Finite Group Databasebeta

← C22×C3×#806 #11857487

Subgroups — C22×C3×#806 #11857487

Order 1152.

2561 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic
2C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×#217C211yesmaximal, characteristic, complemented
4C2×C3×#806C2112yesmaximal, direct product factor
5C22×C3×#99—31nomaximal
6C22×#806C311yesmaximal, characteristic, direct product factor
7C25×C32C2211yescharacteristic
8C24×C3×D3C411yescharacteristic, complemented
9C23×C32×C4—21no—
10C22×C3×#67—21no—
11C22×C3×#67—21no—
12C22×C3×#67—23no—
13C22×C3×#67—23no—
14C22×C3×#67C416yescomplemented
15C22×C3×#67C2216yes—
16C23×C3×Dic3—21no—
17C23×C3×Dic3C411yescharacteristic, complemented
18C2×C32×C22⋊C4—23no—
19C2×C32×C22⋊C4C2216yescomplemented
20C2×C3×#217—23no—
21C2×C3×#217C2216yescomplemented
22C3×#806C22116yesdirect product factor
23C23×C3×D4—31no—
24C23×#67C2×C311yescharacteristic
25C22×C3×C22⋊C4—21no—
26C22×C3×C22⋊C4—31no—
27C22×C3×C22⋊C4D311yescharacteristic, complemented
28C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
29C22×#217C2×C311yescharacteristic, complemented
30C2×C3×#99—312no—
31C2×#806C2×C3112yesdirect product factor
32C24×C32—44no—
33C24×C32C2×C411yescharacteristic
34C24×C32C2×C413yes—
35C24×C32D411yescharacteristic
36C24×C32D411yescharacteristic
37C24×C32D413yes—
38C24×C32D413yes—
39C24×C32C2313yes—
40C23×C3×D3—23no—
41C23×C3×D3—21no—
42C23×C3×D3—44no—
43C23×C3×D3C2×C416yescomplemented
44C22×C32×C4—26no—
45C22×C32×C4—44no—
46C2×C3×#67—26no—
47C2×C3×#67—26no—
48C2×C3×#67—212no—
49C2×C3×#67—26no—
50C2×C3×#67—26no—
51C2×C3×#67—26no—
52C2×C3×#67—26no—
53C2×C3×#67C2×C4112yescomplemented
54C2×C3×#67C2314yes—
55C22×C3×Dic3—23no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—26no—
58C22×C3×Dic3—44no—
59C22×C3×Dic3C2×C416yescomplemented
60C32×C22⋊C4—26no—
61C32×C22⋊C4C2314yescomplemented
62C3×#217—26no—
63C3×#217C2314yescomplemented
64C22×#99—31noSylow
65C25×C3—21no—
66C25×C3—31no—
67C25×C3C2×D311yescharacteristic
68C25×C3C22×C311yescharacteristic
69C24×D3C3×C411yescharacteristic, complemented
70C22×C3×D4—36no—
71C22×C3×D4—36no—
72C22×C3×D4—63no—
73C22×C3×D4—61no—
74C22×C3×D4—63no—
75C22×C3×D4—61no—
76C23×C3×C4—22no—
77C23×C3×C4—21no—
78C23×C3×C4—21no—
79C23×C3×C4—31no—
80C23×C3×C4—61no—
81C22×#67—21no—
82C22×#67—23no—
83C22×#67—21no—
84C22×#67—23no—
85C22×#67C3×C416yescomplemented
86C22×#67C22×C316yes—
87C23×Dic3—21no—
88C23×Dic3C3×C411yescharacteristic, complemented
89C2×C3×C22⋊C4—26no—
90C2×C3×C22⋊C4—23no—
91C2×C3×C22⋊C4—23no—
92C2×C3×C22⋊C4—26no—
93C2×C3×C22⋊C4—36no—
94C2×C3×C22⋊C4—63no—
95C2×C3×C22⋊C4C2×D316yescomplemented
96C2×C3×C22⋊C4C22×C316yescomplemented
97C2×#217—23no—
98C2×#217C22×C316yescomplemented
99C3×#99—316no—
100#806C22×C3116yesdirect product factor
101C23×C32—24no—
102C23×C32—24no—
103C23×C32—24no—
104C23×C32—46no—
105C23×C32—46no—
106C23×C32—46no—
107C23×C32—46no—
108C23×C32C22⋊C413yes—
109C23×C32C22⋊C413yes—
110C23×C32C22⋊C413yes—
111C23×C32C22⋊C416yes—
112C23×C32C22⋊C411yescharacteristic
113C23×C32C22×C413yes—
114C23×C32C22×C413yes—
115C23×C32C2×D413yes—
116C23×C32C2×D413yes—
117C23×C32C2×D413yes—
118C23×C32C2×D413yes—
119C23×C32C2411yescharacteristic
120C22×C3×D3—26no—
121C22×C3×D3—26no—
122C22×C3×D3—412no—
123C22×C3×D3—44no—
124C22×C3×D3—412no—
125C22×C3×D3C22×C414yescomplemented
126C2×C32×C4—24no—
127C2×C32×C4—412no—
128C3×#67—212no—
129C3×#67—212no—
130C3×#67—24no—
131C3×#67—24no—
132C2×C3×Dic3—26no—
133C2×C3×Dic3—26no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3—412no—
136C2×C3×Dic3C22×C414yescomplemented
137C23×D4—31no—
138C22×C22⋊C4—31no—
139C22×C22⋊C4C3×D311yescharacteristic, complemented
140C2×#99—312no—
141C24×C3—21no—
142C24×C3—23no—
143C24×C3—21no—
144C24×C3—23no—
145C24×C3—21no—
146C24×C3—23no—
147C24×C3—23no—
148C24×C3—36no—
149C24×C3—44no—
150C24×C3—44no—
151C24×C3—48no—
152C24×C3—63no—
153C24×C3—61no—
154C24×C3—124no—
155C24×C3C4×D311yescharacteristic
156C24×C3C4×D313yes—
157C24×C3D1211yescharacteristic
158C24×C3D1213yes—
159C24×C3#6711yescharacteristic
160C24×C3#6713yes—
161C24×C3C2×C3×C411yescharacteristic
162C24×C3C2×C3×C413yes—
163C24×C3C3×D411yescharacteristic
164C24×C3C3×D413yes—
165C24×C3C3×D411yescharacteristic
166C24×C3C3×D413yes—
167C24×C3C22×D313yes—
168C24×C3C23×C313yes—
169C23×D3—23no—
170C23×D3—21no—
171C23×D3—44no—
172C23×D3C2×C3×C416yescomplemented
173C2×C3×D4—312no—
174C2×C3×D4—34no—
175C2×C3×D4—66no—
176C2×C3×D4—66no—
177C2×C3×D4—612no—
178C2×C3×D4—66no—
179C2×C3×D4—66no—
180C2×C3×D4—66no—
181C2×C3×D4—66no—
182C22×C3×C4—212no—
183C22×C3×C4—26no—
184C22×C3×C4—26no—
185C22×C3×C4—36no—
186C22×C3×C4—48no—
187C22×C3×C4—44no—
188C22×C3×C4—44no—
189C22×C3×C4—63no—
190C22×C3×C4—61no—
191C22×C3×C4—66no—
192C22×C3×C4—124no—
193C2×#67—26no—
194C2×#67—26no—
195C2×#67—212no—
196C2×#67—26no—
197C2×#67—26no—
198C2×#67—26no—
199C2×#67—26no—
200C2×#67C2×C3×C4112yescomplemented
201C2×#67C23×C314yes—
202C22×Dic3—23no—
203C22×Dic3—21no—
204C22×Dic3—26no—
205C22×Dic3—44no—
206C22×Dic3C2×C3×C416yescomplemented
207C3×C22⋊C4—212no—
208C3×C22⋊C4—26no—
209C3×C22⋊C4—26no—
210C3×C22⋊C4—24no—
211C3×C22⋊C4—34no—
212C3×C22⋊C4—66no—
213C3×C22⋊C4C22×D314yescomplemented
214C3×C22⋊C4C23×C314yescomplemented
215#217—26no—
216#217C23×C314yescomplemented
217C22×C32—26no—
218C22×C32—26no—
219C22×C32—26no—
220C22×C32—26no—
221C22×C32—26no—
222C22×C32—26no—
223C22×C32—46no—
224C22×C32—43no—
225C22×C32—43no—
226C22×C32—43no—
227C22×C32—41no—
228C22×C32#9914yescomplemented
229C22×C32C2×C22⋊C413yes—
230C22×C32C2×C22⋊C413yes—
231C22×C32C2×C22⋊C413yes—
232C22×C32C2×C22⋊C413yes—
233C22×C32C23×C411yescharacteristic
234C22×C32C22×D411yescharacteristic
235C22×C32C22×D411yescharacteristic
236C2×C3×D3—24no—
237C2×C3×D3—412no—
238C2×C3×D3—412no—
239C2×C3×D3—44no—
240C32×C4—44no—
241C3×Dic3—24no—
242C3×Dic3—44no—
243C25—31no—
244C25C2×C3×D311yescharacteristic
245C22×D4—36no—
246C22×D4—36no—
247C22×D4—61no—
248C22×D4—63no—
249C22×D4—61no—
250C22×D4—63no—
251C23×C4—21no—
252C23×C4—31no—
253C23×C4—61no—
254C2×C22⋊C4—23no—
255C2×C22⋊C4—36no—
256C2×C22⋊C4—63no—
257C2×C22⋊C4C2×C3×D316yescomplemented
258#99—316no—
259C23×C3—28no—
260C23×C3—24no—
261C23×C3—24no—
262C23×C3—24no—
263C23×C3—24no—
264C23×C3—24no—
265C23×C3—24no—
266C23×C3—21no—
267C23×C3—23no—
268C23×C3—21no—
269C23×C3—23no—
270C23×C3—23no—
271C23×C3—26no—
272C23×C3—23no—
273C23×C3—23no—
274C23×C3—23no—
275C23×C3—23no—
276C23×C3—23no—
277C23×C3—23no—
278C23×C3—34no—
279C23×C3—44no—
280C23×C3—44no—
281C23×C3—46no—
282C23×C3—46no—
283C23×C3—46no—
284C23×C3—46no—
285C23×C3—46no—
286C23×C3—46no—
287C23×C3—46no—
288C23×C3—46no—
289C23×C3—412no—
290C23×C3—412no—
291C23×C3—412no—
292C23×C3—412no—
293C23×C3—66no—
294C23×C3—66no—
295C23×C3—1212no—
296C23×C3—1212no—
297C23×C3—124no—
298C23×C3(C2×D3)⋊C413yes—
299C23×C3(C2×D3)⋊C413yes—
300C23×C3(C2×D3)⋊C413yes—
301C23×C3(C2×D3)⋊C416yes—
302C23×C3(C2×D3)⋊C411yescharacteristic
303C23×C3C3×C22⋊C413yes—
304C23×C3C3×C22⋊C413yes—
305C23×C3C3×C22⋊C413yes—
306C23×C3C3×C22⋊C416yes—
307C23×C3C3×C22⋊C411yescharacteristic
308C23×C3C2×C4×D313yes—
309C23×C3C2×C4×D313yes—
310C23×C3C2×D1213yes—
311C23×C3C2×D1213yes—
312C23×C3C2×#6713yes—
313C23×C3C2×#6713yes—
314C23×C3C22×C3×C413yes—
315C23×C3C22×C3×C413yes—
316C23×C3C2×C3×D413yes—
317C23×C3C2×C3×D413yes—
318C23×C3C2×C3×D413yes—
319C23×C3C2×C3×D413yes—
320C23×C3C23×D311yescharacteristic
321C23×C3C24×C311yescharacteristic
322C22×D3—26no—
323C22×D3—26no—
324C22×D3—412no—
325C22×D3—44no—
326C22×D3—412no—
327C22×D3C22×C3×C414yescomplemented
328C3×D4—612no—
329C3×D4—612no—
330C3×D4—64no—
331C3×D4—64no—
332C2×C3×C4—28no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—34no—
336C2×C3×C4—424no—
337C2×C3×C4—412no—
338C2×C3×C4—412no—
339C2×C3×C4—66no—
340C2×C3×C4—66no—
341C2×C3×C4—64no—
342C2×C3×C4—1212no—
343#67—212no—
344#67—212no—
345#67—24no—
346#67—24no—
347C2×Dic3—26no—
348C2×Dic3—26no—
349C2×Dic3—24no—
350C2×Dic3—412no—
351C2×Dic3C22×C3×C414yescomplemented
352C2×C32—21no—
353C2×C32—23no—
354C2×C32—21no—
355C2×C32—23no—
356C2×C32—21no—
357C2×C32—23no—
358C2×C32C2×#9916yescomplemented
359C2×C32C22×C22⋊C411yescharacteristic
360C3×D3—44no—
361C24—36no—
362C24—44no—
363C24—63no—
364C24—61no—
365C24—124no—
366C24C3×C4×D311yescharacteristic
367C24C3×C4×D313yes—
368C24C3×D1211yescharacteristic
369C24C3×D1213yes—
370C24C3×#6711yescharacteristic
371C24C3×#6713yes—
372C24C22×C3×D313yes—
373C2×D4—34no—
374C2×D4—312no—
375C2×D4—66no—
376C2×D4—66no—
377C2×D4—612no—
378C2×D4—66no—
379C2×D4—66no—
380C2×D4—66no—
381C2×D4—66no—
382C22×C4—26no—
383C22×C4—36no—
384C22×C4—44no—
385C22×C4—63no—
386C22×C4—61no—
387C22×C4—66no—
388C22×C4—124no—
389C22⋊C4—26no—
390C22⋊C4—34no—
391C22⋊C4—66no—
392C22⋊C4C22×C3×D314yescomplemented
393C22×C3—212no—
394C22×C3—212no—
395C22×C3—26no—
396C22×C3—26no—
397C22×C3—26no—
398C22×C3—26no—
399C22×C3—26no—
400C22×C3—26no—
401C22×C3—26no—
402C22×C3—26no—
403C22×C3—26no—
404C22×C3—26no—
405C22×C3—26no—
406C22×C3—26no—
407C22×C3—23no—
408C22×C3—23no—
409C22×C3—23no—
410C22×C3—23no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—24no—
415C22×C3—46no—
416C22×C3—46no—
417C22×C3—46no—
418C22×C3—46no—
419C22×C3—46no—
420C22×C3—46no—
421C22×C3—43no—
422C22×C3—43no—
423C22×C3—43no—
424C22×C3—43no—
425C22×C3—43no—
426C22×C3—43no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—42no—
430C22×C3—412no—
431C22×C3—46no—
432C22×C3—46no—
433C22×C3—46no—
434C22×C3—64no—
435C22×C3—124no—
436C22×C3—1212no—
437C22×C3—1212no—
438C22×C3#80614yesdirect product factor
439C22×C3C3×#9914yescomplemented
440C22×C3C2×(C2×D3)⋊C413yes—
441C22×C3C2×(C2×D3)⋊C413yes—
442C22×C3C2×(C2×D3)⋊C413yes—
443C22×C3C2×(C2×D3)⋊C413yes—
444C22×C3C2×C3×C22⋊C413yes—
445C22×C3C2×C3×C22⋊C413yes—
446C22×C3C2×C3×C22⋊C413yes—
447C22×C3C2×C3×C22⋊C413yes—
448C22×C3C22×C4×D311yescharacteristic
449C22×C3C22×D1211yescharacteristic
450C22×C3C22×#6711yescharacteristic
451C22×C3C23×C3×C411yescharacteristic
452C22×C3C22×C3×D411yescharacteristic
453C22×C3C22×C3×D411yescharacteristic
454C2×D3—24no—
455C2×D3—412no—
456C2×D3—412no—
457C2×D3—44no—
458C3×C4—48no—
459C3×C4—44no—
460C3×C4—44no—
461C3×C4—64no—
462C3×C4—124no—
463Dic3—24no—
464Dic3—44no—
465C32C22×#9911yescharacteristic, complemented, Sylow
466C23—24no—
467C23—24no—
468C23—24no—
469C23—34no—
470C23—46no—
471C23—46no—
472C23—46no—
473C23—46no—
474C23—66no—
475C23—66no—
476C23—1212no—
477C23—1212no—
478C23—124no—
479C23C3×(C2×D3)⋊C413yes—
480C23C3×(C2×D3)⋊C413yes—
481C23C3×(C2×D3)⋊C413yes—
482C23C3×(C2×D3)⋊C416yes—
483C23C3×(C2×D3)⋊C411yescharacteristic
484C23C2×C3×C4×D313yes—
485C23C2×C3×C4×D313yes—
486C23C2×C3×D1213yes—
487C23C2×C3×D1213yes—
488C23C2×C3×#6713yes—
489C23C2×C3×#6713yes—
490C23C23×C3×D311yescharacteristic
491D4—612no—
492D4—612no—
493D4—64no—
494D4—64no—
495C2×C4—24no—
496C2×C4—34no—
497C2×C4—412no—
498C2×C4—66no—
499C2×C4—66no—
500C2×C4—64no—
501C2×C4—1212no—
502C2×C3—22no—
503C2×C3—26no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—23no—
507C2×C3—21no—
508C2×C3—23no—
509C2×C3—23no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—23no—
513C2×C3—21no—
514C2×C3—23no—
515C2×C3—23no—
516C2×C3—21no—
517C2×C3—26no—
518C2×C3—41no—
519C2×C3—43no—
520C2×C3—41no—
521C2×C3—43no—
522C2×C3—124no—
523C2×C3C2×#80616yesdirect product factor
524C2×C3C2×C3×#9916yescomplemented
525C2×C3C22×(C2×D3)⋊C411yescharacteristic
526C2×C3C22×C3×C22⋊C411yescharacteristic
527D3—44no—
528C22—26no—
529C22—26no—
530C22—26no—
531C22—26no—
532C22—26no—
533C22—26no—
534C22—41no—
535C22—46no—
536C22—43no—
537C22—43no—
538C22—43no—
539C22—64no—
540C22—124no—
541C22—1212no—
542C22—1212no—
543C22C3×#80614yesdirect product factor
544C22C2×C3×(C2×D3)⋊C413yes—
545C22C2×C3×(C2×D3)⋊C413yes—
546C22C2×C3×(C2×D3)⋊C413yes—
547C22C2×C3×(C2×D3)⋊C413yes—
548C22C22×C3×C4×D311yescharacteristic
549C22C22×C3×D1211yescharacteristic
550C22C22×C3×#6711yescharacteristic
551C4—44no—
552C4—64no—
553C4—124no—
554C3—21no—
555C3C22×#80611yescharacteristic, direct product factor
556C3C22×C3×#9911yescharacteristic, complemented
557C2—21no—
558C2—21no—
559C2—23no—
560C2—21no—
561C2—23no—
562C2—23no—
563C2—124no—
564C2C2×C3×#80616yesdirect product factor
565C2C22×C3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC23×C3(C2×D3)⋊C4
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC22×C32×C22⋊C4C2
socleC23×C32C22⋊C4
prime radicalC23×C3×#67C2
cosocleC23×C3C24×C3
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C22×C3×#99
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C25×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C32×C22⋊C4C2semidirect
3. C22×C3×#217C2semidirect
4. C2×C3×#806C2direct (N × H)
6. C22×#806C3direct (N × H)
8. C24×C3×D3C4semidirect
14. C22×C3×#67C4semidirect
17. C23×C3×Dic3C4semidirect
19. C2×C32×C22⋊C4C22semidirect
21. C2×C3×#217C22semidirect
22. C3×#806C22direct (N × H)
27. C22×C3×C22⋊C4D3semidirect
28. C22×C3×C22⋊C4C2×C3semidirect
29. C22×#217C2×C3semidirect
31. C2×#806C2×C3direct (N × H)
43. C23×C3×D3C2×C4semidirect
53. C2×C3×#67C2×C4semidirect
59. C22×C3×Dic3C2×C4semidirect
61. C32×C22⋊C4C23semidirect
63. C3×#217C23semidirect
69. C24×D3C3×C4semidirect
85. C22×#67C3×C4semidirect
88. C23×Dic3C3×C4semidirect
95. C2×C3×C22⋊C4C2×D3semidirect
96. C2×C3×C22⋊C4C22×C3semidirect
98. C2×#217C22×C3semidirect
100. #806C22×C3direct (N × H)
125. C22×C3×D3C22×C4semidirect
136. C2×C3×Dic3C22×C4semidirect
139. C22×C22⋊C4C3×D3semidirect
172. C23×D3C2×C3×C4semidirect
200. C2×#67C2×C3×C4semidirect
206. C22×Dic3C2×C3×C4semidirect
213. C3×C22⋊C4C22×D3semidirect
214. C3×C22⋊C4C23×C3semidirect
216. #217C23×C3semidirect
228. C22×C32#99semidirect
257. C2×C22⋊C4C2×C3×D3semidirect
327. C22×D3C22×C3×C4semidirect
351. C2×Dic3C22×C3×C4semidirect
358. C2×C32C2×#99semidirect
392. C22⋊C4C22×C3×D3semidirect
438. C22×C3#806direct (N × H)
439. C22×C3C3×#99semidirect
465. C32C22×#99semidirect
523. C2×C3C2×#806direct (N × H)
524. C2×C3C2×C3×#99semidirect
543. C22C3×#806direct (N × H)
555. C3C22×#806direct (N × H)
556. C3C22×C3×#99semidirect
564. C2C2×C3×#806direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×C32×C22⋊C42
C22×C3×#2172
C2×C3×#8062
C22×C3×#993
C22×#8063