Finite Group Databasebeta

← C3×#71632 #11787476

Subgroups — C3×#71632 #11787476

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic
3C2×C3×#835C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic
5C3×#4929C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic
7C3×#4524C211yesmaximal, characteristic
8C3×#1878—31nomaximal
9#71632C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
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×#216—22no—
19C2×C3×#216—22no—
20C2×C3×#216C414yescomplemented
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#835—22no—
25C3×C3⋊#95—21no—
26C3×C3⋊#95—21no—
27C3×#810—22no—
28C22×C3×Q16—31no—
29C2×C3×C4×Q8—21no—
30C2×C3×C4×Q8D311yescharacteristic
31C2×C3×C4×Q8C2×C311yescharacteristic
32C22×#216C2×C311yescharacteristic
33C2×C3×#103—31no—
34C2×C3×#103—31no—
35C3×#391—31no—
36C2×#835C2×C311yescharacteristic
37C2×#810C2×C311yescharacteristic
38#4929C2×C311yescharacteristic
39C3×#340—31no—
40C3×#336—31no—
41#4529C2×C311yescharacteristic
42#4524C2×C311yescharacteristic
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8C2×C412yes—
47C2×C32×Q8D412yes—
48C2×C32×Q8D412yes—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C32×C4⋊C4—24no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4D412yes—
65C32×C42—24no—
66C32×C42—21no—
67C32×C42—21no—
68C3×#216—28no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8C2×C412yes—
77#1878—31noSylow
78C22×C3×Q8—21no—
79C22×C3×Q8—31no—
80C22×C3×Q8C2×D311yescharacteristic
81C22×C3×Q8C22×C311yescharacteristic
82C22×Dic6C22×C311yescharacteristic
83C2×C3×Q16—34no—
84C2×C3×Q16—62no—
85C2×C3×Q16—62no—
86C22×C3×C8—31no—
87C22×C3×C8—31no—
88C3×C4×Q8—24no—
89C3×C4×Q8—24no—
90C3×C4×Q8—22no—
91C3×C4×Q8—22no—
92C3×C4×Q8—22no—
93C3×C4×Q8—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C4⋊C4C22×C311yescharacteristic
101C2×C3×C42—22no—
102C2×C3×C42—21no—
103C2×C3×C42—21no—
104C2×C3×C42—21no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C22×C311yescharacteristic
107C2×#216—22no—
108C2×#216—22no—
109C2×#216C3×C414yescomplemented
110C2×C4⋊Dic3C22×C311yescharacteristic
111C22×C3⋊C8C22×C311yescharacteristic
112C22×C3⋊C8C22×C311yescharacteristic
113C3×#103—62no—
114C3×#103—62no—
115C3×#95—61no—
116C3×#95—61no—
117#835—22no—
118C3⋊#95—21no—
119C3⋊#95—21no—
120#810—22no—
121C23×C32C2×D411yescharacteristic
122C32×Q8—22no—
123C32×Q8—22no—
124C32×Q8—22no—
125C32×Q8C22⋊C414yes—
126C2×C32×C4—22no—
127C2×C32×C4—21no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—22no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4Q1612yescomplemented
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3×Dic3—22no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×Dic6—22no—
151C3×Dic6—22no—
152C3×Dic6—41no—
153C3×Dic6—41no—
154C3×C3⋊C8—22no—
155C3×C3⋊C8—41no—
156C22×Q16—31no—
157C2×C4×Q8C3×D311yescharacteristic
158C2×#103—31no—
159C2×#103—31no—
160#391—31no—
161#340—31no—
162#336—31no—
163C2×C3×Q8—22no—
164C2×C3×Q8—22no—
165C2×C3×Q8—22no—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—22no—
175C2×C3×Q8—32no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×Q8C4×D312yes—
182C2×C3×Q8D1212yes—
183C2×C3×Q8#6712yes—
184C2×C3×Q8C2×C3×C412yes—
185C2×C3×Q8C3×D412yes—
186C2×C3×Q8C3×D412yes—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4#6711yescharacteristic
199C22×C3×C4#6711yescharacteristic
200C22×C3×C4C3×D411yescharacteristic
201C22×C3×C4C3×D411yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C23×C311yescharacteristic
204C22×Dic3—21no—
205C22×Dic3—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6C2×C3×C412yes—
212C3×Q16—68no—
213C2×C3×C8—32no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C2×C3×C8—61no—
219C3×C4⋊C4—28no—
220C3×C4⋊C4—24no—
221C3×C4⋊C4—24no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4#6712yes—
229C3×C4⋊C4C3×D412yes—
230C3×C42—28no—
231C3×C42—24no—
232C3×C42—24no—
233C3×C42—22no—
234C3×C42—22no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42—21no—
238C3×C42—21no—
239#216—28no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8C2×C3×C412yes—
248C22×C32C4×D411yescharacteristic
249C22×C32#12011yescharacteristic
250C22×C32#12111yescharacteristic
251C22×C32C2×Q1611yescharacteristic
252C22×C32#13511yescharacteristic
253C22×C32#13711yescharacteristic
254C22×C32#13711yescharacteristic
255C32×C4—24no—
256C32×C4—22no—
257C32×C4—41no—
258C32×C4—42no—
259C32×C4C2×C22⋊C411yescharacteristic
260C32×C4C4×D411yescharacteristic
261C32×C4#12111yescharacteristic
262C32×C4#12311yescharacteristic
263C3×Dic3—42no—
264C3×Dic3—81no—
265C22×Q8—31no—
266C22×Q8C2×C3×D311yescharacteristic
267C2×Q16—34no—
268C2×Q16—62no—
269C2×Q16—62no—
270C22×C8—31no—
271C22×C8—31no—
272C4×Q8—22no—
273C4×Q8—22no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4C2×C3×D311yescharacteristic
277C2×C42—21no—
278C2×C42C2×C3×D311yescharacteristic
279#103—62no—
280#103—62no—
281#95—61no—
282#95—61no—
283C23×C3—21no—
284C23×C3C2×#6711yescharacteristic
285C23×C3C2×C3×D411yescharacteristic
286C3×Q8—24no—
287C3×Q8—24no—
288C3×Q8—24no—
289C3×Q8—22no—
290C3×Q8—22no—
291C3×Q8—22no—
292C3×Q8—22no—
293C3×Q8—22no—
294C3×Q8—22no—
295C3×Q8—24no—
296C3×Q8—62no—
297C3×Q8—62no—
298C3×Q8—121no—
299C3×Q8—121no—
300C3×Q8(C2×D3)⋊C414yes—
301C3×Q8C3×C22⋊C414yes—
302C2×C3×C4—22no—
303C2×C3×C4—24no—
304C2×C3×C4—22no—
305C2×C3×C4—24no—
306C2×C3×C4—24no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—24no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—62no—
343C2×C3×C4—121no—
344C2×C3×C4—121no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4—121no—
348C2×C3×C4#21612yescomplemented
349C2×C3×C4C3×Q1612yescomplemented
350C2×C3×C4C2×C4×D311yescharacteristic
351C2×C3×C4C2×D1211yescharacteristic
352C2×C3×C4#23511yescharacteristic
353C2×C3×C4#23511yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C22×C3×C411yescharacteristic
357C2×C3×C4C2×C3×D411yescharacteristic
358C2×C3×C4C2×C3×D411yescharacteristic
359C2×C3×C4C2×C3×D411yescharacteristic
360C2×C3×C4C3×#4111yescharacteristic
361C2×C3×C4C3×#4111yescharacteristic
362C2×Dic3—22no—
363C2×Dic3—41no—
364C2×Dic3—41no—
365C2×Dic3—41no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368Dic6—22no—
369Dic6—22no—
370Dic6—41no—
371Dic6—41no—
372C3×C8—62no—
373C3×C8—121no—
374C3⋊C8—22no—
375C3⋊C8—41no—
376C2×C32#38611yescharacteristic
377C2×C32C4×Q1611yescharacteristic
378C2×C32#44111yescharacteristic
379C2×C32#45111yescharacteristic
380C2×C32#45211yescharacteristic
381C2×C32#46211yescharacteristic
382C2×C32#46411yescharacteristic
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—61no—
391C2×Q8—61no—
392C2×Q8C3×C4×D312yes—
393C2×Q8C3×D1212yes—
394C2×Q8C3×#6712yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—61no—
398C22×C4—61no—
399C22×C4C3×#6711yescharacteristic
400C22×C4C3×#6711yescharacteristic
401C22×C4C22×C3×D311yescharacteristic
402Q16—68no—
403C2×C8—32no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—61no—
407C2×C8—61no—
408C2×C8—61no—
409C4⋊C4—24no—
410C4⋊C4—21no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4C3×#6712yes—
414C42—24no—
415C42—21no—
416C42—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3C4×#6711yescharacteristic
425C22×C3#93011yescharacteristic
426C22×C3#94211yescharacteristic
427C22×C3C2×#21611yescharacteristic
428C22×C3#95011yescharacteristic
429C22×C3#95111yescharacteristic
430C22×C3#95311yescharacteristic
431C22×C3C3×C4×D411yescharacteristic
432C22×C3C3×#12011yescharacteristic
433C22×C3C3×#12111yescharacteristic
434C22×C3C2×C3×Q1611yescharacteristic
435C22×C3C3×#13511yescharacteristic
436C22×C3C3×#13711yescharacteristic
437C22×C3C3×#13711yescharacteristic
438C3×C4—28no—
439C3×C4—24no—
440C3×C4—24no—
441C3×C4—22no—
442C3×C4—24no—
443C3×C4—22no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—42no—
449C3×C4—44no—
450C3×C4—41no—
451C3×C4—42no—
452C3×C4—41no—
453C3×C4—42no—
454C3×C4—122no—
455C3×C4—241no—
456C3×C4C2×(C2×D3)⋊C411yescharacteristic
457C3×C4C4×#6711yescharacteristic
458C3×C4#92911yescharacteristic
459C3×C4#93011yescharacteristic
460C3×C4C2×C3×C22⋊C411yescharacteristic
461C3×C4C3×C4×D411yescharacteristic
462C3×C4C3×#12111yescharacteristic
463C3×C4C3×#12311yescharacteristic
464Dic3—42no—
465Dic3—81no—
466C32#187811yescharacteristic, complemented, Sylow
467C23C2×C3×#6711yescharacteristic
468Q8—22no—
469Q8—22no—
470Q8—22no—
471Q8—62no—
472Q8—62no—
473Q8—121no—
474Q8—121no—
475Q8C3×(C2×D3)⋊C414yes—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—62no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4C3×#21612yescomplemented
494C2×C4C2×C3×C4×D311yescharacteristic
495C2×C4C2×C3×D1211yescharacteristic
496C2×C4C3×#23511yescharacteristic
497C2×C4C3×#23511yescharacteristic
498C2×C4C2×C3×#6711yescharacteristic
499C2×C4C2×C3×#6711yescharacteristic
500C8—62no—
501C8—121no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3#502811yescharacteristic
510C2×C3C4×#21611yescharacteristic
511C2×C3#503011yescharacteristic
512C2×C3#503111yescharacteristic
513C2×C3#521311yescharacteristic
514C2×C3#522811yescharacteristic
515C2×C3#523911yescharacteristic
516C2×C3C3×#38611yescharacteristic
517C2×C3C3×C4×Q1611yescharacteristic
518C2×C3C3×#44111yescharacteristic
519C2×C3C3×#45111yescharacteristic
520C2×C3C3×#45211yescharacteristic
521C2×C3C3×#46211yescharacteristic
522C2×C3C3×#46411yescharacteristic
523C22C3×C4×#6711yescharacteristic
524C22C3×#93011yescharacteristic
525C22C3×#94211yescharacteristic
526C22C2×C3×#21611yescharacteristic
527C22C3×#95011yescharacteristic
528C22C3×#95111yescharacteristic
529C22C3×#95311yescharacteristic
530C4—24no—
531C4—22no—
532C4—41no—
533C4—42no—
534C4—122no—
535C4—241no—
536C4C2×C3×(C2×D3)⋊C411yescharacteristic
537C4C3×C4×#6711yescharacteristic
538C4C3×#92911yescharacteristic
539C4C3×#93011yescharacteristic
540C3—21no—
541C3#7163211yescharacteristic, direct product factor
542C3C3×#187811yescharacteristic, complemented
543C2C3×#502811yescharacteristic
544C2C3×C4×#21611yescharacteristic
545C2C3×#503011yescharacteristic
546C2C3×#503111yescharacteristic
547C2C3×#521311yescharacteristic
548C2C3×#522811yescharacteristic
549C2C3×#523911yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4×Q8C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4×Q8D3
hypocenterC3C3×#1878
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
9. #71632C3direct (N × H)
20. C2×C3×#216C4semidirect
109. C2×#216C3×C4semidirect
137. C2×C32×C4Q16semidirect
348. C2×C3×C4#216semidirect
349. C2×C3×C4C3×Q16semidirect
466. C32#1878semidirect
493. C2×C4C3×#216semidirect
541. C3#71632direct (N × H)
542. C3C3×#1878semidirect

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×#2162
C2×C3×#8352
C2×C3×#8102
C3×#49292
C3×#45292
C3×#45242
C3×#18783
#716323