Finite Group Databasebeta

← C3×#80319 #11895323

Subgroups — C3×#80319 #11895323

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5713C211yesmaximal, characteristic, complemented
2C3×#5543C211yesmaximal, characteristic, complemented
3C32×#459C211yesmaximal, characteristic
4C3×#5153C212yesmaximal, complemented
5C3×Dic3×D8C212yesmaximal, complemented
6C3×#5070C211yesmaximal, characteristic, complemented
7C3×C4×#214C211yesmaximal, characteristic, complemented
8C3×#4850C211yesmaximal, characteristic, complemented
9C3×#4830C211yesmaximal, characteristic, complemented
10C3×#4768C212yesmaximal, complemented
11C3×#4766C212yesmaximal, complemented
12C3×#3361—31nomaximal
13#80319C311yesmaximal, characteristic, direct product factor
14C2×C32×D8C2212yes—
15C32×#127C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#936—21no—
18C3×#936C2212yes—
19C3×#935—22no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2212yes—
22C3×D4×Dic3C2212yes—
23C2×C3×#214C2211yescharacteristic
24C2×C3×C4⋊Dic3—21no—
25C3×#924—21no—
26C3×#890C2212yes—
27C3×#878—22no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32C32×#102C2212yes—
33C3×#832C2211yescharacteristic
34C3×#832C2212yes—
35C3×#832C2212yes—
36C3×#818C2212yes—
37C3×#816C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#810C2211yescharacteristic
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#559—31no—
44C3×#554—31no—
45#5713C2×C311yescharacteristic, complemented
46#5543C2×C311yescharacteristic, complemented
47C3×#488—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#477—31no—
51C3×#463—32no—
52C3×#459—21no—
53C3×#459D311yescharacteristic
54C3×#459C2×C311yescharacteristic
55C3×C8×Q8—31no—
56C3×C4×SD16—31no—
57C3×C4×D8—32no—
58#5153C2×C312yescomplemented
59Dic3×D8C2×C312yescomplemented
60#5070C2×C311yescharacteristic, complemented
61C4×#214C2×C311yescharacteristic, complemented
62#4850C2×C311yescharacteristic, complemented
63#4830C2×C311yescharacteristic, complemented
64#4768C2×C312yescomplemented
65#4766C2×C312yescomplemented
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3—22no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6D411yescharacteristic
75C2×C3×Dic6C2311yescharacteristic
76C32×D8—24no—
77C2×C32×C8C2312yes—
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42C2311yescharacteristic
81C3×#217—22no—
82C3×#217—22no—
83C3×#217—22no—
84C3×#217—22no—
85C3×#214—22no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—21no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3361—31noSylow
99C2×C3×SD16—31no—
100C2×C3×D8—22no—
101C2×C3×D8C2×D312yes—
102C2×C3×D8C22×C312yes—
103C3×C4⋊Q8—31no—
104C3×#127—21no—
105C3×#127C2×D311yescharacteristic
106C3×#127C22×C311yescharacteristic
107C3×#125—32no—
108C3×#124—32no—
109C3×#124—61no—
110C3×#123—62no—
111C3×C22⋊Q8—62no—
112C3×C22⋊Q8—61no—
113C3×C4×Q8—31no—
114C3×C4×Q8—31no—
115C3×C4×D4—21no—
116C3×C4×D4—32no—
117C3×C4×D4—32no—
118C3×C4×D4—61no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C22×C311yescharacteristic
121C2×C3×C4⋊C4—61no—
122#936—21no—
123#936C22×C312yes—
124#935—22no—
125D4×Dic3—21no—
126D4×Dic3C22×C312yes—
127D4×Dic3C22×C312yes—
128C2×#214C22×C311yescharacteristic
129C2×C4⋊Dic3—21no—
130#924—21no—
131#890C22×C312yes—
132#878—22no—
133#869C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#107—32no—
137C3×#106—31no—
138C3×C4⋊C8—21no—
139C3×C4⋊C8—32no—
140C3×C4⋊C8C2×D311yescharacteristic
141C3×C4⋊C8C22×C311yescharacteristic
142C3×#103—32no—
143C3×#103—31no—
144C3×#102—22no—
145C3×#102—31no—
146C3×#102—32no—
147C3×#102—32no—
148C3×#102C2×D312yes—
149C3×#102C22×C312yes—
150C3×C4×C8—32no—
151C3×C4×C8—31no—
152#832C22×C311yescharacteristic
153#832C22×C312yes—
154#832C22×C312yes—
155#818C22×C312yes—
156#816C22×C312yes—
157Dic3⋊C8C22×C312yes—
158C8×Dic3C22×C312yes—
159#810C22×C311yescharacteristic
160#808C22×C311yescharacteristic
161C4×C3⋊C8C22×C311yescharacteristic
162C23×C32—21no—
163C23×C32—22no—
164C32×D4—22no—
165C32×D4—21no—
166C32×D4—22no—
167C32×D4—42no—
168C32×D4—81no—
169C32×D4#4112yes—
170C2×C32×C4—21no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—82no—
179C2×C3×Dic3—82no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×Dic6—22no—
183C3×Dic6—21no—
184C3×Dic6—21no—
185C3×Dic6—81no—
186C32×C8—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#559—31no—
190#554—31no—
191#488—32no—
192#486—31no—
193#478—32no—
194#477—31no—
195#463—32no—
196#459C3×D311yescharacteristic
197C8×Q8—31no—
198C4×SD16—31no—
199C4×D8—32no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—22no—
209C2×C3×D4—41no—
210C2×C3×D4—41no—
211C2×C3×D4C22×D312yes—
212C2×C3×D4C22×D311yescharacteristic
213C2×C3×D4C23×C312yes—
214C2×C3×D4C23×C311yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—41no—
218C22×C3×C4—62no—
219C22×C3×C4—62no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C2×Dic6—21no—
223C2×Dic6C3×D411yescharacteristic
224C2×Dic6C23×C311yescharacteristic
225C3×SD16—62no—
226C3×D8—24no—
227C3×D8—24no—
228C3×D8—44no—
229C2×C3×C8—22no—
230C2×C3×C8—31no—
231C2×C3×C8—31no—
232C2×C3×C8C22×D312yes—
233C2×C3×C8C23×C312yes—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C4⋊C4C23×C311yescharacteristic
245C3×C22⋊C4—21no—
246C3×C22⋊C4—21no—
247C3×C22⋊C4—41no—
248C3×C22⋊C4—62no—
249C3×C22⋊C4—62no—
250C3×C22⋊C4—62no—
251C3×C22⋊C4—62no—
252C3×C42—21no—
253C3×C42—32no—
254C3×C42—61no—
255C3×C42C22×D311yescharacteristic
256C3×C42C23×C311yescharacteristic
257#217—22no—
258#217—22no—
259#217—22no—
260#217—22no—
261#214—22no—
262C4⋊Dic3—21no—
263C4⋊Dic3—22no—
264C4⋊Dic3C3×D411yescharacteristic
265C4⋊Dic3C23×C311yescharacteristic
266C4⋊Dic3C23×C312yes—
267Dic3⋊C4—21no—
268Dic3⋊C4—22no—
269Dic3⋊C4C3×D412yes—
270C4×Dic3—21no—
271C4×Dic3C23×C312yes—
272C2×C3⋊C8C23×C311yescharacteristic
273C2×C3⋊C8C23×C311yescharacteristic
274C22×C32—22no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—42no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32C22×D411yescharacteristic
281C32×C4—21no—
282C32×C4—41no—
283C32×C4#13512yes—
284C32×C4C2×#4111yescharacteristic
285C32×C42−1+411yescharacteristic
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—41no—
289C3×Dic3—42no—
290C3×Dic3—41no—
291C2×SD16—31no—
292C2×D8C2×C3×D312yes—
293C4⋊Q8—31no—
294#127C2×C3×D311yescharacteristic
295#125—32no—
296#124—32no—
297#124—61no—
298#123—62no—
299C22⋊Q8—62no—
300C22⋊Q8—61no—
301C4×Q8—31no—
302C4×Q8—31no—
303C4×D4—32no—
304C4×D4—32no—
305C4×D4—61no—
306C4×D4C2×C3×D311yescharacteristic
307C2×C4⋊C4—61no—
308#107—32no—
309#106—31no—
310C4⋊C8—32no—
311C4⋊C8C2×C3×D311yescharacteristic
312#103—32no—
313#103—31no—
314#102—31no—
315#102—32no—
316#102—32no—
317#102C2×C3×D312yes—
318C4×C8—32no—
319C4×C8—31no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—41no—
325C23×C3—42no—
326C3×Q8—62no—
327C3×Q8—61no—
328C3×Q8—61no—
329C3×Q8—241no—
330C3×D4—22no—
331C3×D4—21no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—21no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—41no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—42no—
341C3×D4—42no—
342C3×D4—82no—
343C3×D4—81no—
344C3×D4—81no—
345C3×D4—82no—
346C3×D4#23712yes—
347C3×D4C3×#4112yes—
348C2×C3×C4—21no—
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—61no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—82no—
362C2×C3×C4—242no—
363C2×C3×C4—242no—
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C24×C311yescharacteristic
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—22no—
373C2×Dic3—82no—
374C2×Dic3—82no—
375C2×Dic3C2×C3×D412yes—
376C2×Dic3C2×C3×D412yes—
377Dic6—22no—
378Dic6—21no—
379Dic6—21no—
380Dic6—81no—
381C3×C8—22no—
382C3×C8—22no—
383C3×C8—42no—
384C3×C8—61no—
385C3×C8—61no—
386C3⋊C8—21no—
387C3⋊C8—21no—
388C2×C32—42no—
389C2×C32—82no—
390C2×C32#54811yescharacteristic
391C2×C32C2×#13511yescharacteristic
392C2×C32#57611yescharacteristic
393C2×Q8—31no—
394C2×Q8—31no—
395C2×Q8—61no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4C22×C3×D312yes—
399C2×D4C22×C3×D311yescharacteristic
400C22×C4—21no—
401C22×C4—62no—
402C22×C4—62no—
403SD16—62no—
404D8—24no—
405C2×C8—31no—
406C2×C8—31no—
407C2×C8C22×C3×D312yes—
408C4⋊C4—31no—
409C4⋊C4—32no—
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—62no—
413C4⋊C4—62no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C4⋊C4C22×C3×D311yescharacteristic
417C22⋊C4—21no—
418C22⋊C4—62no—
419C22⋊C4—62no—
420C22⋊C4—62no—
421C22⋊C4—62no—
422C42—32no—
423C42—61no—
424C42C22×C3×D311yescharacteristic
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—42no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—81no—
440C22×C3—81no—
441C22×C3—82no—
442C22×C3—82no—
443C22×C3—82no—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C22×C3×D411yescharacteristic
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—62no—
455C3×C4—62no—
456C3×C4—81no—
457C3×C4—121no—
458C3×C4—122no—
459C3×C4—121no—
460C3×C4#91212yes—
461C3×C4C3×#13512yes—
462C3×C4C2×#23711yescharacteristic
463C3×C4#101011yescharacteristic
464C3×C4C2×C3×#4111yescharacteristic
465C3×C4C3×2−1+411yescharacteristic
466Dic3—22no—
467Dic3—22no—
468Dic3—42no—
469Dic3—41no—
470Dic3—41no—
471C32#336111yescharacteristic, complemented, Sylow
472C23—21no—
473C23—22no—
474Q8—62no—
475Q8—61no—
476Q8—61no—
477Q8—241no—
478D4—22no—
479D4—21no—
480D4—22no—
481D4—42no—
482D4—81no—
483D4C3×#23712yes—
484C2×C4—21no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—42no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—62no—
491C2×C4—242no—
492C2×C4—242no—
493C2×C4C3×D3×D411yescharacteristic
494C2×C4C3×D3×D411yescharacteristic
495C2×C4C23×C3×D311yescharacteristic
496C8—22no—
497C8—61no—
498C8—61no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—42no—
503C2×C3—42no—
504C2×C3—82no—
505C2×C3—82no—
506C2×C3—82no—
507C2×C3—162no—
508C2×C3#559811yescharacteristic
509C2×C3C2×#91211yescharacteristic
510C2×C3#577411yescharacteristic
511C2×C3C3×#54811yescharacteristic
512C2×C3C2×C3×#13511yescharacteristic
513C2×C3C3×#57611yescharacteristic
514C22—22no—
515C22—41no—
516C22—41no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22C2×C3×D3×D411yescharacteristic
521C4—21no—
522C4—41no—
523C4—62no—
524C4—62no—
525C4—121no—
526C4—122no—
527C4—121no—
528C4C3×#91212yes—
529C4C2×C3×#23711yescharacteristic
530C4C3×#101011yescharacteristic
531C3—21no—
532C3#8031911yescharacteristic, direct product factor
533C3C3×#336111yescharacteristic, complemented
534C2—42no—
535C2—82no—
536C2C3×#559811yescharacteristic
537C2C2×C3×#91211yescharacteristic
538C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC32×#459C2
socleC22×C32C22×D4
hypercenterC3×#459D3
hypocenterC3C3×#3361
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C3×#5713C2semidirect
2. C3×#5543C2semidirect
4. C3×#5153C2semidirect
5. C3×Dic3×D8C2semidirect
6. C3×#5070C2semidirect
7. C3×C4×#214C2semidirect
8. C3×#4850C2semidirect
9. C3×#4830C2semidirect
10. C3×#4768C2semidirect
11. C3×#4766C2semidirect
13. #80319C3direct (N × H)
45. #5713C2×C3semidirect
46. #5543C2×C3semidirect
58. #5153C2×C3semidirect
59. Dic3×D8C2×C3semidirect
60. #5070C2×C3semidirect
61. C4×#214C2×C3semidirect
62. #4850C2×C3semidirect
63. #4830C2×C3semidirect
64. #4768C2×C3semidirect
65. #4766C2×C3semidirect
471. C32#3361semidirect
532. C3#80319direct (N × H)
533. C3C3×#3361semidirect

Maximal subgroups

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

subgroupindex
C3×#57132
C3×#55432
C32×#4592
C3×#51532
C3×Dic3×D82
C3×#50702
C3×C4×#2142
C3×#48502
C3×#48302
C3×#47682
C3×#47662
C3×#33613
#803193