Finite Group Databasebeta

← C3×#69509 #11775567

Subgroups — C3×#69509 #11775567

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C32×#380C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C3×#4451C214yesmaximal, complemented
5C3×#1519—31nomaximal
6#69509C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C22×C3×#67—21no—
9C22×C3×D12C411yescharacteristic, complemented
10C2×C32×C4⋊C4—21no—
11C2×C32×C22⋊C4—21no—
12C3×#930—21no—
13C3×#930—21no—
14C3×#930C412yescomplemented
15C3×#930C2212yes—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C411yescharacteristic, complemented
18C22×C3×C3⋊C8—21no—
19C32×#95C2212yescomplemented
20C3×#830—21no—
21C3×#830C2212yescomplemented
22C2×C3×#121—31no—
23C2×#930C2×C311yescharacteristic
24C2×C3×C22⋊C8—31no—
25C3×#380—21no—
26C3×#380D311yescharacteristic, complemented
27C3×#380C2×C311yescharacteristic, complemented
28C2×#830C2×C311yescharacteristic, complemented
29C3×#327—34no—
30#4451C2×C314yescomplemented
31C24×C32D411yescharacteristic
32C23×C3×D3—21no—
33C22×C32×C4—22no—
34C22×C32×C4—42no—
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—22no—
42C2×C3×#67—22no—
43C2×C3×#67—42no—
44C2×C3×#67—42no—
45C22×C3×Dic3—21no—
46C2×C3×D12—21no—
47C2×C3×D12—42no—
48C2×C3×D12C2×C412yes—
49C32×C4⋊C4—42no—
50C32×C22⋊C4—42no—
51C3×(C2×D3)⋊C4—22no—
52C3×(C2×D3)⋊C4—22no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3C2×C412yes—
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—42no—
57#1519—31noSylow
58C22×C3×D4—31no—
59C22×C3×D4—61no—
60C23×C3×C4—21no—
61C23×C3×C4C2×D311yescharacteristic
62C23×C3×C4C22×C311yescharacteristic
63C22×#67—21no—
64C22×D12C3×C411yescharacteristic, complemented
65C22×C3×C8—61no—
66C3×#121—32no—
67C3×#121—32no—
68C3×#121—61no—
69C3×#121—61no—
70C2×C3×C4⋊C4—22no—
71C2×C3×C4⋊C4—21no—
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C22⋊C4—22no—
75C2×C3×C22⋊C4—21no—
76C2×C3×C22⋊C4—21no—
77C2×C3×C22⋊C4—61no—
78#930—21no—
79#930—21no—
80#930C3×C412yescomplemented
81#930C22×C312yes—
82C2×(C2×D3)⋊C4—21no—
83C2×C4⋊Dic3C3×C411yescharacteristic, complemented
84C22×C3⋊C8—21no—
85C3×C22⋊C8—32no—
86C3×C22⋊C8—61no—
87C3×#95—22no—
88C3×#95C2×D312yescomplemented
89C3×#95C22×C312yescomplemented
90#830—21no—
91#830C22×C312yescomplemented
92C23×C32—41no—
93C23×C32—41no—
94C23×C32C22⋊C411yescharacteristic
95C23×C32C22⋊C411yescharacteristic
96C23×C32D812yes—
97C23×C32SD1612yes—
98C23×C32C2×D411yescharacteristic
99C22×C3×D3—22no—
100C22×C3×D3—42no—
101C22×C3×D3—42no—
102C22×C3×D3—42no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4—42no—
110C2×C32×C4—42no—
111C2×C32×C4—42no—
112C2×C32×C4C22⋊C411yescharacteristic
113C2×C32×C4C22⋊C411yescharacteristic
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C3×#67—44no—
117C3×#67—42no—
118C3×#67—42no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—42no—
121C3×D12—42no—
122C3×D12—42no—
123C3×C3⋊C8—42no—
124C2×#121—31no—
125C2×C22⋊C8—31no—
126#380C3×D311yescharacteristic, complemented
127#327—34no—
128C24×C3—21no—
129C24×C3—61no—
130C24×C3#6711yescharacteristic
131C24×C3C3×D411yescharacteristic
132C23×D3—21no—
133C2×C3×D4—32no—
134C2×C3×D4—62no—
135C2×C3×D4—62no—
136C2×C3×D4—61no—
137C2×C3×D4—122no—
138C2×C3×D4—122no—
139C2×C3×D4—122no—
140C22×C3×C4—24no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—42no—
150C22×C3×C4—42no—
151C22×C3×C4—44no—
152C22×C3×C4—61no—
153C22×C3×C4C4×D311yescharacteristic
154C22×C3×C4C4×D311yescharacteristic
155C22×C3×C4D1211yescharacteristic
156C22×C3×C4D1211yescharacteristic
157C22×C3×C4#6711yescharacteristic
158C22×C3×C4C2×C3×C411yescharacteristic
159C22×C3×C4C2×C3×C411yescharacteristic
160C22×C3×C4C3×D411yescharacteristic
161C22×C3×C4C3×D411yescharacteristic
162C22×C3×C4C3×D411yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C23×C311yescharacteristic
165C2×#67—22no—
166C2×#67—22no—
167C2×#67—42no—
168C2×#67—42no—
169C22×Dic3—21no—
170C2×D12—21no—
171C2×D12—42no—
172C2×D12C2×C3×C412yes—
173C2×C3×C8—62no—
174C2×C3×C8—122no—
175C3×C4⋊C4—32no—
176C3×C4⋊C4—44no—
177C3×C4⋊C4—42no—
178C3×C4⋊C4—42no—
179C3×C4⋊C4—61no—
180C3×C22⋊C4—44no—
181C3×C22⋊C4—42no—
182C3×C22⋊C4—42no—
183C3×C22⋊C4—62no—
184C3×C22⋊C4—62no—
185(C2×D3)⋊C4—22no—
186(C2×D3)⋊C4—22no—
187C4⋊Dic3—21no—
188C4⋊Dic3C2×C3×C412yes—
189C2×C3⋊C8—22no—
190C2×C3⋊C8—42no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—21no—
197C22×C32—42no—
198C22×C32—42no—
199C22×C32#10212yes—
200C22×C32#10212yes—
201C22×C32C2×C22⋊C411yescharacteristic
202C22×C32C2×D811yescharacteristic
203C22×C32C2×SD1611yescharacteristic
204C2×C3×D3—42no—
205C2×C3×D3—42no—
206C2×C3×D3—42no—
207C2×C3×D3—84no—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4—21no—
211C32×C4—82no—
212C32×C4#9912yes—
213C3×Dic3—42no—
214C22×D4—31no—
215C22×D4—61no—
216C23×C4C2×C3×D311yescharacteristic
217C22×C8—61no—
218#121—32no—
219#121—32no—
220#121—61no—
221#121—61no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—31no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—61no—
226C22⋊C8—32no—
227C22⋊C8—61no—
228#95C2×C3×D312yescomplemented
229C23×C3—21no—
230C23×C3—21no—
231C23×C3—22no—
232C23×C3—22no—
233C23×C3—21no—
234C23×C3—41no—
235C23×C3—41no—
236C23×C3—41no—
237C23×C3—41no—
238C23×C3—42no—
239C23×C3—42no—
240C23×C3—62no—
241C23×C3—122no—
242C23×C3—122no—
243C23×C3—122no—
244C23×C3(C2×D3)⋊C411yescharacteristic
245C23×C3(C2×D3)⋊C411yescharacteristic
246C23×C3#21312yes—
247C23×C3#21512yes—
248C23×C3C3×C22⋊C411yescharacteristic
249C23×C3C3×C22⋊C411yescharacteristic
250C23×C3C3×D812yes—
251C23×C3C3×SD1612yes—
252C23×C3C2×#6711yescharacteristic
253C23×C3C2×C3×D411yescharacteristic
254C22×D3—22no—
255C22×D3—42no—
256C22×D3—42no—
257C22×D3—42no—
258C3×D4—122no—
259C3×D4—124no—
260C3×D4—122no—
261C3×D4—122no—
262C3×D4—122no—
263C2×C3×C4—24no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—42no—
275C2×C3×C4—42no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—44no—
286C2×C3×C4—44no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—44no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—62no—
295C2×C3×C4—122no—
296C2×C3×C4(C2×D3)⋊C411yescharacteristic
297C2×C3×C4(C2×D3)⋊C411yescharacteristic
298C2×C3×C4C3×C22⋊C411yescharacteristic
299C2×C3×C4C3×C22⋊C411yescharacteristic
300C2×C3×C4C2×C4×D311yescharacteristic
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4C22×C3×C411yescharacteristic
303C2×C3×C4C2×C3×D411yescharacteristic
304#67—44no—
305#67—42no—
306#67—42no—
307C2×Dic3—22no—
308C2×Dic3—42no—
309D12—42no—
310D12—42no—
311C3×C8—122no—
312C3⋊C8—42no—
313C2×C32—21no—
314C2×C32—21no—
315C2×C32—22no—
316C2×C32—22no—
317C2×C32C2×#9911yescharacteristic
318C2×C32C2×#10211yescharacteristic
319C2×C32#42111yescharacteristic
320C3×D3—82no—
321C24—61no—
322C24C3×#6711yescharacteristic
323C2×D4—32no—
324C2×D4—62no—
325C2×D4—62no—
326C2×D4—61no—
327C2×D4—122no—
328C2×D4—122no—
329C2×D4—122no—
330C22×C4—22no—
331C22×C4—42no—
332C22×C4—61no—
333C22×C4C3×C4×D311yescharacteristic
334C22×C4C3×C4×D311yescharacteristic
335C22×C4C3×D1211yescharacteristic
336C22×C4C3×D1211yescharacteristic
337C22×C4C3×#6711yescharacteristic
338C22×C4C22×C3×D311yescharacteristic
339C2×C8—62no—
340C2×C8—122no—
341C4⋊C4—32no—
342C4⋊C4—42no—
343C4⋊C4—61no—
344C22⋊C4—42no—
345C22⋊C4—62no—
346C22⋊C4—62no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—44no—
375C22×C3—44no—
376C22×C3—122no—
377C22×C3—122no—
378C22×C3—122no—
379C22×C3—244no—
380C22×C3#80912yes—
381C22×C3#80912yes—
382C22×C3C3×#10212yes—
383C22×C3C3×#10212yes—
384C22×C3C2×(C2×D3)⋊C411yescharacteristic
385C22×C3C2×#21311yescharacteristic
386C22×C3C2×#21511yescharacteristic
387C22×C3C2×C3×C22⋊C411yescharacteristic
388C22×C3C2×C3×D811yescharacteristic
389C22×C3C2×C3×SD1611yescharacteristic
390C2×D3—42no—
391C2×D3—42no—
392C2×D3—42no—
393C2×D3—84no—
394C3×C4—22no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—22no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—84no—
405C3×C4—82no—
406C3×C4—82no—
407C3×C4—122no—
408C3×C4#80612yes—
409C3×C4C3×#9912yes—
410Dic3—42no—
411C32#151911yescharacteristic, complemented, Sylow
412C23—41no—
413C23—41no—
414C23—62no—
415C23—122no—
416C23—122no—
417C23—122no—
418C23C3×(C2×D3)⋊C411yescharacteristic
419C23C3×(C2×D3)⋊C411yescharacteristic
420C23C3×#21312yes—
421C23C3×#21512yes—
422C23C2×C3×#6711yescharacteristic
423D4—122no—
424D4—122no—
425D4—122no—
426D4—124no—
427D4—122no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—62no—
438C2×C4—122no—
439C2×C4C3×(C2×D3)⋊C411yescharacteristic
440C2×C4C3×(C2×D3)⋊C411yescharacteristic
441C2×C4C2×C3×C4×D311yescharacteristic
442C2×C4C2×C3×D1211yescharacteristic
443C8—122no—
444C2×C3—22no—
445C2×C3—22no—
446C2×C3—21no—
447C2×C3—22no—
448C2×C3—22no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—42no—
458C2×C3—42no—
459C2×C3—242no—
460C2×C3C2×#80611yescharacteristic
461C2×C3C2×#80911yescharacteristic
462C2×C3#500511yescharacteristic
463C2×C3C2×C3×#9911yescharacteristic
464C2×C3C2×C3×#10211yescharacteristic
465C2×C3C3×#42111yescharacteristic
466D3—82no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—42no—
474C22—42no—
475C22—122no—
476C22—122no—
477C22—122no—
478C22—244no—
479C22C3×#80912yes—
480C22C3×#80912yes—
481C22C2×C3×(C2×D3)⋊C411yescharacteristic
482C22C2×C3×#21311yescharacteristic
483C22C2×C3×#21511yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—82no—
488C4—122no—
489C4C3×#80612yes—
490C3—21no—
491C3#6950911yescharacteristic, direct product factor
492C3C3×#151911yescharacteristic, complemented
493C2—21no—
494C2—22no—
495C2—21no—
496C2—22no—
497C2—242no—
498C2C2×C3×#80611yescharacteristic
499C2C2×C3×#80911yescharacteristic
500C2C3×#500511yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#380C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#930C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#380D3
hypocenterC3C3×#1519
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
2. C32×#380C2semidirect
3. C2×C3×#830C2semidirect
4. C3×#4451C2semidirect
6. #69509C3direct (N × H)
9. C22×C3×D12C4semidirect
14. C3×#930C4semidirect
17. C2×C3×C4⋊Dic3C4semidirect
19. C32×#95C22semidirect
21. C3×#830C22semidirect
26. C3×#380D3semidirect
27. C3×#380C2×C3semidirect
28. C2×#830C2×C3semidirect
30. #4451C2×C3semidirect
64. C22×D12C3×C4semidirect
80. #930C3×C4semidirect
83. C2×C4⋊Dic3C3×C4semidirect
88. C3×#95C2×D3semidirect
89. C3×#95C22×C3semidirect
91. #830C22×C3semidirect
126. #380C3×D3semidirect
228. #95C2×C3×D3semidirect
411. C32#1519semidirect
491. C3#69509direct (N × H)
492. C3C3×#1519semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C32×#3802
C2×C3×#8302
C3×#44512
C3×#15193
#695093