Finite Group Databasebeta

← C3×#83677 #11896014

Subgroups — C3×#83677 #11896014

Order 1152.

782 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#556C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C3×#5090C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5C3×#5055C212yesmaximal
6C3×#5054C212yesmaximal
7C3×#5030C212yesmaximal, complemented
8C3×#5024C211yesmaximal, characteristic, complemented
9C3×#5020C212yesmaximal, complemented
10C3×C4×#214C211yesmaximal, characteristic
11C3×#5008C211yesmaximal, characteristic
12C3×#3369—31nomaximal
13#83677C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×#126—22no—
16C32×#124C2212yes—
17C32×C22⋊Q8—21no—
18C32×C4×Q8C2212yes—
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×#117—21no—
22C3×Q8×Dic3—21no—
23C2×C3×#216C2212yes—
24C2×C3×#214C2211yescharacteristic
25C3×#888—21no—
26C3×#888—22no—
27C3×#869C2211yescharacteristic
28C3×#869C2212yes—
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2212yes—
31C3×#835C2212yes—
32C3×#835C2212yes—
33C3×#835C2212yes—
34C3×#832C2212yes—
35C3×#832C2211yescharacteristic
36C3×#810C2211yescharacteristic
37C3×#808C2212yes—
38C3×#808C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40C3×C4⋊(C3⋊C8)C2212yes—
41C3×#803C2212yes—
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×Q82—31no—
44C3×#556—21no—
45C3×#556D311yescharacteristic
46C3×#556C2×C311yescharacteristic
47Q8×Dic6C2×C311yescharacteristic, complemented
48C3×#489—32no—
49C3×#487—31no—
50C3×#476—31no—
51C3×#475—32no—
52C3×#464—32no—
53C3×#462—31no—
54C3×#446—31no—
55C3×#441—32no—
56C3×C4×SD16—31no—
57#5090C2×C311yescharacteristic, complemented
58#5079C2×C311yescharacteristic, complemented
59#5055C2×C312yes—
60#5054C2×C312yes—
61#5030C2×C312yescomplemented
62#5024C2×C311yescharacteristic, complemented
63#5020C2×C312yescomplemented
64C4×#214C2×C311yescharacteristic
65#5008C2×C311yescharacteristic
66C2×C32×Q8D411yescharacteristic
67C2×C32×Q8C2312yes—
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6C2311yescharacteristic
73C32×C4⋊C4—21no—
74C32×C4⋊C4—22no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4D411yescharacteristic
77C32×C4⋊C4D412yes—
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—22no—
80C32×C22⋊C4—21no—
81C32×C22⋊C4—22no—
82C32×C42—22no—
83C32×C42C2311yescharacteristic
84C32×C42C2312yes—
85C3×#216—24no—
86C3×#214—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—21no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3—21no—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98#3369—31noSylow
99C2×C3×Q16—32no—
100C2×C3×SD16—31no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—32no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—61no—
105C3×C4⋊Q8—62no—
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C22×C311yescharacteristic
108C3×#126—24no—
109C3×#126—22no—
110C3×#126—22no—
111C3×#124—22no—
112C3×#124C2×D312yes—
113C3×#124C22×C312yes—
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8—21no—
116C3×C22⋊Q8—21no—
117C3×C4×Q8—22no—
118C3×C4×Q8—21no—
119C3×C4×Q8—31no—
120C3×C4×Q8—32no—
121C3×C4×Q8—61no—
122C3×C4×Q8C2×D312yes—
123C3×C4×Q8C2×D311yescharacteristic
124C3×C4×Q8C22×C312yes—
125C3×C4×Q8C22×C311yescharacteristic
126C3×C4×D4—21no—
127C3×C4×D4C2×D311yescharacteristic
128C3×C4×D4C22×C311yescharacteristic
129C3×#117—22no—
130C3×#117—21no—
131C3×#117—21no—
132Q8×Dic3—21no—
133C2×#216C22×C312yes—
134C2×#214C22×C311yescharacteristic
135#888—21no—
136#888—22no—
137#869C22×C311yescharacteristic
138#869C22×C312yes—
139C4×Dic6C22×C311yescharacteristic
140C4×Dic6C22×C312yes—
141C3×#106—31no—
142C3×#106—32no—
143C3×C4⋊C8—31no—
144C3×C4⋊C8—32no—
145C3×#103—32no—
146C3×#103—32no—
147C3×#103—32no—
148C3×#103—31no—
149C3×#102—31no—
150C3×#102—32no—
151C3×#97—32no—
152C3×C4×C8—31no—
153#835C22×C312yes—
154#835C22×C312yes—
155#835C22×C312yes—
156#832C22×C312yes—
157#832C22×C311yescharacteristic
158#810C22×C311yescharacteristic
159#808C22×C312yes—
160#808C22×C311yescharacteristic
161C4⋊(C3⋊C8)C22×C311yescharacteristic
162C4⋊(C3⋊C8)C22×C312yes—
163#803C22×C312yes—
164C4×C3⋊C8C22×C311yescharacteristic
165C23×C32—21no—
166C32×Q8—22no—
167C32×Q8—22no—
168C32×Q8—22no—
169C32×D4—21no—
170C32×D4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—22no—
173C2×C32×C4—42no—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C3×Dic6—21no—
183C3×Dic6—82no—
184C3×Dic6—81no—
185C3×Dic6#4112yes—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—21no—
189Q82—31no—
190#556C3×D311yescharacteristic
191#489—32no—
192#487—31no—
193#476—31no—
194#475—32no—
195#464—32no—
196#462—31no—
197#446—31no—
198#441—32no—
199C4×SD16—31no—
200C2×C3×Q8—21no—
201C2×C3×Q8—22no—
202C2×C3×Q8—31no—
203C2×C3×Q8—62no—
204C2×C3×Q8—61no—
205C2×C3×Q8#6711yescharacteristic
206C2×C3×Q8C3×D411yescharacteristic
207C2×C3×Q8C22×D312yes—
208C2×C3×Q8C23×C312yes—
209C2×C3×D4—21no—
210C2×C3×D4C22×D311yescharacteristic
211C2×C3×D4C23×C311yescharacteristic
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C2×Dic6—22no—
216C2×Dic6—21no—
217C2×Dic6C23×C311yescharacteristic
218C3×Q16—64no—
219C3×SD16—62no—
220C2×C3×C8—31no—
221C2×C3×C8—31no—
222C2×C3×C8—32no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—24no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4#6711yescharacteristic
242C3×C4⋊C4#6712yes—
243C3×C4⋊C4C3×D411yescharacteristic
244C3×C4⋊C4C3×D412yes—
245C3×C4⋊C4C22×D311yescharacteristic
246C3×C4⋊C4C23×C311yescharacteristic
247C3×C22⋊C4—24no—
248C3×C22⋊C4—22no—
249C3×C22⋊C4—24no—
250C3×C22⋊C4—22no—
251C3×C22⋊C4—21no—
252C3×C22⋊C4—22no—
253C3×C22⋊C4—22no—
254C3×C22⋊C4—21no—
255C3×C22⋊C4—22no—
256C3×C42—24no—
257C3×C42—22no—
258C3×C42—22no—
259C3×C42—21no—
260C3×C42—22no—
261C3×C42—62no—
262C3×C42—61no—
263C3×C42C22×D311yescharacteristic
264C3×C42C22×D312yes—
265C3×C42C23×C311yescharacteristic
266C3×C42C23×C312yes—
267#216—24no—
268#214—22no—
269C4⋊Dic3—22no—
270C4⋊Dic3—21no—
271C4⋊Dic3C23×C312yes—
272C4⋊Dic3C23×C311yescharacteristic
273Dic3⋊C4—22no—
274Dic3⋊C4—21no—
275C4×Dic3—22no—
276C4×Dic3—21no—
277C2×C3⋊C8C23×C311yescharacteristic
278C2×C3⋊C8C23×C311yescharacteristic
279C2×C3⋊C8C23×C312yes—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32C22×D411yescharacteristic
284C32×C4—22no—
285C32×C4—22no—
286C32×C4—21no—
287C32×C4—42no—
288C32×C4—41no—
289C32×C4#13712yes—
290C32×C4C2×#4111yescharacteristic
291C32×C42−1+411yescharacteristic
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C2×Q16—32no—
296C2×SD16—31no—
297C4⋊Q8—32no—
298C4⋊Q8—31no—
299C4⋊Q8—61no—
300C4⋊Q8—62no—
301C4⋊Q8C2×C3×D311yescharacteristic
302#126—22no—
303#124C2×C3×D312yes—
304C22⋊Q8—21no—
305C4×Q8—31no—
306C4×Q8—32no—
307C4×Q8—61no—
308C4×Q8C2×C3×D312yes—
309C4×Q8C2×C3×D311yescharacteristic
310C4×D4C2×C3×D311yescharacteristic
311#117—21no—
312#106—31no—
313#106—32no—
314C4⋊C8—31no—
315C4⋊C8—32no—
316#103—32no—
317#103—32no—
318#103—32no—
319#103—31no—
320#102—31no—
321#102—32no—
322#97—32no—
323C4×C8—31no—
324C23×C3—22no—
325C23×C3—21no—
326C23×C3—21no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8—22no—
333C3×Q8—32no—
334C3×Q8—42no—
335C3×Q8—42no—
336C3×Q8—42no—
337C3×Q8—61no—
338C3×Q8—242no—
339C3×Q8—241no—
340C3×D4—21no—
341C3×D4—21no—
342C3×D4—21no—
343C3×D4—21no—
344C3×D4—41no—
345C3×D4—41no—
346C2×C3×C4—22no—
347C2×C3×C4—24no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—44no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—61no—
361C2×C3×C4—62no—
362C2×C3×C4—61no—
363C2×C3×C4C2×#6712yes—
364C2×C3×C4C2×#6712yes—
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×C3×D412yes—
368C2×C3×C4C2×C3×D412yes—
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C2×C3×D411yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C24×C311yescharacteristic
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—21no—
376Dic6—21no—
377Dic6—82no—
378Dic6—81no—
379Dic6C3×#4112yes—
380C3×C8—61no—
381C3×C8—62no—
382C3×C8—61no—
383C3⋊C8—21no—
384C3⋊C8—22no—
385C3⋊C8—21no—
386C2×C32—81no—
387C2×C32#54811yescharacteristic
388C2×C32C2×#13711yescharacteristic
389C2×C32#57711yescharacteristic
390C2×Q8—31no—
391C2×Q8—62no—
392C2×Q8—61no—
393C2×Q8C3×#6711yescharacteristic
394C2×Q8C22×C3×D312yes—
395C2×D4C22×C3×D311yescharacteristic
396C22×C4—21no—
397Q16—64no—
398SD16—62no—
399C2×C8—31no—
400C2×C8—31no—
401C2×C8—32no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—62no—
408C4⋊C4—61no—
409C4⋊C4—62no—
410C4⋊C4—61no—
411C4⋊C4C3×#6711yescharacteristic
412C4⋊C4C3×#6712yes—
413C4⋊C4C22×C3×D311yescharacteristic
414C22⋊C4—22no—
415C22⋊C4—21no—
416C22⋊C4—22no—
417C42—22no—
418C42—62no—
419C42—61no—
420C42C22×C3×D311yescharacteristic
421C42C22×C3×D312yes—
422C22×C3—21no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3C22×#6711yescharacteristic
433C22×C3C22×C3×D411yescharacteristic
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—41no—
446C3×C4—42no—
447C3×C4—44no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—42no—
451C3×C4—42no—
452C3×C4—62no—
453C3×C4—122no—
454C3×C4—121no—
455C3×C4#95112yes—
456C3×C4C3×#13712yes—
457C3×C4D3×#4111yescharacteristic
458C3×C4#101011yescharacteristic
459C3×C4C2×C3×#4111yescharacteristic
460C3×C4C3×2−1+411yescharacteristic
461Dic3—22no—
462Dic3—41no—
463Dic3—42no—
464C32#336911yescharacteristic, complemented, Sylow
465C23—21no—
466Q8—22no—
467Q8—22no—
468Q8—22no—
469Q8—32no—
470Q8—61no—
471Q8—242no—
472Q8—241no—
473D4—21no—
474D4—21no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—42no—
478C2×C4—61no—
479C2×C4—62no—
480C2×C4—61no—
481C2×C4C2×C3×#6712yes—
482C2×C4C2×C3×#6712yes—
483C2×C4C2×C3×#6711yescharacteristic
484C2×C4C2×C3×#6711yescharacteristic
485C2×C4C23×C3×D311yescharacteristic
486C8—61no—
487C8—62no—
488C8—61no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—82no—
493C2×C3—81no—
494C2×C3—81no—
495C2×C3C2×#95111yescharacteristic
496C2×C3#583111yescharacteristic
497C2×C3#583711yescharacteristic
498C2×C3C3×#54811yescharacteristic
499C2×C3C2×C3×#13711yescharacteristic
500C2×C3C3×#57711yescharacteristic
501C22—41no—
502C22—41no—
503C22—41no—
504C22C22×C3×#6711yescharacteristic
505C4—22no—
506C4—22no—
507C4—21no—
508C4—41no—
509C4—42no—
510C4—62no—
511C4—122no—
512C4—121no—
513C4C3×#95112yes—
514C4C3×D3×#4111yescharacteristic
515C4C3×#101011yescharacteristic
516C3—21no—
517C3#8367711yescharacteristic, direct product factor
518C3C3×#336911yescharacteristic, complemented
519C2—81no—
520C2C2×C3×#95111yescharacteristic
521C2C3×#583111yescharacteristic
522C2C3×#583711yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#556C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×#556D3
hypocenterC3C3×#3369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#556

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. C3×#5090C2semidirect
4. C3×#5079C2semidirect
7. C3×#5030C2semidirect
8. C3×#5024C2semidirect
9. C3×#5020C2semidirect
13. #83677C3direct (N × H)
47. Q8×Dic6C2×C3semidirect
57. #5090C2×C3semidirect
58. #5079C2×C3semidirect
61. #5030C2×C3semidirect
62. #5024C2×C3semidirect
63. #5020C2×C3semidirect
464. C32#3369semidirect
517. C3#83677direct (N × H)
518. C3C3×#3369semidirect

Maximal subgroups

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

subgroupindex
C32×#5562
C3×Q8×Dic62
C3×#50902
C3×#50792
C3×#50552
C3×#50542
C3×#50302
C3×#50242
C3×#50202
C3×C4×#2142
C3×#50082
C3×#33693
#836773