Finite Group Databasebeta

← C3×#81813 #11898341

Subgroups — C3×#81813 #11898341

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5671C212yesmaximal, complemented
2C32×#495C211yesmaximal, characteristic
3C3×#5183C211yesmaximal, characteristic, complemented
4C3×Dic3×Q16C211yesmaximal, characteristic, complemented
5C3×#5166C212yesmaximal, complemented
6C3×#5162C212yesmaximal, complemented
7C3×#5155C211yesmaximal, characteristic
8C3×Dic3×D8C211yesmaximal, characteristic
9C3×#5054C212yesmaximal, complemented
10C3×C4×Dic12C211yesmaximal, characteristic, complemented
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3393—31nomaximal
13#81813C311yesmaximal, characteristic, direct product factor
14C2×C32×Q16C2211yescharacteristic
15C2×C32×SD16C2212yes—
16C2×C32×D8C2211yescharacteristic
17C32×#124C2212yes—
18C3×Q8×Dic3C2212yes—
19C3×#944C2212yes—
20C2×C3×#216C2212yes—
21C3×#936C2212yes—
22C3×D4×Dic3C2212yes—
23C2×C3×#214C2212yes—
24C2×C3×Dic12C2211yescharacteristic
25C3×#879—22no—
26C3×#879—22no—
27C3×#878—22no—
28C3×#877—22no—
29C3×C4×Dic6C2212yes—
30C3×C4×Dic6C2211yescharacteristic
31C32×C4×C8C2211yescharacteristic
32C3×#835C2212yes—
33C3×#832C2212yes—
34C3×#818C2211yescharacteristic
35C3×#816C2212yes—
36C3×Dic3⋊C8C2211yescharacteristic
37C3×Dic3⋊C8C2211yescharacteristic
38C3×C8×Dic3C2211yescharacteristic
39C3×C8×Dic3C2211yescharacteristic
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41C3×#556—32no—
42#5671C2×C312yescomplemented
43C3×#495—21no—
44C3×#495—31no—
45C3×#495D311yescharacteristic
46C3×#495C2×C311yescharacteristic
47C3×#494—31no—
48C3×#464—32no—
49C3×#464—32no—
50C3×#461—32no—
51C3×C8×Q8—31no—
52C3×C4×Q16—31no—
53C3×C4×Q16—31no—
54C3×C4×D8—31no—
55#5183C2×C311yescharacteristic, complemented
56Dic3×Q16C2×C311yescharacteristic, complemented
57#5166C2×C312yescomplemented
58#5162C2×C312yescomplemented
59#5155C2×C311yescharacteristic
60Dic3×D8C2×C311yescharacteristic
61#5054C2×C312yescomplemented
62C4×Dic12C2×C311yescharacteristic, complemented
63C8×Dic6C2×C311yescharacteristic, complemented
64C2×C32×Q8C2312yes—
65C2×C32×D4C2312yes—
66C22×C3×Dic3—22no—
67C2×C3×Dic6D411yescharacteristic
68C2×C3×Dic6C2312yes—
69C32×Q16—22no—
70C32×SD16—42no—
71C32×D8—22no—
72C2×C32×C8C2311yescharacteristic
73C2×C32×C8C2311yescharacteristic
74C32×C22⋊C4—22no—
75C32×C22⋊C4—22no—
76C32×C42C2311yescharacteristic
77C3×#217—22no—
78C3×#217—22no—
79C3×#217—22no—
80C3×#216—42no—
81C3×#214—42no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3D411yescharacteristic
84C3×C4⋊Dic3C2312yes—
85C3×Dic3⋊C4—22no—
86C3×Dic3⋊C4—22no—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4D411yescharacteristic
89C3×Dic3⋊C4D411yescharacteristic
90C3×C4×Dic3—22no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3C2311yescharacteristic
93C3×C4×Dic3C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C3×Dic12—22no—
97#3393—31noSylow
98C2×C3×Q16—21no—
99C2×C3×Q16—32no—
100C2×C3×Q16—31no—
101C2×C3×Q16C2×D311yescharacteristic
102C2×C3×Q16C22×C311yescharacteristic
103C2×C3×SD16—22no—
104C2×C3×SD16—32no—
105C2×C3×SD16C2×D312yes—
106C2×C3×SD16C22×C312yes—
107C2×C3×D8—21no—
108C2×C3×D8C2×D311yescharacteristic
109C2×C3×D8C22×C311yescharacteristic
110C3×C4⋊Q8—32no—
111C3×#126—62no—
112C3×#126—62no—
113C3×#124—22no—
114C3×#124—32no—
115C3×#124C2×D312yes—
116C3×#124C22×C312yes—
117C3×C22⋊Q8—62no—
118C3×C4×Q8—31no—
119C3×C4×Q8—32no—
120C3×C4×Q8—32no—
121C3×C4×D4—32no—
122C3×#117—62no—
123Q8×Dic3C22×C312yes—
124#944C22×C312yes—
125C2×#216C22×C312yes—
126#936C22×C312yes—
127D4×Dic3C22×C312yes—
128C2×#214C22×C312yes—
129C2×Dic12C22×C311yescharacteristic
130#879—22no—
131#879—22no—
132#878—22no—
133#877—22no—
134C4×Dic6C22×C312yes—
135C4×Dic6C22×C311yescharacteristic
136C3×#107—31no—
137C3×C4⋊C8—31no—
138C3×C4⋊C8—31no—
139C3×C4⋊C8—31no—
140C3×#103—32no—
141C3×#103—32no—
142C3×#102—32no—
143C3×C4×C8—21no—
144C3×C4×C8—31no—
145C3×C4×C8—31no—
146C3×C4×C8C2×D311yescharacteristic
147C3×C4×C8C22×C311yescharacteristic
148#835C22×C312yes—
149#832C22×C312yes—
150#818C22×C311yescharacteristic
151#816C22×C312yes—
152Dic3⋊C8C22×C311yescharacteristic
153Dic3⋊C8C22×C311yescharacteristic
154C8×Dic3C22×C311yescharacteristic
155C8×Dic3C22×C311yescharacteristic
156C4⋊(C3⋊C8)C22×C311yescharacteristic
157C23×C32—22no—
158C32×Q8—22no—
159C32×Q8—22no—
160C32×D4—22no—
161C32×D4—22no—
162C2×C32×C4—22no—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—44no—
169C2×C3×Dic3C2×D411yescharacteristic
170C2×C3×Dic3C2×D411yescharacteristic
171C2×C3×Dic3C2×D411yescharacteristic
172C2×C3×Dic3C2×D411yescharacteristic
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—22no—
176C32×C8—21no—
177C32×C8#4112yes—
178C3×C3⋊C8—21no—
179C3×C3⋊C8—21no—
180#556—32no—
181#495—31no—
182#495C3×D311yescharacteristic
183#494—31no—
184#464—32no—
185#464—32no—
186#461—32no—
187C8×Q8—31no—
188C4×Q16—31no—
189C4×Q16—31no—
190C4×D8—31no—
191C2×C3×Q8—22no—
192C2×C3×Q8—31no—
193C2×C3×Q8—32no—
194C2×C3×Q8C22×D312yes—
195C2×C3×Q8C23×C312yes—
196C2×C3×D4—22no—
197C2×C3×D4C22×D312yes—
198C2×C3×D4C23×C312yes—
199C22×C3×C4—62no—
200C22×Dic3—22no—
201C2×Dic6C3×D411yescharacteristic
202C2×Dic6C23×C312yes—
203C3×Q16—22no—
204C3×Q16—22no—
205C3×Q16—42no—
206C3×Q16—62no—
207C3×Q16—122no—
208C3×SD16—42no—
209C3×SD16—42no—
210C3×SD16—44no—
211C3×SD16—122no—
212C3×D8—22no—
213C3×D8—22no—
214C3×D8—42no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—31no—
218C2×C3×C8—31no—
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C23×C311yescharacteristic
222C2×C3×C8C23×C311yescharacteristic
223C3×C4⋊C4—31no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—62no—
231C3×C22⋊C4—22no—
232C3×C22⋊C4—22no—
233C3×C22⋊C4—22no—
234C3×C22⋊C4—22no—
235C3×C22⋊C4—42no—
236C3×C22⋊C4—42no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—62no—
240C3×C42—21no—
241C3×C42—31no—
242C3×C42—31no—
243C3×C42—62no—
244C3×C42—62no—
245C3×C42C22×D311yescharacteristic
246C3×C42C23×C311yescharacteristic
247#217—22no—
248#217—22no—
249#217—22no—
250#216—42no—
251#214—42no—
252C4⋊Dic3—22no—
253C4⋊Dic3C3×D411yescharacteristic
254C4⋊Dic3C23×C312yes—
255Dic3⋊C4—22no—
256Dic3⋊C4—22no—
257Dic3⋊C4—22no—
258Dic3⋊C4C3×D411yescharacteristic
259Dic3⋊C4C3×D411yescharacteristic
260C4×Dic3—22no—
261C4×Dic3—22no—
262C4×Dic3C23×C311yescharacteristic
263C4×Dic3C23×C311yescharacteristic
264C2×C3⋊C8C23×C311yescharacteristic
265C2×C3⋊C8C23×C311yescharacteristic
266Dic12—22no—
267C22×C32—42no—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32C22×D411yescharacteristic
271C32×C4—21no—
272C32×C4—21no—
273C32×C4—42no—
274C32×C4C2×#4111yescharacteristic
275C32×C4H(5,𝔽2)11yescharacteristic
276C3×Dic3—21no—
277C3×Dic3—21no—
278C3×Dic3—21no—
279C3×Dic3—42no—
280C3×Dic3—42no—
281C3×Dic3#13512yes—
282C2×Q16—32no—
283C2×Q16—31no—
284C2×Q16C2×C3×D311yescharacteristic
285C2×SD16—32no—
286C2×SD16C2×C3×D312yes—
287C2×D8C2×C3×D311yescharacteristic
288C4⋊Q8—32no—
289#126—62no—
290#126—62no—
291#124—32no—
292#124C2×C3×D312yes—
293C22⋊Q8—62no—
294C4×Q8—31no—
295C4×Q8—32no—
296C4×Q8—32no—
297C4×D4—32no—
298#117—62no—
299#107—31no—
300C4⋊C8—31no—
301C4⋊C8—31no—
302C4⋊C8—31no—
303#103—32no—
304#103—32no—
305#102—32no—
306C4×C8—31no—
307C4×C8—31no—
308C4×C8C2×C3×D311yescharacteristic
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—42no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—42no—
317C3×Q8—42no—
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—62no—
321C3×D4—22no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—42no—
326C3×D4—42no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—31no—
333C2×C3×C4—31no—
334C2×C3×C4—31no—
335C2×C3×C4—31no—
336C2×C3×C4—42no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—124no—
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4C2×C3×D411yescharacteristic
343C2×C3×C4C2×C3×D411yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×C3×C4C24×C311yescharacteristic
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—44no—
349C2×Dic3C2×C3×D411yescharacteristic
350C2×Dic3C2×C3×D411yescharacteristic
351C2×Dic3C2×C3×D411yescharacteristic
352C2×Dic3C2×C3×D411yescharacteristic
353Dic6—22no—
354Dic6—22no—
355Dic6—22no—
356C3×C8—22no—
357C3×C8—21no—
358C3×C8—21no—
359C3×C8—22no—
360C3×C8—61no—
361C3×C8—61no—
362C3×C8#23712yes—
363C3×C8C3×#4112yes—
364C3⋊C8—21no—
365C3⋊C8—21no—
366C2×C32—82no—
367C2×C32#55011yescharacteristic
368C2×C32C2×#13511yescharacteristic
369C2×C32#57811yescharacteristic
370C2×Q8—31no—
371C2×Q8—32no—
372C2×Q8C22×C3×D312yes—
373C2×D4C22×C3×D312yes—
374C22×C4—62no—
375Q16—22no—
376Q16—62no—
377Q16—122no—
378SD16—42no—
379SD16—122no—
380D8—22no—
381C2×C8—31no—
382C2×C8—31no—
383C2×C8C22×C3×D311yescharacteristic
384C2×C8C22×C3×D311yescharacteristic
385C4⋊C4—31no—
386C4⋊C4—31no—
387C4⋊C4—31no—
388C4⋊C4—32no—
389C4⋊C4—62no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—62no—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—62no—
396C22⋊C4—62no—
397C22⋊C4—62no—
398C42—31no—
399C42—31no—
400C42—62no—
401C42—62no—
402C42C22×C3×D311yescharacteristic
403C22×C3—21no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—82no—
411C22×C3—82no—
412C22×C3—82no—
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C22×C3×D411yescharacteristic
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—32no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—61no—
427C3×C4—61no—
428C3×C4—61no—
429C3×C4—82no—
430C3×C4—122no—
431C3×C4—122no—
432C3×C4C2×#23711yescharacteristic
433C3×C4#100411yescharacteristic
434C3×C4C2×C3×#4111yescharacteristic
435C3×C4C3×H(5,𝔽2)11yescharacteristic
436Dic3—21no—
437Dic3—21no—
438Dic3—21no—
439Dic3—42no—
440Dic3—42no—
441Dic3C3×#13512yes—
442C32#339311yescharacteristic, complemented, Sylow
443C23—22no—
444Q8—22no—
445Q8—22no—
446Q8—62no—
447Q8—62no—
448Q8—62no—
449D4—22no—
450D4—22no—
451C2×C4—22no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—124no—
459C2×C4C3×D3×D411yescharacteristic
460C2×C4C3×D3×D411yescharacteristic
461C2×C4C23×C3×D311yescharacteristic
462C8—21no—
463C8—61no—
464C8—61no—
465C8C3×#23712yes—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—82no—
470C2×C3—82no—
471C2×C3—162no—
472C2×C3#571811yescharacteristic
473C2×C3D3×#13511yescharacteristic
474C2×C3#577111yescharacteristic
475C2×C3C3×#55011yescharacteristic
476C2×C3C2×C3×#13511yescharacteristic
477C2×C3C3×#57811yescharacteristic
478C22—42no—
479C22—42no—
480C22—42no—
481C22C2×C3×D3×D411yescharacteristic
482C4—21no—
483C4—21no—
484C4—32no—
485C4—42no—
486C4—61no—
487C4—61no—
488C4—61no—
489C4—122no—
490C4—122no—
491C4C2×C3×#23711yescharacteristic
492C4C3×#100411yescharacteristic
493C3—21no—
494C3#8181311yescharacteristic, direct product factor
495C3C3×#339311yescharacteristic, complemented
496C2—82no—
497C2C3×#571811yescharacteristic
498C2C3×D3×#13511yescharacteristic
499C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#495C2
socleC22×C32C22×D4
prime radicalC2×C32×D8C22
hypercenterC3×#495D3
hypocenterC3C3×#3393
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#495

Complements

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

NH ≅ G/Ntype
1. C3×#5671C2semidirect
3. C3×#5183C2semidirect
4. C3×Dic3×Q16C2semidirect
5. C3×#5166C2semidirect
6. C3×#5162C2semidirect
9. C3×#5054C2semidirect
10. C3×C4×Dic12C2semidirect
11. C3×C8×Dic6C2semidirect
13. #81813C3direct (N × H)
42. #5671C2×C3semidirect
55. #5183C2×C3semidirect
56. Dic3×Q16C2×C3semidirect
57. #5166C2×C3semidirect
58. #5162C2×C3semidirect
61. #5054C2×C3semidirect
62. C4×Dic12C2×C3semidirect
63. C8×Dic6C2×C3semidirect
442. C32#3393semidirect
494. C3#81813direct (N × H)
495. C3C3×#3393semidirect

Maximal subgroups

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

subgroupindex
C3×#56712
C32×#4952
C3×#51832
C3×Dic3×Q162
C3×#51662
C3×#51622
C3×#51552
C3×Dic3×D82
C3×#50542
C3×C4×Dic122
C3×C8×Dic62
C3×#33933
#818133