Finite Group Databasebeta

← C3×#81620 #11895146

Subgroups — C3×#81620 #11895146

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2C3×#5721C211yesmaximal, characteristic, complemented
3C32×#487C211yesmaximal, characteristic, complemented
4C3×#5094C211yesmaximal, characteristic, complemented
5C3×#5083C211yesmaximal, characteristic
6C3×#4818C212yesmaximal
7C3×#4792C212yesmaximal, complemented
8C3×#4791C212yesmaximal, complemented
9C3×#4788C212yesmaximal
10C3×C4×#204C211yesmaximal, characteristic
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3359—31nomaximal
13#81620C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17C3×#946—21no—
18C3×Q8×Dic3C2212yes—
19C3×#944C2212yes—
20C2×C3×#215C2212yes—
21C2×C3×#204C2211yescharacteristic
22C3×#896—22no—
23C3×#893C2212yes—
24C3×#890—21no—
25C3×#889—22no—
26C3×#888C2212yes—
27C3×#887—21no—
28C3×C4×D12C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#103C2212yes—
32C32×#103C2212yes—
33C32×C4×C8C2211yescharacteristic
34C3×#835C2212yes—
35C3×#821C2211yescharacteristic
36C3×#817C2211yescharacteristic
37C3×#816C2211yescharacteristic
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#810C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#557—31no—
44C3×D4×Q8—31no—
45#5727C2×C311yescharacteristic
46#5721C2×C311yescharacteristic, complemented
47C3×#487—21no—
48C3×#487—32no—
49C3×#487D311yescharacteristic, complemented
50C3×#487C2×C311yescharacteristic, complemented
51C3×#475—31no—
52C3×#475—32no—
53C3×#461—31no—
54C3×#461—32no—
55C3×C8×Q8—31no—
56C3×C4×SD16—32no—
57C3×C4×SD16—31no—
58#5094C2×C311yescharacteristic, complemented
59#5083C2×C311yescharacteristic
60#4818C2×C312yes—
61#4792C2×C312yescomplemented
62#4791C2×C312yescomplemented
63#4788C2×C312yes—
64C4×#204C2×C311yescharacteristic
65C8×Dic6C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2312yes—
68C3×D3×Q8—44no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C4⋊C4—21no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yes—
81C32×C42C2311yescharacteristic
82C3×#215—24no—
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
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⋊C8C2312yes—
98C3×#204—22no—
99#3359—31noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C2×C3×SD16—32no—
103C2×C3×SD16—31no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—21no—
106C3×C4⋊Q8—32no—
107C3×C4⋊Q8—32no—
108C3×C4⋊Q8C2×D311yescharacteristic
109C3×C4⋊Q8C2×D311yescharacteristic
110C3×C4⋊Q8C22×C311yescharacteristic
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—32no—
121C3×C4×D4—31no—
122#946—21no—
123Q8×Dic3C22×C312yes—
124#944C22×C312yes—
125C2×#215C22×C312yes—
126C2×#204C22×C311yescharacteristic
127#896—22no—
128#893C22×C312yes—
129#890—21no—
130#889—22no—
131#888C22×C312yes—
132#887—21no—
133C4×D12C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#106—31no—
137C3×#106—32no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8—31no—
140C3×#103—22no—
141C3×#103—22no—
142C3×#103—32no—
143C3×#103—31no—
144C3×#103—32no—
145C3×#103C2×D312yes—
146C3×#103C2×D312yes—
147C3×#103C22×C312yes—
148C3×#103C22×C312yes—
149C3×#102—31no—
150C3×C4×C8—21no—
151C3×C4×C8—32no—
152C3×C4×C8C2×D311yescharacteristic
153C3×C4×C8C22×C311yescharacteristic
154#835C22×C312yes—
155#821C22×C311yescharacteristic
156#817C22×C311yescharacteristic
157#816C22×C311yescharacteristic
158Dic3⋊C8C22×C312yes—
159C8×Dic3C22×C312yes—
160#810C22×C312yes—
161#808C22×C312yes—
162C4⋊(C3⋊C8)C22×C311yescharacteristic
163C22×C3×D3—21no—
164C32×Q8—22no—
165C32×Q8—22no—
166C32×Q8—42no—
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—42no—
180C3×C4×D3—44no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6—44no—
184C3×Dic6SD1614yescomplemented
185C32×C8—21no—
186C32×C8—21no—
187C3×C3⋊C8—22no—
188#557—31no—
189D4×Q8—31no—
190#487—32no—
191#487C3×D311yescharacteristic, complemented
192#475—31no—
193#475—32no—
194#461—31no—
195#461—32no—
196C8×Q8—31no—
197C4×SD16—32no—
198C4×SD16—31no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—22no—
202C2×C3×Q8—31no—
203C2×C3×Q8—31no—
204C2×C3×Q8—41no—
205C2×C3×Q8—62no—
206C2×C3×Q8—124no—
207C2×C3×Q8C22×D312yes—
208C2×C3×Q8C23×C312yes—
209C2×C3×D4—31no—
210C22×C3×C4—62no—
211C22×C3×C4—61no—
212D3×Q8—44no—
213C2×D12C23×C311yescharacteristic
214C2×C4×D3—21no—
215C2×C4×D3—22no—
216C2×Dic6—22no—
217C2×Dic6C3×D411yescharacteristic
218C2×Dic6C23×C311yescharacteristic
219C3×SD16—62no—
220C3×SD16—64no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—32no—
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C23×C311yescharacteristic
227C2×C3×C8C23×C311yescharacteristic
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—41no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4C22×D312yes—
248C3×C4⋊C4C23×C312yes—
249C3×C22⋊C4—62no—
250C3×C22⋊C4—61no—
251C3×C42—21no—
252C3×C42—32no—
253C3×C42—62no—
254C3×C42—61no—
255C3×C42C22×D311yescharacteristic
256C3×C42C23×C311yescharacteristic
257#215—24no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—22no—
260C4⋊Dic3—22no—
261C4⋊Dic3C3×D411yescharacteristic
262C4⋊Dic3C23×C311yescharacteristic
263C4⋊Dic3C23×C311yescharacteristic
264Dic3⋊C4—21no—
265Dic3⋊C4—22no—
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268Dic3⋊C4C3×D412yes—
269C4×Dic3—21no—
270C4×Dic3—22no—
271C4×Dic3C23×C312yes—
272C2×C3⋊C8C23×C312yes—
273#204—22no—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4—42no—
280C32×C4—42no—
281C32×C4C2×SD1612yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3×Dic3—22no—
285C3×Dic3—41no—
286C3×Dic3—41no—
287C3×Dic3—41no—
288C3×Dic3C2×SD1614yes—
289C22×Q8—61no—
290C2×SD16—32no—
291C2×SD16—31no—
292C4⋊Q8—32no—
293C4⋊Q8—32no—
294C4⋊Q8C2×C3×D311yescharacteristic
295C4⋊Q8C2×C3×D311yescharacteristic
296#125—62no—
297#125—61no—
298C22⋊Q8—62no—
299C22⋊Q8—61no—
300C4×Q8—31no—
301C4×Q8—32no—
302C4×Q8—31no—
303C4×Q8—61no—
304C4×D4—32no—
305C4×D4—31no—
306#106—31no—
307#106—32no—
308C4⋊C8—32no—
309C4⋊C8—31no—
310#103—32no—
311#103—31no—
312#103—32no—
313#103C2×C3×D312yes—
314#103C2×C3×D312yes—
315#102—31no—
316C4×C8—32no—
317C4×C8C2×C3×D311yescharacteristic
318C23×C3—61no—
319C22×D3—21no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—22no—
324C3×Q8—34no—
325C3×Q8—42no—
326C3×Q8—42no—
327C3×Q8—42no—
328C3×Q8—42no—
329C3×Q8—61no—
330C3×Q8—61no—
331C3×Q8—82no—
332C3×Q8—124no—
333C3×D4—32no—
334C3×D4—61no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—124no—
350C2×C3×C4—122no—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4C2×C3×D411yescharacteristic
354C2×C3×C4C2×C3×D411yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C24×C311yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3C2×C3×D412yes—
361C2×Dic3C2×C3×D412yes—
362D12—21no—
363D12C3×#4112yes—
364C4×D3—42no—
365C4×D3—44no—
366Dic6—21no—
367Dic6—21no—
368Dic6—44no—
369Dic6C3×SD1614yescomplemented
370C3×C8—21no—
371C3×C8—21no—
372C3×C8—21no—
373C3×C8—21no—
374C3×C8—41no—
375C3×C8—41no—
376C3×C8—62no—
377C3⋊C8—22no—
378C2×C32#54811yescharacteristic
379C2×C32C22×SD1611yescharacteristic
380C2×C32#57811yescharacteristic
381C3×D3—42no—
382C2×Q8—21no—
383C2×Q8—31no—
384C2×Q8—31no—
385C2×Q8—62no—
386C2×Q8—124no—
387C2×Q8C22×C3×D312yes—
388C2×D4—31no—
389C22×C4—62no—
390C22×C4—61no—
391SD16—62no—
392SD16—64no—
393C2×C8—32no—
394C2×C8C22×C3×D311yescharacteristic
395C2×C8C22×C3×D311yescharacteristic
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—32no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—31no—
403C4⋊C4—62no—
404C4⋊C4—62no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—61no—
408C4⋊C4C22×C3×D312yes—
409C22⋊C4—62no—
410C22⋊C4—61no—
411C42—32no—
412C42—62no—
413C42—61no—
414C42C22×C3×D311yescharacteristic
415C22×C3—21no—
416C22×C3—62no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×C3×D411yescharacteristic
421C2×D3—22no—
422C2×D3—41no—
423C2×D3—41no—
424C3×C4—22no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—22no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—34no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—62no—
436C3×C4—82no—
437C3×C4—82no—
438C3×C4—121no—
439C3×C4—121no—
440C3×C4—121no—
441C3×C4D3×SD1612yes—
442C3×C4C2×C3×SD1612yes—
443C3×C4D3×#4111yescharacteristic
444C3×C4#101011yescharacteristic
445C3×C4C2×C3×#4111yescharacteristic
446C3×C4C3×2−1+411yescharacteristic
447Dic3—22no—
448Dic3—41no—
449Dic3—41no—
450Dic3—41no—
451Dic3C2×C3×SD1614yes—
452C32#335911yescharacteristic, complemented, Sylow
453C23—61no—
454Q8—22no—
455Q8—22no—
456Q8—34no—
457Q8—42no—
458Q8—61no—
459Q8—61no—
460Q8—124no—
461D4—32no—
462D4—61no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—124no—
471C2×C4—122no—
472C2×C4C3×D3×D411yescharacteristic
473C2×C4C3×D3×D411yescharacteristic
474C2×C4C23×C3×D311yescharacteristic
475C8—21no—
476C8—21no—
477C8—62no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—122no—
482C2×C3#567711yescharacteristic
483C2×C3C2×D3×SD1611yescharacteristic
484C2×C3#576611yescharacteristic
485C2×C3C3×#54811yescharacteristic
486C2×C3C22×C3×SD1611yescharacteristic
487C2×C3C3×#57811yescharacteristic
488D3—42no—
489C22—62no—
490C22—121no—
491C22—121no—
492C22C2×C3×D3×D411yescharacteristic
493C4—21no—
494C4—34no—
495C4—42no—
496C4—42no—
497C4—62no—
498C4—121no—
499C4—121no—
500C4—121no—
501C4C3×D3×SD1612yes—
502C4C3×D3×#4111yescharacteristic
503C4C3×#101011yescharacteristic
504C3—21no—
505C3#8162011yescharacteristic, direct product factor
506C3C3×#335911yescharacteristic, complemented
507C2—122no—
508C2C3×#567711yescharacteristic
509C2C2×C3×D3×SD1611yescharacteristic
510C2C3×#576611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#487D3
hypocenterC3C3×#3359
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
2. C3×#5721C2semidirect
3. C32×#487C2semidirect
4. C3×#5094C2semidirect
7. C3×#4792C2semidirect
8. C3×#4791C2semidirect
11. C3×C8×Dic6C2semidirect
13. #81620C3direct (N × H)
46. #5721C2×C3semidirect
49. C3×#487D3semidirect
50. C3×#487C2×C3semidirect
58. #5094C2×C3semidirect
61. #4792C2×C3semidirect
62. #4791C2×C3semidirect
65. C8×Dic6C2×C3semidirect
184. C3×Dic6SD16semidirect
191. #487C3×D3semidirect
369. Dic6C3×SD16semidirect
452. C32#3359semidirect
505. C3#81620direct (N × H)
506. C3C3×#3359semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C3×#57212
C32×#4872
C3×#50942
C3×#50832
C3×#48182
C3×#47922
C3×#47912
C3×#47882
C3×C4×#2042
C3×C8×Dic62
C3×#33593
#816203