Finite Group Databasebeta

← C3×#71607 #11786918

Subgroups — C3×#71607 #11786918

Order 1152.

937 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C2×C3×#832C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C2×C3×#808C211yesmaximal, characteristic, complemented
5C3×#4928C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7C3×#4524C211yesmaximal, characteristic, complemented
8C3×#1864—31nomaximal
9#71607C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C23×C32×C4—21no—
12C32×C4×D4—22no—
13C32×C4×D4—22no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C22⋊C4—21no—
16C2×C32×C42C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4—21no—
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#832—22no—
23C3×#832C414yescomplemented
24C3×C3⋊#95—21no—
25C3×#808—22no—
26C2×C3×C4×D4—21no—
27C2×C3×C4×D4D311yescharacteristic
28C2×C3×C4×D4C2×C311yescharacteristic
29C2×C3×#106—31no—
30C2×C3×#102—31no—
31C2×C3×#102—31no—
32C3×#389—31no—
33C2×#832C2×C311yescharacteristic
34C2×#832C2×C311yescharacteristic
35C2×#808C2×C311yescharacteristic, complemented
36#4928C2×C311yescharacteristic, complemented
37C3×#340—31no—
38C3×#336—31no—
39#4529C2×C311yescharacteristic, complemented
40#4524C2×C311yescharacteristic, complemented
41C24×C32—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4C2×C412yes—
46C2×C32×D4D412yes—
47C2×C32×D4Q812yes—
48C22×C32×C4—24no—
49C22×C32×C4—21no—
50C22×C32×C4—42no—
51C22×C32×C4—42no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4D412yes—
59C32×C22⋊C4—24no—
60C32×C42—21no—
61C32×C42—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3C2×C412yescomplemented
66C3×Dic3⋊C4—42no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8C2×C412yescomplemented
73#1864—31noSylow
74C22×C3×D4—21no—
75C22×C3×D4C2×D311yescharacteristic
76C22×C3×D4C22×C311yescharacteristic
77C23×C3×C4—22no—
78C23×C3×C4—21no—
79C23×C3×C4—21no—
80C22×C3×C8—31no—
81C22×C3×C8—31no—
82C3×C4×D4—24no—
83C3×C4×D4—24no—
84C3×C4×D4—22no—
85C3×C4×D4—22no—
86C3×C4×D4—22no—
87C3×C4×D4—22no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—61no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C22×C311yescharacteristic
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—21no—
96C2×C3×C22⋊C4—21no—
97C2×C3×C42—21no—
98C2×C3×C42C2×D311yescharacteristic
99C2×C3×C42C22×C311yescharacteristic
100C2×C4⋊Dic3C22×C311yescharacteristic
101C2×C4⋊Dic3C22×C311yescharacteristic
102C2×Dic3⋊C4—21no—
103C22×C3⋊C8C22×C311yescharacteristic
104C22×C3⋊C8C22×C311yescharacteristic
105C3×#106—62no—
106C3×#102—34no—
107C3×#102—62no—
108C3×#95—61no—
109#832—22no—
110#832C3×C414yescomplemented
111C3⋊#95—21no—
112#808—22no—
113C23×C32—22no—
114C23×C32—22no—
115C23×C32—22no—
116C23×C32—41no—
117C23×C32—41no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32C2×D411yescharacteristic
121C32×D4—22no—
122C32×D4—22no—
123C32×D4—22no—
124C32×D4C4⋊C414yescomplemented
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—22no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—48no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4SD1612yes—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×Q811yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C3×Dic3—22no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149C2×C4×D4C3×D311yescharacteristic
150C2×#106—31no—
151C2×#102—31no—
152C2×#102—31no—
153#389—31no—
154#340—31no—
155#336—31no—
156C24×C3—22no—
157C24×C3—21no—
158C24×C3—21no—
159C2×C3×D4—22no—
160C2×C3×D4—22no—
161C2×C3×D4—22no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4—22no—
171C2×C3×D4Dic612yes—
172C2×C3×D4C4×D312yes—
173C2×C3×D4#6712yes—
174C2×C3×D4C2×C3×C412yes—
175C2×C3×D4C3×D412yes—
176C2×C3×D4C3×Q812yes—
177C22×C3×C4—22no—
178C22×C3×C4—28no—
179C22×C3×C4—24no—
180C22×C3×C4—24no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—44no—
187C22×C3×C4—42no—
188C22×C3×C4—42no—
189C22×C3×C4—44no—
190C22×C3×C4—42no—
191C22×C3×C4—42no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4#6711yescharacteristic
195C22×C3×C4#6711yescharacteristic
196C22×C3×C4C3×D411yescharacteristic
197C22×C3×C4C3×D411yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C23×C311yescharacteristic
200C22×Dic3—21no—
201C22×Dic3—21no—
202C2×C3×C8—32no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—22no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4—122no—
217C3×C4⋊C4#6712yes—
218C3×C4⋊C4C3×D412yes—
219C3×C22⋊C4—28no—
220C3×C22⋊C4—24no—
221C3×C22⋊C4—24no—
222C3×C42—22no—
223C3×C42—22no—
224C3×C42—21no—
225C3×C42—21no—
226C3×C42—21no—
227C3×C42—21no—
228C4⋊Dic3—21no—
229C4⋊Dic3—21no—
230C4⋊Dic3—21no—
231C4⋊Dic3C2×C3×C412yescomplemented
232Dic3⋊C4—42no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8C2×C3×C412yescomplemented
239C22×C32—24no—
240C22×C32—42no—
241C22×C32—42no—
242C22×C32—42no—
243C22×C32—42no—
244C22×C32—42no—
245C22×C32—42no—
246C22×C32C4×D411yescharacteristic
247C22×C32#12011yescharacteristic
248C22×C32C22⋊Q811yescharacteristic
249C22×C32C2×SD1611yescharacteristic
250C22×C32#13511yescharacteristic
251C22×C32AGL(1,ℤ/8)11yescharacteristic
252C22×C32AGL(1,ℤ/8)11yescharacteristic
253C32×C4—22no—
254C32×C4—41no—
255C32×C4—42no—
256C32×C4C2×C4⋊C411yescharacteristic
257C32×C4C4×D411yescharacteristic
258C32×C4C22⋊Q811yescharacteristic
259C32×C4#12311yescharacteristic
260C3×Dic3—42no—
261C3×Dic3—81no—
262C22×D4C2×C3×D311yescharacteristic
263C23×C4—21no—
264C22×C8—31no—
265C22×C8—31no—
266C4×D4—22no—
267C4×D4—22no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—61no—
271C2×C4⋊C4C2×C3×D311yescharacteristic
272C2×C22⋊C4—21no—
273C2×C42C2×C3×D311yescharacteristic
274#106—62no—
275#102—34no—
276#102—62no—
277#95—61no—
278C23×C3—24no—
279C23×C3—24no—
280C23×C3—24no—
281C23×C3—22no—
282C23×C3—22no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—21no—
288C23×C3—42no—
289C23×C3—42no—
290C23×C3—42no—
291C23×C3—42no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—41no—
295C23×C3—41no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3C2×#6711yescharacteristic
301C23×C3C2×C3×D411yescharacteristic
302C3×D4—24no—
303C3×D4—24no—
304C3×D4—24no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—24no—
312C3×D4Dic3⋊C414yescomplemented
313C3×D4C3×C4⋊C414yescomplemented
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—24no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—416no—
340C2×C3×C4—48no—
341C2×C3×C4—48no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—62no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4#21412yes—
355C2×C3×C4C3×SD1612yes—
356C2×C3×C4C2×Dic611yescharacteristic
357C2×C3×C4C2×C4×D311yescharacteristic
358C2×C3×C4#23511yescharacteristic
359C2×C3×C4#23511yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C22×C3×C411yescharacteristic
363C2×C3×C4C2×C3×D411yescharacteristic
364C2×C3×C4C2×C3×D411yescharacteristic
365C2×C3×C4C2×C3×Q811yescharacteristic
366C2×C3×C4C3×#4111yescharacteristic
367C2×C3×C4C3×#4111yescharacteristic
368C2×Dic3—22no—
369C2×Dic3—41no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C3×C8—62no—
375C3×C8—121no—
376C3⋊C8—22no—
377C3⋊C8—41no—
378C2×C32—44no—
379C2×C32#38511yescharacteristic
380C2×C32C4×SD1611yescharacteristic
381C2×C32#44211yescharacteristic
382C2×C32#44911yescharacteristic
383C2×C32#45011yescharacteristic
384C2×C32#47611yescharacteristic
385C2×C32#47811yescharacteristic
386C24—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4C3×Dic612yes—
391C2×D4C3×C4×D312yes—
392C2×D4C3×#6712yes—
393C22×C4—24no—
394C22×C4—21no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—61no—
398C22×C4—61no—
399C22×C4C3×#6711yescharacteristic
400C22×C4C3×#6711yescharacteristic
401C22×C4C22×C3×D311yescharacteristic
402C2×C8—32no—
403C2×C8—61no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—61no—
407C2×C8—61no—
408C4⋊C4—21no—
409C4⋊C4—32no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4—122no—
414C4⋊C4C3×#6712yes—
415C22⋊C4—24no—
416C42—21no—
417C42—21no—
418C22×C3—28no—
419C22×C3—24no—
420C22×C3—24no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—44no—
429C22×C3—44no—
430C22×C3—44no—
431C22×C3—44no—
432C22×C3—44no—
433C22×C3—44no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3#92411yescharacteristic
447C22×C3C4×#6711yescharacteristic
448C22×C3#93211yescharacteristic
449C22×C3C2×#21411yescharacteristic
450C22×C3#94911yescharacteristic
451C22×C3#95011yescharacteristic
452C22×C3#95311yescharacteristic
453C22×C3C3×C4×D411yescharacteristic
454C22×C3C3×#12011yescharacteristic
455C22×C3C3×C22⋊Q811yescharacteristic
456C22×C3C2×C3×SD1611yescharacteristic
457C22×C3C3×#13511yescharacteristic
458C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
459C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
460C3×C4—24no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—44no—
468C3×C4—42no—
469C3×C4—42no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—42no—
473C3×C4—122no—
474C3×C4—241no—
475C3×C4C2×Dic3⋊C411yescharacteristic
476C3×C4#92411yescharacteristic
477C3×C4C4×#6711yescharacteristic
478C3×C4#92911yescharacteristic
479C3×C4C2×C3×C4⋊C411yescharacteristic
480C3×C4C3×C4×D411yescharacteristic
481C3×C4C3×C22⋊Q811yescharacteristic
482C3×C4C3×#12311yescharacteristic
483Dic3—42no—
484Dic3—81no—
485C32#186411yescharacteristic, complemented, Sylow
486C23—22no—
487C23—22no—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23C2×C3×#6711yescharacteristic
494D4—22no—
495D4—22no—
496D4—22no—
497D4C3×Dic3⋊C414yescomplemented
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—48no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—62no—
508C2×C4—121no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4C3×#21412yes—
514C2×C4C2×C3×Dic611yescharacteristic
515C2×C4C2×C3×C4×D311yescharacteristic
516C2×C4C3×#23511yescharacteristic
517C2×C4C3×#23511yescharacteristic
518C2×C4C2×C3×#6711yescharacteristic
519C2×C4C2×C3×#6711yescharacteristic
520C8—62no—
521C8—121no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—48no—
530C2×C3—44no—
531C2×C3—44no—
532C2×C3#500811yescharacteristic
533C2×C3#500911yescharacteristic
534C2×C3#501411yescharacteristic
535C2×C3C4×#21411yescharacteristic
536C2×C3#521011yescharacteristic
537C2×C3#521811yescharacteristic
538C2×C3#523811yescharacteristic
539C2×C3C3×#38511yescharacteristic
540C2×C3C3×C4×SD1611yescharacteristic
541C2×C3C3×#44211yescharacteristic
542C2×C3C3×#44911yescharacteristic
543C2×C3C3×#45011yescharacteristic
544C2×C3C3×#47611yescharacteristic
545C2×C3C3×#47811yescharacteristic
546C22—24no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22C3×#92411yescharacteristic
554C22C3×C4×#6711yescharacteristic
555C22C3×#93211yescharacteristic
556C22C2×C3×#21411yescharacteristic
557C22C3×#94911yescharacteristic
558C22C3×#95011yescharacteristic
559C22C3×#95311yescharacteristic
560C4—22no—
561C4—42no—
562C4—41no—
563C4—122no—
564C4—241no—
565C4C2×C3×Dic3⋊C411yescharacteristic
566C4C3×#92411yescharacteristic
567C4C3×C4×#6711yescharacteristic
568C4C3×#92911yescharacteristic
569C3—21no—
570C3#7160711yescharacteristic, direct product factor
571C3C3×#186411yescharacteristic, complemented
572C2—44no—
573C2C3×#500811yescharacteristic
574C2C3×#500911yescharacteristic
575C2C3×#501411yescharacteristic
576C2C3×C4×#21411yescharacteristic
577C2C3×#521011yescharacteristic
578C2C3×#521811yescharacteristic
579C2C3×#523811yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#1864
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
4. C2×C3×#808C2semidirect
5. C3×#4928C2semidirect
6. C3×#4529C2semidirect
7. C3×#4524C2semidirect
9. #71607C3direct (N × H)
23. C3×#832C4semidirect
35. C2×#808C2×C3semidirect
36. #4928C2×C3semidirect
39. #4529C2×C3semidirect
40. #4524C2×C3semidirect
65. C3×C4⋊Dic3C2×C4semidirect
72. C2×C3×C3⋊C8C2×C4semidirect
110. #832C3×C4semidirect
124. C32×D4C4⋊C4semidirect
231. C4⋊Dic3C2×C3×C4semidirect
238. C2×C3⋊C8C2×C3×C4semidirect
312. C3×D4Dic3⋊C4semidirect
313. C3×D4C3×C4⋊C4semidirect
485. C32#1864semidirect
497. D4C3×Dic3⋊C4semidirect
570. C3#71607direct (N × H)
571. C3C3×#1864semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#8322
C2×C3×#8082
C3×#49282
C3×#45292
C3×#45242
C3×#18643
#716073