Finite Group Databasebeta

← C3×#71629 #11786967

Subgroups — C3×#71629 #11786967

Order 1152.

745 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic
2C2×C3×#835C211yesmaximal, characteristic
3C2×C3×#835C211yesmaximal, characteristic
4C2×C3×#808C211yesmaximal, characteristic
5C3×#4928C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic
7C3×#4524C211yesmaximal, characteristic
8C3×#1865—31nomaximal
9#71629C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C32×C4×Q8—22no—
12C32×C4×Q8—22no—
13C2×C32×C4⋊C4—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C42—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×#835—22no—
23C3×#835C414yescomplemented
24C3×C3⋊#95—21no—
25C3×#808—22no—
26C2×C3×C4×Q8—21no—
27C2×C3×C4×Q8D311yescharacteristic
28C2×C3×C4×Q8C2×C311yescharacteristic
29C2×C3×#106—31no—
30C2×C3×#103—31no—
31C2×C3×#103—31no—
32C3×#389—31no—
33C2×#835C2×C311yescharacteristic
34C2×#835C2×C311yescharacteristic
35C2×#808C2×C311yescharacteristic
36#4928C2×C311yescharacteristic
37C3×#340—31no—
38C3×#336—31no—
39#4529C2×C311yescharacteristic
40#4524C2×C311yescharacteristic
41C2×C32×Q8—21no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8C2×C412yes—
45C2×C32×Q8D412yes—
46C2×C32×Q8Q812yes—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4D411yescharacteristic
50C22×C32×C4D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C32×C4⋊C4—24no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D412yes—
57C32×C42—24no—
58C32×C42—21no—
59C32×C42—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3C2×C412yes—
64C3×Dic3⋊C4—42no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8C2×C412yes—
71#1865—31noSylow
72C22×C3×Q8—21no—
73C22×C3×Q8C2×D311yescharacteristic
74C22×C3×Q8C22×C311yescharacteristic
75C22×C3×C8—31no—
76C22×C3×C8—31no—
77C3×C4×Q8—24no—
78C3×C4×Q8—24no—
79C3×C4×Q8—22no—
80C3×C4×Q8—22no—
81C3×C4×Q8—22no—
82C3×C4×Q8—22no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—61no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C22×C311yescharacteristic
92C2×C3×C42—22no—
93C2×C3×C42—21no—
94C2×C3×C42—21no—
95C2×C3×C42—21no—
96C2×C3×C42C2×D311yescharacteristic
97C2×C3×C42C22×C311yescharacteristic
98C2×C4⋊Dic3C22×C311yescharacteristic
99C2×C4⋊Dic3C22×C311yescharacteristic
100C2×Dic3⋊C4—21no—
101C22×C3⋊C8C22×C311yescharacteristic
102C22×C3⋊C8C22×C311yescharacteristic
103C3×#106—62no—
104C3×#103—34no—
105C3×#103—62no—
106C3×#95—61no—
107#835—22no—
108#835C3×C414yescomplemented
109C3⋊#95—21no—
110#808—22no—
111C23×C32C2×D411yescharacteristic
112C32×Q8—22no—
113C32×Q8—22no—
114C32×Q8—22no—
115C32×Q8C4⋊C414yescomplemented
116C2×C32×C4—22no—
117C2×C32×C4—21no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—22no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4SD1612yes—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×Q811yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3×Dic3—22no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C3×C3⋊C8—22no—
141C3×C3⋊C8—41no—
142C2×C4×Q8C3×D311yescharacteristic
143C2×#106—31no—
144C2×#103—31no—
145C2×#103—31no—
146#389—31no—
147#340—31no—
148#336—31no—
149C2×C3×Q8—22no—
150C2×C3×Q8—22no—
151C2×C3×Q8—22no—
152C2×C3×Q8—21no—
153C2×C3×Q8—21no—
154C2×C3×Q8—21no—
155C2×C3×Q8—21no—
156C2×C3×Q8—21no—
157C2×C3×Q8—21no—
158C2×C3×Q8—22no—
159C2×C3×Q8—22no—
160C2×C3×Q8—22no—
161C2×C3×Q8Dic612yes—
162C2×C3×Q8C4×D312yes—
163C2×C3×Q8#6712yes—
164C2×C3×Q8C2×C3×C412yes—
165C2×C3×Q8C3×D412yes—
166C2×C3×Q8C3×Q812yes—
167C22×C3×C4—22no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4#6711yescharacteristic
179C22×C3×C4#6711yescharacteristic
180C22×C3×C4C3×D411yescharacteristic
181C22×C3×C4C3×D411yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C23×C311yescharacteristic
184C22×Dic3—21no—
185C22×Dic3—21no—
186C2×C3×C8—32no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—28no—
193C3×C4⋊C4—24no—
194C3×C4⋊C4—24no—
195C3×C4⋊C4—22no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—122no—
204C3×C4⋊C4#6712yes—
205C3×C4⋊C4C3×D412yes—
206C3×C42—28no—
207C3×C42—24no—
208C3×C42—24no—
209C3×C42—22no—
210C3×C42—22no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—21no—
218C4⋊Dic3C2×C3×C412yes—
219Dic3⋊C4—42no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8C2×C3×C412yes—
226C22×C32C4×D411yescharacteristic
227C22×C32#12011yescharacteristic
228C22×C32C22⋊Q811yescharacteristic
229C22×C32C2×SD1611yescharacteristic
230C22×C32#13511yescharacteristic
231C22×C32#13711yescharacteristic
232C22×C32#13711yescharacteristic
233C32×C4—24no—
234C32×C4—22no—
235C32×C4—41no—
236C32×C4—42no—
237C32×C4C2×C4⋊C411yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4C22⋊Q811yescharacteristic
240C32×C4#12311yescharacteristic
241C3×Dic3—42no—
242C3×Dic3—81no—
243C22×Q8C2×C3×D311yescharacteristic
244C22×C8—31no—
245C22×C8—31no—
246C4×Q8—22no—
247C4×Q8—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—61no—
252C2×C4⋊C4C2×C3×D311yescharacteristic
253C2×C42—21no—
254C2×C42C2×C3×D311yescharacteristic
255#106—62no—
256#103—34no—
257#103—62no—
258#95—61no—
259C23×C3—21no—
260C23×C3C2×#6711yescharacteristic
261C23×C3C2×C3×D411yescharacteristic
262C3×Q8—24no—
263C3×Q8—24no—
264C3×Q8—24no—
265C3×Q8—22no—
266C3×Q8—22no—
267C3×Q8—22no—
268C3×Q8—22no—
269C3×Q8—22no—
270C3×Q8—22no—
271C3×Q8—24no—
272C3×Q8Dic3⋊C414yescomplemented
273C3×Q8C3×C4⋊C414yescomplemented
274C2×C3×C4—22no—
275C2×C3×C4—24no—
276C2×C3×C4—22no—
277C2×C3×C4—24no—
278C2×C3×C4—24no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—24no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—62no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4#21512yes—
321C2×C3×C4C3×SD1612yes—
322C2×C3×C4C2×Dic611yescharacteristic
323C2×C3×C4C2×C4×D311yescharacteristic
324C2×C3×C4#23511yescharacteristic
325C2×C3×C4#23511yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C22×C3×C411yescharacteristic
329C2×C3×C4C2×C3×D411yescharacteristic
330C2×C3×C4C2×C3×D411yescharacteristic
331C2×C3×C4C2×C3×Q811yescharacteristic
332C2×C3×C4C3×#4111yescharacteristic
333C2×C3×C4C3×#4111yescharacteristic
334C2×Dic3—22no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C3×C8—62no—
341C3×C8—121no—
342C3⋊C8—22no—
343C3⋊C8—41no—
344C2×C32#38511yescharacteristic
345C2×C32C4×SD1611yescharacteristic
346C2×C32#44111yescharacteristic
347C2×C32#44811yescharacteristic
348C2×C32#45211yescharacteristic
349C2×C32#47511yescharacteristic
350C2×C32#47911yescharacteristic
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8C3×Dic612yes—
355C2×Q8C3×C4×D312yes—
356C2×Q8C3×#6712yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4C3×#6711yescharacteristic
362C22×C4C3×#6711yescharacteristic
363C22×C4C22×C3×D311yescharacteristic
364C2×C8—32no—
365C2×C8—61no—
366C2×C8—61no—
367C2×C8—61no—
368C2×C8—61no—
369C2×C8—61no—
370C4⋊C4—24no—
371C4⋊C4—21no—
372C4⋊C4—32no—
373C4⋊C4—61no—
374C4⋊C4—61no—
375C4⋊C4—61no—
376C4⋊C4—122no—
377C4⋊C4C3×#6712yes—
378C42—24no—
379C42—21no—
380C42—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3#92411yescharacteristic
389C22×C3C4×#6711yescharacteristic
390C22×C3C2×#21511yescharacteristic
391C22×C3#94211yescharacteristic
392C22×C3#95011yescharacteristic
393C22×C3#95111yescharacteristic
394C22×C3#95311yescharacteristic
395C22×C3C3×C4×D411yescharacteristic
396C22×C3C3×#12011yescharacteristic
397C22×C3C3×C22⋊Q811yescharacteristic
398C22×C3C2×C3×SD1611yescharacteristic
399C22×C3C3×#13511yescharacteristic
400C22×C3C3×#13711yescharacteristic
401C22×C3C3×#13711yescharacteristic
402C3×C4—28no—
403C3×C4—24no—
404C3×C4—24no—
405C3×C4—22no—
406C3×C4—24no—
407C3×C4—22no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—42no—
413C3×C4—44no—
414C3×C4—41no—
415C3×C4—42no—
416C3×C4—41no—
417C3×C4—42no—
418C3×C4—122no—
419C3×C4—241no—
420C3×C4C2×Dic3⋊C411yescharacteristic
421C3×C4#92411yescharacteristic
422C3×C4C4×#6711yescharacteristic
423C3×C4#92911yescharacteristic
424C3×C4C2×C3×C4⋊C411yescharacteristic
425C3×C4C3×C4×D411yescharacteristic
426C3×C4C3×C22⋊Q811yescharacteristic
427C3×C4C3×#12311yescharacteristic
428Dic3—42no—
429Dic3—81no—
430C32#186511yescharacteristic, complemented, Sylow
431C23C2×C3×#6711yescharacteristic
432Q8—22no—
433Q8—22no—
434Q8—22no—
435Q8C3×Dic3⋊C414yescomplemented
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—62no—
448C2×C4—121no—
449C2×C4—121no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4—121no—
453C2×C4C3×#21512yes—
454C2×C4C2×C3×Dic611yescharacteristic
455C2×C4C2×C3×C4×D311yescharacteristic
456C2×C4C3×#23511yescharacteristic
457C2×C4C3×#23511yescharacteristic
458C2×C4C2×C3×#6711yescharacteristic
459C2×C4C2×C3×#6711yescharacteristic
460C8—62no—
461C8—121no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3#502011yescharacteristic
470C2×C3#502211yescharacteristic
471C2×C3C4×#21511yescharacteristic
472C2×C3#503011yescharacteristic
473C2×C3#521011yescharacteristic
474C2×C3#522711yescharacteristic
475C2×C3#523911yescharacteristic
476C2×C3C3×#38511yescharacteristic
477C2×C3C3×C4×SD1611yescharacteristic
478C2×C3C3×#44111yescharacteristic
479C2×C3C3×#44811yescharacteristic
480C2×C3C3×#45211yescharacteristic
481C2×C3C3×#47511yescharacteristic
482C2×C3C3×#47911yescharacteristic
483C22C3×#92411yescharacteristic
484C22C3×C4×#6711yescharacteristic
485C22C2×C3×#21511yescharacteristic
486C22C3×#94211yescharacteristic
487C22C3×#95011yescharacteristic
488C22C3×#95111yescharacteristic
489C22C3×#95311yescharacteristic
490C4—24no—
491C4—22no—
492C4—41no—
493C4—42no—
494C4—122no—
495C4—241no—
496C4C2×C3×Dic3⋊C411yescharacteristic
497C4C3×#92411yescharacteristic
498C4C3×C4×#6711yescharacteristic
499C4C3×#92911yescharacteristic
500C3—21no—
501C3#7162911yescharacteristic, direct product factor
502C3C3×#186511yescharacteristic, complemented
503C2C3×#502011yescharacteristic
504C2C3×#502211yescharacteristic
505C2C3×C4×#21511yescharacteristic
506C2C3×#503011yescharacteristic
507C2C3×#521011yescharacteristic
508C2C3×#522711yescharacteristic
509C2C3×#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×#1865
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. #71629C3direct (N × H)
23. C3×#835C4semidirect
108. #835C3×C4semidirect
115. C32×Q8C4⋊C4semidirect
272. C3×Q8Dic3⋊C4semidirect
273. C3×Q8C3×C4⋊C4semidirect
430. C32#1865semidirect
435. Q8C3×Dic3⋊C4semidirect
501. C3#71629direct (N × H)
502. C3C3×#1865semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×C3×#8352
C2×C3×#8082
C3×#49282
C3×#45292
C3×#45242
C3×#18653
#716293