Finite Group Databasebeta

← C3×#10590281 #13157295

Subgroups — C3×#10590281 #13157295

Order 1728.

722 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64083C211yesmaximal, characteristic
2C32×#869C211yesmaximal, characteristic, complemented
3C32×C4×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#63564C214yesmaximal, complemented
5C3×#5088—31nomaximal
6C3×#4694—31nomaximal
7#10590281C311yesmaximal, characteristic, direct product factor
8C2×C3×C4⋊(C3⋊D3)—21no—
9C2×C3×C4⋊(C3⋊D3)—21no—
10C2×C3×C4⋊(C3⋊D3)C2212yes—
11C2×C32×Dic6—21no—
12C33×C42C2211yescharacteristic
13C32×C4⋊Dic3—21no—
14C32×C4⋊Dic3C2212yes—
15C2×C32×C3⋊C8C2212yes—
16C32×C4⋊Q8—31no—
17#64083C2×C311yescharacteristic
18C3×#874—31no—
19C3×#874—31no—
20C3×#874—61no—
21C3×#869—21no—
22C3×#869D311yescharacteristic, complemented
23C3×#869C2×C311yescharacteristic, complemented
24C32×C4×C8—31no—
25C3×#821—34no—
26C3×#809—34no—
27C3×C4×C3⋊C8—21no—
28C3×C4×C3⋊C8D311yescharacteristic, complemented
29C3×C4×C3⋊C8C2×C311yescharacteristic, complemented
30#63564C2×C314yescomplemented
31C22×C3×C3⋊D3—22no—
32C2×C33×C4D411yescharacteristic
33C2×C33×C4D411yescharacteristic
34C2×C33×C4C2311yescharacteristic
35C3×C4⋊(C3⋊D3)—24no—
36C3×C4⋊(C3⋊D3)—42no—
37C3×C4⋊(C3⋊D3)—42no—
38C2×C32×Dic3—22no—
39C32×Dic6—42no—
40C32×C3⋊C8—22no—
41C3×#486—91no—
42#5088—31no—
43#4694—31no—
44C2×C32×Q8—61no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)C22×C312yes—
48C2×C3×D12—32no—
49C2×C3×D12—32no—
50C2×C3×D12—62no—
51C2×C3×D12—62no—
52C2×C3×D12—62no—
53C2×C3×D12—61no—
54C2×C3×D12—61no—
55C2×C3×D12—61no—
56C2×C3×D12—61no—
57C2×C3×Dic6—22no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C32×C8—32no—
61C32×C4⋊C4—32no—
62C32×C4⋊C4—61no—
63C32×C42—21no—
64C32×C42—21no—
65C32×C42—21no—
66C32×C42—41no—
67C32×C42C2×D311yescharacteristic
68C32×C42C2×D311yescharacteristic
69C32×C42C22×C311yescharacteristic
70C3×C4⋊Dic3—22no—
71C3×C4⋊Dic3—22no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2×D312yes—
75C3×C4⋊Dic3C22×C312yes—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8C2×D312yes—
78C2×C3×C3⋊C8C22×C312yes—
79C22×C33C2×D411yescharacteristic
80C2×C3×C3⋊D3—42no—
81C2×C3×C3⋊D3—42no—
82C2×C3×C3⋊D3—42no—
83C33×C4D812yes—
84C33×C4SD1612yes—
85C33×C4#4112yes—
86C32×Dic3—42no—
87C3×C4⋊Q8—31no—
88C3×C4⋊Q8—31no—
89C3×C4⋊Q8—61no—
90C3×#127—91no—
91#874—31no—
92#874—31no—
93#874—61no—
94#869C3×D311yescharacteristic, complemented
95C3×#102—94no—
96C3×C4×C8—31no—
97C3×C4×C8—31no—
98C3×C4×C8—61no—
99#821—34no—
100#809—34no—
101C4×C3⋊C8C3×D311yescharacteristic, complemented
102C22×C3⋊D3—22no—
103C22×C3×D3—64no—
104C22×C3×D3—62no—
105C22×C3×D3—62no—
106C32×Q8—122no—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—62no—
120C2×C32×C4D1211yescharacteristic
121C2×C32×C4D1211yescharacteristic
122C2×C32×C4#6711yescharacteristic
123C2×C32×C4#6711yescharacteristic
124C2×C32×C4C3×D411yescharacteristic
125C2×C32×C4C3×D411yescharacteristic
126C2×C32×C4C22×D311yescharacteristic
127C2×C32×C4C22×D311yescharacteristic
128C2×C32×C4C23×C311yescharacteristic
129C4⋊(C3⋊D3)—24no—
130C4⋊(C3⋊D3)—42no—
131C4⋊(C3⋊D3)—42no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C3×D12—64no—
136C3×D12—64no—
137C3×D12—124no—
138C3×D12—124no—
139C3×D12—124no—
140C3×D12—122no—
141C3×D12—122no—
142C3×D12—122no—
143C3×D12—122no—
144C3×Dic6—44no—
145C3×Dic6—42no—
146C3×Dic6—42no—
147C32×C8—62no—
148C3×C3⋊C8—24no—
149C3×C3⋊C8—22no—
150C3×C3⋊C8—22no—
151#486—91noSylow
152C2×C33#12411yescharacteristic
153C2×C33C2×D811yescharacteristic
154C2×C33C2×SD1611yescharacteristic
155C3×C3⋊D3—82no—
156C2×C3×Q8—62no—
157C2×C3×Q8—61no—
158C2×C3×Q8—61no—
159C2×C3×D4—92no—
160C2×C3×D4—181no—
161C2×C3×D4—181no—
162C2×D12—32no—
163C2×D12—32no—
164C2×D12—62no—
165C2×D12—62no—
166C2×D12—62no—
167C2×D12—61no—
168C2×D12—61no—
169C2×D12—61no—
170C2×D12—61no—
171C2×Dic6—21no—
172C2×C3×C8—32no—
173C2×C3×C8—32no—
174C2×C3×C8—62no—
175C3×C4⋊C4—32no—
176C3×C4⋊C4—32no—
177C3×C4⋊C4—62no—
178C3×C4⋊C4—62no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C42—21no—
182C3×C42—21no—
183C3×C42—21no—
184C3×C42—41no—
185C3×C42D3211yescharacteristic
186C3×C42C2×C3×D311yescharacteristic
187C3×C42C2×C3×D311yescharacteristic
188C4⋊Dic3—21no—
189C4⋊Dic3C2×C3×D312yes—
190C2×C3⋊C8C2×C3×D312yes—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—41no—
195C22×C32C2×D1211yescharacteristic
196C22×C32C2×#6711yescharacteristic
197C22×C32C2×C3×D411yescharacteristic
198C2×C3⋊D3—42no—
199C2×C3⋊D3—42no—
200C2×C3⋊D3—42no—
201C2×C3×D3—124no—
202C2×C3×D3—124no—
203C2×C3×D3—124no—
204C2×C3×D3—122no—
205C2×C3×D3—122no—
206C2×C3×D3—122no—
207C2×C3×D3—122no—
208C2×C3×D3—122no—
209C2×C3×D3—122no—
210C32×C4—22no—
211C32×C4—22no—
212C32×C4—22no—
213C32×C4—22no—
214C32×C4—22no—
215C32×C4—22no—
216C32×C4—22no—
217C32×C4—22no—
218C32×C4—22no—
219C32×C4—42no—
220C32×C4—42no—
221C32×C4—42no—
222C32×C4—122no—
223C32×C4#20412yes—
224C32×C4D2412yes—
225C32×C4#21312yes—
226C32×C4#21512yes—
227C32×C4C3×D812yes—
228C32×C4C3×SD1612yes—
229C32×C4#23512yes—
230C32×C4#23912yes—
231C32×C4C3×#4112yes—
232C3×Dic3—44no—
233C3×Dic3—42no—
234C3×Dic3—42no—
235C4⋊Q8—31no—
236#127—91no—
237#102—94no—
238C4×C8—31no—
239C33#48611yescharacteristic, complemented, Sylow
240C23×C3—182no—
241C22×D3—64no—
242C22×D3—62no—
243C22×D3—62no—
244C3×Q8—124no—
245C3×Q8—122no—
246C3×Q8—122no—
247C3×D4—184no—
248C3×D4—362no—
249C3×D4—362no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—64no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4#62611yescharacteristic
266C2×C3×C4#62611yescharacteristic
267C2×C3×C4C3×D1211yescharacteristic
268C2×C3×C4C3×D1211yescharacteristic
269C2×C3×C4C3×#6711yescharacteristic
270C2×C3×C4C3×#6711yescharacteristic
271C2×C3×C4C2×D3211yescharacteristic
272C2×C3×C4C22×C3×D311yescharacteristic
273C2×C3×C4C22×C3×D311yescharacteristic
274C2×Dic3—22no—
275D12—64no—
276D12—64no—
277D12—124no—
278D12—124no—
279D12—124no—
280D12—122no—
281D12—122no—
282D12—122no—
283D12—122no—
284Dic6—42no—
285C3×C8—64no—
286C3×C8—62no—
287C3×C8—62no—
288C3⋊C8—22no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32—21no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32—21no—
298C2×C32—41no—
299C2×C32—41no—
300C2×C32—41no—
301C2×C32#87511yescharacteristic
302C2×C32C2×#20411yescharacteristic
303C2×C32C2×D2411yescharacteristic
304C2×C32C2×#21311yescharacteristic
305C2×C32C2×#21511yescharacteristic
306C2×C32#94711yescharacteristic
307C2×C32C3×#12411yescharacteristic
308C2×C32C2×C3×D811yescharacteristic
309C2×C32C2×C3×SD1611yescharacteristic
310C3⋊D3—82no—
311C3×D3—244no—
312C3×D3—242no—
313C3×D3—242no—
314C2×Q8—61no—
315C2×D4—92no—
316C2×D4—181no—
317C2×D4—181no—
318C2×C8—32no—
319C4⋊C4—32no—
320C4⋊C4—61no—
321C42C3×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—41no—
326C22×C3—362no—
327C22×C3—362no—
328C22×C3—362no—
329C22×C3C2×#62611yescharacteristic
330C22×C3C2×C3×D1211yescharacteristic
331C22×C3C2×C3×#6711yescharacteristic
332C2×D3—124no—
333C2×D3—124no—
334C2×D3—124no—
335C2×D3—122no—
336C2×D3—122no—
337C2×D3—122no—
338C2×D3—122no—
339C2×D3—122no—
340C2×D3—122no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—22no—
348C3×C4—22no—
349C3×C4—22no—
350C3×C4—42no—
351C3×C4—42no—
352C3×C4—42no—
353C3×C4—124no—
354C3×C4—122no—
355C3×C4—122no—
356C3×C4#371412yes—
357C3×C4#371712yes—
358C3×C4C3×#20412yes—
359C3×C4C3×D2412yes—
360C3×C4C3×#21312yes—
361C3×C4C3×#21512yes—
362C3×C4#379912yes—
363C3×C4C3×#23512yes—
364C3×C4C3×#23912yes—
365Dic3—42no—
366C32—21no—
367C32—21no—
368C32—21no—
369C32—41no—
370C32#469411yescharacteristic, complemented
371C32#508811yescharacteristic, complemented
372C32C3×#48611yescharacteristic, complemented
373C23—182no—
374Q8—122no—
375D4—184no—
376D4—362no—
377D4—362no—
378C2×C4—62no—
379C2×C4C3×#62611yescharacteristic
380C2×C4C3×#62611yescharacteristic
381C2×C4C2×C3×D3211yescharacteristic
382C8—62no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—41no—
395C2×C3—722no—
396C2×C3C2×#371411yescharacteristic
397C2×C3C2×#371711yescharacteristic
398C2×C3#6386411yescharacteristic
399C2×C3C3×#87511yescharacteristic
400C2×C3C2×C3×#20411yescharacteristic
401C2×C3C2×C3×D2411yescharacteristic
402C2×C3C2×C3×#21311yescharacteristic
403C2×C3C2×C3×#21511yescharacteristic
404C2×C3C3×#94711yescharacteristic
405D3—244no—
406D3—242no—
407D3—242no—
408C22—362no—
409C22—362no—
410C22—362no—
411C22C2×C3×#62611yescharacteristic
412C4—122no—
413C4C3×#371412yes—
414C4C3×#371712yes—
415C4C3×#379912yes—
416C3—21no—
417C3—21no—
418C3—21no—
419C3—41no—
420C3#1059028111yescharacteristic, direct product factor
421C3C3×#469411yescharacteristic, complemented
422C3C3×#508811yescharacteristic, complemented
423C2—722no—
424C2C2×C3×#371411yescharacteristic
425C2C2×C3×#371711yescharacteristic
426C2C3×#6386411yescharacteristic
subgroupG/H
centerC22×C3C2×#626
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×C42C22
socleC22×C33C2×D4
prime radicalC3×#64083C2
hypercenterC3×C42D32
hypocenterC32C3×#486
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C42

Complements

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

NH ≅ G/Ntype
2. C32×#869C2semidirect
3. C32×C4×C3⋊C8C2semidirect
4. C3×#63564C2semidirect
7. #10590281C3direct (N × H)
22. C3×#869D3semidirect
23. C3×#869C2×C3semidirect
28. C3×C4×C3⋊C8D3semidirect
29. C3×C4×C3⋊C8C2×C3semidirect
30. #63564C2×C3semidirect
94. #869C3×D3semidirect
101. C4×C3⋊C8C3×D3semidirect
239. C33#486semidirect
370. C32#4694semidirect
371. C32#5088semidirect
372. C32C3×#486semidirect
420. C3#10590281direct (N × H)
421. C3C3×#4694semidirect
422. C3C3×#5088semidirect

Maximal subgroups

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

subgroupindex
C3×#640832
C32×#8692
C32×C4×C3⋊C82
C3×#635642
C3×#50883
C3×#46943
#105902813