Finite Group Databasebeta

← C3×#79638 #11898412

Subgroups — C3×#79638 #11898412

Order 1152.

805 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×#5585C211yesmaximal, characteristic, complemented
2C3×#5542C211yesmaximal, characteristic, complemented
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5168C212yesmaximal, complemented
5C3×#5031C211yesmaximal, characteristic, complemented
6C3×#5015C211yesmaximal, characteristic
7C3×#4852C212yesmaximal, complemented
8C3×#4798C212yesmaximal, complemented
9C3×#4787C212yesmaximal, complemented
10C3×#4693C211yesmaximal, characteristic, complemented
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3394—31nomaximal
13#79638C311yesmaximal, characteristic, direct product factor
14C2×C32×SD16C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#947C2212yes—
18C2×C3×#216C2212yes—
19C3×#936C2212yes—
20C2×C3×#213C2212yes—
21C3×#926—21no—
22C3×#924—21no—
23C2×C3×#204C2212yes—
24C2×C3×#204C2212yes—
25C3×#894—22no—
26C3×#893C2212yes—
27C3×#887C2212yes—
28C3×#879—22no—
29C3×#875—21no—
30C3×#874C2211yescharacteristic
31C3×C4×D12—21no—
32C3×#869C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34C32×#106C2211yescharacteristic
35C32×#103C2211yescharacteristic
36C32×#102C2211yescharacteristic
37C32×C4×C8C2211yescharacteristic
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#810C2212yes—
41C3×#809C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#559—31no—
44C3×#556—31no—
45#5585C2×C311yescharacteristic, complemented
46#5542C2×C311yescharacteristic, complemented
47C3×#495—32no—
48C3×#492—31no—
49C3×#464—32no—
50C3×#463—32no—
51C3×#462—31no—
52C3×#459—31no—
53C3×C8×Q8—31no—
54C3×C4×SD16—21no—
55C3×C4×SD16—32no—
56C3×C4×SD16D311yescharacteristic, complemented
57C3×C4×SD16C2×C311yescharacteristic, complemented
58#5168C2×C312yescomplemented
59#5031C2×C311yescharacteristic, complemented
60#5015C2×C311yescharacteristic
61#4852C2×C312yescomplemented
62#4798C2×C312yescomplemented
63#4787C2×C312yescomplemented
64#4693C2×C311yescharacteristic, complemented
65C8×Dic6C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—22no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2312yes—
75C32×SD16—22no—
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84C3×#217—22no—
85C3×#217—22no—
86C3×#216—42no—
87C3×#213—42no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3D411yescharacteristic
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4D412yes—
96C3×C4×Dic3—22no—
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8C2312yes—
99C3×#204—24no—
100C3×#204—42no—
101#3394—31noSylow
102C2×C3×Q16—32no—
103C2×C3×SD16—21no—
104C2×C3×SD16—32no—
105C2×C3×SD16—32no—
106C2×C3×SD16C2×D311yescharacteristic
107C2×C3×SD16C22×C311yescharacteristic
108C2×C3×D8—32no—
109C3×C4⋊Q8—31no—
110C3×#127—31no—
111C3×#126—62no—
112C3×#124—32no—
113C3×#124—32no—
114C3×#124—61no—
115C3×#123—62no—
116C3×C22⋊Q8—61no—
117C3×C4×Q8—21no—
118C3×C4×Q8—31no—
119C3×C4×Q8—32no—
120C3×C4×Q8C2×D311yescharacteristic
121C3×C4×Q8C22×C311yescharacteristic
122C3×C4×D4—21no—
123C3×C4×D4—32no—
124C3×C4×D4—61no—
125C3×C4×D4C2×D311yescharacteristic
126C3×C4×D4C22×C311yescharacteristic
127C3×#117—61no—
128#947C22×C312yes—
129C2×#216C22×C312yes—
130#936C22×C312yes—
131C2×#213C22×C312yes—
132#926—21no—
133#924—21no—
134C2×#204C22×C312yes—
135C2×#204C22×C312yes—
136#894—22no—
137#893C22×C312yes—
138#887C22×C312yes—
139#879—22no—
140#875—21no—
141#874C22×C311yescharacteristic
142C4×D12—21no—
143#869C22×C311yescharacteristic
144C4×Dic6C22×C311yescharacteristic
145C3×#106—21no—
146C3×#106C2×D311yescharacteristic
147C3×#106C22×C311yescharacteristic
148C3×C4⋊C8—32no—
149C3×C4⋊C8—31no—
150C3×#103—21no—
151C3×#103—32no—
152C3×#103C2×D311yescharacteristic
153C3×#103C22×C311yescharacteristic
154C3×#102—21no—
155C3×#102—32no—
156C3×#102C2×D311yescharacteristic
157C3×#102C22×C311yescharacteristic
158C3×C4×C8—21no—
159C3×C4×C8—32no—
160C3×C4×C8C2×D311yescharacteristic
161C3×C4×C8C22×C311yescharacteristic
162Dic3⋊C8C22×C312yes—
163C8×Dic3C22×C312yes—
164#810C22×C312yes—
165#809C22×C312yes—
166C4⋊(C3⋊C8)C22×C311yescharacteristic
167C23×C32—21no—
168C22×C3×D3—22no—
169C32×Q8—21no—
170C32×Q8—21no—
171C32×D4—21no—
172C32×D4—21no—
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
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—22no—
184C3×D12—22no—
185C3×D12—42no—
186C3×D12—81no—
187C3×C4×D3—82no—
188C3×Dic6—22no—
189C3×Dic6—22no—
190C3×Dic6—22no—
191C32×C8—21no—
192C32×C8#4112yes—
193C3×C3⋊C8—22no—
194#559—31no—
195#556—31no—
196#495—32no—
197#492—31no—
198#464—32no—
199#463—32no—
200#462—31no—
201#459—31no—
202C8×Q8—31no—
203C4×SD16—32no—
204C4×SD16C3×D311yescharacteristic, complemented
205C2×C3×Q8—21no—
206C2×C3×Q8—31no—
207C2×C3×Q8—32no—
208C2×C3×Q8C22×D311yescharacteristic
209C2×C3×Q8C23×C311yescharacteristic
210C2×C3×D4—21no—
211C2×C3×D4—32no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C2×C3×D4C22×D311yescharacteristic
215C2×C3×D4C23×C311yescharacteristic
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—41no—
219C22×C3×C4—62no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12C23×C312yes—
223C2×C4×D3—22no—
224C2×Dic6C3×D411yescharacteristic
225C2×Dic6C23×C312yes—
226C3×Q16—122no—
227C3×SD16—24no—
228C3×SD16—22no—
229C3×SD16—22no—
230C3×SD16—64no—
231C3×SD16—122no—
232C3×D8—122no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—32no—
236C2×C3×C8C22×D311yescharacteristic
237C2×C3×C8C22×D311yescharacteristic
238C2×C3×C8C23×C311yescharacteristic
239C2×C3×C8C23×C311yescharacteristic
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—41no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C4⋊C4C23×C311yescharacteristic
253C3×C4⋊C4C23×C311yescharacteristic
254C3×C22⋊C4—21no—
255C3×C22⋊C4—21no—
256C3×C22⋊C4—41no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4—62no—
261C3×C22⋊C4—62no—
262C3×C42—21no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42—32no—
266C3×C42—41no—
267C3×C42—62no—
268C3×C42C22×D311yescharacteristic
269C3×C42C23×C311yescharacteristic
270#217—22no—
271#217—22no—
272#216—42no—
273#213—42no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277C4⋊Dic3—21no—
278C4⋊Dic3—21no—
279C4⋊Dic3C3×D411yescharacteristic
280Dic3⋊C4—22no—
281Dic3⋊C4C3×D412yes—
282C4×Dic3—22no—
283C4×Dic3C23×C312yes—
284C2×C3⋊C8C23×C312yes—
285#204—24no—
286#204—42no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32C22×D411yescharacteristic
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C2×C3×D3—42no—
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—22no—
303C3×Dic3—42no—
304C2×Q16—32no—
305C2×SD16—32no—
306C2×SD16—32no—
307C2×SD16C2×C3×D311yescharacteristic
308C2×D8—32no—
309C4⋊Q8—31no—
310#127—31no—
311#126—62no—
312#124—32no—
313#124—32no—
314#124—61no—
315#123—62no—
316C22⋊Q8—61no—
317C4×Q8—31no—
318C4×Q8—32no—
319C4×Q8C2×C3×D311yescharacteristic
320C4×D4—32no—
321C4×D4—61no—
322C4×D4C2×C3×D311yescharacteristic
323#117—61no—
324#106C2×C3×D311yescharacteristic
325C4⋊C8—32no—
326C4⋊C8—31no—
327#103—32no—
328#103C2×C3×D311yescharacteristic
329#102—32no—
330#102C2×C3×D311yescharacteristic
331C4×C8—32no—
332C4×C8C2×C3×D311yescharacteristic
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—41no—
336C23×C3—62no—
337C22×D3—22no—
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—62no—
347C3×D4—22no—
348C3×D4—21no—
349C3×D4—21no—
350C3×D4—21no—
351C3×D4—21no—
352C3×D4—41no—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—122no—
356C3×D4—241no—
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—21no—
365C2×C3×C4—21no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—62no—
374C2×C3×C4—82no—
375C2×C3×C4—242no—
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
382C2×Dic3—22no—
383C2×Dic3C2×C3×D412yes—
384C2×Dic3C2×C3×D412yes—
385D12—22no—
386D12—22no—
387D12—42no—
388D12—81no—
389C4×D3—82no—
390Dic6—22no—
391Dic6—22no—
392Dic6—22no—
393C3×C8—21no—
394C3×C8—21no—
395C3×C8—22no—
396C3×C8—41no—
397C3×C8—62no—
398C3×C8#23512yes—
399C3×C8C3×#4112yes—
400C3⋊C8—22no—
401C2×C32—81no—
402C2×C32#55011yescharacteristic
403C2×C32C2×#13511yescharacteristic
404C2×C32#57711yescharacteristic
405C3×D3—82no—
406C2×Q8—31no—
407C2×Q8—32no—
408C2×Q8C22×C3×D311yescharacteristic
409C2×D4—32no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4C22×C3×D311yescharacteristic
413C22×C4—21no—
414C22×C4—62no—
415Q16—122no—
416SD16—22no—
417SD16—64no—
418SD16—122no—
419D8—122no—
420C2×C8—32no—
421C2×C8C22×C3×D311yescharacteristic
422C2×C8C22×C3×D311yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—31no—
425C4⋊C4—32no—
426C4⋊C4—62no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4C22×C3×D311yescharacteristic
430C4⋊C4C22×C3×D311yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—62no—
433C22⋊C4—62no—
434C22⋊C4—62no—
435C22⋊C4—62no—
436C22⋊C4—62no—
437C42—21no—
438C42—32no—
439C42—62no—
440C42C22×C3×D311yescharacteristic
441C22×C3—21no—
442C22×C3—42no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—81no—
450C22×C3—81no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C22×C3×D411yescharacteristic
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
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—62no—
474C3×C4—81no—
475C3×C4—81no—
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—22no—
485Dic3—42no—
486C32#339411yescharacteristic, complemented, Sylow
487C23—21no—
488C23—62no—
489Q8—21no—
490Q8—21no—
491Q8—62no—
492Q8—62no—
493Q8—62no—
494D4—21no—
495D4—21no—
496D4—62no—
497D4—62no—
498D4—122no—
499D4—241no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—42no—
506C2×C4—62no—
507C2×C4—242no—
508C2×C4C3×D3×D411yescharacteristic
509C2×C4C3×D3×D411yescharacteristic
510C2×C4C23×C3×D311yescharacteristic
511C8—21no—
512C8—62no—
513C8C3×#23512yes—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—82no—
518C2×C3—81no—
519C2×C3—81no—
520C2×C3—242no—
521C2×C3#555311yescharacteristic
522C2×C3C2×#91611yescharacteristic
523C2×C3#577011yescharacteristic
524C2×C3C3×#55011yescharacteristic
525C2×C3C2×C3×#13511yescharacteristic
526C2×C3C3×#57711yescharacteristic
527D3—82no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—122no—
532C22—122no—
533C22—122no—
534C22C2×C3×D3×D411yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—62no—
540C4—62no—
541C4—122no—
542C4C3×#91612yes—
543C4C2×C3×#23511yescharacteristic
544C4C3×#100911yescharacteristic
545C3—21no—
546C3#7963811yescharacteristic, direct product factor
547C3C3×#339411yescharacteristic, complemented
548C2—81no—
549C2—242no—
550C2C3×#555311yescharacteristic
551C2C2×C3×#91611yescharacteristic
552C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC3×#5015C2
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3394
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×#5585C2semidirect
2. C3×#5542C2semidirect
3. C32×C4×SD16C2semidirect
4. C3×#5168C2semidirect
5. C3×#5031C2semidirect
7. C3×#4852C2semidirect
8. C3×#4798C2semidirect
9. C3×#4787C2semidirect
10. C3×#4693C2semidirect
11. C3×C8×Dic6C2semidirect
13. #79638C3direct (N × H)
45. #5585C2×C3semidirect
46. #5542C2×C3semidirect
56. C3×C4×SD16D3semidirect
57. C3×C4×SD16C2×C3semidirect
58. #5168C2×C3semidirect
59. #5031C2×C3semidirect
61. #4852C2×C3semidirect
62. #4798C2×C3semidirect
63. #4787C2×C3semidirect
64. #4693C2×C3semidirect
65. C8×Dic6C2×C3semidirect
204. C4×SD16C3×D3semidirect
486. C32#3394semidirect
546. C3#79638direct (N × H)
547. C3C3×#3394semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
C3×#55422
C32×C4×SD162
C3×#51682
C3×#50312
C3×#50152
C3×#48522
C3×#47982
C3×#47872
C3×#46932
C3×C8×Dic62
C3×#33943
#796383