Finite Group Databasebeta

← C3×#10590863 #13157826

Subgroups — C3×#10590863 #13157826

Order 1728.

542 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×#63869C211yesmaximal, characteristic, complemented
2C3×#63860C211yesmaximal, characteristic
3C3×#63643C211yesmaximal, characteristic, complemented
4C32×#821C211yesmaximal, characteristic
5C32×C8×Dic3C211yesmaximal, characteristic, complemented
6C3×#63567C211yesmaximal, characteristic, complemented
7C3×#63563C211yesmaximal, characteristic
8C3×#4768—31nomaximal
9C3×#4697—31nomaximal
10#10590863C311yesmaximal, characteristic, direct product factor
11C2×C3×#634C2211yescharacteristic
12C2×C32×D12C2211yescharacteristic
13C2×C33×C8C2211yescharacteristic
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C32×C4⋊Dic3C2211yescharacteristic
16C32×C4×Dic3C2211yescharacteristic
17C2×C32×C3⋊C8C2211yescharacteristic
18C3×#3724—21no—
19C3×Dic3⋊Dic3—21no—
20C3×(C2×D3)⋊Dic3—21no—
21C3×(C2×D3)⋊Dic3—21no—
22C3×#936—31no—
23C3×#890—31no—
24C3×#875—31no—
25C3×#870—31no—
26#63869C2×C311yescharacteristic, complemented
27#63860C2×C311yescharacteristic
28C32×#102—31no—
29C32×C4×C8—31no—
30#63643C2×C311yescharacteristic, complemented
31C3×#832—31no—
32C3×#821—21no—
33C3×#821—31no—
34C3×#821D311yescharacteristic
35C3×#821C2×C311yescharacteristic
36C3×#816—31no—
37C3×#816—31no—
38C3×#816—31no—
39C3×#816—61no—
40C3×C8×Dic3—21no—
41C3×C8×Dic3D311yescharacteristic, complemented
42C3×C8×Dic3C2×C311yescharacteristic, complemented
43C3×#810—31no—
44#63567C2×C311yescharacteristic, complemented
45#63563C2×C311yescharacteristic
46C22×C32×D3—21no—
47C2×C33×C4C2311yescharacteristic
48C2×C3×C3⋊Dic3—21no—
49C2×C3×C3⋊Dic3—21no—
50C3×#634—21no—
51C3×#634—21no—
52C2×C32×Dic3—21no—
53C2×C32×Dic3D411yescharacteristic
54C2×C32×Dic3D411yescharacteristic
55C32×D12—21no—
56C32×D12—21no—
57C33×C8—21no—
58C32×C3⋊C8—21no—
59C3×#488—91no—
60#4768—31no—
61#4697—31no—
62C2×C32×D4—31no—
63C2×#634C22×C311yescharacteristic
64C2×C3×D12—21no—
65C2×C3×D12C2×D311yescharacteristic
66C2×C3×D12C22×C311yescharacteristic
67C2×C3×Dic6—31no—
68C2×C3×Dic6—31no—
69C2×C3×Dic6—61no—
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—
79C32×C42—31no—
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—61no—
89C3×C4⋊Dic3—61no—
90C3×C4⋊Dic3C2×D311yescharacteristic
91C3×C4⋊Dic3C22×C311yescharacteristic
92C3×Dic3⋊C4—61no—
93C3×Dic3⋊C4—61no—
94C3×Dic3⋊C4—61no—
95C3×C4×Dic3—21no—
96C3×C4×Dic3C2×D311yescharacteristic
97C3×C4×Dic3C22×C311yescharacteristic
98C2×C3×C3⋊C8—21no—
99C2×C3×C3⋊C8C2×D311yescharacteristic
100C2×C3×C3⋊C8C22×C311yescharacteristic
101#3724—21no—
102Dic3⋊Dic3—21no—
103(C2×D3)⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105C22×C33C2×D411yescharacteristic
106C2×C32×D3—41no—
107C2×C32×D3—41no—
108C2×C32×D3—41no—
109C33×C4#4111yescharacteristic
110C33×C4#4111yescharacteristic
111C3×C3⋊Dic3—41no—
112C3×C3⋊Dic3—41no—
113C32×Dic3—21no—
114C32×Dic3—21no—
115C32×Dic3—41no—
116C3×#125—91no—
117C3×#124—91no—
118#936—31no—
119#890—31no—
120#875—31no—
121#870—31no—
122C3×#103—91no—
123C3×#103—91no—
124C3×#102—31no—
125C3×#102—31no—
126C3×#102—61no—
127C3×#102—91no—
128C3×C4×C8—31no—
129C3×C4×C8—31no—
130C3×C4×C8—61no—
131#832—31no—
132#821—31no—
133#821C3×D311yescharacteristic
134#816—31no—
135#816—31no—
136#816—31no—
137#816—61no—
138C8×Dic3C3×D311yescharacteristic, complemented
139#810—31no—
140C23×C32—61no—
141C22×C3×D3—21no—
142C22×C3×D3—21no—
143C22×C3×D3—41no—
144C32×D4—61no—
145C32×D4—61no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—31no—
150C2×C32×C4—31no—
151C2×C32×C4—41no—
152C2×C32×C4—61no—
153C2×C32×C4C22×D311yescharacteristic
154C2×C32×C4C22×D311yescharacteristic
155C2×C32×C4C23×C311yescharacteristic
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158#634—21no—
159#634—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—41no—
165C2×C3×Dic3—61no—
166C2×C3×Dic3—61no—
167C2×C3×Dic3—61no—
168C2×C3×Dic3—61no—
169C2×C3×Dic3—121no—
170C2×C3×Dic3—121no—
171C2×C3×Dic3D1211yescharacteristic
172C2×C3×Dic3D1211yescharacteristic
173C2×C3×Dic3C3×D411yescharacteristic
174C2×C3×Dic3C3×D411yescharacteristic
175C3×D12—22no—
176C3×D12—21no—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—21no—
180C3×D12—41no—
181C3×Dic6—62no—
182C3×Dic6—61no—
183C3×Dic6—61no—
184C3×Dic6—61no—
185C3×Dic6—61no—
186C3×Dic6—121no—
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—22no—
196C3×C3⋊C8—21no—
197C3×C3⋊C8—21no—
198#488—91noSylow
199C2×C33#12411yescharacteristic
200C2×C33#13511yescharacteristic
201C2×C33#13511yescharacteristic
202C32×D3—81no—
203C2×C3×Q8—91no—
204C2×C3×D4—31no—
205C2×C3×D4—31no—
206C2×C3×D4—61no—
207C2×D12C2×C3×D311yescharacteristic
208C2×Dic6—31no—
209C2×Dic6—31no—
210C2×Dic6—61no—
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—181no—
226C3×C4⋊C4—181no—
227C3×C22⋊C4—181no—
228C3×C22⋊C4—181no—
229C3×C42—31no—
230C3×C42—31no—
231C3×C42—61no—
232#217—61no—
233#217—61no—
234(C2×D3)⋊C4—61no—
235(C2×D3)⋊C4—61no—
236C4⋊Dic3—31no—
237C4⋊Dic3—31no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3C2×C3×D311yescharacteristic
241Dic3⋊C4—61no—
242Dic3⋊C4—61no—
243Dic3⋊C4—61no—
244C4×Dic3C2×C3×D311yescharacteristic
245C2×C3⋊C8C2×C3×D311yescharacteristic
246C22×C32—21no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—41no—
250C22×C32—121no—
251C22×C32—121no—
252C22×C32—121no—
253C22×C32C2×D1211yescharacteristic
254C22×C32D3×D411yescharacteristic
255C22×C32C2×C3×D411yescharacteristic
256C2×C3×D3—42no—
257C2×C3×D3—41no—
258C2×C3×D3—41no—
259C2×C3×D3—41no—
260C2×C3×D3—41no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C2×C3×D3—81no—
264C2×C3×D3—81no—
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—61no—
275C32×C4—121no—
276C32×C4#23511yescharacteristic
277C32×C4#23511yescharacteristic
278C32×C4#23511yescharacteristic
279C32×C4#23711yescharacteristic
280C32×C4C3×#4111yescharacteristic
281C32×C4C3×#4111yescharacteristic
282C3⋊Dic3—41no—
283C3⋊Dic3—41no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—21no—
287C3×Dic3—21no—
288C3×Dic3—21no—
289C3×Dic3—21no—
290C3×Dic3—41no—
291C3×Dic3—41no—
292C3×Dic3—81no—
293C3×Dic3—122no—
294C3×Dic3—121no—
295C3×Dic3—121no—
296C3×Dic3—121no—
297C3×Dic3—121no—
298C3×Dic3—241no—
299#125—91no—
300#124—91no—
301#103—91no—
302#103—91no—
303#102—31no—
304#102—91no—
305C4×C8—31no—
306C33#48811yescharacteristic, complemented, Sylow
307C23×C3—61no—
308C23×C3—61no—
309C23×C3—121no—
310C22×D3—21no—
311C3×Q8—181no—
312C3×Q8—181no—
313C3×D4—62no—
314C3×D4—61no—
315C3×D4—61no—
316C3×D4—61no—
317C3×D4—61no—
318C3×D4—121no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—31no—
323C2×C3×C4—31no—
324C2×C3×C4—31no—
325C2×C3×C4—31no—
326C2×C3×C4—41no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—121no—
332C2×C3×C4—181no—
333C2×C3×C4—181no—
334C2×C3×C4C2×D3211yescharacteristic
335C2×C3×C4C22×C3×D311yescharacteristic
336C2×C3×C4C22×C3×D311yescharacteristic
337C2×Dic3—21no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3C3×D1211yescharacteristic
345C2×Dic3C3×D1211yescharacteristic
346D12—21no—
347D12—21no—
348Dic6—62no—
349Dic6—61no—
350Dic6—61no—
351Dic6—61no—
352Dic6—61no—
353Dic6—121no—
354C3×C8—22no—
355C3×C8—21no—
356C3×C8—21no—
357C3×C8—21no—
358C3×C8—41no—
359C3×C8—41no—
360C3×C8—42no—
361C3×C8—62no—
362C3×C8—61no—
363C3×C8—61no—
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—241no—
378C2×C32#87511yescharacteristic
379C2×C32#88511yescharacteristic
380C2×C32#90411yescharacteristic
381C2×C32#90411yescharacteristic
382C2×C32#91211yescharacteristic
383C2×C32#91611yescharacteristic
384C2×C32C3×#12411yescharacteristic
385C2×C32C3×#13511yescharacteristic
386C2×C32C3×#13511yescharacteristic
387C3×D3—82no—
388C3×D3—81no—
389C3×D3—81no—
390C2×Q8—91no—
391C2×D4—31no—
392C2×C8—31no—
393C2×C8C3×D3211yescharacteristic
394C4⋊C4—31no—
395C4⋊C4—91no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—31no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—41no—
405C22×C3—122no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3—241no—
413C22×C3—241no—
414C22×C3D3×D1211yescharacteristic
415C22×C3C2×C3×D1211yescharacteristic
416C22×C3C3×D3×D411yescharacteristic
417C2×D3—41no—
418C2×D3—41no—
419C2×D3—41no—
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—62no—
429C3×C4—62no—
430C3×C4—61no—
431C3×C4—61no—
432C3×C4—61no—
433C3×C4—61no—
434C3×C4—121no—
435C3×C4—121no—
436C3×C4—241no—
437C3×C4—361no—
438C3×C4—361no—
439C3×C4#379811yescharacteristic
440C3×C4#380411yescharacteristic
441C3×C4C3×#23511yescharacteristic
442C3×C4C3×#23511yescharacteristic
443C3×C4C3×#23511yescharacteristic
444C3×C4C3×#23711yescharacteristic
445Dic3—21no—
446Dic3—21no—
447Dic3—41no—
448Dic3—122no—
449Dic3—121no—
450Dic3—121no—
451Dic3—121no—
452Dic3—121no—
453Dic3—241no—
454C32—21no—
455C32—21no—
456C32—21no—
457C32—41no—
458C32#469711yescharacteristic, complemented
459C32#476811yescharacteristic, complemented
460C32C3×#48811yescharacteristic, complemented
461C23—61no—
462Q8—181no—
463Q8—181no—
464D4—61no—
465D4—61no—
466C2×C4—31no—
467C2×C4—31no—
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—242no—
487C2×C3—241no—
488C2×C3—241no—
489C2×C3#6380611yescharacteristic
490C2×C3#6380711yescharacteristic
491C2×C3#6385211yescharacteristic
492C2×C3C3×#87511yescharacteristic
493C2×C3C3×#88511yescharacteristic
494C2×C3C3×#90411yescharacteristic
495C2×C3C3×#90411yescharacteristic
496C2×C3C3×#91211yescharacteristic
497C2×C3C3×#91611yescharacteristic
498D3—81no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22C3×D3×D1211yescharacteristic
503C4—61no—
504C4—61no—
505C4—121no—
506C4—361no—
507C4—361no—
508C4C3×#379811yescharacteristic
509C4C3×#380411yescharacteristic
510C3—21no—
511C3—21no—
512C3—21no—
513C3—41no—
514C3#1059086311yescharacteristic, direct product factor
515C3C3×#469711yescharacteristic, complemented
516C3C3×#476811yescharacteristic, complemented
517C2—241no—
518C2C3×#6380611yescharacteristic
519C2C3×#6380711yescharacteristic
520C2C3×#6385211yescharacteristic
subgroupG/H
centerC22×C3D3×D12
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×C8C22
socleC22×C33C2×D4
prime radicalC2×C32×D12C22
hypercenterC2×C3×C8D32
hypocenterC32C3×#488
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
1. C3×#63869C2semidirect
3. C3×#63643C2semidirect
5. C32×C8×Dic3C2semidirect
6. C3×#63567C2semidirect
10. #10590863C3direct (N × H)
26. #63869C2×C3semidirect
30. #63643C2×C3semidirect
41. C3×C8×Dic3D3semidirect
42. C3×C8×Dic3C2×C3semidirect
44. #63567C2×C3semidirect
138. C8×Dic3C3×D3semidirect
306. C33#488semidirect
458. C32#4697semidirect
459. C32#4768semidirect
460. C32C3×#488semidirect
514. C3#10590863direct (N × H)
515. C3C3×#4697semidirect
516. C3C3×#4768semidirect

Maximal subgroups

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

subgroupindex
C3×#638692
C3×#638602
C3×#636432
C32×#8212
C32×C8×Dic32
C3×#635672
C3×#635632
C3×#47683
C3×#46973
#105908633