Finite Group Databasebeta

← C3×#80414 #11895140

Subgroups — C3×#80414 #11895140

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2C3×D4×Dic6C211yesmaximal, characteristic
3C32×#461C211yesmaximal, characteristic
4C3×#5162C212yesmaximal
5C3×Dic3×SD16C212yesmaximal
6C3×#5079C211yesmaximal, characteristic, complemented
7C3×C4×#214C211yesmaximal, characteristic
8C3×#4851C211yesmaximal, characteristic, complemented
9C3×#4830C211yesmaximal, characteristic, complemented
10C3×#4792C212yesmaximal, complemented
11C3×#4791C212yesmaximal, complemented
12C3×#3359—31nomaximal
13#80414C311yesmaximal, characteristic, direct product factor
14C22×C3×Dic6—21no—
15C2×C32×SD16C2212yes—
16C32×C4⋊Q8C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18C3×Q8×Dic3C2212yes—
19C3×#944C2212yes—
20C3×D4×Dic3C2212yes—
21C2×C3×#214C2211yescharacteristic
22C3×#924—21no—
23C3×#890—21no—
24C3×#889—22no—
25C3×#888C2212yes—
26C3×#887—21no—
27C3×#878—22no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32C32×#103C2212yes—
33C3×#835C2212yes—
34C3×#835C2212yes—
35C3×#832C2211yescharacteristic
36C3×#817C2212yes—
37C3×#816C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#810C2211yescharacteristic
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#557—31no—
44C3×D4×Q8—31no—
45#5721C2×C311yescharacteristic, complemented
46D4×Dic6C2×C311yescharacteristic
47C3×#487—31no—
48C3×#487—32no—
49C3×#475—31no—
50C3×#475—32no—
51C3×#461—21no—
52C3×#461—32no—
53C3×#461D311yescharacteristic
54C3×#461C2×C311yescharacteristic
55C3×C8×Q8—31no—
56C3×C4×SD16—32no—
57C3×C4×SD16—31no—
58#5162C2×C312yes—
59Dic3×SD16C2×C312yes—
60#5079C2×C311yescharacteristic, complemented
61C4×#214C2×C311yescharacteristic
62#4851C2×C311yescharacteristic, complemented
63#4830C2×C311yescharacteristic, complemented
64#4792C2×C312yescomplemented
65#4791C2×C312yescomplemented
66C2×C32×Q8C2312yes—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C22×C3×Dic3—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6—44no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2311yescharacteristic
75C32×SD16—24no—
76C2×C32×C8C2312yes—
77C32×C4⋊C4—21no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C22⋊C4—21no—
81C32×C42C2311yescharacteristic
82C3×#217—22no—
83C3×#214—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99#3359—31noSylow
100C22×C3×Q8—61no—
101C22×Dic6—21no—
102C2×C3×SD16—22no—
103C2×C3×SD16—31no—
104C2×C3×SD16C2×D312yes—
105C2×C3×SD16C22×C312yes—
106C3×C4⋊Q8—21no—
107C3×C4⋊Q8—32no—
108C3×C4⋊Q8—32no—
109C3×C4⋊Q8—31no—
110C3×C4⋊Q8C2×D311yescharacteristic
111C3×C4⋊Q8C22×C311yescharacteristic
112C3×#125—62no—
113C3×#125—61no—
114C3×C22⋊Q8—62no—
115C3×C22⋊Q8—61no—
116C3×C4×Q8—31no—
117C3×C4×Q8—32no—
118C3×C4×Q8—31no—
119C3×C4×Q8—61no—
120C3×C4×D4—21no—
121C3×C4×D4—32no—
122C3×C4×D4C2×D311yescharacteristic
123C3×C4×D4C22×C311yescharacteristic
124Q8×Dic3C22×C312yes—
125#944C22×C312yes—
126D4×Dic3C22×C312yes—
127C2×#214C22×C311yescharacteristic
128#924—21no—
129#890—21no—
130#889—22no—
131#888C22×C312yes—
132#887—21no—
133#878—22no—
134#869C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C4×Dic6C22×C311yescharacteristic
137C3×#106—32no—
138C3×#106—31no—
139C3×C4⋊C8—21no—
140C3×C4⋊C8—32no—
141C3×C4⋊C8C2×D311yescharacteristic
142C3×C4⋊C8C22×C311yescharacteristic
143C3×#103—22no—
144C3×#103—32no—
145C3×#103—32no—
146C3×#103—32no—
147C3×#103—31no—
148C3×#103C2×D312yes—
149C3×#103C22×C312yes—
150C3×#102—31no—
151C3×C4×C8—32no—
152C3×C4×C8—31no—
153#835C22×C312yes—
154#835C22×C312yes—
155#832C22×C311yescharacteristic
156#817C22×C312yes—
157#816C22×C312yes—
158Dic3⋊C8C22×C312yes—
159C8×Dic3C22×C312yes—
160#810C22×C311yescharacteristic
161#808C22×C311yescharacteristic
162C4×C3⋊C8C22×C311yescharacteristic
163C23×C32—21no—
164C32×Q8—22no—
165C32×Q8—22no—
166C32×D4—21no—
167C32×D4#4112yes—
168C2×C32×C4—22no—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—44no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6—42no—
183C3×Dic6—44no—
184C3×Dic6SD1614yescomplemented
185C32×C8—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—21no—
188#557—31no—
189D4×Q8—31no—
190#487—31no—
191#487—32no—
192#475—31no—
193#475—32no—
194#461—32no—
195#461C3×D311yescharacteristic
196C8×Q8—31no—
197C4×SD16—32no—
198C4×SD16—31no—
199C2×C3×Q8—22no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—62no—
203C2×C3×Q8—61no—
204C2×C3×Q8—124no—
205C2×C3×Q8C22×D312yes—
206C2×C3×Q8C23×C312yes—
207C2×C3×D4—21no—
208C2×C3×D4C22×D311yescharacteristic
209C2×C3×D4C23×C311yescharacteristic
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—41no—
213C22×C3×C4—62no—
214C22×Dic3—22no—
215C2×Dic6—21no—
216C2×Dic6—22no—
217C2×Dic6—44no—
218C2×Dic6C3×D411yescharacteristic
219C2×Dic6C23×C311yescharacteristic
220C3×SD16—24no—
221C3×SD16—24no—
222C3×SD16—44no—
223C3×SD16—62no—
224C2×C3×C8—22no—
225C2×C3×C8—31no—
226C2×C3×C8—31no—
227C2×C3×C8C22×D312yes—
228C2×C3×C8C23×C312yes—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C4⋊C4C23×C311yescharacteristic
248C3×C22⋊C4—21no—
249C3×C22⋊C4—21no—
250C3×C22⋊C4—41no—
251C3×C22⋊C4—62no—
252C3×C42—21no—
253C3×C42—32no—
254C3×C42—62no—
255C3×C42—61no—
256C3×C42C22×D311yescharacteristic
257C3×C42C23×C311yescharacteristic
258#217—22no—
259#214—22no—
260C4⋊Dic3—21no—
261C4⋊Dic3—22no—
262C4⋊Dic3C3×D411yescharacteristic
263C4⋊Dic3C23×C311yescharacteristic
264C4⋊Dic3C23×C312yes—
265Dic3⋊C4—21no—
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268Dic3⋊C4—22no—
269Dic3⋊C4C3×D412yes—
270C4×Dic3—21no—
271C4×Dic3—22no—
272C4×Dic3C23×C312yes—
273C2×C3⋊C8C23×C311yescharacteristic
274C2×C3⋊C8C23×C311yescharacteristic
275C22×C32—22no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32C22×D411yescharacteristic
279C32×C4—21no—
280C32×C4—42no—
281C32×C4—41no—
282C32×C4C2×SD1612yes—
283C32×C4C2×#4111yescharacteristic
284C32×C42−1+411yescharacteristic
285C3×Dic3—22no—
286C3×Dic3—41no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3C2×SD1614yes—
290C22×Q8—61no—
291C2×SD16—31no—
292C2×SD16C2×C3×D312yes—
293C4⋊Q8—32no—
294C4⋊Q8—32no—
295C4⋊Q8—31no—
296C4⋊Q8C2×C3×D311yescharacteristic
297#125—62no—
298#125—61no—
299C22⋊Q8—62no—
300C22⋊Q8—61no—
301C4×Q8—31no—
302C4×Q8—32no—
303C4×Q8—31no—
304C4×Q8—61no—
305C4×D4—32no—
306C4×D4C2×C3×D311yescharacteristic
307#106—32no—
308#106—31no—
309C4⋊C8—32no—
310C4⋊C8C2×C3×D311yescharacteristic
311#103—32no—
312#103—32no—
313#103—32no—
314#103—31no—
315#103C2×C3×D312yes—
316#102—31no—
317C4×C8—32no—
318C4×C8—31no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3—41no—
322C3×Q8—22no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—34no—
327C3×Q8—42no—
328C3×Q8—42no—
329C3×Q8—61no—
330C3×Q8—61no—
331C3×Q8—124no—
332C3×Q8—122no—
333C3×D4—21no—
334C3×D4—21no—
335C3×D4—22no—
336C3×D4—41no—
337C3×D4#23712yes—
338C3×D4C3×#4112yes—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—41no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—82no—
356C2×C3×C4—124no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×C3×D411yescharacteristic
360C2×C3×C4C2×C3×D411yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C24×C311yescharacteristic
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366C2×Dic3—44no—
367C2×Dic3C2×C3×D412yes—
368C2×Dic3C2×C3×D412yes—
369Dic6—21no—
370Dic6—21no—
371Dic6—42no—
372Dic6—44no—
373Dic6C3×SD1614yescomplemented
374C3×C8—22no—
375C3×C8—22no—
376C3×C8—42no—
377C3×C8—61no—
378C3×C8—61no—
379C3⋊C8—21no—
380C3⋊C8—21no—
381C2×C32—42no—
382C2×C32#54811yescharacteristic
383C2×C32C22×SD1611yescharacteristic
384C2×C32#57811yescharacteristic
385C2×Q8—31no—
386C2×Q8—31no—
387C2×Q8—62no—
388C2×Q8—61no—
389C2×Q8—124no—
390C2×Q8C22×C3×D312yes—
391C2×D4C22×C3×D311yescharacteristic
392C22×C4—21no—
393C22×C4—62no—
394SD16—24no—
395SD16—62no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8C22×C3×D312yes—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—32no—
402C4⋊C4—31no—
403C4⋊C4—31no—
404C4⋊C4—32no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—62no—
408C4⋊C4—62no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4C22×C3×D311yescharacteristic
412C22⋊C4—21no—
413C22⋊C4—62no—
414C42—32no—
415C42—62no—
416C42—61no—
417C42C22×C3×D311yescharacteristic
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—42no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—81no—
427C22×C3—81no—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C22×C3×D411yescharacteristic
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—34no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—62no—
442C3×C4—81no—
443C3×C4—82no—
444C3×C4—122no—
445C3×C4—121no—
446C3×C4—121no—
447C3×C4D3×SD1612yes—
448C3×C4C2×C3×SD1612yes—
449C3×C4C2×#23711yescharacteristic
450C3×C4#101011yescharacteristic
451C3×C4C2×C3×#4111yescharacteristic
452C3×C4C3×2−1+411yescharacteristic
453Dic3—22no—
454Dic3—42no—
455Dic3—41no—
456Dic3—41no—
457Dic3C2×C3×SD1614yes—
458C32#335911yescharacteristic, complemented, Sylow
459C23—21no—
460Q8—22no—
461Q8—22no—
462Q8—34no—
463Q8—61no—
464Q8—61no—
465Q8—124no—
466Q8—122no—
467D4—21no—
468D4C3×#23712yes—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—32no—
472C2×C4—32no—
473C2×C4—42no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—62no—
477C2×C4—124no—
478C2×C4C3×D3×D411yescharacteristic
479C2×C4C3×D3×D411yescharacteristic
480C2×C4C23×C3×D311yescharacteristic
481C8—22no—
482C8—61no—
483C8—61no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—42no—
488C2×C3—42no—
489C2×C3—82no—
490C2×C3#559811yescharacteristic
491C2×C3C2×D3×SD1611yescharacteristic
492C2×C3#577911yescharacteristic
493C2×C3C3×#54811yescharacteristic
494C2×C3C22×C3×SD1611yescharacteristic
495C2×C3C3×#57811yescharacteristic
496C22—22no—
497C22—41no—
498C22—41no—
499C22C2×C3×D3×D411yescharacteristic
500C4—21no—
501C4—34no—
502C4—41no—
503C4—42no—
504C4—62no—
505C4—122no—
506C4—121no—
507C4—121no—
508C4C3×D3×SD1612yes—
509C4C2×C3×#23711yescharacteristic
510C4C3×#101011yescharacteristic
511C3—21no—
512C3#8041411yescharacteristic, direct product factor
513C3C3×#335911yescharacteristic, complemented
514C2—42no—
515C2C3×#559811yescharacteristic
516C2C2×C3×D3×SD1611yescharacteristic
517C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×#461D3
hypocenterC3C3×#3359
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
1. C3×#5721C2semidirect
6. C3×#5079C2semidirect
8. C3×#4851C2semidirect
9. C3×#4830C2semidirect
10. C3×#4792C2semidirect
11. C3×#4791C2semidirect
13. #80414C3direct (N × H)
45. #5721C2×C3semidirect
60. #5079C2×C3semidirect
62. #4851C2×C3semidirect
63. #4830C2×C3semidirect
64. #4792C2×C3semidirect
65. #4791C2×C3semidirect
184. C3×Dic6SD16semidirect
373. Dic6C3×SD16semidirect
458. C32#3359semidirect
512. C3#80414direct (N × H)
513. C3C3×#3359semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
C3×D4×Dic62
C32×#4612
C3×#51622
C3×Dic3×SD162
C3×#50792
C3×C4×#2142
C3×#48512
C3×#48302
C3×#47922
C3×#47912
C3×#33593
#804143