Finite Group Databasebeta

← C3×#81604 #11878891

Subgroups — C3×#81604 #11878891

Order 1152.

817 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic
2C3×D3×C4⋊Q8C211yesmaximal, characteristic
3C32×#487C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5C3×#5092C211yesmaximal, characteristic, complemented
6C3×#4809C214yesmaximal
7C3×#4795C214yesmaximal, complemented
8C3×#4699C211yesmaximal, characteristic, complemented
9C3×#4685C211yesmaximal, characteristic
10C3×#3209—31nomaximal
11#81604C311yesmaximal, characteristic, direct product factor
12C2×C3×D3×Q8C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15C3×#946—21no—
16C3×Q8×Dic3—21no—
17C3×#944C2212yes—
18C2×C3×#216C2214yes—
19C2×C3×Dic12C2214yes—
20C3×#897C2212yes—
21C3×#892—21no—
22C3×D3×C4⋊C4—21no—
23C3×D3×C4⋊C4—21no—
24C3×#890—21no—
25C3×#888—21no—
26C3×#888—21no—
27C3×#887C2212yes—
28C3×C42×D3C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C32×#103C2214yes—
32C32×C4×C8C2211yescharacteristic
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yes—
35C3×#810C2214yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#533—31no—
38C2×C3×C4⋊Q8—31no—
39#5728C2×C311yescharacteristic
40D3×C4⋊Q8C2×C311yescharacteristic
41C3×#494—31no—
42C3×#494—31no—
43C3×#487—21no—
44C3×#487—31no—
45C3×#487D311yescharacteristic, complemented
46C3×#487C2×C311yescharacteristic, complemented
47C3×#462—34no—
48C3×#451—34no—
49C3×#431—31no—
50#5093C2×C311yescharacteristic, complemented
51#5092C2×C311yescharacteristic, complemented
52#4809C2×C314yes—
53#4795C2×C314yescomplemented
54#4699C2×C311yescharacteristic, complemented
55#4685C2×C311yescharacteristic
56C2×C32×Q8—21no—
57C2×C32×Q8C2312yes—
58C3×D3×Q8—44no—
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3D411yescharacteristic
61C2×C3×C4×D3D411yescharacteristic
62C2×C3×C4×D3C2311yescharacteristic
63C2×C3×Dic6—22no—
64C2×C3×Dic6C2312yes—
65C2×C3×Dic6C2312yes—
66C2×C32×C8C2312yes—
67C32×C4⋊C4—21no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C32×C42C2311yescharacteristic
72C3×#216—44no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—22no—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3—22no—
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3D411yescharacteristic
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2312yes—
87C3×Dic12—44no—
88#3209—31noSylow
89C22×C3×Q8—32no—
90C2×D3×Q8C22×C312yes—
91C2×C3×Q16—34no—
92C2×C3×Q16—34no—
93C3×C4⋊Q8—21no—
94C3×C4⋊Q8—21no—
95C3×C4⋊Q8—32no—
96C3×C4⋊Q8—31no—
97C3×C4⋊Q8—31no—
98C3×C4⋊Q8—61no—
99C3×C4⋊Q8—61no—
100C3×C4⋊Q8C2×D311yescharacteristic
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4⋊Q8C22×C311yescharacteristic
103C3×C4⋊Q8C22×C311yescharacteristic
104C3×#125—61no—
105C3×C22⋊Q8—32no—
106C3×C22⋊Q8—61no—
107C3×C4×Q8—32no—
108C3×C4×Q8—61no—
109C3×#117—61no—
110C2×C3×C4⋊C4—61no—
111C2×C3×C4⋊C4—61no—
112C2×C3×C42—31no—
113#946—21no—
114Q8×Dic3—21no—
115#944C22×C312yes—
116C2×#216C22×C314yes—
117C2×Dic12C22×C314yes—
118#897C22×C312yes—
119#892—21no—
120D3×C4⋊C4—21no—
121D3×C4⋊C4—21no—
122#890—21no—
123#888—21no—
124#888—21no—
125#887C22×C312yes—
126C42×D3C22×C311yescharacteristic
127#869C22×C311yescharacteristic
128#869C22×C311yescharacteristic
129C3×C4⋊C8—32no—
130C3×#103—24no—
131C3×#103—34no—
132C3×#103C2×D314yes—
133C3×#103C22×C314yes—
134C3×C22⋊C8—32no—
135C3×C4×C8—21no—
136C3×C4×C8—31no—
137C3×C4×C8C2×D311yescharacteristic
138C3×C4×C8C22×C311yescharacteristic
139(C2×D3)⋊C8C22×C312yes—
140Dic3⋊C8C22×C312yes—
141#810C22×C314yes—
142C4×C3⋊C8C22×C311yescharacteristic
143C22×C3×D3C2×D411yescharacteristic
144C32×Q8—24no—
145C32×Q8—42no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2411yescharacteristic
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×D411yescharacteristic
154C2×C3×Dic3C2×D411yescharacteristic
155C2×C3×Dic3C2×D411yescharacteristic
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3—44no—
159C3×C4×D3Q1614yescomplemented
160C3×Dic6—24no—
161C3×Dic6—24no—
162C3×Dic6—44no—
163C32×C8—22no—
164C3×C3⋊C8—22no—
165#533—31no—
166C2×C4⋊Q8—31no—
167#494—31no—
168#494—31no—
169#487—31no—
170#487C3×D311yescharacteristic, complemented
171#462—34no—
172#451—34no—
173#431—31no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—22no—
177C2×C3×Q8—32no—
178C2×C3×Q8—32no—
179C2×C3×Q8—41no—
180C2×C3×Q8—62no—
181C2×C3×Q8—124no—
182C2×C3×Q8C22×D312yes—
183C2×C3×Q8C23×C312yes—
184C22×C3×C4—31no—
185C22×C3×C4—31no—
186C22×C3×C4—31no—
187C22×C3×C4—62no—
188D3×Q8—44no—
189C2×C4×D3—22no—
190C2×C4×D3C3×D411yescharacteristic
191C2×C4×D3C3×D411yescharacteristic
192C2×C4×D3C23×C311yescharacteristic
193C2×Dic6—22no—
194C2×Dic6C23×C312yes—
195C2×Dic6C23×C312yes—
196C3×Q16—124no—
197C3×Q16—124no—
198C2×C3×C8—22no—
199C2×C3×C8—32no—
200C2×C3×C8C22×D312yes—
201C2×C3×C8C23×C312yes—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—41no—
210C3×C4⋊C4—41no—
211C3×C4⋊C4—41no—
212C3×C4⋊C4—62no—
213C3×C4⋊C4—62no—
214C3×C4⋊C4—62no—
215C3×C4⋊C4—62no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4C22×D312yes—
221C3×C4⋊C4C23×C312yes—
222C3×C22⋊C4—62no—
223C3×C42—21no—
224C3×C42—31no—
225C3×C42—31no—
226C3×C42—31no—
227C3×C42—62no—
228C3×C42C22×D311yescharacteristic
229C3×C42C23×C311yescharacteristic
230#216—44no—
231(C2×D3)⋊C4—22no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—21no—
236C4⋊Dic3—22no—
237Dic3⋊C4—22no—
238Dic3⋊C4—22no—
239Dic3⋊C4—22no—
240C4×Dic3—22no—
241C4×Dic3C3×D411yescharacteristic
242C4×Dic3C3×D411yescharacteristic
243C4×Dic3C23×C311yescharacteristic
244C2×C3⋊C8C23×C312yes—
245Dic12—44no—
246C22×C32C22×D411yescharacteristic
247C2×C3×D3—21no—
248C2×C3×D3—21no—
249C2×C3×D3C2×Q1612yes—
250C32×C4—42no—
251C32×C4—42no—
252C32×C4C2×Q1612yes—
253C32×C4#13712yes—
254C32×C4H(5,𝔽2)12yes—
255C3×Dic3—21no—
256C3×Dic3—21no—
257C3×Dic3—42no—
258C3×Dic3—42no—
259C3×Dic3C2×Q1612yes—
260C22×Q8—32no—
261C2×Q16—34no—
262C2×Q16—34no—
263C4⋊Q8—32no—
264C4⋊Q8—31no—
265C4⋊Q8—31no—
266C4⋊Q8—61no—
267C4⋊Q8—61no—
268C4⋊Q8C2×C3×D311yescharacteristic
269C4⋊Q8C2×C3×D311yescharacteristic
270#125—61no—
271C22⋊Q8—32no—
272C22⋊Q8—61no—
273C4×Q8—32no—
274C4×Q8—61no—
275#117—61no—
276C2×C4⋊C4—61no—
277C2×C4⋊C4—61no—
278C2×C42—31no—
279C4⋊C8—32no—
280#103—34no—
281#103C2×C3×D314yes—
282C22⋊C8—32no—
283C4×C8—31no—
284C4×C8C2×C3×D311yescharacteristic
285C23×C3—31no—
286C22×D3C2×C3×D411yescharacteristic
287C3×Q8—24no—
288C3×Q8—24no—
289C3×Q8—44no—
290C3×Q8—42no—
291C3×Q8—42no—
292C3×Q8—64no—
293C3×Q8—64no—
294C3×Q8—82no—
295C3×Q8—124no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—31no—
304C2×C3×C4—34no—
305C2×C3×C4—31no—
306C2×C3×C4—31no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—124no—
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4C2×C3×D411yescharacteristic
317C2×C3×C4C2×C3×D411yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319C2×C3×C4C24×C311yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3C2×C3×D411yescharacteristic
323C2×Dic3C2×C3×D411yescharacteristic
324C2×Dic3C2×C3×D411yescharacteristic
325C4×D3—22no—
326C4×D3—22no—
327C4×D3—44no—
328C4×D3C3×Q1614yescomplemented
329Dic6—24no—
330Dic6—24no—
331Dic6—44no—
332C3×C8—22no—
333C3×C8—22no—
334C3×C8—42no—
335C3×C8—62no—
336C3⋊C8—22no—
337C2×C32#53511yescharacteristic
338C2×C32C22×Q1611yescharacteristic
339C2×C32C2×#13711yescharacteristic
340C3×D3—22no—
341C2×Q8—21no—
342C2×Q8—32no—
343C2×Q8—32no—
344C2×Q8—62no—
345C2×Q8—124no—
346C2×Q8C22×C3×D312yes—
347C22×C4—31no—
348C22×C4—31no—
349C22×C4—31no—
350C22×C4—62no—
351Q16—124no—
352Q16—124no—
353C2×C8—32no—
354C2×C8C22×C3×D312yes—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—62no—
359C4⋊C4—62no—
360C4⋊C4—62no—
361C4⋊C4—62no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4C22×C3×D312yes—
367C22⋊C4—62no—
368C42—31no—
369C42—31no—
370C42—31no—
371C42—62no—
372C42C22×C3×D311yescharacteristic
373C22×C3—21no—
374C22×C3—32no—
375C22×C3—61no—
376C22×C3—61no—
377C22×C3C2×D3×D411yescharacteristic
378C22×C3C22×C3×D411yescharacteristic
379C2×D3—21no—
380C2×D3—21no—
381C2×D3C2×C3×Q1612yes—
382C3×C4—22no—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—32no—
386C3×C4—42no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—61no—
391C3×C4—61no—
392C3×C4—82no—
393C3×C4—82no—
394C3×C4—122no—
395C3×C4—122no—
396C3×C4#91512yes—
397C3×C4D3×Q1612yes—
398C3×C4C2×C3×Q1612yes—
399C3×C4C3×#13712yes—
400C3×C4#100912yes—
401C3×C4C3×H(5,𝔽2)12yes—
402Dic3—21no—
403Dic3—21no—
404Dic3—42no—
405Dic3—42no—
406Dic3C2×C3×Q1612yes—
407C32#320911yescharacteristic, complemented, Sylow
408C23—31no—
409Q8—24no—
410Q8—42no—
411Q8—64no—
412Q8—64no—
413Q8—124no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—31no—
417C2×C4—34no—
418C2×C4—31no—
419C2×C4—31no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—124no—
425C2×C4C3×D3×D411yescharacteristic
426C2×C4C3×D3×D411yescharacteristic
427C2×C4C23×C3×D311yescharacteristic
428C8—22no—
429C8—62no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—62no—
434C2×C3#567411yescharacteristic
435C2×C3C2×#91511yescharacteristic
436C2×C3C2×D3×Q1611yescharacteristic
437C2×C3C3×#53511yescharacteristic
438C2×C3C22×C3×Q1611yescharacteristic
439C2×C3C2×C3×#13711yescharacteristic
440D3—22no—
441C22—32no—
442C22—61no—
443C22—61no—
444C22C2×C3×D3×D411yescharacteristic
445C4—32no—
446C4—42no—
447C4—42no—
448C4—61no—
449C4—61no—
450C4—122no—
451C4—122no—
452C4C3×#91512yes—
453C4C3×D3×Q1612yes—
454C4C3×#100912yes—
455C3—21no—
456C3#8160411yescharacteristic, direct product factor
457C3C3×#320911yescharacteristic, complemented
458C2—62no—
459C2C3×#567411yescharacteristic
460C2C2×C3×#91511yescharacteristic
461C2C2×C3×D3×Q1611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#487D3
hypocenterC3C3×#3209
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
3. C32×#487C2semidirect
4. C3×#5093C2semidirect
5. C3×#5092C2semidirect
7. C3×#4795C2semidirect
8. C3×#4699C2semidirect
11. #81604C3direct (N × H)
45. C3×#487D3semidirect
46. C3×#487C2×C3semidirect
50. #5093C2×C3semidirect
51. #5092C2×C3semidirect
53. #4795C2×C3semidirect
54. #4699C2×C3semidirect
159. C3×C4×D3Q16semidirect
170. #487C3×D3semidirect
328. C4×D3C3×Q16semidirect
407. C32#3209semidirect
456. C3#81604direct (N × H)
457. C3C3×#3209semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C3×D3×C4⋊Q82
C32×#4872
C3×#50932
C3×#50922
C3×#48092
C3×#47952
C3×#46992
C3×#46852
C3×#32093
#816043