Finite Group Databasebeta

← C3×#10590383 #13157396

Subgroups — C3×#10590383 #13157396

Order 1728.

642 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#634C211yesmaximal, characteristic
2C32×C4×Dic6C211yesmaximal, characteristic
3C2×C3×#3719C211yesmaximal, characteristic
4C32×#803C211yesmaximal, characteristic
5C3×#63573C211yesmaximal, characteristic
6C3×#63567C211yesmaximal, characteristic
7C3×#63566C211yesmaximal, characteristic
8C3×#5030—31nomaximal
9C3×#4716—31nomaximal
10#10590383C311yesmaximal, characteristic, direct product factor
11C2×C3×#634C2211yescharacteristic
12C2×C32×Dic6C2211yescharacteristic
13C33×C42C2211yescharacteristic
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C3×#3750—21no—
16C3×C4×C3⋊Dic3—21no—
17C32×C4⋊Dic3C2211yescharacteristic
18C32×Dic3⋊C4—21no—
19C32×C4×Dic3—21no—
20C2×C32×C3⋊C8C2211yescharacteristic
21C2×C32×C3⋊C8C2211yescharacteristic
22C3×#3719C414yescomplemented
23C32×C4×Q8—31no—
24C4×#634C2×C311yescharacteristic
25C2×C3×#216—31no—
26C2×C3×Dic12—31no—
27C3×C4×Dic6—21no—
28C3×C4×Dic6—31no—
29C3×C4×Dic6—31no—
30C3×C4×Dic6—61no—
31C3×C4×Dic6D311yescharacteristic
32C3×C4×Dic6C2×C311yescharacteristic
33C2×#3719C2×C311yescharacteristic
34C32×#97—31no—
35C3×#835—31no—
36C3×#817—31no—
37C3×#816—31no—
38C3×#816—31no—
39C3×#810—31no—
40C3×#808—31no—
41C3×#803—21no—
42C3×#803D311yescharacteristic
43C3×#803C2×C311yescharacteristic
44#63573C2×C311yescharacteristic
45#63567C2×C311yescharacteristic
46#63566C2×C311yescharacteristic
47C2×C33×C4D411yescharacteristic
48C2×C33×C4D411yescharacteristic
49C2×C33×C4C2311yescharacteristic
50C2×C3×C3⋊Dic3—21no—
51C2×C3×C3⋊Dic3—21no—
52C3×#634—21no—
53C3×#634C2×C412yes—
54C2×C32×Dic3—21no—
55C2×C32×Dic3—21no—
56C32×Dic6—21no—
57C32×Dic6C2×C412yes—
58C32×C3⋊C8—21no—
59C32×C3⋊C8C2×C412yes—
60C3×#441—91no—
61#5030—31no—
62#4716—31no—
63C2×C32×Q8—31no—
64C2×#634C22×C311yescharacteristic
65C2×C3×Dic6—21no—
66C2×C3×Dic6—31no—
67C2×C3×Dic6—31no—
68C2×C3×Dic6—61no—
69C2×C3×Dic6C2×D311yescharacteristic
70C2×C3×Dic6C22×C311yescharacteristic
71C2×C32×C8—31no—
72C2×C32×C8—31no—
73C32×C4⋊C4—31no—
74C32×C4⋊C4—61no—
75C32×C42—21no—
76C32×C42—21no—
77C32×C42—21no—
78C32×C42—41no—
79C32×C42—61no—
80C32×C42C2×D311yescharacteristic
81C32×C42C2×D311yescharacteristic
82C32×C42C22×C311yescharacteristic
83C4⋊(C3⋊Dic3)C22×C311yescharacteristic
84#3750—21no—
85C4×C3⋊Dic3—21no—
86C3×#216—34no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—31no—
89C3×C4⋊Dic3—31no—
90C3×C4⋊Dic3—61no—
91C3×C4⋊Dic3C2×D311yescharacteristic
92C3×C4⋊Dic3C22×C311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—62no—
97C3×Dic3⋊C4—61no—
98C3×Dic3⋊C4—61no—
99C3×C4×Dic3—22no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3—62no—
103C3×C4×Dic3—61no—
104C3×C4×Dic3—61no—
105C2×C3×C3⋊C8—21no—
106C2×C3×C3⋊C8—21no—
107C2×C3×C3⋊C8C2×D311yescharacteristic
108C2×C3×C3⋊C8C2×D311yescharacteristic
109C2×C3×C3⋊C8C22×C311yescharacteristic
110C2×C3×C3⋊C8C22×C311yescharacteristic
111C3×Dic12—34no—
112#3719C3×C414yescomplemented
113C22×C33C2×D411yescharacteristic
114C33×C4—21no—
115C33×C4—21no—
116C33×C4C22×C411yescharacteristic
117C33×C4#4111yescharacteristic
118C3×C3⋊Dic3—22no—
119C3×C3⋊Dic3—41no—
120C32×Dic3—22no—
121C32×Dic3—41no—
122C2×C3×Q16—91no—
123C3×C4×Q8—31no—
124C3×C4×Q8—31no—
125C3×C4×Q8—61no—
126C3×C4×Q8—91no—
127C2×#216—31no—
128C2×Dic12—31no—
129C4×Dic6—31no—
130C4×Dic6—31no—
131C4×Dic6—61no—
132C4×Dic6C3×D311yescharacteristic
133C3×#106—91no—
134C3×#103—91no—
135C3×#103—91no—
136C3×#97—31no—
137C3×#97—31no—
138C3×#97—61no—
139#835—31no—
140#817—31no—
141#816—31no—
142#816—31no—
143#810—31no—
144#808—31no—
145#803C3×D311yescharacteristic
146C32×Q8—32no—
147C32×Q8—61no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—41no—
158C2×C32×C4—41no—
159C2×C32×C4—41no—
160C2×C32×C4—61no—
161C2×C32×C4—61no—
162C2×C32×C4D1211yescharacteristic
163C2×C32×C4D1211yescharacteristic
164C2×C32×C4#6711yescharacteristic
165C2×C32×C4#6711yescharacteristic
166C2×C32×C4C3×D411yescharacteristic
167C2×C32×C4C3×D411yescharacteristic
168C2×C32×C4C22×D311yescharacteristic
169C2×C32×C4C22×D311yescharacteristic
170C2×C32×C4C23×C311yescharacteristic
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173#634—21no—
174#634C2×C3×C412yes—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—62no—
182C2×C3×Dic3—61no—
183C2×C3×Dic3—61no—
184C2×C3×Dic3—62no—
185C2×C3×Dic3—61no—
186C2×C3×Dic3—61no—
187C3×Dic6—22no—
188C3×Dic6—21no—
189C3×Dic6—21no—
190C3×Dic6—22no—
191C3×Dic6—32no—
192C3×Dic6—32no—
193C3×Dic6—62no—
194C3×Dic6—62no—
195C3×Dic6—61no—
196C3×Dic6—61no—
197C3×Dic6C4×D312yes—
198C3×Dic6C2×C3×C412yes—
199C32×C8—32no—
200C32×C8—61no—
201C3×C3⋊C8—22no—
202C3×C3⋊C8—21no—
203C3×C3⋊C8—21no—
204C3×C3⋊C8—22no—
205C3×C3⋊C8C4×D312yes—
206C3×C3⋊C8C2×C3×C412yes—
207#441—91noSylow
208C2×C33C4×D411yescharacteristic
209C2×C33#13711yescharacteristic
210C2×C33#13711yescharacteristic
211C2×C3×Q8—31no—
212C2×C3×Q8—31no—
213C2×C3×Q8—61no—
214C2×C3×Q8—91no—
215C2×Dic6—31no—
216C2×Dic6—31no—
217C2×Dic6—61no—
218C2×Dic6C2×C3×D311yescharacteristic
219C3×Q16—94no—
220C2×C3×C8—31no—
221C2×C3×C8—31no—
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—91no—
233C3×C4⋊C4—181no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42—41no—
238C3×C42—62no—
239C3×C42—61no—
240C3×C42—61no—
241C3×C42—181no—
242C3×C42D3211yescharacteristic
243C3×C42C2×C3×D311yescharacteristic
244C3×C42C2×C3×D311yescharacteristic
245#216—34no—
246C4⋊Dic3—31no—
247C4⋊Dic3—31no—
248C4⋊Dic3—61no—
249C4⋊Dic3C2×C3×D311yescharacteristic
250Dic3⋊C4—21no—
251Dic3⋊C4—62no—
252Dic3⋊C4—61no—
253Dic3⋊C4—61no—
254C4×Dic3—21no—
255C4×Dic3—62no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C2×C3⋊C8C2×C3×D311yescharacteristic
259C2×C3⋊C8C2×C3×D311yescharacteristic
260Dic12—34no—
261C22×C32—21no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32—41no—
265C22×C32C2×D1211yescharacteristic
266C22×C32C2×#6711yescharacteristic
267C22×C32C2×C3×D411yescharacteristic
268C32×C4—21no—
269C32×C4—21no—
270C32×C4—22no—
271C32×C4—22no—
272C32×C4—21no—
273C32×C4—21no—
274C32×C4—21no—
275C32×C4—21no—
276C32×C4—21no—
277C32×C4—21no—
278C32×C4—21no—
279C32×C4—21no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4—42no—
289C32×C4—42no—
290C32×C4—62no—
291C32×C4—121no—
292C32×C4C2×C4×D311yescharacteristic
293C32×C4C2×C4×D311yescharacteristic
294C32×C4#23511yescharacteristic
295C32×C4#23511yescharacteristic
296C32×C4C22×C3×C411yescharacteristic
297C32×C4C3×#4111yescharacteristic
298C3⋊Dic3—22no—
299C3⋊Dic3—41no—
300C3×Dic3—24no—
301C3×Dic3—22no—
302C3×Dic3—22no—
303C3×Dic3—42no—
304C3×Dic3—41no—
305C3×Dic3—41no—
306C3×Dic3—64no—
307C3×Dic3—62no—
308C3×Dic3—62no—
309C3×Dic3—122no—
310C3×Dic3—121no—
311C3×Dic3—121no—
312C2×Q16—91no—
313C4×Q8—31no—
314C4×Q8—91no—
315#106—91no—
316#103—91no—
317#103—91no—
318#97—31no—
319C33#44111yescharacteristic, complemented, Sylow
320C3×Q8—32no—
321C3×Q8—32no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—61no—
325C3×Q8—61no—
326C3×Q8—92no—
327C3×Q8—181no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—62no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—181no—
347C2×C3×C4—181no—
348C2×C3×C4#62611yescharacteristic
349C2×C3×C4#62611yescharacteristic
350C2×C3×C4C3×D1211yescharacteristic
351C2×C3×C4C3×D1211yescharacteristic
352C2×C3×C4C3×#6711yescharacteristic
353C2×C3×C4C3×#6711yescharacteristic
354C2×C3×C4C2×D3211yescharacteristic
355C2×C3×C4C22×C3×D311yescharacteristic
356C2×C3×C4C22×C3×D311yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—62no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—62no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365Dic6—21no—
366Dic6—32no—
367Dic6—32no—
368Dic6—62no—
369Dic6—62no—
370Dic6—61no—
371Dic6—61no—
372Dic6C3×C4×D312yes—
373C3×C8—32no—
374C3×C8—32no—
375C3×C8—62no—
376C3×C8—62no—
377C3×C8—61no—
378C3×C8—61no—
379C3⋊C8—21no—
380C3⋊C8C3×C4×D312yes—
381C2×C32—21no—
382C2×C32—21no—
383C2×C32—21no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32—21no—
387C2×C32—21no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32—41no—
391C2×C32—41no—
392C2×C32—41no—
393C2×C32C4×D1211yescharacteristic
394C2×C32#90911yescharacteristic
395C2×C32#90911yescharacteristic
396C2×C32C4×#6711yescharacteristic
397C2×C32#94211yescharacteristic
398C2×C32#95111yescharacteristic
399C2×C32C3×C4×D411yescharacteristic
400C2×C32C3×#13711yescharacteristic
401C2×C32C3×#13711yescharacteristic
402C2×Q8—31no—
403C2×Q8—91no—
404Q16—94no—
405C2×C8—31no—
406C2×C8—31no—
407C4⋊C4—31no—
408C4⋊C4—61no—
409C4⋊C4—91no—
410C4⋊C4—181no—
411C42—61no—
412C42—181no—
413C42C3×D3211yescharacteristic
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—41no—
418C22×C3C2×#62611yescharacteristic
419C22×C3C2×C3×D1211yescharacteristic
420C22×C3C2×C3×#6711yescharacteristic
421C3×C4—22no—
422C3×C4—22no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—41no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—64no—
444C3×C4—62no—
445C3×C4—62no—
446C3×C4—122no—
447C3×C4—121no—
448C3×C4—121no—
449C3×C4—182no—
450C3×C4—361no—
451C3×C4#379811yescharacteristic
452C3×C4C4×D3211yescharacteristic
453C3×C4C2×C3×C4×D311yescharacteristic
454C3×C4C2×C3×C4×D311yescharacteristic
455C3×C4C3×#23511yescharacteristic
456C3×C4C3×#23511yescharacteristic
457Dic3—22no—
458Dic3—41no—
459Dic3—64no—
460Dic3—62no—
461Dic3—62no—
462Dic3—122no—
463Dic3—121no—
464Dic3—121no—
465C32—21no—
466C32—21no—
467C32—21no—
468C32—41no—
469C32#471611yescharacteristic, complemented
470C32#503011yescharacteristic, complemented
471C32C3×#44111yescharacteristic, complemented
472Q8—32no—
473Q8—61no—
474Q8—92no—
475Q8—181no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4C3×#62611yescharacteristic
481C2×C4C3×#62611yescharacteristic
482C2×C4C2×C3×D3211yescharacteristic
483C8—32no—
484C8—61no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—41no—
495C2×C3—41no—
496C2×C3—41no—
497C2×C3#6383111yescharacteristic
498C2×C3#6383311yescharacteristic
499C2×C3C4×#62611yescharacteristic
500C2×C3C3×C4×D1211yescharacteristic
501C2×C3C3×#90911yescharacteristic
502C2×C3C3×#90911yescharacteristic
503C2×C3C3×C4×#6711yescharacteristic
504C2×C3C3×#94211yescharacteristic
505C2×C3C3×#95111yescharacteristic
506C22C2×C3×#62611yescharacteristic
507C4—21no—
508C4—21no—
509C4—62no—
510C4—121no—
511C4—182no—
512C4—361no—
513C4C3×#379811yescharacteristic
514C4C3×C4×D3211yescharacteristic
515C3—21no—
516C3—21no—
517C3—21no—
518C3—41no—
519C3#1059038311yescharacteristic, direct product factor
520C3C3×#471611yescharacteristic, complemented
521C3C3×#503011yescharacteristic, complemented
522C2C3×#6383111yescharacteristic
523C2C3×#6383311yescharacteristic
524C2C3×C4×#62611yescharacteristic
subgroupG/H
centerC22×C3C2×#626
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC33×C42C22
socle, prime radicalC22×C33C2×D4
cosocleC2×C32×C4C23×C3
hypercenterC3×C42D32
hypocenterC32C3×#441
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C42

Complements

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

NH ≅ G/Ntype
10. #10590383C3direct (N × H)
22. C3×#3719C4semidirect
112. #3719C3×C4semidirect
319. C33#441semidirect
469. C32#4716semidirect
470. C32#5030semidirect
471. C32C3×#441semidirect
519. C3#10590383direct (N × H)
520. C3C3×#4716semidirect
521. C3C3×#5030semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#6342
C32×C4×Dic62
C2×C3×#37192
C32×#8032
C3×#635732
C3×#635672
C3×#635662
C3×#50303
C3×#47163
#105903833