Finite Group Databasebeta

← C3×#83676 #11895509

Subgroups — C3×#83676 #11895509

Order 1152.

778 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#556C211yesmaximal, characteristic
2C3×#5567C211yesmaximal, characteristic, complemented
3C3×#5090C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5C3×#5056C212yesmaximal
6C3×#5054C212yesmaximal
7C3×C4×#216C212yesmaximal, complemented
8C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
9C3×#5022C212yesmaximal, complemented
10C3×C4×#214C211yesmaximal, characteristic
11C3×#5007C211yesmaximal, characteristic
12C3×#3364—31nomaximal
13#83676C311yesmaximal, 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×#944—21no—
23C2×C3×#216C2212yes—
24C2×C3×#214C2211yescharacteristic
25C3×#889—22no—
26C3×#887—21no—
27C3×#870C2212yes—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2212yes—
31C3×#835C2212yes—
32C3×#835C2212yes—
33C3×#835C2212yes—
34C3×#832C2212yes—
35C3×#832C2211yescharacteristic
36C3×#810C2211yescharacteristic
37C3×#808C2211yescharacteristic
38C3×#807C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40C3×C4⋊(C3⋊C8)C2212yes—
41C3×C4×C3⋊C8C2211yescharacteristic
42C3×C4×C3⋊C8C2212yes—
43C3×#557—31no—
44C3×#556—21no—
45C3×#556D311yescharacteristic
46C3×#556C2×C311yescharacteristic
47#5567C2×C311yescharacteristic, complemented
48C3×#488—32no—
49C3×#487—31no—
50C3×#479—32no—
51C3×#474—31no—
52C3×#464—32no—
53C3×#462—31no—
54C3×C8×Q8—31no—
55C3×C4×Q16—32no—
56C3×C4×SD16—31no—
57#5090C2×C311yescharacteristic, complemented
58#5079C2×C311yescharacteristic, complemented
59#5056C2×C312yes—
60#5054C2×C312yes—
61C4×#216C2×C312yescomplemented
62Q8×C3⋊C8C2×C311yescharacteristic, complemented
63#5022C2×C312yescomplemented
64C4×#214C2×C311yescharacteristic
65#5007C2×C311yescharacteristic
66C2×C32×Q8D411yescharacteristic
67C2×C32×Q8C2312yes—
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2311yescharacteristic
72C32×C4⋊C4—21no—
73C32×C4⋊C4—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4D411yescharacteristic
76C32×C4⋊C4D412yes—
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—22no—
79C32×C22⋊C4—21no—
80C32×C22⋊C4—22no—
81C32×C42—22no—
82C32×C42C2311yescharacteristic
83C32×C42C2312yes—
84C3×#216—24no—
85C3×#214—22no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—21no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3—21no—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98#3364—31noSylow
99C2×C3×Q16—32no—
100C2×C3×SD16—31no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—61no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C22×C311yescharacteristic
106C3×#126—24no—
107C3×#126—22no—
108C3×#126—22no—
109C3×#125—32no—
110C3×#125—62no—
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—
132#944—21no—
133C2×#216C22×C312yes—
134C2×#214C22×C311yescharacteristic
135#889—22no—
136#887—21no—
137#870C22×C312yes—
138#869C22×C311yescharacteristic
139C4×Dic6C22×C311yescharacteristic
140C4×Dic6C22×C312yes—
141C3×#107—32no—
142C3×#106—31no—
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×C4×C8—31no—
152C3×C4×C8—32no—
153#835C22×C312yes—
154#835C22×C312yes—
155#835C22×C312yes—
156#832C22×C312yes—
157#832C22×C311yescharacteristic
158#810C22×C311yescharacteristic
159#808C22×C311yescharacteristic
160#807C22×C312yes—
161C4⋊(C3⋊C8)C22×C311yescharacteristic
162C4⋊(C3⋊C8)C22×C312yes—
163C4×C3⋊C8C22×C311yescharacteristic
164C4×C3⋊C8C22×C312yes—
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—21no—
181C2×C3×Dic3—22no—
182C3×Dic6—21no—
183C3×Dic6—42no—
184C3×Dic6#4112yes—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—22no—
187C3×C3⋊C8—21no—
188#557—31no—
189#556C3×D311yescharacteristic
190#488—32no—
191#487—31no—
192#479—32no—
193#474—31no—
194#464—32no—
195#462—31no—
196C8×Q8—31no—
197C4×Q16—32no—
198C4×SD16—31no—
199C2×C3×Q8—21no—
200C2×C3×Q8—22no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×Q8#6711yescharacteristic
204C2×C3×Q8C3×D411yescharacteristic
205C2×C3×Q8C22×D312yes—
206C2×C3×Q8C23×C312yes—
207C2×C3×D4—21no—
208C2×C3×D4C22×D311yescharacteristic
209C2×C3×D4C23×C311yescharacteristic
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C2×Dic6—21no—
214C2×Dic6C23×C311yescharacteristic
215C3×Q16—64no—
216C3×SD16—62no—
217C2×C3×C8—31no—
218C2×C3×C8—32no—
219C2×C3×C8—31no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—24no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—21no—
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—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4#6711yescharacteristic
240C3×C4⋊C4#6712yes—
241C3×C4⋊C4C3×D411yescharacteristic
242C3×C4⋊C4C3×D412yes—
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C4⋊C4C23×C311yescharacteristic
245C3×C22⋊C4—24no—
246C3×C22⋊C4—22no—
247C3×C22⋊C4—24no—
248C3×C22⋊C4—22no—
249C3×C22⋊C4—21no—
250C3×C22⋊C4—22no—
251C3×C22⋊C4—22no—
252C3×C22⋊C4—21no—
253C3×C22⋊C4—22no—
254C3×C42—24no—
255C3×C42—22no—
256C3×C42—22no—
257C3×C42—21no—
258C3×C42—22no—
259C3×C42—62no—
260C3×C42—61no—
261C3×C42C22×D311yescharacteristic
262C3×C42C22×D312yes—
263C3×C42C23×C311yescharacteristic
264C3×C42C23×C312yes—
265#216—24no—
266#214—22no—
267C4⋊Dic3—21no—
268C4⋊Dic3C23×C312yes—
269C4⋊Dic3C23×C311yescharacteristic
270Dic3⋊C4—21no—
271Dic3⋊C4—22no—
272Dic3⋊C4—22no—
273Dic3⋊C4—22no—
274C4×Dic3—22no—
275C4×Dic3—21no—
276C2×C3⋊C8C23×C311yescharacteristic
277C2×C3⋊C8C23×C312yes—
278C2×C3⋊C8C23×C311yescharacteristic
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C32×C4—22no—
284C32×C4—22no—
285C32×C4—21no—
286C32×C4—42no—
287C32×C4—41no—
288C32×C4#13512yes—
289C32×C4C2×#4111yescharacteristic
290C32×C42−1+411yescharacteristic
291C3×Dic3—22no—
292C3×Dic3—42no—
293C3×Dic3—41no—
294C2×Q16—32no—
295C2×SD16—31no—
296C4⋊Q8—31no—
297C4⋊Q8—61no—
298C4⋊Q8C2×C3×D311yescharacteristic
299#126—22no—
300#125—32no—
301#125—62no—
302#124C2×C3×D312yes—
303C22⋊Q8—21no—
304C4×Q8—31no—
305C4×Q8—32no—
306C4×Q8—61no—
307C4×Q8C2×C3×D312yes—
308C4×Q8C2×C3×D311yescharacteristic
309C4×D4C2×C3×D311yescharacteristic
310#117—21no—
311#107—32no—
312#106—31no—
313C4⋊C8—31no—
314C4⋊C8—32no—
315#103—32no—
316#103—32no—
317#103—32no—
318#103—31no—
319#102—31no—
320#102—32no—
321C4×C8—31no—
322C4×C8—32no—
323C23×C3—22no—
324C23×C3—21no—
325C23×C3—21no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8—32no—
333C3×Q8—42no—
334C3×Q8—42no—
335C3×Q8—42no—
336C3×Q8—61no—
337C3×Q8—122no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—21no—
341C3×D4—21no—
342C3×D4—41no—
343C3×D4—41no—
344C2×C3×C4—22no—
345C2×C3×C4—24no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—44no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4C2×#6712yes—
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6712yes—
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×C3×D412yes—
366C2×C3×C4C2×C3×D412yes—
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C24×C311yescharacteristic
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—22no—
374Dic6—21no—
375Dic6—42no—
376Dic6C3×#4112yes—
377C3×C8—61no—
378C3×C8—62no—
379C3×C8—61no—
380C3⋊C8—21no—
381C3⋊C8—22no—
382C3⋊C8—21no—
383C2×C32—81no—
384C2×C32#54811yescharacteristic
385C2×C32C2×#13511yescharacteristic
386C2×C32#57811yescharacteristic
387C2×Q8—31no—
388C2×Q8—61no—
389C2×Q8C3×#6711yescharacteristic
390C2×Q8C22×C3×D312yes—
391C2×D4C22×C3×D311yescharacteristic
392C22×C4—21no—
393Q16—64no—
394SD16—62no—
395C2×C8—31no—
396C2×C8—32no—
397C2×C8—31no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—61no—
404C4⋊C4—62no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—61no—
408C4⋊C4C3×#6711yescharacteristic
409C4⋊C4C3×#6712yes—
410C4⋊C4C22×C3×D311yescharacteristic
411C22⋊C4—22no—
412C22⋊C4—21no—
413C22⋊C4—22no—
414C42—22no—
415C42—62no—
416C42—61no—
417C42C22×C3×D311yescharacteristic
418C42C22×C3×D312yes—
419C22×C3—21no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3C22×#6711yescharacteristic
430C22×C3C22×C3×D411yescharacteristic
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—42no—
441C3×C4—42no—
442C3×C4—41no—
443C3×C4—42no—
444C3×C4—44no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—62no—
450C3×C4—122no—
451C3×C4—121no—
452C3×C4#95012yes—
453C3×C4C3×#13512yes—
454C3×C4D3×#4111yescharacteristic
455C3×C4#101011yescharacteristic
456C3×C4C2×C3×#4111yescharacteristic
457C3×C4C3×2−1+411yescharacteristic
458Dic3—22no—
459Dic3—42no—
460Dic3—41no—
461C32#336411yescharacteristic, complemented, Sylow
462C23—21no—
463Q8—22no—
464Q8—22no—
465Q8—22no—
466Q8—32no—
467Q8—61no—
468Q8—122no—
469D4—21no—
470D4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—42no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—62no—
477C2×C4C2×C3×#6712yes—
478C2×C4C2×C3×#6711yescharacteristic
479C2×C4C2×C3×#6712yes—
480C2×C4C2×C3×#6711yescharacteristic
481C2×C4C23×C3×D311yescharacteristic
482C8—61no—
483C8—62no—
484C8—61no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—82no—
489C2×C3—81no—
490C2×C3—81no—
491C2×C3C2×#95011yescharacteristic
492C2×C3#583111yescharacteristic
493C2×C3#583811yescharacteristic
494C2×C3C3×#54811yescharacteristic
495C2×C3C2×C3×#13511yescharacteristic
496C2×C3C3×#57811yescharacteristic
497C22—41no—
498C22—41no—
499C22—41no—
500C22C22×C3×#6711yescharacteristic
501C4—22no—
502C4—22no—
503C4—21no—
504C4—41no—
505C4—42no—
506C4—62no—
507C4—122no—
508C4—121no—
509C4C3×#95012yes—
510C4C3×D3×#4111yescharacteristic
511C4C3×#101011yescharacteristic
512C3—21no—
513C3#8367611yescharacteristic, direct product factor
514C3C3×#336411yescharacteristic, complemented
515C2—81no—
516C2C2×C3×#95011yescharacteristic
517C2C3×#583111yescharacteristic
518C2C3×#583811yescharacteristic
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×#3364
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×#5567C2semidirect
3. C3×#5090C2semidirect
4. C3×#5079C2semidirect
7. C3×C4×#216C2semidirect
8. C3×Q8×C3⋊C8C2semidirect
9. C3×#5022C2semidirect
13. #83676C3direct (N × H)
47. #5567C2×C3semidirect
57. #5090C2×C3semidirect
58. #5079C2×C3semidirect
61. C4×#216C2×C3semidirect
62. Q8×C3⋊C8C2×C3semidirect
63. #5022C2×C3semidirect
461. C32#3364semidirect
513. C3#83676direct (N × H)
514. C3C3×#3364semidirect

Maximal subgroups

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

subgroupindex
C32×#5562
C3×#55672
C3×#50902
C3×#50792
C3×#50562
C3×#50542
C3×C4×#2162
C3×Q8×C3⋊C82
C3×#50222
C3×C4×#2142
C3×#50072
C3×#33643
#836763