Finite Group Databasebeta

← C3×#80995 #11895922

Subgroups — C3×#80995 #11895922

Order 1152.

818 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2C3×#5553C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic, complemented
6C3×#4891C212yesmaximal, complemented
7C3×#4889C212yesmaximal, complemented
8C3×#4848C211yesmaximal, characteristic, complemented
9C3×#4831C211yesmaximal, characteristic, complemented
10C3×#4764C212yesmaximal, complemented
11C3×#4762C212yesmaximal, complemented
12C3×#3368—31nomaximal
13#80995C311yesmaximal, characteristic, direct product factor
14C2×C3×#235—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×Q8×Dic3—21no—
18C3×#944—21no—
19C3×#940C2212yes—
20C2×C3×#214C2211yescharacteristic
21C3×#930—21no—
22C2×C3×#204C2212yes—
23C3×#893C2212yes—
24C3×#890C2212yes—
25C3×#889—22no—
26C3×#887C2212yes—
27C3×#884—22no—
28C3×#874C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#107C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#102C2212yes—
34C3×#832C2211yescharacteristic
35C3×#821C2212yes—
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×#810C2211yescharacteristic
39C3×#809C2212yes—
40C3×#809C2212yes—
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#557—31no—
44C3×#550—31no—
45#5721C2×C311yescharacteristic, complemented
46#5553C2×C311yescharacteristic
47C3×#490—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#474—21no—
51C3×#474D311yescharacteristic, complemented
52C3×#474C2×C311yescharacteristic, complemented
53C3×#460—31no—
54C3×#460—32no—
55C3×#446—31no—
56C3×#440—32no—
57C3×C4×SD16—31no—
58#5088C2×C311yescharacteristic, complemented
59C4×#214C2×C311yescharacteristic, complemented
60#4891C2×C312yescomplemented
61#4889C2×C312yescomplemented
62#4848C2×C311yescharacteristic, complemented
63#4831C2×C311yescharacteristic, complemented
64#4764C2×C312yescomplemented
65#4762C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C3×#235—44no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6D411yescharacteristic
77C2×C3×Dic6C2311yescharacteristic
78C2×C32×C8C2312yes—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yes—
81C32×C4⋊C4C2311yescharacteristic
82C32×C22⋊C4—21no—
83C32×C42C2311yescharacteristic
84C3×#214—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3—21no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×#204—24no—
99#3368—31noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C2×C3×SD16—31no—
103C2×C3×SD16—32no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—61no—
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C22×C311yescharacteristic
108C3×#127—32no—
109C3×#127—31no—
110C3×#125—32no—
111C3×#125—62no—
112C3×#121—62no—
113C3×#121—61no—
114C3×C4×Q8—31no—
115C3×C4×Q8—32no—
116C3×C4×Q8—31no—
117C3×C4×Q8—61no—
118C3×C4×D4—21no—
119C3×C4×D4—32no—
120C3×C4×D4C2×D311yescharacteristic
121C3×C4×D4C22×C311yescharacteristic
122Q8×Dic3—21no—
123#944—21no—
124#940C22×C312yes—
125C2×#214C22×C311yescharacteristic
126#930—21no—
127C2×#204C22×C312yes—
128#893C22×C312yes—
129#890C22×C312yes—
130#889—22no—
131#887C22×C312yes—
132#884—22no—
133#874C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#107—22no—
137C3×#107C2×D312yes—
138C3×#107C22×C312yes—
139C3×#106—31no—
140C3×C4⋊C8—21no—
141C3×C4⋊C8—32no—
142C3×C4⋊C8C2×D311yescharacteristic
143C3×C4⋊C8C22×C311yescharacteristic
144C3×#103—31no—
145C3×#102—22no—
146C3×#102—31no—
147C3×#102—32no—
148C3×#102—32no—
149C3×#102—32no—
150C3×#102C2×D312yes—
151C3×#102C22×C312yes—
152C3×#97—32no—
153C3×C4×C8—31no—
154#832C22×C311yescharacteristic
155#821C22×C312yes—
156#815C22×C312yes—
157Dic3⋊C8C22×C312yes—
158#810C22×C311yescharacteristic
159#809C22×C312yes—
160#809C22×C312yes—
161#808C22×C311yescharacteristic
162C4×C3⋊C8C22×C311yescharacteristic
163C23×C32—21no—
164C22×C3×D3—22no—
165C32×Q8—42no—
166C32×D4—21no—
167C32×D4—21no—
168C2×C32×C4—22no—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C3×#67—44no—
175C3×#67—82no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—22no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×C4×D3—44no—
185C3×Dic6—22no—
186C3×Dic6—21no—
187C3×Dic6#4112yescomplemented
188C32×C8—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—21no—
191#557—31no—
192#550—31no—
193#490—32no—
194#486—31no—
195#478—32no—
196#474C3×D311yescharacteristic, complemented
197#460—31no—
198#460—32no—
199#446—31no—
200#440—32no—
201C4×SD16—31no—
202C3×#41—124no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—31no—
206C2×C3×Q8—31no—
207C2×C3×Q8—41no—
208C2×C3×D4—21no—
209C2×C3×D4—32no—
210C2×C3×D4—62no—
211C2×C3×D4—62no—
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×#67—22no—
221C2×#67—22no—
222#235—44no—
223C2×D12—21no—
224C2×D12—21no—
225C2×D12C23×C312yes—
226C2×C4×D3—22no—
227C2×Dic6C3×D411yescharacteristic
228C2×Dic6C23×C311yescharacteristic
229C3×SD16—64no—
230C3×SD16—62no—
231C2×C3×C8—22no—
232C2×C3×C8—31no—
233C2×C3×C8—31no—
234C2×C3×C8C22×D312yes—
235C2×C3×C8C23×C312yes—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—41no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4C22×D312yes—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C23×C311yescharacteristic
251C3×C4⋊C4C23×C312yes—
252C3×C22⋊C4—21no—
253C3×C22⋊C4—21no—
254C3×C22⋊C4—41no—
255C3×C22⋊C4—62no—
256C3×C42—21no—
257C3×C42—32no—
258C3×C42—62no—
259C3×C42—61no—
260C3×C42C22×D311yescharacteristic
261C3×C42C23×C311yescharacteristic
262#214—22no—
263(C2×D3)⋊C4—22no—
264C4⋊Dic3—22no—
265C4⋊Dic3C3×D411yescharacteristic
266C4⋊Dic3C23×C311yescharacteristic
267Dic3⋊C4—21no—
268Dic3⋊C4—22no—
269Dic3⋊C4—22no—
270Dic3⋊C4C3×D412yes—
271C4×Dic3—21no—
272C4×Dic3—22no—
273C4×Dic3C23×C312yes—
274C2×C3⋊C8C23×C311yescharacteristic
275C2×C3⋊C8C23×C311yescharacteristic
276#204—24no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32C22×D411yescharacteristic
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C32×C4—21no—
285C32×C4—41no—
286C32×C4—42no—
287C32×C4AGL(1,ℤ/8)12yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C2×#41—61no—
295C2×SD16—31no—
296C2×SD16—32no—
297C4⋊Q8—61no—
298C4⋊Q8C2×C3×D311yescharacteristic
299#127—32no—
300#127—31no—
301#125—32no—
302#125—62no—
303#121—62no—
304#121—61no—
305C4×Q8—31no—
306C4×Q8—32no—
307C4×Q8—31no—
308C4×Q8—61no—
309C4×D4—32no—
310C4×D4C2×C3×D311yescharacteristic
311#107C2×C3×D312yes—
312#106—31no—
313C4⋊C8—32no—
314C4⋊C8C2×C3×D311yescharacteristic
315#103—31no—
316#102—31no—
317#102—32no—
318#102—32no—
319#102—32no—
320#102C2×C3×D312yes—
321#97—32no—
322C4×C8—31no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—41no—
326C23×C3—62no—
327C22×D3—22no—
328C3×Q8—32no—
329C3×Q8—42no—
330C3×Q8—42no—
331C3×Q8—62no—
332C3×Q8—61no—
333C3×Q8—82no—
334C3×D4—22no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—41no—
340C3×D4—62no—
341C3×D4—62no—
342C3×D4—124no—
343C3×D4—122no—
344C3×D4—241no—
345C3×D4—242no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—32no—
354C2×C3×C4—32no—
355C2×C3×C4—41no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—82no—
362C2×C3×C4—124no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C24×C311yescharacteristic
369#67—44no—
370#67—82no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3C2×C3×D412yes—
374C2×Dic3C2×C3×D412yes—
375D12—22no—
376D12—22no—
377D12—42no—
378D12—81no—
379C4×D3—44no—
380Dic6—22no—
381Dic6—21no—
382Dic6C3×#4112yescomplemented
383C3×C8—22no—
384C3×C8—22no—
385C3×C8—42no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—21no—
390C2×C32—81no—
391C2×C32#54811yescharacteristic
392C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
393C2×C32#57711yescharacteristic
394C3×D3—82no—
395#41—124no—
396C2×Q8—21no—
397C2×Q8—31no—
398C2×Q8—31no—
399C2×D4—32no—
400C2×D4—62no—
401C2×D4—62no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4C22×C3×D311yescharacteristic
405C22×C4—21no—
406C22×C4—62no—
407SD16—64no—
408SD16—62no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8C22×C3×D312yes—
412C4⋊C4—21no—
413C4⋊C4—31no—
414C4⋊C4—32no—
415C4⋊C4—31no—
416C4⋊C4—62no—
417C4⋊C4—62no—
418C4⋊C4—62no—
419C4⋊C4—61no—
420C4⋊C4C22×C3×D312yes—
421C4⋊C4C22×C3×D311yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—62no—
424C42—32no—
425C42—62no—
426C42—61no—
427C42C22×C3×D311yescharacteristic
428C22×C3—21no—
429C22×C3—42no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—81no—
437C22×C3—81no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C22×C3×D411yescharacteristic
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—42no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—42no—
454C3×C4—41no—
455C3×C4—42no—
456C3×C4—62no—
457C3×C4—62no—
458C3×C4—62no—
459C3×C4—81no—
460C3×C4—82no—
461C3×C4—121no—
462C3×C4#91112yes—
463C3×C4C3×AGL(1,ℤ/8)12yes—
464C3×C4#100711yescharacteristic
465C3×C4D3×#4111yescharacteristic
466C3×C4C2×C3×#4111yescharacteristic
467C3×C4C3×2−1+411yescharacteristic
468Dic3—22no—
469Dic3—22no—
470Dic3—22no—
471Dic3—41no—
472C32#336811yescharacteristic, complemented, Sylow
473C23—21no—
474C23—62no—
475Q8—32no—
476Q8—42no—
477Q8—62no—
478Q8—61no—
479D4—21no—
480D4—21no—
481D4—62no—
482D4—62no—
483D4—124no—
484D4—122no—
485D4—241no—
486D4—242no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—32no—
490C2×C4—32no—
491C2×C4—42no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—124no—
495C2×C4C3×D3×D411yescharacteristic
496C2×C4C3×D3×D411yescharacteristic
497C2×C4C23×C3×D311yescharacteristic
498C8—22no—
499C8—61no—
500C8—61no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—82no—
505C2×C3—81no—
506C2×C3—81no—
507C2×C3—242no—
508C2×C3#563311yescharacteristic
509C2×C3C2×#91111yescharacteristic
510C2×C3#577811yescharacteristic
511C2×C3C3×#54811yescharacteristic
512C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
513C2×C3C3×#57711yescharacteristic
514D3—82no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—122no—
519C22—122no—
520C22—122no—
521C22C2×C3×D3×D411yescharacteristic
522C4—21no—
523C4—41no—
524C4—42no—
525C4—62no—
526C4—62no—
527C4—62no—
528C4—121no—
529C4C3×#91112yes—
530C4C3×#100711yescharacteristic
531C4C3×D3×#4111yescharacteristic
532C3—21no—
533C3#8099511yescharacteristic, direct product factor
534C3C3×#336811yescharacteristic, complemented
535C2—81no—
536C2—242no—
537C2C3×#563311yescharacteristic
538C2C2×C3×#91111yescharacteristic
539C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC3×#5553C2
hypercenterC3×#474D3
hypocenterC3C3×#3368
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
1. C3×#5721C2semidirect
3. C32×#474C2semidirect
4. C3×#5088C2semidirect
5. C3×C4×#214C2semidirect
6. C3×#4891C2semidirect
7. C3×#4889C2semidirect
8. C3×#4848C2semidirect
9. C3×#4831C2semidirect
10. C3×#4764C2semidirect
11. C3×#4762C2semidirect
13. #80995C3direct (N × H)
45. #5721C2×C3semidirect
51. C3×#474D3semidirect
52. C3×#474C2×C3semidirect
58. #5088C2×C3semidirect
59. C4×#214C2×C3semidirect
60. #4891C2×C3semidirect
61. #4889C2×C3semidirect
62. #4848C2×C3semidirect
63. #4831C2×C3semidirect
64. #4764C2×C3semidirect
65. #4762C2×C3semidirect
187. C3×Dic6#41semidirect
196. #474C3×D3semidirect
382. Dic6C3×#41semidirect
472. C32#3368semidirect
533. C3#80995direct (N × H)
534. C3C3×#3368semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
C3×#55532
C32×#4742
C3×#50882
C3×C4×#2142
C3×#48912
C3×#48892
C3×#48482
C3×#48312
C3×#47642
C3×#47622
C3×#33683
#809953