Finite Group Databasebeta

← C3×#80959 #11897531

Subgroups — C3×#80959 #11897531

Order 1152.

802 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic, complemented
2C3×#5543C211yesmaximal, characteristic, complemented
3C32×#474C211yesmaximal, characteristic, complemented
4C3×#5080C211yesmaximal, characteristic, complemented
5C3×C4×#213C211yesmaximal, characteristic
6C3×#4891C212yesmaximal, complemented
7C3×#4876C212yesmaximal, complemented
8C3×#4842C211yesmaximal, characteristic, complemented
9C3×#4831C211yesmaximal, characteristic, complemented
10C3×#4785C212yesmaximal
11C3×#4761C212yesmaximal, complemented
12C3×#3384—31nomaximal
13#80959C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#946—21no—
18C3×D4×Dic3C2212yes—
19C2×C3×#213C2211yescharacteristic
20C2×C3×C4⋊Dic3—21no—
21C3×#924—21no—
22C3×#896—22no—
23C3×#893C2212yes—
24C3×#890C2212yes—
25C3×#888C2212yes—
26C3×#878—22no—
27C3×C4×D12C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C32×#107C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×#102C2212yes—
33C3×#832C2211yescharacteristic
34C3×#821C2212yes—
35C3×#817C2212yes—
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×#809C2211yescharacteristic
39C3×#808C2212yes—
40C3×#808C2212yes—
41C3×#807C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#554—31no—
44C3×D4×Q8—31no—
45#5727C2×C311yescharacteristic, complemented
46#5543C2×C311yescharacteristic, complemented
47C3×#501—32no—
48C3×#498—31no—
49C3×#478—32no—
50C3×#476—31no—
51C3×#476—32no—
52C3×#474—21no—
53C3×#474D311yescharacteristic, complemented
54C3×#474C2×C311yescharacteristic, complemented
55C3×#446—31no—
56C3×#442—32no—
57C3×C4×D8—31no—
58#5080C2×C311yescharacteristic, complemented
59C4×#213C2×C311yescharacteristic
60#4891C2×C312yescomplemented
61#4876C2×C312yescomplemented
62#4842C2×C311yescharacteristic, complemented
63#4831C2×C311yescharacteristic, complemented
64#4785C2×C312yes—
65#4761C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C22×C3×Dic3—22no—
70C3×D3×Q8—44no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6D411yescharacteristic
77C2×C32×C8C2312yes—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2312yes—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42C2311yescharacteristic
83C3×#217—22no—
84C3×#213Q814yescomplemented
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—22no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2312yes—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3384—31noSylow
99C22×C3×Q8—61no—
100C2×D3×Q8—21no—
101C2×C3×D8—31no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C22×C311yescharacteristic
107C3×#125—32no—
108C3×C22⋊Q8—62no—
109C3×C22⋊Q8—62no—
110C3×C22⋊Q8—61no—
111C3×C22⋊Q8—61no—
112C3×C4×Q8—31no—
113C3×C4×D4—21no—
114C3×C4×D4—32no—
115C3×C4×D4—32no—
116C3×C4×D4—31no—
117C3×C4×D4C2×D311yescharacteristic
118C3×C4×D4C22×C311yescharacteristic
119C2×C3×C4⋊C4—61no—
120#946—21no—
121D4×Dic3C22×C312yes—
122C2×#213C22×C311yescharacteristic
123C2×C4⋊Dic3—21no—
124#924—21no—
125#896—22no—
126#893C22×C312yes—
127#890C22×C312yes—
128#888C22×C312yes—
129#878—22no—
130C4×D12C22×C311yescharacteristic
131#869C22×C311yescharacteristic
132C4×Dic6C22×C311yescharacteristic
133C3×#107—22no—
134C3×#107—31no—
135C3×#107C2×D312yes—
136C3×#107C22×C312yes—
137C3×#106—32no—
138C3×#106—32no—
139C3×#106—32no—
140C3×C4⋊C8—21no—
141C3×C4⋊C8—32no—
142C3×C4⋊C8C2×D311yescharacteristic
143C3×C4⋊C8C22×C311yescharacteristic
144C3×#102—22no—
145C3×#102—31no—
146C3×#102—32no—
147C3×#102—31no—
148C3×#102C2×D312yes—
149C3×#102C22×C312yes—
150C3×#97—32no—
151C3×C4×C8—31no—
152#832C22×C311yescharacteristic
153#821C22×C312yes—
154#817C22×C312yes—
155#815C22×C312yes—
156Dic3⋊C8C22×C312yes—
157#809C22×C311yescharacteristic
158#808C22×C312yes—
159#808C22×C312yes—
160#807C22×C311yescharacteristic
161C4×C3⋊C8C22×C311yescharacteristic
162C23×C32—21no—
163C22×C3×D3—21no—
164C32×Q8—42no—
165C32×D4—21no—
166C32×D4C2×Q812yescomplemented
167C2×C32×C4—21no—
168C2×C32×C4—22no—
169C2×C32×C4—42no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—82no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—21no—
179C3×D12C2×Q812yes—
180C3×C4×D3—44no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183C3×Dic6—44no—
184C3×Dic6—81no—
185C32×C8—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8C2×Q812yescomplemented
188#554—31no—
189D4×Q8—31no—
190#501—32no—
191#498—31no—
192#478—32no—
193#476—31no—
194#476—32no—
195#474C3×D311yescharacteristic, complemented
196#446—31no—
197#442—32no—
198C4×D8—31no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—31no—
202C2×C3×Q8—41no—
203C2×C3×Q8—62no—
204C2×C3×Q8—61no—
205C2×C3×Q8—124no—
206C2×C3×D4—21no—
207C2×C3×D4—31no—
208C2×C3×D4C22×D311yescharacteristic
209C2×C3×D4C23×C311yescharacteristic
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—41no—
213C22×C3×C4—62no—
214C22×C3×C4—62no—
215C22×C3×C4—61no—
216C22×Dic3—22no—
217D3×Q8—44no—
218C2×D12C23×C311yescharacteristic
219C2×C4×D3—21no—
220C2×C4×D3—22no—
221C2×Dic6—22no—
222C2×Dic6—21no—
223C2×Dic6C3×D411yescharacteristic
224C3×D8—34no—
225C2×C3×C8—22no—
226C2×C3×C8—31no—
227C2×C3×C8—31no—
228C2×C3×C8C22×D312yes—
229C2×C3×C8C23×C312yes—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C4⋊C4C22×D312yes—
245C3×C4⋊C4C23×C311yescharacteristic
246C3×C4⋊C4C23×C312yes—
247C3×C22⋊C4—21no—
248C3×C22⋊C4—21no—
249C3×C22⋊C4—41no—
250C3×C22⋊C4—62no—
251C3×C22⋊C4—62no—
252C3×C22⋊C4—61no—
253C3×C42—21no—
254C3×C42—32no—
255C3×C42C22×D311yescharacteristic
256C3×C42C23×C311yescharacteristic
257#217—22no—
258#213C3×Q814yescomplemented
259(C2×D3)⋊C4—21no—
260(C2×D3)⋊C4—22no—
261C4⋊Dic3—21no—
262C4⋊Dic3—22no—
263C4⋊Dic3C3×D411yescharacteristic
264C4⋊Dic3C23×C311yescharacteristic
265C4⋊Dic3C23×C312yes—
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268Dic3⋊C4C3×D412yes—
269C4×Dic3C23×C312yes—
270C2×C3⋊C8C23×C311yescharacteristic
271C2×C3⋊C8C23×C311yescharacteristic
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4—42no—
281C32×C4—41no—
282C32×C4AGL(1,ℤ/8)12yes—
283C32×C4C22×Q811yescharacteristic
284C32×C42−1+411yescharacteristic
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—42no—
289C22×Q8—61no—
290C2×D8—31no—
291C4⋊Q8—32no—
292C4⋊Q8—31no—
293C4⋊Q8C2×C3×D311yescharacteristic
294#125—32no—
295C22⋊Q8—62no—
296C22⋊Q8—62no—
297C22⋊Q8—61no—
298C22⋊Q8—61no—
299C4×Q8—31no—
300C4×D4—32no—
301C4×D4—32no—
302C4×D4—31no—
303C4×D4C2×C3×D311yescharacteristic
304C2×C4⋊C4—61no—
305#107—31no—
306#107C2×C3×D312yes—
307#106—32no—
308#106—32no—
309#106—32no—
310C4⋊C8—32no—
311C4⋊C8C2×C3×D311yescharacteristic
312#102—31no—
313#102—32no—
314#102—31no—
315#102C2×C3×D312yes—
316#97—32no—
317C4×C8—31no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—41no—
321C23×C3—61no—
322C22×D3—21no—
323C3×Q8—42no—
324C3×Q8—42no—
325C3×Q8—62no—
326C3×Q8—82no—
327C3×Q8—124no—
328C3×Q8—241no—
329C3×D4—21no—
330C3×D4—21no—
331C3×D4—22no—
332C3×D4—32no—
333C3×D4—41no—
334C3×D4—61no—
335C3×D4D3×Q812yescomplemented
336C3×D4C2×C3×Q812yescomplemented
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—41no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—82no—
353C2×C3×C4—124no—
354C2×C3×C4—122no—
355C2×C3×C4—242no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C2×C3×D411yescharacteristic
359C2×C3×C4C2×C3×D411yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×C3×C4C24×C311yescharacteristic
362C2×Dic3—21no—
363C2×Dic3—22no—
364C2×Dic3—82no—
365C2×Dic3C2×C3×D412yes—
366C2×Dic3C2×C3×D412yes—
367D12—21no—
368D12C2×C3×Q812yes—
369C4×D3—44no—
370C4×D3—42no—
371Dic6—22no—
372Dic6—44no—
373Dic6—81no—
374C3×C8—22no—
375C3×C8—22no—
376C3×C8—32no—
377C3×C8—42no—
378C3×C8—61no—
379C3⋊C8—21no—
380C3⋊C8C2×C3×Q812yescomplemented
381C2×C32—42no—
382C2×C32D4×Q811yescharacteristic
383C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
384C2×C32#57711yescharacteristic
385C3×D3—42no—
386C2×Q8—21no—
387C2×Q8—31no—
388C2×Q8—62no—
389C2×Q8—61no—
390C2×Q8—124no—
391C2×D4—31no—
392C2×D4C22×C3×D311yescharacteristic
393C22×C4—21no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4—61no—
397D8—34no—
398C2×C8—31no—
399C2×C8—31no—
400C2×C8C22×C3×D312yes—
401C4⋊C4—21no—
402C4⋊C4—31no—
403C4⋊C4—32no—
404C4⋊C4—32no—
405C4⋊C4—31no—
406C4⋊C4—62no—
407C4⋊C4—62no—
408C4⋊C4—62no—
409C4⋊C4—61no—
410C4⋊C4C22×C3×D311yescharacteristic
411C4⋊C4C22×C3×D312yes—
412C22⋊C4—21no—
413C22⋊C4—62no—
414C22⋊C4—62no—
415C22⋊C4—61no—
416C42—32no—
417C42C22×C3×D311yescharacteristic
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—42no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—62no—
427C22×C3—81no—
428C22×C3—81no—
429C22×C3—121no—
430C22×C3—121no—
431C22×C3C2×D3×D411yescharacteristic
432C22×C3C22×C3×D411yescharacteristic
433C2×D3—22no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—41no—
442C3×C4—42no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—42no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—81no—
449C3×C4—82no—
450C3×C4—121no—
451C3×C4—122no—
452C3×C4#91112yes—
453C3×C4C3×AGL(1,ℤ/8)12yes—
454C3×C4C2×D3×Q811yescharacteristic
455C3×C4#101011yescharacteristic
456C3×C4C22×C3×Q811yescharacteristic
457C3×C4C3×2−1+411yescharacteristic
458Dic3—22no—
459Dic3—22no—
460Dic3—41no—
461Dic3—42no—
462C32#338411yescharacteristic, complemented, Sylow
463C23—21no—
464C23—61no—
465Q8—42no—
466Q8—62no—
467Q8—124no—
468Q8—241no—
469D4—21no—
470D4—32no—
471D4—61no—
472D4C3×D3×Q812yescomplemented
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—42no—
478C2×C4—62no—
479C2×C4—61no—
480C2×C4—124no—
481C2×C4—122no—
482C2×C4—242no—
483C2×C4C3×D3×D411yescharacteristic
484C2×C4C3×D3×D411yescharacteristic
485C2×C4C23×C3×D311yescharacteristic
486C8—22no—
487C8—32no—
488C8—61no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—42no—
493C2×C3—42no—
494C2×C3—82no—
495C2×C3—122no—
496C2×C3#563211yescharacteristic
497C2×C3C2×#91111yescharacteristic
498C2×C3#577811yescharacteristic
499C2×C3C3×D4×Q811yescharacteristic
500C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
501C2×C3C3×#57711yescharacteristic
502D3—42no—
503C22—22no—
504C22—41no—
505C22—41no—
506C22—62no—
507C22—121no—
508C22—121no—
509C22C2×C3×D3×D411yescharacteristic
510C4—21no—
511C4—41no—
512C4—42no—
513C4—62no—
514C4—62no—
515C4—121no—
516C4—122no—
517C4C3×#91112yes—
518C4C2×C3×D3×Q811yescharacteristic
519C4C3×#101011yescharacteristic
520C3—21no—
521C3#8095911yescharacteristic, direct product factor
522C3C3×#338411yescharacteristic, complemented
523C2—42no—
524C2—122no—
525C2C3×#563211yescharacteristic
526C2C2×C3×#91111yescharacteristic
527C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC3×#474D3
hypocenterC3C3×#3384
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×#5727C2semidirect
2. C3×#5543C2semidirect
3. C32×#474C2semidirect
4. C3×#5080C2semidirect
6. C3×#4891C2semidirect
7. C3×#4876C2semidirect
8. C3×#4842C2semidirect
9. C3×#4831C2semidirect
11. C3×#4761C2semidirect
13. #80959C3direct (N × H)
45. #5727C2×C3semidirect
46. #5543C2×C3semidirect
53. C3×#474D3semidirect
54. C3×#474C2×C3semidirect
58. #5080C2×C3semidirect
60. #4891C2×C3semidirect
61. #4876C2×C3semidirect
62. #4842C2×C3semidirect
63. #4831C2×C3semidirect
65. #4761C2×C3semidirect
84. C3×#213Q8semidirect
166. C32×D4C2×Q8semidirect
187. C3×C3⋊C8C2×Q8semidirect
195. #474C3×D3semidirect
258. #213C3×Q8semidirect
335. C3×D4D3×Q8semidirect
336. C3×D4C2×C3×Q8semidirect
380. C3⋊C8C2×C3×Q8semidirect
462. C32#3384semidirect
472. D4C3×D3×Q8semidirect
521. C3#80959direct (N × H)
522. C3C3×#3384semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C3×#55432
C32×#4742
C3×#50802
C3×C4×#2132
C3×#48912
C3×#48762
C3×#48422
C3×#48312
C3×#47852
C3×#47612
C3×#33843
#809593