Finite Group Databasebeta

← C3×#10590820 #13157793

Subgroups — C3×#10590820 #13157793

Order 1728.

498 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63872C211yesmaximal, characteristic
2C3×#63843C211yesmaximal, characteristic
3C3×#63641C211yesmaximal, characteristic
4C32×#817C211yesmaximal, characteristic
5C32×#816C211yesmaximal, characteristic
6C3×#63576C211yesmaximal, characteristic
7C3×#63565C211yesmaximal, characteristic
8C3×#4857—31nomaximal
9C3×#4799—31nomaximal
10#10590820C311yesmaximal, characteristic, direct product factor
11C2×C32×Dic6C2211yescharacteristic
12C2×C33×C8C2211yescharacteristic
13C3×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
15C32×C4⋊Dic3C2211yescharacteristic
16C32×C4⋊Dic3C2211yescharacteristic
17C32×C4⋊Dic3C2211yescharacteristic
18C3×Dic3⋊Dic3—21no—
19C3×Dic3⋊Dic3—21no—
20C3×Dic3⋊Dic3—21no—
21C3×Dic32—21no—
22C3×Q8×Dic3—31no—
23C3×#890—31no—
24C3×#890—31no—
25C3×#887—31no—
26#63872C2×C311yescharacteristic
27#63843C2×C311yescharacteristic
28C32×#106—31no—
29C32×#103—31no—
30#63641C2×C311yescharacteristic
31C3×#835—31no—
32C3×#817—21no—
33C3×#817D311yescharacteristic
34C3×#817C2×C311yescharacteristic
35C3×#816—21no—
36C3×#816D311yescharacteristic
37C3×#816C2×C311yescharacteristic
38C3×Dic3⋊C8—31no—
39C3×Dic3⋊C8—31no—
40C3×Dic3⋊C8—61no—
41C3×#810—31no—
42C3×#807—31no—
43C3×#807—31no—
44#63576C2×C311yescharacteristic
45#63565C2×C311yescharacteristic
46C2×C33×C4C2311yescharacteristic
47C2×C3×C3⋊Dic3D411yescharacteristic
48C2×C3×C3⋊Dic3D411yescharacteristic
49C2×C32×Dic3—21no—
50C2×C32×Dic3—21no—
51C2×C32×Dic3—21no—
52C2×C32×Dic3—21no—
53C32×Dic6—21no—
54C32×Dic6Q812yes—
55C33×C8—21no—
56C3×C3⋊(C3⋊C8)—21no—
57C3×#479—91no—
58#4857—31no—
59#4799—31no—
60C2×C32×Q8—31no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2×D311yescharacteristic
63C2×C3×Dic6C22×C311yescharacteristic
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—41no—
68C2×C32×C8C2×D311yescharacteristic
69C2×C32×C8C2×D311yescharacteristic
70C2×C32×C8C22×C311yescharacteristic
71C32×C4⋊C4—31no—
72C32×C4⋊C4—31no—
73C32×C4⋊C4—31no—
74C4×C3⋊Dic3C22×C311yescharacteristic
75C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3—61no—
80C3×C4⋊Dic3—61no—
81C3×C4⋊Dic3—61no—
82C3×C4⋊Dic3C2×D311yescharacteristic
83C3×C4⋊Dic3C2×D311yescharacteristic
84C3×C4⋊Dic3C2×D311yescharacteristic
85C3×C4⋊Dic3C22×C311yescharacteristic
86C3×C4⋊Dic3C22×C311yescharacteristic
87C3×C4⋊Dic3C22×C311yescharacteristic
88C3×Dic3⋊C4—61no—
89C3×Dic3⋊C4—61no—
90C3×Dic3⋊C4—61no—
91C3×C4×Dic3—31no—
92C3×C4×Dic3—31no—
93C3×C4×Dic3—61no—
94C3×C4×Dic3—61no—
95C3×C4×Dic3—61no—
96C2×C3×C3⋊C8—31no—
97C2×C3×C3⋊C8—31no—
98C2×C3×C3⋊C8—61no—
99Dic3⋊Dic3—21no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102Dic32—21no—
103C22×C33C2×D411yescharacteristic
104C33×C4C2×Q811yescharacteristic
105C33×C4#4111yescharacteristic
106C3×C3⋊Dic3—21no—
107C3×C3⋊Dic3—21no—
108C32×Dic3—22no—
109C32×Dic3—41no—
110C32×Dic3—41no—
111C32×Dic3—41no—
112C3×#125—91no—
113C3×C4×Q8—91no—
114Q8×Dic3—31no—
115#890—31no—
116#890—31no—
117#887—31no—
118C3×#107—91no—
119C3×#106—31no—
120C3×#106—31no—
121C3×#106—61no—
122C3×C4⋊C8—91no—
123C3×#103—31no—
124C3×#103—31no—
125C3×#103—61no—
126C3×#103—91no—
127#835—31no—
128#817C3×D311yescharacteristic
129#816C3×D311yescharacteristic
130Dic3⋊C8—31no—
131Dic3⋊C8—31no—
132Dic3⋊C8—61no—
133#810—31no—
134#807—31no—
135#807—31no—
136C32×Q8—32no—
137C32×Q8—61no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—41no—
142C2×C32×C4—61no—
143C2×C32×C4—61no—
144C2×C32×C4—61no—
145C2×C32×C4—61no—
146C2×C32×C4C22×D311yescharacteristic
147C2×C32×C4C22×D311yescharacteristic
148C2×C32×C4C23×C311yescharacteristic
149C2×C3⋊Dic3C3×D411yescharacteristic
150C2×C3⋊Dic3C3×D411yescharacteristic
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—31no—
160C2×C3×Dic3—31no—
161C2×C3×Dic3—31no—
162C2×C3×Dic3—31no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3—41no—
165C2×C3×Dic3—41no—
166C2×C3×Dic3—41no—
167C2×C3×Dic3—61no—
168C2×C3×Dic3—61no—
169C3×Dic6—21no—
170C3×Dic6—21no—
171C3×Dic6—22no—
172C3×Dic6—41no—
173C3×Dic6Dic612yes—
174C3×Dic6C3×Q812yes—
175C32×C8—21no—
176C32×C8—22no—
177C32×C8—21no—
178C32×C8—21no—
179C32×C8—41no—
180C32×C8—41no—
181C32×C8—42no—
182C3⋊(C3⋊C8)—21no—
183C3×C3⋊C8—61no—
184C3×C3⋊C8—61no—
185C3×C3⋊C8—121no—
186#479—91noSylow
187C2×C33C22⋊Q811yescharacteristic
188C2×C33#13511yescharacteristic
189C2×C33#13711yescharacteristic
190C2×C3×Q8—31no—
191C2×C3×Q8—31no—
192C2×C3×Q8—61no—
193C2×Dic6C2×C3×D311yescharacteristic
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—41no—
198C2×C3×C8—91no—
199C2×C3×C8D3211yescharacteristic
200C2×C3×C8C2×C3×D311yescharacteristic
201C2×C3×C8C2×C3×D311yescharacteristic
202C3×C4⋊C4—31no—
203C3×C4⋊C4—31no—
204C3×C4⋊C4—31no—
205C3×C4⋊C4—31no—
206C3×C4⋊C4—31no—
207C3×C4⋊C4—31no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—181no—
212C3×C4⋊C4—181no—
213C3×C4⋊C4—181no—
214C3×C42—91no—
215C3×C42—181no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3C2×C3×D311yescharacteristic
220C4⋊Dic3C2×C3×D311yescharacteristic
221C4⋊Dic3C2×C3×D311yescharacteristic
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225C4×Dic3—31no—
226C4×Dic3—31no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C4×Dic3—61no—
230C2×C3⋊C8—31no—
231C2×C3⋊C8—31no—
232C2×C3⋊C8—61no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32—41no—
237C22×C32D3×D411yescharacteristic
238C22×C32D3×D411yescharacteristic
239C22×C32C2×C3×D411yescharacteristic
240C32×C4—21no—
241C32×C4—21no—
242C32×C4—21no—
243C32×C4—21no—
244C32×C4—21no—
245C32×C4—21no—
246C32×C4—41no—
247C32×C4—41no—
248C32×C4—62no—
249C32×C4—121no—
250C32×C4—121no—
251C32×C4—121no—
252C32×C4C2×Dic611yescharacteristic
253C32×C4#23511yescharacteristic
254C32×C4#23711yescharacteristic
255C32×C4D3×Q811yescharacteristic
256C32×C4C2×C3×Q811yescharacteristic
257C32×C4C3×#4111yescharacteristic
258C3⋊Dic3—21no—
259C3⋊Dic3—21no—
260C3×Dic3—22no—
261C3×Dic3—22no—
262C3×Dic3—42no—
263C3×Dic3—41no—
264C3×Dic3—41no—
265C3×Dic3—41no—
266C3×Dic3—41no—
267C3×Dic3—41no—
268C3×Dic3—41no—
269C3×Dic3—62no—
270C3×Dic3—61no—
271C3×Dic3—61no—
272C3×Dic3—61no—
273C3×Dic3—61no—
274C3×Dic3—81no—
275C3×Dic3—81no—
276C3×Dic3—81no—
277C3×Dic3—121no—
278#125—91no—
279C4×Q8—91no—
280#107—91no—
281#106—31no—
282C4⋊C8—91no—
283#103—31no—
284#103—91no—
285C33#47911yescharacteristic, complemented, Sylow
286C3×Q8—32no—
287C3×Q8—32no—
288C3×Q8—62no—
289C3×Q8—61no—
290C3×Q8—61no—
291C3×Q8—121no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—41no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—91no—
305C2×C3×C4—91no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4C2×D3211yescharacteristic
311C2×C3×C4C22×C3×D311yescharacteristic
312C2×C3×C4C22×C3×D311yescharacteristic
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—31no—
318C2×Dic3—31no—
319C2×Dic3—31no—
320C2×Dic3—31no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323Dic6—21no—
324Dic6C3×Dic612yes—
325C3×C8—22no—
326C3×C8—21no—
327C3×C8—21no—
328C3×C8—21no—
329C3×C8—41no—
330C3×C8—41no—
331C3×C8—42no—
332C3×C8—181no—
333C3⋊C8—61no—
334C3⋊C8—61no—
335C3⋊C8—121no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32—41no—
346C2×C32—41no—
347C2×C32—41no—
348C2×C32#87811yescharacteristic
349C2×C32#89611yescharacteristic
350C2×C32#91511yescharacteristic
351C2×C32#91611yescharacteristic
352C2×C32#91611yescharacteristic
353C2×C32#91811yescharacteristic
354C2×C32C3×C22⋊Q811yescharacteristic
355C2×C32C3×#13511yescharacteristic
356C2×C32C3×#13711yescharacteristic
357C2×Q8—31no—
358C2×C8—91no—
359C2×C8C3×D3211yescharacteristic
360C4⋊C4—31no—
361C4⋊C4—31no—
362C4⋊C4—31no—
363C4⋊C4—181no—
364C4⋊C4—181no—
365C4⋊C4—181no—
366C42—91no—
367C42—181no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—41no—
372C22×C3#380211yescharacteristic
373C22×C3C3×D3×D411yescharacteristic
374C22×C3C3×D3×D411yescharacteristic
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—62no—
384C3×C4—62no—
385C3×C4—122no—
386C3×C4—121no—
387C3×C4—121no—
388C3×C4—121no—
389C3×C4—121no—
390C3×C4—121no—
391C3×C4—121no—
392C3×C4—181no—
393C3×C4—181no—
394C3×C4—241no—
395C3×C4—241no—
396C3×C4—241no—
397C3×C4D3×Dic611yescharacteristic
398C3×C4#380411yescharacteristic
399C3×C4C2×C3×Dic611yescharacteristic
400C3×C4C3×#23511yescharacteristic
401C3×C4C3×#23711yescharacteristic
402C3×C4C3×D3×Q811yescharacteristic
403Dic3—22no—
404Dic3—41no—
405Dic3—41no—
406Dic3—41no—
407Dic3—62no—
408Dic3—61no—
409Dic3—61no—
410Dic3—61no—
411Dic3—61no—
412Dic3—121no—
413C32—21no—
414C32—21no—
415C32—21no—
416C32—41no—
417C32#479911yescharacteristic, complemented
418C32#485711yescharacteristic, complemented
419C32C3×#47911yescharacteristic, complemented
420Q8—32no—
421Q8—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—91no—
427C2×C4—91no—
428C2×C4C2×C3×D3211yescharacteristic
429C8—21no—
430C8—181no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—41no—
441C2×C3—41no—
442C2×C3—41no—
443C2×C3#6380911yescharacteristic
444C2×C3#6381111yescharacteristic
445C2×C3#6389911yescharacteristic
446C2×C3C3×#87811yescharacteristic
447C2×C3C3×#89611yescharacteristic
448C2×C3C3×#91511yescharacteristic
449C2×C3C3×#91611yescharacteristic
450C2×C3C3×#91611yescharacteristic
451C2×C3C3×#91811yescharacteristic
452C22C3×#380211yescharacteristic
453C4—62no—
454C4—121no—
455C4—121no—
456C4—121no—
457C4—181no—
458C4—181no—
459C4C3×D3×Dic611yescharacteristic
460C4C3×#380411yescharacteristic
461C3—21no—
462C3—21no—
463C3—21no—
464C3—41no—
465C3#1059082011yescharacteristic, direct product factor
466C3C3×#479911yescharacteristic, complemented
467C3C3×#485711yescharacteristic, complemented
468C2C3×#6380911yescharacteristic
469C2C3×#6381111yescharacteristic
470C2C3×#6389911yescharacteristic
subgroupG/H
centerC22×C3#3802
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×C8C22
socle, prime radicalC22×C33C2×D4
hypercenterC2×C3×C8D32
hypocenterC32C3×#479
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
10. #10590820C3direct (N × H)
285. C33#479semidirect
417. C32#4799semidirect
418. C32#4857semidirect
419. C32C3×#479semidirect
465. C3#10590820direct (N × H)
466. C3C3×#4799semidirect
467. C3C3×#4857semidirect

Maximal subgroups

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

subgroupindex
C3×#638722
C3×#638432
C3×#636412
C32×#8172
C32×#8162
C3×#635762
C3×#635652
C3×#48573
C3×#47993
#105908203