Finite Group Databasebeta

← C3×#80464 #11896038

Subgroups — C3×#80464 #11896038

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C32×#462C211yesmaximal, characteristic, complemented
4C3×#5185C212yesmaximal
5C3×#5184C212yesmaximal, complemented
6C3×#5079C211yesmaximal, characteristic, complemented
7C3×C4×#215C211yesmaximal, characteristic
8C3×#4842C211yesmaximal, characteristic
9C3×#4831C211yesmaximal, characteristic, complemented
10C3×#4794C212yesmaximal
11C3×#4791C212yesmaximal, complemented
12C3×#3369—31nomaximal
13#80464C311yesmaximal, characteristic, direct product factor
14C2×C32×Q16C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C3×#947C2212yes—
18C3×Q8×Dic3C2212yes—
19C3×Q8×Dic3C2212yes—
20C2×C3×#215C2211yescharacteristic
21C3×#898—22no—
22C3×#897—21no—
23C3×#892—21no—
24C3×#888—22no—
25C3×#888C2212yes—
26C3×C4×D12C2211yescharacteristic
27C3×#869—21no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6—21no—
30C3×C4×Dic6C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32C32×#103C2212yes—
33C3×#835C2211yescharacteristic
34C3×#835C2212yes—
35C3×#835C2212yes—
36C3×#821C2212yes—
37C3×#817C2212yes—
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#809C2211yescharacteristic
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×Q82—31no—
44C3×#556—31no—
45#5732C2×C311yescharacteristic
46Q8×Dic6C2×C311yescharacteristic, complemented
47C3×#489—32no—
48C3×#487—31no—
49C3×#476—31no—
50C3×#475—32no—
51C3×#464—32no—
52C3×#462—21no—
53C3×#462D311yescharacteristic, complemented
54C3×#462C2×C311yescharacteristic, complemented
55C3×#446—31no—
56C3×#441—32no—
57C3×C4×SD16—31no—
58#5185C2×C312yes—
59#5184C2×C312yescomplemented
60#5079C2×C311yescharacteristic, complemented
61C4×#215C2×C311yescharacteristic
62#4842C2×C311yescharacteristic
63#4831C2×C311yescharacteristic, complemented
64#4794C2×C312yes—
65#4791C2×C312yescomplemented
66C2×C32×Q8C2312yes—
67C2×C32×Q8C2311yescharacteristic
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6D411yescharacteristic
73C32×Q16—24no—
74C2×C32×C8C2312yes—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81C3×#215—22no—
82C3×(C2×D3)⋊C4—21no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3—22no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3369—31noSylow
99C2×C3×Q16—22no—
100C2×C3×Q16C2×D312yes—
101C2×C3×Q16C22×C312yes—
102C2×C3×SD16—31no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8—32no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8—61no—
107C3×C4⋊Q8—62no—
108C3×C4⋊Q8C2×D311yescharacteristic
109C3×C4⋊Q8C22×C311yescharacteristic
110C3×#126—62no—
111C3×#124—32no—
112C3×C22⋊Q8—61no—
113C3×C4×Q8—21no—
114C3×C4×Q8—31no—
115C3×C4×Q8—32no—
116C3×C4×Q8—32no—
117C3×C4×Q8—61no—
118C3×C4×Q8C2×D311yescharacteristic
119C3×C4×Q8C22×C311yescharacteristic
120C3×C4×D4—31no—
121C3×#117—61no—
122#947C22×C312yes—
123Q8×Dic3C22×C312yes—
124Q8×Dic3C22×C312yes—
125C2×#215C22×C311yescharacteristic
126#898—22no—
127#897—21no—
128#892—21no—
129#888—22no—
130#888C22×C312yes—
131C4×D12C22×C311yescharacteristic
132#869—21no—
133#869C22×C311yescharacteristic
134C4×Dic6—21no—
135C4×Dic6C22×C311yescharacteristic
136C3×#106—32no—
137C3×#106—31no—
138C3×C4⋊C8—21no—
139C3×C4⋊C8—32no—
140C3×C4⋊C8C2×D311yescharacteristic
141C3×C4⋊C8C22×C311yescharacteristic
142C3×#103—22no—
143C3×#103—31no—
144C3×#103—32no—
145C3×#103—32no—
146C3×#103C2×D312yes—
147C3×#103C22×C312yes—
148C3×#102—32no—
149C3×#102—31no—
150C3×#97—32no—
151C3×C4×C8—31no—
152#835C22×C311yescharacteristic
153#835C22×C312yes—
154#835C22×C312yes—
155#821C22×C312yes—
156#817C22×C312yes—
157#815C22×C312yes—
158Dic3⋊C8C22×C312yes—
159#809C22×C311yescharacteristic
160#808C22×C311yescharacteristic
161C4×C3⋊C8C22×C311yescharacteristic
162C22×C3×D3—21no—
163C32×Q8—21no—
164C32×Q8—22no—
165C32×Q8—22no—
166C32×Q8#4112yes—
167C2×C32×C4—21no—
168C2×C32×C4—22no—
169C2×C32×C4—21no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12—21no—
179C3×C4×D3—42no—
180C3×Dic6—22no—
181C3×Dic6—82no—
182C3×Dic6—81no—
183C32×C8—22no—
184C3×C3⋊C8—21no—
185C3×C3⋊C8—21no—
186Q82—31no—
187#556—31no—
188#489—32no—
189#487—31no—
190#476—31no—
191#475—32no—
192#464—32no—
193#462C3×D311yescharacteristic, complemented
194#446—31no—
195#441—32no—
196C4×SD16—31no—
197C2×C3×Q8—21no—
198C2×C3×Q8—22no—
199C2×C3×Q8—31no—
200C2×C3×Q8—62no—
201C2×C3×Q8—61no—
202C2×C3×Q8C22×D312yes—
203C2×C3×Q8C22×D311yescharacteristic
204C2×C3×Q8C23×C312yes—
205C2×C3×Q8C23×C311yescharacteristic
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C2×D12C23×C311yescharacteristic
209C2×C4×D3—21no—
210C2×Dic6—21no—
211C2×Dic6—22no—
212C2×Dic6C3×D411yescharacteristic
213C3×Q16—24no—
214C3×Q16—24no—
215C3×Q16—44no—
216C3×SD16—62no—
217C2×C3×C8—22no—
218C2×C3×C8—31no—
219C2×C3×C8—31no—
220C2×C3×C8C22×D312yes—
221C2×C3×C8C23×C312yes—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—41no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C4⋊C4C23×C311yescharacteristic
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—61no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—21no—
248C3×C42—32no—
249C3×C42—41no—
250C3×C42—62no—
251C3×C42—62no—
252C3×C42C22×D311yescharacteristic
253C3×C42C23×C311yescharacteristic
254#215—22no—
255(C2×D3)⋊C4—21no—
256(C2×D3)⋊C4—22no—
257(C2×D3)⋊C4—22no—
258C4⋊Dic3—21no—
259C4⋊Dic3—22no—
260C4⋊Dic3—22no—
261C4⋊Dic3C3×D411yescharacteristic
262C4⋊Dic3C23×C311yescharacteristic
263C4⋊Dic3C23×C312yes—
264Dic3⋊C4—22no—
265Dic3⋊C4C3×D412yes—
266C4×Dic3—22no—
267C4×Dic3—22no—
268C4×Dic3C23×C312yes—
269C2×C3⋊C8C23×C311yescharacteristic
270C2×C3⋊C8C23×C311yescharacteristic
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C32×C4—22no—
276C32×C4—21no—
277C32×C4—42no—
278C32×C4—41no—
279C32×C4#13712yes—
280C32×C4C2×#4111yescharacteristic
281C32×C42−1+411yescharacteristic
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—41no—
285C3×Dic3—42no—
286C2×Q16C2×C3×D312yes—
287C2×SD16—31no—
288C4⋊Q8—32no—
289C4⋊Q8—31no—
290C4⋊Q8—61no—
291C4⋊Q8—62no—
292C4⋊Q8C2×C3×D311yescharacteristic
293#126—62no—
294#124—32no—
295C22⋊Q8—61no—
296C4×Q8—31no—
297C4×Q8—32no—
298C4×Q8—32no—
299C4×Q8—61no—
300C4×Q8C2×C3×D311yescharacteristic
301C4×D4—31no—
302#117—61no—
303#106—32no—
304#106—31no—
305C4⋊C8—32no—
306C4⋊C8C2×C3×D311yescharacteristic
307#103—31no—
308#103—32no—
309#103—32no—
310#103C2×C3×D312yes—
311#102—32no—
312#102—31no—
313#97—32no—
314C4×C8—31no—
315C23×C3—61no—
316C22×D3—21no—
317C3×Q8—21no—
318C3×Q8—21no—
319C3×Q8—22no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—22no—
324C3×Q8—41no—
325C3×Q8—42no—
326C3×Q8—42no—
327C3×Q8—62no—
328C3×Q8—241no—
329C3×Q8—242no—
330C3×Q8#23712yes—
331C3×Q8C3×#4112yes—
332C3×D4—61no—
333C3×D4—61no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—42no—
348C2×C3×C4—61no—
349C2×C3×C4—62no—
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—22no—
359C2×Dic3C2×C3×D412yes—
360C2×Dic3C2×C3×D412yes—
361D12—21no—
362D12—21no—
363C4×D3—42no—
364Dic6—22no—
365Dic6—82no—
366Dic6—81no—
367C3×C8—22no—
368C3×C8—22no—
369C3×C8—42no—
370C3×C8—61no—
371C3×C8—61no—
372C3⋊C8—21no—
373C3⋊C8—21no—
374C2×C32#54811yescharacteristic
375C2×C32C2×#13711yescharacteristic
376C2×C32#57711yescharacteristic
377C3×D3—81no—
378C2×Q8—31no—
379C2×Q8—62no—
380C2×Q8—61no—
381C2×Q8C22×C3×D312yes—
382C2×Q8C22×C3×D311yescharacteristic
383C2×D4—31no—
384C22×C4—61no—
385Q16—24no—
386SD16—62no—
387C2×C8—31no—
388C2×C8—31no—
389C2×C8C22×C3×D312yes—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—31no—
394C4⋊C4—32no—
395C4⋊C4—32no—
396C4⋊C4—31no—
397C4⋊C4—62no—
398C4⋊C4—62no—
399C4⋊C4—62no—
400C4⋊C4—61no—
401C4⋊C4C22×C3×D311yescharacteristic
402C22⋊C4—62no—
403C22⋊C4—62no—
404C22⋊C4—61no—
405C42—21no—
406C42—32no—
407C42—62no—
408C42—62no—
409C42C22×C3×D311yescharacteristic
410C22×C3—21no—
411C22×C3—121no—
412C22×C3—121no—
413C22×C3—121no—
414C22×C3C2×D3×D411yescharacteristic
415C22×C3C22×C3×D411yescharacteristic
416C2×D3—41no—
417C2×D3—41no—
418C2×D3—41no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—22no—
422C3×C4—22no—
423C3×C4—22no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—41no—
427C3×C4—42no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—62no—
433C3×C4—62no—
434C3×C4—82no—
435C3×C4—81no—
436C3×C4—121no—
437C3×C4—122no—
438C3×C4#91812yes—
439C3×C4C3×#13712yes—
440C3×C4C2×#23711yescharacteristic
441C3×C4#101011yescharacteristic
442C3×C4C2×C3×#4111yescharacteristic
443C3×C4C3×2−1+411yescharacteristic
444Dic3—22no—
445Dic3—22no—
446Dic3—41no—
447Dic3—42no—
448C32#336911yescharacteristic, complemented, Sylow
449C23—61no—
450Q8—21no—
451Q8—22no—
452Q8—22no—
453Q8—62no—
454Q8—241no—
455Q8—242no—
456Q8C3×#23712yes—
457D4—61no—
458D4—61no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—32no—
463C2×C4—32no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—122no—
467C2×C4C3×D3×D411yescharacteristic
468C2×C4C3×D3×D411yescharacteristic
469C2×C4C23×C3×D311yescharacteristic
470C8—22no—
471C8—61no—
472C8—61no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—241no—
477C2×C3#559811yescharacteristic
478C2×C3C2×#91811yescharacteristic
479C2×C3#577811yescharacteristic
480C2×C3C3×#54811yescharacteristic
481C2×C3C2×C3×#13711yescharacteristic
482C2×C3C3×#57711yescharacteristic
483D3—81no—
484C22—121no—
485C22—121no—
486C22—121no—
487C22C2×C3×D3×D411yescharacteristic
488C4—21no—
489C4—22no—
490C4—41no—
491C4—42no—
492C4—62no—
493C4—62no—
494C4—121no—
495C4—122no—
496C4C3×#91812yes—
497C4C2×C3×#23711yescharacteristic
498C4C3×#101011yescharacteristic
499C3—21no—
500C3#8046411yescharacteristic, direct product factor
501C3C3×#336911yescharacteristic, complemented
502C2—241no—
503C2C3×#559811yescharacteristic
504C2C2×C3×#91811yescharacteristic
505C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#462D3
hypocenterC3C3×#3369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. C32×#462C2semidirect
5. C3×#5184C2semidirect
6. C3×#5079C2semidirect
9. C3×#4831C2semidirect
11. C3×#4791C2semidirect
13. #80464C3direct (N × H)
46. Q8×Dic6C2×C3semidirect
53. C3×#462D3semidirect
54. C3×#462C2×C3semidirect
59. #5184C2×C3semidirect
60. #5079C2×C3semidirect
63. #4831C2×C3semidirect
65. #4791C2×C3semidirect
193. #462C3×D3semidirect
448. C32#3369semidirect
500. C3#80464direct (N × H)
501. C3C3×#3369semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
C3×Q8×Dic62
C32×#4622
C3×#51852
C3×#51842
C3×#50792
C3×C4×#2152
C3×#48422
C3×#48312
C3×#47942
C3×#47912
C3×#33693
#804643