Finite Group Databasebeta

← C3×#70383 #11788190

Subgroups — C3×#70383 #11788190

Order 1152.

801 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5828C211yesmaximal, characteristic
2C2×C3×#872C211yesmaximal, characteristic, complemented
3C2×C32×#104C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5C3×#5126C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1897—31nomaximal
9#70383C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C3×#946C412yescomplemented
15C3×#938C412yescomplemented
16C3×#937—21no—
17C3×#935—21no—
18C3×C4×#67—22no—
19C2×C3×(C2×D3)⋊C4—21no—
20C3×#926C2211yescharacteristic
21C2×C3×Dic3⋊C4—21no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C3×#872—22no—
25C3×#872—22no—
26C32×#104—22no—
27C3×#837—22no—
28C3×(C2×D3)⋊C8—22no—
29C3×#525—31no—
30C2×C3×#117—31no—
31#5828C2×C311yescharacteristic
32C2×#872C2×C311yescharacteristic, complemented
33C2×C3×#104—21no—
34C2×C3×#104—31no—
35C2×C3×#104D311yescharacteristic, complemented
36C2×C3×#104C2×C311yescharacteristic, complemented
37C3×#407—31no—
38C2×#837C2×C311yescharacteristic, complemented
39#5126C2×C311yescharacteristic, complemented
40C3×#339—31no—
41C3×#339—31no—
42#4555C2×C311yescharacteristic, complemented
43#4523C2×C311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C32×#41—21no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41—21no—
49C2×C32×Q8C2×C411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4C2×C411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C3×#67—22no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3C2×C412yes—
63C2×C3×C4×D3D412yes—
64C32×M16—21no—
65C32×M16—21no—
66C2×C32×C8—21no—
67C32×C42—21no—
68C32×C42D412yescomplemented
69C3×#217—21no—
70C3×#217—22no—
71C3×(C2×D3)⋊C4—24no—
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3C2×C412yes—
74C3×Dic3⋊C4—24no—
75C3×Dic3⋊C4—22no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3D412yescomplemented
79C3×#208—21no—
80C3×#208—21no—
81C2×C3×C3⋊C8—21no—
82#1897—31noSylow
83C2×C3×#41—21no—
84C2×C3×#41C2×D311yescharacteristic
85C2×C3×#41C22×C311yescharacteristic
86C23×C3×C4—31no—
87C22×C4×D3C22×C311yescharacteristic
88C2×C3×M16—21no—
89C2×C3×M16—31no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C22×C311yescharacteristic
92C3×#123—61no—
93C3×C22⋊Q8—32no—
94C3×#121—32no—
95C3×#120—61no—
96C3×C4×D4—62no—
97C3×#117—31no—
98C3×#117—62no—
99C3×#117—62no—
100C2×C3×C4⋊C4—61no—
101C2×C3×C22⋊C4—61no—
102C2×C3×C42—21no—
103C2×C3×C42—31no—
104C2×C3×C42C2×D311yescharacteristic
105C2×C3×C42C22×C311yescharacteristic
106#946C3×C412yescomplemented
107#938C3×C412yescomplemented
108#937—21no—
109#935—21no—
110C4×#67—22no—
111C2×(C2×D3)⋊C4—21no—
112#926C22×C311yescharacteristic
113C2×Dic3⋊C4—21no—
114C2×C4×Dic3C22×C311yescharacteristic
115C2×#208C22×C311yescharacteristic
116#872—22no—
117#872—22no—
118C3×#104—24no—
119C3×#104—22no—
120C3×#104—22no—
121C3×#104—62no—
122C3×C22⋊C8—62no—
123#837—22no—
124(C2×D3)⋊C8—22no—
125C23×C32—21no—
126C23×C32C2×D411yescharacteristic
127C22×C3×D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—42no—
130C22×C3×D3C22⋊C412yes—
131C32×Q8—21no—
132C32×Q8—21no—
133C32×D4—21no—
134C32×D4—21no—
135C32×D4—41no—
136C32×D4—41no—
137C2×C32×C4—21no—
138C2×C32×C4—22no—
139C2×C32×C4—42no—
140C2×C32×C4—41no—
141C2×C32×C4—41no—
142C2×C32×C4C22×C411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C3×#67—44no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—42no—
154C2×C3×Dic3C22⋊C412yes—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C32×C8—41no—
160C3×C3⋊C8—41no—
161#525—31no—
162C2×#117—31no—
163C2×#104—31no—
164C2×#104C3×D311yescharacteristic, complemented
165#407—31no—
166#339—31no—
167#339—31no—
168C24×C3—31no—
169C23×D3C3×D411yescharacteristic
170C3×#41—22no—
171C3×#41—22no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—41no—
181C3×#41—41no—
182C2×C3×Q8—21no—
183C2×C3×Q8C4×D311yescharacteristic
184C2×C3×Q8C2×C3×C411yescharacteristic
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—41no—
189C2×C3×D4—62no—
190C2×C3×D4C4×D311yescharacteristic
191C2×C3×D4C2×C3×C411yescharacteristic
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—31no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—41no—
201C22×C3×C4—41no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C23×C311yescharacteristic
209C2×#67—22no—
210C22×Dic3—21no—
211C22×Dic3C3×D411yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C4×D3—21no—
215C2×C4×D3—21no—
216C2×C4×D3C2×C3×C412yes—
217C2×C4×D3C3×D412yes—
218C3×M16—22no—
219C3×M16—21no—
220C3×M16—21no—
221C3×M16—21no—
222C3×M16—21no—
223C3×M16—41no—
224C3×M16—61no—
225C3×M16—61no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—41no—
229C2×C3×C8—61no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—64no—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—64no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—61no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—22no—
240C3×C42—32no—
241C3×C42—41no—
242C3×C42—61no—
243C3×C42—61no—
244C3×C42#6712yescomplemented
245C3×C42C3×D412yescomplemented
246#217—21no—
247#217—22no—
248(C2×D3)⋊C4—24no—
249(C2×D3)⋊C4—22no—
250C4⋊Dic3C2×C3×C412yes—
251Dic3⋊C4—24no—
252Dic3⋊C4—22no—
253C4×Dic3—21no—
254C4×Dic3—21no—
255C4×Dic3C3×D412yescomplemented
256#208—21no—
257#208—21no—
258C2×C3⋊C8—21no—
259C22×C32—22no—
260C22×C32—41no—
261C22×C32—42no—
262C22×C32C2×C22⋊C411yescharacteristic
263C22×C32#12011yescharacteristic
264C22×C32#12311yescharacteristic
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C2×C3×D3—22no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C32×C4—42no—
271C32×C4—41no—
272C32×C4C4×D411yescharacteristic
273C32×C4C4×D411yescharacteristic
274C32×C4#12111yescharacteristic
275C32×C4#12111yescharacteristic
276C3×Dic3—22no—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C2×#41C2×C3×D311yescharacteristic
280C23×C4—31no—
281C2×M16—31no—
282C2×M16C2×C3×D311yescharacteristic
283#123—61no—
284C22⋊Q8—32no—
285#121—32no—
286#120—61no—
287C4×D4—62no—
288#117—31no—
289#117—62no—
290#117—62no—
291C2×C4⋊C4—61no—
292C2×C22⋊C4—61no—
293C2×C42—31no—
294C2×C42C2×C3×D311yescharacteristic
295#104—22no—
296#104—62no—
297C22⋊C8—62no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—32no—
302C23×C3—41no—
303C23×C3—61no—
304C23×C3—61no—
305C23×C3—122no—
306C23×C3D3×D411yescharacteristic
307C23×C3C2×C3×D411yescharacteristic
308C22×D3—21no—
309C22×D3—21no—
310C22×D3—42no—
311C22×D3C3×C22⋊C412yes—
312C3×Q8—22no—
313C3×Q8—21no—
314C3×Q8—21no—
315C3×Q8—21no—
316C3×Q8—21no—
317C3×Q8—41no—
318C3×D4—22no—
319C3×D4—21no—
320C3×D4—21no—
321C3×D4—21no—
322C3×D4—21no—
323C3×D4—41no—
324C3×D4—42no—
325C3×D4—42no—
326C3×D4—41no—
327C3×D4—41no—
328C3×D4—41no—
329C3×D4—41no—
330C3×D4—124no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—32no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—44no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—122no—
362C2×C3×C4C2×C4×D311yescharacteristic
363C2×C3×C4#23511yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4#23711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C22×C3×C411yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C2×C3×D411yescharacteristic
371C2×C3×C4C2×C3×D411yescharacteristic
372C2×C3×C4C3×#4111yescharacteristic
373C2×C3×C4C3×#4111yescharacteristic
374#67—44no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—42no—
380C2×Dic3C3×C22⋊C412yes—
381C4×D3—22no—
382C4×D3—22no—
383C4×D3—22no—
384C4×D3—22no—
385C3×C8—42no—
386C3×C8—41no—
387C3×C8—41no—
388C3×C8—121no—
389C3⋊C8—41no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32—81no—
393C2×C32#38611yescharacteristic
394C2×C32#42112yes—
395C3×D3—42no—
396C24—31no—
397#41—21no—
398#41—21no—
399#41—21no—
400#41—21no—
401C2×Q8C3×C4×D311yescharacteristic
402C2×D4—21no—
403C2×D4—62no—
404C2×D4C3×C4×D311yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—31no—
408C22×C4—32no—
409C22×C4—32no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4C22×C3×D311yescharacteristic
416M16—21no—
417M16—21no—
418M16—61no—
419M16—61no—
420C2×C8—21no—
421C2×C8—61no—
422C4⋊C4—32no—
423C4⋊C4—62no—
424C4⋊C4—64no—
425C22⋊C4—62no—
426C22⋊C4—64no—
427C22⋊C4—62no—
428C22⋊C4—61no—
429C42—21no—
430C42—32no—
431C42—61no—
432C42—61no—
433C42C3×#6712yescomplemented
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3—62no—
448C22×C3—82no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3D3×C22⋊C411yescharacteristic
452C22×C3#88311yescharacteristic
453C22×C3#93711yescharacteristic
454C22×C3C2×C3×C22⋊C411yescharacteristic
455C22×C3C3×#12011yescharacteristic
456C22×C3C3×#12311yescharacteristic
457C2×D3—22no—
458C2×D3—22no—
459C2×D3—22no—
460C2×D3—42no—
461C2×D3—42no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—42no—
467C3×C4—42no—
468C3×C4—42no—
469C3×C4—44no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—62no—
473C3×C4—122no—
474C3×C4—122no—
475C3×C4#67⋊C411yescharacteristic
476C3×C4#88411yescharacteristic
477C3×C4C4×#6711yescharacteristic
478C3×C4#93811yescharacteristic
479C3×C4C3×C4×D411yescharacteristic
480C3×C4C3×C4×D411yescharacteristic
481C3×C4C3×#12111yescharacteristic
482C3×C4C3×#12111yescharacteristic
483Dic3—22no—
484Dic3—42no—
485Dic3—42no—
486C32#189711yescharacteristic, complemented, Sylow
487C23—21no—
488C23—32no—
489C23—61no—
490C23—61no—
491C23—122no—
492C23C3×D3×D411yescharacteristic
493Q8—21no—
494Q8—21no—
495D4—21no—
496D4—21no—
497D4—41no—
498D4—41no—
499D4—124no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—32no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—122no—
515C2×C4C2×C3×C4×D311yescharacteristic
516C2×C4C3×#23511yescharacteristic
517C2×C4C3×D3×D411yescharacteristic
518C2×C4C3×D3×D411yescharacteristic
519C2×C4C3×#23711yescharacteristic
520C2×C4C2×C3×#6711yescharacteristic
521C8—41no—
522C8—121no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—22no—
529C2×C3—41no—
530C2×C3—41no—
531C2×C3—82no—
532C2×C3—81no—
533C2×C3—81no—
534C2×C3—122no—
535C2×C3#482112yes—
536C2×C3#495611yescharacteristic
537C2×C3C3×#38611yescharacteristic
538C2×C3C3×#42112yes—
539D3—42no—
540C22—22no—
541C22—41no—
542C22—42no—
543C22—62no—
544C22—62no—
545C22—62no—
546C22—122no—
547C22—122no—
548C22C3×D3×C22⋊C411yescharacteristic
549C22C3×#88311yescharacteristic
550C22C3×#93711yescharacteristic
551C4—42no—
552C4—41no—
553C4—62no—
554C4—122no—
555C4—122no—
556C4C3×#67⋊C411yescharacteristic
557C4C3×#88411yescharacteristic
558C4C3×C4×#6711yescharacteristic
559C4C3×#93811yescharacteristic
560C3—21no—
561C3#7038311yescharacteristic, direct product factor
562C3C3×#189711yescharacteristic, complemented
563C2—21no—
564C2—21no—
565C2—81no—
566C2—122no—
567C2C3×#482112yes—
568C2C3×#495611yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#5828C2
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#104D3
hypocenterC3C3×#1897
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
2. C2×C3×#872C2semidirect
3. C2×C32×#104C2semidirect
4. C2×C3×#837C2semidirect
5. C3×#5126C2semidirect
6. C3×#4555C2semidirect
7. C3×#4523C2semidirect
9. #70383C3direct (N × H)
14. C3×#946C4semidirect
15. C3×#938C4semidirect
32. C2×#872C2×C3semidirect
35. C2×C3×#104D3semidirect
36. C2×C3×#104C2×C3semidirect
38. C2×#837C2×C3semidirect
39. #5126C2×C3semidirect
42. #4555C2×C3semidirect
43. #4523C2×C3semidirect
68. C32×C42D4semidirect
78. C3×C4×Dic3D4semidirect
106. #946C3×C4semidirect
107. #938C3×C4semidirect
164. C2×#104C3×D3semidirect
244. C3×C42#67semidirect
245. C3×C42C3×D4semidirect
255. C4×Dic3C3×D4semidirect
433. C42C3×#67semidirect
486. C32#1897semidirect
561. C3#70383direct (N × H)
562. C3C3×#1897semidirect

Maximal subgroups

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

subgroupindex
C3×#58282
C2×C3×#8722
C2×C32×#1042
C2×C3×#8372
C3×#51262
C3×#45552
C3×#45232
C3×#18973
#703833