Finite Group Databasebeta

← C3×#83640 #11887591

Subgroups — C3×#83640 #11887591

Order 1152.

890 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#554C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5091C211yesmaximal, characteristic, complemented
5C3×#5051C212yesmaximal, complemented
6C3×#5050C212yesmaximal, complemented
7C3×#5031C211yesmaximal, characteristic, complemented
8C3×C4×#216C211yesmaximal, characteristic, complemented
9C3×D4×C3⋊C8C211yesmaximal, characteristic
10C3×#4970C212yesmaximal, complemented
11C2×C3×#810C212yesmaximal, complemented
12C3×#3299—31nomaximal
13#83640C311yesmaximal, characteristic, direct product factor
14C22×C3×Dic6C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#125—21no—
17C32×C22⋊Q8—22no—
18C32×C22⋊Q8C2212yes—
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4—21no—
21C32×C4×D4C2211yescharacteristic
22C2×C32×C4⋊C4C2212yes—
23C2×C3×#216C2211yescharacteristic
24C2×C3×#216C2212yes—
25C3×D4×Dic3—21no—
26C3×#924C2212yes—
27C22×C3×C3⋊C8C2212yes—
28C3×#888—21no—
29C3×#878—22no—
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C3×#835C2211yescharacteristic
33C3×#830C2212yes—
34C3×#810C2211yescharacteristic
35C3×#810C2212yes—
36C3×#810C2212yes—
37C3×#810C2212yes—
38C3×#810C2212yes—
39C3×#807C2211yescharacteristic
40C3×#807C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#554—21no—
44C3×#554D311yescharacteristic
45C3×#554C2×C311yescharacteristic
46C3×D4×Q8—31no—
47D4×Dic6C2×C311yescharacteristic
48C3×#487—31no—
49C3×#484—32no—
50C3×#477—31no—
51C3×#467—32no—
52C3×#462—31no—
53C3×#451—32no—
54C3×C4×Q16—31no—
55C3×C8×D4—31no—
56C2×C3×#103—32no—
57#5093C2×C311yescharacteristic, complemented
58#5091C2×C311yescharacteristic, complemented
59#5051C2×C312yescomplemented
60#5050C2×C312yescomplemented
61#5031C2×C311yescharacteristic, complemented
62C4×#216C2×C311yescharacteristic, complemented
63D4×C3⋊C8C2×C311yescharacteristic
64#4970C2×C312yescomplemented
65C2×#810C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2311yescharacteristic
68C2×C32×D4D411yescharacteristic
69C22×C32×C4—22no—
70C22×C32×C4C2312yes—
71C22×C3×Dic3—22no—
72C2×C3×Dic6—24no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6—42no—
75C2×C3×Dic6C2312yes—
76C2×C3×Dic6C2311yescharacteristic
77C32×C4⋊C4—22no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4—22no—
81C32×C4⋊C4D411yescharacteristic
82C32×C4⋊C4C2311yescharacteristic
83C32×C4⋊C4C2312yes—
84C32×C22⋊C4—22no—
85C32×C22⋊C4D412yes—
86C32×C42—21no—
87C32×C42C2311yescharacteristic
88C3×#217—22no—
89C3×#216—22no—
90C3×#216—42no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—21no—
97C2×C3×C3⋊C8—42no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2311yescharacteristic
101#3299—31noSylow
102C22×C3×Q8—32no—
103C22×Dic6C22×C312yes—
104C2×C3×Q16—31no—
105C2×C3×Q16—32no—
106C22×C3×C8—32no—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8—31no—
109C3×C4⋊Q8—61no—
110C3×C4⋊Q8C2×D311yescharacteristic
111C3×C4⋊Q8C22×C311yescharacteristic
112C3×#125—22no—
113C3×#125—21no—
114C3×#125—21no—
115C3×C22⋊Q8—24no—
116C3×C22⋊Q8—22no—
117C3×C22⋊Q8—22no—
118C3×C22⋊Q8—22no—
119C3×C22⋊Q8—32no—
120C3×C22⋊Q8—62no—
121C3×C22⋊Q8C2×D312yes—
122C3×C22⋊Q8C22×C312yes—
123C3×C4×Q8—21no—
124C3×C4×Q8—31no—
125C3×C4×Q8C2×D311yescharacteristic
126C3×C4×Q8C22×C311yescharacteristic
127C3×C4×D4—22no—
128C3×C4×D4—21no—
129C3×C4×D4—21no—
130C3×C4×D4—21no—
131C3×C4×D4—61no—
132C3×C4×D4C2×D311yescharacteristic
133C3×C4×D4C22×C311yescharacteristic
134C2×C3×C4⋊C4—22no—
135C2×C3×C4⋊C4C2×D312yes—
136C2×C3×C4⋊C4C22×C312yes—
137C2×#216C22×C311yescharacteristic
138C2×#216C22×C312yes—
139D4×Dic3—21no—
140#924C22×C312yes—
141C22×C3⋊C8C22×C312yes—
142#888—21no—
143#878—22no—
144#869C22×C311yescharacteristic
145C4×Dic6C22×C311yescharacteristic
146C3×#107—31no—
147C3×#107—32no—
148C3×C4⋊C8—31no—
149C3×#103—31no—
150C3×#103—31no—
151C3×#103—32no—
152C3×#103—32no—
153C3×#103—32no—
154C3×#103—32no—
155C3×C22⋊C8—32no—
156C3×C4×C8—31no—
157#835C22×C311yescharacteristic
158#830C22×C312yes—
159#810C22×C311yescharacteristic
160#810C22×C312yes—
161#810C22×C312yes—
162#810C22×C312yes—
163#810C22×C312yes—
164#807C22×C311yescharacteristic
165#807C22×C312yes—
166C4⋊(C3⋊C8)C22×C311yescharacteristic
167C4×C3⋊C8C22×C311yescharacteristic
168C23×C32C2×D412yes—
169C32×Q8—21no—
170C32×Q8—21no—
171C32×Q8—81no—
172C32×D4Q1614yescomplemented
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—82no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—44no—
187C3×Dic6—21no—
188C3×Dic6—22no—
189C3×Dic6—22no—
190C3×Dic6—44no—
191C3×Dic6#4112yes—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—22no—
195#554C3×D311yescharacteristic
196D4×Q8—31no—
197#487—31no—
198#484—32no—
199#477—31no—
200#467—32no—
201#462—31no—
202#451—32no—
203C4×Q16—31no—
204C8×D4—31no—
205C2×#103—32no—
206C2×C3×Q8—22no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—31no—
211C2×C3×Q8—32no—
212C2×C3×Q8—64no—
213C2×C3×Q8—62no—
214C2×C3×Q8—122no—
215C2×C3×Q8C22×D311yescharacteristic
216C2×C3×Q8C23×C311yescharacteristic
217C2×C3×D4—21no—
218C2×C3×D4#6711yescharacteristic
219C2×C3×D4C3×D411yescharacteristic
220C22×C3×C4—24no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—62no—
225C22×C3×C4C22×D312yes—
226C22×C3×C4C23×C312yes—
227C22×Dic3—22no—
228C2×Dic6—24no—
229C2×Dic6—22no—
230C2×Dic6—42no—
231C2×Dic6C23×C312yes—
232C2×Dic6C23×C311yescharacteristic
233C3×Q16—62no—
234C3×Q16—122no—
235C2×C3×C8—31no—
236C2×C3×C8—31no—
237C2×C3×C8—32no—
238C2×C3×C8—122no—
239C3×C4⋊C4—24no—
240C3×C4⋊C4—22no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—24no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—22no—
247C3×C4⋊C4—22no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4#6711yescharacteristic
260C3×C4⋊C4C3×D411yescharacteristic
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C4⋊C4C22×D312yes—
263C3×C4⋊C4C23×C311yescharacteristic
264C3×C4⋊C4C23×C312yes—
265C3×C22⋊C4—24no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—62no—
270C3×C22⋊C4#6712yes—
271C3×C22⋊C4C3×D412yes—
272C3×C42—22no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—61no—
277C3×C42C22×D311yescharacteristic
278C3×C42C23×C311yescharacteristic
279#217—22no—
280#216—22no—
281#216—42no—
282C4⋊Dic3—21no—
283C4⋊Dic3—21no—
284C4⋊Dic3C23×C311yescharacteristic
285Dic3⋊C4—21no—
286Dic3⋊C4—22no—
287C4×Dic3—21no—
288C2×C3⋊C8—42no—
289C2×C3⋊C8C23×C311yescharacteristic
290C2×C3⋊C8C23×C311yescharacteristic
291C2×C3⋊C8C23×C312yes—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32C2×Q1614yes—
295C22×C32C22×D411yescharacteristic
296C32×C4—22no—
297C32×C4—21no—
298C32×C4—41no—
299C32×C4—41no—
300C32×C4—42no—
301C32×C4C2×Q1612yes—
302C32×C4C2×#4111yescharacteristic
303C32×C4H(5,𝔽2)11yescharacteristic
304C3×Dic3—22no—
305C3×Dic3—42no—
306C3×Dic3—41no—
307C22×Q8—32no—
308C2×Q16—31no—
309C2×Q16—32no—
310C22×C8—32no—
311C4⋊Q8—31no—
312C4⋊Q8—61no—
313C4⋊Q8C2×C3×D311yescharacteristic
314#125—21no—
315C22⋊Q8—22no—
316C22⋊Q8—32no—
317C22⋊Q8—62no—
318C22⋊Q8C2×C3×D312yes—
319C4×Q8—31no—
320C4×Q8C2×C3×D311yescharacteristic
321C4×D4—21no—
322C4×D4—61no—
323C4×D4C2×C3×D311yescharacteristic
324C2×C4⋊C4C2×C3×D312yes—
325#107—31no—
326#107—32no—
327C4⋊C8—31no—
328#103—31no—
329#103—31no—
330#103—32no—
331#103—32no—
332#103—32no—
333#103—32no—
334C22⋊C8—32no—
335C4×C8—31no—
336C23×C3—22no—
337C23×C3C2×#6712yes—
338C23×C3C2×C3×D412yes—
339C3×Q8—21no—
340C3×Q8—21no—
341C3×Q8—21no—
342C3×Q8—21no—
343C3×Q8—32no—
344C3×Q8—41no—
345C3×Q8—41no—
346C3×Q8—61no—
347C3×Q8—62no—
348C3×Q8—62no—
349C3×Q8—81no—
350C3×Q8—81no—
351C3×Q8—82no—
352C3×Q8—124no—
353C3×D4—24no—
354C3×D4#21614yescomplemented
355C3×D4C3×Q1614yescomplemented
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—24no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—62no—
378C2×C3×C4—82no—
379C2×C3×C4—82no—
380C2×C3×C4—84no—
381C2×C3×C4—124no—
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C2×#6712yes—
384C2×C3×C4C2×#6711yescharacteristic
385C2×C3×C4C2×C3×D411yescharacteristic
386C2×C3×C4C2×C3×D412yes—
387C2×C3×C4C2×C3×D411yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C24×C311yescharacteristic
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—22no—
393C2×Dic3—44no—
394Dic6—21no—
395Dic6—22no—
396Dic6—22no—
397Dic6—44no—
398Dic6C3×#4112yes—
399C3×C8—61no—
400C3×C8—61no—
401C3×C8—62no—
402C3⋊C8—21no—
403C3⋊C8—21no—
404C3⋊C8—22no—
405C2×C32—24no—
406C2×C32#54611yescharacteristic
407C2×C32C22×Q1611yescharacteristic
408C2×C32#57711yescharacteristic
409C2×Q8—21no—
410C2×Q8—31no—
411C2×Q8—32no—
412C2×Q8—64no—
413C2×Q8—62no—
414C2×Q8—122no—
415C2×Q8C22×C3×D311yescharacteristic
416C2×D4C3×#6711yescharacteristic
417C22×C4—22no—
418C22×C4—62no—
419C22×C4C22×C3×D312yes—
420Q16—62no—
421Q16—122no—
422C2×C8—31no—
423C2×C8—31no—
424C2×C8—32no—
425C2×C8—122no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—31no—
431C4⋊C4—61no—
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—62no—
440C22⋊C4C3×#6712yes—
441C42—21no—
442C42—61no—
443C42C22×C3×D311yescharacteristic
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—24no—
449C22×C3—21no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3C2×#21614yes—
453C22×C3C2×C3×Q1614yes—
454C22×C3C22×#6711yescharacteristic
455C22×C3C22×C3×D411yescharacteristic
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—42no—
464C3×C4—41no—
465C3×C4—42no—
466C3×C4—44no—
467C3×C4—42no—
468C3×C4—41no—
469C3×C4—42no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—42no—
473C3×C4—41no—
474C3×C4—62no—
475C3×C4—122no—
476C3×C4—121no—
477C3×C4C2×#21612yes—
478C3×C4C2×C3×Q1612yes—
479C3×C4D3×#4111yescharacteristic
480C3×C4#100911yescharacteristic
481C3×C4C2×C3×#4111yescharacteristic
482C3×C4C3×H(5,𝔽2)11yescharacteristic
483Dic3—22no—
484Dic3—41no—
485Dic3—42no—
486C32#329911yescharacteristic, complemented, Sylow
487C23C2×C3×#6712yes—
488Q8—21no—
489Q8—21no—
490Q8—32no—
491Q8—61no—
492Q8—62no—
493Q8—62no—
494Q8—81no—
495Q8—124no—
496D4C3×#21614yescomplemented
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—62no—
505C2×C4—82no—
506C2×C4—124no—
507C2×C4C2×C3×#6711yescharacteristic
508C2×C4C2×C3×#6712yes—
509C2×C4C2×C3×#6711yescharacteristic
510C2×C4C23×C3×D311yescharacteristic
511C8—61no—
512C8—61no—
513C8—62no—
514C2×C3—24no—
515C2×C3—24no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—44no—
520C2×C3C22×#21611yescharacteristic
521C2×C3#582911yescharacteristic
522C2×C3#583611yescharacteristic
523C2×C3C3×#54611yescharacteristic
524C2×C3C22×C3×Q1611yescharacteristic
525C2×C3C3×#57711yescharacteristic
526C22—22no—
527C22—22no—
528C22C2×C3×#21614yes—
529C22C22×C3×#6711yescharacteristic
530C4—22no—
531C4—21no—
532C4—41no—
533C4—41no—
534C4—42no—
535C4—62no—
536C4—122no—
537C4—121no—
538C4C2×C3×#21612yes—
539C4C3×D3×#4111yescharacteristic
540C4C3×#100911yescharacteristic
541C3—21no—
542C3#8364011yescharacteristic, direct product factor
543C3C3×#329911yescharacteristic, complemented
544C2—24no—
545C2C22×C3×#21611yescharacteristic
546C2C3×#582911yescharacteristic
547C2C3×#583611yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#554C2
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenterC3×#554D3
hypocenterC3C3×#3299
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#554

Complements

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

NH ≅ G/Ntype
3. C3×#5093C2semidirect
4. C3×#5091C2semidirect
5. C3×#5051C2semidirect
6. C3×#5050C2semidirect
7. C3×#5031C2semidirect
8. C3×C4×#216C2semidirect
10. C3×#4970C2semidirect
11. C2×C3×#810C2semidirect
13. #83640C3direct (N × H)
57. #5093C2×C3semidirect
58. #5091C2×C3semidirect
59. #5051C2×C3semidirect
60. #5050C2×C3semidirect
61. #5031C2×C3semidirect
62. C4×#216C2×C3semidirect
64. #4970C2×C3semidirect
65. C2×#810C2×C3semidirect
172. C32×D4Q16semidirect
354. C3×D4#216semidirect
355. C3×D4C3×Q16semidirect
486. C32#3299semidirect
496. D4C3×#216semidirect
542. C3#83640direct (N × H)
543. C3C3×#3299semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
C3×D4×Dic62
C3×#50932
C3×#50912
C3×#50512
C3×#50502
C3×#50312
C3×C4×#2162
C3×D4×C3⋊C82
C3×#49702
C2×C3×#8102
C3×#32993
#836403