Finite Group Databasebeta

← C3×#81091 #11896023

Subgroups — C3×#81091 #11896023

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5722C211yesmaximal, characteristic, complemented
2C3×#5542C211yesmaximal, characteristic
3C32×#476C211yesmaximal, characteristic
4C3×#5093C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic
6C3×#4854C212yesmaximal, complemented
7C3×#4853C212yesmaximal, complemented
8C3×#4849C211yesmaximal, characteristic, complemented
9C3×#4831C211yesmaximal, characteristic, complemented
10C3×#4767C212yesmaximal
11C3×#4765C212yesmaximal
12C3×#3369—31nomaximal
13#81091C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16C3×#944—22no—
17C3×#936C2212yes—
18C2×C3×#214C2211yescharacteristic
19C3×#926—21no—
20C3×#924—21no—
21C2×C3×Dic12C2212yes—
22C3×#888—21no—
23C3×#888C2212yes—
24C3×#887—21no—
25C3×#887C2212yes—
26C3×#887C2212yes—
27C3×#879—22no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#102C2212yes—
34C3×#832C2211yescharacteristic
35C3×#816C2212yes—
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×#810C2211yescharacteristic
39C3×#810C2212yes—
40C3×#810C2212yes—
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×Q82—31no—
44C3×#556—31no—
45#5722C2×C311yescharacteristic, complemented
46#5542C2×C311yescharacteristic
47C3×#489—32no—
48C3×#487—31no—
49C3×#476—21no—
50C3×#476D311yescharacteristic
51C3×#476C2×C311yescharacteristic
52C3×#475—32no—
53C3×#464—32no—
54C3×#462—31no—
55C3×#446—31no—
56C3×#441—32no—
57C3×C4×SD16—31no—
58#5093C2×C311yescharacteristic, complemented
59C4×#214C2×C311yescharacteristic
60#4854C2×C312yescomplemented
61#4853C2×C312yescomplemented
62#4849C2×C311yescharacteristic, complemented
63#4831C2×C311yescharacteristic, complemented
64#4767C2×C312yes—
65#4765C2×C312yes—
66C2×C32×Q8—21no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×C3×Dic6C2311yescharacteristic
73C2×C32×C8C2312yes—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77C32×C22⋊C4—21no—
78C32×C42C2311yescharacteristic
79C3×#217—22no—
80C3×#217—22no—
81C3×#214—22no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×Dic3⋊C4—21no—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—21no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C3×Dic12—24no—
98#3369—31noSylow
99C2×C3×Q16—32no—
100C2×C3×SD16—31no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—32no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—61no—
105C3×C4⋊Q8—62no—
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C22×C311yescharacteristic
108C3×#126—62no—
109C3×#124—32no—
110C3×C22⋊Q8—61no—
111C3×C4×Q8—31no—
112C3×C4×Q8—32no—
113C3×C4×Q8—32no—
114C3×C4×Q8—31no—
115C3×C4×Q8—61no—
116C3×C4×D4—21no—
117C3×C4×D4C2×D311yescharacteristic
118C3×C4×D4C22×C311yescharacteristic
119C3×#117—61no—
120#944—22no—
121#936C22×C312yes—
122C2×#214C22×C311yescharacteristic
123#926—21no—
124#924—21no—
125C2×Dic12C22×C312yes—
126#888—21no—
127#888C22×C312yes—
128#887—21no—
129#887C22×C312yes—
130#887C22×C312yes—
131#879—22no—
132#869C22×C311yescharacteristic
133C4×Dic6C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C3×#106—22no—
136C3×#106—31no—
137C3×#106C2×D312yes—
138C3×#106C22×C312yes—
139C3×C4⋊C8—21no—
140C3×C4⋊C8—32no—
141C3×C4⋊C8C2×D311yescharacteristic
142C3×C4⋊C8C22×C311yescharacteristic
143C3×#103—32no—
144C3×#103—31no—
145C3×#103—32no—
146C3×#103—32no—
147C3×#102—22no—
148C3×#102—31no—
149C3×#102C2×D312yes—
150C3×#102C22×C312yes—
151C3×#97—32no—
152C3×C4×C8—31no—
153#832C22×C311yescharacteristic
154#816C22×C312yes—
155#815C22×C312yes—
156Dic3⋊C8C22×C312yes—
157#810C22×C311yescharacteristic
158#810C22×C312yes—
159#810C22×C312yes—
160#808C22×C311yescharacteristic
161C4×C3⋊C8C22×C311yescharacteristic
162C23×C32—21no—
163C32×Q8—81no—
164C32×D4—21no—
165C32×D4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—22no—
168C2×C32×C4—42no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×Dic6—22no—
178C3×Dic6—21no—
179C3×Dic6—22no—
180C3×Dic6—22no—
181C3×Dic6—82no—
182C3×Dic6#4112yes—
183C32×C8—22no—
184C3×C3⋊C8—21no—
185C3×C3⋊C8—21no—
186Q82—31no—
187#556—31no—
188#489—32no—
189#487—31no—
190#476C3×D311yescharacteristic
191#475—32no—
192#464—32no—
193#462—31no—
194#446—31no—
195#441—32no—
196C4×SD16—31no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8—31no—
201C2×C3×Q8—32no—
202C2×C3×Q8—41no—
203C2×C3×Q8—62no—
204C2×C3×D4—21no—
205C2×C3×D4C22×D311yescharacteristic
206C2×C3×D4C23×C311yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—41no—
210C2×Dic6—22no—
211C2×Dic6C3×D411yescharacteristic
212C2×Dic6C23×C312yes—
213C2×Dic6C23×C311yescharacteristic
214C3×Q16—64no—
215C3×SD16—62no—
216C2×C3×C8—22no—
217C2×C3×C8—31no—
218C2×C3×C8—31no—
219C2×C3×C8C22×D312yes—
220C2×C3×C8C23×C312yes—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4C22×D312yes—
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C4⋊C4C23×C311yescharacteristic
238C3×C4⋊C4C23×C312yes—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—41no—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C42—21no—
245C3×C42—32no—
246C3×C42—62no—
247C3×C42—62no—
248C3×C42—61no—
249C3×C42C22×D311yescharacteristic
250C3×C42C23×C311yescharacteristic
251#217—22no—
252#217—22no—
253#214—22no—
254C4⋊Dic3—21no—
255C4⋊Dic3—21no—
256C4⋊Dic3C3×D411yescharacteristic
257C4⋊Dic3C23×C311yescharacteristic
258Dic3⋊C4—21no—
259Dic3⋊C4—22no—
260Dic3⋊C4—22no—
261Dic3⋊C4—22no—
262Dic3⋊C4C3×D412yes—
263C4×Dic3—21no—
264C4×Dic3—22no—
265C4×Dic3—22no—
266C4×Dic3C23×C312yes—
267C2×C3⋊C8C23×C311yescharacteristic
268C2×C3⋊C8C23×C311yescharacteristic
269Dic12—24no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32C22×D411yescharacteristic
274C32×C4—21no—
275C32×C4—41no—
276C32×C4—42no—
277C32×C4#13712yes—
278C32×C4C2×#4111yescharacteristic
279C32×C42−1+411yescharacteristic
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—42no—
284C3×Dic3—41no—
285C2×Q16—32no—
286C2×SD16—31no—
287C4⋊Q8—32no—
288C4⋊Q8—31no—
289C4⋊Q8—61no—
290C4⋊Q8—62no—
291C4⋊Q8C2×C3×D311yescharacteristic
292#126—62no—
293#124—32no—
294C22⋊Q8—61no—
295C4×Q8—31no—
296C4×Q8—32no—
297C4×Q8—32no—
298C4×Q8—31no—
299C4×Q8—61no—
300C4×D4C2×C3×D311yescharacteristic
301#117—61no—
302#106—31no—
303#106C2×C3×D312yes—
304C4⋊C8—32no—
305C4⋊C8C2×C3×D311yescharacteristic
306#103—32no—
307#103—31no—
308#103—32no—
309#103—32no—
310#102—31no—
311#102C2×C3×D312yes—
312#97—32no—
313C4×C8—31no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—41no—
317C3×Q8—32no—
318C3×Q8—62no—
319C3×Q8—61no—
320C3×Q8—62no—
321C3×Q8—62no—
322C3×Q8—81no—
323C3×Q8—81no—
324C3×Q8—82no—
325C3×Q8—242no—
326C3×D4—22no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—21no—
331C3×D4—41no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—41no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—61no—
348C2×C3×C4—82no—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4C2×C3×D411yescharacteristic
352C2×C3×C4C2×C3×D411yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C24×C311yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—22no—
358C2×Dic3C2×C3×D412yes—
359C2×Dic3C2×C3×D412yes—
360Dic6—22no—
361Dic6—21no—
362Dic6—22no—
363Dic6—22no—
364Dic6—82no—
365Dic6C3×#4112yes—
366C3×C8—22no—
367C3×C8—22no—
368C3×C8—42no—
369C3×C8—61no—
370C3×C8—61no—
371C3⋊C8—21no—
372C3⋊C8—21no—
373C2×C32—81no—
374C2×C32#54811yescharacteristic
375C2×C32C2×#13711yescharacteristic
376C2×C32#57711yescharacteristic
377C2×Q8—21no—
378C2×Q8—31no—
379C2×Q8—31no—
380C2×Q8—32no—
381C2×Q8—62no—
382C2×D4C22×C3×D311yescharacteristic
383C22×C4—21no—
384Q16—64no—
385SD16—62no—
386C2×C8—31no—
387C2×C8—31no—
388C2×C8C22×C3×D312yes—
389C4⋊C4—21no—
390C4⋊C4—31no—
391C4⋊C4—32no—
392C4⋊C4—31no—
393C4⋊C4—62no—
394C4⋊C4—62no—
395C4⋊C4—62no—
396C4⋊C4—61no—
397C4⋊C4—61no—
398C4⋊C4—61no—
399C4⋊C4C22×C3×D312yes—
400C4⋊C4C22×C3×D311yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—62no—
403C22⋊C4—62no—
404C42—32no—
405C42—62no—
406C42—62no—
407C42—61no—
408C42C22×C3×D311yescharacteristic
409C22×C3—21no—
410C22×C3—42no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—81no—
418C22×C3—81no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×C3×D411yescharacteristic
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—22no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—42no—
429C3×C4—41no—
430C3×C4—42no—
431C3×C4—62no—
432C3×C4—62no—
433C3×C4—62no—
434C3×C4—81no—
435C3×C4—82no—
436C3×C4—122no—
437C3×C4—121no—
438C3×C4#91512yes—
439C3×C4C3×#13712yes—
440C3×C4#100711yescharacteristic
441C3×C4D3×#4111yescharacteristic
442C3×C4C2×C3×#4111yescharacteristic
443C3×C4C3×2−1+411yescharacteristic
444Dic3—22no—
445Dic3—22no—
446Dic3—22no—
447Dic3—41no—
448Dic3—42no—
449C32#336911yescharacteristic, complemented, Sylow
450C23—21no—
451Q8—32no—
452Q8—62no—
453Q8—61no—
454Q8—62no—
455Q8—62no—
456Q8—81no—
457Q8—242no—
458D4—21no—
459D4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—32no—
463C2×C4—32no—
464C2×C4—42no—
465C2×C4—61no—
466C2×C4—62no—
467C2×C4—61no—
468C2×C4C3×D3×D411yescharacteristic
469C2×C4C3×D3×D411yescharacteristic
470C2×C4C23×C3×D311yescharacteristic
471C8—22no—
472C8—61no—
473C8—61no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—82no—
478C2×C3—81no—
479C2×C3—81no—
480C2×C3#563311yescharacteristic
481C2×C3C2×#91511yescharacteristic
482C2×C3#577511yescharacteristic
483C2×C3C3×#54811yescharacteristic
484C2×C3C2×C3×#13711yescharacteristic
485C2×C3C3×#57711yescharacteristic
486C22—41no—
487C22—41no—
488C22—41no—
489C22C2×C3×D3×D411yescharacteristic
490C4—21no—
491C4—41no—
492C4—42no—
493C4—62no—
494C4—62no—
495C4—62no—
496C4—121no—
497C4—122no—
498C4C3×#91512yes—
499C4C3×#100711yescharacteristic
500C4C3×D3×#4111yescharacteristic
501C3—21no—
502C3#8109111yescharacteristic, direct product factor
503C3C3×#336911yescharacteristic, complemented
504C2—81no—
505C2C3×#563311yescharacteristic
506C2C2×C3×#91511yescharacteristic
507C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#476C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×#476D3
hypocenterC3C3×#3369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
1. C3×#5722C2semidirect
4. C3×#5093C2semidirect
6. C3×#4854C2semidirect
7. C3×#4853C2semidirect
8. C3×#4849C2semidirect
9. C3×#4831C2semidirect
13. #81091C3direct (N × H)
45. #5722C2×C3semidirect
58. #5093C2×C3semidirect
60. #4854C2×C3semidirect
61. #4853C2×C3semidirect
62. #4849C2×C3semidirect
63. #4831C2×C3semidirect
449. C32#3369semidirect
502. C3#81091direct (N × H)
503. C3C3×#3369semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
C3×#55422
C32×#4762
C3×#50932
C3×C4×#2142
C3×#48542
C3×#48532
C3×#48492
C3×#48312
C3×#47672
C3×#47652
C3×#33693
#810913