Finite Group Databasebeta

← C3×#10590562 #13157549

Subgroups — C3×#10590562 #13157549

Order 1728.

526 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#890C211yesmaximal, characteristic
2C3×#63866C211yesmaximal, characteristic
3C3×#63637C211yesmaximal, characteristic
4C32×#810C211yesmaximal, characteristic
5C3×#63567C211yesmaximal, characteristic
6C3×#63565C211yesmaximal, characteristic
7C3×#63554C211yesmaximal, characteristic
8C3×#5069—31nomaximal
9C3×#4797—31nomaximal
10#10590562C311yesmaximal, characteristic, direct product factor
11C2×C3×#634C2211yescharacteristic
12C2×C32×Dic6C2211yescharacteristic
13C33×C4⋊C4C2211yescharacteristic
14C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
15C32×C4⋊Dic3—21no—
16C32×C4⋊Dic3C2211yescharacteristic
17C32×Dic3⋊C4—21no—
18C32×C4×Dic3C2211yescharacteristic
19C2×C32×C3⋊C8C2211yescharacteristic
20C3×Dic3⋊Dic3—21no—
21C3×Dic3⋊Dic3—21no—
22C32×#125—31no—
23C3×#944—31no—
24C3×#890—21no—
25C3×#890D311yescharacteristic
26C3×#890C2×C311yescharacteristic
27C3×#869—31no—
28#63866C2×C311yescharacteristic
29C32×#103—31no—
30#63637C2×C311yescharacteristic
31C3×#835—31no—
32C3×#816—31no—
33C3×#815—31no—
34C3×#810—21no—
35C3×#810—31no—
36C3×#810—31no—
37C3×#810—31no—
38C3×#810—31no—
39C3×#810—61no—
40C3×#810D311yescharacteristic
41C3×#810C2×C311yescharacteristic
42C3×#803—31no—
43#63567C2×C311yescharacteristic
44#63565C2×C311yescharacteristic
45#63554C2×C311yescharacteristic
46C2×C33×C4—21no—
47C2×C33×C4C2311yescharacteristic
48C2×C3×C3⋊Dic3—21no—
49C3×#634—21no—
50C3×#634—21no—
51C2×C32×Dic3—21no—
52C2×C32×Dic3—21no—
53C2×C32×Dic3D411yescharacteristic
54C2×C32×Dic3D411yescharacteristic
55C32×Dic6—21no—
56C32×Dic6—21no—
57C3×C3⋊(C3⋊C8)—21no—
58C32×C3⋊C8—21no—
59C3×#491—91no—
60#5069—31no—
61#4797—31no—
62C2×C32×Q8—31no—
63C2×#634C22×C311yescharacteristic
64C2×C3×Dic6—21no—
65C2×C3×Dic6—31no—
66C2×C3×Dic6—31no—
67C2×C3×Dic6—61no—
68C2×C3×Dic6C2×D311yescharacteristic
69C2×C3×Dic6C22×C311yescharacteristic
70C2×C32×C8—31no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4—31no—
75C32×C4⋊C4—41no—
76C32×C4⋊C4—61no—
77C32×C4⋊C4—61no—
78C32×C4⋊C4C2×D311yescharacteristic
79C32×C4⋊C4C2×D311yescharacteristic
80C32×C4⋊C4C22×C311yescharacteristic
81C32×C42—31no—
82C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—61no—
88C3×C4⋊Dic3—61no—
89C3×C4⋊Dic3C2×D311yescharacteristic
90C3×C4⋊Dic3C22×C311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—61no—
95C3×Dic3⋊C4—61no—
96C3×C4×Dic3—21no—
97C3×C4×Dic3C2×D311yescharacteristic
98C3×C4×Dic3C22×C311yescharacteristic
99C2×C3×C3⋊C8—21no—
100C2×C3×C3⋊C8—31no—
101C2×C3×C3⋊C8—31no—
102C2×C3×C3⋊C8—61no—
103C2×C3×C3⋊C8C2×D311yescharacteristic
104C2×C3×C3⋊C8C22×C311yescharacteristic
105Dic3⋊Dic3—21no—
106Dic3⋊Dic3—21no—
107C22×C33C2×D411yescharacteristic
108C33×C4—41no—
109C33×C4#4111yescharacteristic
110C33×C4#4111yescharacteristic
111C3×C3⋊Dic3—41no—
112C32×Dic3—21no—
113C32×Dic3—21no—
114C32×Dic3—41no—
115C32×Dic3—41no—
116C3×C4⋊Q8—91no—
117C3×#125—31no—
118C3×#125—31no—
119C3×#125—61no—
120#944—31no—
121#890C3×D311yescharacteristic
122#869—31no—
123C3×#103—31no—
124C3×#103—31no—
125C3×#103—61no—
126C3×#103—91no—
127C3×#103—91no—
128C3×#103—91no—
129C3×#97—91no—
130#835—31no—
131#816—31no—
132#815—31no—
133#810—31no—
134#810—31no—
135#810—31no—
136#810—31no—
137#810—61no—
138#810C3×D311yescharacteristic
139#803—31no—
140C32×Q8—61no—
141C32×Q8—61no—
142C2×C32×C4—21no—
143C2×C32×C4—22no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
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—41no—
153C2×C32×C4—41no—
154C2×C32×C4—42no—
155C2×C32×C4—61no—
156C2×C32×C4—61no—
157C2×C32×C4C22×D311yescharacteristic
158C2×C32×C4C22×D311yescharacteristic
159C2×C32×C4C23×C311yescharacteristic
160C2×C3⋊Dic3—21no—
161#634—21no—
162#634—21no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—61no—
172C2×C3×Dic3—61no—
173C2×C3×Dic3—121no—
174C2×C3×Dic3#6711yescharacteristic
175C2×C3×Dic3#6711yescharacteristic
176C2×C3×Dic3C3×D411yescharacteristic
177C2×C3×Dic3C3×D411yescharacteristic
178C3×Dic6—22no—
179C3×Dic6—21no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6—41no—
184C3×Dic6—62no—
185C3×Dic6—61no—
186C3×Dic6—61no—
187C3×Dic6—61no—
188C3×Dic6—61no—
189C3×Dic6—121no—
190C32×C8—61no—
191C3⋊(C3⋊C8)—21no—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—41no—
195C3×C3⋊C8—61no—
196C3×C3⋊C8—61no—
197C3×C3⋊C8—121no—
198#491—91noSylow
199C2×C33#12411yescharacteristic
200C2×C33#13711yescharacteristic
201C2×C33#13711yescharacteristic
202C2×C3×Q8—31no—
203C2×C3×Q8—31no—
204C2×C3×Q8—61no—
205C2×C3×Q8—91no—
206C2×Dic6—31no—
207C2×Dic6—31no—
208C2×Dic6—61no—
209C2×Dic6C2×C3×D311yescharacteristic
210C2×C3×C8—31no—
211C2×C3×C8—31no—
212C2×C3×C8—61no—
213C2×C3×C8—91no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—31no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—41no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—181no—
228C3×C4⋊C4—181no—
229C3×C4⋊C4D3211yescharacteristic
230C3×C4⋊C4C2×C3×D311yescharacteristic
231C3×C4⋊C4C2×C3×D311yescharacteristic
232C3×C42—31no—
233C3×C42—31no—
234C3×C42—61no—
235C4⋊Dic3—21no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3C2×C3×D311yescharacteristic
239Dic3⋊C4—21no—
240Dic3⋊C4—61no—
241Dic3⋊C4—61no—
242C4×Dic3C2×C3×D311yescharacteristic
243C2×C3⋊C8—31no—
244C2×C3⋊C8—31no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8C2×C3×D311yescharacteristic
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—21no—
250C22×C32—41no—
251C22×C32D3×D411yescharacteristic
252C22×C32C2×#6711yescharacteristic
253C22×C32C2×C3×D411yescharacteristic
254C32×C4—21no—
255C32×C4—21no—
256C32×C4—21no—
257C32×C4—21no—
258C32×C4—21no—
259C32×C4—21no—
260C32×C4—41no—
261C32×C4—41no—
262C32×C4—41no—
263C32×C4—42no—
264C32×C4—41no—
265C32×C4—41no—
266C32×C4—61no—
267C32×C4—61no—
268C32×C4—81no—
269C32×C4—81no—
270C32×C4—82no—
271C32×C4—121no—
272C32×C4—121no—
273C32×C4#23511yescharacteristic
274C32×C4#23711yescharacteristic
275C32×C4#23911yescharacteristic
276C32×C4#23911yescharacteristic
277C32×C4C3×#4111yescharacteristic
278C32×C4C3×#4111yescharacteristic
279C3⋊Dic3—41no—
280C3×Dic3—21no—
281C3×Dic3—21no—
282C3×Dic3—21no—
283C3×Dic3—21no—
284C3×Dic3—41no—
285C3×Dic3—41no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C3×Dic3—41no—
291C3×Dic3—41no—
292C3×Dic3—122no—
293C3×Dic3—121no—
294C3×Dic3—121no—
295C4⋊Q8—91no—
296#125—31no—
297#103—31no—
298#103—91no—
299#103—91no—
300#103—91no—
301#97—91no—
302C33#49111yescharacteristic, complemented, Sylow
303C3×Q8—62no—
304C3×Q8—61no—
305C3×Q8—61no—
306C3×Q8—61no—
307C3×Q8—61no—
308C3×Q8—121no—
309C3×Q8—181no—
310C3×Q8—181no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—31no—
319C2×C3×C4—31no—
320C2×C3×C4—31no—
321C2×C3×C4—31no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—42no—
325C2×C3×C4—41no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—62no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—121no—
334C2×C3×C4—181no—
335C2×C3×C4C2×D3211yescharacteristic
336C2×C3×C4C22×C3×D311yescharacteristic
337C2×C3×C4C22×C3×D311yescharacteristic
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—121no—
343C2×Dic3C3×#6711yescharacteristic
344C2×Dic3C3×#6711yescharacteristic
345Dic6—21no—
346Dic6—21no—
347Dic6—62no—
348Dic6—61no—
349Dic6—61no—
350Dic6—61no—
351Dic6—61no—
352Dic6—121no—
353C3×C8—61no—
354C3×C8—61no—
355C3×C8—121no—
356C3×C8—181no—
357C3⋊C8—21no—
358C3⋊C8—61no—
359C3⋊C8—61no—
360C3⋊C8—121no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32—21no—
364C2×C32—21no—
365C2×C32—21no—
366C2×C32—21no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32—21no—
370C2×C32—41no—
371C2×C32—41no—
372C2×C32—41no—
373C2×C32#88511yescharacteristic
374C2×C32#91511yescharacteristic
375C2×C32#91811yescharacteristic
376C2×C32#94711yescharacteristic
377C2×C32#95111yescharacteristic
378C2×C32#95111yescharacteristic
379C2×C32C3×#12411yescharacteristic
380C2×C32C3×#13711yescharacteristic
381C2×C32C3×#13711yescharacteristic
382C2×Q8—31no—
383C2×Q8—91no—
384C2×C8—31no—
385C2×C8—91no—
386C4⋊C4—31no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4C3×D3211yescharacteristic
392C42—31no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—41no—
397C22×C3D3×#6711yescharacteristic
398C22×C3C3×D3×D411yescharacteristic
399C22×C3C2×C3×#6711yescharacteristic
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—42no—
407C3×C4—41no—
408C3×C4—41no—
409C3×C4—41no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—61no—
413C3×C4—61no—
414C3×C4—61no—
415C3×C4—61no—
416C3×C4—81no—
417C3×C4—81no—
418C3×C4—82no—
419C3×C4—121no—
420C3×C4—121no—
421C3×C4—122no—
422C3×C4—122no—
423C3×C4—121no—
424C3×C4—121no—
425C3×C4—121no—
426C3×C4—121no—
427C3×C4—361no—
428C3×C4#379611yescharacteristic
429C3×C4#379911yescharacteristic
430C3×C4C3×#23511yescharacteristic
431C3×C4C3×#23711yescharacteristic
432C3×C4C3×#23911yescharacteristic
433C3×C4C3×#23911yescharacteristic
434Dic3—21no—
435Dic3—21no—
436Dic3—41no—
437Dic3—41no—
438Dic3—122no—
439Dic3—121no—
440Dic3—121no—
441C32—21no—
442C32—21no—
443C32—21no—
444C32—41no—
445C32#479711yescharacteristic, complemented
446C32#506911yescharacteristic, complemented
447C32C3×#49111yescharacteristic, complemented
448Q8—61no—
449Q8—61no—
450Q8—181no—
451Q8—181no—
452C2×C4—21no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—181no—
458C2×C4C2×C3×D3211yescharacteristic
459C8—61no—
460C8—181no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—41no—
471C2×C3—41no—
472C2×C3—41no—
473C2×C3#6390711yescharacteristic
474C2×C3#6392911yescharacteristic
475C2×C3#6394311yescharacteristic
476C2×C3C3×#88511yescharacteristic
477C2×C3C3×#91511yescharacteristic
478C2×C3C3×#91811yescharacteristic
479C2×C3C3×#94711yescharacteristic
480C2×C3C3×#95111yescharacteristic
481C2×C3C3×#95111yescharacteristic
482C22C3×D3×#6711yescharacteristic
483C4—41no—
484C4—61no—
485C4—61no—
486C4—121no—
487C4—121no—
488C4—361no—
489C4C3×#379611yescharacteristic
490C4C3×#379911yescharacteristic
491C3—21no—
492C3—21no—
493C3—21no—
494C3—41no—
495C3#1059056211yescharacteristic, direct product factor
496C3C3×#479711yescharacteristic, complemented
497C3C3×#506911yescharacteristic, complemented
498C2C3×#6390711yescharacteristic
499C2C3×#6392911yescharacteristic
500C2C3×#6394311yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×C4⋊C4C22
socle, prime radicalC22×C33C2×D4
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
10. #10590562C3direct (N × H)
302. C33#491semidirect
445. C32#4797semidirect
446. C32#5069semidirect
447. C32C3×#491semidirect
495. C3#10590562direct (N × H)
496. C3C3×#4797semidirect
497. C3C3×#5069semidirect

Maximal subgroups

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

subgroupindex
C32×#8902
C3×#638662
C3×#636372
C32×#8102
C3×#635672
C3×#635652
C3×#635542
C3×#50693
C3×#47973
#105905623