Finite Group Databasebeta

← C3×#79680 #11888024

Subgroups — C3×#79680 #11888024

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5584C211yesmaximal, characteristic, complemented
2C3×#5555C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5173C212yesmaximal, complemented
5C3×#5031C211yesmaximal, characteristic, complemented
6C3×#5007C211yesmaximal, characteristic, complemented
7C3×#4868C212yesmaximal, complemented
8C3×#4813C212yesmaximal, complemented
9C3×#4772C212yesmaximal, complemented
10C3×C8×D12C211yesmaximal, characteristic, complemented
11C3×#4681C211yesmaximal, characteristic, complemented
12C3×#3302—31nomaximal
13#79680C311yesmaximal, characteristic, direct product factor
14C2×C3×#237C2212yes—
15C2×C32×SD16C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18C3×#946C2212yes—
19C2×C3×#216C2212yes—
20C3×#930—21no—
21C2×C3×C4⋊Dic3—21no—
22C2×C3×D3×C8C2212yes—
23C3×#898—22no—
24C3×#897C2212yes—
25C3×#892C2212yes—
26C3×#886—22no—
27C3×#875—21no—
28C3×C4×D12C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C3×C4×Dic6—21no—
32C32×#106C2211yescharacteristic
33C32×#103C2211yescharacteristic
34C32×#102C2211yescharacteristic
35C32×C4×C8C2211yescharacteristic
36C3×#832C2212yes—
37C3×(C2×D3)⋊C8C2212yes—
38C3×#816C2212yes—
39C3×#816C2212yes—
40C3×#810C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#556—31no—
44C3×#547—31no—
45#5584C2×C311yescharacteristic, complemented
46#5555C2×C311yescharacteristic
47C3×#487—31no—
48C3×#485—32no—
49C3×#474—31no—
50C3×#467—32no—
51C3×#462—31no—
52C3×#452—32no—
53C3×C4×SD16—21no—
54C3×C4×SD16D311yescharacteristic, complemented
55C3×C4×SD16C2×C311yescharacteristic, complemented
56C3×C8×D4—31no—
57C3×#416—32no—
58#5173C2×C312yescomplemented
59#5031C2×C311yescharacteristic, complemented
60#5007C2×C311yescharacteristic, complemented
61#4868C2×C312yescomplemented
62#4813C2×C312yescomplemented
63#4772C2×C312yescomplemented
64C8×D12C2×C311yescharacteristic, complemented
65#4681C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×#67—22no—
70C22×C3×Dic3—22no—
71C3×#237—24no—
72C3×#237—42no—
73C2×C3×D12D411yescharacteristic
74C2×C3×C4×D3C2312yes—
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2312yes—
77C32×SD16—22no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C4⋊C4C2311yescharacteristic
83C32×C22⋊C4—21no—
84C32×C42—21no—
85C32×C42C2311yescharacteristic
86C3×#216—42no—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×(C2×D3)⋊C4D412yes—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3D411yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×Dic3⋊C4—22no—
98C3×C4×Dic3—22no—
99C2×C3×C3⋊C8C2312yes—
100C3×D3×C8—42no—
101#3302—31noSylow
102C2×C3×#41—32no—
103C2×#237C22×C312yes—
104C2×C3×Q16—32no—
105C2×C3×SD16—21no—
106C2×C3×SD16C2×D311yescharacteristic
107C2×C3×SD16C22×C311yescharacteristic
108C22×C3×C8—32no—
109C3×C4⋊Q8—31no—
110C3×C4⋊Q8—31no—
111C3×#126—62no—
112C3×#124—61no—
113C3×#123—62no—
114C3×C22⋊Q8—32no—
115C3×C22⋊Q8—32no—
116C3×#121—61no—
117C3×C4×Q8—21no—
118C3×C4×Q8—61no—
119C3×C4×Q8C2×D311yescharacteristic
120C3×C4×Q8C22×C311yescharacteristic
121C3×C4×D4—21no—
122C3×C4×D4—31no—
123C3×C4×D4C2×D311yescharacteristic
124C3×C4×D4C22×C311yescharacteristic
125C3×#117—32no—
126C2×C3×C4⋊C4—61no—
127#946C22×C312yes—
128C2×#216C22×C312yes—
129#930—21no—
130C2×C4⋊Dic3—21no—
131C2×D3×C8C22×C312yes—
132#898—22no—
133#897C22×C312yes—
134#892C22×C312yes—
135#886—22no—
136#875—21no—
137C4×D12C22×C311yescharacteristic
138#869C22×C311yescharacteristic
139#869C22×C311yescharacteristic
140C4×Dic6—21no—
141C3×#107—32no—
142C3×#106—21no—
143C3×#106C2×D311yescharacteristic
144C3×#106C22×C311yescharacteristic
145C3×C4⋊C8—31no—
146C3×#103—21no—
147C3×#103—32no—
148C3×#103—32no—
149C3×#103—32no—
150C3×#103C2×D311yescharacteristic
151C3×#103C22×C311yescharacteristic
152C3×#102—21no—
153C3×#102—32no—
154C3×#102C2×D311yescharacteristic
155C3×#102C22×C311yescharacteristic
156C3×C22⋊C8—32no—
157C3×C4×C8—21no—
158C3×C4×C8C2×D311yescharacteristic
159C3×C4×C8C22×C311yescharacteristic
160#832C22×C312yes—
161(C2×D3)⋊C8C22×C312yes—
162#816C22×C312yes—
163#816C22×C312yes—
164#810C22×C312yes—
165#807C22×C312yes—
166C4⋊(C3⋊C8)C22×C311yescharacteristic
167C23×C32—21no—
168C22×C3×D3C2×D412yes—
169C32×Q8—21no—
170C32×Q8—21no—
171C32×D4—21no—
172C32×D4#4112yes—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—42no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C3×#67—44no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—44no—
184C2×C3×Dic3C2×D412yes—
185C3×D12—22no—
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3×Dic6—22no—
189C3×Dic6—22no—
190C3×Dic6—42no—
191C32×C8—21no—
192C32×C8—21no—
193C3×C3⋊C8—22no—
194#556—31no—
195#547—31no—
196#487—31no—
197#485—32no—
198#474—31no—
199#467—32no—
200#462—31no—
201#452—32no—
202C4×SD16C3×D311yescharacteristic, complemented
203C8×D4—31no—
204#416—32no—
205C3×#41—64no—
206C3×#41—122no—
207C2×C3×Q8—21no—
208C2×C3×Q8—32no—
209C2×C3×Q8—61no—
210C2×C3×Q8C22×D311yescharacteristic
211C2×C3×Q8C23×C311yescharacteristic
212C2×C3×D4—21no—
213C2×C3×D4—31no—
214C2×C3×D4—62no—
215C2×C3×D4C22×D311yescharacteristic
216C2×C3×D4C23×C311yescharacteristic
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—32no—
220C22×C3×C4—41no—
221C22×C3×C4—62no—
222C2×#67—22no—
223C22×Dic3—22no—
224#237—24no—
225#237—42no—
226C2×D12C3×D411yescharacteristic
227C2×C4×D3C23×C312yes—
228C2×Dic6—21no—
229C2×Dic6C23×C312yes—
230C3×Q16—122no—
231C3×SD16—24no—
232C3×SD16—22no—
233C3×SD16—22no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—32no—
237C2×C3×C8—122no—
238C2×C3×C8C22×D311yescharacteristic
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C23×C311yescharacteristic
241C2×C3×C8C23×C311yescharacteristic
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—32no—
248C3×C4⋊C4—41no—
249C3×C4⋊C4—62no—
250C3×C4⋊C4—62no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4C22×D311yescharacteristic
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C4⋊C4C23×C311yescharacteristic
257C3×C4⋊C4C23×C311yescharacteristic
258C3×C22⋊C4—21no—
259C3×C22⋊C4—21no—
260C3×C22⋊C4—32no—
261C3×C22⋊C4—41no—
262C3×C22⋊C4—62no—
263C3×C22⋊C4—62no—
264C3×C22⋊C4—62no—
265C3×C42—21no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—41no—
269C3×C42—62no—
270C3×C42C22×D311yescharacteristic
271C3×C42C23×C311yescharacteristic
272#216—42no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4C3×D412yes—
277C4⋊Dic3—21no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—22no—
281C4⋊Dic3C3×D411yescharacteristic
282C4⋊Dic3C23×C312yes—
283Dic3⋊C4—22no—
284C4×Dic3—22no—
285C2×C3⋊C8C23×C312yes—
286D3×C8—42no—
287C22×C32—22no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32C22×D411yescharacteristic
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C32×C4—21no—
295C32×C4—41no—
296C32×C4—41no—
297C32×C4—41no—
298C32×C4#13512yes—
299C32×C4C2×#4111yescharacteristic
300C32×C4H(5,𝔽2)11yescharacteristic
301C3×Dic3—22no—
302C3×Dic3—42no—
303C3×Dic3—42no—
304C2×#41—32no—
305C2×Q16—32no—
306C2×SD16C2×C3×D311yescharacteristic
307C22×C8—32no—
308C4⋊Q8—31no—
309C4⋊Q8—31no—
310#126—62no—
311#124—61no—
312#123—62no—
313C22⋊Q8—32no—
314C22⋊Q8—32no—
315#121—61no—
316C4×Q8—61no—
317C4×Q8C2×C3×D311yescharacteristic
318C4×D4—31no—
319C4×D4C2×C3×D311yescharacteristic
320#117—32no—
321C2×C4⋊C4—61no—
322#107—32no—
323#106C2×C3×D311yescharacteristic
324C4⋊C8—31no—
325#103—32no—
326#103—32no—
327#103—32no—
328#103C2×C3×D311yescharacteristic
329#102—32no—
330#102C2×C3×D311yescharacteristic
331C22⋊C8—32no—
332C4×C8C2×C3×D311yescharacteristic
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—32no—
336C23×C3—41no—
337C22×D3C2×C3×D412yes—
338C3×Q8—22no—
339C3×Q8—21no—
340C3×Q8—21no—
341C3×Q8—21no—
342C3×Q8—21no—
343C3×Q8—41no—
344C3×Q8—62no—
345C3×Q8—62no—
346C3×Q8—122no—
347C3×D4—21no—
348C3×D4—21no—
349C3×D4—22no—
350C3×D4—41no—
351C3×D4—62no—
352C3×D4—124no—
353C3×D4#23512yes—
354C3×D4C3×#4112yes—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—32no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—82no—
375C2×C3×C4—124no—
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4C2×C3×D411yescharacteristic
379C2×C3×C4C2×C3×D411yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381C2×C3×C4C24×C311yescharacteristic
382#67—44no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—44no—
386C2×Dic3C2×C3×D412yes—
387D12—22no—
388C4×D3—22no—
389C4×D3—22no—
390Dic6—22no—
391Dic6—22no—
392Dic6—42no—
393C3×C8—22no—
394C3×C8—21no—
395C3×C8—21no—
396C3×C8—21no—
397C3×C8—21no—
398C3×C8—41no—
399C3×C8—62no—
400C3⋊C8—22no—
401C2×C32—42no—
402C2×C32#54611yescharacteristic
403C2×C32C2×#13511yescharacteristic
404C2×C32#57811yescharacteristic
405C3×D3—42no—
406#41—64no—
407#41—122no—
408C2×Q8—32no—
409C2×Q8—61no—
410C2×Q8C22×C3×D311yescharacteristic
411C2×D4—31no—
412C2×D4—62no—
413C2×D4C22×C3×D311yescharacteristic
414C22×C4—21no—
415C22×C4—32no—
416C22×C4—62no—
417Q16—122no—
418SD16—22no—
419C2×C8—32no—
420C2×C8—122no—
421C2×C8C22×C3×D311yescharacteristic
422C2×C8C22×C3×D311yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—31no—
425C4⋊C4—32no—
426C4⋊C4—62no—
427C4⋊C4—62no—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4C22×C3×D311yescharacteristic
432C4⋊C4C22×C3×D311yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—32no—
435C22⋊C4—62no—
436C22⋊C4—62no—
437C22⋊C4—62no—
438C42—21no—
439C42—62no—
440C42C22×C3×D311yescharacteristic
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—42no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—81no—
453C22×C3—81no—
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C22×C3×D411yescharacteristic
456C2×D3—22no—
457C2×D3—22no—
458C2×D3—22no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—41no—
465C3×C4—42no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—62no—
473C3×C4—81no—
474C3×C4—81no—
475C3×C4—122no—
476C3×C4—122no—
477C3×C4#91612yes—
478C3×C4C3×#13512yes—
479C3×C4C2×#23511yescharacteristic
480C3×C4#100911yescharacteristic
481C3×C4C2×C3×#4111yescharacteristic
482C3×C4C3×H(5,𝔽2)11yescharacteristic
483Dic3—22no—
484Dic3—42no—
485Dic3—42no—
486C32#330211yescharacteristic, complemented, Sylow
487C23—21no—
488C23—32no—
489Q8—21no—
490Q8—21no—
491Q8—62no—
492Q8—62no—
493Q8—122no—
494D4—21no—
495D4—62no—
496D4—124no—
497D4C3×#23512yes—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—32no—
502C2×C4—42no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—124no—
508C2×C4C3×D3×D411yescharacteristic
509C2×C4C3×D3×D411yescharacteristic
510C2×C4C23×C3×D311yescharacteristic
511C8—21no—
512C8—21no—
513C8—62no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—42no—
518C2×C3—42no—
519C2×C3—82no—
520C2×C3—122no—
521C2×C3#555011yescharacteristic
522C2×C3C2×#91611yescharacteristic
523C2×C3#577111yescharacteristic
524C2×C3C3×#54611yescharacteristic
525C2×C3C2×C3×#13511yescharacteristic
526C2×C3C3×#57811yescharacteristic
527D3—42no—
528C22—22no—
529C22—41no—
530C22—41no—
531C22—62no—
532C22—62no—
533C22—62no—
534C22C2×C3×D3×D411yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—62no—
540C4—122no—
541C4—122no—
542C4C3×#91612yes—
543C4C2×C3×#23511yescharacteristic
544C4C3×#100911yescharacteristic
545C3—21no—
546C3#7968011yescharacteristic, direct product factor
547C3C3×#330211yescharacteristic, complemented
548C2—42no—
549C2—122no—
550C2C3×#555011yescharacteristic
551C2C2×C3×#91611yescharacteristic
552C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC3×#5555C2
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3302
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C3×#5584C2semidirect
3. C32×C4×SD16C2semidirect
4. C3×#5173C2semidirect
5. C3×#5031C2semidirect
6. C3×#5007C2semidirect
7. C3×#4868C2semidirect
8. C3×#4813C2semidirect
9. C3×#4772C2semidirect
10. C3×C8×D12C2semidirect
11. C3×#4681C2semidirect
13. #79680C3direct (N × H)
45. #5584C2×C3semidirect
54. C3×C4×SD16D3semidirect
55. C3×C4×SD16C2×C3semidirect
58. #5173C2×C3semidirect
59. #5031C2×C3semidirect
60. #5007C2×C3semidirect
61. #4868C2×C3semidirect
62. #4813C2×C3semidirect
63. #4772C2×C3semidirect
64. C8×D12C2×C3semidirect
65. #4681C2×C3semidirect
202. C4×SD16C3×D3semidirect
486. C32#3302semidirect
546. C3#79680direct (N × H)
547. C3C3×#3302semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
C3×#55552
C32×C4×SD162
C3×#51732
C3×#50312
C3×#50072
C3×#48682
C3×#48132
C3×#47722
C3×C8×D122
C3×#46812
C3×#33023
#796803