Finite Group Databasebeta

← C3×#78131 #11808784

Subgroups — C3×#78131 #11808784

Order 1152.

1203 conjugacy classes of subgroups.

The subgroup lattice has 583 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic
2C2×C3×#887C211yesmaximal, characteristic, complemented
3C32×#400C211yesmaximal, characteristic, complemented
4C3×#4991C211yesmaximal, characteristic
5C3×#4985C211yesmaximal, characteristic, complemented
6C3×#4675C212yesmaximal, complemented
7C3×#4673C212yesmaximal, complemented
8C3×#4672C211yesmaximal, characteristic
9C3×#4666C212yesmaximal, complemented
10C3×#4666C212yesmaximal, complemented
11C3×#4648C211yesmaximal, characteristic, complemented
12C3×#2398—31nomaximal
13#78131C311yesmaximal, characteristic, direct product factor
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×Dic6C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#893—24no—
31C3×#887—24no—
32C32×#95C2211yescharacteristic
33C32×#95C2212yes—
34C32×#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C2×C3×C4×Q8—31no—
40C2×C3×C4×D4—31no—
41C2×#893C2×C311yescharacteristic
42C2×#887C2×C311yescharacteristic, complemented
43C3×#400—21no—
44C3×#400—31no—
45C3×#400D311yescharacteristic, complemented
46C3×#400C2×C311yescharacteristic, complemented
47C3×#397—32no—
48C3×#394—31no—
49C3×#394—31no—
50C3×#393—32no—
51C3×C4×C22⋊C4—32no—
52C3×C4×C22⋊C4—32no—
53C3×#376—31no—
54#4991C2×C311yescharacteristic
55#4985C2×C311yescharacteristic, complemented
56#4675C2×C312yescomplemented
57#4673C2×C312yescomplemented
58#4672C2×C311yescharacteristic
59#4666C2×C312yescomplemented
60#4666C2×C312yescomplemented
61#4648C2×C311yescharacteristic, complemented
62C23×C3×D3C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×D12—24no—
74C2×C3×D12—22no—
75C2×C3×C4×D3—24no—
76C2×C3×C4×D3—24no—
77C2×C3×C4×D3—24no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—22no—
81C32×C4⋊C4—22no—
82C32×C4⋊C4—22no—
83C3×(C2×D3)⋊C4—24no—
84C3×(C2×D3)⋊C4—24no—
85C3×(C2×D3)⋊C4—24no—
86C3×(C2×D3)⋊C4—24no—
87C3×(C2×D3)⋊C4—24no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—22no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3—24no—
93C3×C4×Dic3D414yes—
94#2398—31noSylow
95C22×C3×Q8—31no—
96C22×C3×D4—31no—
97C23×C3×C4—32no—
98C22×D12C22×C311yescharacteristic
99C22×C4×D3C22×C312yes—
100C22×Dic6C22×C311yescharacteristic
101C3×C4×Q8—64no—
102C3×C4×D4—64no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C22×C311yescharacteristic
110C2×C3×C4⋊C4C22×C311yescharacteristic
111C2×C3×C22⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C22⋊C4—32no—
116C2×C3×C42—31no—
117C2×C3×C42—32no—
118C2×C3×C42—31no—
119C2×C3×C42—31no—
120C2×(C2×D3)⋊C4C22×C312yes—
121C2×(C2×D3)⋊C4C22×C312yes—
122C2×(C2×D3)⋊C4C22×C312yes—
123C2×(C2×D3)⋊C4C22×C312yes—
124C2×(C2×D3)⋊C4C22×C312yes—
125C2×Dic3⋊C4C22×C311yescharacteristic
126C2×Dic3⋊C4C22×C311yescharacteristic
127C2×C4×Dic3C22×C312yes—
128C2×C4×Dic3C22×C311yescharacteristic
129C2×C4×Dic3C22×C311yescharacteristic
130C2×C4×Dic3C22×C311yescharacteristic
131#893—24no—
132#887—24no—
133C3×#95—21no—
134C3×#95—22no—
135C3×#95—22no—
136C3×#95—32no—
137C3×#95—31no—
138C3×#95—32no—
139C3×#95—32no—
140C3×#95C2×D311yescharacteristic
141C3×#95C2×D312yes—
142C3×#95C2×D312yes—
143C3×#95C22×C311yescharacteristic
144C3×#95C22×C312yes—
145C3×#95C22×C312yes—
146C3⋊#95C22×C312yes—
147C3⋊#95C22×C311yescharacteristic
148C3⋊#95C22×C312yes—
149C3⋊#95C22×C312yes—
150C23×C32C2411yescharacteristic
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3#4114yes—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—22no—
161C2×C32×C4—21no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D412yes—
170C2×C32×C4#4112yes—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3#4112yes—
183C2×C3×Dic3#4114yes—
184C3×D12—28no—
185C3×C4×D3—48no—
186C3×Dic6—28no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189#400—31no—
190#400C3×D311yescharacteristic, complemented
191#397—32no—
192#394—31no—
193#394—31no—
194#393—32no—
195C4×C22⋊C4—32no—
196C4×C22⋊C4—32no—
197#376—31no—
198C24×C3—32no—
199C23×D3C23×C312yes—
200C2×C3×Q8—62no—
201C2×C3×Q8—62no—
202C2×C3×Q8—62no—
203C2×C3×D4—64no—
204C2×C3×D4—62no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—32no—
214C22×C3×C4—31no—
215C22×C3×C4—64no—
216C22×C3×C4—64no—
217C22×C3×C4—64no—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C23×C312yes—
224C22×C3×C4C23×C312yes—
225C22×C3×C4C23×C311yescharacteristic
226C22×C3×C4C23×C311yescharacteristic
227C22×C3×C4C23×C311yescharacteristic
228C22×Dic3C23×C312yes—
229C22×Dic3C23×C311yescharacteristic
230C22×Dic3C23×C311yescharacteristic
231C22×Dic3C23×C311yescharacteristic
232C22×Dic3C23×C311yescharacteristic
233C2×D12—24no—
234C2×D12—22no—
235C2×C4×D3—24no—
236C2×C4×D3—24no—
237C2×C4×D3—24no—
238C2×Dic6—22no—
239C2×Dic6—22no—
240C2×Dic6—22no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—22no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—42no—
246C3×C4⋊C4—42no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C22⋊C4—64no—
250C3×C22⋊C4—64no—
251C3×C22⋊C4—64no—
252C3×C22⋊C4—64no—
253C3×C22⋊C4—64no—
254C3×C42—34no—
255C3×C42—64no—
256C3×C42—62no—
257C3×C42—62no—
258(C2×D3)⋊C4—24no—
259(C2×D3)⋊C4—24no—
260(C2×D3)⋊C4—24no—
261(C2×D3)⋊C4—24no—
262(C2×D3)⋊C4—24no—
263Dic3⋊C4—22no—
264Dic3⋊C4—22no—
265C4×Dic3—22no—
266C4×Dic3—22no—
267C4×Dic3—24no—
268C4×Dic3C3×D414yes—
269C22×C32C22×D411yescharacteristic
270C22×C32C2×#4111yescharacteristic
271C22×C32C2×#4112yes—
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4112yes—
274C2×C3×D3—24no—
275C2×C3×D3—24no—
276C2×C3×D3—24no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C32×C4—22no—
282C32×C4—22no—
283C32×C4—41no—
284C32×C4—42no—
285C32×C4—42no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—41no—
289C3×Dic3—42no—
290C3×Dic3#12414yes—
291C22×Q8—31no—
292C22×D4—31no—
293C23×C4—32no—
294C4×Q8—64no—
295C4×D4—64no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—31no—
298C2×C4⋊C4C2×C3×D311yescharacteristic
299C2×C4⋊C4C2×C3×D311yescharacteristic
300C2×C22⋊C4—32no—
301C2×C22⋊C4—32no—
302C2×C22⋊C4—32no—
303C2×C22⋊C4—32no—
304C2×C22⋊C4—32no—
305C2×C42—31no—
306C2×C42—31no—
307C2×C42—31no—
308C2×C42—32no—
309#95—32no—
310#95—31no—
311#95—32no—
312#95—32no—
313#95C2×C3×D311yescharacteristic
314#95C2×C3×D312yes—
315#95C2×C3×D312yes—
316C23×C3—21no—
317C23×C3—34no—
318C23×C3—62no—
319C23×C3—62no—
320C23×C3—62no—
321C23×C3—62no—
322C23×C3—62no—
323C23×C3—62no—
324C23×C3C23×D311yescharacteristic
325C23×C3C24×C311yescharacteristic
326C22×D3—22no—
327C22×D3—22no—
328C22×D3—22no—
329C22×D3—22no—
330C22×D3—22no—
331C22×D3—22no—
332C22×D3C3×#4114yes—
333C3×Q8—68no—
334C3×D4—68no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—32no—
360C2×C3×C4—34no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—41no—
364C2×C3×C4—42no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—128no—
384C2×C3×C4D3×D412yes—
385C2×C3×C4#23912yes—
386C2×C3×C4C2×C3×D412yes—
387C2×C3×C4C3×#4112yes—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3C2×C3×D412yes—
398C2×Dic3C2×C3×D412yes—
399C2×Dic3C3×#4112yes—
400C2×Dic3C3×#4114yes—
401D12—28no—
402C4×D3—48no—
403Dic6—28no—
404C2×C32#52511yescharacteristic
405C2×C32#52511yescharacteristic
406C2×C32C2×#12411yescharacteristic
407C2×C32#52912yes—
408C2×C32#52912yes—
409C3×D3—44no—
410C24—32no—
411C2×Q8—62no—
412C2×Q8—62no—
413C2×Q8—62no—
414C2×D4—64no—
415C2×D4—62no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—32no—
420C22×C4—31no—
421C22×C4—64no—
422C22×C4—64no—
423C22×C4—64no—
424C22×C4C22×C3×D312yes—
425C22×C4C22×C3×D312yes—
426C22×C4C22×C3×D311yescharacteristic
427C22×C4C22×C3×D311yescharacteristic
428C22×C4C22×C3×D311yescharacteristic
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—62no—
432C4⋊C4—62no—
433C22⋊C4—64no—
434C22⋊C4—64no—
435C22⋊C4—64no—
436C22⋊C4—64no—
437C22⋊C4—64no—
438C42—34no—
439C42—62no—
440C42—62no—
441C42—64no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—64no—
448C22×C3—64no—
449C22×C3—64no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C2×#23911yescharacteristic
456C22×C3D3×#4112yes—
457C22×C3D3×#4112yes—
458C22×C3D3×#4111yescharacteristic
459C22×C3C22×C3×D411yescharacteristic
460C22×C3C2×C3×#4111yescharacteristic
461C22×C3C2×C3×#4112yes—
462C22×C3C2×C3×#4111yescharacteristic
463C22×C3C2×C3×#4112yes—
464C2×D3—24no—
465C2×D3—24no—
466C2×D3—24no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—42no—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—22no—
475C3×C4—34no—
476C3×C4—42no—
477C3×C4—42no—
478C3×C4—41no—
479C3×C4—42no—
480C3×C4—42no—
481C3×C4—41no—
482C3×C4—42no—
483C3×C4—42no—
484C3×C4—62no—
485C3×C4—62no—
486C3×C4—81no—
487C3×C4—82no—
488C3×C4—82no—
489C3×C4—121no—
490C3×C4—122no—
491Dic3—22no—
492Dic3—22no—
493Dic3—41no—
494Dic3—42no—
495Dic3C3×#12414yes—
496C32#239811yescharacteristic, complemented, Sylow
497C23—34no—
498C23—62no—
499C23—62no—
500C23—62no—
501C23—62no—
502C23—62no—
503C23—62no—
504C23C23×C3×D311yescharacteristic
505Q8—68no—
506D4—68no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—32no—
519C2×C4—34no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—128no—
532C2×C4C3×D3×D412yes—
533C2×C4C3×#23912yes—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3—22no—
539C2×C3—124no—
540C2×C3#562711yescharacteristic
541C2×C3#565611yescharacteristic
542C2×C3D3×#12411yescharacteristic
543C2×C3#569112yes—
544C2×C3#570612yes—
545C2×C3C3×#52511yescharacteristic
546C2×C3C3×#52511yescharacteristic
547C2×C3C2×C3×#12411yescharacteristic
548C2×C3C3×#52912yes—
549C2×C3C3×#52912yes—
550D3—44no—
551C22—64no—
552C22—64no—
553C22—64no—
554C22—122no—
555C22—122no—
556C22—122no—
557C22—122no—
558C22C2×C3×D3×D411yescharacteristic
559C22C2×C3×#23911yescharacteristic
560C22C3×D3×#4111yescharacteristic
561C22C3×D3×#4112yes—
562C22C3×D3×#4112yes—
563C4—22no—
564C4—22no—
565C4—34no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—62no—
570C4—62no—
571C4—121no—
572C4—122no—
573C3—21no—
574C3#7813111yescharacteristic, direct product factor
575C3C3×#239811yescharacteristic, complemented
576C2—124no—
577C2C3×#562711yescharacteristic
578C2C3×#565611yescharacteristic
579C2C3×D3×#12411yescharacteristic
580C2C3×#569112yes—
581C2C3×#570612yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#400C2
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC3×#400D3
hypocenterC3C3×#2398
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#400

Complements

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

NH ≅ G/Ntype
2. C2×C3×#887C2semidirect
3. C32×#400C2semidirect
5. C3×#4985C2semidirect
6. C3×#4675C2semidirect
7. C3×#4673C2semidirect
9. C3×#4666C2semidirect
10. C3×#4666C2semidirect
11. C3×#4648C2semidirect
13. #78131C3direct (N × H)
42. C2×#887C2×C3semidirect
45. C3×#400D3semidirect
46. C3×#400C2×C3semidirect
55. #4985C2×C3semidirect
56. #4675C2×C3semidirect
57. #4673C2×C3semidirect
59. #4666C2×C3semidirect
60. #4666C2×C3semidirect
61. #4648C2×C3semidirect
190. #400C3×D3semidirect
496. C32#2398semidirect
574. C3#78131direct (N × H)
575. C3C3×#2398semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×C3×#8872
C32×#4002
C3×#49912
C3×#49852
C3×#46752
C3×#46732
C3×#46722
C3×#46662
C3×#46482
C3×#23983
#781313