Finite Group Databasebeta

← C3×#79913 #11898424

Subgroups — C3×#79913 #11898424

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C32×C8×Q8C211yesmaximal, characteristic, complemented
4C3×#4849C211yesmaximal, characteristic, complemented
5C3×#4845C212yesmaximal, complemented
6C3×#4844C212yesmaximal, complemented
7C3×#4843C211yesmaximal, characteristic
8C3×#4696C212yesmaximal, complemented
9C3×#4693C211yesmaximal, characteristic, complemented
10C3×C4×#204C212yesmaximal, complemented
11C3×C4×#204C211yesmaximal, characteristic, complemented
12C3×#3394—31nomaximal
13#79913C311yesmaximal, characteristic, direct product factor
14C32×C4×Q8C2211yescharacteristic
15C3×#947—21no—
16C3×#946—21no—
17C2×C3×Dic12C2212yes—
18C2×C3×D24C2212yes—
19C2×C3×#204C2212yes—
20C2×C3×#204C2211yescharacteristic
21C2×C3×#204C2212yes—
22C3×#898—22no—
23C3×#894—22no—
24C3×#893—21no—
25C3×#892—21no—
26C3×#875C2212yes—
27C3×#875C2212yes—
28C3×#874C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×C4×D12C2212yes—
31C3×#869C2211yescharacteristic
32C3×C4×Dic6C2212yes—
33C3×C4×Dic6C2211yescharacteristic
34C32×C4⋊C8C2211yescharacteristic
35C32×C4⋊C8C2212yes—
36C32×C4×C8C2211yescharacteristic
37C32×C4×C8C2212yes—
38C3×#821C2212yes—
39C3×#821C2211yescharacteristic
40C3×#817C2211yescharacteristic
41C3×#816C2212yes—
42C3×#816C2211yescharacteristic
43C3×#559—31no—
44C3×#556—31no—
45#5585C2×C311yescharacteristic, complemented
46#5584C2×C311yescharacteristic, complemented
47C3×#495—32no—
48C3×#492—31no—
49C3×#464—32no—
50C3×#463—32no—
51C3×#462—31no—
52C3×#459—31no—
53C3×C8×Q8—21no—
54C3×C8×Q8D311yescharacteristic, complemented
55C3×C8×Q8C2×C311yescharacteristic, complemented
56C3×C4×SD16—31no—
57C3×C4×SD16—32no—
58#4849C2×C311yescharacteristic, complemented
59#4845C2×C312yescomplemented
60#4844C2×C312yescomplemented
61#4843C2×C311yescharacteristic
62#4696C2×C312yescomplemented
63#4693C2×C311yescharacteristic, complemented
64C4×#204C2×C312yescomplemented
65C4×#204C2×C311yescharacteristic, complemented
66C2×C32×Q8D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—22no—
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2312yes—
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4D411yescharacteristic
79C32×C4⋊C4D412yes—
80C32×C42C2311yescharacteristic
81C32×C42C2312yes—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3—21no—
96C3×Dic12—42no—
97C3×D24—42no—
98C3×#204—24no—
99C3×#204—22no—
100C3×#204—42no—
101#3394—31noSylow
102C2×C3×Q16—32no—
103C2×C3×SD16—32no—
104C2×C3×SD16—31no—
105C2×C3×SD16—32no—
106C2×C3×D8—32no—
107C3×C4⋊Q8—31no—
108C3×#127—31no—
109C3×#126—62no—
110C3×#124—32no—
111C3×#124—32no—
112C3×#124—61no—
113C3×#123—62no—
114C3×C22⋊Q8—61no—
115C3×C4×Q8—21no—
116C3×C4×Q8—31no—
117C3×C4×Q8—32no—
118C3×C4×Q8C2×D311yescharacteristic
119C3×C4×Q8C22×C311yescharacteristic
120C3×C4×D4—32no—
121C3×C4×D4—31no—
122C3×C4×D4—61no—
123C3×#117—61no—
124#947—21no—
125#946—21no—
126C2×Dic12C22×C312yes—
127C2×D24C22×C312yes—
128C2×#204C22×C312yes—
129C2×#204C22×C311yescharacteristic
130C2×#204C22×C312yes—
131#898—22no—
132#894—22no—
133#893—21no—
134#892—21no—
135#875C22×C312yes—
136#875C22×C312yes—
137#874C22×C311yescharacteristic
138C4×D12C22×C311yescharacteristic
139C4×D12C22×C312yes—
140#869C22×C311yescharacteristic
141C4×Dic6C22×C312yes—
142C4×Dic6C22×C311yescharacteristic
143C3×#106—31no—
144C3×C4⋊C8—21no—
145C3×C4⋊C8—22no—
146C3×C4⋊C8C2×D311yescharacteristic
147C3×C4⋊C8C2×D312yes—
148C3×C4⋊C8C22×C311yescharacteristic
149C3×C4⋊C8C22×C312yes—
150C3×#103—32no—
151C3×#103—31no—
152C3×#102—32no—
153C3×#102—31no—
154C3×C4×C8—21no—
155C3×C4×C8—22no—
156C3×C4×C8C2×D311yescharacteristic
157C3×C4×C8C2×D312yes—
158C3×C4×C8C22×C311yescharacteristic
159C3×C4×C8C22×C312yes—
160#821C22×C312yes—
161#821C22×C311yescharacteristic
162#817C22×C311yescharacteristic
163#816C22×C312yes—
164#816C22×C311yescharacteristic
165C22×C3×D3—21no—
166C22×C3×D3—22no—
167C32×Q8—22no—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C3×D12—22no—
178C3×D12—21no—
179C3×D12—22no—
180C3×D12—21no—
181C3×D12—42no—
182C3×D12—81no—
183C3×C4×D3—42no—
184C3×C4×D3—82no—
185C3×Dic6—22no—
186C3×Dic6—21no—
187C3×Dic6—22no—
188C3×Dic6—21no—
189C32×C8—21no—
190C32×C8—22no—
191C32×C8#4112yes—
192#559—31no—
193#556—31no—
194#495—32no—
195#492—31no—
196#464—32no—
197#463—32no—
198#462—31no—
199#459—31no—
200C8×Q8C3×D311yescharacteristic, complemented
201C4×SD16—31no—
202C4×SD16—32no—
203C2×C3×Q8—21no—
204C2×C3×Q8—31no—
205C2×C3×Q8—32no—
206C2×C3×Q8D1211yescharacteristic
207C2×C3×Q8C3×D411yescharacteristic
208C2×C3×D4—31no—
209C2×C3×D4—32no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C22×C3×C4—61no—
213C22×C3×C4—62no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12C23×C312yes—
217C2×D12C23×C311yescharacteristic
218C2×C4×D3—21no—
219C2×C4×D3—22no—
220C2×Dic6C23×C312yes—
221C2×Dic6C23×C311yescharacteristic
222C3×Q16—122no—
223C3×SD16—64no—
224C3×SD16—62no—
225C3×SD16—122no—
226C3×D8—122no—
227C2×C3×C8—21no—
228C2×C3×C8—22no—
229C2×C3×C8—21no—
230C2×C3×C8C22×D312yes—
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C23×C311yescharacteristic
234C2×C3×C8C23×C312yes—
235C2×C3×C8C23×C311yescharacteristic
236C3×C4⋊C4—21no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4D1211yescharacteristic
245C3×C4⋊C4D1212yes—
246C3×C4⋊C4C3×D411yescharacteristic
247C3×C4⋊C4C3×D412yes—
248C3×C22⋊C4—62no—
249C3×C22⋊C4—62no—
250C3×C22⋊C4—61no—
251C3×C22⋊C4—62no—
252C3×C22⋊C4—62no—
253C3×C22⋊C4—62no—
254C3×C42—22no—
255C3×C42—21no—
256C3×C42—62no—
257C3×C42—61no—
258C3×C42C22×D312yes—
259C3×C42C22×D311yescharacteristic
260C3×C42C23×C311yescharacteristic
261C3×C42C23×C312yes—
262(C2×D3)⋊C4—22no—
263(C2×D3)⋊C4—21no—
264(C2×D3)⋊C4—22no—
265(C2×D3)⋊C4—22no—
266(C2×D3)⋊C4—22no—
267(C2×D3)⋊C4—22no—
268C4⋊Dic3—21no—
269C4⋊Dic3—21no—
270C4⋊Dic3C23×C311yescharacteristic
271C4⋊Dic3C23×C311yescharacteristic
272Dic3⋊C4—21no—
273Dic3⋊C4—22no—
274C4×Dic3—22no—
275C4×Dic3—21no—
276Dic12—42no—
277D24—42no—
278#204—24no—
279#204—22no—
280#204—42no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—42no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C2×C3×D3—42no—
286C2×C3×D3—42no—
287C2×C3×D3—41no—
288C32×C4—22no—
289C32×C4—22no—
290C32×C4—21no—
291C32×C4#13512yes—
292C32×C4C2×#4111yescharacteristic
293C32×C4H(5,𝔽2)11yescharacteristic
294C3×Dic3—42no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C3×Dic3—41no—
298C2×Q16—32no—
299C2×SD16—32no—
300C2×SD16—31no—
301C2×SD16—32no—
302C2×D8—32no—
303C4⋊Q8—31no—
304#127—31no—
305#126—62no—
306#124—32no—
307#124—32no—
308#124—61no—
309#123—62no—
310C22⋊Q8—61no—
311C4×Q8—32no—
312C4×Q8—31no—
313C4×Q8C2×C3×D311yescharacteristic
314C4×D4—31no—
315C4×D4—32no—
316C4×D4—61no—
317#117—61no—
318#106—31no—
319C4⋊C8C2×C3×D311yescharacteristic
320C4⋊C8C2×C3×D312yes—
321#103—32no—
322#103—31no—
323#102—32no—
324#102—31no—
325C4×C8C2×C3×D311yescharacteristic
326C4×C8C2×C3×D312yes—
327C23×C3—61no—
328C23×C3—62no—
329C22×D3—21no—
330C22×D3—22no—
331C3×Q8—24no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—61no—
335C3×Q8—62no—
336C3×Q8—62no—
337C3×Q8—61no—
338C3×D4—61no—
339C3×D4—62no—
340C3×D4—61no—
341C3×D4—62no—
342C3×D4—122no—
343C3×D4—241no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4—122no—
354C2×C3×C4—242no—
355C2×C3×C4C2×D1212yes—
356C2×C3×C4C2×D1212yes—
357C2×C3×C4C2×D1211yescharacteristic
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4C2×C3×D412yes—
360C2×C3×C4C2×C3×D411yescharacteristic
361C2×C3×C4C2×C3×D412yes—
362C2×C3×C4C2×C3×D411yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364C2×C3×C4C24×C311yescharacteristic
365C2×Dic3—21no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369D12—22no—
370D12—21no—
371D12—22no—
372D12—21no—
373D12—42no—
374D12—81no—
375C4×D3—42no—
376C4×D3—82no—
377Dic6—22no—
378Dic6—21no—
379Dic6—22no—
380Dic6—21no—
381C3×C8—22no—
382C3×C8—21no—
383C3×C8—21no—
384C3×C8—22no—
385C3×C8—22no—
386C3×C8—42no—
387C3×C8—41no—
388C3×C8#23912yes—
389C3×C8C3×#4112yes—
390C2×C32#55011yescharacteristic
391C2×C32C2×#13511yescharacteristic
392C2×C32#57711yescharacteristic
393C3×D3—81no—
394C3×D3—82no—
395C2×Q8—31no—
396C2×Q8—32no—
397C2×Q8C3×D1211yescharacteristic
398C2×D4—31no—
399C2×D4—32no—
400C2×D4—61no—
401C2×D4—61no—
402C22×C4—61no—
403C22×C4—62no—
404Q16—122no—
405SD16—64no—
406SD16—62no—
407SD16—122no—
408D8—122no—
409C2×C8C22×C3×D312yes—
410C2×C8C22×C3×D311yescharacteristic
411C2×C8C22×C3×D311yescharacteristic
412C4⋊C4—31no—
413C4⋊C4—31no—
414C4⋊C4—61no—
415C4⋊C4—62no—
416C4⋊C4—61no—
417C4⋊C4—61no—
418C4⋊C4C3×D1211yescharacteristic
419C4⋊C4C3×D1212yes—
420C22⋊C4—62no—
421C22⋊C4—62no—
422C22⋊C4—61no—
423C22⋊C4—62no—
424C22⋊C4—62no—
425C22⋊C4—62no—
426C42—62no—
427C42—61no—
428C42C22×C3×D312yes—
429C42C22×C3×D311yescharacteristic
430C22×C3—21no—
431C22×C3—121no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3—122no—
437C22×C3C22×D1211yescharacteristic
438C22×C3C22×C3×D411yescharacteristic
439C2×D3—41no—
440C2×D3—42no—
441C2×D3—42no—
442C2×D3—41no—
443C2×D3—42no—
444C2×D3—41no—
445C3×C4—24no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—21no—
452C3×C4—22no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—42no—
456C3×C4—41no—
457C3×C4—121no—
458C3×C4—121no—
459C3×C4—121no—
460C3×C4—122no—
461C3×C4#90412yes—
462C3×C4C3×#13512yes—
463C3×C4C2×#23911yescharacteristic
464C3×C4#100911yescharacteristic
465C3×C4C2×C3×#4111yescharacteristic
466C3×C4C3×H(5,𝔽2)11yescharacteristic
467Dic3—41no—
468Dic3—41no—
469Dic3—42no—
470Dic3—41no—
471C32#339411yescharacteristic, complemented, Sylow
472C23—61no—
473C23—62no—
474Q8—22no—
475Q8—61no—
476Q8—62no—
477Q8—62no—
478Q8—61no—
479D4—61no—
480D4—62no—
481D4—61no—
482D4—62no—
483D4—122no—
484D4—241no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—122no—
490C2×C4—242no—
491C2×C4C2×C3×D1212yes—
492C2×C4C2×C3×D1212yes—
493C2×C4C2×C3×D1211yescharacteristic
494C2×C4C2×C3×D1211yescharacteristic
495C2×C4C23×C3×D311yescharacteristic
496C8—22no—
497C8—21no—
498C8C3×#23912yes—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—241no—
503C2×C3—242no—
504C2×C3#557711yescharacteristic
505C2×C3C2×#90411yescharacteristic
506C2×C3#575111yescharacteristic
507C2×C3C3×#55011yescharacteristic
508C2×C3C2×C3×#13511yescharacteristic
509C2×C3C3×#57711yescharacteristic
510D3—81no—
511D3—82no—
512C22—122no—
513C22—121no—
514C22—121no—
515C22—122no—
516C22—121no—
517C22—122no—
518C22C22×C3×D1211yescharacteristic
519C4—22no—
520C4—21no—
521C4—22no—
522C4—121no—
523C4—121no—
524C4—122no—
525C4—121no—
526C4C3×#90412yes—
527C4C2×C3×#23911yescharacteristic
528C4C3×#100911yescharacteristic
529C3—21no—
530C3#7991311yescharacteristic, direct product factor
531C3C3×#339411yescharacteristic, complemented
532C2—242no—
533C2—241no—
534C2C3×#557711yescharacteristic
535C2C2×C3×#90411yescharacteristic
536C2C3×#575111yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C8×Q8C2
socleC22×C32C22×D4
prime radicalC3×#4843C2
hypercenterC3×C8×Q8D3
hypocenterC3C3×#3394
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5585C2semidirect
2. C3×#5584C2semidirect
3. C32×C8×Q8C2semidirect
4. C3×#4849C2semidirect
5. C3×#4845C2semidirect
6. C3×#4844C2semidirect
8. C3×#4696C2semidirect
9. C3×#4693C2semidirect
10. C3×C4×#204C2semidirect
11. C3×C4×#204C2semidirect
13. #79913C3direct (N × H)
45. #5585C2×C3semidirect
46. #5584C2×C3semidirect
54. C3×C8×Q8D3semidirect
55. C3×C8×Q8C2×C3semidirect
58. #4849C2×C3semidirect
59. #4845C2×C3semidirect
60. #4844C2×C3semidirect
62. #4696C2×C3semidirect
63. #4693C2×C3semidirect
64. C4×#204C2×C3semidirect
65. C4×#204C2×C3semidirect
200. C8×Q8C3×D3semidirect
471. C32#3394semidirect
530. C3#79913direct (N × H)
531. 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×#55842
C32×C8×Q82
C3×#48492
C3×#48452
C3×#48442
C3×#48432
C3×#46962
C3×#46932
C3×C4×#2042
C3×#33943
#799133