Finite Group Databasebeta

← C3×#10590682 #13157684

Subgroups — C3×#10590682 #13157684

Order 1728.

566 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Dic3C211yesmaximal, characteristic
2C3×#63856C211yesmaximal, characteristic
3C3×#63645C211yesmaximal, characteristic, complemented
4C32×(C2×D3)⋊C8C211yesmaximal, characteristic
5C32×#816C211yesmaximal, characteristic, complemented
6C3×#63575C211yesmaximal, characteristic, complemented
7C3×#63566C211yesmaximal, characteristic, complemented
8C3×#4811—31nomaximal
9C3×#4722—31nomaximal
10#10590682C311yesmaximal, characteristic, direct product factor
11C2×C32×C4×D3C2211yescharacteristic
12C2×C32×Dic6C2211yescharacteristic
13C2×C3×D3×Dic3—21no—
14C2×C33×C8C2211yescharacteristic
15C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C32×C4⋊Dic3C2211yescharacteristic
18C2×C32×C3⋊C8C2211yescharacteristic
19C3×#3724—21no—
20C3×Dic3⋊Dic3—21no—
21C3×(C2×D3)⋊Dic3—21no—
22C3×#946—31no—
23C2×C3×C4⋊Dic3—31no—
24C3×#924—31no—
25C3×D3×C4⋊C4—31no—
26D3×C4⋊Dic3C2×C311yescharacteristic
27#63856C2×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—31no—
38C3×#818—61no—
39C3×#816—21no—
40C3×#816—31no—
41C3×#816D311yescharacteristic, complemented
42C3×#816C2×C311yescharacteristic, complemented
43C3×#807—31no—
44#63575C2×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—
57C3×D3×Dic3—42no—
58C33×C8—21no—
59C32×C3⋊C8—21no—
60C3×#484—91no—
61#4811—31no—
62#4722—31no—
63C2×C32×Q8—31no—
64C22×C32×C4—31no—
65C22×C3×Dic3—61no—
66C2×C3×C4×D3—21no—
67C2×C3×C4×D3—61no—
68C2×C3×C4×D3C2×D311yescharacteristic
69C2×C3×C4×D3C22×C311yescharacteristic
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2×D311yescharacteristic
72C2×C3×Dic6C22×C311yescharacteristic
73C2×D3×Dic3—21no—
74C2×C32×C8—21no—
75C2×C32×C8—21no—
76C2×C32×C8—21no—
77C2×C32×C8—31no—
78C2×C32×C8—41no—
79C2×C32×C8C2×D311yescharacteristic
80C2×C32×C8C2×D311yescharacteristic
81C2×C32×C8C22×C311yescharacteristic
82C32×C4⋊C4—31no—
83C4⋊(C3⋊Dic3)C22×C311yescharacteristic
84C4⋊(C3⋊Dic3)C22×C311yescharacteristic
85C3×#217—61no—
86C3×(C2×D3)⋊C4—61no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—31no—
89C3×C4⋊Dic3—31no—
90C3×C4⋊Dic3—31no—
91C3×C4⋊Dic3—31no—
92C3×C4⋊Dic3—61no—
93C3×C4⋊Dic3—61no—
94C3×C4⋊Dic3—61no—
95C3×C4⋊Dic3C2×D311yescharacteristic
96C3×C4⋊Dic3C22×C311yescharacteristic
97C3×Dic3⋊C4—61no—
98C3×Dic3⋊C4—61no—
99C3×Dic3⋊C4—61no—
100C2×C3×C3⋊C8—21no—
101C2×C3×C3⋊C8C2×D311yescharacteristic
102C2×C3×C3⋊C8C22×C311yescharacteristic
103#3724—21no—
104Dic3⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106C22×C33C2×D411yescharacteristic
107C2×C32×D3—21no—
108C2×C32×D3—21no—
109C2×C32×D3Q1612yes—
110C33×C4#4111yescharacteristic
111C33×C4#4111yescharacteristic
112C3×C3⋊Dic3—41no—
113C3×C3⋊Dic3—41no—
114C32×Dic3—21no—
115C32×Dic3—41no—
116C32×Dic3—41no—
117C3×C22⋊Q8—91no—
118C2×C3×C4⋊C4—91no—
119#946—31no—
120C2×C4⋊Dic3—31no—
121#924—31no—
122D3×C4⋊C4—31no—
123C3×#107—91no—
124C3×#107—91no—
125C3×#103—31no—
126C3×#103—31no—
127C3×#103—61no—
128C3×#103—91no—
129C3×C22⋊C8—31no—
130C3×C22⋊C8—31no—
131C3×C22⋊C8—61no—
132#835—31no—
133(C2×D3)⋊C8C3×D311yescharacteristic
134#818—31no—
135#818—31no—
136#818—31no—
137#818—61no—
138#816—31no—
139#816C3×D311yescharacteristic, complemented
140#807—31no—
141C23×C32—31no—
142C22×C3×D3—21no—
143C22×C3×D3D1211yescharacteristic
144C22×C3×D3C3×D411yescharacteristic
145C32×Q8—61no—
146C32×Q8—61no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—31no—
151C2×C32×C4—41no—
152C2×C32×C4—61no—
153C2×C32×C4—61no—
154C2×C32×C4—61no—
155C2×C32×C4—61no—
156C2×C32×C4C22×D311yescharacteristic
157C2×C32×C4C22×D311yescharacteristic
158C2×C32×C4C23×C311yescharacteristic
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—21no—
166C2×C3×Dic3—41no—
167C2×C3×Dic3—41no—
168C2×C3×Dic3—61no—
169C2×C3×Dic3—61no—
170C2×C3×Dic3—61no—
171C2×C3×Dic3—61no—
172C2×C3×Dic3—121no—
173C2×C3×Dic3—121no—
174C2×C3×Dic3—122no—
175C2×C3×Dic3D1211yescharacteristic
176C2×C3×Dic3C3×D411yescharacteristic
177C3×C4×D3—21no—
178C3×C4×D3—21no—
179C3×C4×D3—21no—
180C3×C4×D3—21no—
181C3×C4×D3—41no—
182C3×C4×D3—41no—
183C3×C4×D3—122no—
184C3×Dic6—22no—
185C3×Dic6—21no—
186C3×Dic6—21no—
187C3×Dic6—21no—
188C3×Dic6—21no—
189C3×Dic6—41no—
190D3×Dic3—42no—
191C32×C8—21no—
192C32×C8—22no—
193C32×C8—21no—
194C32×C8—21no—
195C32×C8—41no—
196C32×C8—41no—
197C32×C8—42no—
198C32×C8—61no—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—41no—
202#484—91noSylow
203C2×C33#12311yescharacteristic
204C2×C33C2×Q1611yescharacteristic
205C2×C33AGL(1,ℤ/8)11yescharacteristic
206C32×D3—22no—
207C2×C3×Q8—31no—
208C2×C3×Q8—31no—
209C2×C3×Q8—61no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—61no—
213C22×C3×C4—181no—
214C22×Dic3—61no—
215C2×C4×D3—61no—
216C2×C4×D3C2×C3×D311yescharacteristic
217C2×Dic6C2×C3×D311yescharacteristic
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—31no—
222C2×C3×C8—31no—
223C2×C3×C8—41no—
224C2×C3×C8—61no—
225C2×C3×C8D3211yescharacteristic
226C2×C3×C8C2×C3×D311yescharacteristic
227C2×C3×C8C2×C3×D311yescharacteristic
228C3×C4⋊C4—31no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—91no—
232C3×C4⋊C4—91no—
233C3×C4⋊C4—181no—
234C3×C4⋊C4—181no—
235C3×C22⋊C4—181no—
236#217—61no—
237(C2×D3)⋊C4—61no—
238C4⋊Dic3—31no—
239C4⋊Dic3—31no—
240C4⋊Dic3—31no—
241C4⋊Dic3—31no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3C2×C3×D311yescharacteristic
246Dic3⋊C4—61no—
247Dic3⋊C4—61no—
248Dic3⋊C4—61no—
249C2×C3⋊C8C2×C3×D311yescharacteristic
250C22×C32—21no—
251C22×C32—21no—
252C22×C32—21no—
253C22×C32—32no—
254C22×C32—41no—
255C22×C32—61no—
256C22×C32—61no—
257C22×C32C2×D1211yescharacteristic
258C22×C32D3×D411yescharacteristic
259C22×C32C2×C3×D411yescharacteristic
260C2×C3×D3—21no—
261C2×C3×D3—21no—
262C2×C3×D3—21no—
263C2×C3×D3—21no—
264C2×C3×D3—22no—
265C2×C3×D3—41no—
266C2×C3×D3—41no—
267C2×C3×D3Dic1212yes—
268C2×C3×D3C3×Q1612yes—
269C32×C4—21no—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4—21no—
273C32×C4—21no—
274C32×C4—21no—
275C32×C4—41no—
276C32×C4—41no—
277C32×C4—61no—
278C32×C4—121no—
279C32×C4—121no—
280C32×C4#23511yescharacteristic
281C32×C4#23711yescharacteristic
282C32×C4#23711yescharacteristic
283C32×C4#23711yescharacteristic
284C32×C4C3×#4111yescharacteristic
285C32×C4C3×#4111yescharacteristic
286C3⋊Dic3—41no—
287C3⋊Dic3—41no—
288C3×Dic3—21no—
289C3×Dic3—21no—
290C3×Dic3—41no—
291C3×Dic3—42no—
292C3×Dic3—41no—
293C3×Dic3—41no—
294C3×Dic3—41no—
295C3×Dic3—41no—
296C3×Dic3—81no—
297C3×Dic3—121no—
298C3×Dic3—121no—
299C3×Dic3—121no—
300C3×Dic3—121no—
301C3×Dic3—241no—
302C3×Dic3—241no—
303C22⋊Q8—91no—
304C2×C4⋊C4—91no—
305#107—91no—
306#107—91no—
307#103—31no—
308#103—91no—
309C22⋊C8—31no—
310C33#48411yescharacteristic, complemented, Sylow
311C23×C3—31no—
312C23×C3—31no—
313C23×C3—61no—
314C22×D3C3×D1211yescharacteristic
315C3×Q8—62no—
316C3×Q8—61no—
317C3×Q8—61no—
318C3×Q8—61no—
319C3×Q8—61no—
320C3×Q8—121no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
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—61no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4—181no—
341C2×C3×C4—181no—
342C2×C3×C4—362no—
343C2×C3×C4C2×D3211yescharacteristic
344C2×C3×C4C22×C3×D311yescharacteristic
345C2×C3×C4C22×C3×D311yescharacteristic
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—122no—
355C2×Dic3C3×D1211yescharacteristic
356C4×D3—21no—
357C4×D3—21no—
358C4×D3—122no—
359Dic6—21no—
360Dic6—21no—
361C3×C8—22no—
362C3×C8—21no—
363C3×C8—21no—
364C3×C8—21no—
365C3×C8—41no—
366C3×C8—41no—
367C3×C8—42no—
368C3×C8—61no—
369C3×C8—61no—
370C3×C8—121no—
371C3⋊C8—21no—
372C2×C32—21no—
373C2×C32—21no—
374C2×C32—21no—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32—21no—
380C2×C32—21no—
381C2×C32—41no—
382C2×C32—41no—
383C2×C32—41no—
384C2×C32—62no—
385C2×C32#88311yescharacteristic
386C2×C32#88611yescharacteristic
387C2×C32C2×Dic1211yescharacteristic
388C2×C32#90811yescharacteristic
389C2×C32#91411yescharacteristic
390C2×C32D3×Q1611yescharacteristic
391C2×C32C3×#12311yescharacteristic
392C2×C32C2×C3×Q1611yescharacteristic
393C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
394C3×D3—22no—
395C3×D3—22no—
396C3×D3—42no—
397C2×Q8—31no—
398C22×C4—31no—
399C22×C4—181no—
400C2×C8—31no—
401C2×C8C3×D3211yescharacteristic
402C4⋊C4—31no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C22⋊C4—181no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—32no—
412C22×C3—32no—
413C22×C3—41no—
414C22×C3—62no—
415C22×C3—61no—
416C22×C3—61no—
417C22×C3—61no—
418C22×C3—61no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3D3×D1211yescharacteristic
422C22×C3C2×C3×D1211yescharacteristic
423C22×C3C3×D3×D411yescharacteristic
424C2×D3—21no—
425C2×D3—21no—
426C2×D3C3×Dic1212yes—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—41no—
434C3×C4—41no—
435C3×C4—61no—
436C3×C4—61no—
437C3×C4—121no—
438C3×C4—122no—
439C3×C4—121no—
440C3×C4—121no—
441C3×C4—121no—
442C3×C4—121no—
443C3×C4—241no—
444C3×C4—361no—
445C3×C4—361no—
446C3×C4#379511yescharacteristic
447C3×C4#380511yescharacteristic
448C3×C4C3×#23511yescharacteristic
449C3×C4C3×#23711yescharacteristic
450C3×C4C3×#23711yescharacteristic
451C3×C4C3×#23711yescharacteristic
452Dic3—21no—
453Dic3—41no—
454Dic3—41no—
455Dic3—121no—
456Dic3—121no—
457Dic3—121no—
458Dic3—121no—
459Dic3—241no—
460Dic3—241no—
461C32—21no—
462C32—21no—
463C32—21no—
464C32—41no—
465C32#472211yescharacteristic, complemented
466C32#481111yescharacteristic, complemented
467C32C3×#48411yescharacteristic, complemented
468C23—31no—
469Q8—61no—
470Q8—61no—
471C2×C4—31no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—362no—
479C2×C4C2×C3×D3211yescharacteristic
480C8—21no—
481C8—61no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—41no—
492C2×C3—41no—
493C2×C3—41no—
494C2×C3—62no—
495C2×C3—62no—
496C2×C3—122no—
497C2×C3#6379411yescharacteristic
498C2×C3D3×Dic1211yescharacteristic
499C2×C3#6389111yescharacteristic
500C2×C3C3×#88311yescharacteristic
501C2×C3C3×#88611yescharacteristic
502C2×C3C2×C3×Dic1211yescharacteristic
503C2×C3C3×#90811yescharacteristic
504C2×C3C3×#91411yescharacteristic
505C2×C3C3×D3×Q1611yescharacteristic
506D3—22no—
507C22—32no—
508C22—61no—
509C22—61no—
510C22C3×D3×D1211yescharacteristic
511C4—61no—
512C4—121no—
513C4—121no—
514C4—361no—
515C4—361no—
516C4C3×#379511yescharacteristic
517C4C3×#380511yescharacteristic
518C3—21no—
519C3—21no—
520C3—21no—
521C3—41no—
522C3#1059068211yescharacteristic, direct product factor
523C3C3×#472211yescharacteristic, complemented
524C3C3×#481111yescharacteristic, complemented
525C2—62no—
526C2C3×#6379411yescharacteristic
527C2C3×D3×Dic1211yescharacteristic
528C2C3×#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×#484
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×#63575C2semidirect
7. C3×#63566C2semidirect
10. #10590682C3direct (N × H)
30. #63645C2×C3semidirect
41. C3×#816D3semidirect
42. C3×#816C2×C3semidirect
44. #63575C2×C3semidirect
45. #63566C2×C3semidirect
139. #816C3×D3semidirect
310. C33#484semidirect
465. C32#4722semidirect
466. C32#4811semidirect
467. C32C3×#484semidirect
522. C3#10590682direct (N × H)
523. C3C3×#4722semidirect
524. C3C3×#4811semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Dic32
C3×#638562
C3×#636452
C32×(C2×D3)⋊C82
C32×#8162
C3×#635752
C3×#635662
C3×#48113
C3×#47223
#105906823