Finite Group Databasebeta

← C3×Dic3×#99 #11783752

Subgroups — C3×Dic3×#99 #11783752

Order 1152.

929 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C2×C32×#99C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4C3×Dic3×C22⋊C4C212yesmaximal, complemented
5C3×#4527C212yesmaximal, complemented
6C3×C4×#99—31nomaximal
7Dic3×#99C311yesmaximal, characteristic, direct product factor
8C22×C32×D4C2211yescharacteristic
9C23×C3×Dic3C411yescharacteristic, complemented
10C23×C3×Dic3C2211yescharacteristic
11C2×C32×C22⋊C4C2212yes—
12C2×C3×#217C411yescharacteristic, complemented
13C2×C3×#217C2211yescharacteristic
14C2×C3×#217C2212yes—
15C3×D4×Dic3—22no—
16C3×D4×Dic3—22no—
17C2×C3×C4⋊Dic3C411yescharacteristic, complemented
18C2×C3×C4×Dic3—22no—
19C2×C3×C4×Dic3C411yescharacteristic, complemented
20C32×#99C414yescomplemented
21C3×#834C414yescomplemented
22C3×C3⋊#95—22no—
23C2×C3×C4×D4—31no—
24C2×D4×Dic3C2×C311yescharacteristic
25C2×C3×#99—21no—
26C2×C3×#99—31no—
27C2×C3×#99D311yescharacteristic
28C2×C3×#99C2×C311yescharacteristic
29C3×C4×C22⋊C4—32no—
30C2×#834C2×C311yescharacteristic
31Dic3×C22⋊C4C2×C312yescomplemented
32C3×#342—32no—
33#4527C2×C312yescomplemented
34C24×C32C2×C411yescharacteristic
35C24×C32C2311yescharacteristic
36C2×C32×D4—22no—
37C2×C32×D4—22no—
38C2×C32×D4C2×C412yes—
39C2×C32×D4C2×C412yes—
40C22×C32×C4—22no—
41C22×C32×C4C2×C411yescharacteristic
42C22×C3×Dic3—22no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—42no—
46C22×C3×Dic3—42no—
47C22×C3×Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C22×C3×Dic3C2×C411yescharacteristic
50C22×C3×Dic3C2×C411yescharacteristic
51C22×C3×Dic3D412yes—
52C22×C3×Dic3D412yes—
53C32×C22⋊C4—22no—
54C32×C22⋊C4C2×C414yescomplemented
55C3×#217—22no—
56C3×#217—22no—
57C3×#217—22no—
58C3×#217C2×C414yescomplemented
59C3×C4⋊Dic3—22no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C3×C4×Dic3—44no—
63C4×#99—31noSylow
64C22×C3×D4—21no—
65C22×C3×D4C2×D311yescharacteristic
66C22×C3×D4C22×C311yescharacteristic
67C23×C3×C4—31no—
68C23×C3×C4—31no—
69C23×Dic3C3×C411yescharacteristic, complemented
70C23×Dic3C22×C311yescharacteristic
71C3×C4×D4—62no—
72C3×C4×D4—62no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C22⋊C4—22no—
75C2×C3×C22⋊C4—32no—
76C2×C3×C22⋊C4—31no—
77C2×C3×C22⋊C4—31no—
78C2×C3×C22⋊C4C2×D312yes—
79C2×C3×C22⋊C4C22×C312yes—
80C2×C3×C42—31no—
81C2×C3×C42—62no—
82C2×#217C3×C411yescharacteristic, complemented
83C2×#217C22×C311yescharacteristic
84C2×#217C22×C312yes—
85D4×Dic3—22no—
86D4×Dic3—22no—
87C2×C4⋊Dic3C3×C411yescharacteristic, complemented
88C2×C4×Dic3—22no—
89C2×C4×Dic3C3×C411yescharacteristic, complemented
90C3×#99—24no—
91C3×#99—34no—
92C3×#99Dic314yesdirect product factor
93C3×#99C3×C414yescomplemented
94C3×#95—62no—
95#834C3×C414yescomplemented
96C3⋊#95—22no—
97C23×C32—21no—
98C23×C32—21no—
99C23×C32—41no—
100C23×C32—41no—
101C23×C32—41no—
102C23×C32—41no—
103C23×C32C4212yescomplemented
104C23×C32C22×C411yescharacteristic
105C23×C32C22×C411yescharacteristic
106C23×C32C22×C411yescharacteristic
107C23×C32C2×D412yes—
108C23×C32#4112yes—
109C32×D4—24no—
110C32×D4—24no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—24no—
114C2×C32×C4—42no—
115C2×C32×C4—42no—
116C2×C32×C4C4212yescomplemented
117C2×C3×Dic3—24no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—41no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—42no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3C22⋊C411yescharacteristic
131C2×C3×Dic3C22⋊C412yes—
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C4×D4—31no—
134C2×#99—31no—
135C2×#99C3×D311yescharacteristic
136C4×C22⋊C4—32no—
137#342—32no—
138C24×C3—21no—
139C24×C3—21no—
140C24×C3C4×D311yescharacteristic
141C24×C3C2×C3×C411yescharacteristic
142C24×C3C22×D311yescharacteristic
143C24×C3C23×C311yescharacteristic
144C2×C3×D4—22no—
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—22no—
148C2×C3×D4—22no—
149C2×C3×D4—22no—
150C2×C3×D4—42no—
151C2×C3×D4—42no—
152C2×C3×D4C4×D312yes—
153C2×C3×D4C2×Dic312yes—
154C2×C3×D4C2×C3×C412yes—
155C2×C3×D4C2×C3×C412yes—
156C22×C3×C4—22no—
157C22×C3×C4—22no—
158C22×C3×C4—21no—
159C22×C3×C4—31no—
160C22×C3×C4—32no—
161C22×C3×C4—31no—
162C22×C3×C4—32no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—42no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4—62no—
169C22×C3×C4—122no—
170C22×C3×C4—122no—
171C22×C3×C4C4×D311yescharacteristic
172C22×C3×C4C2×C3×C411yescharacteristic
173C22×Dic3—22no—
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—42no—
177C22×Dic3—42no—
178C22×Dic3C2×C3×C411yescharacteristic
179C22×Dic3C2×C3×C411yescharacteristic
180C22×Dic3C2×C3×C411yescharacteristic
181C22×Dic3C2×C3×C411yescharacteristic
182C22×Dic3C3×D412yes—
183C22×Dic3C3×D412yes—
184C3×C4⋊C4—62no—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—22no—
187C3×C22⋊C4—24no—
188C3×C22⋊C4—34no—
189C3×C22⋊C4—42no—
190C3×C22⋊C4—62no—
191C3×C22⋊C4—62no—
192C3×C22⋊C4—62no—
193C3×C22⋊C4C2×Dic314yescomplemented
194C3×C22⋊C4C2×C3×C414yescomplemented
195C3×C42—61no—
196C3×C42—61no—
197C3×C42—124no—
198#217—22no—
199#217—22no—
200#217—22no—
201#217C2×C3×C414yescomplemented
202C4⋊Dic3—22no—
203C4×Dic3—21no—
204C4×Dic3—21no—
205C4×Dic3—44no—
206C22×C32—22no—
207C22×C32—21no—
208C22×C32—22no—
209C22×C32—21no—
210C22×C32—22no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32—42no—
214C22×C32—42no—
215C22×C32—42no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32C2×C4211yescharacteristic
219C22×C32C2×C22⋊C411yescharacteristic
220C22×C32#11711yescharacteristic
221C22×C32C4×D412yes—
222C22×C32C4×D412yes—
223C32×C4—22no—
224C32×C4—44no—
225C3×Dic3—21no—
226C3×Dic3—22no—
227C3×Dic3—44no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3#9912yesdirect product factor
231C22×D4C2×C3×D311yescharacteristic
232C23×C4—31no—
233C23×C4—31no—
234C4×D4—62no—
235C4×D4—62no—
236C2×C4⋊C4—31no—
237C2×C22⋊C4—32no—
238C2×C22⋊C4—31no—
239C2×C22⋊C4—31no—
240C2×C22⋊C4C2×C3×D312yes—
241C2×C42—31no—
242C2×C42—62no—
243#99—34no—
244#99C3×Dic314yesdirect product factor
245#95—62no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—22no—
254C23×C3—22no—
255C23×C3—21no—
256C23×C3—41no—
257C23×C3—41no—
258C23×C3—41no—
259C23×C3—41no—
260C23×C3—41no—
261C23×C3—41no—
262C23×C3—41no—
263C23×C3—41no—
264C23×C3—41no—
265C23×C3—41no—
266C23×C3—81no—
267C23×C3—81no—
268C23×C3—81no—
269C23×C3—81no—
270C23×C3C4×Dic312yescomplemented
271C23×C3C3×C4212yescomplemented
272C23×C3C2×C4×D311yescharacteristic
273C23×C3C2×C4×D311yescharacteristic
274C23×C3D3×D412yes—
275C23×C3#23712yes—
276C23×C3C22×Dic311yescharacteristic
277C23×C3C22×C3×C411yescharacteristic
278C23×C3C22×C3×C411yescharacteristic
279C23×C3C22×C3×C411yescharacteristic
280C23×C3C2×C3×D412yes—
281C23×C3C3×#4112yes—
282C3×D4—24no—
283C3×D4—24no—
284C3×D4—24no—
285C3×D4—24no—
286C3×D4—44no—
287C3×D4—44no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—22no—
295C2×C3×C4—31no—
296C2×C3×C4—31no—
297C2×C3×C4—32no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—44no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4—64no—
306C2×C3×C4—62no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—64no—
310C2×C3×C4—82no—
311C2×C3×C4—82no—
312C2×C3×C4—122no—
313C2×C3×C4—122no—
314C2×C3×C4—121no—
315C2×C3×C4—122no—
316C2×C3×C4—122no—
317C2×C3×C4—122no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4C4×Dic312yescomplemented
321C2×C3×C4C3×C4212yescomplemented
322C2×Dic3—24no—
323C2×Dic3—22no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—24no—
327C2×Dic3—41no—
328C2×Dic3—42no—
329C2×Dic3—42no—
330C2×Dic3—42no—
331C2×Dic3—42no—
332C2×Dic3—42no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3C3×C22⋊C411yescharacteristic
336C2×Dic3C3×C22⋊C412yes—
337C2×Dic3C3×C22⋊C411yescharacteristic
338C2×C32—22no—
339C2×C32—22no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—42no—
343C2×C32C4×C22⋊C411yescharacteristic
344C2×C32C2×#9911yescharacteristic
345C2×C32#41011yescharacteristic
346C24C3×C4×D311yescharacteristic
347C24C22×C3×D311yescharacteristic
348C2×D4—22no—
349C2×D4—22no—
350C2×D4C3×C4×D312yes—
351C2×D4C2×C3×Dic312yes—
352C22×C4—22no—
353C22×C4—31no—
354C22×C4—32no—
355C22×C4—31no—
356C22×C4—32no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—62no—
362C22×C4—122no—
363C22×C4—122no—
364C22×C4C3×C4×D311yescharacteristic
365C4⋊C4—62no—
366C22⋊C4—22no—
367C22⋊C4—34no—
368C22⋊C4—62no—
369C22⋊C4—62no—
370C22⋊C4—62no—
371C22⋊C4C2×C3×Dic314yescomplemented
372C42—61no—
373C42—61no—
374C42—124no—
375C22×C3—22no—
376C22×C3—21no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—22no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3—42no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—81no—
410C22×C3—81no—
411C22×C3—81no—
412C22×C3—82no—
413C22×C3—81no—
414C22×C3—82no—
415C22×C3—82no—
416C22×C3#87711yescharacteristic
417C22×C3D3×C22⋊C411yescharacteristic
418C22×C3#67⋊C412yes—
419C22×C3C2×C4×Dic311yescharacteristic
420C22×C3D4×Dic312yes—
421C22×C3C2×C3×C4211yescharacteristic
422C22×C3C2×C3×C22⋊C411yescharacteristic
423C22×C3C3×#11711yescharacteristic
424C22×C3C3×C4×D412yes—
425C22×C3C3×C4×D412yes—
426C3×C4—22no—
427C3×C4—22no—
428C3×C4—32no—
429C3×C4—42no—
430C3×C4—44no—
431C3×C4—44no—
432C3×C4—61no—
433C3×C4—62no—
434C3×C4—84no—
435C3×C4—124no—
436C3×C4—121no—
437C3×C4—121no—
438Dic3—21no—
439Dic3—22no—
440Dic3—44no—
441Dic3—41no—
442Dic3—41no—
443Dic3C3×#9912yesdirect product factor
444C32C4×#9911yescharacteristic, complemented, Sylow
445C23—21no—
446C23—21no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23C3×C4×Dic312yescomplemented
452C23C2×C3×C4×D311yescharacteristic
453C23C2×C3×C4×D311yescharacteristic
454C23C3×D3×D412yes—
455C23C3×#23712yes—
456C23C22×C3×Dic311yescharacteristic
457D4—24no—
458D4—24no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—24no—
462C2×C4—31no—
463C2×C4—31no—
464C2×C4—32no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—64no—
468C2×C4—62no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—64no—
472C2×C4—122no—
473C2×C4—122no—
474C2×C4—121no—
475C2×C4—122no—
476C2×C4—122no—
477C2×C4—122no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4C3×C4×Dic312yescomplemented
481C2×C3—22no—
482C2×C3—22no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—22no—
486C2×C3—22no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—42no—
493C2×C3—41no—
494C2×C3—41no—
495C2×C3—42no—
496C2×C3—42no—
497C2×C3—42no—
498C2×C3—82no—
499C2×C3#474011yescharacteristic
500C2×C3D3×#9911yescharacteristic
501C2×C3Dic3×C22⋊C411yescharacteristic
502C2×C3C3×C4×C22⋊C411yescharacteristic
503C2×C3C2×C3×#9911yescharacteristic
504C2×C3C3×#41011yescharacteristic
505C22—22no—
506C22—21no—
507C22—22no—
508C22—21no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—41no—
513C22—42no—
514C22—42no—
515C22—41no—
516C22—41no—
517C22C3×#87711yescharacteristic
518C22C3×D3×C22⋊C411yescharacteristic
519C22C3×#67⋊C412yes—
520C22C2×C3×C4×Dic311yescharacteristic
521C22C3×D4×Dic312yes—
522C4—22no—
523C4—32no—
524C4—44no—
525C4—61no—
526C4—62no—
527C4—124no—
528C4—121no—
529C4—121no—
530C3—21no—
531C3Dic3×#9911yescharacteristic, direct product factor
532C3C3×C4×#9911yescharacteristic, complemented
533C2—22no—
534C2—22no—
535C2—21no—
536C2—21no—
537C2—42no—
538C2C3×#474011yescharacteristic
539C2C3×D3×#9911yescharacteristic
540C2C3×Dic3×C22⋊C411yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C2×C3×C42
FrattiniC24C22×C3×D3
FittingC2×C32×#99C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C32×D4C22
cosocleC24×C3C23×C3
hypercenterC2×C3×#99D3
hypocenterC3C3×C4×#99
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×#99

Complements

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

NH ≅ G/Ntype
4. C3×Dic3×C22⋊C4C2semidirect
5. C3×#4527C2semidirect
7. Dic3×#99C3direct (N × H)
9. C23×C3×Dic3C4semidirect
12. C2×C3×#217C4semidirect
17. C2×C3×C4⋊Dic3C4semidirect
19. C2×C3×C4×Dic3C4semidirect
20. C32×#99C4semidirect
21. C3×#834C4semidirect
31. Dic3×C22⋊C4C2×C3semidirect
33. #4527C2×C3semidirect
54. C32×C22⋊C4C2×C4semidirect
58. C3×#217C2×C4semidirect
69. C23×Dic3C3×C4semidirect
82. C2×#217C3×C4semidirect
87. C2×C4⋊Dic3C3×C4semidirect
89. C2×C4×Dic3C3×C4semidirect
92. C3×#99Dic3direct (N × H)
93. C3×#99C3×C4semidirect
95. #834C3×C4semidirect
103. C23×C32C42semidirect
116. C2×C32×C4C42semidirect
193. C3×C22⋊C4C2×Dic3semidirect
194. C3×C22⋊C4C2×C3×C4semidirect
201. #217C2×C3×C4semidirect
230. C3×Dic3#99direct (N × H)
244. #99C3×Dic3direct (N × H)
270. C23×C3C4×Dic3semidirect
271. C23×C3C3×C42semidirect
320. C2×C3×C4C4×Dic3semidirect
321. C2×C3×C4C3×C42semidirect
371. C22⋊C4C2×C3×Dic3semidirect
443. Dic3C3×#99direct (N × H)
444. C32C4×#99semidirect
451. C23C3×C4×Dic3semidirect
480. C2×C4C3×C4×Dic3semidirect
531. C3Dic3×#99direct (N × H)
532. C3C3×C4×#99semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×C32×#992
C2×C3×#8342
C3×Dic3×C22⋊C42
C3×#45272
C3×C4×#993
Dic3×#993