Finite Group Databasebeta

← C3×#83689 #11895521

Subgroups — C3×#83689 #11895521

Order 1152.

772 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic
5C3×#5068C212yesmaximal
6C3×#5063C212yesmaximal, complemented
7C3×#5031C211yesmaximal, characteristic, complemented
8C3×C4×#216C212yesmaximal, complemented
9C3×#5028C212yesmaximal
10C3×C4×#215C211yesmaximal, characteristic
11C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
12C3×#3364—31nomaximal
13#83689C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#125—22no—
17C32×#125C2212yes—
18C32×C4×Q8—21no—
19C32×C4×Q8C2211yescharacteristic
20C32×C4×Q8C2212yes—
21C32×C4×Q8C2211yescharacteristic
22C3×#946—21no—
23C2×C3×#216C2212yes—
24C2×C3×#215C2211yescharacteristic
25C3×#898—22no—
26C3×#892—21no—
27C3×#875C2212yes—
28C3×C4×D12C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×C4×Dic6C2212yes—
31C3×#835C2211yescharacteristic
32C3×#810C2212yes—
33C3×#810C2212yes—
34C3×#810C2212yes—
35C3×#809C2211yescharacteristic
36C3×#809C2212yes—
37C3×#808C2211yescharacteristic
38C3×#807C2212yes—
39C3×C4⋊(C3⋊C8)C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41C3×C4×C3⋊C8C2211yescharacteristic
42C3×C4×C3⋊C8C2212yes—
43C3×#557—21no—
44C3×#557D311yescharacteristic, complemented
45C3×#557C2×C311yescharacteristic, complemented
46C3×#556—31no—
47#5584C2×C311yescharacteristic
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#5093C2×C311yescharacteristic, complemented
58#5087C2×C311yescharacteristic
59#5068C2×C312yes—
60#5063C2×C312yescomplemented
61#5031C2×C311yescharacteristic, complemented
62C4×#216C2×C312yescomplemented
63#5028C2×C312yes—
64C4×#215C2×C311yescharacteristic
65Q8×C3⋊C8C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×Q8D411yescharacteristic
68C2×C32×Q8C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6C2312yes—
72C32×C4⋊C4—22no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4—22no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—22no—
77C32×C4⋊C4D411yescharacteristic
78C32×C4⋊C4D412yes—
79C32×C4⋊C4C2312yes—
80C32×C4⋊C4C2311yescharacteristic
81C32×C42—22no—
82C32×C42—21no—
83C32×C42C2312yes—
84C32×C42C2311yescharacteristic
85C3×#216—24no—
86C3×#215—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—22no—
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—22no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C22×C311yescharacteristic
108C3×#126—62no—
109C3×#125—24no—
110C3×#125—22no—
111C3×#125—22no—
112C3×#125—22no—
113C3×#125C2×D312yes—
114C3×#125C22×C312yes—
115C3×#124—32no—
116C3×C22⋊Q8—61no—
117C3×C4×Q8—22no—
118C3×C4×Q8—21no—
119C3×C4×Q8—21no—
120C3×C4×Q8—21no—
121C3×C4×Q8—22no—
122C3×C4×Q8—21no—
123C3×C4×Q8—32no—
124C3×C4×Q8C2×D311yescharacteristic
125C3×C4×Q8C2×D312yes—
126C3×C4×Q8C2×D311yescharacteristic
127C3×C4×Q8C22×C311yescharacteristic
128C3×C4×Q8C22×C312yes—
129C3×C4×Q8C22×C311yescharacteristic
130C3×C4×D4—31no—
131C3×#117—61no—
132#946—21no—
133C2×#216C22×C312yes—
134C2×#215C22×C311yescharacteristic
135#898—22no—
136#892—21no—
137#875C22×C312yes—
138C4×D12C22×C311yescharacteristic
139#869C22×C311yescharacteristic
140C4×Dic6C22×C312yes—
141C3×#107—32no—
142C3×#106—31no—
143C3×C4⋊C8—31no—
144C3×C4⋊C8—32no—
145C3×#103—31no—
146C3×#103—32no—
147C3×#103—32no—
148C3×#103—32no—
149C3×#102—31no—
150C3×#102—32no—
151C3×C4×C8—31no—
152C3×C4×C8—32no—
153#835C22×C311yescharacteristic
154#810C22×C312yes—
155#810C22×C312yes—
156#810C22×C312yes—
157#809C22×C311yescharacteristic
158#809C22×C312yes—
159#808C22×C311yescharacteristic
160#807C22×C312yes—
161C4⋊(C3⋊C8)C22×C312yes—
162C4⋊(C3⋊C8)C22×C311yescharacteristic
163C4×C3⋊C8C22×C311yescharacteristic
164C4×C3⋊C8C22×C312yes—
165C22×C3×D3—21no—
166C32×Q8—21no—
167C32×Q8—22no—
168C32×Q8—42no—
169C32×Q8#4112yes—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—22no—
173C2×C32×C4C2×D412yes—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C3×D12—21no—
181C3×D12—21no—
182C3×C4×D3—42no—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—22no—
187C3×C3⋊C8—21no—
188#557C3×D311yescharacteristic, complemented
189#556—31no—
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—22no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—32no—
205C2×C3×Q8#6711yescharacteristic
206C2×C3×Q8C3×D411yescharacteristic
207C2×C3×Q8C22×D311yescharacteristic
208C2×C3×Q8C23×C311yescharacteristic
209C2×C3×D4—31no—
210C22×C3×C4—61no—
211C2×D12C23×C311yescharacteristic
212C2×C4×D3—21no—
213C2×Dic6C23×C312yes—
214C3×Q16—64no—
215C3×SD16—62no—
216C2×C3×C8—31no—
217C2×C3×C8—32no—
218C2×C3×C8—31no—
219C3×C4⋊C4—24no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—24no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—24no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4#6711yescharacteristic
243C3×C4⋊C4#6712yes—
244C3×C4⋊C4C3×D411yescharacteristic
245C3×C4⋊C4C3×D412yes—
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C4⋊C4C22×D312yes—
248C3×C4⋊C4C23×C312yes—
249C3×C4⋊C4C23×C311yescharacteristic
250C3×C22⋊C4—62no—
251C3×C22⋊C4—61no—
252C3×C22⋊C4—62no—
253C3×C42—24no—
254C3×C42—22no—
255C3×C42—22no—
256C3×C42—21no—
257C3×C42—22no—
258C3×C42—21no—
259C3×C42—22no—
260C3×C42—21no—
261C3×C42—62no—
262C3×C42C22×D311yescharacteristic
263C3×C42C22×D312yes—
264C3×C42C23×C312yes—
265C3×C42C23×C311yescharacteristic
266#216—24no—
267#215—22no—
268(C2×D3)⋊C4—21no—
269(C2×D3)⋊C4—22no—
270(C2×D3)⋊C4—22no—
271C4⋊Dic3—21no—
272C4⋊Dic3—21no—
273C4⋊Dic3C23×C311yescharacteristic
274Dic3⋊C4—22no—
275C4×Dic3—22no—
276C2×C3⋊C8C23×C311yescharacteristic
277C2×C3⋊C8C23×C312yes—
278C2×C3⋊C8C23×C311yescharacteristic
279C22×C32C22×D411yescharacteristic
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C32×C4—22no—
284C32×C4—22no—
285C32×C4—22no—
286C32×C4—21no—
287C32×C4—42no—
288C32×C4—41no—
289C32×C4#13512yes—
290C32×C4C2×#4111yescharacteristic
291C32×C42−1+411yescharacteristic
292C3×Dic3—42no—
293C3×Dic3—41no—
294C2×Q16—32no—
295C2×SD16—31no—
296C4⋊Q8—21no—
297C4⋊Q8—31no—
298C4⋊Q8C2×C3×D311yescharacteristic
299#126—62no—
300#125—22no—
301#125C2×C3×D312yes—
302#124—32no—
303C22⋊Q8—61no—
304C4×Q8—21no—
305C4×Q8—32no—
306C4×Q8C2×C3×D311yescharacteristic
307C4×Q8C2×C3×D312yes—
308C4×Q8C2×C3×D311yescharacteristic
309C4×D4—31no—
310#117—61no—
311#107—32no—
312#106—31no—
313C4⋊C8—31no—
314C4⋊C8—32no—
315#103—31no—
316#103—32no—
317#103—32no—
318#103—32no—
319#102—31no—
320#102—32no—
321C4×C8—31no—
322C4×C8—32no—
323C23×C3—61no—
324C22×D3—21no—
325C3×Q8—22no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—22no—
331C3×Q8—42no—
332C3×Q8—44no—
333C3×Q8—42no—
334C3×Q8—42no—
335C3×Q8—62no—
336C3×Q8—62no—
337C3×Q8#23912yes—
338C3×Q8C3×#4112yes—
339C3×D4—61no—
340C3×D4—61no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
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—61no—
356C2×C3×C4—62no—
357C2×C3×C4—122no—
358C2×C3×C4C2×#6712yes—
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6712yes—
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×C3×D412yes—
363C2×C3×C4C2×C3×D412yes—
364C2×C3×C4C2×C3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C24×C311yescharacteristic
368C2×Dic3—21no—
369C2×Dic3—22no—
370D12—21no—
371D12—21no—
372C4×D3—42no—
373Dic6—22no—
374Dic6—22no—
375C3×C8—61no—
376C3×C8—62no—
377C3×C8—61no—
378C3⋊C8—21no—
379C3⋊C8—22no—
380C3⋊C8—21no—
381C2×C32#54811yescharacteristic
382C2×C32C2×#13511yescharacteristic
383C2×C32#57811yescharacteristic
384C3×D3—81no—
385C2×Q8—21no—
386C2×Q8—32no—
387C2×Q8C3×#6711yescharacteristic
388C2×Q8C22×C3×D311yescharacteristic
389C2×D4—31no—
390C22×C4—61no—
391Q16—64no—
392SD16—62no—
393C2×C8—31no—
394C2×C8—32no—
395C2×C8—31no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—31no—
402C4⋊C4—61no—
403C4⋊C4—62no—
404C4⋊C4—61no—
405C4⋊C4C3×#6711yescharacteristic
406C4⋊C4C3×#6712yes—
407C4⋊C4C22×C3×D311yescharacteristic
408C4⋊C4C22×C3×D312yes—
409C22⋊C4—62no—
410C22⋊C4—61no—
411C22⋊C4—62no—
412C42—22no—
413C42—21no—
414C42—62no—
415C42C22×C3×D311yescharacteristic
416C42C22×C3×D312yes—
417C22×C3—21no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3C22×#6711yescharacteristic
422C22×C3C22×C3×D411yescharacteristic
423C2×D3—41no—
424C2×D3—41no—
425C2×D3—41no—
426C3×C4—24no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—21no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—42no—
439C3×C4—42no—
440C3×C4—41no—
441C3×C4—44no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4—41no—
445C3×C4—42no—
446C3×C4—41no—
447C3×C4—122no—
448C3×C4—121no—
449C3×C4#95012yes—
450C3×C4C3×#13512yes—
451C3×C4C2×#23911yescharacteristic
452C3×C4#100711yescharacteristic
453C3×C4C2×C3×#4111yescharacteristic
454C3×C4C3×2−1+411yescharacteristic
455Dic3—41no—
456Dic3—42no—
457C32#336411yescharacteristic, complemented, Sylow
458C23—61no—
459Q8—22no—
460Q8—21no—
461Q8—42no—
462Q8—62no—
463Q8—62no—
464Q8C3×#23912yes—
465D4—61no—
466D4—61no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—61no—
471C2×C4—62no—
472C2×C4—122no—
473C2×C4C2×C3×#6712yes—
474C2×C4C2×C3×#6711yescharacteristic
475C2×C4C2×C3×#6712yes—
476C2×C4C2×C3×#6711yescharacteristic
477C2×C4C23×C3×D311yescharacteristic
478C8—61no—
479C8—62no—
480C8—61no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—241no—
485C2×C3#581711yescharacteristic
486C2×C3C2×#95011yescharacteristic
487C2×C3#583811yescharacteristic
488C2×C3C3×#54811yescharacteristic
489C2×C3C2×C3×#13511yescharacteristic
490C2×C3C3×#57811yescharacteristic
491D3—81no—
492C22—121no—
493C22—121no—
494C22—121no—
495C22C22×C3×#6711yescharacteristic
496C4—22no—
497C4—22no—
498C4—22no—
499C4—21no—
500C4—42no—
501C4—41no—
502C4—122no—
503C4—121no—
504C4C3×#95012yes—
505C4C2×C3×#23911yescharacteristic
506C4C3×#100711yescharacteristic
507C3—21no—
508C3#8368911yescharacteristic, direct product factor
509C3C3×#336411yescharacteristic, complemented
510C2—241no—
511C2C3×#581711yescharacteristic
512C2C2×C3×#95011yescharacteristic
513C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#557C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#557D3
hypocenterC3C3×#3364
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
3. C3×#5093C2semidirect
6. C3×#5063C2semidirect
7. C3×#5031C2semidirect
8. C3×C4×#216C2semidirect
11. C3×Q8×C3⋊C8C2semidirect
13. #83689C3direct (N × H)
44. C3×#557D3semidirect
45. C3×#557C2×C3semidirect
57. #5093C2×C3semidirect
60. #5063C2×C3semidirect
61. #5031C2×C3semidirect
62. C4×#216C2×C3semidirect
65. Q8×C3⋊C8C2×C3semidirect
188. #557C3×D3semidirect
457. C32#3364semidirect
508. C3#83689direct (N × H)
509. C3C3×#3364semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
C3×#55842
C3×#50932
C3×#50872
C3×#50682
C3×#50632
C3×#50312
C3×C4×#2162
C3×#50282
C3×C4×#2152
C3×Q8×C3⋊C82
C3×#33643
#836893