Finite Group Databasebeta

← C3×#10591370 #13158379

Subgroups — C3×#10591370 #13158379

Order 1728.

1762 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic
2C22×C3×#624C212yesmaximal
3C32×C3⋊#95C212yesmaximal, complemented
4C3×#63579C212yesmaximal, complemented
5C3×D3×#95—32nomaximal
6#10591370C311yesmaximal, 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—
13C2×C3×#624—24no—
14C2×C3×#624—24no—
15C2×C3×#624C418yescomplemented
16C22×C4×C3⋊D3C2×C311yescharacteristic
17C22×C3×C4×D3—32no—
18C22×C3×C4×D3—34no—
19C22×C3×C4×D3—61no—
20C22×#624C2×C312yes—
21C32×#95—32no—
22C3×C3⋊#95—22no—
23C3×C3⋊#95—34no—
24C3×C3⋊#95D312yescomplemented
25C3×C3⋊#95C2×C312yescomplemented
26#63579C2×C312yescomplemented
27C23×C33C2311yescharacteristic
28C22×C3×C3⋊D3C2×C414yes—
29C22×C3×C3⋊D3C2×C412yes—
30C22×C3×C3⋊D3D412yes—
31C22×C3×C3⋊D3D414yes—
32C22×C3×C3⋊D3Q812yes—
33C2×C33×C4—22no—
34C2×C33×C4C2×C412yescomplemented
35C2×C3×C3⋊Dic3—22no—
36C2×C3×C3⋊Dic3C2×C412yescomplemented
37C3×C4×C3⋊D3—28no—
38C2×C32×Dic3—24no—
39C2×C32×Dic3—24no—
40C2×C32×Dic3C2×C418yescomplemented
41C3×#624—216no—
42C2×C3×#95—91no—
43D3×#95—32no—
44C23×C3⋊D3C22×C311yescharacteristic
45C23×C3×D3—32no—
46C23×C3×D3—61no—
47C22×C32×C4—21no—
48C22×C32×C4—22no—
49C22×C32×C4—34no—
50C22×C32×C4—41no—
51C22×C32×C4C2×D312yes—
52C22×C32×C4C22×C311yescharacteristic
53C22×C3⋊Dic3C22×C311yescharacteristic
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3C3×C414yescomplemented
56C22×C3×Dic3—24no—
57C22×C3×Dic3—32no—
58C22×C3×Dic3—61no—
59C22×C3×Dic3C2×D314yes—
60C22×C3×Dic3C22×C314yes—
61C2×C3×C4×D3—38no—
62C2×C3×C4×D3—316no—
63C2×C3×C4×D3—68no—
64C2×C3×C4×D3—68no—
65C2×C3×C4×D3—68no—
66C2×C3×C4×D3—64no—
67C2×C3×C4×D3—68no—
68C2×#624—24no—
69C2×#624—24no—
70C2×#624C3×C418yescomplemented
71C22×C33C22×C412yes—
72C22×C33C22×C411yescharacteristic
73C22×C33C2×D411yescharacteristic
74C22×C33C2×D412yes—
75C22×C33C2×Q811yescharacteristic
76C2×C3×C3⋊D3C4214yes—
77C2×C3×C3⋊D3C22⋊C418yes—
78C2×C3×C3⋊D3C22⋊C414yes—
79C2×C3×C3⋊D3C4⋊C418yes—
80C2×C3×C3⋊D3C4⋊C414yes—
81C33×C4—22no—
82C3×C3⋊Dic3—22no—
83C32×Dic3—28no—
84C23×C3×C4—92no—
85C23×C3×C4—91no—
86C22×C4×D3—32no—
87C22×C4×D3—34no—
88C22×C4×D3—61no—
89C3×#95—32no—
90C3×#95—32no—
91C3×#95—62no—
92C3×#95—92no—
93C3⋊#95—34no—
94C3⋊#95C3×D312yescomplemented
95C23×C32—21no—
96C23×C32—22no—
97C23×C32—41no—
98C23×C32C22×D312yes—
99C23×C32C23×C311yescharacteristic
100C22×C3⋊D3C2×C3×C414yes—
101C22×C3⋊D3C2×C3×C412yes—
102C22×C3⋊D3C3×D412yes—
103C22×C3⋊D3C3×D414yes—
104C22×C3⋊D3C3×Q812yes—
105C22×C3×D3—38no—
106C22×C3×D3—34no—
107C22×C3×D3—34no—
108C22×C3×D3—38no—
109C22×C3×D3—34no—
110C22×C3×D3—64no—
111C22×C3×D3—62no—
112C22×C3×D3—62no—
113C22×C3×D3—64no—
114C22×C3×D3—62no—
115C2×C32×C4—22no—
116C2×C32×C4—24no—
117C2×C32×C4—24no—
118C2×C32×C4—22no—
119C2×C32×C4—24no—
120C2×C32×C4—38no—
121C2×C32×C4—42no—
122C2×C32×C4—44no—
123C2×C32×C4—44no—
124C2×C32×C4—64no—
125C2×C32×C4—64no—
126C2×C32×C4C4×D314yescomplemented
127C2×C32×C4C2×C3×C412yescomplemented
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C2×C3×C412yescomplemented
130C4×C3⋊D3—28no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3—28no—
136C2×C3×Dic3—34no—
137C2×C3×Dic3—44no—
138C2×C3×Dic3—44no—
139C2×C3×Dic3—62no—
140C2×C3×Dic3—64no—
141C2×C3×Dic3—64no—
142C2×C3×Dic3C4×D318yescomplemented
143C2×C3×Dic3C2×C3×C418yescomplemented
144C3×C4×D3—632no—
145C3×C4×D3—616no—
146C3×C4×D3—616no—
147#624—216no—
148C2×#95—91noSylow
149C2×C33C2×C4211yescharacteristic
150C2×C33C2×C22⋊C412yes—
151C2×C33C2×C22⋊C411yescharacteristic
152C2×C33C2×C4⋊C412yes—
153C2×C33C2×C4⋊C411yescharacteristic
154C3×C3⋊D3#9518yescomplemented
155C24×C3—91no—
156C23×D3—32no—
157C23×D3—61no—
158C22×C3×C4—21no—
159C22×C3×C4—22no—
160C22×C3×C4—34no—
161C22×C3×C4—34no—
162C22×C3×C4—41no—
163C22×C3×C4—64no—
164C22×C3×C4—98no—
165C22×C3×C4—91no—
166C22×C3×C4—94no—
167C22×C3×C4—184no—
168C22×C3×C4—184no—
169C22×C3×C4—184no—
170C22×C3×C4D3211yescharacteristic
171C22×C3×C4C2×C3×D312yes—
172C22×Dic3—32no—
173C22×Dic3—61no—
174C22×Dic3C2×C3×D314yes—
175C2×C4×D3—38no—
176C2×C4×D3—316no—
177C2×C4×D3—64no—
178C2×C4×D3—68no—
179C2×C4×D3—68no—
180C2×C4×D3—68no—
181C2×C4×D3—68no—
182C22×C32—21no—
183C22×C32—22no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32—22no—
187C22×C32—24no—
188C22×C32—22no—
189C22×C32—22no—
190C22×C32—24no—
191C22×C32—22no—
192C22×C32—41no—
193C22×C32—42no—
194C22×C32—42no—
195C22×C32—41no—
196C22×C32—41no—
197C22×C32C2×C4×D314yes—
198C22×C32C2×C4×D312yes—
199C22×C32D3×D412yes—
200C22×C32D3×D414yes—
201C22×C32D3×Q812yes—
202C22×C32C22×C3×C412yes—
203C22×C32C22×C3×C411yescharacteristic
204C22×C32C2×C3×D411yescharacteristic
205C22×C32C2×C3×D412yes—
206C22×C32C2×C3×Q811yescharacteristic
207C2×C3⋊D3C3×C4214yes—
208C2×C3⋊D3C3×C22⋊C418yes—
209C2×C3⋊D3C3×C22⋊C414yes—
210C2×C3⋊D3C3×C4⋊C418yes—
211C2×C3⋊D3C3×C4⋊C414yes—
212C2×C3×D3—38no—
213C2×C3×D3—316no—
214C2×C3×D3—38no—
215C2×C3×D3—316no—
216C2×C3×D3—38no—
217C2×C3×D3—64no—
218C2×C3×D3—64no—
219C2×C3×D3—68no—
220C2×C3×D3—68no—
221C2×C3×D3—64no—
222C32×C4—22no—
223C32×C4—24no—
224C32×C4—24no—
225C32×C4—44no—
226C32×C4—44no—
227C32×C4—68no—
228C3⋊Dic3—22no—
229C3×Dic3—28no—
230C3×Dic3—28no—
231C3×Dic3—48no—
232C3×Dic3—64no—
233C3×Dic3—64no—
234C23×C4—92no—
235C23×C4—91no—
236#95—32no—
237#95—92no—
238C33C2×#9511yescharacteristic, complemented, Sylow
239C23×C3—22no—
240C23×C3—21no—
241C23×C3—41no—
242C23×C3—92no—
243C23×C3—94no—
244C23×C3—92no—
245C23×C3—92no—
246C23×C3—94no—
247C23×C3C2×D3211yescharacteristic
248C23×C3C22×C3×D312yes—
249C22×D3—38no—
250C22×D3—34no—
251C22×D3—34no—
252C22×D3—38no—
253C22×D3—34no—
254C22×D3—62no—
255C22×D3—64no—
256C22×D3—64no—
257C22×D3—62no—
258C22×D3—62no—
259C2×C3×C4—24no—
260C2×C3×C4—22no—
261C2×C3×C4—24no—
262C2×C3×C4—22no—
263C2×C3×C4—24no—
264C2×C3×C4—38no—
265C2×C3×C4—38no—
266C2×C3×C4—44no—
267C2×C3×C4—44no—
268C2×C3×C4—42no—
269C2×C3×C4—68no—
270C2×C3×C4—64no—
271C2×C3×C4—64no—
272C2×C3×C4—64no—
273C2×C3×C4—64no—
274C2×C3×C4—92no—
275C2×C3×C4—124no—
276C2×C3×C4—124no—
277C2×C3×C4—188no—
278C2×C3×C4—1816no—
279C2×C3×C4—182no—
280C2×C3×C4#62412yescomplemented
281C2×C3×C4C3×C4×D314yescomplemented
282C2×Dic3—24no—
283C2×Dic3—24no—
284C2×Dic3—34no—
285C2×Dic3—62no—
286C2×Dic3—64no—
287C2×Dic3—64no—
288C2×Dic3C3×C4×D318yescomplemented
289C4×D3—632no—
290C4×D3—616no—
291C4×D3—616no—
292C2×C32—24no—
293C2×C32—22no—
294C2×C32—24no—
295C2×C32—22no—
296C2×C32—21no—
297C2×C32—22no—
298C2×C32—21no—
299C2×C32—22no—
300C2×C32—21no—
301C2×C32—22no—
302C2×C32—41no—
303C2×C32—41no—
304C2×C32—42no—
305C2×C32—42no—
306C2×C32—41no—
307C2×C32C42×D312yes—
308C2×C32D3×C22⋊C414yes—
309C2×C32D3×C22⋊C412yes—
310C2×C32D3×C4⋊C414yes—
311C2×C32D3×C4⋊C412yes—
312C2×C32C2×C3×C4211yescharacteristic
313C2×C32C2×C3×C22⋊C412yes—
314C2×C32C2×C3×C22⋊C411yescharacteristic
315C2×C32C2×C3×C4⋊C412yes—
316C2×C32C2×C3×C4⋊C411yescharacteristic
317C3⋊D3C3×#9518yescomplemented
318C3×D3—316no—
319C3×D3—68no—
320C24—91no—
321C22×C4—34no—
322C22×C4—98no—
323C22×C4—91no—
324C22×C4—94no—
325C22×C4—184no—
326C22×C4—184no—
327C22×C4—184no—
328C22×C4C3×D3211yescharacteristic
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—24no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—24no—
339C22×C3—41no—
340C22×C3—42no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—42no—
344C22×C3—94no—
345C22×C3—98no—
346C22×C3—94no—
347C22×C3—98no—
348C22×C3—94no—
349C22×C3#379711yescharacteristic
350C22×C3C4×D3212yes—
351C22×C3#380211yescharacteristic
352C22×C3C2×#62411yescharacteristic
353C22×C3#381112yes—
354C22×C3C2×C3×C4×D314yes—
355C22×C3C2×C3×C4×D312yes—
356C22×C3C3×D3×D412yes—
357C22×C3C3×D3×D414yes—
358C22×C3C3×D3×Q812yes—
359C2×D3—38no—
360C2×D3—316no—
361C2×D3—316no—
362C2×D3—38no—
363C2×D3—38no—
364C2×D3—64no—
365C2×D3—64no—
366C2×D3—68no—
367C2×D3—68no—
368C2×D3—64no—
369C3×C4—24no—
370C3×C4—24no—
371C3×C4—22no—
372C3×C4—44no—
373C3×C4—44no—
374C3×C4—68no—
375C3×C4—68no—
376C3×C4—128no—
377C3×C4—182no—
378Dic3—28no—
379Dic3—64no—
380Dic3—64no—
381C32—22no—
382C32—21no—
383C32—41no—
384C32D3×#9512yescomplemented
385C32C2×C3×#9511yescharacteristic, complemented
386C23—92no—
387C23—94no—
388C23—92no—
389C23—92no—
390C23—94no—
391C23C2×C3×D3211yescharacteristic
392C2×C4—22no—
393C2×C4—38no—
394C2×C4—64no—
395C2×C4—64no—
396C2×C4—92no—
397C2×C4—188no—
398C2×C4—1816no—
399C2×C4—182no—
400C2×C4C3×#62412yescomplemented
401C2×C3—21no—
402C2×C3—22no—
403C2×C3—21no—
404C2×C3—22no—
405C2×C3—22no—
406C2×C3—24no—
407C2×C3—21no—
408C2×C3—22no—
409C2×C3—24no—
410C2×C3—22no—
411C2×C3—41no—
412C2×C3—41no—
413C2×C3—42no—
414C2×C3—41no—
415C2×C3—42no—
416C2×C3—98no—
417C2×C3C4×#62411yescharacteristic
418C2×C3#6388312yes—
419C2×C3#6390011yescharacteristic
420C2×C3#6392112yes—
421C2×C3#6397411yescharacteristic
422C2×C3C3×C42×D312yes—
423C2×C3C3×D3×C22⋊C412yes—
424C2×C3C3×D3×C22⋊C414yes—
425C2×C3C3×D3×C4⋊C414yes—
426C2×C3C3×D3×C4⋊C412yes—
427D3—316no—
428D3—68no—
429C22—94no—
430C22—94no—
431C22—98no—
432C22—94no—
433C22—98no—
434C22C3×#379711yescharacteristic
435C22C3×C4×D3212yes—
436C22C3×#380211yescharacteristic
437C22C2×C3×#62411yescharacteristic
438C22C3×#381112yes—
439C4—22no—
440C4—68no—
441C4—182no—
442C3—21no—
443C3—22no—
444C3—41no—
445C3#1059137011yescharacteristic, direct product factor
446C3C3×D3×#9512yescomplemented
447C2—98no—
448C2C3×C4×#62411yescharacteristic
449C2C3×#6388312yes—
450C2C3×#6390011yescharacteristic
451C2C3×#6392112yes—
452C2C3×#6397411yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C2×C3×C42
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C3×C3⋊D3C22
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#95
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
3. C32×C3⋊#95C2semidirect
4. C3×#63579C2semidirect
6. #10591370C3direct (N × H)
11. C2×C3×C4×C3⋊D3C4semidirect
15. C2×C3×#624C4semidirect
24. C3×C3⋊#95D3semidirect
25. C3×C3⋊#95C2×C3semidirect
26. #63579C2×C3semidirect
34. C2×C33×C4C2×C4semidirect
36. C2×C3×C3⋊Dic3C2×C4semidirect
40. C2×C32×Dic3C2×C4semidirect
55. C2×C4×C3⋊D3C3×C4semidirect
70. C2×#624C3×C4semidirect
94. C3⋊#95C3×D3semidirect
126. C2×C32×C4C4×D3semidirect
127. C2×C32×C4C2×C3×C4semidirect
129. C2×C3⋊Dic3C2×C3×C4semidirect
142. C2×C3×Dic3C4×D3semidirect
143. C2×C3×Dic3C2×C3×C4semidirect
154. C3×C3⋊D3#95semidirect
238. C33C2×#95semidirect
280. C2×C3×C4#624semidirect
281. C2×C3×C4C3×C4×D3semidirect
288. C2×Dic3C3×C4×D3semidirect
317. C3⋊D3C3×#95semidirect
384. C32D3×#95semidirect
385. C32C2×C3×#95semidirect
400. C2×C4C3×#624semidirect
445. C3#10591370direct (N × H)
446. C3C3×D3×#95semidirect

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
C22×C3×#6242
C32×C3⋊#952
C3×#635792
C3×D3×#953
#105913703