Finite Group Databasebeta

← C3×#79568 #11895204

Subgroups — C3×#79568 #11895204

Order 1152.

767 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5543C211yesmaximal, characteristic, complemented
2C3×#5542C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic
4C3×#5153C212yesmaximal
5C3×#5019C211yesmaximal, characteristic, complemented
6C3×#5008C211yesmaximal, characteristic, complemented
7C3×#4877C212yesmaximal, complemented
8C3×#4768C212yesmaximal, complemented
9C3×#4758C212yesmaximal, complemented
10C3×#4681C211yesmaximal, characteristic, complemented
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3360—31nomaximal
13#79568C311yesmaximal, characteristic, direct product factor
14C2×C32×D8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#936C2212yes—
18C3×D4×Dic3C2212yes—
19C2×C3×#214C2212yes—
20C3×#926—21no—
21C2×C3×C4⋊Dic3—21no—
22C3×#924—21no—
23C3×#924—21no—
24C3×#890C2212yes—
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×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#810C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#556—31no—
44C3×#554—31no—
45#5543C2×C311yescharacteristic, complemented
46#5542C2×C311yescharacteristic, complemented
47C3×#488—32no—
48C3×#487—31no—
49C3×#479—32no—
50C3×#476—31no—
51C3×#463—32no—
52C3×#461—31no—
53C3×C8×Q8—31no—
54C3×C4×SD16—32no—
55C3×C4×D8—21no—
56C3×C4×D8D311yescharacteristic
57C3×C4×D8C2×C311yescharacteristic
58#5153C2×C312yes—
59#5019C2×C311yescharacteristic, complemented
60#5008C2×C311yescharacteristic, complemented
61#4877C2×C312yescomplemented
62#4768C2×C312yescomplemented
63#4758C2×C312yescomplemented
64#4681C2×C311yescharacteristic, complemented
65C8×Dic6C2×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×Dic6D411yescharacteristic
73C2×C3×Dic6C2312yes—
74C32×D8—22no—
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C4⋊C4C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C22⋊C4—21no—
81C32×C42C2311yescharacteristic
82C3×#217—22no—
83C3×#217—22no—
84C3×#217—22no—
85C3×#214—24no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2312yes—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98#3360—31noSylow
99C2×C3×SD16—32no—
100C2×C3×D8—21no—
101C2×C3×D8C2×D311yescharacteristic
102C2×C3×D8C22×C311yescharacteristic
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—31no—
105C3×#126—62no—
106C3×#125—32no—
107C3×#124—32no—
108C3×C22⋊Q8—62no—
109C3×C22⋊Q8—61no—
110C3×C22⋊Q8—61no—
111C3×C4×Q8—31no—
112C3×C4×Q8—32no—
113C3×C4×D4—21no—
114C3×C4×D4—21no—
115C3×C4×D4—32no—
116C3×C4×D4C2×D311yescharacteristic
117C3×C4×D4C2×D311yescharacteristic
118C3×C4×D4C22×C311yescharacteristic
119C3×C4×D4C22×C311yescharacteristic
120C3×#117—61no—
121C2×C3×C4⋊C4—61no—
122#936C22×C312yes—
123D4×Dic3C22×C312yes—
124C2×#214C22×C312yes—
125#926—21no—
126C2×C4⋊Dic3—21no—
127#924—21no—
128#924—21no—
129#890C22×C312yes—
130#887C22×C312yes—
131#879—22no—
132#878—22no—
133#869C22×C311yescharacteristic
134#869C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#107—21no—
137C3×#107C2×D311yescharacteristic
138C3×#107C22×C311yescharacteristic
139C3×#106—32no—
140C3×C4⋊C8—32no—
141C3×C4⋊C8—31no—
142C3×#103—32no—
143C3×#103—32no—
144C3×#103—32no—
145C3×#102—21no—
146C3×#102—21no—
147C3×#102—32no—
148C3×#102C2×D311yescharacteristic
149C3×#102C2×D311yescharacteristic
150C3×#102C22×C311yescharacteristic
151C3×#102C22×C311yescharacteristic
152C3×C4×C8—21no—
153C3×C4×C8—32no—
154C3×C4×C8C2×D311yescharacteristic
155C3×C4×C8C22×C311yescharacteristic
156#832C22×C312yes—
157#816C22×C312yes—
158#816C22×C312yes—
159Dic3⋊C8C22×C312yes—
160C8×Dic3C22×C312yes—
161#810C22×C312yes—
162#808C22×C312yes—
163C4⋊(C3⋊C8)C22×C311yescharacteristic
164C23×C32—21no—
165C23×C32—21no—
166C32×D4—21no—
167C32×D4—21no—
168C32×D4—21no—
169C32×D4#4112yes—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—42no—
173C2×C32×C4—42no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—82no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—81no—
186C32×C8—21no—
187C32×C8—21no—
188C3×C3⋊C8—22no—
189#556—31no—
190#554—31no—
191#488—32no—
192#487—31no—
193#479—32no—
194#476—31no—
195#463—32no—
196#461—31no—
197C8×Q8—31no—
198C4×SD16—32no—
199C4×D8C3×D311yescharacteristic
200C2×C3×Q8—31no—
201C2×C3×Q8—32no—
202C2×C3×Q8—61no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4C22×D311yescharacteristic
206C2×C3×D4C22×D311yescharacteristic
207C2×C3×D4C23×C311yescharacteristic
208C2×C3×D4C23×C311yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—41no—
214C22×C3×C4—41no—
215C22×C3×C4—62no—
216C22×Dic3—22no—
217C2×Dic6—21no—
218C2×Dic6C3×D411yescharacteristic
219C2×Dic6C23×C312yes—
220C3×SD16—64no—
221C3×D8—24no—
222C3×D8—22no—
223C3×D8—22no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—32no—
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C23×C311yescharacteristic
230C2×C3×C8C23×C311yescharacteristic
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C4⋊C4C23×C311yescharacteristic
245C3×C4⋊C4C23×C311yescharacteristic
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4—21no—
249C3×C22⋊C4—21no—
250C3×C22⋊C4—41no—
251C3×C22⋊C4—41no—
252C3×C22⋊C4—62no—
253C3×C22⋊C4—62no—
254C3×C22⋊C4—62no—
255C3×C42—21no—
256C3×C42—32no—
257C3×C42—62no—
258C3×C42C22×D311yescharacteristic
259C3×C42C23×C311yescharacteristic
260#217—22no—
261#217—22no—
262#217—22no—
263#214—24no—
264C4⋊Dic3—21no—
265C4⋊Dic3—21no—
266C4⋊Dic3—21no—
267C4⋊Dic3—22no—
268C4⋊Dic3C3×D411yescharacteristic
269C4⋊Dic3C23×C312yes—
270Dic3⋊C4—22no—
271Dic3⋊C4—22no—
272Dic3⋊C4C3×D412yes—
273C4×Dic3—22no—
274C4×Dic3C23×C312yes—
275C2×C3⋊C8C23×C312yes—
276C22×C32—22no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C32×C4—21no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4#13512yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C2×SD16—32no—
294C2×D8C2×C3×D311yescharacteristic
295C4⋊Q8—31no—
296C4⋊Q8—31no—
297#126—62no—
298#125—32no—
299#124—32no—
300C22⋊Q8—62no—
301C22⋊Q8—61no—
302C22⋊Q8—61no—
303C4×Q8—31no—
304C4×Q8—32no—
305C4×D4—32no—
306C4×D4C2×C3×D311yescharacteristic
307C4×D4C2×C3×D311yescharacteristic
308#117—61no—
309C2×C4⋊C4—61no—
310#107C2×C3×D311yescharacteristic
311#106—32no—
312C4⋊C8—32no—
313C4⋊C8—31no—
314#103—32no—
315#103—32no—
316#103—32no—
317#102—32no—
318#102C2×C3×D311yescharacteristic
319#102C2×C3×D311yescharacteristic
320C4×C8—32no—
321C4×C8C2×C3×D311yescharacteristic
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—41no—
327C23×C3—41no—
328C3×Q8—62no—
329C3×Q8—62no—
330C3×Q8—62no—
331C3×Q8—241no—
332C3×D4—22no—
333C3×D4—21no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—22no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4#23512yes—
343C3×D4C3×#4112yes—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—82no—
362C2×C3×C4—82no—
363C2×C3×C4—242no—
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C24×C311yescharacteristic
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—82no—
373C2×Dic3C2×C3×D412yes—
374C2×Dic3C2×C3×D412yes—
375Dic6—22no—
376Dic6—22no—
377Dic6—22no—
378Dic6—81no—
379C3×C8—22no—
380C3×C8—21no—
381C3×C8—21no—
382C3×C8—21no—
383C3×C8—21no—
384C3×C8—41no—
385C3×C8—62no—
386C3⋊C8—22no—
387C2×C32—42no—
388C2×C32—81no—
389C2×C32#54811yescharacteristic
390C2×C32C2×#13511yescharacteristic
391C2×C32#57711yescharacteristic
392C2×Q8—31no—
393C2×Q8—32no—
394C2×Q8—61no—
395C2×D4C22×C3×D311yescharacteristic
396C2×D4C22×C3×D311yescharacteristic
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—62no—
400SD16—64no—
401D8—22no—
402C2×C8—32no—
403C2×C8C22×C3×D311yescharacteristic
404C2×C8C22×C3×D311yescharacteristic
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—32no—
408C4⋊C4—62no—
409C4⋊C4—62no—
410C4⋊C4—62no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C4⋊C4C22×C3×D311yescharacteristic
415C4⋊C4C22×C3×D311yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—62no—
419C22⋊C4—62no—
420C22⋊C4—62no—
421C42—32no—
422C42—62no—
423C42C22×C3×D311yescharacteristic
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—81no—
440C22×C3—81no—
441C22×C3—81no—
442C22×C3—81no—
443C22×C3C2×D3×D411yescharacteristic
444C22×C3C22×C3×D411yescharacteristic
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—41no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—81no—
458C3×C4—81no—
459C3×C4—122no—
460C3×C4—122no—
461C3×C4#91212yes—
462C3×C4C3×#13512yes—
463C3×C4C2×#23511yescharacteristic
464C3×C4#101011yescharacteristic
465C3×C4C2×C3×#4111yescharacteristic
466C3×C4C3×2−1+411yescharacteristic
467Dic3—22no—
468Dic3—22no—
469Dic3—42no—
470Dic3—42no—
471C32#336011yescharacteristic, complemented, Sylow
472C23—21no—
473C23—21no—
474Q8—62no—
475Q8—62no—
476Q8—62no—
477Q8—241no—
478D4—21no—
479D4—21no—
480D4—21no—
481D4C3×#23512yes—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—242no—
491C2×C4C3×D3×D411yescharacteristic
492C2×C4C3×D3×D411yescharacteristic
493C2×C4C23×C3×D311yescharacteristic
494C8—21no—
495C8—21no—
496C8—62no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—42no—
501C2×C3—42no—
502C2×C3—82no—
503C2×C3—82no—
504C2×C3—81no—
505C2×C3—81no—
506C2×C3#555211yescharacteristic
507C2×C3C2×#91211yescharacteristic
508C2×C3#577011yescharacteristic
509C2×C3C3×#54811yescharacteristic
510C2×C3C2×C3×#13511yescharacteristic
511C2×C3C3×#57711yescharacteristic
512C22—22no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22C2×C3×D3×D411yescharacteristic
519C4—21no—
520C4—41no—
521C4—41no—
522C4—62no—
523C4—62no—
524C4—122no—
525C4—122no—
526C4C3×#91212yes—
527C4C2×C3×#23511yescharacteristic
528C4C3×#101011yescharacteristic
529C3—21no—
530C3#7956811yescharacteristic, direct product factor
531C3C3×#336011yescharacteristic, complemented
532C2—42no—
533C2—81no—
534C2C3×#555211yescharacteristic
535C2C2×C3×#91211yescharacteristic
536C2C3×#577011yescharacteristic
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×#3360
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×#5543C2semidirect
2. C3×#5542C2semidirect
5. C3×#5019C2semidirect
6. C3×#5008C2semidirect
7. C3×#4877C2semidirect
8. C3×#4768C2semidirect
9. C3×#4758C2semidirect
10. C3×#4681C2semidirect
11. C3×C8×Dic6C2semidirect
13. #79568C3direct (N × H)
45. #5543C2×C3semidirect
46. #5542C2×C3semidirect
59. #5019C2×C3semidirect
60. #5008C2×C3semidirect
61. #4877C2×C3semidirect
62. #4768C2×C3semidirect
63. #4758C2×C3semidirect
64. #4681C2×C3semidirect
65. C8×Dic6C2×C3semidirect
471. C32#3360semidirect
530. C3#79568direct (N × H)
531. C3C3×#3360semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
C3×#55422
C32×C4×D82
C3×#51532
C3×#50192
C3×#50082
C3×#48772
C3×#47682
C3×#47582
C3×#46812
C3×C8×Dic62
C3×#33603
#795683