Finite Group Databasebeta

← C3×#68307 #11775564

Subgroups — C3×#68307 #11775564

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#121C211yesmaximal, characteristic
2C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
3C3×#4667C211yesmaximal, characteristic, complemented
4C32×#327C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic, complemented
7C3×#4451C211yesmaximal, characteristic, complemented
8C3×#1519—31nomaximal
9#68307C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×D4—21no—
11C2×C3×D3×D4C411yescharacteristic, complemented
12C22×C3×C4×D3C2211yescharacteristic
13C32×#121C2211yescharacteristic
14C3×#939—21no—
15C3×#938C411yescharacteristic, complemented
16C3×#930C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×Dic3⋊C4—21no—
19C2×C3×D3×C8—21no—
20C3×#895C411yescharacteristic, complemented
21C3×D3×C4⋊C4C411yescharacteristic, complemented
22C3×#884—21no—
23C3×D3×C22⋊C4—21no—
24C32×C22⋊C8C2211yescharacteristic, complemented
25C32×#95C2211yescharacteristic, complemented
26C3×C3⋊#95C2211yescharacteristic, complemented
27C3×#830C2211yescharacteristic, complemented
28C3×(C2×D3)⋊C8—21no—
29C2×C3×#121—31no—
30D3×#121C2×C311yescharacteristic
31C2×C3×C22⋊C8—31no—
32C3×#380—31no—
33D3×C22⋊C8C2×C311yescharacteristic, complemented
34#4667C2×C311yescharacteristic, complemented
35C3×#327—21no—
36C3×#327—31no—
37C3×#327—31no—
38C3×#327—31no—
39C3×#327D311yescharacteristic, complemented
40C3×#327C2×C311yescharacteristic, complemented
41#4537C2×C311yescharacteristic, complemented
42#4470C2×C311yescharacteristic, complemented
43#4451C2×C311yescharacteristic, complemented
44C23×C3×D3—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4C2×C411yescharacteristic
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C3×D3×D4—42no—
56C3×D3×D4—42no—
57C3×D3×D4—42no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—42no—
62C2×C3×C4×D3C2×C411yescharacteristic
63C2×C3×C4×D3C2×C411yescharacteristic
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3D411yescharacteristic
66C2×C32×C8—21no—
67C32×C4⋊C4C2×C411yescharacteristic
68C32×C22⋊C4—21no—
69C3×#217—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×(C2×D3)⋊C4—21no—
72C3×(C2×D3)⋊C4—42no—
73C3×C4⋊Dic3C2×C411yescharacteristic
74C3×Dic3⋊C4—21no—
75C3×Dic3⋊C4—42no—
76C2×C3×C3⋊C8—21no—
77C3×D3×C8—42no—
78#1519—31noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—31no—
82C2×D3×D4—21no—
83C2×D3×D4C3×C411yescharacteristic, complemented
84C22×C4×D3C22×C311yescharacteristic
85C22×C3×C8—61no—
86C3×#121—21no—
87C3×#121—31no—
88C3×#121—31no—
89C3×#121—31no—
90C3×#121—61no—
91C3×#121—61no—
92C3×#121C2×D311yescharacteristic
93C3×#121C22×C311yescharacteristic
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—61no—
96C2×C3×C22⋊C4—61no—
97C2×C3×C22⋊C4—61no—
98#939—21no—
99#938C3×C411yescharacteristic, complemented
100#930C22×C311yescharacteristic
101C2×(C2×D3)⋊C4—21no—
102C2×Dic3⋊C4—21no—
103C2×D3×C8—21no—
104#895C3×C411yescharacteristic, complemented
105D3×C4⋊C4C3×C411yescharacteristic, complemented
106#884—21no—
107D3×C22⋊C4—21no—
108C3×C22⋊C8—21no—
109C3×C22⋊C8—31no—
110C3×C22⋊C8—61no—
111C3×C22⋊C8C2×D311yescharacteristic, complemented
112C3×C22⋊C8C22×C311yescharacteristic, complemented
113C3×#95—21no—
114C3×#95—31no—
115C3×#95C2×D311yescharacteristic, complemented
116C3×#95C22×C311yescharacteristic, complemented
117C3⋊#95C22×C311yescharacteristic, complemented
118#830C22×C311yescharacteristic, complemented
119(C2×D3)⋊C8—21no—
120C23×C32—21no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—21no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—42no—
126C22×C3×D3—42no—
127C22×C3×D3—42no—
128C22×C3×D3C22⋊C411yescharacteristic
129C22×C3×D3C22⋊C411yescharacteristic
130C22×C3×D3D812yes—
131C22×C3×D3SD1612yes—
132C32×D4—41no—
133C32×D4—41no—
134C32×D4—41no—
135C2×C32×C4—21no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C3×#67—41no—
143C3×#67—41no—
144C3×#67—42no—
145C3×#67—42no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3C22⋊C411yescharacteristic
152C2×C3×Dic3C22⋊C411yescharacteristic
153C3×D12—41no—
154C3×D12—42no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×C4×D3—41no—
158C3×C4×D3—41no—
159C3×C4×D3—42no—
160C32×C8—41no—
161C3×C3⋊C8—41no—
162C2×#121—31no—
163C2×C22⋊C8—31no—
164#380—31no—
165#327—31no—
166#327—31no—
167#327—31no—
168#327C3×D311yescharacteristic, complemented
169C24×C3—31no—
170C24×C3—61no—
171C23×D3—21no—
172C23×D3C3×D411yescharacteristic
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—31no—
177C2×C3×D4—41no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—122no—
183C2×C3×D4—122no—
184C2×C3×D4—122no—
185C2×C3×D4C4×D311yescharacteristic
186C2×C3×D4C2×C3×C411yescharacteristic
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—41no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4—122no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C23×C311yescharacteristic
201C2×#67—21no—
202C2×#67—21no—
203C2×#67—21no—
204C22×Dic3—21no—
205C22×Dic3C3×D411yescharacteristic
206D3×D4—42no—
207D3×D4—42no—
208D3×D4—42no—
209C2×D12—21no—
210C2×D12C2×C3×C411yescharacteristic
211C2×C4×D3—21no—
212C2×C4×D3—42no—
213C2×C4×D3C2×C3×C411yescharacteristic
214C2×C4×D3C2×C3×C411yescharacteristic
215C2×C4×D3C3×D411yescharacteristic
216C2×C4×D3C3×D411yescharacteristic
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—41no—
220C2×C3×C8—61no—
221C2×C3×C8—122no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—122no—
226C3×C4⋊C4C4×D311yescharacteristic
227C3×C4⋊C4C2×C3×C411yescharacteristic
228C3×C22⋊C4—21no—
229C3×C22⋊C4—21no—
230C3×C22⋊C4—41no—
231C3×C22⋊C4—61no—
232C3×C22⋊C4—61no—
233C3×C22⋊C4—61no—
234C3×C22⋊C4—122no—
235#217—21no—
236(C2×D3)⋊C4—21no—
237(C2×D3)⋊C4—21no—
238(C2×D3)⋊C4—42no—
239C4⋊Dic3C2×C3×C411yescharacteristic
240Dic3⋊C4—21no—
241Dic3⋊C4—42no—
242C2×C3⋊C8—21no—
243D3×C8—42no—
244C22×C32—21no—
245C22×C32—21no—
246C22×C32—41no—
247C22×C32—41no—
248C22×C32—41no—
249C22×C32C2×C22⋊C411yescharacteristic
250C22×C32C2×D811yescharacteristic
251C22×C32C2×SD1611yescharacteristic
252C2×C3×D3—21no—
253C2×C3×D3—21no—
254C2×C3×D3—21no—
255C2×C3×D3—21no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C2×C3×D3—41no—
259C2×C3×D3—41no—
260C2×C3×D3—41no—
261C2×C3×D3—84no—
262C2×C3×D3#10212yes—
263C2×C3×D3#10212yes—
264C32×C4—21no—
265C32×C4—21no—
266C32×C4—41no—
267C32×C4—81no—
268C3×Dic3—21no—
269C3×Dic3—41no—
270C3×Dic3—81no—
271C3×Dic3#9912yes—
272C22×D4—31no—
273C22×D4—61no—
274C23×C4—31no—
275C22×C8—61no—
276#121—31no—
277#121—31no—
278#121—31no—
279#121—61no—
280#121—61no—
281#121C2×C3×D311yescharacteristic
282C2×C4⋊C4—31no—
283C2×C4⋊C4—61no—
284C2×C22⋊C4—61no—
285C2×C22⋊C4—61no—
286C22⋊C8—31no—
287C22⋊C8—61no—
288C22⋊C8C2×C3×D311yescharacteristic, complemented
289#95—31no—
290#95C2×C3×D311yescharacteristic, complemented
291C23×C3—21no—
292C23×C3—21no—
293C23×C3—21no—
294C23×C3—31no—
295C23×C3—31no—
296C23×C3—32no—
297C23×C3—32no—
298C23×C3—41no—
299C23×C3—61no—
300C23×C3—121no—
301C23×C3—121no—
302C23×C3—122no—
303C23×C3—122no—
304C23×C3—122no—
305C23×C3D3×D411yescharacteristic
306C23×C3C2×C3×D411yescharacteristic
307C22×D3—21no—
308C22×D3—41no—
309C22×D3—41no—
310C22×D3—42no—
311C22×D3—42no—
312C22×D3—42no—
313C22×D3C3×C22⋊C411yescharacteristic
314C22×D3C3×C22⋊C411yescharacteristic
315C22×D3C3×D812yes—
316C22×D3C3×SD1612yes—
317C3×D4—41no—
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—41no—
321C3×D4—41no—
322C3×D4—41no—
323C3×D4—81no—
324C3×D4—81no—
325C3×D4—81no—
326C3×D4—121no—
327C3×D4—122no—
328C3×D4—122no—
329C3×D4—122no—
330C3×D4—121no—
331C3×D4—121no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—31no—
337C2×C3×C4—31no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—42no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—81no—
353C2×C3×C4—81no—
354C2×C3×C4—81no—
355C2×C3×C4—121no—
356C2×C3×C4—121no—
357C2×C3×C4—122no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4C2×C4×D311yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4C22×C3×C411yescharacteristic
364C2×C3×C4C2×C3×D411yescharacteristic
365#67—41no—
366#67—41no—
367#67—42no—
368#67—42no—
369C2×Dic3—22no—
370C2×Dic3—21no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3C3×C22⋊C411yescharacteristic
375C2×Dic3C3×C22⋊C411yescharacteristic
376D12—41no—
377D12—42no—
378C4×D3—22no—
379C4×D3—22no—
380C4×D3—41no—
381C4×D3—41no—
382C4×D3—42no—
383C3×C8—41no—
384C3×C8—41no—
385C3×C8—81no—
386C3×C8—121no—
387C3⋊C8—41no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32—81no—
391C2×C32C2×#9911yescharacteristic
392C2×C32C2×#10211yescharacteristic
393C2×C32#42111yescharacteristic
394C3×D3—22no—
395C3×D3—22no—
396C3×D3—81no—
397C24—31no—
398C24—61no—
399C2×D4—21no—
400C2×D4—31no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—122no—
406C2×D4—122no—
407C2×D4—122no—
408C2×D4C3×C4×D311yescharacteristic
409C22×C4—21no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—122no—
418C22×C4C22×C3×D311yescharacteristic
419C2×C8—21no—
420C2×C8—61no—
421C2×C8—122no—
422C4⋊C4—31no—
423C4⋊C4—61no—
424C4⋊C4—122no—
425C4⋊C4C3×C4×D311yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—61no—
428C22⋊C4—61no—
429C22⋊C4—61no—
430C22⋊C4—122no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—32no—
439C22×C3—32no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—61no—
449C22×C3—61no—
450C22×C3—61no—
451C22×C3—61no—
452C22×C3—81no—
453C22×C3—81no—
454C22×C3—81no—
455C22×C3—122no—
456C22×C3—122no—
457C22×C3—121no—
458C22×C3—121no—
459C22×C3—121no—
460C22×C3—244no—
461C22×C3D3×C22⋊C411yescharacteristic
462C22×C3D3×D811yescharacteristic
463C22×C3D3×SD1611yescharacteristic
464C22×C3C2×C3×C22⋊C411yescharacteristic
465C22×C3C2×C3×D811yescharacteristic
466C22×C3C2×C3×SD1611yescharacteristic
467C2×D3—21no—
468C2×D3—21no—
469C2×D3—21no—
470C2×D3—21no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—41no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—84no—
477C2×D3C3×#10212yes—
478C2×D3C3×#10212yes—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—32no—
484C3×C4—41no—
485C3×C4—41no—
486C3×C4—41no—
487C3×C4—41no—
488C3×C4—61no—
489C3×C4—81no—
490C3×C4—81no—
491C3×C4—81no—
492C3×C4—82no—
493C3×C4—121no—
494C3×C4—241no—
495Dic3—21no—
496Dic3—41no—
497Dic3—81no—
498Dic3C3×#9912yes—
499C32#151911yescharacteristic, complemented, Sylow
500C23—21no—
501C23—31no—
502C23—31no—
503C23—32no—
504C23—32no—
505C23—61no—
506C23—121no—
507C23—121no—
508C23—122no—
509C23—122no—
510C23—122no—
511C23C3×D3×D411yescharacteristic
512D4—41no—
513D4—41no—
514D4—41no—
515D4—121no—
516D4—122no—
517D4—122no—
518D4—122no—
519D4—121no—
520D4—121no—
521C2×C4—21no—
522C2×C4—31no—
523C2×C4—31no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—61no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C4—122no—
535C2×C4—121no—
536C2×C4—121no—
537C2×C4—121no—
538C2×C4C2×C3×C4×D311yescharacteristic
539C2×C4C3×D3×D411yescharacteristic
540C8—41no—
541C8—121no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—41no—
550C2×C3—41no—
551C2×C3—62no—
552C2×C3—62no—
553C2×C3—81no—
554C2×C3—81no—
555C2×C3—161no—
556C2×C3—241no—
557C2×C3D3×#9911yescharacteristic
558C2×C3D3×#10211yescharacteristic
559C2×C3#482111yescharacteristic
560C2×C3C2×C3×#9911yescharacteristic
561C2×C3C2×C3×#10211yescharacteristic
562C2×C3C3×#42111yescharacteristic
563D3—22no—
564D3—22no—
565D3—81no—
566C22—21no—
567C22—21no—
568C22—32no—
569C22—32no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—61no—
574C22—61no—
575C22—61no—
576C22—61no—
577C22—122no—
578C22—122no—
579C22—121no—
580C22—121no—
581C22—121no—
582C22—244no—
583C22C3×D3×C22⋊C411yescharacteristic
584C22C3×D3×D811yescharacteristic
585C22C3×D3×SD1611yescharacteristic
586C4—21no—
587C4—21no—
588C4—32no—
589C4—41no—
590C4—61no—
591C4—81no—
592C4—121no—
593C4—241no—
594C3—21no—
595C3#6830711yescharacteristic, direct product factor
596C3C3×#151911yescharacteristic, complemented
597C2—21no—
598C2—21no—
599C2—62no—
600C2—62no—
601C2—81no—
602C2—241no—
603C2C3×D3×#9911yescharacteristic
604C2C3×D3×#10211yescharacteristic
605C2C3×#482111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#327C2
socleC22×C32C2×C22⋊C4
prime radicalC3×D3×#121C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#327D3
hypocenterC3C3×#1519
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
2. C3×D3×C22⋊C8C2semidirect
3. C3×#4667C2semidirect
4. C32×#327C2semidirect
5. C3×#4537C2semidirect
6. C3×#4470C2semidirect
7. C3×#4451C2semidirect
9. #68307C3direct (N × H)
11. C2×C3×D3×D4C4semidirect
15. C3×#938C4semidirect
20. C3×#895C4semidirect
21. C3×D3×C4⋊C4C4semidirect
24. C32×C22⋊C8C22semidirect
25. C32×#95C22semidirect
26. C3×C3⋊#95C22semidirect
27. C3×#830C22semidirect
33. D3×C22⋊C8C2×C3semidirect
34. #4667C2×C3semidirect
39. C3×#327D3semidirect
40. C3×#327C2×C3semidirect
41. #4537C2×C3semidirect
42. #4470C2×C3semidirect
43. #4451C2×C3semidirect
83. C2×D3×D4C3×C4semidirect
99. #938C3×C4semidirect
104. #895C3×C4semidirect
105. D3×C4⋊C4C3×C4semidirect
111. C3×C22⋊C8C2×D3semidirect
112. C3×C22⋊C8C22×C3semidirect
115. C3×#95C2×D3semidirect
116. C3×#95C22×C3semidirect
117. C3⋊#95C22×C3semidirect
118. #830C22×C3semidirect
168. #327C3×D3semidirect
288. C22⋊C8C2×C3×D3semidirect
290. #95C2×C3×D3semidirect
499. C32#1519semidirect
595. C3#68307direct (N × H)
596. C3C3×#1519semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1212
C3×D3×C22⋊C82
C3×#46672
C32×#3272
C3×#45372
C3×#44702
C3×#44512
C3×#15193
#683073