Finite Group Databasebeta

← C3×#69967 #11773849

Subgroups — C3×#69967 #11773849

Order 1152.

975 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4C3×#4468C214yesmaximal, complemented
5C3×#1462—31nomaximal
6#69967C311yesmaximal, characteristic, direct product factor
7C24×C3×D3C411yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C23×C3×Dic3C411yescharacteristic
10C2×C32×M16—21no—
11C2×C3×(C2×D3)⋊C4—21no—
12C2×C3×(C2×D3)⋊C4—21no—
13C2×C3×(C2×D3)⋊C4—21no—
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4C412yes—
16C2×C3×(C2×D3)⋊C4C2212yes—
17C2×C3×#208—21no—
18C32×C22⋊C8—21no—
19C32×C22⋊C8C2212yescomplemented
20C3×#830—21no—
21C3×#830C2212yescomplemented
22C22×C3×C22⋊C4—31no—
23C22×(C2×D3)⋊C4C2×C311yescharacteristic
24C3×#407—21no—
25C3×#407—31no—
26C3×#407D311yescharacteristic, complemented
27C3×#407C2×C311yescharacteristic, complemented
28#5207C2×C311yescharacteristic, complemented
29C3×#323—34no—
30#4468C2×C314yescomplemented
31C24×C32C2×C411yescharacteristic
32C23×C3×D3—21no—
33C23×C3×D3—21no—
34C23×C3×D3—24no—
35C23×C3×D3—42no—
36C23×C3×D3—42no—
37C23×C3×D3C2×C412yes—
38C22×C32×C4—42no—
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—42no—
48C22×C3×Dic3C2×C412yes—
49C32×M16—42no—
50C2×C32×C8—22no—
51C3×(C2×D3)⋊C4—22no—
52C3×(C2×D3)⋊C4—22no—
53C3×(C2×D3)⋊C4—22no—
54C3×(C2×D3)⋊C4—22no—
55C3×#208—42no—
56C2×C3×C3⋊C8—22no—
57#1462—31noSylow
58C25×C3—31no—
59C24×D3C3×C411yescharacteristic
60C23×C3×C4—21no—
61C23×C3×C4—31no—
62C23×C3×C4C2×D311yescharacteristic
63C23×C3×C4C22×C311yescharacteristic
64C23×Dic3C3×C411yescharacteristic
65C2×C3×M16—22no—
66C2×C3×M16—21no—
67C2×C3×M16—21no—
68C2×C3×M16—61no—
69C2×C3×C22⋊C4—32no—
70C2×C3×C22⋊C4—32no—
71C2×C3×C22⋊C4—61no—
72C2×C3×C22⋊C4—61no—
73C2×C3×C22⋊C4—61no—
74C2×C3×C22⋊C4—61no—
75C2×(C2×D3)⋊C4—21no—
76C2×(C2×D3)⋊C4—21no—
77C2×(C2×D3)⋊C4—21no—
78C2×(C2×D3)⋊C4—21no—
79C2×(C2×D3)⋊C4C3×C412yes—
80C2×(C2×D3)⋊C4C22×C312yes—
81C2×#208—21no—
82C3×C22⋊C8—22no—
83C3×C22⋊C8—21no—
84C3×C22⋊C8—21no—
85C3×C22⋊C8—22no—
86C3×C22⋊C8—32no—
87C3×C22⋊C8—61no—
88C3×C22⋊C8C2×D312yescomplemented
89C3×C22⋊C8C22×C312yescomplemented
90#830—21no—
91#830C22×C312yescomplemented
92C23×C32—22no—
93C23×C32—22no—
94C23×C32—22no—
95C23×C32C22⋊C411yescharacteristic
96C23×C32C22⋊C411yescharacteristic
97C23×C32C22×C411yescharacteristic
98C22×C3×D3—24no—
99C22×C3×D3—24no—
100C22×C3×D3—22no—
101C22×C3×D3—22no—
102C22×C3×D3—416no—
103C22×C3×D3—42no—
104C22×C3×D3—42no—
105C22×C3×D3—42no—
106C22×C3×D3—42no—
107C22×C3×D3—42no—
108C22×C3×D3—42no—
109C22×C3×D3M1614yescomplemented
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4C22⋊C411yescharacteristic
117C2×C32×C4C22⋊C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3×Dic3—22no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—42no—
124C32×C8—42no—
125C3×C3⋊C8—42no—
126C22×C22⋊C4—31no—
127#407—31no—
128#407C3×D311yescharacteristic, complemented
129#323—34no—
130C24×C3—21no—
131C24×C3—32no—
132C24×C3—64no—
133C24×C3—61no—
134C24×C3—61no—
135C24×C3—122no—
136C24×C3—122no—
137C24×C3C4×D311yescharacteristic
138C24×C3C2×C3×C411yescharacteristic
139C23×D3—21no—
140C23×D3—21no—
141C23×D3—24no—
142C23×D3—42no—
143C23×D3—42no—
144C23×D3C2×C3×C412yes—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—32no—
152C22×C3×C4—42no—
153C22×C3×C4—42no—
154C22×C3×C4—44no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4—122no—
158C22×C3×C4C4×D311yescharacteristic
159C22×C3×C4D1211yescharacteristic
160C22×C3×C4D1211yescharacteristic
161C22×C3×C4#6711yescharacteristic
162C22×C3×C4#6711yescharacteristic
163C22×C3×C4C2×C3×C411yescharacteristic
164C22×C3×C4C3×D411yescharacteristic
165C22×C3×C4C3×D411yescharacteristic
166C22×C3×C4C3×D411yescharacteristic
167C22×C3×C4C3×D411yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C23×C311yescharacteristic
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—42no—
173C22×Dic3C2×C3×C412yes—
174C3×M16—44no—
175C3×M16—42no—
176C3×M16—42no—
177C3×M16—122no—
178C2×C3×C8—24no—
179C2×C3×C8—22no—
180C2×C3×C8—22no—
181C2×C3×C8—62no—
182C3×C22⋊C4—62no—
183C3×C22⋊C4—62no—
184C3×C22⋊C4—62no—
185C3×C22⋊C4—62no—
186(C2×D3)⋊C4—22no—
187(C2×D3)⋊C4—22no—
188(C2×D3)⋊C4—22no—
189(C2×D3)⋊C4—22no—
190#208—42no—
191C2×C3⋊C8—22no—
192C22×C32—28no—
193C22×C32—21no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32—21no—
199C22×C32#9912yes—
200C22×C32#10012yes—
201C22×C32C2×C22⋊C411yescharacteristic
202C22×C32C2×M1612yes—
203C2×C3×D3—24no—
204C2×C3×D3—48no—
205C2×C3×D3—48no—
206C2×C3×D3—44no—
207C2×C3×D3—42no—
208C2×C3×D3—42no—
209C2×C3×D3—44no—
210C32×C4—21no—
211C32×C4—21no—
212C32×C4—21no—
213C32×C4—21no—
214C3×Dic3—42no—
215C25—31no—
216C23×C4—31no—
217C23×C4C2×C3×D311yescharacteristic
218C2×M16—21no—
219C2×M16—61no—
220C2×C22⋊C4—32no—
221C2×C22⋊C4—32no—
222C2×C22⋊C4—61no—
223C2×C22⋊C4—61no—
224C2×C22⋊C4—61no—
225C2×C22⋊C4—61no—
226C22⋊C8—21no—
227C22⋊C8—32no—
228C22⋊C8—61no—
229C22⋊C8C2×C3×D312yescomplemented
230C23×C3—22no—
231C23×C3—22no—
232C23×C3—22no—
233C23×C3—22no—
234C23×C3—22no—
235C23×C3—22no—
236C23×C3—21no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—34no—
240C23×C3—42no—
241C23×C3—42no—
242C23×C3—42no—
243C23×C3—64no—
244C23×C3—64no—
245C23×C3—62no—
246C23×C3—62no—
247C23×C3—122no—
248C23×C3—122no—
249C23×C3—1216no—
250C23×C3—122no—
251C23×C3—122no—
252C23×C3—122no—
253C23×C3—122no—
254C23×C3(C2×D3)⋊C411yescharacteristic
255C23×C3(C2×D3)⋊C411yescharacteristic
256C23×C3C3×C22⋊C411yescharacteristic
257C23×C3C3×C22⋊C411yescharacteristic
258C23×C3C2×C4×D311yescharacteristic
259C23×C3C22×C3×C411yescharacteristic
260C22×D3—24no—
261C22×D3—24no—
262C22×D3—22no—
263C22×D3—22no—
264C22×D3—416no—
265C22×D3—42no—
266C22×D3—42no—
267C22×D3—42no—
268C22×D3—42no—
269C22×D3—42no—
270C22×D3—42no—
271C22×D3C3×M1614yescomplemented
272C2×C3×C4—24no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—42no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
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—122no—
297C2×C3×C4—122no—
298C2×C3×C4(C2×D3)⋊C411yescharacteristic
299C2×C3×C4(C2×D3)⋊C411yescharacteristic
300C2×C3×C4C3×C22⋊C411yescharacteristic
301C2×C3×C4C3×C22⋊C411yescharacteristic
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C2×C3×D411yescharacteristic
305C2×C3×C4C2×C3×D411yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—42no—
308C2×Dic3—42no—
309C2×Dic3—42no—
310C3×C8—44no—
311C3×C8—42no—
312C3×C8—42no—
313C3×C8—122no—
314C3⋊C8—42no—
315C2×C32—22no—
316C2×C32—22no—
317C2×C32—22no—
318C2×C32#40711yescharacteristic
319C2×C32C2×#9911yescharacteristic
320C2×C32C2×#10011yescharacteristic
321C3×D3—44no—
322C24—32no—
323C24—64no—
324C24—61no—
325C24—61no—
326C24—122no—
327C24—122no—
328C24C3×C4×D311yescharacteristic
329C22×C4—32no—
330C22×C4—42no—
331C22×C4—61no—
332C22×C4—61no—
333C22×C4—122no—
334C22×C4C3×C4×D311yescharacteristic
335C22×C4C3×D1211yescharacteristic
336C22×C4C3×D1211yescharacteristic
337C22×C4C3×#6711yescharacteristic
338C22×C4C3×#6711yescharacteristic
339C22×C4C22×C3×D311yescharacteristic
340M16—42no—
341M16—122no—
342C2×C8—22no—
343C2×C8—62no—
344C22⋊C4—62no—
345C22⋊C4—62no—
346C22⋊C4—62no—
347C22⋊C4—62no—
348C22×C3—28no—
349C22×C3—28no—
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—22no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—48no—
373C22×C3—64no—
374C22×C3—124no—
375C22×C3—128no—
376C22×C3—128no—
377C22×C3—124no—
378C22×C3—122no—
379C22×C3—122no—
380C22×C3#80612yes—
381C22×C3#82312yes—
382C22×C3C3×#9912yes—
383C22×C3C3×#10012yes—
384C22×C3D3×M1612yes—
385C22×C3C2×(C2×D3)⋊C411yescharacteristic
386C22×C3C2×C3×C22⋊C411yescharacteristic
387C22×C3C2×C3×M1612yes—
388C2×D3—24no—
389C2×D3—48no—
390C2×D3—48no—
391C2×D3—44no—
392C2×D3—42no—
393C2×D3—42no—
394C2×D3—44no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—41no—
406C3×C4—41no—
407C3×C4—122no—
408Dic3—42no—
409C32#146211yescharacteristic, complemented, Sylow
410C23—22no—
411C23—22no—
412C23—22no—
413C23—34no—
414C23—64no—
415C23—64no—
416C23—62no—
417C23—62no—
418C23—122no—
419C23—122no—
420C23—1216no—
421C23—122no—
422C23—122no—
423C23—122no—
424C23—122no—
425C23C3×(C2×D3)⋊C411yescharacteristic
426C23C3×(C2×D3)⋊C411yescharacteristic
427C23C2×C3×C4×D311yescharacteristic
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—62no—
435C2×C4—122no—
436C2×C4—122no—
437C2×C4—122no—
438C2×C4C3×(C2×D3)⋊C411yescharacteristic
439C2×C4C3×(C2×D3)⋊C411yescharacteristic
440C2×C4C2×C3×D1211yescharacteristic
441C2×C4C2×C3×#6711yescharacteristic
442C8—42no—
443C8—122no—
444C2×C3—22no—
445C2×C3—22no—
446C2×C3—22no—
447C2×C3—22no—
448C2×C3—22no—
449C2×C3—22no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—42no—
454C2×C3—42no—
455C2×C3—42no—
456C2×C3—124no—
457C2×C3C2×#80611yescharacteristic
458C2×C3#512611yescharacteristic
459C2×C3C2×#82311yescharacteristic
460C2×C3C3×#40711yescharacteristic
461C2×C3C2×C3×#9911yescharacteristic
462C2×C3C2×C3×#10011yescharacteristic
463D3—44no—
464C22—28no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—64no—
472C22—124no—
473C22—124no—
474C22—128no—
475C22—128no—
476C22—122no—
477C22—122no—
478C22C3×#80612yes—
479C22C3×#82312yes—
480C22C3×D3×M1612yes—
481C22C2×C3×(C2×D3)⋊C411yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—122no—
487C3—21no—
488C3#6996711yescharacteristic, direct product factor
489C3C3×#146211yescharacteristic, complemented
490C2—22no—
491C2—22no—
492C2—22no—
493C2—124no—
494C2C2×C3×#80611yescharacteristic
495C2C3×#512611yescharacteristic
496C2C2×C3×#82311yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C3×D3C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#407D3
hypocenterC3C3×#1462
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
2. C32×#407C2semidirect
3. C3×#5207C2semidirect
4. C3×#4468C2semidirect
6. #69967C3direct (N × H)
19. C32×C22⋊C8C22semidirect
21. C3×#830C22semidirect
26. C3×#407D3semidirect
27. C3×#407C2×C3semidirect
28. #5207C2×C3semidirect
30. #4468C2×C3semidirect
88. C3×C22⋊C8C2×D3semidirect
89. C3×C22⋊C8C22×C3semidirect
91. #830C22×C3semidirect
109. C22×C3×D3M16semidirect
128. #407C3×D3semidirect
229. C22⋊C8C2×C3×D3semidirect
271. C22×D3C3×M16semidirect
409. C32#1462semidirect
488. C3#69967direct (N × H)
489. C3C3×#1462semidirect

Maximal subgroups

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

subgroupindex
C22×C3×(C2×D3)⋊C42
C32×#4072
C3×#52072
C3×#44682
C3×#14623
#699673