Finite Group Databasebeta

← C3×#80873 #11878561

Subgroups — C3×#80873 #11878561

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5608C212yesmaximal, complemented
2C32×#469C211yesmaximal, characteristic, complemented
3C3×#5158C212yesmaximal, complemented
4C3×#5137C211yesmaximal, characteristic, complemented
5C3×#5129C211yesmaximal, characteristic, complemented
6C3×#5041C212yesmaximal, complemented
7C3×#4862C212yesmaximal, complemented
8C3×#4783C212yesmaximal, complemented
9C3×#4777C212yesmaximal, complemented
10C3×#3204—31nomaximal
11#80873C311yesmaximal, characteristic, direct product factor
12C2×C3×#237C2212yes—
13C2×C3×#235C2211yescharacteristic
14C2×C32×D8C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C32×#121C2212yes—
17C3×#939—22no—
18C3×#938—22no—
19C3×#938C2212yes—
20C2×C3×#214C2212yes—
21C3×#924C2212yes—
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C3×#897C2212yes—
25C3×D3×C4⋊C4C2212yes—
26C3×#884—22no—
27C3×#878—22no—
28C32×#106C2211yescharacteristic
29C32×#102C2212yes—
30C3×#832C2212yes—
31C3×(C2×D3)⋊C8C2212yes—
32C3×(C2×D3)⋊C8C2212yes—
33C3×#817C2211yescharacteristic
34C3×#816C2212yes—
35C3×#810C2212yes—
36C3×#808C2212yes—
37C3×#537—32no—
38#5608C2×C312yescomplemented
39C3×#483—32no—
40C3×#481—32no—
41C3×#470—31no—
42C3×#469—21no—
43C3×#469D311yescharacteristic, complemented
44C3×#469C2×C311yescharacteristic, complemented
45C3×#465—32no—
46C3×#452—32no—
47C3×#449—32no—
48C3×#408—31no—
49#5158C2×C312yescomplemented
50#5137C2×C311yescharacteristic, complemented
51#5129C2×C311yescharacteristic, complemented
52#5041C2×C312yescomplemented
53#4862C2×C312yescomplemented
54#4783C2×C312yescomplemented
55#4777C2×C312yescomplemented
56C2×C32×D4—22no—
57C2×C32×D4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C2×C3×#67—22no—
60C2×C3×#67—22no—
61C2×C3×#67D412yes—
62C22×C3×Dic3—22no—
63C3×#237—42no—
64C3×#237—42no—
65C3×#235—41no—
66C3×#235—41no—
67C2×C3×D12D411yescharacteristic
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3C2312yes—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C32×D8—41no—
73C32×M16—41no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77C32×C22⋊C4—22no—
78C3×#217—22no—
79C3×#217—22no—
80C3×#214—42no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×Dic3⋊C4—22no—
86C2×C3×C3⋊C8—41no—
87C2×C3×C3⋊C8C2312yes—
88C3×Dic12—41no—
89#3204—31noSylow
90C2×C3×#41—31no—
91C2×C3×#41—32no—
92C2×#237C22×C312yes—
93C2×#235C22×C311yescharacteristic
94C2×C3×Q16—31no—
95C2×C3×SD16—32no—
96C2×C3×D8—21no—
97C2×C3×D8C2×D311yescharacteristic
98C2×C3×D8C22×C311yescharacteristic
99C2×C3×M16—21no—
100C2×C3×M16C2×D311yescharacteristic
101C2×C3×M16C22×C311yescharacteristic
102C22×C3×C8—31no—
103C3×C22⋊Q8—32no—
104C3×C22⋊Q8—32no—
105C3×C22⋊Q8—62no—
106C3×#121—22no—
107C3×#121—32no—
108C3×#121—62no—
109C3×#121—62no—
110C3×#121—62no—
111C3×#121C2×D312yes—
112C3×#121C22×C312yes—
113C2×C3×C4⋊C4—32no—
114#939—22no—
115#938—22no—
116#938C22×C312yes—
117C2×#214C22×C312yes—
118#924C22×C312yes—
119C22×C3⋊C8C22×C311yescharacteristic
120C2×Dic12C22×C311yescharacteristic
121#897C22×C312yes—
122D3×C4⋊C4C22×C312yes—
123#884—22no—
124#878—22no—
125C3×#106—21no—
126C3×#106—31no—
127C3×#106—32no—
128C3×#106C2×D311yescharacteristic
129C3×#106C22×C311yescharacteristic
130C3×#103—32no—
131C3×#103—32no—
132C3×#102—22no—
133C3×#102—32no—
134C3×#102C2×D312yes—
135C3×#102C22×C312yes—
136C3×C22⋊C8—32no—
137C3×C22⋊C8—32no—
138#832C22×C312yes—
139(C2×D3)⋊C8C22×C312yes—
140(C2×D3)⋊C8C22×C312yes—
141#817C22×C311yescharacteristic
142#816C22×C312yes—
143#810C22×C312yes—
144#808C22×C312yes—
145C23×C32—22no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3C2×D412yes—
148C32×D4—22no—
149C32×D4—22no—
150C32×D4—82no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—22no—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2411yescharacteristic
156C3×#67—42no—
157C3×#67—44no—
158C3×#67—82no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—44no—
162C2×C3×Dic3C2×D412yes—
163C3×D12—41no—
164C3×C4×D3—22no—
165C3×C4×D3—22no—
166C3×C4×D3—82no—
167C3×Dic6—22no—
168C3×Dic6—22no—
169C3×Dic6—41no—
170C32×C8—21no—
171C32×C8—21no—
172C3×C3⋊C8—22no—
173#537—32no—
174#483—32no—
175#481—32no—
176#470—31no—
177#469C3×D311yescharacteristic, complemented
178#465—32no—
179#452—32no—
180#449—32no—
181#408—31no—
182C3×#41—121no—
183C3×#41—121no—
184C3×#41—122no—
185C3×#41—122no—
186C2×C3×Q8—31no—
187C2×C3×Q8—32no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—32no—
192C2×C3×D4—31no—
193C2×C3×D4—42no—
194C2×C3×D4—62no—
195C2×C3×D4—62no—
196C2×C3×D4C22×D312yes—
197C2×C3×D4C23×C312yes—
198C22×C3×C4—21no—
199C22×C3×C4—32no—
200C22×C3×C4—62no—
201C22×C3×C4—62no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C23×C311yescharacteristic
204C2×#67—22no—
205C2×#67—22no—
206C2×#67C3×D412yes—
207C22×Dic3—22no—
208#237—42no—
209#237—42no—
210#235—41no—
211#235—41no—
212C2×D12C3×D411yescharacteristic
213C2×C4×D3—22no—
214C2×C4×D3C23×C312yes—
215C2×Dic6C3×D411yescharacteristic
216C2×Dic6C23×C312yes—
217C3×Q16—121no—
218C3×SD16—122no—
219C3×D8—41no—
220C3×D8—41no—
221C3×D8—42no—
222C3×M16—41no—
223C3×M16—41no—
224C3×M16—42no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—32no—
228C2×C3×C8—121no—
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C23×C311yescharacteristic
232C2×C3×C8C23×C311yescharacteristic
233C3×C4⋊C4—22no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4C22×D312yes—
239C3×C4⋊C4C23×C312yes—
240C3×C22⋊C4—22no—
241C3×C22⋊C4—22no—
242C3×C22⋊C4—42no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—62no—
245C3×C22⋊C4—62no—
246#217—22no—
247#217—22no—
248#214—42no—
249(C2×D3)⋊C4—22no—
250C4⋊Dic3—22no—
251C4⋊Dic3C23×C312yes—
252Dic3⋊C4—22no—
253Dic3⋊C4—22no—
254C2×C3⋊C8—41no—
255C2×C3⋊C8C23×C312yes—
256Dic12—41no—
257C22×C32—21no—
258C22×C32—22no—
259C22×C32—42no—
260C22×C32—42no—
261C22×C32—42no—
262C22×C32C22×D411yescharacteristic
263C2×C3×D3—22no—
264C2×C3×D3—22no—
265C2×C3×D3—22no—
266C32×C4—21no—
267C32×C4—42no—
268C32×C4H(5,𝔽2)11yescharacteristic
269C32×C4H(5,𝔽2)11yescharacteristic
270C3×Dic3—22no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C2×#41—31no—
274C2×#41—32no—
275C2×Q16—31no—
276C2×SD16—32no—
277C2×D8C2×C3×D311yescharacteristic
278C2×M16C2×C3×D311yescharacteristic
279C22×C8—31no—
280C22⋊Q8—32no—
281C22⋊Q8—32no—
282C22⋊Q8—62no—
283#121—32no—
284#121—62no—
285#121—62no—
286#121—62no—
287#121C2×C3×D312yes—
288C2×C4⋊C4—32no—
289#106—31no—
290#106—32no—
291#106C2×C3×D311yescharacteristic
292#103—32no—
293#103—32no—
294#102—32no—
295#102C2×C3×D312yes—
296C22⋊C8—32no—
297C22⋊C8—32no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—21no—
301C23×C3—32no—
302C23×C3—42no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×C3×D411yescharacteristic
305C22×D3C2×C3×D412yes—
306C3×Q8—62no—
307C3×Q8—62no—
308C3×Q8—121no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—22no—
312C3×D4—22no—
313C3×D4—42no—
314C3×D4—42no—
315C3×D4—82no—
316C3×D4—82no—
317C3×D4—84no—
318C3×D4—121no—
319C3×D4—122no—
320C3×D4—124no—
321C3×D4—242no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—32no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—42no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—124no—
339C2×C3×C4—242no—
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4C2×C3×D411yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C24×C311yescharacteristic
344#67—42no—
345#67—44no—
346#67—82no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—44no—
350C2×Dic3C2×C3×D412yes—
351D12—41no—
352C4×D3—22no—
353C4×D3—22no—
354C4×D3—82no—
355Dic6—22no—
356Dic6—22no—
357Dic6—41no—
358C3×C8—22no—
359C3×C8—21no—
360C3×C8—21no—
361C3×C8—21no—
362C3×C8—21no—
363C3×C8—41no—
364C3×C8—62no—
365C3⋊C8—22no—
366C2×C32—41no—
367C2×C32—82no—
368C2×C32#53411yescharacteristic
369C2×C32#57712yes—
370C3×D3—42no—
371#41—121no—
372#41—121no—
373#41—122no—
374#41—122no—
375C2×Q8—31no—
376C2×Q8—32no—
377C2×D4—22no—
378C2×D4—32no—
379C2×D4—31no—
380C2×D4—62no—
381C2×D4—62no—
382C2×D4C22×C3×D312yes—
383C22×C4—32no—
384C22×C4—62no—
385C22×C4—62no—
386C22×C4C22×C3×D311yescharacteristic
387Q16—121no—
388SD16—122no—
389D8—41no—
390M16—41no—
391C2×C8—32no—
392C2×C8—121no—
393C2×C8C22×C3×D311yescharacteristic
394C2×C8C22×C3×D311yescharacteristic
395C4⋊C4—32no—
396C4⋊C4—62no—
397C4⋊C4—62no—
398C4⋊C4—62no—
399C4⋊C4C22×C3×D312yes—
400C22⋊C4—22no—
401C22⋊C4—62no—
402C22⋊C4—62no—
403C22⋊C4—62no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—41no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—62no—
418C22×C3—62no—
419C22×C3—62no—
420C22×C3—82no—
421C22×C3—82no—
422C22×C3—82no—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C22×C3×D411yescharacteristic
425C2×D3—22no—
426C2×D3—22no—
427C2×D3—22no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—41no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—62no—
436C3×C4—82no—
437C3×C4—122no—
438C3×C4—122no—
439C3×C4#100411yescharacteristic
440C3×C4#100911yescharacteristic
441C3×C4C3×H(5,𝔽2)11yescharacteristic
442C3×C4C3×H(5,𝔽2)11yescharacteristic
443Dic3—22no—
444Dic3—42no—
445Dic3—42no—
446C32#320411yescharacteristic, complemented, Sylow
447C23—22no—
448C23—32no—
449C23C3×D3×D411yescharacteristic
450Q8—62no—
451Q8—62no—
452Q8—121no—
453D4—22no—
454D4—22no—
455D4—82no—
456D4—121no—
457D4—122no—
458D4—124no—
459D4—242no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—32no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—124no—
469C2×C4—242no—
470C2×C4C3×D3×D411yescharacteristic
471C2×C4C23×C3×D311yescharacteristic
472C8—21no—
473C8—21no—
474C8—62no—
475C2×C3—22no—
476C2×C3—21no—
477C2×C3—41no—
478C2×C3—41no—
479C2×C3—81no—
480C2×C3—82no—
481C2×C3—82no—
482C2×C3—122no—
483C2×C3—162no—
484C2×C3#560511yescharacteristic
485C2×C3#577512yes—
486C2×C3C3×#53411yescharacteristic
487C2×C3C3×#57712yes—
488D3—42no—
489C22—22no—
490C22—21no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—62no—
495C22—62no—
496C22—62no—
497C22C2×C3×D3×D411yescharacteristic
498C4—21no—
499C4—42no—
500C4—62no—
501C4—122no—
502C4—122no—
503C4C3×#100411yescharacteristic
504C4C3×#100911yescharacteristic
505C3—21no—
506C3#8087311yescharacteristic, direct product factor
507C3C3×#320411yescharacteristic, complemented
508C2—41no—
509C2—82no—
510C2—122no—
511C2C3×#560511yescharacteristic
512C2C3×#577512yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#469C2
socleC22×C32C22×D4
hypercenterC3×#469D3
hypocenterC3C3×#3204
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#469

Complements

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

NH ≅ G/Ntype
1. C3×#5608C2semidirect
2. C32×#469C2semidirect
3. C3×#5158C2semidirect
4. C3×#5137C2semidirect
5. C3×#5129C2semidirect
6. C3×#5041C2semidirect
7. C3×#4862C2semidirect
8. C3×#4783C2semidirect
9. C3×#4777C2semidirect
11. #80873C3direct (N × H)
38. #5608C2×C3semidirect
43. C3×#469D3semidirect
44. C3×#469C2×C3semidirect
49. #5158C2×C3semidirect
50. #5137C2×C3semidirect
51. #5129C2×C3semidirect
52. #5041C2×C3semidirect
53. #4862C2×C3semidirect
54. #4783C2×C3semidirect
55. #4777C2×C3semidirect
177. #469C3×D3semidirect
446. C32#3204semidirect
506. C3#80873direct (N × H)
507. C3C3×#3204semidirect

Maximal subgroups

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

subgroupindex
C3×#56082
C32×#4692
C3×#51582
C3×#51372
C3×#51292
C3×#50412
C3×#48622
C3×#47832
C3×#47772
C3×#32043
#808733