Finite Group Databasebeta

← C2×C3×#4755 #11867962

Subgroups — C2×C3×#4755 #11867962

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#216C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic
3C2×C3×#909C211yesmaximal, characteristic
4C2×C3×#907C211yesmaximal, characteristic
5C2×C32×#101C211yesmaximal, characteristic, complemented
6C2×C3×#824C211yesmaximal, characteristic, complemented
7C2×C3×#822C211yesmaximal, characteristic, complemented
8C3×#4755C218yesmaximal, direct product factor
9C2×C3×#473—31nomaximal
10C2×#4755C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×C3×#216—21no—
17C2×C3×#216—21no—
18C2×C3×#216—21no—
19C2×C3×#216—22no—
20C2×C3×#216C2214yescomplemented
21C3×#942—22no—
22C3×#942C2214yes—
23C2×C3×#215—21no—
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#909—22no—
27C3×#909C2214yes—
28C3×#907—22no—
29C3×#907C2214yes—
30C2×C3×Dic12—21no—
31C2×C3×#204—21no—
32C2×C3×ΓL(1,𝔽25)—21no—
33C2×C3×D3×C8—21no—
34C32×#101C2214yescomplemented
35C3×#824C2214yescomplemented
36C3×#822C2214yescomplemented
37C2×C3×#137—31no—
38C2×C3×#137—31no—
39C22×C3×Q16—31no—
40C2×C3×#131—31no—
41C22×#216C2×C311yescharacteristic, complemented
42C2×#942C2×C311yescharacteristic
43C2×#909C2×C311yescharacteristic
44C2×#907C2×C311yescharacteristic
45C3×#473—38no—
46C2×C3×#108—31no—
47C2×C3×#101—21no—
48C2×C3×#101—31no—
49C2×C3×#101D311yescharacteristic, complemented
50C2×C3×#101C2×C311yescharacteristic, complemented
51C2×#824C2×C311yescharacteristic, complemented
52C2×#822C2×C311yescharacteristic, complemented
53#4755C2×C318yesdirect product factor
54C2×C32×Q8—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8—21no—
57C2×C32×Q8—21no—
58C2×C32×Q8—21no—
59C2×C32×Q8C2312yes—
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C2×C3×#67—21no—
63C22×C3×Dic3—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235D412yes—
67C3×#235C2312yes—
68C2×C3×D12D411yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6D411yescharacteristic
76C2×C3×Dic6C2312yes—
77C32×M16—21no—
78C32×M16—21no—
79C32×M16C2312yes—
80C32×M16C2312yes—
81C2×C32×C8—21no—
82C2×C32×C8—21no—
83C3×#216—24no—
84C3×#216—24no—
85C3×#216—24no—
86C3×#215—24no—
87C3×#208—21no—
88C3×#208C2312yes—
89C2×C3×C3⋊C8—21no—
90C2×C3×C3⋊C8D411yescharacteristic
91C2×C3×C3⋊C8D411yescharacteristic
92C2×C3×C3⋊C8D412yes—
93C2×C3×C3⋊C8C2312yes—
94C3×Dic12—24no—
95C3×#204—24no—
96C3×ΓL(1,𝔽25)—24no—
97C3×D3×C8—24no—
98C2×#473—31noSylow
99C2×C3×#41—31no—
100C22×C3×Q8—21no—
101C22×C3×Q8—31no—
102C22×C3×Q8C2×D311yescharacteristic
103C22×C3×Q8C22×C311yescharacteristic
104C2×#235C22×C311yescharacteristic
105C22×Dic6C22×C311yescharacteristic
106C3×#137—34no—
107C3×#137—34no—
108C3×#137—62no—
109C3×#137—62no—
110C2×C3×Q16—34no—
111C2×C3×Q16—61no—
112C2×C3×Q16—61no—
113C2×C3×Q16—61no—
114C2×C3×Q16—62no—
115C2×C3×Q16—61no—
116C2×C3×SD16—61no—
117C2×C3×SD16—61no—
118C3×#131—34no—
119C3×#131—62no—
120C2×C3×M16—21no—
121C2×C3×M16—21no—
122C2×C3×M16—31no—
123C2×C3×M16—61no—
124C2×C3×M16C2×D311yescharacteristic
125C2×C3×M16C2×D311yescharacteristic
126C2×C3×M16C22×C311yescharacteristic
127C2×C3×M16C22×C311yescharacteristic
128C22×C3×C8—31no—
129C22×C3×C8—61no—
130C2×#216—21no—
131C2×#216—21no—
132C2×#216—21no—
133C2×#216—22no—
134C2×#216C22×C314yescomplemented
135#942—22no—
136#942C22×C314yes—
137C2×#215—21no—
138C2×#208C22×C311yescharacteristic
139C22×C3⋊C8C22×C311yescharacteristic
140#909—22no—
141#909C22×C314yes—
142#907—22no—
143#907C22×C314yes—
144C2×Dic12—21no—
145C2×#204—21no—
146C2×ΓL(1,𝔽25)—21no—
147C2×D3×C8—21no—
148C3×#108—34no—
149C3×#101—24no—
150C3×#101—34no—
151C3×#101C2×D314yescomplemented
152C3×#101C22×C314yescomplemented
153#824C22×C314yescomplemented
154#822C22×C314yescomplemented
155C23×C32#4111yescharacteristic
156C22×C3×D3—21no—
157C32×Q8—22no—
158C32×Q8—22no—
159C32×Q8—41no—
160C32×Q8—41no—
161C2×C32×C4—22no—
162C2×C32×C4—41no—
163C2×C32×C4—41no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4#4111yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C3×#67—22no—
171C3×#67—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—41no—
175C2×C3×Dic3—41no—
176C3×D12—21no—
177C3×D12C2×D412yes—
178C3×C4×D3—22no—
179C3×C4×D3—22no—
180C3×Dic6—21no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—41no—
184C3×Dic6—41no—
185C3×Dic6C2×D412yes—
186C32×C8—22no—
187C32×C8—22no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8C2×D412yes—
190C3×C3⋊C8C2×D412yes—
191C2×#137—31no—
192C2×#137—31no—
193C22×Q16—31no—
194C2×#131—31no—
195#473—38no—
196C2×#108—31no—
197C2×#101—31no—
198C2×#101C3×D311yescharacteristic, complemented
199C3×#41—32no—
200C3×#41—32no—
201C3×#41—61no—
202C3×#41—61no—
203C2×C3×Q8—22no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—22no—
215C2×C3×Q8—31no—
216C2×C3×Q8—32no—
217C2×C3×Q8—41no—
218C2×C3×Q8—41no—
219C2×C3×Q8—41no—
220C2×C3×Q8—41no—
221C2×C3×Q8—61no—
222C2×C3×Q8—61no—
223C2×C3×Q8—61no—
224C2×C3×Q8—61no—
225C2×C3×Q8—61no—
226C2×C3×Q8C22×D312yes—
227C2×C3×Q8C23×C312yes—
228C2×C3×D4—31no—
229C2×C3×D4—61no—
230C22×C3×C4—22no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C23×C311yescharacteristic
238C2×#67—21no—
239C22×Dic3—21no—
240#235—21no—
241#235—21no—
242#235C3×D412yes—
243#235C23×C312yes—
244C2×D12C3×D411yescharacteristic
245C2×C4×D3—21no—
246C2×Dic6—21no—
247C2×Dic6—21no—
248C2×Dic6—21no—
249C2×Dic6—21no—
250C2×Dic6—21no—
251C2×Dic6C3×D411yescharacteristic
252C2×Dic6C23×C312yes—
253C3×Q16—64no—
254C3×Q16—64no—
255C3×Q16—64no—
256C3×Q16—64no—
257C3×SD16—64no—
258C3×SD16—64no—
259C3×M16—21no—
260C3×M16—21no—
261C3×M16—21no—
262C3×M16—21no—
263C3×M16—22no—
264C3×M16—22no—
265C3×M16—32no—
266C3×M16—41no—
267C3×M16—41no—
268C3×M16—64no—
269C3×M16—61no—
270C3×M16C22×D312yes—
271C3×M16C22×D312yes—
272C3×M16C23×C312yes—
273C3×M16C23×C312yes—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—31no—
279C2×C3×C8—31no—
280C2×C3×C8—32no—
281C2×C3×C8—32no—
282C2×C3×C8—41no—
283C2×C3×C8—41no—
284C2×C3×C8—64no—
285C2×C3×C8—61no—
286#216—24no—
287#216—24no—
288#216—24no—
289#215—24no—
290#208—21no—
291#208C23×C312yes—
292C2×C3⋊C8—21no—
293C2×C3⋊C8C3×D411yescharacteristic
294C2×C3⋊C8C3×D411yescharacteristic
295C2×C3⋊C8C3×D412yes—
296C2×C3⋊C8C23×C312yes—
297Dic12—24no—
298#204—24no—
299ΓL(1,𝔽25)—24no—
300D3×C8—24no—
301C22×C32—22no—
302C22×C32#12111yescharacteristic
303C22×C32#12111yescharacteristic
304C22×C32C2×#4111yescharacteristic
305C2×C3×D3—22no—
306C2×C3×D3—42no—
307C32×C4—42no—
308C32×C4#12111yescharacteristic
309C32×C4#12111yescharacteristic
310C32×C4C22×D411yescharacteristic
311C32×C4C22×D411yescharacteristic
312C3×Dic3—22no—
313C3×Dic3—42no—
314C2×#41—31no—
315C22×Q8—31no—
316C22×Q8C2×C3×D311yescharacteristic
317#137—34no—
318#137—34no—
319#137—62no—
320#137—62no—
321C2×Q16—34no—
322C2×Q16—61no—
323C2×Q16—61no—
324C2×Q16—61no—
325C2×Q16—62no—
326C2×Q16—61no—
327C2×SD16—61no—
328C2×SD16—61no—
329#131—34no—
330#131—62no—
331C2×M16—31no—
332C2×M16—61no—
333C2×M16C2×C3×D311yescharacteristic
334C2×M16C2×C3×D311yescharacteristic
335C22×C8—31no—
336C22×C8—61no—
337#108—34no—
338#101—34no—
339#101C2×C3×D314yescomplemented
340C23×C3—21no—
341C23×C3—61no—
342C23×C3#23511yescharacteristic
343C23×C3C3×#4111yescharacteristic
344C22×D3—21no—
345C3×Q8—22no—
346C3×Q8—22no—
347C3×Q8—22no—
348C3×Q8—22no—
349C3×Q8—32no—
350C3×Q8—42no—
351C3×Q8—42no—
352C3×Q8—42no—
353C3×Q8—42no—
354C3×Q8—41no—
355C3×Q8—41no—
356C3×Q8—41no—
357C3×Q8—41no—
358C3×Q8—61no—
359C3×Q8—62no—
360C3×Q8—62no—
361C3×Q8—121no—
362C3×Q8—121no—
363C3×D4—32no—
364C3×D4—62no—
365C3×D4—62no—
366C3×D4—61no—
367C2×C3×C4—24no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—61no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—121no—
387C2×C3×C4—121no—
388C2×C3×C4#23511yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4C2×C3×D411yescharacteristic
394C2×C3×C4C2×C3×D411yescharacteristic
395C2×C3×C4C2×C3×D411yescharacteristic
396C2×C3×C4C2×C3×D411yescharacteristic
397C2×C3×C4C3×#4111yescharacteristic
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C24×C311yescharacteristic
400#67—22no—
401#67—22no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—41no—
405C2×Dic3—41no—
406D12—21no—
407D12C2×C3×D412yes—
408C4×D3—22no—
409C4×D3—22no—
410Dic6—21no—
411Dic6—22no—
412Dic6—22no—
413Dic6—41no—
414Dic6—41no—
415Dic6C2×C3×D412yes—
416C3×C8—22no—
417C3×C8—22no—
418C3×C8—22no—
419C3×C8—22no—
420C3×C8—32no—
421C3×C8—32no—
422C3×C8—42no—
423C3×C8—42no—
424C3×C8—62no—
425C3⋊C8—22no—
426C3⋊C8C2×C3×D412yes—
427C3⋊C8C2×C3×D412yes—
428C2×C32—21no—
429C2×C32—21no—
430C2×C32#47312yescomplemented
431C2×C32C2×#12111yescharacteristic
432C3×D3—42no—
433#41—32no—
434#41—32no—
435#41—61no—
436#41—61no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—32no—
443C2×Q8—31no—
444C2×Q8—61no—
445C2×Q8—61no—
446C2×Q8—61no—
447C2×Q8—61no—
448C2×Q8—61no—
449C2×Q8C22×C3×D312yes—
450C2×D4—31no—
451C2×D4—61no—
452C22×C4—21no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4C22×C3×D311yescharacteristic
456Q16—64no—
457Q16—64no—
458Q16—64no—
459Q16—64no—
460SD16—64no—
461SD16—64no—
462M16—21no—
463M16—21no—
464M16—32no—
465M16—64no—
466M16—61no—
467M16C22×C3×D312yes—
468M16C22×C3×D312yes—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—32no—
472C2×C8—31no—
473C2×C8—31no—
474C2×C8—32no—
475C2×C8—64no—
476C2×C8—61no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—42no—
483C22×C3—62no—
484C22×C3—122no—
485C22×C3#88411yescharacteristic
486C22×C3#88411yescharacteristic
487C22×C3C3×#12111yescharacteristic
488C22×C3C3×#12111yescharacteristic
489C22×C3C2×#23511yescharacteristic
490C22×C3C2×C3×#4111yescharacteristic
491C2×D3—22no—
492C2×D3—42no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—44no—
498C3×C4—42no—
499C3×C4—42no—
500C3×C4—62no—
501C3×C4—122no—
502C3×C4#88411yescharacteristic
503C3×C4#88411yescharacteristic
504C3×C4C3×#12111yescharacteristic
505C3×C4C3×#12111yescharacteristic
506C3×C4C2×D3×D411yescharacteristic
507C3×C4C2×D3×D411yescharacteristic
508C3×C4C22×C3×D411yescharacteristic
509C3×C4C22×C3×D411yescharacteristic
510Dic3—22no—
511Dic3—42no—
512C32C2×#47311yescharacteristic, complemented, Sylow
513C23—61no—
514C23C3×#23511yescharacteristic
515Q8—22no—
516Q8—22no—
517Q8—32no—
518Q8—41no—
519Q8—41no—
520Q8—61no—
521Q8—62no—
522Q8—62no—
523Q8—121no—
524Q8—121no—
525D4—32no—
526D4—62no—
527D4—62no—
528D4—61no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—61no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—121no—
537C2×C4—121no—
538C2×C4C3×#23511yescharacteristic
539C2×C4C3×D3×D411yescharacteristic
540C2×C4C3×D3×D411yescharacteristic
541C2×C4C3×D3×D411yescharacteristic
542C2×C4C3×D3×D411yescharacteristic
543C2×C4C23×C3×D311yescharacteristic
544C8—22no—
545C8—22no—
546C8—32no—
547C8—32no—
548C8—62no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—22no—
555C2×C3—41no—
556C2×C3—41no—
557C2×C3—122no—
558C2×C3#475512yesdirect product factor
559C2×C3C3×#47312yescomplemented
560C2×C3C2×#88411yescharacteristic
561C2×C3C2×C3×#12111yescharacteristic
562D3—42no—
563C22—22no—
564C22—62no—
565C22—122no—
566C22C3×#88411yescharacteristic
567C22C3×#88411yescharacteristic
568C22C2×C3×#23511yescharacteristic
569C4—42no—
570C4—62no—
571C4—122no—
572C4C3×#88411yescharacteristic
573C4C3×#88411yescharacteristic
574C4C2×C3×D3×D411yescharacteristic
575C4C2×C3×D3×D411yescharacteristic
576C3—21no—
577C3C2×#475511yescharacteristic, direct product factor
578C3C2×C3×#47311yescharacteristic, complemented
579C2—21no—
580C2—21no—
581C2—122no—
582C2C3×#475512yesdirect product factor
583C2C2×C3×#88411yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#101C2
socleC22×C32#121
prime radicalC2×C3×#235C22
hypercenterC2×C3×#101D3
hypocenterC3C2×C3×#473
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#101

Complements

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

NH ≅ G/Ntype
1. C22×C3×#216C2semidirect
5. C2×C32×#101C2semidirect
6. C2×C3×#824C2semidirect
7. C2×C3×#822C2semidirect
8. C3×#4755C2direct (N × H)
10. C2×#4755C3direct (N × H)
20. C2×C3×#216C22semidirect
34. C32×#101C22semidirect
35. C3×#824C22semidirect
36. C3×#822C22semidirect
41. C22×#216C2×C3semidirect
49. C2×C3×#101D3semidirect
50. C2×C3×#101C2×C3semidirect
51. C2×#824C2×C3semidirect
52. C2×#822C2×C3semidirect
53. #4755C2×C3direct (N × H)
134. C2×#216C22×C3semidirect
151. C3×#101C2×D3semidirect
152. C3×#101C22×C3semidirect
153. #824C22×C3semidirect
154. #822C22×C3semidirect
198. C2×#101C3×D3semidirect
339. #101C2×C3×D3semidirect
430. C2×C32#473semidirect
512. C32C2×#473semidirect
558. C2×C3#4755direct (N × H)
559. C2×C3C3×#473semidirect
577. C3C2×#4755direct (N × H)
578. C3C2×C3×#473semidirect
582. C2C3×#4755direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2162
C2×C3×#9422
C2×C3×#9092
C2×C3×#9072
C2×C32×#1012
C2×C3×#8242
C2×C3×#8222
C3×#47552
C2×C3×#4733
C2×#47553