Finite Group Databasebeta

← C3×#70382 #11788156

Subgroups — C3×#70382 #11788156

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5828C211yesmaximal, characteristic
2C2×C3×C42×D3C211yesmaximal, 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×#1896—31nomaximal
9#70382C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C3×C4×D3—21no—
12C22×C3×C4×D3C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C3×#946C412yescomplemented
16C3×#938C412yescomplemented
17C3×#937—21no—
18C3×#935—21no—
19C3×C4×#67—22no—
20C3×#926C2211yescharacteristic
21C2×C3×C4×Dic3—21no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C3×C42×D3—22no—
25C3×C42×D3—22no—
26C32×#104—22no—
27C3×#837—22no—
28C3×(C2×D3)⋊C8—22no—
29C3×#525—31no—
30C22×C3×C42—31no—
31#5828C2×C311yescharacteristic
32C2×C42×D3C2×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, complemented
50C2×C32×D4—21no—
51C2×C32×D4C2×C411yescharacteristic, complemented
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—28no—
59C2×C3×C4×D3—24no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×C4×D3C2×C412yes—
65C2×C3×C4×D3D412yes—
66C32×M16—21no—
67C32×M16—21no—
68C2×C32×C8—21no—
69C32×C42—21no—
70C32×C42D412yescomplemented
71C3×#217—21no—
72C3×#217—22no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3C2×C412yescomplemented
75C3×Dic3⋊C4—22no—
76C3×C4×Dic3—24no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79C3×C4×Dic3D412yescomplemented
80C3×#208—21no—
81C3×#208—21no—
82C2×C3×C3⋊C8—21no—
83#1896—31noSylow
84C2×C3×#41—21no—
85C2×C3×#41C2×D311yescharacteristic
86C2×C3×#41C22×C311yescharacteristic
87C23×C3×C4—31no—
88C23×C3×C4—61no—
89C22×C4×D3—21no—
90C22×C4×D3C22×C311yescharacteristic
91C2×C3×M16—21no—
92C2×C3×M16—31no—
93C2×C3×M16C2×D311yescharacteristic
94C2×C3×M16C22×C311yescharacteristic
95C3×#123—61no—
96C3×C22⋊Q8—32no—
97C3×#121—32no—
98C3×#120—61no—
99C3×C4×D4—62no—
100C3×#117—31no—
101C2×C3×C42—21no—
102C2×C3×C42—31no—
103C2×C3×C42—62no—
104C2×C3×C42—61no—
105C2×C3×C42—62no—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C22×C311yescharacteristic
108#946C3×C412yescomplemented
109#938C3×C412yescomplemented
110#937—21no—
111#935—21no—
112C4×#67—22no—
113#926C22×C311yescharacteristic
114C2×C4×Dic3—21no—
115C2×C4×Dic3C22×C311yescharacteristic
116C2×#208C22×C311yescharacteristic
117C42×D3—22no—
118C42×D3—22no—
119C3×#104—24no—
120C3×#104—22no—
121C3×#104—22no—
122C3×#104—62no—
123C3×C22⋊C8—62no—
124#837—22no—
125(C2×D3)⋊C8—22no—
126C23×C32—21no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—21no—
129C22×C3×D3—21no—
130C22×C3×D3—24no—
131C22×C3×D3C22⋊C412yes—
132C32×Q8—21no—
133C32×Q8—21no—
134C32×D4—21no—
135C32×D4—21no—
136C32×D4—41no—
137C32×D4—41no—
138C2×C32×C4—24no—
139C2×C32×C4—22no—
140C2×C32×C4—21no—
141C2×C32×C4—41no—
142C2×C32×C4—41no—
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C3×#67—44no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3C22⋊C412yes—
156C3×C4×D3—216no—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C32×C8—41no—
162C3×C3⋊C8—41no—
163#525—31no—
164C22×C42—31no—
165C2×#104—31no—
166C2×#104C3×D311yescharacteristic, complemented
167#407—31no—
168#339—31no—
169#339—31no—
170C24×C3—31no—
171C23×D3C3×D411yescharacteristic
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—21no—
181C3×#41—21no—
182C3×#41—41no—
183C3×#41—41no—
184C2×C3×Q8—21no—
185C2×C3×Q8C4×D311yescharacteristic, complemented
186C2×C3×Q8C2×C3×C411yescharacteristic, complemented
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—41no—
191C2×C3×D4—62no—
192C2×C3×D4C4×D311yescharacteristic, complemented
193C2×C3×D4C2×C3×C411yescharacteristic, complemented
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—32no—
201C22×C3×C4—32no—
202C22×C3×C4—41no—
203C22×C3×C4—41no—
204C22×C3×C4—64no—
205C22×C3×C4—68no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×C3×C4—61no—
209C22×C3×C4—61no—
210C22×C3×C4—61no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C23×C311yescharacteristic
213C2×#67—22no—
214C22×Dic3—21no—
215C22×Dic3C3×D411yescharacteristic
216C2×C4×D3—24no—
217C2×C4×D3—28no—
218C2×C4×D3—21no—
219C2×C4×D3—21no—
220C2×C4×D3—21no—
221C2×C4×D3—21no—
222C2×C4×D3C2×C3×C412yes—
223C2×C4×D3C3×D412yes—
224C3×M16—22no—
225C3×M16—21no—
226C3×M16—21no—
227C3×M16—21no—
228C3×M16—21no—
229C3×M16—41no—
230C3×M16—61no—
231C3×M16—61no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—41no—
235C2×C3×C8—61no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—62no—
240C3×C22⋊C4—61no—
241C3×C42—21no—
242C3×C42—21no—
243C3×C42—22no—
244C3×C42—32no—
245C3×C42—41no—
246C3×C42—64no—
247C3×C42—61no—
248C3×C42—61no—
249C3×C42#6712yescomplemented
250C3×C42C3×D412yescomplemented
251#217—21no—
252#217—22no—
253(C2×D3)⋊C4—22no—
254C4⋊Dic3C2×C3×C412yescomplemented
255Dic3⋊C4—22no—
256C4×Dic3—24no—
257C4×Dic3—21no—
258C4×Dic3—21no—
259C4×Dic3C3×D412yescomplemented
260#208—21no—
261#208—21no—
262C2×C3⋊C8—21no—
263C22×C32—22no—
264C22×C32—41no—
265C22×C32—42no—
266C22×C32C2×C22⋊C411yescharacteristic
267C22×C32#12011yescharacteristic
268C22×C32#12311yescharacteristic
269C2×C3×D3—24no—
270C2×C3×D3—24no—
271C2×C3×D3—22no—
272C2×C3×D3—22no—
273C2×C3×D3#10414yescomplemented
274C32×C4—24no—
275C32×C4—41no—
276C32×C4C4×D411yescharacteristic
277C32×C4C4×D411yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12111yescharacteristic
280C3×Dic3—24no—
281C3×Dic3—22no—
282C3×Dic3—42no—
283C2×#41C2×C3×D311yescharacteristic
284C23×C4—31no—
285C23×C4—61no—
286C2×M16—31no—
287C2×M16C2×C3×D311yescharacteristic
288#123—61no—
289C22⋊Q8—32no—
290#121—32no—
291#120—61no—
292C4×D4—62no—
293#117—31no—
294C2×C42—31no—
295C2×C42—62no—
296C2×C42—61no—
297C2×C42—62no—
298C2×C42C2×C3×D311yescharacteristic
299#104—22no—
300#104—62no—
301C22⋊C8—62no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—32no—
306C23×C3—41no—
307C23×C3—64no—
308C23×C3—61no—
309C23×C3—61no—
310C23×C3D3×D411yescharacteristic
311C23×C3C2×C3×D411yescharacteristic
312C22×D3—21no—
313C22×D3—21no—
314C22×D3—24no—
315C22×D3C3×C22⋊C412yes—
316C3×Q8—22no—
317C3×Q8—21no—
318C3×Q8—21no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—41no—
322C3×D4—22no—
323C3×D4—21no—
324C3×D4—21no—
325C3×D4—21no—
326C3×D4—21no—
327C3×D4—41no—
328C3×D4—42no—
329C3×D4—42no—
330C3×D4—41no—
331C3×D4—41no—
332C3×D4—41no—
333C3×D4—41no—
334C3×D4—124no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—32no—
348C2×C3×C4—42no—
349C2×C3×C4—41no—
350C2×C3×C4—44no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—616no—
358C2×C3×C4—64no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—61no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4C2×C4×D311yescharacteristic
368C2×C3×C4#23511yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C22×C3×C411yescharacteristic
374C2×C3×C4C2×C3×D411yescharacteristic
375C2×C3×C4C2×C3×D411yescharacteristic
376C2×C3×C4C2×C3×D411yescharacteristic
377C2×C3×C4C3×#4111yescharacteristic
378C2×C3×C4C3×#4111yescharacteristic
379#67—44no—
380C2×Dic3—24no—
381C2×Dic3—21no—
382C2×Dic3—22no—
383C2×Dic3—21no—
384C2×Dic3—22no—
385C2×Dic3C3×C22⋊C412yes—
386C4×D3—216no—
387C4×D3—22no—
388C4×D3—22no—
389C4×D3—22no—
390C4×D3—22no—
391C3×C8—42no—
392C3×C8—41no—
393C3×C8—41no—
394C3×C8—121no—
395C3⋊C8—41no—
396C2×C32—21no—
397C2×C32—21no—
398C2×C32—81no—
399C2×C32#38611yescharacteristic
400C2×C32C2×#10412yes—
401C3×D3—24no—
402C24—31no—
403#41—21no—
404#41—21no—
405#41—21no—
406#41—21no—
407C2×Q8C3×C4×D311yescharacteristic, complemented
408C2×D4—21no—
409C2×D4—62no—
410C2×D4C3×C4×D311yescharacteristic, complemented
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—31no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—64no—
417C22×C4—68no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—61no—
423C22×C4C22×C3×D311yescharacteristic
424M16—21no—
425M16—21no—
426M16—61no—
427M16—61no—
428C2×C8—21no—
429C2×C8—61no—
430C4⋊C4—32no—
431C4⋊C4—62no—
432C22⋊C4—62no—
433C22⋊C4—62no—
434C22⋊C4—61no—
435C42—21no—
436C42—32no—
437C42—64no—
438C42—61no—
439C42—61no—
440C42C3×#6712yescomplemented
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—34no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—64no—
454C22×C3—64no—
455C22×C3—62no—
456C22×C3—62no—
457C22×C3—82no—
458C22×C3D3×C22⋊C411yescharacteristic
459C22×C3#88311yescharacteristic
460C22×C3#93711yescharacteristic
461C22×C3C2×C3×C22⋊C411yescharacteristic
462C22×C3C3×#12011yescharacteristic
463C22×C3C3×#12311yescharacteristic
464C2×D3—24no—
465C2×D3—24no—
466C2×D3—22no—
467C2×D3—22no—
468C2×D3C3×#10414yescomplemented
469C3×C4—24no—
470C3×C4—24no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—44no—
476C3×C4—42no—
477C3×C4—41no—
478C3×C4—41no—
479C3×C4—64no—
480C3×C4—62no—
481C3×C4—122no—
482C3×C4#67⋊C411yescharacteristic
483C3×C4#88411yescharacteristic
484C3×C4C4×#6711yescharacteristic
485C3×C4#93811yescharacteristic
486C3×C4C3×C4×D411yescharacteristic
487C3×C4C3×C4×D411yescharacteristic
488C3×C4C3×#12111yescharacteristic
489C3×C4C3×#12111yescharacteristic
490Dic3—24no—
491Dic3—22no—
492Dic3—42no—
493C32#189611yescharacteristic, complemented, Sylow
494C23—21no—
495C23—32no—
496C23—64no—
497C23—61no—
498C23—61no—
499C23C3×D3×D411yescharacteristic
500Q8—21no—
501Q8—21no—
502D4—21no—
503D4—21no—
504D4—41no—
505D4—41no—
506D4—124no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—32no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—616no—
514C2×C4—64no—
515C2×C4—61no—
516C2×C4—62no—
517C2×C4—61no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4C2×C3×C4×D311yescharacteristic
524C2×C4C3×#23511yescharacteristic
525C2×C4C3×D3×D411yescharacteristic
526C2×C4C3×D3×D411yescharacteristic
527C2×C4C3×#23711yescharacteristic
528C2×C4C2×C3×#6711yescharacteristic
529C8—41no—
530C8—121no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3—41no—
538C2×C3—41no—
539C2×C3—64no—
540C2×C3—82no—
541C2×C3—81no—
542C2×C3—81no—
543C2×C3D3×#10412yes—
544C2×C3#495611yescharacteristic
545C2×C3C3×#38611yescharacteristic
546C2×C3C2×C3×#10412yes—
547D3—24no—
548C22—22no—
549C22—34no—
550C22—41no—
551C22—42no—
552C22—64no—
553C22—64no—
554C22—62no—
555C22—62no—
556C22C3×D3×C22⋊C411yescharacteristic
557C22C3×#88311yescharacteristic
558C22C3×#93711yescharacteristic
559C4—24no—
560C4—41no—
561C4—64no—
562C4—62no—
563C4—122no—
564C4C3×#67⋊C411yescharacteristic
565C4C3×#88411yescharacteristic
566C4C3×C4×#6711yescharacteristic
567C4C3×#93811yescharacteristic
568C3—21no—
569C3#7038211yescharacteristic, direct product factor
570C3C3×#189611yescharacteristic, complemented
571C2—21no—
572C2—21no—
573C2—64no—
574C2—81no—
575C2C3×D3×#10412yes—
576C2C3×#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×#1896
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×C42×D3C2semidirect
3. C2×C32×#104C2semidirect
4. C2×C3×#837C2semidirect
5. C3×#5126C2semidirect
6. C3×#4555C2semidirect
7. C3×#4523C2semidirect
9. #70382C3direct (N × H)
15. C3×#946C4semidirect
16. C3×#938C4semidirect
32. C2×C42×D3C2×C3semidirect
35. C2×C3×#104D3semidirect
36. C2×C3×#104C2×C3semidirect
38. C2×#837C2×C3semidirect
39. #5126C2×C3semidirect
42. #4555C2×C3semidirect
43. #4523C2×C3semidirect
49. C2×C32×Q8C2×C4semidirect
51. C2×C32×D4C2×C4semidirect
70. C32×C42D4semidirect
74. C3×C4⋊Dic3C2×C4semidirect
79. C3×C4×Dic3D4semidirect
108. #946C3×C4semidirect
109. #938C3×C4semidirect
166. C2×#104C3×D3semidirect
185. C2×C3×Q8C4×D3semidirect
186. C2×C3×Q8C2×C3×C4semidirect
192. C2×C3×D4C4×D3semidirect
193. C2×C3×D4C2×C3×C4semidirect
249. C3×C42#67semidirect
250. C3×C42C3×D4semidirect
254. C4⋊Dic3C2×C3×C4semidirect
259. C4×Dic3C3×D4semidirect
273. C2×C3×D3#104semidirect
407. C2×Q8C3×C4×D3semidirect
410. C2×D4C3×C4×D3semidirect
440. C42C3×#67semidirect
468. C2×D3C3×#104semidirect
493. C32#1896semidirect
569. C3#70382direct (N × H)
570. C3C3×#1896semidirect

Maximal subgroups

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

subgroupindex
C3×#58282
C2×C3×C42×D32
C2×C32×#1042
C2×C3×#8372
C3×#51262
C3×#45552
C3×#45232
C3×#18963
#703823