Finite Group Databasebeta

← C3×#71633 #11787572

Subgroups — C3×#71633 #11787572

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×C3×#835C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic
5C3×#4939C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7C3×#4524C211yesmaximal, characteristic, complemented
8C3×#1880—31nomaximal
9#71633C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C32×C4×Q8—22no—
13C32×C4×Q8—22no—
14C2×C32×C4⋊C4—21no—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C42—21no—
17C2×C32×C42C2211yescharacteristic
18C2×C3×#215—22no—
19C2×C3×#215—22no—
20C2×C3×#215C414yescomplemented
21C2×C3×(C2×D3)⋊C4—21no—
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#835—22no—
27C3×#809—22no—
28C22×C3×SD16—31no—
29C2×C3×C4×Q8—21no—
30C2×C3×C4×Q8D311yescharacteristic, complemented
31C2×C3×C4×Q8C2×C311yescharacteristic, complemented
32C22×#215C2×C311yescharacteristic
33C2×C3×#103—31no—
34C2×C3×#102—31no—
35C3×#390—31no—
36C2×#835C2×C311yescharacteristic, complemented
37C2×#809C2×C311yescharacteristic
38#4939C2×C311yescharacteristic
39C3×#340—31no—
40C3×#336—31no—
41#4529C2×C311yescharacteristic, complemented
42#4524C2×C311yescharacteristic, complemented
43C23×C3×D3—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8C2×C412yes—
48C2×C32×Q8D412yes—
49C2×C32×Q8D412yes—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C32×C4⋊C4—24no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4D412yes—
65C32×C42—24no—
66C32×C42—21no—
67C32×C42—21no—
68C3×#215—28no—
69C3×(C2×D3)⋊C4—42no—
70C3×(C2×D3)⋊C4—42no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8C2×C412yes—
79#1880—31noSylow
80C22×C3×Q8—21no—
81C22×C3×Q8C2×D311yescharacteristic
82C22×C3×Q8C22×C311yescharacteristic
83C22×C3×D4—31no—
84C22×D12C22×C311yescharacteristic
85C2×C3×SD16—34no—
86C2×C3×SD16—62no—
87C2×C3×SD16—62no—
88C22×C3×C8—31no—
89C22×C3×C8—31no—
90C3×C4×Q8—24no—
91C3×C4×Q8—24no—
92C3×C4×Q8—22no—
93C3×C4×Q8—22no—
94C3×C4×Q8—22no—
95C3×C4×Q8—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C4⋊C4C22×C311yescharacteristic
103C2×C3×C22⋊C4—61no—
104C2×C3×C22⋊C4—61no—
105C2×C3×C42—22no—
106C2×C3×C42—21no—
107C2×C3×C42—21no—
108C2×C3×C42—21no—
109C2×C3×C42C2×D311yescharacteristic
110C2×C3×C42C22×C311yescharacteristic
111C2×#215—22no—
112C2×#215—22no—
113C2×#215C3×C414yescomplemented
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×C4⋊Dic3C22×C311yescharacteristic
117C22×C3⋊C8C22×C311yescharacteristic
118C22×C3⋊C8C22×C311yescharacteristic
119C3×#103—62no—
120C3×#102—62no—
121#835—22no—
122#809—22no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C32×Q8—22no—
132C32×Q8—22no—
133C32×Q8—22no—
134C32×Q8C22⋊C414yescomplemented
135C2×C32×C4—22no—
136C2×C32×C4—21no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—22no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4—41no—
145C2×C32×C4—41no—
146C2×C32×C4SD1612yescomplemented
147C2×C32×C4C22×C411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C2×C32×C4#4111yescharacteristic
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—41no—
159C3×D12—41no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C22×SD16—31no—
163C2×C4×Q8C3×D311yescharacteristic, complemented
164C2×#103—31no—
165C2×#102—31no—
166#390—31no—
167#340—31no—
168#336—31no—
169C24×C3—61no—
170C23×D3—21no—
171C2×C3×Q8—22no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8C4×D312yes—
184C2×C3×Q8D1212yes—
185C2×C3×Q8#6712yes—
186C2×C3×Q8C2×C3×C412yes—
187C2×C3×Q8C3×D412yes—
188C2×C3×Q8C3×D412yes—
189C2×C3×D4—32no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—61no—
205C22×C3×C4#6711yescharacteristic
206C22×C3×C4#6711yescharacteristic
207C22×C3×C4C3×D411yescharacteristic
208C22×C3×C4C3×D411yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C23×C311yescharacteristic
211C22×Dic3—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12C2×C3×C412yes—
218C3×SD16—68no—
219C2×C3×C8—32no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C3×C4⋊C4—28no—
226C3×C4⋊C4—24no—
227C3×C4⋊C4—24no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4#6712yes—
235C3×C4⋊C4C3×D412yes—
236C3×C22⋊C4—122no—
237C3×C22⋊C4—122no—
238C3×C42—28no—
239C3×C42—24no—
240C3×C42—24no—
241C3×C42—22no—
242C3×C42—22no—
243C3×C42—21no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42—21no—
247#215—28no—
248(C2×D3)⋊C4—42no—
249(C2×D3)⋊C4—42no—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8C2×C3×C412yes—
258C22×C32C4×D411yescharacteristic
259C22×C32#12011yescharacteristic
260C22×C32#12111yescharacteristic
261C22×C32C2×SD1611yescharacteristic
262C22×C32#13511yescharacteristic
263C22×C32AGL(1,ℤ/8)11yescharacteristic
264C22×C32#13711yescharacteristic
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—81no—
269C2×C3×D3—81no—
270C2×C3×D3—81no—
271C2×C3×D3—81no—
272C32×C4—24no—
273C32×C4—22no—
274C32×C4—41no—
275C32×C4—42no—
276C32×C4C2×C22⋊C411yescharacteristic
277C32×C4C4×D411yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12311yescharacteristic
280C3×Dic3—81no—
281C22×Q8C2×C3×D311yescharacteristic
282C22×D4—31no—
283C2×SD16—34no—
284C2×SD16—62no—
285C2×SD16—62no—
286C22×C8—31no—
287C22×C8—31no—
288C4×Q8—22no—
289C4×Q8—22no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4C2×C3×D311yescharacteristic
293C2×C22⋊C4—61no—
294C2×C22⋊C4—61no—
295C2×C42—21no—
296C2×C42C2×C3×D311yescharacteristic
297#103—62no—
298#102—62no—
299C23×C3—21no—
300C23×C3—62no—
301C23×C3—121no—
302C23×C3—121no—
303C23×C3—121no—
304C23×C3—121no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3C2×#6711yescharacteristic
308C23×C3C2×C3×D411yescharacteristic
309C22×D3—22no—
310C22×D3—41no—
311C22×D3—41no—
312C22×D3—41no—
313C22×D3—41no—
314C22×D3—41no—
315C22×D3—41no—
316C3×Q8—24no—
317C3×Q8—24no—
318C3×Q8—24no—
319C3×Q8—22no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—24no—
326C3×Q8(C2×D3)⋊C414yescomplemented
327C3×Q8C3×C22⋊C414yescomplemented
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—121no—
331C3×D4—121no—
332C2×C3×C4—22no—
333C2×C3×C4—24no—
334C2×C3×C4—22no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—24no—
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—21no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—121no—
373C2×C3×C4—121no—
374C2×C3×C4—121no—
375C2×C3×C4#21512yescomplemented
376C2×C3×C4C3×SD1612yescomplemented
377C2×C3×C4C2×C4×D311yescharacteristic
378C2×C3×C4C2×D1211yescharacteristic
379C2×C3×C4#23511yescharacteristic
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4C2×#6711yescharacteristic
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C22×C3×C411yescharacteristic
384C2×C3×C4C2×C3×D411yescharacteristic
385C2×C3×C4C2×C3×D411yescharacteristic
386C2×C3×C4C2×C3×D411yescharacteristic
387C2×C3×C4C3×#4111yescharacteristic
388C2×C3×C4C3×#4111yescharacteristic
389C2×Dic3—41no—
390C2×Dic3—41no—
391C2×Dic3—41no—
392D12—22no—
393D12—22no—
394D12—41no—
395D12—41no—
396C3×C8—62no—
397C3×C8—121no—
398C3⋊C8—22no—
399C3⋊C8—41no—
400C2×C32#38611yescharacteristic
401C2×C32C4×SD1611yescharacteristic
402C2×C32#44011yescharacteristic
403C2×C32#44811yescharacteristic
404C2×C32#44911yescharacteristic
405C2×C32#46011yescharacteristic
406C2×C32#46411yescharacteristic
407C3×D3—82no—
408C24—61no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8C3×C4×D312yes—
413C2×Q8C3×D1212yes—
414C2×Q8C3×#6712yes—
415C2×D4—32no—
416C2×D4—61no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—61no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—61no—
424C22×C4C3×#6711yescharacteristic
425C22×C4C3×#6711yescharacteristic
426C22×C4C22×C3×D311yescharacteristic
427SD16—68no—
428C2×C8—32no—
429C2×C8—61no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C4⋊C4—24no—
435C4⋊C4—21no—
436C4⋊C4—61no—
437C4⋊C4—61no—
438C4⋊C4C3×#6712yes—
439C22⋊C4—122no—
440C22⋊C4—122no—
441C42—24no—
442C42—21no—
443C42—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3—241no—
455C22×C3—241no—
456C22×C3—241no—
457C22×C3—241no—
458C22×C3C4×#6711yescharacteristic
459C22×C3#93011yescharacteristic
460C22×C3C2×#21511yescharacteristic
461C22×C3#94211yescharacteristic
462C22×C3#94911yescharacteristic
463C22×C3#95011yescharacteristic
464C22×C3#95311yescharacteristic
465C22×C3C3×C4×D411yescharacteristic
466C22×C3C3×#12011yescharacteristic
467C22×C3C3×#12111yescharacteristic
468C22×C3C2×C3×SD1611yescharacteristic
469C22×C3C3×#13511yescharacteristic
470C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
471C22×C3C3×#13711yescharacteristic
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—81no—
476C2×D3—81no—
477C2×D3—81no—
478C2×D3—81no—
479C3×C4—28no—
480C3×C4—24no—
481C3×C4—24no—
482C3×C4—22no—
483C3×C4—24no—
484C3×C4—22no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—42no—
490C3×C4—44no—
491C3×C4—41no—
492C3×C4—42no—
493C3×C4—41no—
494C3×C4—42no—
495C3×C4—241no—
496C3×C4C2×(C2×D3)⋊C411yescharacteristic
497C3×C4C4×#6711yescharacteristic
498C3×C4#92911yescharacteristic
499C3×C4#93011yescharacteristic
500C3×C4C2×C3×C22⋊C411yescharacteristic
501C3×C4C3×C4×D411yescharacteristic
502C3×C4C3×#12111yescharacteristic
503C3×C4C3×#12311yescharacteristic
504Dic3—81no—
505C32#188011yescharacteristic, complemented, Sylow
506C23—62no—
507C23—121no—
508C23—121no—
509C23—121no—
510C23—121no—
511C23—121no—
512C23—121no—
513C23C2×C3×#6711yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—22no—
517Q8C3×(C2×D3)⋊C414yescomplemented
518D4—62no—
519D4—62no—
520D4—121no—
521D4—121no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—121no—
534C2×C4—121no—
535C2×C4—121no—
536C2×C4C3×#21512yescomplemented
537C2×C4C2×C3×C4×D311yescharacteristic
538C2×C4C2×C3×D1211yescharacteristic
539C2×C4C3×#23511yescharacteristic
540C2×C4C3×#23511yescharacteristic
541C2×C4C2×C3×#6711yescharacteristic
542C2×C4C2×C3×#6711yescharacteristic
543C8—62no—
544C8—121no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—242no—
553C2×C3C4×#21511yescharacteristic
554C2×C3#502611yescharacteristic
555C2×C3#502711yescharacteristic
556C2×C3#502811yescharacteristic
557C2×C3#521311yescharacteristic
558C2×C3#522711yescharacteristic
559C2×C3#523811yescharacteristic
560C2×C3C3×#38611yescharacteristic
561C2×C3C3×C4×SD1611yescharacteristic
562C2×C3C3×#44011yescharacteristic
563C2×C3C3×#44811yescharacteristic
564C2×C3C3×#44911yescharacteristic
565C2×C3C3×#46011yescharacteristic
566C2×C3C3×#46411yescharacteristic
567D3—82no—
568C22—122no—
569C22—122no—
570C22—122no—
571C22—241no—
572C22—241no—
573C22—241no—
574C22—241no—
575C22C3×C4×#6711yescharacteristic
576C22C3×#93011yescharacteristic
577C22C2×C3×#21511yescharacteristic
578C22C3×#94211yescharacteristic
579C22C3×#94911yescharacteristic
580C22C3×#95011yescharacteristic
581C22C3×#95311yescharacteristic
582C4—24no—
583C4—22no—
584C4—41no—
585C4—42no—
586C4—241no—
587C4C2×C3×(C2×D3)⋊C411yescharacteristic
588C4C3×C4×#6711yescharacteristic
589C4C3×#92911yescharacteristic
590C4C3×#93011yescharacteristic
591C3—21no—
592C3#7163311yescharacteristic, direct product factor
593C3C3×#188011yescharacteristic, complemented
594C2—242no—
595C2C3×C4×#21511yescharacteristic
596C2C3×#502611yescharacteristic
597C2C3×#502711yescharacteristic
598C2C3×#502811yescharacteristic
599C2C3×#521311yescharacteristic
600C2C3×#522711yescharacteristic
601C2C3×#523811yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4×Q8C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4×Q8D3
hypocenterC3C3×#1880
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
3. C2×C3×#835C2semidirect
6. C3×#4529C2semidirect
7. C3×#4524C2semidirect
9. #71633C3direct (N × H)
20. C2×C3×#215C4semidirect
30. C2×C3×C4×Q8D3semidirect
31. C2×C3×C4×Q8C2×C3semidirect
36. C2×#835C2×C3semidirect
41. #4529C2×C3semidirect
42. #4524C2×C3semidirect
113. C2×#215C3×C4semidirect
134. C32×Q8C22⋊C4semidirect
146. C2×C32×C4SD16semidirect
163. C2×C4×Q8C3×D3semidirect
326. C3×Q8(C2×D3)⋊C4semidirect
327. C3×Q8C3×C22⋊C4semidirect
375. C2×C3×C4#215semidirect
376. C2×C3×C4C3×SD16semidirect
505. C32#1880semidirect
517. Q8C3×(C2×D3)⋊C4semidirect
536. C2×C4C3×#215semidirect
592. C3#71633direct (N × H)
593. C3C3×#1880semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C22×C3×#2152
C2×C3×#8352
C2×C3×#8092
C3×#49392
C3×#45292
C3×#45242
C3×#18803
#716333