Finite Group Databasebeta

← C3×#81621 #11895225

Subgroups — C3×#81621 #11895225

Order 1152.

749 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2C3×#5730C211yesmaximal, characteristic, complemented
3C32×#487C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×#5083C211yesmaximal, characteristic, complemented
6C3×#4819C212yesmaximal
7C3×#4800C212yesmaximal, complemented
8C3×#4796C212yesmaximal, complemented
9C3×#4788C212yesmaximal, complemented
10C3×C4×D24C211yesmaximal, characteristic
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3360—31nomaximal
13#81621C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C3×#947C2212yes—
17C3×#946—22no—
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2212yes—
20C2×C3×D24C2211yescharacteristic
21C3×#898—22no—
22C3×#897—21no—
23C3×#897—21no—
24C3×#893C2212yes—
25C3×#892—21no—
26C3×D3×C4⋊C4—21no—
27C3×#890C2212yes—
28C3×C4×D12C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#103C2212yes—
32C32×#103C2212yes—
33C32×C4×C8C2211yescharacteristic
34C3×#835C2212yes—
35C3×#821C2211yescharacteristic
36C3×#821C2211yescharacteristic
37C3×#818C2211yescharacteristic
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#809C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#556—31no—
44C3×#554—31no—
45#5732C2×C311yescharacteristic, complemented
46#5730C2×C311yescharacteristic, complemented
47C3×#488—32no—
48C3×#487—21no—
49C3×#487D311yescharacteristic, complemented
50C3×#487C2×C311yescharacteristic, complemented
51C3×#479—32no—
52C3×#476—31no—
53C3×#463—32no—
54C3×#461—31no—
55C3×C8×Q8—31no—
56C3×C4×SD16—32no—
57C3×C4×D8—31no—
58#5084C2×C311yescharacteristic, complemented
59#5083C2×C311yescharacteristic, complemented
60#4819C2×C312yes—
61#4800C2×C312yescomplemented
62#4796C2×C312yescomplemented
63#4788C2×C312yescomplemented
64C4×D24C2×C311yescharacteristic
65C8×Dic6C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—22no—
73C2×C3×Dic6D411yescharacteristic
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2312yes—
80C32×C42C2311yescharacteristic
81C3×#215—24no—
82C3×(C2×D3)⋊C4—21no—
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2312yes—
97C3×D24—22no—
98#3360—31noSylow
99C2×C3×SD16—32no—
100C2×C3×D8—31no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C22×C311yescharacteristic
106C3×C4⋊Q8C22×C311yescharacteristic
107C3×#126—62no—
108C3×#125—32no—
109C3×#124—32no—
110C3×C22⋊Q8—61no—
111C3×C22⋊Q8—61no—
112C3×C22⋊Q8—62no—
113C3×C4×Q8—31no—
114C3×C4×Q8—32no—
115C3×C4×D4—32no—
116C3×C4×D4—31no—
117C3×C4×D4—31no—
118C3×#117—61no—
119C2×C3×C4⋊C4—61no—
120#947C22×C312yes—
121#946—22no—
122Q8×Dic3C22×C312yes—
123C2×#215C22×C312yes—
124C2×D24C22×C311yescharacteristic
125#898—22no—
126#897—21no—
127#897—21no—
128#893C22×C312yes—
129#892—21no—
130D3×C4⋊C4—21no—
131#890C22×C312yes—
132C4×D12C22×C311yescharacteristic
133C4×D12C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C3×#107—31no—
136C3×#106—32no—
137C3×C4⋊C8—32no—
138C3×C4⋊C8—31no—
139C3×#103—22no—
140C3×#103—22no—
141C3×#103—32no—
142C3×#103C2×D312yes—
143C3×#103C2×D312yes—
144C3×#103C22×C312yes—
145C3×#103C22×C312yes—
146C3×#102—31no—
147C3×#102—31no—
148C3×#102—32no—
149C3×C4×C8—21no—
150C3×C4×C8—32no—
151C3×C4×C8C2×D311yescharacteristic
152C3×C4×C8C22×C311yescharacteristic
153#835C22×C312yes—
154#821C22×C311yescharacteristic
155#821C22×C311yescharacteristic
156#818C22×C311yescharacteristic
157Dic3⋊C8C22×C312yes—
158C8×Dic3C22×C312yes—
159#809C22×C312yes—
160#808C22×C312yes—
161C4⋊(C3⋊C8)C22×C311yescharacteristic
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C32×Q8—22no—
165C32×Q8—22no—
166C32×Q8—81no—
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×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—21no—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12#4112yes—
180C3×C4×D3—42no—
181C3×C4×D3—42no—
182C3×C4×D3—82no—
183C3×Dic6—22no—
184C32×C8—21no—
185C32×C8—21no—
186C3×C3⋊C8—22no—
187#556—31no—
188#554—31no—
189#488—32no—
190#487C3×D311yescharacteristic, complemented
191#479—32no—
192#476—31no—
193#463—32no—
194#461—31no—
195C8×Q8—31no—
196C4×SD16—32no—
197C4×D8—31no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—22no—
201C2×C3×Q8—31no—
202C2×C3×Q8—41no—
203C2×C3×Q8C22×D312yes—
204C2×C3×Q8C23×C312yes—
205C2×C3×D4—31no—
206C2×C3×D4—31no—
207C22×C3×C4—62no—
208C22×C3×C4—61no—
209C22×C3×C4—61no—
210C2×D12C23×C311yescharacteristic
211C2×D12C23×C311yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C4×D3—22no—
215C2×Dic6C3×D411yescharacteristic
216C3×SD16—64no—
217C3×D8—62no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—32no—
221C2×C3×C8C22×D311yescharacteristic
222C2×C3×C8C22×D311yescharacteristic
223C2×C3×C8C23×C311yescharacteristic
224C2×C3×C8C23×C311yescharacteristic
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—41no—
237C3×C4⋊C4—41no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4C22×D312yes—
243C3×C4⋊C4C23×C312yes—
244C3×C22⋊C4—62no—
245C3×C22⋊C4—62no—
246C3×C22⋊C4—62no—
247C3×C22⋊C4—61no—
248C3×C22⋊C4—61no—
249C3×C42—21no—
250C3×C42—32no—
251C3×C42—62no—
252C3×C42C22×D311yescharacteristic
253C3×C42C23×C311yescharacteristic
254#215—24no—
255(C2×D3)⋊C4—21no—
256(C2×D3)⋊C4—21no—
257(C2×D3)⋊C4—22no—
258(C2×D3)⋊C4—22no—
259(C2×D3)⋊C4—22no—
260C4⋊Dic3—22no—
261C4⋊Dic3—22no—
262C4⋊Dic3C3×D411yescharacteristic
263C4⋊Dic3C23×C311yescharacteristic
264C4⋊Dic3C23×C311yescharacteristic
265Dic3⋊C4—22no—
266Dic3⋊C4C3×D412yes—
267C4×Dic3—22no—
268C4×Dic3C23×C312yes—
269C2×C3⋊C8C23×C312yes—
270D24—22no—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—22no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4—42no—
280C32×C4—42no—
281C32×C4#13512yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—41no—
287C3×Dic3—41no—
288C2×SD16—32no—
289C2×D8—31no—
290C4⋊Q8C2×C3×D311yescharacteristic
291C4⋊Q8C2×C3×D311yescharacteristic
292#126—62no—
293#125—32no—
294#124—32no—
295C22⋊Q8—61no—
296C22⋊Q8—61no—
297C22⋊Q8—62no—
298C4×Q8—31no—
299C4×Q8—32no—
300C4×D4—32no—
301C4×D4—31no—
302C4×D4—31no—
303#117—61no—
304C2×C4⋊C4—61no—
305#107—31no—
306#106—32no—
307C4⋊C8—32no—
308C4⋊C8—31no—
309#103—32no—
310#103C2×C3×D312yes—
311#103C2×C3×D312yes—
312#102—31no—
313#102—31no—
314#102—32no—
315C4×C8—32no—
316C4×C8C2×C3×D311yescharacteristic
317C23×C3—61no—
318C23×C3—61no—
319C22×D3—21no—
320C22×D3—21no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—42no—
326C3×Q8—42no—
327C3×Q8—62no—
328C3×Q8—81no—
329C3×Q8—81no—
330C3×Q8—82no—
331C3×D4—32no—
332C3×D4—61no—
333C3×D4—61no—
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—122no—
349C2×C3×C4—122no—
350C2×C3×C4—242no—
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×Dic3C2×C3×D412yes—
360C2×Dic3C2×C3×D412yes—
361D12—21no—
362D12—21no—
363D12—21no—
364D12C3×#4112yes—
365C4×D3—42no—
366C4×D3—42no—
367C4×D3—82no—
368Dic6—22no—
369C3×C8—21no—
370C3×C8—21no—
371C3×C8—21no—
372C3×C8—21no—
373C3×C8—41no—
374C3×C8—41no—
375C3×C8—62no—
376C3⋊C8—22no—
377C2×C32#54811yescharacteristic
378C2×C32C2×#13511yescharacteristic
379C2×C32#57711yescharacteristic
380C3×D3—42no—
381C3×D3—81no—
382C2×Q8—21no—
383C2×Q8—31no—
384C2×Q8C22×C3×D312yes—
385C2×D4—31no—
386C2×D4—31no—
387C22×C4—62no—
388C22×C4—61no—
389C22×C4—61no—
390SD16—64no—
391D8—62no—
392C2×C8—32no—
393C2×C8C22×C3×D311yescharacteristic
394C2×C8C22×C3×D311yescharacteristic
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—31no—
399C4⋊C4—32no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—62no—
405C4⋊C4C22×C3×D312yes—
406C22⋊C4—62no—
407C22⋊C4—62no—
408C22⋊C4—62no—
409C22⋊C4—61no—
410C22⋊C4—61no—
411C42—32no—
412C42—62no—
413C42C22×C3×D311yescharacteristic
414C22×C3—21no—
415C22×C3—62no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3C2×D3×D411yescharacteristic
422C22×C3C22×C3×D411yescharacteristic
423C2×D3—22no—
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—41no—
427C2×D3—41no—
428C2×D3—41no—
429C3×C4—22no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—42no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—62no—
440C3×C4—62no—
441C3×C4—82no—
442C3×C4—82no—
443C3×C4—121no—
444C3×C4—121no—
445C3×C4#91912yes—
446C3×C4C3×#13512yes—
447C3×C4D3×#4111yescharacteristic
448C3×C4#101011yescharacteristic
449C3×C4C2×C3×#4111yescharacteristic
450C3×C4C3×2−1+411yescharacteristic
451Dic3—22no—
452Dic3—22no—
453Dic3—41no—
454Dic3—41no—
455C32#336011yescharacteristic, complemented, Sylow
456C23—61no—
457C23—61no—
458Q8—22no—
459Q8—22no—
460Q8—62no—
461Q8—81no—
462D4—32no—
463D4—61no—
464D4—61no—
465D4—61no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—32no—
469C2×C4—32no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—122no—
473C2×C4—122no—
474C2×C4—242no—
475C2×C4C3×D3×D411yescharacteristic
476C2×C4C3×D3×D411yescharacteristic
477C2×C4C23×C3×D311yescharacteristic
478C8—21no—
479C8—21no—
480C8—62no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—122no—
485C2×C3—241no—
486C2×C3#567711yescharacteristic
487C2×C3#576211yescharacteristic
488C2×C3C2×#91911yescharacteristic
489C2×C3C3×#54811yescharacteristic
490C2×C3C2×C3×#13511yescharacteristic
491C2×C3C3×#57711yescharacteristic
492D3—42no—
493D3—81no—
494C22—62no—
495C22—121no—
496C22—121no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22C2×C3×D3×D411yescharacteristic
501C4—21no—
502C4—42no—
503C4—42no—
504C4—62no—
505C4—62no—
506C4—121no—
507C4—121no—
508C4C3×#91912yes—
509C4C3×D3×#4111yescharacteristic
510C4C3×#101011yescharacteristic
511C3—21no—
512C3#8162111yescharacteristic, direct product factor
513C3C3×#336011yescharacteristic, complemented
514C2—122no—
515C2—241no—
516C2C3×#567711yescharacteristic
517C2C3×#576211yescharacteristic
518C2C2×C3×#91911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC3×#487D3
hypocenterC3C3×#3360
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
1. C3×#5732C2semidirect
2. C3×#5730C2semidirect
3. C32×#487C2semidirect
4. C3×#5084C2semidirect
5. C3×#5083C2semidirect
7. C3×#4800C2semidirect
8. C3×#4796C2semidirect
9. C3×#4788C2semidirect
11. C3×C8×Dic6C2semidirect
13. #81621C3direct (N × H)
45. #5732C2×C3semidirect
46. #5730C2×C3semidirect
49. C3×#487D3semidirect
50. C3×#487C2×C3semidirect
58. #5084C2×C3semidirect
59. #5083C2×C3semidirect
61. #4800C2×C3semidirect
62. #4796C2×C3semidirect
63. #4788C2×C3semidirect
65. C8×Dic6C2×C3semidirect
190. #487C3×D3semidirect
455. C32#3360semidirect
512. C3#81621direct (N × H)
513. C3C3×#3360semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
C3×#57302
C32×#4872
C3×#50842
C3×#50832
C3×#48192
C3×#48002
C3×#47962
C3×#47882
C3×C4×D242
C3×C8×Dic62
C3×#33603
#816213