Finite Group Databasebeta

← C3×#87015 #11903749

Subgroups — C3×#87015 #11903749

Order 1152.

2236 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2C3×#5728C213yesmaximal, complemented
3C3×#5727C213yesmaximal, complemented
4C3×#5690C216yesmaximal, complemented
5C3×#5688C216yesmaximal, complemented
6C3×#5579C213yesmaximal, complemented
7C3×C4×#239C211yesmaximal, characteristic
8C3×C4×#239C212yesmaximal
9C3×C4×D3×Q8C213yesmaximal, complemented
10C3×#5569C212yesmaximal, complemented
11C3×Q8×Dic6C211yesmaximal, characteristic, complemented
12C3×Q8×#41—31nomaximal
13#87015C311yesmaximal, characteristic, direct product factor
14C2×C3×#239C2211yescharacteristic
15C2×C3×D3×Q8C2213yes—
16C32×C4⋊Q8C2213yes—
17C32×#125C2216yes—
18C32×C4×Q8C2211yescharacteristic
19C32×C4×Q8C2212yes—
20C32×C4×Q8C2213yes—
21C3×#946C2216yes—
22C3×Q8×Dic3C2212yes—
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2213yes—
25C3×#897C2216yes—
26C3×#896C22112yes—
27C3×#896C22112yes—
28C3×#893C2213yes—
29C3×#893C2216yes—
30C3×#892C2213yes—
31C3×#892C2216yes—
32C3×D3×C4⋊C4C2213yes—
33C3×D3×C4⋊C4C2216yes—
34C3×#890C2216yes—
35C3×#888C2216yes—
36C3×#888C2216yes—
37C3×#887C2211yescharacteristic
38C3×#887C2216yes—
39C3×#887C2216yes—
40C3×C4×D12C2216yes—
41C3×C4×D12C2213yes—
42C3×C42×D3C2216yes—
43C3×C42×D3C2213yes—
44C3×#870C2216yes—
45C3×#869C2213yes—
46C3×C4×Dic6C2213yes—
47C3×C4×Dic6C2216yes—
48C3×Q82—31no—
49C3×#557—21no—
50C3×#557—32no—
51C3×#557D311yescharacteristic, complemented
52C3×#557C2×C311yescharacteristic, complemented
53C3×#554—36no—
54C3×#554—33no—
55C3×D4×Q8—33no—
56C3×#533—33no—
57C3×#533—36no—
58C3×C4×#41—32no—
59C3×C4×#41—31no—
60C2×C3×C4×Q8—33no—
61#5728C2×C313yescomplemented
62#5727C2×C313yescomplemented
63#5690C2×C316yescomplemented
64#5688C2×C316yescomplemented
65#5579C2×C313yescomplemented
66C4×#239C2×C312yes—
67C4×#239C2×C311yescharacteristic
68C4×D3×Q8C2×C313yescomplemented
69#5569C2×C312yescomplemented
70Q8×Dic6C2×C311yescharacteristic, complemented
71C2×C32×Q8C2313yes—
72C2×C32×Q8C2311yescharacteristic
73C3×#239Q818yescomplemented
74C3×D3×Q8—212no—
75C2×C3×D12C2313yes—
76C2×C3×C4×D3C2316yes—
77C2×C3×C4×D3C2313yes—
78C2×C3×C4×D3C2313yes—
79C2×C3×C4×D3C2316yes—
80C2×C3×C4×D3C2313yes—
81C2×C3×Dic6C2316yes—
82C2×C3×Dic6C2316yes—
83C2×C3×Dic6C2311yescharacteristic
84C32×C4⋊C4C2311yescharacteristic
85C32×C4⋊C4C2316yes—
86C32×C4⋊C4C2316yes—
87C32×C4⋊C4C2313yes—
88C32×C4⋊C4C2316yes—
89C32×C42C2316yes—
90C32×C42C2313yes—
91C3×(C2×D3)⋊C4C2316yes—
92C3×(C2×D3)⋊C4C23112yes—
93C3×C4⋊Dic3C2313yes—
94C3×C4⋊Dic3C2316yes—
95C3×C4⋊Dic3C2316yes—
96C3×C4⋊Dic3C2313yes—
97C3×Dic3⋊C4C2316yes—
98C3×Dic3⋊C4C23112yes—
99C3×Dic3⋊C4C2312yes—
100C3×Dic3⋊C4C2316yes—
101C3×C4×Dic3C2313yes—
102C3×C4×Dic3C2312yes—
103C3×C4×Dic3C2316yes—
104C3×C4×Dic3C2311yescharacteristic
105C3×C4×Dic3C2316yes—
106C3×C4×Dic3C2313yes—
107Q8×#41—31noSylow
108C2×C3×#41—31no—
109C22×C3×Q8—33no—
110C2×#239C22×C311yescharacteristic
111C2×D3×Q8C22×C313yes—
112C3×C4⋊Q8—23no—
113C3×C4⋊Q8—36no—
114C3×C4⋊Q8—36no—
115C3×C4⋊Q8—33no—
116C3×C4⋊Q8C2×D313yes—
117C3×C4⋊Q8C22×C313yes—
118C3×#125—26no—
119C3×#125—36no—
120C3×#125—36no—
121C3×#125C2×D316yes—
122C3×#125C22×C316yes—
123C3×C22⋊Q8—36no—
124C3×C22⋊Q8—312no—
125C3×C22⋊Q8—312no—
126C3×C22⋊Q8—36no—
127C3×C4×Q8—23no—
128C3×C4×Q8—22no—
129C3×C4×Q8—21no—
130C3×C4×Q8—32no—
131C3×C4×Q8—33no—
132C3×C4×Q8—31no—
133C3×C4×Q8—31no—
134C3×C4×Q8—36no—
135C3×C4×Q8—36no—
136C3×C4×Q8—33no—
137C3×C4×Q8—36no—
138C3×C4×Q8C2×D311yescharacteristic
139C3×C4×Q8C2×D313yes—
140C3×C4×Q8C2×D312yes—
141C3×C4×Q8C22×C311yescharacteristic
142C3×C4×Q8C22×C312yes—
143C3×C4×Q8C22×C313yes—
144C3×C4×D4—36no—
145C3×C4×D4—33no—
146C3×C4×D4—33no—
147C3×C4×D4—36no—
148C3×#117—36no—
149C3×#117—33no—
150C2×C3×C4⋊C4—36no—
151C2×C3×C4⋊C4—33no—
152C2×C3×C42—33no—
153C2×C3×C42—36no—
154#946C22×C316yes—
155Q8×Dic3C22×C313yes—
156Q8×Dic3C22×C312yes—
157Q8×Dic3C22×C311yescharacteristic
158#897C22×C316yes—
159#896C22×C3112yes—
160#896C22×C3112yes—
161#893C22×C313yes—
162#893C22×C316yes—
163#892C22×C313yes—
164#892C22×C316yes—
165D3×C4⋊C4C22×C316yes—
166D3×C4⋊C4C22×C313yes—
167#890C22×C316yes—
168#888C22×C316yes—
169#888C22×C316yes—
170#887C22×C316yes—
171#887C22×C316yes—
172#887C22×C311yescharacteristic
173C4×D12C22×C316yes—
174C4×D12C22×C313yes—
175C42×D3C22×C316yes—
176C42×D3C22×C313yes—
177#870C22×C316yes—
178#869C22×C313yes—
179C4×Dic6C22×C316yes—
180C4×Dic6C22×C313yes—
181C22×C3×D3C2413yes—
182C32×Q8—26no—
183C32×Q8C2×Q814yescomplemented
184C2×C32×C4C2412yes—
185C2×C32×C4C2416yes—
186C2×C32×C4C2413yes—
187C2×C32×C4C2413yes—
188C2×C32×C4C2411yescharacteristic
189C2×C3×Dic3C2411yescharacteristic
190C2×C3×Dic3C2413yes—
191C2×C3×Dic3C2416yes—
192C2×C3×Dic3C2411yescharacteristic
193C2×C3×Dic3C2412yes—
194C3×D12C2×Q8112yescomplemented
195C3×C4×D3—26no—
196C3×C4×D3—212no—
197C3×C4×D3—46no—
198C3×C4×D3—43no—
199C3×C4×D3C2×Q8112yescomplemented
200C3×Dic6—212no—
201C3×Dic6—46no—
202C3×Dic6#4114yescomplemented
203Q82—31no—
204#557—32no—
205#557C3×D311yescharacteristic, complemented
206#554—36no—
207#554—33no—
208D4×Q8—33no—
209#533—33no—
210#533—36no—
211C4×#41—32no—
212C4×#41—31no—
213C2×C4×Q8—33no—
214C3×#41—38no—
215C2×C3×Q8—21no—
216C2×C3×Q8—23no—
217C2×C3×Q8—31no—
218C2×C3×Q8—36no—
219C2×C3×Q8—36no—
220C2×C3×Q8—612no—
221C2×C3×Q8C22×D313yes—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×Q8C23×C313yes—
224C2×C3×Q8C23×C311yescharacteristic
225C2×C3×D4—33no—
226C22×C3×C4—33no—
227C22×C3×C4—36no—
228C22×C3×C4—33no—
229C22×C3×C4—33no—
230C22×C3×C4—36no—
231#239C3×Q818yescomplemented
232D3×Q8—212no—
233C2×D12C23×C313yes—
234C2×C4×D3C23×C313yes—
235C2×C4×D3C23×C316yes—
236C2×C4×D3C23×C316yes—
237C2×C4×D3C23×C313yes—
238C2×C4×D3C23×C313yes—
239C2×Dic6C23×C316yes—
240C2×Dic6C23×C316yes—
241C2×Dic6C23×C311yescharacteristic
242C3×C4⋊C4—21no—
243C3×C4⋊C4—26no—
244C3×C4⋊C4—23no—
245C3×C4⋊C4—26no—
246C3×C4⋊C4—26no—
247C3×C4⋊C4—32no—
248C3×C4⋊C4—36no—
249C3×C4⋊C4—36no—
250C3×C4⋊C4—312no—
251C3×C4⋊C4—36no—
252C3×C4⋊C4—33no—
253C3×C4⋊C4—33no—
254C3×C4⋊C4—36no—
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C4⋊C4C22×D316yes—
257C3×C4⋊C4C22×D316yes—
258C3×C4⋊C4C22×D313yes—
259C3×C4⋊C4C22×D316yes—
260C3×C4⋊C4C23×C311yescharacteristic
261C3×C4⋊C4C23×C316yes—
262C3×C4⋊C4C23×C316yes—
263C3×C4⋊C4C23×C313yes—
264C3×C4⋊C4C23×C316yes—
265C3×C22⋊C4—312no—
266C3×C22⋊C4—36no—
267C3×C42—26no—
268C3×C42—23no—
269C3×C42—32no—
270C3×C42—31no—
271C3×C42—36no—
272C3×C42—33no—
273C3×C42—33no—
274C3×C42—36no—
275C3×C42C22×D316yes—
276C3×C42C22×D313yes—
277C3×C42C23×C313yes—
278C3×C42C23×C316yes—
279(C2×D3)⋊C4C23×C316yes—
280(C2×D3)⋊C4C23×C3112yes—
281C4⋊Dic3C23×C313yes—
282C4⋊Dic3C23×C316yes—
283C4⋊Dic3C23×C316yes—
284C4⋊Dic3C23×C313yes—
285Dic3⋊C4C23×C312yes—
286Dic3⋊C4C23×C316yes—
287Dic3⋊C4C23×C316yes—
288Dic3⋊C4C23×C3112yes—
289C4×Dic3C23×C316yes—
290C4×Dic3C23×C313yes—
291C4×Dic3C23×C312yes—
292C4×Dic3C23×C311yescharacteristic
293C4×Dic3C23×C313yes—
294C4×Dic3C23×C316yes—
295C22×C32C2511yescharacteristic
296C2×C3×D3—23no—
297C2×C3×D3—23no—
298C2×C3×D3C22×Q816yes—
299C32×C4—26no—
300C32×C4—23no—
301C32×C4—22no—
302C32×C4C22×Q816yes—
303C32×C4C2×#4112yes—
304C3×Dic3—23no—
305C3×Dic3—26no—
306C3×Dic3—21no—
307C3×Dic3C22×Q812yes—
308C3×Dic3C2×#4114yes—
309C2×#41—31no—
310C22×Q8—33no—
311C4⋊Q8—36no—
312C4⋊Q8—36no—
313C4⋊Q8—33no—
314C4⋊Q8C2×C3×D313yes—
315#125—36no—
316#125—36no—
317#125C2×C3×D316yes—
318C22⋊Q8—36no—
319C22⋊Q8—312no—
320C22⋊Q8—312no—
321C22⋊Q8—36no—
322C4×Q8—33no—
323C4×Q8—31no—
324C4×Q8—32no—
325C4×Q8—31no—
326C4×Q8—36no—
327C4×Q8—36no—
328C4×Q8—33no—
329C4×Q8—36no—
330C4×Q8C2×C3×D313yes—
331C4×Q8C2×C3×D312yes—
332C4×Q8C2×C3×D311yescharacteristic
333C4×D4—36no—
334C4×D4—33no—
335C4×D4—33no—
336C4×D4—36no—
337#117—36no—
338#117—33no—
339C2×C4⋊C4—36no—
340C2×C4⋊C4—33no—
341C2×C42—33no—
342C2×C42—36no—
343C23×C3—33no—
344C22×D3C24×C313yes—
345C3×Q8—26no—
346C3×Q8—26no—
347C3×Q8—24no—
348C3×Q8—34no—
349C3×Q8—46no—
350C3×Q8—612no—
351C3×Q8—126no—
352C3×Q8D3×Q814yescomplemented
353C3×Q8C2×C3×Q814yescomplemented
354C3×D4—312no—
355C2×C3×C4—23no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—23no—
359C2×C3×C4—26no—
360C2×C3×C4—31no—
361C2×C3×C4—32no—
362C2×C3×C4—312no—
363C2×C3×C4—31no—
364C2×C3×C4—33no—
365C2×C3×C4—36no—
366C2×C3×C4—612no—
367C2×C3×C4—66no—
368C2×C3×C4—126no—
369C2×C3×C4—123no—
370C2×C3×C4C23×D312yes—
371C2×C3×C4C23×D316yes—
372C2×C3×C4C23×D313yes—
373C2×C3×C4C23×D313yes—
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C24×C312yes—
376C2×C3×C4C24×C316yes—
377C2×C3×C4C24×C313yes—
378C2×C3×C4C24×C313yes—
379C2×C3×C4C24×C311yescharacteristic
380C2×Dic3C24×C311yescharacteristic
381C2×Dic3C24×C313yes—
382C2×Dic3C24×C316yes—
383C2×Dic3C24×C311yescharacteristic
384C2×Dic3C24×C312yes—
385D12C2×C3×Q8112yescomplemented
386C4×D3—26no—
387C4×D3—212no—
388C4×D3—46no—
389C4×D3—43no—
390C4×D3C2×C3×Q8112yescomplemented
391Dic6—212no—
392Dic6—46no—
393Dic6C3×#4114yescomplemented
394C2×C32C23×Q811yescharacteristic
395C2×C32C22×#4111yescharacteristic
396C2×C32#58511yescharacteristic
397C3×D3—26no—
398#41—38no—
399C2×Q8—31no—
400C2×Q8—36no—
401C2×Q8—36no—
402C2×Q8—612no—
403C2×Q8C22×C3×D313yes—
404C2×Q8C22×C3×D311yescharacteristic
405C2×D4—33no—
406C22×C4—33no—
407C22×C4—36no—
408C22×C4—33no—
409C22×C4—33no—
410C22×C4—36no—
411C4⋊C4—32no—
412C4⋊C4—36no—
413C4⋊C4—36no—
414C4⋊C4—36no—
415C4⋊C4—33no—
416C4⋊C4—33no—
417C4⋊C4—36no—
418C4⋊C4—312no—
419C4⋊C4C22×C3×D311yescharacteristic
420C4⋊C4C22×C3×D316yes—
421C4⋊C4C22×C3×D316yes—
422C4⋊C4C22×C3×D313yes—
423C4⋊C4C22×C3×D316yes—
424C22⋊C4—312no—
425C22⋊C4—36no—
426C42—32no—
427C42—31no—
428C42—36no—
429C42—33no—
430C42—33no—
431C42—36no—
432C42C22×C3×D316yes—
433C42C22×C3×D313yes—
434C22×C3—21no—
435C22×C3—36no—
436C22×C3—63no—
437C22×C3—63no—
438C22×C3C24×D311yescharacteristic
439C22×C3C25×C311yescharacteristic
440C2×D3—23no—
441C2×D3—23no—
442C2×D3C22×C3×Q816yes—
443C3×C4—26no—
444C3×C4—22no—
445C3×C4—23no—
446C3×C4—26no—
447C3×C4—23no—
448C3×C4—22no—
449C3×C4—26no—
450C3×C4—22no—
451C3×C4—32no—
452C3×C4—34no—
453C3×C4—46no—
454C3×C4—42no—
455C3×C4—43no—
456C3×C4—63no—
457C3×C4—61no—
458C3×C4—66no—
459C3×C4C2×D3×Q816yes—
460C3×C4D3×#4112yes—
461C3×C4C22×C3×Q816yes—
462C3×C4C2×C3×#4112yes—
463Dic3—23no—
464Dic3—26no—
465Dic3—21no—
466Dic3C22×C3×Q812yes—
467Dic3C2×C3×#4114yes—
468C32Q8×#4111yescharacteristic, complemented, Sylow
469C23—33no—
470Q8—26no—
471Q8—34no—
472Q8—612no—
473Q8—126no—
474Q8C3×D3×Q814yescomplemented
475D4—312no—
476C2×C4—31no—
477C2×C4—32no—
478C2×C4—312no—
479C2×C4—31no—
480C2×C4—33no—
481C2×C4—36no—
482C2×C4—612no—
483C2×C4—66no—
484C2×C4—126no—
485C2×C4—123no—
486C2×C4C23×C3×D312yes—
487C2×C4C23×C3×D316yes—
488C2×C4C23×C3×D313yes—
489C2×C4C23×C3×D313yes—
490C2×C4C23×C3×D311yescharacteristic
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—66no—
495C2×C3C22×D3×Q811yescharacteristic
496C2×C3C2×D3×#4111yescharacteristic
497C2×C3#596811yescharacteristic
498C2×C3C23×C3×Q811yescharacteristic
499C2×C3C22×C3×#4111yescharacteristic
500C2×C3C3×#58511yescharacteristic
501D3—26no—
502C22—36no—
503C22—63no—
504C22—63no—
505C22C24×C3×D311yescharacteristic
506C4—26no—
507C4—22no—
508C4—23no—
509C4—32no—
510C4—34no—
511C4—63no—
512C4—61no—
513C4—66no—
514C4C2×C3×D3×Q816yes—
515C4C3×D3×#4112yes—
516C3—21no—
517C3#8701511yescharacteristic, direct product factor
518C3C3×Q8×#4111yescharacteristic, complemented
519C2—66no—
520C2C22×C3×D3×Q811yescharacteristic
521C2C2×C3×D3×#4111yescharacteristic
522C2C3×#596811yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#557C2
socleC22×C32C25
prime radicalC2×C3×#239C22
hypercenterC3×#557D3
hypocenterC3C3×Q8×#41
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
2. C3×#5728C2semidirect
3. C3×#5727C2semidirect
4. C3×#5690C2semidirect
5. C3×#5688C2semidirect
6. C3×#5579C2semidirect
9. C3×C4×D3×Q8C2semidirect
10. C3×#5569C2semidirect
11. C3×Q8×Dic6C2semidirect
13. #87015C3direct (N × H)
51. C3×#557D3semidirect
52. C3×#557C2×C3semidirect
61. #5728C2×C3semidirect
62. #5727C2×C3semidirect
63. #5690C2×C3semidirect
64. #5688C2×C3semidirect
65. #5579C2×C3semidirect
68. C4×D3×Q8C2×C3semidirect
69. #5569C2×C3semidirect
70. Q8×Dic6C2×C3semidirect
73. C3×#239Q8semidirect
183. C32×Q8C2×Q8semidirect
194. C3×D12C2×Q8semidirect
199. C3×C4×D3C2×Q8semidirect
202. C3×Dic6#41semidirect
205. #557C3×D3semidirect
231. #239C3×Q8semidirect
352. C3×Q8D3×Q8semidirect
353. C3×Q8C2×C3×Q8semidirect
385. D12C2×C3×Q8semidirect
390. C4×D3C2×C3×Q8semidirect
393. Dic6C3×#41semidirect
468. C32Q8×#41semidirect
474. Q8C3×D3×Q8semidirect
517. C3#87015direct (N × H)
518. C3C3×Q8×#41semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
C3×#57282
C3×#57272
C3×#56902
C3×#56882
C3×#55792
C3×C4×#2392
C3×C4×D3×Q82
C3×#55692
C3×Q8×Dic62
C3×Q8×#413
#870153