Finite Group Databasebeta

← C3×D3×#323 #11773706

Subgroups — C3×D3×#323 #11773706

Order 1152.

961 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C22⋊C4C211yesmaximal, characteristic
2C3×D3×C22⋊C8C212yesmaximal, complemented
3C32×#323C211yesmaximal, characteristic, complemented
4C3×#4525C211yesmaximal, characteristic, complemented
5C3×#4468C212yesmaximal, complemented
6C2×C3×#323—31nomaximal
7D3×#323C311yesmaximal, characteristic, direct product factor
8C24×C3×D3C411yescharacteristic
9C22×C3×C4×D3C411yescharacteristic
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×C3×#217C411yescharacteristic
13C2×C3×(C2×D3)⋊C4C411yescharacteristic
14C2×C3×(C2×D3)⋊C4C2211yescharacteristic
15C2×C3×D3×C8—22no—
16C3×D3×C22⋊C4—22no—
17C3×D3×C22⋊C4—22no—
18C32×C22⋊C8C2212yescomplemented
19C3×#830C2212yescomplemented
20C3×(C2×D3)⋊C8—22no—
21C22×C3×C22⋊C4—31no—
22C2×D3×C22⋊C4C2×C311yescharacteristic
23C2×C3×C22⋊C8—32no—
24D3×C22⋊C8C2×C312yescomplemented
25C3×#323—21no—
26C3×#323—31no—
27C3×#323—32no—
28C3×#323D311yescharacteristic, direct product factor
29C3×#323C2×C311yescharacteristic, complemented
30#4525C2×C311yescharacteristic, complemented
31#4468C2×C312yescomplemented
32C24×C32C2×C411yescharacteristic
33C23×C3×D3—21no—
34C23×C3×D3—21no—
35C23×C3×D3—22no—
36C23×C3×D3—42no—
37C23×C3×D3—42no—
38C23×C3×D3C814yescomplemented
39C23×C3×D3C2×C411yescharacteristic
40C23×C3×D3C2×C411yescharacteristic
41C22×C32×C4C2×C411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3C2×C411yescharacteristic
44C22×C3×Dic3C2×C411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—42no—
48C2×C3×C4×D3—42no—
49C2×C3×C4×D3D412yes—
50C2×C3×C4×D3D412yes—
51C2×C32×C8—22no—
52C32×C22⋊C4—22no—
53C3×#217—22no—
54C3×(C2×D3)⋊C4—22no—
55C3×(C2×D3)⋊C4—22no—
56C2×C3×C3⋊C8—22no—
57C3×D3×C8—44no—
58C2×#323—31noSylow
59C25×C3—31no—
60C24×D3C3×C411yescharacteristic
61C23×C3×C4—31no—
62C23×C3×C4—31no—
63C22×C4×D3C3×C411yescharacteristic
64C22×C4×D3C22×C311yescharacteristic
65C22×C3×C8—62no—
66C2×C3×C22⋊C4—21no—
67C2×C3×C22⋊C4—31no—
68C2×C3×C22⋊C4—31no—
69C2×C3×C22⋊C4—31no—
70C2×C3×C22⋊C4—62no—
71C2×C3×C22⋊C4—62no—
72C2×C3×C22⋊C4C2×D311yescharacteristic
73C2×C3×C22⋊C4C22×C311yescharacteristic
74C2×#217C3×C411yescharacteristic
75C2×(C2×D3)⋊C4C3×C411yescharacteristic
76C2×(C2×D3)⋊C4C22×C311yescharacteristic
77C2×D3×C8—22no—
78D3×C22⋊C4—22no—
79D3×C22⋊C4—22no—
80C3×C22⋊C8—22no—
81C3×C22⋊C8—32no—
82C3×C22⋊C8—62no—
83C3×C22⋊C8C2×D312yescomplemented
84C3×C22⋊C8C22×C312yescomplemented
85#830C22×C312yescomplemented
86(C2×D3)⋊C8—22no—
87C23×C32—21no—
88C23×C32—21no—
89C23×C32—41no—
90C23×C32—41no—
91C23×C32C2×C812yescomplemented
92C23×C32C22×C411yescharacteristic
93C22×C3×D3—22no—
94C22×C3×D3—22no—
95C22×C3×D3—21no—
96C22×C3×D3—21no—
97C22×C3×D3—24no—
98C22×C3×D3—24no—
99C22×C3×D3—42no—
100C22×C3×D3—42no—
101C22×C3×D3—48no—
102C22×C3×D3—48no—
103C22×C3×D3—42no—
104C22×C3×D3—42no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C22×C3×D3C22⋊C411yescharacteristic
108C22×C3×D3C22⋊C411yescharacteristic
109C22×C3×D3C2×C812yes—
110C22×C3×D3C2×C812yescomplemented
111C22×C3×D3M1612yes—
112C2×C32×C4—21no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C2×D412yes—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3C22⋊C412yes—
120C3×C4×D3—24no—
121C3×C4×D3—42no—
122C3×C4×D3—42no—
123C3×C4×D3—42no—
124C32×C8—42no—
125C3×C3⋊C8—42no—
126C22×C22⋊C4—31no—
127C2×C22⋊C8—32no—
128#323—31no—
129#323—32no—
130#323C3×D311yescharacteristic, direct product factor
131C24×C3—21no—
132C24×C3—31no—
133C24×C3—34no—
134C24×C3—31no—
135C24×C3—62no—
136C24×C3—61no—
137C24×C3—61no—
138C24×C3—122no—
139C24×C3—122no—
140C24×C3C4×D311yescharacteristic
141C24×C3C2×C3×C411yescharacteristic
142C23×D3—21no—
143C23×D3—21no—
144C23×D3—22no—
145C23×D3—42no—
146C23×D3—42no—
147C23×D3C3×C814yescomplemented
148C23×D3C2×C3×C411yescharacteristic
149C23×D3C2×C3×C411yescharacteristic
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—31no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4—31no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4—122no—
159C22×C3×C4—122no—
160C22×C3×C4C4×D311yescharacteristic
161C22×C3×C4C2×C3×C411yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C23×C311yescharacteristic
164C22×Dic3C2×C3×C411yescharacteristic
165C22×Dic3C2×C3×C411yescharacteristic
166C2×C4×D3—21no—
167C2×C4×D3—21no—
168C2×C4×D3—42no—
169C2×C4×D3—42no—
170C2×C4×D3C3×D412yes—
171C2×C4×D3C3×D412yes—
172C2×C3×C8—22no—
173C2×C3×C8—22no—
174C2×C3×C8—42no—
175C2×C3×C8—62no—
176C2×C3×C8—124no—
177C3×C22⋊C4—22no—
178C3×C22⋊C4—22no—
179C3×C22⋊C4—42no—
180C3×C22⋊C4—62no—
181C3×C22⋊C4—62no—
182C3×C22⋊C4—62no—
183#217—22no—
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—22no—
186C2×C3⋊C8—22no—
187D3×C8—44no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—22no—
191C22×C32—42no—
192C22×C32—42no—
193C22×C32—41no—
194C22×C32—41no—
195C22×C32C2×C22⋊C411yescharacteristic
196C22×C32C22×C811yescharacteristic
197C22×C32C2×M1611yescharacteristic
198C2×C3×D3—21no—
199C2×C3×D3—21no—
200C2×C3×D3—24no—
201C2×C3×D3—24no—
202C2×C3×D3—22no—
203C2×C3×D3—48no—
204C2×C3×D3—42no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C2×C3×D3—48no—
208C2×C3×D3—42no—
209C2×C3×D3C22⋊C812yes—
210C2×C3×D3C22⋊C812yes—
211C2×C3×D3#9912yes—
212C2×C3×D3#10012yes—
213C32×C4—22no—
214C32×C4—41no—
215C3×Dic3—22no—
216C3×Dic3—41no—
217C25—31no—
218C23×C4—31no—
219C23×C4—31no—
220C22×C8—62no—
221C2×C22⋊C4—31no—
222C2×C22⋊C4—31no—
223C2×C22⋊C4—31no—
224C2×C22⋊C4—62no—
225C2×C22⋊C4—62no—
226C2×C22⋊C4C2×C3×D311yescharacteristic
227C22⋊C8—32no—
228C22⋊C8—62no—
229C22⋊C8C2×C3×D312yescomplemented
230C23×C3—21no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—22no—
235C23×C3—21no—
236C23×C3—31no—
237C23×C3—31no—
238C23×C3—32no—
239C23×C3—32no—
240C23×C3—32no—
241C23×C3—41no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—41no—
245C23×C3—41no—
246C23×C3—41no—
247C23×C3—62no—
248C23×C3—62no—
249C23×C3—64no—
250C23×C3—64no—
251C23×C3—61no—
252C23×C3—61no—
253C23×C3—81no—
254C23×C3—81no—
255C23×C3—121no—
256C23×C3—121no—
257C23×C3—122no—
258C23×C3—122no—
259C23×C3—128no—
260C23×C3—128no—
261C23×C3—122no—
262C23×C3—122no—
263C23×C3D3×C812yescomplemented
264C23×C3C2×C3×C812yescomplemented
265C23×C3C2×C4×D311yescharacteristic
266C23×C3C22×C3×C411yescharacteristic
267C22×D3—22no—
268C22×D3—22no—
269C22×D3—21no—
270C22×D3—21no—
271C22×D3—24no—
272C22×D3—24no—
273C22×D3—42no—
274C22×D3—42no—
275C22×D3—48no—
276C22×D3—48no—
277C22×D3—42no—
278C22×D3—42no—
279C22×D3—41no—
280C22×D3—41no—
281C22×D3C3×C22⋊C411yescharacteristic
282C22×D3C3×C22⋊C411yescharacteristic
283C22×D3C2×C3×C812yes—
284C22×D3C2×C3×C812yescomplemented
285C22×D3C3×M1612yes—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—32no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—64no—
296C2×C3×C4—61no—
297C2×C3×C4—81no—
298C2×C3×C4—81no—
299C2×C3×C4—122no—
300C2×C3×C4—122no—
301C2×C3×C4—122no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4D3×D412yes—
305C2×C3×C4C2×C3×D412yes—
306C2×Dic3—21no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3C3×C22⋊C412yes—
310C4×D3—24no—
311C4×D3—42no—
312C4×D3—42no—
313C4×D3—42no—
314C3×C8—42no—
315C3×C8—42no—
316C3×C8—82no—
317C3×C8—122no—
318C3⋊C8—42no—
319C2×C32—21no—
320C2×C32—21no—
321C2×C32—42no—
322C2×C32C2×C22⋊C811yescharacteristic
323C2×C32C2×#9911yescharacteristic
324C2×C32C2×#10011yescharacteristic
325C3×D3—22no—
326C3×D3—42no—
327C3×D3#32314yesdirect product factor
328C24—31no—
329C24—34no—
330C24—31no—
331C24—61no—
332C24—61no—
333C24—62no—
334C24—122no—
335C24—122no—
336C24C3×C4×D311yescharacteristic
337C22×C4—31no—
338C22×C4—32no—
339C22×C4—32no—
340C22×C4—31no—
341C22×C4—61no—
342C22×C4—61no—
343C22×C4—122no—
344C22×C4—122no—
345C22×C4C3×C4×D311yescharacteristic
346C22×C4C22×C3×D311yescharacteristic
347C2×C8—22no—
348C2×C8—62no—
349C2×C8—124no—
350C22⋊C4—22no—
351C22⋊C4—62no—
352C22⋊C4—62no—
353C22⋊C4—62no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—32no—
364C22×C3—32no—
365C22×C3—32no—
366C22×C3—32no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—64no—
379C22×C3—64no—
380C22×C3—61no—
381C22×C3—61no—
382C22×C3—62no—
383C22×C3—81no—
384C22×C3—81no—
385C22×C3—82no—
386C22×C3—82no—
387C22×C3—122no—
388C22×C3—122no—
389C22×C3—128no—
390C22×C3—128no—
391C22×C3—121no—
392C22×C3—121no—
393C22×C3D3×C22⋊C411yescharacteristic
394C22×C3C2×D3×C811yescharacteristic
395C22×C3D3×M1611yescharacteristic
396C22×C3C2×C3×C22⋊C411yescharacteristic
397C22×C3C22×C3×C811yescharacteristic
398C22×C3C2×C3×M1611yescharacteristic
399C2×D3—21no—
400C2×D3—21no—
401C2×D3—24no—
402C2×D3—24no—
403C2×D3—22no—
404C2×D3—48no—
405C2×D3—42no—
406C2×D3—41no—
407C2×D3—41no—
408C2×D3—48no—
409C2×D3—42no—
410C2×D3C3×C22⋊C812yes—
411C2×D3C3×C22⋊C812yes—
412C2×D3C3×#9912yes—
413C2×D3C3×#10012yes—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—42no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—62no—
420C3×C4—81no—
421C3×C4—121no—
422Dic3—22no—
423Dic3—41no—
424C32C2×#32311yescharacteristic, complemented, Sylow
425C23—21no—
426C23—21no—
427C23—31no—
428C23—31no—
429C23—32no—
430C23—32no—
431C23—32no—
432C23—41no—
433C23—41no—
434C23—62no—
435C23—62no—
436C23—64no—
437C23—64no—
438C23—61no—
439C23—61no—
440C23—121no—
441C23—121no—
442C23—122no—
443C23—122no—
444C23—128no—
445C23—128no—
446C23—122no—
447C23—122no—
448C23C3×D3×C812yescomplemented
449C23C2×C3×C4×D311yescharacteristic
450C2×C4—21no—
451C2×C4—32no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—64no—
455C2×C4—61no—
456C2×C4—122no—
457C2×C4—122no—
458C2×C4—122no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4C3×D3×D412yes—
462C8—42no—
463C8—122no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—34no—
472C2×C3—41no—
473C2×C3—41no—
474C2×C3—42no—
475C2×C3—42no—
476C2×C3—62no—
477C2×C3—82no—
478C2×C3—122no—
479C2×C3D3×C22⋊C811yescharacteristic
480C2×C3D3×#9911yescharacteristic
481C2×C3D3×#10011yescharacteristic
482C2×C3C2×C3×C22⋊C811yescharacteristic
483C2×C3C2×C3×#9911yescharacteristic
484C2×C3C2×C3×#10011yescharacteristic
485D3—22no—
486D3—42no—
487D3C3×#32314yesdirect product factor
488C22—21no—
489C22—21no—
490C22—22no—
491C22—32no—
492C22—32no—
493C22—32no—
494C22—32no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—64no—
500C22—64no—
501C22—61no—
502C22—61no—
503C22—62no—
504C22—122no—
505C22—122no—
506C22—128no—
507C22—128no—
508C22—121no—
509C22—121no—
510C22C3×D3×C22⋊C411yescharacteristic
511C22C2×C3×D3×C811yescharacteristic
512C22C3×D3×M1611yescharacteristic
513C4—22no—
514C4—41no—
515C4—62no—
516C4—121no—
517C3—21no—
518C3D3×#32311yescharacteristic, direct product factor
519C3C2×C3×#32311yescharacteristic, complemented
520C2—21no—
521C2—21no—
522C2—34no—
523C2—42no—
524C2—62no—
525C2—122no—
526C2C3×D3×C22⋊C811yescharacteristic
527C2C3×D3×#9911yescharacteristic
528C2C3×D3×#10011yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC32×#323C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C3×D3C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#323D3
hypocenterC3C2×C3×#323
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#323

Complements

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

NH ≅ G/Ntype
2. C3×D3×C22⋊C8C2semidirect
3. C32×#323C2semidirect
4. C3×#4525C2semidirect
5. C3×#4468C2semidirect
7. D3×#323C3direct (N × H)
18. C32×C22⋊C8C22semidirect
19. C3×#830C22semidirect
24. D3×C22⋊C8C2×C3semidirect
28. C3×#323D3direct (N × H)
29. C3×#323C2×C3semidirect
30. #4525C2×C3semidirect
31. #4468C2×C3semidirect
38. C23×C3×D3C8semidirect
83. C3×C22⋊C8C2×D3semidirect
84. C3×C22⋊C8C22×C3semidirect
85. #830C22×C3semidirect
91. C23×C32C2×C8semidirect
110. C22×C3×D3C2×C8semidirect
130. #323C3×D3direct (N × H)
147. C23×D3C3×C8semidirect
229. C22⋊C8C2×C3×D3semidirect
263. C23×C3D3×C8semidirect
264. C23×C3C2×C3×C8semidirect
284. C22×D3C2×C3×C8semidirect
327. C3×D3#323direct (N × H)
424. C32C2×#323semidirect
448. C23C3×D3×C8semidirect
487. D3C3×#323direct (N × H)
518. C3D3×#323direct (N × H)
519. C3C2×C3×#323semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C22⋊C42
C3×D3×C22⋊C82
C32×#3232
C3×#45252
C3×#44682
C2×C3×#3233
D3×#3233