Finite Group Databasebeta

← C3×#68281 #11775414

Subgroups — C3×#68281 #11775414

Order 1152.

549 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5596C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3C3×#4651C211yesmaximal, characteristic, complemented
4C32×#327C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic, complemented
7C3×#4451C211yesmaximal, characteristic, complemented
8C3×#1514—31nomaximal
9#68281C311yesmaximal, characteristic, direct product factor
10C2×C3×#237—21no—
11C32×#121C2211yescharacteristic
12C3×#940C411yescharacteristic, complemented
13C3×#939—21no—
14C3×D4×Dic3C411yescharacteristic, complemented
15C3×#930C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C3×#893C411yescharacteristic, complemented
18C3×#888C411yescharacteristic, complemented
19C3×#885—21no—
20C3×#67⋊C4—21no—
21C32×C22⋊C8C2211yescharacteristic
22C32×#95C2211yescharacteristic
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#815—21no—
28C3×Dic3⋊C8—21no—
29C3×#532—31no—
30#5596C2×C311yescharacteristic
31C3×#432—31no—
32C3×#383—31no—
33#4719C2×C311yescharacteristic, complemented
34#4651C2×C311yescharacteristic, complemented
35C3×#327—21no—
36C3×#327—31no—
37C3×#327—31no—
38C3×#327—31no—
39C3×#327D311yescharacteristic, complemented
40C3×#327C2×C311yescharacteristic, complemented
41#4537C2×C311yescharacteristic, complemented
42#4470C2×C311yescharacteristic, complemented
43#4451C2×C311yescharacteristic, complemented
44C2×C32×D4—21no—
45C2×C32×D4C2×C411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C3×#237—42no—
56C3×#237—42no—
57C2×C3×D12C2×C411yescharacteristic
58C2×C3×C4×D3—21no—
59C2×C3×Dic6—21no—
60C2×C32×C8—21no—
61C32×C4⋊C4C2×C411yescharacteristic
62C32×C22⋊C4—21no—
63C3×#217—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3C2×C411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3C2×C411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C3×C4×Dic3D411yescharacteristic
72C2×C3×C3⋊C8—21no—
73#1514—31noSylow
74C2×C3×#41—61no—
75C2×#237—21no—
76C3×C4⋊Q8—31no—
77C3×#127—31no—
78C3×#124—61no—
79C3×#121—21no—
80C3×#121—31no—
81C3×#121—61no—
82C3×#121C2×D311yescharacteristic
83C3×#121C22×C311yescharacteristic
84C3×C4×D4—31no—
85C3×C4×D4—31no—
86C3×C4×D4—61no—
87C2×C3×C42—31no—
88#940C3×C411yescharacteristic, complemented
89#939—21no—
90D4×Dic3C3×C411yescharacteristic, complemented
91#930C22×C311yescharacteristic
92C2×C4×Dic3C22×C311yescharacteristic
93#893C3×C411yescharacteristic, complemented
94#888C3×C411yescharacteristic, complemented
95#885—21no—
96#67⋊C4—21no—
97C3×C4⋊C8—61no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8—31no—
100C3×C22⋊C8C2×D311yescharacteristic
101C3×C22⋊C8C22×C311yescharacteristic
102C3×#97—61no—
103C3×#95—21no—
104C3×#95—31no—
105C3×#95—61no—
106C3×#95—61no—
107C3×#95C2×D311yescharacteristic
108C3×#95C22×C311yescharacteristic
109C3⋊#95—21no—
110C3⋊#95—21no—
111C3⋊#95C22×C311yescharacteristic
112#830C22×C311yescharacteristic
113#815—21no—
114Dic3⋊C8—21no—
115C23×C32—21no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C32×D4—41no—
119C32×D4—41no—
120C32×D4—41no—
121C2×C32×C4—21no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C3×#67—42no—
129C3×#67—42no—
130C3×#67—41no—
131C3×#67—41no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—42no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3C22⋊C411yescharacteristic
142C2×C3×Dic3C22⋊C411yescharacteristic
143C2×C3×Dic3C22⋊C411yescharacteristic
144C3×D12—41no—
145C3×C4×D3—42no—
146C3×Dic6—42no—
147C32×C8—41no—
148C3×C3⋊C8—41no—
149#532—31no—
150#432—31no—
151#383—31no—
152#327—31no—
153#327—31no—
154#327—31no—
155#327C3×D311yescharacteristic, complemented
156C3×#41—122no—
157C3×#41—122no—
158C2×C3×Q8—61no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—31no—
163C2×C3×D4—41no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4C4×D311yescharacteristic
168C2×C3×D4C2×C3×C411yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—41no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C23×C311yescharacteristic
180C2×#67—21no—
181C2×#67—21no—
182C2×#67—21no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3C3×D411yescharacteristic
186C22×Dic3C3×D411yescharacteristic
187#237—42no—
188#237—42no—
189C2×D12C2×C3×C411yescharacteristic
190C2×C4×D3—21no—
191C2×Dic6—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—41no—
195C2×C3×C8—61no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4C4×D311yescharacteristic
200C3×C4⋊C4C2×C3×C411yescharacteristic
201C3×C22⋊C4—21no—
202C3×C22⋊C4—21no—
203C3×C22⋊C4—41no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206C3×C22⋊C4—61no—
207C3×C42—31no—
208C3×C42—31no—
209C3×C42—31no—
210C3×C42—31no—
211#217—21no—
212(C2×D3)⋊C4—21no—
213(C2×D3)⋊C4—21no—
214C4⋊Dic3C2×C3×C411yescharacteristic
215Dic3⋊C4—21no—
216C4×Dic3C2×C3×C411yescharacteristic
217C4×Dic3C2×C3×C411yescharacteristic
218C4×Dic3C3×D411yescharacteristic
219C4×Dic3C3×D411yescharacteristic
220C2×C3⋊C8—21no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32—41no—
224C22×C32—41no—
225C22×C32—41no—
226C22×C32C2×C22⋊C411yescharacteristic
227C22×C32AGL(1,ℤ/8)11yescharacteristic
228C22×C32AGL(1,ℤ/8)11yescharacteristic
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C32×C4—21no—
233C32×C4—21no—
234C32×C4—41no—
235C32×C4—81no—
236C3×Dic3—21no—
237C3×Dic3—21no—
238C3×Dic3—21no—
239C3×Dic3—21no—
240C3×Dic3—41no—
241C3×Dic3—81no—
242C2×#41—61no—
243C4⋊Q8—31no—
244#127—31no—
245#124—61no—
246#121—31no—
247#121—61no—
248#121C2×C3×D311yescharacteristic
249C4×D4—31no—
250C4×D4—31no—
251C4×D4—61no—
252C2×C42—31no—
253C4⋊C8—61no—
254C22⋊C8—31no—
255C22⋊C8C2×C3×D311yescharacteristic
256#97—61no—
257#95—31no—
258#95—61no—
259#95—61no—
260#95C2×C3×D311yescharacteristic
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—41no—
265C23×C3—61no—
266C23×C3D3×D411yescharacteristic
267C23×C3C2×C3×D411yescharacteristic
268C22×D3—21no—
269C3×Q8—122no—
270C3×D4—41no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—81no—
277C3×D4—81no—
278C3×D4—81no—
279C3×D4—121no—
280C3×D4—122no—
281C3×D4—122no—
282C3×D4—121no—
283C3×D4—121no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—31no—
289C2×C3×C4—31no—
290C2×C3×C4—31no—
291C2×C3×C4—31no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—42no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—81no—
306C2×C3×C4—81no—
307C2×C3×C4—81no—
308C2×C3×C4—122no—
309C2×C3×C4—121no—
310C2×C3×C4—122no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4C22×C3×C411yescharacteristic
317C2×C3×C4C2×C3×D411yescharacteristic
318#67—42no—
319#67—42no—
320#67—41no—
321#67—41no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—41no—
326C2×Dic3—42no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3C3×C22⋊C411yescharacteristic
331C2×Dic3C3×C22⋊C411yescharacteristic
332C2×Dic3C3×C22⋊C411yescharacteristic
333C2×Dic3C3×C22⋊C411yescharacteristic
334D12—41no—
335C4×D3—42no—
336Dic6—42no—
337C3×C8—41no—
338C3×C8—41no—
339C3×C8—81no—
340C3×C8—121no—
341C3⋊C8—41no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—81no—
345C2×C32#41011yescharacteristic
346C2×C32#41811yescharacteristic
347C2×C32#42111yescharacteristic
348C3×D3—81no—
349#41—122no—
350#41—122no—
351C2×Q8—61no—
352C2×D4—21no—
353C2×D4—31no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4C3×C4×D311yescharacteristic
358C22×C4—21no—
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4—61no—
364C22×C4C22×C3×D311yescharacteristic
365C2×C8—21no—
366C2×C8—61no—
367C4⋊C4—31no—
368C4⋊C4—61no—
369C4⋊C4C3×C4×D311yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C42—31no—
375C42—31no—
376C42—31no—
377C42—31no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—81no—
394C22×C3—81no—
395C22×C3—81no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3—121no—
399C22×C3D3×C22⋊C411yescharacteristic
400C22×C3#91111yescharacteristic
401C22×C3#91411yescharacteristic
402C22×C3C2×C3×C22⋊C411yescharacteristic
403C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
404C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—41no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—41no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—61no—
417C3×C4—61no—
418C3×C4—61no—
419C3×C4—61no—
420C3×C4—81no—
421C3×C4—81no—
422C3×C4—81no—
423C3×C4—82no—
424C3×C4—121no—
425C3×C4—241no—
426Dic3—21no—
427Dic3—21no—
428Dic3—21no—
429Dic3—21no—
430Dic3—41no—
431Dic3—81no—
432C32#151411yescharacteristic, complemented, Sylow
433C23—21no—
434C23—61no—
435C23C3×D3×D411yescharacteristic
436Q8—122no—
437D4—41no—
438D4—41no—
439D4—41no—
440D4—121no—
441D4—122no—
442D4—122no—
443D4—121no—
444D4—121no—
445C2×C4—21no—
446C2×C4—31no—
447C2×C4—31no—
448C2×C4—31no—
449C2×C4—31no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—122no—
458C2×C4—121no—
459C2×C4—122no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4C2×C3×C4×D311yescharacteristic
464C2×C4C3×D3×D411yescharacteristic
465C8—41no—
466C8—121no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—41no—
475C2×C3—41no—
476C2×C3—81no—
477C2×C3—81no—
478C2×C3—161no—
479C2×C3—241no—
480C2×C3#474011yescharacteristic
481C2×C3#477011yescharacteristic
482C2×C3#482111yescharacteristic
483C2×C3C3×#41011yescharacteristic
484C2×C3C3×#41811yescharacteristic
485C2×C3C3×#42111yescharacteristic
486D3—81no—
487C22—21no—
488C22—21no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—121no—
493C22—121no—
494C22—121no—
495C22C3×D3×C22⋊C411yescharacteristic
496C22C3×#91111yescharacteristic
497C22C3×#91411yescharacteristic
498C4—21no—
499C4—21no—
500C4—41no—
501C4—61no—
502C4—61no—
503C4—61no—
504C4—61no—
505C4—81no—
506C4—121no—
507C4—241no—
508C3—21no—
509C3#6828111yescharacteristic, direct product factor
510C3C3×#151411yescharacteristic, complemented
511C2—21no—
512C2—21no—
513C2—81no—
514C2—241no—
515C2C3×#474011yescharacteristic
516C2C3×#477011yescharacteristic
517C2C3×#482111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#327C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#5596C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#327D3
hypocenterC3C3×#1514
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
2. C3×#4719C2semidirect
3. C3×#4651C2semidirect
4. C32×#327C2semidirect
5. C3×#4537C2semidirect
6. C3×#4470C2semidirect
7. C3×#4451C2semidirect
9. #68281C3direct (N × H)
12. C3×#940C4semidirect
14. C3×D4×Dic3C4semidirect
17. C3×#893C4semidirect
18. C3×#888C4semidirect
33. #4719C2×C3semidirect
34. #4651C2×C3semidirect
39. C3×#327D3semidirect
40. C3×#327C2×C3semidirect
41. #4537C2×C3semidirect
42. #4470C2×C3semidirect
43. #4451C2×C3semidirect
88. #940C3×C4semidirect
90. D4×Dic3C3×C4semidirect
93. #893C3×C4semidirect
94. #888C3×C4semidirect
155. #327C3×D3semidirect
432. C32#1514semidirect
509. C3#68281direct (N × H)
510. C3C3×#1514semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
C3×#47192
C3×#46512
C32×#3272
C3×#45372
C3×#44702
C3×#44512
C3×#15143
#682813