Finite Group Databasebeta

← C3×#69651 #11794049

Subgroups — C3×#69651 #11794049

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#214C211yesmaximal, characteristic
2C32×#390C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C3×#4929C211yesmaximal, characteristic, complemented
6C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2055—31nomaximal
9#69651C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C22⋊C4—21no—
14C2×C32×C22⋊C4—21no—
15C2×C32×C42C2211yescharacteristic
16C2×C3×#214—22no—
17C2×C3×#214—22no—
18C2×C3×#214—22no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#832—22no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×#810—22no—
26C3×C4⋊(C3⋊C8)—22no—
27C22×C3×SD16—31no—
28C22×#214C2×C311yescharacteristic
29C2×C3×C4⋊C8—31no—
30C2×C3×#103—31no—
31C2×C3×#102—31no—
32C3×#391—31no—
33C3×#390—21no—
34C3×#390D311yescharacteristic
35C3×#390C2×C311yescharacteristic
36C2×#832C2×C311yescharacteristic
37C2×#810C2×C311yescharacteristic, complemented
38#4929C2×C311yescharacteristic, complemented
39C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
40C3×#340—31no—
41#4529C2×C311yescharacteristic, complemented
42C24×C32—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4D412yes—
49C22×C32×C4—21no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4D411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6D412yes—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C32×C22⋊C4—42no—
64C32×C22⋊C4—42no—
65C32×C42—21no—
66C32×C42—21no—
67C3×#214—28no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D412yes—
76#2055—31noSylow
77C22×C3×Q8—31no—
78C22×C3×D4—21no—
79C22×C3×D4C2×D311yescharacteristic
80C22×C3×D4C22×C311yescharacteristic
81C22×Dic6C22×C311yescharacteristic
82C2×C3×SD16—62no—
83C2×C3×SD16—62no—
84C2×C3×SD16—62no—
85C22×C3×C8—31no—
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C22×C311yescharacteristic
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—21no—
94C2×C3×C22⋊C4—21no—
95C2×C3×C22⋊C4—21no—
96C2×C3×C22⋊C4—21no—
97C2×C3×C42—21no—
98C2×C3×C42C2×D311yescharacteristic
99C2×C3×C42C22×C311yescharacteristic
100C2×#214—22no—
101C2×#214—22no—
102C2×#214—22no—
103C2×C4⋊Dic3C22×C311yescharacteristic
104C22×C3⋊C8C22×C311yescharacteristic
105C22×C3⋊C8C22×C311yescharacteristic
106C3×C4⋊C8—62no—
107C3×#103—62no—
108C3×#102—62no—
109C3×#95—61no—
110C3×#95—61no—
111#832—22no—
112C3⋊#95—21no—
113C3⋊#95—21no—
114#810—22no—
115C4⋊(C3⋊C8)—22no—
116C23×C32—22no—
117C23×C32—41no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32C2×D411yescharacteristic
124C32×D4—22no—
125C32×D4—22no—
126C32×D4—41no—
127C32×D4—41no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4SD1612yescomplemented
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3×Dic3—22no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×Dic6—22no—
150C3×Dic6—22no—
151C3×Dic6—41no—
152C3×Dic6—41no—
153C3×C3⋊C8—22no—
154C3×C3⋊C8—41no—
155C22×SD16—31no—
156C2×C4⋊C8—31no—
157C2×#103—31no—
158C2×#102—31no—
159#391—31no—
160#390C3×D311yescharacteristic
161#340—31no—
162C24×C3—22no—
163C24×C3—21no—
164C24×C3—21no—
165C2×C3×Q8—32no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—22no—
183C2×C3×D4—41no—
184C2×C3×D4—41no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4D1212yes—
188C2×C3×D4C3×D412yes—
189C22×C3×C4—22no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4#6711yescharacteristic
198C22×C3×C4#6711yescharacteristic
199C22×C3×C4C3×D411yescharacteristic
200C22×C3×C4C3×D411yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C23×C311yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—21no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6C3×D412yes—
211C3×SD16—68no—
212C2×C3×C8—32no—
213C2×C3×C8—61no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—41no—
223C3×C4⋊C4—41no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C22⋊C4—44no—
227C3×C22⋊C4—42no—
228C3×C22⋊C4—42no—
229C3×C22⋊C4—44no—
230C3×C22⋊C4—42no—
231C3×C22⋊C4—42no—
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42—41no—
237C3×C42—41no—
238#214—28no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8C3×D412yes—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32—42no—
250C22×C32—81no—
251C22×C32—81no—
252C22×C32—81no—
253C22×C32—81no—
254C22×C32#12111yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32#12111yescharacteristic
257C22×C32C2×SD1611yescharacteristic
258C22×C32#13511yescharacteristic
259C22×C32AGL(1,ℤ/8)11yescharacteristic
260C22×C32#13711yescharacteristic
261C32×C4—22no—
262C32×C4—41no—
263C32×C4—81no—
264C32×C4#12011yescharacteristic
265C32×C4#12311yescharacteristic
266C32×C4#12311yescharacteristic
267C32×C4#12411yescharacteristic
268C3×Dic3—42no—
269C3×Dic3—81no—
270C22×Q8—31no—
271C22×D4C2×C3×D311yescharacteristic
272C2×SD16—62no—
273C2×SD16—62no—
274C2×SD16—62no—
275C22×C8—31no—
276C22×C8—31no—
277C2×C4⋊C4—31no—
278C2×C4⋊C4C2×C3×D311yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C42C2×C3×D311yescharacteristic
282C4⋊C8—62no—
283#103—62no—
284#102—62no—
285#95—61no—
286#95—61no—
287C23×C3—24no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—21no—
291C23×C3—42no—
292C23×C3—42no—
293C23×C3—42no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3—42no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3C2×#6711yescharacteristic
310C23×C3C2×C3×D411yescharacteristic
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—121no—
314C3×Q8—121no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—42no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—42no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—41no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
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—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—62no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4#21412yescomplemented
365C2×C3×C4C3×SD1612yescomplemented
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4#23511yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23711yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4C2×C3×D411yescharacteristic
373C2×C3×C4C2×C3×D411yescharacteristic
374C2×C3×C4C2×C3×D411yescharacteristic
375C2×C3×C4C3×#4111yescharacteristic
376C2×C3×C4C3×#4111yescharacteristic
377C2×C3×C4C3×#4111yescharacteristic
378C2×Dic3—22no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383C2×Dic3—41no—
384Dic6—22no—
385Dic6—22no—
386Dic6—41no—
387Dic6—41no—
388C3×C8—62no—
389C3×C8—121no—
390C3⋊C8—22no—
391C3⋊C8—41no—
392C2×C32—82no—
393C2×C32#39411yescharacteristic
394C2×C32#46011yescharacteristic
395C2×C32#46111yescharacteristic
396C2×C32#46311yescharacteristic
397C2×C32#46411yescharacteristic
398C2×C32#46511yescharacteristic
399C2×C32#46811yescharacteristic
400C24—21no—
401C2×Q8—32no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8—61no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4C3×D1212yes—
413C22×C4—21no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4C3×#6711yescharacteristic
417C22×C4C3×#6711yescharacteristic
418C22×C4C22×C3×D311yescharacteristic
419SD16—68no—
420C2×C8—32no—
421C2×C8—61no—
422C2×C8—61no—
423C2×C8—61no—
424C2×C8—61no—
425C2×C8—61no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C22⋊C4—42no—
431C22⋊C4—42no—
432C42—21no—
433C42—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—82no—
451C22×C3—82no—
452C22×C3—82no—
453C22×C3—82no—
454C22×C3—81no—
455C22×C3—81no—
456C22×C3—81no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3#93011yescharacteristic
463C22×C3#93211yescharacteristic
464C22×C3C2×#21411yescharacteristic
465C22×C3#93811yescharacteristic
466C22×C3#93911yescharacteristic
467C22×C3#95011yescharacteristic
468C22×C3#95111yescharacteristic
469C22×C3C3×#12111yescharacteristic
470C22×C3C3×#12111yescharacteristic
471C22×C3C3×#12111yescharacteristic
472C22×C3C2×C3×SD1611yescharacteristic
473C22×C3C3×#13511yescharacteristic
474C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
475C22×C3C3×#13711yescharacteristic
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—42no—
483C3×C4—42no—
484C3×C4—41no—
485C3×C4—41no—
486C3×C4—82no—
487C3×C4—81no—
488C3×C4—81no—
489C3×C4—122no—
490C3×C4—241no—
491C3×C4#88211yescharacteristic
492C3×C4#88311yescharacteristic
493C3×C4#88511yescharacteristic
494C3×C4#88611yescharacteristic
495C3×C4C3×#12011yescharacteristic
496C3×C4C3×#12311yescharacteristic
497C3×C4C3×#12311yescharacteristic
498C3×C4C3×#12411yescharacteristic
499Dic3—42no—
500Dic3—81no—
501C32#205511yescharacteristic, complemented, Sylow
502C23—22no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23C2×C3×#6711yescharacteristic
510Q8—62no—
511Q8—62no—
512Q8—121no—
513Q8—121no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—62no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4C3×#21412yescomplemented
533C2×C4C2×C3×D1211yescharacteristic
534C2×C4C3×#23511yescharacteristic
535C2×C4C3×D3×D411yescharacteristic
536C2×C4C3×D3×D411yescharacteristic
537C2×C4C3×#23711yescharacteristic
538C2×C4C3×#23711yescharacteristic
539C8—62no—
540C8—121no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—84no—
549C2×C3—82no—
550C2×C3—82no—
551C2×C3#496111yescharacteristic
552C2×C3#501611yescharacteristic
553C2×C3#501911yescharacteristic
554C2×C3#504111yescharacteristic
555C2×C3#504211yescharacteristic
556C2×C3#505411yescharacteristic
557C2×C3#507511yescharacteristic
558C2×C3C3×#39411yescharacteristic
559C2×C3C3×#46011yescharacteristic
560C2×C3C3×#46111yescharacteristic
561C2×C3C3×#46311yescharacteristic
562C2×C3C3×#46411yescharacteristic
563C2×C3C3×#46511yescharacteristic
564C2×C3C3×#46811yescharacteristic
565C22—42no—
566C22—42no—
567C22—42no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22C3×#93011yescharacteristic
573C22C3×#93211yescharacteristic
574C22C2×C3×#21411yescharacteristic
575C22C3×#93811yescharacteristic
576C22C3×#93911yescharacteristic
577C22C3×#95011yescharacteristic
578C22C3×#95111yescharacteristic
579C4—22no—
580C4—41no—
581C4—81no—
582C4—122no—
583C4—241no—
584C4C3×#88211yescharacteristic
585C4C3×#88311yescharacteristic
586C4C3×#88511yescharacteristic
587C4C3×#88611yescharacteristic
588C3—21no—
589C3#6965111yescharacteristic, direct product factor
590C3C3×#205511yescharacteristic, complemented
591C2—82no—
592C2C3×#496111yescharacteristic
593C2C3×#501611yescharacteristic
594C2C3×#501911yescharacteristic
595C2C3×#504111yescharacteristic
596C2C3×#504211yescharacteristic
597C2C3×#505411yescharacteristic
598C2C3×#507511yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenterC3×#390D3
hypocenterC3C3×#2055
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
4. C2×C3×#810C2semidirect
5. C3×#4929C2semidirect
6. C2×C3×C4⋊(C3⋊C8)C2semidirect
7. C3×#4529C2semidirect
9. #69651C3direct (N × H)
37. C2×#810C2×C3semidirect
38. #4929C2×C3semidirect
39. C2×C4⋊(C3⋊C8)C2×C3semidirect
41. #4529C2×C3semidirect
136. C2×C32×C4SD16semidirect
364. C2×C3×C4#214semidirect
365. C2×C3×C4C3×SD16semidirect
501. C32#2055semidirect
532. C2×C4C3×#214semidirect
589. C3#69651direct (N × H)
590. C3C3×#2055semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2142
C32×#3902
C2×C3×#8322
C2×C3×#8102
C3×#49292
C2×C3×C4⋊(C3⋊C8)2
C3×#45292
C3×#20553
#696513