Finite Group Databasebeta

← C3×#76893 #11808781

Subgroups — C3×#76893 #11808781

Order 1152.

1255 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C2×C3×#887C211yesmaximal, characteristic, complemented
3C32×#394C211yesmaximal, characteristic
4C3×#5222C211yesmaximal, characteristic
5C3×#4986C211yesmaximal, characteristic, complemented
6C3×#4952C212yesmaximal, complemented
7C3×#4947C212yesmaximal, complemented
8C3×Dic3×C22⋊C4C212yesmaximal, complemented
9C3×Dic3×C22⋊C4C212yesmaximal, complemented
10C3×#4659C211yesmaximal, characteristic, complemented
11C3×#4648C211yesmaximal, characteristic, complemented
12C3×#2398—31nomaximal
13#76893C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C22×C3×Dic6C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4C2212yes—
19C2×C32×C22⋊C4C2212yes—
20C2×C3×#217C2212yes—
21C2×C3×#217C2212yes—
22C2×C3×#217C2212yes—
23C3×D4×Dic3—24no—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#887—24no—
32C32×#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C2×C3×C4×Q8—31no—
40C2×C3×C4×D4—31no—
41C2×D4×Dic3C2×C311yescharacteristic
42C2×#887C2×C311yescharacteristic, complemented
43C3×#400—31no—
44C3×#400—31no—
45C3×#397—32no—
46C3×#394—21no—
47C3×#394—31no—
48C3×#394D311yescharacteristic
49C3×#394C2×C311yescharacteristic
50C3×#393—32no—
51C3×C4×C22⋊C4—32no—
52C3×C4×C22⋊C4—32no—
53C3×#376—31no—
54#5222C2×C311yescharacteristic
55#4986C2×C311yescharacteristic, complemented
56#4952C2×C312yescomplemented
57#4947C2×C312yescomplemented
58Dic3×C22⋊C4C2×C312yescomplemented
59Dic3×C22⋊C4C2×C312yescomplemented
60#4659C2×C311yescharacteristic, complemented
61#4648C2×C311yescharacteristic, complemented
62C24×C32C2312yes—
63C2×C32×D4—24no—
64C2×C32×D4—22no—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3×Dic3—24no—
70C22×C3×Dic3—24no—
71C22×C3×Dic3—24no—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C2×C3×Dic6—22no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—22no—
81C32×C4⋊C4—22no—
82C32×C22⋊C4—24no—
83C32×C22⋊C4—24no—
84C3×#217—24no—
85C3×#217—24no—
86C3×#217—24no—
87C3×C4⋊Dic3—22no—
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—21no—
97C22×C3×D4C2×D311yescharacteristic
98C22×C3×D4C22×C311yescharacteristic
99C23×C3×C4—32no—
100C23×Dic3C22×C312yes—
101C22×Dic6C22×C311yescharacteristic
102C3×C4×Q8—64no—
103C3×C4×D4—64no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C22×C311yescharacteristic
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C22⋊C4C2×D312yes—
116C2×C3×C22⋊C4C2×D312yes—
117C2×C3×C22⋊C4C22×C312yes—
118C2×C3×C22⋊C4C22×C312yes—
119C2×C3×C42—31no—
120C2×C3×C42—32no—
121C2×C3×C42—31no—
122C2×C3×C42—31no—
123C2×#217C22×C312yes—
124C2×#217C22×C312yes—
125C2×#217C22×C312yes—
126D4×Dic3—24no—
127C2×C4⋊Dic3C22×C311yescharacteristic
128C2×Dic3⋊C4C22×C311yescharacteristic
129C2×Dic3⋊C4C22×C311yescharacteristic
130C2×C4×Dic3C22×C312yes—
131C2×C4×Dic3C22×C311yescharacteristic
132C2×C4×Dic3C22×C311yescharacteristic
133C2×C4×Dic3C22×C311yescharacteristic
134#887—24no—
135C3×#95—21no—
136C3×#95—32no—
137C3×#95—31no—
138C3×#95—32no—
139C3×#95—32no—
140C3×#95—32no—
141C3×#95—32no—
142C3×#95C2×D311yescharacteristic
143C3×#95C22×C311yescharacteristic
144C3⋊#95C22×C312yes—
145C3⋊#95C22×C311yescharacteristic
146C3⋊#95C22×C312yes—
147C3⋊#95C22×C312yes—
148C3⋊#95C22×C312yes—
149C3⋊#95C22×C312yes—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32#4114yes—
157C23×C32C2411yescharacteristic
158C32×D4—28no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—22no—
162C2×C32×C4—21no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D412yes—
168C2×C32×C4#4112yes—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—48no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C2×C3×Dic3#4112yes—
185C2×C3×Dic3#4114yes—
186C3×Dic6—28no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189#400—31no—
190#400—31no—
191#397—32no—
192#394—31no—
193#394C3×D311yescharacteristic
194#393—32no—
195C4×C22⋊C4—32no—
196C4×C22⋊C4—32no—
197#376—31no—
198C24×C3—22no—
199C24×C3C22×D312yes—
200C24×C3C23×C312yes—
201C2×C3×Q8—62no—
202C2×C3×Q8—62no—
203C2×C3×Q8—62no—
204C2×C3×D4—24no—
205C2×C3×D4—24no—
206C2×C3×D4—22no—
207C2×C3×D4—22no—
208C2×C3×D4—42no—
209C2×C3×D4—44no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—31no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4—31no—
220C22×C3×C4—64no—
221C22×C3×C4—64no—
222C22×C3×C4—64no—
223C22×C3×C4C22×D312yes—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C23×C312yes—
228C22×C3×C4C23×C311yescharacteristic
229C22×C3×C4C23×C311yescharacteristic
230C22×C3×C4C23×C311yescharacteristic
231C22×Dic3—24no—
232C22×Dic3—24no—
233C22×Dic3—24no—
234C22×Dic3C23×C312yes—
235C22×Dic3C23×C312yes—
236C22×Dic3C23×C311yescharacteristic
237C22×Dic3C23×C311yescharacteristic
238C22×Dic3C23×C311yescharacteristic
239C22×Dic3C23×C311yescharacteristic
240C2×Dic6—22no—
241C2×Dic6—22no—
242C2×Dic6—22no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—42no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C22⋊C4—24no—
250C3×C22⋊C4—24no—
251C3×C22⋊C4—24no—
252C3×C22⋊C4—24no—
253C3×C22⋊C4—44no—
254C3×C22⋊C4—44no—
255C3×C22⋊C4—64no—
256C3×C22⋊C4—64no—
257C3×C22⋊C4—64no—
258C3×C42—34no—
259C3×C42—64no—
260C3×C42—62no—
261C3×C42—62no—
262#217—24no—
263#217—24no—
264#217—24no—
265C4⋊Dic3—22no—
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268C4×Dic3—22no—
269C4×Dic3—22no—
270C4×Dic3—24no—
271C4×Dic3C3×D414yes—
272C22×C32—24no—
273C22×C32—24no—
274C22×C32—24no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32—42no—
278C22×C32—42no—
279C22×C32C22×D411yescharacteristic
280C22×C32C2×#4112yes—
281C22×C32C2×#4111yescharacteristic
282C22×C32C2×#4111yescharacteristic
283C22×C32C2×#4112yes—
284C32×C4—22no—
285C32×C4—22no—
286C32×C4—41no—
287C32×C4—42no—
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C3×Dic3#12414yes—
294C22×Q8—31no—
295C22×D4C2×C3×D311yescharacteristic
296C23×C4—32no—
297C4×Q8—64no—
298C4×D4—64no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4C2×C3×D311yescharacteristic
303C2×C22⋊C4—32no—
304C2×C22⋊C4—32no—
305C2×C22⋊C4—32no—
306C2×C22⋊C4C2×C3×D312yes—
307C2×C22⋊C4C2×C3×D312yes—
308C2×C42—31no—
309C2×C42—31no—
310C2×C42—31no—
311C2×C42—32no—
312#95—32no—
313#95—31no—
314#95—32no—
315#95—32no—
316#95—32no—
317#95—32no—
318#95C2×C3×D311yescharacteristic
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—21no—
332C23×C3—24no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3#23714yes—
340C23×C3C3×#4114yes—
341C23×C3C23×D311yescharacteristic
342C23×C3C24×C311yescharacteristic
343C3×Q8—68no—
344C3×D4—28no—
345C3×D4—28no—
346C3×D4—48no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—32no—
366C2×C3×C4—34no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—41no—
376C2×C3×C4—42no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—128no—
390C2×C3×C4D3×D412yes—
391C2×C3×C4#23712yes—
392C2×C3×C4C2×C3×D412yes—
393C2×C3×C4C3×#4112yes—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—48no—
407C2×Dic3C2×C3×D412yes—
408C2×Dic3C2×C3×D412yes—
409C2×Dic3C3×#4112yes—
410C2×Dic3C3×#4114yes—
411Dic6—28no—
412C2×C32—44no—
413C2×C32#52511yescharacteristic
414C2×C32#52511yescharacteristic
415C2×C32C2×#12411yescharacteristic
416C2×C32#52912yes—
417C2×C32#52912yes—
418C24C22×C3×D312yes—
419C2×Q8—62no—
420C2×Q8—62no—
421C2×Q8—62no—
422C2×D4—24no—
423C2×D4—22no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—32no—
428C22×C4—32no—
429C22×C4—31no—
430C22×C4—64no—
431C22×C4—64no—
432C22×C4—64no—
433C22×C4C22×C3×D312yes—
434C22×C4C22×C3×D311yescharacteristic
435C22×C4C22×C3×D311yescharacteristic
436C22×C4C22×C3×D311yescharacteristic
437C4⋊C4—22no—
438C4⋊C4—62no—
439C4⋊C4—62no—
440C4⋊C4—62no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—64no—
444C22⋊C4—64no—
445C22⋊C4—64no—
446C42—34no—
447C42—62no—
448C42—62no—
449C42—64no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—24no—
453C22×C3—24no—
454C22×C3—24no—
455C22×C3—24no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—44no—
462C22×C3—44no—
463C22×C3—44no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—42no—
472C22×C3—82no—
473C22×C3—82no—
474C22×C3—82no—
475C22×C3—82no—
476C22×C3C2×D3×D411yescharacteristic
477C22×C3C2×#23712yes—
478C22×C3C2×#23711yescharacteristic
479C22×C3D3×#4111yescharacteristic
480C22×C3D3×#4112yes—
481C22×C3C22×C3×D411yescharacteristic
482C22×C3C2×C3×#4112yes—
483C22×C3C2×C3×#4111yescharacteristic
484C22×C3C2×C3×#4111yescharacteristic
485C22×C3C2×C3×#4112yes—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—22no—
490C3×C4—34no—
491C3×C4—42no—
492C3×C4—42no—
493C3×C4—41no—
494C3×C4—41no—
495C3×C4—42no—
496C3×C4—42no—
497C3×C4—62no—
498C3×C4—62no—
499C3×C4—81no—
500C3×C4—82no—
501C3×C4—122no—
502C3×C4—122no—
503C3×C4—121no—
504Dic3—22no—
505Dic3—22no—
506Dic3—41no—
507Dic3—42no—
508Dic3—42no—
509Dic3C3×#12414yes—
510C32#239811yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23C3×#23714yes—
518C23C23×C3×D311yescharacteristic
519Q8—68no—
520D4—28no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—32no—
530C2×C4—34no—
531C2×C4—32no—
532C2×C4—32no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—128no—
546C2×C4C3×D3×D412yes—
547C2×C4C3×#23712yes—
548C2×C3—21no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—44no—
554C2×C3—44no—
555C2×C3—84no—
556C2×C3#558611yescharacteristic
557C2×C3#560012yes—
558C2×C3#560611yescharacteristic
559C2×C3#564912yes—
560C2×C3D3×#12411yescharacteristic
561C2×C3C3×#52511yescharacteristic
562C2×C3C3×#52511yescharacteristic
563C2×C3C2×C3×#12411yescharacteristic
564C2×C3C3×#52912yes—
565C2×C3C3×#52912yes—
566C22—24no—
567C22—24no—
568C22—24no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22C2×C3×D3×D411yescharacteristic
574C22C2×C3×#23712yes—
575C22C2×C3×#23711yescharacteristic
576C22C3×D3×#4112yes—
577C22C3×D3×#4111yescharacteristic
578C4—22no—
579C4—22no—
580C4—34no—
581C4—41no—
582C4—42no—
583C4—62no—
584C4—62no—
585C4—121no—
586C4—122no—
587C4—122no—
588C3—21no—
589C3#7689311yescharacteristic, direct product factor
590C3C3×#239811yescharacteristic, complemented
591C2—44no—
592C2C3×#558611yescharacteristic
593C2C3×#560012yes—
594C2C3×#560611yescharacteristic
595C2C3×#564912yes—
596C2C3×D3×#12411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#394C2
socleC23×C32C24
prime radicalC22×C32×D4C22
hypercenterC3×#394D3
hypocenterC3C3×#2398
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#394

Complements

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

NH ≅ G/Ntype
2. C2×C3×#887C2semidirect
5. C3×#4986C2semidirect
6. C3×#4952C2semidirect
7. C3×#4947C2semidirect
8. C3×Dic3×C22⋊C4C2semidirect
9. C3×Dic3×C22⋊C4C2semidirect
10. C3×#4659C2semidirect
11. C3×#4648C2semidirect
13. #76893C3direct (N × H)
42. C2×#887C2×C3semidirect
55. #4986C2×C3semidirect
56. #4952C2×C3semidirect
57. #4947C2×C3semidirect
58. Dic3×C22⋊C4C2×C3semidirect
59. Dic3×C22⋊C4C2×C3semidirect
60. #4659C2×C3semidirect
61. #4648C2×C3semidirect
510. C32#2398semidirect
589. C3#76893direct (N × H)
590. C3C3×#2398semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×C3×#8872
C32×#3942
C3×#52222
C3×#49862
C3×#49522
C3×#49472
C3×Dic3×C22⋊C42
C3×#46592
C3×#46482
C3×#23983
#768933