×C4×Dic3C22×C312yes—
119C2×C4×Dic3C22×C311yescharacteristic
120C2×C4×Dic3C22×C312yes—
121C2×C4×Dic3C22×C312yes—
122C3×#95—22no—
123C3×#95—32no—
124C3×#95—32no—
125C3×#95—32no—
126C3×#95—32no—
127C3×#95C2×D312yes—
128C3×#95C22×C312yes—
129C3⋊#95C22×C312yes—
130C3⋊#95C22×C312yes—
131C3⋊#95C22×C312yes—
132C3⋊#95C22×C312yes—
133C23×C32—21no—
134C23×C32—21no—
135C23×C32—22no—
136C23×C32—22no—
137C23×C32—22no—
138C23×C32—22no—
139C23×C32—21no—
140C23×C32—21no—
141C23×C32C22×C412yes—
142C23×C32C22×C412yes—
143C23×C32C2411yescharacteristic
144C32×D4—44no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—44no—
153C2×C32×C4C22×C412yes—
154C2×C32×C4#4114yes—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—44no—
165C2×C3×Dic3C22×C414yes—
166C2×C3×Dic3C22×C414yes—
167C2×C3×Dic3#4114yes—
168C2×#123—31no—
169#390—31no—
170#388—32no—
171#388—32no—
172#387—32no—
173#386C3×D311yescharacteristic
174C4×C4⋊C4—32no—
175C4×C22⋊C4—32no—
176C4×C22⋊C4—32no—
177C24×C3—21no—
178C24×C3—21no—
179C24×C3C22×D311yescharacteristic
180C24×C3C22×D311yescharacteristic
181C24×C3C23×C311yescharacteristic
182C24×C3C23×C311yescharacteristic
183C2×C3×D4—24no—
184C2×C3×D4—41no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—42no—
189C2×C3×D4—42no—
190C2×C3×D4C4×D314yes—
191C2×C3×D4C2×C3×C414yes—
192C22×C3×C4—24no—
193C22×C3×C4—24no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—34no—
201C22×C3×C4—32no—
202C22×C3×C4—44no—
203C22×C3×C4—41no—
204C22×C3×C4—41no—
205C22×C3×C4—42no—
206C22×C3×C4—121no—
207C22×C3×C4—121no—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D312yes—
211C22×C3×C4C23×C312yes—
212C22×C3×C4C23×C311yescharacteristic
213C22×C3×C4C23×C312yes—
214C22×Dic3—41no—
215C22×Dic3—41no—
216C22×Dic3C2×C3×C414yescomplemented
217C22×Dic3C23×C312yes—
218C22×Dic3C23×C312yes—
219C22×Dic3C23×C312yes—
220C22×Dic3C23×C312yes—
221C3×C4⋊C4—38no—
222C3×C4⋊C4—64no—
223C3×C4⋊C4—121no—
224C3×C22⋊C4—24no—
225C3×C22⋊C4—24no—
226C3×C22⋊C4—38no—
227C3×C22⋊C4—34no—
228C3×C22⋊C4—44no—
229C3×C22⋊C4—41no—
230C3×C22⋊C4—41no—
231C3×C22⋊C4—42no—
232C3×C22⋊C4—64no—
233C3×C22⋊C4—64no—
234C3×C42—64no—
235C3×C42—122no—
236C3×C42—121no—
237C3×C42—122no—
238#217—24no—
239#217—24no—
240#217C2×C3×C418yes—
241#217C2×C3×C414yescomplemented
242C4⋊Dic3—41no—
243Dic3⋊C4—24no—
244Dic3⋊C4C2×C3×C418yescomplemented
245C4×Dic3—24no—
246C4×Dic3—41no—
247C4×Dic3—42no—
248C4×Dic3—42no—
249C22×C32—22no—
250C22×C32—24no—
251C22×C32—24no—
252C22×C32—22no—
253C22×C32—41no—
254C22×C32—42no—
255C22×C32—41no—
256C22×C32—41no—
257C22×C32—42no—
258C22×C32—41no—
259C22×C32C23×C411yescharacteristic
260C22×C32C2×#4112yes—
261C22×C32C2×#4112yes—
262C22×C32H(5,𝔽2)11yescharacteristic
263C22×C32H(5,𝔽2)11yescharacteristic
264C32×C4—22no—
265C32×C4—24no—
266C32×C4—42no—
267C3×Dic3—24no—
268C3×Dic3—24no—
269C3×Dic3—24no—
270C3×Dic3—42no—
271C22×D4C2×C3×D311yescharacteristic
272C23×C4—31no—
273C23×C4C2×C3×D311yescharacteristic
274#123—38no—
275C2×C4⋊C4—32no—
276C2×C4⋊C4—32no—
277C2×C4⋊C4—31no—
278C2×C22⋊C4—32no—
279C2×C22⋊C4—31no—
280C2×C22⋊C4—32no—
281C2×C22⋊C4—32no—
282C2×C22⋊C4C2×C3×D312yes—
283C2×C22⋊C4C2×C3×D311yescharacteristic
284C2×C42—32no—
285C2×C42—32no—
286C2×C42—32no—
287C2×C42—31no—
288#95—32no—
289#95—32no—
290#95—32no—
291#95—32no—
292#95C2×C3×D312yes—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—42no—
320C23×C3C2×C4×D312yes—
321C23×C3C2×C4×D312yes—
322C23×C3C22×C3×C412yes—
323C23×C3C22×C3×C412yes—
324C23×C3C23×D311yescharacteristic
325C23×C3C24×C311yescharacteristic
326C3×D4—44no—
327C3×D4—44no—
328C3×D4—48no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—24no—
345C2×C3×C4—34no—
346C2×C3×C4—34no—
347C2×C3×C4—34no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—44no—
356C2×C3×C4—44no—
357C2×C3×C4—48no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—124no—
368C2×C3×C4C2×C4×D312yes—
369C2×C3×C4#23714yes—
370C2×C3×C4C22×C3×C412yes—
371C2×C3×C4C3×#4114yes—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—44no—
382C2×Dic3C22×C3×C414yes—
383C2×Dic3C22×C3×C414yes—
384C2×Dic3C3×#4114yes—
385C2×C32—42no—
386C2×C32—42no—
387C2×C32C4×#4112yes—
388C2×C32#51811yescharacteristic
389C2×C32#55111yescharacteristic
390C2×C32#55312yes—
391C2×C32#55911yescharacteristic
392C24C22×C3×D311yescharacteristic
393C24C22×C3×D311yescharacteristic
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C3×C4×D314yes—
397C22×C4—24no—
398C22×C4—32no—
399C22×C4—32no—
400C22×C4—32no—
401C22×C4—34no—
402C22×C4—32no—
403C22×C4—41no—
404C22×C4—121no—
405C22×C4—121no—
406C22×C4C22×C3×D312yes—
407C22×C4C22×C3×D311yescharacteristic
408C22×C4C22×C3×D312yes—
409C4⋊C4—38no—
410C4⋊C4—64no—
411C4⋊C4—121no—
412C22⋊C4—24no—
413C22⋊C4—38no—
414C22⋊C4—34no—
415C22⋊C4—41no—
416C22⋊C4—64no—
417C22⋊C4—64no—
418C42—64no—
419C42—122no—
420C42—121no—
421C42—122no—
422C22×C3—24no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—24no—
426C22×C3—24no—
427C22×C3—24no—
428C22×C3—24no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—44no—
437C22×C3—42no—
438C22×C3—44no—
439C22×C3—42no—
440C22×C3—44no—
441C22×C3—42no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—81no—
455C22×C3—82no—
456C22×C3—81no—
457C22×C3C22×C4×D311yescharacteristic
458C22×C3C2×#23712yes—
459C22×C3#100411yescharacteristic
460C22×C3#100411yescharacteristic
461C22×C3D3×#4112yes—
462C22×C3C23×C3×C411yescharacteristic
463C22×C3C2×C3×#4112yes—
464C22×C3C2×C3×#4112yes—
465C22×C3C3×H(5,𝔽2)11yescharacteristic
466C22×C3C3×H(5,𝔽2)11yescharacteristic
467C3×C4—22no—
468C3×C4—24no—
469C3×C4—22no—
470C3×C4—24no—
471C3×C4—44no—
472C3×C4—42no—
473C3×C4—42no—
474C3×C4—42no—
475C3×C4—64no—
476C3×C4—64no—
477C3×C4—64no—
478C3×C4—82no—
479C3×C4—122no—
480Dic3—24no—
481Dic3—24no—
482Dic3—24no—
483Dic3—42no—
484C32#237411yescharacteristic, complemented, Sylow
485C23—22no—
486C23—22no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—22no—
492C23—22no—
493C23C2×C3×C4×D312yes—
494C23C2×C3×C4×D312yes—
495C23C23×C3×D311yescharacteristic
496D4—44no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—34no—
505C2×C4—34no—
506C2×C4—34no—
507C2×C4—44no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—124no—
518C2×C4C2×C3×C4×D312yes—
519C2×C4C3×#23714yes—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—22no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—44no—
526C2×C3—42no—
527C2×C3—42no—
528C2×C3—42no—
529C2×C3—42no—
530C2×C3—82no—
531C2×C3#548611yescharacteristic
532C2×C3C4×#23712yes—
533C2×C3#558711yescharacteristic
534C2×C3#561412yes—
535C2×C3#566411yescharacteristic
536C2×C3C3×C4×#4112yes—
537C2×C3C3×#51811yescharacteristic
538C2×C3C3×#55111yescharacteristic
539C2×C3C3×#55312yes—
540C2×C3C3×#55911yescharacteristic
541C22—24no—
542C22—24no—
543C22—22no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—42no—
549C22—41no—
550C22—41no—
551C22C22×C3×C4×D311yescharacteristic
552C22C2×C3×#23712yes—
553C22C3×#100411yescharacteristic
554C22C3×#100411yescharacteristic
555C22C3×D3×#4112yes—
556C4—24no—
557C4—22no—
558C4—42no—
559C4—64no—
560C4—64no—
561C4—64no—
562C4—122no—
563C3—21no—
564C3#7468111yescharacteristic, direct product factor
565C3C3×#237411yescharacteristic, complemented
566C2—42no—
567C2—42no—
568C2C3×#548611yescharacteristic
569C2C3×C4×#23712yes—
570C2C3×#558711yescharacteristic
571C2C3×#561412yes—
572C2C3×#566411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
prime radicalC22×C32×D4C22
cosocleC23×C3C24×C3
hypercenterC3×#386D3
hypocenterC3C3×#2374
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
4. C3×C4×#217C2semidirect
5. C3×#4944C2semidirect
6. C3×#4944C2semidirect
7. C3×Dic3×C22⋊C4C2semidirect
8. C3×#4655C2semidirect
9. C3×#4649C2semidirect
11. #74681C3direct (N × H)
21. C3×#935C4semidirect
47. C4×#217C2×C3semidirect
48. #4944C2×C3semidirect
49. #4944C2×C3semidirect
50. Dic3×C22⋊C4C2×C3semidirect
51. #4655C2×C3semidirect
52. #4649C2×C3semidirect
65. C22×C3×Dic3C2×C4semidirect
75. C3×#217C2×C4semidirect
78. C3×Dic3⋊C4C2×C4semidirect
114. #935C3×C4semidirect
216. C22×Dic3C2×C3×C4semidirect
241. #217C2×C3×C4semidirect
244. Dic3⋊C4C2×C3×C4semidirect
484. C32#2374semidirect
564. C3#74681direct (N × H)
565. C3C3×#2374semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9352
C32×#3862
C3×#52212
C3×C4×#2172
C3×#49442
C3×Dic3×C22⋊C42
C3×#46552
C3×#46492
C3×#23743
#746813