Finite Group Databasebeta

← C3×#10590677 #13157797

Subgroups — C3×#10590677 #13157797

Order 1728.

614 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63909C211yesmaximal, characteristic
2C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#63648C211yesmaximal, characteristic, complemented
4C32×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
5C32×#817C211yesmaximal, characteristic, complemented
6C3×#63573C211yesmaximal, characteristic, complemented
7C3×#63564C211yesmaximal, characteristic, complemented
8C3×#4863—31nomaximal
9C3×#4735—31nomaximal
10#10590677C311yesmaximal, characteristic, direct product factor
11C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C32×C4×D3C2211yescharacteristic
13C2×C3×#626—21no—
14C2×C3×D3×Dic3—21no—
15C2×C33×C8C2211yescharacteristic
16C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C32×C4⋊Dic3C2211yescharacteristic
18C32×C4⋊Dic3C2211yescharacteristic
19C2×C32×C3⋊C8C2211yescharacteristic
20C3×Dic3⋊Dic3—21no—
21C3×#3722—21no—
22C3×#930—31no—
23C2×C3×C4⋊Dic3—31no—
24C3×#895—31no—
25C3×D3×C4⋊C4—31no—
26#63909C2×C311yescharacteristic
27D3×C4⋊Dic3C2×C311yescharacteristic, complemented
28C32×#106—31no—
29C32×C22⋊C8—31no—
30#63648C2×C311yescharacteristic, complemented
31C3×#821—31no—
32C3×#821—31no—
33C3×#821—31no—
34C3×#821—61no—
35C3×(C2×D3)⋊C8—21no—
36C3×(C2×D3)⋊C8D311yescharacteristic, complemented
37C3×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
38C3×#817—21no—
39C3×#817—31no—
40C3×#817D311yescharacteristic, complemented
41C3×#817C2×C311yescharacteristic, complemented
42C3×#809—31no—
43C3×#808—31no—
44#63573C2×C311yescharacteristic, complemented
45#63564C2×C311yescharacteristic, complemented
46C22×C3×C3⋊D3—21no—
47C22×C32×D3D411yescharacteristic
48C2×C33×C4C2311yescharacteristic
49C2×C3×C3⋊Dic3—21no—
50C3×C4⋊(C3⋊D3)—21no—
51C3×C4⋊(C3⋊D3)—21no—
52C2×C32×Dic3—21no—
53C2×C32×Dic3—21no—
54C2×C32×Dic3D411yescharacteristic
55C32×C4×D3—21no—
56C32×C4×D3—21no—
57C3×#626—42no—
58C3×D3×Dic3—42no—
59C33×C8—21no—
60C32×C3⋊C8—21no—
61C3×#481—91no—
62#4863—31no—
63#4735—31no—
64C22×C32×C4—31no—
65C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
66C2×C3×#67—61no—
67C22×C3×Dic3—61no—
68C2×C3×D12—31no—
69C2×C3×D12—31no—
70C2×C3×D12—61no—
71C2×C3×D12—61no—
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—61no—
74C2×C3×C4×D3C2×D311yescharacteristic
75C2×C3×C4×D3C22×C311yescharacteristic
76C2×#626—21no—
77C2×D3×Dic3—21no—
78C2×C32×C8—21no—
79C2×C32×C8—21no—
80C2×C32×C8—21no—
81C2×C32×C8—31no—
82C2×C32×C8—41no—
83C2×C32×C8C2×D311yescharacteristic
84C2×C32×C8C2×D311yescharacteristic
85C2×C32×C8C22×C311yescharacteristic
86C32×C4⋊C4—31no—
87C32×C4⋊C4—31no—
88C4⋊(C3⋊Dic3)C22×C311yescharacteristic
89C3×(C2×D3)⋊C4—61no—
90C3×(C2×D3)⋊C4—61no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—31no—
94C3×C4⋊Dic3—31no—
95C3×C4⋊Dic3—61no—
96C3×C4⋊Dic3—61no—
97C3×C4⋊Dic3C2×D311yescharacteristic
98C3×C4⋊Dic3C2×D311yescharacteristic
99C3×C4⋊Dic3C22×C311yescharacteristic
100C3×C4⋊Dic3C22×C311yescharacteristic
101C3×Dic3⋊C4—61no—
102C2×C3×C3⋊C8—21no—
103C2×C3×C3⋊C8C2×D311yescharacteristic
104C2×C3×C3⋊C8C22×C311yescharacteristic
105Dic3⋊Dic3—21no—
106#3722—21no—
107C22×C33C2×D411yescharacteristic
108C2×C3×C3⋊D3—41no—
109C2×C3×C3⋊D3—41no—
110C2×C3×C3⋊D3—41no—
111C2×C32×D3—21no—
112C2×C32×D3—21no—
113C2×C32×D3SD1612yes—
114C33×C4#4111yescharacteristic
115C33×C4#4111yescharacteristic
116C3×C3⋊Dic3—41no—
117C32×Dic3—21no—
118C32×Dic3—41no—
119C32×Dic3—41no—
120C3×#121—91no—
121C2×C3×C4⋊C4—91no—
122#930—31no—
123C2×C4⋊Dic3—31no—
124#895—31no—
125D3×C4⋊C4—31no—
126C3×#106—31no—
127C3×#106—31no—
128C3×#106—61no—
129C3×#106—91no—
130C3×#102—91no—
131C3×#102—91no—
132C3×C22⋊C8—31no—
133C3×C22⋊C8—31no—
134C3×C22⋊C8—61no—
135#821—31no—
136#821—31no—
137#821—31no—
138#821—61no—
139(C2×D3)⋊C8C3×D311yescharacteristic, complemented
140#817—31no—
141#817C3×D311yescharacteristic, complemented
142#809—31no—
143#808—31no—
144C23×C32—31no—
145C22×C3⋊D3—21no—
146C22×C3×D3—21no—
147C22×C3×D3—61no—
148C22×C3×D3—61no—
149C22×C3×D3—121no—
150C22×C3×D3D1211yescharacteristic
151C22×C3×D3C3×D411yescharacteristic
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—31no—
156C2×C32×C4—41no—
157C2×C32×C4—61no—
158C2×C32×C4—61no—
159C2×C32×C4—61no—
160C2×C32×C4—61no—
161C2×C32×C4C22×D311yescharacteristic
162C2×C32×C4C22×D311yescharacteristic
163C2×C32×C4C23×C311yescharacteristic
164C2×C3⋊Dic3—21no—
165C4⋊(C3⋊D3)—21no—
166C4⋊(C3⋊D3)—21no—
167C3×#67—122no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—41no—
174C2×C3×Dic3—41no—
175C2×C3×Dic3—61no—
176C2×C3×Dic3—61no—
177C2×C3×Dic3—121no—
178C2×C3×Dic3—122no—
179C2×C3×Dic3D1211yescharacteristic
180C2×C3×Dic3C3×D411yescharacteristic
181C3×D12—62no—
182C3×D12—61no—
183C3×D12—61no—
184C3×D12—61no—
185C3×D12—61no—
186C3×D12—121no—
187C3×D12—122no—
188C3×C4×D3—21no—
189C3×C4×D3—21no—
190C3×C4×D3—21no—
191C3×C4×D3—21no—
192C3×C4×D3—41no—
193C3×C4×D3—41no—
194C3×C4×D3—122no—
195#626—42no—
196D3×Dic3—42no—
197C32×C8—21no—
198C32×C8—22no—
199C32×C8—21no—
200C32×C8—21no—
201C32×C8—41no—
202C32×C8—41no—
203C32×C8—42no—
204C32×C8—61no—
205C3×C3⋊C8—21no—
206C3×C3⋊C8—21no—
207C3×C3⋊C8—41no—
208#481—91noSylow
209C2×C33#12311yescharacteristic
210C2×C33C2×SD1611yescharacteristic
211C2×C33AGL(1,ℤ/8)11yescharacteristic
212C3×C3⋊D3—81no—
213C32×D3—22no—
214C2×C3×D4—91no—
215C2×C3×D4—181no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4—61no—
219C22×C3×C4—181no—
220C2×#67—61no—
221C22×Dic3—61no—
222C2×D12—31no—
223C2×D12—31no—
224C2×D12—61no—
225C2×D12—61no—
226C2×C4×D3—61no—
227C2×C4×D3C2×C3×D311yescharacteristic
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—31no—
232C2×C3×C8—31no—
233C2×C3×C8—41no—
234C2×C3×C8—61no—
235C2×C3×C8D3211yescharacteristic
236C2×C3×C8C2×C3×D311yescharacteristic
237C2×C3×C8C2×C3×D311yescharacteristic
238C3×C4⋊C4—31no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—91no—
245C3×C4⋊C4—181no—
246C3×C22⋊C4—181no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249C4⋊Dic3—31no—
250C4⋊Dic3—31no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3C2×C3×D311yescharacteristic
254C4⋊Dic3C2×C3×D311yescharacteristic
255Dic3⋊C4—61no—
256C2×C3⋊C8C2×C3×D311yescharacteristic
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32—32no—
261C22×C32—41no—
262C22×C32—61no—
263C22×C32—61no—
264C22×C32C2×D1211yescharacteristic
265C22×C32D3×D411yescharacteristic
266C22×C32C2×C3×D411yescharacteristic
267C2×C3⋊D3—41no—
268C2×C3⋊D3—41no—
269C2×C3⋊D3—41no—
270C2×C3×D3—21no—
271C2×C3×D3—21no—
272C2×C3×D3—21no—
273C2×C3×D3—21no—
274C2×C3×D3—22no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—122no—
278C2×C3×D3—121no—
279C2×C3×D3—121no—
280C2×C3×D3—121no—
281C2×C3×D3—121no—
282C2×C3×D3—121no—
283C2×C3×D3—121no—
284C2×C3×D3—241no—
285C2×C3×D3—241no—
286C2×C3×D3#20412yes—
287C2×C3×D3C3×SD1612yes—
288C32×C4—21no—
289C32×C4—21no—
290C32×C4—21no—
291C32×C4—21no—
292C32×C4—21no—
293C32×C4—21no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4—61no—
297C32×C4—121no—
298C32×C4—121no—
299C32×C4#23511yescharacteristic
300C32×C4#23711yescharacteristic
301C32×C4#23711yescharacteristic
302C32×C4#23911yescharacteristic
303C32×C4C3×#4111yescharacteristic
304C32×C4C3×#4111yescharacteristic
305C3⋊Dic3—41no—
306C3×Dic3—21no—
307C3×Dic3—21no—
308C3×Dic3—41no—
309C3×Dic3—41no—
310C3×Dic3—41no—
311C3×Dic3—41no—
312C3×Dic3—41no—
313C3×Dic3—81no—
314C3×Dic3—81no—
315C3×Dic3—121no—
316C3×Dic3—121no—
317C3×Dic3—241no—
318#121—91no—
319C2×C4⋊C4—91no—
320#106—31no—
321#106—91no—
322#102—91no—
323#102—91no—
324C22⋊C8—31no—
325C33#48111yescharacteristic, complemented, Sylow
326C23×C3—31no—
327C23×C3—31no—
328C23×C3—61no—
329C23×C3—181no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—121no—
333C22×D3C3×D1211yescharacteristic
334C3×D4—181no—
335C3×D4—181no—
336C3×D4—362no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—31no—
341C2×C3×C4—31no—
342C2×C3×C4—41no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4—181no—
357C2×C3×C4—362no—
358C2×C3×C4C2×D3211yescharacteristic
359C2×C3×C4C22×C3×D311yescharacteristic
360C2×C3×C4C22×C3×D311yescharacteristic
361#67—122no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—121no—
367C2×Dic3—122no—
368C2×Dic3C3×D1211yescharacteristic
369D12—62no—
370D12—61no—
371D12—61no—
372D12—61no—
373D12—61no—
374D12—121no—
375D12—122no—
376C4×D3—21no—
377C4×D3—21no—
378C4×D3—122no—
379C3×C8—22no—
380C3×C8—21no—
381C3×C8—21no—
382C3×C8—21no—
383C3×C8—41no—
384C3×C8—41no—
385C3×C8—42no—
386C3×C8—61no—
387C3×C8—61no—
388C3×C8—121no—
389C3⋊C8—21no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—21no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32—21no—
397C2×C32—21no—
398C2×C32—21no—
399C2×C32—41no—
400C2×C32—41no—
401C2×C32—41no—
402C2×C32—62no—
403C2×C32#88611yescharacteristic
404C2×C32#89411yescharacteristic
405C2×C32C2×#20411yescharacteristic
406C2×C32#90811yescharacteristic
407C2×C32D3×SD1611yescharacteristic
408C2×C32#91411yescharacteristic
409C2×C32C3×#12311yescharacteristic
410C2×C32C2×C3×SD1611yescharacteristic
411C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
412C3⋊D3—81no—
413C3×D3—22no—
414C3×D3—22no—
415C3×D3—42no—
416C3×D3—242no—
417C3×D3—241no—
418C3×D3—241no—
419C2×D4—91no—
420C2×D4—181no—
421C22×C4—31no—
422C22×C4—181no—
423C2×C8—31no—
424C2×C8C3×D3211yescharacteristic
425C4⋊C4—31no—
426C4⋊C4—31no—
427C4⋊C4—91no—
428C4⋊C4—181no—
429C22⋊C4—181no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—32no—
434C22×C3—32no—
435C22×C3—41no—
436C22×C3—62no—
437C22×C3—61no—
438C22×C3—61no—
439C22×C3—61no—
440C22×C3—61no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—361no—
444C22×C3—361no—
445C22×C3—361no—
446C22×C3D3×D1211yescharacteristic
447C22×C3C2×C3×D1211yescharacteristic
448C22×C3C3×D3×D411yescharacteristic
449C2×D3—21no—
450C2×D3—21no—
451C2×D3—122no—
452C2×D3—121no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—241no—
459C2×D3—241no—
460C2×D3C3×#20412yes—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—61no—
470C3×C4—61no—
471C3×C4—121no—
472C3×C4—121no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4—121no—
476C3×C4—241no—
477C3×C4—241no—
478C3×C4—361no—
479C3×C4#379611yescharacteristic
480C3×C4#380411yescharacteristic
481C3×C4C3×#23511yescharacteristic
482C3×C4C3×#23711yescharacteristic
483C3×C4C3×#23711yescharacteristic
484C3×C4C3×#23911yescharacteristic
485Dic3—21no—
486Dic3—41no—
487Dic3—41no—
488Dic3—121no—
489Dic3—121no—
490Dic3—241no—
491C32—21no—
492C32—21no—
493C32—21no—
494C32—41no—
495C32#473511yescharacteristic, complemented
496C32#486311yescharacteristic, complemented
497C32C3×#48111yescharacteristic, complemented
498C23—31no—
499C23—181no—
500D4—181no—
501D4—181no—
502D4—362no—
503C2×C4—31no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—181no—
509C2×C4—362no—
510C2×C4C2×C3×D3211yescharacteristic
511C8—21no—
512C8—61no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—41no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—62no—
526C2×C3—62no—
527C2×C3—122no—
528C2×C3—721no—
529C2×C3D3×#20411yescharacteristic
530C2×C3#6379411yescharacteristic
531C2×C3#6389011yescharacteristic
532C2×C3C3×#88611yescharacteristic
533C2×C3C3×#89411yescharacteristic
534C2×C3C2×C3×#20411yescharacteristic
535C2×C3C3×#90811yescharacteristic
536C2×C3C3×D3×SD1611yescharacteristic
537C2×C3C3×#91411yescharacteristic
538D3—22no—
539D3—242no—
540D3—241no—
541D3—241no—
542C22—32no—
543C22—61no—
544C22—61no—
545C22—361no—
546C22—361no—
547C22—361no—
548C22C3×D3×D1211yescharacteristic
549C4—61no—
550C4—121no—
551C4—121no—
552C4—361no—
553C4C3×#379611yescharacteristic
554C4C3×#380411yescharacteristic
555C3—21no—
556C3—21no—
557C3—21no—
558C3—41no—
559C3#1059067711yescharacteristic, direct product factor
560C3C3×#473511yescharacteristic, complemented
561C3C3×#486311yescharacteristic, complemented
562C2—62no—
563C2—721no—
564C2C3×D3×#20411yescharacteristic
565C2C3×#6379411yescharacteristic
566C2C3×#6389011yescharacteristic
subgroupG/H
centerC22×C3D3×D12
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×C8C22
socleC22×C33C2×D4
prime radicalC3×#63909C2
hypercenterC2×C3×C8D32
hypocenterC32C3×#481
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
2. C3×D3×C4⋊Dic3C2semidirect
3. C3×#63648C2semidirect
4. C32×(C2×D3)⋊C8C2semidirect
5. C32×#817C2semidirect
6. C3×#63573C2semidirect
7. C3×#63564C2semidirect
10. #10590677C3direct (N × H)
27. D3×C4⋊Dic3C2×C3semidirect
30. #63648C2×C3semidirect
36. C3×(C2×D3)⋊C8D3semidirect
37. C3×(C2×D3)⋊C8C2×C3semidirect
40. C3×#817D3semidirect
41. C3×#817C2×C3semidirect
44. #63573C2×C3semidirect
45. #63564C2×C3semidirect
139. (C2×D3)⋊C8C3×D3semidirect
141. #817C3×D3semidirect
325. C33#481semidirect
495. C32#4735semidirect
496. C32#4863semidirect
497. C32C3×#481semidirect
559. C3#10590677direct (N × H)
560. C3C3×#4735semidirect
561. C3C3×#4863semidirect

Maximal subgroups

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

subgroupindex
C3×#639092
C3×D3×C4⋊Dic32
C3×#636482
C32×(C2×D3)⋊C82
C32×#8172
C3×#635732
C3×#635642
C3×#48633
C3×#47353
#105906773