Finite Group Databasebeta

← #13161490

Subgroups — #13161490

Order 1728.

554 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64079C211yesmaximal, characteristic
2C3×C4×#634C211yesmaximal, characteristic
3C3×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
4#11722080C211yesmaximal, characteristic
5#11722079C211yesmaximal, characteristic
6#11722076C211yesmaximal, characteristic
7#11722076C211yesmaximal, characteristic
8#10590302—31nomaximal
9#10590292—31nomaximal
10#10590286—31nomaximal
11C2×C3×#634C2211yescharacteristic
12C33×C42C2211yescharacteristic
13C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C3×#3750—21no—
17C3×#3750—21no—
18C3×#3750—21no—
19C3×C4×C3⋊Dic3—21no—
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
22#64079D311yescharacteristic
23C4×#634D311yescharacteristic
24C3×#870—31no—
25C3×#870—31no—
26C3×#870—61no—
27C3×C4×Dic6—31no—
28C3×C4×Dic6—31no—
29C3×C4×Dic6—61no—
30C4⋊(C3⋊(C3⋊C8))D311yescharacteristic
31C3×C4⋊(C3⋊C8)—31no—
32C3×C4⋊(C3⋊C8)—31no—
33C3×C4⋊(C3⋊C8)—61no—
34#63576—31no—
35#63575—31no—
36#63575—31no—
37#63574—31no—
38#63573—31no—
39#63573—31no—
40#63567—31no—
41#63567—31no—
42#63566—31no—
43#63566—31no—
44#63565—31no—
45#63565—31no—
46C2×C33×C4D411yescharacteristic
47C2×C33×C4D411yescharacteristic
48C2×C33×C4C2311yescharacteristic
49C2×C3×C3⋊Dic3—21no—
50C2×C3×C3⋊Dic3—21no—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C3×#634—21no—
54C3×#634Q812yes—
55C3×C3⋊(C3⋊C8)—21no—
56C3×C3⋊(C3⋊C8)—21no—
57#5063—91no—
58#5022—91no—
59#4829—91no—
60C2×#634C2×D311yescharacteristic
61C2×C3×Dic6—31no—
62C2×C3×Dic6—31no—
63C2×C3×Dic6—61no—
64C32×C42—21no—
65C32×C42—21no—
66C32×C42—21no—
67C32×C42—41no—
68C32×C42C2×D311yescharacteristic
69C32×C42C2×D311yescharacteristic
70C32×C42C2×D311yescharacteristic
71C4⋊(C3⋊Dic3)C2×D311yescharacteristic
72C4⋊(C3⋊Dic3)C2×D311yescharacteristic
73C4⋊(C3⋊Dic3)C2×D311yescharacteristic
74#3750—21no—
75#3750—21no—
76#3750—21no—
77C4×C3⋊Dic3—21no—
78C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
79C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
80C3×C4⋊Dic3—31no—
81C3×C4⋊Dic3—31no—
82C3×C4⋊Dic3—31no—
83C3×C4⋊Dic3—31no—
84C3×C4⋊Dic3—31no—
85C3×C4⋊Dic3—31no—
86C3×C4⋊Dic3—61no—
87C3×C4⋊Dic3—61no—
88C3×C4⋊Dic3—61no—
89C3×Dic3⋊C4—62no—
90C3×Dic3⋊C4—62no—
91C3×Dic3⋊C4—62no—
92C3×Dic3⋊C4—61no—
93C3×Dic3⋊C4—61no—
94C3×Dic3⋊C4—61no—
95C3×Dic3⋊C4—61no—
96C3×Dic3⋊C4—61no—
97C3×Dic3⋊C4—61no—
98C3×C4×Dic3—62no—
99C3×C4×Dic3—61no—
100C3×C4×Dic3—61no—
101C2×C3×C3⋊C8—31no—
102C2×C3×C3⋊C8—31no—
103C2×C3×C3⋊C8—31no—
104C2×C3×C3⋊C8—31no—
105C2×C3×C3⋊C8—61no—
106C2×C3×C3⋊C8—61no—
107C22×C33C2×D411yescharacteristic
108C33×C4—21no—
109C33×C4—21no—
110C33×C4C2×Q811yescharacteristic
111C33×C4#4111yescharacteristic
112C3×C3⋊Dic3—22no—
113C3×C3⋊Dic3—41no—
114C3×C3⋊Dic3—41no—
115C3×C3⋊Dic3—41no—
116C3×#125—91no—
117C3×C4×Q8—91no—
118#870—31no—
119#870—31no—
120#870—61no—
121C4×Dic6—31no—
122C4×Dic6—31no—
123C4×Dic6—61no—
124C3×C4⋊C8—91no—
125#835—91no—
126#835—91no—
127#818—91no—
128#817—91no—
129#816—91no—
130#816—91no—
131#810—91no—
132#810—91no—
133#808—91no—
134#808—91no—
135#807—91no—
136#807—91no—
137C4⋊(C3⋊C8)—31no—
138C4⋊(C3⋊C8)—31no—
139C4⋊(C3⋊C8)—61no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—41no—
150C2×C32×C4—41no—
151C2×C32×C4—41no—
152C2×C32×C4D1211yescharacteristic
153C2×C32×C4D1211yescharacteristic
154C2×C32×C4#6711yescharacteristic
155C2×C32×C4#6711yescharacteristic
156C2×C32×C4#6711yescharacteristic
157C2×C32×C4#6711yescharacteristic
158C2×C32×C4C22×D311yescharacteristic
159C2×C32×C4C22×D311yescharacteristic
160C2×C32×C4C22×D311yescharacteristic
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165#634—21no—
166#634Dic612yes—
167C2×C3×Dic3—62no—
168C2×C3×Dic3—61no—
169C2×C3×Dic3—61no—
170C2×C3×Dic3—62no—
171C2×C3×Dic3—62no—
172C2×C3×Dic3—62no—
173C2×C3×Dic3—61no—
174C2×C3×Dic3—61no—
175C2×C3×Dic3—61no—
176C2×C3×Dic3—61no—
177C2×C3×Dic3—61no—
178C2×C3×Dic3—61no—
179C3×Dic6—32no—
180C3×Dic6—32no—
181C3×Dic6—62no—
182C3×Dic6—62no—
183C3×Dic6—61no—
184C3×Dic6—61no—
185C3⋊(C3⋊C8)—21no—
186C3⋊(C3⋊C8)—21no—
187C3×C3⋊C8—61no—
188C3×C3⋊C8—61no—
189C3×C3⋊C8—61no—
190C3×C3⋊C8—61no—
191C3×C3⋊C8—121no—
192C3×C3⋊C8—121no—
193#479—271noSylow
194C2×C33C22⋊Q811yescharacteristic
195C2×C33#13511yescharacteristic
196C2×C33#13711yescharacteristic
197C2×C3×Q8—91no—
198C2×Dic6—31no—
199C2×Dic6—31no—
200C2×Dic6—61no—
201C2×C3×C8—91no—
202C2×C3×C8—91no—
203C3×C4⋊C4—91no—
204C3×C4⋊C4—91no—
205C3×C4⋊C4—91no—
206C3×C4⋊C4—181no—
207C3×C4⋊C4—181no—
208C3×C4⋊C4—181no—
209C3×C42—21no—
210C3×C42—21no—
211C3×C42—21no—
212C3×C42—41no—
213C3×C42—181no—
214C3×C42D3211yescharacteristic
215C3×C42D3211yescharacteristic
216C3×C42D3211yescharacteristic
217C4⋊Dic3—31no—
218C4⋊Dic3—31no—
219C4⋊Dic3—31no—
220C4⋊Dic3—31no—
221C4⋊Dic3—31no—
222C4⋊Dic3—31no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226Dic3⋊C4—62no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—61no—
230Dic3⋊C4—61no—
231Dic3⋊C4—61no—
232Dic3⋊C4—61no—
233Dic3⋊C4—61no—
234Dic3⋊C4—61no—
235C4×Dic3—62no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238C2×C3⋊C8—31no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—31no—
241C2×C3⋊C8—31no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C22×C32—21no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32—41no—
248C22×C32C2×D1211yescharacteristic
249C22×C32C2×#6711yescharacteristic
250C22×C32C2×#6711yescharacteristic
251C32×C4—21no—
252C32×C4—21no—
253C32×C4—22no—
254C32×C4—22no—
255C32×C4—21no—
256C32×C4—21no—
257C32×C4—21no—
258C32×C4—21no—
259C32×C4—21no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4—21no—
263C32×C4—21no—
264C32×C4—21no—
265C32×C4—41no—
266C32×C4—41no—
267C32×C4—41no—
268C32×C4—41no—
269C32×C4—41no—
270C32×C4—41no—
271C32×C4—42no—
272C32×C4—42no—
273C32×C4C2×Dic611yescharacteristic
274C32×C4#23511yescharacteristic
275C32×C4#23711yescharacteristic
276C32×C4D3×Q811yescharacteristic
277C32×C4D3×Q811yescharacteristic
278C32×C4#23911yescharacteristic
279C3⋊Dic3—22no—
280C3⋊Dic3—41no—
281C3⋊Dic3—41no—
282C3⋊Dic3—41no—
283C3×Dic3—64no—
284C3×Dic3—62no—
285C3×Dic3—62no—
286C3×Dic3—122no—
287C3×Dic3—122no—
288C3×Dic3—122no—
289C3×Dic3—121no—
290C3×Dic3—121no—
291C3×Dic3—121no—
292C3×Dic3—121no—
293C3×Dic3—121no—
294C3×Dic3—121no—
295#125—91no—
296C4×Q8—91no—
297#107—271no—
298#106—271no—
299C4⋊C8—91no—
300#103—271no—
301#103—271no—
302C33#47911yescharacteristic, complemented, Sylow
303C3×Q8—92no—
304C3×Q8—181no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—181no—
318C2×C3×C4—181no—
319C2×C3×C4—181no—
320C2×C3×C4—181no—
321C2×C3×C4#62511yescharacteristic
322C2×C3×C4#62511yescharacteristic
323C2×C3×C4#62611yescharacteristic
324C2×C3×C4#62611yescharacteristic
325C2×C3×C4#62611yescharacteristic
326C2×C3×C4#62611yescharacteristic
327C2×C3×C4C2×D3211yescharacteristic
328C2×C3×C4C2×D3211yescharacteristic
329C2×C3×C4C2×D3211yescharacteristic
330C2×Dic3—62no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342Dic6—32no—
343Dic6—32no—
344Dic6—62no—
345Dic6—62no—
346Dic6—61no—
347Dic6—61no—
348C3×C8—181no—
349C3×C8—181no—
350C3⋊C8—61no—
351C3⋊C8—61no—
352C3⋊C8—61no—
353C3⋊C8—61no—
354C3⋊C8—121no—
355C3⋊C8—121no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32—21no—
364C2×C32—21no—
365C2×C32—41no—
366C2×C32—41no—
367C2×C32—41no—
368C2×C32#89711yescharacteristic
369C2×C32#90411yescharacteristic
370C2×C32#90911yescharacteristic
371C2×C32#92411yescharacteristic
372C2×C32#94211yescharacteristic
373C2×C32#94611yescharacteristic
374C2×C32#95011yescharacteristic
375C2×C32#95011yescharacteristic
376C2×C32#95111yescharacteristic
377C2×Q8—91no—
378C2×C8—91no—
379C2×C8—91no—
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C42—181no—
387C42#111311yescharacteristic
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3C2×#62511yescharacteristic
393C22×C3C2×#62611yescharacteristic
394C22×C3C2×#62611yescharacteristic
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—41no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—42no—
414C3×C4—42no—
415C3×C4—41no—
416C3×C4—41no—
417C3×C4—182no—
418C3×C4—361no—
419C3×C4—361no—
420C3×C4—361no—
421C3×C4D3×Dic611yescharacteristic
422C3×C4D3×Dic611yescharacteristic
423C3×C4#379511yescharacteristic
424C3×C4#379611yescharacteristic
425C3×C4#379711yescharacteristic
426C3×C4#379911yescharacteristic
427Dic3—64no—
428Dic3—62no—
429Dic3—62no—
430Dic3—122no—
431Dic3—122no—
432Dic3—122no—
433Dic3—121no—
434Dic3—121no—
435Dic3—121no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439C32—21no—
440C32—21no—
441C32—21no—
442C32—41no—
443C32#482911yescharacteristic, complemented
444C32#502211yescharacteristic, complemented
445C32#506311yescharacteristic, complemented
446Q8—92no—
447Q8—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4#629511yescharacteristic
453C2×C4#629511yescharacteristic
454C2×C4C2×#111311yescharacteristic
455C8—181no—
456C8—181no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3#6382211yescharacteristic
470C2×C3#6382711yescharacteristic
471C2×C3#6382911yescharacteristic
472C2×C3#6382911yescharacteristic
473C2×C3#6383111yescharacteristic
474C2×C3#6383311yescharacteristic
475C2×C3#6385611yescharacteristic
476C2×C3#6385711yescharacteristic
477C2×C3#6387111yescharacteristic
478C22C2×#629511yescharacteristic
479C4—21no—
480C4—21no—
481C4—182no—
482C4—361no—
483C4—361no—
484C4—361no—
485C4#8904011yescharacteristic
486C4#8904111yescharacteristic
487C3—21no—
488C3—21no—
489C3—21no—
490C3—41no—
491C3#1059028611yescharacteristic, complemented
492C3#1059029211yescharacteristic, complemented
493C3#1059030211yescharacteristic, complemented
494C2#1172366011yescharacteristic
495C2#1172366311yescharacteristic
496C2#1172367411yescharacteristic
subgroupG/H
centerC22C2×#6295
commutator, cosocleC2×C33×C4C23
FrattiniC2×C4C2×#1113
FittingC33×C42C22
socle, prime radicalC22×C33C2×D4
hypercenterC42#1113
hypocenterC33#479
LCSG ▷ C2×C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
302. C33#479semidirect
443. C32#4829semidirect
444. C32#5022semidirect
445. C32#5063semidirect
491. C3#10590286semidirect
492. C3#10590292semidirect
493. C3#10590302semidirect

Maximal subgroups

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

subgroupindex
C3×#640792
C3×C4×#6342
C3×C4⋊(C3⋊(C3⋊C8))2
#117220802
#117220792
#117220762
#105903023
#105902923
#105902863