Finite Group Databasebeta

← C3×#79589 #11860845

Subgroups — C3×#79589 #11860845

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic
2C3×#5546C212yesmaximal, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4C3×Dic3×D8C211yesmaximal, characteristic, complemented
5C3×#5018C212yesmaximal, complemented
6C3×D3×#107C211yesmaximal, characteristic, complemented
7C3×#4873C211yesmaximal, characteristic, complemented
8C3×#4771C212yesmaximal, complemented
9C3×#4757C212yesmaximal, complemented
10C3×C4×Dic12C211yesmaximal, characteristic, complemented
11C3×#4689C211yesmaximal, characteristic, complemented
12C3×#2951—31nomaximal
13#79589C311yesmaximal, characteristic, direct product factor
14C2×C3×#237C2212yes—
15C2×C32×D8C2211yescharacteristic
16C32×C4×D4C2212yes—
17C3×D4×Dic3C2212yes—
18C2×C3×#214C2212yes—
19C3×C4×#67—22no—
20C2×C3×Dic3⋊C4—22no—
21C3×#912C418yescomplemented
22C2×C3×Dic12C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×D3×C4⋊C4C2212yes—
26C3×#887C2212yes—
27C3×#67⋊C4—22no—
28C3×#877—22no—
29C3×#872C2211yescharacteristic
30C3×C4×Dic6C2212yes—
31C32×#107C2211yescharacteristic
32C32×#102C2212yes—
33C32×C4×C8C2211yescharacteristic
34C3×#832C2212yes—
35C3×#818C2211yescharacteristic
36C3×#816C2212yes—
37C3×#815C2211yescharacteristic
38C3×C8×Dic3C2211yescharacteristic
39C3×#810C2212yes—
40C3×#807C2212yes—
41C3×#803C2211yescharacteristic
42C2×C3×#135—31no—
43C3×#520—32no—
44C2×#912C2×C311yescharacteristic
45#5546C2×C312yescomplemented
46C3×#440—32no—
47C3×#440—32no—
48C3×C4×Q16—31no—
49C3×C4×Q16—31no—
50C3×C4×D8—21no—
51C3×C4×D8—31no—
52C3×C4×D8D311yescharacteristic, complemented
53C3×C4×D8C2×C311yescharacteristic, complemented
54C2×C3×#107—31no—
55C3×#417—32no—
56C3×#405—31no—
57Dic3×D8C2×C311yescharacteristic, complemented
58#5018C2×C312yescomplemented
59D3×#107C2×C311yescharacteristic, complemented
60#4873C2×C311yescharacteristic, complemented
61#4771C2×C312yescomplemented
62#4757C2×C312yescomplemented
63C4×Dic12C2×C311yescharacteristic, complemented
64#4689C2×C311yescharacteristic, complemented
65C2×C32×D4C2312yes—
66C22×C32×C4—22no—
67C2×C3×#67—22no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3—22no—
70C3×#237—24no—
71C3×#237C2×C418yescomplemented
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×Dic6C2312yes—
75C32×D8C2×C414yescomplemented
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4C2312yes—
79C32×C22⋊C4—22no—
80C32×C42C2311yescharacteristic
81C3×#217—22no—
82C3×#214C2×C418yescomplemented
83C3×(C2×D3)⋊C4D411yescharacteristic
84C3×(C2×D3)⋊C4D411yescharacteristic
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4—22no—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D411yescharacteristic
90C3×Dic3⋊C4D411yescharacteristic
91C3×C4×Dic3—22no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C3×Dic12C2×C414yescomplemented
97C3×ΓL(1,𝔽25)—22no—
98C3×D3×C8C2×C414yescomplemented
99#2951—31noSylow
100C2×C3×#41—32no—
101C2×#237C22×C312yes—
102C3×#135—38no—
103C2×C3×Q16—31no—
104C2×C3×SD16—32no—
105C2×C3×D8—21no—
106C2×C3×D8C2×D311yescharacteristic
107C2×C3×D8C22×C311yescharacteristic
108C2×C3×M16—31no—
109C22×C3×C8—31no—
110C3×C4×Q8—32no—
111C3×C4×Q8—32no—
112C3×C4×D4—22no—
113C3×C4×D4—32no—
114C3×C4×D4—62no—
115C3×C4×D4—62no—
116C3×C4×D4C2×D312yes—
117C3×C4×D4C22×C312yes—
118C3×#117—31no—
119C3×#117—62no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4—62no—
122D4×Dic3C22×C312yes—
123C2×#214C22×C312yes—
124C4×#67—22no—
125C2×Dic3⋊C4—22no—
126#912C3×C418yescomplemented
127C2×Dic12C22×C311yescharacteristic
128C2×ΓL(1,𝔽25)C22×C311yescharacteristic
129C2×D3×C8C22×C311yescharacteristic
130D3×C4⋊C4C22×C312yes—
131#887C22×C312yes—
132#67⋊C4—22no—
133#877—22no—
134#872C22×C311yescharacteristic
135C4×Dic6C22×C312yes—
136C3×#107—21no—
137C3×#107—31no—
138C3×#107—32no—
139C3×#107C2×D311yescharacteristic
140C3×#107C22×C311yescharacteristic
141C3×#103—32no—
142C3×#103—32no—
143C3×#102—22no—
144C3×#102—32no—
145C3×#102C2×D312yes—
146C3×#102C22×C312yes—
147C3×#97—31no—
148C3×#97—31no—
149C3×C4×C8—21no—
150C3×C4×C8—31no—
151C3×C4×C8C2×D311yescharacteristic
152C3×C4×C8C22×C311yescharacteristic
153#832C22×C312yes—
154#818C22×C311yescharacteristic
155#816C22×C312yes—
156#815C22×C311yescharacteristic
157C8×Dic3C22×C311yescharacteristic
158#810C22×C312yes—
159#807C22×C312yes—
160#803C22×C311yescharacteristic
161C23×C32—22no—
162C22×C3×D3C2×D411yescharacteristic
163C32×D4—22no—
164C32×D4C22×C414yes—
165C2×C32×C4—22no—
166C2×C32×C4—82no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C3×#67—28no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—28no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—82no—
175C2×C3×Dic3C2×D411yescharacteristic
176C2×C3×Dic3C2×D411yescharacteristic
177C2×C3×Dic3C2×D411yescharacteristic
178C3×C4×D3—82no—
179C3×C4×D3C22×C412yes—
180C3×C4×D3#4112yes—
181C3×Dic6—22no—
182C3×Dic6C22×C414yes—
183C32×C8—21no—
184C32×C8C22×C412yes—
185C3×C3⋊C8—21no—
186C3×C3⋊C8C22×C412yes—
187C2×#135—31no—
188#520—32no—
189#440—32no—
190#440—32no—
191C4×Q16—31no—
192C4×Q16—31no—
193C4×D8—31no—
194C4×D8C3×D311yescharacteristic, complemented
195C2×#107—31no—
196#417—32no—
197#405—31no—
198C3×#41—38no—
199C3×#41—64no—
200C2×C3×Q8—32no—
201C2×C3×D4—22no—
202C2×C3×D4—62no—
203C2×C3×D4C22×D312yes—
204C2×C3×D4C23×C312yes—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—31no—
208C22×C3×C4—42no—
209C22×C3×C4—62no—
210C22×C3×C4—62no—
211C22×C3×C4—62no—
212C2×#67—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215#237—24no—
216#237C2×C3×C418yescomplemented
217C2×C4×D3—22no—
218C2×C4×D3C23×C311yescharacteristic
219C2×Dic6C23×C312yes—
220C3×Q16—34no—
221C3×SD16—38no—
222C3×D8—24no—
223C3×D8C4×D314yescomplemented
224C3×D8C2×C3×C414yescomplemented
225C3×M16—62no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—31no—
229C2×C3×C8—34no—
230C2×C3×C8—31no—
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C23×C311yescharacteristic
234C2×C3×C8C23×C311yescharacteristic
235C3×C4⋊C4—22no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4C22×D312yes—
243C3×C4⋊C4C23×C312yes—
244C3×C22⋊C4—22no—
245C3×C22⋊C4—22no—
246C3×C22⋊C4—31no—
247C3×C22⋊C4—31no—
248C3×C22⋊C4—42no—
249C3×C22⋊C4—62no—
250C3×C42—21no—
251C3×C42—31no—
252C3×C42—62no—
253C3×C42—62no—
254C3×C42C22×D311yescharacteristic
255C3×C42C23×C311yescharacteristic
256#217—22no—
257#214C2×C3×C418yescomplemented
258(C2×D3)⋊C4C3×D411yescharacteristic
259(C2×D3)⋊C4C3×D411yescharacteristic
260C4⋊Dic3C23×C312yes—
261Dic3⋊C4—22no—
262Dic3⋊C4—22no—
263Dic3⋊C4—22no—
264Dic3⋊C4C3×D411yescharacteristic
265Dic3⋊C4C3×D411yescharacteristic
266C4×Dic3—22no—
267C4×Dic3—22no—
268C4×Dic3C23×C311yescharacteristic
269C2×C3⋊C8C23×C311yescharacteristic
270C2×C3⋊C8C23×C311yescharacteristic
271Dic12C2×C3×C414yescomplemented
272ΓL(1,𝔽25)—22no—
273D3×C8C2×C3×C414yescomplemented
274C22×C32—24no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32C22×D411yescharacteristic
278C2×C3×D3—21no—
279C2×C3×D3—21no—
280C2×C3×D3C4×D412yes—
281C32×C4—21no—
282C32×C4—21no—
283C32×C4—42no—
284C32×C4C23×C411yescharacteristic
285C32×C4C2×#4111yescharacteristic
286C3×Dic3—24no—
287C3×Dic3—21no—
288C3×Dic3—21no—
289C3×Dic3—42no—
290C3×Dic3C4×D412yes—
291C2×#41—32no—
292#135—38no—
293C2×Q16—31no—
294C2×SD16—32no—
295C2×D8C2×C3×D311yescharacteristic
296C2×M16—31no—
297C22×C8—31no—
298C4×Q8—32no—
299C4×Q8—32no—
300C4×D4—32no—
301C4×D4—62no—
302C4×D4—62no—
303C4×D4C2×C3×D312yes—
304#117—31no—
305#117—62no—
306C2×C4⋊C4—32no—
307C2×C4⋊C4—62no—
308#107—31no—
309#107—32no—
310#107C2×C3×D311yescharacteristic
311#103—32no—
312#103—32no—
313#102—32no—
314#102C2×C3×D312yes—
315#97—31no—
316#97—31no—
317C4×C8—31no—
318C4×C8C2×C3×D311yescharacteristic
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—31no—
322C23×C3—42no—
323C22×D3C2×C3×D411yescharacteristic
324C3×Q8—34no—
325C3×Q8—62no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—24no—
329C3×D4—42no—
330C3×D4—68no—
331C3×D4C2×C4×D314yes—
332C3×D4C22×C3×C414yes—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—31no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—31no—
342C2×C3×C4—31no—
343C2×C3×C4—42no—
344C2×C3×C4—68no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—82no—
348C2×C3×C4—82no—
349C2×C3×C4—84no—
350C2×C3×C4—242no—
351C2×C3×C4—242no—
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4C2×C3×D411yescharacteristic
355C2×C3×C4C2×C3×D411yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C24×C311yescharacteristic
358#67—28no—
359C2×Dic3—22no—
360C2×Dic3—28no—
361C2×Dic3—22no—
362C2×Dic3—82no—
363C2×Dic3C2×C3×D411yescharacteristic
364C2×Dic3C2×C3×D411yescharacteristic
365C2×Dic3C2×C3×D411yescharacteristic
366C4×D3—82no—
367C4×D3C22×C3×C412yes—
368C4×D3C3×#4112yes—
369Dic6—22no—
370Dic6C22×C3×C414yes—
371C3×C8—21no—
372C3×C8—21no—
373C3×C8—22no—
374C3×C8—32no—
375C3×C8—41no—
376C3×C8—61no—
377C3×C8C2×C4×D312yes—
378C3×C8C22×C3×C412yes—
379C3⋊C8—21no—
380C3⋊C8C22×C3×C412yes—
381C2×C32—44no—
382C2×C32C2×C4×D411yescharacteristic
383C2×C32#57611yescharacteristic
384C2×C32#57811yescharacteristic
385C3×D3—22no—
386#41—38no—
387#41—64no—
388C2×Q8—32no—
389C2×D4—62no—
390C2×D4C22×C3×D312yes—
391C22×C4—22no—
392C22×C4—31no—
393C22×C4—62no—
394C22×C4—62no—
395C22×C4—62no—
396Q16—34no—
397SD16—38no—
398D8C3×C4×D314yescomplemented
399M16—62no—
400C2×C8—31no—
401C2×C8—34no—
402C2×C8—31no—
403C2×C8C22×C3×D311yescharacteristic
404C2×C8C22×C3×D311yescharacteristic
405C4⋊C4—31no—
406C4⋊C4—31no—
407C4⋊C4—32no—
408C4⋊C4—62no—
409C4⋊C4—62no—
410C4⋊C4—62no—
411C4⋊C4C22×C3×D312yes—
412C22⋊C4—22no—
413C22⋊C4—31no—
414C22⋊C4—31no—
415C22⋊C4—62no—
416C42—31no—
417C42—62no—
418C42—62no—
419C42C22×C3×D311yescharacteristic
420C22×C3—24no—
421C22×C3—24no—
422C22×C3—21no—
423C22×C3—32no—
424C22×C3—44no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—61no—
430C22×C3—61no—
431C22×C3—82no—
432C22×C3—82no—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×C3×D411yescharacteristic
435C2×D3—21no—
436C2×D3—21no—
437C2×D3C3×C4×D412yes—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—32no—
446C3×C4—41no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—61no—
450C3×C4—61no—
451C3×C4—64no—
452C3×C4—82no—
453C3×C4—122no—
454C3×C4C22×C4×D311yescharacteristic
455C3×C4D3×#4111yescharacteristic
456C3×C4C23×C3×C411yescharacteristic
457C3×C4C2×C3×#4111yescharacteristic
458Dic3—21no—
459Dic3—21no—
460Dic3—24no—
461Dic3—42no—
462Dic3C3×C4×D412yes—
463C32#295111yescharacteristic, complemented, Sylow
464C23—22no—
465C23—31no—
466Q8—34no—
467Q8—62no—
468D4—22no—
469D4—68no—
470D4C2×C3×C4×D314yes—
471C2×C4—22no—
472C2×C4—31no—
473C2×C4—32no—
474C2×C4—32no—
475C2×C4—31no—
476C2×C4—31no—
477C2×C4—68no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—82no—
481C2×C4—242no—
482C2×C4—242no—
483C2×C4C3×D3×D411yescharacteristic
484C2×C4C3×D3×D411yescharacteristic
485C2×C4C23×C3×D311yescharacteristic
486C8—21no—
487C8—32no—
488C8—61no—
489C8C2×C3×C4×D312yes—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—44no—
494C2×C3—44no—
495C2×C3—62no—
496C2×C3—84no—
497C2×C3C4×D3×D411yescharacteristic
498C2×C3#575711yescharacteristic
499C2×C3#577111yescharacteristic
500C2×C3C2×C3×C4×D411yescharacteristic
501C2×C3C3×#57611yescharacteristic
502C2×C3C3×#57811yescharacteristic
503D3—22no—
504C22—24no—
505C22—32no—
506C22—42no—
507C22—42no—
508C22—61no—
509C22—61no—
510C22C2×C3×D3×D411yescharacteristic
511C4—21no—
512C4—21no—
513C4—32no—
514C4—42no—
515C4—61no—
516C4—61no—
517C4—64no—
518C4—122no—
519C4C22×C3×C4×D311yescharacteristic
520C4C3×D3×#4111yescharacteristic
521C3—21no—
522C3#7958911yescharacteristic, direct product factor
523C3C3×#295111yescharacteristic, complemented
524C2—44no—
525C2—62no—
526C2C3×C4×D3×D411yescharacteristic
527C2C3×#575711yescharacteristic
528C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
prime radicalC2×C3×#912C2
cosocleC2×C3×C4C24×C3
hypercenterC3×C4×D8D3
hypocenterC3C3×#2951
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
2. C3×#5546C2semidirect
3. C32×C4×D8C2semidirect
4. C3×Dic3×D8C2semidirect
5. C3×#5018C2semidirect
6. C3×D3×#107C2semidirect
7. C3×#4873C2semidirect
8. C3×#4771C2semidirect
9. C3×#4757C2semidirect
10. C3×C4×Dic12C2semidirect
11. C3×#4689C2semidirect
13. #79589C3direct (N × H)
21. C3×#912C4semidirect
45. #5546C2×C3semidirect
52. C3×C4×D8D3semidirect
53. C3×C4×D8C2×C3semidirect
57. Dic3×D8C2×C3semidirect
58. #5018C2×C3semidirect
59. D3×#107C2×C3semidirect
60. #4873C2×C3semidirect
61. #4771C2×C3semidirect
62. #4757C2×C3semidirect
63. C4×Dic12C2×C3semidirect
64. #4689C2×C3semidirect
71. C3×#237C2×C4semidirect
75. C32×D8C2×C4semidirect
82. C3×#214C2×C4semidirect
96. C3×Dic12C2×C4semidirect
98. C3×D3×C8C2×C4semidirect
126. #912C3×C4semidirect
194. C4×D8C3×D3semidirect
216. #237C2×C3×C4semidirect
223. C3×D8C4×D3semidirect
224. C3×D8C2×C3×C4semidirect
257. #214C2×C3×C4semidirect
271. Dic12C2×C3×C4semidirect
273. D3×C8C2×C3×C4semidirect
398. D8C3×C4×D3semidirect
463. C32#2951semidirect
522. C3#79589direct (N × H)
523. C3C3×#2951semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
C3×#55462
C32×C4×D82
C3×Dic3×D82
C3×#50182
C3×D3×#1072
C3×#48732
C3×#47712
C3×#47572
C3×C4×Dic122
C3×#46892
C3×#29513
#795893