Finite Group Databasebeta

← C3×#79970 #11895830

Subgroups — C3×#79970 #11895830

Order 1152.

791 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5584C211yesmaximal, characteristic, complemented
2C3×Q8×D12C211yesmaximal, characteristic, complemented
3C32×#446C211yesmaximal, characteristic, complemented
4C3×#4850C212yesmaximal, complemented
5C3×#4846C211yesmaximal, characteristic, complemented
6C3×#4844C212yesmaximal
7C3×#4841C211yesmaximal, characteristic, complemented
8C3×#4714C212yesmaximal, complemented
9C3×#4710C212yesmaximal, complemented
10C3×C4×D24C211yesmaximal, characteristic
11C3×#4681C211yesmaximal, characteristic, complemented
12C3×#3367—31nomaximal
13#79970C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8—21no—
15C32×C4×Q8C2211yescharacteristic
16C3×#946—21no—
17C2×C3×D24C2211yescharacteristic
18C2×C3×#204C2212yes—
19C3×#898—22no—
20C3×#897—21no—
21C3×#897—22no—
22C3×#892—21no—
23C3×#875C2212yes—
24C3×C4×D12C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2212yes—
27C3×#869C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C3×#869C2212yes—
30C3×C4×Dic6C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×C4⋊C8C2212yes—
33C32×#97C2212yes—
34C32×C4×C8C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#821C2211yescharacteristic
37C3×#821C2212yes—
38C3×#818C2211yescharacteristic
39C3×#818C2212yes—
40C3×#816C2212yes—
41C3×#816C2212yes—
42C3×#816C2212yes—
43C3×#556—31no—
44C3×D4×Q8—31no—
45#5584C2×C311yescharacteristic, complemented
46Q8×D12C2×C311yescharacteristic, complemented
47C3×#489—32no—
48C3×#487—31no—
49C3×#477—32no—
50C3×#474—31no—
51C3×#463—32no—
52C3×#461—31no—
53C3×#446—21no—
54C3×#446D311yescharacteristic, complemented
55C3×#446C2×C311yescharacteristic, complemented
56C3×#440—32no—
57C3×C4×D8—31no—
58#4850C2×C312yescomplemented
59#4846C2×C311yescharacteristic, complemented
60#4844C2×C312yes—
61#4841C2×C311yescharacteristic, complemented
62#4714C2×C312yescomplemented
63#4710C2×C312yescomplemented
64C4×D24C2×C311yescharacteristic
65#4681C2×C311yescharacteristic, complemented
66C2×C32×Q8D411yescharacteristic
67C3×D3×Q8—44no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—21no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2312yes—
76C2×C32×C8C2312yes—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C32×C4⋊C4D411yescharacteristic
80C32×C4⋊C4D412yes—
81C32×C42C2311yescharacteristic
82C32×C42C2312yes—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—22no—
97C3×D24—22no—
98C3×#204—24no—
99#3367—31noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C2×C3×SD16—32no—
103C2×C3×D8—31no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8—32no—
106C3×C4⋊Q8—31no—
107C3×#126—62no—
108C3×#124—32no—
109C3×C22⋊Q8—61no—
110C3×C22⋊Q8—61no—
111C3×C22⋊Q8—62no—
112C3×C4×Q8—21no—
113C3×C4×Q8—32no—
114C3×C4×Q8C2×D311yescharacteristic
115C3×C4×Q8C22×C311yescharacteristic
116C3×C4×D4—31no—
117C3×C4×D4—31no—
118C3×C4×D4—32no—
119C3×#117—61no—
120#946—21no—
121C2×D24C22×C311yescharacteristic
122C2×#204C22×C312yes—
123#898—22no—
124#897—21no—
125#897—22no—
126#892—21no—
127#875C22×C312yes—
128C4×D12C22×C311yescharacteristic
129C4×D12C22×C311yescharacteristic
130C4×D12C22×C312yes—
131#869C22×C311yescharacteristic
132#869C22×C311yescharacteristic
133#869C22×C312yes—
134C4×Dic6C22×C312yes—
135C3×#107—31no—
136C3×#107—32no—
137C3×C4⋊C8—21no—
138C3×C4⋊C8—22no—
139C3×C4⋊C8C2×D311yescharacteristic
140C3×C4⋊C8C2×D312yes—
141C3×C4⋊C8C22×C311yescharacteristic
142C3×C4⋊C8C22×C312yes—
143C3×#103—32no—
144C3×#103—32no—
145C3×#103—32no—
146C3×#102—31no—
147C3×#102—31no—
148C3×#102—32no—
149C3×#97—22no—
150C3×#97C2×D312yes—
151C3×#97C22×C312yes—
152C3×C4×C8—21no—
153C3×C4×C8C2×D311yescharacteristic
154C3×C4×C8C22×C311yescharacteristic
155#821C22×C311yescharacteristic
156#821C22×C311yescharacteristic
157#821C22×C312yes—
158#818C22×C311yescharacteristic
159#818C22×C312yes—
160#816C22×C312yes—
161#816C22×C312yes—
162#816C22×C312yes—
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C32×Q8—22no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C3×D12—21no—
176C3×D12—21no—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—44no—
180C3×C4×D3—42no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—44no—
185C3×Dic6—42no—
186C32×C8—21no—
187C32×C8—22no—
188C32×C8—21no—
189#556—31no—
190D4×Q8—31no—
191#489—32no—
192#487—31no—
193#477—32no—
194#474—31no—
195#463—32no—
196#461—31no—
197#446C3×D311yescharacteristic, complemented
198#440—32no—
199C4×D8—31no—
200C2×C3×Q8—21no—
201C2×C3×Q8—32no—
202C2×C3×Q8—62no—
203C2×C3×Q8—61no—
204C2×C3×Q8—124no—
205C2×C3×Q8D1211yescharacteristic
206C2×C3×Q8C3×D411yescharacteristic
207C2×C3×D4—31no—
208C2×C3×D4—31no—
209C22×C3×C4—61no—
210C22×C3×C4—62no—
211C22×C3×C4—61no—
212D3×Q8—44no—
213C2×D12C23×C311yescharacteristic
214C2×D12C23×C311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—22no—
217C2×C4×D3—21no—
218C2×Dic6—22no—
219C2×Dic6—21no—
220C2×Dic6C23×C312yes—
221C3×SD16—64no—
222C3×D8—62no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—22no—
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D312yes—
229C2×C3×C8C23×C311yescharacteristic
230C2×C3×C8C23×C311yescharacteristic
231C2×C3×C8C23×C312yes—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4D1211yescharacteristic
243C3×C4⋊C4D1212yes—
244C3×C4⋊C4C3×D411yescharacteristic
245C3×C4⋊C4C3×D412yes—
246C3×C22⋊C4—62no—
247C3×C22⋊C4—62no—
248C3×C22⋊C4—61no—
249C3×C22⋊C4—61no—
250C3×C22⋊C4—62no—
251C3×C42—21no—
252C3×C42—22no—
253C3×C42—62no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D312yes—
256C3×C42C23×C311yescharacteristic
257C3×C42C23×C312yes—
258(C2×D3)⋊C4—22no—
259(C2×D3)⋊C4—21no—
260(C2×D3)⋊C4—21no—
261(C2×D3)⋊C4—22no—
262(C2×D3)⋊C4—22no—
263C4⋊Dic3—21no—
264C4⋊Dic3—22no—
265C4⋊Dic3—21no—
266C4⋊Dic3—21no—
267C4⋊Dic3C23×C312yes—
268C4⋊Dic3C23×C311yescharacteristic
269C4⋊Dic3C23×C311yescharacteristic
270Dic3⋊C4—22no—
271C4×Dic3—22no—
272D24—22no—
273#204—24no—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C32×C4—22no—
282C32×C4—22no—
283C32×C4—21no—
284C32×C4AGL(1,ℤ/8)12yes—
285C32×C4C2×#4111yescharacteristic
286C32×C42−1+411yescharacteristic
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3—42no—
290C3×Dic3—41no—
291C22×Q8—61no—
292C2×SD16—32no—
293C2×D8—31no—
294C4⋊Q8—31no—
295C4⋊Q8—32no—
296C4⋊Q8—31no—
297#126—62no—
298#124—32no—
299C22⋊Q8—61no—
300C22⋊Q8—61no—
301C22⋊Q8—62no—
302C4×Q8—32no—
303C4×Q8C2×C3×D311yescharacteristic
304C4×D4—31no—
305C4×D4—32no—
306C4×D4—31no—
307#117—61no—
308#107—31no—
309#107—32no—
310C4⋊C8C2×C3×D311yescharacteristic
311C4⋊C8C2×C3×D312yes—
312#103—32no—
313#103—32no—
314#103—32no—
315#102—31no—
316#102—31no—
317#102—32no—
318#97C2×C3×D312yes—
319C4×C8C2×C3×D311yescharacteristic
320C23×C3—61no—
321C23×C3—61no—
322C22×D3—21no—
323C22×D3—21no—
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—42no—
327C3×Q8—62no—
328C3×Q8—62no—
329C3×Q8—124no—
330C3×Q8—122no—
331C3×D4—32no—
332C3×D4—61no—
333C3×D4—61no—
334C3×D4—61no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—61no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—61no—
344C2×C3×C4—124no—
345C2×C3×C4—122no—
346C2×C3×C4—122no—
347C2×C3×C4C2×D1212yes—
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4C2×D1212yes—
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4C2×C3×D412yes—
352C2×C3×C4C2×C3×D412yes—
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×Dic3—21no—
360C2×Dic3—22no—
361D12—21no—
362D12—21no—
363D12—21no—
364D12C3×#4112yes—
365C4×D3—44no—
366C4×D3—42no—
367C4×D3—42no—
368Dic6—22no—
369Dic6—22no—
370Dic6—44no—
371Dic6—42no—
372C3×C8—22no—
373C3×C8—21no—
374C3×C8—21no—
375C3×C8—22no—
376C3×C8—22no—
377C3×C8—21no—
378C3×C8—21no—
379C3×C8—41no—
380C3×C8—42no—
381C2×C32#54811yescharacteristic
382C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
383C2×C32#57811yescharacteristic
384C3×D3—42no—
385C3×D3—81no—
386C2×Q8—32no—
387C2×Q8—62no—
388C2×Q8—61no—
389C2×Q8—124no—
390C2×Q8C3×D1211yescharacteristic
391C2×D4—31no—
392C2×D4—31no—
393C22×C4—61no—
394C22×C4—62no—
395C22×C4—61no—
396SD16—64no—
397D8—62no—
398C2×C8C22×C3×D311yescharacteristic
399C2×C8C22×C3×D311yescharacteristic
400C2×C8C22×C3×D312yes—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—31no—
404C4⋊C4—61no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—61no—
408C4⋊C4—61no—
409C4⋊C4C3×D1211yescharacteristic
410C4⋊C4C3×D1212yes—
411C22⋊C4—62no—
412C22⋊C4—62no—
413C22⋊C4—61no—
414C22⋊C4—61no—
415C22⋊C4—62no—
416C42—62no—
417C42C22×C3×D311yescharacteristic
418C42C22×C3×D312yes—
419C22×C3—21no—
420C22×C3—62no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3C22×D1211yescharacteristic
427C22×C3C22×C3×D411yescharacteristic
428C2×D3—22no—
429C2×D3—41no—
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—41no—
433C2×D3—41no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—41no—
446C3×C4—122no—
447C3×C4—121no—
448C3×C4—121no—
449C3×C4—122no—
450C3×C4#90812yes—
451C3×C4C3×AGL(1,ℤ/8)12yes—
452C3×C4#100711yescharacteristic
453C3×C4D3×#4111yescharacteristic
454C3×C4C2×C3×#4111yescharacteristic
455C3×C4C3×2−1+411yescharacteristic
456Dic3—41no—
457Dic3—42no—
458Dic3—41no—
459Dic3—42no—
460C32#336711yescharacteristic, complemented, Sylow
461C23—61no—
462C23—61no—
463Q8—22no—
464Q8—62no—
465Q8—62no—
466Q8—124no—
467Q8—122no—
468D4—32no—
469D4—61no—
470D4—61no—
471D4—61no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—61no—
476C2×C4—124no—
477C2×C4—122no—
478C2×C4—122no—
479C2×C4C2×C3×D1212yes—
480C2×C4C2×C3×D1211yescharacteristic
481C2×C4C2×C3×D1212yes—
482C2×C4C2×C3×D1211yescharacteristic
483C2×C4C23×C3×D311yescharacteristic
484C8—21no—
485C8—21no—
486C8—22no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—122no—
491C2×C3—241no—
492C2×C3#557611yescharacteristic
493C2×C3C2×#90811yescharacteristic
494C2×C3#575311yescharacteristic
495C2×C3C3×#54811yescharacteristic
496C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
497C2×C3C3×#57811yescharacteristic
498D3—42no—
499D3—81no—
500C22—62no—
501C22—121no—
502C22—121no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22C22×C3×D1211yescharacteristic
507C4—22no—
508C4—22no—
509C4—21no—
510C4—122no—
511C4—121no—
512C4—121no—
513C4—122no—
514C4C3×#90812yes—
515C4C3×#100711yescharacteristic
516C4C3×D3×#4111yescharacteristic
517C3—21no—
518C3#7997011yescharacteristic, direct product factor
519C3C3×#336711yescharacteristic, complemented
520C2—122no—
521C2—241no—
522C2C3×#557611yescharacteristic
523C2C2×C3×#90811yescharacteristic
524C2C3×#575311yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#446C2
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC3×#446D3
hypocenterC3C3×#3367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#446

Complements

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

NH ≅ G/Ntype
1. C3×#5584C2semidirect
2. C3×Q8×D12C2semidirect
3. C32×#446C2semidirect
4. C3×#4850C2semidirect
5. C3×#4846C2semidirect
7. C3×#4841C2semidirect
8. C3×#4714C2semidirect
9. C3×#4710C2semidirect
11. C3×#4681C2semidirect
13. #79970C3direct (N × H)
45. #5584C2×C3semidirect
46. Q8×D12C2×C3semidirect
54. C3×#446D3semidirect
55. C3×#446C2×C3semidirect
58. #4850C2×C3semidirect
59. #4846C2×C3semidirect
61. #4841C2×C3semidirect
62. #4714C2×C3semidirect
63. #4710C2×C3semidirect
65. #4681C2×C3semidirect
197. #446C3×D3semidirect
460. C32#3367semidirect
518. C3#79970direct (N × H)
519. C3C3×#3367semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
C3×Q8×D122
C32×#4462
C3×#48502
C3×#48462
C3×#48442
C3×#48412
C3×#47142
C3×#47102
C3×C4×D242
C3×#46812
C3×#33673
#799703