Finite Group Databasebeta

← C3×#79571 #11895818

Subgroups — C3×#79571 #11895818

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5542C211yesmaximal, characteristic, complemented
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic
4C3×#5153C212yesmaximal
5C3×#5019C211yesmaximal, characteristic, complemented
6C3×#5007C211yesmaximal, characteristic, complemented
7C3×#4875C212yesmaximal, complemented
8C3×#4765C212yesmaximal, complemented
9C3×#4757C212yesmaximal, complemented
10C3×#4681C211yesmaximal, characteristic, complemented
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3367—31nomaximal
13#79571C311yesmaximal, characteristic, direct product factor
14C22×C3×Dic6—21no—
15C2×C32×D8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18C3×#936C2212yes—
19C3×D4×Dic3C2212yes—
20C2×C3×#214C2212yes—
21C3×#926—21no—
22C3×#924—21no—
23C3×#924—21no—
24C3×#888C2212yes—
25C3×#887C2212yes—
26C3×#879—22no—
27C3×#878—22no—
28C3×#869C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#107C2211yescharacteristic
32C32×#102C2211yescharacteristic
33C32×#102C2211yescharacteristic
34C32×C4×C8C2211yescharacteristic
35C3×#832C2212yes—
36C3×#816C2212yes—
37C3×#816C2212yes—
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#810C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#556—31no—
44C3×D4×Q8—31no—
45#5542C2×C311yescharacteristic, complemented
46D4×Dic6C2×C311yescharacteristic, complemented
47C3×#489—32no—
48C3×#487—31no—
49C3×#477—32no—
50C3×#474—31no—
51C3×#463—32no—
52C3×#461—31no—
53C3×#446—31no—
54C3×#440—32no—
55C3×C4×D8—21no—
56C3×C4×D8D311yescharacteristic
57C3×C4×D8C2×C311yescharacteristic
58#5153C2×C312yes—
59#5019C2×C311yescharacteristic, complemented
60#5007C2×C311yescharacteristic, complemented
61#4875C2×C312yescomplemented
62#4765C2×C312yescomplemented
63#4757C2×C312yescomplemented
64#4681C2×C311yescharacteristic, complemented
65#4679C2×C311yescharacteristic, complemented
66C2×C32×D4C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C3×Dic3—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—44no—
74C2×C3×Dic6D411yescharacteristic
75C2×C3×Dic6C2312yes—
76C32×D8—22no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C32×C4⋊C4C2311yescharacteristic
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C22⋊C4—21no—
83C32×C42C2311yescharacteristic
84C3×#217—22no—
85C3×#217—22no—
86C3×#217—22no—
87C3×#214—24no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4D412yes—
96C3×C4×Dic3—22no—
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8C2312yes—
99#3367—31noSylow
100C22×C3×Q8—61no—
101C22×Dic6—21no—
102C2×C3×SD16—32no—
103C2×C3×D8—21no—
104C2×C3×D8C2×D311yescharacteristic
105C2×C3×D8C22×C311yescharacteristic
106C3×C4⋊Q8—32no—
107C3×C4⋊Q8—31no—
108C3×C4⋊Q8—31no—
109C3×#126—62no—
110C3×#124—32no—
111C3×C22⋊Q8—62no—
112C3×C22⋊Q8—61no—
113C3×C22⋊Q8—61no—
114C3×C4×Q8—31no—
115C3×C4×Q8—32no—
116C3×C4×D4—21no—
117C3×C4×D4—21no—
118C3×C4×D4—32no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C2×D311yescharacteristic
121C3×C4×D4C22×C311yescharacteristic
122C3×C4×D4C22×C311yescharacteristic
123C3×#117—61no—
124#936C22×C312yes—
125D4×Dic3C22×C312yes—
126C2×#214C22×C312yes—
127#926—21no—
128#924—21no—
129#924—21no—
130#888C22×C312yes—
131#887C22×C312yes—
132#879—22no—
133#878—22no—
134#869C22×C311yescharacteristic
135#869C22×C311yescharacteristic
136C4×Dic6C22×C311yescharacteristic
137C3×#107—21no—
138C3×#107—32no—
139C3×#107C2×D311yescharacteristic
140C3×#107C22×C311yescharacteristic
141C3×C4⋊C8—32no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144C3×#103—32no—
145C3×#103—32no—
146C3×#102—21no—
147C3×#102—21no—
148C3×#102—32no—
149C3×#102C2×D311yescharacteristic
150C3×#102C2×D311yescharacteristic
151C3×#102C22×C311yescharacteristic
152C3×#102C22×C311yescharacteristic
153C3×#97—32no—
154C3×C4×C8—21no—
155C3×C4×C8C2×D311yescharacteristic
156C3×C4×C8C22×C311yescharacteristic
157#832C22×C312yes—
158#816C22×C312yes—
159#816C22×C312yes—
160#815C22×C312yes—
161Dic3⋊C8C22×C312yes—
162#810C22×C312yes—
163#807C22×C312yes—
164C4⋊(C3⋊C8)C22×C311yescharacteristic
165C23×C32—21no—
166C23×C32—21no—
167C32×D4—21no—
168C32×D4—21no—
169C32×D4—21no—
170C32×D4#4112yes—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—42no—
174C2×C32×C4—42no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—44no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×Dic6—44no—
187C3×Dic6—42no—
188C32×C8—21no—
189C32×C8—21no—
190C3×C3⋊C8—22no—
191#556—31no—
192D4×Q8—31no—
193#489—32no—
194#487—31no—
195#477—32no—
196#474—31no—
197#463—32no—
198#461—31no—
199#446—31no—
200#440—32no—
201C4×D8C3×D311yescharacteristic
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8—62no—
205C2×C3×Q8—61no—
206C2×C3×Q8—124no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4C22×D311yescharacteristic
210C2×C3×D4C22×D311yescharacteristic
211C2×C3×D4C23×C311yescharacteristic
212C2×C3×D4C23×C311yescharacteristic
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—41no—
218C22×C3×C4—41no—
219C22×C3×C4—62no—
220C22×Dic3—22no—
221C2×Dic6—21no—
222C2×Dic6—22no—
223C2×Dic6—44no—
224C2×Dic6C3×D411yescharacteristic
225C2×Dic6C23×C312yes—
226C3×SD16—64no—
227C3×D8—24no—
228C3×D8—22no—
229C3×D8—22no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—32no—
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C22×D311yescharacteristic
235C2×C3×C8C23×C311yescharacteristic
236C2×C3×C8C23×C311yescharacteristic
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—32no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C23×C311yescharacteristic
250C3×C4⋊C4C23×C311yescharacteristic
251C3×C22⋊C4—21no—
252C3×C22⋊C4—21no—
253C3×C22⋊C4—21no—
254C3×C22⋊C4—21no—
255C3×C22⋊C4—41no—
256C3×C22⋊C4—41no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—62no—
260C3×C42—21no—
261C3×C42—32no—
262C3×C42—62no—
263C3×C42C22×D311yescharacteristic
264C3×C42C23×C311yescharacteristic
265#217—22no—
266#217—22no—
267#217—22no—
268#214—24no—
269C4⋊Dic3—21no—
270C4⋊Dic3—21no—
271C4⋊Dic3—21no—
272C4⋊Dic3C3×D411yescharacteristic
273C4⋊Dic3C23×C312yes—
274Dic3⋊C4—22no—
275Dic3⋊C4—22no—
276Dic3⋊C4C3×D412yes—
277C4×Dic3—22no—
278C4×Dic3C23×C312yes—
279C2×C3⋊C8C23×C312yes—
280C22×C32—22no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32C22×D411yescharacteristic
287C32×C4—21no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4AGL(1,ℤ/8)12yes—
291C32×C4C2×#4111yescharacteristic
292C32×C42−1+411yescharacteristic
293C3×Dic3—22no—
294C3×Dic3—22no—
295C3×Dic3—42no—
296C3×Dic3—42no—
297C22×Q8—61no—
298C2×SD16—32no—
299C2×D8C2×C3×D311yescharacteristic
300C4⋊Q8—32no—
301C4⋊Q8—31no—
302C4⋊Q8—31no—
303#126—62no—
304#124—32no—
305C22⋊Q8—62no—
306C22⋊Q8—61no—
307C22⋊Q8—61no—
308C4×Q8—31no—
309C4×Q8—32no—
310C4×D4—32no—
311C4×D4C2×C3×D311yescharacteristic
312C4×D4C2×C3×D311yescharacteristic
313#117—61no—
314#107—32no—
315#107C2×C3×D311yescharacteristic
316C4⋊C8—32no—
317C4⋊C8—31no—
318#103—32no—
319#103—32no—
320#103—32no—
321#102—32no—
322#102C2×C3×D311yescharacteristic
323#102C2×C3×D311yescharacteristic
324#97—32no—
325C4×C8C2×C3×D311yescharacteristic
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—41no—
331C23×C3—41no—
332C3×Q8—62no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—124no—
336C3×Q8—122no—
337C3×D4—22no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—21no—
341C3×D4—21no—
342C3×D4—21no—
343C3×D4—21no—
344C3×D4—22no—
345C3×D4—41no—
346C3×D4—41no—
347C3×D4#23512yes—
348C3×D4C3×#4112yes—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—82no—
367C2×C3×C4—82no—
368C2×C3×C4—124no—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4C2×C3×D411yescharacteristic
372C2×C3×C4C2×C3×D411yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C24×C311yescharacteristic
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—44no—
378C2×Dic3C2×C3×D412yes—
379C2×Dic3C2×C3×D412yes—
380Dic6—22no—
381Dic6—22no—
382Dic6—22no—
383Dic6—44no—
384Dic6—42no—
385C3×C8—22no—
386C3×C8—21no—
387C3×C8—21no—
388C3×C8—21no—
389C3×C8—21no—
390C3×C8—41no—
391C3×C8—62no—
392C3⋊C8—22no—
393C2×C32—42no—
394C2×C32—81no—
395C2×C32#54811yescharacteristic
396C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
397C2×C32#57811yescharacteristic
398C2×Q8—31no—
399C2×Q8—32no—
400C2×Q8—62no—
401C2×Q8—61no—
402C2×Q8—124no—
403C2×D4C22×C3×D311yescharacteristic
404C2×D4C22×C3×D311yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—62no—
408SD16—64no—
409D8—22no—
410C2×C8—32no—
411C2×C8C22×C3×D311yescharacteristic
412C2×C8C22×C3×D311yescharacteristic
413C4⋊C4—31no—
414C4⋊C4—32no—
415C4⋊C4—32no—
416C4⋊C4—62no—
417C4⋊C4—62no—
418C4⋊C4—61no—
419C4⋊C4—61no—
420C4⋊C4—61no—
421C4⋊C4C22×C3×D311yescharacteristic
422C4⋊C4C22×C3×D311yescharacteristic
423C22⋊C4—21no—
424C22⋊C4—21no—
425C22⋊C4—62no—
426C22⋊C4—62no—
427C22⋊C4—62no—
428C42—32no—
429C42—62no—
430C42C22×C3×D311yescharacteristic
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—81no—
447C22×C3—81no—
448C22×C3—81no—
449C22×C3—81no—
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C22×C3×D411yescharacteristic
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—22no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—41no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4—41no—
462C3×C4—62no—
463C3×C4—62no—
464C3×C4—81no—
465C3×C4—81no—
466C3×C4—122no—
467C3×C4—122no—
468C3×C4#91112yes—
469C3×C4C3×AGL(1,ℤ/8)12yes—
470C3×C4C2×#23511yescharacteristic
471C3×C4#101011yescharacteristic
472C3×C4C2×C3×#4111yescharacteristic
473C3×C4C3×2−1+411yescharacteristic
474Dic3—22no—
475Dic3—22no—
476Dic3—42no—
477Dic3—42no—
478C32#336711yescharacteristic, complemented, Sylow
479C23—21no—
480C23—21no—
481Q8—62no—
482Q8—62no—
483Q8—62no—
484Q8—124no—
485Q8—122no—
486D4—21no—
487D4—21no—
488D4—21no—
489D4C3×#23512yes—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—124no—
499C2×C4C3×D3×D411yescharacteristic
500C2×C4C3×D3×D411yescharacteristic
501C2×C4C23×C3×D311yescharacteristic
502C8—21no—
503C8—21no—
504C8—62no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—42no—
509C2×C3—42no—
510C2×C3—82no—
511C2×C3—82no—
512C2×C3—81no—
513C2×C3—81no—
514C2×C3#555211yescharacteristic
515C2×C3C2×#91111yescharacteristic
516C2×C3#577111yescharacteristic
517C2×C3C3×#54811yescharacteristic
518C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
519C2×C3C3×#57811yescharacteristic
520C22—22no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C2×C3×D3×D411yescharacteristic
527C4—21no—
528C4—41no—
529C4—41no—
530C4—62no—
531C4—62no—
532C4—122no—
533C4—122no—
534C4C3×#91112yes—
535C4C2×C3×#23511yescharacteristic
536C4C3×#101011yescharacteristic
537C3—21no—
538C3#7957111yescharacteristic, direct product factor
539C3C3×#336711yescharacteristic, complemented
540C2—42no—
541C2—81no—
542C2C3×#555211yescharacteristic
543C2C2×C3×#91111yescharacteristic
544C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
prime radicalC2×C32×D8C22
hypercenterC3×C4×D8D3
hypocenterC3C3×#3367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5542C2semidirect
2. C3×D4×Dic6C2semidirect
5. C3×#5019C2semidirect
6. C3×#5007C2semidirect
7. C3×#4875C2semidirect
8. C3×#4765C2semidirect
9. C3×#4757C2semidirect
10. C3×#4681C2semidirect
11. C3×#4679C2semidirect
13. #79571C3direct (N × H)
45. #5542C2×C3semidirect
46. D4×Dic6C2×C3semidirect
59. #5019C2×C3semidirect
60. #5007C2×C3semidirect
61. #4875C2×C3semidirect
62. #4765C2×C3semidirect
63. #4757C2×C3semidirect
64. #4681C2×C3semidirect
65. #4679C2×C3semidirect
478. C32#3367semidirect
538. C3#79571direct (N × H)
539. C3C3×#3367semidirect

Maximal subgroups

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

subgroupindex
C3×#55422
C3×D4×Dic62
C32×C4×D82
C3×#51532
C3×#50192
C3×#50072
C3×#48752
C3×#47652
C3×#47572
C3×#46812
C3×#46792
C3×#33673
#795713