Finite Group Databasebeta

← C3×#80370 #11895634

Subgroups — C3×#80370 #11895634

Order 1152.

760 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5713C211yesmaximal, characteristic
2C3×#5570C211yesmaximal, characteristic, complemented
3C32×#460C211yesmaximal, characteristic
4C3×#5166C212yesmaximal, complemented
5C3×Dic3×SD16C212yesmaximal, complemented
6C3×#5070C211yesmaximal, characteristic
7C3×C4×#216C211yesmaximal, characteristic, complemented
8C3×#4851C211yesmaximal, characteristic, complemented
9C3×#4830C211yesmaximal, characteristic, complemented
10C3×#4768C212yesmaximal, complemented
11C3×#4763C212yesmaximal, complemented
12C3×#3365—31nomaximal
13#80370C311yesmaximal, characteristic, direct product factor
14C2×C32×SD16C2212yes—
15C32×#127C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C3×Q8×Dic3C2212yes—
18C2×C3×#216C2211yescharacteristic
19C3×#936—21no—
20C3×#936C2212yes—
21C3×#935—22no—
22C3×D4×Dic3—21no—
23C3×D4×Dic3C2212yes—
24C3×#890—22no—
25C3×#890C2212yes—
26C3×#869—21no—
27C3×#869C2211yescharacteristic
28C3×C4×Dic6—21no—
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32C32×#102C2212yes—
33C3×#835C2211yescharacteristic
34C3×#832C2212yes—
35C3×#832C2212yes—
36C3×#817C2212yes—
37C3×#816C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#810C2211yescharacteristic
41C3×#807C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#559—31no—
44C3×#557—31no—
45#5713C2×C311yescharacteristic
46#5570C2×C311yescharacteristic, complemented
47C3×#488—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#475—31no—
51C3×#464—32no—
52C3×#460—21no—
53C3×#460D311yescharacteristic
54C3×#460C2×C311yescharacteristic
55C3×C8×Q8—31no—
56C3×C4×Q16—31no—
57C3×C4×SD16—32no—
58#5166C2×C312yescomplemented
59Dic3×SD16C2×C312yescomplemented
60#5070C2×C311yescharacteristic
61C4×#216C2×C311yescharacteristic, complemented
62#4851C2×C311yescharacteristic, complemented
63#4830C2×C311yescharacteristic, complemented
64#4768C2×C312yescomplemented
65#4763C2×C312yescomplemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4C2312yes—
70C22×C3×Dic3—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C32×SD16—24no—
75C2×C32×C8C2312yes—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C42—21no—
79C32×C42C2311yescharacteristic
80C3×#217—22no—
81C3×#217—22no—
82C3×#217—22no—
83C3×#216—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3—21no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3365—31noSylow
99C2×C3×Q16—31no—
100C2×C3×SD16—22no—
101C2×C3×SD16C2×D312yes—
102C2×C3×SD16C22×C312yes—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—61no—
105C3×#127—21no—
106C3×#127C2×D311yescharacteristic
107C3×#127C22×C311yescharacteristic
108C3×#125—32no—
109C3×#125—62no—
110C3×#124—32no—
111C3×#124—61no—
112C3×#123—62no—
113C3×C4×Q8—21no—
114C3×C4×Q8—31no—
115C3×C4×Q8—32no—
116C3×C4×Q8—31no—
117C3×C4×Q8—61no—
118C3×C4×Q8C2×D311yescharacteristic
119C3×C4×Q8C22×C311yescharacteristic
120C3×C4×D4—32no—
121C3×C4×D4—61no—
122Q8×Dic3C22×C312yes—
123C2×#216C22×C311yescharacteristic
124#936—21no—
125#936C22×C312yes—
126#935—22no—
127D4×Dic3—21no—
128D4×Dic3C22×C312yes—
129#890—22no—
130#890C22×C312yes—
131#869—21no—
132#869C22×C311yescharacteristic
133C4×Dic6—21no—
134C4×Dic6C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#107—31no—
137C3×#106—32no—
138C3×C4⋊C8—21no—
139C3×C4⋊C8—32no—
140C3×C4⋊C8C2×D311yescharacteristic
141C3×C4⋊C8C22×C311yescharacteristic
142C3×#103—31no—
143C3×#103—32no—
144C3×#103—31no—
145C3×#102—22no—
146C3×#102—32no—
147C3×#102—32no—
148C3×#102C2×D312yes—
149C3×#102C22×C312yes—
150C3×C4×C8—32no—
151C3×C4×C8—31no—
152#835C22×C311yescharacteristic
153#832C22×C312yes—
154#832C22×C312yes—
155#817C22×C312yes—
156#816C22×C312yes—
157Dic3⋊C8C22×C312yes—
158C8×Dic3C22×C312yes—
159#810C22×C311yescharacteristic
160#807C22×C311yescharacteristic
161C4×C3⋊C8C22×C311yescharacteristic
162C23×C32—22no—
163C32×Q8—21no—
164C32×Q8#4112yes—
165C32×D4—22no—
166C32×D4—22no—
167C32×D4—42no—
168C32×D4—81no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—82no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×Dic6—22no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6—42no—
184C32×C8—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#559—31no—
188#557—31no—
189#488—32no—
190#486—31no—
191#478—32no—
192#475—31no—
193#464—32no—
194#460C3×D311yescharacteristic
195C8×Q8—31no—
196C4×Q16—31no—
197C4×SD16—32no—
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8—31no—
201C2×C3×Q8—61no—
202C2×C3×Q8C22×D311yescharacteristic
203C2×C3×Q8C23×C311yescharacteristic
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—22no—
209C2×C3×D4—41no—
210C2×C3×D4—41no—
211C2×C3×D4C22×D312yes—
212C2×C3×D4C23×C312yes—
213C22×C3×C4—62no—
214C22×Dic3—22no—
215C2×Dic6—21no—
216C2×Dic6C3×D411yescharacteristic
217C2×Dic6C23×C311yescharacteristic
218C3×Q16—62no—
219C3×SD16—24no—
220C3×SD16—24no—
221C3×SD16—44no—
222C2×C3×C8—22no—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C2×C3×C8C22×D312yes—
226C2×C3×C8C23×C312yes—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C4⋊C4C23×C311yescharacteristic
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—62no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—21no—
248C3×C42—32no—
249C3×C42—41no—
250C3×C42—62no—
251C3×C42—61no—
252C3×C42C22×D311yescharacteristic
253C3×C42C23×C311yescharacteristic
254#217—22no—
255#217—22no—
256#217—22no—
257#216—22no—
258C4⋊Dic3—21no—
259C4⋊Dic3—22no—
260C4⋊Dic3—22no—
261C4⋊Dic3C3×D411yescharacteristic
262C4⋊Dic3C23×C311yescharacteristic
263C4⋊Dic3C23×C312yes—
264Dic3⋊C4—21no—
265Dic3⋊C4—22no—
266Dic3⋊C4C3×D412yes—
267C4×Dic3—21no—
268C4×Dic3—22no—
269C4×Dic3C23×C312yes—
270C2×C3⋊C8C23×C311yescharacteristic
271C2×C3⋊C8C23×C311yescharacteristic
272C22×C32—42no—
273C22×C32—42no—
274C22×C32—42no—
275C22×C32C22×D411yescharacteristic
276C32×C4—22no—
277C32×C4—21no—
278C32×C4—41no—
279C32×C4#13512yes—
280C32×C4C2×#4111yescharacteristic
281C32×C42−1+411yescharacteristic
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—41no—
285C3×Dic3—42no—
286C3×Dic3—41no—
287C2×Q16—31no—
288C2×SD16C2×C3×D312yes—
289C4⋊Q8—31no—
290C4⋊Q8—61no—
291#127C2×C3×D311yescharacteristic
292#125—32no—
293#125—62no—
294#124—32no—
295#124—61no—
296#123—62no—
297C4×Q8—31no—
298C4×Q8—32no—
299C4×Q8—31no—
300C4×Q8—61no—
301C4×Q8C2×C3×D311yescharacteristic
302C4×D4—32no—
303C4×D4—61no—
304#107—31no—
305#106—32no—
306C4⋊C8—32no—
307C4⋊C8C2×C3×D311yescharacteristic
308#103—31no—
309#103—32no—
310#103—31no—
311#102—32no—
312#102—32no—
313#102C2×C3×D312yes—
314C4×C8—32no—
315C4×C8—31no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—42no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—22no—
322C3×Q8—41no—
323C3×Q8—62no—
324C3×Q8—61no—
325C3×Q8—61no—
326C3×Q8—122no—
327C3×Q8#23712yes—
328C3×Q8C3×#4112yes—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—42no—
334C3×D4—42no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—82no—
338C3×D4—81no—
339C3×D4—81no—
340C3×D4—82no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—242no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C2×C3×D411yescharacteristic
359C2×C3×C4C2×C3×D411yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×C3×C4C24×C311yescharacteristic
362C2×Dic3—22no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—82no—
366C2×Dic3C2×C3×D412yes—
367C2×Dic3C2×C3×D412yes—
368Dic6—22no—
369Dic6—21no—
370Dic6—21no—
371Dic6—42no—
372C3×C8—22no—
373C3×C8—22no—
374C3×C8—42no—
375C3×C8—61no—
376C3×C8—61no—
377C3⋊C8—21no—
378C3⋊C8—21no—
379C2×C32—82no—
380C2×C32#54811yescharacteristic
381C2×C32C2×#13511yescharacteristic
382C2×C32#57711yescharacteristic
383C2×Q8—31no—
384C2×Q8—31no—
385C2×Q8—61no—
386C2×Q8C22×C3×D311yescharacteristic
387C2×D4—21no—
388C2×D4—21no—
389C2×D4C22×C3×D312yes—
390C22×C4—62no—
391Q16—62no—
392SD16—24no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8C22×C3×D312yes—
396C4⋊C4—21no—
397C4⋊C4—31no—
398C4⋊C4—32no—
399C4⋊C4—32no—
400C4⋊C4—31no—
401C4⋊C4—62no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—61no—
405C4⋊C4—61no—
406C4⋊C4C22×C3×D311yescharacteristic
407C22⋊C4—62no—
408C22⋊C4—62no—
409C22⋊C4—62no—
410C42—21no—
411C42—32no—
412C42—62no—
413C42—61no—
414C42C22×C3×D311yescharacteristic
415C22×C3—21no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—82no—
423C22×C3—82no—
424C22×C3—82no—
425C22×C3C2×D3×D411yescharacteristic
426C22×C3C22×C3×D411yescharacteristic
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—41no—
435C3×C4—42no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—62no—
439C3×C4—62no—
440C3×C4—81no—
441C3×C4—122no—
442C3×C4—121no—
443C3×C4—121no—
444C3×C4#91612yes—
445C3×C4C3×#13512yes—
446C3×C4C2×#23711yescharacteristic
447C3×C4#101011yescharacteristic
448C3×C4C2×C3×#4111yescharacteristic
449C3×C4C3×2−1+411yescharacteristic
450Dic3—22no—
451Dic3—22no—
452Dic3—42no—
453Dic3—41no—
454Dic3—41no—
455C32#336511yescharacteristic, complemented, Sylow
456C23—22no—
457Q8—21no—
458Q8—62no—
459Q8—61no—
460Q8—61no—
461Q8—122no—
462Q8C3×#23712yes—
463D4—22no—
464D4—22no—
465D4—42no—
466D4—81no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—242no—
475C2×C4C3×D3×D411yescharacteristic
476C2×C4C3×D3×D411yescharacteristic
477C2×C4C23×C3×D311yescharacteristic
478C8—22no—
479C8—61no—
480C8—61no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—82no—
485C2×C3—82no—
486C2×C3—162no—
487C2×C3#559811yescharacteristic
488C2×C3C2×#91611yescharacteristic
489C2×C3#577511yescharacteristic
490C2×C3C3×#54811yescharacteristic
491C2×C3C2×C3×#13511yescharacteristic
492C2×C3C3×#57711yescharacteristic
493C22—42no—
494C22—42no—
495C22—42no—
496C22C2×C3×D3×D411yescharacteristic
497C4—21no—
498C4—22no—
499C4—41no—
500C4—62no—
501C4—62no—
502C4—122no—
503C4—121no—
504C4—121no—
505C4C3×#91612yes—
506C4C2×C3×#23711yescharacteristic
507C4C3×#101011yescharacteristic
508C3—21no—
509C3#8037011yescharacteristic, direct product factor
510C3C3×#336511yescharacteristic, complemented
511C2—82no—
512C2C3×#559811yescharacteristic
513C2C2×C3×#91611yescharacteristic
514C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#460C2
socleC22×C32C22×D4
prime radicalC32×#127C22
hypercenterC3×#460D3
hypocenterC3C3×#3365
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
2. C3×#5570C2semidirect
4. C3×#5166C2semidirect
5. C3×Dic3×SD16C2semidirect
7. C3×C4×#216C2semidirect
8. C3×#4851C2semidirect
9. C3×#4830C2semidirect
10. C3×#4768C2semidirect
11. C3×#4763C2semidirect
13. #80370C3direct (N × H)
46. #5570C2×C3semidirect
58. #5166C2×C3semidirect
59. Dic3×SD16C2×C3semidirect
61. C4×#216C2×C3semidirect
62. #4851C2×C3semidirect
63. #4830C2×C3semidirect
64. #4768C2×C3semidirect
65. #4763C2×C3semidirect
455. C32#3365semidirect
509. C3#80370direct (N × H)
510. C3C3×#3365semidirect

Maximal subgroups

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

subgroupindex
C3×#57132
C3×#55702
C32×#4602
C3×#51662
C3×Dic3×SD162
C3×#50702
C3×C4×#2162
C3×#48512
C3×#48302
C3×#47682
C3×#47632
C3×#33653
#803703