Finite Group Databasebeta

← C3×#78694 #11857539

Subgroups — C3×#78694 #11857539

Order 1152.

1679 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
1C2×C3×#1009C211yesmaximal, characteristic
2C3×#5521C212yesmaximal, complemented
3C32×#410C211yesmaximal, characteristic, complemented
4C3×#5240C211yesmaximal, characteristic, complemented
5C3×#5006C212yesmaximal, complemented
6C3×D3×#99C218yesmaximal, complemented
7C3×#2883—31nomaximal
8#78694C311yesmaximal, characteristic, direct product factor
9C2×C32×#41C2211yescharacteristic
10C3×#1009—24no—
11C3×#1009—24no—
12C2×C3×#239C412yescomplemented
13C2×C3×D3×D4C412yescomplemented
14C2×C3×D3×D4C2214yes—
15C2×C3×#235C412yescomplemented
16C2×C3×#235C2211yescharacteristic
17C22×C3×D12C412yescomplemented
18C22×C3×D12C2211yescharacteristic
19C32×#117C2212yescomplemented
20C3×#926C2212yescomplemented
21C3×#893—24no—
22C3×D3×C22⋊C4C2218yescomplemented
23C3×C4×D12—24no—
24C32×#99C2214yescomplemented
25C3×#834C2214yescomplemented
26C3×#806C2218yescomplemented
27C2×C3×H(5,𝔽2)—31no—
28C2×#1009C2×C311yescharacteristic
29C3×#518—32no—
30#5521C2×C312yescomplemented
31C3×#410—21no—
32C3×#410—31no—
33C3×#410—32no—
34C3×#410D311yescharacteristic, complemented
35C3×#410C2×C311yescharacteristic, complemented
36C2×C3×#99—38no—
37#5240C2×C311yescharacteristic, complemented
38#5006C2×C312yescomplemented
39D3×#99C2×C318yescomplemented
40C23×C3×D3C2×C414yescomplemented
41C23×C3×D3C2312yes—
42C32×#41—22no—
43C32×#41—22no—
44C2×C32×Q8C2×C411yescharacteristic, complemented
45C2×C32×D4C2×C411yescharacteristic, complemented
46C2×C32×D4C2312yes—
47C22×C32×C4C2×C412yescomplemented
48C22×C32×C4C2311yescharacteristic
49C2×C3×#67C2×C414yescomplemented
50C2×C3×#67C2312yes—
51C3×#239—28no—
52C3×D3×D4—216no—
53C3×D3×D4—28no—
54C3×#235—22no—
55C3×#235—22no—
56C3×#235—24no—
57C3×#235—24no—
58C2×C3×D12—24no—
59C2×C3×D12—24no—
60C2×C3×D12C2×C412yes—
61C2×C3×D12C2×C412yes—
62C2×C3×D12C2×C411yescharacteristic, complemented
63C2×C3×D12C2×C414yescomplemented
64C2×C3×D12D414yes—
65C2×C3×D12D414yes—
66C2×C3×C4×D3—28no—
67C2×C3×C4×D3C2×C414yescomplemented
68C2×C3×C4×D3C2×C412yescomplemented
69C2×C3×Dic6C2×C411yescharacteristic, complemented
70C32×C4⋊C4—22no—
71C32×C22⋊C4C2314yes—
72C32×C42—22no—
73C3×#217C2314yes—
74C3×(C2×D3)⋊C4—28no—
75C3×C4⋊Dic3—22no—
76C3×C4×Dic3—22no—
77#2883—31noSylow
78C3×H(5,𝔽2)—64no—
79C3×H(5,𝔽2)—64no—
80C2×C3×#41—21no—
81C2×C3×#41—32no—
82C2×C3×#41—32no—
83C2×C3×#41—31no—
84C2×C3×#41C2×D311yescharacteristic
85C2×C3×#41C22×C311yescharacteristic
86C22×C3×D4—32no—
87C22×C3×D4—34no—
88C22×C3×D4—32no—
89C22×C3×D4—31no—
90#1009—24no—
91#1009—24no—
92C2×#239C3×C412yescomplemented
93C2×D3×D4C3×C412yescomplemented
94C2×D3×D4C22×C314yes—
95C2×#235C3×C412yescomplemented
96C2×#235C22×C311yescharacteristic
97C22×D12C3×C412yescomplemented
98C22×D12C22×C311yescharacteristic
99C3×C4×D4—64no—
100C3×C4×D4—64no—
101C3×#117—22no—
102C3×#117—32no—
103C3×#117C2×D312yescomplemented
104C3×#117C22×C312yescomplemented
105C2×C3×C22⋊C4—38no—
106#926C22×C312yescomplemented
107#893—24no—
108D3×C22⋊C4C22×C318yescomplemented
109C4×D12—24no—
110C3×#99—24no—
111C3×#99—34no—
112C3×#99—38no—
113C3×#99C2×D314yescomplemented
114C3×#99C22×C314yescomplemented
115#834C22×C314yescomplemented
116#806C22×C318yescomplemented
117C23×C32C22×C412yes—
118C23×C32C2411yescharacteristic
119C22×C3×D3—28no—
120C22×C3×D3—82no—
121C22×C3×D3—84no—
122C22×C3×D3C22×C412yes—
123C22×C3×D3C22×C414yes—
124C22×C3×D3C2×D418yes—
125C32×Q8—22no—
126C32×D4—24no—
127C32×D4—22no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—24no—
131C2×C32×C4C22×C412yes—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D412yes—
136C3×#67—24no—
137C3×#67—28no—
138C2×C3×Dic3—24no—
139C2×C3×Dic3C22×C412yes—
140C3×D12—28no—
141C3×D12—21no—
142C3×D12—21no—
143C3×D12C22⋊C414yes—
144C3×D12C22⋊C414yes—
145C3×D12C22⋊C418yes—
146C3×C4×D3—28no—
147C3×C4×D3—24no—
148C3×C4×D3—88no—
149C3×Dic6—21no—
150C3×Dic6—21no—
151C2×H(5,𝔽2)—31no—
152#518—32no—
153#410—31no—
154#410—32no—
155#410C3×D311yescharacteristic, complemented
156C2×#99—38no—
157C24×C3—32no—
158C24×C3—34no—
159C23×D3C2×C3×C414yescomplemented
160C23×D3C23×C312yes—
161C3×#41—22no—
162C3×#41—22no—
163C3×#41—22no—
164C3×#41—22no—
165C3×#41—42no—
166C3×#41—42no—
167C3×#41—64no—
168C3×#41—64no—
169C3×#41—68no—
170C3×#41—62no—
171C3×#41—62no—
172C2×C3×Q8—21no—
173C2×C3×Q8—31no—
174C2×C3×Q8C4×D311yescharacteristic, complemented
175C2×C3×Q8C2×C3×C411yescharacteristic, complemented
176C2×C3×D4—21no—
177C2×C3×D4—22no—
178C2×C3×D4—34no—
179C2×C3×D4—32no—
180C2×C3×D4—32no—
181C2×C3×D4—32no—
182C2×C3×D4—34no—
183C2×C3×D4—31no—
184C2×C3×D4—34no—
185C2×C3×D4—34no—
186C2×C3×D4—64no—
187C2×C3×D4—64no—
188C2×C3×D4—68no—
189C2×C3×D4—616no—
190C2×C3×D4C4×D311yescharacteristic, complemented
191C2×C3×D4C2×C3×C411yescharacteristic, complemented
192C2×C3×D4C22×D312yes—
193C2×C3×D4C23×C312yes—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—34no—
197C22×C3×C4—32no—
198C22×C3×C4—68no—
199C22×C3×C4C4×D312yescomplemented
200C22×C3×C4C2×C3×C412yescomplemented
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C23×C311yescharacteristic
203C2×#67C2×C3×C414yescomplemented
204C2×#67C23×C312yes—
205#239—28no—
206D3×D4—216no—
207D3×D4—28no—
208#235—22no—
209#235—22no—
210#235—24no—
211#235—24no—
212C2×D12—24no—
213C2×D12—24no—
214C2×D12C2×C3×C412yes—
215C2×D12C2×C3×C412yes—
216C2×D12C2×C3×C411yescharacteristic, complemented
217C2×D12C2×C3×C414yescomplemented
218C2×D12C3×D414yes—
219C2×D12C3×D414yes—
220C2×C4×D3—28no—
221C2×C4×D3C2×C3×C414yescomplemented
222C2×C4×D3C2×C3×C412yescomplemented
223C2×Dic6C2×C3×C411yescharacteristic, complemented
224C3×C4⋊C4—22no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—42no—
227C3×C4⋊C4—62no—
228C3×C22⋊C4—24no—
229C3×C22⋊C4—34no—
230C3×C22⋊C4—68no—
231C3×C22⋊C4C22×D314yes—
232C3×C22⋊C4C23×C314yes—
233C3×C42—22no—
234C3×C42—22no—
235C3×C42—42no—
236C3×C42—62no—
237#217C23×C314yes—
238(C2×D3)⋊C4—28no—
239C4⋊Dic3—22no—
240C4×Dic3—22no—
241C22×C32—22no—
242C22×C32—41no—
243C22×C32—42no—
244C22×C32C23×C411yescharacteristic
245C22×C32C22×D412yes—
246C2×C3×D3—22no—
247C2×C3×D3—48no—
248C2×C3×D3—44no—
249C2×C3×D3—42no—
250C2×C3×D3—88no—
251C2×C3×D3C2×C22⋊C418yes—
252C32×C4—22no—
253C32×C4—44no—
254C32×C4C2×C22⋊C411yescharacteristic
255C32×C4C2×C22⋊C411yescharacteristic
256C32×C4C2×C22⋊C412yes—
257C3×Dic3—22no—
258C3×Dic3—44no—
259H(5,𝔽2)—64no—
260H(5,𝔽2)—64no—
261C2×#41—32no—
262C2×#41—32no—
263C2×#41—31no—
264C2×#41C2×C3×D311yescharacteristic
265C22×D4—32no—
266C22×D4—34no—
267C22×D4—32no—
268C22×D4—31no—
269C4×D4—64no—
270C4×D4—64no—
271#117—32no—
272#117C2×C3×D312yescomplemented
273C2×C22⋊C4—38no—
274#99—34no—
275#99—38no—
276#99C2×C3×D314yescomplemented
277C23×C3—21no—
278C23×C3—22no—
279C23×C3—34no—
280C23×C3—38no—
281C23×C3—32no—
282C23×C3—68no—
283C23×C3—242no—
284C23×C3—244no—
285C23×C3C2×C4×D312yes—
286C23×C3C22×C3×C412yes—
287C23×C3C23×D311yescharacteristic
288C23×C3C24×C311yescharacteristic
289C22×D3—28no—
290C22×D3—82no—
291C22×D3—84no—
292C22×D3C22×C3×C412yes—
293C22×D3C22×C3×C414yes—
294C22×D3C2×C3×D418yes—
295C3×Q8—22no—
296C3×Q8—22no—
297C3×Q8—42no—
298C3×Q8—61no—
299C3×Q8—61no—
300C3×D4—24no—
301C3×D4—24no—
302C3×D4—22no—
303C3×D4—22no—
304C3×D4—34no—
305C3×D4—34no—
306C3×D4—38no—
307C3×D4—42no—
308C3×D4—44no—
309C3×D4—68no—
310C3×D4—68no—
311C3×D4—64no—
312C3×D4—61no—
313C3×D4—61no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—24no—
319C2×C3×C4—24no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—32no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—44no—
329C2×C3×C4—68no—
330C2×C3×C4—64no—
331C2×C3×C4—64no—
332C2×C3×C4—248no—
333C2×C3×C4C2×C4×D312yes—
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4D3×D412yes—
337C2×C3×C4D3×D412yes—
338C2×C3×C4C22×C3×C412yes—
339C2×C3×C4C22×C3×C411yescharacteristic
340C2×C3×C4C22×C3×C411yescharacteristic
341C2×C3×C4C2×C3×D412yes—
342C2×C3×C4C2×C3×D412yes—
343#67—24no—
344#67—28no—
345C2×Dic3—24no—
346C2×Dic3C22×C3×C412yes—
347D12—28no—
348D12—21no—
349D12—21no—
350D12C3×C22⋊C414yes—
351D12C3×C22⋊C414yes—
352D12C3×C22⋊C418yes—
353C4×D3—28no—
354C4×D3—24no—
355C4×D3—88no—
356Dic6—21no—
357Dic6—21no—
358C2×C32—22no—
359C2×C32—21no—
360C2×C32—42no—
361C2×C32C22×C22⋊C411yescharacteristic
362C3×D3—28no—
363C3×D3—42no—
364C24—32no—
365C24—34no—
366#41—22no—
367#41—22no—
368#41—64no—
369#41—64no—
370#41—68no—
371#41—62no—
372#41—62no—
373C2×Q8—31no—
374C2×Q8C3×C4×D311yescharacteristic, complemented
375C2×D4—32no—
376C2×D4—34no—
377C2×D4—32no—
378C2×D4—32no—
379C2×D4—34no—
380C2×D4—31no—
381C2×D4—34no—
382C2×D4—34no—
383C2×D4—64no—
384C2×D4—64no—
385C2×D4—68no—
386C2×D4—616no—
387C2×D4C3×C4×D311yescharacteristic, complemented
388C2×D4C22×C3×D312yes—
389C22×C4—34no—
390C22×C4—32no—
391C22×C4—68no—
392C22×C4C3×C4×D312yescomplemented
393C22×C4C22×C3×D311yescharacteristic
394C4⋊C4—22no—
395C4⋊C4—62no—
396C22⋊C4—34no—
397C22⋊C4—68no—
398C22⋊C4C22×C3×D314yes—
399C42—22no—
400C42—62no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—38no—
406C22×C3—42no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—62no—
412C22×C3—81no—
413C22×C3—82no—
414C22×C3—128no—
415C22×C3—124no—
416C22×C3—122no—
417C22×C3—248no—
418C22×C3C22×C4×D311yescharacteristic
419C22×C3C2×D3×D412yes—
420C22×C3C23×C3×C411yescharacteristic
421C22×C3C22×C3×D412yes—
422C2×D3—22no—
423C2×D3—48no—
424C2×D3—44no—
425C2×D3—42no—
426C2×D3—88no—
427C2×D3C2×C3×C22⋊C418yes—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—22no—
433C3×C4—42no—
434C3×C4—44no—
435C3×C4—44no—
436C3×C4—62no—
437C3×C4—84no—
438C3×C4—124no—
439C3×C4D3×C22⋊C411yescharacteristic
440C3×C4D3×C22⋊C411yescharacteristic
441C3×C4D3×C22⋊C412yes—
442C3×C4C2×C3×C22⋊C411yescharacteristic
443C3×C4C2×C3×C22⋊C411yescharacteristic
444C3×C4C2×C3×C22⋊C412yes—
445Dic3—22no—
446Dic3—44no—
447C32#288311yescharacteristic, complemented, Sylow
448C23—34no—
449C23—38no—
450C23—32no—
451C23—68no—
452C23—242no—
453C23—244no—
454C23C2×C3×C4×D312yes—
455C23C23×C3×D311yescharacteristic
456Q8—22no—
457Q8—61no—
458Q8—61no—
459D4—24no—
460D4—22no—
461D4—34no—
462D4—34no—
463D4—38no—
464D4—68no—
465D4—68no—
466D4—64no—
467D4—61no—
468D4—61no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—32no—
473C2×C4—68no—
474C2×C4—64no—
475C2×C4—64no—
476C2×C4—248no—
477C2×C4C2×C3×C4×D312yes—
478C2×C4C2×C3×C4×D311yescharacteristic
479C2×C4C2×C3×C4×D311yescharacteristic
480C2×C4C3×D3×D412yes—
481C2×C4C3×D3×D412yes—
482C2×C3—22no—
483C2×C3—21no—
484C2×C3—22no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—42no—
488C2×C3—41no—
489C2×C3—42no—
490C2×C3—42no—
491C2×C3—68no—
492C2×C3—82no—
493C2×C3—122no—
494C2×C3C2×D3×C22⋊C411yescharacteristic
495C2×C3C22×C3×C22⋊C411yescharacteristic
496D3—28no—
497D3—42no—
498C22—22no—
499C22—38no—
500C22—41no—
501C22—42no—
502C22—62no—
503C22—128no—
504C22—124no—
505C22—122no—
506C22—248no—
507C22C22×C3×C4×D311yescharacteristic
508C22C2×C3×D3×D412yes—
509C4—22no—
510C4—44no—
511C4—62no—
512C4—124no—
513C4C3×D3×C22⋊C411yescharacteristic
514C4C3×D3×C22⋊C411yescharacteristic
515C4C3×D3×C22⋊C412yes—
516C3—21no—
517C3#7869411yescharacteristic, direct product factor
518C3C3×#288311yescharacteristic, complemented
519C2—22no—
520C2—21no—
521C2—42no—
522C2—68no—
523C2—122no—
524C2C2×C3×D3×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C3C2×D3×C22⋊C4
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#410C2
socleC2×C32C22×C22⋊C4
prime radicalC2×C3×#1009C2
cosocleC23×C3C24×C3
hypercenterC3×#410D3
hypocenterC3C3×#2883
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#410

Complements

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

NH ≅ G/Ntype
2. C3×#5521C2semidirect
3. C32×#410C2semidirect
4. C3×#5240C2semidirect
5. C3×#5006C2semidirect
6. C3×D3×#99C2semidirect
8. #78694C3direct (N × H)
12. C2×C3×#239C4semidirect
13. C2×C3×D3×D4C4semidirect
15. C2×C3×#235C4semidirect
17. C22×C3×D12C4semidirect
19. C32×#117C22semidirect
20. C3×#926C22semidirect
22. C3×D3×C22⋊C4C22semidirect
24. C32×#99C22semidirect
25. C3×#834C22semidirect
26. C3×#806C22semidirect
30. #5521C2×C3semidirect
34. C3×#410D3semidirect
35. C3×#410C2×C3semidirect
37. #5240C2×C3semidirect
38. #5006C2×C3semidirect
39. D3×#99C2×C3semidirect
40. C23×C3×D3C2×C4semidirect
44. C2×C32×Q8C2×C4semidirect
45. C2×C32×D4C2×C4semidirect
47. C22×C32×C4C2×C4semidirect
49. C2×C3×#67C2×C4semidirect
62. C2×C3×D12C2×C4semidirect
63. C2×C3×D12C2×C4semidirect
67. C2×C3×C4×D3C2×C4semidirect
68. C2×C3×C4×D3C2×C4semidirect
69. C2×C3×Dic6C2×C4semidirect
92. C2×#239C3×C4semidirect
93. C2×D3×D4C3×C4semidirect
95. C2×#235C3×C4semidirect
97. C22×D12C3×C4semidirect
103. C3×#117C2×D3semidirect
104. C3×#117C22×C3semidirect
106. #926C22×C3semidirect
108. D3×C22⋊C4C22×C3semidirect
113. C3×#99C2×D3semidirect
114. C3×#99C22×C3semidirect
115. #834C22×C3semidirect
116. #806C22×C3semidirect
155. #410C3×D3semidirect
159. C23×D3C2×C3×C4semidirect
174. C2×C3×Q8C4×D3semidirect
175. C2×C3×Q8C2×C3×C4semidirect
190. C2×C3×D4C4×D3semidirect
191. C2×C3×D4C2×C3×C4semidirect
199. C22×C3×C4C4×D3semidirect
200. C22×C3×C4C2×C3×C4semidirect
203. C2×#67C2×C3×C4semidirect
216. C2×D12C2×C3×C4semidirect
217. C2×D12C2×C3×C4semidirect
221. C2×C4×D3C2×C3×C4semidirect
222. C2×C4×D3C2×C3×C4semidirect
223. C2×Dic6C2×C3×C4semidirect
272. #117C2×C3×D3semidirect
276. #99C2×C3×D3semidirect
374. C2×Q8C3×C4×D3semidirect
387. C2×D4C3×C4×D3semidirect
392. C22×C4C3×C4×D3semidirect
447. C32#2883semidirect
517. C3#78694direct (N × H)
518. C3C3×#2883semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C3×#55212
C32×#4102
C3×#52402
C3×#50062
C3×D3×#992
C3×#28833
#786943