Finite Group Databasebeta

← C3×#10591355 #13158303

Subgroups — C3×#10591355 #13158303

Order 1728.

1378 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#3724C212yesmaximal, complemented
3C2×C3×#3722C212yesmaximal
4C32×C3⋊#95C212yesmaximal, complemented
5C3×#4667—32nomaximal
6#10591355C311yesmaximal, characteristic, direct product factor
7C23×C3×C3⋊D3C2211yescharacteristic
8C22×C33×C4C2211yescharacteristic
9C22×C3×C3⋊Dic3C2211yescharacteristic
10C2×C3×C4×C3⋊D3—24no—
11C2×C3×C4×C3⋊D3C414yescomplemented
12C22×C32×Dic3C2214yes—
13C3×#3724—24no—
14C3×#3722—24no—
15C22×C4×C3⋊D3C2×C311yescharacteristic
16C22×C3×C4×D3—32no—
17C22×C3×C4×D3—61no—
18C2×C3×(C2×D3)⋊C4—34no—
19C2×C3×Dic3⋊C4—34no—
20C2×#3724C2×C312yescomplemented
21C2×#3722C2×C312yes—
22C32×#95—32no—
23C3×C3⋊#95—22no—
24C3×C3⋊#95D312yescomplemented
25C3×C3⋊#95C2×C312yescomplemented
26C23×C33C2311yescharacteristic
27C22×C3×C3⋊D3—22no—
28C22×C3×C3⋊D3—22no—
29C22×C3×C3⋊D3C2×C412yes—
30C22×C3×C3⋊D3D412yes—
31C22×C3×C3⋊D3Q812yes—
32C2×C33×C4—22no—
33C2×C33×C4C2×C412yes—
34C2×C3×C3⋊Dic3C2×C412yes—
35C2×C3×C3⋊Dic3D414yes—
36C3×C4×C3⋊D3—28no—
37C2×C32×Dic3—24no—
38C2×C32×Dic3—24no—
39C2×C32×Dic3—24no—
40C3×#380—91no—
41#4667—32no—
42C23×C3⋊D3C22×C311yescharacteristic
43C23×C3×D3—32no—
44C23×C3×D3—61no—
45C22×C32×C4—21no—
46C22×C32×C4—22no—
47C22×C32×C4—34no—
48C22×C32×C4—41no—
49C22×C32×C4C2×D312yes—
50C22×C32×C4C22×C311yescharacteristic
51C22×C3⋊Dic3C22×C311yescharacteristic
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3C3×C414yescomplemented
54C22×C3×Dic3—24no—
55C22×C3×Dic3—32no—
56C22×C3×Dic3—61no—
57C22×C3×Dic3C2×D314yes—
58C22×C3×Dic3C22×C314yes—
59C2×C3×C4×D3—38no—
60C2×C3×C4×D3—68no—
61C2×C3×C4×D3—64no—
62C2×C3×C4×D3—68no—
63C3×(C2×D3)⋊C4—68no—
64C3×Dic3⋊C4—68no—
65#3724—24no—
66#3722—24no—
67C22×C33C22×C411yescharacteristic
68C22×C33C2×D412yes—
69C22×C33C2×D411yescharacteristic
70C22×C33C2×Q811yescharacteristic
71C22×C33#4112yes—
72C2×C3×C3⋊D3—22no—
73C2×C3×C3⋊D3—22no—
74C2×C3×C3⋊D3—24no—
75C2×C3×C3⋊D3—24no—
76C2×C3×C3⋊D3C4⋊C414yescomplemented
77C33×C4—22no—
78C3×C3⋊Dic3C22⋊C414yescomplemented
79C32×Dic3—44no—
80C23×C3×C4—91no—
81C22×C4×D3—32no—
82C22×C4×D3—61no—
83C2×C3×C4⋊C4—92no—
84C2×C3×C22⋊C4—92no—
85C2×(C2×D3)⋊C4—34no—
86C2×Dic3⋊C4—34no—
87C3×#95—32no—
88C3×#95—32no—
89C3×#95—62no—
90C3⋊#95C3×D312yescomplemented
91C23×C32—21no—
92C23×C32—22no—
93C23×C32—41no—
94C23×C32C22×D312yes—
95C23×C32C23×C311yescharacteristic
96C22×C3⋊D3—22no—
97C22×C3⋊D3—22no—
98C22×C3⋊D3C2×C3×C412yes—
99C22×C3⋊D3C3×D412yes—
100C22×C3⋊D3C3×Q812yes—
101C22×C3×D3—34no—
102C22×C3×D3—34no—
103C22×C3×D3—34no—
104C22×C3×D3—62no—
105C22×C3×D3—62no—
106C22×C3×D3—62no—
107C22×C3×D3—64no—
108C22×C3×D3—64no—
109C22×C3×D3—64no—
110C22×C3×D3—64no—
111C2×C32×C4—22no—
112C2×C32×C4—24no—
113C2×C32×C4—24no—
114C2×C32×C4—22no—
115C2×C32×C4—24no—
116C2×C32×C4—42no—
117C2×C32×C4—44no—
118C2×C32×C4—44no—
119C2×C32×C4—64no—
120C2×C32×C4—64no—
121C2×C32×C4—64no—
122C2×C32×C4C4×D314yes—
123C2×C32×C4C2×C3×C412yes—
124C2×C3⋊Dic3C2×C3×C412yes—
125C2×C3⋊Dic3C3×D414yes—
126C4×C3⋊D3—28no—
127C2×C3×Dic3—28no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—34no—
135C2×C3×Dic3—38no—
136C2×C3×Dic3—44no—
137C2×C3×Dic3—44no—
138C2×C3×Dic3—62no—
139C2×C3×Dic3—64no—
140C3×C4×D3—616no—
141C3×C4×D3—616no—
142#380—91noSylow
143C2×C33C2×C22⋊C411yescharacteristic
144C2×C33C2×C4⋊C411yescharacteristic
145C2×C33#11711yescharacteristic
146C2×C33#12112yes—
147C2×C33C22⋊Q812yes—
148C3×C3⋊D3—24no—
149C24×C3—91no—
150C23×D3—32no—
151C23×D3—61no—
152C22×C3×C4—21no—
153C22×C3×C4—22no—
154C22×C3×C4—34no—
155C22×C3×C4—34no—
156C22×C3×C4—41no—
157C22×C3×C4—64no—
158C22×C3×C4—91no—
159C22×C3×C4—94no—
160C22×C3×C4—184no—
161C22×C3×C4D3211yescharacteristic
162C22×C3×C4C2×C3×D312yes—
163C22×Dic3—32no—
164C22×Dic3—61no—
165C22×Dic3C2×C3×D314yes—
166C2×C4×D3—38no—
167C2×C4×D3—64no—
168C2×C4×D3—68no—
169C2×C4×D3—68no—
170C3×C4⋊C4—184no—
171C3×C22⋊C4—184no—
172(C2×D3)⋊C4—68no—
173Dic3⋊C4—68no—
174C22×C32—21no—
175C22×C32—22no—
176C22×C32—21no—
177C22×C32—21no—
178C22×C32—22no—
179C22×C32—22no—
180C22×C32—24no—
181C22×C32—22no—
182C22×C32—24no—
183C22×C32—22no—
184C22×C32—41no—
185C22×C32—42no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32—42no—
189C22×C32C2×C4×D312yes—
190C22×C32#23514yes—
191C22×C32D3×D412yes—
192C22×C32D3×D414yes—
193C22×C32D3×Q812yes—
194C22×C32C22×C3×C411yescharacteristic
195C22×C32C2×C3×D412yes—
196C22×C32C2×C3×D411yescharacteristic
197C22×C32C2×C3×Q811yescharacteristic
198C22×C32C3×#4112yes—
199C2×C3⋊D3—22no—
200C2×C3⋊D3—22no—
201C2×C3⋊D3—24no—
202C2×C3⋊D3—24no—
203C2×C3⋊D3C3×C4⋊C414yescomplemented
204C2×C3×D3—38no—
205C2×C3×D3—64no—
206C2×C3×D3—64no—
207C2×C3×D3—68no—
208C2×C3×D3—64no—
209C2×C3×D3—68no—
210C2×C3×D3—64no—
211C2×C3×D3—64no—
212C2×C3×D3—68no—
213C2×C3×D3—68no—
214C32×C4—22no—
215C32×C4—24no—
216C32×C4—24no—
217C32×C4—44no—
218C32×C4—44no—
219C32×C4—124no—
220C3⋊Dic3C3×C22⋊C414yescomplemented
221C3×Dic3—38no—
222C3×Dic3—48no—
223C3×Dic3—44no—
224C3×Dic3—44no—
225C3×Dic3—64no—
226C23×C4—91no—
227C2×C4⋊C4—92no—
228C2×C22⋊C4—92no—
229#95—32no—
230C33#38011yescharacteristic, complemented, Sylow
231C23×C3—22no—
232C23×C3—21no—
233C23×C3—41no—
234C23×C3—92no—
235C23×C3—92no—
236C23×C3—92no—
237C23×C3—182no—
238C23×C3—182no—
239C23×C3C2×D3211yescharacteristic
240C23×C3C22×C3×D312yes—
241C22×D3—34no—
242C22×D3—34no—
243C22×D3—34no—
244C22×D3—62no—
245C22×D3—62no—
246C22×D3—62no—
247C22×D3—64no—
248C22×D3—64no—
249C22×D3—64no—
250C22×D3—64no—
251C2×C3×C4—24no—
252C2×C3×C4—22no—
253C2×C3×C4—24no—
254C2×C3×C4—22no—
255C2×C3×C4—24no—
256C2×C3×C4—44no—
257C2×C3×C4—44no—
258C2×C3×C4—42no—
259C2×C3×C4—68no—
260C2×C3×C4—64no—
261C2×C3×C4—64no—
262C2×C3×C4—64no—
263C2×C3×C4—64no—
264C2×C3×C4—64no—
265C2×C3×C4—64no—
266C2×C3×C4—92no—
267C2×C3×C4—94no—
268C2×C3×C4—124no—
269C2×C3×C4—124no—
270C2×C3×C4—188no—
271C2×C3×C4#62412yes—
272C2×C3×C4C3×C4×D314yes—
273C2×Dic3—24no—
274C2×Dic3—24no—
275C2×Dic3—24no—
276C2×Dic3—34no—
277C2×Dic3—38no—
278C2×Dic3—62no—
279C2×Dic3—64no—
280C4×D3—616no—
281C4×D3—616no—
282C2×C32—22no—
283C2×C32—24no—
284C2×C32—22no—
285C2×C32—24no—
286C2×C32—22no—
287C2×C32—21no—
288C2×C32—21no—
289C2×C32—22no—
290C2×C32—21no—
291C2×C32—22no—
292C2×C32—41no—
293C2×C32—41no—
294C2×C32—41no—
295C2×C32—42no—
296C2×C32—42no—
297C2×C32#87212yes—
298C2×C32D3×C22⋊C412yes—
299C2×C32#88414yes—
300C2×C32D3×C4⋊C412yes—
301C2×C32#89614yes—
302C2×C32C2×C3×C22⋊C411yescharacteristic
303C2×C32C2×C3×C4⋊C411yescharacteristic
304C2×C32C3×#11711yescharacteristic
305C2×C32C3×#12112yes—
306C2×C32C3×C22⋊Q812yes—
307C3⋊D3—24no—
308C3×D3—68no—
309C3×D3—68no—
310C24—91no—
311C22×C4—34no—
312C22×C4—91no—
313C22×C4—94no—
314C22×C4—184no—
315C22×C4C3×D3211yescharacteristic
316C4⋊C4—184no—
317C22⋊C4—184no—
318C22×C3—21no—
319C22×C3—22no—
320C22×C3—24no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—22no—
326C22×C3—22no—
327C22×C3—24no—
328C22×C3—41no—
329C22×C3—42no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—42no—
333C22×C3—94no—
334C22×C3—184no—
335C22×C3—182no—
336C22×C3—184no—
337C22×C3—182no—
338C22×C3#379711yescharacteristic
339C22×C3#379812yes—
340C22×C3#380211yescharacteristic
341C22×C3C2×#62411yescharacteristic
342C22×C3#381112yes—
343C22×C3C2×C3×C4×D312yes—
344C22×C3C3×#23514yes—
345C22×C3C3×D3×D412yes—
346C22×C3C3×D3×D414yes—
347C22×C3C3×D3×Q812yes—
348C2×D3—38no—
349C2×D3—64no—
350C2×D3—64no—
351C2×D3—68no—
352C2×D3—64no—
353C2×D3—68no—
354C2×D3—64no—
355C2×D3—68no—
356C2×D3—68no—
357C2×D3—64no—
358C3×C4—24no—
359C3×C4—24no—
360C3×C4—22no—
361C3×C4—44no—
362C3×C4—44no—
363C3×C4—94no—
364C3×C4—128no—
365C3×C4—124no—
366C3×C4—124no—
367Dic3—38no—
368Dic3—44no—
369Dic3—64no—
370C32—22no—
371C32—21no—
372C32—41no—
373C32#466712yescomplemented
374C32C3×#38011yescharacteristic, complemented
375C23—92no—
376C23—92no—
377C23—92no—
378C23—182no—
379C23—182no—
380C23C2×C3×D3211yescharacteristic
381C2×C4—22no—
382C2×C4—64no—
383C2×C4—64no—
384C2×C4—64no—
385C2×C4—92no—
386C2×C4—94no—
387C2×C4—188no—
388C2×C4C3×#62412yes—
389C2×C3—21no—
390C2×C3—22no—
391C2×C3—22no—
392C2×C3—24no—
393C2×C3—21no—
394C2×C3—22no—
395C2×C3—21no—
396C2×C3—22no—
397C2×C3—24no—
398C2×C3—22no—
399C2×C3—41no—
400C2×C3—42no—
401C2×C3—41no—
402C2×C3—41no—
403C2×C3—42no—
404C2×C3—184no—
405C2×C3#6386512yes—
406C2×C3#6387411yescharacteristic
407C2×C3#6390011yescharacteristic
408C2×C3#6391212yes—
409C2×C3#6397411yescharacteristic
410C2×C3C3×#87212yes—
411C2×C3C3×D3×C22⋊C412yes—
412C2×C3C3×#88414yes—
413C2×C3C3×D3×C4⋊C412yes—
414C2×C3C3×#89614yes—
415D3—68no—
416D3—68no—
417C22—94no—
418C22—182no—
419C22—184no—
420C22—182no—
421C22—184no—
422C22C3×#379711yescharacteristic
423C22C3×#379812yes—
424C22C3×#380211yescharacteristic
425C22C2×C3×#62411yescharacteristic
426C22C3×#381112yes—
427C4—22no—
428C4—94no—
429C4—124no—
430C3—21no—
431C3—22no—
432C3—41no—
433C3#1059135511yescharacteristic, direct product factor
434C3C3×#466712yescomplemented
435C2—184no—
436C2C3×#6386512yes—
437C2C3×#6387411yescharacteristic
438C2C3×#6390011yescharacteristic
439C2C3×#6391212yes—
440C2C3×#6397411yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C3×C3⋊D3C22
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#380
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3724C2semidirect
4. C32×C3⋊#95C2semidirect
6. #10591355C3direct (N × H)
11. C2×C3×C4×C3⋊D3C4semidirect
20. C2×#3724C2×C3semidirect
24. C3×C3⋊#95D3semidirect
25. C3×C3⋊#95C2×C3semidirect
53. C2×C4×C3⋊D3C3×C4semidirect
76. C2×C3×C3⋊D3C4⋊C4semidirect
78. C3×C3⋊Dic3C22⋊C4semidirect
90. C3⋊#95C3×D3semidirect
203. C2×C3⋊D3C3×C4⋊C4semidirect
220. C3⋊Dic3C3×C22⋊C4semidirect
230. C33#380semidirect
373. C32#4667semidirect
374. C32C3×#380semidirect
433. C3#10591355direct (N × H)
434. C3C3×#4667semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×C3⋊D32
C2×C3×#37242
C2×C3×#37222
C32×C3⋊#952
C3×#46673
#105913553