Finite Group Databasebeta

← C3×#10590649 #13157811

Subgroups — C3×#10590649 #13157811

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×#63916C211yesmaximal, characteristic
2C3×#63900C211yesmaximal, characteristic, complemented
3C3×#63647C211yesmaximal, characteristic, complemented
4C32×#821C211yesmaximal, characteristic, complemented
5C32×#817C211yesmaximal, characteristic, complemented
6C3×#63574C211yesmaximal, characteristic, complemented
7C3×#63562C211yesmaximal, characteristic, complemented
8C3×#4863—31nomaximal
9C3×#4777—31nomaximal
10#10590649C311yesmaximal, characteristic, direct product factor
11C2×C3×C4×C3⋊D3C2211yescharacteristic
12C2×C32×D12C2211yescharacteristic
13C2×C3×#626—21no—
14C2×C3×#624—21no—
15C2×C33×C8C2211yescharacteristic
16C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
17C32×C4⋊Dic3C2211yescharacteristic
18C32×C4⋊Dic3C2211yescharacteristic
19C32×C4⋊Dic3C2211yescharacteristic
20C3×#3724—21no—
21C3×(C2×D3)⋊Dic3—21no—
22C3×#938—31no—
23C3×#895—31no—
24C3×D3×C4⋊C4—31no—
25C3×D3×C4⋊C4—31no—
26#63916C2×C311yescharacteristic
27#63900C2×C311yescharacteristic, complemented
28C32×#106—31no—
29C32×#102—31no—
30#63647C2×C311yescharacteristic, complemented
31C3×#832—31no—
32C3×#821—21no—
33C3×#821D311yescharacteristic, complemented
34C3×#821C2×C311yescharacteristic, complemented
35C3×(C2×D3)⋊C8—31no—
36C3×(C2×D3)⋊C8—31no—
37C3×(C2×D3)⋊C8—61no—
38C3×#817—21no—
39C3×#817D311yescharacteristic, complemented
40C3×#817C2×C311yescharacteristic, complemented
41C3×#809—31no—
42C3×#808—31no—
43C3×#808—31no—
44#63574C2×C311yescharacteristic, complemented
45#63562C2×C311yescharacteristic, complemented
46C22×C3×C3⋊D3D411yescharacteristic
47C22×C32×D3—21no—
48C2×C33×C4C2311yescharacteristic
49C2×C3×C3⋊Dic3D411yescharacteristic
50C3×C4×C3⋊D3—21no—
51C3×C4×C3⋊D3—21no—
52C2×C32×Dic3—21no—
53C2×C32×Dic3—21no—
54C2×C32×Dic3—21no—
55C32×D12—21no—
56C32×D12—21no—
57C3×#626—42no—
58C3×#624—42no—
59C33×C8—21no—
60C3×C3⋊(C3⋊C8)—21no—
61C3×#481—91no—
62#4863—31no—
63#4777—31no—
64C2×C32×D4—31no—
65C2×C4×C3⋊D3C22×C311yescharacteristic
66C2×C3×#67—61no—
67C2×C3×D12—21no—
68C2×C3×D12—61no—
69C2×C3×D12C2×D311yescharacteristic
70C2×C3×D12C22×C311yescharacteristic
71C2×C3×C4×D3—31no—
72C2×C3×C4×D3—31no—
73C2×C3×C4×D3—61no—
74C2×C3×C4×D3—61no—
75C2×C3×C4×D3—61no—
76C2×#626—21no—
77C2×#624—21no—
78C2×C32×C8—21no—
79C2×C32×C8—21no—
80C2×C32×C8—21no—
81C2×C32×C8—41no—
82C2×C32×C8C2×D311yescharacteristic
83C2×C32×C8C2×D311yescharacteristic
84C2×C32×C8C22×C311yescharacteristic
85C32×C4⋊C4—31no—
86C32×C4⋊C4—31no—
87C32×C4⋊C4—31no—
88C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
89C3×#217—61no—
90C3×(C2×D3)⋊C4—61no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2×D311yescharacteristic
95C3×C4⋊Dic3C2×D311yescharacteristic
96C3×C4⋊Dic3C2×D311yescharacteristic
97C3×C4⋊Dic3C22×C311yescharacteristic
98C3×C4⋊Dic3C22×C311yescharacteristic
99C3×C4⋊Dic3C22×C311yescharacteristic
100C3×Dic3⋊C4—61no—
101C3×Dic3⋊C4—61no—
102C2×C3×C3⋊C8—31no—
103C2×C3×C3⋊C8—31no—
104C2×C3×C3⋊C8—61no—
105#3724—21no—
106(C2×D3)⋊Dic3—21no—
107C22×C33C2×D411yescharacteristic
108C2×C3×C3⋊D3—21no—
109C2×C3×C3⋊D3—21no—
110C2×C3×C3⋊D3SD1612yes—
111C2×C32×D3—41no—
112C2×C32×D3—41no—
113C2×C32×D3—41no—
114C33×C4#4111yescharacteristic
115C33×C4#4111yescharacteristic
116C3×C3⋊Dic3—21no—
117C32×Dic3—41no—
118C32×Dic3—41no—
119C32×Dic3—41no—
120C3×#121—91no—
121C2×C3×C4⋊C4—91no—
122#938—31no—
123#895—31no—
124D3×C4⋊C4—31no—
125D3×C4⋊C4—31no—
126C3×#106—31no—
127C3×#106—31no—
128C3×#106—61no—
129C3×#106—91no—
130C3×#102—31no—
131C3×#102—31no—
132C3×#102—61no—
133C3×#102—91no—
134C3×C22⋊C8—91no—
135#832—31no—
136#821C3×D311yescharacteristic, complemented
137(C2×D3)⋊C8—31no—
138(C2×D3)⋊C8—31no—
139(C2×D3)⋊C8—61no—
140#817C3×D311yescharacteristic, complemented
141#809—31no—
142#808—31no—
143#808—31no—
144C23×C32—61no—
145C22×C3⋊D3C3×D411yescharacteristic
146C22×C3×D3—21no—
147C22×C3×D3—21no—
148C22×C3×D3—31no—
149C22×C3×D3—31no—
150C22×C3×D3—41no—
151C22×C3×D3—61no—
152C32×D4—61no—
153C32×D4—61no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—41no—
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⋊Dic3C3×D411yescharacteristic
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—21no—
174C2×C3×Dic3—31no—
175C2×C3×Dic3—31no—
176C2×C3×Dic3—41no—
177C2×C3×Dic3—41no—
178C2×C3×Dic3—41no—
179C2×C3×Dic3—61no—
180C3×D12—22no—
181C3×D12—21no—
182C3×D12—21no—
183C3×D12—21no—
184C3×D12—21no—
185C3×D12—41no—
186C3×D12—122no—
187C3×C4×D3—61no—
188C3×C4×D3—61no—
189C3×C4×D3—61no—
190C3×C4×D3—61no—
191C3×C4×D3—121no—
192C3×C4×D3—121no—
193C3×C4×D3—122no—
194C3×C4×D3—122no—
195#626—42no—
196#624—42no—
197C32×C8—21no—
198C32×C8—22no—
199C32×C8—21no—
200C32×C8—21no—
201C32×C8—41no—
202C32×C8—41no—
203C32×C8—42no—
204C3⋊(C3⋊C8)—21no—
205C3×C3⋊C8—61no—
206C3×C3⋊C8—61no—
207C3×C3⋊C8—121no—
208#481—91noSylow
209C2×C33#12311yescharacteristic
210C2×C33C2×SD1611yescharacteristic
211C2×C33AGL(1,ℤ/8)11yescharacteristic
212C3×C3⋊D3—22no—
213C32×D3—81no—
214C2×C3×D4—31no—
215C2×C3×D4—31no—
216C2×C3×D4—61no—
217C2×C3×D4—181no—
218C22×C3×C4—91no—
219C22×C3×C4—181no—
220C2×#67—61no—
221C2×D12—61no—
222C2×D12C2×C3×D311yescharacteristic
223C2×C4×D3—31no—
224C2×C4×D3—31no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—41no—
232C2×C3×C8—91no—
233C2×C3×C8D3211yescharacteristic
234C2×C3×C8C2×C3×D311yescharacteristic
235C2×C3×C8C2×C3×D311yescharacteristic
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
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—61no—
245C3×C4⋊C4—181no—
246C3×C22⋊C4—181no—
247#217—61no—
248(C2×D3)⋊C4—61no—
249C4⋊Dic3C2×C3×D311yescharacteristic
250C4⋊Dic3C2×C3×D311yescharacteristic
251C4⋊Dic3C2×C3×D311yescharacteristic
252Dic3⋊C4—61no—
253Dic3⋊C4—61no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—61no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32—41no—
261C22×C32—121no—
262C22×C32—121no—
263C22×C32—121no—
264C22×C32D3×D411yescharacteristic
265C22×C32D3×D411yescharacteristic
266C22×C32C2×C3×D411yescharacteristic
267C2×C3⋊D3—21no—
268C2×C3⋊D3—21no—
269C2×C3⋊D3C3×SD1612yes—
270C2×C3×D3—32no—
271C2×C3×D3—32no—
272C2×C3×D3—42no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—62no—
280C2×C3×D3—61no—
281C2×C3×D3—61no—
282C2×C3×D3—61no—
283C2×C3×D3—61no—
284C2×C3×D3—81no—
285C2×C3×D3—81no—
286C2×C3×D3—121no—
287C2×C3×D3—121no—
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—121no—
297C32×C4—121no—
298C32×C4—121no—
299C32×C4#23511yescharacteristic
300C32×C4#23511yescharacteristic
301C32×C4#23711yescharacteristic
302C32×C4#23911yescharacteristic
303C32×C4C3×#4111yescharacteristic
304C32×C4C3×#4111yescharacteristic
305C3⋊Dic3—21no—
306C3×Dic3—41no—
307C3×Dic3—41no—
308C3×Dic3—41no—
309C3×Dic3—41no—
310C3×Dic3—41no—
311C3×Dic3—41no—
312C3×Dic3—61no—
313C3×Dic3—61no—
314C3×Dic3—81no—
315C3×Dic3—81no—
316C3×Dic3—81no—
317C3×Dic3—121no—
318#121—91no—
319C2×C4⋊C4—91no—
320#106—31no—
321#106—91no—
322#102—31no—
323#102—91no—
324C22⋊C8—91no—
325C33#48111yescharacteristic, complemented, Sylow
326C23×C3—61no—
327C23×C3—61no—
328C23×C3—91no—
329C23×C3—121no—
330C22×D3—21no—
331C22×D3—31no—
332C22×D3—31no—
333C22×D3—61no—
334C3×D4—62no—
335C3×D4—61no—
336C3×D4—61no—
337C3×D4—61no—
338C3×D4—61no—
339C3×D4—121no—
340C3×D4—362no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—41no—
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—91no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—181no—
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—21no—
365C2×Dic3—31no—
366C2×Dic3—31no—
367C2×Dic3—61no—
368D12—21no—
369D12—21no—
370D12—122no—
371C4×D3—61no—
372C4×D3—61no—
373C4×D3—61no—
374C4×D3—61no—
375C4×D3—121no—
376C4×D3—121no—
377C4×D3—122no—
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—181no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C3⋊C8—121no—
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—241no—
403C2×C32#88311yescharacteristic
404C2×C32#89411yescharacteristic
405C2×C32#91111yescharacteristic
406C2×C32D3×SD1611yescharacteristic
407C2×C32D3×SD1611yescharacteristic
408C2×C32#91411yescharacteristic
409C2×C32C3×#12311yescharacteristic
410C2×C32C2×C3×SD1611yescharacteristic
411C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
412C3⋊D3—22no—
413C3×D3—62no—
414C3×D3—62no—
415C3×D3—82no—
416C3×D3—81no—
417C3×D3—81no—
418C3×D3—122no—
419C2×D4—31no—
420C2×D4—181no—
421C22×C4—91no—
422C22×C4—181no—
423C2×C8—91no—
424C2×C8C3×D3211yescharacteristic
425C4⋊C4—31no—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—181no—
429C22⋊C4—181no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—41no—
434C22×C3—92no—
435C22×C3—122no—
436C22×C3—121no—
437C22×C3—121no—
438C22×C3—121no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3—181no—
443C22×C3—181no—
444C22×C3—241no—
445C22×C3—241no—
446C22×C3#380211yescharacteristic
447C22×C3C3×D3×D411yescharacteristic
448C22×C3C3×D3×D411yescharacteristic
449C2×D3—32no—
450C2×D3—32no—
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—62no—
455C2×D3—61no—
456C2×D3—61no—
457C2×D3—61no—
458C2×D3—61no—
459C2×D3—121no—
460C2×D3—121no—
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—121no—
470C3×C4—121no—
471C3×C4—121no—
472C3×C4—121no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4—181no—
476C3×C4—241no—
477C3×C4—241no—
478C3×C4—241no—
479C3×C4#379911yescharacteristic
480C3×C4#380411yescharacteristic
481C3×C4C3×#23511yescharacteristic
482C3×C4C3×#23511yescharacteristic
483C3×C4C3×#23711yescharacteristic
484C3×C4C3×#23911yescharacteristic
485Dic3—41no—
486Dic3—41no—
487Dic3—41no—
488Dic3—61no—
489Dic3—61no—
490Dic3—121no—
491C32—21no—
492C32—21no—
493C32—21no—
494C32—41no—
495C32#477711yescharacteristic, complemented
496C32#486311yescharacteristic, complemented
497C32C3×#48111yescharacteristic, complemented
498C23—61no—
499C23—91no—
500D4—61no—
501D4—61no—
502D4—362no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—91no—
507C2×C4—181no—
508C2×C4—181no—
509C2×C4—362no—
510C2×C4C2×C3×D3211yescharacteristic
511C8—21no—
512C8—181no—
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—182no—
526C2×C3—242no—
527C2×C3—241no—
528C2×C3—241no—
529C2×C3#6379611yescharacteristic
530C2×C3#6379811yescharacteristic
531C2×C3#6385411yescharacteristic
532C2×C3C3×#88311yescharacteristic
533C2×C3C3×#89411yescharacteristic
534C2×C3C3×#91111yescharacteristic
535C2×C3C3×D3×SD1611yescharacteristic
536C2×C3C3×D3×SD1611yescharacteristic
537C2×C3C3×#91411yescharacteristic
538D3—62no—
539D3—62no—
540D3—81no—
541D3—122no—
542C22—92no—
543C22—121no—
544C22—121no—
545C22—121no—
546C22—181no—
547C22—181no—
548C22C3×#380211yescharacteristic
549C4—121no—
550C4—121no—
551C4—121no—
552C4—181no—
553C4C3×#379911yescharacteristic
554C4C3×#380411yescharacteristic
555C3—21no—
556C3—21no—
557C3—21no—
558C3—41no—
559C3#1059064911yescharacteristic, direct product factor
560C3C3×#477711yescharacteristic, complemented
561C3C3×#486311yescharacteristic, complemented
562C2—182no—
563C2—241no—
564C2C3×#6379611yescharacteristic
565C2C3×#6379811yescharacteristic
566C2C3×#6385411yescharacteristic
subgroupG/H
centerC22×C3#3802
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×C8C22
socleC22×C33C2×D4
prime radicalC3×#63916C2
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×#63900C2semidirect
3. C3×#63647C2semidirect
4. C32×#821C2semidirect
5. C32×#817C2semidirect
6. C3×#63574C2semidirect
7. C3×#63562C2semidirect
10. #10590649C3direct (N × H)
27. #63900C2×C3semidirect
30. #63647C2×C3semidirect
33. C3×#821D3semidirect
34. C3×#821C2×C3semidirect
39. C3×#817D3semidirect
40. C3×#817C2×C3semidirect
44. #63574C2×C3semidirect
45. #63562C2×C3semidirect
136. #821C3×D3semidirect
140. #817C3×D3semidirect
325. C33#481semidirect
495. C32#4777semidirect
496. C32#4863semidirect
497. C32C3×#481semidirect
559. C3#10590649direct (N × H)
560. C3C3×#4777semidirect
561. C3C3×#4863semidirect

Maximal subgroups

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

subgroupindex
C3×#639162
C3×#639002
C3×#636472
C32×#8212
C32×#8172
C3×#635742
C3×#635622
C3×#48633
C3×#47773
#105906493