Finite Group Databasebeta

← C3×D3×#836 #13158639

Subgroups — C3×D3×#836 #13158639

Order 1728.

854 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×Q8C211yesmaximal, characteristic
2C3×D3×#208C212yesmaximal
3C3×#63663C211yesmaximal, characteristic, complemented
4C32×#836C211yesmaximal, characteristic, complemented
5C3×#63560C212yesmaximal, complemented
6C2×C3×#836—31nomaximal
7C3×D3×#101—31nomaximal
8D3×#836C311yesmaximal, characteristic, direct product factor
9C2×C33×Q8C2211yescharacteristic
10C32×D3×Q8—22no—
11C32×D3×Q8—22no—
12C2×C32×C4×D3C412yes—
13C2×C32×C4×D3C2211yescharacteristic
14C2×C32×Dic6C412yes—
15C2×C32×Dic6C2211yescharacteristic
16C3×#3748C2212yes—
17C32×#208C2212yes—
18C3×#3711—22no—
19C3×D3×C3⋊C8—22no—
20C22×C32×Q8—31no—
21C2×C3×D3×Q8—21no—
22C2×C3×D3×Q8D311yescharacteristic
23C2×C3×D3×Q8C2×C311yescharacteristic
24C2×C3×#208—32no—
25C3×D3×M16—32no—
26D3×#208C2×C312yes—
27C32×#101—31no—
28#63663C2×C311yescharacteristic, complemented
29C3×#836—21no—
30C3×#836—31no—
31C3×#836—31no—
32C3×#836—32no—
33C3×#836—61no—
34C3×#836D311yescharacteristic, direct product factor
35C3×#836C2×C311yescharacteristic, complemented
36C3×#824—32no—
37#63560C2×C312yescomplemented
38C22×C32×D3C2×C411yescharacteristic
39C33×Q8—22no—
40C2×C33×C4C2×C412yes—
41C2×C33×C4C2311yescharacteristic
42C2×C32×Dic3C2×C412yes—
43C2×C32×Dic3C2×C411yescharacteristic
44C32×C4×D3—22no—
45C32×C4×D3—22no—
46C32×C4×D3D412yes—
47C32×C4×D3D412yes—
48C32×Dic6—22no—
49C32×Dic6—24no—
50C3×C3⋊(C3⋊C8)—22no—
51C32×C3⋊C8—22no—
52C2×C3×#101—91no—
53C2×#836—31no—
54D3×#101—31no—
55C2×C32×Q8—21no—
56C2×C32×Q8—21no—
57C2×C32×Q8—21no—
58C2×C32×Q8—32no—
59C2×C32×Q8—31no—
60C2×C32×Q8—41no—
61C2×C32×Q8—62no—
62C2×C32×Q8—62no—
63C2×C32×Q8C2×D311yescharacteristic
64C2×C32×Q8C2×D311yescharacteristic
65C2×C32×Q8C22×C311yescharacteristic
66C22×C32×C4—31no—
67C22×C32×C4—32no—
68C3×D3×Q8—24no—
69C3×D3×Q8—24no—
70C3×D3×Q8—22no—
71C3×D3×Q8—22no—
72C3×D3×Q8—22no—
73C3×D3×Q8—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3Dic312yes—
77C2×C3×C4×D3C3×C412yes—
78C2×C3×C4×D3C2×D311yescharacteristic
79C2×C3×C4×D3C22×C311yescharacteristic
80C2×C3×Dic6—22no—
81C2×C3×Dic6—21no—
82C2×C3×Dic6Dic312yes—
83C2×C3×Dic6C3×C412yes—
84C2×C3×Dic6C2×D311yescharacteristic
85C2×C3×Dic6C22×C311yescharacteristic
86C32×M16—32no—
87#3748C22×C312yes—
88C3×#208—22no—
89C3×#208—32no—
90C3×#208—32no—
91C3×#208—62no—
92C3×#208—62no—
93C3×#208C2×D312yes—
94C3×#208C22×C312yes—
95C2×C3×C3⋊C8—62no—
96C3×ΓL(1,𝔽25)—62no—
97C3×D3×C8—62no—
98#3711—22no—
99D3×C3⋊C8—22no—
100C22×C33C22×C411yescharacteristic
101C2×C32×D3—22no—
102C2×C32×D3C22⋊C411yescharacteristic
103C2×C32×D3C22⋊C411yescharacteristic
104C33×C4—22no—
105C33×C4C2×D412yes—
106C32×Dic3—22no—
107C32×Dic3C22⋊C412yes—
108C22×C3×Q8—31no—
109C22×C3×Q8—31no—
110C22×C3×Q8—61no—
111C2×D3×Q8C3×D311yescharacteristic
112C2×C3×M16—92no—
113C2×#208—32no—
114D3×M16—32no—
115C3×#101—31no—
116C3×#101—31no—
117C3×#101—61no—
118C3×#101—92no—
119C3×#101—91no—
120#836—31no—
121#836—31no—
122#836—32no—
123#836—61no—
124#836C3×D311yescharacteristic, direct product factor
125#824—32no—
126C23×C32—31no—
127C22×C3×D3—21no—
128C22×C3×D3C2×Dic311yescharacteristic
129C22×C3×D3C2×C3×C411yescharacteristic
130C32×Q8—22no—
131C32×Q8—24no—
132C32×Q8—22no—
133C32×Q8—22no—
134C32×Q8—42no—
135C32×Q8—42no—
136C32×Q8—44no—
137C32×Q8—64no—
138C32×Q8—62no—
139C2×C32×C4—22no—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—31no—
146C2×C32×C4—32no—
147C2×C32×C4—32no—
148C2×C32×C4—32no—
149C2×C32×C4—42no—
150C2×C32×C4—41no—
151C2×C32×C4—62no—
152C2×C32×C4—62no—
153C2×C32×C4C4×D312yes—
154C2×C32×C4C2×Dic312yes—
155C2×C32×C4C2×C3×C412yes—
156C2×C32×C4C22×D311yescharacteristic
157C2×C32×C4C22×D311yescharacteristic
158C2×C32×C4C23×C311yescharacteristic
159C2×C3×Dic3—22no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3C2×Dic312yes—
162C2×C3×Dic3C2×Dic311yescharacteristic
163C2×C3×Dic3C2×C3×C412yes—
164C2×C3×Dic3C2×C3×C411yescharacteristic
165C3×C4×D3—24no—
166C3×C4×D3—24no—
167C3×C4×D3—22no—
168C3×C4×D3—22no—
169C3×C4×D3—22no—
170C3×C4×D3—22no—
171C3×C4×D3—22no—
172C3×C4×D3—22no—
173C3×C4×D3#6712yes—
174C3×C4×D3#6712yes—
175C3×C4×D3C3×D412yes—
176C3×C4×D3C3×D412yes—
177C3×Dic6—24no—
178C3×Dic6—28no—
179C3×Dic6—22no—
180C3×Dic6—22no—
181C3×Dic6—24no—
182C3×Dic6—24no—
183C32×C8—62no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—22no—
186C3×C3⋊C8—22no—
187C3×C3⋊C8—42no—
188C3×C3⋊C8—62no—
189C3×C3⋊C8—62no—
190C3×C3⋊C8—122no—
191C2×#101—91noSylow
192C2×C33—21no—
193C2×C33C2×C22⋊C411yescharacteristic
194C32×D3—21no—
195C32×D3#10112yescomplemented
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—32no—
200C2×C3×Q8—32no—
201C2×C3×Q8—31no—
202C2×C3×Q8—31no—
203C2×C3×Q8—41no—
204C2×C3×Q8—62no—
205C2×C3×Q8—61no—
206C2×C3×Q8—62no—
207C2×C3×Q8—62no—
208C2×C3×Q8—62no—
209C2×C3×Q8—62no—
210C2×C3×Q8—64no—
211C2×C3×Q8—64no—
212C2×C3×Q8D3211yescharacteristic
213C2×C3×Q8C2×C3×D311yescharacteristic
214C2×C3×Q8C2×C3×D311yescharacteristic
215C22×C3×C4—31no—
216C22×C3×C4—31no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4—61no—
220C22×C3×C4—62no—
221D3×Q8—22no—
222D3×Q8—22no—
223C2×C4×D3C3×Dic312yes—
224C2×C4×D3C2×C3×D311yescharacteristic
225C2×Dic6C3×Dic312yes—
226C2×Dic6C2×C3×D311yescharacteristic
227C3×M16—32no—
228C3×M16—32no—
229C3×M16—62no—
230C3×M16—92no—
231C3×M16—182no—
232C2×C3×C8—182no—
233#208—32no—
234#208—32no—
235#208—62no—
236#208—62no—
237#208C2×C3×D312yes—
238C2×C3⋊C8—62no—
239ΓL(1,𝔽25)—62no—
240D3×C8—62no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32—31no—
245C22×C32—31no—
246C22×C32—41no—
247C22×C32—62no—
248C22×C32C2×C4×D311yescharacteristic
249C22×C32C22×Dic311yescharacteristic
250C22×C32C22×C3×C411yescharacteristic
251C2×C3×D3—24no—
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254C2×C3×D3—21no—
255C2×C3×D3—21no—
256C2×C3×D3#21711yescharacteristic
257C2×C3×D3#21711yescharacteristic
258C2×C3×D3C3×C22⋊C411yescharacteristic
259C2×C3×D3C3×C22⋊C411yescharacteristic
260C32×C4—22no—
261C32×C4—24no—
262C32×C4—22no—
263C32×C4—22no—
264C32×C4—22no—
265C32×C4—22no—
266C32×C4—22no—
267C32×C4—32no—
268C32×C4—42no—
269C32×C4—42no—
270C32×C4—42no—
271C32×C4—44no—
272C32×C4—62no—
273C32×C4D3×D412yes—
274C32×C4C2×#6712yes—
275C32×C4C2×C3×D412yes—
276C3×Dic3—24no—
277C3×Dic3—22no—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3#21712yes—
281C3×Dic3C3×C22⋊C412yes—
282C22×Q8—31no—
283C2×M16—92no—
284#101—31no—
285#101—92no—
286#101—91no—
287C33C2×#10111yescharacteristic, complemented, Sylow
288C23×C3—31no—
289C23×C3—31no—
290C23×C3—61no—
291C22×D3C2×C3×Dic311yescharacteristic
292C3×Q8—24no—
293C3×Q8—22no—
294C3×Q8—22no—
295C3×Q8—22no—
296C3×Q8—42no—
297C3×Q8—42no—
298C3×Q8—44no—
299C3×Q8—64no—
300C3×Q8—64no—
301C3×Q8—68no—
302C3×Q8—64no—
303C3×Q8—62no—
304C3×Q8—62no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—31no—
312C2×C3×C4—31no—
313C2×C3×C4—32no—
314C2×C3×C4—32no—
315C2×C3×C4—32no—
316C2×C3×C4—32no—
317C2×C3×C4—32no—
318C2×C3×C4—32no—
319C2×C3×C4—42no—
320C2×C3×C4—41no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—61no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—64no—
330C2×C3×C4—64no—
331C2×C3×C4D3×Dic312yes—
332C2×C3×C4C3×C4×D312yes—
333C2×C3×C4C2×C3×Dic312yes—
334C2×C3×C4C2×D3211yescharacteristic
335C2×C3×C4C22×C3×D311yescharacteristic
336C2×C3×C4C22×C3×D311yescharacteristic
337C2×Dic3C2×C3×Dic312yes—
338C2×Dic3C2×C3×Dic311yescharacteristic
339C4×D3—22no—
340C4×D3—22no—
341C4×D3C3×#6712yes—
342C4×D3C3×#6712yes—
343Dic6—22no—
344Dic6—24no—
345C3×C8—62no—
346C3×C8—62no—
347C3×C8—122no—
348C3×C8—182no—
349C3⋊C8—22no—
350C3⋊C8—62no—
351C3⋊C8—62no—
352C3⋊C8—122no—
353C2×C32—21no—
354C2×C32—22no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—32no—
361C2×C32—41no—
362C2×C32—41no—
363C2×C32—41no—
364C2×C32—42no—
365C2×C32—61no—
366C2×C32D3×C22⋊C411yescharacteristic
367C2×C32C2×#21711yescharacteristic
368C2×C32C2×C3×C22⋊C411yescharacteristic
369C3×D3—22no—
370C3×D3—21no—
371C3×D3—21no—
372C3×D3—22no—
373C3×D3#83612yesdirect product factor
374C3×D3C3×#10112yescomplemented
375C2×Q8—32no—
376C2×Q8—31no—
377C2×Q8—62no—
378C2×Q8—62no—
379C2×Q8C3×D3211yescharacteristic
380C22×C4—31no—
381C22×C4—32no—
382M16—32no—
383M16—92no—
384M16—182no—
385C2×C8—182no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—31no—
390C22×C3—31no—
391C22×C3—31no—
392C22×C3—31no—
393C22×C3—41no—
394C22×C3—61no—
395C22×C3—61no—
396C22×C3—62no—
397C22×C3—62no—
398C22×C3—64no—
399C22×C3C2×D3×Dic311yescharacteristic
400C22×C3C2×C3×C4×D311yescharacteristic
401C22×C3C22×C3×Dic311yescharacteristic
402C2×D3—22no—
403C2×D3C3×#21711yescharacteristic
404C2×D3C3×#21711yescharacteristic
405C3×C4—24no—
406C3×C4—22no—
407C3×C4—22no—
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—32no—
413C3×C4—32no—
414C3×C4—42no—
415C3×C4—42no—
416C3×C4—44no—
417C3×C4—42no—
418C3×C4—62no—
419C3×C4—64no—
420C3×C4—62no—
421C3×C4—62no—
422C3×C4D3×#6712yes—
423C3×C4C3×D3×D412yes—
424C3×C4C2×C3×#6712yes—
425Dic3—22no—
426Dic3C3×#21712yes—
427C32—21no—
428C32—21no—
429C32—21no—
430C32—41no—
431C32D3×#10111yescharacteristic, complemented
432C32C2×#83611yescharacteristic, complemented
433C32C2×C3×#10111yescharacteristic, complemented
434C23—31no—
435Q8—22no—
436Q8—64no—
437Q8—62no—
438C2×C4—31no—
439C2×C4—32no—
440C2×C4—32no—
441C2×C4—32no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4C3×D3×Dic312yes—
445C2×C4C2×C3×D3211yescharacteristic
446C8—62no—
447C8—182no—
448C2×C3—22no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—32no—
456C2×C3—32no—
457C2×C3—41no—
458C2×C3—41no—
459C2×C3—42no—
460C2×C3—41no—
461C2×C3—62no—
462C2×C3—62no—
463C2×C3—61no—
464C2×C3—61no—
465C2×C3D3×#21711yescharacteristic
466C2×C3C3×D3×C22⋊C411yescharacteristic
467C2×C3C2×C3×#21711yescharacteristic
468D3—21no—
469D3C3×#83612yesdirect product factor
470C22—31no—
471C22—31no—
472C22—62no—
473C22C2×C3×D3×Dic311yescharacteristic
474C4—22no—
475C4—32no—
476C4—62no—
477C4C3×D3×#6712yes—
478C3—21no—
479C3—21no—
480C3—21no—
481C3—41no—
482C3D3×#83611yescharacteristic, direct product factor
483C3C3×D3×#10111yescharacteristic, complemented
484C3C2×C3×#83611yescharacteristic, complemented
485C2—21no—
486C2—32no—
487C2—61no—
488C2C3×D3×#21711yescharacteristic
subgroupG/H
centerC2×C3D3×#217
commutatorC22×C32C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC2×C33×Q8C22
socleC2×C33C2×C22⋊C4
prime radicalC22×C32×D3C2×C4
cosocleC2×C32×C4C23×C3
hypercenterC2×C3×Q8D32
hypocenterC32C2×C3×#101
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×Q8

Complements

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

NH ≅ G/Ntype
3. C3×#63663C2semidirect
4. C32×#836C2semidirect
5. C3×#63560C2semidirect
8. D3×#836C3direct (N × H)
28. #63663C2×C3semidirect
34. C3×#836D3direct (N × H)
35. C3×#836C2×C3semidirect
37. #63560C2×C3semidirect
124. #836C3×D3direct (N × H)
195. C32×D3#101semidirect
287. C33C2×#101semidirect
373. C3×D3#836direct (N × H)
374. C3×D3C3×#101semidirect
431. C32D3×#101semidirect
432. C32C2×#836semidirect
433. C32C2×C3×#101semidirect
469. D3C3×#836direct (N × H)
482. C3D3×#836direct (N × H)
483. C3C3×D3×#101semidirect
484. C3C2×C3×#836semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×Q82
C3×D3×#2082
C3×#636632
C32×#8362
C3×#635602
C2×C3×#8363
C3×D3×#1013
D3×#8363