Finite Group Databasebeta

← C2×C3×#4802 #11857854

Subgroups — C2×C3×#4802 #11857854

Order 1152.

1585 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic
2C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic
3C2×C3×#892C211yesmaximal, characteristic
4C2×C32×#103C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×C3×#810C211yesmaximal, characteristic, complemented
8C3×#4802C218yesmaximal, direct product factor
9C2×C3×#419—31nomaximal
10C2×#4802C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C2×C3×D3×Q8—24no—
13C2×C3×D3×Q8—22no—
14C2×C3×D3×Q8C418yescomplemented
15C2×C3×D3×Q8C2214yes—
16C22×C3×C4×D3—21no—
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6—21no—
19C22×C3×Dic6C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)—24no—
27C2×C3×ΓL(1,𝔽25)C2214yes—
28C3×#892—22no—
29C3×#892C2214yes—
30C32×#103C2214yescomplemented
31C3×#835C2214yescomplemented
32C3×#816C2214yescomplemented
33C3×#810C2214yescomplemented
34C23×C3×Q8—31no—
35C22×D3×Q8C2×C311yescharacteristic
36C22×C3×M16—31no—
37C2×C3×#117—31no—
38C22×ΓL(1,𝔽25)C2×C311yescharacteristic
39C2×#892C2×C311yescharacteristic
40C3×#419—38no—
41C2×C3×#103—21no—
42C2×C3×#103—31no—
43C2×C3×#103—31no—
44C2×C3×#103—31no—
45C2×C3×#103D311yescharacteristic, complemented
46C2×C3×#103C2×C311yescharacteristic, complemented
47C2×#835C2×C311yescharacteristic, complemented
48C2×#816C2×C311yescharacteristic, complemented
49C2×#810C2×C311yescharacteristic, complemented
50#4802C2×C318yesdirect product factor
51C23×C3×D3D411yescharacteristic
52C2×C32×Q8—22no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2×C414yes—
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C3×D3×Q8—216no—
63C3×D3×Q8—28no—
64C3×D3×Q8C2×C4116yescomplemented
65C2×C3×C4×D3—28no—
66C2×C3×C4×D3—24no—
67C2×C3×C4×D3C2×C414yes—
68C2×C3×C4×D3D412yes—
69C2×C3×C4×D3D414yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—28no—
74C2×C3×Dic6—24no—
75C2×C3×Dic6C2×C414yes—
76C2×C3×Dic6C2312yes—
77C2×C32×C8—22no—
78C2×C32×C8C2312yes—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yes—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3—24no—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8C2312yes—
87C3×ΓL(1,𝔽25)—28no—
88C2×#419—31noSylow
89C22×C3×Q8—21no—
90C22×C3×Q8—38no—
91C22×C3×Q8—34no—
92C22×C3×Q8—31no—
93C22×C3×Q8—61no—
94C22×C3×Q8—62no—
95C22×C3×Q8—64no—
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×Q8C22×C311yescharacteristic
98C23×C3×C4—31no—
99C23×C3×C4—61no—
100C2×D3×Q8—24no—
101C2×D3×Q8—22no—
102C2×D3×Q8C3×C418yescomplemented
103C2×D3×Q8C22×C314yes—
104C22×C4×D3—21no—
105C22×C4×D3C22×C311yescharacteristic
106C22×Dic6—21no—
107C22×Dic6C22×C311yescharacteristic
108C2×C3×M16—34no—
109C2×C3×M16—64no—
110C22×C3×C8—21no—
111C22×C3×C8—31no—
112C22×C3×C8C2×D311yescharacteristic
113C22×C3×C8C22×C311yescharacteristic
114C3×#117—34no—
115C3×#117—62no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C3×C4⋊C4C22×C311yescharacteristic
120C2×C3×C22⋊C4—61no—
121C2×C3×C42—61no—
122C2×(C2×D3)⋊C4—21no—
123C2×C4⋊Dic3C22×C311yescharacteristic
124C2×C4×Dic3—21no—
125C22×C3⋊C8C22×C311yescharacteristic
126C2×ΓL(1,𝔽25)—24no—
127C2×ΓL(1,𝔽25)C22×C314yes—
128#892—22no—
129#892C22×C314yes—
130C3×#103—24no—
131C3×#103—34no—
132C3×#103—34no—
133C3×#103—34no—
134C3×#103C2×D314yescomplemented
135C3×#103C22×C314yescomplemented
136#835C22×C314yescomplemented
137#816C22×C314yescomplemented
138#810C22×C314yescomplemented
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3C22⋊C414yes—
143C22×C3×D3C2×D412yes—
144C32×Q8—24no—
145C32×Q8—22no—
146C32×Q8C22×C414yes—
147C2×C32×C4—24no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—42no—
151C2×C32×C4C22×C412yes—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2411yescharacteristic
155C2×C3×Dic3—24no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C22⋊C414yes—
160C2×C3×Dic3C2×D412yes—
161C3×C4×D3—216no—
162C3×C4×D3C22⋊C418yes—
163C3×C4×D3C22×C414yes—
164C3×C4×D3C2×D414yes—
165C3×Dic6—24no—
166C3×Dic6—22no—
167C3×Dic6—216no—
168C3×Dic6C22×C414yes—
169C32×C8—22no—
170C3×C3⋊C8—22no—
171C23×Q8—31no—
172C22×M16—31no—
173C2×#117—31no—
174#419—38no—
175C2×#103—31no—
176C2×#103—31no—
177C2×#103—31no—
178C2×#103C3×D311yescharacteristic, complemented
179C24×C3—31no—
180C23×D3C3×D411yescharacteristic
181C2×C3×Q8—22no—
182C2×C3×Q8—21no—
183C2×C3×Q8—22no—
184C2×C3×Q8—21no—
185C2×C3×Q8—24no—
186C2×C3×Q8—22no—
187C2×C3×Q8—316no—
188C2×C3×Q8—34no—
189C2×C3×Q8—32no—
190C2×C3×Q8—41no—
191C2×C3×Q8—42no—
192C2×C3×Q8—68no—
193C2×C3×Q8—64no—
194C2×C3×Q8—616no—
195C2×C3×Q8—68no—
196C2×C3×Q8—62no—
197C2×C3×Q8—61no—
198C2×C3×Q8C4×D314yes—
199C2×C3×Q8C2×C3×C414yes—
200C2×C3×Q8C22×D312yes—
201C2×C3×Q8C23×C312yes—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—31no—
208C22×C3×C4—34no—
209C22×C3×C4—32no—
210C22×C3×C4—34no—
211C22×C3×C4—32no—
212C22×C3×C4—41no—
213C22×C3×C4—41no—
214C22×C3×C4—68no—
215C22×C3×C4—64no—
216C22×C3×C4—61no—
217C22×C3×C4—61no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C23×C311yescharacteristic
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3C3×D411yescharacteristic
223D3×Q8—216no—
224D3×Q8—28no—
225D3×Q8C2×C3×C4116yescomplemented
226C2×C4×D3—28no—
227C2×C4×D3—24no—
228C2×C4×D3C2×C3×C414yes—
229C2×C4×D3C3×D412yes—
230C2×C4×D3C3×D414yes—
231C2×C4×D3C23×C312yes—
232C2×Dic6—21no—
233C2×Dic6—22no—
234C2×Dic6—28no—
235C2×Dic6—24no—
236C2×Dic6C2×C3×C414yes—
237C2×Dic6C23×C312yes—
238C3×M16—68no—
239C2×C3×C8—22no—
240C2×C3×C8—22no—
241C2×C3×C8—22no—
242C2×C3×C8—32no—
243C2×C3×C8—42no—
244C2×C3×C8—62no—
245C2×C3×C8C22×D312yes—
246C2×C3×C8C23×C312yes—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—41no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4C22×D312yes—
254C3×C4⋊C4C23×C312yes—
255C3×C22⋊C4—64no—
256C3×C42—64no—
257(C2×D3)⋊C4—24no—
258C4⋊Dic3—21no—
259C4⋊Dic3C23×C312yes—
260C4×Dic3—24no—
261C2×C3⋊C8—22no—
262C2×C3⋊C8C23×C312yes—
263ΓL(1,𝔽25)—28no—
264C22×C32C2×C22⋊C412yes—
265C22×C32#13712yes—
266C22×C32#13712yes—
267C22×C32C22×D411yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—28no—
271C2×C3×D3C2×C22⋊C414yes—
272C32×C4—24no—
273C32×C4—42no—
274C32×C4C2×C22⋊C412yes—
275C32×C4C23×C411yescharacteristic
276C32×C4C22×D411yescharacteristic
277C3×Dic3—24no—
278C3×Dic3—42no—
279C3×Dic3C2×C22⋊C414yes—
280C22×Q8—38no—
281C22×Q8—34no—
282C22×Q8—31no—
283C22×Q8—61no—
284C22×Q8—62no—
285C22×Q8—64no—
286C22×Q8C2×C3×D311yescharacteristic
287C23×C4—31no—
288C23×C4—61no—
289C2×M16—34no—
290C2×M16—64no—
291C22×C8—31no—
292C22×C8C2×C3×D311yescharacteristic
293#117—34no—
294#117—62no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4C2×C3×D311yescharacteristic
297C2×C22⋊C4—61no—
298C2×C42—61no—
299#103—34no—
300#103—34no—
301#103—34no—
302#103C2×C3×D314yescomplemented
303C23×C3—21no—
304C23×C3—34no—
305C23×C3—32no—
306C23×C3—62no—
307C23×C3—62no—
308C23×C3D3×D411yescharacteristic
309C23×C3C2×C3×D411yescharacteristic
310C22×D3—22no—
311C22×D3—22no—
312C22×D3C3×C22⋊C414yes—
313C22×D3C2×C3×D412yes—
314C3×Q8—24no—
315C3×Q8—24no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—24no—
319C3×Q8—34no—
320C3×Q8—44no—
321C3×Q8—42no—
322C3×Q8—616no—
323C3×Q8—64no—
324C3×Q8—62no—
325C3×Q8C2×C4×D314yes—
326C3×Q8C22×C3×C414yes—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—34no—
338C2×C3×C4—32no—
339C2×C3×C4—38no—
340C2×C3×C4—34no—
341C2×C3×C4—34no—
342C2×C3×C4—44no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—616no—
348C2×C3×C4—64no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—82no—
352C2×C3×C4—122no—
353C2×C3×C4C2×C4×D312yes—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D412yes—
356C2×C3×C4C22×C3×C412yes—
357C2×C3×C4C2×C3×D411yescharacteristic
358C2×C3×C4C2×C3×D412yes—
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C24×C311yescharacteristic
361C2×Dic3—24no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—42no—
365C2×Dic3C3×C22⋊C414yes—
366C2×Dic3C2×C3×D412yes—
367C4×D3—216no—
368C4×D3C3×C22⋊C418yes—
369C4×D3C22×C3×C414yes—
370C4×D3C2×C3×D414yes—
371Dic6—24no—
372Dic6—22no—
373Dic6—216no—
374Dic6C22×C3×C414yes—
375C3×C8—22no—
376C3×C8—22no—
377C3×C8—42no—
378C3×C8—62no—
379C3⋊C8—22no—
380C2×C32#41914yescomplemented
381C2×C32C22×C22⋊C411yescharacteristic
382C2×C32C2×#13711yescharacteristic
383C2×C32C2×#13711yescharacteristic
384C3×D3—24no—
385C24—31no—
386C2×Q8—22no—
387C2×Q8—21no—
388C2×Q8—316no—
389C2×Q8—32no—
390C2×Q8—34no—
391C2×Q8—68no—
392C2×Q8—64no—
393C2×Q8—616no—
394C2×Q8—68no—
395C2×Q8—62no—
396C2×Q8—61no—
397C2×Q8C3×C4×D314yes—
398C2×Q8C22×C3×D312yes—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—31no—
402C22×C4—32no—
403C22×C4—34no—
404C22×C4—32no—
405C22×C4—34no—
406C22×C4—68no—
407C22×C4—64no—
408C22×C4—61no—
409C22×C4—61no—
410C22×C4C22×C3×D311yescharacteristic
411M16—68no—
412C2×C8—22no—
413C2×C8—32no—
414C2×C8—62no—
415C2×C8C22×C3×D312yes—
416C4⋊C4—21no—
417C4⋊C4—32no—
418C4⋊C4—61no—
419C4⋊C4C22×C3×D312yes—
420C22⋊C4—64no—
421C42—64no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—21no—
426C22×C3—34no—
427C22×C3—62no—
428C22×C3—62no—
429C22×C3—68no—
430C22×C3D3×C22⋊C412yes—
431C22×C3#91512yes—
432C22×C3#91812yes—
433C22×C3C2×C3×C22⋊C412yes—
434C22×C3C3×#13712yes—
435C22×C3C3×#13712yes—
436C22×C3C2×D3×D411yescharacteristic
437C22×C3C22×C3×D411yescharacteristic
438C2×D3—22no—
439C2×D3—22no—
440C2×D3—28no—
441C2×D3C2×C3×C22⋊C414yes—
442C3×C4—24no—
443C3×C4—24no—
444C3×C4—22no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—34no—
448C3×C4—44no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—64no—
452C3×C4—82no—
453C3×C4—122no—
454C3×C4D3×C22⋊C412yes—
455C3×C4C2×C3×C22⋊C412yes—
456C3×C4C22×C4×D311yescharacteristic
457C3×C4C2×D3×D411yescharacteristic
458C3×C4C23×C3×C411yescharacteristic
459C3×C4C22×C3×D411yescharacteristic
460Dic3—24no—
461Dic3—42no—
462Dic3C2×C3×C22⋊C414yes—
463C32C2×#41911yescharacteristic, complemented, Sylow
464C23—34no—
465C23—32no—
466C23—62no—
467C23—62no—
468C23C3×D3×D411yescharacteristic
469Q8—24no—
470Q8—22no—
471Q8—34no—
472Q8—616no—
473Q8—64no—
474Q8—62no—
475Q8C2×C3×C4×D314yes—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—34no—
480C2×C4—32no—
481C2×C4—38no—
482C2×C4—34no—
483C2×C4—34no—
484C2×C4—42no—
485C2×C4—616no—
486C2×C4—64no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—122no—
490C2×C4C2×C3×C4×D312yes—
491C2×C4C3×D3×D411yescharacteristic
492C2×C4C3×D3×D412yes—
493C2×C4C23×C3×D311yescharacteristic
494C8—22no—
495C8—62no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—24no—
499C2×C3—21no—
500C2×C3—64no—
501C2×C3#480214yesdirect product factor
502C2×C3C3×#41914yescomplemented
503C2×C3C2×D3×C22⋊C411yescharacteristic
504C2×C3C2×#91511yescharacteristic
505C2×C3C2×#91811yescharacteristic
506C2×C3C22×C3×C22⋊C411yescharacteristic
507C2×C3C2×C3×#13711yescharacteristic
508C2×C3C2×C3×#13711yescharacteristic
509D3—24no—
510C22—34no—
511C22—62no—
512C22—62no—
513C22—68no—
514C22C3×D3×C22⋊C412yes—
515C22C3×#91512yes—
516C22C3×#91812yes—
517C22C2×C3×D3×D411yescharacteristic
518C4—24no—
519C4—34no—
520C4—42no—
521C4—64no—
522C4—122no—
523C4C3×D3×C22⋊C412yes—
524C4C22×C3×C4×D311yescharacteristic
525C4C2×C3×D3×D411yescharacteristic
526C3—21no—
527C3C2×#480211yescharacteristic, direct product factor
528C3C2×C3×#41911yescharacteristic, complemented
529C2—64no—
530C2C3×#480214yesdirect product factor
531C2C2×C3×D3×C22⋊C411yescharacteristic
532C2C2×C3×#91511yescharacteristic
533C2C2×C3×#91811yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×#103D3
hypocenterC3C2×C3×#419
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
4. C2×C32×#103C2semidirect
5. C2×C3×#835C2semidirect
6. C2×C3×#816C2semidirect
7. C2×C3×#810C2semidirect
8. C3×#4802C2direct (N × H)
10. C2×#4802C3direct (N × H)
14. C2×C3×D3×Q8C4semidirect
30. C32×#103C22semidirect
31. C3×#835C22semidirect
32. C3×#816C22semidirect
33. C3×#810C22semidirect
45. C2×C3×#103D3semidirect
46. C2×C3×#103C2×C3semidirect
47. C2×#835C2×C3semidirect
48. C2×#816C2×C3semidirect
49. C2×#810C2×C3semidirect
50. #4802C2×C3direct (N × H)
64. C3×D3×Q8C2×C4semidirect
102. C2×D3×Q8C3×C4semidirect
134. C3×#103C2×D3semidirect
135. C3×#103C22×C3semidirect
136. #835C22×C3semidirect
137. #816C22×C3semidirect
138. #810C22×C3semidirect
178. C2×#103C3×D3semidirect
225. D3×Q8C2×C3×C4semidirect
302. #103C2×C3×D3semidirect
380. C2×C32#419semidirect
463. C32C2×#419semidirect
501. C2×C3#4802direct (N × H)
502. C2×C3C3×#419semidirect
527. C3C2×#4802direct (N × H)
528. C3C2×C3×#419semidirect
530. C2C3×#4802direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C22×C3×ΓL(1,𝔽25)2
C2×C3×#8922
C2×C32×#1032
C2×C3×#8352
C2×C3×#8162
C2×C3×#8102
C3×#48022
C2×C3×#4193
C2×#48023