Finite Group Databasebeta

← C3×#80371 #11895937

Subgroups — C3×#80371 #11895937

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic
2C3×#5570C211yesmaximal, characteristic, complemented
3C32×#460C211yesmaximal, characteristic, complemented
4C3×#5164C212yesmaximal, complemented
5C3×#5163C212yesmaximal, complemented
6C3×#5070C211yesmaximal, characteristic, complemented
7C3×C4×#215C211yesmaximal, characteristic, complemented
8C3×#4846C211yesmaximal, characteristic, complemented
9C3×#4831C211yesmaximal, characteristic, complemented
10C3×#4766C212yesmaximal, complemented
11C3×#4764C212yesmaximal, complemented
12C3×#3368—31nomaximal
13#80371C311yesmaximal, characteristic, direct product factor
14C2×C3×#237—21no—
15C2×C32×SD16C2212yes—
16C32×#127C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2211yescharacteristic
20C3×#940C2212yes—
21C3×#939—22no—
22C3×#938—21no—
23C3×D4×Dic3C2212yes—
24C3×#890—22no—
25C3×#890C2212yes—
26C3×C4×D12C2211yescharacteristic
27C3×#869—21no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6—21no—
30C3×C4×Dic6C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32C32×#102C2212yes—
33C3×#835C2211yescharacteristic
34C3×#832C2212yes—
35C3×#832C2212yes—
36C3×#821C2212yes—
37C3×#818C2212yes—
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#809C2211yescharacteristic
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#557—31no—
44C3×#550—31no—
45#5718C2×C311yescharacteristic
46#5570C2×C311yescharacteristic, complemented
47C3×#490—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#474—31no—
51C3×#460—21no—
52C3×#460—32no—
53C3×#460D311yescharacteristic, complemented
54C3×#460C2×C311yescharacteristic, complemented
55C3×#446—31no—
56C3×#440—32no—
57C3×C4×SD16—31no—
58#5164C2×C312yescomplemented
59#5163C2×C312yescomplemented
60#5070C2×C311yescharacteristic, complemented
61C4×#215C2×C311yescharacteristic, complemented
62#4846C2×C311yescharacteristic, complemented
63#4831C2×C311yescharacteristic, complemented
64#4766C2×C312yescomplemented
65#4764C2×C312yescomplemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4C2312yes—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—44no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6D411yescharacteristic
78C32×SD16—24no—
79C2×C32×C8C2312yes—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84C3×#217—22no—
85C3×#215—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99#3368—31noSylow
100C2×C3×#41—61no—
101C2×#237—21no—
102C2×C3×SD16—22no—
103C2×C3×SD16—31no—
104C2×C3×SD16C2×D312yes—
105C2×C3×SD16C22×C312yes—
106C3×C4⋊Q8—31no—
107C3×C4⋊Q8—61no—
108C3×#127—21no—
109C3×#127—32no—
110C3×#127C2×D311yescharacteristic
111C3×#127C22×C311yescharacteristic
112C3×#125—32no—
113C3×#125—62no—
114C3×#121—61no—
115C3×#121—62no—
116C3×C4×Q8—21no—
117C3×C4×Q8—31no—
118C3×C4×Q8—32no—
119C3×C4×Q8—61no—
120C3×C4×Q8C2×D311yescharacteristic
121C3×C4×Q8C22×C311yescharacteristic
122C3×C4×D4—32no—
123C3×C4×D4—31no—
124Q8×Dic3C22×C312yes—
125C2×#215C22×C311yescharacteristic
126#940C22×C312yes—
127#939—22no—
128#938—21no—
129D4×Dic3C22×C312yes—
130#890—22no—
131#890C22×C312yes—
132C4×D12C22×C311yescharacteristic
133#869—21no—
134#869C22×C311yescharacteristic
135C4×Dic6—21no—
136C4×Dic6C22×C311yescharacteristic
137C3×#107—32no—
138C3×#106—31no—
139C3×C4⋊C8—21no—
140C3×C4⋊C8—32no—
141C3×C4⋊C8C2×D311yescharacteristic
142C3×C4⋊C8C22×C311yescharacteristic
143C3×#103—31no—
144C3×#102—22no—
145C3×#102—32no—
146C3×#102—32no—
147C3×#102—32no—
148C3×#102—31no—
149C3×#102C2×D312yes—
150C3×#102C22×C312yes—
151C3×#97—32no—
152C3×C4×C8—31no—
153#835C22×C311yescharacteristic
154#832C22×C312yes—
155#832C22×C312yes—
156#821C22×C312yes—
157#818C22×C312yes—
158#815C22×C312yes—
159Dic3⋊C8C22×C312yes—
160#809C22×C311yescharacteristic
161#808C22×C311yescharacteristic
162C4×C3⋊C8C22×C311yescharacteristic
163C23×C32—22no—
164C22×C3×D3—21no—
165C32×Q8—21no—
166C32×Q8#4112yescomplemented
167C32×D4—22no—
168C32×D4—22no—
169C32×D4—42no—
170C32×D4—81no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C3×#67—44no—
177C3×#67—82no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—44no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—21no—
184C3×D12—21no—
185C3×C4×D3—42no—
186C3×Dic6—22no—
187C3×Dic6—42no—
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#474—31no—
197#460—32no—
198#460C3×D311yescharacteristic, complemented
199#446—31no—
200#440—32no—
201C4×SD16—31no—
202C3×#41—124no—
203C2×C3×Q8—21no—
204C2×C3×Q8—31no—
205C2×C3×Q8—61no—
206C2×C3×Q8C22×D311yescharacteristic
207C2×C3×Q8C23×C311yescharacteristic
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—22no—
213C2×C3×D4—31no—
214C2×C3×D4—41no—
215C2×C3×D4—41no—
216C2×C3×D4—62no—
217C2×C3×D4—62no—
218C2×C3×D4C22×D312yes—
219C2×C3×D4C23×C312yes—
220C22×C3×C4—62no—
221C22×C3×C4—61no—
222C2×#67—22no—
223C2×#67—22no—
224C22×Dic3—22no—
225#237—44no—
226C2×D12C23×C311yescharacteristic
227C2×C4×D3—21no—
228C2×Dic6—21no—
229C2×Dic6C3×D411yescharacteristic
230C3×SD16—24no—
231C3×SD16—24no—
232C3×SD16—44no—
233C3×SD16—62no—
234C2×C3×C8—22no—
235C2×C3×C8—31no—
236C2×C3×C8—31no—
237C2×C3×C8C22×D312yes—
238C2×C3×C8C23×C312yes—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—41no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4—62no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C4⋊C4C23×C311yescharacteristic
253C3×C22⋊C4—62no—
254C3×C22⋊C4—61no—
255C3×C42—21no—
256C3×C42—21no—
257C3×C42—21no—
258C3×C42—32no—
259C3×C42—41no—
260C3×C42—62no—
261C3×C42C22×D311yescharacteristic
262C3×C42C23×C311yescharacteristic
263#217—22no—
264#215—22no—
265(C2×D3)⋊C4—21no—
266C4⋊Dic3—21no—
267C4⋊Dic3—22no—
268C4⋊Dic3—22no—
269C4⋊Dic3C3×D411yescharacteristic
270C4⋊Dic3C23×C311yescharacteristic
271C4⋊Dic3C23×C312yes—
272Dic3⋊C4—22no—
273Dic3⋊C4C3×D412yes—
274C4×Dic3—22no—
275C4×Dic3C23×C312yes—
276C2×C3⋊C8C23×C311yescharacteristic
277C2×C3⋊C8C23×C311yescharacteristic
278C22×C32—42no—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C32×C4—22no—
286C32×C4—21no—
287C32×C4—41no—
288C32×C4AGL(1,ℤ/8)12yes—
289C32×C4C2×#4111yescharacteristic
290C32×C42−1+411yescharacteristic
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—42no—
294C3×Dic3—41no—
295C2×#41—61no—
296C2×SD16—31no—
297C2×SD16C2×C3×D312yes—
298C4⋊Q8—31no—
299C4⋊Q8—61no—
300#127—32no—
301#127C2×C3×D311yescharacteristic
302#125—32no—
303#125—62no—
304#121—61no—
305#121—62no—
306C4×Q8—31no—
307C4×Q8—32no—
308C4×Q8—61no—
309C4×Q8C2×C3×D311yescharacteristic
310C4×D4—32no—
311C4×D4—31no—
312#107—32no—
313#106—31no—
314C4⋊C8—32no—
315C4⋊C8C2×C3×D311yescharacteristic
316#103—31no—
317#102—32no—
318#102—32no—
319#102—32no—
320#102—31no—
321#102C2×C3×D312yes—
322#97—32no—
323C4×C8—31no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—42no—
327C23×C3—61no—
328C22×D3—21no—
329C3×Q8—21no—
330C3×Q8—21no—
331C3×Q8—22no—
332C3×Q8—41no—
333C3×Q8—62no—
334C3×Q8—122no—
335C3×Q8#23712yescomplemented
336C3×Q8C3×#4112yescomplemented
337C3×D4—22no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—42no—
342C3×D4—42no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—61no—
346C3×D4—61no—
347C3×D4—82no—
348C3×D4—81no—
349C3×D4—81no—
350C3×D4—82no—
351C3×D4—124no—
352C3×D4—242no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—32no—
361C2×C3×C4—32no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—62no—
365C2×C3×C4—61no—
366C2×C3×C4—124no—
367C2×C3×C4—122no—
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4C2×C3×D411yescharacteristic
371C2×C3×C4C2×C3×D411yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C24×C311yescharacteristic
374#67—44no—
375#67—82no—
376C2×Dic3—22no—
377C2×Dic3—21no—
378C2×Dic3—44no—
379C2×Dic3C2×C3×D412yes—
380C2×Dic3C2×C3×D412yes—
381D12—21no—
382D12—21no—
383C4×D3—42no—
384Dic6—22no—
385Dic6—42no—
386C3×C8—22no—
387C3×C8—22no—
388C3×C8—42no—
389C3×C8—61no—
390C3×C8—61no—
391C3⋊C8—21no—
392C3⋊C8—21no—
393C2×C32—82no—
394C2×C32#54811yescharacteristic
395C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
396C2×C32#57711yescharacteristic
397C3×D3—81no—
398#41—124no—
399C2×Q8—31no—
400C2×Q8—61no—
401C2×Q8C22×C3×D311yescharacteristic
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—31no—
405C2×D4—62no—
406C2×D4—62no—
407C2×D4C22×C3×D312yes—
408C22×C4—62no—
409C22×C4—61no—
410SD16—24no—
411SD16—62no—
412C2×C8—31no—
413C2×C8—31no—
414C2×C8C22×C3×D312yes—
415C4⋊C4—21no—
416C4⋊C4—31no—
417C4⋊C4—32no—
418C4⋊C4—32no—
419C4⋊C4—31no—
420C4⋊C4—62no—
421C4⋊C4—62no—
422C4⋊C4—62no—
423C4⋊C4—61no—
424C4⋊C4C22×C3×D311yescharacteristic
425C22⋊C4—62no—
426C22⋊C4—61no—
427C42—21no—
428C42—32no—
429C42—62no—
430C42C22×C3×D311yescharacteristic
431C22×C3—21no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—82no—
439C22×C3—82no—
440C22×C3—82no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C22×C3×D411yescharacteristic
446C2×D3—41no—
447C2×D3—41no—
448C2×D3—41no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—41no—
457C3×C4—42no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—81no—
463C3×C4—121no—
464C3×C4—122no—
465C3×C4#91412yes—
466C3×C4C3×AGL(1,ℤ/8)12yes—
467C3×C4C2×#23711yescharacteristic
468C3×C4#101011yescharacteristic
469C3×C4C2×C3×#4111yescharacteristic
470C3×C4C3×2−1+411yescharacteristic
471Dic3—22no—
472Dic3—22no—
473Dic3—42no—
474Dic3—41no—
475C32#336811yescharacteristic, complemented, Sylow
476C23—22no—
477C23—61no—
478Q8—21no—
479Q8—62no—
480Q8—122no—
481Q8C3×#23712yescomplemented
482D4—22no—
483D4—22no—
484D4—42no—
485D4—61no—
486D4—61no—
487D4—81no—
488D4—124no—
489D4—242no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—62no—
495C2×C4—61no—
496C2×C4—124no—
497C2×C4—122no—
498C2×C4C3×D3×D411yescharacteristic
499C2×C4C3×D3×D411yescharacteristic
500C2×C4C23×C3×D311yescharacteristic
501C8—22no—
502C8—61no—
503C8—61no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—82no—
508C2×C3—82no—
509C2×C3—162no—
510C2×C3—241no—
511C2×C3#559811yescharacteristic
512C2×C3C2×#91411yescharacteristic
513C2×C3#577511yescharacteristic
514C2×C3C3×#54811yescharacteristic
515C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
516C2×C3C3×#57711yescharacteristic
517D3—81no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—121no—
522C22—121no—
523C22—121no—
524C22C2×C3×D3×D411yescharacteristic
525C4—21no—
526C4—22no—
527C4—41no—
528C4—62no—
529C4—62no—
530C4—121no—
531C4—122no—
532C4C3×#91412yes—
533C4C2×C3×#23711yescharacteristic
534C4C3×#101011yescharacteristic
535C3—21no—
536C3#8037111yescharacteristic, direct product factor
537C3C3×#336811yescharacteristic, complemented
538C2—82no—
539C2—241no—
540C2C3×#559811yescharacteristic
541C2C2×C3×#91411yescharacteristic
542C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#460C2
socleC22×C32C22×D4
prime radicalC3×#5718C2
hypercenterC3×#460D3
hypocenterC3C3×#3368
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
2. C3×#5570C2semidirect
3. C32×#460C2semidirect
4. C3×#5164C2semidirect
5. C3×#5163C2semidirect
6. C3×#5070C2semidirect
7. C3×C4×#215C2semidirect
8. C3×#4846C2semidirect
9. C3×#4831C2semidirect
10. C3×#4766C2semidirect
11. C3×#4764C2semidirect
13. #80371C3direct (N × H)
46. #5570C2×C3semidirect
53. C3×#460D3semidirect
54. C3×#460C2×C3semidirect
58. #5164C2×C3semidirect
59. #5163C2×C3semidirect
60. #5070C2×C3semidirect
61. C4×#215C2×C3semidirect
62. #4846C2×C3semidirect
63. #4831C2×C3semidirect
64. #4766C2×C3semidirect
65. #4764C2×C3semidirect
166. C32×Q8#41semidirect
198. #460C3×D3semidirect
335. C3×Q8#237semidirect
336. C3×Q8C3×#41semidirect
475. C32#3368semidirect
481. Q8C3×#237semidirect
536. C3#80371direct (N × H)
537. C3C3×#3368semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
C3×#55702
C32×#4602
C3×#51642
C3×#51632
C3×#50702
C3×C4×#2152
C3×#48462
C3×#48312
C3×#47662
C3×#47642
C3×#33683
#803713