Finite Group Databasebeta

← C3×#10590710 #13157820

Subgroups — C3×#10590710 #13157820

Order 1728.

534 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63856C211yesmaximal, characteristic
2C3×#63841C211yesmaximal, characteristic
3C3×#63645C211yesmaximal, characteristic, complemented
4C32×(C2×D3)⋊C8C211yesmaximal, characteristic
5C32×#816C211yesmaximal, characteristic, complemented
6C3×#63573C211yesmaximal, characteristic, complemented
7C3×#63566C211yesmaximal, characteristic, complemented
8C3×#4814—31nomaximal
9C3×#4723—31nomaximal
10#10590710C311yesmaximal, characteristic, direct product factor
11C2×C32×C4×D3C2211yescharacteristic
12C2×C32×Dic6C2211yescharacteristic
13C2×C33×C8C2211yescharacteristic
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C32×C4⋊Dic3C2211yescharacteristic
17C2×C32×C3⋊C8C2211yescharacteristic
18C3×#3724—21no—
19C3×(C2×D3)⋊Dic3—21no—
20C3×(C2×D3)⋊Dic3—21no—
21C3×Dic32—21no—
22C3×#946—31no—
23C3×#926—31no—
24C3×#924—31no—
25C3×#892—31no—
26#63856C2×C311yescharacteristic
27#63841C2×C311yescharacteristic
28C32×#103—31no—
29C32×C22⋊C8—31no—
30#63645C2×C311yescharacteristic, complemented
31C3×#835—31no—
32C3×(C2×D3)⋊C8—21no—
33C3×(C2×D3)⋊C8D311yescharacteristic
34C3×(C2×D3)⋊C8C2×C311yescharacteristic
35C3×#818—31no—
36C3×#818—31no—
37C3×#818—61no—
38C3×#817—31no—
39C3×#816—21no—
40C3×#816—31no—
41C3×#816D311yescharacteristic, complemented
42C3×#816C2×C311yescharacteristic, complemented
43C3×#808—31no—
44#63573C2×C311yescharacteristic, complemented
45#63566C2×C311yescharacteristic, complemented
46C22×C32×D3D411yescharacteristic
47C2×C33×C4C2311yescharacteristic
48C2×C3×C3⋊Dic3—21no—
49C2×C3×C3⋊Dic3—21no—
50C2×C32×Dic3—21no—
51C2×C32×Dic3—21no—
52C2×C32×Dic3D411yescharacteristic
53C32×C4×D3—21no—
54C32×C4×D3—21no—
55C32×Dic6—21no—
56C32×Dic6—21no—
57C33×C8—21no—
58C32×C3⋊C8—21no—
59C3×#485—91no—
60#4814—31no—
61#4723—31no—
62C2×C32×Q8—31no—
63C22×C32×C4—31no—
64C2×C3×C4×D3—21no—
65C2×C3×C4×D3C2×D311yescharacteristic
66C2×C3×C4×D3C22×C311yescharacteristic
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2×D311yescharacteristic
69C2×C3×Dic6C22×C311yescharacteristic
70C2×C32×C8—21no—
71C2×C32×C8—21no—
72C2×C32×C8—21no—
73C2×C32×C8—31no—
74C2×C32×C8—41no—
75C2×C32×C8C2×D311yescharacteristic
76C2×C32×C8C2×D311yescharacteristic
77C2×C32×C8C22×C311yescharacteristic
78C32×C4⋊C4—31no—
79C4⋊(C3⋊Dic3)C22×C311yescharacteristic
80C4⋊(C3⋊Dic3)C22×C311yescharacteristic
81C3×#217—61no—
82C3×#217—61no—
83C3×(C2×D3)⋊C4—61no—
84C3×(C2×D3)⋊C4—61no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—31no—
87C3×C4⋊Dic3—31no—
88C3×C4⋊Dic3—31no—
89C3×C4⋊Dic3—31no—
90C3×C4⋊Dic3—61no—
91C3×C4⋊Dic3—61no—
92C3×C4⋊Dic3C2×D311yescharacteristic
93C3×C4⋊Dic3C22×C311yescharacteristic
94C3×Dic3⋊C4—61no—
95C3×Dic3⋊C4—61no—
96C3×C4×Dic3—61no—
97C3×C4×Dic3—61no—
98C2×C3×C3⋊C8—21no—
99C2×C3×C3⋊C8C2×D311yescharacteristic
100C2×C3×C3⋊C8C22×C311yescharacteristic
101#3724—21no—
102(C2×D3)⋊Dic3—21no—
103(C2×D3)⋊Dic3—21no—
104Dic32—21no—
105C22×C33C2×D411yescharacteristic
106C2×C32×D3—21no—
107C2×C32×D3—21no—
108C2×C32×D3—21no—
109C33×C4#4111yescharacteristic
110C33×C4#4111yescharacteristic
111C3×C3⋊Dic3—41no—
112C3×C3⋊Dic3—41no—
113C32×Dic3—21no—
114C32×Dic3—41no—
115C32×Dic3—41no—
116C3×C22⋊Q8—91no—
117C3×#117—91no—
118#946—31no—
119#926—31no—
120#924—31no—
121#892—31no—
122C3×#107—91no—
123C3×#106—91no—
124C3×#103—31no—
125C3×#103—31no—
126C3×#103—61no—
127C3×#103—91no—
128C3×C22⋊C8—31no—
129C3×C22⋊C8—31no—
130C3×C22⋊C8—61no—
131#835—31no—
132(C2×D3)⋊C8C3×D311yescharacteristic
133#818—31no—
134#818—31no—
135#818—61no—
136#817—31no—
137#816—31no—
138#816C3×D311yescharacteristic, complemented
139#808—31no—
140C23×C32—31no—
141C22×C3×D3—21no—
142C22×C3×D3D1211yescharacteristic
143C22×C3×D3C3×D411yescharacteristic
144C32×Q8—61no—
145C32×Q8—61no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—31no—
150C2×C32×C4—41no—
151C2×C32×C4—61no—
152C2×C32×C4—61no—
153C2×C32×C4—61no—
154C2×C32×C4—61no—
155C2×C32×C4C22×D311yescharacteristic
156C2×C32×C4C22×D311yescharacteristic
157C2×C32×C4C23×C311yescharacteristic
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—41no—
166C2×C3×Dic3—41no—
167C2×C3×Dic3—61no—
168C2×C3×Dic3—61no—
169C2×C3×Dic3—61no—
170C2×C3×Dic3—61no—
171C2×C3×Dic3—121no—
172C2×C3×Dic3—121no—
173C2×C3×Dic3D1211yescharacteristic
174C2×C3×Dic3C3×D411yescharacteristic
175C3×C4×D3—21no—
176C3×C4×D3—21no—
177C3×C4×D3—21no—
178C3×C4×D3—21no—
179C3×C4×D3—41no—
180C3×C4×D3—41no—
181C3×Dic6—22no—
182C3×Dic6—21no—
183C3×Dic6—21no—
184C3×Dic6—21no—
185C3×Dic6—21no—
186C3×Dic6—41no—
187C32×C8—21no—
188C32×C8—22no—
189C32×C8—21no—
190C32×C8—21no—
191C32×C8—41no—
192C32×C8—41no—
193C32×C8—42no—
194C32×C8—61no—
195C3×C3⋊C8—21no—
196C3×C3⋊C8—21no—
197C3×C3⋊C8—41no—
198#485—91noSylow
199C2×C33#12311yescharacteristic
200C2×C33#13511yescharacteristic
201C2×C33#13711yescharacteristic
202C32×D3—41no—
203C2×C3×Q8—31no—
204C2×C3×Q8—31no—
205C2×C3×Q8—61no—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C22×C3×C4—61no—
209C2×C4×D3C2×C3×D311yescharacteristic
210C2×Dic6C2×C3×D311yescharacteristic
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—31no—
215C2×C3×C8—31no—
216C2×C3×C8—41no—
217C2×C3×C8—61no—
218C2×C3×C8D3211yescharacteristic
219C2×C3×C8C2×C3×D311yescharacteristic
220C2×C3×C8C2×C3×D311yescharacteristic
221C3×C4⋊C4—31no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—91no—
225C3×C4⋊C4—91no—
226C3×C4⋊C4—181no—
227C3×C22⋊C4—181no—
228C3×C22⋊C4—181no—
229C3×C42—181no—
230#217—61no—
231#217—61no—
232(C2×D3)⋊C4—61no—
233(C2×D3)⋊C4—61no—
234C4⋊Dic3—31no—
235C4⋊Dic3—31no—
236C4⋊Dic3—31no—
237C4⋊Dic3—31no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3C2×C3×D311yescharacteristic
241Dic3⋊C4—61no—
242Dic3⋊C4—61no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C2×C3⋊C8C2×C3×D311yescharacteristic
246C22×C32—21no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—41no—
250C22×C32—61no—
251C22×C32—61no—
252C22×C32—61no—
253C22×C32C2×D1211yescharacteristic
254C22×C32D3×D411yescharacteristic
255C22×C32C2×C3×D411yescharacteristic
256C2×C3×D3—22no—
257C2×C3×D3—21no—
258C2×C3×D3—21no—
259C2×C3×D3—21no—
260C2×C3×D3—21no—
261C2×C3×D3—21no—
262C2×C3×D3—21no—
263C2×C3×D3—41no—
264C2×C3×D3—41no—
265C32×C4—21no—
266C32×C4—21no—
267C32×C4—21no—
268C32×C4—21no—
269C32×C4—21no—
270C32×C4—21no—
271C32×C4—41no—
272C32×C4—41no—
273C32×C4—61no—
274C32×C4—121no—
275C32×C4—121no—
276C32×C4#23511yescharacteristic
277C32×C4#23711yescharacteristic
278C32×C4#23711yescharacteristic
279C32×C4#23711yescharacteristic
280C32×C4C3×#4111yescharacteristic
281C32×C4C3×#4111yescharacteristic
282C3⋊Dic3—41no—
283C3⋊Dic3—41no—
284C3×Dic3—21no—
285C3×Dic3—21no—
286C3×Dic3—41no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C3×Dic3—41no—
291C3×Dic3—41no—
292C3×Dic3—81no—
293C3×Dic3—121no—
294C3×Dic3—121no—
295C3×Dic3—121no—
296C3×Dic3—121no—
297C3×Dic3—241no—
298C3×Dic3—241no—
299C22⋊Q8—91no—
300#117—91no—
301#107—91no—
302#106—91no—
303#103—31no—
304#103—91no—
305C22⋊C8—31no—
306C33#48511yescharacteristic, complemented, Sylow
307C23×C3—31no—
308C23×C3—31no—
309C23×C3—61no—
310C22×D3C3×D1211yescharacteristic
311C3×Q8—62no—
312C3×Q8—61no—
313C3×Q8—61no—
314C3×Q8—61no—
315C3×Q8—61no—
316C3×Q8—121no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—31no—
321C2×C3×C4—31no—
322C2×C3×C4—41no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4—181no—
337C2×C3×C4—181no—
338C2×C3×C4C2×D3211yescharacteristic
339C2×C3×C4C22×C3×D311yescharacteristic
340C2×C3×C4C22×C3×D311yescharacteristic
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3C3×D1211yescharacteristic
350C4×D3—21no—
351C4×D3—21no—
352Dic6—21no—
353Dic6—21no—
354C3×C8—22no—
355C3×C8—21no—
356C3×C8—21no—
357C3×C8—21no—
358C3×C8—41no—
359C3×C8—41no—
360C3×C8—42no—
361C3×C8—61no—
362C3×C8—61no—
363C3×C8—121no—
364C3⋊C8—21no—
365C2×C32—21no—
366C2×C32—21no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32—21no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32—21no—
373C2×C32—21no—
374C2×C32—41no—
375C2×C32—41no—
376C2×C32—41no—
377C2×C32—121no—
378C2×C32#88311yescharacteristic
379C2×C32#88611yescharacteristic
380C2×C32#90411yescharacteristic
381C2×C32#90911yescharacteristic
382C2×C32#91511yescharacteristic
383C2×C32#91911yescharacteristic
384C2×C32C3×#12311yescharacteristic
385C2×C32C3×#13511yescharacteristic
386C2×C32C3×#13711yescharacteristic
387C3×D3—42no—
388C3×D3—41no—
389C3×D3—41no—
390C2×Q8—31no—
391C22×C4—31no—
392C2×C8—31no—
393C2×C8C3×D3211yescharacteristic
394C4⋊C4—31no—
395C4⋊C4—91no—
396C4⋊C4—91no—
397C4⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—181no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—41no—
405C22×C3—62no—
406C22×C3—61no—
407C22×C3—61no—
408C22×C3—61no—
409C22×C3—61no—
410C22×C3—61no—
411C22×C3—61no—
412C22×C3—121no—
413C22×C3—121no—
414C22×C3D3×D1211yescharacteristic
415C22×C3C2×C3×D1211yescharacteristic
416C22×C3C3×D3×D411yescharacteristic
417C2×D3—21no—
418C2×D3—21no—
419C2×D3—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—61no—
429C3×C4—61no—
430C3×C4—121no—
431C3×C4—122no—
432C3×C4—121no—
433C3×C4—121no—
434C3×C4—121no—
435C3×C4—121no—
436C3×C4—241no—
437C3×C4—361no—
438C3×C4—361no—
439C3×C4#379511yescharacteristic
440C3×C4#380511yescharacteristic
441C3×C4C3×#23511yescharacteristic
442C3×C4C3×#23711yescharacteristic
443C3×C4C3×#23711yescharacteristic
444C3×C4C3×#23711yescharacteristic
445Dic3—21no—
446Dic3—41no—
447Dic3—41no—
448Dic3—121no—
449Dic3—121no—
450Dic3—121no—
451Dic3—121no—
452Dic3—241no—
453Dic3—241no—
454C32—21no—
455C32—21no—
456C32—21no—
457C32—41no—
458C32#472311yescharacteristic, complemented
459C32#481411yescharacteristic, complemented
460C32C3×#48511yescharacteristic, complemented
461C23—31no—
462Q8—61no—
463Q8—61no—
464C2×C4—31no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4C2×C3×D3211yescharacteristic
472C8—21no—
473C8—61no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—41no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—122no—
487C2×C3—121no—
488C2×C3—121no—
489C2×C3#6380011yescharacteristic
490C2×C3#6380811yescharacteristic
491C2×C3#6389111yescharacteristic
492C2×C3C3×#88311yescharacteristic
493C2×C3C3×#88611yescharacteristic
494C2×C3C3×#90411yescharacteristic
495C2×C3C3×#90911yescharacteristic
496C2×C3C3×#91511yescharacteristic
497C2×C3C3×#91911yescharacteristic
498D3—41no—
499C22—61no—
500C22—61no—
501C22—61no—
502C22C3×D3×D1211yescharacteristic
503C4—61no—
504C4—121no—
505C4—121no—
506C4—361no—
507C4—361no—
508C4C3×#379511yescharacteristic
509C4C3×#380511yescharacteristic
510C3—21no—
511C3—21no—
512C3—21no—
513C3—41no—
514C3#1059071011yescharacteristic, direct product factor
515C3C3×#472311yescharacteristic, complemented
516C3C3×#481411yescharacteristic, complemented
517C2—121no—
518C2C3×#6380011yescharacteristic
519C2C3×#6380811yescharacteristic
520C2C3×#6389111yescharacteristic
subgroupG/H
centerC22×C3D3×D12
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×C8C22
socleC22×C33C2×D4
prime radicalC22×C32×D3D4
hypercenterC2×C3×C8D32
hypocenterC32C3×#485
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
3. C3×#63645C2semidirect
5. C32×#816C2semidirect
6. C3×#63573C2semidirect
7. C3×#63566C2semidirect
10. #10590710C3direct (N × H)
30. #63645C2×C3semidirect
41. C3×#816D3semidirect
42. C3×#816C2×C3semidirect
44. #63573C2×C3semidirect
45. #63566C2×C3semidirect
138. #816C3×D3semidirect
306. C33#485semidirect
458. C32#4723semidirect
459. C32#4814semidirect
460. C32C3×#485semidirect
514. C3#10590710direct (N × H)
515. C3C3×#4723semidirect
516. C3C3×#4814semidirect

Maximal subgroups

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

subgroupindex
C3×#638562
C3×#638412
C3×#636452
C32×(C2×D3)⋊C82
C32×#8162
C3×#635732
C3×#635662
C3×#48143
C3×#47233
#105907103