Finite Group Databasebeta

← C3×#82041 #11899763

Subgroups — C3×#82041 #11899763

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5771C211yesmaximal, characteristic, complemented
2C3×#5766C211yesmaximal, characteristic, complemented
3C32×#510C211yesmaximal, characteristic, complemented
4C3×#5194C211yesmaximal, characteristic, complemented
5C2×C3×#829C211yesmaximal, characteristic, complemented
6C3×#4918C212yesmaximal, complemented
7C3×D3×Q32C212yesmaximal, complemented
8C3×#4916C212yesmaximal, complemented
9C3×#4915C212yesmaximal, complemented
10C3×#4909C211yesmaximal, characteristic, complemented
11C3×#4907C211yesmaximal, characteristic, complemented
12C3×#3417—31nomaximal
13#82041C311yesmaximal, characteristic, direct product factor
14C3×#1010—21no—
15C3×#1007—21no—
16C32×#135C2211yescharacteristic
17C2×C32×Q16C2211yescharacteristic
18C3×#951—21no—
19C3×#942—21no—
20C3×#919C2212yes—
21C3×#918—22no—
22C3×D3×Q16C2212yes—
23C3×D3×Q16C2212yes—
24C3×#915—22no—
25C3×#912C2212yes—
26C2×C3×Dic12C2211yescharacteristic
27C3×#904C2211yescharacteristic
28C3×#901C2211yescharacteristic
29C32×Q32C2212yes—
30C32×SD32C2212yes—
31C32×M32C2211yescharacteristic
32C3×#829C2212yes—
33C3×#829C2212yes—
34C3×#829C2211yescharacteristic
35C3×#828C2211yescharacteristic
36C3×#827C2211yescharacteristic
37C3×#826C2211yescharacteristic
38C2×C3×C3⋊C16C2211yescharacteristic
39C3×Dic24C2212yes—
40C3×#800C2212yes—
41C3×#798C2212yes—
42C3×D3×C16C2212yes—
43C3×#578—31no—
44C3×#578—31no—
45#5771C2×C311yescharacteristic, complemented
46#5766C2×C311yescharacteristic, complemented
47C3×#510—21no—
48C3×#510—32no—
49C3×#510—32no—
50C3×#510—31no—
51C3×#510D311yescharacteristic, complemented
52C3×#510C2×C311yescharacteristic, complemented
53C3×#508—31no—
54C3×#508—32no—
55C2×C3×Q32—31no—
56C2×C3×Q32—32no—
57C3×#504—31no—
58#5194C2×C311yescharacteristic, complemented
59C2×#829C2×C311yescharacteristic, complemented
60#4918C2×C312yescomplemented
61D3×Q32C2×C312yescomplemented
62#4916C2×C312yescomplemented
63#4915C2×C312yescomplemented
64#4909C2×C311yescharacteristic, complemented
65#4907C2×C311yescharacteristic, complemented
66C32×#41—21no—
67C2×C32×Q8—21no—
68C3×#239—22no—
69C3×#239—41no—
70C3×D3×Q8—22no—
71C3×D3×Q8—22no—
72C3×D3×Q8—41no—
73C3×#237—22no—
74C3×#237—42no—
75C3×#235—21no—
76C3×#235—42no—
77C3×#235—41no—
78C3×#235D411yescharacteristic
79C2×C3×Dic6—21no—
80C2×C3×Dic6—41no—
81C32×Q16—21no—
82C32×Q16C2311yescharacteristic
83C32×Q16C2312yes—
84C32×SD16—21no—
85C32×D8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C3×#216—22no—
88C3×#216—22no—
89C3×#215—22no—
90C3×#214—22no—
91C3×#208D411yescharacteristic
92C3×Dic12—21no—
93C3×Dic12C2311yescharacteristic
94C3×Dic12C2312yes—
95C3×D24C2311yescharacteristic
96C3×#204—21no—
97C3×ΓL(1,𝔽25)D412yes—
98C3×D3×C8C2312yes—
99C32×C16C2312yes—
100C3×C3⋊C16C2311yescharacteristic
101C3×C3⋊C16C2311yescharacteristic
102#3417—31noSylow
103C3×2−1+4—61no—
104C3×2−1+4—61no—
105#1010—21no—
106#1007—21no—
107C3×#137—62no—
108C3×#137—62no—
109C3×#137—61no—
110C3×#137—61no—
111C3×#135—21no—
112C3×#135—32no—
113C3×#135—32no—
114C3×#135—31no—
115C3×#135C2×D311yescharacteristic
116C3×#135C22×C311yescharacteristic
117C2×C3×Q16—21no—
118C2×C3×Q16—32no—
119C2×C3×Q16—32no—
120C2×C3×Q16—31no—
121C2×C3×Q16C2×D311yescharacteristic
122C2×C3×Q16C22×C311yescharacteristic
123C3×#131—31no—
124#951—21no—
125#942—21no—
126#919C22×C312yes—
127#918—22no—
128D3×Q16C22×C312yes—
129D3×Q16C22×C312yes—
130#915—22no—
131#912C22×C312yes—
132C2×Dic12C22×C311yescharacteristic
133#904C22×C311yescharacteristic
134#901C22×C311yescharacteristic
135C3×Q32—22no—
136C3×Q32—31no—
137C3×Q32—32no—
138C3×Q32—32no—
139C3×Q32—32no—
140C3×Q32C2×D312yes—
141C3×Q32C22×C312yes—
142C3×SD32—22no—
143C3×SD32—31no—
144C3×SD32—31no—
145C3×SD32—32no—
146C3×SD32C2×D312yes—
147C3×SD32C22×C312yes—
148C3×D16—31no—
149C3×M32—21no—
150C3×M32—32no—
151C3×M32C2×D311yescharacteristic
152C3×M32C22×C311yescharacteristic
153C2×C3×C16—31no—
154C2×C3×C16—32no—
155#829C22×C312yes—
156#829C22×C312yes—
157#829C22×C311yescharacteristic
158#828C22×C311yescharacteristic
159#827C22×C311yescharacteristic
160#826C22×C311yescharacteristic
161C2×C3⋊C16C22×C311yescharacteristic
162Dic24C22×C312yes—
163#800C22×C312yes—
164#798C22×C312yes—
165D3×C16C22×C312yes—
166C32×Q8—22no—
167C32×Q8—21no—
168C32×Q8—41no—
169C32×D4—21no—
170C32×D4—41no—
171C2×C32×C4—41no—
172C2×C32×C4—41no—
173C2×C32×C4C2×D411yescharacteristic
174C3×#67—41no—
175C3×#67—42no—
176C3×#67D812yes—
177C2×C3×Dic3—41no—
178C2×C3×Dic3—42no—
179C3×D12—21no—
180C3×D12—42no—
181C3×D12D811yescharacteristic
182C3×C4×D3—42no—
183C3×C4×D3—42no—
184C3×C4×D3—41no—
185C3×C4×D3—42no—
186C3×C4×D3C2×D412yes—
187C3×Dic6—21no—
188C3×Dic6—22no—
189C3×Dic6—41no—
190C3×Dic6—42no—
191C3×Dic6—42no—
192C3×Dic6D811yescharacteristic
193C32×C8C2×D411yescharacteristic
194C32×C8C2411yescharacteristic
195C3×C3⋊C8C2×D412yes—
196#578—31no—
197#578—31no—
198#510—32no—
199#510—32no—
200#510—31no—
201#510C3×D311yescharacteristic, complemented
202#508—31no—
203#508—32no—
204C2×Q32—31no—
205C2×Q32—32no—
206#504—31no—
207C3×#41—21no—
208C3×#41—21no—
209C3×#41—31no—
210C3×#41—41no—
211C3×#41—62no—
212C3×#41—62no—
213C3×#41—61no—
214C3×#41—122no—
215C3×#41—121no—
216C3×#41—122no—
217C3×#41—121no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—41no—
221C2×C3×Q8—62no—
222C2×C3×Q8—62no—
223C2×C3×Q8—61no—
224C2×C3×Q8—121no—
225C2×C3×Q8—121no—
226#239—22no—
227#239—41no—
228D3×Q8—22no—
229D3×Q8—22no—
230D3×Q8—41no—
231#237—22no—
232#237—42no—
233#235—21no—
234#235—42no—
235#235—41no—
236#235C3×D411yescharacteristic
237C2×Dic6—21no—
238C2×Dic6—41no—
239C3×Q16—21no—
240C3×Q16—21no—
241C3×Q16—22no—
242C3×Q16—21no—
243C3×Q16—31no—
244C3×Q16—32no—
245C3×Q16—41no—
246C3×Q16—62no—
247C3×Q16—62no—
248C3×Q16—61no—
249C3×Q16C22×D311yescharacteristic
250C3×Q16C22×D312yes—
251C3×Q16C23×C311yescharacteristic
252C3×Q16C23×C312yes—
253C3×SD16—21no—
254C3×SD16—21no—
255C3×SD16—41no—
256C3×SD16—62no—
257C3×SD16—62no—
258C3×SD16—61no—
259C3×D8—21no—
260C3×D8—31no—
261C3×D8C22×D311yescharacteristic
262C3×D8C23×C311yescharacteristic
263C3×M16—31no—
264C3×M16—32no—
265C2×C3×C8—21no—
266C2×C3×C8—32no—
267C2×C3×C8C22×D311yescharacteristic
268C2×C3×C8C23×C311yescharacteristic
269#216—22no—
270#216—22no—
271#215—22no—
272#214—22no—
273#208C3×D411yescharacteristic
274Dic12—21no—
275Dic12C23×C312yes—
276Dic12C23×C311yescharacteristic
277D24C23×C311yescharacteristic
278#204—21no—
279ΓL(1,𝔽25)C3×D412yes—
280D3×C8C23×C312yes—
281C3×C16—22no—
282C3×C16—31no—
283C3×C16—31no—
284C3×C16C22×D312yes—
285C3×C16C23×C312yes—
286C3⋊C16C23×C311yescharacteristic
287C3⋊C16C23×C311yescharacteristic
288C22×C32—41no—
289C22×C32C2×D811yescharacteristic
290C2×C3×D3—41no—
291C2×C3×D3C2×D812yes—
292C32×C4—41no—
293C32×C4—42no—
294C32×C4C2×D811yescharacteristic
295C32×C4C22×D411yescharacteristic
296C3×Dic3—41no—
297C3×Dic3—42no—
298C3×Dic3C2×D812yes—
2992−1+4—61no—
3002−1+4—61no—
301#137—62no—
302#137—62no—
303#137—61no—
304#137—61no—
305#135—32no—
306#135—32no—
307#135—31no—
308#135C2×C3×D311yescharacteristic
309C2×Q16—32no—
310C2×Q16—32no—
311C2×Q16—31no—
312C2×Q16C2×C3×D311yescharacteristic
313#131—31no—
314Q32—31no—
315Q32—32no—
316Q32—32no—
317Q32—32no—
318Q32C2×C3×D312yes—
319SD32—31no—
320SD32—31no—
321SD32—32no—
322SD32C2×C3×D312yes—
323D16—31no—
324M32—32no—
325M32C2×C3×D311yescharacteristic
326C2×C16—31no—
327C2×C16—32no—
328C3×Q8—21no—
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—21no—
332C3×Q8—31no—
333C3×Q8—41no—
334C3×Q8—42no—
335C3×Q8—41no—
336C3×Q8—41no—
337C3×Q8—61no—
338C3×Q8—62no—
339C3×Q8—81no—
340C3×Q8—122no—
341C3×Q8—122no—
342C3×Q8—121no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—32no—
346C3×D4—31no—
347C3×D4—41no—
348C3×D4—41no—
349C3×D4—41no—
350C3×D4—61no—
351C3×D4—81no—
352C3×D4—122no—
353C3×D4—122no—
354C3×D4—121no—
355C2×C3×C4—21no—
356C2×C3×C4—32no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—81no—
362C2×C3×C4—81no—
363C2×C3×C4—122no—
364C2×C3×C4—122no—
365C2×C3×C4—122no—
366C2×C3×C4—122no—
367C2×C3×C4—121no—
368C2×C3×C4—121no—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4C2×C3×D411yescharacteristic
371#67—41no—
372#67—42no—
373#67C3×D812yes—
374C2×Dic3—41no—
375C2×Dic3—42no—
376D12—21no—
377D12—42no—
378D12C3×D811yescharacteristic
379C4×D3—42no—
380C4×D3—42no—
381C4×D3—41no—
382C4×D3—42no—
383C4×D3C2×C3×D412yes—
384Dic6—21no—
385Dic6—22no—
386Dic6—41no—
387Dic6—42no—
388Dic6—42no—
389Dic6C3×D811yescharacteristic
390C3×C8—21no—
391C3×C8—21no—
392C3×C8—32no—
393C3×C8D3×D411yescharacteristic
394C3×C8C2×C3×D411yescharacteristic
395C3×C8C23×D311yescharacteristic
396C3×C8C24×C311yescharacteristic
397C3⋊C8C2×C3×D412yes—
398C2×C32—21no—
399C2×C32—81no—
400C2×C32C22×D811yescharacteristic
401C3×D3—22no—
402C3×D3—81no—
403#41—21no—
404#41—31no—
405#41—62no—
406#41—62no—
407#41—61no—
408#41—122no—
409#41—121no—
410#41—122no—
411#41—121no—
412C2×Q8—21no—
413C2×Q8—62no—
414C2×Q8—62no—
415C2×Q8—61no—
416C2×Q8—121no—
417C2×Q8—121no—
418Q16—21no—
419Q16—31no—
420Q16—32no—
421Q16—62no—
422Q16—62no—
423Q16—61no—
424Q16C22×C3×D311yescharacteristic
425Q16C22×C3×D312yes—
426SD16—21no—
427SD16—62no—
428SD16—62no—
429SD16—61no—
430D8—31no—
431D8C22×C3×D311yescharacteristic
432M16—31no—
433M16—32no—
434C2×C8—32no—
435C2×C8C22×C3×D311yescharacteristic
436C16—31no—
437C16—31no—
438C16C22×C3×D312yes—
439C22×C3—21no—
440C22×C3—32no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—81no—
444C22×C3—121no—
445C22×C3D3×D811yescharacteristic
446C22×C3C2×C3×D811yescharacteristic
447C2×D3—41no—
448C2×D3C2×C3×D812yes—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—32no—
452C3×C4—41no—
453C3×C4—42no—
454C3×C4—41no—
455C3×C4—42no—
456C3×C4—81no—
457C3×C4—82no—
458C3×C4—122no—
459C3×C4—121no—
460C3×C4D3×D811yescharacteristic
461C3×C4C2×C3×D811yescharacteristic
462C3×C4C2×D3×D411yescharacteristic
463C3×C4C22×C3×D411yescharacteristic
464Dic3—41no—
465Dic3—42no—
466Dic3C2×C3×D812yes—
467C32#341711yescharacteristic, complemented, Sylow
468Q8—21no—
469Q8—22no—
470Q8—31no—
471Q8—41no—
472Q8—62no—
473Q8—61no—
474Q8—122no—
475Q8—122no—
476Q8—121no—
477D4—21no—
478D4—32no—
479D4—31no—
480D4—41no—
481D4—61no—
482D4—122no—
483D4—122no—
484D4—121no—
485C2×C4—32no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—122no—
489C2×C4—122no—
490C2×C4—122no—
491C2×C4—122no—
492C2×C4—121no—
493C2×C4—121no—
494C2×C4C3×D3×D411yescharacteristic
495C8—32no—
496C8C3×D3×D411yescharacteristic
497C8C23×C3×D311yescharacteristic
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—41no—
502C2×C3—62no—
503C2×C3—81no—
504C2×C3—81no—
505C2×C3—161no—
506C2×C3—241no—
507C2×C3C2×D3×D811yescharacteristic
508C2×C3C22×C3×D811yescharacteristic
509D3—22no—
510D3—81no—
511C22—32no—
512C22—41no—
513C22—121no—
514C22C3×D3×D811yescharacteristic
515C4—32no—
516C4—41no—
517C4—42no—
518C4—122no—
519C4—121no—
520C4C3×D3×D811yescharacteristic
521C4C2×C3×D3×D411yescharacteristic
522C3—21no—
523C3#8204111yescharacteristic, direct product factor
524C3C3×#341711yescharacteristic, complemented
525C2—21no—
526C2—62no—
527C2—81no—
528C2—241no—
529C2C2×C3×D3×D811yescharacteristic
subgroupG/H
centerC2×C3C2×D3×D8
commutator, cosocleC3×C8C24×C3
FrattiniC8C23×C3×D3
FittingC32×#510C2
socleC2×C32C22×D8
hypercenterC3×#510D3
hypocenterC3C3×#3417
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#510

Complements

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

NH ≅ G/Ntype
1. C3×#5771C2semidirect
2. C3×#5766C2semidirect
3. C32×#510C2semidirect
4. C3×#5194C2semidirect
5. C2×C3×#829C2semidirect
6. C3×#4918C2semidirect
7. C3×D3×Q32C2semidirect
8. C3×#4916C2semidirect
9. C3×#4915C2semidirect
10. C3×#4909C2semidirect
11. C3×#4907C2semidirect
13. #82041C3direct (N × H)
45. #5771C2×C3semidirect
46. #5766C2×C3semidirect
51. C3×#510D3semidirect
52. C3×#510C2×C3semidirect
58. #5194C2×C3semidirect
59. C2×#829C2×C3semidirect
60. #4918C2×C3semidirect
61. D3×Q32C2×C3semidirect
62. #4916C2×C3semidirect
63. #4915C2×C3semidirect
64. #4909C2×C3semidirect
65. #4907C2×C3semidirect
201. #510C3×D3semidirect
467. C32#3417semidirect
523. C3#82041direct (N × H)
524. C3C3×#3417semidirect

Maximal subgroups

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

subgroupindex
C3×#57712
C3×#57662
C32×#5102
C3×#51942
C2×C3×#8292
C3×#49182
C3×D3×Q322
C3×#49162
C3×#49152
C3×#49092
C3×#49072
C3×#34173
#820413