Finite Group Databasebeta

← C2×C3×#4658 #11808507

Subgroups — C2×C3×#4658 #11808507

Order 1152.

1373 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic3⋊C4C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×C32×#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C2×C3×C3⋊#95C211yesmaximal, characteristic
7C2×C3×C3⋊#95C211yesmaximal, characteristic
8C3×#4658C218yesmaximal, direct product factor
9C2×C3×#400—31nomaximal
10C2×#4658C311yesmaximal, characteristic, direct product factor
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C2×C3×Dic3⋊C4—24no—
19C2×C3×Dic3⋊C4—24no—
20C2×C3×Dic3⋊C4C2214yes—
21C2×C3×Dic3⋊C4C2214yes—
22C32×#95C2214yes—
23C3×C3⋊#95C2214yes—
24C3×C3⋊#95C2214yes—
25C3×C3⋊#95C2214yes—
26C3×C3⋊#95C2214yes—
27C22×C3×C4⋊C4—31no—
28C22×C3×C4⋊C4—31no—
29C22×Dic3⋊C4C2×C311yescharacteristic
30C22×Dic3⋊C4C2×C311yescharacteristic
31C3×#400—38no—
32C2×C3×#95—21no—
33C2×C3×#95—31no—
34C2×C3×#95—31no—
35C2×C3×#95—31no—
36C2×C3×#95—31no—
37C2×C3×#95D311yescharacteristic
38C2×C3×#95C2×C311yescharacteristic
39C2×C3⋊#95C2×C311yescharacteristic
40C2×C3⋊#95C2×C311yescharacteristic
41C2×C3⋊#95C2×C311yescharacteristic
42C2×C3⋊#95C2×C311yescharacteristic
43#4658C2×C318yesdirect product factor
44C24×C32C2311yescharacteristic
45C22×C32×C4—22no—
46C22×C32×C4—22no—
47C22×C32×C4—22no—
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4—22no—
51C22×C32×C4—22no—
52C22×C32×C4—22no—
53C22×C32×C4—22no—
54C22×C32×C4C2312yes—
55C22×C32×C4C2312yes—
56C22×C32×C4C2312yes—
57C22×C3×Dic3—22no—
58C22×C3×Dic3—22no—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—22no—
61C22×C3×Dic3—22no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C22×C3×Dic3—22no—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—22no—
67C22×C3×Dic3D414yes—
68C22×C3×Dic3Q814yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C3×Dic3⋊C4—28no—
74C3×Dic3⋊C4—28no—
75C2×#400—31noSylow
76C23×C3×C4—21no—
77C23×C3×C4—21no—
78C23×C3×C4—21no—
79C23×C3×C4—31no—
80C23×C3×C4—31no—
81C23×C3×C4—31no—
82C23×C3×C4—31no—
83C23×C3×C4C2×D311yescharacteristic
84C23×C3×C4C2×D311yescharacteristic
85C23×C3×C4C2×D311yescharacteristic
86C23×C3×C4C22×C311yescharacteristic
87C23×C3×C4C22×C311yescharacteristic
88C23×C3×C4C22×C311yescharacteristic
89C23×Dic3C22×C311yescharacteristic
90C23×Dic3C22×C311yescharacteristic
91C23×Dic3C22×C311yescharacteristic
92C23×Dic3C22×C311yescharacteristic
93C2×C3×C4⋊C4—34no—
94C2×C3×C4⋊C4—34no—
95C2×C3×C4⋊C4—64no—
96C2×C3×C4⋊C4—64no—
97C2×Dic3⋊C4—24no—
98C2×Dic3⋊C4—24no—
99C2×Dic3⋊C4C22×C314yes—
100C2×Dic3⋊C4C22×C314yes—
101C3×#95—24no—
102C3×#95—34no—
103C3×#95—34no—
104C3×#95—34no—
105C3×#95—34no—
106C3×#95C2×D314yes—
107C3×#95C22×C314yes—
108C3⋊#95C22×C314yes—
109C3⋊#95C22×C314yes—
110C3⋊#95C22×C314yes—
111C3⋊#95C22×C314yes—
112C23×C32C2×D412yes—
113C23×C32C2×Q812yes—
114C23×C32#4112yes—
115C23×C32#4112yes—
116C23×C32#4112yes—
117C23×C32#4112yes—
118C23×C32#4112yes—
119C23×C32C2411yescharacteristic
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—22no—
129C2×C32×C4—44no—
130C2×C32×C4—44no—
131C2×C32×C4—44no—
132C2×C3×Dic3—28no—
133C2×C3×Dic3—28no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—44no—
145C2×C3×Dic3—44no—
146C2×C3×Dic3C2×D414yes—
147C2×C3×Dic3C2×Q814yes—
148C22×C4⋊C4—31no—
149C22×C4⋊C4—31no—
150#400—38no—
151C2×#95—31no—
152C2×#95—31no—
153C2×#95—31no—
154C2×#95—31no—
155C2×#95C3×D311yescharacteristic
156C24×C3—21no—
157C24×C3C22×D311yescharacteristic
158C24×C3C23×C311yescharacteristic
159C22×C3×C4—24no—
160C22×C3×C4—24no—
161C22×C3×C4—24no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—34no—
184C22×C3×C4—34no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4—42no—
190C22×C3×C4—42no—
191C22×C3×C4—42no—
192C22×C3×C4—42no—
193C22×C3×C4—42no—
194C22×C3×C4—42no—
195C22×C3×C4—62no—
196C22×C3×C4—62no—
197C22×C3×C4—62no—
198C22×C3×C4—62no—
199C22×C3×C4—62no—
200C22×C3×C4—62no—
201C22×C3×C4—62no—
202C22×C3×C4—62no—
203C22×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4C22×D312yes—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C23×C312yes—
209C22×C3×C4C23×C312yes—
210C22×C3×C4C23×C312yes—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3C3×D414yes—
222C22×Dic3C3×Q814yes—
223C22×Dic3C23×C312yes—
224C22×Dic3C23×C312yes—
225C22×Dic3C23×C312yes—
226C22×Dic3C23×C312yes—
227C3×C4⋊C4—68no—
228C3×C4⋊C4—68no—
229Dic3⋊C4—28no—
230Dic3⋊C4—28no—
231C22×C32C22⋊Q814yes—
232C22×C32#12314yes—
233C22×C32#12414yes—
234C22×C32#12514yes—
235C22×C32#12514yes—
236C22×C32#12614yes—
237C22×C32#12614yes—
238C22×C32C22×D411yescharacteristic
239C22×C32C22×Q811yescharacteristic
240C22×C32C2×#4111yescharacteristic
241C22×C32C2×#4111yescharacteristic
242C22×C32C2×#4111yescharacteristic
243C22×C32C2×#4111yescharacteristic
244C22×C32C2×#4111yescharacteristic
245C32×C4—42no—
246C32×C4—42no—
247C32×C4—42no—
248C3×Dic3—24no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C3×Dic3—42no—
252C23×C4—31no—
253C23×C4—31no—
254C23×C4—31no—
255C23×C4—31no—
256C23×C4C2×C3×D311yescharacteristic
257C23×C4C2×C3×D311yescharacteristic
258C23×C4C2×C3×D311yescharacteristic
259C2×C4⋊C4—34no—
260C2×C4⋊C4—34no—
261C2×C4⋊C4—64no—
262C2×C4⋊C4—64no—
263#95—34no—
264#95—34no—
265#95—34no—
266#95—34no—
267#95C2×C3×D314yes—
268C23×C3—21no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3#23512yes—
277C23×C3#23512yes—
278C23×C3#23512yes—
279C23×C3D3×D412yes—
280C23×C3#23712yes—
281C23×C3#23712yes—
282C23×C3D3×Q812yes—
283C23×C3C2×C3×D412yes—
284C23×C3C2×C3×Q812yes—
285C23×C3C3×#4112yes—
286C23×C3C3×#4112yes—
287C23×C3C3×#4112yes—
288C23×C3C3×#4112yes—
289C23×C3C3×#4112yes—
290C23×C3C23×D311yescharacteristic
291C23×C3C24×C311yescharacteristic
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—24no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—34no—
314C2×C3×C4—34no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—48no—
322C2×C3×C4—48no—
323C2×C3×C4—48no—
324C2×C3×C4—44no—
325C2×C3×C4—44no—
326C2×C3×C4—44no—
327C2×C3×C4—44no—
328C2×C3×C4—44no—
329C2×C3×C4—44no—
330C2×C3×C4—68no—
331C2×C3×C4—68no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—124no—
343C2×C3×C4—124no—
344C2×Dic3—28no—
345C2×Dic3—28no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—44no—
357C2×Dic3—44no—
358C2×Dic3C2×C3×D414yes—
359C2×Dic3C2×C3×Q814yes—
360C2×C32#40018yescomplemented
361C2×C32C2×C22⋊Q811yescharacteristic
362C2×C32C2×#12311yescharacteristic
363C2×C32C2×#12411yescharacteristic
364C2×C32C2×#12511yescharacteristic
365C2×C32C2×#12511yescharacteristic
366C2×C32C2×#12611yescharacteristic
367C2×C32C2×#12611yescharacteristic
368C24C22×C3×D311yescharacteristic
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—32no—
379C22×C4—32no—
380C22×C4—34no—
381C22×C4—34no—
382C22×C4—32no—
383C22×C4—32no—
384C22×C4—62no—
385C22×C4—62no—
386C22×C4—62no—
387C22×C4—62no—
388C22×C4—62no—
389C22×C4—62no—
390C22×C4—62no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4C22×C3×D312yes—
395C22×C4C22×C3×D312yes—
396C22×C4C22×C3×D312yes—
397C4⋊C4—68no—
398C4⋊C4—68no—
399C22×C3—24no—
400C22×C3—24no—
401C22×C3—24no—
402C22×C3—24no—
403C22×C3—24no—
404C22×C3—24no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—24no—
413C22×C3#87614yes—
414C22×C3#87914yes—
415C22×C3#88314yes—
416C22×C3#88514yes—
417C22×C3#88914yes—
418C22×C3#88914yes—
419C22×C3#89614yes—
420C22×C3C3×C22⋊Q814yes—
421C22×C3C3×#12314yes—
422C22×C3C3×#12414yes—
423C22×C3C3×#12514yes—
424C22×C3C3×#12514yes—
425C22×C3C3×#12614yes—
426C22×C3C3×#12614yes—
427C22×C3C2×#23511yescharacteristic
428C22×C3C2×#23511yescharacteristic
429C22×C3C2×#23511yescharacteristic
430C22×C3C2×D3×D411yescharacteristic
431C22×C3C2×#23711yescharacteristic
432C22×C3C2×#23711yescharacteristic
433C22×C3C2×D3×Q811yescharacteristic
434C22×C3C22×C3×D411yescharacteristic
435C22×C3C22×C3×Q811yescharacteristic
436C22×C3C2×C3×#4111yescharacteristic
437C22×C3C2×C3×#4111yescharacteristic
438C22×C3C2×C3×#4111yescharacteristic
439C22×C3C2×C3×#4111yescharacteristic
440C22×C3C2×C3×#4111yescharacteristic
441C3×C4—44no—
442C3×C4—44no—
443C3×C4—44no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—42no—
450C3×C4—64no—
451C3×C4—64no—
452C3×C4—122no—
453C3×C4—122no—
454Dic3—24no—
455Dic3—24no—
456Dic3—42no—
457Dic3—42no—
458C32C2×#40011yescharacteristic, complemented, Sylow
459C23C3×#23512yes—
460C23C3×#23512yes—
461C23C3×#23512yes—
462C23C3×D3×D412yes—
463C23C3×#23712yes—
464C23C3×#23712yes—
465C23C3×D3×Q812yes—
466C23C23×C3×D311yescharacteristic
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—34no—
477C2×C4—34no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—68no—
482C2×C4—68no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—124no—
494C2×C4—124no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—28no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3#465818yesdirect product factor
504C2×C3C3×#40018yescomplemented
505C2×C3C2×#87611yescharacteristic
506C2×C3C2×#87911yescharacteristic
507C2×C3C2×#88311yescharacteristic
508C2×C3C2×#88511yescharacteristic
509C2×C3C2×#88911yescharacteristic
510C2×C3C2×#88911yescharacteristic
511C2×C3C2×#89611yescharacteristic
512C2×C3C2×C3×C22⋊Q811yescharacteristic
513C2×C3C2×C3×#12311yescharacteristic
514C2×C3C2×C3×#12411yescharacteristic
515C2×C3C2×C3×#12511yescharacteristic
516C2×C3C2×C3×#12511yescharacteristic
517C2×C3C2×C3×#12611yescharacteristic
518C2×C3C2×C3×#12611yescharacteristic
519C22C3×#87614yes—
520C22C3×#87914yes—
521C22C3×#88314yes—
522C22C3×#88514yes—
523C22C3×#88914yes—
524C22C3×#88914yes—
525C22C3×#89614yes—
526C22C2×C3×#23511yescharacteristic
527C22C2×C3×#23511yescharacteristic
528C22C2×C3×#23511yescharacteristic
529C22C2×C3×D3×D411yescharacteristic
530C22C2×C3×#23711yescharacteristic
531C22C2×C3×#23711yescharacteristic
532C22C2×C3×D3×Q811yescharacteristic
533C4—42no—
534C4—42no—
535C4—42no—
536C4—64no—
537C4—64no—
538C4—122no—
539C4—122no—
540C3—21no—
541C3C2×#465811yescharacteristic, direct product factor
542C3C2×C3×#40011yescharacteristic, complemented
543C2C3×#465818yesdirect product factor
544C2C2×C3×#87611yescharacteristic
545C2C2×C3×#87911yescharacteristic
546C2C2×C3×#88311yescharacteristic
547C2C2×C3×#88511yescharacteristic
548C2C2×C3×#88911yescharacteristic
549C2C2×C3×#88911yescharacteristic
550C2C2×C3×#89611yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socle, prime radicalC24×C32C23
hypercenterC2×C3×#95D3
hypocenterC3C2×C3×#400
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
8. C3×#4658C2direct (N × H)
10. C2×#4658C3direct (N × H)
43. #4658C2×C3direct (N × H)
360. C2×C32#400semidirect
458. C32C2×#400semidirect
503. C2×C3#4658direct (N × H)
504. C2×C3C3×#400semidirect
541. C3C2×#4658direct (N × H)
542. C3C2×C3×#400semidirect
543. C2C3×#4658direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Dic3⋊C42
C2×C32×#952
C2×C3×C3⋊#952
C3×#46582
C2×C3×#4003
C2×#46583