Finite Group Databasebeta

← C3×#83664 #11888000

Subgroups — C3×#83664 #11888000

Order 1152.

878 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#556C211yesmaximal, characteristic, complemented
2C3×#5551C211yesmaximal, characteristic
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5C3×#5051C212yesmaximal, complemented
6C3×#5047C212yesmaximal, complemented
7C3×#5031C211yesmaximal, characteristic, complemented
8C3×C4×#215C211yesmaximal, characteristic, complemented
9C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
10C3×#5002C212yesmaximal, complemented
11C3×#4996C212yesmaximal, complemented
12C3×#3302—31nomaximal
13#83664C311yesmaximal, characteristic, direct product factor
14C2×C3×#235C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#126—22no—
17C32×#124—21no—
18C32×C22⋊Q8C2212yes—
19C32×C4×Q8—21no—
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C32×#117C2212yes—
23C2×C3×#216C2212yes—
24C2×C3×#215C2211yescharacteristic
25C3×#938—21no—
26C3×#924C2212yes—
27C22×C3×C3⋊C8C2212yes—
28C3×D3×C4⋊C4—21no—
29C3×#883—22no—
30C3×C4×D12C2211yescharacteristic
31C3×#869C2211yescharacteristic
32C3×#835C2211yescharacteristic
33C3×#830C2212yes—
34C3×#810C2212yes—
35C3×#810C2212yes—
36C3×#810C2212yes—
37C3×#809C2211yescharacteristic
38C3×#809C2212yes—
39C3×#808C2211yescharacteristic
40C3×#807C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#556—21no—
44C3×#556D311yescharacteristic, complemented
45C3×#556C2×C311yescharacteristic, complemented
46C3×#547—31no—
47#5551C2×C311yescharacteristic
48C3×#487—31no—
49C3×#485—32no—
50C3×#474—31no—
51C3×#467—32no—
52C3×#462—31no—
53C3×#452—32no—
54C3×C4×SD16—31no—
55C3×C8×D4—31no—
56C3×#416—32no—
57#5093C2×C311yescharacteristic, complemented
58#5087C2×C311yescharacteristic, complemented
59#5051C2×C312yescomplemented
60#5047C2×C312yescomplemented
61#5031C2×C311yescharacteristic, complemented
62C4×#215C2×C311yescharacteristic, complemented
63D4×C3⋊C8C2×C311yescharacteristic, complemented
64#5002C2×C312yescomplemented
65#4996C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2311yescharacteristic
68C2×C32×D4D411yescharacteristic
69C22×C32×C4C2312yes—
70C2×C3×#67—22no—
71C3×#235—24no—
72C3×#235—42no—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—21no—
76C2×C3×Dic6C2312yes—
77C32×C4⋊C4—22no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4D411yescharacteristic
81C32×C4⋊C4C2312yes—
82C32×C4⋊C4C2311yescharacteristic
83C32×C22⋊C4—22no—
84C32×C22⋊C4—22no—
85C32×C22⋊C4D412yes—
86C32×C42—22no—
87C32×C42—21no—
88C32×C42C2311yescharacteristic
89C3×#217—22no—
90C3×#216—42no—
91C3×#215—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—22no—
97C2×C3×C3⋊C8—42no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2311yescharacteristic
101#3302—31noSylow
102C2×C3×#41—32no—
103C2×#235C22×C312yes—
104C2×C3×Q16—32no—
105C2×C3×SD16—31no—
106C22×C3×C8—32no—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8—31no—
109C3×C4⋊Q8C2×D311yescharacteristic
110C3×C4⋊Q8C22×C311yescharacteristic
111C3×#126—24no—
112C3×#126—22no—
113C3×#126—22no—
114C3×#124—22no—
115C3×#124—21no—
116C3×#124—21no—
117C3×#123—62no—
118C3×C22⋊Q8—22no—
119C3×C22⋊Q8—32no—
120C3×C22⋊Q8C2×D312yes—
121C3×C22⋊Q8C22×C312yes—
122C3×#121—61no—
123C3×C4×Q8—22no—
124C3×C4×Q8—21no—
125C3×C4×Q8—21no—
126C3×C4×Q8—21no—
127C3×C4×Q8C2×D311yescharacteristic
128C3×C4×Q8C22×C311yescharacteristic
129C3×C4×D4—21no—
130C3×C4×D4—31no—
131C3×C4×D4C2×D311yescharacteristic
132C3×C4×D4C22×C311yescharacteristic
133C3×#117—22no—
134C3×#117C2×D312yes—
135C3×#117C22×C312yes—
136C2×C3×C4⋊C4—61no—
137C2×#216C22×C312yes—
138C2×#215C22×C311yescharacteristic
139#938—21no—
140#924C22×C312yes—
141C22×C3⋊C8C22×C312yes—
142D3×C4⋊C4—21no—
143#883—22no—
144C4×D12C22×C311yescharacteristic
145#869C22×C311yescharacteristic
146C3×#107—32no—
147C3×#106—31no—
148C3×C4⋊C8—31no—
149C3×#103—31no—
150C3×#103—32no—
151C3×#103—32no—
152C3×#103—32no—
153C3×#102—31no—
154C3×#102—32no—
155C3×C22⋊C8—32no—
156C3×C4×C8—31no—
157#835C22×C311yescharacteristic
158#830C22×C312yes—
159#810C22×C312yes—
160#810C22×C312yes—
161#810C22×C312yes—
162#809C22×C311yescharacteristic
163#809C22×C312yes—
164#808C22×C311yescharacteristic
165#807C22×C312yes—
166C4⋊(C3⋊C8)C22×C311yescharacteristic
167C4×C3⋊C8C22×C311yescharacteristic
168C23×C32C2×D412yes—
169C22×C3×D3—21no—
170C32×Q8—21no—
171C32×Q8—21no—
172C32×Q8—42no—
173C32×D4—22no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C3×#67—44no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C3×D12—21no—
187C3×D12#4112yes—
188C3×C4×D3—44no—
189C3×C4×D3—42no—
190C3×Dic6—22no—
191C3×Dic6—22no—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—22no—
195#556C3×D311yescharacteristic, complemented
196#547—31no—
197#487—31no—
198#485—32no—
199#474—31no—
200#467—32no—
201#462—31no—
202#452—32no—
203C4×SD16—31no—
204C8×D4—31no—
205#416—32no—
206C3×#41—64no—
207C3×#41—122no—
208C2×C3×Q8—22no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—32no—
213C2×C3×Q8C22×D311yescharacteristic
214C2×C3×Q8C23×C311yescharacteristic
215C2×C3×D4—21no—
216C2×C3×D4—31no—
217C2×C3×D4—62no—
218C2×C3×D4#6711yescharacteristic
219C2×C3×D4C3×D411yescharacteristic
220C22×C3×C4—22no—
221C22×C3×C4—61no—
222C22×C3×C4—62no—
223C22×C3×C4C22×D312yes—
224C22×C3×C4C23×C312yes—
225C2×#67—22no—
226#235—24no—
227#235—42no—
228C2×D12C23×C311yescharacteristic
229C2×C4×D3—21no—
230C2×C4×D3—22no—
231C2×Dic6C23×C312yes—
232C3×Q16—122no—
233C3×SD16—62no—
234C2×C3×C8—31no—
235C2×C3×C8—31no—
236C2×C3×C8—32no—
237C2×C3×C8—122no—
238C3×C4⋊C4—24no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—22no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—62no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4#6711yescharacteristic
255C3×C4⋊C4C3×D411yescharacteristic
256C3×C4⋊C4C22×D311yescharacteristic
257C3×C4⋊C4C22×D312yes—
258C3×C4⋊C4C23×C312yes—
259C3×C4⋊C4C23×C311yescharacteristic
260C3×C22⋊C4—24no—
261C3×C22⋊C4—24no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—22no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—61no—
269C3×C22⋊C4#6712yes—
270C3×C22⋊C4C3×D412yes—
271C3×C42—24no—
272C3×C42—22no—
273C3×C42—22no—
274C3×C42—21no—
275C3×C42—22no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42C22×D311yescharacteristic
279C3×C42C23×C311yescharacteristic
280#217—22no—
281#216—42no—
282#215—22no—
283(C2×D3)⋊C4—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3C23×C311yescharacteristic
287Dic3⋊C4—22no—
288C2×C3⋊C8—42no—
289C2×C3⋊C8C23×C311yescharacteristic
290C2×C3⋊C8C23×C311yescharacteristic
291C2×C3⋊C8C23×C312yes—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32—22no—
295C22×C32C22×D411yescharacteristic
296C2×C3×D3—22no—
297C2×C3×D3—41no—
298C2×C3×D3—41no—
299C32×C4—22no—
300C32×C4—21no—
301C32×C4—41no—
302C32×C4—42no—
303C32×C4—41no—
304C32×C4#13512yes—
305C32×C4C2×#4111yescharacteristic
306C32×C4H(5,𝔽2)11yescharacteristic
307C3×Dic3—42no—
308C3×Dic3—41no—
309C2×#41—32no—
310C2×Q16—32no—
311C2×SD16—31no—
312C22×C8—32no—
313C4⋊Q8—31no—
314C4⋊Q8C2×C3×D311yescharacteristic
315#126—22no—
316#124—21no—
317#123—62no—
318C22⋊Q8—32no—
319C22⋊Q8C2×C3×D312yes—
320#121—61no—
321C4×Q8—21no—
322C4×Q8C2×C3×D311yescharacteristic
323C4×D4—31no—
324C4×D4C2×C3×D311yescharacteristic
325#117C2×C3×D312yes—
326C2×C4⋊C4—61no—
327#107—32no—
328#106—31no—
329C4⋊C8—31no—
330#103—31no—
331#103—32no—
332#103—32no—
333#103—32no—
334#102—31no—
335#102—32no—
336C22⋊C8—32no—
337C4×C8—31no—
338C23×C3—22no—
339C23×C3—61no—
340C23×C3C2×#6712yes—
341C23×C3C2×C3×D412yes—
342C22×D3—21no—
343C3×Q8—21no—
344C3×Q8—21no—
345C3×Q8—21no—
346C3×Q8—21no—
347C3×Q8—41no—
348C3×Q8—41no—
349C3×Q8—44no—
350C3×Q8—42no—
351C3×Q8—42no—
352C3×Q8—62no—
353C3×Q8—62no—
354C3×D4—22no—
355C3×D4—22no—
356C3×D4—32no—
357C3×D4—42no—
358C3×D4—61no—
359C3×D4—124no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—24no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—61no—
380C2×C3×C4—62no—
381C2×C3×C4—124no—
382C2×C3×C4—122no—
383C2×C3×C4C2×#6712yes—
384C2×C3×C4C2×#6711yescharacteristic
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C2×C3×D412yes—
387C2×C3×C4C2×C3×D411yescharacteristic
388C2×C3×C4C2×C3×D411yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C24×C311yescharacteristic
391#67—44no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394D12—21no—
395D12C3×#4112yes—
396C4×D3—44no—
397C4×D3—42no—
398Dic6—22no—
399Dic6—22no—
400C3×C8—61no—
401C3×C8—61no—
402C3×C8—62no—
403C3⋊C8—21no—
404C3⋊C8—21no—
405C3⋊C8—22no—
406C2×C32—42no—
407C2×C32#54611yescharacteristic
408C2×C32C2×#13511yescharacteristic
409C2×C32#57811yescharacteristic
410C3×D3—42no—
411#41—64no—
412#41—122no—
413C2×Q8—21no—
414C2×Q8—32no—
415C2×Q8C22×C3×D311yescharacteristic
416C2×D4—31no—
417C2×D4—62no—
418C2×D4C3×#6711yescharacteristic
419C22×C4—61no—
420C22×C4—62no—
421C22×C4C22×C3×D312yes—
422Q16—122no—
423SD16—62no—
424C2×C8—31no—
425C2×C8—31no—
426C2×C8—32no—
427C2×C8—122no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—31no—
432C4⋊C4—61no—
433C4⋊C4—62no—
434C4⋊C4—61no—
435C4⋊C4C3×#6711yescharacteristic
436C4⋊C4C22×C3×D311yescharacteristic
437C4⋊C4C22×C3×D312yes—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—62no—
441C22⋊C4—61no—
442C22⋊C4C3×#6712yes—
443C42—22no—
444C42—21no—
445C42C22×C3×D311yescharacteristic
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—22no—
452C22×C3—21no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—62no—
457C22×C3—121no—
458C22×C3—121no—
459C22×C3C22×#6711yescharacteristic
460C22×C3C22×C3×D411yescharacteristic
461C2×D3—22no—
462C2×D3—41no—
463C2×D3—41no—
464C3×C4—21no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—22no—
468C3×C4—22no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—42no—
472C3×C4—41no—
473C3×C4—44no—
474C3×C4—42no—
475C3×C4—42no—
476C3×C4—42no—
477C3×C4—41no—
478C3×C4—42no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—121no—
483C3×C4—122no—
484C3×C4#95012yes—
485C3×C4C3×#13512yes—
486C3×C4D3×#4111yescharacteristic
487C3×C4#100911yescharacteristic
488C3×C4C2×C3×#4111yescharacteristic
489C3×C4C3×H(5,𝔽2)11yescharacteristic
490Dic3—41no—
491Dic3—42no—
492C32#330211yescharacteristic, complemented, Sylow
493C23—61no—
494C23C2×C3×#6712yes—
495Q8—21no—
496Q8—21no—
497Q8—42no—
498Q8—62no—
499Q8—62no—
500D4—22no—
501D4—32no—
502D4—61no—
503D4—124no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—61no—
510C2×C4—62no—
511C2×C4—124no—
512C2×C4—122no—
513C2×C4C2×C3×#6712yes—
514C2×C4C2×C3×#6711yescharacteristic
515C2×C4C2×C3×#6711yescharacteristic
516C2×C4C23×C3×D311yescharacteristic
517C8—61no—
518C8—61no—
519C8—62no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—42no—
524C2×C3—42no—
525C2×C3—82no—
526C2×C3—122no—
527C2×C3C2×#95011yescharacteristic
528C2×C3#582911yescharacteristic
529C2×C3#583811yescharacteristic
530C2×C3C3×#54611yescharacteristic
531C2×C3C2×C3×#13511yescharacteristic
532C2×C3C3×#57811yescharacteristic
533D3—42no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—62no—
538C22—121no—
539C22—121no—
540C22C22×C3×#6711yescharacteristic
541C4—22no—
542C4—21no—
543C4—42no—
544C4—41no—
545C4—41no—
546C4—121no—
547C4—122no—
548C4C3×#95012yes—
549C4C3×D3×#4111yescharacteristic
550C4C3×#100911yescharacteristic
551C3—21no—
552C3#8366411yescharacteristic, direct product factor
553C3C3×#330211yescharacteristic, complemented
554C2—42no—
555C2—122no—
556C2C2×C3×#95011yescharacteristic
557C2C3×#582911yescharacteristic
558C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#556C2
socleC22×C32C22×D4
prime radicalC3×#5551C2
hypercenterC3×#556D3
hypocenterC3C3×#3302
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#556

Complements

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

NH ≅ G/Ntype
1. C32×#556C2semidirect
3. C3×#5093C2semidirect
4. C3×#5087C2semidirect
5. C3×#5051C2semidirect
6. C3×#5047C2semidirect
7. C3×#5031C2semidirect
8. C3×C4×#215C2semidirect
9. C3×D4×C3⋊C8C2semidirect
10. C3×#5002C2semidirect
11. C3×#4996C2semidirect
13. #83664C3direct (N × H)
44. C3×#556D3semidirect
45. C3×#556C2×C3semidirect
57. #5093C2×C3semidirect
58. #5087C2×C3semidirect
59. #5051C2×C3semidirect
60. #5047C2×C3semidirect
61. #5031C2×C3semidirect
62. C4×#215C2×C3semidirect
63. D4×C3⋊C8C2×C3semidirect
64. #5002C2×C3semidirect
65. #4996C2×C3semidirect
195. #556C3×D3semidirect
492. C32#3302semidirect
552. C3#83664direct (N × H)
553. C3C3×#3302semidirect

Maximal subgroups

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

subgroupindex
C32×#5562
C3×#55512
C3×#50932
C3×#50872
C3×#50512
C3×#50472
C3×#50312
C3×C4×#2152
C3×D4×C3⋊C82
C3×#50022
C3×#49962
C3×#33023
#836643