Finite Group Databasebeta

← C3×#10590495 #13157463

Subgroups — C3×#10590495 #13157463

Order 1728.

520 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64099C211yesmaximal, characteristic
2C3×#63843C211yesmaximal, characteristic
3C32×#810C211yesmaximal, characteristic
4C32×#808C211yesmaximal, characteristic
5C3×#63575C211yesmaximal, characteristic
6C3×#63572C211yesmaximal, characteristic
7C3×#63566C211yesmaximal, characteristic
8C3×#4857—31nomaximal
9C3×#4796—31nomaximal
10#10590495C311yesmaximal, characteristic, direct product factor
11C2×C32×Dic6C2211yescharacteristic
12C33×C4⋊C4C2211yescharacteristic
13C3×C4⋊(C3⋊Dic3)—21no—
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C3×#3750—21no—
16C3×C4×C3⋊Dic3C2211yescharacteristic
17C32×C4⋊Dic3C2211yescharacteristic
18C2×C32×C3⋊C8C2211yescharacteristic
19C2×C32×C3⋊C8C2211yescharacteristic
20C3×Dic3⋊Dic3—21no—
21C3×Dic32—21no—
22#64099C2×C311yescharacteristic
23C3×Q8×Dic3—31no—
24C3×#890—31no—
25C3×#890—31no—
26C3×#890—61no—
27C3×#887—31no—
28#63843C2×C311yescharacteristic
29C32×#106—31no—
30C32×#103—31no—
31C3×#835—31no—
32C3×#818—31no—
33C3×#816—31no—
34C3×Dic3⋊C8—31no—
35C3×Dic3⋊C8—31no—
36C3×#810—21no—
37C3×#810D311yescharacteristic
38C3×#810C2×C311yescharacteristic
39C3×#808—21no—
40C3×#808D311yescharacteristic
41C3×#808C2×C311yescharacteristic
42C3×#807—31no—
43#63575C2×C311yescharacteristic
44#63572C2×C311yescharacteristic
45#63566C2×C311yescharacteristic
46C2×C33×C4—21no—
47C2×C33×C4C2311yescharacteristic
48C2×C3×C3⋊Dic3—21no—
49C2×C3×C3⋊Dic3D411yescharacteristic
50C2×C3×C3⋊Dic3D411yescharacteristic
51C2×C32×Dic3—21no—
52C2×C32×Dic3—21no—
53C32×Dic6—21no—
54C32×Dic6Q812yes—
55C32×C3⋊C8—21no—
56C32×C3⋊C8—21no—
57C3×#479—91no—
58#4857—31no—
59#4796—31no—
60C2×C32×Q8—31no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2×D311yescharacteristic
63C2×C3×Dic6C22×C311yescharacteristic
64C2×C32×C8—31no—
65C2×C32×C8—31no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4—31no—
70C32×C4⋊C4—41no—
71C32×C4⋊C4C2×D311yescharacteristic
72C32×C4⋊C4C2×D311yescharacteristic
73C32×C4⋊C4C22×C311yescharacteristic
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)C22×C311yescharacteristic
76#3750—21no—
77C4×C3⋊Dic3C22×C311yescharacteristic
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3—31no—
80C3×C4⋊Dic3—31no—
81C3×C4⋊Dic3—61no—
82C3×C4⋊Dic3—61no—
83C3×C4⋊Dic3—61no—
84C3×C4⋊Dic3—61no—
85C3×C4⋊Dic3—62no—
86C3×C4⋊Dic3C2×D311yescharacteristic
87C3×C4⋊Dic3C22×C311yescharacteristic
88C3×Dic3⋊C4—61no—
89C3×Dic3⋊C4—61no—
90C3×Dic3⋊C4—61no—
91C3×Dic3⋊C4—62no—
92C3×C4×Dic3—31no—
93C3×C4×Dic3—31no—
94C3×C4×Dic3—61no—
95C3×C4×Dic3—61no—
96C3×C4×Dic3—61no—
97C2×C3×C3⋊C8—21no—
98C2×C3×C3⋊C8—21no—
99C2×C3×C3⋊C8C2×D311yescharacteristic
100C2×C3×C3⋊C8C2×D311yescharacteristic
101C2×C3×C3⋊C8C22×C311yescharacteristic
102C2×C3×C3⋊C8C22×C311yescharacteristic
103Dic3⋊Dic3—21no—
104Dic32—21no—
105C22×C33C2×D411yescharacteristic
106C33×C4—41no—
107C33×C4C2×Q811yescharacteristic
108C33×C4#4111yescharacteristic
109C3×C3⋊Dic3—21no—
110C3×C3⋊Dic3—21no—
111C3×C3⋊Dic3—41no—
112C32×Dic3—22no—
113C32×Dic3—41no—
114C3×#125—91no—
115C3×C4×Q8—91no—
116Q8×Dic3—31no—
117#890—31no—
118#890—31no—
119#890—61no—
120#887—31no—
121C3×#107—91no—
122C3×#106—31no—
123C3×#106—31no—
124C3×#106—61no—
125C3×C4⋊C8—91no—
126C3×#103—31no—
127C3×#103—31no—
128C3×#103—61no—
129C3×#103—91no—
130#835—31no—
131#818—31no—
132#816—31no—
133Dic3⋊C8—31no—
134Dic3⋊C8—31no—
135#810C3×D311yescharacteristic
136#808C3×D311yescharacteristic
137#807—31no—
138C32×Q8—32no—
139C32×Q8—61no—
140C2×C32×C4—21no—
141C2×C32×C4—22no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4—41no—
148C2×C32×C4—41no—
149C2×C32×C4—41no—
150C2×C32×C4—42no—
151C2×C32×C4—61no—
152C2×C32×C4—61no—
153C2×C32×C4C22×D311yescharacteristic
154C2×C32×C4C22×D311yescharacteristic
155C2×C32×C4C23×C311yescharacteristic
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C3×D411yescharacteristic
158C2×C3⋊Dic3C3×D411yescharacteristic
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—31no—
164C2×C3×Dic3—31no—
165C2×C3×Dic3—31no—
166C2×C3×Dic3—31no—
167C2×C3×Dic3—41no—
168C2×C3×Dic3—41no—
169C2×C3×Dic3—61no—
170C2×C3×Dic3—61no—
171C2×C3×Dic3—62no—
172C2×C3×Dic3—61no—
173C2×C3×Dic3—61no—
174C3×Dic6—21no—
175C3×Dic6—21no—
176C3×Dic6—22no—
177C3×Dic6—41no—
178C3×Dic6Dic612yes—
179C3×Dic6C3×Q812yes—
180C32×C8—61no—
181C32×C8—61no—
182C3×C3⋊C8—22no—
183C3×C3⋊C8—21no—
184C3×C3⋊C8—21no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—41no—
188#479—91noSylow
189C2×C33C22⋊Q811yescharacteristic
190C2×C33#13511yescharacteristic
191C2×C33#13711yescharacteristic
192C2×C3×Q8—31no—
193C2×C3×Q8—31no—
194C2×C3×Q8—61no—
195C2×Dic6C2×C3×D311yescharacteristic
196C2×C3×C8—31no—
197C2×C3×C8—31no—
198C2×C3×C8—31no—
199C2×C3×C8—31no—
200C2×C3×C8—61no—
201C2×C3×C8—61no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—31no—
206C3×C4⋊C4—31no—
207C3×C4⋊C4—41no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—91no—
210C3×C4⋊C4—181no—
211C3×C4⋊C4—181no—
212C3×C4⋊C4—181no—
213C3×C4⋊C4D3211yescharacteristic
214C3×C4⋊C4C2×C3×D311yescharacteristic
215C3×C4⋊C4C2×C3×D311yescharacteristic
216C3×C42—91no—
217C3×C42—181no—
218C4⋊Dic3—31no—
219C4⋊Dic3—31no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—62no—
225C4⋊Dic3C2×C3×D311yescharacteristic
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229Dic3⋊C4—62no—
230C4×Dic3—31no—
231C4×Dic3—31no—
232C4×Dic3—61no—
233C4×Dic3—61no—
234C4×Dic3—61no—
235C2×C3⋊C8C2×C3×D311yescharacteristic
236C2×C3⋊C8C2×C3×D311yescharacteristic
237C22×C32—21no—
238C22×C32—21no—
239C22×C32—21no—
240C22×C32—41no—
241C22×C32D3×D411yescharacteristic
242C22×C32D3×D411yescharacteristic
243C22×C32C2×C3×D411yescharacteristic
244C32×C4—21no—
245C32×C4—21no—
246C32×C4—21no—
247C32×C4—21no—
248C32×C4—21no—
249C32×C4—21no—
250C32×C4—41no—
251C32×C4—41no—
252C32×C4—41no—
253C32×C4—42no—
254C32×C4—41no—
255C32×C4—41no—
256C32×C4—62no—
257C32×C4—81no—
258C32×C4—81no—
259C32×C4—82no—
260C32×C4—121no—
261C32×C4C2×Dic611yescharacteristic
262C32×C4#23511yescharacteristic
263C32×C4#23711yescharacteristic
264C32×C4D3×Q811yescharacteristic
265C32×C4C2×C3×Q811yescharacteristic
266C32×C4C3×#4111yescharacteristic
267C3⋊Dic3—21no—
268C3⋊Dic3—21no—
269C3⋊Dic3—41no—
270C3×Dic3—22no—
271C3×Dic3—22no—
272C3×Dic3—42no—
273C3×Dic3—41no—
274C3×Dic3—41no—
275C3×Dic3—61no—
276C3×Dic3—61no—
277C3×Dic3—61no—
278C3×Dic3—61no—
279C3×Dic3—81no—
280C3×Dic3—121no—
281C3×Dic3—121no—
282C3×Dic3—122no—
283C3×Dic3—121no—
284C3×Dic3—121no—
285#125—91no—
286C4×Q8—91no—
287#107—91no—
288#106—31no—
289C4⋊C8—91no—
290#103—31no—
291#103—91no—
292C33#47911yescharacteristic, complemented, Sylow
293C3×Q8—32no—
294C3×Q8—32no—
295C3×Q8—62no—
296C3×Q8—61no—
297C3×Q8—61no—
298C3×Q8—121no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—42no—
309C2×C3×C4—41no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—91no—
315C2×C3×C4—91no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—181no—
319C2×C3×C4C2×D3211yescharacteristic
320C2×C3×C4C22×C3×D311yescharacteristic
321C2×C3×C4C22×C3×D311yescharacteristic
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—31no—
325C2×Dic3—31no—
326C2×Dic3—31no—
327C2×Dic3—31no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—62no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333Dic6—21no—
334Dic6C3×Dic612yes—
335C3×C8—62no—
336C3×C8—61no—
337C3×C8—61no—
338C3×C8—61no—
339C3×C8—61no—
340C3×C8—121no—
341C3⋊C8—21no—
342C3⋊C8—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32—21no—
351C2×C32—21no—
352C2×C32—41no—
353C2×C32—41no—
354C2×C32—41no—
355C2×C32#87811yescharacteristic
356C2×C32#89611yescharacteristic
357C2×C32#91511yescharacteristic
358C2×C32#91511yescharacteristic
359C2×C32#91611yescharacteristic
360C2×C32#91911yescharacteristic
361C2×C32C3×C22⋊Q811yescharacteristic
362C2×C32C3×#13511yescharacteristic
363C2×C32C3×#13711yescharacteristic
364C2×Q8—31no—
365C2×C8—31no—
366C2×C8—31no—
367C4⋊C4—31no—
368C4⋊C4—91no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C4⋊C4—181no—
372C4⋊C4C3×D3211yescharacteristic
373C42—91no—
374C42—181no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—41no—
379C22×C3#381111yescharacteristic
380C22×C3C3×D3×D411yescharacteristic
381C22×C3C3×D3×D411yescharacteristic
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—42no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4—41no—
394C3×C4—62no—
395C3×C4—62no—
396C3×C4—81no—
397C3×C4—81no—
398C3×C4—82no—
399C3×C4—122no—
400C3×C4—121no—
401C3×C4—121no—
402C3×C4—181no—
403C3×C4—181no—
404C3×C4—241no—
405C3×C4—361no—
406C3×C4D3×Dic611yescharacteristic
407C3×C4#379511yescharacteristic
408C3×C4C2×C3×Dic611yescharacteristic
409C3×C4C3×#23511yescharacteristic
410C3×C4C3×#23711yescharacteristic
411C3×C4C3×D3×Q811yescharacteristic
412Dic3—22no—
413Dic3—41no—
414Dic3—61no—
415Dic3—61no—
416Dic3—61no—
417Dic3—61no—
418Dic3—121no—
419Dic3—121no—
420Dic3—122no—
421Dic3—121no—
422Dic3—121no—
423C32—21no—
424C32—21no—
425C32—21no—
426C32—41no—
427C32#479611yescharacteristic, complemented
428C32#485711yescharacteristic, complemented
429C32C3×#47911yescharacteristic, complemented
430Q8—32no—
431Q8—61no—
432C2×C4—21no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—91no—
436C2×C4—91no—
437C2×C4—181no—
438C2×C4C2×C3×D3211yescharacteristic
439C8—61no—
440C8—61no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3#6389611yescharacteristic
454C2×C3#6393111yescharacteristic
455C2×C3#6395011yescharacteristic
456C2×C3C3×#87811yescharacteristic
457C2×C3C3×#89611yescharacteristic
458C2×C3C3×#91511yescharacteristic
459C2×C3C3×#91511yescharacteristic
460C2×C3C3×#91611yescharacteristic
461C2×C3C3×#91911yescharacteristic
462C22C3×#381111yescharacteristic
463C4—41no—
464C4—62no—
465C4—121no—
466C4—181no—
467C4—181no—
468C4—361no—
469C4C3×D3×Dic611yescharacteristic
470C4C3×#379511yescharacteristic
471C3—21no—
472C3—21no—
473C3—21no—
474C3—41no—
475C3#1059049511yescharacteristic, direct product factor
476C3C3×#479611yescharacteristic, complemented
477C3C3×#485711yescharacteristic, complemented
478C2C3×#6389611yescharacteristic
479C2C3×#6393111yescharacteristic
480C2C3×#6395011yescharacteristic
subgroupG/H
centerC22×C3#3811
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×C4⋊C4C22
socle, prime radicalC22×C33C2×D4
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#479
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
10. #10590495C3direct (N × H)
292. C33#479semidirect
427. C32#4796semidirect
428. C32#4857semidirect
429. C32C3×#479semidirect
475. C3#10590495direct (N × H)
476. C3C3×#4796semidirect
477. C3C3×#4857semidirect

Maximal subgroups

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

subgroupindex
C3×#640992
C3×#638432
C32×#8102
C32×#8082
C3×#635752
C3×#635722
C3×#635662
C3×#48573
C3×#47963
#105904953