Finite Group Databasebeta

← C3×#71681 #11788068

Subgroups — C3×#71681 #11788068

Order 1152.

1077 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2C23×C3×C3⋊C8C211yesmaximal, characteristic, complemented
3C2×C3×#832C212yesmaximal, complemented
4C3×#5212C211yesmaximal, characteristic, complemented
5C3×#4529C212yesmaximal, complemented
6C3×#1893—31nomaximal
7#71681C311yesmaximal, characteristic, direct product factor
8C22×C32×D4—21no—
9C22×C32×D4C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C32×#121—22no—
12C32×#121C414yescomplemented
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C22⋊C4—21no—
15C2×C3×#217—21no—
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8—22no—
18C22×C3×C3⋊C8—24no—
19C22×C3×C3⋊C8C2212yes—
20C3×#832—24no—
21C3×C3⋊#95—21no—
22C23×C3×C8—31no—
23C2×C3×#121—21no—
24C2×C3×#121D311yescharacteristic
25C2×C3×#121C2×C311yescharacteristic
26C23×C3⋊C8C2×C311yescharacteristic, complemented
27C2×C3×#102—32no—
28C3×#380—31no—
29C2×#832C2×C312yescomplemented
30#5212C2×C311yescharacteristic, complemented
31C3×#340—32no—
32#4529C2×C312yescomplemented
33C24×C32—21no—
34C24×C32D411yescharacteristic
35C2×C32×D4—24no—
36C2×C32×D4—22no—
37C2×C32×D4—21no—
38C2×C32×D4—22no—
39C2×C32×D4—42no—
40C2×C32×D4—42no—
41C2×C32×D4C2×C412yes—
42C22×C32×C4—22no—
43C22×C32×C4—22no—
44C22×C32×C4—21no—
45C22×C32×C4C2×C412yes—
46C22×C32×C4D411yescharacteristic
47C22×C32×C4D412yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3—22no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4C2×C412yes—
52C32×C22⋊C4—24no—
53C3×#217—42no—
54C3×C4⋊Dic3—22no—
55C3×C4⋊Dic3—22no—
56C2×C3×C3⋊C8—28no—
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8—22no—
59C2×C3×C3⋊C8D414yescomplemented
60#1893—31noSylow
61C22×C3×D4—22no—
62C22×C3×D4—21no—
63C22×C3×D4—21no—
64C22×C3×D4—21no—
65C22×C3×D4C2×D311yescharacteristic
66C22×C3×D4C22×C311yescharacteristic
67C23×C3×C4—21no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C22×C311yescharacteristic
70C22×C3×C8—32no—
71C22×C3×C8—64no—
72C22×C3×C8—62no—
73C3×#121—24no—
74C3×#121—22no—
75C3×#121—22no—
76C3×#121—24no—
77C3×#121Dic314yescomplemented
78C3×#121C3×C414yescomplemented
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C4⋊C4C2×D311yescharacteristic
82C2×C3×C4⋊C4C22×C311yescharacteristic
83C2×C3×C22⋊C4—22no—
84C2×C3×C22⋊C4—21no—
85C2×C3×C22⋊C4—21no—
86C2×C3×C22⋊C4—61no—
87C2×#217—21no—
88C2×C4⋊Dic3C22×C312yes—
89C22×C3⋊C8—22no—
90C22×C3⋊C8—24no—
91C22×C3⋊C8C22×C312yes—
92C3×#102—64no—
93C3×#95—61no—
94#832—24no—
95C3⋊#95—21no—
96C23×C32—22no—
97C23×C32—22no—
98C23×C32—22no—
99C23×C32—42no—
100C23×C32—41no—
101C23×C32—41no—
102C23×C32—42no—
103C23×C32C22⋊C412yes—
104C23×C32D812yes—
105C23×C32SD1612yes—
106C23×C32C2×D411yescharacteristic
107C32×D4—24no—
108C32×D4—48no—
109C32×D4—41no—
110C32×D4—41no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—24no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4C22⋊C412yes—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4112yes—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—42no—
126C3×C3⋊C8—24no—
127C23×C8—31no—
128C2×#121C3×D311yescharacteristic
129C2×#102—32no—
130#380—31no—
131#340—32no—
132C24×C3—22no—
133C24×C3—21no—
134C24×C3—21no—
135C24×C3—21no—
136C24×C3#6711yescharacteristic
137C24×C3C3×D411yescharacteristic
138C2×C3×D4—28no—
139C2×C3×D4—22no—
140C2×C3×D4—24no—
141C2×C3×D4—24no—
142C2×C3×D4—22no—
143C2×C3×D4—22no—
144C2×C3×D4—21no—
145C2×C3×D4—22no—
146C2×C3×D4—21no—
147C2×C3×D4—22no—
148C2×C3×D4—22no—
149C2×C3×D4—42no—
150C2×C3×D4—42no—
151C2×C3×D4—44no—
152C2×C3×D4—44no—
153C2×C3×D4—42no—
154C2×C3×D4—42no—
155C2×C3×D4—42no—
156C2×C3×D4—42no—
157C2×C3×D4C2×Dic312yes—
158C2×C3×D4C2×C3×C412yes—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C22×C3×C4—42no—
171C22×C3×C4—42no—
172C22×C3×C4—62no—
173C22×C3×C4C2×Dic312yes—
174C22×C3×C4#6711yescharacteristic
175C22×C3×C4#6712yes—
176C22×C3×C4C2×C3×C412yes—
177C22×C3×C4C3×D411yescharacteristic
178C22×C3×C4C3×D412yes—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C23×C311yescharacteristic
181C22×Dic3—22no—
182C2×C3×C8—34no—
183C2×C3×C8—68no—
184C2×C3×C8—62no—
185C2×C3×C8—62no—
186C3×C4⋊C4—22no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—62no—
191C3×C4⋊C4—62no—
192C3×C4⋊C4C2×Dic312yes—
193C3×C4⋊C4C2×C3×C412yes—
194C3×C22⋊C4—28no—
195C3×C22⋊C4—24no—
196C3×C22⋊C4—24no—
197C3×C22⋊C4—122no—
198#217—42no—
199C4⋊Dic3—22no—
200C4⋊Dic3—22no—
201C2×C3⋊C8—28no—
202C2×C3⋊C8—22no—
203C2×C3⋊C8—22no—
204C2×C3⋊C8C3×D414yescomplemented
205C22×C32—22no—
206C22×C32—22no—
207C22×C32—24no—
208C22×C32—24no—
209C22×C32—42no—
210C22×C32—42no—
211C22×C32—42no—
212C22×C32—82no—
213C22×C32—82no—
214C22×C32#10214yescomplemented
215C22×C32C2×C22⋊C411yescharacteristic
216C22×C32#12112yes—
217C22×C32C2×D811yescharacteristic
218C22×C32C2×SD1611yescharacteristic
219C22×C32#13512yes—
220C32×C4—22no—
221C32×C4—42no—
222C32×C4C4×D412yes—
223C32×C4#12011yescharacteristic
224C32×C4#12311yescharacteristic
225C3×Dic3—82no—
226C22×D4—21no—
227C22×D4C2×C3×D311yescharacteristic
228C23×C4C2×C3×D311yescharacteristic
229C22×C8—32no—
230C22×C8—64no—
231C22×C8—62no—
232#121—22no—
233#121C3×Dic314yescomplemented
234C2×C4⋊C4—32no—
235C2×C4⋊C4C2×C3×D311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—61no—
238#102—64no—
239#95—61no—
240C23×C3—22no—
241C23×C3—22no—
242C23×C3—22no—
243C23×C3—22no—
244C23×C3—24no—
245C23×C3—22no—
246C23×C3—22no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—21no—
251C23×C3—42no—
252C23×C3—42no—
253C23×C3—42no—
254C23×C3—42no—
255C23×C3—44no—
256C23×C3—44no—
257C23×C3—41no—
258C23×C3—41no—
259C23×C3—42no—
260C23×C3—42no—
261C23×C3—42no—
262C23×C3—41no—
263C23×C3—41no—
264C23×C3—42no—
265C23×C3#21312yes—
266C23×C3#21412yes—
267C23×C3#21712yes—
268C23×C3C3×C22⋊C412yes—
269C23×C3C3×D812yes—
270C23×C3C3×SD1612yes—
271C23×C3C2×#6711yescharacteristic
272C23×C3C2×C3×D411yescharacteristic
273C3×D4—24no—
274C3×D4—24no—
275C3×D4—44no—
276C3×D4—42no—
277C3×D4—42no—
278C3×D4—416no—
279C3×D4—48no—
280C3×D4—48no—
281C3×D4—41no—
282C3×D4—41no—
283C3×D4—41no—
284C3×D4—41no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—24no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—24no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—24no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—44no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—122no—
312C2×C3×C4—122no—
313C2×C3×C4—122no—
314C2×C3×C4#21712yes—
315C2×C3×C4C3×C22⋊C412yes—
316C2×C3×C4D3×D412yes—
317C2×C3×C4#23712yes—
318C2×C3×C4C22×Dic311yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C22×C3×C411yescharacteristic
321C2×C3×C4C2×C3×D412yes—
322C2×C3×C4C2×C3×D411yescharacteristic
323C2×C3×C4C3×#4112yes—
324C2×Dic3—42no—
325C2×Dic3—42no—
326C2×Dic3—42no—
327C3×C8—64no—
328C3⋊C8—24no—
329C2×C32—24no—
330C2×C32—82no—
331C2×C32#38611yescharacteristic
332C2×C32C2×#10211yescharacteristic
333C2×C32#41611yescharacteristic
334C2×C32#46512yes—
335C2×C32#46612yes—
336C24—21no—
337C24C3×#6711yescharacteristic
338C2×D4—24no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—21no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4C2×C3×Dic312yes—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—62no—
349C22×C4C2×C3×Dic312yes—
350C22×C4C3×#6711yescharacteristic
351C22×C4C3×#6712yes—
352C22×C4C22×C3×D311yescharacteristic
353C2×C8—34no—
354C2×C8—68no—
355C2×C8—62no—
356C2×C8—62no—
357C4⋊C4—21no—
358C4⋊C4—62no—
359C4⋊C4—62no—
360C4⋊C4C2×C3×Dic312yes—
361C22⋊C4—24no—
362C22⋊C4—122no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—24no—
368C22×C3—24no—
369C22×C3—24no—
370C22×C3—24no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—24no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3—44no—
380C22×C3—44no—
381C22×C3—44no—
382C22×C3—44no—
383C22×C3—44no—
384C22×C3—42no—
385C22×C3—42no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—84no—
391C22×C3—84no—
392C22×C3—82no—
393C22×C3—82no—
394C22×C3—82no—
395C22×C3—82no—
396C22×C3#83214yescomplemented
397C22×C3C3×#10214yescomplemented
398C22×C3C2×#21311yescharacteristic
399C22×C3C2×#21411yescharacteristic
400C22×C3#93912yes—
401C22×C3#95012yes—
402C22×C3C2×#21711yescharacteristic
403C22×C3C2×C3×C22⋊C411yescharacteristic
404C22×C3C3×#12112yes—
405C22×C3C2×C3×D811yescharacteristic
406C22×C3C2×C3×SD1611yescharacteristic
407C22×C3C3×#13512yes—
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—42no—
414C3×C4—44no—
415C3×C4—42no—
416C3×C4—42no—
417C3×C4—242no—
418C3×C4D4×Dic312yes—
419C3×C4#93511yescharacteristic
420C3×C4#93711yescharacteristic
421C3×C4C3×C4×D412yes—
422C3×C4C3×#12011yescharacteristic
423C3×C4C3×#12311yescharacteristic
424Dic3—82no—
425C32#189311yescharacteristic, complemented, Sylow
426C23—22no—
427C23—22no—
428C23—22no—
429C23—41no—
430C23—41no—
431C23—42no—
432C23—42no—
433C23C3×#21312yes—
434C23C3×#21412yes—
435C23C3×#21712yes—
436C23C2×C3×#6711yescharacteristic
437D4—24no—
438D4—48no—
439D4—41no—
440D4—41no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—122no—
449C2×C4—122no—
450C2×C4—122no—
451C2×C4C3×#21712yes—
452C2×C4C3×D3×D412yes—
453C2×C4C3×#23712yes—
454C2×C4C22×C3×Dic311yescharacteristic
455C2×C4C2×C3×#6711yescharacteristic
456C8—64no—
457C2×C3—24no—
458C2×C3—24no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—22no—
463C2×C3—22no—
464C2×C3—44no—
465C2×C3—84no—
466C2×C3—82no—
467C2×C3—82no—
468C2×C3#503812yes—
469C2×C3#504112yes—
470C2×C3C2×#83211yescharacteristic
471C2×C3#522011yescharacteristic
472C2×C3#523311yescharacteristic
473C2×C3C3×#38611yescharacteristic
474C2×C3C2×C3×#10211yescharacteristic
475C2×C3C3×#41611yescharacteristic
476C2×C3C3×#46512yes—
477C2×C3C3×#46612yes—
478C22—22no—
479C22—22no—
480C22—24no—
481C22—24no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—82no—
486C22—82no—
487C22C3×#83214yescomplemented
488C22C2×C3×#21311yescharacteristic
489C22C2×C3×#21411yescharacteristic
490C22C3×#93912yes—
491C22C3×#95012yes—
492C22C2×C3×#21711yescharacteristic
493C4—22no—
494C4—42no—
495C4—242no—
496C4C3×D4×Dic312yes—
497C4C3×#93511yescharacteristic
498C4C3×#93711yescharacteristic
499C3—21no—
500C3#7168111yescharacteristic, direct product factor
501C3C3×#189311yescharacteristic, complemented
502C2—24no—
503C2—82no—
504C2C3×#503812yes—
505C2C3×#504112yes—
506C2C2×C3×#83211yescharacteristic
507C2C3×#522011yescharacteristic
508C2C3×#523311yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
Fitting, prime radicalC2×C32×#121C2
socleC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#121D3
hypocenterC3C3×#1893
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
2. C23×C3×C3⋊C8C2semidirect
3. C2×C3×#832C2semidirect
4. C3×#5212C2semidirect
5. C3×#4529C2semidirect
7. #71681C3direct (N × H)
12. C32×#121C4semidirect
26. C23×C3⋊C8C2×C3semidirect
29. C2×#832C2×C3semidirect
30. #5212C2×C3semidirect
32. #4529C2×C3semidirect
59. C2×C3×C3⋊C8D4semidirect
77. C3×#121Dic3semidirect
78. C3×#121C3×C4semidirect
204. C2×C3⋊C8C3×D4semidirect
214. C22×C32#102semidirect
233. #121C3×Dic3semidirect
396. C22×C3#832semidirect
397. C22×C3C3×#102semidirect
425. C32#1893semidirect
487. C22C3×#832semidirect
500. C3#71681direct (N × H)
501. C3C3×#1893semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C23×C3×C3⋊C82
C2×C3×#8322
C3×#52122
C3×#45292
C3×#18933
#716813